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Sample records for cauchy problem

  1. Abstract Cauchy problems three approaches

    CERN Document Server

    Melnikova, Irina V

    2001-01-01

    Although the theory of well-posed Cauchy problems is reasonably understood, ill-posed problems-involved in a numerous mathematical models in physics, engineering, and finance- can be approached in a variety of ways. Historically, there have been three major strategies for dealing with such problems: semigroup, abstract distribution, and regularization methods. Semigroup and distribution methods restore well-posedness, in a modern weak sense. Regularization methods provide approximate solutions to ill-posed problems. Although these approaches were extensively developed over the last decades by many researchers, nowhere could one find a comprehensive treatment of all three approaches.Abstract Cauchy Problems: Three Approaches provides an innovative, self-contained account of these methods and, furthermore, demonstrates and studies some of the profound connections between them. The authors discuss the application of different methods not only to the Cauchy problem that is not well-posed in the classical sense, b...

  2. Beginnings of the Cauchy problem

    OpenAIRE

    Choquet-Bruhat, Yvonne

    2014-01-01

    Brief account of results on the Cauchy problem for the Einstein equations starting with early the works of Darmois and Lichnerowicz and going up to the proofs of the existence and uniqueness of solutions global in space and local in time, in Sobolev spaces, for the general equations either in vacuum or with classical sources.

  3. The Cauchy problem and Hadamard's example

    Directory of Open Access Journals (Sweden)

    Oleg Yaremko

    2013-05-01

    Full Text Available Integral representation for harmonic function  in the ring. We prove the existence and uniqueness of solutions of the Cauchy problem for the Laplace equation in the circle. Integral representation for the solution of the Cauchy problem was found.

  4. CAUCHY PROBLEM OF ONE TYPE OF ATMOSPHERE EVOLUTION EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    HE Juan-xiong; HE You-hua

    2006-01-01

    One type of evolution atmosphere equations was discussed. It is found that according to the stratification theory, (i) the inertial force has no influence on the criterion of the well-posed Cauchy problem; (ii) the compressibility plays no role on the well-posed condition of the Cauchy problem of the viscid atmosphere equations, but changes the well-posed condition of the viscid atmosphere equations; (iii) this type of atmosphere evolution equations is ill-posed on the hyperplane t = 0 in spite of its compressibility and viscosity; (iv) the Cauchy problem of compressible viscosity atmosphere with still initial motion is ill-posed.

  5. The Cauchy problem of f(R) gravity

    OpenAIRE

    Lanahan-Tremblay, Nicolas; Faraoni, Valerio

    2007-01-01

    The initial value problem of metric and Palatini f(R)gravity is studied by using the dynamical equivalence between these theories and Brans-Dicke gravity. The Cauchy problem is well-formulated for metric f(R)gravity in the presence of matter and well-posed in vacuo. For Palatini f(R)gravity, instead, the Cauchy problem is not well-formulated.

  6. The local Cauchy problem for dissipative plasmas; Le probleme de Cauchy local pour les plasmas dissipatifs

    Energy Technology Data Exchange (ETDEWEB)

    Giovangigli, V.; Graille, B. [Ecole Polytechnique, CMAP, 91 - Palaiseau (France)

    2005-01-01

    We investigate a system of partial differential equations modeling dissipative plasmas. Transport fluxes are anisotropic linear combinations of gradients and also include zeroth order contributions due to electromagnetic forces. There are also source terms depending on the solution gradient. By using entropic variables, we first recast the system in a partially symmetric form and next in the form of a quasilinear partially symmetric hyperbolic-parabolic system. Using a result of Vol'Pert and Hudjaev, we prove local existence and uniqueness of a bounded smooth solution to the Cauchy problem. (authors)

  7. On the Cauchy Problem Describing an Electron-Phonon Interaction

    Institute of Scientific and Technical Information of China (English)

    Jo(a)o-Paulo DIAS; Mário FIGUEIRA; Filipe OLIVEIRA

    2011-01-01

    In this paper, a model is derived to describe a quartic anharmonic interatomic interaction with an external potential involving a pair electron-phonon. The authors study the corresponding Cauchy Problem in the semilinear and quasilinear cases.

  8. Form methods for autonomous and non-autonomous Cauchy problems

    OpenAIRE

    Thomaschewski, Sonja

    2003-01-01

    Die vorliegende Dissertation stellt einige Resultate vor, die aus Untersuchungen von Formmethoden hervorgingen. Diese spielen eine wichtige Rolle für Evolutionsgleichungen, wenn sich diese als abstraktes Cauchy-Problem schreiben lassen, bei dem der lineare Operator zu einer Sesquilinearform assoziiert ist. Dies ist der Fall für die meisten partiellen Differentialgleichungen. Falls diese Form dicht definiert, stetig und elliptisch ist, so ist das zugehörige abstrakte Cauchy-Problem wohlgestell...

  9. Invariance of the Cauchy mean-value expression with an application to the problem of representation of Cauchy means

    Directory of Open Access Journals (Sweden)

    Lucio R. Berrone

    2005-01-01

    Full Text Available The notion of invariance under transformations (changes of coordinates of the Cauchy mean-value expression is introduced and then used in furnishing a suitable two-variable version of a result by L. Losonczi on equality of many-variable Cauchy means. An assessment of the methods used by Losonczi and Matkowski is made and an alternative way is proposed to solve the problem of representation of two-variable Cauchy means.

  10. Cauchy problem for Laplace equation: An observer based approach

    KAUST Repository

    Majeed, Muhammad Usman

    2013-10-01

    A method to solve Cauchy Problem for Laplace equation using state observers is proposed. It is known that this problem is ill-posed. The domain under consideration is simple lipschitz in 2 with a hole. The idea is to recover the solution over whole domain from the observations on outer boundary. Proposed approach adapts one of the space variables as a time variable. The observer developed to solve Cauchy problem for the Laplace\\'s equation is compuationally robust and accurate. © 2013 IEEE.

  11. Existence and Regularity for Boundary Cauchy Problems with Infinite Delay

    Directory of Open Access Journals (Sweden)

    Jung-Chan Chang

    2014-01-01

    Full Text Available The aim of this work is to investigate a class of boundary Cauchy problems with infinite delay. We give some sufficient conditions ensuring the uniqueness, existence, and regularity of solutions. For illustration, we apply the result to an age dependent population equation, which covers some special cases considered in some recent papers.

  12. Existence and Regularity for Boundary Cauchy Problems with Infinite Delay

    OpenAIRE

    Jung-Chan Chang

    2014-01-01

    The aim of this work is to investigate a class of boundary Cauchy problems with infinite delay. We give some sufficient conditions ensuring the uniqueness, existence, and regularity of solutions. For illustration, we apply the result to an age dependent population equation, which covers some special cases considered in some recent papers.

  13. Applications of elliptic Carleman inequalities to Cauchy and inverse problems

    CERN Document Server

    Choulli, Mourad

    2016-01-01

    This book presents a unified approach to studying the stability of both elliptic Cauchy problems and selected inverse problems. Based on elementary Carleman inequalities, it establishes three-ball inequalities, which are the key to deriving logarithmic stability estimates for elliptic Cauchy problems and are also useful in proving stability estimates for certain elliptic inverse problems. The book presents three inverse problems, the first of which consists in determining the surface impedance of an obstacle from the far field pattern. The second problem investigates the detection of corrosion by electric measurement, while the third concerns the determination of an attenuation coefficient from internal data, which is motivated by a problem encountered in biomedical imaging.

  14. The stability for the Cauchy problem for elliptic equations

    CERN Document Server

    Alessandrini, Giovanni; Rosset, Edi; Vessella, Sergio

    2009-01-01

    We discuss the ill-posed Cauchy problem for elliptic equations, which is pervasive in inverse boundary value problems modeled by elliptic equations. We provide essentially optimal stability results, in wide generality and under substantially minimal assumptions. As a general scheme in our arguments, we show that all such stability results can be derived by the use of a single building brick, the three-spheres inequality.

  15. The Cauchy problem for higher order abstract differential equations

    CERN Document Server

    Xiao, Ti-Jun

    1998-01-01

    This monograph is the first systematic exposition of the theory of the Cauchy problem for higher order abstract linear differential equations, which covers all the main aspects of the developed theory. The main results are complete with detailed proofs and established recently, containing the corresponding theorems for first and incomplete second order cases and therefore for operator semigroups and cosine functions. They will find applications in many fields. The special power of treating the higher order problems directly is demonstrated, as well as that of the vector-valued Laplace transforms in dealing with operator differential equations and operator families. The reader is expected to have a knowledge of complex and functional analysis.

  16. PERIODIC BOUNDARY VALUE PROBLEM AND CAUCHY PROBLEM OF THE GENERALIZED CUBIC DOUBLE DISPERSION EQUATION

    Institute of Scientific and Technical Information of China (English)

    Chen Guowang; Xue Hongxia

    2008-01-01

    In this article, the existence, uniqueness and regularities of the global gener-alized solution and global classical solution for the periodic boundary value problem and the Cauchy problem of the general cubic double dispersion equation utt -uxx-auxxtt+bux4 - duxxt= f(u)xx are proved, and the sufficient conditions of blow-up of the solutions for the Cauchy problems in finite time are given.

  17. Oscillatory solutions of the Cauchy problem for linear differential equations

    Directory of Open Access Journals (Sweden)

    Gro Hovhannisyan

    2015-06-01

    Full Text Available We consider the Cauchy problem for second and third order linear differential equations with constant complex coefficients. We describe necessary and sufficient conditions on the data for the existence of oscillatory solutions. It is known that in the case of real coefficients the oscillatory behavior of solutions does not depend on initial values, but we show that this is no longer true in the complex case: hence in practice it is possible to control oscillatory behavior by varying the initial conditions. Our Proofs are based on asymptotic analysis of the zeros of solutions, represented as linear combinations of exponential functions.

  18. On the Cauchy problem for the damped Boussinesq equation

    OpenAIRE

    Varlamov, Vladimir

    1996-01-01

    A classic solution to the Cauchy problem for the damped Boussinesq equation $u_{tt}-2Bu_{txx}=-\\alpha u_{xxxx}+u_{xx}-\\beta(u^2)_{xx}$, $x\\in\\Bbb R^1$, $t>0$, $\\alpha, B=\\text{const}>0$, $\\beta=\\text{const}\\in\\Bbb R^1$, with small initial data is constructed by means of the application of both the spectral and perturbation theories. Large time asymptotics of this solution are obtained. Its main term accounts for two solitons traveling in opposite directions. Each of th...

  19. Cauchy problems of pseudo-parabolic equations with inhomogeneous terms

    Science.gov (United States)

    Li, Zhongping; Du, Wanjuan

    2015-12-01

    This paper deals with Cauchy problems of pseudo-parabolic equations with inhomogeneous terms. The aim of the paper is to study the influence of the inhomogeneous term on the asymptotic behavior of solutions. We at first determine the critical Fujita exponent and then give the secondary critical exponent on the decay asymptotic behavior of an initial value at infinity. Furthermore, the precise estimate of life span for the blow-up solution is obtained. Our results show that the asymptotic behavior of solutions is seriously affected by the inhomogeneous term.

  20. Cauchy problem in spacetimes with closed timelike curves

    International Nuclear Information System (INIS)

    The laws of physics might permit the existence, in the real Universe, of closed timelike curves (CTC's). Macroscopic CTC's might be a semiclassical consequence of Planck-scale, quantum gravitational, Lorentzian foam, if such foam exists. If CTC's are permitted, then the semiclassical laws of physics (the laws with gravity classical and other fields quantized or classical) should be augmented by a principle of self-consistency, which states that a local solution to the equations of physics can occur in the real Universe only if it can be extended to be part of a global solution, one which is well defined throughout the (nonsingular regions of) classical spacetime. The consequences of this principle are explored for the Cauchy problem of the evolution of a classical, massless scalar field Φ (satisfying □Φ=0) in several model spacetimes with CTC's

  1. A NOTE ON "THE CAUCHY PROBLEM FOR COUPLED IMBQ EQUATIONS"

    Institute of Scientific and Technical Information of China (English)

    Hongxia GUO; Guowang CHEN

    2013-01-01

    In this article,we prove that the Cauchy problem for a N-dimensional system of nonlinear wave equations utt-a△utt =△f(u,v),x ∈ RN,t > 0,vtt-a△vtt =△g(u,v),x ∈ RN,t > 0 admits a unique global generalized solution in C3([0,∞); Wm,p(RN) ∩ L∞(RN) f∩ L2(RN))(m ≥ 0 is an integer,1 ≤ p ≤ ∞) and a unique global classical solution in C3([0,∞); Wm,p ∩ L∞ ∩ L2) (m > 2 + N/p),the sufficient conditions of the blow up of the solution in finite time are given,and also two examples are given.

