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Sample records for mathematical formulation solution

  1. Generic Mathematical Programming Formulation and Solution for Computer-Aided Molecular Design

    DEFF Research Database (Denmark)

    Zhang, Lei; Cignitti, Stefano; Gani, Rafiqul

    2015-01-01

    This short communication presents a generic mathematical programming formulation for Computer-Aided Molecular Design (CAMD). A given CAMD problem, based on target properties, is formulated as a Mixed Integer Linear/Non-Linear Program (MILP/MINLP). The mathematical programming model presented here......, which is formulated as an MILP/MINLP problem, considers first-order and second-order molecular groups for molecular structure representation and property estimation. It is shown that various CAMD problems can be formulated and solved through this model....

  2. Solution of the mathematical adjoint equations for an interface current nodal formulation

    International Nuclear Information System (INIS)

    Yang, W.S.; Taiwo, T.A.; Khalil, H.

    1994-01-01

    Two techniques for solving the mathematical adjoint equations of an interface current nodal method are described. These techniques are the ''similarity transformation'' procedure and a direct solution scheme. A theoretical basis is provided for the similarity transformation procedure originally proposed by Lawrence. It is shown that the matrices associated with the mathematical and physical adjoint equations are similar to each other for the flat transverse leakage approximation but not for the quadratic leakage approximation. It is also shown that a good approximate solution of the mathematical adjoint for the quadratic transverse leakage approximation is obtained by applying the similarity transformation for the flat transverse leakage approximation to the physical adjoint solution. The direct solution scheme, which was developed as an alternative to the similarity transformation procedure, yields the correct mathematical adjoint solution for both flat and quadratic transverse leakage approximations. In this scheme, adjoint nodal equations are cast in a form very similar to that of the forward equations by employing a linear transformation of the adjoint partial currents. This enables the use of the forward solution algorithm with only minor modifications for solving the mathematical adjoint equations. By using the direct solution scheme as a reference method, it is shown that while the results computed with the similarity transformation procedure are approximate, they are sufficiently accurate for calculations of global and local reactivity changes resulting from coolant voiding in a liquid-metal reactor

  3. Mathematical model formulation and validation of water and solute transport in whole hamster pancreatic islets.

    Science.gov (United States)

    Benson, James D; Benson, Charles T; Critser, John K

    2014-08-01

    Optimization of cryopreservation protocols for cells and tissues requires accurate models of heat and mass transport. Model selection often depends on the configuration of the tissue. Here, a mathematical and conceptual model of water and solute transport for whole hamster pancreatic islets has been developed and experimentally validated incorporating fundamental biophysical data from previous studies on individual hamster islet cells while retaining whole-islet structural information. It describes coupled transport of water and solutes through the islet by three methods: intracellularly, intercellularly, and in combination. In particular we use domain decomposition techniques to couple a transmembrane flux model with an interstitial mass transfer model. The only significant undetermined variable is the cellular surface area which is in contact with the intercellularly transported solutes, Ais. The model was validated and Ais determined using a 3×3 factorial experimental design blocked for experimental day. Whole islet physical experiments were compared with model predictions at three temperatures, three perfusing solutions, and three islet size groups. A mean of 4.4 islets were compared at each of the 27 experimental conditions and found to correlate with a coefficient of determination of 0.87±0.06 (mean ± SD). Only the treatment variable of perfusing solution was found to be significant (p<0.05). We have devised a model that retains much of the intrinsic geometric configuration of the system, and thus fewer laboratory experiments are needed to determine model parameters and thus to develop new optimized cryopreservation protocols. Additionally, extensions to ovarian follicles and other concentric tissue structures may be made. Copyright © 2014 Elsevier Inc. All rights reserved.

  4. Mathematical Formulation and Comparison of Solution Approaches for the Vehicle Routing Problem with Access Time Windows

    Directory of Open Access Journals (Sweden)

    Rafael Grosso

    2018-01-01

    Full Text Available The application of the principles of sustainability to the implementation of urban freight policies requires the estimation of all the costs and externalities involved. We focus here on the case of access time windows, which ban the access of freight vehicles to central urban areas in many European cities. Even though this measure seeks to reduce congestion and emissions in the most crowded periods of the day, it also imposes additional costs for carriers and results in higher emissions and energy consumption. We present here a mathematical model for the Vehicle Routing Problem with Access Time Windows, a variant of the VRP suitable for planning delivery routes in a city subject to this type of accessibility restriction. We use the model to find exact solutions to small problem instances based on a case study and then compare the performance over larger instances of a modified savings algorithm, a genetic algorithm, and a tabu search procedure, with the results showing no clear prevalence of any of them, but confirming the significance of those additional costs and externalities.

  5. Transport of fluid and solutes in the body I. Formulation of a mathematical model.

    Science.gov (United States)

    Gyenge, C C; Bowen, B D; Reed, R K; Bert, J L

    1999-09-01

    A compartmental model of short-term whole body fluid, protein, and ion distribution and transport is formulated. The model comprises four compartments: a vascular and an interstitial compartment, each with an embedded cellular compartment. The present paper discusses the assumptions on which the model is based and describes the equations that make up the model. Fluid and protein transport parameters from a previously validated model as well as ionic exchange parameters from the literature or from statistical estimation [see companion paper: C. C. Gyenge, B. D. Bowen, R. K. Reed, and J. L. Bert. Am. J. Physiol. 277 (Heart Circ. Physiol. 46): H1228-H1240, 1999] are used in formulating the model. The dynamic model has the ability to simulate 1) transport across the capillary membrane of fluid, proteins, and small ions and their distribution between the vascular and interstitial compartments; 2) the changes in extracellular osmolarity; 3) the distribution and transport of water and ions associated with each of the cellular compartments; 4) the cellular transmembrane potential; and 5) the changes of volume in the four fluid compartments. The validation and testing of the proposed model against available experimental data are presented in the companion paper.

  6. On Scalar Energy: Mathematical Formulation

    International Nuclear Information System (INIS)

    Hathout, A.M.

    2011-01-01

    A new kind of electromagnetic waves (EMW), which exists only in vacuum of the empty space, will be discussed and mathematically formulated in this paper. The mathematical existence of this energy was first proposed in a series of groundbreaking equations by Scottish Mathematician, James Clerk Maxwell, in the mid of 1800 and 39;s. This energy is called scalar energy. It is characterized by both particle and wave like. The waves of this energy are called longitudinal EMW to distinguish them from transverse EM, the kind we are familiar with in our daily life. Teslas name of this energy is scalar energy or zero point energy. It is aimed at this paper to explain more details and to verify the scalar EM concept in vacuum.

  7. Mathematical Formulation of Multilayer Networks

    Science.gov (United States)

    De Domenico, Manlio; Solé-Ribalta, Albert; Cozzo, Emanuele; Kivelä, Mikko; Moreno, Yamir; Porter, Mason A.; Gómez, Sergio; Arenas, Alex

    2013-10-01

    A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems are very rich. Achieving a deep understanding of such systems necessitates generalizing “traditional” network theory, and the newfound deluge of data now makes it possible to test increasingly general frameworks for the study of networks. In particular, although adjacency matrices are useful to describe traditional single-layer networks, such a representation is insufficient for the analysis and description of multiplex and time-dependent networks. One must therefore develop a more general mathematical framework to cope with the challenges posed by multilayer complex systems. In this paper, we introduce a tensorial framework to study multilayer networks, and we discuss the generalization of several important network descriptors and dynamical processes—including degree centrality, clustering coefficients, eigenvector centrality, modularity, von Neumann entropy, and diffusion—for this framework. We examine the impact of different choices in constructing these generalizations, and we illustrate how to obtain known results for the special cases of single-layer and multiplex networks. Our tensorial approach will be helpful for tackling pressing problems in multilayer complex systems, such as inferring who is influencing whom (and by which media) in multichannel social networks and developing routing techniques for multimodal transportation systems.

  8. Classical and Weak Solutions for Two Models in Mathematical Finance

    Science.gov (United States)

    Gyulov, Tihomir B.; Valkov, Radoslav L.

    2011-12-01

    We study two mathematical models, arising in financial mathematics. These models are one-dimensional analogues of the famous Black-Scholes equation on finite interval. The main difficulty is the degeneration at the both ends of the space interval. First, classical solutions are studied. Positivity and convexity properties of the solutions are discussed. Variational formulation in weighted Sobolev spaces is introduced and existence and uniqueness of the weak solution is proved. Maximum principle for weak solution is discussed.

  9. Mathematical formulation and numerical simulation of bird flu infection process within a poultry farm

    Science.gov (United States)

    Putri, Arrival Rince; Nova, Tertia Delia; Watanabe, M.

    2016-02-01

    Bird flu infection processes within a poultry farm are formulated mathematically. A spatial effect is taken into account for the virus concentration with a diffusive term. An infection process is represented in terms of a traveling wave solutions. For a small removal rate, a singular perturbation analysis lead to existence of traveling wave solutions, that correspond to progressive infection in one direction.

  10. Scaffolding Mathematical Modelling with a Solution Plan

    Science.gov (United States)

    Schukajlow, Stanislaw; Kolter, Jana; Blum, Werner

    2015-01-01

    In the study presented in this paper, we examined the possibility to scaffold mathematical modelling with strategies. The strategies were prompted using an instrument called "solution plan" as a scaffold. The effects of this step by step instrument on mathematical modelling competency and on self-reported strategies were tested using…

  11. A Mathematical Formulation of the SCOLE Control Problem. Part 2: Optimal Compensator Design

    Science.gov (United States)

    Balakrishnan, A. V.

    1988-01-01

    The study initiated in Part 1 of this report is concluded and optimal feedback control (compensator) design for stability augmentation is considered, following the mathematical formulation developed in Part 1. Co-located (rate) sensors and (force and moment) actuators are assumed, and allowing for both sensor and actuator noise, stabilization is formulated as a stochastic regulator problem. Specializing the general theory developed by the author, a complete, closed form solution (believed to be new with this report) is obtained, taking advantage of the fact that the inherent structural damping is light. In particular, it is possible to solve in closed form the associated infinite-dimensional steady-state Riccati equations. The SCOLE model involves associated partial differential equations in a single space variable, but the compensator design theory developed is far more general since it is given in the abstract wave equation formulation. The results thus hold for any multibody system so long as the basic model is linear.

  12. A mathematical formulation for large strain analysis of geologic continua

    International Nuclear Information System (INIS)

    Chaudhary, A.B.; Vakili, J.E.; Hume, H.R.

    1987-12-01

    A solution method is presented for finite-deformation analysis of geologic materials. The principle of virtual work is used to state the equations of equilibrium in a weak form. These equations are linearized about the last-established equilibrium configuration. A material constitutive relationship between the Green-Naghdi stress rate and the rate-of-deformation tensor is used to obtain the current stresses. The finite-element governing equations are expressed in a form suitable for an iterative solution strategy. The obtained gradient matrix contains the effects of both material and geometric nonlinearities. The primary application area of this formulation is the analysis of long-term deformation response of the region adjoining the mining shafts and the waste emplacement rooms within a nuclear waste repository. In this region, the strains are expected to be large, and the infinitesimal strain analysis would introduce inaccuracies in the solution. 19 refs., 6 figs

  13. Initial value formulation for the spherically symmetric dust solution

    International Nuclear Information System (INIS)

    Liu, H.

    1990-01-01

    An initial value formulation for the dust solution with spherical symmetry is given explicitly in which the initial distributions of dust and its velocity on an initial surface are chosen to be the initial data. As special cases, the Friedmann universe, the Schwarzschild solution in comoving coordinates, and a spherically symmetric and radially inhomogeneous cosmological model are derived

  14. 21 CFR 864.2875 - Balanced salt solutions or formulations.

    Science.gov (United States)

    2010-04-01

    ... 21 Food and Drugs 8 2010-04-01 2010-04-01 false Balanced salt solutions or formulations. 864.2875 Section 864.2875 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) MEDICAL DEVICES HEMATOLOGY AND PATHOLOGY DEVICES Cell And Tissue Culture Products § 864.2875...

  15. Cleaning UF membranes with simple and formulated solutions

    NARCIS (Netherlands)

    Levitsky, I.; Duek, A.; Naim, R.; Arkhangelsky, E.; Gitis, V.

    2012-01-01

    The ultrafiltration membranes fouled by proteins are typically cleaned by consecutive soaking in alkali, surfactant and oxidizing solutions. We combined all three chemicals into a formulated cleaning agent and examined its efficiency to restore the water flux without damaging the membrane or

  16. Mathematical models and heuristic solutions for container positioning problems in port terminals

    DEFF Research Database (Denmark)

    Kallehauge, Louise Sibbesen

    2008-01-01

    presents an efficient solution algorithm for the CPP. Based on a number of new concepts, an event-based construction heuristic is developed and its ability to solve real-life problem instances is established. The backbone of the algorithm is a list of events, corresponding to a sequence of operations...... by constructing mathematical programming formulations of the problem and developing an efficient heuristic algorithm for its solution. The thesis consists of an introduction, two main chapters concerning new mathematical formulations and a new heuristic for the CPP, technical issues, computational results...... concerning the subject is reviewed. The research presented in this thesis is divided into two main parts: Construction and investigation of new mathematical programming formulations of the CPP and development and implementation of a new event-based heuristic for the problem. The first part presents three...

  17. End-Member Formulation of Solid Solutions and Reactive Transport

    Energy Technology Data Exchange (ETDEWEB)

    Lichtner, Peter C. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

    2015-09-01

    A model for incorporating solid solutions into reactive transport equations is presented based on an end-member representation. Reactive transport equations are solved directly for the composition and bulk concentration of the solid solution. Reactions of a solid solution with an aqueous solution are formulated in terms of an overall stoichiometric reaction corresponding to a time-varying composition and exchange reactions, equivalent to reaction end-members. Reaction rates are treated kinetically using a transition state rate law for the overall reaction and a pseudo-kinetic rate law for exchange reactions. The composition of the solid solution at the onset of precipitation is assumed to correspond to the least soluble composition, equivalent to the composition at equilibrium. The stoichiometric saturation determines if the solid solution is super-saturated with respect to the aqueous solution. The method is implemented for a simple prototype batch reactor using Mathematica for a binary solid solution. Finally, the sensitivity of the results on the kinetic rate constant for a binary solid solution is investigated for reaction of an initially stoichiometric solid phase with an undersaturated aqueous solution.

  18. Non-Perturbative Formulation of Time-Dependent String Solutions

    CERN Document Server

    Alexandre, J; Mavromatos, Nikolaos E; Alexandre, Jean; Ellis, John; Mavromatos, Nikolaos E.

    2006-01-01

    We formulate here a new world-sheet renormalization-group technique for the bosonic string, which is non-perturbative in the Regge slope alpha' and based on a functional method for controlling the quantum fluctuations, whose magnitudes are scaled by the value of alpha'. Using this technique we exhibit, in addition to the well-known linear-dilaton cosmology, a new, non-perturbative time-dependent background solution. Using the reparametrization invariance of the string S-matrix, we demonstrate that this solution is conformally invariant to alpha', and we give a heuristic inductive argument that conformal invariance can be maintained to all orders in alpha'. This new time-dependent string solution may be applicable to primordial cosmology or to the exit from linear-dilaton cosmology at large times.

  19. Poisson-Fermi Formulation of Nonlocal Electrostatics in Electrolyte Solutions

    Directory of Open Access Journals (Sweden)

    Liu Jinn-Liang

    2017-10-01

    Full Text Available We present a nonlocal electrostatic formulation of nonuniform ions and water molecules with interstitial voids that uses a Fermi-like distribution to account for steric and correlation efects in electrolyte solutions. The formulation is based on the volume exclusion of hard spheres leading to a steric potential and Maxwell’s displacement field with Yukawa-type interactions resulting in a nonlocal electric potential. The classical Poisson-Boltzmann model fails to describe steric and correlation effects important in a variety of chemical and biological systems, especially in high field or large concentration conditions found in and near binding sites, ion channels, and electrodes. Steric effects and correlations are apparent when we compare nonlocal Poisson-Fermi results to Poisson-Boltzmann calculations in electric double layer and to experimental measurements on the selectivity of potassium channels for K+ over Na+.

  20. mathematical model of thermal explosion, the dual variational formulation of nonlinear problem, alternative functional

    Directory of Open Access Journals (Sweden)

    V. S. Zarubin

    2016-01-01

    in its plane, and in the circular cylinder unlimited in length.An approximate numerical solution of the differential equation that is included in a nonlinear mathematical model of the thermal explosion enables us to obtain quantitative estimates of combination of determining parameters at which the limit state occurs in areas of not only canonical form. A capability to study of the thermal explosion state can be extended in the context of development of mathematical modeling methods, including methods of model analysis to describe the thermal state of solids.To analyse a mathematical model of the thermal explosion in a homogeneous solid the paper uses a variational approach based on the dual variational formulation of the appropriate nonlinear stationary problem of heat conduction in such a body. This formulation contains two alternative functional reaching the matching values in their stationary points corresponding to the true temperature distribution. This functional feature allows you to not only get an approximate quantitative estimate of the combination of parameters that determine the thermal explosion state, but also to find the greatest possible error in such estimation.

  1. Fluid dynamics and mass transfer in variably saturated porous media: formulation and applications of a mathematical model

    International Nuclear Information System (INIS)

    Sharma, D.

    1982-01-01

    This paper presents the formulation and applications of a mathematical model designed to predict the fluid dynamics and associated mass transfers in variably saturated porous media. Novelties in the formulation are emphasized and demonstrated to provide several computational advantages. The numerical procedure employed is of the integrated finite-difference variety which employs a hybrid differencing scheme. This procedure, while solving the coupled governing equations in conservative form, permits accommodation of substantial heterogeneities and anisotropies in material properties of the porous media. Accordingly, it is capable of making reliable predictions of steeply varying moisture and chemical-specie concentration fronts. The paper provides several examples of application of the model to the solution of practical problems. It is demonstrated that economical solutions to highly non-linear problems associated with solid and liquid waste disposal practices can be obtained

  2. Mathematical Formulation Requirements and Specifications for the Process Models

    International Nuclear Information System (INIS)

    Steefel, C.; Moulton, D.; Pau, G.; Lipnikov, K.; Meza, J.; Lichtner, P.; Wolery, T.; Bacon, D.; Spycher, N.; Bell, J.; Moridis, G.; Yabusaki, S.; Sonnenthal, E.; Zyvoloski, G.; Andre, B.; Zheng, L.; Davis, J.

    2010-01-01

    The Advanced Simulation Capability for Environmental Management (ASCEM) is intended to be a state-of-the-art scientific tool and approach for understanding and predicting contaminant fate and transport in natural and engineered systems. The ASCEM program is aimed at addressing critical EM program needs to better understand and quantify flow and contaminant transport behavior in complex geological systems. It will also address the long-term performance of engineered components including cementitious materials in nuclear waste disposal facilities, in order to reduce uncertainties and risks associated with DOE EM's environmental cleanup and closure activities. Building upon national capabilities developed from decades of Research and Development in subsurface geosciences, computational and computer science, modeling and applied mathematics, and environmental remediation, the ASCEM initiative will develop an integrated, open-source, high-performance computer modeling system for multiphase, multicomponent, multiscale subsurface flow and contaminant transport. This integrated modeling system will incorporate capabilities for predicting releases from various waste forms, identifying exposure pathways and performing dose calculations, and conducting systematic uncertainty quantification. The ASCEM approach will be demonstrated on selected sites, and then applied to support the next generation of performance assessments of nuclear waste disposal and facility decommissioning across the EM complex. The Multi-Process High Performance Computing (HPC) Simulator is one of three thrust areas in ASCEM. The other two are the Platform and Integrated Toolsets (dubbed the Platform) and Site Applications. The primary objective of the HPC Simulator is to provide a flexible and extensible computational engine to simulate the coupled processes and flow scenarios described by the conceptual models developed using the ASCEM Platform. The graded and iterative approach to assessments naturally

  3. Mathematical Formulation Requirements and Specifications for the Process Models

    Energy Technology Data Exchange (ETDEWEB)

    Steefel, C.; Moulton, D.; Pau, G.; Lipnikov, K.; Meza, J.; Lichtner, P.; Wolery, T.; Bacon, D.; Spycher, N.; Bell, J.; Moridis, G.; Yabusaki, S.; Sonnenthal, E.; Zyvoloski, G.; Andre, B.; Zheng, L.; Davis, J.

    2010-11-01

    The Advanced Simulation Capability for Environmental Management (ASCEM) is intended to be a state-of-the-art scientific tool and approach for understanding and predicting contaminant fate and transport in natural and engineered systems. The ASCEM program is aimed at addressing critical EM program needs to better understand and quantify flow and contaminant transport behavior in complex geological systems. It will also address the long-term performance of engineered components including cementitious materials in nuclear waste disposal facilities, in order to reduce uncertainties and risks associated with DOE EM's environmental cleanup and closure activities. Building upon national capabilities developed from decades of Research and Development in subsurface geosciences, computational and computer science, modeling and applied mathematics, and environmental remediation, the ASCEM initiative will develop an integrated, open-source, high-performance computer modeling system for multiphase, multicomponent, multiscale subsurface flow and contaminant transport. This integrated modeling system will incorporate capabilities for predicting releases from various waste forms, identifying exposure pathways and performing dose calculations, and conducting systematic uncertainty quantification. The ASCEM approach will be demonstrated on selected sites, and then applied to support the next generation of performance assessments of nuclear waste disposal and facility decommissioning across the EM complex. The Multi-Process High Performance Computing (HPC) Simulator is one of three thrust areas in ASCEM. The other two are the Platform and Integrated Toolsets (dubbed the Platform) and Site Applications. The primary objective of the HPC Simulator is to provide a flexible and extensible computational engine to simulate the coupled processes and flow scenarios described by the conceptual models developed using the ASCEM Platform. The graded and iterative approach to assessments

  4. Mathematical formulation of biomechanical parameters used in orthodontic treatment

    Science.gov (United States)

    Balakrishna, A.; Vamsi, Ch. Raghu; Rao, V. D. Prasad; Swamy, Ch. Kishore; Kuladeep, B.

    2015-05-01

    Orthodontic Treatment is being widely practiced around the world for teeth straightening and extraction to improve alignment of remaining teeth. Here, forces are applied to correct the position of teeth. The force applied on the teeth isn't calibrated and applied arbitrarily based on the recommendations from scientific research and experience of the orthodontist. The number of settings and the total time required for the completion of treatment also remains arbitrary. So, there is a need for determining the force which is actually acting on the teeth and determining the optimal force required for the treatment of each and every individual case. In this paper a mathematical relation is derived between the force applied on the tooth and tooth displacement by considering a 2nd order non-homogeneous linear differential equation. As the tooth displacement is not a direct function of force applied, Biomechanical parameters like mass of tooth, stiffness and damping coefficient of periodontal ligament & alveolar bone are involved in the differential equation. By solving the equation, tooth displacement thereby, tooth velocity can be obtained for a particular force. On the other hand, based on the dimensions of the model, orthodontist could determine the total tooth displacement required for each setting of the treatment, so that, the total displacement is covered. The orthodontist uses the data and applies the required force on to the teeth, based on which the orthodontist can plan his treatment procedure and reduce the number of settings, total treatment time and also increases the success rate of the treatment.

  5. On matrix diffusion: formulations, solution methods and qualitative effects

    Science.gov (United States)

    Carrera, Jesús; Sánchez-Vila, Xavier; Benet, Inmaculada; Medina, Agustín; Galarza, Germán; Guimerà, Jordi

    Matrix diffusion has become widely recognized as an important transport mechanism. Unfortunately, accounting for matrix diffusion complicates solute-transport simulations. This problem has led to simplified formulations, partly motivated by the solution method. As a result, some confusion has been generated about how to properly pose the problem. One of the objectives of this work is to find some unity among existing formulations and solution methods. In doing so, some asymptotic properties of matrix diffusion are derived. Specifically, early-time behavior (short tests) depends only on φm2RmDm / Lm2, whereas late-time behavior (long tracer tests) depends only on φmRm, and not on matrix diffusion coefficient or block size and shape. The latter is always true for mean arrival time. These properties help in: (a) analyzing the qualitative behavior of matrix diffusion; (b) explaining one paradox of solute transport through fractured rocks (the apparent dependence of porosity on travel time); (c) discriminating between matrix diffusion and other problems (such as kinetic sorption or heterogeneity); and (d) describing identifiability problems and ways to overcome them. RésuméLa diffusion matricielle est un phénomène reconnu maintenant comme un mécanisme de transport important. Malheureusement, la prise en compte de la diffusion matricielle complique la simulation du transport de soluté. Ce problème a conduit à des formulations simplifiées, en partie à cause de la méthode de résolution. Il s'en est suivi une certaine confusion sur la façon de poser correctement le problème. L'un des objectifs de ce travail est de trouver une certaine unité parmi les formulations et les méthodes de résolution. C'est ainsi que certaines propriétés asymptotiques de la diffusion matricielle ont été dérivées. En particulier, le comportement à l'origine (expériences de traçage courtes) dépend uniquement du terme φm2RmDm / Lm2, alors que le comportement à long terme

  6. A mathematical formulation for interface-based modular product design with geometric and weight constraints

    Science.gov (United States)

    Jung-Woon Yoo, John

    2016-06-01

    Since customer preferences change rapidly, there is a need for design processes with shorter product development cycles. Modularization plays a key role in achieving mass customization, which is crucial in today's competitive global market environments. Standardized interfaces among modularized parts have facilitated computational product design. To incorporate product size and weight constraints during computational design procedures, a mixed integer programming formulation is presented in this article. Product size and weight are two of the most important design parameters, as evidenced by recent smart-phone products. This article focuses on the integration of geometric, weight and interface constraints into the proposed mathematical formulation. The formulation generates the optimal selection of components for a target product, which satisfies geometric, weight and interface constraints. The formulation is verified through a case study and experiments are performed to demonstrate the performance of the formulation.

  7. FORMULATION OF MATHEMATICAL PROBLEM DESCRIBING PHYSICAL AND CHEMICAL PROCESSES AT CONCRETE CORROSION

    Directory of Open Access Journals (Sweden)

    Sergey V. Fedosov

    2017-06-01

    Full Text Available The article deals with the relevance of new scientific research focused on modeling of physical and chemical processes occurring in the cement concrete at their exploitation. The basic types of concrete corrosion are described. The problem of mass transfer processes in a flat reinforced concrete wall at concrete corrosion of the first and the second types has been mathematically formulated.

  8. Solutions manual to accompany finite mathematics models and applications

    CERN Document Server

    Morris, Carla C

    2015-01-01

    A solutions manual to accompany Finite Mathematics: Models and Applications In order to emphasize the main concepts of each chapter, Finite Mathematics: Models and Applications features plentiful pedagogical elements throughout such as special exercises, end notes, hints, select solutions, biographies of key mathematicians, boxed key principles, a glossary of important terms and topics, and an overview of use of technology. The book encourages the modeling of linear programs and their solutions and uses common computer software programs such as LINDO. In addition to extensive chapters on pr

  9. Logic and discrete mathematics a concise introduction : solutions manual

    CERN Document Server

    Conradie, Willem; Robinson, Claudette

    2015-01-01

    Solutions manual to accompany Logic and Discrete Mathematics: A Concise Introduction This book features a unique combination of comprehensive coverage of logic with a solid exposition of the most important fields of discrete mathematics, presenting material that has been tested and refined by the authors in university courses taught over more than a decade. Written in a clear and reader-friendly style, each section ends with an extensive set of exercises, most of them provided with complete solutions which are available in this accompanying solutions manual.

  10. Formulation of coarse mesh finite difference to calculate mathematical adjoint flux

    International Nuclear Information System (INIS)

    Pereira, Valmir; Martinez, Aquilino Senra; Silva, Fernando Carvalho da

    2002-01-01

    The objective of this work is the obtention of the mathematical adjoint flux, having as its support the nodal expansion method (NEM) for coarse mesh problems. Since there are difficulties to evaluate this flux by using NEM. directly, a coarse mesh finite difference program was developed to obtain this adjoint flux. The coarse mesh finite difference formulation (DFMG) adopted uses results of the direct calculation (node average flux and node face averaged currents) obtained by NEM. These quantities (flux and currents) are used to obtain the correction factors which modify the classical finite differences formulation . Since the DFMG formulation is also capable of calculating the direct flux it was also tested to obtain this flux and it was verified that it was able to reproduce with good accuracy both the flux and the currents obtained via NEM. In this way, only matrix transposition is needed to calculate the mathematical adjoint flux. (author)

  11. Soliton-type solutions for two models in mathematical physics

    Science.gov (United States)

    Al-Ghafri, K. S.

    2018-04-01

    In this paper, the generalised Klein-Gordon and Kadomtsov-Petviashvili Benjamin-Bona-Mahony equations with power law nonlinearity are investigated. Our study is based on reducing the form of both equations to a first-order ordinary differential equation having the travelling wave solutions. Subsequently, soliton-type solutions such as compacton and solitary pattern solutions are obtained analytically. Additionally, the peaked soliton has been derived where it exists under a specific restrictions. In addition to the soliton solutions, the mathematical method which is exploited in this work also creates a few amount of travelling wave solutions.

  12. Formulation and solution of the classical seashell problem

    International Nuclear Information System (INIS)

    Illert, C.

    1987-01-01

    Despite an extensive scholarly literature dating back to classical times, seashell geometries have hiterto resisted rigorous theoretical analysis, leaving applied scientists to adopt a directionless empirical approach toward classification. The voluminousness of recent paleontological literature demonstrates the importance of this problem to applied scientists, but in no way reflects corresponding conceptual or theoretical advances beyond the XIX century thinking which was so ably summarized by Sir D'Arcy Wentworth Thompson in 1917. However, in this foundation paper for the newly emerging science of theoretical conchology, unifying theoretical considerations for the first time, permits a rigorous formulation and a complete solution of the problem of biological shell geometries. Shell coiling about the axis of symmetry can be deduced from first principles using energy considerations associated with incremental growth. The present paper shows that those shell apertures which are incurved (''cowrielike''), outflared (''stromblike'') or even backturned (''Opisthostomoidal'') are merely special cases of a much broader spectrum of ''allowable'' energy-efficient growth trajectories (tensile elastic clockspring spirals), many of which were widely used by Cretaceous ammonites. Energy considerations also dictate shell growth along the axis of symmetry, thus seashell spires can be understood in terms of certain special figures of revolution (Moebius elastic conoids), the better-known coeloconoidal and cyrtoconoidal shell spires being only two special cases arising from a whole class of topologically possible, energy efficient and biologically observed geometries. The ''wires'' and ''conoids'' of the present paper are instructive conceptual simplifications sufficient for present purposes. A second paper will later deal with generalized tubular surfaces in thre

  13. AUTOMATION PROGRAM FOR RECOGNITION OF ALGORITHM SOLUTION OF MATHEMATIC TASK

    Directory of Open Access Journals (Sweden)

    Denis N. Butorin

    2014-01-01

    Full Text Available In the article are been describing technology for manage of testing task in computer program. It was found for recognition of algorithm solution of mathematic task. There are been justifi ed the using hierarchical structure for a special set of testing questions. Also, there has been presented the release of the described tasks in the computer program openSEE. 

  14. AUTOMATION PROGRAM FOR RECOGNITION OF ALGORITHM SOLUTION OF MATHEMATIC TASK

    OpenAIRE

    Denis N. Butorin

    2014-01-01

    In the article are been describing technology for manage of testing task in computer program. It was found for recognition of algorithm solution of mathematic task. There are been justifi ed the using hierarchical structure for a special set of testing questions. Also, there has been presented the release of the described tasks in the computer program openSEE. 

  15. The mathematical models of solution mining and case study

    International Nuclear Information System (INIS)

    Jacobson, R.H.; Waskovsky, J.; Wang Xiwen; Wang Haifeng

    1991-01-01

    The mathematical model of parameters which describe solution mining and the principle of ore leaching are presented theoretically and thoroughly with the emphasis on in-situ leaching with a biolixiviant, furthermore, the example of bioleach mining, or biomining, in an abandoned underground copper mine is discussed

  16. A mathematical solution for the parameters of three interfering resonances

    Science.gov (United States)

    Han, X.; Shen, C. P.

    2018-04-01

    The multiple-solution problem in determining the parameters of three interfering resonances from a fit to an experimentally measured distribution is considered from a mathematical viewpoint. It is shown that there are four numerical solutions for a fit with three coherent Breit-Wigner functions. Although explicit analytical formulae cannot be derived in this case, we provide some constraint equations between the four solutions. For the cases of nonrelativistic and relativistic Breit-Wigner forms of amplitude functions, a numerical method is provided to derive the other solutions from that already obtained, based on the obtained constraint equations. In real experimental measurements with more complicated amplitude forms similar to Breit-Wigner functions, the same method can be deduced and performed to get numerical solutions. The good agreement between the solutions found using this mathematical method and those directly from the fit verifies the correctness of the constraint equations and mathematical methodology used. Supported by National Natural Science Foundation of China (NSFC) (11575017, 11761141009), the Ministry of Science and Technology of China (2015CB856701) and the CAS Center for Excellence in Particle Physics (CCEPP)

  17. Exact Solutions for Nonlinear Differential Difference Equations in Mathematical Physics

    Directory of Open Access Journals (Sweden)

    Khaled A. Gepreel

    2013-01-01

    Full Text Available We modified the truncated expansion method to construct the exact solutions for some nonlinear differential difference equations in mathematical physics via the general lattice equation, the discrete nonlinear Schrodinger with a saturable nonlinearity, the quintic discrete nonlinear Schrodinger equation, and the relativistic Toda lattice system. Also, we put a rational solitary wave function method to find the rational solitary wave solutions for some nonlinear differential difference equations. The proposed methods are more effective and powerful to obtain the exact solutions for nonlinear difference differential equations.

  18. Existence of Periodic Solutions and Stability of Zero Solution of a Mathematical Model of Schistosomiasis

    Directory of Open Access Journals (Sweden)

    Lin Li

    2014-01-01

    Full Text Available A mathematical model on schistosomiasis governed by periodic differential equations with a time delay was studied. By discussing boundedness of the solutions of this model and construction of a monotonic sequence, the existence of positive periodic solution was shown. The conditions under which the model admits a periodic solution and the conditions under which the zero solution is globally stable are given, respectively. Some numerical analyses show the conditional coexistence of locally stable zero solution and periodic solutions and that it is an effective treatment by simply reducing the population of snails and enlarging the death ratio of snails for the control of schistosomiasis.

  19. Supplemental mathematical formulations, Atmospheric pathway: The Multimedia Environmental Pollutant Assessment System (MEPAS)

    International Nuclear Information System (INIS)

    Droppo, J.G.; Buck, J.W.

    1996-03-01

    The Multimedia Environmental Pollutant Assessment System (MEPAS) is an integrated software implementation of physics-based fate and transport models for health and environmental risk assessments of both radioactive and hazardous pollutants. This atmospheric component report is one of a series of formulation reports that document the MEPAS mathematical models. MEPAS is a ''multimedia'' model; pollutant transport is modeled within, through, and between multiple media (air, soil, groundwater, and surface water). The estimated concentrations in the various media are used to compute exposures and impacts to the environment, to maximum individuals, and to populations

  20. Mathematical Formulation of Relationship between Applied Marketing Effort and Potential Ability of Determining Market Share

    Directory of Open Access Journals (Sweden)

    Mokhtar M. Metwally

    2008-01-01

    Full Text Available The aim of this paper is to formulate the mathematical relationship between firms potential ability and their applied efforts to attract the body of unattached customers. A method is devised in this paper by which management techniques imposed by a particular firm can evaluate its market share. This paper demonstrates the relationship between the applied marketing effort of management and the potential ability of the firm in determining its market share. This paper also investigates the effect of a number of simultaneous marketing impulses on the movement of the body of unattached customers and hence on the size of the market share.

  1. Systematic network synthesis and design: Problem formulation, superstructure generation, data management and solution

    DEFF Research Database (Denmark)

    Quaglia, Alberto; Gargalo, Carina L.; Chairakwongsa, Siwanat

    2015-01-01

    when large problems are considered. In an earlier work, we proposed a computer-aided framework for synthesis and design of process networks. In this contribution, we expand the framework by including methods and tools developed to structure, automate and simplify the mathematical formulation......The developments obtained in recent years in the field of mathematical programming considerably reduced the computational time and resources needed to solve large and complex Mixed Integer Non Linear Programming (MINLP) problems. Nevertheless, the application of these methods in industrial practice...... is still limited by the complexity associated with the mathematical formulation of some problems. In particular, the tasks of design space definition and representation as superstructure, as well as the data collection, validation and handling may become too complex and cumbersome to execute, especially...

  2. An MPCC Formulation and Its Smooth Solution Algorithm for Continuous Network Design Problem

    Directory of Open Access Journals (Sweden)

    Guangmin Wang

    2017-12-01

    Full Text Available Continuous network design problem (CNDP is searching for a transportation network configuration to minimize the sum of the total system travel time and the investment cost of link capacity expansions by considering that the travellers follow a traditional Wardrop user equilibrium (UE to choose their routes. In this paper, the CNDP model can be formulated as mathematical programs with complementarity constraints (MPCC by describing UE as a non-linear complementarity problem (NCP. To address the difficulty resulting from complementarity constraints in MPCC, they are substituted by the Fischer-Burmeister (FB function, which can be smoothed by the introduction of the smoothing parameter. Therefore, the MPCC can be transformed into a well-behaved non-linear program (NLP by replacing the complementarity constraints with a smooth equation. Consequently, the solver such as LINDOGLOBAL in GAMS can be used to solve the smooth approximate NLP to obtain the solution to MPCC for modelling CNDP. The numerical experiments on the example from the literature demonstrate that the proposed algorithm is feasible.

  3. Gelatin behaviour in dilute aqueous solution : designing a nanoparticulate formulation

    OpenAIRE

    Farrugia, Claude; Groves, Michael J.

    1999-01-01

    Although it has been claimed that nanoparticles can be produced from gelatin, a naturally occurring polypeptide, the commercial conversion of animal collagen to gelatin results in a heterogeneous product with a wide molecular-weight range. This is probably responsible for the widely observed variation in the experimental conditions required for nanoparticle formation. In this study, 0.2% w/v aqueous B225 gelatin solutions were incubated under various conditions of time, temperature, pH an...

  4. A Continuous Formulation for Logical Decisions in Differential Algebraic Systems using Mathematical Programs with Complementarity Constraints

    Directory of Open Access Journals (Sweden)

    Kody M. Powell

    2016-03-01

    Full Text Available This work presents a methodology to represent logical decisions in differential algebraic equation simulation and constrained optimization problems using a set of continuous algebraic equations. The formulations may be used when state variables trigger a change in process dynamics, and introduces a pseudo-binary decision variable, which is continuous, but should only have valid solutions at values of either zero or one within a finite time horizon. This formulation enables dynamic optimization problems with logical disjunctions to be solved by simultaneous solution methods without using methods such as mixed integer programming. Several case studies are given to illustrate the value of this methodology including nonlinear model predictive control of a chemical reactor using a surge tank with overflow to buffer disturbances in feed flow rate. Although this work contains novel methodologies for solving dynamic algebraic equation (DAE constrained problems where the system may experience an abrupt change in dynamics that may otherwise require a conditional statement, there remain substantial limitations to this methodology, including a limited domain where problems may converge and the possibility for ill-conditioning. Although the problems presented use only continuous algebraic equations, the formulation has inherent non-smoothness. Hence, these problems must be solved with care and only in select circumstances, such as in simulation or situations when the solution is expected to be near the solver’s initial point.

  5. Mathematical modeling of solute transport in the subsurface

    International Nuclear Information System (INIS)

    Naymik, T.G.

    1987-01-01

    A review of key works on solute transport models indicates that solute transport processes with the exception of advection are still poorly understood. Solute transport models generally do a good job when they are used to test scientific concepts and hypotheses, investigate natural processes, systematically store and manage data, and simulate mass balance of solutes under certain natural conditions. Solute transport models generally are not good for predicting future conditions with a high degree of certainty, or for determining concentrations precisely. The mathematical treatment of solute transport far surpasses their understanding of the process. Investigations of the extent of groundwater contamination and methods to remedy existing problems show the along-term nature of the hazard. Industrial organic compounds may be immiscible in water, highly volatile, or complexed with inorganic as well as other organic compounds; many remain stable in nature almost indefinitely. In the worst case, future disposal of hazardous waste may be restricted to deep burial, as is proposed for radioactive wastes. For investigations pertinent to transport of radionuclides from a geologic repository, the process cannot be fully understood without adequate thermodynamic and kinetic data bases

  6. Xyce parallel electronic simulator design : mathematical formulation, version 2.0.

    Energy Technology Data Exchange (ETDEWEB)

    Hoekstra, Robert John; Waters, Lon J.; Hutchinson, Scott Alan; Keiter, Eric Richard; Russo, Thomas V.

    2004-06-01

    This document is intended to contain a detailed description of the mathematical formulation of Xyce, a massively parallel SPICE-style circuit simulator developed at Sandia National Laboratories. The target audience of this document are people in the role of 'service provider'. An example of such a person would be a linear solver expert who is spending a small fraction of his time developing solver algorithms for Xyce. Such a person probably is not an expert in circuit simulation, and would benefit from an description of the equations solved by Xyce. In this document, modified nodal analysis (MNA) is described in detail, with a number of examples. Issues that are unique to circuit simulation, such as voltage limiting, are also described in detail.

  7. Mathematical modeling of the dynamic stability of fluid conveying pipe based on integral equation formulations

    International Nuclear Information System (INIS)

    Elfelsoufi, Z.; Azrar, L.

    2016-01-01

    In this paper, a mathematical modeling of flutter and divergence analyses of fluid conveying pipes based on integral equation formulations is presented. Dynamic stability problems related to fluid pressure, velocity, tension, topography slope and viscoelastic supports and foundations are formulated. A methodological approach is presented and the required matrices, associated to the influencing fluid and pipe parameters, are explicitly given. Internal discretizations are used allowing to investigate the deformation, the bending moment, slope and shear force at internal points. Velocity–frequency, pressure-frequency and tension-frequency curves are analyzed for various fluid parameters and internal elastic supports. Critical values of divergence and flutter behaviors with respect to various fluid parameters are investigated. This model is general and allows the study of dynamic stability of tubes crossed by stationary and instationary fluid on various types of supports. Accurate predictions can be obtained and are of particular interest for a better performance and for an optimal safety of piping system installations. - Highlights: • Modeling the flutter and divergence of fluid conveying pipes based on RBF. • Dynamic analysis of a fluid conveying pipe with generalized boundary conditions. • Considered parameters fluid are the pressure, tension, slopes topography, velocity. • Internal support increase the critical velocity value. • This methodologies determine the fluid parameters effects.

  8. Bogolyubov renormalization group and symmetry of solution in mathematical physics

    International Nuclear Information System (INIS)

    Shirkov, D.V.; Kovalev, V.F.

    2000-01-01

    Evolution of the concept known in the theoretical physics as the Renormalization Group (RG) is presented. The corresponding symmetry, that has been first introduced in QFT in mid-fifties, is a continuous symmetry of a solution with respect to transformation involving parameters (e.g., of boundary condition) specifying some particular solution. After short detour into Wilson's discrete semi-group, we follow the expansion of QFT RG and argue that the underlying transformation, being considered as a reparametrization one, is closely related to the self-similarity property. It can be treated as its generalization, the Functional Self-similarity (FS). Then, we review the essential progress during the last decade of the FS concept in application to boundary value problem formulated in terms of differential equations. A summary of a regular approach recently devised for discovering the RG = FS symmetries with the help of the modern Lie group analysis and some of its applications are given. As a main physical illustration, we give application of a new approach to solution for a problem of self-focusing laser beam in a nonlinear medium

  9. Mathematical bridges

    CERN Document Server

    Andreescu, Titu; Tetiva, Marian

    2017-01-01

    Building bridges between classical results and contemporary nonstandard problems, Mathematical Bridges embraces important topics in analysis and algebra from a problem-solving perspective. Blending old and new techniques, tactics and strategies used in solving challenging mathematical problems, readers will discover numerous genuine mathematical gems throughout that will heighten their appreciation of the inherent beauty of mathematics. Most of the problems are original to the authors and are intertwined in a well-motivated exposition driven by representative examples. The book is structured to assist the reader in formulating and proving conjectures, as well as devising solutions to important mathematical problems by making connections between various concepts and ideas from different areas of mathematics. Instructors and educators teaching problem-solving courses or organizing mathematics clubs, as well as motivated mathematics students from high school juniors to college seniors, will find Mathematical Bri...

  10. Using Assessment for Learning Mathematics with Mobile Tablet Based Solutions

    Directory of Open Access Journals (Sweden)

    Ghislain Maurice Norbert Isabwe

    2014-03-01

    Full Text Available This article discusses assessment for learning in mathematics subjects. Teachers of large classes face the challenge of regularly assessing studentsཿ ongoing mathematical learning achievements. Taking the complexity of assessment and feedback for learning as a background, we have developed a new approach to the assessment for learning mathematics at university level. We devised mobile tablet technology supported assessment processes, and we carried out user studies in both Rwanda and Norway. Results of our study indicated that students found it fruitful to be involved in assessing other studentsཿ mathematics work, i.e. assessing fellow studentsཿ answers to mathematical tasks. By being involved in the assessment process, the students expected mathematical learning gains. Their providing and obtaining of feedback to/from their fellow students using technology supported tools were highly appreciated as regards their own mathematical learning process.

  11. Mathematical description of adsorption and transport of reactive solutes in soil: a review of selected literature

    International Nuclear Information System (INIS)

    Travis, C.C.

    1978-10-01

    This report reviews selected literature related to the mathematical description of the transport of reactive solutes through soil. The primary areas of the literature reviewed are (1) mathematical models in current use for description of the adsorption-desorption interaction between the soil solution and the soil matrix and (2) analytic solutions of the differential equations describing the convective-dispersive transport of reactive solutes through soil

  12. Formulation and Development of Metered Dose Inhalations of Salbutamol in Solution Form

    Science.gov (United States)

    Khale, Anubha; Bajaj, Amrita

    2011-01-01

    In the present study attempts were made to prepare metered dose inhalation of salbutamol in solution form and compared it with the marketed metered dose inhalation in suspension form. Solution form of the drug was found better than marketed suspension formulation with respect to homogeneity and content uniformity. Propellant blend P-11 and P-12 in the proportion 30:70 was selected as it gave optimum vapour pressure. Surfactant oleic acid in concentration 10 mg per can was selected as it gave best results with clarity, spray pattern, vapour pressure, content per spray and rate of evaporation. Ethyl alcohol 2 ml per can was used as a cosolvent to give a clear solution, optimum vapour pressure, maximum content per spray and fair rate of evaporation. The selected formulation was subjected to the physico-chemical evaluation tests as per the standard pharmacopoeial procedures and the characteristics of the formulations were further compared with a conventional marketed formulation. In vitro study reveled the net respirable fraction was better than marketed preparation. PMID:22923867

  13. Notes on the students’ solutions of Mathematical Olympiad problems

    OpenAIRE

    Veilande, Ingrida

    2015-01-01

    The quality of mathematics education in schools of Latvia can be evaluated by several criteria: on national level – by the results of centralized examination, by diagnostic tests, by students’ achievements in educational Olympiads, and in international comparison – by analysis of results of students’ assessment programs such as TIMSS and PISA. These statistics identify the major problems in mathematics education.

  14. Relative bioavailability of diclofenac potassium from softgel capsule versus powder for oral solution and immediate-release tablet formulation.

    Science.gov (United States)

    Bende, Girish; Biswal, Shibadas; Bhad, Prafulla; Chen, Yuming; Salunke, Atish; Winter, Serge; Wagner, Robert; Sunkara, Gangadhar

    2016-01-01

    The oral bioavailability of diclofenac potassium 50 mg administered as a soft gelatin capsule (softgel capsule), powder for oral solution (oral solution), and tablet was evaluated in a randomized, open-label, 3-period, 6-sequence crossover study in healthy adults. Plasma diclofenac concentrations were measured using a validated liquid chromatography-mass spectrometry/mass spectrometry method, and pharmacokinetic analysis was performed by noncompartmental methods. The median time to achieve peak plasma concentrations of diclofenac was 0.5, 0.25, and 0.75 hours with the softgel capsule, oral solution, and tablet formulations, respectively. The geometric mean ratio and associated 90%CI for AUCinf, and Cmax of the softgel capsule formulation relative to the oral solution formulation were 0.97 (0.95-1.00) and 0.85 (0.76-0.95), respectively. The geometric mean ratio and associated 90%CI for AUCinf and Cmax of the softgel capsule formulation relative to the tablet formulation were 1.04 (1.00-1.08) and 1.67 (1.43-1.96), respectively. In conclusion, the exposure (AUC) of diclofenac with the new diclofenac potassium softgel capsule formulation was comparable to that of the existing oral solution and tablet formulations. The peak plasma concentration of diclofenac from the new softgel capsule was 67% higher than the existing tablet formulation, whereas it was 15% lower in comparison with the oral solution formulation. © 2015, The American College of Clinical Pharmacology.

  15. Spectral theory and quantum mechanics mathematical foundations of quantum theories, symmetries and introduction to the algebraic formulation

    CERN Document Server

    Moretti, Valter

    2017-01-01

    This book discusses the mathematical foundations of quantum theories. It offers an introductory text on linear functional analysis with a focus on Hilbert spaces, highlighting the spectral theory features that are relevant in physics. After exploring physical phenomenology, it then turns its attention to the formal and logical aspects of the theory. Further, this Second Edition collects in one volume a number of useful rigorous results on the mathematical structure of quantum mechanics focusing in particular on von Neumann algebras, Superselection rules, the various notions of Quantum Symmetry and Symmetry Groups, and including a number of fundamental results on the algebraic formulation of quantum theories. Intended for Master's and PhD students, both in physics and mathematics, the material is designed to be self-contained: it includes a summary of point-set topology and abstract measure theory, together with an appendix on differential geometry. The book also benefits established researchers by organizing ...

