calculus: Topics by WorldWideScience.org

Stein method for invariant measures of diffusions via Malliavin calculus

... such as biology, physics, geology, materials science, engineering, computer science, and mathematics ... expected to produce course and curricular materials that will be of national interest and widely ...

Drinking water composition and incidence of urinary calculus: introducing a new index.

Given a random variable $F$ regular enough in the sense of the Malliavin calculus, we are able to measure the distance between its law and almost any continuous probability law on the real line. The bounds are given in terms of the Malliavin derivative of $F$. Our approach is based on the theory of It\\^o diffusions and the stochastic calculus of variations. Several examples are considered in order to illustrate our general results.

2011-01-01

The Bedwyr system for model checking over syntactic expressions

INTRODUCTION. We searched for a pathophysiologically based feature of major water electrolytes, which may define water quality better than the water hardness, respecting urinary calculus formation. MATERIALS AND METHODS. Utilizing a multistage stratified sampling, 2310 patients were diagnosed in the imaging centers of the provincial capitals in Iran between 2007 and 2008. These were composed of 1755 patients who were settled residents of 24 provincial capitals. Data on the regional drinking water composition, obtained from an accredited registry, and their relationships with the region's incidence of urinary calculi were evaluated by metaregression models. The stone risk index (defined as the ratio of calcium to magnesium-bicarbonate product in drinking water) was used to assess the risk of calculus formation. RESULTS. No correlation was found between the urinary calculus incidence and the amount of calcium, bicarbonate, or ...

2011-01-01

Digital Libraries: From Process Modelling to Grid-based Service Oriented Architecture

Bedwyr is a generalization of logic programming that allows model checking directly on syntactic expressions possibly containing bindings. This system, written in OCaml, is a direct implementation of two recent advances in the theory of proof search. The first is centered on the fact that both finite success and finite failure can be captured in the sequent calculus by incorporating inference rules for {\\em definitions} that allow {\\em fixed points} to be explored. As a result, proof search in such a sequent calculus can capture simple model checking problems as well as may and must behavior in operational semantics. The second is that higher-order abstract syntax is directly supported using term-level $\\lambda$-binders and the quantifier known as $\

2007-01-01

A Novel Approach for Complete Identification of Dynamic Fractional Order Systems Using Stochastic Optimization Algorithms and Fractional Calculus

Graphical Business Process Modelling Languages (BPML) like Role Activity Diagrams (RAD) provide ease and flexibility for modelling business behaviour. However, these languages show limited applicability in terms of enactment over distributed systems paradigms like Service Oriented Architecture (SOA) based grid computing. This paper investigates RAD modelling of a Scientific Publishing Process (SPP) for Digital Libraries (DL) and tries to determine the suitability of Pi-Calculus based formal approaches to enact SOA based grid computing. In order to achieve this purpose, the Pi-Calculus based formal transformation from a RAD model of SPP for DL draws attention towards a number of challenging issues including issues that require particular design considerations for appropriate enactment in a SOA based grid system.

2006-01-01

Quantum deformation of BRST algebra

This contribution deals with identification of fractional-order dynamical systems. System identification, which refers to estimation of process parameters, is a necessity in control theory. Real processes are usually of fractional order as opposed to the ideal integral order models. A simple and elegant scheme of estimating the parameters for such a fractional order process is proposed. This method employs fractional calculus theory to find equations relating the parameters that are to be estimated, and then estimates the process parameters after solving the simultaneous equations. The said simultaneous equations are generated and updated using particle swarm optimization (PSO) technique, the fitness function being the sum of squared deviations from the actual set of observations. The data used for the calculations are intentionally corrupted to simulate real-life conditions. Results show that the proposed scheme offers a very high degree of accuracy even for ...

2008-01-01

Physicochemical basis for formation of renal stones of calcium phosphate origin: calculation of the degree of saturation of urine with respect to brushite

We investigate the q-deformation of the BRST algebra, the algebra of the ghost, matter and gauge fields on one spacetime point using the result of the bicovariant differential calculus. There are two nilpotent operations in the algebra, the BRST transformation #delta#_B and the derivative d. We show that one can define the covariant commutation relations among the fields and their derivatives consistently with these two operations as well as the *-operation, the antimultiplicative inner involution. (orig.).