  2. A Generalized Cauchy Distribution Framework for Problems Requiring Robust Behavior

    Directory of Open Access Journals (Sweden)

    Carrillo RafaelE

    2010-01-01

    Full Text Available Statistical modeling is at the heart of many engineering problems. The importance of statistical modeling emanates not only from the desire to accurately characterize stochastic events, but also from the fact that distributions are the central models utilized to derive sample processing theories and methods. The generalized Cauchy distribution (GCD family has a closed-form pdf expression across the whole family as well as algebraic tails, which makes it suitable for modeling many real-life impulsive processes. This paper develops a GCD theory-based approach that allows challenging problems to be formulated in a robust fashion. Notably, the proposed framework subsumes generalized Gaussian distribution (GGD family-based developments, thereby guaranteeing performance improvements over traditional GCD-based problem formulation techniques. This robust framework can be adapted to a variety of applications in signal processing. As examples, we formulate four practical applications under this framework: (1 filtering for power line communications, (2 estimation in sensor networks with noisy channels, (3 reconstruction methods for compressed sensing, and (4 fuzzy clustering.

  3. Origins and development of the Cauchy problem in general relativity

    Science.gov (United States)

    Ringström, Hans

    2015-06-01

    The seminal work of Yvonne Choquet-Bruhat published in 1952 demonstrates that it is possible to formulate Einstein's equations as an initial value problem. The purpose of this article is to describe the background to and impact of this achievement, as well as the result itself. In some respects, the idea of viewing the field equations of general relativity as a system of evolution equations goes back to Einstein himself; in an argument justifying that gravitational waves propagate at the speed of light, Einstein used a special choice of coordinates to derive a system of wave equations for the linear perturbations on a Minkowski background. Over the following decades, Hilbert, de Donder, Lanczos, Darmois and many others worked to put Einstein's ideas on a more solid footing. In fact, the issue of local uniqueness (giving a rigorous justification for the statement that the speed of propagation of the gravitational field is bounded by that of light) was already settled in the 1930s by the work of Stellmacher. However, the first person to demonstrate both local existence and uniqueness in a setting in which the notion of finite speed of propagation makes sense was Yvonne Choquet-Bruhat. In this sense, her work lays the foundation for the formulation of Einstein's equations as an initial value problem. Following a description of the results of Choquet-Bruhat, we discuss the development of three research topics that have their origin in her work. The first one is local existence. One reason for addressing it is that it is at the heart of the original paper. Moreover, it is still an active and important research field, connected to the problem of characterizing the asymptotic behaviour of solutions that blow up in finite time. As a second topic, we turn to the questions of global uniqueness and strong cosmic censorship. These questions are of fundamental importance to anyone interested in justifying that the Cauchy problem makes sense globally. They are also closely

  4. Uniformizable Cauchy spaces

    Directory of Open Access Journals (Sweden)

    Eva Lowen-Colebunders

    1982-09-01

    Full Text Available A family C of filters on a set X is uniformizable if there is a uniformity on X such that C is its collection of Cauchy filters. Using the theory of completions and Cauchy continuous maps for Cauchy spaces, we obtain characterizations of uniformizable Cauchy spaces. In particular, given a Cauchy structure C on X we investigate under what conditions the filter u(C=⋂F∈CF×F is a uniformity and C is its collection of Cauchy filters. This problem is treated using Cauchy covering systems.

  5. THE CAUCHY PROBLEM FOR THE SYSTEM OF EQUATIONS OF THERMOELASTICITY IN E^n

    Directory of Open Access Journals (Sweden)

    Ikbol E. Niyozov

    2014-05-01

    Full Text Available ABSTRACT: In this paper we consider the problem of analytical continuation of solutions to the system of equations of thermoelasticity in a bounded domain from their values and values of their strains on a part of the boundary of this domain, i.e., we study the Cauchy problem. ABSTRAK: Di dalam kajian ini, kami menyelidiki masalah keselanjaran analitik bagi penyelesaian-penyelesaian terhadap sistem persamaan-persamaan termoelastik di dalam domain bersempadan berdasarkan nilai-nilainya dan nilai tegasannya bagi sebahagian daripada sempadan domain tersebut, iaitu kami mengkaji masalah Cauchy.

  6. The Cauchy problem for a modified Camassa-Holm equation with analytic initial data

    OpenAIRE

    Gorsky, Jennifer M.

    2004-01-01

    We show that the periodic Cauchy problem for a modified Camassa-Holm equation with analytic initial data is analytic in the space variable $x$ for time near zero. By differentiating the equation and the initial condition with respect to $x$ we obtain a sequence of initial-value problems of KdV-type equations. These, written in the form of integral equations, define a mapping on a Banach space whose elements are sequences of functions equipped with a norm expressing the Cauchy e...

  7. An optimal iterative algorithm to solve Cauchy problem for Laplace equation

    KAUST Repository

    Majeed, Muhammad Usman

    2015-05-25

    An optimal mean square error minimizer algorithm is developed to solve severely ill-posed Cauchy problem for Laplace equation on an annulus domain. The mathematical problem is presented as a first order state space-like system and an optimal iterative algorithm is developed that minimizes the mean square error in states. Finite difference discretization schemes are used to discretize first order system. After numerical discretization algorithm equations are derived taking inspiration from Kalman filter however using one of the space variables as a time-like variable. Given Dirichlet and Neumann boundary conditions are used on the Cauchy data boundary and fictitious points are introduced on the unknown solution boundary. The algorithm is run for a number of iterations using the solution of previous iteration as a guess for the next one. The method developed happens to be highly robust to noise in Cauchy data and numerically efficient results are illustrated.

  8. A class of neutral functional differential equations and the abstract Cauchy problem

    International Nuclear Information System (INIS)

    In this paper we establish the basic equivalence between the generalized solutions of a certain class of Neutral Functional Differential Equations and the trajectories of the associated abstract Cauchy problem. These results have applications in several fields including Mathematical Biology, Ecology and Control Theory. (author)

  9. The Cauchy problem for a model of immiscible gas flow with large data

    Energy Technology Data Exchange (ETDEWEB)

    Sande, Hilde

    2008-12-15

    The thesis consists of an introduction and two papers; 1. The solution of the Cauchy problem with large data for a model of a mixture of gases. 2. Front tracking for a model of immiscible gas flow with large data. (AG) refs, figs

  10. Global 1 Estimation of the Cauchy Problem Solutions to the Navier-Stokes Equation

    OpenAIRE

    Asset Durmagambetov; Leyla Fazilova

    2014-01-01

    The analytic properties of the scattering amplitude are discussed, and a representation of the potential is obtained using the scattering amplitude. A uniform time estimation of the Cauchy problem solution for the Navier-Stokes equations is provided. The paper also describes the time blowup of classical solutions for the Navier-Stokes equations by the smoothness assumption.  

  11. The Cauchy Problem for Schrödinger Equations with Time-Dependent Hamiltonian

    Directory of Open Access Journals (Sweden)

    Massimo Cicognani

    2014-12-01

    Full Text Available We consider the Cauchy problem for a Schrödinger equation with an Hamiltonian depending also on the time variable and that may vanish at t = 0. We find optimal Levi conditions for well-posedness in Sobolev and Gevrey spaces.

  12. Cauchy Problem of Some Doubly Degenerate Parabolic Equations with Initial Datum a Measure

    Institute of Scientific and Technical Information of China (English)

    Hui Jun FAN

    2004-01-01

    This paper discusses the Cauchy problem of the equation ut=△·(|△um|p-2△um)-uq with initial datum a measure. Under the assumption of the parameters, one proves the existence and non-existence of the non-negative generalized solution.

  13. On the quasilinear Cauchy problem for a hyperbolic functional differential equation

    Directory of Open Access Journals (Sweden)

    Elżbieta Puźniakowska-Gałuch

    2015-01-01

    Full Text Available The Cauchy problem for hyperbolic functional differential equations is considered. Volterra and Fredholm dependence are considered. A theorem on the local existence of generalized solutions defined on the Haar pyramid is proved. A result on differentiability of a solution with respect to initial data is proved.

  14. The Cauchy problem for the homogeneous Monge-Ampere equation, III. Lifespan

    CERN Document Server

    Rubinstein, Yanir A

    2012-01-01

    We prove several results on the lifespan, regularity, and uniqueness of solutions of the Cauchy problem for the homogeneous complex and real Monge-Ampere equations (HCMA/HRMA) under various a priori regularity conditions. We use methods of characteristics in both the real and complex settings to bound the lifespan of solutions with prescribed regularity. In the complex domain, we characterize the C^3 lifespan of the HCMA in terms of analytic continuation of Hamiltonian mechanics and intersection of complex time characteristics. We use a conservation law type argument to prove uniqueness of solutions of the Cauchy problem for the HCMA. We then prove that the Cauchy problem is ill-posed in C^3, in the sense that there exists a dense set of C^3 Cauchy data for which there exists no C^3 solution even for a short time. In the real domain we show that the HRMA is equivalent to a Hamilton--Jacobi equation, and use the equivalence to prove that any differentiable weak solution is smooth, so that the differentiable li...

  15. Numerical analysis of Cauchy-type problem arising in electrical engineering

    OpenAIRE

    Dücker, Monika

    2010-01-01

    Inverse problems arise often in physical and technical processes. In this dissertation we consider problems of Cauchy-type based on the application of hybrid insulation. The experimental setup takes place at the NTNU Trondheim which placed at the disposal the measurements for the calculation. In this case we search Dirichlet or Neumann control for given Neumann measurements. After describing the problem of hybrid insulation and introducing the basic principals of functional analysis we analys...

  16. A robust data completion method for 2D Laplacian Cauchy problems

    International Nuclear Information System (INIS)

    The purpose is to propose an improved regularization method for data completion problems. This method is presented on the Cauchy problem for the Laplace equation in 2D situations. Many numerical simulations using finite element method highlight the efficiency of this new approach. In particular, it gives reconstructions with an increased accuracy, it is stable with respect to strong perturbations on the data and is able to deblur noisy data.

  17. A robust data completion method for 2D Laplacian Cauchy problems

    Energy Technology Data Exchange (ETDEWEB)

    Delvare, F [Laboratoire Energetique Explosions Structures and Institut PRISME, Universite d' Orleans and ENSI de Bourges, 88 Boulevard Lahitolle, 18020 Bourges Cedex (France); Cimetiere, A [Laboratoire de Metallurgie Physique, Universite de Poitiers and ENSMA Poitiers, Boulevard Marie et Pierre CURIE, Teleport 2, BP 30179, 86962 Futuroscope Chasseneuil Cedex (France)], E-mail: franck.delvare@ensi-bourges.fr, E-mail: alain.cimetiere@univ-poitiers.fr

    2008-11-01

    The purpose is to propose an improved regularization method for data completion problems. This method is presented on the Cauchy problem for the Laplace equation in 2D situations. Many numerical simulations using finite element method highlight the efficiency of this new approach. In particular, it gives reconstructions with an increased accuracy, it is stable with respect to strong perturbations on the data and is able to deblur noisy data.

  18. Global existence and decay of solutions of the Cauchy problem in thermoelasticity with second sound

    KAUST Repository

    Kasimov, Aslan R.