  16. Una formulación matemática y de solución para programar cirugías con restricciones de recursos humanos en el hospital público A mathematical formulation and solution to schedule surgeries with human resource constraints in a public hospital

    Directory of Open Access Journals (Sweden)

    Lorena Pradenas Rojas

    2012-08-01

    Full Text Available Actualmente, los hospitales públicos nacionales e internacionales presentan demandas que sobrepasan la capacidad de atención, lo que ha provocado un creciente interés por usar herramientas de gestión en los centros clínicos que les permita realizar de forma eficiente y eficaz la entrega de servicios a los distintos pacientes. El presente estudio aporta una nueva forma de abordar el problema de programación de cirugías, desde la programación matemática, presentando un modelo de optimización multiobjetivo y un algoritmo metaheurístico implementado computacionalmente, que permite la programación semanal de intervenciones quirúrgicas, cumpliendo con los requerimientos de pabellones y personal especializado necesario para su realización. Se utiliza una instancia de prueba, donde el tiempo de ejecución del algoritmo, implementado en C++, fue de siete minutos para 191 cirugías en lista de espera. El tiempo alcanzado es considerablemente menor a la programación realizada con un sistema manual, como los actualmente usados en hospitales públicos.Currently, national and international public hospitals have demands that exceed their service capacity, which has caused a growing interest in management sciences to deliver these medical centers the tools that will enable them to perform efficiently and effectively, delivering services to different patients. This study provides a new way of approaching the problem of surgical scheduling using mathematical programming, presenting a multi-objective optimization model and a metaheuristic algorithm implemented computationall. The solution allows weekly schedule of surgical procedure and complying with the requirements of the flag and expertise necessary for realization. We ordered test instances where the execution time of the algorithm, coded in C++, was 7 minutes for a 191 surgeries waiting list, which is a considerable less amount of time to this schedule than using a manual approach. The latest

  17. MATHEMATICAL MODELLING OF PREFERED SOLUTIONS CHOICE FUNCTION FOR TUBULAR GAS HEATERS BY EXPERIMENTAL INFORMATIONS

    Directory of Open Access Journals (Sweden)

    BARSUK R. V.

    2016-08-01

    Full Text Available Annotation. Problems formulation. The article deals with choice functions building of preferred solutions by experimental information for tubular gas heater working on fuel granules - pellets.Further choice functions using for making technical solutions by tubular gas heaters construction and designing. Recently research analysis. There are works about choice functions construction by separate presents are examined. But full chose functions building by separate presents are not examined. Aims and tasks. There are setting aim to develop full choice functions mathematical model on separate presents by authors. The expert are connect to primary experimental data’s evaluation that estimates separate results by output functions (criteria. Its evaluations issue in experimental points paired comparison’s table form. Thus, there are necessary construct binary choice relations presents on experimental “points” set by expert that then using for full choice function’s constructing. Conclusions. There are choice function’s construction’s sequence are sets. There are posed point comparison results that characterized tubular gas heater’s condition with expert’s evaluation using. Also posed output functions comparisons by which can be characterized improving tubular gas heater’s performance or vice versa.

  18. Formulation and stability of an extemporaneous 0.02% chlorhexidine digluconate ophthalmic solution.

    Science.gov (United States)

    Lin, Shu-Chiao; Huang, Chih-Fen; Shen, Li-Jiuan; Wang, Hsueh-Ju; Lin, Chia-Yu; Wu, Fe-Lin Lin

    2015-12-01

    Acanthamoeba keratitis is difficult to treat because Acanthamoeba cysts are resistant to the majority of antimicrobial agents. Despite the efficacy of 0.02% chlorhexidine in treating Acanthamoeba keratitis, a lack of data in the literature regarding the formulation's stability limits its clinical use. The objective of this study was to develop an optimal extemporaneous 0.02% chlorhexidine digluconate ophthalmic formulation for patients in need. With available active pharmaceutical ingredients, 0.02% chlorhexidine digluconate sample solutions were prepared by diluting with BSS Plus Solution or acetate buffer. Influences of the buffer, type of container, and temperature under daily-open condition were assessed based on the changes of pH values and chlorhexidine concentrations of the test samples weekly. To determine the beyond-use date, the optimal samples were stored at 2-8°C or room temperature, and analyzed at time 0 and at Week 1, Week 2, Week 3, Week 4, Week 5, Week 8, Week 12, and Week 24. Despite chlorhexidine exhibiting better stability in acetate buffer than in BSS solution, its shelf-life was stability at 2-25°C for 6 months after being sealed and for 1 month after opening. This finding will enable us to prepare 0.02% chlorhexidine digluconate ophthalmic solutions based on a doctor's prescription. Copyright © 2014. Published by Elsevier B.V.

  19. A mathematical formulation of the Mahaux-Weidenmueller formula for the scattering matrix

    International Nuclear Information System (INIS)

    Christiansen, T J; Zworski, M

    2009-01-01

    This paper gives a mathematical exposition of a formula for the scattering matrix for a manifold with infinite cylindrical ends or a waveguide. This formula is well known in the physics literature and we show that a variant of this formula gives the scattering matrix of the mathematics literature. Moreover, we bound the difference between the scattering matrix and an approximation of it computed using a finite rank approximation of the interaction matrix.

  20. Formulation of natural convection around repository for dual reciprocity boundary element solution

    International Nuclear Information System (INIS)

    Vrankar, L.; Sarler, B.

    1998-01-01

    The disposal of high-level radioactive wastes in deep geological formations is of pronounced technological importance for nuclear safety. The understanding of related fluid flow, heat and mass transport in geological systems is of great interest. This article prepares necessary physical, mathematical and numerical fundamentals for computational modeling of related phenomena. The porous media is described by the simple Darcy law and momentum-energy coupling is due to Boussinesq approximation. The Dual Reciprocity of Boundary Element Method (DRBEM) is used for solving coupled mass, momentum and energy equations in two-dimensions for the steady buoyancy induced convection problem in an semi-infinite porous media. It is structured by weighting with the fundamental solution of the Laplace equation. The inverse multi quadrics are used in the DRBEM transformation. The solution is obtained in an iterative way.(author)

  1. Theoretical study on the sound absorption of electrolytic solutions. I. Theoretical formulation

    Science.gov (United States)

    Yamaguchi, T.; Matsuoka, T.; Koda, S.

    2007-04-01

    A theory is formulated that describes the sound absorption of electrolytic solutions due to the relative motion of ions, including the formation of ion pairs. The theory is based on the Kubo-Green formula for the bulk viscosity. The time correlation function of the pressure is projected onto the bilinear product of the density modes of ions. The time development of the product of density modes is described by the diffusive limit of the generalized Langevin equation, and approximate expressions for the three- and four-body correlation functions required are given with the hypernetted-chain integral equation theory. Calculations on the aqueous solutions of model electrolytes are performed. It is demonstrated that the theory describes both the activated barrier crossing between contact and solvent-separated ion pairs and the Coulombic correlation between ions.

  2. A mathematical model of a steady flow through the Kaplan turbine - The existence of a weak solution in the case of an arbitrarily large inflow

    Science.gov (United States)

    Neustupa, Tomáš

    2017-07-01

    The paper presents the mathematical model of a steady 2-dimensional viscous incompressible flow through a radial blade machine. The corresponding boundary value problem is studied in the rotating frame. We provide the classical and weak formulation of the problem. Using a special form of the so called "artificial" or "natural" boundary condition on the outflow, we prove the existence of a weak solution for an arbitrarily large inflow.

  3. PEGylated polylysine dendrimers increase lymphatic exposure to doxorubicin when compared to PEGylated liposomal and solution formulations of doxorubicin.

    Science.gov (United States)

    Ryan, Gemma M; Kaminskas, Lisa M; Bulitta, Jürgen B; McIntosh, Michelle P; Owen, David J; Porter, Christopher J H

    2013-11-28

    Improved delivery of chemotherapeutic drugs to the lymphatic system has the potential to augment outcomes for cancer therapy by enhancing activity against lymph node metastases. Uptake of small molecule chemotherapeutics into the lymphatic system, however, is limited. Nano-sized drug carriers have the potential to promote access to the lymphatics, but to this point, this has not been examined in detail. The current study therefore evaluated the lymphatic exposure of doxorubicin after subcutaneous and intravenous administration as a simple solution formulation or when formulated as a doxorubicin loaded PEGylated poly-lysine dendrimer (hydrodynamic diameter 12 nm), a PEGylated liposome (100 nm) and various pluronic micellar formulations (~5 nm) to thoracic lymph duct cannulated rats. Plasma and lymph pharmacokinetics were analysed by compartmental pharmacokinetic modelling in S-ADAPT, and Berkeley Madonna software was used to predict the lymphatic exposure of doxorubicin over an extended period of time. The micelle formulations displayed poor in vivo stability, resulting in doxorubicin profiles that were similar to that observed after administration of the doxorubicin solution formulation. In contrast, the dendrimer formulation significantly increased the recovery of doxorubicin in the thoracic lymph after both intravenous and subcutaneous dosing when compared to the solution or micellar formulation. Dendrimer-doxorubicin also resulted in increases in lymphatic doxorubicin concentrations when compared to the liposome formulation, although liposomal doxorubicin did increase lymphatic transport when compared to the solution formulation. Specifically, the dendrimer formulation increased the recovery of doxorubicin in the lymph up to 30 h post dose by up to 685 fold and 3.7 fold when compared to the solution and liposomal formulations respectively. Using the compartmental model to predict lymphatic exposure to longer time periods suggested that doxorubicin exposure to

  4. Formulation and stability of an extemporaneously compounded oral solution of chlorpromazine HCl.

    Science.gov (United States)

    Prohotsky, Daniel L; Juba, Katherine M; Zhao, Fang

    2014-12-01

    Chlorpromazine is a phenothiazine antipsychotic which is often used in hospice and palliative care to treat hiccups, delirium, and nausea. With the discontinuation of the commercial oral solution concentrate, there is a need to prepare this product by extemporaneous compounding. This study was initiated to identify an easy-to-prepare formulation for the compounding pharmacist. A stability study was also conducted to select the proper storage conditions and establish the beyond-use date. Chlorpromazine HCl powder and the Ora-Sweet® syrup vehicle were used to prepare the 100 mg/mL solution. Once the feasibility was established, a batch of the solution was prepared and packaged in amber plastic prescription bottles for a stability study. These samples were stored at refrigeration (2-8°C) or room temperature (20-25°C) for up to 3 months. At each monthly time point, the samples were evaluated by visual inspection, pH measurement, and high performance liquid chromatography (HPLC). A separate forced stability study was conducted to confirm that the HPLC method was stability indicating. A clear and colorless solution of 100 mg/mL chlorpromazine HCl was obtained by dissolving the drug powder in Ora-Sweet® with moderate agitation. The stability study results indicated that this solution product remained unchanged in visual appearance or pH at both refrigeration and room temperature for up to 3 months. The HPLC results also confirmed that all stability samples retained 93.6-101.4% of initial drug concentration. Chlorpromazine HCl solution 100 mg/mL can be compounded extemporaneously by dissolving chlorpromazine HCl drug powder in Ora-Sweet®. The resulting product is stable for at least three months in amber plastic prescription bottles stored at either refrigeration or room temperature.

  5. Principles of mathematical economics II solutions manual, supplementary materials and supplementary exercises

    CERN Document Server

    Vali, Shapoor

    2015-01-01

    This manual provides solutions to approximately 500 problems appeared in various chapters of the text Principles of Mathematical Economics. In some cases, a detailed solution with the additional discussion is provided. At the end of each chapter, new sets of exercises are given.

  6. MATHEMATICAL FORMULATION OF PLASTIC CHARACTERISTICS OF WIRE OF STEEL 70 AT HIGH-SPEED WIRE DRAWING

    Directory of Open Access Journals (Sweden)

    Yu. L. Bobarikin

    2011-01-01

    Full Text Available The carried out numerical experiments subject to initial and boundary conditions indicate that mathematical model of elastic-plastic characteristics of steel 90 can be used for numerical calculations of wire drawing routes for this grade of steel.

  7. A Mathematical Model of Solute Coupled Water Transport in Toad Intestine Incorporating Recirculation of the Actively Transported Solute

    DEFF Research Database (Denmark)

    Larsen, Erik Hviid; Sørensen, Jakob Balslev; Sørensen, Jens Nørkær

    2000-01-01

    those of tight junction and interspace basement membrane by convection-diffusion. With solute permeability of paracellular pathway large relative to paracellular water flow, the paracellular flux ratio of the solute (influx/outflux) is small (2-4) in agreement with experiments. The virtual solute......A mathematical model of an absorbing leaky epithelium is developed for analysis of solute coupled water transport. The non-charged driving solute diffuses into cells and is pumped from cells into the lateral intercellular space (lis). All membranes contain water channels with the solute passing...... increases with hydraulic conductance of the pathway carrying water from mucosal solution into lis. Uphill water transport is accomplished, but with high hydraulic conductance of cell membranes strength of transport is obscured by water flow through cells. Anomalous solvent drag occurs when back flux...

  8. Mathematical modeling of fluid and solute transport in peritoneal dialysis

    OpenAIRE

    Waniewski, Jacek

    2001-01-01

    Optimization of peritoneal dialysis schedule and dialysis fluid composition needs, among others, methods for quantitative assessment of fluid and solute transport. Furthermore, an integrative quantitative description of physiological processes within the tissue, which contribute to the net transfer of fluid and solutes, is necessary for interpretation of the data and for predictions of the outcome of possible intervention into the peritoneal transport system. The current pro...

  9. Generalized dynamics of soft-matter quasicrystals mathematical models and solutions

    CERN Document Server

    Fan, Tian-You

    2017-01-01

    The book systematically introduces the mathematical models and solutions of generalized hydrodynamics of soft-matter quasicrystals (SMQ). It provides methods for solving the initial-boundary value problems in these systems. The solutions obtained demonstrate the distribution, deformation and motion of the soft-matter quasicrystals, and determine the stress, velocity and displacement fields. The interactions between phonons, phasons and fluid phonons are discussed in some fundamental materials samples. Mathematical solutions for solid and soft-matter quasicrystals are compared, to help readers to better understand the featured properties of SMQ.

  10. Mathematical modelling and numerical solution of swelling of cartilaginous tissues. Part II: Mixed hybrid finite element solution

    NARCIS (Netherlands)

    Malakpoor, K.; Kaasschieter, E.F.; Huyghe, J.M.R.J.

    2007-01-01

    The swelling and shrinkage of biological tissues are modelled by a four-component mixture theory [J.M. Huyghe and J.D. Janssen, Int. J. Engng. Sci. 35 (1997) 793-802; K. Malakpoor, E.F. Kaasschieter and J.M. Huyghe, Mathematical modelling and numerical solution of swelling of cartilaginous tissues.

  11. Mathematical model for the formulation of runoff scenarios before possible variants of the climatic change

    International Nuclear Information System (INIS)

    Dominguez Calle, Efrain Antonio

    2001-01-01

    The application of mathematical modelling to evaluate the hydrological response of different river basins under multiple climate scenarios has become a wide spread tool. However, most of the existing models demand high volumes of data and high data quality. Usually, in Latin America not only the amount of data is scarce, but also the quality of it is very poor, so it is difficult to implement mathematical models with good validation results. Additionally, those models have to be applied over big geographical regions making the hydrological modelling process an almost impossible task. All these factors are pointing to the necessity to develop low data demanding models with few data quality requirements. In this light, this paper shows an attempt to develop a hydrological model under these restrictions. The results shown are concerned with the validation assessment of a study case in Colombia over an extensive region for the Catatumbo watershed. Finally, the improvements currently under implementation are shown

  12. Mathematical Formulation used by MATLAB Code to Convert FTIR Interferograms to Calibrated Spectra

    Energy Technology Data Exchange (ETDEWEB)

    Armstrong, Derek Elswick [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2016-07-19

    This report discusses the mathematical procedures used to convert raw interferograms from Fourier transform infrared (FTIR) sensors to calibrated spectra. The work discussed in this report was completed as part of the Helios project at Los Alamos National Laboratory. MATLAB code was developed to convert the raw interferograms to calibrated spectra. The report summarizes the developed MATLAB scripts and functions, along with a description of the mathematical methods used by the code. The first step in working with raw interferograms is to convert them to uncalibrated spectra by applying an apodization function to the raw data and then by performing a Fourier transform. The developed MATLAB code also addresses phase error correction by applying the Mertz method. This report provides documentation for the MATLAB scripts.

  13. Computer Facilitated Mathematical Methods in Chemical Engineering--Similarity Solution

    Science.gov (United States)

    Subramanian, Venkat R.

    2006-01-01

    High-performance computers coupled with highly efficient numerical schemes and user-friendly software packages have helped instructors to teach numerical solutions and analysis of various nonlinear models more efficiently in the classroom. One of the main objectives of a model is to provide insight about the system of interest. Analytical…

  14. A matrix formulation of Frobenius power series solutions using products of 4X4 matrices

    Directory of Open Access Journals (Sweden)

    Jeremy Mandelkern

    2015-08-01

    Full Text Available In Coddington and Levison [7, p. 119, Thm. 4.1] and Balser [4, p. 18-19, Thm. 5], matrix formulations of Frobenius theory, near a regular singular point, are given using 2X2 matrix recurrence relations yielding fundamental matrices consisting of two linearly independent solutions together with their quasi-derivatives. In this article we apply a reformulation of these matrix methods to the Bessel equation of nonintegral order. The reformulated approach of this article differs from [7] and [4] by its implementation of a new ``vectorization'' procedure that yields recurrence relations of an altogether different form: namely, it replaces the implicit 2X2 matrix recurrence relations of both [7] and [4] by explicit 4X4 matrix recurrence relations that are implemented by means only of 4X4 matrix products. This new idea of using a vectorization procedure may further enable the development of symbolic manipulator programs for matrix forms of the Frobenius theory.

  15. The Henry-Saltwater Intrusion Benchmark – Alternatives in Multiphysics Formulations and Solution Strategies

    Directory of Open Access Journals (Sweden)

    E Holzbecher

    2016-03-01

    Full Text Available In a classical paper Henry set up a conceptual model for simulating saltwater intrusion into coastal aquifers. Up to now the problem has been taken up by software developers and modellers as a benchmark for codes simulating coupled flow and transport in porous media. The Henry test case has been treated using different numerical methods based on various formulations of differential equations. We compare several of these approaches using multiphysics software. We model the problem using Finite Elements, utilizing the primitive variables and the streamfunction approach, both with and without using the Oberbeck-Boussinesq assumption. We compare directly coupled solvers with segregated solver strategies. Changing finite element orders and mesh refinement, we find that models based on the streamfunction converge 2-4 times faster than runs based on primitive variables. Concerning the solution strategy, we find an advantage of Picard iterations compared to monolithic Newton iterations.

  16. Exact and Numerical Solutions of a Spatially-Distributed Mathematical Model for Fluid and Solute Transport in Peritoneal Dialysis

    Directory of Open Access Journals (Sweden)

    Roman Cherniha

    2016-06-01

    Full Text Available The nonlinear mathematical model for solute and fluid transport induced by the osmotic pressure of glucose and albumin with the dependence of several parameters on the hydrostatic pressure is described. In particular, the fractional space available for macromolecules (albumin was used as a typical example and fractional fluid void volume were assumed to be different functions of hydrostatic pressure. In order to find non-uniform steady-state solutions analytically, some mathematical restrictions on the model parameters were applied. Exact formulae (involving hypergeometric functions for the density of fluid flux from blood to tissue and the fluid flux across tissues were constructed. In order to justify the applicability of the analytical results obtained, a wide range of numerical simulations were performed. It was found that the analytical formulae can describe with good approximation the fluid and solute transport (especially the rate of ultrafiltration for a wide range of values of the model parameters.

  17. Optimization of energy and water use in multipurpose batch plants using an improved mathematical formulation

    CSIR Research Space (South Africa)

    Seid, ER

    2014-05-01

    Full Text Available and its as- sociated thermal storage policy for recircu- lated hot/cold heat storage medium (HEN). Most of the previous works solved this se- quentially. Foo et al. (2008) extended the minimum units targeting and network evo- lution techniques that were...) reviewed these techniques based on graphical-based pinch analysis and mathematical optimization approach. The seminal work on pinch analysis application to batch water network was reported by Wang and Smith (1994). Foo et al. (2005) proposed a time...

  18. Osteoprotegerin in bone metastases: mathematical solution to the puzzle.

    Directory of Open Access Journals (Sweden)

    Marc D Ryser

    Full Text Available Bone is a common site for cancer metastasis. To create space for their growth, cancer cells stimulate bone resorbing osteoclasts. Cytokine RANKL is a key osteoclast activator, while osteoprotegerin (OPG is a RANKL decoy receptor and an inhibitor of osteoclastogenesis. Consistently, systemic application of OPG decreases metastatic tumor burden in bone. However, OPG produced locally by cancer cells was shown to enhance osteolysis and tumor growth. We propose that OPG produced by cancer cells causes a local reduction in RANKL levels, inducing a steeper RANKL gradient away from the tumor and towards the bone tissue, resulting in faster resorption and tumor expansion. We tested this hypothesis using a mathematical model of nonlinear partial differential equations describing the spatial dynamics of OPG, RANKL, PTHrP, osteoclasts, tumor and bone mass. We demonstrate that at lower expression rates, tumor-derived OPG enhances the chemotactic RANKL gradient and osteolysis, whereas at higher expression rates OPG broadly inhibits RANKL and decreases osteolysis and tumor burden. Moreover, tumor expression of a soluble mediator inducing RANKL in the host tissue, such as PTHrP, is important for correct orientation of the RANKL gradient. A meta-analysis of OPG, RANKL and PTHrP expression in normal prostate, carcinoma and metastatic tissues demonstrated an increase in expression of OPG, but not RANKL, in metastatic prostate cancer, and positive correlation between OPG and PTHrP in metastatic prostate cancer. The proposed mechanism highlights the importance of the spatial distribution of receptors, decoys and ligands, and can be applied to other systems involving regulation of spatially anisotropic processes.

  19. Coupled Fluid, Energy, and Solute Transport (CFEST) model: Formulation and user's manual

    International Nuclear Information System (INIS)

    Gupta, S.K.; Cole, C.R.; Kincaid, C.T.; Monti, A.M.

    1987-10-01

    The CFEST (Coupled Fluid, Energy, and Solute Transport) code has been developed to analyze coupled hydrologic, thermal, and solute transport processes. It treats single-pahse Darcy ground-water flow in a horizontal or vertical plane, or in fully three-dimensional space under nonisothermal conditions. The code has the capability to model discontinuous and continuous layering, time-dependent and constant sources/sinks, and transient as well as steady-stae ground-water flow. The code offers a wide choice of boundary conditions such as precsribed heads, nodal injection or withdrawal, constant or spatially varying infiltration rates, and welemental source/sink. Initial conditions for the flow analysis can be prescribed pressure or hydraulic head. The heterogeneity in aquifer permeability and porosity can be described by geologic unit or explicity for given elements. Three-dimensional elelments are generated from user-defined well logs at each surface node. To facilitate interaction between disciplines, support programs are provided to plot the finite element grid, well logs, contour maps of input and output parameters, and vertical cross sections. Ground-water travel paths and times and volumetric rates from a specified point can be determined from support programs. This report includes governing partial differential equations, finite element formulation, a use's manual, verification test examples, sample problems, and source listings. 36 refs., 121 figs., 36 tabs

  20. Fast estimation of space-robots inertia parameters: A modular mathematical formulation

    Science.gov (United States)

    Nabavi Chashmi, Seyed Yaser; Malaek, Seyed Mohammad-Bagher

    2016-10-01

    This work aims to propose a new technique that considerably helps enhance time and precision needed to identify ;Inertia Parameters (IPs); of a typical Autonomous Space-Robot (ASR). Operations might include, capturing an unknown Target Space-Object (TSO), ;active space-debris removal; or ;automated in-orbit assemblies;. In these operations generating precise successive commands are essential to the success of the mission. We show how a generalized, repeatable estimation-process could play an effective role to manage the operation. With the help of the well-known Force-Based approach, a new ;modular formulation; has been developed to simultaneously identify IPs of an ASR while it captures a TSO. The idea is to reorganize the equations with associated IPs with a ;Modular Set; of matrices instead of a single matrix representing the overall system dynamics. The devised Modular Matrix Set will then facilitate the estimation process. It provides a conjugate linear model in mass and inertia terms. The new formulation is, therefore, well-suited for ;simultaneous estimation processes; using recursive algorithms like RLS. Further enhancements would be needed for cases the effect of center of mass location becomes important. Extensive case studies reveal that estimation time is drastically reduced which in-turn paves the way to acquire better results.

  1. Advances in mathematical economics

    CERN Document Server

    Maruyama, Toru

    2015-01-01

    The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.

  2. Advances in mathematical economics

    CERN Document Server

    Maruyama, Toru

    2014-01-01

    A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research.

  3. Advances in mathematical economics

    CERN Document Server

    Yamazaki, Akira

    2006-01-01

    A lot of economic problems can formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who were seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking for effective mathematical tools for their researchers.

  4. Advances in mathematical economics

    CERN Document Server

    Yamazaki, Akira

    2006-01-01

    A lot of economic problems can formulated as constrained optimizations and equilibration of their solutions.Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who were seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking for effective mathematical tools for their researchers.

  5. Advances in mathematical economics

    CERN Document Server

    Maruyama, Toru

    2017-01-01

    The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.

  6. Advances in mathematical economics

    CERN Document Server

    Maruyama, Toru

    2016-01-01

    The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.

  7. A new mathematical formulation of the line-by-line method in case of weak line overlapping

    Science.gov (United States)

    Ishov, Alexander G.; Krymova, Natalie V.

    1994-01-01

    A rigorous mathematical proof is presented for multiline representation on the equivalent width of a molecular band which consists in the general case of n overlapping spectral lines. The multiline representation includes a principal term and terms of minor significance. The principal term is the equivalent width of the molecular band consisting of the same n nonoverlapping spectral lines. The terms of minor significance take into consideration the overlapping of two, three and more spectral lines. They are small in case of the weak overlapping of spectral lines in the molecular band. The multiline representation can be easily generalized for optically inhomogeneous gas media and holds true for combinations of molecular bands. If the band lines overlap weakly the standard formulation of line-by-line method becomes too labor-consuming. In this case the multiline representation permits line-by-line calculations to be performed more effectively. Other useful properties of the multiline representation are pointed out.

  8. Electromagnetic Modeling of the Propagation Characteristics of Satellite Communications Through Composite Precipitation Layers, Part1: Mathematical Formulation

    Directory of Open Access Journals (Sweden)

    H.M. Al-Rizzo

    2000-12-01

    Full Text Available A systematic and general formulation of a Propagation Simulation Program (PSP is developed for the coherent field of microwave and millimeter wave carrier signals traversing intermediate layered precipitation media, taking into account the random behavior of particle size, orientation, shape and concentration distributions.  Based on a rigorous solution of the volumetric multiple-scattering integral equations, the formalism offers the capability of treating the potential transmission impairments on satellite-earth links and radar remote sensing generated by composite atmospheric layers of precipitation in conjunction with the finite polarization isolation of dual-polarized transmitting and receiving antennas. A multi-layered formulation is employed which encompasses an ensemble of discrete particles comprising an arbitrary mixture of ice crystals, melting snow and raindrops that may exist simultaneously along satellite-earth communication paths.

  9. Mathematical formulation of temperature fluctuation and control rod vibration in PARR

    International Nuclear Information System (INIS)

    Ansari, S.A.; Ayazuddin, S.K.

    This report describes the mathematical interpretation of experimental neutron noise spectra obtained for PARR core. A one dimensional thermal-hydraulic model of PARR core was developed to calculate the magnitude of neutron noise as a result of fluctuation in the core inlet coolant temperature. The sink structure of the neutron power spectral density as well as the dependence of observed neutron spectra on coolant velocity is also explained by the thermal hydraulic model. An attempt is made to explain the phenomena of control rod vibration by a simple eigen frequency vibration model. The calculated neutron power spectral density due to vibration and temperature noise were added and compared with the experimental power spectra obtained for PARR. (orig./A.B.)

  10. Salbutamol sulphate-ethylcellulose microparticles: formulation and in-vitro evaluation with emphasis on mathematical approaches

    Directory of Open Access Journals (Sweden)

    G Murtaza

    2009-10-01

    Full Text Available "n "nBackground and the purpose of the study: This study reports the laboratory optimization for the preparation of salbutamol sulphate-ethylcellulose microparticles by a non-solvent addition coacervation technique through adjustment of the ratio of salbutamol sulphate to ethylcellulose. The variation of drug release between the microparticles and tabletted microparticles was also investigated. "nMethods: In vitro release profiles of developed microparticles and tabletted microparticles were studied using USP XXIV dissolution apparatus I and II, respectively, in 450 ml double distilled water at 50 rpm maintained at 37°C. "nResults: White microparticles with no definite shape having good entrapment efficiency (96.68 to 97.83% and production yield (97.48 ± 1.21 to 98.35 ± 1.08% were obtained. In this investigation, initial burst effect was observed in the drug release behavior. The rate of drug release from microparticles decreased as the concentration of polyisobutylene was increased from 6% to 12% during microencapsulation. The release pattern of tabletted microparticles was affected significantly (p < 0.05 by the addition of hydroxy propyl methyl cellulose (HPMC as excepient and insignificantly (p > 0.05 by the type of dissolution media and stirring speed. Tabletted microparticles showed good stability and reproducibility. Ethylcellulose was found to be compatible with salbutamol sulphate. The drug release from all formulations was best fit to Higuchi's equation and the mechanism of drug release was anomalous diffusion from all formulations. "nConclusion: The results of this study suggest that by using ethylcellulose it is possible to design a single-unit, sustained-release oral dosage form of salbutamol sulphate for indication of twice a day.

  11. The CFEST-INV stochastic hydrology code: Mathematical formulation, application, and user's manual

    International Nuclear Information System (INIS)

    Devary, J.L.

    1987-06-01

    Performance assessments of a nuclear waste repository must consider the hydrologic, thermal, mechanical, and geochemical environments of a candidate site. Predictions of radionuclide transport requires estimating water movement as a function of pressure, temperature, and solute concentration. CFEST (Coupled Fluid, Energy, and Solute Transport), is a finite-element based groundwater code that can be used to simultaneously solve the partial differential equations for pressure head, solute temperature, and solute concentration. The CFEST code has been designed to support site, repository, and waste package subsystem assessments. CFEST-INV is a stochastic hydrology code that was developed to augment the CFEST code in data processing; model calibration; performance prediction; error propagation; and data collection guidance. The CFEST-INV code utilizes kriging, finite-element modeling, adjoint-sensitivity, statistical-inverse, first-order variance, and Monte-Carlo techniques to develop performance (measure) driven data collection schemes and to determine the waste isolation capabilities (including uncertainties) of candidate repository sites. This report contains the basic physical and numerical principles of the CFEST-INV code, its input parameters, verification exercises, a user's manual, and the code's application history. 18 refs., 16 figs., 6 tabs

  12. Development of a mathematical model of a packed column for benzene removal from salt solutions

    International Nuclear Information System (INIS)

    Georgeton, G.K.

    1989-01-01

    A mathematical model of a packed column was developed to describe the removal of benzene from radioactive salt solutions at the Savannah River Site. The model was developed from existing, generalized mass transfer correlations for randomly dumped packing, and the correlations were adapted for structured packing. Thermophysical data specific to the solutions of interest were incorporated into the model. Verification of the code was completed using operating data from stripping columns at other locations

  13. The Way Adults with Orientation to Mathematics Teaching Cope with the Solution of Everyday Real-World Problems

    Science.gov (United States)

    Gazit, Avikam; Patkin, Dorit

    2012-01-01

    The article aims to check the way adults, "some who are" practicing mathematics teachers at elementary school, "some who are" academicians making a career change to mathematics teachers at junior high school and the "rest who are" pre-service mathematics teachers at elementary school, cope with the solution of…

  14. Incorporating electrokinetic effects in the porochemoelastic inclined wellbore formulation and solution

    Directory of Open Access Journals (Sweden)

    Vinh X. Nguyen

    2010-03-01

    Full Text Available The porochemoelectroelastic analytical models and solutions have been used to describe the response of chemically active and electrically charged saturated porous media such as clays, shales, and biological tissues. However, these attempts have been restricted to one-dimensional consolidation problems, which are very limited in practice and not general enough to serve as benchmark solutions for numerical validation. This work summarizes the general linear porochemoelectroelastic formulation and presents the solution of an inclined wellbore drilled in a fluid-saturated chemically active and ionized formation, such as shale, and subjected to a three-dimensional in-situ state of stress. The analytical solution to this geometry incorporates the coupled solid deformation and simultaneous fluid/ion flows induced by the combined influences of pore pressure, chemical potential, and electrical potential gradients under isothermal conditions. The formation pore fluid is modeled as an electrolyte solution comprised of a solvent and one type of dissolved cation and anion. The analytical approach also integrates into the solution the quantitative use of the cation exchange capacity (CEC commonly obtained from laboratory measurements on shale samples. The results for stresses and pore pressure distributions due to the coupled electrochemical effects are illustrated and plotted in the vicinity of the inclined wellbore and compared with the classical porochemoelastic and poroelastic solutions.Modelos analíticos poroelásticos incluindo acoplamento químico e elétrico e soluções têm sido utilizados paradescrever a resposta de meios porosos saturados ativos química e eletricamente tais como argilas, folhelhos e tecidos biológicos. Entretanto tais tentativas têm sido restritas a problemas de consolidação unidimensional os quais exibem limitações na prática não constituindo exemplos realistas para validação de soluções numéricas. Este trabalho

  15. Formulations to overcome the divergence of iterative method of fixed-point in nonlinear equations solution

    Directory of Open Access Journals (Sweden)

    Wilson Rodríguez Calderón

    2015-04-01

    Full Text Available When we need to determine the solution of a nonlinear equation there are two options: closed-methods which use intervals that contain the root and during the iterative process reduce the size of natural way, and, open-methods that represent an attractive option as they do not require an initial interval enclosure. In general, we know open-methods are more efficient computationally though they do not always converge. In this paper we are presenting a divergence case analysis when we use the method of fixed point iteration to find the normal height in a rectangular channel using the Manning equation. To solve this problem, we propose applying two strategies (developed by authors that allow to modifying the iteration function making additional formulations of the traditional method and its convergence theorem. Although Manning equation is solved with other methods like Newton when we use the iteration method of fixed-point an interesting divergence situation is presented which can be solved with a convergence higher than quadratic over the initial iterations. The proposed strategies have been tested in two cases; a study of divergence of square root of real numbers was made previously by authors for testing. Results in both cases have been successful. We present comparisons because are important for seeing the advantage of proposed strategies versus the most representative open-methods.

  16. Optimal Water-Power Flow Problem: Formulation and Distributed Optimal Solution

    Energy Technology Data Exchange (ETDEWEB)

    Dall-Anese, Emiliano [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Zhao, Changhong [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Zamzam, Admed S. [University of Minnesota; Sidiropoulos, Nicholas D. [University of Minnesota; Taylor, Josh A. [University of Toronto

    2018-01-12

    This paper formalizes an optimal water-power flow (OWPF) problem to optimize the use of controllable assets across power and water systems while accounting for the couplings between the two infrastructures. Tanks and pumps are optimally managed to satisfy water demand while improving power grid operations; {for the power network, an AC optimal power flow formulation is augmented to accommodate the controllability of water pumps.} Unfortunately, the physics governing the operation of the two infrastructures and coupling constraints lead to a nonconvex (and, in fact, NP-hard) problem; however, after reformulating OWPF as a nonconvex, quadratically-constrained quadratic problem, a feasible point pursuit-successive convex approximation approach is used to identify feasible and optimal solutions. In addition, a distributed solver based on the alternating direction method of multipliers enables water and power operators to pursue individual objectives while respecting the couplings between the two networks. The merits of the proposed approach are demonstrated for the case of a distribution feeder coupled with a municipal water distribution network.

  17. M3 version 3.0: Concepts, methods, and mathematical formulation

    Energy Technology Data Exchange (ETDEWEB)

    Gomez, Javier B. [Univ. of Zaragoza (Spain). Dept. of Earth Sciences; Laaksoharju, Marcus [Geopoint AB, Sollentuna (Sweden); Skaarman, Erik [Abscondo, Bromma (Sweden); Gurban, Ioana [3D-Terra, Montreal, PQ (Canada)

    2006-07-15

    Hydrochemical evaluation is a complex type of work, carried out by specialists. The outcome of this work is generally presented as qualitative models and process descriptions of a site. To support and help quantify the processes in an objective way, a multivariate mathematical tool named M (Multivariate Mixing and Mass balance calculations) has been constructed. The computer code can be used to trace the origin of the groundwater and calculate the mixing portions and mass balances even from ambiguous groundwater data. The groundwater composition used traditionally to describe the reactions taking place in the bedrock can now be used to trace the present and past groundwater flow with increased accuracy. The M code is a groundwater response model, which means that the changes in the groundwater chemistry in terms of sources and sinks are traced in relation to an ideal mixing model. The complexity of the measured groundwater data determines the configuration of the ideal mixing model. Deviations or similarities with the ideal mixing model are interpreted as being due to mixing or reactions. Assumptions concerning important mineral phases altering the groundwater or uncertainties associated with thermodynamic constants do not affect the modelling because the calculations are solely based on the measured groundwater composition. M uses the opposite approach to that of many standard hydrochemical models. In M mixing is evaluated and calculated first. The constituents that cannot be described by mixing are described by reactions. The M model consists of three steps: the first is a standard principal component analysis, followed by mixing and finally mass balance calculations. The measured groundwater composition can be described in terms of mixing portions in % and the sink/sources of an element associated with reactions are reported in mg/l.

  18. M3 version 3.0: Concepts, methods, and mathematical formulation

    International Nuclear Information System (INIS)

    Gomez, Javier B.; Skaarman, Erik; Gurban, Ioana

    2006-07-01

    Hydrochemical evaluation is a complex type of work, carried out by specialists. The outcome of this work is generally presented as qualitative models and process descriptions of a site. To support and help quantify the processes in an objective way, a multivariate mathematical tool named M (Multivariate Mixing and Mass balance calculations) has been constructed. The computer code can be used to trace the origin of the groundwater and calculate the mixing portions and mass balances even from ambiguous groundwater data. The groundwater composition used traditionally to describe the reactions taking place in the bedrock can now be used to trace the present and past groundwater flow with increased accuracy. The M code is a groundwater response model, which means that the changes in the groundwater chemistry in terms of sources and sinks are traced in relation to an ideal mixing model. The complexity of the measured groundwater data determines the configuration of the ideal mixing model. Deviations or similarities with the ideal mixing model are interpreted as being due to mixing or reactions. Assumptions concerning important mineral phases altering the groundwater or uncertainties associated with thermodynamic constants do not affect the modelling because the calculations are solely based on the measured groundwater composition. M uses the opposite approach to that of many standard hydrochemical models. In M mixing is evaluated and calculated first. The constituents that cannot be described by mixing are described by reactions. The M model consists of three steps: the first is a standard principal component analysis, followed by mixing and finally mass balance calculations. The measured groundwater composition can be described in terms of mixing portions in % and the sink/sources of an element associated with reactions are reported in mg/l

  19. [Efficient Pharmaceutical Formulation Designs and Their Development Using Mathematical and Statistical Analysis].

    Science.gov (United States)

    Iwao, Yasunori

    2015-01-01

    With the aim of directly predicting the functionality and mechanism of pharmaceutical excipients, we investigated an analysis method based on available surface area (S(t)), which is the surface area of a drug in direct contact with the external solvent during dissolution. First, to study the effect of lubricant concentration on the dissolution rate of acetaminophen (APAP), the dissolution behaviors as well as the change over time in S(t) of APAP tablets were examined. In the dissolution tests, a retarded dissolution of APAP was not observed with new lubricant triglycerin full behenate (TR-FB), whereas magnesium stearate (Mg-St) retarded the dissolution. The S(t) profiles for APAP with Mg-St at>0.5% showed downward curvature indicating a gradual decrease in surface area over time. Conversely, with TR-FB, even when its concentration was increased, the S(t) profile for APAP had a maximum value. The differences between Mg-St and TR-FB could be explained by the differences in extensibility deriving from their morphology. Next, we evaluated the effect of disintegtant concentration using five disintegrants. When disintegrant was added to ethenzamide tablet formulation, an increase in the dissolution rate and S(t) dependent on disintegrant concentration was observed, according to the type of disintegrant. It was found that the water absorption ability of disintegrants had strong correlations with the parameters of S(t). Taken together, this study demonstrates that analysis of S(t) can directly provide useful information, especially about the functionality of pharmaceutical excipients.

  20. Jacobi Elliptic Solutions for Nonlinear Differential Difference Equations in Mathematical Physics

    Directory of Open Access Journals (Sweden)

    Khaled A. Gepreel

    2012-01-01

    Full Text Available We put a direct new method to construct the rational Jacobi elliptic solutions for nonlinear differential difference equations which may be called the rational Jacobi elliptic functions method. We use the rational Jacobi elliptic function method to construct many new exact solutions for some nonlinear differential difference equations in mathematical physics via the lattice equation and the discrete nonlinear Schrodinger equation with a saturable nonlinearity. The proposed method is more effective and powerful to obtain the exact solutions for nonlinear differential difference equations.

  1. [Application of fuzzy mathematics on modifying taste of oral solution of traditional Chinese drug].

    Science.gov (United States)

    Wang, Youjie; Feng, Yi; Zhang, Bo

    2009-01-01

    To apply Fuzzy mathematical methods to choose the best taste modifying prescription of oral solution of traditional Chinese drug. Jin-Fukang oral solution was used as a model drug. The oral solution was prepared in different taste modifying prescriptions, whose tastes were evaluated by the fuzzy quality synthetic evaluation system. Compound-sweeteners with Sucralose and Erythritol was the best choice. Fuzzy integrated evaluation can be used to evaluate the taste of traditional Chinese medicinal pharmaceuticals, which overcame the artificial factors and achieve more objective conclusion.

  2. Sanskrit-Prakrit interaction in elementary mathematics as reflected in Arabic and Italian formulations of the rule of three – and something more on the rule elsewhere

    DEFF Research Database (Denmark)

    Høyrup, Jens

    2012-01-01

    because the erudite astronomer-mathematicians use commercial arithmetic as the introduction to mathematics. But we have no surviving vernacular texts. From Brahmagupta onward, however, the standard Sanskrit formulation is supplemented by the observation that two of the known magnitudes are similar in kind...

  3. Formulation of coarse mesh finite difference to calculate mathematical adjoint flux; Formulacao de diferencas finitas de malha grossa para calculo do fluxo adjunto matematico

    Energy Technology Data Exchange (ETDEWEB)

    Pereira, Valmir; Martinez, Aquilino Senra; Silva, Fernando Carvalho da [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear

    2002-07-01

    The objective of this work is the obtention of the mathematical adjoint flux, having as its support the nodal expansion method (NEM) for coarse mesh problems. Since there are difficulties to evaluate this flux by using NEM. directly, a coarse mesh finite difference program was developed to obtain this adjoint flux. The coarse mesh finite difference formulation (DFMG) adopted uses results of the direct calculation (node average flux and node face averaged currents) obtained by NEM. These quantities (flux and currents) are used to obtain the correction factors which modify the classical finite differences formulation . Since the DFMG formulation is also capable of calculating the direct flux it was also tested to obtain this flux and it was verified that it was able to reproduce with good accuracy both the flux and the currents obtained via NEM. In this way, only matrix transposition is needed to calculate the mathematical adjoint flux. (author)

  4. Formulation and solution of the classical seashell problem. Pt. 1. Seashell geometry

    Energy Technology Data Exchange (ETDEWEB)

    Illert, C.

    1987-07-01

    Despite an extensive scholarly literature dating back to classical times, seashell geometries have hitherto resisted rigorous theoretical analysis, leaving applied scientists to adopt a directionless empirical approach toward classification. The voluminousness of recent palaeontological literature demonstrates the importance of this problem to applied scientists, but in no way reflects corresponding conceptual or theoretical advances beyond the XIX century thinking which was so ably summarized by Sir D'Arcy Wentworth Thompson in 1917. However, in this foundation paper for the newly emerging science of theoretical conchology, unifying theoretical considerations for the first time, permits a rigorous formulation and a complete solution of the problem of biological shell geometries. Shell coiling about the axis of symmetry can be deduced from first principles using energy considerations associated with incremental growth. The present paper shows that those shell apertures which are incurved ('cowrielike'), outflared ('stromblike') or even backturned ('opisthostomoidal') are merely special cases of a much broader spectrum of 'allowable' energy-efficient growth trajectories (tensile elastic clockspring spirals), many of which were widely used by Cretaceous ammonites. Energy considerations also dictate shell growth along the axis of symmetry, thus seashell spires can be understood in terms of certain special figures of revolution (Moebius elastic conoids), the better-known coeloconoidal and cyrtoconoidal shell spires being only two special cases arising from a whole class of topologically possible, energy efficient and biologically observed geometries. The 'wires' and 'conoids' of the present paper are instructive conceptual simplifications sufficient for present purposes. A second paper will later deal with generalized tubular surfaces in three dimensions.

  5. Various Solution Methods, Accompanied by Dynamic Investigation, for the Same Problem as a Means for Enriching the Mathematical Toolbox

    Science.gov (United States)

    Oxman, Victor; Stupel, Moshe

    2018-01-01

    A geometrical task is presented with multiple solutions using different methods, in order to show the connection between various branches of mathematics and to highlight the importance of providing the students with an extensive 'mathematical toolbox'. Investigation of the property that appears in the task was carried out using a computerized tool.

  6. A mathematical model for chemical reactions with actinide elements in the aqueous nitric acid solution: REACT

    International Nuclear Information System (INIS)

    Tachimori, Shoichi

    1990-02-01

    A mathematical model of chemical reactions with actinide elements: REACT code, was developed to simulate change of valency states of U, Pu and Np in the aqueous nitric acid solution. Twenty seven rate equations for the redox reactions involving some reductants, disproportionation reactions, and radiolytic growth and decay reaction of nitrous acid were programmed in the code . Eight numerical solution methods such as Porsing method to solve the rate equations were incorporated parallel as options depending on the characteristics of the reaction systems. The present report gives a description of the REACT code, e.g., chemical reactions and their rate equations, numerical solution methods, and some examples of the calculation results. A manual and a source file of the program was attached to the appendix. (author)

  7. SLATEC-4.1, Subroutine Library for Solution of Mathematical Problems

    International Nuclear Information System (INIS)

    Boland, W.R.

    1999-01-01

    1 - Description of problem or function: SLATEC4.1 is a large collection of FORTRAN mathematical subprograms brought together in a joint effort by the Air Force Phillips Laboratory, Lawrence Livermore National Laboratory, Los Alamos National Laboratory, Magnetic Fusion Energy Computing Center, National Institute of Standards and Technology, Sandia National Laboratories (Albuquerque and Livermore), and Oak Ridge National Laboratory. SLATEC is characterized by portability, good numerical technology, good documentation, robustness, and quality assurance. The library can be divided into the following subsections following the lines of the GAMS classification system: Error Analysis, Elementary and Special Functions, Elementary Vector Operations, Solutions of Systems of Linear Equations, Eigen analysis, QR Decomposition, Singular Value Decomposition, Overdetermined or Underdetermined Systems, Interpolation, Solution of Nonlinear Equations, Optimization, Quadrature, Ordinary Differential Equations, Partial Differential Equations, Fast Fourier Transforms, Approximation, Pseudo-random Number Generation, Sorting, Machine Constants, and Diagnostics and Error Handling. 2 - Method of solution: This information is provided by comments within the individual library subroutines

  8. Collection of proceedings of the international conference on programming and mathematical methods for solution of physical problems

    International Nuclear Information System (INIS)

    1994-01-01

    Traditional International Conference on programming and mathematical methods for solution of physical problems took place in Dubna in Jun, 14-19, 1993. More than 160 scientists from 14 countries participated in the Conference. They presented about 120 reports, the range of problems including computerized information complexes, experimental data acquisition and processing systems, mathematical simulation and calculation experiment in physics, analytical and numerical methods for solution of physical problems

  9. Thermodynamic investigation of the interaction between cyclodextrins and preservatives - Application and verification in a mathematical model to determine the needed preservative surplus in aqueous cyclodextrin formulations.

    Science.gov (United States)

    Holm, René; Olesen, Niels Erik; Alexandersen, Signe Dalgaard; Dahlgaard, Birgitte N; Westh, Peter; Mu, Huiling

    2016-05-25

    Preservatives are inactivated when added to conserve aqueous cyclodextrin (CD) formulations due to complex formation between CDs and the preservative. To maintain the desired conservation effect the preservative needs to be added in apparent surplus to account for this inactivation. The purpose of the present work was to establish a mathematical model, which defines this surplus based upon knowledge of stability constants and the minimal concentration of preservation to inhibit bacterial growth. The stability constants of benzoic acid, methyl- and propyl-paraben with different frequently used βCDs were determined by isothermal titration calorimetry. Based upon this knowledge mathematical models were constructed to account for the equilibrium systems and to calculate the required concentration of the preservations, which was evaluated experimentally based upon the USP/Ph. Eur./JP monograph. The mathematical calculations were able to predict the needed concentration of preservation in the presence of CDs; it clearly demonstrated the usefulness of including all underlying chemical equilibria in a mathematical model, such that the formulation design can be based on quantitative arguments. Copyright © 2015 Elsevier B.V. All rights reserved.

  10. Mathematics

    CERN Document Server

    Eringen, A Cemal

    2013-01-01

    Continuum Physics: Volume 1 - Mathematics is a collection of papers that discusses certain selected mathematical methods used in the study of continuum physics. Papers in this collection deal with developments in mathematics in continuum physics and its applications such as, group theory functional analysis, theory of invariants, and stochastic processes. Part I explains tensor analysis, including the geometry of subspaces and the geometry of Finsler. Part II discusses group theory, which also covers lattices, morphisms, and crystallographic groups. Part III reviews the theory of invariants th

  11. Integral equation solution for truncated slab structures by using a fringe current formulation

    DEFF Research Database (Denmark)

    Jørgensen, Erik; Toccafondi, A.; Maci, S.

    1999-01-01

    Full-wave solutions of truncated dielectric slab problems are interesting for a variety of engineering applications, in particular patch antennas on finite ground planes. For this application a canonical reference solution is that of a semi-infinite slab illuminated by a line source. Standard int...