1993-01-01

UK PubMed Central (United Kingdom)

Brushite (CaHPO₄·2H₂O) was considered to govern the formation of renal calculus of calcium phosphate origin. The degree of saturation of urine with respect to this phase...Full Text Available

1969-10-01

Formal Analysis of UMTS Privacy

Feynman integral calculus

The ubiquitous presence of mobile communication devices and the continuous development of mo- bile data applications, which results in high level of mobile devices' activity and exchanged data, often transparent to the user, makes privacy preservation an important feature of mobile telephony systems. We present a formal analysis of the UMTS Authentication and Key Agreement protocol, using the applied pi-calculus and the ProVerif tool. We formally verify the model with respect to privacy properties. We show a linkability attack which makes it possible, for individuals with low-cost equipment, to trace UMTS subscribers. The attack exploits information leaked by poorly designed error messages.

2011-01-01

A finite-dimensional fermionic TQFT

The goal of the book is to summarize those methods for evaluating Feynman integrals that have been developed over a span of more than fifty years. The book characterizes the most powerful methods and illustrates them with numerous examples starting from very simple ones and progressing to nontrivial examples. The book demonstrates how to choose adequate methods and combine evaluation methods in a non-trivial way. The most powerful methods are characterized and then illustrated through numerous examples. This is an updated textbook version of the previous book (Evaluating Feynman integrals, STMP 211) of the author. (orig.)

2006-07-01

A Remark on Gauge Transformations and the Moving Frame Method

A fermionic - based on Grassmann--Berezin calculus of anticommuting variables - topological quantum field theory (TQFT) is considered, mainly in three dimensions. It is defined for piecewise-linear manifolds and, for a given triangulation, deals only with a finite number of variables. Despite its simple nature, it can distiguish between lens spaces L(7,1) and L(7,2). And despite its origin from a kind of Reidemeister torsion, it does this without using nontrivial representations of the fundamental group. Also, symbolic calculations are presented giving strong evidence of existence of similar theory in four dimensions.

2011-01-01

Concepts in radiation protection

In this note we give a shorter proof of recent regularity results by Riviere and Riviere-Struwe. We differ from the mentioned articles only in using the direct method of Helein's moving frame to construct a suitable gauge transformation. Though this is neither new nor surprising, it enables us to describe a proof of regularity using besides the duality of Hardy- and BMO-space only elementary arguments of calculus of variations and algebraic identities. Moreover, we remark that in order to prove Hildebrandt's conjecture one can avoid the Nash-Moser imbedding theorem. There are no new results presented here, nor are there any techniques we could claim originality for.

2009-01-01

Random learning units using WIRIS quizzes in Moodle

This monograph provides basic notions and principles in dosimetry and radiation protection in compliance with two fundamental works: IAEA Safety Series No.115 - International Basic Safety Standards for Protection against Ionizing Radiation and for the Safety of Radiation Sources - and Publication no. 60 of International Commission on Radiological Protection. After the review of quantities and units necessary in radiation protection, the book presents the new values of dose limits as well as the values of 'radiation weighting factor', 'tissue weighting factor' and 'conversion factor intake-dose' (committed effective dose per unit intake) by ingestion and inhalation for 30 most important radionuclides. The new values of dose limits, lower than the old values, are a challenge for the radiation protection, especially of the 'public' where the dose limit diminished by a factor of five relative to the earlier edition. The new value of dose limit for public, 1 mSv per year (obviously over the ...

1996-01-01

British Library Electronic Table of Contents (United Kingdom)

Moodle is an extended learning management system for developing learning units, including mathematically-based subjects. A wide variety of material can be developed in Moodle which contains facilities for forums, questionnaires, lessons, tasks, wikis, glossaries and chats. Therefore, the Moodle platform provides a meeting point for those working in a mathematics course. Mathematics requires special materials and activities: The material must include mathematical objects and the activities included in the virtual course must be able to do mathematical computations. WIRIS is a powerful software for educational environments. It has libraries for calculus, algebra, geometry and much more. In this article, examples showing the use of WIRIS in numerical methods and examples of using a new tool, ...