    2013-06-04

    We consider the one-dimensional Cauchy problem in non-linear thermoelasticity with second sound, where the heat conduction is modelled by Cattaneo\\'s law. After presenting decay estimates for solutions to the linearized problem, including refined estimates for data in weighted Lebesgue-spaces, we prove a global existence theorem for small data together with improved decay estimates, in particular for derivatives of the solutions. © 2013 Taylor & Francis.

  19. The Cauchy problem for the homogeneous Monge-Ampere equation, I. Toeplitz quantization

    CERN Document Server

    Rubinstein, Yanir A

    2010-01-01

    The Cauchy problem for the homogeneous (real and complex) Monge-Ampere equation (HRMA/HCMA) arises from the initial value problem for geodesics in the space of Kahler metrics. It is an ill-posed problem. We conjecture that, in its lifespan, the solution can be obtained by Toeplitz quantizing the Hamiltonian flow defined by the Cauchy data, analytically continuing the quantization, and then taking a kind of logarithmic classical limit. In this article, we prove that in the case of torus invariant metrics (where the HCMA reduces to the HRMA) this ``quantum analytic continuation potential" coincides with the well-known Legendre transform potential, and hence solves the equation as long as it is smooth. In the sequel we prove that the Legendre transform potential ceases to solve the HRMA after that time.

  20. The Fujita exponent for the Cauchy problem in the hyperbolic space

    Science.gov (United States)

    Bandle, Catherine; Pozio, Maria Assunta; Tesei, Alberto

    It is well known that the heat kernel in the hyperbolic space has a different behavior for large times than the one in the Euclidean space. The main purpose of this paper is to study its effect on the positive solutions of Cauchy problems with power nonlinearities. Existence and non-existence results for local solutions are derived. Emphasis is put on their long time behavior and on Fujita's phenomenon. To have the same situation as for the Cauchy problem in R, namely finite time blow up for all solutions if the exponent is smaller than a critical value and existence of global solutions only for powers above the critical exponent, we must introduce a weight depending exponentially on the time. In this respect the situation is similar to problems in bounded domains with Dirichlet boundary conditions. Important tools are estimates for the heat kernel in the hyperbolic space and comparison principles.

  1. On the Cauchy problem for some fractional order partial differential equations

    CERN Document Server

    Moustafa, O L

    2003-01-01

    In the present paper, we study the Cauchy problem for a fractional order partial differential equation of the form D sub t supalpha((partial deriv u(x,t))/(partial deriv t))-SIGMA sub a sub b sub s sub ( sub q sub ) sub = sub 2 sub m a sub q (x,t)D sub x sup q u(x,t)=SIGMA sub a sub b sub s sub ( sub q sub ) subapprox sub 2 sub m b sub q (x,t)D sub x sup q u(x,t) where 0Cauchy problem is studied, also a continuity property is considered.

  2. On the Cauchy problem for some fractional order partial differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Moustafa, Osama L. E-mail: olmoustafa@yahoo.com

    2003-09-01

    In the present paper, we study the Cauchy problem for a fractional order partial differential equation of the form D{sub t}{sup {alpha}}(({partial_derivative}u(x,t))/({partial_derivative}t))-{sigma}{sub abs(q)=2m}a{sub q}(x,t)D{sub x}{sup q}u(x,t)={sigma}{sub abs(q){approx}}{sub 2m}b{sub q}(x,t)D{sub x}{sup q}u(x,t) where 0<{alpha}{<=}1 and {sigma}{sub abs(q)=2m}a{sub q}(x,t)D{sub x}{sup q} is a uniformly elliptic partial differential operator. The existence and uniqueness of the solution of the considered Cauchy problem is studied, also a continuity property is considered.

  3. Global existence for weak solutions of the Cauchy problem in a model of radiation hydrodynamics

    Czech Academy of Sciences Publication Activity Database

    Ducomet, B.; Nečasová, Šárka

    2014-01-01

    Roč. 420, č. 1 (2014), s. 464-482. ISSN 0022-247X R&D Projects: GA ČR GAP201/10/1920; GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Cauchy problem * Navier - Stokes -Fourier system * radiation hydrodynamics Subject RIV: BA - General Mathematics Impact factor: 1.120, year: 2014 http://www.sciencedirect.com/science/article/pii/S0022247X14004855

  4. On the Cauchy problem for a doubly nonlinear degenerate parabolic equation with strongly nonlinear sources

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    In this article, we consider the existence of local and global solution to the Cauchy problem of a doubly nonlinear equation. By introducing the norms |||f|||h and h, we give the suffcient and necessary conditions on the initial value to the existence of local solution of doubly nonlinear equation. Moreover some results on the global existence and nonexistence of solutions are considered.

  5. Initial surface disturbance on a shear current: the Cauchy--Poisson problem with a twist

    OpenAIRE

    Ellingsen, Simen Å.

    2014-01-01

    We solve for the first time the classical linear Cauchy--Poisson problem for the time evolution an initial surface disturbance when a uniform shear current is present beneath the surface. The solution is general, including the effects of gravity, surface tension and constant finite depth. The particular case of an initially Gaussian disturbance of width $b$ is studied for different values of three system parameters: a "shear Froude number" $S\\sqrt{b/g}$ ($S$ is the uniform vorticity), the Bon...

  6. On the Blow-up Phenomena of Cauchy Problem for the Camassa- Holm Equation

    Institute of Scientific and Technical Information of China (English)

    LIU Yongqin; WANG Weike

    2006-01-01

    We focus on the blow-up phenomena of Cauchy problem for the Camassa-Holm equation. Blow-up can occur only in the form of wave-breaking, i.e. the solution is bounded but its slope becomes unbounded in finite time. We proved that there is such a point that its slope becomes infinite exactly at breaking time. We also gave the precise blow-up rate and the blow-up set.

  7. Probability representations of Cauchy problem solutions for quantum mechanics equations

    International Nuclear Information System (INIS)

    Probability representations of quantum mechanics equations in a number of cases allow to see a new interpretation of the generally accepted notions; they also serve as a theoretical basis of the numerical solution of a problems. Probability representations of the solutions of Schroedinger equations and Dirac-Pauli vector equations are presented. In addition, the Heisenberg picture of quantum mechanics equation is considered

  8. On Classical Solutions to the Cauchy Problem of the Two-Dimensional Barotropic Compressible Navier-Stokes Equations with Vacuum

    OpenAIRE

    Li, Jing; Liang, Zhilei

    2013-01-01

    This paper concerns the Cauchy problem of the barotropic compressible Navier-Stokes equations on the whole two-dimensional space with vacuum as far field density. In particular, the initial density can have compact support. When the shear and the bulk viscosities are a positive constant and a power function of the density respectively, it is proved that the two-dimensional Cauchy problem of the compressible Navier-Stokes equations admits a unique local strong solution provided the initial den...

  9. Efficient numerical method for solving Cauchy problem for the Gamma equation

    Science.gov (United States)

    Koleva, Miglena N.

    2011-12-01

    In this work we consider Cauchy problem for the so called Gamma equation, derived by transforming the fully nonlinear Black-Scholes equation for option price into a quasilinear parabolic equation for the second derivative (Greek) Γ = VSS of the option price V. We develop an efficient numerical method for solving the model problem concerning different volatility terms. Using suitable change of variables the problem is transformed on finite interval, keeping original behavior of the solution at the infinity. Then we construct Picard-Newton algorithm with adaptive mesh step in time, which can be applied also in the case of non-differentiable functions. Results of numerical simulations are given.

  10. GENERAL CAUCHY PROBLEM FOR THE LINEAR SHALLOW -WATER EQUATIONS ON AN EQUATORIAL BETA-PLANE

    Institute of Scientific and Technical Information of China (English)

    SHEN Chun; SHI Wei-hui

    2006-01-01

    Based on the theory of stratification, the well-posedness of the initial value problem for the linear shallow-water equations on an equatorial beta-plane was discussed. The sufficient and necessary conditions of the existence and uniqueness for the local solution of the equations were presented and the existence conditions for formal solutions of the equations were also given. For the Cauchy problem on the hyper-plane, the local analytic solution were worked out and a special case was discussed. Finally, an example was used to explain the variety of formal solutions for the ill-posed problem.

  11. A Series Solution of the Cauchy Problem for Turing Reaction-diffsion Model

    OpenAIRE

    L. Päivärinta; Shidfar, A.; A. Molabahrami

    2011-01-01

    In this paper, the series pattern solution of the Cauchy problem for Turing reaction-diffusion model is obtained by using the homotopy analysis method (HAM). Turing reaction-diffusion model is nonlinear reaction-diffusion system which usually has power-law nonlinearities or may be rewritten in the form of power-law nonlinearities. Using the HAM, it is possible to find the exact solution or an approximate solution of the problem. This technique provides a series of functions which converges ra...

  12. A remark on the Cauchy problem for the generalized Benney-Luke equation

    OpenAIRE

    Quintero, José Raúl

    2008-01-01

    In this article, we address the well posedness of the Cauchy problem associated with the generalized Benney--Luke equation in $\\mathbb R^{1+2}:$ \\begin{multline*} \\Phi_{tt} - \\Delta \\Phi + a \\Delta^2 \\Phi - b \\Delta \\Phi_{tt} + \\theta\\Big ( \\Phi_t \\big [\\partial_{x} \\big [ \\big (\\partial_{x} \\Phi \\big )^{p} \\big ]+ \\partial_{y} \\big [ \\big (\\partial_{y}\\Phi \\big )^{p} \\big ] \\big ] \\\\ + 2 \\big [ \\big (\\partial_{x} \\Phi \\big )^{p}\\Phi_{xt}+ \\big (\\partial_{y} \\Phi \\big )^{p}\\Phi...

  13. On the Cauchy problem for nonlinear Schrödinger equations with rotation

    KAUST Repository

    Antonelli, Paolo

    2011-10-01

    We consider the Cauchy problem for (energy-subcritical) nonlinear Schrödinger equations with sub-quadratic external potentials and an additional angular momentum rotation term. This equation is a well-known model for superuid quantum gases in rotating traps. We prove global existence (in the energy space) for defocusing nonlinearities without any restriction on the rotation frequency, generalizing earlier results given in [11, 12]. Moreover, we find that the rotation term has a considerable in fiuence in proving finite time blow-up in the focusing case.

  14. Well-Posedness of the Cauchy Problem for a Space-Dependent Anyon Boltzmann Equation

    OpenAIRE

    Arkeryd, Leif; Nouri, Anne

    2015-01-01

    A fully non-linear kinetic Boltzmann equation for anyons is studied in a periodic 1d setting with large initial data. Strong L 1 solutions are obtained for the Cauchy problem. The main results concern global existence, uniqueness and stabililty. We use the Bony functional, the two-dimensional velocity frame specific for anyons, and an initial layer analysis that moves the solution away from a critical value. 1 Anyons and the Boltzmann equation. Let us first recall the definition of anyon. Con...

  15. The Cauchy problem for the homogeneous Monge-Ampere equation, II. Legendre transform

    CERN Document Server

    Rubinstein, Yanir A

    2010-01-01

    We continue our study of the Cauchy problem for the homogeneous (real and complex) Monge-Ampere equation (HRMA/HCMA). In the prequel a quantum mechanical approach for solving the HCMA was developed, and was shown to coincide with the well-known Legendre transform approach in the case of the HRMA. In this article---that uses only tools of convex analysis and can be read independently---we prove that the candidate solution produced by these methods ceases to solve the HRMA, even in a weak sense, as soon as it ceases to be differentiable.

  16. The Cauchy problem for the (generalized) Kadomtsev-Petviashvili-Burgers equation

    OpenAIRE

    Molinet, Luc

    2000-01-01

    We investigate the Cauchy problem for the generalized Kadomtsev-Petviashvili-Burgers (KP-Burgers) equation in Sobolev spaces. This nonlinear wave equation has both dispersive and dissipative parts which makes it quite particular. After showing local existence by contraction principle for initial data $ \\varphi\\in H^s(\\mathbb R^2) $ such that $ {\\mathcal F}^{-1} (\\frac{k_2}{k_1} \\widehat{\\varphi})\\in H^r(\\mathbb R^2) $, $ 0{\\leqslant} r {\\leqslant} s- 1 $, we try to extend the s...