  12. Formulation and stability of an extemporaneous 0.02% chlorhexidine digluconate ophthalmic solution

    Directory of Open Access Journals (Sweden)

    Shu-Chiao Lin

    2015-12-01

    Conclusion: The acetate-buffered 0.02% chlorhexidine digluconate ophthalmic solution stored in light-resistant high-density polyethylene eyedroppers demonstrated excellent stability at 2–25°C for 6 months after being sealed and for 1 month after opening. This finding will enable us to prepare 0.02% chlorhexidine digluconate ophthalmic solutions based on a doctor's prescription.

  13. A stabilized finite element formulation for the solution of the Navier-Stokes equations in axisymmetric geometry

    International Nuclear Information System (INIS)

    Souza, Altivo Monteiro de

    2008-12-01

    The world energy consumption has been increasing strongly in recent years. Nuclear energy has been regarded as a suitable option to supply this growing energy demand in industrial scale. In view of the need of improving the understanding and capacity of analysis of nuclear power plants, modern simulation techniques for flow and heat transfer problems are gaining greater importance. A large number of problems found in nuclear reactor engineering can be dealt assuming axial symmetry. Thus, in this work a stabilized finite element formulation for the solution of the Navier-Stokes and energy equations for axisymmetric problems have been developed and tested. The formulation has been implemented in the NS S OLVER M PI 2 D A program developed at the Parallel Computation Laboratory of the Instituto de Engenharia Nuclear (LCP/IEN) and is now available either for safety analysis or design of nuclear systems. (author)

  14. Influence of formulation and processing variables on properties of itraconazole nanoparticles made by advanced evaporative precipitation into aqueous solution.

    Science.gov (United States)

    Bosselmann, Stephanie; Nagao, Masao; Chow, Keat T; Williams, Robert O

    2012-09-01

    Nanoparticles, of the poorly water-soluble drug, itraconazole (ITZ), were produced by the Advanced Evaporative Precipitation into Aqueous Solution process (Advanced EPAS). This process combines emulsion templating and EPAS processing to provide improved control over the size distribution of precipitated particles. Specifically, oil-in-water emulsions containing the drug and suitable stabilizers are sprayed into a heated aqueous solution to induce precipitation of the drug in form of nanoparticles. The influence of processing parameters (temperature and volume of the heated aqueous solution; type of nozzle) and formulation aspects (stabilizer concentrations; total solid concentrations) on the size of suspended ITZ particles, as determined by laser diffraction, was investigated. Furthermore, freeze-dried ITZ nanoparticles were evaluated regarding their morphology, crystallinity, redispersibility, and dissolution behavior. Results indicate that a robust precipitation process was developed such that size distribution of dispersed nanoparticles was shown to be largely independent across the different processing and formulation parameters. Freeze-drying of colloidal dispersions resulted in micron-sized agglomerates composed of spherical, sub-300-nm particles characterized by reduced crystallinity and high ITZ potencies of up to 94% (w/w). The use of sucrose prevented particle agglomeration and resulted in powders that were readily reconstituted and reached high and sustained supersaturation levels upon dissolution in aqueous media.

  15. REUSING STOCKS SOLUTIONS WITH DIFFERENT FORMULATED FOR ORCHID FERTILIZER ACCLIMATIZATION PHASE

    Directory of Open Access Journals (Sweden)

    C. G. C. Issa

    2018-04-01

    Full Text Available Orchids are ornamental plants that stand out by their colors, types, shapes, size, beauty. Additionally, some species have aromas. This diversity of orchids makes it be greatly appreciated as potted plants, landscaping, with high commercial value. The aim of this study was to evaluate the development of orchids at different levels of fertilization by reusing nutrients added to the culture medium for cultivation in vitro is also analyzing the different times of acclimatization. The micropropagated orchids removed from the growth chamber, were transported to greenhouse composing the different treatments for acclimatization (0, 10, 20, 30, 40 and 50 days. To be transplanted were placed in pine bark substrate and Sphagnum being placed in trays. After 30 days the seedlings were transplanted to styrofoam trays was initiated plant fertilization weekly with different formulated by administering 5 ml each (1 humic acid, 2nd potassium nitrate (KNO3, 3rd humic acid + Nitrate potassium (KNO3, 4th calcium chloride (CaCl2, 5 ° control. Six months after withdrawal of the growth room the plants was carried out the evaluation of the experiment where the plant survival was evaluated by the number of shoots, number of leaves, the length of the largest leaf and root presence. The experimental design was completely randomized in a factorial 6x5, with the time of acclimatization (0, 10, 20, 30, 40 and 50 days the first factor and the second, the type of fertilizer used (4 formulated and the witness with 8 replicates per treatment. The data were submitted to deviance analysis in the software R. In this study, the need to fertilize with nutrient rich formulations for orchids in the acclimatization phase was contacted and that these should remain for a few days inside the jars in a greenhouse environment.

  16. MATHEMATICAL SOLUTIONS FOR OPTIMAL DIMENSIONING OF NUMBER AND HEIGHTS OF SOME HYDROTECHNIQUE ON TORRENTIAL FORMATION

    Directory of Open Access Journals (Sweden)

    Nicolae Petrescu

    2010-01-01

    Full Text Available This paper is intended to achieve a mathematical model for the optimal dimensioning of number and heights of somedams/thresholds during a downpour, a decrease of water flow rate being obtained and by the solid material depositionsbehind the constructions a new smaller slope of the valley that changes the torrential nature that had before theconstruction is obtained.The choice of the dam and its characteristic dimensions may be an optimization issue and the location of dams on thetorrential (rainfall aspect is dictated by the capabilities of the foundation and restraint so that the chosen solutions willhave to comply with these sites. Finally, the choice of optimal solution to limit torrential (rainfall aspect will be basedon a calculation where the number of thresholds / dams can be a variable related to this, their height properly varying.The calculation method presented is an attempt to demonstrate the multiple opportunities available to implement atechnical issue solving conditions offered by the mathematics against soil erosion, which now is currently very topicalon the environmental protection.

  17. Self-similar cosmological solutions with dark energy. I. Formulation and asymptotic analysis

    International Nuclear Information System (INIS)

    Harada, Tomohiro; Maeda, Hideki; Carr, B. J.

    2008-01-01

    Based on the asymptotic analysis of ordinary differential equations, we classify all spherically symmetric self-similar solutions to the Einstein equations which are asymptotically Friedmann at large distances and contain a perfect fluid with equation of state p=(γ-1)μ with 0 1). However, in the latter case there is an additional parameter associated with the weak discontinuity at the sonic point and the solutions are only asymptotically 'quasi-Friedmann', in the sense that they exhibit an angle deficit at large distances. In the 0<γ<2/3 case, there is no sonic point and there exists a one-parameter family of solutions which are genuinely asymptotically Friedmann at large distances. We find eight classes of asymptotic behavior: Friedmann or quasi-Friedmann or quasistatic or constant-velocity at large distances, quasi-Friedmann or positive-mass singular or negative-mass singular at small distances, and quasi-Kantowski-Sachs at intermediate distances. The self-similar asymptotically quasistatic and quasi-Kantowski-Sachs solutions are analytically extendible and of great cosmological interest. We also investigate their conformal diagrams. The results of the present analysis are utilized in an accompanying paper to obtain and physically interpret numerical solutions

  18. Methods for constructing exact solutions of partial differential equations mathematical and analytical techniques with applications to engineering

    CERN Document Server

    Meleshko, Sergey V

    2005-01-01

    Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.

  19. Development of a new version of the Liverpool Malaria Model. I. Refining the parameter settings and mathematical formulation of basic processes based on a literature review

    Directory of Open Access Journals (Sweden)

    Jones Anne E

    2011-02-01

    Full Text Available Abstract Background A warm and humid climate triggers several water-associated diseases such as malaria. Climate- or weather-driven malaria models, therefore, allow for a better understanding of malaria transmission dynamics. The Liverpool Malaria Model (LMM is a mathematical-biological model of malaria parasite dynamics using daily temperature and precipitation data. In this study, the parameter settings of the LMM are refined and a new mathematical formulation of key processes related to the growth and size of the vector population are developed. Methods One of the most comprehensive studies to date in terms of gathering entomological and parasitological information from the literature was undertaken for the development of a new version of an existing malaria model. The knowledge was needed to allow the justification of new settings of various model parameters and motivated changes of the mathematical formulation of the LMM. Results The first part of the present study developed an improved set of parameter settings and mathematical formulation of the LMM. Important modules of the original LMM version were enhanced in order to achieve a higher biological and physical accuracy. The oviposition as well as the survival of immature mosquitoes were adjusted to field conditions via the application of a fuzzy distribution model. Key model parameters, including the mature age of mosquitoes, the survival probability of adult mosquitoes, the human blood index, the mosquito-to-human (human-to-mosquito transmission efficiency, the human infectious age, the recovery rate, as well as the gametocyte prevalence, were reassessed by means of entomological and parasitological observations. This paper also revealed that various malaria variables lack information from field studies to be set properly in a malaria modelling approach. Conclusions Due to the multitude of model parameters and the uncertainty involved in the setting of parameters, an extensive

  20. Mathematics

    CERN Document Server

    Stein, Sherman K

    2010-01-01

    Anyone can appreciate the beauty, depth, and vitality of mathematics with the help of this highly readable text, specially developed from a college course designed to appeal to students in a variety of fields. Readers with little mathematical background are exposed to a broad range of subjects chosen from number theory, topology, set theory, geometry, algebra, and analysis. Starting with a survey of questions on weight, the text discusses the primes, the fundamental theorem of arithmetic, rationals and irrationals, tiling, tiling and electricity, probability, infinite sets, and many other topi

  1. Formulation and make-up of simulated concentrated water, high ionic content aqueous solution

    International Nuclear Information System (INIS)

    Gdowski, G.

    1997-01-01

    This procedure describes the formulation and make-up of Simulated Concentrated Water (SCW), a high-ionic-content water to be used for Activity E-20-50 Long-Term Corrosion Studies. This water has an ionic content which is nominally a factor of a thousand higher than that of representative waters at or near Yucca Mountain. Representative waters were chosen as J-13 well water [Harrar, 1990] and perched water at Yucca Mountain [Glassley, 1996]. J-13 well water is obtained from ground water that is in contact with the Topopah Spring tuff, which is the repository horizon rock. The perched water is located in the Topopah Spring tuff, but below the repository horizon and above the water table. A nominal thousand times higher ionic content was chosen to simulate the water that would result from the wetting of salts which have been previously deposited on a container surface

  2. On the use of formulations in person-centred, solution-focused short-term psychotherapy.

    Science.gov (United States)

    Fitzgerald, Pamela; Leudar, Ivan

    2012-01-01

    According to Carl Rogers, therapy must be non-directive in order to be effective. This means that the therapist needs to be trained to work within the clients' frame of reference and do so in their practice. Conversation analytic research, however, suggests that therapists who claim to practise non-directive, non-authoritarian therapy nevertheless exercise subtle means of influencing their clients (e.g. through active listening, see Fitzgerald and Leudar 2010). The questions are: what in practice counts as being non-directive and how (relatively) nondirective psychotherapy is accomplished in practice. The present paper focuses on formulations which are one of the therapist's most useful tools and we demonstrate how these are used to guide clients to think along lines conducive to change.

  3. Multimode Preemptive Resource Investment Problem Subject to Due Dates for Activities: Formulation and Solution Procedure

    Directory of Open Access Journals (Sweden)

    Behrouz Afshar-Nadjafi

    2014-01-01

    Full Text Available The preemptive Multimode resource investment problem is investigated. The Objective is to minimize the total renewable/nonrenewable resource costs and earliness-tardiness costs by a given project deadline and due dates for activities. In this problem setting preemption is allowed with no setup cost or time. The project contains activities interrelated by finish-start type precedence relations with a time lag of zero, which require a set of renewable and nonrenewable resources. The problem formed in this way is an NP-hard. A mixed integer programming formulation is proposed for the problem and parameters tuned genetic algorithm (GA is proposed to solve it. To evaluate the performance of the proposed algorithm, 120 test problems are used. Comparative statistical results reveal that the proposed GA is efficient and effective in terms of the objective function and computational times.

  4. Formulation and make-up of simulate dilute water, low ionic content aqueous solution

    International Nuclear Information System (INIS)

    Gdowski, G.

    1997-01-01

    This procedure describes the formulation and make-up of Simulated Dilute Water (SOW), a low-ionic-content water to be used for Activity E-20-50, Long-Term Corrosion Studies. This water has an ionic content which is nominally a factor of ten higher than that of representative waters at or near Yucca Mountain. Representative waters were chosen as J-13 well water [Harrar, 1990] and perched water at Yucca Mountain [Glassley, 1996]. J-13 well water is obtained from ground water that is in contact with the Topopah Spring tuff, which is the repository horizon rock. The perched water is located in the Topopah Spring tuff, but below the repository horizon and above the water table. A nominal times ten higher ionic content was chosen to simulate the effect of ionic concentrating due to elevated temperature water flowing through fractures where salts and minerals have been deposited due to evaporation and boiling

  5. The double travelling salesman problem with multiple stacks - Formulation and heuristic solution approaches

    DEFF Research Database (Denmark)

    Petersen, Hanne Løhmann; Madsen, Oli B.G.

    2009-01-01

    This paper introduces the double travelling salesman problem with multiple stacks and presents four different metaheuristic approaches to its solution. The double TSP with multiple stacks is concerned with determining the shortest route performing pickups and deliveries in two separated networks...

  6. Mathematics

    International Nuclear Information System (INIS)

    Demazure, M.

    1988-01-01

    The 1988 progress report of the Mathematics center (Polytechnic School, France), is presented. The Center is composed of different research teams: analysis, Riemann geometry, group theory, formal calculus and algorithm geometry, dynamical systems, topology and singularity. For each team, the members, the research topics, the national and international cooperations, are given. The papers concerning the investigations carried out in 1988, are listed [fr

  7. Head to head comparison of the formulation and stability of concentrated solutions of HESylated versus PEGylated anakinra.

    Science.gov (United States)

    Liebner, Robert; Meyer, Martin; Hey, Thomas; Winter, Gerhard; Besheer, Ahmed

    2015-02-01

    Although PEGylation of biologics is currently the gold standard for half-life extension, the technology has a number of limitations, most importantly the non-biodegradability of PEG and the extremely high viscosity at high concentrations. HESylation is a promising alternative based on coupling to the biodegradable polymer hydroxyethyl starch (HES). In this study, we are comparing HESylation with PEGylation regarding the effect on the protein's physicochemical properties, as well as on formulation at high concentrations, where protein stability and viscosity can be compromised. For this purpose, the model protein anakinra is coupled to HES or PEG by reductive amination. Results show that coupling of HES or PEG had practically no effect on the protein's secondary structure, and that it reduced protein affinity by one order of magnitude, with HESylated anakinra more affine than the PEGylated protein. The viscosity of HESylated anakinra at protein concentrations up to 75 mg/mL was approximately 40% lower than that of PEG-anakinra. Both conjugates increased the apparent melting temperature of anakinra in concentrated solutions. Finally, HESylated anakinra was superior to PEG-anakinra regarding monomer recovery after 8 weeks of storage at 40°C. These results show that HESylating anakinra offers formulation advantages compared with PEGylation, especially for concentrated protein solutions. © 2014 Wiley Periodicals, Inc. and the American Pharmacists Association.

  8. Study on the influence of finite element formulation and equation of motion solution scheme on FEM analysis results based on the asymmetrically loaded plate problem

    Directory of Open Access Journals (Sweden)

    Marcin Krzeszowiec

    2015-03-01

    Full Text Available Computer simulations of physical phenomena are at the moment common both in science and industry. The possibility of finding approximate solutions for complicated systems of differential equations, mathematically describing issues in the fields of mechanics, physics or chemistry, allows for shorten design and research time, often significantly reducing the need for expensive experimental studies or costly production of prototypes. However, the mentioned prevalence of these methods, particularly the Finite Element Method, resulted in analysis outcomes to be often in advance regarded as accurate ones. The purpose of the article is to showcase, on a simple stress analysis problem, how parameters such as the density of the finite element mesh, finite element formulation or integration scheme significantly influence on the simulation results and how easy it is to end up with the results that do not hold any physical sense, despite the fact that all the basic assumptions of correct analysis (suitable boundary conditions, total system energy stored etc. have been met. The results of this study can serve as a warning against premature conclusion drawing from calculations carried out by means of FEM simulation.[b]Keywords[/b]: computational mechanics, finite element method, shell elements, numerical integration

  9. THE NONISOTHERMAL STAGE OF MAGNETIC STAR FORMATION. I. FORMULATION OF THE PROBLEM AND METHOD OF SOLUTION

    International Nuclear Information System (INIS)

    Kunz, Matthew W.; Mouschovias, Telemachos Ch.

    2009-01-01

    We formulate the problem of the formation and subsequent evolution of fragments (or cores) in magnetically supported, self-gravitating molecular clouds in two spatial dimensions. The six-fluid (neutrals, electrons, molecular and atomic ions, positively charged, negatively charged, and neutral grains) physical system is governed by the radiation, nonideal magnetohydrodynamic equations. The magnetic flux is not assumed to be frozen in any of the charged species. Its evolution is determined by a newly derived generalized Ohm's law, which accounts for the contributions of both elastic and inelastic collisions to ambipolar diffusion and Ohmic dissipation. The species abundances are calculated using an extensive chemical-equilibrium network. Both MRN and uniform grain size distributions are considered. The thermal evolution of the protostellar core and its effect on the dynamics are followed by employing the gray flux-limited diffusion approximation. Realistic temperature-dependent grain opacities are used that account for a variety of grain compositions. We have augmented the publicly available Zeus-MP code to take into consideration all these effects and have modified several of its algorithms to improve convergence, accuracy, and efficiency. Results of magnetic star formation simulations that accurately track the evolution of a protostellar fragment from a density ≅10 3 cm -3 to a density ≅10 15 cm -3 , while rigorously accounting for both nonideal MHD processes and radiative transfer, are presented in a separate paper.

  10. Multiphase flow experiments, mathematical modeling and numerical simulation of the water - gas - solute movement

    Science.gov (United States)

    Li, Y.; Ma, X.; Su, N.

    2013-12-01

    The movement of water and solute into and through the vadose zone is, in essence, an issue of immiscible displacement in pore-space network of a soil. Therefore, multiphase flow and transport in porous media, referring to three medium: air, water, and the solute, pose one of the largest unresolved challenges for porous medium fluid seepage. However, this phenomenon has always been largely neglected. It is expected that a reliable analysis model of the multi-phase flow in soil can truly reflect the process of natural movement about the infiltration, which is impossible to be observed directly. In such cases, geophysical applications of the nuclear magnetic resonance (NMR) provides the opportunity to measure the water movements into soils directly over a large scale from tiny pore to regional scale, accordingly enable it available both on the laboratory and on the field. In addition, the NMR provides useful information about the pore space properties. In this study, we proposed both laboratory and field experiments to measure the multi-phase flow parameters, together with optimize the model in computer programming based on the fractional partial differential equations (fPDE). In addition, we establish, for the first time, an infiltration model including solute flowing with water, which has huge influence on agriculture and soil environment pollution. Afterwards, with data collected from experiments, we simulate the model and analyze the spatial variability of parameters. Simulations are also conducted according to the model to evaluate the effects of airflow on water infiltration and other effects such as solute and absorption. It has significant meaning to oxygen irrigation aiming to higher crop yield, and shed more light into the dam slope stability. In summary, our framework is a first-time model added in solute to have a mathematic analysis with the fPDE and more instructive to agriculture activities.

  11. A Mathematical Model of Repeated Impregnation of Porous Bodies with Solutions of Polymers

    Directory of Open Access Journals (Sweden)

    I. V. Glebov

    2015-01-01

    Full Text Available The paper describes basic methods of impregnating porous bodies with solutions of polymers and their use to manufacture prepregs. It also describes the existing methods of manufacturing multilayer prepregs to produce aerospace coating of the spacecraft "Soyuz". It is shown that these prepregs have to meet high requirements for the content of the polymer, as compared with other composite materials, about 35 - 40% of the mass. Methods used for their manufacturing are long-term and non-controllable. The assumption is made that using the vacuum impregnation technology of a woven material will allow to accelerate the manufacturing process of these prepregs and improve their quality.In reviewing the technical literature have been found works on modeling the processes of impregnation, but they are aimed only at studying the speed of the woven material impregnation by various fluids and determining the time of impregnation. There were no models found to define prepreg parameters during the process of multiple impregnations. The aim of this work is to develop the simple mathematical model, which enables us to predict the polymer content of volatile products in the prepreg after each cycle of multiple impregnation of woven material with a solution of the polymer.To consider the vacuum impregnation method are used the prepregs based on silica and silica-nylon stitch-bonding fabric and bakelite varnish LBS-4 containing 50 - 60% of phenol resin and the solvent with minor impurities of pure phenol and water, as an example. To describe the process of vacuum impregnation of the porous work-piece is developed a mathematical description of the process of filling the porous space of the material with a varnish. It is assumed that the varnish components fill the porous space of the material in the same proportion as they are contained in the varnish.It is shown that a single impregnation cannot ensure the content of phenol resin in the prepreg over 32%, which does

  12. Cloud point extraction of vanadium in pharmaceutical formulations, dialysate and parenteral solutions using 8-hydroxyquinoline and nonionic surfactant

    International Nuclear Information System (INIS)

    Khan, Sumaira; Kazi, Tasneem G.; Baig, Jameel A.; Kolachi, Nida F.; Afridi, Hassan I.; Wadhwa, Sham Kumar; Shah, Abdul Q.; Kandhro, Ghulam A.; Shah, Faheem

    2010-01-01

    A cloud point extraction (CPE) method has been developed for the determination of trace quantity of vanadium ions in pharmaceutical formulations (PF), dialysate (DS) and parenteral solutions (PS). The CPE of vanadium (V) using 8-hydroxyquinoline (oxine) as complexing reagent and mediated by nonionic surfactant (Triton X-114) was investigated. The parameters that affect the extraction efficiency of CPE, such as pH of sample solution, concentration of oxine and Triton X-114, equilibration temperature and time period for shaking were investigated in detail. The validity of CPE of V was checked by standard addition method in real samples. The extracted surfactant-rich phase was diluted with nitric acid in ethanol, prior to subjecting electrothermal atomic absorption spectrometry. Under these conditions, the preconcentration of 50 mL sample solutions, allowed raising an enrichment factor of 125-fold. The lower limit of detection obtained under the optimal conditions was 42 ng/L. The proposed method has been successfully applied to the determination of trace quantity of V in various pharmaceutical preparations with satisfactory results. The concentration ranges of V in PF, DS and PS samples were found in the range of 10.5-15.2, 0.65-1.32 and 1.76-6.93 μg/L, respectively.

  13. Short-term dissolution experiments on various cement formulations in standard Canadian shield saline solution in the presence of clay

    International Nuclear Information System (INIS)

    Heimann, R.B.; Stanchell, M.A.T.

    1986-12-01

    A commercially available sulphate-resisting portland cement (SRPC) and three cement formulations derived from it by adding 10 and 20 vol% silica fume or 35 vol% fly-ash have been leached in Standard Canadian Shield Saline Solution (SCSSS) with added calcium-montmorillonite or sodium-montmorillonite at 150 degrees C for 14 days. The leach solutions have been analyzed by atomic absorption spectroscopy for silicon, magensium, iron and potassium, and by inductively coupled plasma spectrometry for aluminum and phosphorous. The surfaces of the leached samples have been investigated by scanning electron microscopy in conjunction with energy-dispersive X-ray spectroscopy, and by X-ray powder diffraction methods. Cumulative pore size distrubtion curves have been recorded for as-cured and leached cement samples. It has been shown that the presence of clay accelerates the rate of dissolution of the various cements, and that the pH of the leaching solutions plays a dominant role in the elemental release kinetics

  14. Formulation of Low Peclet Number Based Grid Expansion Factor for the Solution of the Convection Diffusion Equation

    Directory of Open Access Journals (Sweden)

    A. Abdullah

    2018-04-01

    Full Text Available Convection-diffusion problems, due to its fundamental nature, are found in various science and engineering applications. In this research, the importance of the relationship between grid structure and flow parameters in such problems is emphasized. In particular, we propose a systematic technique in the selection of the grid expansion factor based on its logarithmic relationship with low Peclet number. Such linear mathematical connection between the two non-dimensional parameters serves as a guideline for more structured decision-making and improves the heuristic process in the determination of the computational domain grid for the numerical solution of convection-diffusion equations especially in the prediction of the concentration of the scalar. Results confirm the effectiveness of the new approach.

  15. Material degradation due to moisture and temperature. Part 1: mathematical model, analysis, and analytical solutions

    Science.gov (United States)

    Xu, C.; Mudunuru, M. K.; Nakshatrala, K. B.

    2016-11-01

    The mechanical response, serviceability, and load-bearing capacity of materials and structural components can be adversely affected due to external stimuli, which include exposure to a corrosive chemical species, high temperatures, temperature fluctuations (i.e., freezing-thawing), cyclic mechanical loading, just to name a few. It is, therefore, of paramount importance in several branches of engineering—ranging from aerospace engineering, civil engineering to biomedical engineering—to have a fundamental understanding of degradation of materials, as the materials in these applications are often subjected to adverse environments. As a result of recent advancements in material science, new materials such as fiber-reinforced polymers and multi-functional materials that exhibit high ductility have been developed and widely used, for example, as infrastructural materials or in medical devices (e.g., stents). The traditional small-strain approaches of modeling these materials will not be adequate. In this paper, we study degradation of materials due to an exposure to chemical species and temperature under large strain and large deformations. In the first part of our research work, we present a consistent mathematical model with firm thermodynamic underpinning. We then obtain semi-analytical solutions of several canonical problems to illustrate the nature of the quasi-static and unsteady behaviors of degrading hyperelastic solids.

  16. Comment on: "Corrections to the Mathematical Formulation of a Backwards Lagrangian Particle Dispersion Model" by Gibson and Sailor (2012: Boundary-Layer Meteorology 145, 399-406)

    Science.gov (United States)

    Stöckl, Stefan; Rotach, Mathias W.; Kljun, Natascha

    2018-01-01

    We discuss the results of Gibson and Sailor (Boundary-Layer Meteorol 145:399-406, 2012) who suggest several corrections to the mathematical formulation of the Lagrangian particle dispersion model of Rotach et al. (Q J R Meteorol Soc 122:367-389, 1996). While most of the suggested corrections had already been implemented in the 1990s, one suggested correction raises a valid point, but results in a violation of the well-mixed criterion. Here we improve their idea and test the impact on model results using a well-mixed test and a comparison with wind-tunnel experimental data. The new approach results in similar dispersion patterns as the original approach, while the approach suggested by Gibson and Sailor leads to erroneously reduced concentrations near the ground in convective and especially forced convective conditions.

  17. From everyday problem to a mathematical solution - understanding student reasoning by identifying their chain of reference

    DEFF Research Database (Denmark)

    Dreyøe, Jonas; Larsen, Dorte Moeskær; Misfeldt, Morten

    2018-01-01

    This paper investigates a group of students’ reasoning in an inquiry-oriented and open mathematical investigation developed as a part of a large-scale intervention. We focus on the role of manipulatives, articulations, and representations in collaborative mathematical reasoning among grade 5......, manipulatives, and reasoning in a way that allows us to follow the material traces of students’ mathematical reasoning and hence discuss the possibilities, limitations, and pedagogical consequences of the application of Latour’s (1999) framework....

  18. Preliminary Formulation of Finite Element Solution for the 1-D, 1-G Time Dependent Neutron Diffusion Equation without Consideration about Delay Neutron

    Energy Technology Data Exchange (ETDEWEB)

    Ryu, Eun Hyun; Song, Yong Mann; Park, Joo Hwan [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)

    2013-05-15

    If time-dependent equation is solved with the FEM, the limitation of the input geometry will disappear. It has often been pointed out that the numerical methods implemented in the RFSP code are not state-of-the-art. Although an acceleration method such as the Coarse Mesh Finite Difference (CMFD) for Finite Difference Method (FDM) does not exist for the FEM, one should keep in mind that the number of time steps for the transient simulation is not large. The rigorous formulation in this study will richen the theoretical basis of the FEM and lead to an extension of the dynamics code to deal with a more complicated problem. In this study, the formulation for the 1-D, 1-G Time Dependent Neutron Diffusion Equation (TDNDE) without consideration of the delay neutron will first be done. A problem including one multiplying medium will be solved. Also several conclusions from a comparison between the numerical and analytic solutions, a comparison between solutions with various element orders, and a comparison between solutions with different time differencing will be made to be certain about the formulation and FEM solution. By investigating various cases with different values of albedo, theta, and the order of elements, it can be concluded that the finite element solution is agree well with the analytic solution. The higher the element order used, the higher the accuracy improvements are obtained.

  19. Formulación de metotrexato 50 mg solución inyectable Formulation of metotrexate 50 mg injectable solution

    Directory of Open Access Journals (Sweden)

    Armando Gato del Monte

    2006-08-01

    possible to obtain a formulation of metotrexate 50 mg injectable solution with adequate characteristics, and physical, chemical, biological and microbiological stability. The formulation was industrially escalated and was bottled in ampuls that meet the established quality parameters satisfactorily. The quality parameters of the finished product that appear in the USP 26 were proved by the stability study of these batches. An expiration date of 2 years was established under the conditions of controlled temperature 2-8 ºC and protected from light

  20. Mathematical evaluation of similarity factor using various weighing approaches on aceclofenac marketed formulations by model-independent method.

    Science.gov (United States)

    Soni, T G; Desai, J U; Nagda, C D; Gandhi, T R; Chotai, N P

    2008-01-01

    The US Food and Drug Administration's (FDA's) guidance for industry on dissolution testing of immediate-release solid oral dosage forms describes that drug dissolution may be the rate limiting step for drug absorption in the case of low solubility/high permeability drugs (BCS class II drugs). US FDA Guidance describes the model-independent mathematical approach proposed by Moore and Flanner for calculating a similarity factor (f2) of dissolution across a suitable time interval. In the present study, the similarity factor was calculated on dissolution data of two marketed aceclofenac tablets (a BCS class II drug) using various weighing approaches proposed by Gohel et al. The proposed approaches were compared with a conventional approach (W = 1). On the basis of consideration of variability, preference is given in the order of approach 3 > approach 2 > approach 1 as approach 3 considers batch-to-batch as well as within-samples variability and shows best similarity profile. Approach 2 considers batch-to batch variability with higher specificity than approach 1.

  1. Multiphysics Simulation of Welding-Arc and Nozzle-Arc System: Mathematical-Model, Solution-Methodology and Validation

    Science.gov (United States)

    Pawar, Sumedh; Sharma, Atul

    2018-01-01

    This work presents mathematical model and solution methodology for a multiphysics engineering problem on arc formation during welding and inside a nozzle. A general-purpose commercial CFD solver ANSYS FLUENT 13.0.0 is used in this work. Arc formation involves strongly coupled gas dynamics and electro-dynamics, simulated by solution of coupled Navier-Stoke equations, Maxwell's equations and radiation heat-transfer equation. Validation of the present numerical methodology is demonstrated with an excellent agreement with the published results. The developed mathematical model and the user defined functions (UDFs) are independent of the geometry and are applicable to any system that involves arc-formation, in 2D axisymmetric coordinates system. The high-pressure flow of SF6 gas in the nozzle-arc system resembles arc chamber of SF6 gas circuit breaker; thus, this methodology can be extended to simulate arcing phenomenon during current interruption.

  2. Formulating a poorly water soluble drug into an oral solution suitable for paediatric patients; lorazepam as a model drug

    NARCIS (Netherlands)

    A.C. Van Der Vossen (Anna C.); I. Van Der Velde (Iris); O. Smeets (Oscar); Postma, D.J.; Eckhardt, M.; A. Vermes (Andras); B.C.P. Koch (Birgit C. P.); A.G. Vulto (Arnold); L.M. Hanff (Lidwien)

    2017-01-01

    textabstractIntroduction Many drugs are unavailable in suitable oral paediatric dosage forms, and pharmacists often have to compound drugs to provide paediatric patients with an acceptable formulation in the right dose. Liquid formulations offer the advantage of dosing flexibility and ease of

  3. Micosoft Excel Sensitivity Analysis for Linear and Stochastic Program Feed Formulation

    Science.gov (United States)

    Sensitivity analysis is a part of mathematical programming solutions and is used in making nutritional and economic decisions for a given feed formulation problem. The terms, shadow price and reduced cost, are familiar linear program (LP) terms to feed formulators. Because of the nonlinear nature of...

  4. Variable thickness transient ground-water flow model. Volume 1. Formulation

    International Nuclear Information System (INIS)

    Reisenauer, A.E.

    1979-12-01

    Mathematical formulation for the variable thickness transient (VTT) model of an aquifer system is presented. The basic assumptions are described. Specific data requirements for the physical parameters are discussed. The boundary definitions and solution techniques of the numerical formulation of the system of equations are presented

  5. Application of High-Resolution Ultrasonic Spectroscopy for analysis of complex formulations. Compressibility of solutes and solute particles in liquid mixtures

    International Nuclear Information System (INIS)

    Buckin, V

    2012-01-01

    The paper describes key aspects of interpretation of compressibility of solutes in liquid mixtures obtained through high-resolution measurements of ultrasonic parameters. It examines the fundamental relationships between the characteristics of solutes and the contributions of solutes to compressibility of liquid mixtures expressed through apparent adiabatic compressibility of solutes, and adiabatic compressibility of solute particles. In addition, it analyses relationships between the adiabatic compressibility of solutes and the measured ultrasonic characteristics of mixtures. Especial attention is given to the effects of solvents on the measured adiabatic compressibility of solutes and on concentration increment of ultrasonic velocity of solutes in mixtures.

  6. Mathematical Formulation of the Remote Electric and Magnetic Emissions of the Lightning Dart Leader and Return Stroke

    Science.gov (United States)

    Thiemann, Edward M. B.

    analytic solution to Maxwell's Equations for the lightning leader followed by a novel return stroke model. I model the leader as a downward propagating boxcar function of uniform charge density and constant velocity, and the subsequent return stroke is modeled as an upward propagating boxcar with a time dependent velocity. Charge conservation is applied to ensure self-consistency of the driving current and charge sources, and physical observations are used to support model development. The resulting transient electric and magnetic fields are presented at various distances and delay times and compared with measured waveforms and previously published models.

  7. Mathematics of quantum mechanics. Foundations, examples, problems, solutions; Mathematik der Quantenmechanik. Grundlagen, Beispiele, Aufgaben, Loesungen

    Energy Technology Data Exchange (ETDEWEB)

    Korsch, Hans Juergen

    2013-07-01

    This book mediates the fundamental terms and methods, which are necessary for an understanding of quantum mechanics. It shows, how mathematics can contribute to the understanding of quantum mechanics. The presented quantum-mechanical problems aim at the illustration and exercise of the most important mathematical methods. Because of the clear and understandable presentation and the numerous completely calculated examples and problems this book is suited for the self-study, for the accompanying of courses on quantum physics, for the accomplishment of exercise problems, and for the preparation on examinations.

  8. Mathematical methods in the solution of the the Hamilton-Darwin and the Takagi-Taupin equations

    International Nuclear Information System (INIS)

    Werner, S.A.; Berliner, R.R.; Arif, M.; Missouri Univ., Columbia

    1986-01-01

    The diffraction of neutrons by a single crystal is intrinsically a multiple scattering problem. For an ideally imperfect mosaic crystal the Hamilton-Darwin transfer equations describe the coupling of the incident and diffracted beams; whereas, for a perfect crystal one must use the dynamical theory of diffraction, which can be recast in the form of two coupled partial differential equations commonly referred to as the Takagi-Taupin equations. From a mathematical point of view these two problems are equivalent, although the physical manifestations of the solutions are quite different. For the occasion of Professor Shull's seventieth birthday celebration, we bring together in this paper some of the mathematical techniques which we have found useful in elucidating the subtleties of the Bragg diffraction of neutron by crystals. (orig.)

  9. Symbolic Computations and Exact and Explicit Solutions of Some Nonlinear Evolution Equations in Mathematical Physics

    International Nuclear Information System (INIS)

    Oezis, Turgut; Aslan, Imail

    2009-01-01

    With the aid of symbolic computation system Mathematica, several explicit solutions for Fisher's equation and CKdV equation are constructed by utilizing an auxiliary equation method, the so called G'/G-expansion method, where the new and more general forms of solutions are also constructed. When the parameters are taken as special values, the previously known solutions are recovered. (general)

  10. Numerical methods for solution of some nonlinear problems of mathematical physics

    International Nuclear Information System (INIS)

    Zhidkov, E.P.

    1981-01-01

    The continuous analog of the Newton method and its application to some nonlinear problems of mathematical physics using a computer is considered. It is shown that the application of this method in JINR to the wide range of nonlinear problems has shown its universality and high efficiency [ru

  11. Formulation and solutions of fractional continuously variable order mass–spring–damper systems controlled by viscoelastic and viscous–viscoelastic dampers

    Directory of Open Access Journals (Sweden)

    S Saha Ray

    2016-05-01

    Full Text Available This article presents the formulation and a new approach to find analytic solutions for fractional continuously variable order dynamic models, namely, fractional continuously variable order mass–spring–damper systems. Here, we use the viscoelastic and viscous–viscoelastic dampers for describing the damping nature of the oscillating systems, where the order of fractional derivative varies continuously. Here, we handle the continuous changing nature of fractional order derivative for dynamic systems, which has not been studied yet. By successive recursive method, here we find the solution of fractional continuously variable order mass–spring–damper systems and then obtain closed-form solutions. We then present and discuss the solutions obtained in the cases with continuously variable order of damping for oscillator through graphical plots.

  12. New mathematical method for the solution of gas-gas equilibria with special application to HTGR primary-coolant environments

    International Nuclear Information System (INIS)

    Bongartz, K.

    1983-07-01

    A new mathematical method and corresponding computer program have been developed that provide a general method for the numerical solution of an equilibrium problem involving the chemical interactions of gaseous species. The method and computer code were developed to calculate the equilibrium concentrations of impurity gases, such as CO, CO 2 , H 2 , H 2 O, CH 4 , and O 2 , which may be approached as the result of gaseous chemical reactions occurring within the hot primary coolant helium of a high-temperature gas-cooled reactor (HTGR). The method, however, can be applied to any gas mixture

  13. Asymptotic Normality of the Optimal Solution in Multiresponse Surface Mathematical Programming

    OpenAIRE

    Díaz-García, José A.; Caro-Lopera, Francisco J.

    2015-01-01

    An explicit form for the perturbation effect on the matrix of regression coeffi- cients on the optimal solution in multiresponse surface methodology is obtained in this paper. Then, the sensitivity analysis of the optimal solution is studied and the critical point characterisation of the convex program, associated with the optimum of a multiresponse surface, is also analysed. Finally, the asymptotic normality of the optimal solution is derived by the standard methods.

  14. Distribution-valued weak solutions to a parabolic problem arising in financial mathematics

    Directory of Open Access Journals (Sweden)

    Michael Eydenberg

    2009-07-01

    Full Text Available We study distribution-valued solutions to a parabolic problem that arises from a model of the Black-Scholes equation in option pricing. We give a minor generalization of known existence and uniqueness results for solutions in bounded domains $Omega subset mathbb{R}^{n+1}$ to give existence of solutions for certain classes of distributions $fin mathcal{D}'(Omega$. We also study growth conditions for smooth solutions of certain parabolic equations on $mathbb{R}^nimes (0,T$ that have initial values in the space of distributions.

  15. Uniqueness of solutions for a mathematical model for magneto-viscoelastic flows

    Science.gov (United States)

    Schlömerkemper, A.; Žabenský, J.

    2018-06-01

    We investigate uniqueness of weak solutions for a system of partial differential equations capturing behavior of magnetoelastic materials. This system couples the Navier–Stokes equations with evolutionary equations for the deformation gradient and for the magnetization obtained from a special case of the micromagnetic energy. It turns out that the conditions on uniqueness coincide with those for the well-known Navier–Stokes equations in bounded domains: weak solutions are unique in two spatial dimensions, and weak solutions satisfying the Prodi–Serrin conditions are unique among all weak solutions in three dimensions. That is, we obtain the so-called weak-strong uniqueness result in three spatial dimensions.

  16. Advances in mathematical economics

    CERN Document Server

    Yamazaki, Akira

    2005-01-01

    A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. The editorial board of this series comprises the following prominent economists and mathematicians: Managing Editors: S. Kusuoka (Univ. Tokyo), T. Maruyama (Keio Univ.). Editors: R. Anderson (U.C. Berkeley), C. Castaing (Univ. Montpellier), F.H. Clarke (Univ. Lyon I), G. Debreu (U.C. Berkeley), E. Dierker (Univ. Vienna), D. Duffie (Stanford Univ.), L.C. Evans (U.C. Berkeley), T. Fujimoto (Okayama Univ.), J.-M. Grandmont...

  17. Mathematical simulation of the drying of suspensions and colloidal solutions by their depressurization

    Science.gov (United States)

    Lashkov, V. A.; Levashko, E. I.; Safin, R. G.

    2006-05-01

    The heat and mass transfer in the process of drying of high-humidity materials by their depressurization has been investigated. The results of experimental investigation and mathematical simulation of the indicated process are presented. They allow one to determine the regularities of this process and predict the quality of the finished product. A technological scheme and an engineering procedure for calculating the drying of the liquid base of a soap are presented.

  18. Computing the stability of steady-state solutions of mathematical models of the electrical activity in the heart.

    Science.gov (United States)

    Tveito, Aslak; Skavhaug, Ola; Lines, Glenn T; Artebrant, Robert

    2011-08-01

    Instabilities in the electro-chemical resting state of the heart can generate ectopic waves that in turn can initiate arrhythmias. We derive methods for computing the resting state for mathematical models of the electro-chemical process underpinning a heartbeat, and we estimate the stability of the resting state by invoking the largest real part of the eigenvalues of a linearized model. The implementation of the methods is described and a number of numerical experiments illustrate the feasibility of the methods. In particular, we test the methods for problems where we can compare the solutions with analytical results, and problems where we have solutions computed by independent software. The software is also tested for a fairly realistic 3D model. Copyright © 2011 Elsevier Ltd. All rights reserved.

  19. Langevin formulation of quantum dynamics

    International Nuclear Information System (INIS)

    Roncadelli, M.

    1989-03-01

    We first show that nonrelativistic quantum mechanics formulated at imaginary-(h/2 π) can formally be viewed as the Fokker-Planck description of a frictionless brownian motion, which occurs (in general) in an absorbing medium. We next offer a new formulation of quantum mechanics, which is basically the Langevin treatment of this brownian motion. Explicitly, we derive a noise-average representation for the transition probability W(X'',t''|X',t'), in terms of the solutions to a Langevin equation with a Gaussian white-noise. Upon analytic continuation back to real-(h/2 π),W(X'',t''|X',t') becomes the propagator of the original Schroedinger equation. Our approach allows for a straightforward application to quantum dynamical problems of the mathematical techniques of classical stochastic processes. Moreover, computer simulations of quantum mechanical systems can be carried out by using numerical programs based on the Langevin dynamics. (author). 19 refs, 1 tab

  20. Thermodynamically accurate modeling of the catalytic cycle of photosynthetic oxygen evolution: a mathematical solution to asymmetric Markov chains.

    Science.gov (United States)

    Vinyard, David J; Zachary, Chase E; Ananyev, Gennady; Dismukes, G Charles

    2013-07-01

    Forty-three years ago, Kok and coworkers introduced a phenomenological model describing period-four oscillations in O2 flash yields during photosynthetic water oxidation (WOC), which had been first reported by Joliot and coworkers. The original two-parameter Kok model was subsequently extended in its level of complexity to better simulate diverse data sets, including intact cells and isolated PSII-WOCs, but at the expense of introducing physically unrealistic assumptions necessary to enable numerical solutions. To date, analytical solutions have been found only for symmetric Kok models (inefficiencies are equally probable for all intermediates, called "S-states"). However, it is widely accepted that S-state reaction steps are not identical and some are not reversible (by thermodynamic restraints) thereby causing asymmetric cycles. We have developed a mathematically more rigorous foundation that eliminates unphysical assumptions known to be in conflict with experiments and adopts a new experimental constraint on solutions. This new algorithm termed STEAMM for S-state Transition Eigenvalues of Asymmetric Markov Models enables solutions to models having fewer adjustable parameters and uses automated fitting to experimental data sets, yielding higher accuracy and precision than the classic Kok or extended Kok models. This new tool provides a general mathematical framework for analyzing damped oscillations arising from any cycle period using any appropriate Markov model, regardless of symmetry. We illustrate applications of STEAMM that better describe the intrinsic inefficiencies for photon-to-charge conversion within PSII-WOCs that are responsible for damped period-four and period-two oscillations of flash O2 yields across diverse species, while using simpler Markov models free from unrealistic assumptions. Copyright © 2013 Elsevier B.V. All rights reserved.

  1. Validation of a stability-indicating hydrophilic interaction liquid chromatographic method for the quantitative determination of vitamin k3 (menadione sodium bisulfite) in injectable solution formulation.

    Science.gov (United States)

    Ghanem, Mashhour M; Abu-Lafi, Saleh A; Hallak, Hussein O

    2013-01-01

    A simple, specific, accurate, and stability-indicating method was developed and validated for the quantitative determination of menadione sodium bisulfite in the injectable solution formulation. The method is based on zwitterionic hydrophilic interaction liquid chromatography (ZIC-HILIC) coupled with a photodiode array detector. The desired separation was achieved on the ZIC-HILIC column (250 mm × 4.6 mm, 5 μm) at 25°C temperature. The optimized mobile phase consisted of an isocratic solvent mixture of 200mM ammonium acetate (NH4AC) solution and acetonitrile (ACN) (20:80; v/v) pH-adjusted to 5.7 by glacial acetic acid. The mobile phase was fixed at 0.5 ml/min and the analytes were monitored at 261 nm using a photodiode array detector. The effects of the chromatographic conditions on the peak retention, peak USP tailing factor, and column efficiency were systematically optimized. Forced degradation experiments were carried out by exposing menadione sodium bisulfite standard and the injectable solution formulation to thermal, photolytic, oxidative, and acid-base hydrolytic stress conditions. The degradation products were well-resolved from the main peak and the excipients, thus proving that the method is a reliable, stability-indicating tool. The method was validated as per ICH and USP guidelines (USP34/NF29) and found to be adequate for the routine quantitative estimation of menadione sodium bisulfite in commercially available menadione sodium bisulfite injectable solution dosage forms.

  2. A combined finite element-boundary integral formulation for solution of two-dimensional scattering problems via CGFFT. [Conjugate Gradient Fast Fourier Transformation

    Science.gov (United States)

    Collins, Jeffery D.; Volakis, John L.; Jin, Jian-Ming

    1990-01-01

    A new technique is presented for computing the scattering by 2-D structures of arbitrary composition. The proposed solution approach combines the usual finite element method with the boundary-integral equation to formulate a discrete system. This is subsequently solved via the conjugate gradient (CG) algorithm. A particular characteristic of the method is the use of rectangular boundaries to enclose the scatterer. Several of the resulting boundary integrals are therefore convolutions and may be evaluated via the fast Fourier transform (FFT) in the implementation of the CG algorithm. The solution approach offers the principal advantage of having O(N) memory demand and employs a 1-D FFT versus a 2-D FFT as required with a traditional implementation of the CGFFT algorithm. The speed of the proposed solution method is compared with that of the traditional CGFFT algorithm, and results for rectangular bodies are given and shown to be in excellent agreement with the moment method.

  3. New Solutions of Three Nonlinear Space- and Time-Fractional Partial Differential Equations in Mathematical Physics

    International Nuclear Information System (INIS)

    Yao Ruo-Xia; Wang Wei; Chen Ting-Hua

    2014-01-01

    Motivated by the widely used ansätz method and starting from the modified Riemann—Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper. (general)

  4. Mathematical and physical aspects of controlling the exact solutions of the 3D Gross-Pitaevskii equation

    International Nuclear Information System (INIS)

    Fedele, Renato; Jovanovic, Dusan; De Nicola, Sergio; Eliasson, Bengt; Shukla, Padma K.

    2010-01-01

    The possibility of the decomposition of the three-dimensional (3D) Gross-Pitaevskii equation (GPE) into a pair of coupled Schroedinger-type equations, is investigated. It is shown that, under suitable mathematical conditions, it is possible to construct the exact controlled solutions of the 3D GPE from the solutions of a linear 2D Schroedinger equation coupled with a 1D nonlinear Schroedinger equation (the transverse and longitudinal components of the GPE, respectively). The coupling between these two equations is the functional of the transverse and the longitudinal profiles. The applied method of nonlinear decomposition, called the controlling potential method (CPM), yields the full 3D solution in the form of the product of the solutions of the transverse and longitudinal components of the GPE. It is shown that the CPM constitutes a variational principle and sets up a condition on the controlling potential well. Its physical interpretation is given in terms of the minimization of the (energy) effects introduced by the control. The method is applied to the case of a parabolic external potential to construct analytically an exact BEC state in the form of a bright soliton, for which the quantitative comparison between the external and controlling potentials is presented.

  5. Inverse operator theory method mathematics-mechanization for the solutions of nonlinear equations and some typical applications in nonlinear physics

    International Nuclear Information System (INIS)

    Fang Jinqing; Yao Weiguang

    1992-12-01

    Inverse operator theory method (IOTM) has developed rapidly in the last few years. It is an effective and useful procedure for quantitative solution of nonlinear or stochastic continuous dynamical systems. Solutions are obtained in series form for deterministic equations, and in the case of stochastic equation it gives statistic measures of the solution process. A very important advantage of the IOTM is to eliminate a number of restrictive and assumption on the nature of stochastic processes. Therefore, it provides more realistic solutions. The IOTM and its mathematics-mechanization (MM) are briefly introduced. They are used successfully to study the chaotic behaviors of the nonlinear dynamical systems for the first time in the world. As typical examples, the Lorentz equation, generalized Duffing equation, two coupled generalized Duffing equations are investigated by the use of the IOTM and the MM. The results are in good agreement with ones by the Runge-Kutta method (RKM). It has higher accuracy and faster convergence. So the IOTM realized by the MM is of potential application valuable in nonlinear science

  6. Renormgroup symmetry for solution functionals

    International Nuclear Information System (INIS)

    Shirkov, D.V.; Kovalev, V.F.