2011-01-01

Quantification of the influence of the choice of the algorithm and planning system on the calculation of a treatment plan

Partition Functions of Normal Factor Graphs

In this work an analysis of the influence of the choice of the algorithm or planning system, on the calculus of the same treatment plan is introduced. For this purpose specific software has been developed for comparing plans of a series of IMRT cases of prostate and head and neck cancer calculated using the convolution, superposition and fast superposition algorithms implemented in the XiO 4.40 planning system (CMS). It has also been used for the comparison of the same treatment plan for lung pathology calculated in XiO with the mentioned algorithms, and calculated in the Plan 4.1 planning system (Brainlab) using its pencil beam algorithm. Differences in dose among the treatment plans have been quantified using a set of metrics. The recommendation for the dosimetrist of a careful choice of the algorithm has been numerically confirmed. (Author).

On the Reinhardt Conjecture

One of the most common types of functions in mathematics, physics, and engineering is a sum of products, sometimes called a partition function. After "normalization," a sum of products has a natural graphical representation, called a normal factor graph (NFG), in which vertices represent factors, edges represent internal variables, and half-edges represent the external variables of the partition function. In physics, so-called trace diagrams share similar features. We believe that the conceptual framework of representing sums of products as partition functions of NFGs is an important and intuitive paradigm that, surprisingly, does not seem to have been introduced explicitly in the previous factor graph literature. Of particular interest are NFG modifications that leave the partition function invariant. A simple subclass of such NFG modifications offers a unifying view of the Fourier transform, tree-based reparameterization, loop calculus, and the Legendre ...

2011-01-01

Neutrinos and long-range weak forces in cosmology

In 1934, Reinhardt asked for the centrally symmetric convex domain in the plane whose best lattice packing has the lowest density. He conjectured that the unique solution up to an affine transformation is the smoothed octagon (an octagon rounded at corners by arcs of hyperbolas). This article offers a detailed strategy of proof. In particular, we show that the problem is an instance of the classical problem of Bolza in the calculus of variations. A minimizing solution is known to exist. The boundary of every minimizer is a differentiable curve with Lipschitz continuous derivative. If a minimizer is piecewise analytic, then it is a smoothed polygon (a polygon rounded at corners by arcs of hyperbolas). To complete the proof of the Reinhardt conjecture, the assumption of piecewise analyticity must be removed, and the conclusion of smoothed polygon must be strengthened to smoothed octagon.

2011-01-01

An Intrinsic Approach to Forces in Magnetoelectric Media

The Lorentz and coordinate covariant calculus of spinors in Riemannian spacetime, which is the mathematical model for the description of the quantum mechanics of elementary particles with spin interacting with the classical gravitation field, is explored. The Dirac equation describing the interaction of neutrinos with the gravitational fields of the Robertson-Walker cosmological world models is separated, and the spectrum of eigenfunctions and eigenvalues for particular choices of the set of quantum numbers is given explicitly for the k = 0 and k = +1 models, although only the radial equations determining the final quantum number are given for the k = -1 model. The mathematical theory of the motion of a perfect fluid whose elements interact via long-range neutrino-exchange forces, as well as gravitationally, is developed. The formalism for calculating, by calculating the Bogoliubov transformation of the Fock space operators that instantaneously diagonalize their ...

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Three-dimensional mise-a-la-masse modeling using horizontal well; Suihei kosei wo mochiita ryuden den`iho no sanjigen modeling

This paper offers a conceptually straightforward method for the calculation of stresses in polarisable media based on the notion of a drive form and its property of being closed in spacetimes with symmetry. After an outline of the notation required to exploit the powerful exterior calculus of differential forms, a discussion of the relation between Killing isometries and conservation laws for smooth and distributional drive forms is given. Instantaneous forces on isolated spacetime domains and regions with interfaces are defined, based on manifestly covariant equations of motion. The remaining sections apply these notions to media that sustain electromagnetic stresses, with emphasis on homogeneous magnetoelectric material. An explicit calculation of the average pressure exerted by a monochromatic wave normally incident on a homogeneous, magnetoelectric slab in vacuo is presented and the concluding section summarizes how this pressure depends on the parameters in ...

2008-01-01

Plasma membrane as the target site of cholic acid analogs.