  17. Two-point boundary value and Cauchy formulations in an axisymmetrical MHD equilibrium problem

    International Nuclear Information System (INIS)

    In this paper we present two equilibrium solvers for axisymmetrical toroidal configurations, both based on the expansion in poloidal angle method. The first one has been conceived as a two-point boundary value solver in a system of coordinates with straight field lines, while the second one uses a well-conditioned Cauchy formulation of the problem in a general curvilinear coordinate system. In order to check the capability of our moment methods to describe equilibrium accurately, a comparison of the moment solutions with analytical solutions obtained for a Solov'ev equilibrium has been performed. (author)

  18. A Series Solution of the Cauchy Problem for Turing Reaction-diffusion Model

    Directory of Open Access Journals (Sweden)

    L. Päivärinta

    2011-12-01

    Full Text Available In this paper, the series pattern solution of the Cauchy problem for Turing reaction-diffusion model is obtained by using the homotopy analysis method (HAM. Turing reaction-diffusion model is nonlinear reaction-diffusion system which usually has power-law nonlinearities or may be rewritten in the form of power-law nonlinearities. Using the HAM, it is possible to find the exact solution or an approximate solution of the problem. This technique provides a series of functions which converges rapidly to the exact solution of the problem. The efficiency of the approach will be shown by applying the procedure on two problems. Furthermore, the so-called homotopy-Pade technique (HPT is applied to enlarge the convergence region and rate of solution series given by the HAM.

  19. A dimension decomposition approach based on iterative observer design for an elliptic Cauchy problem

    KAUST Repository

    Majeed, Muhammad Usman

    2015-07-13

    A state observer inspired iterative algorithm is presented to solve boundary estimation problem for Laplace equation using one of the space variables as a time-like variable. Three dimensional domain with two congruent parallel surfaces is considered. Problem is set up in cartesian co-ordinates and Laplace equation is re-written as a first order state equation with state operator matrix A and measurements are provided on the Cauchy data surface with measurement operator C. Conditions for the existence of strongly continuous semigroup generated by A are studied. Observability conditions for pair (C, A) are provided in infinite dimensional setting. In this given setting, special observability result obtained allows to decompose three dimensional problem into a set of independent two dimensional sub-problems over rectangular cross-sections. Numerical simulation results are provided.

  20. On the Regularity of the Solutions for Cauchy Problem of Incompressible 3D Navier-Stokes Equation

    OpenAIRE

    Lin, Qun

    2013-01-01

    In this paper we will prove that the vorticity belongs to $L^{\\infty}(0, T; L^2(R^3))$ for the Cauchy problem of 3D incompressible Navier-Stokes equation, then the existence of a global smooth solution is obtained. Our approach is to construct a set of auxiliary problems to approximate the original one for vorticity equation.

  1. Cauchy problem for multiscale conservation laws: Application to structured cell populations

    CERN Document Server

    Shang, Peipei

    2010-01-01

    In this paper, we study a vector conservation law that models the growth and selection of ovarian follicles. During each ovarian cycle, only a definite number of follicles ovulate, while the others undergo a degeneration process called atresia. This work is motivated by a multiscale mathematical model starting on the cellular scale, where ovulation or atresia result from a hormonally controlled selection process. A two-dimensional conservation law describes the age and maturity structuration of the follicular cell populations. The densities intersect through a coupled hyperbolic system between different follicles and cell phases, which results in a vector conservation law and coupling boundary conditions. The maturity velocity functions possess both a local and nonlocal character. We prove the existence and uniqueness of the weak solution to the Cauchy problem with bounded initial and boundary data.

  2. Uniqueness of solutions of a generalized Cauchy problem for a system of first order partial functional differential equations

    Directory of Open Access Journals (Sweden)

    Milena Netka

    2009-01-01

    Full Text Available The paper is concerned with weak solutions of a generalized Cauchy problem for a nonlinear system of first order differential functional equations. A theorem on the uniqueness of a solution is proved. Nonlinear estimates of the Perron type are assumed. A method of integral functional inequalities is used.

  3. Existence of Mild Solutions for Nonlocal Cauchy Problem for Fractional Neutral Integro-Differential Equation with Unbounded Delay

    OpenAIRE

    dos Santos, J. P. C.; Vijayakumar, V.; R. Murugesu

    2013-01-01

    In this article, we study the existence of mild solutions for the nonlocal Cauchy problem for a class of abstract fractional neutral integro-differential equations with infinite delay. The results are obtained by using the theory of resolvent operators. Finally, an application is given to illustrate the theory.

  4. Cauchy-Neumann Problem for Second-Order General Schrödinger Equations in Cylinders with Nonsmooth Bases

    Directory of Open Access Journals (Sweden)

    Nguyen Manh Hung

    2009-01-01

    Full Text Available The main goal of this paper is to obtain the regularity of weak solutions of Cauchy-Neumann problems for the second-order general Schrödinger equations in domains with conical points on the boundary of the bases.

  5. The exact solution of the Cauchy problem for two generalized linear vectorial Fokker-Planck equations: algebraic approach

    International Nuclear Information System (INIS)

    The exact solutions of the Cauchy problem for two equations which are slight generalization of the so-called linear vectorial Fokker-Planck equation are found using the disentangling techniques of Feynman and algebraic (operational) methods. This approach may be considered as a generalization of the Suzuki's method for solving the one-dimensional linear Pokker-Planck equation

  6. The Cauchy problem for metric-affine f(R)-gravity in presence of perfect-fluid matter

    CERN Document Server

    Capozziello, S

    2009-01-01

    The Cauchy problem for metric-affine f(R)-gravity `a la Palatini and with torsion, in presence of perfect fluid matter acting as source, is discussed following the well-known Bruhat prescriptions for General Relativity. The problem results well-formulated and well-posed when the perfect-fluid form of the stress-energy tensor is preserved under conformal transformations. The key role of conservation laws in Jordan and in Einstein frame is also discussed.

  7. Initial surface disturbance on a shear current: the Cauchy--Poisson problem with a twist

    CERN Document Server

    Ellingsen, Simen Å

    2014-01-01

    We solve for the first time the classical linear Cauchy--Poisson problem for the time evolution an initial surface disturbance when a uniform shear current is present beneath the surface. The solution is general, including the effects of gravity, surface tension and constant finite depth. The particular case of an initially Gaussian disturbance of width $b$ is studied for different values of three system parameters: a "shear Froude number" $S\\sqrt{b/g}$ ($S$ is the uniform vorticity), the Bond number and the depth relative to the initial perturbation width. Different phase and group velocity in different directions yield very different wave patterns in different parameter regimes when the shear is strong, and the well known pattern of diverging ring waves in the absence of shear can take on very different qualitative behaviours. For a given shear Froude number, both finite depth and nonzero capillary effects are found to weaken the influence of the shear on the resulting wave pattern. The various patterns are...

  8. Well-posedness of the Cauchy problem for models of large amplitude internal waves

    International Nuclear Information System (INIS)

    We consider in this paper the 'shallow-water/shallow-water' asymptotic model obtained in Choi and Camassa (1999 J. Fluid Mech. 396 1–36), Craig et al (2005 Commun. Pure. Appl. Math. 58 1587–641) (one-dimensional interface) and Bona et al (2008 J. Math. Pures Appl. 89 538–66) (two-dimensional interface) from the two-layer system with rigid lid, for the description of large amplitude internal waves at the interface of two layers of immiscible fluids of different densities. For one-dimensional interfaces, this system is of hyperbolic type and its local well-posedness does not raise serious difficulties, although other issues (blow-up, loss of hyperbolicity, etc) turn out to be delicate. For two-dimensional interfaces, the system is nonlocal. Nevertheless, we prove that it conserves some properties of 'hyperbolic type' and show that the associated Cauchy problem is locally well posed in suitable Sobolev classes provided some natural restrictions are imposed on the data. These results are illustrated by numerical simulations with emphasis on the formation of shock waves

  9. Well-posedness of the Cauchy problem for the stochastic system for the Lorenz model for a baroclinic atmosphere

    International Nuclear Information System (INIS)

    The paper is concerned with the Cauchy problem for a nonlinear system of partial differential equations with parameters. This system describes the two-layer quasi-solenoidal Lorenz model for a baroclinic atmosphere on a rotating two-dimensional sphere. The right-hand side of the system is perturbed by white noise, and random initial data is considered. This system is shown to be uniquely solvable, and an estimate for the continuous dependence of the solution on the set of random initial data and the right-hand side is established on a finite time interval. In passing, an estimate for the continuous dependence on the set of parameters, the initial data, and the right-hand side is obtained on a finite time interval for the solution of the Cauchy problem with deterministic initial data and deterministic right-hand side. Bibliography: 32 titles.

  10. ON THE STABILITY OF THE POSITIVE RADIAL STEADY STATES FOR A SEMILINEAR CAUCHY PROBLEM INVOLVING CRITICAL EXPONENTS

    Institute of Scientific and Technical Information of China (English)

    Deng Yinbin; Yang Fen

    2008-01-01

    This article is contributed to the Cauchy problem u/t = △u + K(ㄧxㄧ)up in Rn x (0,T), u(x,0) =(ψ)(x) in Rn; with initial function(ψ)≠0. The stability of positive radial steady state, which are positive solutions of △u + K(ㄧxㄧ)up =0, is obtained when p is critical for general K(ㄧxㄧ).

  11. On the Cauchy problem for the Korteweg–de Vries equation with steplike finite-gap initial data: I. Schwartz-type perturbations

    International Nuclear Information System (INIS)

    We solve the Cauchy problem for the Korteweg–de Vries equation with initial conditions which are steplike Schwartz-type perturbations of finite-gap potentials under the assumption that the respective spectral bands either coincide or are disjoint

  12. El problema de Cauchy asociado a una ecuación del tipo Kuramoto-Sivashisky bidimensional periódica / The problem of Cauchy associated to an equation of type Kuramoto-Sivashisky two-dimensional periodic

    OpenAIRE

    Campos Palomino, Juvitsa Milena

    2009-01-01

    El propósito de este trabajo es abordar la buena colocación en los espacios de Sobolev Hs(T2) para s≥1 del problema de Cauchy asociado a una ecuación del tipo Kuramoto-Sivashisky bidimensional periódica; que modela fenómenos físicos que ocurren en películas delgadas y plasma. / Abstract. The purpose of this work is to establish the well-posedness in the spaces Sobolev spaces Hs(T2) para s≥1 for the Cauchy problem associated for the Kuramoto-Sivashisky two-dimensional equation in the periodica...

  13. Diffuse interface methods for inverse problems: case study for an elliptic Cauchy problem

    Science.gov (United States)

    Burger, Martin; Løseth Elvetun, Ole; Schlottbom, Matthias

    2015-12-01

    Many inverse problems have to deal with complex, evolving and often not exactly known geometries, e.g. as domains of forward problems modeled by partial differential equations. This makes it desirable to use methods which are robust with respect to perturbed or not well resolved domains, and which allow for efficient discretizations not resolving any fine detail of those geometries. For forward problems in partial differential equations methods based on diffuse interface representations have gained strong attention in the last years, but so far they have not been considered systematically for inverse problems. In this work we introduce a diffuse domain method as a tool for the solution of variational inverse problems. As a particular example we study ECG inversion in further detail. ECG inversion is a linear inverse source problem with boundary measurements governed by an anisotropic diffusion equation, which naturally cries for solutions under changing geometries, namely the beating heart. We formulate a regularization strategy using Tikhonov regularization and, using standard source conditions, we prove convergence rates. A special property of our approach is that not only operator perturbations are introduced by the diffuse domain method, but more important we have to deal with topologies which depend on a parameter \\varepsilon in the diffuse domain method, i.e. we have to deal with \\varepsilon -dependent forward operators and \\varepsilon -dependent norms. In particular the appropriate function spaces for the unknown and the data depend on \\varepsilon . This prevents the application of some standard convergence techniques for inverse problems, in particular interpreting the perturbations as data errors in the original problem does not yield suitable results. We consequently develop a novel approach based on saddle-point problems. The numerical solution of the problem is discussed as well and results for several computational experiments are reported. In

  14. The Cauchy problem for metric-affine f(R)-gravity in the presence of perfect-fluid matter

    International Nuclear Information System (INIS)

    The Cauchy problem for metric-affine f(R)-gravity in the manner of Palatini and with torsion, in the presence of perfect fluid matter acting as a source, is discussed following the well-known Bruhat prescriptions for general relativity. The problem results in being well formulated and well posed when the perfect-fluid form of the stress-energy tensor is preserved under conformal transformations and the set of viable f(R)-models is not empty. The key role of conservation laws in the Jordan and in the Einstein frame is also discussed.