    2004-01-01

    The paper contains generalization of the renormgroup algorithm for boundary value problems of mathematical physics and related concept of the renormgroup symmetry, formulated earlier by the authors with reference to models based on differential equations. These algorithm and symmetry are formulated now for models with nonlocal (integral) equations. We discuss in detail and illustrate by examples the applications of the generalized algorithm to models with nonlocal terms which appear as linear functionals of the solution. (author)

  7. Adaptive solution of the multigroup diffusion equation on irregular structured grids using a conforming finite element method formulation

    International Nuclear Information System (INIS)

    Ragusa, J. C.

    2004-01-01

    In this paper, a method for performing spatially adaptive computations in the framework of multigroup diffusion on 2-D and 3-D Cartesian grids is investigated. The numerical error, intrinsic to any computer simulation of physical phenomena, is monitored through an a posteriori error estimator. In a posteriori analysis, the computed solution itself is used to assess the accuracy. By efficiently estimating the spatial error, the entire computational process is controlled through successively adapted grids. Our analysis is based on a finite element solution of the diffusion equation. Bilinear test functions are used. The derived a posteriori error estimator is therefore based on the Hessian of the numerical solution. (authors)

  8. Mathematical modeling and exact solutions to rotating flows of a Burgers' fluid

    International Nuclear Information System (INIS)

    Hayat, T.

    2005-12-01

    The aim of this study is to provide the modeling and exact analytic solutions for hydromagnetic oscillatory rotating flows of an incompressible Burgers' fluid bounded by a plate. The governing time-dependent equation for the Burgers' fluid is different than those from the Navier-Stokes' equation. The entire system is assumed to rotate around an axis normal to the plate. The governing equations for this investigation are solved analytically for two physical problems. The solutions for the three cases, when the two times angular velocity is greater than the frequency of oscillation or it is smaller than the frequency or it is equal to the frequency (resonant case), are discussed in second problem. In Burgers' fluid, it is also found that hydromagnetic solution in the resonant case satisfies the boundary condition at infinity. Moreover, the obtained analytical results reduce to several previously published results as the special cases. (author)

  9. Mathematical Model of Age Aggression

    OpenAIRE

    Golovinski, P. A.

    2013-01-01

    We formulate a mathematical model of competition for resources between representatives of different age groups. A nonlinear kinetic integral-differential equation of the age aggression describes the process of redistribution of resources. It is shown that the equation of the age aggression has a stationary solution, in the absence of age-dependency in the interaction of different age groups. A numerical simulation of the evolution of resources for different initial distributions has done. It ...

  10. Optimal solutions for a bio mathematical model for the evolution of smoking habit

    Science.gov (United States)

    Sikander, Waseem; Khan, Umar; Ahmed, Naveed; Mohyud-Din, Syed Tauseef

    In this study, we apply Variation of Parameter Method (VPM) coupled with an auxiliary parameter to obtain the approximate solutions for the epidemic model for the evolution of smoking habit in a constant population. Convergence of the developed algorithm, namely VPM with an auxiliary parameter is studied. Furthermore, a simple way is considered for obtaining an optimal value of auxiliary parameter via minimizing the total residual error over the domain of problem. Comparison of the obtained results with standard VPM shows that an auxiliary parameter is very feasible and reliable in controlling the convergence of approximate solutions.

  11. An explicit solution of the mathematical model for osmotic desalination process

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Do Yeon; Gu, Boram; Yang, Dae Ryook [Korea University, Seoul (Korea, Republic of)

    2013-09-15

    Membrane processes such as reverse osmosis and forward osmosis for seawater desalination have gained attention in recent years. Mathematical models have been used to interpret the mechanism of membrane processes. The membrane process model, consisting of flux and concentration polarization (CP) models, is coupled with balance equations and solved simultaneously. This set of model equations is, however, implicit and nonlinear; consequently, the model must be solved iteratively and numerically, which is time- and cost-intensive. We suggest a method to transform implicit equations to their explicit form, in order to avoid an iterative procedure. In addition, the performance of five solving methods, including the method that we suggest, is tested and compared for accuracy, computation time, and robustness based on input conditions. Our proposed method shows the best performance based on the robustness of various simulation conditions, accuracy, and a cost-effective computation time.

  12. MATHEMATICAL MODELING AND NUMERICAL SOLUTION OF IRON CORROSION PROBLEM BASED ON CONDENSATION CHEMICAL PROPERTIES

    Directory of Open Access Journals (Sweden)

    Basuki Widodo

    2012-02-01

    Full Text Available Corrosion process is a natural case that happened at the various metals, where the corrosion process in electrochemical can be explained by using galvanic cell. The iron corrosion process is based on the acidity degree (pH of a condensation, iron concentration and condensation temperature of electrolyte. Those are applied at electrochemistry cell. The iron corrosion process at this electrochemical cell also able to generate electrical potential and electric current during the process takes place. This paper considers how to build a mathematical model of iron corrosion, electrical potential and electric current. The mathematical model further is solved using the finite element method. This iron corrosion model is built based on the iron concentration, condensation temperature, and iteration time applied. In the electric current density model, the current based on electric current that is happened at cathode and anode pole and the iteration time applied. Whereas on the potential  electric model, it is based on the beginning of electric potential and the iteration time applied. The numerical results show that the part of iron metal, that is gristle caused by corrosion, is the part of metal that has function as anode and it has some influences, such as time depth difference, iron concentration and condensation temperature on the iron corrosion process and the sum of reduced mass during corrosion process. Moreover, difference influence of time and beginning electric potential has an effect on the electric potential, which emerges during corrosion process at the electrochemical cell. Whereas, at the electrical current is also influenced by difference of depth time and condensation temperature applied.Keywords: Iron Corrosion, Concentration of iron, Electrochemical Cell and Finite Element Method

  13. Mathematical solution of multilevel fractional programming problem with fuzzy goal programming approach

    Science.gov (United States)

    Lachhwani, Kailash; Poonia, Mahaveer Prasad

    2012-08-01

    In this paper, we show a procedure for solving multilevel fractional programming problems in a large hierarchical decentralized organization using fuzzy goal programming approach. In the proposed method, the tolerance membership functions for the fuzzily described numerator and denominator part of the objective functions of all levels as well as the control vectors of the higher level decision makers are respectively defined by determining individual optimal solutions of each of the level decision makers. A possible relaxation of the higher level decision is considered for avoiding decision deadlock due to the conflicting nature of objective functions. Then, fuzzy goal programming approach is used for achieving the highest degree of each of the membership goal by minimizing negative deviational variables. We also provide sensitivity analysis with variation of tolerance values on decision vectors to show how the solution is sensitive to the change of tolerance values with the help of a numerical example.

  14. Approximate Mathematical Modeling of Osmotic Dehydration of Cone-Shaped Fruits and Vegetables in Hypertonic Solutions

    Directory of Open Access Journals (Sweden)

    Mohammad Sirousazar

    2017-07-01

    Full Text Available Water loss kinetics in osmotic dehydration of cone-shaped fruits and vegetables was modeled on the basis of diffusion mechanism, using the Fick’s second law. The model was developed by taking into account the influences of the fruit geometrical characteristics, initial water content of fruit, water diffusion coefficient in fruit, and the water concentration in hypertonic solution. Based on the obtained model, it was shown that the water diffusion coefficient and the initial water concentration of fruit have direct effects on the dehydration rate and also inverse influence on the dehydration duration. The geometrical parameters of fruit and water concentration in hypertonic solution showed direct effect on the dehydration duration as well as inverse effect on the dehydration rate. The presented model seems to be useful tool to predict the dehydration kinetics of cone-shaped fruit during osmotic dehydration process and to optimize the process prior to perform the experiments.

  15. A Bi-Modal Routing Problem with Cyclical and One-Way Trips: Formulation and Heuristic Solution

    Directory of Open Access Journals (Sweden)

    Grinde Roger B.

    2017-12-01

    Full Text Available A bi-modal routing problem is solved using a heuristic approach. Motivated by a recreational hiking application, the problem is similar to routing problems in business with two transport modes. The problem decomposes into a set covering problem (SCP and an asymmetric traveling salesperson problem (ATSP, corresponding to a hiking time objective and a driving distance objective. The solution algorithm considers hiking time first, but finds all alternate optimal solutions, as inputs to the driving distance problem. Results show the trade-offs between the two objectives.

  16. Approximate Mathematical Modeling of Osmotic Dehydration of Cone-Shaped Fruits and Vegetables in Hypertonic Solutions

    OpenAIRE

    Mohammad Sirousazar

    2017-01-01

    Water loss kinetics in osmotic dehydration of cone-shaped fruits and vegetables was modeled on the basis of diffusion mechanism, using the Fick’s second law. The model was developed by taking into account the influences of the fruit geometrical characteristics, initial water content of fruit, water diffusion coefficient in fruit, and the water concentration in hypertonic solution. Based on the obtained model, it was shown that the water diffusion coefficient and the initial water concentratio...

  17. A solution procedure for mixed-integer nonlinear programming formulation of supply chain planning with quantity discounts under demand uncertainty

    Science.gov (United States)

    Yin, Sisi; Nishi, Tatsushi

    2014-11-01

    Quantity discount policy is decision-making for trade-off prices between suppliers and manufacturers while production is changeable due to demand fluctuations in a real market. In this paper, quantity discount models which consider selection of contract suppliers, production quantity and inventory simultaneously are addressed. The supply chain planning problem with quantity discounts under demand uncertainty is formulated as a mixed-integer nonlinear programming problem (MINLP) with integral terms. We apply an outer-approximation method to solve MINLP problems. In order to improve the efficiency of the proposed method, the problem is reformulated as a stochastic model replacing the integral terms by using a normalisation technique. We present numerical examples to demonstrate the efficiency of the proposed method.

  18. A mathematical model for the transfer of soil solutes to runoff under water scouring.

    Science.gov (United States)

    Yang, Ting; Wang, Quanjiu; Wu, Laosheng; Zhang, Pengyu; Zhao, Guangxu; Liu, Yanli

    2016-11-01

    The transfer of nutrients from soil to runoff often causes unexpected pollution in water bodies. In this study, a mathematical model that relates to the detachment of soil particles by water flow and the degree of mixing between overland flow and soil nutrients was proposed. The model assumes that the mixing depth is an integral of average water flow depth, and it was evaluated by experiments with three water inflow rates to bare soil surfaces and to surfaces with eight treatments of different stone coverages. The model predicted outflow rates were compared with the experimentally observed data to test the accuracy of the infiltration parameters obtained by curve fitting the models to the data. Further analysis showed that the comprehensive mixing coefficient (ke) was linearly correlated with Reynolds' number Re (R(2)>0.9), and this relationship was verified by comparing the simulated potassium concentration and cumulative mass with observed data, respectively. The best performance with the bias error analysis (Nash Sutcliffe coefficient of efficiency (NS), relative error (RE) and the coefficient of determination (R(2))) showed that the predicted data by the proposed model was in good agreement with the measured data. Thus the model can be used to guide soil-water and fertilization management to minimize nutrient runoff from cropland. Copyright © 2016 Elsevier B.V. All rights reserved.

  19. Phase Relations in Ternary Systems in the Subsolidus Region: Methods to Formulate Solid Solution Equations and to Find Particular Compositions

    Science.gov (United States)

    Alvarez-Montan~o, Victor E.; Farías, Mario H.; Brown, Francisco; Mun~oz-Palma, Iliana C.; Cubillas, Fernando; Castillon-Barraza, Felipe F.

    2017-01-01

    A good understanding of ternary phase diagrams is required to advance and/or to reproduce experimental research in solid-state and materials chemistry. The aim of this paper is to describe the solutions to problems that appear when studying or determining ternary phase diagrams. A brief description of the principal features shown in phase diagrams…

  20. Use of a screening method to determine excipients which optimize the extent and stability of supersaturated drug solutions and application of this system to solid formulation design.

    Science.gov (United States)

    Vandecruys, Roger; Peeters, Jef; Verreck, Geert; Brewster, Marcus E

    2007-09-05

    Assessing the effect of excipients on the ability to attain and maintain supersaturation of drug-based solution may provide useful information for the design of solid formulations. Judicious selection of materials that affect either the extent or stability of supersaturating drug delivery systems may be enabling for poorly soluble drug candidates or other difficult-to-formulate compounds. The technique suggested herein is aimed at providing a screening protocol to allow preliminary assessment of these factors based on small to moderate amounts of drug substance. A series of excipients were selected that may, by various mechanisms, affect supersaturation including pharmaceutical polymers such as HMPC and PVP, surfactants such as Polysorbate 20, Cremophor RH40 and TPGS and hydrophilic cyclodextrins such as HPbetaCD. Using a co-solvent based method and 25 drug candidates, the data suggested, on the whole, that the surfactants and the selected cyclodextrin seemed to best augment the extent of supersaturation but had variable benefits as stabilizers, while the pharmaceutical polymers had useful effect on supersaturation stability but were less helpful in increasing the extent of supersaturation. Using these data, a group of simple solid dosage forms were prepared and tested in the dog for one of the drug candidates. Excipients that gave the best extent and stability for the formed supersaturated solution in the screening assay also gave the highest oral bioavailability in the dog.

  1. Dual Treatments as Starting Point for Integrative Perceptions in Teaching Mathematics

    Science.gov (United States)

    Kërënxhi, Svjetllana; Gjoci, Pranvera

    2015-01-01

    In this paper, we recommend mathematical teaching through dual treatments. The dual treatments notion, classified in dual interpretations, dual analyses, dual solutions, and dual formulations, is explained through concrete examples taken from mathematical textbooks of elementary education. Dual treatments provide opportunities for creating…

  2. Nanomedicine formulations for the delivery of antiviral drugs: a promising solution for the treatment of viral infections.

    Science.gov (United States)

    Lembo, David; Donalisio, Manuela; Civra, Andrea; Argenziano, Monica; Cavalli, Roberta

    2018-01-01

    Viral infections represent a public health problem and one of the leading causes of global mortality. Nanomedicine strategies can be considered a powerful tool to enhance the effectiveness of antiviral drugs, often associated with solubility and bioavailability issues. Consequently, high doses and frequent administrations are required, resulting in adverse side effects. To overcome these limitations, various nanomedicine platforms have been designed. Areas covered: This review focuses on the state of the art of organic-based nanoparticles for the delivery of approved antivirals. A brief description of the main characteristics of nanocarriers is followed by an overview of the most promising research addressing the treatment of most important viral infections. Expert opinion: The activity of antiviral drugs could be improved with nanomedicine formulations. Indeed, nanoparticles can affect the fate of the encapsulated drugs, allowing controlled release kinetics, enhanced bioavailability, modified pharmacokinetics, and reduced side effects. In addition, the physicochemical properties of nanocarriers can enable their capability to target specific sites and to interact with virus structures. In this regard, nanomedicines can be considered an opportunity to enhance the therapeutic index of antivirals. Efficacy, safety, and manufacturing issues need to be carefully assessed to bring this promising approach to the clinic.

  3. Ocular pharmacokinetics of bimatoprost formulated in DuraSite compared to bimatoprost 0.03% ophthalmic solution in pigmented rabbit eyes

    Directory of Open Access Journals (Sweden)

    Shafiee A

    2013-07-01

    Full Text Available Afshin Shafiee,1 Lyle M Bowman,2 Eddie Hou,2 Kamran Hosseini1,3 1Preclinical, 2Development, 3Clinical, InSite Vision, Alameda, CA, USA Purpose: To compare the aqueous humor (AH and iris-ciliary body (ICB concentration of bimatoprost in rabbit eyes treated with ISV-215 (0.03% bimatoprost formulated in DuraSite with the marketed product bimatoprost 0.03% ophthalmic solution. Methods: The left eye of rabbits received a single topical instillation of either ISV-215 (n = 32 eyes or bimatoprost 0.03% (n = 32 eyes. At predetermined time points, levels of bimatoprost and bimatoprost acid in the AH and the ICB were quantified by HPLC-MS/MS. Results: Both bimatoprost and bimatoprost acid were detected in the AH and the ICB within 15 minutes of dosing. Bimatoprost acid concentrations in both compartments were markedly higher than bimatoprost. There was a statistically significant (P < 0.01 increase in the concentration of the prodrug in the AH and its acid form in the ICB in animals treated with ISV-215 compared to bimatoprost 0.03%. In the ISV-215-treated rabbit eyes, the highest concentrations of bimatoprost and bimatoprost acid were in the ICB and AH, respectively, while in the bimatoprost 0.03%-treated eyes, no differences in the drug content of the selected ocular tissues were observed. Conclusions: Bimatoprost 0.03% formulated in DuraSite has superior ocular distribution and area under the curve compared to bimatoprost 0.03% in rabbit eyes. This improvement in the pharmacokinetic parameters of ISV-215 may provide us with a better platform to optimize a bimatoprost formulation that offers the same degree of efficacy in lowering intraocular pressure and improved therapeutic index in glaucomatous patients by lessening the ocular side effects associated with long-term use of topical prostaglandin F2α analogs. Keywords: drug delivery, intraocular pressure, glaucoma, aqueous humor, prostaglandin (PGF2α analogs

  4. Mathematical scandals

    CERN Document Server

    Pappas, Theoni

    1997-01-01

    In this highly readable volume of vignettes of mathematical scandals and gossip, Theoni Pappas assembles 29 fascinating stories of intrigue and the bizarre ? in short, the human background of the history of mathematics. Might a haberdasher have changed Einstein's life? Why was the first woman mathematician murdered? How come there's no Nobel Prize in mathematics?Mathematics is principally about numbers, equations, and solutions, all of them precise and timeless. But, behind this arcane matter lies the sometimes sordid world of real people, whose rivalries and deceptions

  5. A Novel Hybridization of Applied Mathematical, Operations Research and Risk-based Methods to Achieve an Optimal Solution to a Challenging Subsurface Contamination Problem

    Science.gov (United States)

    Johnson, K. D.; Pinder, G. F.

    2013-12-01

    The objective of the project is the creation of a new, computationally based, approach to the collection, evaluation and use of data for the purpose of determining optimal strategies for investment in the solution of remediation of contaminant source areas and similar environmental problems. The research focuses on the use of existing mathematical tools assembled in a unique fashion. The area of application of this new capability is optimal (least-cost) groundwater contamination source identification; we wish to identify the physical environments wherein it may be cost-prohibitive to identify a contaminant source, the optimal strategy to protect the environment from additional insult and formulate strategies for cost-effective environmental restoration. The computational underpinnings of the proposed approach encompass the integration into a unique of several known applied-mathematical tools. The resulting tool integration achieves the following: 1) simulate groundwater flow and contaminant transport under uncertainty, that is when the physical parameters such as hydraulic conductivity are known to be described by a random field; 2) define such a random field from available field data or be able to provide insight into the sampling strategy needed to create such a field; 3) incorporate subjective information, such as the opinions of experts on the importance of factors such as locations of waste landfills; 4) optimize a search strategy for finding a potential source location and to optimally combine field information with model results to provide the best possible representation of the mean contaminant field and its geostatistics. Our approach combines in a symbiotic manner methodologies found in numerical simulation, random field analysis, Kalman filtering, fuzzy set theory and search theory. Testing the algorithm for this stage of the work, we will focus on fabricated field situations wherein we can a priori specify the degree of uncertainty associated with the

  6. Mathematical modelling, variational formulation and numerical simulation of the energy transfer process in a gray plate in the presence of a thermal radiant source

    International Nuclear Information System (INIS)

    Gama, R.M.S. da.

    1992-05-01

    The energy transfer process in a gray, opaque and rigid plate, heated by an external thermal radiant source, is considered. The source is regarded as a spherical black body, with radius a (a → 0) and uniform heat generation, placed above the plate. A mathematical model is constructed, assuming that the heat transfer from/to the plate takes place by thermal radiation. The obtained mathematical model is nonlinear. Is presented a suitable variational principle which is employed for simulating some particular cases. (author)

  7. Dispersive traveling wave solutions of the Equal-Width and Modified Equal-Width equations via mathematical methods and its applications

    Science.gov (United States)

    Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

    2018-06-01

    The Equal-Width and Modified Equal-Width equations are used as a model in partial differential equations for the simulation of one-dimensional wave transmission in nonlinear media with dispersion processes. In this article we have employed extend simple equation method and the exp(-varphi(ξ)) expansion method to construct the exact traveling wave solutions of equal width and modified equal width equations. The obtained results are novel and have numerous applications in current areas of research in mathematical physics. It is exposed that our method, with the help of symbolic computation, provides a effective and powerful mathematical tool for solving different kind nonlinear wave problems.

  8. Thermodynamic investigation of the interaction between cyclodextrins and preservatives - Application and verification in a mathematical model to determine the needed preservative surplus in aqueous cyclodextrin formulations

    DEFF Research Database (Denmark)

    Holm, René; Olesen, Niels Erik; Alexandersen, Signe Dalgaard

    2016-01-01

    Preservatives are inactivated when added to conserve aqueous cyclodextrin (CD) formulations due to complex formation between CDs and the preservative. To maintain the desired conservation effect the preservative needs to be added in apparent surplus to account for this inactivation. The purpose o...

  9. Mathematical physiology

    CERN Document Server

    Sneyd, James

    2009-01-01

    There has been a long history of interaction between mathematics and physiology. This book looks in detail at a wide selection of mathematical models in physiology, showing how physiological problems can be formulated and studied mathematically, and how such models give rise to interesting and challenging mathematical questions. With its coverage of many recent models it gives an overview of the field, while many older models are also discussed, to put the modern work in context. In this second edition the coverage of basic principles has been expanded to include such topics as stochastic differential equations, Markov models and Gibbs free energy, and the selection of models has also been expanded to include some of the basic models of fluid transport, respiration/perfusion, blood diseases, molecular motors, smooth muscle, neuroendrocine cells, the baroreceptor loop, turboglomerular oscillations, blood clotting and the retina. Owing to this extensive coverage, the second edition is published in two volumes. ...

  10. The Mathematical modelling of environmental pollution using the ...

    African Journals Online (AJOL)

    In this paper environmental pollution has been modeled mathematically using the Freundlich non-linear contaminant transport formulation. An analytical solution of lower order perturbation of the concentration C(x,f) is obtained. Flow profiles for various values of molecular diffusion D and the velocity U are studied and the ...

  11. Proceedings – Mathematical Sciences | Indian Academy of Sciences

    Indian Academy of Sciences (India)

    Home; Journals; Proceedings – Mathematical Sciences; Volume 116; Issue 1. Volume 116, Issue 1. February 2006, pages 1-119. pp 1-8 .... in probability but for which no r.c.l.l. solution exists. pp 97-119. Formulation of the Problem of Sonic Boom by a Maneuvering Aerofoil as a One-Parameter Family of Cauchy Problems.

  12. Closed-Form Solutions of the Thomas-Fermi in Heavy Atoms and the Langmuir-Blodgett in Current Flow ODEs in Mathematical Physics

    Directory of Open Access Journals (Sweden)

    Efstathios E. Theotokoglou

    2015-01-01

    Full Text Available Two kinds of second-order nonlinear, ordinary differential equations (ODEs appearing in mathematical physics are analyzed in this paper. The first one concerns the Thomas-Fermi (TF equation, while the second concerns the Langmuir-Blodgett (LB equation in current flow. According to a mathematical methodology recently developed, the exact analytic solutions of both TF and LB ODEs are proposed. Both of these are nonlinear of the second order and by a series of admissible functional transformations are reduced to Abel’s equations of the second kind of the normal form. The closed form solutions of the TF and LB equations in the phase and physical plane are given. Finally a new interesting result has been obtained related to the derivative of the TF function at the limit.

  13. Dissolution profiles of perindopril and indapamide in their fixed-dose formulations by a new HPLC method and different mathematical approaches

    Directory of Open Access Journals (Sweden)

    Gumieniczek Anna

    2015-09-01

    Full Text Available A new HPLC method was introduced and validated for simultaneous determination of perindopril and indapamide. Validation procedure included specificity, sensitivity, robustness, stability, linearity, precision and accuracy. The method was used for the dissolution test of perindopril and indapamide in three fixed-dose formulations. The dissolution procedure was optimized using different media, different pH of the buffer, surfactants, paddle speed and temperature. Similarity of dissolution profiles was estimated using different model-independent and model-dependent methods and, additionally, by principal component analysis (PCA. Also, some kinetic models were checked for dissolved amounts of drugs as a function of time.

  14. Mathematical aspects of quantum field theory

    CERN Document Server

    de Faria, Edson

    2010-01-01

    Over the last century quantum field theory has made a significant impact on the formulation and solution of mathematical problems and inspired powerful advances in pure mathematics. However, most accounts are written by physicists, and mathematicians struggle to find clear definitions and statements of the concepts involved. This graduate-level introduction presents the basic ideas and tools from quantum field theory to a mathematical audience. Topics include classical and quantum mechanics, classical field theory, quantization of classical fields, perturbative quantum field theory, renormalization, and the standard model. The material is also accessible to physicists seeking a better understanding of the mathematical background, providing the necessary tools from differential geometry on such topics as connections and gauge fields, vector and spinor bundles, symmetries and group representations.

  15. Methods of mathematical modelling continuous systems and differential equations

    CERN Document Server

    Witelski, Thomas

    2015-01-01

    This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.

  16. VEDIC MATHEMATICS

    Directory of Open Access Journals (Sweden)

    Sead Rešić

    2015-09-01

    Full Text Available It is very difficult to motivate students when it comes to a school subject like Mathematics. Teachers spend a lot of time trying to find something that will arouse interest in students. It is particularly difficult to find materials that are motivating enough for students that they eagerly wait for the next lesson. One of the solutions may be found in Vedic Mathematics. Traditional methods of teaching Mathematics create fear of this otherwise interesting subject in the majority of students. Fear increases failure. Often the traditional, conventional mathematical methods consist of very long lessons which are difficult to understand. Vedic Mathematics is an ancient system that is very flexible and encourages the development of intuition and innovation. It is a mental calculating tool that does not require a calculator because the calculator is embedded in each of us. Starting from the above problems of fear and failure in Mathematics, the goal of this paper is to do research with the control and the experimental group and to compare the test results. Two tests should be done for each of the groups. The control group would do the tests in the conventional way. The experimental group would do the first test in a conventional manner and then be subjected to different treatment, that is to say, be taught on the basis of Vedic Mathematics. After that, the second group would do the second test according to the principles of Vedic Mathematics. Expectations are that after short lectures on Vedic mathematics results of the experimental group would improve and that students will show greater interest in Mathematics.

  17. Two-dimensional interaction of a shear flow with a free surface in a stratified fluid and its solitary-wave solutions via mathematical methods

    Science.gov (United States)

    Seadawy, Aly R.

    2017-12-01

    In this study, we presented the problem formulations of models for internal solitary waves in a stratified shear flow with a free surface. The nonlinear higher order of extended KdV equations for the free surface displacement is generated. We derived the coefficients of the nonlinear higher-order extended KdV equation in terms of integrals of the modal function for the linear long-wave theory. The wave amplitude potential and the fluid pressure of the extended KdV equation in the form of solitary-wave solutions are deduced. We discussed and analyzed the stability of the obtained solutions and the movement role of the waves by making graphs of the exact solutions.

  18. Formulation of similarity porous media systems

    International Nuclear Information System (INIS)

    Anderson, R.M.; Ford, W.T.; Ruttan, A.; Strauss, M.J.

    1982-01-01

    The mathematical formulation of the Porous Media System (PMS) describing two-phase, immiscible, compressible fluid flow in linear, homogeneous porous media is reviewed and expanded. It is shown that families of common vertex, coaxial parabolas and families of parallel lines are the only families of curves on which solutions of the PMS may be constant. A coordinate transformation is used to change the partial differential equations of the PMS to a system of ordinary differential equations, referred to as a similarity Porous Media System (SPMS), in which the independent variable denotes movement from curve to curve in a selected family of curves. Properties of solutions of the first boundary value problem are developed for the SPMS

  19. Mathematical Perspectives

    Energy Technology Data Exchange (ETDEWEB)

    Glimm, J.

    2009-10-14

    Progress for the past decade or so has been extraordinary. The solution of Fermat's Last Theorem [11] and of the Poincare Conjecture [1] have resolved two of the most outstanding challenges to mathematics. For both cases, deep and advanced theories and whole subfields of mathematics came into play and were developed further as part of the solutions. And still the future is wide open. Six of the original seven problems from the Clay Foundation challenge remain open, the 23 DARPA challenge problems are open. Entire new branches of mathematics have been developed, including financial mathematics and the connection between geometry and string theory, proposed to solve the problems of quantized gravity. New solutions of the Einstein equations, inspired by shock wave theory, suggest a cosmology model which fits accelerating expansion of the universe possibly eliminating assumptions of 'dark matter'. Intellectual challenges and opportunities for mathematics are greater than ever. The role of mathematics in society continues to grow; with this growth comes new opportunities and some growing pains; each will be analyzed here. We see a broadening of the intellectual and professional opportunities and responsibilities for mathematicians. These trends are also occuring across all of science. The response can be at the level of the professional societies, which can work to deepen their interactions, not only within the mathematical sciences, but also with other scientific societies. At a deeper level, the choices to be made will come from individual mathematicians. Here, of course, the individual choices will be varied, and we argue for respect and support for this diversity of responses. In such a manner, we hope to preserve the best of the present while welcoming the best of the new.

  20. Mathematical simulation of the behaviour of the spent organic extractive solution near the injection well area in the case of underground disposal

    International Nuclear Information System (INIS)

    Istomin, A.D.; Noskov, M.D.; Balakhonov, V.G.; Zubkov, A.A.; Egorov, G.F.

    2005-01-01

    A mathematical model is presented of the processes in the collector seam under combined disposal of organic and radioactive wastes in porous geological strata of deep bedding. The model describes filtration, mass transfer, sorption and desorption of radionuclides, radioactive decay, decomposition of organic components and heat transfer. The computer software is developed. The results of simulating the thermal field dynamics, behaviour of the components of the spent organic extractive solution and water radioactive wastes in the collector seam of deep bedding are presented [ru

  1. Conformal and covariant Z4 formulation of the Einstein equations: Strongly hyperbolic first-order reduction and solution with discontinuous Galerkin schemes

    Science.gov (United States)

    Dumbser, Michael; Guercilena, Federico; Köppel, Sven; Rezzolla, Luciano; Zanotti, Olindo

    2018-04-01

    We present a strongly hyperbolic first-order formulation of the Einstein equations based on the conformal and covariant Z4 system (CCZ4) with constraint-violation damping, which we refer to as FO-CCZ4. As CCZ4, this formulation combines the advantages of a conformal and traceless formulation, with the suppression of constraint violations given by the damping terms, but being first order in time and space, it is particularly suited for a discontinuous Galerkin (DG) implementation. The strongly hyperbolic first-order formulation has been obtained by making careful use of first and second-order ordering constraints. A proof of strong hyperbolicity is given for a selected choice of standard gauges via an analytical computation of the entire eigenstructure of the FO-CCZ4 system. The resulting governing partial differential equations system is written in nonconservative form and requires the evolution of 58 unknowns. A key feature of our formulation is that the first-order CCZ4 system decouples into a set of pure ordinary differential equations and a reduced hyperbolic system of partial differential equations that contains only linearly degenerate fields. We implement FO-CCZ4 in a high-order path-conservative arbitrary-high-order-method-using-derivatives (ADER)-DG scheme with adaptive mesh refinement and local time-stepping, supplemented with a third-order ADER-WENO subcell finite-volume limiter in order to deal with singularities arising with black holes. We validate the correctness of the formulation through a series of standard tests in vacuum, performed in one, two and three spatial dimensions, and also present preliminary results on the evolution of binary black-hole systems. To the best of our knowledge, these are the first successful three-dimensional simulations of moving punctures carried out with high-order DG schemes using a first-order formulation of the Einstein equations.

  2. Exact Solutions to the Double Travelling Salesman Problem with Multiple Stacks

    DEFF Research Database (Denmark)

    Petersen, Hanne L.; Archetti, Claudia; Speranza, M. Grazia

    2010-01-01

    In this paper we present mathematical programming formulations and solution approaches for the optimal solution of the Double Travelling Salesman Problem with Multiple Stacks (DTSPMS). A set of orders is given, each one requiring transportation of one item from a customer in a pickup region...

  3. Mathematical Modeling of Diverse Phenomena

    Science.gov (United States)

    Howard, J. C.

    1979-01-01

    Tensor calculus is applied to the formulation of mathematical models of diverse phenomena. Aeronautics, fluid dynamics, and cosmology are among the areas of application. The feasibility of combining tensor methods and computer capability to formulate problems is demonstrated. The techniques described are an attempt to simplify the formulation of mathematical models by reducing the modeling process to a series of routine operations, which can be performed either manually or by computer.

  4. Fundamental concepts of mathematics

    CERN Document Server

    Goodstein, R L

    Fundamental Concepts of Mathematics, 2nd Edition provides an account of some basic concepts in modern mathematics. The book is primarily intended for mathematics teachers and lay people who wants to improve their skills in mathematics. Among the concepts and problems presented in the book include the determination of which integral polynomials have integral solutions; sentence logic and informal set theory; and why four colors is enough to color a map. Unlike in the first edition, the second edition provides detailed solutions to exercises contained in the text. Mathematics teachers and people

  5. The Radiation Problem from a Vertical Hertzian Dipole Antenna above Flat and Lossy Ground: Novel Formulation in the Spectral Domain with Closed-Form Analytical Solution in the High Frequency Regime

    Directory of Open Access Journals (Sweden)

    K. Ioannidi

    2014-01-01

    Full Text Available We consider the problem of radiation from a vertical short (Hertzian dipole above flat lossy ground, which represents the well-known “Sommerfeld radiation problem” in the literature. The problem is formulated in a novel spectral domain approach, and by inverse three-dimensional Fourier transformation the expressions for the received electric and magnetic (EM field in the physical space are derived as one-dimensional integrals over the radial component of wavevector, in cylindrical coordinates. This formulation appears to have inherent advantages over the classical formulation by Sommerfeld, performed in the spatial domain, since it avoids the use of the so-called Hertz potential and its subsequent differentiation for the calculation of the received EM field. Subsequent use of the stationary phase method in the high frequency regime yields closed-form analytical solutions for the received EM field vectors, which coincide with the corresponding reflected EM field originating from the image point. In this way, we conclude that the so-called “space wave” in the literature represents the total solution of the Sommerfeld problem in the high frequency regime, in which case the surface wave can be ignored. Finally, numerical results are presented, in comparison with corresponding numerical results based on Norton’s solution of the problem.

  6. On the non-uniqueness of the nodal mathematical adjoint

    International Nuclear Information System (INIS)

    Müller, Erwin

    2014-01-01

    Highlights: • We evaluate three CMFD schemes for computing the nodal mathematical adjoint. • The nodal mathematical adjoint is not unique and can be non-positive (nonphysical). • Adjoint and forward eigenmodes are compatible if produced by the same CMFD method. • In nodal applications the excited eigenmodes are purely mathematical entities. - Abstract: Computation of the neutron adjoint flux within the framework of modern nodal diffusion methods is often facilitated by reducing the nodal equation system for the forward flux into a simpler coarse-mesh finite-difference form and then transposing the resultant matrix equations. The solution to the transposed problem is known as the nodal mathematical adjoint. Since the coarse-mesh finite-difference reduction of a given nodal formulation can be obtained in a number of ways, different nodal mathematical adjoint solutions can be computed. This non-uniqueness of the nodal mathematical adjoint challenges the credibility of the reduction strategy and demands a verdict as to its suitability in practical applications. This is the matter under consideration in this paper. A selected number of coarse-mesh finite-difference reduction schemes are described and compared. Numerical calculations are utilised to illustrate the differences in the adjoint solutions as well as to appraise the impact on such common applications as the computation of core point kinetics parameters. Recommendations are made for the proper application of the coarse-mesh finite-difference reduction approach to the nodal mathematical adjoint problem

  7. Economic assessment and pathogenic bacteria inhibition of bovine hide presoaking solutions formulated with enzymes that can remove adobe-type manure

    Science.gov (United States)

    The presoaking formulations that have recently been developed are effective in removing the damaging adobe type bovine manure and eco-friendly because the ingredients used are recycled and required only a quarter of the amount of biocide and surfactant that the industry is commonly using. The goal ...

  8. Approximate Analytical Solutions for Mathematical Model of Tumour Invasion and Metastasis Using Modified Adomian Decomposition and Homotopy Perturbation Methods

    Directory of Open Access Journals (Sweden)

    Norhasimah Mahiddin

    2014-01-01

    Full Text Available The modified decomposition method (MDM and homotopy perturbation method (HPM are applied to obtain the approximate solution of the nonlinear model of tumour invasion and metastasis. The study highlights the significant features of the employed methods and their ability to handle nonlinear partial differential equations. The methods do not need linearization and weak nonlinearity assumptions. Although the main difference between MDM and Adomian decomposition method (ADM is a slight variation in the definition of the initial condition, modification eliminates massive computation work. The approximate analytical solution obtained by MDM logically contains the solution obtained by HPM. It shows that HPM does not involve the Adomian polynomials when dealing with nonlinear problems.

  9. Improving the Ability of Mathematic Representation Capabilities and Students Skills in Importing Square Forms to Square Using Variation Solutions

    Science.gov (United States)

    Nirawati, R.

    2018-04-01

    This research was conducted to see whether the variation of the solution is acceptable and easy to understand by students with different level of ability so that it can be seen the difference of students ability in facilitating the quadratic form in the upper, middle and lower groups. This research used experimental method with factorial design. Based on the result of final test analysis, there were differences of students ability in upper group, medium group, and lower group in putting squared form based on the use certain variation of solution.

  10. Design of future municipal wastewater treatment plants: A mathematical approach to manage complexity and identify optimal solutions

    DEFF Research Database (Denmark)

    Bozkurt, Hande; Quaglia, Alberto; Gernaey, Krist

    The increasing number of alternative wastewater treatment (WWT) technologies and stricter effluent requirements imposed by regulations make the early stage decision making for WWTP layout design, which is currently based on expert decisions and previous experiences, much harder. This paper...... therefore proposes a new approach based on mathematical programming to manage the complexity of the problem and generate/identify novel and optimal WWTP layouts for municipal/domestic wastewater treatment. Towards this end, after developing a database consisting of primary, secondary and tertiary WWT...... solved to obtain the optimal WWT network and the optimal wastewater and sludge flow through the network. The tool is evaluated on a case study, which was chosen as the Benchmark Simulation Model no.1 (BSM1) and many retrofitting options for obtaining a cost-effective treatment were investigated...

  11. Mathematical Representation of VoIP Connection Delay

    Directory of Open Access Journals (Sweden)

    M. Halas

    2007-09-01

    Full Text Available The main topic of this article is to define mathematical formulation of VoIP connection delay model. It handles about all partial delay components, the mechanism of their generation, facilities and their mathematical formulation. Thereafter based on mathematical formulation of all partial delay components, the final mathematical model of whole VoIP call delay is created. In conclusion of this article the results of the designed mathematical model are compared with the experimentally gained results.

  12. Comments on alternate formulations for preequilibrium decay

    International Nuclear Information System (INIS)

    Blann, M.

    1978-01-01

    The physical and mathematical differences of several formulations for preequilibrium decay are discussed. Mathematical models and examples are presented or referred to in order to illustrate what the author believes to be errors in the exciton formulation as being due to improper inclusion of spectator effects. An earlier work of Gadioli et al. is reinterpreted, and quotations therein to work of the present author are corrected

  13. Mathematical literacy skills of students' in term of gender differences

    Science.gov (United States)

    Lailiyah, Siti

    2017-08-01

    Good mathematical literacy skills will hopefully help maximize the tasks and role of the prospective teacher in activities. Mathematical literacy focus on students' ability to analyze, justify, and communicate ideas effectively, formulate, solve and interpret mathematical problems in a variety of forms and situations. The purpose of this study is to describe the mathematical literacy skills of the prospective teacher in term of gender differences. This research used a qualitative approach with a case study. Subjects of this study were taken from two male students and two female students of the mathematics education prospective teacher who have followed Community Service Program (CSP) in literacy. Data were collected through methods think a loud and interviews. Four prospective teachers were asked to fill mathematical literacy test and video taken during solving this test. Students are required to convey loud what he was thinking when solving problems. After students get the solution, researchers grouped the students' answers and results think aloud. Furthermore, the data are grouped and analyzed according to indicators of mathematical literacy skills. Male students have good of each indicator in mathematical literacy skills (the first indicator to the sixth indicator). Female students have good of mathematical literacy skills (the first indicator, the second indicator, the third indicator, the fourth indicator and the sixth indicator), except for the fifth indicators that are enough.

  14. Single-particle Schroedinger fluid. I. Formulation

    International Nuclear Information System (INIS)

    Kan, K.K.; Griffin, J.J.

    1976-01-01

    The problem of a single quantal particle moving in a time-dependent external potential well is formulated specifically to emphasize and develop the fluid dynamical aspects of the matter flow. This idealized problem, the single-particle Schroedinger fluid, is shown to exhibit already a remarkably rich variety of fluid dynamical features, including compressible flow and line vortices. It provides also a sufficient framework to encompass simultaneously various simplified fluidic models for nuclei which have earlier been postulated on an ad hoc basis, and to illuminate their underlying restrictions. Explicit solutions of the single-particle Schroedinger fluid problem are studied in the adiabatic limit for their mathematical and physical implications (especially regarding the collective kinetic energy). The basic generalizations for extension of the treatment to the many-body Schroedinger fluid are set forth

  15. On the conservation laws and solutions of a (2+1) dimensional KdV-mKdV equation of mathematical physics

    Science.gov (United States)

    Motsepa, Tanki; Masood Khalique, Chaudry

    2018-05-01

    In this paper, we study a (2+1) dimensional KdV-mKdV equation, which models many physical phenomena of mathematical physics. This equation has two integral terms in it. By an appropriate substitution, we convert this equation into two partial differential equations, which do not have integral terms and are equivalent to the original equation. We then work with the system of two equations and obtain its exact travelling wave solutions in form of Jacobi elliptic functions. Furthermore, we employ the multiplier method to construct conservation laws for the system. Finally, we revert the results obtained into the original variables of the (2+1) dimensional KdV-mKdV equation.

  16. On interior regularity of solutions of a class of almost-hypoelliptic equations. Armenian Journal of Mathematics

    Directory of Open Access Journals (Sweden)

    Hayk Ghazaryan

    2010-06-01

    Full Text Available In this paper it is proved that all distributional solutions of the non-degenerate, almost hypoelliptic (hypoelliptic by the one of variables equation $P(Du = P(D_{1},D_{2}u = 0$ are infinitely differentiable in the certain strip in $E^{2}$ under a priori assumption that they and its certain derivatives are square integrable with a certain exponential weight.

  17. Ether formulations of relativity

    International Nuclear Information System (INIS)

    Duffy, M.C.

    1980-01-01

    Contemporary ether theories are surveyed and criticised, especially those formally identical to orthodox Relativity. The historical development of Relativity, Special and General, in terms of an ether, is briefly indicated. Classical interpretations of Generalized Relativity using ether are compared to Euclidean formulations using a background space. The history of a sub-group of theories, formulating a 'new' Relativity involving modified transforms, is outlined. According to the theory with which they agree, recent supposed detections of drift are classified and criticised. Cosmological evidence suggesting an ether is mentioned. Only ether theories formally identical to Relativity have been published in depth. They stand criticised as being contrary to the positivist spirit. The history of mechanical analogues is traced, from Hartley's representing gravitating matter as spherical standing waves, to recent suggestions that vortex-sponge might model electromagnetic, quantum, uncertainty and faster-than-light phenomena. Contemporary theories are particular physical theories, themselves 'second interpretations' of a primary mathematical model. Mechanical analogues are auxiliary, not necessary, to other theory, disclosing relationships between classical and non-classical descriptions of assemblies charging state. The ether-relativity polemic, part of a broader dispute about relativity, is founded on mistaken conceptions of the roles of mathematical and physical models, mechanical analogues; and a distored view of history, which indicates that ether theories have become relativistic. (author)

  18. A stabilized finite element formulation for the solution of the Navier-Stokes equations in axisymmetric geometry; Uma formulacao estabilizada de elementos finitos para solucao das equacoes de Navier-Stokes em geometria axissimetrica

    Energy Technology Data Exchange (ETDEWEB)

    Souza, Altivo Monteiro de

    2008-12-15

    The world energy consumption has been increasing strongly in recent years. Nuclear energy has been regarded as a suitable option to supply this growing energy demand in industrial scale. In view of the need of improving the understanding and capacity of analysis of nuclear power plants, modern simulation techniques for flow and heat transfer problems are gaining greater importance. A large number of problems found in nuclear reactor engineering can be dealt assuming axial symmetry. Thus, in this work a stabilized finite element formulation for the solution of the Navier-Stokes and energy equations for axisymmetric problems have been developed and tested. The formulation has been implemented in the NS{sub S}OLVER{sub M}PI{sub 2}D{sub A} program developed at the Parallel Computation Laboratory of the Instituto de Engenharia Nuclear (LCP/IEN) and is now available either for safety analysis or design of nuclear systems. (author)

  19. Mathematical and physical model of gravity-fed infusion outflow: application to soft-bag-packed solutions.

    Science.gov (United States)

    Simon, N; Décaudin, B; Lannoy, D; Barthélémy, C; Lemdani, M; Odou, P

    2011-12-01

    Gravity-fed infusion (GFI) systems are acknowledged as being unable to keep their flow-rate constant. This may affect drug plasma levels such as aminoglycosides. Numerous factors have previously been cited, but their relative importance has never been quantified so far. The objective of this work is to identify the main factors that influence GFI in vitro outflow and to propose a mathematical model of flow-rate evolution as a function of time. In this model, pressure loss and infusion device creep have been considered as the main variation factors. Concomitantly, two experiments were undertaken. Firstly, the flow-rate evolution of an in vitro infusion of 250 mL of dextrose 5% was assessed. Secondly, the creep occurring on an infusion device was measured through a stress relaxation experiment. The experimental infusion flow-rate decreased by as much as 28.5% over 1 h. Simulated and experimental data are well correlated (r = 0.987; P model should help to explain the differences observed in drug plasma levels with gravity-fed devices.

  20. A variational formulation for linear models in coupled dynamic thermoelasticity

    International Nuclear Information System (INIS)

    Feijoo, R.A.; Moura, C.A. de.

    1981-07-01

    A variational formulation for linear models in coupled dynamic thermoelasticity which quite naturally motivates the design of a numerical scheme for the problem, is studied. When linked to regularization or penalization techniques, this algorithm may be applied to more general models, namely, the ones that consider non-linear constraints associated to variational inequalities. The basic postulates of Mechanics and Thermodynamics as well as some well-known mathematical techniques are described. A thorough description of the algorithm implementation with the finite-element method is also provided. Proofs for existence and uniqueness of solutions and for convergence of the approximations are presented, and some numerical results are exhibited. (Author) [pt

  1. Post-processing application of chemical solutions for control of Listeria monocytogenes, cultured under different conditions, on commercial smoked sausage formulated with and without potassium lactate-sodium diacetate.

    Science.gov (United States)

    Geornaras, Ifigenia; Skandamis, Panagiotis N; Belk, Keith E; Scanga, John A; Kendall, Patricia A; Smith, Gary C; Sofos, John N

    2006-12-01

    This study evaluated post-processing chemical solutions for their antilisterial effects on commercial smoked sausage formulated with or without 1.5% potassium lactate plus 0.05% sodium diacetate, and contaminated (approximately 3-4 log cfu/cm(2)) with 10-strain composite Listeria monocytogenes inocula prepared under various conditions. Inoculated samples were left untreated, or were immersed (2 min, 25 +/- 2 degrees C) in solutions of acetic acid (2.5%), lactic acid (2.5%), potassium benzoate (5%) or Nisaplin (0.5%, equivalent to 5000 IU/ml of nisin) alone, and in sequence (Nisaplin followed by acetic acid, lactic acid or potassium benzoate), before vacuum packaging and storage at 10 degrees C (48 days). Acetic acid, lactic acid or potassium benzoate applied alone reduced initial L. monocytogenes populations by 0.4-1.5 log cfu/cm(2), while treatments including Nisaplin caused reductions of 2.1-3.3 log cfu/cm(2). L. monocytogenes on untreated sausage formulated with antimicrobials had a lag phase duration of 10.2 days and maximum specific growth rate (mu(max)) of 0.089 per day, compared to no lag phase and mu(max) of 0.300 per day for L. monocytogenes on untreated product that did not contain antimicrobials in the formulation. The immersion treatments inhibited growth of the pathogen for 4.9-14.8 days on sausage formulated without potassium lactate-sodium diacetate; however, in all cases significant (P meat processors in their efforts to select required regulatory alternatives for control of post-processing contamination in meat products.

  2. Mathematical simulation and calculation of continuous countercurrent process of ion-exchange extraction of strontium from strongly mineralized solutions

    International Nuclear Information System (INIS)

    Nikashina, V.A.; Venitsianov, E.V.; Ivanov, V.A.; Gur'yanova, L.N.; Nikolaev, N.P.; Baturova, L.L.; Moskovskij Gosudarstvennyj Univ., Moscow

    1993-01-01

    A program 'Countercurrent' is developed for the simulation of a continuous ion-exchange extraction of strontium from the strongly mineralized solutions containing NaCl and CaCl 2 using carboxylic cation exchanger KB-4 in countercurrent columns. The use of the program allows one to calculate the consitions of Ca and Sr separation depending on the modes of operation at the stage of sorption as well as regeneration, to calculate a residual Sr content on an overloaded sorbent and Sr separation on an incompletely regenerated KB-4, and to find the optimal separation conditions

  3. Chromium (VI) ion adsorption by grafted cross-linked chitosan beads in aqueous solution - a mathematical and statistical modeling study.