The 3-D model program was developed to apply a mise-a-la-masse method to linear current sources with optional shapes. Mise-a-la-masse method is a bipolar mapping survey method using current sources installed in wells, and recently has been widely used for direct exploration of geothermal reservoirs. This method is also used for monitoring underground fluid as electrode arrangement of fluid flow tomography for surveying underground fluid (geothermal fluid, underground water, petroleum). In the geothermal reservoir exploration, the casing pipes of wells are used as linear current sources, and measured data are processed as those based on vertical current source. In the largely inclined well, the inclination of current sources should be considered. The 3-D modeling program was developed by difference calculus using the theoretical potential equation and apparent resistivity based on linear current sources with optional 3-D shapes. The numerical model experiment result ...

1996-10-01

Optimal Control of Thermo--Fluid Phenomena in Variable Domains

Although the mechanism is unknown, Calculus Bovis and its active components, cholic acid analogs (CAAs), have been used in China to treat a wide range of diseases. Based on the previous finding that the potency of CAA is strongly dependent on the intrinsic surface activity, this paper aimed to investigate the role of the plasma membrane in the pharmacological activity of CAAs. First, CAAs (0.1 mM) caused a surface activity-dependent depression on ATPase activity in the cell membrane extract, but it had no effects on other cellular extracts, suggesting an indispensable role of the membrane environment for pharmacological activity. Second, CAAs lowered the membrane fluidity of cultured Caco-2 cells with the same rank-order of potency sequence. Third, the hypothesis that any functional protein located on the membrane is influenced by changes in cellular membrane fluidity was supported by: ileal contraction that was induced by acetylcholine and mediated by the ...

2011-08-03

Accuracy of FEM 3-D modeling in the electromagnetic methods; Denjiho ni okeru FEM 3 jigen modeling no seido

This presentation concerns our continued research on adjoint--based optimization of viscous incompressible flows (the Navier--Stokes problem) coupled with heat conduction involving change of phase (the Stefan problem), and occurring in domains with variable boundaries. This problem is motivated by optimization of advanced welding techniques used in automotive manufacturing, where the goal is to determine an optimal heat input, so as to obtain a desired shape of the weld pool surface upon solidification. We argue that computation of sensitivities (gradients) in such free--boundary problems requires the use of the shape--differential calculus as a key ingredient. We also show that, with such tools available, the computational solution of the direct and inverse (optimization) problems can in fact be achieved in a similar manner and in a comparable computational time. Our presentation will address certain mathematical and computational aspects of the method. As an ...

2008-11-01

Revisit to the helicity and the generalized self-organization theory

Analytical methods considering 3-D resistivity distribution, in particular, finite element method (FEM) were studied to improve the reliability of electromagnetic exploration. Integral equation, difference calculus, FEM and hybrid method are generally used as computational 3-D modeling method. FEM is widely used in various fields because FEM can easily handle complicated shapes and boundaries. However, in electromagnetic method, the assumption of continuous electric field is pointed out as important problem. The normal (orthogonal) component of current density should be continuous at the boundary between media with different conductivities, while this means that the normal component of electric field is discontinuous. In FEM, this means that current channeling is not properly considered, resulting in poor accuracy. Unless this problem is solved, FEM modeling is not practical. As one of the solutions, it is promising to specifically incorporate interior boundary ...

1996-10-01

On the calculation of scattered fields by 3-D structure in the time-domain electromagnetic (TDEM) method; Jikan ryoiki denjiho ni okeru sanjigen kozo kara no sanranba no keisan ni tsuite

It is clarified that the so-caned 'helicity conservation law' is never the conservation equation of the helicity K itself', but is merely 'the time change rate equation of K', which is passively and resultantly determined by the mutually independent volume and surface integral terms. It is shown that since the total helicity K can never be conserved in the real experimental systems, the conjecture of the total helicity invariance is not physically available to real magnetized plasmas in an exact sense. The well-known relaxation theory by Dr. J. B. Taylor is clarified to be neither the variational principle nor the energy principle, but be merely a mathematical calculation, using the variational calculus in order to find the minimum magnetic energy solution from the set of solutions having the same value of K. With the use of auto-correlations for physical quantities, it is presented that a novel basic formulation of an ...

2000-09-01