  15. The Cauchy problem for metric-affine f(R)-gravity in the presence of perfect-fluid matter

    Science.gov (United States)

    Capozziello, S.; Vignolo, S.

    2009-09-01

    The Cauchy problem for metric-affine f(R)-gravity in the manner of Palatini and with torsion, in the presence of perfect fluid matter acting as a source, is discussed following the well-known Bruhat prescriptions for general relativity. The problem results in being well formulated and well posed when the perfect-fluid form of the stress-energy tensor is preserved under conformal transformations and the set of viable f(R)-models is not empty. The key role of conservation laws in the Jordan and in the Einstein frame is also discussed.

  16. The Cauchy problem for metric-affine f(R)-gravity in the presence of perfect-fluid matter

    Energy Technology Data Exchange (ETDEWEB)

    Capozziello, S [Dipartimento di Scienze Fisiche, Universita ' Federico II' di Napoli and INFN Sez. di Napoli, Compl. Univ. Monte S. Angelo Ed. N, via Cinthia, I-80126 Napoli (Italy); Vignolo, S [DIPTEM Sez. Metodi e Modelli Matematici, Universita di Genova, Piazzale Kennedy, Pad. D-16129 Genova (Italy)

    2009-09-07

    The Cauchy problem for metric-affine f(R)-gravity in the manner of Palatini and with torsion, in the presence of perfect fluid matter acting as a source, is discussed following the well-known Bruhat prescriptions for general relativity. The problem results in being well formulated and well posed when the perfect-fluid form of the stress-energy tensor is preserved under conformal transformations and the set of viable f(R)-models is not empty. The key role of conservation laws in the Jordan and in the Einstein frame is also discussed.

  17. A Semi-linear Backward Parabolic Cauchy Problem with Unbounded Coefficients of Hamilton–Jacobi–Bellman Type and Applications to Optimal Control

    International Nuclear Information System (INIS)

    We obtain weighted uniform estimates for the gradient of the solutions to a class of linear parabolic Cauchy problems with unbounded coefficients. Such estimates are then used to prove existence and uniqueness of the mild solution to a semi-linear backward parabolic Cauchy problem, where the differential equation is the Hamilton–Jacobi–Bellman equation of a suitable optimal control problem. Via backward stochastic differential equations, we show that the mild solution is indeed the value function of the controlled equation and that the feedback law is verified

  18. A Semi-linear Backward Parabolic Cauchy Problem with Unbounded Coefficients of Hamilton–Jacobi–Bellman Type and Applications to Optimal Control

    Energy Technology Data Exchange (ETDEWEB)

    Addona, Davide, E-mail: d.addona@campus.unimib.it [Università degli Studi di Milano Bicocca, (MILANO BICOCCA) Dipartimento di Matematica (Italy)

    2015-08-15

    We obtain weighted uniform estimates for the gradient of the solutions to a class of linear parabolic Cauchy problems with unbounded coefficients. Such estimates are then used to prove existence and uniqueness of the mild solution to a semi-linear backward parabolic Cauchy problem, where the differential equation is the Hamilton–Jacobi–Bellman equation of a suitable optimal control problem. Via backward stochastic differential equations, we show that the mild solution is indeed the value function of the controlled equation and that the feedback law is verified.

  19. Cauchy problem of semi-linear parabolic equations with weak data in homogeneous space and application to the Navier-Stokes equations

    Institute of Scientific and Technical Information of China (English)

    苗长兴

    2003-01-01

    In this paper we study the Cauchy problem for a class of semi-linear parabolic type equations withweak data in the homogeneous spaces. We give a method which can be used to construct local mild solutionsof the abstract Cauchy problem in Cσ,s,p and Lq([O, T);Hs,p) by introducing the concept of both admissiblequintuplet and compatible space and establishing time-space estimates for solutions to the linear parabolic typeequations. For the small data, we prove that these results can be extended globally in time. We also study theregularity of the solution to the abstract Cauchy problem for nonlinear parabolic type equations in Cσ,s,p. Asan application, we obtain the same result for Navier-Stokes equations with weak initial data in homogeneousSobolev spaces.

  20. Global Existence and Large Time Asymptotic Behavior of Strong Solutions to the Cauchy Problem of 2D Density-Dependent Navier-Stokes Equations with Vacuum

    OpenAIRE

    Lv, Boqiang; Shi, Xiaoding; Zhong, Xin

    2015-01-01

    We are concerned with the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible Navier-Stokes equations with vacuum as far-field density. It is proved that if the initial density decays not too slow at infinity, the 2D Cauchy problem of the density-dependent Navier-Stokes equations on the whole space $\\mathbb{R}^2$ admits a unique global strong solution. Note that the initial data can be arbitrarily large and the initial density can contain vacuum states and even have compa...

  1. Exponential Decay for the Semilinear Cauchy-Ventcel Problem with Localized Damping

    Directory of Open Access Journals (Sweden)

    Mohamed Medjden

    2004-11-01

    Full Text Available Le but de ce travail est d’ étudier la décroissance exponentielle del’énergie des solutions losque le temps tend vers l’infini du problème aux limites de Cauchy-Ventcel semi-linéaire dissipatif dans un domaine borné. On donne des conditions suffisantes sur les non linéarités de f et g pour avoir la décroissance exponentielle de l’énergie. Ce problème décrit les vibrations d’un corps élastiqueavec un raidisseur mince sur le bord. La méthode de démonstration est basée sur les techniques de multiplicateurs et un principe de continuation unique qui permettent d’estimer l’énergie totale des solutions.

  2. On the theory of generalized entropy solutions of the Cauchy problem for a class of non-strictly hyperbolic systems of conservation laws

    International Nuclear Information System (INIS)

    Many-dimensional non-strictly hyperbolic systems of conservation laws with a radially degenerate flux function are considered. For such systems the set of entropies is defined and described, the concept of generalized entropy solution of the Cauchy problem is introduced, and the properties of generalized entropy solutions are studied. The class of strong generalized entropy solutions is distinguished, in which the Cauchy problem in question is uniquely soluble. A condition on the initial data is described that ensures that the generalized entropy solution is strong and therefore unique. Under this condition the convergence of the 'vanishing viscosity' method is established. An example presented in the paper shows that a generalized entropy solution is not necessarily unique in the general case

  3. Superfluidity of Minkowskian Higgs vacuum with BPS monopoles quantized by Dirac may be described as Cauchy problem to Gribov ambiguity equation

    CERN Document Server

    Lantsman, L

    2006-01-01

    We show that manifest superfluid properties of the Minkowskian Higgs model with vacuum BPS monopoles quantized by Dirac may be described in the framework of the Cauchy problem to the Gribov ambiguity equation. The latter equation specifies the ambiguity in choosing the covariant Coulomb (transverse) gauge for Yang-Mills fields represented as topological Dirac variables, may be treated as solutions to the Gauss law constraint at the removal of temporal components of these fields. We demonstrate that the above Cauchy problem comes just to fixing the covariant Coulomb gauge for topological Dirac variables in the given initial time instant $t_0$ and finding the solutions to the Gribov ambiguity equation in the shape of vacuum BPS monopoles and excitations over the BPS monopole vacuum referring to the class of multipoles. The next goal of the present study will be specifying the look of Gribov topological multipliers entering Dirac variables in the Minkowskian Higgs model quantized by Dirac, especially at the spat...

  4. Global Well-Posedness of Classical Solutions to the Cauchy problem of Two-Dimensional Baratropic Compressible Navier-Stokes System with Vacuum and Large Initial Data

    OpenAIRE

    Huang, Xiangdi; Li, Jing

    2012-01-01

    For smooth initial data, we establish the global existence and uniqueness of strong and classical solutions to the Cauchy problem for the barotropic compressible Navier-Stokes equations in two spatial dimensions with vacuum state as far field and with no restrictions on the size of initial data provided the shear viscosity is a positive constant and the bulk one is $\\lambda = \\rho^{\\beta}$ with $\\beta>4/3$.

  5. Some analytical properties of dissolving operators related with the Cauchy problem for a class of nonautonomous partial differential equations. Part 1

    Directory of Open Access Journals (Sweden)

    Marzena Pytel-Kudela

    2006-01-01

    Full Text Available The analytical properties of dissolving operators related with the Cauchy problem for a class of nonautonomous partial differential equations in Hilbert spaces are studied using theory of bi-linear forms in respectively rigged Hilbert spaces triples. Theorems specifying the existence of a dissolving operator for a class of adiabatically perturbed nonautonomous partial differential equations are stated. Some applications of the results obtained are discussed.

  6. Cauchy problems for fifth-order KdV equations in weighted Sobolev spaces

    Directory of Open Access Journals (Sweden)

    Eddye Bustamante

    2015-05-01

    Full Text Available In this work we study the initial-value problem for the fifth-order Korteweg-de Vries equation $$ \\partial_{t}u+\\partial_{x}^{5}u+u^k\\partial_{x}u=0, \\quad x,t\\in \\mathbb{R}, \\; k=1,2, $$ in weighted Sobolev spaces $H^s(\\mathbb{R}\\cap L^2(\\langle x \\rangle^{2r}dx$. We prove local and global results. For the case $k=2$ we point out the relationship between decay and regularity of solutions of the initial-value problem.

  7. On analytic continuability of the missing Cauchy datum for Helmholtz boundary problems

    DEFF Research Database (Denmark)

    Karamehmedovic, Mirza

    2015-01-01

    We relate the domains of analytic continuation of Dirichlet and Neumann boundary data for Helmholtz problems in two or more independent variables. The domains are related à priori, locally and explicitly in terms of complex polyrectangular neighbourhoods of planar pieces of the boundary. To this...

  8. Cauchy problem for doubly nonlinear parabolic equations with time-dependent source%具时间依赖源的双非线性抛物方程的 Cauchy 问题

    Institute of Scientific and Technical Information of China (English)

    成军祥; 尚海锋

    2013-01-01

    研究了方程ut-div(|Dum|p-2 Dum )=t-σuq的Cauchy问题,其中m>0, p>1。 此方程为双非线性抛物方程,根据参数m, p的不同取值,方程主部会发生双重退化或双重奇异性。 本文利用先验估计和紧性方法以及对参数m, p作精细划分,得到了测度初值解的最优存在性。%The Cauchy problem of the equation.

  9. On analytic continuability of the missing Cauchy datum for Helmholtz boundary problems

    OpenAIRE

    Karamehmedovic, Mirza

    2015-01-01

    We relate the domains of analytic continuation of Dirichlet and Neumann boundary data for Helmholtz problems in two or more independent variables. The domains are related à priori, locally and explicitly in terms of complex polyrectangular neighbourhoods of planar pieces of the boundary. To this end we identify and characterise a special subspace of the standard pseudodifferential operators with real-analytic symbols. The result is applicable in the estimation of the domain of analytic contin...