    Science.gov (United States)

    Igberase, E; Osifo, P; Ofomaja, A

    2017-12-01

    Chitosan outstanding qualities and efficient way of binding metal ions even to near zero concentration is the major reason for special attention. Modification of chitosan allows the polymer to be applied in numerous field of research. Depending on the modification techniques, chitosan possesses increased adsorption capacity. In this study chitosan beads (CS) were formulated from chitosan flakes, the beads were cross-linked with glutaraldehyde and thereafter grafted with ethyldiaminetetraacetic acid. The stability and amine concentration of the beads were determined. The chemical functionalities of the beads were obtained by Fourier transform infrared spectroscopy, X-ray diffraction and thermogravimetric analysis (TGA). However, in the adsorption studies with Cr(VI), the number of runs in the experiment was obtained by response surface methodology (RSM), and the maximum adsorption capacity (Q m ) from each run was determined from the Langmuir model. The results of the experiment showed that the non-modified beads were soluble at pH 1-4 and insoluble at pH 5, while the modified beads were insoluble at pH 1-6. The amine concentration of CS, CCS and grafted cross-linked chitosan beads (GCCS) were 4.4, 3.8 and 5.0 mmol/g, respectively. The point of zero charge (pH PZC ) of GCCS was found to be 4.4. The quadratic model was significant and adequate in describing the experimental data. The difference between experimental and predicted Q m was negligible. From the design matrix and results, increased Q m was achieved at pH 5, contact time 70 min, temperature 45°C, adsorbent dosage 5 g and initial concentration 70 mg/l. The desorption of the beads loaded with Cr(VI) was successful with 0.5 M HCl eluant and contact time of 180 min, leading to cost minimization.

  4. About solution of multipoint boundary problem of static analysis of deep beam with the use of combined application of finite element method and discrete-continual finite element method. part 1: formulation of the problem and general principles of approximation

    Directory of Open Access Journals (Sweden)

    Lyakhovich Leonid

    2017-01-01

    Full Text Available This paper is devoted to formulation and general principles of approximation of multipoint boundary problem of static analysis of deep beam with the use of combined application of finite element method (FEM discrete-continual finite element method (DCFEM. The field of application of DCFEM comprises structures with regular physical and geometrical parameters in some dimension (“basic” dimension. DCFEM presupposes finite element approximation for non-basic dimension while in the basic dimension problem remains continual. DCFEM is based on analytical solutions of resulting multipoint boundary problems for systems of ordinary differential equations with piecewise-constant coefficients.

  5. How to solve mathematical problems

    CERN Document Server

    Wickelgren, Wayne A

    1995-01-01

    Seven problem-solving techniques include inference, classification of action sequences, subgoals, contradiction, working backward, relations between problems, and mathematical representation. Also, problems from mathematics, science, and engineering with complete solutions.

  6. BUILDING CONCEPTUAL AND MATHEMATICAL MODEL FOR WATER FLOW AND SOLUTE TRANSPORT IN THE UNSATURATED ZONE AT KOSNICA SITE

    Directory of Open Access Journals (Sweden)

    Stanko Ružičić

    2012-12-01

    Full Text Available Conceptual model of flow and solute transport in unsaturated zone at Kosnica site, which is the basis for modeling pollution migration through the unsaturated zone to groundwater, is set up. The main characteristics of the unsaturated zone of the Kosnica site are described. Detailed description of investigated profile of unsaturated zone, with all necessary analytical results performed and used in building of conceptual models, is presented. Experiments that are in progress and processes which are modeled are stated. Monitoring of parameters necessary for calibration of models is presented. The ultimate goal of research is risk assessment of groundwater contamination at Kosnica site that has its source in or on unsaturated zone.

  7. Mathematical simulation and calculation of the continuous countercurrent process of ion-exchange extraction of strontium from strongly mineralized solutions

    International Nuclear Information System (INIS)

    Nikashina, V.A.; Guryanova, L.N.; Baturova, L.L.; Venetsianov, E.V.; Ivanov, V.A.; Nikolaev, N.P.

    1993-01-01

    The program open-quotes Countercurrentclose quotes is developed for the simulation of a continuous ion-exchange extraction of strontium from strongly mineralized NaCl and CaCl 2 solutions using a KB-4 carboxylic cation-exchanger in the countercurrent columns. The program allows one to Calculate the conditions of Ca and Sr separation depending on the mode of operation at the sorption and regeneration stages, the residual Sr content on the overloaded sorbent, and the Sr separation on incompletely regenerated KB-4. It also makes it possible to find the optimal separation conditions. The program open-quotes Countercurrentclose quotes can be also used to simulate other ion-exchange processes

  8. Study of Mo (VI Removal from Aqueous Solution: Application of Different Mathematical Models to Continuous Biosorption Data

    Directory of Open Access Journals (Sweden)

    Fatemeh Kafshgari

    2013-01-01

    Full Text Available Molybdenum (VI biosorption process was investigated by marine algae Cystoseria indica pretreated with 0.1 M CaCl2 solution in a packed bed column. The biosorbent was characterized by FTIR, BET and SEM analyses. The results showed that Mo (VI ions should be chelated with the hydroxyl, carboxyl and amine groups of the biomass. The effects of inlet metal concentration and flow rate on biosorption process were investigated and the experimental breakthrough curves were obtained. Results showed that the maximum biosorption capacity of Ca-pretreated C. indica for Mo (VI was found to be 18.32 mg/g at optimum flow rate of (1.4 mL/min. The controlled-rate step shifted from external to internal mass transfer limitations, as the flow rate increased. Also, it was observed that the breakthrough and exhaustion time decreased from 17.14 hr to 9.05 hr and from 0.006 h to 0.002 hr respectively, with the increase of flow rate from 0.7 to 2.1 ML/min. The increase in the initial concentration of Mo (VI solution from 30 to 95 ml min-1 increases the adsorption capacity from 18.32 to 30.19 mg/g and decreases the percentage of Mo (VI removal from 61 to 38%. Also, the treated volume was the greatest (1.42 L at the lowest inlet concentration. Column data obtained under different conditions were described using the Thomas, Yoon and Nelson, Yan and Belter models. The breakthrough curve predictions by Belter model were found to be very satisfactory.

  9. Investigation of optimal manufacturing process for freeze-dried formulations: Observation of frozen solutions by low temperature X-ray diffraction measurements

    International Nuclear Information System (INIS)

    Egawa, Hiroaki; Yonemochi, Etsuo; Terada, Katsuhide

    2005-01-01

    Freeze-drying is used for the production of sterile injections in the pharmaceutical industry. However, most pharmaceutical compounds are obtained as less stable amorphous form. Freeze crystallization by annealing is an effective method for pharmaceutical compounds that fail to crystallize in the freeze-drying process. Crystallization occurs in the frozen solution during the thermal treatment. In order to establish suitable annealing conditions efficiently, it is important to observe the crystallization process directly in the frozen solution. Recently, low temperature X-ray diffraction has been used to observe frozen solutions. In order to investigate the crystallization process kinetically, the temperature of the low temperature X-ray diffraction instrument must be accurately controlled. We calibrated the temperature of X-ray diffraction instrument by measuring eutectic temperatures of solutions for a series of compounds. Each eutectic crystal was observed in frozen solution with ice crystal below the eutectic temperature. Eutectic temperatures were detected by the decrease in diffraction intensity associated with heating from below the eutectic temperature. Good correlation was obtained between values in the literature and experimental values

  10. An overview of the formulation, existence and uniqueness issues for the initial value problem raised by the dynamics of discrete systems with unilateral contact and dry friction

    Science.gov (United States)

    Ballard, Patrick; Charles, Alexandre

    2018-03-01

    In the end of the seventies, Schatzman and Moreau undertook to revisit the venerable dynamics of rigid bodies with contact and dry friction in the light of more recent mathematics. One claimed objective was to reach, for the first time, a mathematically consistent formulation of an initial value problem associated with the dynamics. The purpose of this article is to make a review of the today state-of-art concerning not only the formulation, but also the issues of existence and uniqueness of solution. xml:lang="fr"

  11. Mathematics and electromagnetism

    International Nuclear Information System (INIS)

    Rodriguez Danta, M.

    2000-01-01

    Symbiosis between mathematics and electromagnetism is analyzed in a simple and concise manner by taking a historical perspective. The universal tool character of mathematical models allowed the transfer of models from several branches of physics into the realm of electromagnetism by drawing analogies. The mutual interdependence between covariant formulation and tensor calculus is marked. The paper focuses on the guiding idea of field theory and Maxwell's equations. Likewise, geometrization of interactions in connection with gauge fields is also noted. (Author)

  12. Applied mathematical methods in nuclear thermal hydraulics

    International Nuclear Information System (INIS)

    Ransom, V.H.; Trapp, J.A.

    1983-01-01

    Applied mathematical methods are used extensively in modeling of nuclear reactor thermal-hydraulic behavior. This application has required significant extension to the state-of-the-art. The problems encountered in modeling of two-phase fluid transients and the development of associated numerical solution methods are reviewed and quantified using results from a numerical study of an analogous linear system of differential equations. In particular, some possible approaches for formulating a well-posed numerical problem for an ill-posed differential model are investigated and discussed. The need for closer attention to numerical fidelity is indicated

  13. A computationally effective formulation of the thermodynamic properties of LiBr-H2O solutions from 273 to 500 K over full composition range

    Czech Academy of Sciences Publication Activity Database

    Pátek, Jaroslav; Klomfar, Jaroslav

    2006-01-01

    Roč. 29, č. 4 (2006), s. 566-578 ISSN 0140-7007 Institutional research plan: CEZ:AV0Z20760514 Keywords : water-lithium bromide * aqueous solution * thermodynamic properties Subject RIV: BJ - Thermodynamics Impact factor: 0.936, year: 2006

  14. The mathematical foundations of gauge theories

    International Nuclear Information System (INIS)

    Marathe, K.B.; Martucci, G.

    1992-01-01

    Theoretical physicists tend to discuss their theories in the language of mathematics. However, the adequate mathematical formulation may not yet be available when the physical law is first discovered. Mathematical physicists trying to develop the relevant mathematics for these theories, may obtain new insights into old mathematical structures. Gauge Theory is such a gift from physics to mathematics. This book presents a self-contained development of a differential geometric formulation of gauge theories, in particular, the theory of Yang-Mills fields. (author). refs.; figs.; tabs

  15. Applied mathematics

    International Nuclear Information System (INIS)

    Nedelec, J.C.

    1988-01-01

    The 1988 progress report of the Applied Mathematics center (Polytechnic School, France), is presented. The research fields of the Center are the scientific calculus, the probabilities and statistics and the video image synthesis. The research topics developed are: the analysis of numerical methods, the mathematical analysis of the physics and mechanics fundamental models, the numerical solution of complex models related to the industrial problems, the stochastic calculus and the brownian movement, the stochastic partial differential equations, the identification of the adaptive filtering parameters, the discrete element systems, statistics, the stochastic control and the development, the image synthesis techniques for education and research programs. The published papers, the congress communications and the thesis are listed [fr

  16. International Mathematical Internet Olympiad

    Directory of Open Access Journals (Sweden)

    Alexander Domoshnitsky

    2012-10-01

    Full Text Available Modern Internet technologies open new possibilities in wide spectrum of traditional methods used in mathematical education. One of the areas, where these technologies can be efficiently used, is an organization of mathematical competitions. Contestants can stay at their schools or universities and try to solve as many mathematical problems as possible and then submit their solutions through Internet. Simple Internet technologies supply audio and video connection between participants and organizers.

  17. Equations of mathematical physics

    CERN Document Server

    Tikhonov, A N

    2011-01-01

    Mathematical physics plays an important role in the study of many physical processes - hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced-undergraduate or graduate-level text considers only those problems leading to partial differential equations. The authors - two well-known Russian mathematicians - have focused on typical physical processes and the principal types of equations deailing with them. Special attention is paid throughout to mathematical formulation, ri

  18. Mathematical modelling techniques

    CERN Document Server

    Aris, Rutherford

    1995-01-01

    ""Engaging, elegantly written."" - Applied Mathematical ModellingMathematical modelling is a highly useful methodology designed to enable mathematicians, physicists and other scientists to formulate equations from a given nonmathematical situation. In this elegantly written volume, a distinguished theoretical chemist and engineer sets down helpful rules not only for setting up models but also for solving the mathematical problems they pose and for evaluating models.The author begins with a discussion of the term ""model,"" followed by clearly presented examples of the different types of mode

  19. Mathematics for physicists

    CERN Document Server

    Martin, B R

    2015-01-01

    Mathematics for Physicists is a relatively short volume covering all the essential mathematics needed for a typical first degree in physics, from a starting point that is compatible with modern school mathematics syllabuses. Early chapters deliberately overlap with senior school mathematics, to a degree that will depend on the background of the individual reader, who may quickly skip over those topics with which he or she is already familiar. The rest of the book covers the mathematics that is usually compulsory for all students in their first two years of a typical university physics degree, plus a little more. There are worked examples throughout the text, and chapter-end problem sets. Mathematics for Physicists features: * Interfaces with modern school mathematics syllabuses * All topics usually taught in the first two years of a physics degree * Worked examples throughout * Problems in every chapter, with answers to selected questions at the end of the book and full solutions on a website This text will ...

  20. Multiple excitation of supports - Part 1. Formulation

    International Nuclear Information System (INIS)

    Galeao, A.C.N.R.; Barbosa, H.J.C.

    1980-12-01

    The formulation and the solution of a simple specific problem of support movement are presented. The formulation is extended to the general case of infinitesimal elasticity where the approximated solutions are obtained by the variational formulation with spatial discretization by Finite Element Method. Finally, the present usual numerical techniques for the treatment of the resulting ordinary differential equations system are discused: Direct integration, Modal overlap, Spectral response. (E.G.) [pt

  1. Dissolution enhancement and mathematical modeling of removal of residual trichloroethene in sands by ozonation during flushing with micro-nano-bubble solution

    Science.gov (United States)

    Sung, Menghau; Teng, Chun-Hao; Yang, Tsung-Hsien

    2017-07-01

    Soil flushing using micro-nano-sized bubbles (MNB) in water as the flushing solution was tested in laboratory sand columns for the cleanup of residual trichloroethene (TCE) non-aqueous-phase-liquid (NAPL). Experiments considering flushing with MNB as well as ozone MNB (OZMNB) in water to treat soils contaminated with residual TCE liquid were conducted to examine effects of ozone on dissolution enhancement. The degrees of residual TCE saturation in soils, ranging from 0.44% to 7.6%, were tested. During flushings, aqueous TCE concentrations at the column exit were monitored and TCE masses remained in the columns after flushing were determined. Experimental results between runs with MNB and OZMNB in water revealed that dissolution enhancement was dependent on residual saturation conditions, and the maximum enhancement was around 9%. Governing equations consisting of three coupled partial differential equations (PDEs) were developed to model the system, and high-order finite difference (HOFD) method was employed to solve these PDEs. From mathematical modeling of reactive mass transfer under low residual saturation conditions (0.44% and 1.9%), experimental data were simulated and important controlling mechanisms were identified. It was concluded that a specific parameter pertinent to NAPL-water interfacial area in the Sherwood number had to be modified to satisfactorily describe the dissolution of TCE in the presence of MNB in water.

  2. An explanation for the physical instability of a marketed fixed dose combination (FDC) formulation containing isoniazid and ethambutol and proposed solutions.

    Science.gov (United States)

    Bhutani, Hemant; Mariappan, T T; Singh, Saranjit

    2004-07-01

    formulation.

  3. Sensitive determination of adenosine disodium triphosphate in soil, milk, and pharmaceutical formulation by enoxacin–europium (III) fluorescence complex in solution

    International Nuclear Information System (INIS)

    Alam, Al-Mahmnur; Kamruzzaman, Mohammad; Hak Lee, Sang; Ho Kim, Young; Jin Jo, Hae; Hong Kim, Sung; Park, Sang-Ryoul

    2012-01-01

    A new spectroflurometric method for the determination of adenosine disodium triphosphate (ATP) is developed. Fluorometric interaction between ATP and enoxacin (ENX)–Eu 3+ complex was studied using UV–vis and fluorescence spectroscopy. Weak luminescence spectra of Eu 3+ were enhanced after complexation with ENX at 589 nm and 614 nm upon excitation at 395 nm due to energy transfer from the ligand to the lanthanide ion. It was observed that luminescence spectrum of Eu 3+ was strongly enhanced further at 614 nm after incorporation of ATP into the ENX–Eu 3+ complex. Under optimal conditions, the enhancement of luminescence at 614 nm was responded linearly with the concentration of ATP. The linearity was maintained in the range of 1.5×10 −10 –1.15×10 −8 M (R=0.9973) with the limit of detection (3σ) of 4.71×10 −11 M. The relative standard deviation (RSD) for 9 repeated measurements of 1×10 −9 M ATP was 1.25%. Successful determinations of ATP in soil, milk, and a pharmaceutical formulation with the proposed method were demonstrated. - Highlights: ► Weak luminescence of Eu 3+ was enhanced at 614 nm after formation of complex with ENX. ► Energy transfer occurs through FRET from ENX to Eu 3+ upon excitation. ► Luminescence signal was further enhanced when ATP conjugates with ENX–Eu 3+ complex. ► Luminescence intensity of Eu 3+ at 614 nm was correlated with concentration of ATP. ► The method was applied to determine ATP in soil, milk, and pharmaceutical samples.

  4. Solutions Network Formulation Report. NASA's Potential Contributions for Using Solar Ultraviolet Radiation in Conjunction with Photocatalysis for Urban Air Pollution Mitigation and Increasing Air Quality

    Science.gov (United States)

    Underwood, Lauren; Ryan, Robert E.

    2007-01-01

    This Candidate Solution is based on using NASA Earth science research on atmospheric ozone and aerosols data as a means to predict and evaluate the effectiveness of photocatalytically created surfaces (building materials like glass, tile and cement) for air pollution mitigation purposes. When these surfaces are exposed to near UV light, organic molecules, like air pollutants and smog precursors, will degrade into environmentally friendly compounds. U.S. EPA (Environmental Protection Agency) is responsible for forecasting daily air quality by using the Air Quality Index (AQI) that is provided by AIRNow. EPA is partnered with AIRNow and is responsible for calculating the AQI for five major air pollutants that are regulated by the Clean Air Act. In this Solution, UV irradiance data acquired from the satellite mission Aura and the OMI Surface UV algorithm will be used to help understand both the efficacy and efficiency of the photocatalytic decomposition process these surfaces facilitate, and their ability to reduce air pollutants. Prediction models that estimate photocatalytic function do not exist. NASA UV irradiance data will enable this capability, so that air quality agencies that are run by state and local officials can develop and implement programs that utilize photocatalysis for urban air pollution control and, enable them to make effective decisions about air pollution protection programs.

  5. Mathematics for quantum chemistry

    CERN Document Server

    Anderson, Jay Martin

    2005-01-01

    This concise volume offers undergraduates an introduction to mathematical formalism in problems of molecular structure and motion. The main topics cover the calculus of orthogonal functions, algebra of vector spaces, and Lagrangian and Hamiltonian formulation of classical mechanics and applications to molecular motion. Answers to problems. 1966 edition.

  6. Solving applied mathematical problems with Matlab

    CERN Document Server

    Xue, Dingyu

    2008-01-01

    Computer Mathematics Language-An Overview. Fundamentals of MATLAB Programming. Calculus Problems. MATLAB Computations of Linear Algebra Problems. Integral Transforms and Complex Variable Functions. Solutions to Nonlinear Equations and Optimization Problems. MATLAB Solutions to Differential Equation Problems. Solving Interpolations and Approximations Problems. Solving Probability and Mathematical Statistics Problems. Nontraditional Solution Methods for Mathematical Problems.

  7. Application of modified homotopy perturbation method and amplitude frequency formulation to strongly nonlinear oscillators

    Directory of Open Access Journals (Sweden)

    seyd ghasem enayati

    2017-01-01

    Full Text Available In this paper, two powerful analytical methods known as modified homotopy perturbation method and Amplitude Frequency Formulation called respectively MHPM and AFF, are introduced to derive approximate solutions of a system of ordinary differential equations appear in mechanical applications. These methods convert a difficult problem into a simple one, which can be easily handled. The obtained solutions are compared with numerical fourth order runge-kutta method to show the applicability and accuracy of both MHPM and AFF in solving this sample problem. The results attained in this paper confirm the idea that MHPM and AFF are powerful mathematical tools and they can be applied to linear and nonlinear problems.

  8. Exact and heuristic solutions to the Double TSP with Multiple Stacks

    DEFF Research Database (Denmark)

    Petersen, Hanne Løhmann; Archetti, Claudia; Madsen, Oli B.G.

    -pallet, which can be loaded in 3 stacks in a standard 40 foot container. Different exact and heuristic solution approaches to the DTSPMS have been implemented and tested. The exact approaches are based on different mathematical formulations of the problem which are solved using branch-and-cut. One formulation...... instances. The implemented heuristics include tabu search, simulated annealing and large neighbourhood search. Particularly the LNS approach shows promising results. It finds the known optimal solution of smaller instances (15 orders) within 10 seconds in most cases, and in 3 minutes it finds solutions...

  9. Students’ Mathematical Literacy in Solving PISA Problems Based on Keirsey Personality Theory

    Science.gov (United States)

    Masriyah; Firmansyah, M. H.

    2018-01-01

    This research is descriptive-qualitative research. The purpose is to describe students’ mathematical literacy in solving PISA on space and shape content based on Keirsey personality theory. The subjects are four junior high school students grade eight with guardian, artisan, rational or idealist personality. Data collecting methods used test and interview. Data of Keirsey Personality test, PISA test, and interview were analysed. Profile of mathematical literacy of each subject are described as follows. In formulating, guardian subject identified mathematical aspects are formula of rectangle area and sides length; significant variables are terms/conditions in problem and formula of ever encountered question; translated into mathematical language those are measurement and arithmetic operations. In employing, he devised and implemented strategies using ease of calculation on area-subtraction principle; declared truth of result but the reason was less correct; didn’t use and switch between different representations. In interpreting, he declared result as area of house floor; declared reasonableness according measurement estimation. In formulating, artisan subject identified mathematical aspects are plane and sides length; significant variables are solution procedure on both of daily problem and ever encountered question; translated into mathematical language those are measurement, variables, and arithmetic operations as well as symbol representation. In employing, he devised and implemented strategies using two design comparison; declared truth of result without reason; used symbol representation only. In interpreting, he expressed result as floor area of house; declared reasonableness according measurement estimation. In formulating, rational subject identified mathematical aspects are scale and sides length; significant variables are solution strategy on ever encountered question; translated into mathematical language those are measurement, variable, arithmetic

  10. Generalized Analytical Treatment Of The Source Strength In The Solution Of The Diffusion Equation

    International Nuclear Information System (INIS)

    Essa, Kh.S.M.; EI-Otaify, M.S.

    2007-01-01

    The source release strength (which is an integral part of the mathematical formulation of the diffusion equation) together with the boundary conditions leads to three different forms of the diffusion equation. The obtained forms have been solved analytically under different boundary conditions, by using transformation of axis, cosine, and Fourier transformation. Three equivalent alternative mathematical formulations of the problem have been obtained. The estimated solution of the concentrations at the ground source has been used for comparison with observed concentrations data for SF 6 tracer experiments in low wind and unstable conditions at lIT Delhi sports ground. A good agreement between estimated and observed concentrations is found

  11. Advanced engineering mathematics

    CERN Document Server

    Jeffrey, Alan

    2001-01-01

    Advanced Engineering Mathematics provides comprehensive and contemporary coverage of key mathematical ideas, techniques, and their widespread applications, for students majoring in engineering, computer science, mathematics and physics. Using a wide range of examples throughout the book, Jeffrey illustrates how to construct simple mathematical models, how to apply mathematical reasoning to select a particular solution from a range of possible alternatives, and how to determine which solution has physical significance. Jeffrey includes material that is not found in works of a similar nature, such as the use of the matrix exponential when solving systems of ordinary differential equations. The text provides many detailed, worked examples following the introduction of each new idea, and large problem sets provide both routine practice, and, in many cases, greater challenge and insight for students. Most chapters end with a set of computer projects that require the use of any CAS (such as Maple or Mathematica) th...

  12. Mathematics Underground

    Science.gov (United States)

    Luther, Kenneth H.

    2012-01-01

    Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…

  13. Open problems in mathematics

    CERN Document Server

    Nash, Jr, John Forbes

    2016-01-01

    The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nash’s legendary mathematical achievements. The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory, cryptography, theoretical computer sc...

  14. Solutions Network Formulation Report. Visible/Infrared Imager/Radiometer Suite and Advanced Microwave Scanning Radiometer Data Products for National Drought Monitor Decision Support

    Science.gov (United States)

    Estep, Leland

    2007-01-01

    Drought effects are either direct or indirect depending on location, population, and regional economic vitality. Common direct effects of drought are reduced crop, rangeland, and forest productivity; increased fire hazard; reduced water levels; increased livestock and wildlife mortality rates; and damage to wildlife and fish habitat. Indirect impacts follow on the heels of direct impacts. For example, a reduction in crop, rangeland, and forest productivity may result in reduced income for farmers and agribusiness, increased prices for food and timber, unemployment, reduced tax revenues, increased crime, foreclosures on bank loans to farmers and businesses, migration, and disaster relief programs. In the United States alone, drought is estimated to result in annual losses of between $6 - 8 billion. Recent sustained drought in the United States has made decision-makers aware of the impacts of climate change on society and environment. The eight major droughts that occurred in the United States between 1980 and 1999 accounted for the largest percentage of weather-related monetary losses. Monitoring drought and its impact that occurs at a variety of scales is an important government activity -- not only nationally but internationally as well. The NDMC (National Drought Mitigation Center) and the USDA (U.S. Department of Agriculture) RMA (Risk Management Agency) have partnered together to develop a DM-DSS (Drought Monitoring Decision Support System). This monitoring system will be an interactive portal that will provide users the ability to visualize and assess drought at all levels. This candidate solution incorporates atmospherically corrected VIIRS data products, such as NDVI (Normalized Difference Vegetation Index) and Ocean SST (sea surface temperature), and AMSR-E soil moisture data products into two NDMC vegetation indices -- VegDRI (Vegetation Drought Response Index) and VegOUT (Vegetation Outlook) -- which are then input into the DM-DSS.

  15. The mathematical career of Pierre de Fermat 1601-1665

    CERN Document Server

    Mahoney, Michael Sean

    1994-01-01

    Hailed as one of the greatest mathematical results of the twentieth century, the recent proof of Fermat's Last Theorem by Andrew Wiles brought to public attention the enigmatic problem-solver Pierre de Fermat, who centuries ago stated his famous conjecture in a margin of a book, writing that he did not have enough room to show his "truly marvelous demonstration" Along with formulating this proposition-xn+yn=zn has no rational solution for n > 2-Fermat, an inventor of analytic geometry, also laid the foundations of differential and integral calculus, established, together with Pascal, the conceptual guidelines of the theory of probability, and created modern number theory. In one of the first full-length investigations of Fermat's life and work, Michael Sean Mahoney provides rare insight into the mathematical genius of a hobbyist who never sought to publish his work, yet who ranked with his contemporaries Pascal and Descartes in shaping the course of modern mathematics.

  16. Mathematics Connection

    African Journals Online (AJOL)

    MATHEMATICS CONNECTION aims at providing a forum topromote the development of Mathematics Education in Ghana. Articles that seekto enhance the teaching and/or learning of mathematics at all levels of theeducational system are welcome.

  17. Solutions Network Formulation Report. Integration of OMI and TES Aerosol Products into the EPA Regional Planning Organizations' FASTNET Aerosol Tracking and Analysis Tool

    Science.gov (United States)

    Knowlton, Kelly; Andrews, Jane C.

    2006-01-01

    Every year, more than 280 million visitors tour our Nation s most treasured parks and wilderness areas. Unfortunately, many visitors are unable to see the spectacular vistas they expect because of white or brown haze in the air. Most of this haze is not natural; it is air pollution, carried by the wind often hundreds of miles from its origin. Some of the pollutants have been linked to serious health problems, such as asthma and other lung disorders, and even premature death. In addition, nitrates and sulfates contribute to acid rain formation, which contaminates rivers and lakes and erodes buildings and historical monuments. The U.S. Environmental Protection Agency RPOs (Regional Planning Organizations) have been tasked with monitoring and determining the nature and origin of haze in Class I scenic areas, and finding ways to reduce haze in order to improve visibility in these areas. The RPOs have developed an Internet-based air quality DST (Decision Support Tool) called FASTNET (Fast Aerosol Sensing Tools for Natural Event Tracking). While FASTNET incorporates a few satellite datasets, most of the data utilized by this DST comes from ground-based instrument networks. The problem is that in many areas the sensors are sparsely located, with long distances between them, causing difficulties in tracking haze over the United States, determining its source, and analyzing its content. Satellite data could help to fill in the data gaps and to supplement and verify ground-recorded air quality data. Although satellite data are now being used for air quality research applications, such data are not routinely used for environmental decision support, in part because of limited resources, difficulties with interdisciplinary data interpretation, and the need for advanced inter-agency partnerships. As a result, the validation and verification of satellite data for air quality operational system applications has been limited This candidate solution evaluates the usefulness of OMI

  18. Profile of male-field dependent (FD) prospective teacher's reflective thinking in solving contextual mathematical problem

    Science.gov (United States)

    Agustan, S.; Juniati, Dwi; Siswono, Tatag Yuli Eko

    2017-08-01

    Reflective thinking is an important component in the world of education, especially in professional education of teachers. In learning mathematics, reflective thinking is one way to solve mathematical problem because it can improve student's curiosity when student faces a mathematical problem. Reflective thinking is also a future competence that should be taught to students to face the challenges and to respond of demands of the 21st century. There are many factors which give impact toward the student's reflective thinking when student solves mathematical problem. One of them is cognitive style. For this reason, reflective thinking and cognitive style are important things in solving contextual mathematical problem. This research paper describes aspect of reflective thinking in solving contextual mathematical problem involved solution by using some mathematical concept, namely linear program, algebra arithmetic operation, and linear equations of two variables. The participant, in this research paper, is a male-prospective teacher who has Field Dependent. The purpose of this paper is to describe aspect of prospective teachers' reflective thinking in solving contextual mathematical problem. This research paper is a descriptive by using qualitative approach. To analyze the data, the researchers focus in four main categories which describe prospective teacher's activities using reflective thinking, namely; (a) formulation and synthesis of experience, (b) orderliness of experience, (c) evaluating the experience and (d) testing the selected solution based on the experience.

  19. Handbook of mathematics

    CERN Document Server

    Bronshtein, I N; Musiol, Gerhard; Mühlig, Heiner

    2015-01-01

    This guide book to mathematics contains in handbook form the fundamental working knowledge of mathematics which is needed as an everyday guide for working scientists and engineers, as well as for students. Easy to understand, and convenient to use, this guide book gives concisely the information necessary to evaluate most problems which occur in concrete applications. In the newer editions emphasis was laid on those fields of mathematics that became more important for the formulation and modeling of technical and natural processes, namely Numerical Mathematics, Probability Theory and Statistics, as well as Information Processing. Besides many enhancements and  new paragraphs,  new sections on Geometric and Coordinate Transformations, Quaternions and Applications, and Lie Groups and Lie Algebras were added for the sixth edition.

  20. Elastic interaction of a crack with a microcrack array. I - Formulation of the problem and general form of the solution. II - Elastic solution for two crack configurations (piecewise constant and linear approximations)

    Science.gov (United States)

    Chudnovsky, A.; Dolgopolsky, A.; Kachanov, M.

    1987-01-01

    The elastic interactions of a two-dimensional configuration consisting of a crack with an array of microcracks located near the tip are studied. The general form of the solution is based on the potential representations and approximations of tractions on the microcracks by polynomials. In the second part, the technique is applied to two simple two-dimensional configurations involving one and two microcracks. The problems of stress shielding and stress amplification (the reduction or increase of the effective stress intensity factor due to the presence of microcracks) are discussed, and the refinements introduced by higher order polynomial approximations are illustrated.

  1. Mathematical Footprints Discovering Mathematics Everywhere

    CERN Document Server

    Pappas, Theoni

    1999-01-01

    MATHEMATICAL FOOTPRINTS takes a creative look at the role mathematics has played since prehistoric times, and will play in the future, and uncovers mathematics where you least expect to find it from its many uses in medicine, the sciences, and its appearance in art to its patterns in nature and its central role in the development of computers. Pappas presents mathematical ideas in a readable non-threatening manner. MATHEMATICAL FOOTPRINTS is another gem by the creator of THE MATHEMATICS CALENDAR and author of THE JOY OF MATHEMATICS. "Pappas's books have been gold mines of mathematical ent

  2. Crystallization Formulation Lab

    Data.gov (United States)

    Federal Laboratory Consortium — The Crystallization Formulation Lab fills a critical need in the process development and optimization of current and new explosives and energetic formulations. The...

  3. Effect of slip on heat transfer and entropy generation characteristics of simplified Phan-Thien–Tanner fluids with viscous dissipation under uniform heat flux boundary conditions: Exponential formulation

    International Nuclear Information System (INIS)

    Anand, Vishal

    2016-01-01

    Highlights: • Exponential formulation of s-PTT model used. • Heat transfer and entropy generation characteristics studied. • Effects of three slip laws examined. • Exponential formulation more accurate than linear formulation. - Abstract: This study concerns the heat transfer and entropy generation characteristics of viscoelastic fluid flow modeled by the exponential formulation of simplified Phan-Thien–Tanner (s-PTT) model. This is the first such study in literature of thermal behavior of viscoelastic fluids modeled by the exponential formulation of s-PTT model. The flow between two parallel plates is laminar, hydrodynamically and thermally fully developed, viscous dissipative and subject to uniform heat flux on the walls. The slip velocity boundary condition is imposed on the fluid–solid interface and the slip is captured by three slip laws, namely, Navier's non-linear slip law, Hatzikiriakos slip law, and asymptotic slip law. The governing equations have been solved analytically. Closed form solutions for the velocity distribution have been derived while the temperature distribution is presented in terms of an infinite but convergent series. The results pertaining to the three slip laws have been presented in detail. Finally, a comparison has been made between the results for exponential formulation and those for the linear formulation of the s-PTT model. The comparison shows that results for linear formulation deviate significantly from those for exponential formulation and thus the accuracy of the exponential formulation justifies the extra mathematical complexity which it entails.

  4. New Challenges in the Teaching of Mathematics.

    Science.gov (United States)

    Bourguignon, Jean Pierre

    The manifold but discrete presence of mathematics in many objects or services imposes new constraints to the teaching of mathematics. If citizens need to be comfortable in various situations with a variety of mathematical tools, the learning of mathematics requires that one starts with simple concepts. This paper proposes some solutions to solve…

  5. Vibratory gyroscopes : identification of mathematical model from test data

    CSIR Research Space (South Africa)

    Shatalov, MY

    2007-05-01

    Full Text Available Simple mathematical model of vibratory gyroscopes imperfections is formulated, which includes anisotropic damping and variation of mass-stiffness parameters and their harmonics. The method of identification of parameters of the mathematical model...

  6. Mathematical marriages: intercourse between mathematics and Semiotic choice.

    Science.gov (United States)

    Wagner, Roy

    2009-04-01

    This paper examines the interaction between Semiotic choices and the presentation and solution of a family of contemporary mathematical problems centred around the so-called 'stable marriage problem'. I investigate how a socially restrictive choice of signs impacts mathematical production both in terms of problem formation and of solutions. I further note how the choice of gendered language ends up constructing a reality, which duplicates the very structural framework that it imported into mathematical analysis in the first place. I go on to point out some semiotic lines of flight from this interlocking grip of mathematics and gendered language.

  7. Mathematics and Measurement.

    Science.gov (United States)

    Boisvert, R F; Donahue, M J; Lozier, D W; McMichael, R; Rust, B W

    2001-01-01

    In this paper we describe the role that mathematics plays in measurement science at NIST. We first survey the history behind NIST's current work in this area, starting with the NBS Math Tables project of the 1930s. We then provide examples of more recent efforts in the application of mathematics to measurement science, including the solution of ill-posed inverse problems, characterization of the accuracy of software for micromagnetic modeling, and in the development and dissemination of mathematical reference data. Finally, we comment on emerging issues in measurement science to which mathematicians will devote their energies in coming years.

  8. Formulation of Thermosensitive Hydrogel Containing Cyclodextrin ...

    African Journals Online (AJOL)

    Materials. Chitosan (deacetylation degree, DDA = 80 %) was obtained from HiMedia Laboratories Pvt. ... Sterile formulations were ... Chilled β-GP aqueous solution (sterilized through ..... generally decreasing away from the center of the tumor.

  9. Methods of applied mathematics

    CERN Document Server

    Hildebrand, Francis B

    1992-01-01

    This invaluable book offers engineers and physicists working knowledge of a number of mathematical facts and techniques not commonly treated in courses in advanced calculus, but nevertheless extremely useful when applied to typical problems in many different fields. It deals principally with linear algebraic equations, quadratic and Hermitian forms, operations with vectors and matrices, the calculus of variations, and the formulations and theory of linear integral equations. Annotated problems and exercises accompany each chapter.

  10. A direct comparison of physical block occupancy versus timed block occupancy in train timetabling formulations

    DEFF Research Database (Denmark)

    Harrod, Steven; Schlechte, Thomas

    2013-01-01

    Two fundamental mathematical formulations for railway timetabling are compared on a common set of sample problems, representing both multiple track high density services in Europe and single track bidirectional operations in North America. One formulation, ACP, enforces against conflicts by const......Two fundamental mathematical formulations for railway timetabling are compared on a common set of sample problems, representing both multiple track high density services in Europe and single track bidirectional operations in North America. One formulation, ACP, enforces against conflicts...

  11. A General State-Space Formulation for Online Scheduling

    Directory of Open Access Journals (Sweden)

    Dhruv Gupta

    2017-11-01

    Full Text Available We present a generalized state-space model formulation particularly motivated by an online scheduling perspective, which allows modeling (1 task-delays and unit breakdowns; (2 fractional delays and unit downtimes, when using discrete-time grid; (3 variable batch-sizes; (4 robust scheduling through the use of conservative yield estimates and processing times; (5 feedback on task-yield estimates before the task finishes; (6 task termination during its execution; (7 post-production storage of material in unit; and (8 unit capacity degradation and maintenance. Through these proposed generalizations, we enable a natural way to handle routinely encountered disturbances and a rich set of corresponding counter-decisions. Thereby, greatly simplifying and extending the possible application of mathematical programming based online scheduling solutions to diverse application settings. Finally, we demonstrate the effectiveness of this model on a case study from the field of bio-manufacturing.

  12. Mathematics disorder

    Science.gov (United States)

    ... this page: //medlineplus.gov/ency/article/001534.htm Mathematics disorder To use the sharing features on this page, please enable JavaScript. Mathematics disorder is a condition in which a child's ...

  13. Diseño de una formulación de ciclosporina A solución oral con alto grado de dispersión Design of a formulation of highly dispersed cyclosporine A oral solution

    Directory of Open Access Journals (Sweden)

    Suslebys Salomón Izquierdo

    2013-03-01

    properties, is used in the transplantation of solid organs, bone marrow, and in some stages of certain autoimmune diseases. In Cuba, the Cyclosporine A oral solution causes gastrointestinal absorption problems. Objectives: to achieve a pre-concentrated micro-emulsion containing highly dispersed cyclosporine A that may be equal to or higher than the one in the commercial formulation. Methods: study of percentages of emulsifiers and of hydrophilic lipophilic balance (HLB, at some intervals that allow obtaining self-emulsifying systems through a multilevel factorial design. The percent transmittance was used as the response variable in determining the formulation dispersion degree. The evaluation of the organoleptic characteristics of the selected formulation, the rheological study, the microbial count and the antimicrobial effectiveness estimation were all performed. Results: the studied factors have a significant influence on the transmittance percentage, the formulation with the highest degree of dispersion was achieved when using 60% of emulsifiers and an HLB of 11.5, being transmittance values of 95.03%, which were significantly higher than those of the leading product in the form of soft capsules, equal to 84.6%. Organoleptically speaking, the product meets the characteristics of a clear brilliant fluid without suspended particles and Newtonian behavior from the rheological point of view. The bacteria and fungi count met requirements of U.S. Pharmacopoeia for oral solutions. Conclusions: a pre-concentrate highly dispersed CsA microemulsion was achieved in a drinkable solution meeting the physical requirements and microbiological criteria established for this type of dosage form.

  14. Mathematical Chemistry

    OpenAIRE

    Trinajstić, Nenad; Gutman, Ivan

    2002-01-01

    A brief description is given of the historical development of mathematics and chemistry. A path leading to the meeting of these two sciences is described. An attempt is made to define mathematical chemistry, and journals containing the term mathematical chemistry in their titles are noted. In conclusion, the statement is made that although chemistry is an experimental science aimed at preparing new compounds and materials, mathematics is very useful in chemistry, among other things, to produc...

  15. Rainforest Mathematics

    Science.gov (United States)

    Kilpatrick, Jeremy

    2014-01-01

    This paper addresses the contested way that ethnomathematics has sometimes been received by mathematicians and others and what that disagreement might suggest about issues in mathematics education; namely, (a) the relation of ethnomathematics to academic mathematics; (b) recent efforts to reform secondary school mathematics so that it prepares…

  16. Mathematical modeling with multidisciplinary applications

    CERN Document Server

    Yang, Xin-She

    2013-01-01

    Features mathematical modeling techniques and real-world processes with applications in diverse fields Mathematical Modeling with Multidisciplinary Applications details the interdisciplinary nature of mathematical modeling and numerical algorithms. The book combines a variety of applications from diverse fields to illustrate how the methods can be used to model physical processes, design new products, find solutions to challenging problems, and increase competitiveness in international markets. Written by leading scholars and international experts in the field, the

  17. Mathematical modelling

    DEFF Research Database (Denmark)

    Blomhøj, Morten

    2004-01-01

    Developing competences for setting up, analysing and criticising mathematical models are normally seen as relevant only from and above upper secondary level. The general belief among teachers is that modelling activities presuppose conceptual understanding of the mathematics involved. Mathematical...... roots for the construction of important mathematical concepts. In addition competences for setting up, analysing and criticising modelling processes and the possible use of models is a formative aim in this own right for mathematics teaching in general education. The paper presents a theoretical...... modelling, however, can be seen as a practice of teaching that place the relation between real life and mathematics into the centre of teaching and learning mathematics, and this is relevant at all levels. Modelling activities may motivate the learning process and help the learner to establish cognitive...

  18. Discrete Mathematics

    DEFF Research Database (Denmark)

    Sørensen, John Aasted

    2011-01-01

    The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...

  19. Mathematical Modeling and Pure Mathematics

    Science.gov (United States)

    Usiskin, Zalman

    2015-01-01

    Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…

  20. An introduction to mathematical modeling

    CERN Document Server

    Bender, Edward A

    2000-01-01

    Employing a practical, ""learn by doing"" approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields - including science, engineering, and operations research - to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The

  1. Mathematics for multimedia

    CERN Document Server

    Wickerhauser, Mladen Victor

    2003-01-01

    Mathematics and Multimedia focuses on the mathematics behind multimedia applications. This timely and thoroughly modern text is a rigorous survey of selected results from algebra and analysis, requiring only undergraduate math skills.The topics are `gems' chosen for their usefulness in understanding and creating application software for multimedia signal processing and communication.The book is aimed at a wide audience, including computer science and mathematics majors and those interested in employing mathematics in multimedia design and implementation. For the instructor, the material is divided into six chapters that may be presented in six lecture hours each. Thus, the entire text may be covered in one semester, with time left for examinations and student projects. For the student,there are more than 100 exercises with complete solutions, and numerous example programs in Standard C. Each chapter ends with suggestions for further reading. A companion website provides more insight for both instructors and s...

  2. Unsteady analytical solutions to the Poisson–Nernst–Planck equations

    International Nuclear Information System (INIS)

    Schönke, Johannes

    2012-01-01

    It is shown that the Poisson–Nernst–Planck equations for a single ion species can be formulated as one equation in terms of the electric field. This previously not analyzed equation shows similarities to the vector Burgers equation and is identical with it in the one dimensional case. Several unsteady exact solutions for one and multidimensional cases are presented. Besides new mathematical insights which these first known unsteady solutions give, they can serve as test cases in computer simulations to analyze numerical algorithms and to verify code. (paper)

  3. Mathematical olympiad challenges

    CERN Document Server

    Andreescu, Titu

    2000-01-01

    Mathematical Olympiad Challenges is a rich collection of problems put together by two experienced and well-known professors and coaches of the U.S. International Mathematical Olympiad Team. Hundreds of beautiful, challenging, and instructive problems from algebra, geometry, trigonometry, combinatorics, and number theory were selected from numerous mathematical competitions and journals. An important feature of the work is the comprehensive background material provided with each grouping of problems. The problems are clustered by topic into self-contained sections with solutions provided separately. All sections start with an essay discussing basic facts and one or two representative examples. A list of carefully chosen problems follows and the reader is invited to take them on. Additionally, historical insights and asides are presented to stimulate further inquiry. The emphasis throughout is on encouraging readers to move away from routine exercises and memorized algorithms toward creative solutions to open-e...

  4. The challenge of computer mathematics.

    Science.gov (United States)

    Barendregt, Henk; Wiedijk, Freek

    2005-10-15

    Progress in the foundations of mathematics has made it possible to formulate all thinkable mathematical concepts, algorithms and proofs in one language and in an impeccable way. This is not in spite of, but partially based on the famous results of Gödel and Turing. In this way statements are about mathematical objects and algorithms, proofs show the correctness of statements and computations, and computations are dealing with objects and proofs. Interactive computer systems for a full integration of defining, computing and proving are based on this. The human defines concepts, constructs algorithms and provides proofs, while the machine checks that the definitions are well formed and the proofs and computations are correct. Results formalized so far demonstrate the feasibility of this 'computer mathematics'. Also there are very good applications. The challenge is to make the systems more mathematician-friendly, by building libraries and tools. The eventual goal is to help humans to learn, develop, communicate, referee and apply mathematics.

  5. Theoretical Mathematics

    Science.gov (United States)

    Stöltzner, Michael

    Answering to the double-faced influence of string theory on mathematical practice and rigour, the mathematical physicists Arthur Jaffe and Frank Quinn have contemplated the idea that there exists a `theoretical' mathematics (alongside `theoretical' physics) whose basic structures and results still require independent corroboration by mathematical proof. In this paper, I shall take the Jaffe-Quinn debate mainly as a problem of mathematical ontology and analyse it against the backdrop of two philosophical views that are appreciative towards informal mathematical development and conjectural results: Lakatos's methodology of proofs and refutations and John von Neumann's opportunistic reading of Hilbert's axiomatic method. The comparison of both approaches shows that mitigating Lakatos's falsificationism makes his insights about mathematical quasi-ontology more relevant to 20th century mathematics in which new structures are introduced by axiomatisation and not necessarily motivated by informal ancestors. The final section discusses the consequences of string theorists' claim to finality for the theory's mathematical make-up. I argue that ontological reductionism as advocated by particle physicists and the quest for mathematically deeper axioms do not necessarily lead to identical results.

  6. A Mathematical Private Eye

    Science.gov (United States)

    Lee, Ji-Eun; Kim, Kyoung-Tae

    2007-01-01

    This article proposes an instructional idea where students can figure out an individual's secret personal information using the power of mathematics, particularly the power of algebraic thinking. The proposed examples in this article start with a personalized context that other people do not know and end up with generalized patterns of solutions.…

  7. Mathematical modelling of membrane separation

    DEFF Research Database (Denmark)

    Vinther, Frank

    This thesis concerns mathematical modelling of membrane separation. The thesis consists of introductory theory on membrane separation, equations of motion, and properties of dextran, which will be the solute species throughout the thesis. Furthermore, the thesis consist of three separate mathemat......This thesis concerns mathematical modelling of membrane separation. The thesis consists of introductory theory on membrane separation, equations of motion, and properties of dextran, which will be the solute species throughout the thesis. Furthermore, the thesis consist of three separate...... mathematical models, each with a different approach to membrane separation. The first model is a statistical model investigating the interplay between solute shape and the probability of entering the membrane. More specific the transition of solute particles from being spherical to becoming more elongated...

  8. Variational principles are a powerful tool also for formulating field theories

    OpenAIRE

    Dell'Isola , Francesco; Placidi , Luca

    2012-01-01

    Variational principles and calculus of variations have always been an important tool for formulating mathematical models for physical phenomena. Variational methods give an efficient and elegant way to formulate and solve mathematical problems that are of interest for scientists and engineers and are the main tool for the axiomatization of physical theories

  9. Formulation and numerical analysis of nonisothermal multiphase flow in porous media

    International Nuclear Information System (INIS)

    Martinez, M.J.

    1995-06-01

    A mathematical formulation is presented for describing the transport of air, water and energy through porous media. The development follows a continuum mechanics approach. The theory assumes the existence of various average macroscopic variables which describe the state of the system. Balance equations for mass and energy are formulated in terms of these macroscopic variables. The system is supplemented with constitutive equations relating fluxes to the state variables, and with transport property specifications. Specification of various mixing rules and thermodynamic relations completes the system of equations. A numerical simulation scheme, employing the method of lines, is described for one-dimensional flow. The numerical method is demonstrated on sample problems involving nonisothermal flow of air and water. The implementation is verified by comparison with existing numerical solutions

  10. Mathematical models in medicine: Diseases and epidemics

    International Nuclear Information System (INIS)

    Witten, M.

    1987-01-01

    This volume presents the numerous applications of mathematics in the life sciences and medicine, and demonstrates how mathematics and computers have taken root in these fields. The work covers a variety of techniques and applications including mathematical and modelling methodology, modelling/simulation technology, and philosophical issues in model formulation, leading to speciality medical modelling, artificial intelligence, psychiatric models, medical decision making, and molecular modelling

  11. Quaternionic formulation of the exact parity model

    Energy Technology Data Exchange (ETDEWEB)

    Brumby, S.P.; Foot, R.; Volkas, R.R.

    1996-02-28

    The exact parity model (EPM) is a simple extension of the standard model which reinstates parity invariance as an unbroken symmetry of nature. The mirror matter sector of the model can interact with ordinary matter through gauge boson mixing, Higgs boson mixing and, if neutrinos are massive, through neutrino mixing. The last effect has experimental support through the observed solar and atmospheric neutrino anomalies. In the paper it is shown that the exact parity model can be formulated in a quaternionic framework. This suggests that the idea of mirror matter and exact parity may have profound implications for the mathematical formulation of quantum theory. 13 refs.

  12. Quaternionic formulation of the exact parity model

    International Nuclear Information System (INIS)

    Brumby, S.P.; Foot, R.; Volkas, R.R.

    1996-01-01

    The exact parity model (EPM) is a simple extension of the standard model which reinstates parity invariance as an unbroken symmetry of nature. The mirror matter sector of the model can interact with ordinary matter through gauge boson mixing, Higgs boson mixing and, if neutrinos are massive, through neutrino mixing. The last effect has experimental support through the observed solar and atmospheric neutrino anomalies. In the paper it is shown that the exact parity model can be formulated in a quaternionic framework. This suggests that the idea of mirror matter and exact parity may have profound implications for the mathematical formulation of quantum theory. 13 refs

  13. Super-Group Field Cosmology in Batalin-Vilkovisky Formulation

    Science.gov (United States)

    Upadhyay, Sudhaker

    2016-09-01

    In this paper we study the third quantized super-group field cosmology, a model in multiverse scenario, in Batalin-Vilkovisky (BV) formulation. Further, we propose the superfield/super-antifield dependent BRST symmetry transformations. Within this formulation we establish connection between the two different solutions of the quantum master equation within the BV formulation.

  14. A simple formulation and solution to the replacement problem: a practical tool to assess the economic cow value, the value of a new pregnancy, and the cost of a pregnancy loss.

    Science.gov (United States)

    Cabrera, V E

    2012-08-01

    This study contributes to the research literature by providing a new formulation for the cow replacement problem, and it also contributes to the Extension deliverables by providing a user-friendly decision support system tool that would more likely be adopted and applied for practical decision making. The cow value, its related values of a new pregnancy and a pregnancy loss, and their associated replacement policies determine profitability in dairy farming. One objective of this study was to present a simple, interactive, dynamic, and robust formulation of the cow value and the replacement problem, including expectancy of the future production of the cow and the genetic gain of the replacement. The proven hypothesis of this study was that all the above requirements could be achieved by using a Markov chain algorithm. The Markov chain model allowed (1) calculation of a forward expected value of a studied cow and its replacement; (2) use of a single model (the Markov chain) to calculate both the replacement policies and the herd statistics; (3) use of a predefined, preestablished farm reproductive replacement policy; (4) inclusion of a farmer's assessment of the expected future performance of a cow; (5) inclusion of a farmer's assessment of genetic gain with a replacement; and (6) use of a simple spreadsheet or an online system to implement the decision support system. Results clearly demonstrated that the decision policies found with the Markov chain model were consistent with more complex dynamic programming models. The final user-friendly decision support tool is available at http://dairymgt.info/ → Tools → The Economic Value of a Dairy Cow. This tool calculates the cow value instantaneously and is highly interactive, dynamic, and robust. When a Wisconsin dairy farm was studied using the model, the solution policy called for replacing nonpregnant cows 11 mo after calving or months in milk (MIM) if in the first lactation and 9 MIM if in later lactations. The

  15. Mathematics everywhere

    CERN Document Server

    Aigner, Martin; Spain, Philip G

    2010-01-01

    Mathematics is all around us. Often we do not realize it, though. Mathematics Everywhere is a collection of presentations on the role of mathematics in everyday life, through science, technology, and culture. The common theme is the unique position of mathematics as the art of pure thought and at the same time as a universally applicable science. The authors are renowned mathematicians; their presentations cover a wide range of topics. From compact discs to the stock exchange, from computer tomography to traffic routing, from electronic money to climate change, they make the "math inside" unde

  16. Financial mathematics

    CERN Document Server

    Jothi, A Lenin

    2009-01-01

    Financial services, particularly banking and insurance services is the prominent sector for the development of a nation. After the liberalisation of financial sector in India, the scope of getting career opportunities has been widened. It is heartening to note that various universities in India have introduced professional courses on banking and insurance. A new field of applied mathematics has come into prominence under the name of Financial Mathematics. Financial mathematics has attained much importance in the recent years because of the role played by mathematical concepts in decision - m

  17. Engineering mathematics

    CERN Document Server

    Stroud, K A

    2013-01-01

    A groundbreaking and comprehensive reference that's been a bestseller since it first debuted in 1970, the new seventh edition of Engineering Mathematics has been thoroughly revised and expanded. Providing a broad mathematical survey, this innovative volume covers a full range of topics from the very basic to the advanced. Whether you're an engineer looking for a useful on-the-job reference or want to improve your mathematical skills, or you are a student who needs an in-depth self-study guide, Engineering Mathematics is sure to come in handy time and time again.

  18. Mathematical Analysis of the Solidification Behavior of Plain Steel Based on Solute- and Heat-Transfer Equations in the Liquid-Solid Zone

    Science.gov (United States)

    Fujimura, Toshio; Takeshita, Kunimasa; Suzuki, Ryosuke O.

    2018-04-01

    An analytical approximate solution to non-linear solute- and heat-transfer equations in the unsteady-state mushy zone of Fe-C plain steel has been obtained, assuming a linear relationship between the solid fraction and the temperature of the mushy zone. The heat transfer equations for both the solid and liquid zone along with the boundary conditions have been linked with the equations to solve the whole equations. The model predictions ( e.g., the solidification constants and the effective partition ratio) agree with the generally accepted values and with a separately performed numerical analysis. The solidus temperature predicted by the model is in the intermediate range of the reported formulas. The model and Neuman's solution are consistent in the low carbon range. A conventional numerical heat analysis ( i.e., an equivalent specific heat method using the solidus temperature predicted by the model) is consistent with the model predictions for Fe-C plain steels. The model presented herein simplifies the computations to solve the solute- and heat-transfer simultaneous equations while searching for a solidus temperature as a part of the solution. Thus, this model can reduce the complexity of analyses considering the heat- and solute-transfer phenomena in the mushy zone.

  19. Sequential mathematical solution for authentication and authorization technique implementing encryption methodology creating secure transaction using various methods also at quantum level

    Science.gov (United States)

    Gharami, Snigdha; Dinakaran, M.

    2017-11-01

    We see challenges in authenticating each aspect of electronic usage, starting from transaction to social interaction the authenticity and availability of correct information is guided in various ways. Authentication and authorization follow one another; a process of authentication is calculated on multiple layers of steps. In this paper we discuss various possibilities of modifying and using ways to deal with authentication and authorization mechanism. Idea is to work through authentication with mathematical calculations. We will go through various scenarios and find out the system of information that fits best at the moment of need. We will take account of new approaches of authentication and authorization while working on mathematical paradigm of information. The paper also takes an eye on quantum cryptography and discusses on how it could help one in the present scenario. This paper is divided into sections discussing on various paradigm of authentication and how one can achieve it in secure way, this paper is part of research work where analysis of various constraints are to be followed in the extended research work.

  20. Different mathematical processing of absorption, ratio and derivative spectra for quantification of mixtures containing minor component: An application to the analysis of the recently co-formulated antidiabetic drugs; canagliflozin and metformin

    Science.gov (United States)

    Lotfy, Hayam M.; Mohamed, Dalia; Elshahed, Mona S.

    2018-01-01

    In the presented work several spectrophotometric methods were performed for the quantification of canagliflozin (CGZ) and metformin hydrochloride (MTF) simultaneously in their binary mixture. Two of these methods; response correlation (RC) and advanced balance point-spectrum subtraction (ABP-SS) were developed and introduced for the first time in this work, where the latter method (ABP-SS) was performed on both the zero order and the first derivative spectra of the drugs. Besides, two recently established methods; advanced amplitude modulation (AAM) and advanced absorbance subtraction (AAS) were also accomplished. All the proposed methods were validated in accordance to the ICH guidelines, where all methods were proved to be accurate and precise. Additionally, the linearity range, limit of detection and limit of quantification were determined and the selectivity was examined through the analysis of laboratory prepared mixtures and the combined dosage form of the drugs. The proposed methods were capable of determining the two drugs in the ratio present in the pharmaceutical formulation CGZ:MTF (1:17) without the requirement of any preliminary separation, further dilution or standard spiking. The results obtained by the proposed methods were in compliance with the reported chromatographic method when compared statistically, proving the absence of any significant difference in accuracy and precision between the proposed and reported methods.

  1. Numerical bifurcation analysis of conformal formulations of the Einstein constraints

    International Nuclear Information System (INIS)

    Holst, M.; Kungurtsev, V.

    2011-01-01

    The Einstein constraint equations have been the subject of study for more than 50 years. The introduction of the conformal method in the 1970s as a parametrization of initial data for the Einstein equations led to increased interest in the development of a complete solution theory for the constraints, with the theory for constant mean curvature (CMC) spatial slices and closed manifolds completely developed by 1995. The first general non-CMC existence result was establish by Holst et al. in 2008, with extensions to rough data by Holst et al. in 2009, and to vacuum spacetimes by Maxwell in 2009. The non-CMC theory remains mostly open; moreover, recent work of Maxwell on specific symmetry models sheds light on fundamental nonuniqueness problems with the conformal method as a parametrization in non-CMC settings. In parallel with these mathematical developments, computational physicists have uncovered surprising behavior in numerical solutions to the extended conformal thin sandwich formulation of the Einstein constraints. In particular, numerical evidence suggests the existence of multiple solutions with a quadratic fold, and a recent analysis of a simplified model supports this conclusion. In this article, we examine this apparent bifurcation phenomena in a methodical way, using modern techniques in bifurcation theory and in numerical homotopy methods. We first review the evidence for the presence of bifurcation in the Hamiltonian constraint in the time-symmetric case. We give a brief introduction to the mathematical framework for analyzing bifurcation phenomena, and then develop the main ideas behind the construction of numerical homotopy, or path-following, methods in the analysis of bifurcation phenomena. We then apply the continuation software package AUTO to this problem, and verify the presence of the fold with homotopy-based numerical methods. We discuss these results and their physical significance, which lead to some interesting remaining questions to

  2. Mathematical logic

    CERN Document Server

    Kleene, Stephen Cole

    1967-01-01

    Undergraduate students with no prior instruction in mathematical logic will benefit from this multi-part text. Part I offers an elementary but thorough overview of mathematical logic of 1st order. Part II introduces some of the newer ideas and the more profound results of logical research in the 20th century. 1967 edition.

  3. Making Mathematics.

    Science.gov (United States)

    Huckstep, Peter

    2002-01-01

    Contends teachers must resist the temptation to suggest that, while children can create stories and melodies, they cannot create mathematics. Quotes mathematician G. H. Hardy: "A mathematician, like a painter or poet, is a 'maker' of patterns." Considers mathematics should be able to stand up for itself. (BT)

  4. Mathematical psychology.

    Science.gov (United States)

    Batchelder, William H

    2010-09-01

    Mathematical psychology is a sub-field of psychology that started in the 1950s and has continued to grow as an important contributor to formal psychological theory, especially in the cognitive areas of psychology such as learning, memory, classification, choice response time, decision making, attention, and problem solving. In addition, there are several scientific sub-areas that were originated by mathematical psychologists such as the foundations of measurement, stochastic memory models, and psychologically motivated reformulations of expected utility theory. Mathematical psychology does not include all uses of mathematics and statistics in psychology, and indeed there is a long history of such uses especially in the areas of perception and psychometrics. What is most unique about mathematical psychology is its approach to theory construction. While accepting the behaviorist dictum that the data in psychology must be observable and replicable, mathematical models are specified in terms of unobservable formal constructs that can predict detailed aspects of data across multiple experimental and natural settings. By now almost all the substantive areas of cognitive and experimental psychology have formal mathematical models and theories, and many of these are due to researchers that identify with mathematical psychology. Copyright © 2010 John Wiley & Sons, Ltd. For further resources related to this article, please visit the WIREs website. Copyright © 2010 John Wiley & Sons, Ltd.

  5. Mathematics 2

    CERN Document Server

    Kodaira, Kunihiko

    1996-01-01

    This is the translation from the Japanese textbook for the grade 11 course, "General Mathematics". It is part of the easier of the three elective courses in mathematics offered at this level and is taken by about 40% of students. The book covers basic notions of probability and statistics, vectors, exponential, logarithmic, and trigonometric functions, and an introduction to differentiation and integration.

  6. Computational mathematics in China

    CERN Document Server

    Shi, Zhong-Ci

    1994-01-01

    This volume describes the most significant contributions made by Chinese mathematicians over the past decades in various areas of computational mathematics. Some of the results are quite important and complement Western developments in the field. The contributors to the volume range from noted senior mathematicians to promising young researchers. The topics include finite element methods, computational fluid mechanics, numerical solutions of differential equations, computational methods in dynamical systems, numerical algebra, approximation, and optimization. Containing a number of survey articles, the book provides an excellent way for Western readers to gain an understanding of the status and trends of computational mathematics in China.

  7. Mathematical models in radiogeochronology

    International Nuclear Information System (INIS)

    Abril, J.M.; Garcia Leon, M.

    1991-01-01

    The study of activity vs. depth profiles in sediment cores of some man-made and natural ocurring radionuclides have shown to be a poweful tool for dating purposes. Nevertheless, in most cases, an adecuate interpretation of such profiles requires mathematical models. In this paper, by considering the sediment as a continuum, a general equation for diffusion of radionuclides through it is obtained. Consequentely, some previously published dating models are found to be particular solutions of such general advenction-diffusion problem. Special emphasis is given to the mathematical treatment of compactation effect and time dependent problems. (author)

  8. Discrete Mathematics

    DEFF Research Database (Denmark)

    Sørensen, John Aasted

    2011-01-01

    ; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics...... to new problems. Relations and functions: Define a product set; define and apply equivalence relations; construct and apply functions. Apply these concepts to new problems. Natural numbers and induction: Define the natural numbers; apply the principle of induction to verify a selection of properties...

  9. Mathematical biology

    CERN Document Server

    Murray, James D

    1993-01-01

    The book is a textbook (with many exercises) giving an in-depth account of the practical use of mathematical modelling in the biomedical sciences. The mathematical level required is generally not high and the emphasis is on what is required to solve the real biological problem. The subject matter is drawn, e.g. from population biology, reaction kinetics, biological oscillators and switches, Belousov-Zhabotinskii reaction, reaction-diffusion theory, biological wave phenomena, central pattern generators, neural models, spread of epidemics, mechanochemical theory of biological pattern formation and importance in evolution. Most of the models are based on real biological problems and the predictions and explanations offered as a direct result of mathematical analysis of the models are important aspects of the book. The aim is to provide a thorough training in practical mathematical biology and to show how exciting and novel mathematical challenges arise from a genuine interdisciplinary involvement with the biosci...

  10. Mathematics unbound

    CERN Document Server

    Parshall, Karen Hunger

    2002-01-01

    Although today's mathematical research community takes its international character very much for granted, this "global nature" is relatively recent, having evolved over a period of roughly 150 years-from the beginning of the nineteenth century to the middle of the twentieth century. During this time, the practice of mathematics changed from being centered on a collection of disparate national communities to being characterized by an international group of scholars for whom the goal of mathematical research and cooperation transcended national boundaries. Yet, the development of an international community was far from smooth and involved obstacles such as war, political upheaval, and national rivalries. Until now, this evolution has been largely overlooked by historians and mathematicians alike. This book addresses the issue by bringing together essays by twenty experts in the history of mathematics who have investigated the genesis of today's international mathematical community. This includes not only develo...

  11. Mathematical problems in meteorological modelling

    CERN Document Server

    Csomós, Petra; Faragó, István; Horányi, András; Szépszó, Gabriella

    2016-01-01

    This book deals with mathematical problems arising in the context of meteorological modelling. It gathers and presents some of the most interesting and important issues from the interaction of mathematics and meteorology. It is unique in that it features contributions on topics like data assimilation, ensemble prediction, numerical methods, and transport modelling, from both mathematical and meteorological perspectives. The derivation and solution of all kinds of numerical prediction models require the application of results from various mathematical fields. The present volume is divided into three parts, moving from mathematical and numerical problems through air quality modelling, to advanced applications in data assimilation and probabilistic forecasting. The book arose from the workshop “Mathematical Problems in Meteorological Modelling” held in Budapest in May 2014 and organized by the ECMI Special Interest Group on Numerical Weather Prediction. Its main objective is to highlight the beauty of the de...

  12. High-Order Entropy Stable Formulations for Computational Fluid Dynamics

    Science.gov (United States)

    Carpenter, Mark H.; Fisher, Travis C.

    2013-01-01

    A systematic approach is presented for developing entropy stable (SS) formulations of any order for the Navier-Stokes equations. These SS formulations discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality. They are valid for smooth as well as discontinuous flows provided sufficient dissipation is added at shocks and discontinuities. Entropy stable formulations exist for all diagonal norm, summation-by-parts (SBP) operators, including all centered finite-difference operators, Legendre collocation finite-element operators, and certain finite-volume operators. Examples are presented using various entropy stable formulations that demonstrate the current state-of-the-art of these schemes.

  13. An exact approach for aggregated formulations

    DEFF Research Database (Denmark)

    Gamst, Mette; Spoorendonk, Simon; Røpke, Stefan

    Aggregating formulations is a powerful approach for problems to take on tractable forms. Aggregation may lead to loss of information, i.e. the aggregated formulation may be an approximation of the original problem. In branch-and-bound context, aggregation can also complicate branching, e.g. when...... optimality cannot be guaranteed by branching on aggregated variables. We present a generic exact solution method to remedy the drawbacks of aggregation. It combines the original and aggregated formulations and applies Benders' decomposition. We apply the method to the Split Delivery Vehicle Routing Problem....

  14. THE IMPORTANCE OF LIMIT SOLUTIONS & TEMPORAL AND SPATIAL SCALES IN THE TEACHING OF TRANSPORT PHENOMENA

    Directory of Open Access Journals (Sweden)

    SÁVIO LEANDRO BERTOLI

    2016-07-01

    Full Text Available In the engineering courses the field of Transport Phenomena is of significant importance and it is in several disciplines relating to Fluid Mechanics, Heat and Mass Transfer. In these disciplines, problems involving these phenomena are mathematically formulated and analytical solutions are obtained whenever possible. The aim of this paper is to emphasize the possibility of extending aspects of the teaching-learning in this area by a method based on time scales and limit solutions. Thus, aspects relative to the phenomenology naturally arise during the definition of the scales and / or by determining the limit solutions. Aspects concerning the phenomenology of the limit problems are easily incorporated into the proposed development, which contributes significantly to the understanding of physics inherent in the mathematical modeling of each limiting case studied. Finally the study aims to disseminate the use of the limit solutions and of the time scales in the general fields of engineering.

  15. assessment of concentration of air pollutants using analytical and numerical solution of the atmospheric diffusion equation

    International Nuclear Information System (INIS)

    Esmail, S.F.H.

    2011-01-01

    The mathematical formulation of numerous physical problems a results in differential equations actually partial or ordinary differential equations.In our study we are interested in solutions of partial differential equations.The aim of this work is to calculate the concentrations of the pollution, by solving the atmospheric diffusion equation(ADE) using different mathematical methods of solution. It is difficult to solve the general form of ADE analytically, so we use some assumptions to get its solution.The solutions of it depend on the eddy diffusivity profiles(k) and the wind speed u. We use some physical assumptions to simplify its formula and solve it. In the present work, we solve the ADE analytically in three dimensions using Green's function method, Laplace transform method, normal mode method and these separation of variables method. Also, we use ADM as a numerical method. Finally, comparisons are made with the results predicted by the previous methods and the observed data.

  16. Data assimilation a mathematical introduction

    CERN Document Server

    Law, Kody; Zygalakis, Konstantinos

    2015-01-01

    This book provides a systematic treatment of the mathematical underpinnings of work in data assimilation, covering both theoretical and computational approaches. Specifically the authors develop a unified mathematical framework in which a Bayesian formulation of the problem provides the bedrock for the derivation, development and analysis of algorithms; the many examples used in the text, together with the algorithms which are introduced and discussed, are all illustrated by the MATLAB software detailed in the book and made freely available online. The book is organized into nine chapters: the first contains a brief introduction to the mathematical tools around which the material is organized; the next four are concerned with discrete time dynamical systems and discrete time data; the last four are concerned with continuous time dynamical systems and continuous time data and are organized analogously to the corresponding discrete time chapters. This book is aimed at mathematical researchers interested in a sy...

  17. Mathematical methods in engineering

    CERN Document Server

    Machado, José

    2014-01-01

    This book presents a careful selection of the contributions presented at the Mathematical Methods in Engineering (MME10) International Symposium, held at the Polytechnic Institute of Coimbra- Engineering Institute of Coimbra (IPC/ISEC), Portugal, October 21-24, 2010. The volume discusses recent developments about theoretical and applied mathematics toward the solution of engineering problems, thus covering a wide range of topics, such as:  Automatic Control, Autonomous Systems, Computer Science, Dynamical Systems and Control,  Electronics, Finance and Economics, Fluid Mechanics and Heat Transfer, Fractional Mathematics, Fractional Transforms and Their Applications,  Fuzzy Sets and Systems, Image and Signal Analysis, Image Processing, Mechanics, Mechatronics, Motor Control and Human Movement Analysis, Nonlinear Dynamics, Partial Differential Equations, Robotics, Acoustics, Vibration and Control, and Wavelets.

  18. Basic engineering mathematics

    CERN Document Server

    Bird, John

    2014-01-01

    Introductory mathematics written specifically for students new to engineering Now in its sixth edition, Basic Engineering Mathematics is an established textbook that has helped thousands of students to succeed in their exams. John Bird's approach is based on worked examples and interactive problems. This makes it ideal for students from a wide range of academic backgrounds as the student can work through the material at their own pace. Mathematical theories are explained in a straightforward manner, being supported by practical engineering examples and applications in order to ensure that readers can relate theory to practice. The extensive and thorough topic coverage makes this an ideal text for introductory level engineering courses. This title is supported by a companion website with resources for both students and lecturers, including lists of essential formulae, multiple choice tests, full solutions for all 1,600 further questions contained within the practice exercises, and biographical information on t...

  19. Engineering mathematics

    CERN Document Server

    Bird, John

    2014-01-01

    A practical introduction to the core mathematics required for engineering study and practiceNow in its seventh edition, Engineering Mathematics is an established textbook that has helped thousands of students to succeed in their exams.John Bird's approach is based on worked examples and interactive problems. This makes it ideal for students from a wide range of academic backgrounds as the student can work through the material at their own pace. Mathematical theories are explained in a straightforward manner, being supported by practical engineering examples and applications in order to ensure

  20. Mathematical physics

    CERN Document Server

    Geroch, Robert

    1985-01-01

    Mathematical Physics is an introduction to such basic mathematical structures as groups, vector spaces, topological spaces, measure spaces, and Hilbert space. Geroch uses category theory to emphasize both the interrelationships among different structures and the unity of mathematics. Perhaps the most valuable feature of the book is the illuminating intuitive discussion of the ""whys"" of proofs and of axioms and definitions. This book, based on Geroch's University of Chicago course, will be especially helpful to those working in theoretical physics, including such areas as relativity, particle

  1. Applied mathematics

    CERN Document Server

    Logan, J David

    2013-01-01

    Praise for the Third Edition"Future mathematicians, scientists, and engineers should find the book to be an excellent introductory text for coursework or self-study as well as worth its shelf space for reference." -MAA Reviews Applied Mathematics, Fourth Edition is a thoroughly updated and revised edition on the applications of modeling and analyzing natural, social, and technological processes. The book covers a wide range of key topics in mathematical methods and modeling and highlights the connections between mathematics and the applied and nat

  2. Speed mathematics

    CERN Document Server

    Handley, Bill

    2012-01-01

    This new, revised edition of the bestselling Speed Mathematics features new chapters on memorising numbers and general information, calculating statistics and compound interest, square roots, logarithms and easy trig calculations. Written so anyone can understand, this book teaches simple strategies that will enable readers to make lightning-quick calculations. People who excel at mathematics use better strategies than the rest of us; they are not necessarily more intelligent. With Speed Mathematics you'll discover methods to make maths easy and fun. This book is perfect for stud

  3. REACT-Mod: a mathematical model for transient calculation of chemical reactions with U-Pu-Np-Tc in the aqueous nitric acid solution

    International Nuclear Information System (INIS)

    Tachimori, Shoichi; Kitamura, Tatsuaki.

    1996-10-01

    A computer code REACT-Mod which simulates various chemical reactions in an aqueous nitric acid solution involving uranium, plutonium, neptunium, technetium etc. e.g., redox, radiolytic and disproportionation reactions of 68, was developed based on the kinetics model. The numerical solution method adopted in the code are two, a kinetics model totally based on the rate law of which differential equations are solved by the modified Porsing method, and a two-step model based on both the rate law and equilibrium law. Only the former treats 27 radiolytic reactions. The latter is beneficially used to have a quick and approximate result by economical computation. The present report aims not only to explain the concept, chemical reactions treated and characteristics of the model but also to provide details of the program for users of the REACT-Mod code. (author)

  4. Mathematical omnibus thirty lectures on classic mathematics

    CERN Document Server

    Fuchs, Dmitry; Fuchs, Dmitry

    2007-01-01

    The book consists of thirty lectures on diverse topics, covering much of the mathematical landscape rather than focusing on one area. The reader will learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and will discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology. The reader's effort will be rewarded in seeing the harmony of each subject. The common thread in the selected subjects is their illustration of the unity and beauty of mathematics. Most lectures contain exercises, and solutions or answers are given to selected exercises. A special feature of the book is an abundance of drawings (more than four hundred), artwork by an accomplished artist, and about a hundred portraits of mathematicians. Almost every lecture contains surprises for even the seasoned researcher.

  5. A time-dependent multi-layered mathematical model of filtration and solute exchange, the revised Starling principle and the Landis experiments

    Directory of Open Access Journals (Sweden)

    Laura Facchini

    2017-10-01

    Full Text Available Cell oxygenation and nutrition is vitally important for human and animal life. Oxygen and nutrients are transported by the blood stream and cross microvessel walls to penetrate the cell’s membrane. Pathological alterations in the transport of oxygen, and other nutrition elements, across microvessel walls may have serious consequences to cell life, possibly leading to localized cell necrosis. We present a transient model of plasma filtration and solute transport across microvessel walls by coupling flow and transport equations, the latter being non-linear in solute concentration. The microvessel wall is modeled through the superimposition of two or more membranes with different physical properties, representing key structural elements. With this model, the combined effect of the endothelial cells, the glycocalyx and other coating membranes specific of certain microvessels, can be analyzed. We investigate the role of transient external pressures in the study of trans-vascular filtration and solute exchange during the drop of blood capillary pressure due to the pathological decrease of blood volume called hypovolaemia, as well as hemorrhage. We discuss the advantage of using a multi-layered model, rather than a model considering the microvessel wall as a single and homogeneous membrane.

  6. Kinetics on Demand Is a Simple Mathematical Solution that Fits Recorded Caffeine-Induced Luminal SR Ca2+ Changes in Smooth Muscle Cells.

    Directory of Open Access Journals (Sweden)

    Norma C Perez-Rosas

    Full Text Available The process of Ca2+ release from sarcoplasmic reticulum (SR comprises 4 phases in smooth muscle cells. Phase 1 is characterized by a large increase of the intracellular Ca2+ concentration ([Ca2+]i with a minimal reduction of the free luminal SR [Ca2+] ([Ca2+]FSR. Importantly, active SR Ca2+ ATPases (SERCA pumps are necessary for phase 1 to occur. This situation cannot be explained by the standard kinetics that involves a fixed amount of luminal Ca2+ binding sites. A new mathematical model was developed that assumes an increasing SR Ca2+ buffering capacity in response to an increase of the luminal SR [Ca2+] that is called Kinetics-on-Demand (KonD model. This approach can explain both phase 1 and the refractory period associated with a recovered [Ca2+]FSR. Additionally, our data suggest that active SERCA pumps are a requisite for KonD to be functional; otherwise luminal SR Ca2+ binding proteins switch to standard kinetics. The importance of KonD Ca2+ binding properties is twofold: a more efficient Ca2+ release process and that [Ca2+]FSR and Ca2+-bound to SR proteins ([Ca2+]BSR can be regulated separately allowing for Ca2+ release to occur (provided by Ca2+-bound to luminal Ca2+ binding proteins without an initial reduction of the [Ca2+]FSR.

  7. Focus group discussion in mathematical physics learning

    Science.gov (United States)

    Ellianawati; Rudiana, D.; Sabandar, J.; Subali, B.

    2018-03-01

    The Focus Group Discussion (FGD) activity in Mathematical Physics learning has helped students perform the stages of problem solving reflectively. The FGD implementation was conducted to explore the problems and find the right strategy to improve the students' ability to solve the problem accurately which is one of reflective thinking component that has been difficult to improve. The research method used is descriptive qualitative by using single subject response in Physics student. During the FGD process, one student was observed of her reflective thinking development in solving the physics problem. The strategy chosen in the discussion activity was the Cognitive Apprenticeship-Instruction (CA-I) syntax. Based on the results of this study, it is obtained the information that after going through a series of stages of discussion, the students' reflective thinking skills is increased significantly. The scaffolding stage in the CA-I model plays an important role in the process of solving physics problems accurately. Students are able to recognize and formulate problems by describing problem sketches, identifying the variables involved, applying mathematical equations that accord to physics concepts, executing accurately, and applying evaluation by explaining the solution to various contexts.

  8. Construction mathematics

    CERN Document Server

    Virdi, Surinder; Virdi, Narinder Kaur

    2014-01-01

    Construction Mathematics is an introductory level mathematics text, written specifically for students of construction and related disciplines. Learn by tackling exercises based on real-life construction maths. Examples include: costing calculations, labour costs, cost of materials and setting out of building components. Suitable for beginners and easy to follow throughout. Learn the essential basic theory along with the practical necessities. The second edition of this popular textbook is fully updated to match new curricula, and expanded to include even more learning exercises. End of chapter exercises cover a range of theoretical as well as practical problems commonly found in construction practice, and three detailed assignments based on practical tasks give students the opportunity to apply all the knowledge they have gained. Construction Mathematics addresses all the mathematical requirements of Level 2 construction NVQs from City & Guilds/CITB and Edexcel courses, including the BTEC First Diploma in...

  9. Mathematical modelling

    CERN Document Server

    2016-01-01

    This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.

  10. Algorithmic mathematics

    CERN Document Server

    Hougardy, Stefan

    2016-01-01

    Algorithms play an increasingly important role in nearly all fields of mathematics. This book allows readers to develop basic mathematical abilities, in particular those concerning the design and analysis of algorithms as well as their implementation. It presents not only fundamental algorithms like the sieve of Eratosthenes, the Euclidean algorithm, sorting algorithms, algorithms on graphs, and Gaussian elimination, but also discusses elementary data structures, basic graph theory, and numerical questions. In addition, it provides an introduction to programming and demonstrates in detail how to implement algorithms in C++. This textbook is suitable for students who are new to the subject and covers a basic mathematical lecture course, complementing traditional courses on analysis and linear algebra. Both authors have given this "Algorithmic Mathematics" course at the University of Bonn several times in recent years.

  11. Mathematical modeling

    CERN Document Server

    Eck, Christof; Knabner, Peter

    2017-01-01

    Mathematical models are the decisive tool to explain and predict phenomena in the natural and engineering sciences. With this book readers will learn to derive mathematical models which help to understand real world phenomena. At the same time a wealth of important examples for the abstract concepts treated in the curriculum of mathematics degrees are given. An essential feature of this book is that mathematical structures are used as an ordering principle and not the fields of application. Methods from linear algebra, analysis and the theory of ordinary and partial differential equations are thoroughly introduced and applied in the modeling process. Examples of applications in the fields electrical networks, chemical reaction dynamics, population dynamics, fluid dynamics, elasticity theory and crystal growth are treated comprehensively.

  12. Audits of radiopharmaceutical formulations

    International Nuclear Information System (INIS)

    Castronovo, F.P. Jr.

    1992-01-01

    A procedure for auditing radiopharmaceutical formulations is described. To meet FDA guidelines regarding the quality of radiopharmaceuticals, institutional radioactive drug research committees perform audits when such drugs are formulated away from an institutional pharmacy. All principal investigators who formulate drugs outside institutional pharmacies must pass these audits before they can obtain a radiopharmaceutical investigation permit. The audit team meets with the individual who performs the formulation at the site of drug preparation to verify that drug formulations meet identity, strength, quality, and purity standards; are uniform and reproducible; and are sterile and pyrogen free. This team must contain an expert knowledgeable in the preparation of radioactive drugs; a radiopharmacist is the most qualified person for this role. Problems that have been identified by audits include lack of sterility and apyrogenicity testing, formulations that are open to the laboratory environment, failure to use pharmaceutical-grade chemicals, inadequate quality control methods or records, inadequate training of the person preparing the drug, and improper unit dose preparation. Investigational radiopharmaceutical formulations, including nonradiolabeled drugs, must be audited before they are administered to humans. A properly trained pharmacist should be a member of the audit team

  13. Mathematical statistics

    CERN Document Server

    Pestman, Wiebe R

    2009-01-01

    This textbook provides a broad and solid introduction to mathematical statistics, including the classical subjects hypothesis testing, normal regression analysis, and normal analysis of variance. In addition, non-parametric statistics and vectorial statistics are considered, as well as applications of stochastic analysis in modern statistics, e.g., Kolmogorov-Smirnov testing, smoothing techniques, robustness and density estimation. For students with some elementary mathematical background. With many exercises. Prerequisites from measure theory and linear algebra are presented.

  14. Mathematics revealed

    CERN Document Server

    Berman, Elizabeth

    1979-01-01

    Mathematics Revealed focuses on the principles, processes, operations, and exercises in mathematics.The book first offers information on whole numbers, fractions, and decimals and percents. Discussions focus on measuring length, percent, decimals, numbers as products, addition and subtraction of fractions, mixed numbers and ratios, division of fractions, addition, subtraction, multiplication, and division. The text then examines positive and negative numbers and powers and computation. Topics include division and averages, multiplication, ratios, and measurements, scientific notation and estim

  15. Discrete Mathematics

    DEFF Research Database (Denmark)

    Sørensen, John Aasted

    2010-01-01

    The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18...

  16. Discrete Mathematics

    DEFF Research Database (Denmark)

    Sørensen, John Aasted

    2010-01-01

    The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15...

  17. Reactive decontamination formulation

    Science.gov (United States)

    Giletto, Anthony [College Station, TX; White, William [College Station, TX; Cisar, Alan J [Cypress, TX; Hitchens, G Duncan [Bryan, TX; Fyffe, James [Bryan, TX

    2003-05-27

    The present invention provides a universal decontamination formulation and method for detoxifying chemical warfare agents (CWA's) and biological warfare agents (BWA's) without producing any toxic by-products, as well as, decontaminating surfaces that have come into contact with these agents. The formulation includes a sorbent material or gel, a peroxide source, a peroxide activator, and a compound containing a mixture of KHSO.sub.5, KHSO.sub.4 and K.sub.2 SO.sub.4. The formulation is self-decontaminating and once dried can easily be wiped from the surface being decontaminated. A method for decontaminating a surface exposed to chemical or biological agents is also disclosed.

  18. Some unsolved problems in discrete mathematics and mathematical cybernetics

    Energy Technology Data Exchange (ETDEWEB)

    Korshunov, Aleksei D [S.L. Sobolev Institute for Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk (Russian Federation)

    2009-10-31

    There are many unsolved problems in discrete mathematics and mathematical cybernetics. Writing a comprehensive survey of such problems involves great difficulties. First, such problems are rather numerous and varied. Second, they greatly differ from each other in degree of completeness of their solution. Therefore, even a comprehensive survey should not attempt to cover the whole variety of such problems; only the most important and significant problems should be reviewed. An impersonal choice of problems to include is quite hard. This paper includes 13 unsolved problems related to combinatorial mathematics and computational complexity theory. The problems selected give an indication of the author's studies for 50 years; for this reason, the choice of the problems reviewed here is, to some extent, subjective. At the same time, these problems are very difficult and quite important for discrete mathematics and mathematical cybernetics. Bibliography: 74 items.

  19. Some unsolved problems in discrete mathematics and mathematical cybernetics

    Science.gov (United States)

    Korshunov, Aleksei D.

    2009-10-01

    There are many unsolved problems in discrete mathematics and mathematical cybernetics. Writing a comprehensive survey of such problems involves great difficulties. First, such problems are rather numerous and varied. Second, they greatly differ from each other in degree of completeness of their solution. Therefore, even a comprehensive survey should not attempt to cover the whole variety of such problems; only the most important and significant problems should be reviewed. An impersonal choice of problems to include is quite hard. This paper includes 13 unsolved problems related to combinatorial mathematics and computational complexity theory. The problems selected give an indication of the author's studies for 50 years; for this reason, the choice of the problems reviewed here is, to some extent, subjective. At the same time, these problems are very difficult and quite important for discrete mathematics and mathematical cybernetics. Bibliography: 74 items.

  20. Some unsolved problems in discrete mathematics and mathematical cybernetics

    International Nuclear Information System (INIS)

    Korshunov, Aleksei D

    2009-01-01

    There are many unsolved problems in discrete mathematics and mathematical cybernetics. Writing a comprehensive survey of such problems involves great difficulties. First, such problems are rather numerous and varied. Second, they greatly differ from each other in degree of completeness of their solution. Therefore, even a comprehensive survey should not attempt to cover the whole variety of such problems; only the most important and significant problems should be reviewed. An impersonal choice of problems to include is quite hard. This paper includes 13 unsolved problems related to combinatorial mathematics and computational complexity theory. The problems selected give an indication of the author's studies for 50 years; for this reason, the choice of the problems reviewed here is, to some extent, subjective. At the same time, these problems are very difficult and quite important for discrete mathematics and mathematical cybernetics. Bibliography: 74 items.

  1. Life insurance mathematics

    CERN Document Server

    Gerber, Hans U

    1997-01-01

    This concise introduction to life contingencies, the theory behind the actuarial work around life insurance and pension funds, will appeal to the reader who likes applied mathematics. In addition to model of life contingencies, the theory of compound interest is explained and it is shown how mortality and other rates can be estimated from observations. The probabilistic model is used consistently throughout the book. Numerous exercises (with answers and solutions) have been added, and for this third edition several misprints have been corrected.

  2. Studies in mathematics and mechanics

    CERN Document Server

    von Mises, Richard

    2013-01-01

    Studies in Mathematics and Mechanics is a collection of studies presented to Professor Richard von Mises as a token of reverence and appreciation on the occasion of his seventieth birthday which occurred on April 19, 1953. von Mises' thought has been a stimulus in many seemingly unconnected fields of mathematics, science, and philosophy, to which he has contributed decisive results and new formulations of fundamental concepts. The book contains 42 chapters organized into five parts. Part I contains papers on algebra, number theory and geometry. These include a study of Poincaré's representatio

  3. Mathematical methods of classical physics

    CERN Document Server

    Cortés, Vicente

    2017-01-01

    This short primer, geared towards students with a strong interest in mathematically rigorous approaches, introduces the essentials of classical physics, briefly points out its place in the history of physics and its relation to modern physics, and explains what benefits can be gained from a mathematical perspective. As a starting point, Newtonian mechanics is introduced and its limitations are discussed. This leads to and motivates the study of different formulations of classical mechanics, such as Lagrangian and Hamiltonian mechanics, which are the subjects of later chapters. In the second part, a chapter on classical field theories introduces more advanced material. Numerous exercises are collected in the appendix.

  4. Current problems in applied mathematics and mathematical physics

    Science.gov (United States)

    Samarskii, A. A.

    Papers are presented on such topics as mathematical models in immunology, mathematical problems of medical computer tomography, classical orthogonal polynomials depending on a discrete variable, and boundary layer methods for singular perturbation problems in partial derivatives. Consideration is also given to the computer simulation of supernova explosion, nonstationary internal waves in a stratified fluid, the description of turbulent flows by unsteady solutions of the Navier-Stokes equations, and the reduced Galerkin method for external diffraction problems using the spline approximation of fields.

  5. Preparation of radiopharmaceutical formulations

    International Nuclear Information System (INIS)

    Simon, J.; Garlich, J.R.; Frank, R.K.; McMillan, K.

    1998-01-01

    Radiopharmaceutical formulations for complexes comprising at least one radionuclide complexed with a ligand, or its physiologically-acceptable salts thereof, especially 153 samarium-ethylenediaminetetramethylenephosphonic acid, which optionally contains a divalent metal ion, e.g. calcium, and is frozen, thawed, and then administered by injection. Alternatively, the radiopharmaceutical formulations must contain the divalent metal and are frozen only if the time before administration is sufficiently long to cause concern for radiolysis of the ligand. 2 figs., 9 tabs

  6. Tariff formulation and equalization

    International Nuclear Information System (INIS)

    Svartsund, Trond

    2003-01-01

    The primary goal of the transmission tariff is to provide for socioeconomic use of the transmission grid. The present tariff structure is basically right. The responsibility for the formulation of the tariff resides with the local grid owner. This must take place in agreement with the current regulations which are passed by the authorities. The formulation must be adaptable to the local requirements. EBL (Norwegian Electricity Industry Association) is content with the current regulations

  7. Mathematics of the quantum informatics. An introduction; Mathematik der Quanteninformatik. Eine Einfuehrung

    Energy Technology Data Exchange (ETDEWEB)

    Scherer, Wolfgang

    2016-07-01

    Starting from the physical foundations all mathematics required for the quantum informatics are introduced and explained. The essential aspects of the quantum informatics are mathematically formulated. All statements made are also proved in the book.

  8. A locally conservative non-negative finite element formulation for anisotropic advective-diffusive-reactive systems

    Science.gov (United States)

    Mudunuru, M. K.; Shabouei, M.; Nakshatrala, K.

    2015-12-01

    Advection-diffusion-reaction (ADR) equations appear in various areas of life sciences, hydrogeological systems, and contaminant transport. Obtaining stable and accurate numerical solutions can be challenging as the underlying equations are coupled, nonlinear, and non-self-adjoint. Currently, there is neither a robust computational framework available nor a reliable commercial package known that can handle various complex situations. Herein, the objective of this poster presentation is to present a novel locally conservative non-negative finite element formulation that preserves the underlying physical and mathematical properties of a general linear transient anisotropic ADR equation. In continuous setting, governing equations for ADR systems possess various important properties. In general, all these properties are not inherited during finite difference, finite volume, and finite element discretizations. The objective of this poster presentation is two fold: First, we analyze whether the existing numerical formulations (such as SUPG and GLS) and commercial packages provide physically meaningful values for the concentration of the chemical species for various realistic benchmark problems. Furthermore, we also quantify the errors incurred in satisfying the local and global species balance for two popular chemical kinetics schemes: CDIMA (chlorine dioxide-iodine-malonic acid) and BZ (Belousov--Zhabotinsky). Based on these numerical simulations, we show that SUPG and GLS produce unphysical values for concentration of chemical species due to the violation of the non-negative constraint, contain spurious node-to-node oscillations, and have large errors in local and global species balance. Second, we proposed a novel finite element formulation to overcome the above difficulties. The proposed locally conservative non-negative computational framework based on low-order least-squares finite elements is able to preserve these underlying physical and mathematical properties

  9. Mathematical physics applied mathematics for scientists and engineers

    CERN Document Server

    Kusse, Bruce R

    2006-01-01

    What sets this volume apart from other mathematics texts is its emphasis on mathematical tools commonly used by scientists and engineers to solve real-world problems. Using a unique approach, it covers intermediate and advanced material in a manner appropriate for undergraduate students. Based on author Bruce Kusse's course at the Department of Applied and Engineering Physics at Cornell University, Mathematical Physics begins with essentials such as vector and tensor algebra, curvilinear coordinate systems, complex variables, Fourier series, Fourier and Laplace transforms, differential and integral equations, and solutions to Laplace's equations

  10. Mathematical concepts

    CERN Document Server

    Jost, Jürgen

    2015-01-01

    The main intention of this book is to describe and develop the conceptual, structural and abstract thinking of mathematics. Specific mathematical structures are used to illustrate the conceptual approach; providing a deeper insight into mutual relationships and abstract common features. These ideas are carefully motivated, explained and illustrated by examples so that many of the more technical proofs can be omitted. The book can therefore be used: ·         simply as an overview of the panorama of mathematical structures and the relations between them, to be supplemented by more detailed texts whenever you want to acquire a working knowledge of some structure ·         by itself as a first introduction to abstract mathematics ·         together with existing textbooks, to put their results into a more general perspective ·         to gain a new and hopefully deeper perspective after having studied such textbooks Mathematical Concepts has a broader scope and is less detaile...

  11. Simultaneously Exploiting Two Formulations: an Exact Benders Decomposition Approach

    DEFF Research Database (Denmark)

    Lusby, Richard Martin; Gamst, Mette; Spoorendonk, Simon

    When modelling a given problem using linear programming techniques several possibilities often exist, and each results in a different mathematical formulation of the problem. Usually, advantages and disadvantages can be identified in any single formulation. In this paper we consider mixed integer...... to the standard branch-and-price approach from the literature, the method shows promising performance and appears to be an attractive alternative....

  12. Mathematical foundations of biomechanics.

    Science.gov (United States)

    Niederer, Peter F

    2010-01-01

    The aim of biomechanics is the analysis of the structure and function of humans, animals, and plants by means of the methods of mechanics. Its foundations are in particular embedded in mathematics, physics, and informatics. Due to the inherent multidisciplinary character deriving from its aim, biomechanics has numerous connections and overlapping areas with biology, biochemistry, physiology, and pathophysiology, along with clinical medicine, so its range is enormously wide. This treatise is mainly meant to serve as an introduction and overview for readers and students who intend to acquire a basic understanding of the mathematical principles and mechanics that constitute the foundation of biomechanics; accordingly, its contents are limited to basic theoretical principles of general validity and long-range significance. Selected examples are included that are representative for the problems treated in biomechanics. Although ultimate mathematical generality is not in the foreground, an attempt is made to derive the theory from basic principles. A concise and systematic formulation is thereby intended with the aim that the reader is provided with a working knowledge. It is assumed that he or she is familiar with the principles of calculus, vector analysis, and linear algebra.

  13. Mathematical biophysics

    CERN Document Server

    Rubin, Andrew

    2014-01-01

    This book presents concise descriptions and analysis of the classical and modern models used in mathematical biophysics. The authors ask the question "what new information can be provided by the models that cannot be obtained directly from experimental data?" Actively developing fields such as regulatory mechanisms in cells and subcellular systems and electron transport and energy transport in membranes are addressed together with more classical topics such as metabolic processes, nerve conduction and heart activity, chemical kinetics, population dynamics, and photosynthesis. The main approach is to describe biological processes using different mathematical approaches necessary to reveal characteristic features and properties of simulated systems. With the emergence of powerful mathematics software packages such as MAPLE, Mathematica, Mathcad, and MatLab, these methodologies are now accessible to a wide audience. Provides succinct but authoritative coverage of a broad array of biophysical topics and models Wr...

  14. Mathematical tapas

    CERN Document Server

    Hiriart-Urruty, Jean-Baptiste

    This book contains a collection of exercises (called “tapas”) at undergraduate level, mainly from the fields of real analysis, calculus, matrices, convexity, and optimization. Most of the problems presented here are non-standard and some require broad knowledge of different mathematical subjects in order to be solved. The author provides some hints and (partial) answers and also puts these carefully chosen exercises into context, presents information on their origins, and comments on possible extensions. With stars marking the levels of difficulty, these tapas show or prove something interesting, challenge the reader to solve and learn, and may have surprising results. This first volume of Mathematical Tapas will appeal to mathematicians, motivated undergraduate students from science-based areas, and those generally interested in mathematics.

  15. Mathematical writing

    CERN Document Server

    Vivaldi, Franco

    2014-01-01

    This book teaches the art of writing mathematics, an essential -and difficult- skill for any mathematics student.   The book begins with an informal introduction on basic writing principles and a review of the essential dictionary for mathematics. Writing techniques are developed gradually, from the small to the large: words, phrases, sentences, paragraphs, to end with short compositions. These may represent the introduction of a concept, the abstract of a presentation or the proof of a theorem. Along the way the student will learn how to establish a coherent notation, mix words and symbols effectively, write neat formulae, and structure a definition.   Some elements of logic and all common methods of proofs are featured, including various versions of induction and existence proofs. The book concludes with advice on specific aspects of thesis writing (choosing of a title, composing an abstract, compiling a bibliography) illustrated by large number of real-life examples. Many exercises are included; over 150...

  16. Physical mathematics

    CERN Document Server

    Cahill, Kevin

    2013-01-01

    Unique in its clarity, examples and range, Physical Mathematics explains as simply as possible the mathematics that graduate students and professional physicists need in their courses and research. The author illustrates the mathematics with numerous physical examples drawn from contemporary research. In addition to basic subjects such as linear algebra, Fourier analysis, complex variables, differential equations and Bessel functions, this textbook covers topics such as the singular-value decomposition, Lie algebras, the tensors and forms of general relativity, the central limit theorem and Kolmogorov test of statistics, the Monte Carlo methods of experimental and theoretical physics, the renormalization group of condensed-matter physics and the functional derivatives and Feynman path integrals of quantum field theory.

  17. The functions of mathematical physics

    CERN Document Server

    Hochstadt, Harry

    2012-01-01

    A modern classic, this clearly written, incisive textbook provides a comprehensive, detailed survey of the functions of mathematical physics, a field of study straddling the somewhat artificial boundary between pure and applied mathematics.In the 18th and 19th centuries, the theorists who devoted themselves to this field - pioneers such as Gauss, Euler, Fourier, Legendre, and Bessel - were searching for mathematical solutions to physical problems. Today, although most of the functions have practical applications, in areas ranging from the quantum-theoretical model of the atom to the vibrating

  18. Mathematical methods in systems biology.

    Science.gov (United States)

    Kashdan, Eugene; Duncan, Dominique; Parnell, Andrew; Schattler, Heinz

    2016-12-01

    The editors of this Special Issue of Mathematical Biosciences and Engineering were the organizers for the Third International Workshop "Mathematical Methods in System Biology" that took place on June 15-18, 2015 at the University College Dublin in Ireland. As stated in the workshop goals, we managed to attract a good mix of mathematicians and statisticians working on biological and medical applications with biologists and clinicians interested in presenting their challenging problems and looking to find mathematical and statistical tools for their solutions.