  10. Uniqueness and stability of solution for Cauchy problem of degenerate quasilinear parabolic equations

    Institute of Scientific and Technical Information of China (English)

    2005-01-01

    [1]Oleinik, O. A., Samokhin,V. N., Mathematical Models in Boundary Layer Theorem, Boca Raton; Chapman and Hall/CRC, 1999.[2]Volpert, A.I., Hudjaev, S.I., On the problem for quasilinear degenerate parabolic equations of second order(Russian), Mat. Sb., 1967, 3: 374-396.[3]Zhao, J., Uniqueness of solutions of quasilinear degenerate parabolic equations, Northeastern Math. J., 1985,1(2): 153-165.[4]Wu, Z., Yin, J., Some properties of functions in BVx and their applications to the uniqueness of solutions for degenerate quasilinear parabolic equations, Northeastern Math. J., 1989,5(4): 395-422.[5]Brezis, H., Crandall, M.G., Uniqueness of solutions of the initial value problem for ut- △ψ(u) = 0, J.Math. Pures et Appl., 1979, 58: 153-163.[6]Kruzkov, S.N., First order quasilinear equations in several independent varaiables, Math. USSR-Sb., 1970, 10:217-243.[7]Cockburn, B., Gripenberg, G., Continious dependence on the nonlinearities of solutions of degenerate parabolic equations, J. Diff. Equatiaons, 1999, 151: 231-251.[8]Volpert, A.I., BV space and quasilinear equations, Mat. Sb., 1967, 73: 255-302.[9]Volpert, A.I., Hudjave, S.I., Analysis of class of discontinuous functions and the equations of mathematical physics (Russian), Izda. Nauka Moskwa, 1975.[10]Evans, L.C., Weak convergence methods for nonlinear partial differential equations, Conference Board of the Mathematical Sciences, Regional Conferences Series in Mathematics Number 74, 1998.[11]Wu, Z., Zhao, J., Yin, J., et al., Nonlinear Diffusion Equations, Singapore: Word Scientific, 2001.

  11. A large time asymptotics for the solution of the Cauchy problem for the Novikov-Veselov equation at negative energy with non-singular scattering data

    CERN Document Server

    Kazeykina, Anna

    2011-01-01

    In the present paper we are concerned with the Novikov--Veselov equation at negative energy, i.e. with the $(2 + 1)$--dimensional analog of the KdV equation integrable by the method of inverse scattering for the two--dimensional Schr\\"odinger equation at negative energy. We show that the solution of the Cauchy problem for this equation with non--singular scattering data behaves asymptotically as $\\frac{\\const}{t^{3/4}}$ in the uniform norm at large times $t$. We also present some arguments which indicate that this asymptotics is optimal.

  12. Sharp three sphere inequality for perturbations of a product of two second order elliptic operators and stability for the Cauchy problem for the anisotropic plate equation

    CERN Document Server

    Morassi, Antonino; Vessella, Sergio

    2010-01-01

    We prove a sharp three sphere inequality for solutions to third order perturbations of a product of two second order elliptic operators with real coefficients. Then we derive various kinds of quantitative estimates of unique continuation for the anisotropic plate equation. Among these, we prove a stability estimate for the Cauchy problem for such an equation and we illustrate some applications to the size estimates of an unknown inclusion made of different material that might be present in the plate. The paper is self-contained and the Carleman estimate, from which the sharp three sphere inequality is derived, is proved in an elementary and direct way based on standard integration by parts.

  13. Ordered Cauchy spaces

    Directory of Open Access Journals (Sweden)

    D. C. Kent

    1985-01-01

    Full Text Available This paper is concerned with the notion of “ordered Cauchy space” which is given a simple internal characterization in Section 2. It gives a discription of the category of ordered Cauchy spaces which have ordered completions, and a construction of the “fine completion functor” on this category. Sections 4 through 6 deals with certain classes of ordered Cauchy spaces which have ordered completions; examples are given which show that the fine completion does not preserve such properties as uniformizability, regularity, or total boundedness. From these results, it is evident that a further study of ordered Cauchy completions is needed.

  14. On the comparison of Cauchy mean values

    OpenAIRE

    Losonczi László

    2002-01-01

    Suppose that and exist, with , on . Then there is (moreover if ) such that where denotes the divided difference of at the points . This is the Cauchy Mean Value Theorem for divided differences (see e.g. [4]). If the function is invertible then is a mean value of . It is called the Cauchy mean of the numbers and will be denoted by ). Here we completely solve the comparison problem of Cauchy means in the special cases and . In the general case we find necessary conditions (which ar...

  15. Minimization of a constitutive law error functional to solve a Cauchy problem arising in plasma physics: the reconstruction of the magnetic flux in the vacuum surrounding the plasma in a Tokamak

    CERN Document Server

    Faugeras, Blaise; Blum, Jacques; Boulbe, Cedric

    2010-01-01

    A numerical method for the computation of the magnetic flux in the vacuum surrounding the plasma in a Tokamak is investigated. It is based on the formulation of a Cauchy problem which is solved through the minimization of a constitutive law error functional. Several numerical experiments are conducted which show the efficiency of the method.

  16. Asymptotic expansion of the solution of a Cauchy problem for singularly perturbed differential-operational nonlinear equation

    International Nuclear Information System (INIS)

    A formal asymptotic expansion of a solution of the initial problem for a singularly perturbed differential-operational nonlinear equation in a small parameter has been constructed in the critical case. Splash functions of and boundary functions have been estimated of found and assessment of the residual member of the expansion has been obtained

  17. Cauchy cluster process

    DEFF Research Database (Denmark)

    Ghorbani, Mohammad

    2013-01-01

    In this paper we introduce an instance of the well-know Neyman–Scott cluster process model with clusters having a long tail behaviour. In our model the offspring points are distributed around the parent points according to a circular Cauchy distribution. Using a modified Cramér-von Misses test...... statistic and the simulated pointwise envelopes it is shown that this model fits better than the Thomas process to the frequently analyzed long-leaf pine data-set....

  18. The Einstein Equations and the Large Scale Behavior of Gravitational Fields: 50 years of the Cauchy Problem in General Relativity

    International Nuclear Information System (INIS)

    Cosmology is a discipline that encompasses many diverse aspects of physics and astronomy. This is part of its attraction, but also a reason why it is difficult for new researchers to acquire sufficient grounding to enable them to make significant contributions early in their careers. For this reason there are many cosmology textbooks aimed at the advanced undergraduate/beginning postgraduate level. Physical Foundations of Cosmology by Viatcheslav Mukhanov is a worthy new addition to this genre. Like most of its competitors it does not attempt to cover every single aspect of the subject but chooses a particular angle and tries to unify its treatment around that direction. Mukhanov has chosen to focus on the fundamental principles underlying modern cosmological research at the expense of some detail at the frontiers. The book places great emphasis on the particle-astrophysics interface and issues connected with the thermal history of the big-bang model. The treatment of big-bang nucleosynthesis is done in much more detail than in most texts at a similar level, for example. It also contains a very extended and insightful discussion of inflationary models. Mukhanov makes great use of approximate analytical arguments to develop physical intuition rather than concentrating on numerical approaches. The book is quite mathematical, but not in a pedantically formalistic way. There is much use of 'order-of-magnitude' dimensional arguments which undergraduate students often find difficult to get the hang of, but which they would do well to assimilate as early as possible in their research careers. The text is peppered with problems for the reader to solve, some straightforward and some exceedingly difficult. Solutions are not provided. The price to be paid for this foundational approach is that there is not much about observational cosmology in this book, and neither is there much about galaxy formation or large-scale structure. It also neglects some of the trendier recent

  19. THE CAUCHY-KOVALEVSKAYA THEOREM-OLD AND NEW

    Institute of Scientific and Technical Information of China (English)

    W. Tutschke

    2005-01-01

    The paper surveys interactions between complex and functional-analytic methods in the Cauchy-Kovalevskaya theory. For instance, the behaviour of the derivative of a bounded holomorphic function led to abstract versions of the Cauchy-Kovalevskaya Theorem.Recent trends in the Cauchy-Kovalevskaya theory are based on the concept of associated differential operators. Since an evolution operator may posses several associated operators, initial data may be decomposed into components belonging to different associated spaces. This technique makes it also possible to solve ill-posed initial value problems.

  20. 带势的非线性Klein-Gordon方程柯西问题的稳定和不稳定集%Stable and Unstable Sets for the Cauchy Problem for Nonlinear Klein-Gordon Equation with Potential

    Institute of Scientific and Technical Information of China (English)

    蒋毅; 成和平; 孟宪良; 蒲成林

    2006-01-01

    For the Cauchy problem for the nonlinear Klein-Gordon equation with potential,we define new stable and unstable sets for the initial data.We prove that if during the evolution enters into the unstable set,the solution blows up in finite time.If during the evolution enters into the stable set,the solution is global.By using scaling argument,we also answer the question of how small the initial data are the global solution of the Cauchy problem exists.%对带势的非线性Klein-Gordon方程柯西问题,我们定义了新的对于初值的稳定和不稳定集.我们证明了如果发展进入了不稳定集,解在有限时间内爆破;如果发展进入了稳定集,解整体存在.运用势并讨论,我们回答了当初值为多少时,柯西问题的整体解存在.

  1. Identifiability of surface sources from Cauchy data

    International Nuclear Information System (INIS)

    We explore the reconstruction of surface sources from single Cauchy data on the potential. Identifiability is first proven when the location of these sources is known and their density is to be sought. We also investigate the ill-posedness degree to establish that the problem is severely ill-posed, and exhibit the necessary orthogonality conditions fulfilled by exact Cauchy data, for which the process of recovering the density function of the sources succeeds. We later turn to the more difficult reconstruction of the location, the shape and the density function of the sources. Identifiability cannot be obtained for general geometries. Nevertheless, under some acceptable assumptions on the size and the location of these sources, we are able to state identifiability results

  2. Conservation law for the Cauchy-Navier equation of elastodynamics wave via Fourier transform

    OpenAIRE

    Van Vinh, Nguyen; Minh, Nguyen Tuan

    2012-01-01

    In this paper, we use the method of Fourier analysis to derive the formula of the total energy for the Cauchy problem of the Cauchy-Navier elastodynamics wave equation describing the motion of an isotropic elastic body. The conservation law of the total energy is obtained and consequently, the global uniqueness of the solution to the problem is implied.

  3. 一个退化抛物-双曲方程柯西问题熵解的唯一性%Uniqueness of the Entropy Solutions to Cauchy Problem for a Degenerate Parabolic-Hyperbolic Equation

    Institute of Scientific and Technical Information of China (English)

    郝兴文; 王钦

    2011-01-01

    Kuznetsov方法是估计双曲型方程熵解与它的数值解之间误差的有效方法,文中应用该方法证明一个二阶退化抛物-双曲方程熵解的唯一性,并用双变量方法得到了熵解在初值的L1连续性.%Kuznetsov's method is a useful tool to establish the error estimate between numerical solutions and entropy weak solution for hyperbolic equation.This paper uses this method to prove the uniqueness to the Cauchy problem of a special example of second order degenerate parabolic-hyperbolic equation,Meanwhile,the paper obtained that entropy solutions are continuous at t=0 in the sense of L1 norm by the double variable device.

  4. The regularity series of a Cauchy space

    Directory of Open Access Journals (Sweden)

    Darrell C. Kent

    1984-03-01

    Full Text Available This study extends the notion of regularity series from convergence spaces to Cauchy spaces, and includes an investigation of related topics such as that T2 and T3 modifications of a Cauchy space and their behavior relative to certain types of quotient maps. These concepts are applied to obtain a new characterization of Cauchy spaces which have T3 completions.

  5. On Bimodal Offset Cauchy Distribution

    Directory of Open Access Journals (Sweden)

    Girija S.V.S.