  19. Mathematical Lives

    CERN Document Server

    Bartocci, Claudio; Guerraggio, Angelo; Lucchetti, Roberto; Williams, Kim

    2011-01-01

    Steps forward in mathematics often reverberate in other scientific disciplines, and give rise to innovative conceptual developments or find surprising technological applications. This volume brings to the forefront some of the proponents of the mathematics of the twentieth century, who have put at our disposal new and powerful instruments for investigating the reality around us. The portraits present people who have impressive charisma and wide-ranging cultural interests, who are passionate about defending the importance of their own research, are sensitive to beauty, and attentive to the soci

  20. Mathematical programming in multiperson cooperative games

    Energy Technology Data Exchange (ETDEWEB)

    Lucas, W.

    1994-12-31

    Many fundamental solution notions in mathematical economics relate to mathematical programming. This includes various types of equilibrium points for the noncooperative (strategic) competitions, as well as the core for the cooperative (coalitional) models. This talk concerns alternate cooperative solution concepts such as various nucleoli points and other proposed fairness outcomes. These concepts become of particular interest for those cases when the core is an empty set. Recent results on these alternate solutions for classes of assignment games will be presented.

  1. Quotable Quotes in Mathematics

    Science.gov (United States)

    Lo, Bruce W. N.

    1983-01-01

    As a way to dispel negative feelings toward mathematics, a variety of quotations are given. They are categorized by: what mathematics is, mathematicians, mathematics and other disciplines, different areas of mathematics, mathematics and humor, applications of mathematics, and pure versus applied mathematics. (MNS)

  2. On Newton-Raphson formulation and algorithm for displacement based structural dynamics problem with quadratic damping nonlinearity

    Directory of Open Access Journals (Sweden)

    Koh Kim Jie

    2017-01-01

    Full Text Available Quadratic damping nonlinearity is challenging for displacement based structural dynamics problem as the problem is nonlinear in time derivative of the primitive variable. For such nonlinearity, the formulation of tangent stiffness matrix is not lucid in the literature. Consequently, ambiguity related to kinematics update arises when implementing the time integration-iterative algorithm. In present work, an Euler-Bernoulli beam vibration problem with quadratic damping nonlinearity is addressed as the main source of quadratic damping nonlinearity arises from drag force estimation, which is generally valid only for slender structures. Employing Newton-Raphson formulation, tangent stiffness components associated with quadratic damping nonlinearity requires velocity input for evaluation purpose. For this reason, two mathematically equivalent algorithm structures with different kinematics arrangement are tested. Both algorithm structures result in the same accuracy and convergence characteristic of solution.

  3. Approximate solutions of pulse transport in turbulent flow in narrow fuel element bundle geometries, using the FE method

    International Nuclear Information System (INIS)

    Kaiser, H.G.

    1985-01-01

    The author is concerned with the flow conditions in case of narrow fuel element grids of pressurised-water reactors. Starting from the mathematical formulation of the flow processes for incompressible, isothermal flows, models of the turbulence characteristics are being developed. Besides turbulence models, and network structure the finite element method is treated as numeric solution process. Finally the results are summarized and discussed. (HAG) [de

  4. Granulated decontamination formulations

    Science.gov (United States)

    Tucker, Mark D.

    2007-10-02

    A decontamination formulation and method of making that neutralizes the adverse health effects of both chemical and biological compounds, especially chemical warfare (CW) and biological warfare (BW) agents, and toxic industrial chemicals. The formulation provides solubilizing compounds that serve to effectively render the chemical and biological compounds, particularly CW and BW compounds, susceptible to attack, and at least one reactive compound that serves to attack (and detoxify or kill) the compound. The formulation includes at least one solubilizing agent, a reactive compound, a sorbent additive, and water. A highly adsorbent sorbent additive (e.g., amorphous silica, sorbitol, mannitol, etc.) is used to "dry out" one or more liquid ingredients into a dry, free-flowing powder that has an extended shelf life, and is more convenient to handle and mix in the field.

  5. Mathematical cosmology

    International Nuclear Information System (INIS)

    Wainwright, J.

    1990-01-01

    The workshop on mathematical cosmology was devoted to four topics of current interest. This report contains a brief discussion of the historical background of each topic and a concise summary of the content of each talk. The topics were; the observational cosmology program, the cosmological perturbation program, isotropic singularities, and the evolution of Bianchi cosmologies. (author)

  6. Mathematical quantization

    CERN Document Server

    Weaver, Nik

    2001-01-01

    With a unique approach and presenting an array of new and intriguing topics, Mathematical Quantization offers a survey of operator algebras and related structures from the point of view that these objects are quantizations of classical mathematical structures. This approach makes possible, with minimal mathematical detail, a unified treatment of a variety of topics.Detailed here for the first time, the fundamental idea of mathematical quantization is that sets are replaced by Hilbert spaces. Building on this idea, and most importantly on the fact that scalar-valued functions on a set correspond to operators on a Hilbert space, one can determine quantum analogs of a variety of classical structures. In particular, because topologies and measure classes on a set can be treated in terms of scalar-valued functions, we can transfer these constructions to the quantum realm, giving rise to C*- and von Neumann algebras.In the first half of the book, the author quickly builds the operator algebra setting. He uses this ...

  7. Mathematical stereochemistry

    CERN Document Server

    Fujita, Shinsaku

    2015-01-01

    Chirality and stereogenicity are closely related concepts and their differentiation and description is still a challenge in chemoinformatics. A new stereoisogram approach, developed by the author, is introduced in this book, providing a theoretical framework for mathematical aspects of modern stereochemistry. The discussion covers point-groups and permutation symmetry and exemplifies the concepts using organic molecules and inorganic complexes.

  8. Mathematical Formulation of the Arsenal Exchange Model. Revision 7

    Science.gov (United States)

    1973-06-01

    budgec is not desirable for some reason or another. Further, suppose that the analyst is willing to spend B bidget units inefficiently but only as...his stockpile is depleted,-11 max E n \\ u .; will have been achieved. * rin the groused r ;.rget case, the incremental deployments...installation. Because of the J Look-ahead feature of the program which skips over cavities, the first potential deployment increment available to

  9. A robust mathematical formulation for multipurpose batch plants

    CSIR Research Space (South Africa)

    Seid, R

    2012-01-01

    Full Text Available stream_source_info Seid_2011_ABSTRACT ONLY.pdf.txt stream_content_type text/plain stream_size 2104 Content-Encoding ISO-8859-1 stream_name Seid_2011_ABSTRACT ONLY.pdf.txt Content-Type text/plain; charset=ISO-8859...

  10. The Remedial Action Priority System (RAPS): Mathematical formulations

    International Nuclear Information System (INIS)

    Whelan, G.; Strenge, D.L.; Droppo, J.G. Jr.; Steelman, B.L.; Buck, J.W.

    1987-08-01

    The Remedial Action Priority System (RAPS) represents a methodology that prioritizes inactive hazardous and radioactive mixed-waste disposal sites in a scientific and objective manner based on limited site information. This methodology is intended to bridge the technology gap between the initial site evaluation using the Hazard Ranking System (HRS) and the time-consuming process of actual field site characterization, assessment, and remediation efforts. The RAPS methodology provides the US Department of Energy with a management tool for assistance in prioritizing funding and human resource allocations for further investigations and possible remediations at its inactive waste sites. Use of RAPS will help DOE ensure that those sites posing the highest potential risk are addressed first. Chapters 1 through 10 were processed separately for the Energy Data Base

  11. Coastal Modeling System: Mathematical Formulations and Numerical Methods

    Science.gov (United States)

    2014-03-01

    ta l a nd H yd ra ul ic s La bo ra to ry Alejandro Sánchez, Weiming Wu, Honghai Li, Mitch Brown, Chris Reed, Julie Rosati, and Zeki Demirbilek...radiation stresses ( ijS ) are calculated using linear wave theory as (Longuet- Higgins and Stewart 1961; Dean and Dalrymple 1984) ( , )ij w g i j ij gS E f...Army Engineer Research and Development Center. Longuet- Higgins , M. S., and R. W. Stewart. 1961. The changes in amplitude of short gravity waves on

  12. Progress, Wealth, and Mathematics Achievement

    DEFF Research Database (Denmark)

    Valero, Paola

    2013-01-01

    I am interested in discussing the historical conditions that make it possible to formulate the idea that the mathematical qualifications of citizens in modern states is connected to the progress and economic development of nations. I interconnect apparently unrelated areas in an attempt to shed l......, H. (1899). Préface. L' Enseignement Mathématique, 1(1), 1-5. Popkewitz, T. S. (2008). Cosmopolitanism and the age of school reform: Science, education, and making society by making the child. New York: Routledge....... to the end of the 19th century. During the second half of the 19th century, mathematics teachers in different countries struggled to make mathematics part of the classic school curricula. During the second industrialization, the justification for the need for mathematics education was formulated in the first...... as a result, among others, of the growing series of comparative information on educational achievement and development. Such reports can be seen as performances of the comparative logic of Modernity that operates differential positioning, not only among individuals but also among nations, with respect to what...

  13. Mathematics and electromagnetism; Matematicas y electromagnetismo

    Energy Technology Data Exchange (ETDEWEB)

    Rodriguez Danta, M.

    2000-07-01

    Symbiosis between mathematics and electromagnetism is analyzed in a simple and concise manner by taking a historical perspective. The universal tool character of mathematical models allowed the transfer of models from several branches of physics into the realm of electromagnetism by drawing analogies. The mutual interdependence between covariant formulation and tensor calculus is marked. The paper focuses on the guiding idea of field theory and Maxwell's equations. Likewise, geometrization of interactions in connection with gauge fields is also noted. (Author)

  14. Rival approaches to mathematical modelling in immunology

    Science.gov (United States)

    Andrew, Sarah M.; Baker, Christopher T. H.; Bocharov, Gennady A.

    2007-08-01

    In order to formulate quantitatively correct mathematical models of the immune system, one requires an understanding of immune processes and familiarity with a range of mathematical techniques. Selection of an appropriate model requires a number of decisions to be made, including a choice of the modelling objectives, strategies and techniques and the types of model considered as candidate models. The authors adopt a multidisciplinary perspective.

  15. Two-dimensional finite element solution for the simultaneous transport of water and solutes through a nonhomogeneous aquifer under transient saturated unsaturated flow conditions

    International Nuclear Information System (INIS)

    Gureghian, A.B.

    1979-01-01

    A mathematical model of ground water transport through an aquifer is presented. The solute of interest is a metal tracer or radioactive material which may undergo decay through a sorbing unconfined aquifer. The subject is developed under the following headings: flow equation, solute equation, boundary conditions, finite element formulation, element formulation, solution scheme (flow equation, solute equation), results and discussions, water movement in a ditch drained aquifer under transient state, water and solute movement in a homogeneous and unsaturated soil, transport of 226 Ra in nonhomogeneous aquifer, tailings pond lined, and tailings pond unlined. It is concluded that this mathematical model may have a wide variety of applications. The uranium milling industry may find it useful to evaluate the hydrogeological suitability of their disposal sites. It may prove suited for the design of clay disposal ponds destined to hold hazardous liquids. It may also provide a means of estimating the long-term impact of radionuclides or other pollutants on the quality of ground water. 31 references, 9 figures, 3 tables

  16. Derivation and computation of discrete-delay and continuous-delay SDEs in mathematical biology.

    Science.gov (United States)

    Allen, Edward J

    2014-06-01

    Stochastic versions of several discrete-delay and continuous-delay differential equations, useful in mathematical biology, are derived from basic principles carefully taking into account the demographic, environmental, or physiological randomness in the dynamic processes. In particular, stochastic delay differential equation (SDDE) models are derived and studied for Nicholson's blowflies equation, Hutchinson's equation, an SIS epidemic model with delay, bacteria/phage dynamics, and glucose/insulin levels. Computational methods for approximating the SDDE models are described. Comparisons between computational solutions of the SDDEs and independently formulated Monte Carlo calculations support the accuracy of the derivations and of the computational methods.

  17. The Telegraph Equation and Its Solution by Reduced Differential Transform Method

    Directory of Open Access Journals (Sweden)

    Vineet K. Srivastava

    2013-01-01

    Full Text Available One-dimensional second-order hyperbolic telegraph equation was formulated using Ohm’s law and solved by a recent and reliable semianalytic method, namely, the reduced differential transform method (RDTM. Using this method, it is possible to find the exact solution or a closed approximate solution of a differential equation. Three numerical examples have been carried out in order to check the effectiveness, the accuracy, and convergence of the method. The RDTM is a powerful mathematical technique for solving wide range of problems arising in science and engineering fields.

  18. The language of mathematics telling mathematical tales

    CERN Document Server

    Barton, Bill

    2008-01-01

    Everyday mathematical ideas are expressed differently in different languages. This book probes those differences and explores their implications for mathematics education, arguing for alternatives to how we teach and learn mathematics.

  19. Correlation of spacecraft thermal mathematical models to reference data

    Science.gov (United States)

    Torralbo, Ignacio; Perez-Grande, Isabel; Sanz-Andres, Angel; Piqueras, Javier

    2018-03-01

    Model-to-test correlation is a frequent problem in spacecraft-thermal control design. The idea is to determine the values of the parameters of the thermal mathematical model (TMM) that allows reaching a good fit between the TMM results and test data, in order to reduce the uncertainty of the mathematical model. Quite often, this task is performed manually, mainly because a good engineering knowledge and experience is needed to reach a successful compromise, but the use of a mathematical tool could facilitate this work. The correlation process can be considered as the minimization of the error of the model results with regard to the reference data. In this paper, a simple method is presented suitable to solve the TMM-to-test correlation problem, using Jacobian matrix formulation and Moore-Penrose pseudo-inverse, generalized to include several load cases. Aside, in simple cases, this method also allows for analytical solutions to be obtained, which helps to analyze some problems that appear when the Jacobian matrix is singular. To show the implementation of the method, two problems have been considered, one more academic, and the other one the TMM of an electronic box of PHI instrument of ESA Solar Orbiter mission, to be flown in 2019. The use of singular value decomposition of the Jacobian matrix to analyze and reduce these models is also shown. The error in parameter space is used to assess the quality of the correlation results in both models.

  20. On the Correct Formulation of the First Law of Thermodynamics

    Science.gov (United States)

    Kalanov, Temur Z.

    2006-04-01

    The critical analysis of the generally accepted formulation of the first law of thermodynamics is proposed. The purpose of the analysis is to prove that the standard formulation contains a mathematical error and to offer the correct formulation. The correct formulation is based on the concepts of function and differential of function. Really, if internal energy Uof a system is a function of two independent variables Q=Q(t) (describing of the thermal form of energy) and R=R(t) (describing non-thermal form of energy), then the correct formulation of the first law of thermodynamics is: dU(Q,R)dt=( UQ )RdQdt+( UR )QdRdt, where t and -( UR )Q / ( UR )Q ( UQ ) . - ( UQ )R are time and measure of mutual transformation of forms of energy, correspondingly. General conclusion: standard thermodynamics is incorrect.

  1. Rethinking logic logic in relation to mathematics, evolution, and method

    CERN Document Server

    Cellucci, Carlo

    2014-01-01

    This book examines the limitations of mathematical logic and proposes a new approach intended to overcome them. Formulates new rules of discovery, such as induction, analogy, generalization, specialization, metaphor, metonymy, definition and diagrams.

  2. METHOD OF GREEN FUNCTIONS IN MATHEMATICAL MODELLING FOR TWO-POINT BOUNDARY-VALUE PROBLEMS

    Directory of Open Access Journals (Sweden)

    E. V. Dikareva

    2015-01-01

    Full Text Available Summary. In many applied problems of control, optimization, system theory, theoretical and construction mechanics, for problems with strings and nods structures, oscillation theory, theory of elasticity and plasticity, mechanical problems connected with fracture dynamics and shock waves, the main instrument for study these problems is a theory of high order ordinary differential equations. This methodology is also applied for studying mathematical models in graph theory with different partitioning based on differential equations. Such equations are used for theoretical foundation of mathematical models but also for constructing numerical methods and computer algorithms. These models are studied with use of Green function method. In the paper first necessary theoretical information is included on Green function method for multi point boundary-value problems. The main equation is discussed, notions of multi-point boundary conditions, boundary functionals, degenerate and non-degenerate problems, fundamental matrix of solutions are introduced. In the main part the problem to study is formulated in terms of shocks and deformations in boundary conditions. After that the main results are formulated. In theorem 1 conditions for existence and uniqueness of solutions are proved. In theorem 2 conditions are proved for strict positivity and equal measureness for a pair of solutions. In theorem 3 existence and estimates are proved for the least eigenvalue, spectral properties and positivity of eigenfunctions. In theorem 4 the weighted positivity is proved for the Green function. Some possible applications are considered for a signal theory and transmutation operators.

  3. A Spreadsheet-Based, Matrix Formulation Linear Programming Lesson

    DEFF Research Database (Denmark)

    Harrod, Steven

    2009-01-01

    The article focuses on the spreadsheet-based, matrix formulation linear programming lesson. According to the article, it makes a higher level of theoretical mathematics approachable by a wide spectrum of students wherein many may not be decision sciences or quantitative methods majors. Moreover...

  4. The mathematics of superoscillations

    CERN Document Server

    Aharonov, Yakir; Sabadini, Irene; Tollaksen, J

    2017-01-01

    In the past 50 years, quantum physicists have discovered, and experimentally demonstrated, a phenomenon which they termed superoscillations. Aharonov and his collaborators showed that superoscillations naturally arise when dealing with weak values, a notion that provides a fundamentally different way to regard measurements in quantum physics. From a mathematical point of view, superoscillating functions are a superposition of small Fourier components with a bounded Fourier spectrum, which result, when appropriately summed, in a shift that can be arbitrarily large, and well outside the spectrum. The purpose of this work is twofold: on one hand the authors provide a self-contained survey of the existing literature, in order to offer a systematic mathematical approach to superoscillations; on the other hand, they obtain some new and unexpected results, by showing that superoscillating sequences can be seen of as solutions to a large class of convolution equations and can therefore be treated within the theory of...

  5. Understanding engineering mathematics

    CERN Document Server

    Cox, Bill

    2001-01-01

    * Unique interactive style enables students to diagnose their strengths and weaknesses and focus their efforts where needed* Ideal for self-study and tutorial work, building from an initially supportive approach to the development of independent learning skills * Free website includes solutions to all exercises, additional topics and applications, guide to learning mathematics, and practice materialStudents today enter engineering courses with a wide range of mathematical skills, due to the many different pre-university qualifications studied. Bill Cox''s aim is for students to gain a thorough understanding of the maths they are studying, by first strengthening their background in the essentials of each topic. His approach allows a unique self-paced study style, in which students Review their strengths and weaknesses through self-administered diagnostic tests, then focus on Revision where they need it, to finally Reinforce the skills required.The book is structured around a highly successful ''transition'' ma...

  6. Radiation treatment of combustion gases: formulation and test of a reaction model

    International Nuclear Information System (INIS)

    Busi, F.; D'Angelantonio, M.; Mulazzani, Q.G.; Raffaelli, V.; Tubertini, O.

    1985-01-01

    A generalized kinetic mechanism for radiation induced oxidation of nitrogen oxides from exhaust gases in the absence of sulfur dioxide is formulated. The responses obtained by the mathematical simulation are in good agreement with reported experimental results. (author)

  7. Understanding in mathematics

    CERN Document Server

    Sierpinska, Anna

    1994-01-01

    The concept of understanding in mathematics with regard to mathematics education is considered in this volume, the main problem for mathematics teachers being how to facilitate their students'' understanding of the mathematics being taught.

  8. Mathematical epidemiology

    CERN Document Server

    Driessche, Pauline; Wu, Jianhong

    2008-01-01

    Based on lecture notes of two summer schools with a mixed audience from mathematical sciences, epidemiology and public health, this volume offers a comprehensive introduction to basic ideas and techniques in modeling infectious diseases, for the comparison of strategies to plan for an anticipated epidemic or pandemic, and to deal with a disease outbreak in real time. It covers detailed case studies for diseases including pandemic influenza, West Nile virus, and childhood diseases. Models for other diseases including Severe Acute Respiratory Syndrome, fox rabies, and sexually transmitted infections are included as applications. Its chapters are coherent and complementary independent units. In order to accustom students to look at the current literature and to experience different perspectives, no attempt has been made to achieve united writing style or unified notation. Notes on some mathematical background (calculus, matrix algebra, differential equations, and probability) have been prepared and may be downlo...

  9. An integer programming formulation of the parsimonious loss of heterozygosity problem.

    Science.gov (United States)

    Catanzaro, Daniele; Labbé, Martine; Halldórsson, Bjarni V

    2013-01-01

    A loss of heterozygosity (LOH) event occurs when, by the laws of Mendelian inheritance, an individual should be heterozygote at a given site but, due to a deletion polymorphism, is not. Deletions play an important role in human disease and their detection could provide fundamental insights for the development of new diagnostics and treatments. In this paper, we investigate the parsimonious loss of heterozygosity problem (PLOHP), i.e., the problem of partitioning suspected polymorphisms from a set of individuals into a minimum number of deletion areas. Specifically, we generalize Halldórsson et al.'s work by providing a more general formulation of the PLOHP and by showing how one can incorporate different recombination rates and prior knowledge about the locations of deletions. Moreover, we show that the PLOHP can be formulated as a specific version of the clique partition problem in a particular class of graphs called undirected catch-point interval graphs and we prove its general $({\\cal NP})$-hardness. Finally, we provide a state-of-the-art integer programming (IP) formulation and strengthening valid inequalities to exactly solve real instances of the PLOHP containing up to 9,000 individuals and 3,000 SNPs. Our results give perspectives on the mathematics of the PLOHP and suggest new directions on the development of future efficient exact solution approaches.

  10. Dilemma in Teaching Mathematics

    Science.gov (United States)

    Md Kamaruddin, Nafisah Kamariah; Md Amin, Zulkarnain

    2012-01-01

    The challenge in mathematics education is finding the best way to teach mathematics. When students learn the reasoning and proving in mathematics, they will be proficient in mathematics. Students must know mathematics before they can apply it. Symbolism and logic is the key to both the learning of mathematics and its effective application to…

  11. The mathematical model of dynamic stabilization system for autonomous car

    Science.gov (United States)

    Saikin, A. M.; Buznikov, S. E.; Shabanov, N. S.; Elkin, D. S.

    2018-02-01

    Leading foreign companies and domestic enterprises carry out extensive researches and developments in the field of control systems for autonomous cars and in the field of improving driver assistance systems. The search for technical solutions, as a rule, is based on heuristic methods and does not always lead to satisfactory results. The purpose of this research is to formalize the road safety problem in the terms of modern control theory, to construct the adequate mathematical model for solving it, including the choice of software and hardware environment. For automatic control of the object, it is necessary to solve the problem of dynamic stabilization in the most complete formulation. The solution quality of the problem on a finite time interval is estimated by the value of the quadratic functional. Car speed, turn angle and additional yaw rate (during car drift or skidding) measurements are performed programmatically by the original virtual sensors. The limit speeds at which drift, skidding or rollover begins are calculated programmatically taking into account the friction coefficient identified in motion. The analysis of the results confirms both the adequacy of the mathematical models and the algorithms and the possibility of implementing the system in the minimal technical configuration.

  12. The Construction of Mathematical Literacy Problems for Geometry

    Science.gov (United States)

    Malasari, P. N.; Herman, T.; Jupri, A.

    2017-09-01

    The students of junior high school should have mathematical literacy ability to formulate, apply, and interpret mathematics in problem solving of daily life. Teaching these students are not enough by giving them ordinary mathematics problems. Teaching activities for these students brings consequence for teacher to construct mathematical literacy problems. Therefore, the aim of this study is to construct mathematical literacy problems to assess mathematical literacy ability. The steps of this study that consists of analysing, designing, theoretical validation, revising, limited testing to students, and evaluating. The data was collected with written test to 38 students of grade IX at one of state junior high school. Mathematical literacy problems consist of three essays with three indicators and three levels at polyhedron subject. The Indicators are formulating and employing mathematics. The results show that: (1) mathematical literacy problems which are constructed have been valid and practical, (2) mathematical literacy problems have good distinguishing characteristics and adequate distinguishing characteristics, (3) difficulty levels of problems are easy and moderate. The final conclusion is mathematical literacy problems which are constructed can be used to assess mathematical literacy ability.

  13. Analytical solutions for benchmarking cold regions subsurface water flow and energy transport models: one-dimensional soil thaw with conduction and advection

    Science.gov (United States)

    Kurylyk, Barret L.; McKenzie, Jeffrey M; MacQuarrie, Kerry T. B.; Voss, Clifford I.

    2014-01-01

    Numerous cold regions water flow and energy transport models have emerged in recent years. Dissimilarities often exist in their mathematical formulations and/or numerical solution techniques, but few analytical solutions exist for benchmarking flow and energy transport models that include pore water phase change. This paper presents a detailed derivation of the Lunardini solution, an approximate analytical solution for predicting soil thawing subject to conduction, advection, and phase change. Fifteen thawing scenarios are examined by considering differences in porosity, surface temperature, Darcy velocity, and initial temperature. The accuracy of the Lunardini solution is shown to be proportional to the Stefan number. The analytical solution results obtained for soil thawing scenarios with water flow and advection are compared to those obtained from the finite element model SUTRA. Three problems, two involving the Lunardini solution and one involving the classic Neumann solution, are recommended as standard benchmarks for future model development and testing.

  14. Formulating viscous hydrodynamics for large velocity gradients

    International Nuclear Information System (INIS)

    Pratt, Scott

    2008-01-01

    Viscous corrections to relativistic hydrodynamics, which are usually formulated for small velocity gradients, have recently been extended from Navier-Stokes formulations to a class of treatments based on Israel-Stewart equations. Israel-Stewart treatments, which treat the spatial components of the stress-energy tensor τ ij as dynamical objects, introduce new parameters, such as the relaxation times describing nonequilibrium behavior of the elements τ ij . By considering linear response theory and entropy constraints, we show how the additional parameters are related to fluctuations of τ ij . Furthermore, the Israel-Stewart parameters are analyzed for their ability to provide stable and physical solutions for sound waves. Finally, it is shown how these parameters, which are naturally described by correlation functions in real time, might be constrained by lattice calculations, which are based on path-integral formulations in imaginary time

  15. XI. The Relation between Mathematics and Physic

    Indian Academy of Sciences (India)

    of mathematics in this scheme is to represent the laws of motion by equations, and to obtain solutions ... What makes the theory of relativity so acceptable to physicists in spite of its going against the principle of simplicity is its great mathematical peauty. This is a quality ... The difference may be expressed concisely, but in·a ...

  16. Discrete Mathematics Course Supported by CAS MATHEMATICA

    Science.gov (United States)

    Ivanov, O. A.; Ivanova, V. V.; Saltan, A. A.

    2017-01-01

    In this paper, we discuss examples of assignments for a course in discrete mathematics for undergraduate students majoring in business informatics. We consider several problems with computer-based solutions and discuss general strategies for using computers in teaching mathematics and its applications. In order to evaluate the effectiveness of our…

  17. Mathematical Model of a Lithium/Thionyl Chloride Battery

    Energy Technology Data Exchange (ETDEWEB)

    Jain, M.; Jungst, R.G.; Nagasubramanian, G.; Weidner, J.W.

    1998-11-24

    A mathematical model of a spirally wound lithium/thionyl chloride primary battery has been developed ~d used for parameter estimation and design studies. The model formulation is based on the fimdarnental Consemation laws using porous electrode theory and concentrated solution theory. The model is used to estimate the difision coefficient and the kinetic parameters for the reactions at the anode and the cathode as a function of temperature. These parameters are obtained by fitting the simulated capacity and average cell voltage to experimental data over a wide range of temperatures (-55 to 49"C) and discharge loads (10 to 250 ohms). The experiments were performed on D-sized, cathode-limited, spirally wound lithium/thionyl chloride cells. The model is also used to study the effkct of cathode thickness on the cell capacity as a finction of temperature, and it was found that the optimum thickness for the cathode- limited design is temperature and load dependent.

  18. Determination of flexibility factors in curved pipes with end restraints using a semi-analytic formulation

    International Nuclear Information System (INIS)

    Fonseca, E.M.M.; Melo, F.J.M.Q. de; Oliveira, C.A.M.

    2002-01-01

    Piping systems are structural sets used in the chemical industry, conventional or nuclear power plants and fluid transport in general-purpose process equipment. They include curved elements built as parts of toroidal thin-walled structures. The mechanical behaviour of such structural assemblies is of leading importance for satisfactory performance and safety standards of the installations. This paper presents a semi-analytic formulation based on Fourier trigonometric series for solving the pure bending problem in curved pipes. A pipe element is considered as a part of a toroidal shell. A displacement formulation pipe element was developed with Fourier series. The solution of this problem is solved from a system of differential equations using mathematical software. To build-up the solution, a simple but efficient deformation model, from a semi-membrane behaviour, was followed here, given the geometry and thin shell assumption. The flexibility factors are compared with the ASME code for some elbow dimensions adopted from ISO 1127. The stress field distribution was also calculated

  19. Teaching Mathematical Modeling in Mathematics Education

    Science.gov (United States)

    Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant

    2016-01-01

    Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…

  20. Doing Mathematics with Purpose: Mathematical Text Types

    Science.gov (United States)

    Dostal, Hannah M.; Robinson, Richard

    2018-01-01

    Mathematical literacy includes learning to read and write different types of mathematical texts as part of purposeful mathematical meaning making. Thus in this article, we describe how learning to read and write mathematical texts (proof text, algorithmic text, algebraic/symbolic text, and visual text) supports the development of students'…

  1. Teachers' Mathematics as Mathematics-at-Work

    Science.gov (United States)

    Bednarz, Nadine; Proulx, Jérôme

    2017-01-01

    Through recognising mathematics teachers as professionals who use mathematics in their workplace, this article traces a parallel between the mathematics enacted by teachers in their practice and the mathematics used in workplaces found in studies of professionals (e.g. nurses, engineers, bankers). This parallel is developed through the five…

  2. Relationship between the generalized equivalent uniform dose formulation and the Poisson statistics-based tumor control probability model

    International Nuclear Information System (INIS)

    Zhou Sumin; Das, Shiva; Wang Zhiheng; Marks, Lawrence B.

    2004-01-01

    The generalized equivalent uniform dose (GEUD) model uses a power-law formalism, where the outcome is related to the dose via a power law. We herein investigate the mathematical compatibility between this GEUD model and the Poisson statistics based tumor control probability (TCP) model. The GEUD and TCP formulations are combined and subjected to a compatibility constraint equation. This compatibility constraint equates tumor control probability from the original heterogeneous target dose distribution to that from the homogeneous dose from the GEUD formalism. It is shown that this constraint equation possesses a unique, analytical closed-form solution which relates radiation dose to the tumor cell survival fraction. It is further demonstrated that, when there is no positive threshold or finite critical dose in the tumor response to radiation, this relationship is not bounded within the realistic cell survival limits of 0%-100%. Thus, the GEUD and TCP formalisms are, in general, mathematically inconsistent. However, when a threshold dose or finite critical dose exists in the tumor response to radiation, there is a unique mathematical solution for the tumor cell survival fraction that allows the GEUD and TCP formalisms to coexist, provided that all portions of the tumor are confined within certain specific dose ranges

  3. Mathematical and numerical methods for partial differential equations applications for engineering sciences

    CERN Document Server

    Chaskalovic, Joël

    2014-01-01

    This self-tutorial offers a concise yet thorough introduction into the mathematical analysis of approximation methods for partial differential equation. A particular emphasis is put on finite element methods. The unique approach first summarizes and outlines the finite-element mathematics in general and then, in the second and major part, formulates problem examples that clearly demonstrate the techniques of functional analysis via numerous and diverse exercises. The solutions of the problems are given directly afterwards. Using this approach, the author motivates and encourages the reader to actively acquire the knowledge of finite- element methods instead of passively absorbing the material, as in most standard textbooks. This English edition is based on the Finite Element Methods for Engineering Sciences by Joel Chaskalovic

  4. Learning to Calculate and Learning Mathematics.

    Science.gov (United States)

    Fearnley-Sander, Desmond

    1980-01-01

    A calculator solution of a simple computational problem is discussed with emphasis on its ramifications for the understanding of some fundamental theorems of pure mathematics and techniques of computing. (Author/MK)

  5. A mathematical model for iodine kinetics

    International Nuclear Information System (INIS)

    Silva, E.A.T. da.

    1976-01-01

    A mathematical model for the iodine kinetics in thyroid is presented followed by its analytical solution. An eletroanalogical model is also developed for a simplified stage and another is proposed for the main case [pt

  6. Foundations and fundamental concepts of mathematics

    CERN Document Server

    Eves, Howard

    1997-01-01

    Third edition of popular undergraduate-level text offers historic overview, readable treatment of mathematics before Euclid, Euclid's Elements, non-Euclidean geometry, algebraic structure, formal axiomatics, sets, more. Problems, some with solutions. Bibliography.

  7. Hamiltonian formulation of reduced magnetohydrodynamics

    International Nuclear Information System (INIS)

    Morrison, P.J.; Hazeltine, R.D.

    1983-07-01

    Reduced magnetohydrodynamics (RMHD) has become a principal tool for understanding nonlinear processes, including disruptions, in tokamak plasmas. Although analytical studies of RMHD turbulence have been useful, the model's impressive ability to simulate tokamak fluid behavior has been revealed primarily by numerical solution. The present work describes a new analytical approach, not restricted to turbulent regimes, based on Hamiltonian field theory. It is shown that the nonlinear (ideal) RMHD system, in both its high-beta and low-beta versions, can be expressed in Hanmiltonian form. Thus a Poisson bracket, [ , ], is constructed such that each RMHD field quantitity, xi/sub i/, evolves according to xi/sub i/ = [xi/sub i/,H], where H is the total field energy. The new formulation makes RMHD accessible to the methodology of Hamiltonian mechanics; it has lead, in particular, to the recognition of new RMHD invariants and even exact, nonlinear RMHD solutions. A canonical version of the Poisson bracket, which requires the introduction of additional fields, leads to a nonlinear variational principle for time-dependent RMHD

  8. Discovering Mathematics with Magma Reducing the Abstract to the Concrete

    CERN Document Server

    Bosma, Wieb

    2006-01-01

    With a design based on the ontology and semantics of algebra, Magma enables users to rapidly formulate and perform calculations in the more abstract parts of mathematics. This book introduces the role Magma plays in advanced mathematical research through 14 case studies which, in most cases, describe computations underpinning theoretical results.

  9. PROBLEMS OF MATHEMATICAL MODELING OF THE ENTERPRISES ORGANIZATIONAL STRUCTURE

    Directory of Open Access Journals (Sweden)

    N. V. Andrianov

    2006-01-01

    Full Text Available The analysis of the mathematical models which can be used at optimization of the control system of the enterprise organizational structure is presented. The new approach to the mathematical modeling of the enterprise organizational structure, based on using of temporary characteristics of the control blocks working, is formulated

  10. On Double-Entry Bookkeeping: The Mathematical Treatment

    Science.gov (United States)

    Ellerman, David

    2014-01-01

    Double-entry bookkeeping (DEB) implicitly uses a specific mathematical construction, the group of differences using pairs of unsigned numbers ("T-accounts"). That construction was only formulated abstractly in mathematics in the nineteenth century, even though DEB had been used in the business world for over five centuries. Yet the…

  11. Critical analysis of the policy practice of mathematics education in ...

    African Journals Online (AJOL)

    Ensuring a smooth mathematics education programme requires the formulation and implementation of appropriate instructional policies. This study is a survey of some practices of the instructional policies and their influence on mathematics education. Completed Basic School Annual Census (CBSAC) forms and ...

  12. Optimal timing of joint replacement using mathematical programming and stochastic programming models.

    Science.gov (United States)

    Keren, Baruch; Pliskin, Joseph S

    2011-12-01

    The optimal timing for performing radical medical procedures as joint (e.g., hip) replacement must be seriously considered. In this paper we show that under deterministic assumptions the optimal timing for joint replacement is a solution of a mathematical programming problem, and under stochastic assumptions the optimal timing can be formulated as a stochastic programming problem. We formulate deterministic and stochastic models that can serve as decision support tools. The results show that the benefit from joint replacement surgery is heavily dependent on timing. Moreover, for a special case where the patient's remaining life is normally distributed along with a normally distributed survival of the new joint, the expected benefit function from surgery is completely solved. This enables practitioners to draw the expected benefit graph, to find the optimal timing, to evaluate the benefit for each patient, to set priorities among patients and to decide if joint replacement should be performed and when.

  13. Mathematical intuitionism

    CERN Document Server

    Dragalin, A G

    1988-01-01

    This monograph is intended to present the most important methods of proof theory in intuitionistic logic, assuming the reader to have mastered an introductory course in mathematical logic. The book starts with purely syntactical methods based on Gentzen's cut-elimination theorem, followed by intuitionistic arithmetic where Kleene's realizability method plays a central role. The author then studies algebraic models and completeness theorems for them. After giving a survey on the principles of intuitionistic analysis, the last part of the book presents the cut-elimination theorem in intuitionistic simple theory of types with an extensionality rule.

  14. Teachers' knowledge about language in mathematics professional development courses : From an intended curriculum to a curriculum in action

    NARCIS (Netherlands)

    Maaike Hajer; Eva Norén

    2017-01-01

    Explicit language objectives are included in the Swedish national curriculum for mathematics. The curriculum states that students should be given opportunities to develop the ability to formulate problems, use and analyse mathematical concepts and relationships between concepts, show and follow

  15. A Framework of Mathematics Inductive Reasoning

    Science.gov (United States)

    Christou, Constantinos; Papageorgiou, Eleni

    2007-01-01

    Based on a synthesis of the literature in inductive reasoning, a framework for prescribing and assessing mathematics inductive reasoning of primary school students was formulated and validated. The major constructs incorporated in this framework were students' cognitive abilities of finding similarities and/or dissimilarities among attributes and…

  16. Formulation of lubricating grease using Beeswax thickener

    Science.gov (United States)

    Suhaila, N.; Japar, A.; Aizudin, M.; Aziz, A.; Najib Razali, Mohd

    2018-04-01

    The issues on environmental pollution has brought the industries to seek the alternative green solutions for lubricating grease formulation. The significant challenges in producing modified grease are in which considering the chosen thickener as one of the environmental friendly material. The main purposes of the current research were to formulate lubricant grease using different types of base oils and to study the effect of thickener on the formulated lubricant grease. Used oil and motor oil were used as the base oils for the grease preparation. Beeswax and Damar were used as thickener and additive. The grease is tested based on its consistency, stability and oil bleeding. The prepared greases achieved grease consistency of grade 2 and 3 except for grease with unfiltered used oil. Grease formulated with used oil and synthetic oil tend to harden and loss its lubricating ability under high temperature compared to motor oil’ grease. Grease modification using environmental friendly thickener were successfully formulated but it is considered as a low temperature grease as the beeswax have low melting point of 62°C-65°C.

  17. Mathematical foundations of the Burrus techniques for spectral unfolding

    International Nuclear Information System (INIS)

    Rust, B.W.

    1976-01-01

    This paper treats the numerical solution of the first kind Fredholm integral equation in the case where the normal nonuniqueness and ill-conditioning problems are further aggravated by the presence of stochastic measuring errors. The basic ideas, due originally to Walter R. Burrus, of the techniques described are to seek statistical confidence interval estimates for the solution and to make the intervals as small as possible by using physically motivated a priori information to constrain the size of the set of permissible solutions. When these constraints are added to the classical linear regression model, the resulting interval estimation problems can be formulated in terms of parametric quadratic programming, but the solution of such problems is difficult and costly. Two more practicable methods have been developed which give suboptimal bounds, i.e., intervals which are somewhat wider than the optimally narrow ones that would be obtained from the quadratic programming procedure. One method uses various linear programming approximations while the other uses a constrained least squares procedure reminiscent of the Phillips-Twomey-Tikonov smoothing and regularizing techniques. Both methods are illustrated by mathematical and physically motivated examples

  18. Mathematical techniques for biology and medicine

    CERN Document Server

    Simon, William

    1986-01-01

    Suitable for both graduate and undergraduate courses, this text recalls basic concepts of calculus and shows how problems can be formulated in terms of differential equations. Fully worked-out solutions to selected problems. Fourth edition.

  19. Meeting in mathematics

    DEFF Research Database (Denmark)

    Mogensen, Arne; Georgiev, Vladimir; Ulovec, Andreas

    To encourage many more young people to appreciate the real nature and spirit of mathematics and possibly to be enrolled in mathematics study it is important to involve them in doing mathematics (not just learning about mathematics). This goal could be achieved if mathematics teachers are prepared...... to identify and work with mathematically gifted students (without loosing the rest). The book offers chapters on gifted students, mathematical competences and other issues....

  20. Formulation and Evaluation of Bioadhesive Cyproheptadine Tablets ...

    African Journals Online (AJOL)

    Results: The shear stress of 3 % solution of HPMC was greater than that of an equivalent concentration of Carbopol 934P. The values of K, n, R2 and detachment force for the optimized formulation (F0) were 0.269, 0.696, 0.964 and 0.066 Newton (N), respectively, and showed good correlation with the predicted values, thus ...

  1. Path Integral Formulation of Anomalous Diffusion Processes

    OpenAIRE

    Friedrich, Rudolf; Eule, Stephan

    2011-01-01

    We present the path integral formulation of a broad class of generalized diffusion processes. Employing the path integral we derive exact expressions for the path probability densities and joint probability distributions for the class of processes under consideration. We show that Continuous Time Random Walks (CTRWs) are included in our framework. A closed expression for the path probability distribution of CTRWs is found in terms of their waiting time distribution as the solution of a Dyson ...

  2. Mathematical aspects of finite element methods for incompressible viscous flows

    Science.gov (United States)

    Gunzburger, M. D.

    1986-01-01

    Mathematical aspects of finite element methods are surveyed for incompressible viscous flows, concentrating on the steady primitive variable formulation. The discretization of a weak formulation of the Navier-Stokes equations are addressed, then the stability condition is considered, the satisfaction of which insures the stability of the approximation. Specific choices of finite element spaces for the velocity and pressure are then discussed. Finally, the connection between different weak formulations and a variety of boundary conditions is explored.

  3. Element free Galerkin formulation of composite beam with longitudinal slip

    Energy Technology Data Exchange (ETDEWEB)

    Ahmad, Dzulkarnain; Mokhtaram, Mokhtazul Haizad [Department of Civil Engineering, Universiti Selangor, Bestari Jaya, Selangor (Malaysia); Badli, Mohd Iqbal; Yassin, Airil Y. Mohd [Faculty of Civil Engineering, Universiti Teknologi Malaysia, Skudai, Johor (Malaysia)

    2015-05-15

    Behaviour between two materials in composite beam is assumed partially interact when longitudinal slip at its interfacial surfaces is considered. Commonly analysed by the mesh-based formulation, this study used meshless formulation known as Element Free Galerkin (EFG) method in the beam partial interaction analysis, numerically. As meshless formulation implies that the problem domain is discretised only by nodes, the EFG method is based on Moving Least Square (MLS) approach for shape functions formulation with its weak form is developed using variational method. The essential boundary conditions are enforced by Langrange multipliers. The proposed EFG formulation gives comparable results, after been verified by analytical solution, thus signify its application in partial interaction problems. Based on numerical test results, the Cubic Spline and Quartic Spline weight functions yield better accuracy for the EFG formulation, compares to other proposed weight functions.

  4. Systematic Equation Formulation

    DEFF Research Database (Denmark)

    Lindberg, Erik

    2007-01-01

    A tutorial giving a very simple introduction to the set-up of the equations used as a model for an electrical/electronic circuit. The aim is to find a method which is as simple and general as possible with respect to implementation in a computer program. The “Modified Nodal Approach”, MNA, and th......, and the “Controlled Source Approach”, CSA, for systematic equation formulation are investigated. It is suggested that the kernel of the P Spice program based on MNA is reprogrammed....

  5. A mathematical primer on quantum mechanics

    CERN Document Server

    Teta, Alessandro

    2018-01-01

    This book offers a rigorous yet elementary approach to quantum mechanics that will meet the needs of Master’s-level Mathematics students and is equally suitable for Physics students who are interested in gaining a deeper understanding of the mathematical structure of the theory. Throughout the coverage, which is limited to single-particle quantum mechanics, the focus is on formulating theory and developing applications in a mathematically precise manner. Following a review of selected key concepts in classical physics and the historical background, the basic elements of the theory of operators in Hilbert spaces are presented and used to formulate the rules of quantum mechanics. The discussion then turns to free particles, harmonic oscillators, delta potential, and hydrogen atoms, providing rigorous proofs of the corresponding dynamical properties. Starting from an analysis of these applications, readers are subsequently introduced to more advanced topics such as the classical limit, scattering theory, and s...

  6. Mathematics, the Computer, and the Impact on Mathematics Education.

    Science.gov (United States)

    Tooke, D. James

    2001-01-01

    Discusses the connection between mathematics and the computer; mathematics curriculum; mathematics instruction, including teachers learning to use computers; and the impact of the computer on learning mathematics. (LRW)

  7. A new high accuracy non-polynomial tension spline method for the solution of one dimensional wave equation in polar co-ordinates

    Directory of Open Access Journals (Sweden)

    Venu Gopal

    2014-07-01

    Full Text Available In this paper, we propose a new three-level implicit nine point compact finite difference formulation of O(k2 + h4 based on non-polynomial tension spline approximation in r-direction and finite difference approximation in t-direction for the numerical solution of one dimensional wave equation in polar co-ordinates. We describe the mathematical formulation procedure in details and also discuss the stability of the method. Numerical results are provided to justify the usefulness of the proposed method.

  8. Drug delivery and formulations.

    Science.gov (United States)

    Breitkreutz, Jörg; Boos, Joachim

    2011-01-01

    Paediatric drug delivery is a major challenge in drug development. Because of the heterogeneous nature of the patient group, ranging from newborns to adolescents, there is a need to use appropriate excipients, drug dosage forms and delivery devices for different age groups. So far, there is a lack of suitable and safe drug formulations for children, especially for the very young and seriously ill patients. The new EU legislation will enforce paediatric clinical trials and drug development. Current advances in paediatric drug delivery include interesting new concepts such as fast-dissolving drug formulations, including orodispersible tablets and oral thin strips (buccal wafers), and multiparticulate dosage forms based on mini-tabletting or pelletization technologies. Parenteral administration is likely to remain the first choice for children in the neonatal period and for emergency cases. Alternative routes of administration include transdermal, pulmonary and nasal drug delivery systems. A few products are already available on the market, but others still need further investigations and clinical proof of concept.

  9. Contemplating Symbolic Literacy of First Year Mathematics Students

    Science.gov (United States)

    Bardini, Caroline; Pierce, Robyn; Vincent, Jill

    2015-01-01

    Analysis of mathematical notations must consider both syntactical aspects of symbols and the underpinning mathematical concept(s) conveyed. We argue that the construct of "syntax template" provides a theoretical framework to analyse undergraduate mathematics students' written solutions, where we have identified several types of…

  10. Motivation and Achievement of Middle School Mathematics Students

    Science.gov (United States)

    Herges, Rebecca M.; Duffield, Stacy; Martin, William; Wageman, Justin

    2017-01-01

    Mathematics achievement among K-12 students has been a long-standing concern in schools across the United States. A possible solution to this mathematics achievement problem is student motivation. A survey was administered to 65 mathematics students at a Midwestern middle school to determine their beliefs and attitudes related to motivation and…

  11. The mathematics of various entertaining subjects

    CERN Document Server

    Rosenhouse, Jason

    Volume 1 : The history of mathematics is filled with major breakthroughs resulting from solutions to recreational problems. Problems of interest to gamblers led to the modern theory of probability, for example, and surreal numbers were inspired by the game of Go. Yet even with such groundbreaking findings and a wealth of popular-level books exploring puzzles and brainteasers, research in recreational mathematics has often been neglected. The Mathematics of Various Entertaining Subjects brings together authors from a variety of specialties to present fascinating problems and solutions in recreational mathematics. Contributors to the book show how sophisticated mathematics can help construct mazes that look like famous people, how the analysis of crossword puzzles has much in common with understanding epidemics, and how the theory of electrical circuits is useful in understanding the classic Towers of Hanoi puzzle. The card game SET is related to the theory of error-correcting codes, and simple tic-tac-toe tak...

  12. Authenticity of Mathematical Modeling

    Science.gov (United States)

    Tran, Dung; Dougherty, Barbara J.

    2014-01-01

    Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…

  13. A course of higher mathematics

    CERN Document Server

    Smirnov, Vladimir Ivanovich

    1964-01-01

    A Course of Higher Mathematics, Volume II: Advanced Calculus covers the theory of functions of real variable in advanced calculus. This volume is divided into seven chapters and begins with a full discussion of the solution of ordinary differential equations with many applications to the treatment of physical problems. This topic is followed by an account of the properties of multiple integrals and of line integrals, with a valuable section on the theory of measurable sets and of multiple integrals. The subsequent chapters deal with the mathematics necessary to the examination of problems in

  14. DEVELOPMENT OF MAPLE IN TRAINING HIGHER MATHEMATICS

    Directory of Open Access Journals (Sweden)

    Volodymyr M. Mykhalevych

    2011-03-01

    Full Text Available The relevance of the material presented in this paper due to the need to develop and implement new information technologies in teaching higher mathematics with the use of systems of symbolic mathematics. Brief analysis of the Maple and Mathematica is given. The basic results of authors on working out of a training complex on higher mathematics are given. The complex was created in an environment of symbolic mathematics Maple. Procedure simulators, which give the whole process of model solutions of mathematical problems are a major element of the complex. The results of such procedures for typical problems from different sections of higher mathematics in accordance with the program for technical universities are represented. Questions the benefits and methods of using such programs, in particular those related to deficits of licensed copies of Maple was touched.

  15. Solutions Network Formulation Report. Reducing Light Pollution in U.S. Coastal Regions Using the High Sensitivity Cameras on the SAC-C and Aquarius/SAC-D Satellites

    Science.gov (United States)

    Andrews, Jane C.; Knowlton, Kelly

    2007-01-01

    Light pollution has significant adverse biological effects on humans, animals, and plants and has resulted in the loss of our ability to view the stars and planets of the universe. Over half of the U.S. population resides in coastal regions where it is no longer possible to see the stars and planets in the night sky. Forty percent of the entire U.S. population is never exposed to conditions dark enough for their eyes to convert to night vision capabilities. In coastal regions, urban lights shine far out to sea where they are augmented by the output from fishing boat, cruise ship and oil platform floodlights. The proposed candidate solution suggests using HSCs (high sensitivity cameras) onboard the SAC-C and Aquarius/SAC-D satellites to quantitatively evaluate light pollution at high spatial resolution. New products modeled after pre-existing, radiance-calibrated, global nighttime lights products would be integrated into a modified Garstang model where elevation, mountain screening, Rayleigh scattering, Mie scattering by aerosols, and atmospheric extinction along light paths and curvature of the Earth would be taken into account. Because the spatial resolution of the HSCs on SAC-C and the future Aquarius/SAC-D missions is greater than that provided by the DMSP (Defense Meteorological Satellite Program) OLS (Operational Linescan System) or VIIRS (Visible/Infrared Imager/Radiometer Suite), it may be possible to obtain more precise light intensity data for analytical DSSs and the subsequent reduction in coastal light pollution.

  16. Mathematical foundations of event trees

    International Nuclear Information System (INIS)

    Papazoglou, Ioannis A.

    1998-01-01

    A mathematical foundation from first principles of event trees is presented. The main objective of this formulation is to offer a formal basis for developing automated computer assisted construction techniques for event trees. The mathematical theory of event trees is based on the correspondence between the paths of the tree and the elements of the outcome space of a joint event. The concept of a basic cylinder set is introduced to describe joint event outcomes conditional on specific outcomes of basic events or unconditional on the outcome of basic events. The concept of outcome space partition is used to describe the minimum amount of information intended to be preserved by the event tree representation. These concepts form the basis for an algorithm for systematic search for and generation of the most compact (reduced) form of an event tree consistent with the minimum amount of information the tree should preserve. This mathematical foundation allows for the development of techniques for automated generation of event trees corresponding to joint events which are formally described through other types of graphical models. Such a technique has been developed for complex systems described by functional blocks and it is reported elsewhere. On the quantification issue of event trees, a formal definition of a probability space corresponding to the event tree outcomes is provided. Finally, a short discussion is offered on the relationship of the presented mathematical theory with the more general use of event trees in reliability analysis of dynamic systems

  17. Vozy formule 1

    OpenAIRE

    Zbožínek, Adam

    2009-01-01

    Tato práce uvádí základní pravidla a předpoklady pro konstrukci a použití vozů formule 1. Hlavní zaměření je na aerodynamiku, která je nejdůležitější disciplínou v tomto motoristickém sportu, dále je tato práce zaměřena na základní faktory týkající se motoru vozu, kol, nové technologie KERS a provedení volantu. This work shows basic rules and conditions for construction and use of cars formula 1. The main part of this work focus on the aerodynamics which is the most important discipline of...

  18. Assessment of strategy formulation

    DEFF Research Database (Denmark)

    Acur, Nuran; Englyst, Linda

    2006-01-01

    of the success criteria through face-to-face interviews with 46 managers, workshops involving 40 managers, and two in-depth case studies. The success criteria have been slightly modified due to the empirical results, to yield the assessment tool. Findings – The resulting assessment tool integrates three generic...... approaches to strategy assessment, namely the goal-centred, comparative and improvement approaches, as found in the literature. Furthermore, it encompasses three phases of strategy formulation processes: strategic thinking, strategic planning and embedding of strategy. The tool reflects that the different......, but cases and managerial perceptions indicate that the need for accurate and detailed plans might be overrated in the literature, as implementation relies heavily on continuous improvement and empowerment. Concerning embedding, key aspects relate both to the goal-centred and improvement approaches, while...

  19. Teaching mathematics using excel

    OpenAIRE

    Bonello, Mary Rose; Camilleri, Silvana

    2004-01-01

    'Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning.' (Principles and Standards for School Mathematics-NCTM April 2000)

  20. Figures of thought mathematics and mathematical texts

    CERN Document Server

    Reed, David

    2003-01-01

    Examines the ways in which mathematical works can be read as texts, examines their textual strategiesand demonstrates that such readings provide a rich source of philosophical debate regarding mathematics.

  1. Slag-based saltstone formulations

    International Nuclear Information System (INIS)

    Langton, C.A.

    1987-01-01

    Approximately 400 x 10 6 liters of low-level alkaline salt solution will be treated at the Savannah River Plant (SRP) Defense Waste Processing Facility (DWPF) prior to disposal in concrete vaults at SRP. Treatment involves removal of CS + and Sr +2 followed by solidification and stabilization of potential contaminants in saltstone, a hydrated ceramic waste form. Chromium, technetium, and nitrate releases from saltstone can be significantly reduced by substituting hydraulic blast furnace slag for portland cement in the formulation designs. Slag-based mixes are also compatible with Class F fly ash used in saltstone as a functional extender to control heat of hydration and reduce permeability. A monolithic waste form is produced by the hydration of the slag and fly ash. Soluble ion release (NO 3 - ) is controlled by the saltstone microstructure. Chromium and technetium are less leachable from slag mixes compared to cement-based waste forms because these species are chemically reduced to a lower valence state by ferrous iron in the slag and precipitated as relatively insoluble phases, such as CR(OH) 3 and TcO 2 . 5 refs., 4 figs., 4 tabs

  2. Slag-based saltstone formulations

    International Nuclear Information System (INIS)

    Langton, C.A.

    1987-08-01

    Approximately 400 x 10 6 L of low-level alkaline salt solution will be treated at the Savannah River Plant (SRP) Defense Waste Processing Facility (DWPF) prior to disposal in concrete vaults at SRP. Treatment involves removal of Cs + and Sr +2 , followed by solidification and stabilization of potential contaminants in saltstone, a hydrated ceramic wasteform. Chromium, technetium, and nitrate releases from saltstone can be significantly reduced by substituting hydraulic blast furnace slag for portland cement in the formulation designs. Slag-based mixes are also compatible with the Class F flyash used in saltstone as a functional extender to control heat of hydration and reduce permeability. (Class F flyash is also locally available at SRP.) A monolithic wasteform is produced by the hydration of the slag and flyash. Soluble ion release (NO 3- ) is controlled by the saltstone microstructure. Chromium and technetium are less leachable from slag mixes because these species are chemically reduced to a lower valence state by ferrous iron in the slag and are precipitated as relatively insoluble phases, such as Cr(OH) 3 and TcO 2 . 3 refs., 3 figs., 2 tabs

  3. Mathematical Modelling Approach in Mathematics Education

    Science.gov (United States)

    Arseven, Ayla

    2015-01-01

    The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…

  4. Discrete Mathematics and the Secondary Mathematics Curriculum.

    Science.gov (United States)

    Dossey, John

    Discrete mathematics, the mathematics of decision making for finite settings, is a topic of great interest in mathematics education at all levels. Attention is being focused on resolving the diversity of opinion concerning the exact nature of the subject, what content the curriculum should contain, who should study that material, and how that…

  5. Introducing philosophy of mathematics

    CERN Document Server

    Friend, Michele

    2014-01-01

    What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual acc

  6. Quantum Gravity Mathematical Models and Experimental Bounds

    CERN Document Server

    Fauser, Bertfried; Zeidler, Eberhard

    2007-01-01

    The construction of a quantum theory of gravity is the most fundamental challenge confronting contemporary theoretical physics. The different physical ideas which evolved while developing a theory of quantum gravity require highly advanced mathematical methods. This book presents different mathematical approaches to formulate a theory of quantum gravity. It represents a carefully selected cross-section of lively discussions about the issue of quantum gravity which took place at the second workshop "Mathematical and Physical Aspects of Quantum Gravity" in Blaubeuren, Germany. This collection covers in a unique way aspects of various competing approaches. A unique feature of the book is the presentation of different approaches to quantum gravity making comparison feasible. This feature is supported by an extensive index. The book is mainly addressed to mathematicians and physicists who are interested in questions related to mathematical physics. It allows the reader to obtain a broad and up-to-date overview on ...

  7. Application of UV Imaging in Formulation Development.

    Science.gov (United States)

    Sun, Yu; Østergaard, Jesper

    2017-05-01

    Efficient drug delivery is dependent on the drug substance dissolving in the body fluids, being released from dosage forms and transported to the site of action. A fundamental understanding of the interplay between the physicochemical properties of the active compound and pharmaceutical excipients defining formulation behavior after exposure to the aqueous environments and pharmaceutical performance is critical in pharmaceutical development, manufacturing and quality control of drugs. UV imaging has been explored as a tool for qualitative and quantitative characterization of drug dissolution and release with the characteristic feature of providing real-time visualization of the solution phase drug transport in the vicinity of the formulation. Events occurring during drug dissolution and release, such as polymer swelling, drug precipitation/recrystallization, or solvent-mediated phase transitions related to the structural properties of the drug substance or formulation can be monitored. UV imaging is a non-intrusive and simple-to-operate analytical technique which holds potential for providing a mechanistic foundation for formulation development. This review aims to cover applications of UV imaging in the early and late phase pharmaceutical development with a special focus on the relation between structural properties and performance. Potential areas of future advancement and application are also discussed.

  8. Conductometry of electrolyte solutions

    Science.gov (United States)

    Safonova, Lyubov P.; Kolker, Arkadii M.

    1992-09-01

    A review is given of the theories of the electrical conductance of electrolyte solutions of different ionic strengths and concentrations, and of the models of ion association. An analysis is made of the methods for mathematical processing of experimental conductometric data. An account is provided of various theories describing the dependence of the limiting value of the ionic electrical conductance on the properties of the solute and solvent. The bibliography includes 115 references.

  9. Development of formulation device for periodontal disease.

    Science.gov (United States)

    Sato, Yasuhiko; Oba, Takuma; Watanabe, Norio; Danjo, Kazumi

    2012-01-01

    In addition to providing standard surgical treatment that removes the plaque and infected tissues, medications that can regenerate periodontal tissue are also required in the treatment of periodontal disease. As a form of regenerative medication, various growth factors are expected to be used while treating periodontal disease. A protein-like growth factor is often developed as a lyophilized product with dissolution liquid, considering its instability in the solution state. We have clarified that the formulation for periodontal disease needs to be viscous. When the lyophilized product was dissolved using a sticky solution, various problems were encountered, difficulty in dissolving and air bubbles, for example, and some efforts were needed to prepare the formulation. In this research, to identify the problem of preparing a viscous formulation, a lyophilized product (placebo) and sticky liquid were prepared by using vial and ampoule as the conventional containers. Based on these problems, a prototype administration device was developed, and its functionality was confirmed. As a result, it was suggested that the device with a useful mixing system that could shorten the preparation time was developed.

  10. Quantitative HPLC Analysis of an Analgesic/Caffeine Formulation: Determination of Caffeine

    Science.gov (United States)

    Ferguson, Glenda K.

    1998-04-01

    A modern high performance liquid chromatography (HPLC) laboratory experiment which entails the separation of acetaminophen, aspirin, and caffeine and the quantitative assay of caffeine in commercial mixtures of these compounds has been developed. Our HPLC protocol resolves these compounds in only three minutes with a straightforward chromatographic apparatus which consists of a C-18 column, an isocratic mobile phase, UV detection at 254 nm, and an integrator; an expensive, sophisticated system is not required. The separation is both repeatable and rapid. Moreover, the experiment can be completed in a single three-hour period. The experiment is appropriate for any chemistry student who has completed a minimum of one year of general chemistry and is ideal for an analytical or instrumental analysis course. The experiment detailed herein involves the determination of caffeine in Goody's Extra Strength Headache Powders, a commercially available medication which contains acetaminophen, aspirin, and caffeine as active ingredients. However, the separation scheme is not limited to this brand of medication nor is it limited to caffeine as the analyte. With only minor procedural modifications, students can simultaneously quantitate all of these compounds in a commercial mixture. In our procedure, students prepare a series of four caffeine standard solutions as well as a solution from a pharmaceutical analgesic/caffeine mixture, chromatographically analyze each solution in quadruplicate, and plot relative average caffeine standard peak area versus concentration. From the mathematical relationship that results, the concentration of caffeine in the commercial formulation is obtained. Finally, the absolute standard deviation of the mean concentration is calculated.

  11. How students process equations in solving quantitative synthesis problems? Role of mathematical complexity in students’ mathematical performance

    Directory of Open Access Journals (Sweden)

    Bashirah Ibrahim

    2017-10-01

    Full Text Available We examine students’ mathematical performance on quantitative “synthesis problems” with varying mathematical complexity. Synthesis problems are tasks comprising multiple concepts typically taught in different chapters. Mathematical performance refers to the formulation, combination, and simplification of equations. Generally speaking, formulation and combination of equations require conceptual reasoning; simplification of equations requires manipulation of equations as computational tools. Mathematical complexity is operationally defined by the number and the type of equations to be manipulated concurrently due to the number of unknowns in each equation. We use two types of synthesis problems, namely, sequential and simultaneous tasks. Sequential synthesis tasks require a chronological application of pertinent concepts, and simultaneous synthesis tasks require a concurrent application of the pertinent concepts. A total of 179 physics major students from a second year mechanics course participated in the study. Data were collected from written tasks and individual interviews. Results show that mathematical complexity negatively influences the students’ mathematical performance on both types of synthesis problems. However, for the sequential synthesis tasks, it interferes only with the students’ simplification of equations. For the simultaneous synthesis tasks, mathematical complexity additionally impedes the students’ formulation and combination of equations. Several reasons may explain this difference, including the students’ different approaches to the two types of synthesis problems, cognitive load, and the variation of mathematical complexity within each synthesis type.

  12. Mathematical programs with complementarity constraints in traffic and telecommunications networks.

    Science.gov (United States)

    Ralph, Daniel

    2008-06-13

    Given a suitably parametrized family of equilibrium models and a higher level criterion by which to measure an equilibrium state, mathematical programs with equilibrium constraints (MPECs) provide a framework for improving or optimizing the equilibrium state. An example is toll design in traffic networks, which attempts to reduce total travel time by choosing which arcs to toll and what toll levels to impose. Here, a Wardrop equilibrium describes the traffic response to each toll design. Communication networks also have a deep literature on equilibrium flows that suggest some MPECs. We focus on mathematical programs with complementarity constraints (MPCCs), a subclass of MPECs for which the lower level equilibrium system can be formulated as a complementarity problem and therefore, importantly, as a nonlinear program (NLP). Although MPECs and MPCCs are typically non-convex, which is a consequence of the upper level objective clashing with the users' objectives in the lower level equilibrium program, the last decade of research has paved the way for finding local solutions of MPCCs via standard NLP techniques.

  13. Attractors for equations of mathematical physics

    CERN Document Server

    Chepyzhov, Vladimir V

    2001-01-01

    One of the major problems in the study of evolution equations of mathematical physics is the investigation of the behavior of the solutions to these equations when time is large or tends to infinity. The related important questions concern the stability of solutions or the character of the instability if a solution is unstable. In the last few decades, considerable progress in this area has been achieved in the study of autonomous evolution partial differential equations. For a number of basic evolution equations of mathematical physics, it was shown that the long time behavior of their soluti

  14. Mathematics related anxiety: Mathematics bogeyman or not?

    Directory of Open Access Journals (Sweden)

    Videnović Marina

    2011-01-01

    Full Text Available Data of the PISA 2003 survey indicate high levels of mathematics anxiety of students in Serbia. More than half of our students worry whether they will have difficulties in mathematics class or whether they will earn poor marks. Aims of this study therefore are: examining relationship between math anxiety and achievement at mathematics literacy scale; establishing possible predictors of math anxiety and identification of students' groups in relations to their relationship towards mathematics as a subject. Mathematics anxiety is statistically negatively correlated with school achievement and achievement at mathematics literacy scale. Socio-demographic factors, motivational and cognitive aspects related to learning mathematics, perception of school and classroom climate explain 40% variance of mathematics anxiety. Based on students' relationship towards mathematics they cam be divided into three groups; while dimensions that apart them are uninterested-interested in mathematics and presence-absence of anxiety. The group displaying anxiety scores lowest among the three. Applying qualitative analysis students' and teachers' attitudes on specific issues related to teaching and learning mathematics was examined.

  15. Expansion of thermodynamic model of solute permeation through reverse osmosis membrane

    International Nuclear Information System (INIS)

    Nishimaki, Kenzo; Koyama, Akio

    1994-01-01

    Many studies have been performed on permeation mechanism of solute and solvent in membrane separation process like reverse osmosis or ultrafiltration, and several models of solute/solvent permeation through membrane are proposed. Among these models, Kedem and Katchalsky, based on the theory of thermodynamics of irreversible processes, formulated the one-solute permeation process in their mathematical model, which treats membrane as a black box, not giving consideration to membrane structure and to interaction between membrane material and permeates, viz. solute and solvent. According to this theory, the driving force of solute/solvent permeation through membrane is the difference of their chemical potential between both sides of membrane, and the linear phenomenological equation is applied to describing the relation between driving force and flux of solute/solvent. This equation can be applied to the irreversible process only when the process is almost in equilibrium. This condition is supposed to be satisfied in the solute/solvent permeation process through compact membrane with fine pores like reverse osmosis membrane. When reverse osmosis is applied to treatment process for liquid waste, which usually contains a lot of solutes as contaminants, we can not predict the behavior of contaminants by the above one-solute process model. In the case of multi-solutes permeation process for liquid waste, the number of parameter in thermodynamic model increases rapidly with the number of solute, because of coupling phenomenon among solutes. In this study, we expanded the above thermodynamic model to multi-solute process applying operational calculus to the differential equations which describe the irreversible process of the system, and expressed concisely solute concentration vector as a matrix product. In this way, we predict the behavior of solutes in multi-solutes process, using values of parameters obtained in two-solutes process. (author)

  16. TEACHING MATHEMATICAL DISCIPLINES AT THE MEDICAL UNIVERSITY

    Directory of Open Access Journals (Sweden)

    V. Ya. Gelman

    2018-01-01

    Full Text Available Introduction.In programs of training of students of medical specialties, Mathematics is a subject of basic education, i.e. non-core discipline. However, studying Mathematics is extremely important for future physicians, as recently there has been an impetuous development of mathematization in the field of health care. Today, a set of the new medical devices, the equipment and high technologies are being developed based on the mathematical modeling, analysis and forecasting. Mathematical methods are widely applied to diagnostics, development of life-support systems and the description of various biological processes both at the molecular level,  and at the level of a whole organism, its systems, bodies and tissues. The solution of many medical tasks in the field of taxonomy, genetics, and organization of medical service is impossible without knowledge of mathematics. Unfortunately, along with the evident importance of mathematical preparation for a medical profession, its need is poorly realized not only by junior students, but even by some teachers of specialized departments of medical schools.The aim of the publication is to discuss the problems that arise in the teaching of mathematical disciplines to students at a medical school and to suggest possible solutions to these problems.Methodology and research methods. The study is based on the use of modeling of the educational process. The methods of analysis, generalization and the method of expert assessments were applied in the course of the research.Results and scientific novelty. The aspects of mathematical preparation at the university are considered on the basis of the application of the multiplicative model of training quality. It is shown that the main students’ learning difficulties in Mathematics are connected with the following factors: the initial level of mathematical preparation of students and their motivation; outdated methods of Mathematics teaching and academic content

  17. Baseline LAW Glass Formulation Testing

    International Nuclear Information System (INIS)

    Kruger, Albert A.; Mooers, Cavin; Bazemore, Gina; Pegg, Ian L.; Hight, Kenneth; Lai, Shan Tao; Buechele, Andrew; Rielley, Elizabeth; Gan, Hao; Muller, Isabelle S.; Cecil, Richard

    2013-01-01

    The major objective of the baseline glass formulation work was to develop and select glass formulations that are compliant with contractual and processing requirements for each of the LAW waste streams. Other objectives of the work included preparation and characterization of glasses with respect to the properties of interest, optimization of sulfate loading in the glasses, evaluation of ability to achieve waste loading limits, testing to demonstrate compatibility of glass melts with melter materials of construction, development of glass formulations to support ILAW qualification activities, and identification of glass formulation issues with respect to contract specifications and processing requirements

  18. Ionic solubility and solutal advection governed augmented evaporation kinetics of salt solution pendant droplets

    Science.gov (United States)

    Jaiswal, Vivek; Harikrishnan, A. R.; Khurana, Gargi; Dhar, Purbarun

    2018-01-01

    The presence of dispersed inclusions is known to modify the interfacial characteristics in liquids by adsorption-desorption of the ions at interfaces. The present article reports the influencing role of dissolved ions in a polar fluid on its evaporation dynamics. The evaporation dynamics of pendant droplets of aqueous solutions of variant simple salts and concentrations have been experimentally studied. The presence of salts is observed to enhance the evaporation rate (obeying the classical D2 law), and the enhancement has been found to hold a direct proportionality to the concentration of the dissolved salt. Furthermore, it is observed that the degree of enhancement in the evaporation rate is also directly proportional to the solubility of the salt in question. The phenomenon is explained based on the chemical kinetics and thermodynamics of hydration of the ionic species in the polar fluid. The classical evaporation rate constant formulation is found to be inadequate in modeling the enhanced species transport. Additional probing via particle image velocimetry reveals augmented internal circulation within the evaporating salt based drops compared to pure water. Mapping the dynamic surface tension reveals that a salt concentration gradient is generated between the bulk and periphery of the droplet and it could be responsible for the internal advection cells visualized. A thermo-solutal Marangoni and Rayleigh convection based mathematical formulation has been put forward, and it is shown that the enhanced solute-thermal convection could play a major role in enhanced evaporation. The internal circulation mapped from experiments is found to be in good quantitative agreement with the model predictions. Scaling analysis further reveals that the stability of the solutal Marangoni convection surpasses the thermal counterpart with higher salt concentration and solubility. The present article sheds insight into the possible domineering role of conjugate thermohydraulic and

  19. The existence and global attractivity of almost periodic sequence solution of discrete-time neural networks

    International Nuclear Information System (INIS)

    Huang Zhenkun; Wang Xinghua; Gao Feng

    2006-01-01

    In this Letter, we discuss discrete-time analogue of a continuous-time cellular neural network. Sufficient conditions are obtained for the existence of a unique almost periodic sequence solution which is globally attractive. Our results demonstrate dynamics of the formulated discrete-time analogue as mathematical models for the continuous-time cellular neural network in almost periodic case. Finally, a computer simulation illustrates the suitability of our discrete-time analogue as numerical algorithms in simulating the continuous-time cellular neural network conveniently

  20. Making Sense of Mathematics

    Science.gov (United States)

    Umphrey, Jan

    2011-01-01

    The National Council of Teachers of Mathematics (NCTM) is a voice and advocate for mathematics educators, working to ensure that all students receive equitable mathematics learning of the highest quality. To help teachers and school leaders understand the Common Core State Standards for Mathematics (CCSSM) and to point out how the CCSSM can be…

  1. Mathematics through Millenia

    DEFF Research Database (Denmark)

    Hansen, Vagn Lundsgaard

    2005-01-01

    A brief tour through the history of mathematics from the very beginnings to modern times, with an emphasis on the main contributions and important periods of mathematics in various civilizations.......A brief tour through the history of mathematics from the very beginnings to modern times, with an emphasis on the main contributions and important periods of mathematics in various civilizations....

  2. Mathematics through millenia

    DEFF Research Database (Denmark)

    Hansen, Vagn Lundsgaard

    A brief tour through the history of mathematics from the very beginnings to modern times, with an emphasis on the main contributions and important periods of mathematics in various civilizations.......A brief tour through the history of mathematics from the very beginnings to modern times, with an emphasis on the main contributions and important periods of mathematics in various civilizations....

  3. Using Mathematics, Mathematical Applications, Mathematical Modelling, and Mathematical Literacy: A Theoretical Study

    Science.gov (United States)

    Mumcu, Hayal Yavuz

    2016-01-01

    The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…

  4. Governing the Modern, Neoliberal Child through ICT Research in Mathematics Education

    DEFF Research Database (Denmark)

    Valero, Paola; Knijnik, Gelsa

    2015-01-01

    Research on the pedagogical uses of ICT for the learning of mathematics formulates cultural thesis about the desired subject of education and society, and thereby contribute to fabricate the rational, Modern, self-regulated, entrepreneurial neoliberal child. Using the Foucauldian notion...... of governmentality, the section Technology in the mathematics curriculum in the Third International Mathematics Education Research Handbook is discursively analyzed. We problematize how mathematics education research on ICT devices pedagogical technologies that steer the conduct of children to become the desired...

  5. Significance of Strain in Formulation in Theory of Solid Mechanics

    Science.gov (United States)

    Patnaik, Surya N.; Coroneos, Rula M.; Hopkins, Dale A.

    2003-01-01

    The basic theory of solid mechanics was deemed complete circa 1860 when St. Venant provided the strain formulation or the field compatibility condition. The strain formulation was incomplete. The missing portion has been formulated and identified as the boundary compatibility condition (BCC). The BCC, derived through a variational formulation, has been verified through integral theorem and solution of problems. The BCC, unlike the field counterpart, do not trivialize when expressed in displacements. Navier s method and the stiffness formulation have to account for the extra conditions especially at the inter-element boundaries in a finite element model. Completion of the strain formulation has led to the revival of the direct force calculation methods: the Integrated Force Method (IFM) and its dual (IFMD) for finite element analysis, and the completed Beltrami-Michell formulation (CBMF) in elasticity. The benefits from the new methods in elasticity, in finite element analysis, and in design optimization are discussed. Existing solutions and computer codes may have to be adjusted for the compliance of the new conditions. Complacency because the discipline is over a century old and computer codes have been developed for half a century can lead to stagnation of the discipline.

  6. Teaching Students to Formulate Questions

    Science.gov (United States)

    Jensen-Vallin, Jacqueline

    2017-01-01

    As STEM educators, we know it is beneficial to train students to think critically and mathematically during their early mathematical lives. To this end, the author teaches the College Algebra/Precalculus course in a flipped classroom version of an inquiry-based learning style. However, the techniques described in this paper can be applied to a…

  7. Reforming Science and Mathematics Education

    Science.gov (United States)

    Lagowski, J. J.

    1995-09-01

    Since 1991, the National Science Foundation has signed cooperative agreements with 26 states to undertake ambitious and comprehensive initiatives to reform science, mathematics, and technology education. Collectively, those agreements are known as the State Systemic Initiatives (SSI's). Two complimentary programs, The Urban and Rural Systemic Initiatives (USI's and RSI's), address similar reforms in the nation's largest cities and poorest rural areas. The SSI Program departs significantly from past NSF practice in several ways. The funding is for a longer term and is larger in amount, and the NSF is taking a more activist role, seeking to leverage state and private funds and promote the coordination of programs within states. The Initiatives also have a stronger policy orientation than previous NSF programs have had. The NSF strategy is a reflection of the growing and widely held view that meaningful reforms in schools are most likely to be achieved through state initiatives that set clear and ambitious learning goals and standards; align all of the available policy levers in support of reform; stimulate school-level initiatives; and mobilize human and financial resources to support these changes. Two premises underlie systemic reform: (1) all children can meet significantly higher standards if they are asked to do so and given adequate opportunities to master the content, and (2) state and local policy changes can create opportunities by giving schools strong and consistent signals about the changes in practice and performance that are expected. Because this is an enormous investment of Federal resources that is intended to bring about deep, systemic improvement in the nation's ability to teach science and mathematics effectively, the NSF has contracted with a consortium of independent evaluators to conduct a review of the program. The first of the SSI's were funded in 1991, sufficiently long ago to begin to formulate some initial impressions of their impact. Take

  8. Integrated Sensing and Processing (ISP). A Mathematical Methodology for Managing and Integrating Sensors and Processors in Distributed Systems for Radar and Communication

    National Research Council Canada - National Science Library

    Spooner, Chad M

    2005-01-01

    .... The approach is to consider systems of targets and sensors in as general a general mathematical formulation as possible, to develop mathematical tools to study such systems, and to apply the tools...

  9. Stochastic optimization: beyond mathematical programming

    CERN Multimedia

    CERN. Geneva

    2015-01-01

    Stochastic optimization, among which bio-inspired algorithms, is gaining momentum in areas where more classical optimization algorithms fail to deliver satisfactory results, or simply cannot be directly applied. This presentation will introduce baseline stochastic optimization algorithms, and illustrate their efficiency in different domains, from continuous non-convex problems to combinatorial optimization problem, to problems for which a non-parametric formulation can help exploring unforeseen possible solution spaces.

  10. A course in mathematical methods for physicists

    CERN Document Server

    Herman, Russell L

    2014-01-01

    Based on the author’s junior-level undergraduate course, this introductory textbook is designed for a course in mathematical physics. Focusing on the physics of oscillations and waves, A Course in Mathematical Methods for Physicists helps students understand the mathematical techniques needed for their future studies in physics. It takes a bottom-up approach that emphasizes physical applications of the mathematics. The book offers: •A quick review of mathematical prerequisites, proceeding to applications of differential equations and linear algebra •Classroom-tested explanations of complex and Fourier analysis for trigonometric and special functions •Coverage of vector analysis and curvilinear coordinates for solving higher dimensional problems •Sections on nonlinear dynamics, variational calculus, numerical solutions of differential equations, and Green's functions

  11. Fundamental theories of waves and particles formulated without classical mass

    Science.gov (United States)

    Fry, J. L.; Musielak, Z. E.

    2010-12-01

    Quantum and classical mechanics are two conceptually and mathematically different theories of physics, and yet they do use the same concept of classical mass that was originally introduced by Newton in his formulation of the laws of dynamics. In this paper, physical consequences of using the classical mass by both theories are explored, and a novel approach that allows formulating fundamental (Galilean invariant) theories of waves and particles without formally introducing the classical mass is presented. In this new formulation, the theories depend only on one common parameter called 'wave mass', which is deduced from experiments for selected elementary particles and for the classical mass of one kilogram. It is shown that quantum theory with the wave mass is independent of the Planck constant and that higher accuracy of performing calculations can be attained by such theory. Natural units in connection with the presented approach are also discussed and justification beyond dimensional analysis is given for the particular choice of such units.

  12. Discrete mathematics course supported by CAS MATHEMATICA

    Science.gov (United States)

    Ivanov, O. A.; Ivanova, V. V.; Saltan, A. A.

    2017-08-01

    In this paper, we discuss examples of assignments for a course in discrete mathematics for undergraduate students majoring in business informatics. We consider several problems with computer-based solutions and discuss general strategies for using computers in teaching mathematics and its applications. In order to evaluate the effectiveness of our approach, we conducted an anonymous survey. The results of the survey provide evidence that our approach contributes to high outcomes and aligns with the course aims and objectives.

  13. Mathematics without boundaries surveys in pure mathematics

    CERN Document Server

    Pardalos, Panos

    2014-01-01

    The contributions in this volume have been written by eminent scientists from the international mathematical community and present significant advances in several theories, methods and problems of Mathematical Analysis, Discrete Mathematics, Geometry and their Applications. The chapters focus on both old and recent developments in Functional Analysis, Harmonic Analysis, Complex Analysis, Operator Theory, Combinatorics, Functional Equations, Differential Equations as well as a variety of Applications. The book also contains some review works, which could prove particularly useful for a broader audience of readers in Mathematical Sciences, and especially to graduate students looking for the  latest information.

  14. Kant's Schematism and the Foundations of Mathematics

    DEFF Research Database (Denmark)

    Jørgensen, Klaus Frovin

    The theory of schematism was initiated by I. Kant, who, however, was never precise with respect to what he understood under this theory. I give---based on the theoretical works of Kant---an interpretation of the most important aspects of Kant's theory of schematism. In doing this I show how...... show that, contrary to Kant's own intentions, he was not up-to-date on mathematics. And in fact, it was because of this that it was possible for him to formulate his rather rigid theory concerning the unique characterizations of intuition and understanding. I show how phenomena in the mathematics...... of the time of Kant should have had an effect on him. He should have remained more critical towards his formulation and demarcation of intuition, understanding and reason. Finally I show how D. Hilbert in fact gives the necessary generalization of Kant's philosophy. This generalization provides us...

  15. European Success Stories in Industrial Mathematics

    CERN Document Server

    Esteban, Maria J; Lery, Thibaut; Maday, Yvon

    2011-01-01

    This unique book presents real world success stories of collaboration between mathematicians and industrial partners, showcasing first-hand case studies, and lessons learned from the experiences, technologies, and business challenges that led to the successful development of industrial solutions based on mathematics. It shows the crucial contribution of mathematics to innovation and to the industrial creation of value, and the key position of mathematics in the handling of complex systems, amplifying innovation. Each story describes the challenge that led to the industrial cooperation, how the

  16. International Conference on Applied Mathematics and Informatics

    CERN Document Server

    Vasilieva, Olga

    2015-01-01

    This book highlights recent compelling research results and trends in various aspects of contemporary mathematics, emphasizing applications to real-world situations. The chapters present exciting new findings and developments in situations where mathematical rigor is combined with common sense. A multi-disciplinary approach, both within each chapter and in the volume as a whole, leads to practical insights that may result in a more synthetic understanding of specific global issues—as well as their possible solutions. The volume will be of interest not only to experts in mathematics, but also to graduate students, scientists, and practitioners from other fields including physics, biology, geology, management, and medicine.

  17. Mathematical analysis, approximation theory and their applications

    CERN Document Server

    Gupta, Vijay

    2016-01-01

    Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.

  18. Mathematical and information maintenance of biometric systems

    Science.gov (United States)

    Boriev, Z.; Sokolov, S.; Nyrkov, A.; Nekrasova, A.

    2016-04-01

    This article describes the different mathematical methods for processing biometric data. A brief overview of methods for personality recognition by means of a signature is conducted. Mathematical solutions of a dynamic authentication method are considered. Recommendations on use of certain mathematical methods, depending on specific tasks, are provided. Based on the conducted analysis of software and the choice made in favor of the wavelet analysis, a brief basis for its use in the course of software development for biometric personal identification is given for the purpose of its practical application.

  19. Applied mathematics for science and engineering

    CERN Document Server

    Glasgow, Larry A

    2014-01-01

    Prepare students for success in using applied mathematics for engineering practice and post-graduate studies moves from one mathematical method to the next sustaining reader interest and easing the application of the techniques Uses different examples from chemical, civil, mechanical and various other engineering fields Based on a decade's worth of the authors lecture notes detailing the topic of applied mathematics for scientists and engineers Concisely writing with numerous examples provided including historical perspectives as well as a solutions manual for academic adopters

  20. Optimal Component Lumping: problem formulation and solution techniques

    DEFF Research Database (Denmark)

    Lin, Bao; Leibovici, Claude F.; Jørgensen, Sten Bay

    2008-01-01

    This paper presents a systematic method for optimal lumping of a large number of components in order to minimize the loss of information. In principle, a rigorous composition-based model is preferable to describe a system accurately. However, computational intensity and numerical issues restrict ...

  1. Mathematical models for therapeutic approaches to control HIV disease transmission

    CERN Document Server

    Roy, Priti Kumar

    2015-01-01

    The book discusses different therapeutic approaches based on different mathematical models to control the HIV/AIDS disease transmission. It uses clinical data, collected from different cited sources, to formulate the deterministic as well as stochastic mathematical models of HIV/AIDS. It provides complementary approaches, from deterministic and stochastic points of view, to optimal control strategy with perfect drug adherence and also tries to seek viewpoints of the same issue from different angles with various mathematical models to computer simulations. The book presents essential methods and techniques for students who are interested in designing epidemiological models on HIV/AIDS. It also guides research scientists, working in the periphery of mathematical modeling, and helps them to explore a hypothetical method by examining its consequences in the form of a mathematical modelling and making some scientific predictions. The model equations, mathematical analysis and several numerical simulations that are...

  2. The analytical solution to the 1D diffusion equation in heterogeneous media

    International Nuclear Information System (INIS)

    Ganapol, B.D.; Nigg, D.W.

    2011-01-01

    The analytical solution to the time-independent multigroup diffusion equation in heterogeneous plane cylindrical and spherical media is presented. The solution features the simplicity of the one-group formulation while addressing the complication of multigroup diffusion in a fully heterogeneous medium. Beginning with the vector form of the diffusion equation, the approach, based on straightforward mathematics, resolves a set of coupled second order ODEs. The analytical form is facilitated through matrix diagonalization of the neutron interaction matrix rendering the multigroup solution as a series of one-group solutions which, when re-assembled, gives the analytical solution. Customized Eigenmode solutions of the one-group diffusion operator then represent the homogeneous solution in a uniform spatial domain. Once the homogeneous solution is known, the particular solution naturally emerges through variation of parameters. The analytical expression is then numerically implemented through recurrence. Finally, we apply the theory to assess the accuracy of a second order finite difference scheme and to a 1D slab BWR reactor in the four-group approximation. (author)

  3. Mathematics and physics of neutron radiography

    International Nuclear Information System (INIS)

    Harms, A.A.; Wyman, D.R.

    1985-01-01

    This book provides detailed descriptions and analyses of selected experiments and their mathematical characterization. Also included are illustrative and quantitative procedures for applications. This book also discusses the radiography, nondestructive testing and nuclear reactor utilization. The contents discussed are: I: Introduction. II: Component Characterization. III: Object-Image Relations. IV: Rectangular Geometry. V: Cylindrical Geometry. VI: Two-Dimensional Analysis. VII: Object Scattering. VIII: Linear Systems Formulation. IX: Selected Topics. X: Neutron Radiographs. XI: Bibliography and References. Subject Index

  4. An Invitation to Mathematics

    CERN Document Server

    Schleicher, Dierk

    2011-01-01

    This "Invitation to Mathematics" consists of 14 contributions, many from the world's leading mathematicians, which introduce the readers to exciting aspects of current mathematical research. The contributions are as varied as the personalities of active mathematicians, but together they show mathematics as a rich and lively field of research. The contributions are written for interested students at the age of transition between high school and university who know high school mathematics and perhaps competition mathematics and who want to find out what current research mathematics is

  5. Peridynamic Formulation for Coupled Thermoelectric Phenomena

    Directory of Open Access Journals (Sweden)

    Migbar Assefa

    2017-01-01

    Full Text Available Modeling of heat and electrical current flow simultaneously in thermoelectric convertor using classical theories do not consider the influence of defects in the material. This is because traditional methods are developed based on partial differential equations (PDEs and lead to infinite fluxes at the discontinuities. The usual way of solving such PDEs is by using numerical technique, like Finite Element Method (FEM. Although FEM is robust and versatile, it is not suitable to model evolving discontinuities. To avoid such shortcomings, we propose the concept of peridynamic theory to derive the balance of energy and charge equations in the coupled thermoelectric phenomena. Therefore, this paper presents the transport of heat and charge in thermoelectric material in the framework of peridynamic (PD theory. To illustrate the reliability of the PD formulation, numerical examples are presented and results are compared with those from literature, analytical solutions, or finite element solutions.

  6. Novel Formulations for Antimicrobial Peptides

    Directory of Open Access Journals (Sweden)

    Ana Maria Carmona-Ribeiro

    2014-10-01

    Full Text Available Peptides in general hold much promise as a major ingredient in novel supramolecular assemblies. They may become essential in vaccine design, antimicrobial chemotherapy, cancer immunotherapy, food preservation, organs transplants, design of novel materials for dentistry, formulations against diabetes and other important strategical applications. This review discusses how novel formulations may improve the therapeutic index of antimicrobial peptides by protecting their activity and improving their bioavailability. The diversity of novel formulations using lipids, liposomes, nanoparticles, polymers, micelles, etc., within the limits of nanotechnology may also provide novel applications going beyond antimicrobial chemotherapy.

  7. Novel Formulations for Antimicrobial Peptides

    Science.gov (United States)

    Carmona-Ribeiro, Ana Maria; Carrasco, Letícia Dias de Melo

    2014-01-01

    Peptides in general hold much promise as a major ingredient in novel supramolecular assemblies. They may become essential in vaccine design, antimicrobial chemotherapy, cancer immunotherapy, food preservation, organs transplants, design of novel materials for dentistry, formulations against diabetes and other important strategical applications. This review discusses how novel formulations may improve the therapeutic index of antimicrobial peptides by protecting their activity and improving their bioavailability. The diversity of novel formulations using lipids, liposomes, nanoparticles, polymers, micelles, etc., within the limits of nanotechnology may also provide novel applications going beyond antimicrobial chemotherapy. PMID:25302615

  8. Equations in mathematical physics a practical course

    CERN Document Server

    Pikulin, Victor P

    2001-01-01

    This handbook is addressed to students of technology institutf's where a course on mathematical physics of relatively reduced volume is offered, as well as to engineers and scientists. The aim of the handbook is to treat (demonstrate) the basic methods for solving the simplest problems of classical mathematical physics. The most basic among the methods considered hrre i8 the superposition method. It allows one, based on particular linearly indepmdent HolutionH (solution "atoms"), to obtain the solution of a given problem. To that end the "Hupply" of solution atoms must be complete. This method is a development of the well-known method of particular solutions from the theory of ordinar~' differelltial equations. In contrast to the case of ordinary differential equations, where the number of linearly independent 80lutions is always finite, for a linear partial differrntial equation a complete "supply" of solution atoms is always infinite. This infinite set of Holutions may be discrete (for example, for regular ...

  9. GENERAL TASKS OF MATHEMATICAL EDUCATION DEVELOPMENT

    Directory of Open Access Journals (Sweden)

    V. A. Testov

    2014-01-01

    Full Text Available The paper discusses basic implementation aspects of the Mathematical Education Development Concept, adopted by the Russian Government in 2013. According to the above document, the main problems of mathematical education include: low motivation of secondary and higher school students for studying the discipline, resulted from underestimation of mathematical knowledge; and outdated educational content, overloaded by technical elements. In the author’s opinion, a number of important new mathematical fields, developed over the last years, - the graph theory, discrete mathematics, encoding theory, fractal geometry, etc – have a large methodological and applied educational potential. However, these new subdisciplines have very little representation both in the secondary and higher school mathematical curricula. As a solution for overcoming the gap between the latest scientific achievements and pedagogical practices, the author recommends integration of the above mentioned mathematical disciplines in educational curricula instead of some outdated technical issues. In conclusion, the paper emphasizes the need for qualified mathematical teachers’ training for solving the problems of students’ motivation development and content updates.

  10. PROFICIENT CLASSROOM MANAGEMENT THROUGH FOCUSED MATHEMATIC TEACHING

    Directory of Open Access Journals (Sweden)

    Marcus Samuelsson

    2017-12-01

    Full Text Available A not entirely unusual position among teachers is that they believe that they must first establish a peaceful classroom before they can begin to teach the subject. This research, shows how a proficient mathematics teacher teaches his subject and thereby creates a quiet and focused classroom and exerts effective leadership, just by teaching mathematics. The researchers observed a male mathematics teacher for almost half a year, i.e. one semester. The results of research present several patterns that the researchers saw during the observations of his teaching. The teacher showed an interest in each student’s mathematical thinking and expressed explicitly how students were expected to learn mathematics. He also directed students’ attention to mathematics and established a culture where all solutions were important in the teaching process. In the teaching process, he used multiple representations to motivate students and a lot of supportive expressions that made them feel that they were able to learn mathematics. He worked patiently to establish structures, and there was almost no disruptive behaviour. Students simply did not have time to interfere because they were so engaged in learning mathematics.

  11. Bilevel formulation of a policy design problem considering multiple objectives and incomplete preferences

    Science.gov (United States)

    Hawthorne, Bryant; Panchal, Jitesh H.

    2014-07-01

    A bilevel optimization formulation of policy design problems considering multiple objectives and incomplete preferences of the stakeholders is presented. The formulation is presented for Feed-in-Tariff (FIT) policy design for decentralized energy infrastructure. The upper-level problem is the policy designer's problem and the lower-level problem is a Nash equilibrium problem resulting from market interactions. The policy designer has two objectives: maximizing the quantity of energy generated and minimizing policy cost. The stakeholders decide on quantities while maximizing net present value and minimizing capital investment. The Nash equilibrium problem in the presence of incomplete preferences is formulated as a stochastic linear complementarity problem and solved using expected value formulation, expected residual minimization formulation, and the Monte Carlo technique. The primary contributions in this article are the mathematical formulation of the FIT policy, the extension of computational policy design problems to multiple objectives, and the consideration of incomplete preferences of stakeholders for policy design problems.

  12. Solid effervescent formulations as new approach for topical minoxidil delivery.

    Science.gov (United States)

    Pereira, Maíra N; Schulte, Heidi L; Duarte, Natane; Lima, Eliana M; Sá-Barreto, Livia L; Gratieri, Tais; Gelfuso, Guilherme M; Cunha-Filho, Marcilio S S

    2017-01-01

    Currently marketed minoxidil formulations present inconveniences that range from a grease hard aspect they leave on the hair to more serious adverse reactions as scalp dryness and irritation. In this paper we propose a novel approach for minoxidil sulphate (MXS) delivery based on a solid effervescent formulation. The aim was to investigate whether the particle mechanical movement triggered by effervescence would lead to higher follicle accumulation. Preformulation studies using thermal, spectroscopic and morphological analysis demonstrated the compatibility between effervescent salts and the drug. The effervescent formulation demonstrated a 2.7-fold increase on MXS accumulation into hair follicles casts compared to the MXS solution (22.0±9.7μg/cm 2 versus 8.3±4.0μg/cm 2 ) and a significant drug increase (around 4-fold) in remaining skin (97.1±29.2μg/cm 2 ) compared to the drug solution (23.5±6.1μg/cm 2 ). The effervescent formulations demonstrated a prominent increase of drug permeation highly dependent on the effervescent mixture concentration in the formulation, confirming the hypothesis of effervescent reaction favoring drug penetration. Clinically, therapy effectiveness could be improved, increasing the administration interval, hence, patient compliance. More studies to investigate the follicular targeting potential and safety of new formulations are needed. Copyright © 2016 Elsevier B.V. All rights reserved.

  13. From Religion to Dialectics and Mathematics

    Directory of Open Access Journals (Sweden)

    Achtner Wolfgang

    2016-03-01

    Full Text Available Hermann Grassmann is known to be the founder of modern vector and tensor calculus. Having as a theologian no formal education in mathematics at a university he got his basic ideas for this mathematical innovation at least to some extent from listening to Schleiermacher’s lectures on Dialectics and, together with his brother Robert, reading its publication in 1839. The paper shows how the idea of unity and various levels of reality first formulated in Schleiermacher’s talks about religion in 1799 were transformed by him into a philosophical system in his dialectics and then were picked up by Grassmann and operationalized in his philosophical-mathematical treatise on the extension theory (German: Ausdehnungslehre in 1844.

  14. Mathematics in computed tomography and related techniques

    International Nuclear Information System (INIS)

    Sawicka, B.

    1992-01-01

    The mathematical basis of computed tomography (CT) was formulated in 1917 by Radon. His theorem states that the 2-D function f(x,y) can be determined at all points from a complete set of its line integrals. Modern methods of image reconstruction include three approaches: algebraic reconstruction techniques with simultaneous iterative reconstruction or simultaneous algebraic reconstruction; convolution back projection; and the Fourier transform method. There is no one best approach. Because the experimental data do not strictly satisfy theoretical models, a number of effects have to be taken into account; in particular, the problems of beam geometry, finite beam dimensions and distribution, beam scattering, and the radiation source spectrum. Tomography with truncated data is of interest, employing mathematical approximations to compensate for the unmeasured projection data. Mathematical techniques in image processing and data analysis are also extensively used. 13 refs

  15. Brain Functors: A Mathematical Model of Intentional Perception and Action

    OpenAIRE

    David Ellerman

    2016-01-01

    Category theory has foundational importance because it provides conceptual lenses to characterize what is important and universal in mathematics - with adjunctions being the primary lens. If adjunctions are so important in mathematics, then perhaps they will isolate concepts of some importance in the empirical sciences. But the applications of adjunctions have been hampered by an overly restrictive formulation that avoids heteromorphisms or hets. By reformulating an adjunction using hets, it ...

  16. Continuum mechanics and thermodynamics in the Hamilton and the Godunov-type formulations

    Science.gov (United States)

    Peshkov, Ilya; Pavelka, Michal; Romenski, Evgeniy; Grmela, Miroslav

    2018-01-01

    Continuum mechanics with dislocations, with the Cattaneo-type heat conduction, with mass transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of the Godunov-type system of the first-order, symmetric hyperbolic partial differential equations (SHTC equations). The compatibility with thermodynamics of the time reversible part of the governing equations is mathematically expressed in the former formulation as degeneracy of the Hamiltonian structure and in the latter formulation as the existence of a companion conservation law. In both formulations the time irreversible part represents gradient dynamics. The Godunov-type formulation brings the mathematical rigor (the local well posedness of the Cauchy initial value problem) and the possibility to discretize while keeping the physical content of the governing equations (the Godunov finite volume discretization).

  17. The argument of mathematics

    CERN Document Server

    Aberdein, Andrew

    2014-01-01

    This book presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. It offers large array of examples ranging from the history of mathematics to formal proof verification.

  18. Mathematical knowledge in teaching

    CERN Document Server

    Rowland, Tim

    2011-01-01

    This book examines issues of considerable significance in addressing global aspirations to raise standards of teaching and learning in mathematics by developing approaches to characterizing, assessing and developing mathematical knowledge for teaching.

  19. Developing My Mathematics Identity

    Science.gov (United States)

    Gonzalez, Lidia

    2016-01-01

    Assuming the role of storyteller, the author uses her experiences as a graduate student and beginning teacher to reflect critically on issues related to mathematics, mathematics education, gender, and diversity.

  20. Journal of applied mathematics

    National Research Council Canada - National Science Library

    2001-01-01

    "[The] Journal of Applied Mathematics is a refereed journal devoted to the publication of original research papers and review articles in all areas of applied, computational, and industrial mathematics...