    2013-05-01

    Full Text Available The bivariate Cauchy distribution has received applications in many areas, including biological analyses, clinical trials, stochastic modeling of decreasing failure rate life components, study of labour turnover, queuing theory and reliability (Nayak (1987 and Lee and Gross (1991. In the study of biological analyses, clinical trials and reliability circular distributions will yield suitable results. Circular data arises in a number of different areas such as geological, meteorological, biological and industrial sciences. It is not suggestive to use standard statistical techniques to model circular data, due to the circular geometry of the sample space (p.2 Jammalamadaka and Sen Gupta (2001. It is possible to construct a circular model by transforming a bivariate linear random variate to just its directional component and the resultant model is called ‘offset distribution’. In the literature most of the available circular models were constructed by wrapping a linear model. In recent years some wrapped models were constructed by Dattatreya Rao et al (2007. Here an attempt is made to exploit method of offsetting on Bivariate Cauchy distribution to construct a circular model named by us “OFFSET CAUCHY DISTRIBUTION (OC”. The characteristic function of the Offset Cauchy model is derived and its characteristics are discussed.

  6. Control of Cauchy System for an Elliptic Operator

    Institute of Scientific and Technical Information of China (English)

    G.MASSENGO MOPHOU; O.NAKOULIMA

    2009-01-01

    The control of a Cauchy system for an elliptic operator seems to be globally an open problem. In this paper, we analyze this problem using a regularization method which consists in viewing a singular problem as a limit of a family of well-posed problems. Following this analysis and assuming that the interior of considered convex is non-empty, we obtain a singular optimality system (S.O.S.) for the considered control problem.

  7. Variational approach for restoring blurred images with cauchy noise

    DEFF Research Database (Denmark)

    Sciacchitano, Federica; Dong, Yiqiu; Zeng, Tieyong

    2015-01-01

    model, we add a quadratic penalty term, which guarantees the uniqueness of the solution. Due to the convexity of our model, the primal dual algorithm is employed to solve the minimization problem. Experimental results show the effectiveness of the proposed method for simultaneously deblurring and...... denoising images corrupted by Cauchy noise. Comparison with other existing and well-known methods is provided as well....

  8. Uniqueness theorems for Cauchy integrals

    CERN Document Server

    Melnikov, Mark; Volberg, Alexander

    2007-01-01

    If $\\mu$ is a finite complex measure in the complex plane $\\C$ we denote by $C^\\mu$ its Cauchy integral defined in the sense of principal value. The measure $\\mu$ is called reflectionless if it is continuous (has no atoms) and $C^\\mu=0$ at $\\mu$-almost every point. We show that if $\\mu$ is reflectionless and its Cauchy maximal function $C^\\mu_*$ is summable with respect to $|\\mu|$ then $\\mu$ is trivial. An example of a reflectionless measure whose maximal function belongs to the "weak" $L^1$ is also constructed, proving that the above result is sharp in its scale. We also give a partial geometric description of the set of reflectionless measures on the line and discuss connections of our results with the notion of sets of finite perimeter in the sense of De Giorgi.

  9. Ideal-quasi-Cauchy sequences

    CERN Document Server

    Cakalli, Huseyin

    2012-01-01

    An ideal $I$ is a family of subsets of positive integers $\\textbf{N}$ which is closed under taking finite unions and subsets of its elements. A sequence $(x_n)$ of real numbers is said to be $I$-convergent to a real number $L$, if for each \\;$ \\varepsilon> 0$ the set $\\{n:|x_{n}-L|\\geq \\varepsilon\\}$ belongs to $I$. We introduce $I$-ward compactness of a subset of $\\textbf{R}$, the set of real numbers, and $I$-ward continuity of a real function in the senses that a subset $E$ of $\\textbf{R}$ is $I$-ward compact if any sequence $(x_{n})$ of points in $E$ has an $I$-quasi-Cauchy subsequence, and a real function is $I$-ward continuous if it preserves $I$-quasi-Cauchy sequences where a sequence $(x_{n})$ is called to be $I$-quasi-Cauchy when $(\\Delta x_{n})$ is $I$-convergent to 0. We obtain results related to $I$-ward continuity, $I$-ward compactness, ward continuity, ward compactness, ordinary compactness, ordinary continuity, $\\delta$-ward continuity, and slowly oscillating continuity.

  10. Complex integration and Cauchy's theorem

    CERN Document Server

    Watson, GN

    2012-01-01

    This brief monograph by one of the great mathematicians of the early twentieth century offers a single-volume compilation of propositions employed in proofs of Cauchy's theorem. Developing an arithmetical basis that avoids geometrical intuitions, Watson also provides a brief account of the various applications of the theorem to the evaluation of definite integrals.Author G. N. Watson begins by reviewing various propositions of Poincaré's Analysis Situs, upon which proof of the theorem's most general form depends. Subsequent chapters examine the calculus of residues, calculus optimization, the

  11. A local existence theorem of the solution of the Cauchy problem for BBGKY chain of equations represented in cumulant expansions in the space E_{ξ}

    Directory of Open Access Journals (Sweden)

    Myhaylo O. Stashenko

    2004-01-01

    Full Text Available It is proved convergence of solution in cumulant expansions of the initial value problem for BBGKY chain of equations of non-symmetrical one-dimensional system of particles which interact via a short-range potential in the space \\(E_{\\xi}\\ of the sequences of continuous bounded functions.

  12. The log-convexity of the poly-Cauchy numbers

    OpenAIRE

    Komatsu, Takao; Zhao, Feng-Zhen

    2016-01-01

    In 2013, Komatsu introduced the poly-Cauchy numbers, which generalize Cauchy numbers. Several generalizations of poly-Cauchy numbers have been considered since then. One particular type of generalizations is that of multiparameter-poly-Cauchy numbers. In this paper, we study the log-convexity of the multiparameter-poly-Cauchy numbers of the first kind and of the second kind. In addition, we also discuss the log-behavior of multiparameter-poly-Cauchy numbers.

  13. A Cauchy-Dirac delta function

    OpenAIRE

    Katz, Mikhail G.; Tall, David

    2012-01-01

    The Dirac delta function has solid roots in 19th century work in Fourier analysis and singular integrals by Cauchy and others, anticipating Dirac's discovery by over a century, and illuminating the nature of Cauchy's infinitesimals and his infinitesimal definition of delta.

  14. The Cauchy method of residues

    CERN Document Server

    Mitrinović, Dragoslav S

    1993-01-01

    Volume 1, i. e. the monograph The Cauchy Method of Residues - Theory and Applications published by D. Reidel Publishing Company in 1984 is the only book that covers all known applications of the calculus of residues. They range from the theory of equations, theory of numbers, matrix analysis, evaluation of real definite integrals, summation of finite and infinite series, expansions of functions into infinite series and products, ordinary and partial differential equations, mathematical and theoretical physics, to the calculus of finite differences and difference equations. The appearance of Volume 1 was acknowledged by the mathematical community. Favourable reviews and many private communications encouraged the authors to continue their work, the result being the present book, Volume 2, a sequel to Volume 1. We mention that Volume 1 is a revised, extended and updated translation of the book Cauchyjev raeun ostataka sa primenama published in Serbian by Nau~na knjiga, Belgrade in 1978, whereas the greater part ...

  15. El Cours d’Analyse de Cauchy

    OpenAIRE

    Pérez, Javier; Aizpuru, Antonio

    1999-01-01

    En este artículo presentamos un estudio contextualizado de Cours d’Analyse de Cauchy, analizando su significado e importancia. Presentamos especial atención al grado de elaboración teórica de límites, continuidad, series, números reales funciones y series completas, relacionando las aportaciones de Cauchi del nivel conceptual anterior a esta ahora.

  16. 带线性坍塌项和竞争势的非线性波动方程柯西问题的稳定集和不稳定集%Stable and Unstable Sets for the Cauchy Problem of the Nonlinear Wave Equation With Linear Damping and Potential Terms

    Institute of Scientific and Technical Information of China (English)

    蒋毅

    2011-01-01

    For the Cauchy problem of the nonlinear wave equation with linear damping and potential terms, we define new stable and unstable sets for the initial data. We prove that if during the evolution enters into the unstable set, the solution blows up in finite time. If during the evolution enters into the stable set, the solution is global. By using scaling argument, we also answer the question of how small the initial data are, the global solution of the Cauchy oroblem exists.%本文考虑带线性坍塌项和竞争势的非线性波动方程柯西问题.定义了新的稳定集和不稳定集,证明了如果初值进入不稳定集,则解在有限时间爆破;如果初值进入稳定集,则整体解存在.运用势井讨论,回答了当初值在多么小的时候,该柯西问题的整体解存在.

  17. Cauchy-characteristic evolution and waveforms

    International Nuclear Information System (INIS)

    This paper investigates a new method for computing waveforms generated by independent sources. A global spacetime evolution algorithms based on the Cauchy initial-value approach is used for the bounded interior area and the same algorithm based on the characteristic hypersurfaces is used for the exterior region. Both methods are equated at the common interface

  18. Cauchy-characteristic evolution and waveforms

    Energy Technology Data Exchange (ETDEWEB)

    Bishop, N.T. [Univ. of South Africa, Pretoria (South Africa); Holvorcem, P.R.; Matzner, R.A. [Univ. of Texas, Austin, TX (United States)]|[Pennsylvania State Univ., University Park, PA (United States)] [and others

    1997-09-01

    This paper investigates a new method for computing waveforms generated by independent sources. A global spacetime evolution algorithms based on the Cauchy initial-value approach is used for the bounded interior area and the same algorithm based on the characteristic hypersurfaces is used for the exterior region. Both methods are equated at the common interface.

  19. Dirac Equation with External Potential and Initial Data on Cauchy Surfaces

    CERN Document Server

    Deckert, D -A

    2014-01-01

    With this paper we provide a mathematical review on the initial-value problem of the one-particle Dirac equation on space-like Cauchy hypersurfaces for compactly supported external potentials. We, first, discuss the physically relevant spaces of solutions and initial values in position and mass shell representation; second, review the action of the Poincar\\'e group as well as gauge transformations on those spaces; third, introduce generalized Fourier transforms between those spaces and prove convenient Paley-Wiener- and Sobolev-type estimates. These generalized Fourier transforms immediately allow the construction of a unitary evolution operator for the free Dirac equation between the Hilbert spaces of square-integrable wave functions of two respective Cauchy surfaces. With a Picard-Lindel\\"of argument this evolution map is generalized to the Dirac evolution including the external potential. For the latter we introduce a convenient interaction picture on Cauchy surfaces. These tools immediately provide anothe...

  20. Moving Heat Source Reconstruction from the Cauchy Boundary Data

    Directory of Open Access Journals (Sweden)

    Nilson C. Roberty

    2010-01-01

    Full Text Available We consider the problem of reconstruction of an unknown characteristic transient thermal source inside a domain. By introducing the definition of an extended dirichlet-to-Neumann map in the time-space cylinder and the adoption of the anisotropic Sobolev-Hilbert spaces, we can treat the problem with methods similar to those used in the analysis of the stationary source reconstruction problem. Further, the finite difference θ scheme applied to the transient heat conduction equation leads to a model based on a sequence of modified Helmholtz equation solutions. For each modified Helmholtz equation the characteristic star-shape source function may be reconstructed uniquely from the Cauchy boundary data. Using representation formula, we establish reciprocity functional mapping functions that are solutions of the modified Helmholtz equation to their integral in the unknown characteristic support.

  1. External Field QED on Cauchy Surfaces

    CERN Document Server

    Deckert, D -A

    2015-01-01

    The Shale-Stinespring Theorem (1965) together with Ruijsenaar's criterion (1977) provide a necessary and sufficient condition for the implementability of the evolution of external field quantum electrodynamics between constant-time hyperplanes on standard Fock space. The assertion states that an implementation is possible if and only if the spacial components of the external electromagnetic four-vector potential $A_\\mu$ are zero. We generalize this result to smooth, space-like Cauchy surfaces and, for general $A_\\mu$, show how the second-quantized Dirac evolution can always be implemented as a map between varying Fock spaces. Furthermore, we give equivalence classes of polarizations, including an explicit representative, that give rise to those admissible Fock spaces. We prove that the polarization classes only depend on the tangential components of $A_\\mu$ w.r.t. the particular Cauchy surface, and show that they behave naturally under Lorentz and gauge transformations.

  2. Molecular dynamics at constant Cauchy stress

    Science.gov (United States)

    Miller, Ronald E.; Tadmor, Ellad B.; Gibson, Joshua S.; Bernstein, Noam; Pavia, Fabio

    2016-05-01

    The Parrinello-Rahman algorithm for imposing a general state of stress in periodic molecular dynamics simulations is widely used in the literature and has been implemented in many readily available molecular dynamics codes. However, what is often overlooked is that this algorithm controls the second Piola-Kirchhoff stress as opposed to the true (Cauchy) stress. This can lead to misinterpretation of simulation results because (1) the true stress that is imposed during the simulation depends on the deformation of the periodic cell, (2) the true stress is potentially very different from the imposed second Piola-Kirchhoff stress, and (3) the true stress can vary significantly during the simulation even if the imposed second Piola-Kirchhoff is constant. We propose a simple modification to the algorithm that allows the true Cauchy stress to be controlled directly. We then demonstrate the efficacy of the new algorithm with the example of martensitic phase transformations under applied stress.

  3. The random conductance model with Cauchy tails

    CERN Document Server

    Barlow, Martin T

    2009-01-01

    We consider a random walk in an i.i.d. Cauchy-tailed conductances environment. We obtain a quenched functional CLT for the suitably rescaled random walk, and, as a key step in the arguments, we improve the local limit theorem for $p^\\om_{n^2 t}(0,y)$ in [BD09, Theorem 5.14] to a result which gives uniform convergence for $p^\\om_{n^2 t}(x,y)$ for all $x, y$ in a ball.

  4. The Southampton Cauchy-characteristic matching project

    International Nuclear Information System (INIS)

    The Southampton Numerical Relativity Group have set up a long term project concerned with investigating Cauchy-characteristic matching (CCM) codes in numerical relativity. The CCM approach has two distinct features. Firstly, it dispenses with an outer boundary condition and replaces this with matching conditions at an interface residing in the vacuum between the Cauchy and characteristic regions. A successful CCM code leads to a transparent interface and so avoids the spurious reflections which plague most codes employing outer boundary conditions. Secondly, by employing a compactified coordinate, it proves possible to generate global solutions. This means that gravitational waves can be identified unambiguously at future null infinity. To date, cylindrical codes have been developed which have been checked against the exact solutions of Weber-Wheeler, Safier-Stark-Piran and Xanthopoulos. In addition, a cylindrical code has been constructed for investigating dynamic cosmic strings. Recently a master vacuum axi-symmetric CCM code has been completed which consists of four independent modules comprising an interior Cauchy code, an exterior characteristic code together with injection and extraction codes. The main goal of this work is to construct a 3 dimensional code possessing the characteristic, injection and extraction modules which can be attached to an interior code based on a finite grid. Such a code should lead to the construction of more accurate templates which are needed in the search for gravitational waves. (author)

  5. Une remarque sur le problème de Cauchy pour l'opérateur différentiel de partie principale à coefficients polynomiaux

    OpenAIRE

    Hamada, Yûsaku

    2000-01-01

    In our preceding article, by applying the results of Bieberbach, Fatou and Picard, we have studied the domain of holomorphy of the solution of the Cauchy problem for the differential operator with coefficients of entire functions. In this article, by employing the results of the modular function and its ordinary differential equation, we give a remark on the domain of holomorphy of the solution of the Cauchy problem for the differential operator of principal part with polynomial coefficients.

  6. Proof of linear instability of the Reissner-Nordstr\\"om Cauchy horizon under scalar perturbations

    CERN Document Server

    Luk, Jonathan

    2015-01-01

    It has long been suggested that solutions to linear scalar wave equation $$\\Box_g\\phi=0$$ on a fixed subextremal Reissner-Nordstr\\"om spacetime with non-vanishing charge are generically singular at the Cauchy horizon. We prove that generic smooth and compactly supported initial data on a Cauchy hypersurface indeed give rise to solutions with infinite nondegenerate energy near the Cauchy horizon in the interior of the black hole. In particular, the solution generically does not belong to $W^{1,2}_{loc}$. This instability is related to the celebrated blue shift effect in the interior of the black hole. The problem is motivated by the strong cosmic censorship conjecture and it is expected that for the full nonlinear Einstein-Maxwell system, this instability leads to a singular Cauchy horizon for generic small perturbations of Reissner-Nordstr\\"om spacetime. Moreover, in addition to the instability result, we also show as a consequence of the proof that Price's law decay is generically sharp along the event horiz...

  7. Structure of the Cauchy horizon singularity

    CERN Document Server

    Burko, L M

    1999-01-01

    We study the Cauchy horizon (CH) singularity of a spherical charged black hole perturbed nonlinearly by a self-gravitating massless scalar field. We show numerically that the singularity is weak both at the early and at the late sections of the CH, where the focusing of the area coordinate $r$ is strong. In the early section the metric perturbations vanish, and the fields behave according to perturbation analysis. We find exact analytical expressions for the gradients of $r$ and of the scalar field, which are valid at both sections. We then verify these analytical results numerically.

  8. Application of geometric algebra to electromagnetic scattering the Clifford-Cauchy-Dirac technique

    CERN Document Server

    Seagar, Andrew

    2016-01-01

    This work presents the Clifford-Cauchy-Dirac (CCD) technique for solving problems involving the scattering of electromagnetic radiation from materials of all kinds. It allows anyone who is interested to master techniques that lead to simpler and more efficient solutions to problems of electromagnetic scattering than are currently in use. The technique is formulated in terms of the Cauchy kernel, single integrals, Clifford algebra and a whole-field approach. This is in contrast to many conventional techniques that are formulated in terms of Green's functions, double integrals, vector calculus and the combined field integral equation (CFIE). Whereas these conventional techniques lead to an implementation using the method of moments (MoM), the CCD technique is implemented as alternating projections onto convex sets in a Banach space. The ultimate outcome is an integral formulation that lends itself to a more direct and efficient solution than conventionally is the case, and applies without exception to all types...

  9. Self-accelerating Massive Gravity: Superluminality, Cauchy Surfaces and Strong Coupling

    CERN Document Server

    Motloch, Pavel; Joyce, Austin; Motohashi, Hayato

    2015-01-01

    Self-accelerating solutions in massive gravity provide explicit, calculable examples that exhibit the general interplay between superluminality, the well-posedness of the Cauchy problem, and strong coupling. For three particular classes of vacuum solutions, one of which is new to this work, we construct the conformal diagram for the characteristic surfaces on which isotropic stress-energy perturbations propagate. With one exception, all solutions necessarily possess spacelike characteristics, indicating perturbative superluminality. Foliating the spacetime with these surfaces gives a pathological frame where kinetic terms of the perturbations vanish, confusing the Hamiltonian counting of degrees of freedom. This frame dependence distinguishes the vanishing of kinetic terms from strong coupling of perturbations or an ill-posed Cauchy problem. We give examples where spacelike characteristics do and do not originate from a point where perturbation theory breaks down and where spacelike surfaces do or do not inte...

  10. Cauchy-Rassias Stability of Cauchy-Jensen Additive Mappings in Banach Spaces

    Institute of Scientific and Technical Information of China (English)

    Choonkil BAAK

    2006-01-01

    Let X, Y be vector spaces. It is shown that if a mapping f: X → Y satisfiesf(x+y/2+z)+f(x-y/2+z)=f(x)+2f(z), (0.1)f(x+y/2+z)-f(x-y/2+z)= f(y), (0.2)or2f(x+y/2+z)=f(x)+f(y)+2f(z) (0.3)for all x, y, z ∈ X, then the mapping f: X → Y is Cauchy additive.Furthermore, we prove the Cauchy-Rassias stability of the functional equations (0.1), (0.2) and (0.3) in Banach spaces. The results are applied to investigate isomorphisms between unital Banach algebra.

  11. Abstract Description of Internet Traffic of Generalized Cauchy Type

    Directory of Open Access Journals (Sweden)

    Ming Li

    2012-01-01

    . Therefore, there is a limitation for fGn to accurately model traffic. Recently, the generalized Cauchy (GC process was introduced to model traffic with the flexibility to separately measure the fractal dimension DGC and the Hurst parameter HGC of traffic. However, there is a fundamental problem whether or not there exists the generality that the GC model is more conformable with real traffic than single parameter models, such as fGn, irrelevant of traffic traces used in experimental verification. The solution to that problem remains unknown but is desired for model evaluation in traffic theory or for model selection against specific issues, such as queuing analysis relating to the autocorrelation function (ACF of arrival traffic. The key contribution of this paper is our solution to that fundamental problem (see Theorem 3.17 with the following features in analysis. (i Set-valued analysis of the traffic of the fGn type. (ii Set-valued analysis of the traffic of the GC type. (iii Revealing the generality previously mentioned by comparing metrics of the traffic of the fGn type to that of the GC type.

  12. Cauchy Based Matched Filter for Retinal Vessels Detection

    OpenAIRE

    Zolfagharnasab, Hooshiar; Naghsh-Nilchi, Ahmad Reza

    2014-01-01

    In this paper, a novel matched filter based on a new kernel function with Cauchy distribution is introduced to improve the accuracy of the automatic retinal vessel detection compared with other available matched filter-based methods, most notably, the methods built on Gaussian distribution function. Several experiments are conducted to pick the best values of the parameters for the new designed filter, including both Cauchy function parameters as well as the matched filter parameters such as ...

  13. Cauchy-Kowalevski and polynomial ordinary differential equations

    Directory of Open Access Journals (Sweden)

    Roger J. Thelwell

    2012-01-01

    Full Text Available The Cauchy-Kowalevski Theorem is the foremost result guaranteeing existence and uniqueness of local solutions for analytic quasilinear partial differential equations with Cauchy initial data. The techniques of Cauchy-Kowalevski may also be applied to initial-value ordinary differential equations. These techniques, when applied in the polynomial ordinary differential equation setting, lead one naturally to a method in which coefficients of the series solution are easily computed in a recursive manner, and an explicit majorization admits a clear a priori error bound. The error bound depends only on immediately observable quantities of the polynomial system; coefficients, initial conditions, and polynomial degree. The numerous benefits of the polynomial system are shown for a specific example.

  14. Nonlocal Cauchy problem for nonlinear mixed integrodifferential equations

    Directory of Open Access Journals (Sweden)

    H.L. Tidke

    2010-12-01

    Full Text Available The present paper investigates the existence and uniqueness of mild and strong solutions of a nonlinear mixed Volterra-Fredholm integrodifferential equation with nonlocal condition. The results obtained by using Schauder fixed point theorem and the theory of semigroups.

  15. ON CAUCHY-POMPEIU FORMULA FOR FUNCTIONS WITH VALUES IN A UNIVERSAL CLIFFORD ALGEBRA

    Institute of Scientific and Technical Information of China (English)

    2003-01-01

    This paper obtains the Cauchy-Pompeiu formula on certain distinguishedboundary for functions with values in a universal Clifford algebra. This formula is just anextension of the Cauchy's integral formula obtained in [11].

  16. A Cauchy-Davenport theorem for linear maps

    OpenAIRE

    Herdade, Simao; Kim, John; Kopparty, Swastik

    2015-01-01

    We prove a version of the Cauchy-Davenport theorem for general linear maps. For subsets $A,B$ of the finite field $\\mathbb{F}_p$, the classical Cauchy-Davenport theorem gives a lower bound for the size of the sumset $A+B$ in terms of the sizes of the sets $A$ and $B$. Our theorem considers a general linear map $L: \\mathbb{F}_p^n \\to \\mathbb{F}_p^m$, and subsets $A_1, \\ldots, A_n \\subseteq \\mathbb{F}_p$, and gives a lower bound on the size of $L(A_1 \\times A_2 \\times \\ldots \\times A_n)$ in ter...

  17. On cosmic censorship: do compact Cauchy horizons imply symmetry?

    International Nuclear Information System (INIS)

    The basic idea of Cosmic Censorship is that, in a physically reasonable spacetime, an observer should not encounter any naked singularities. The authors discuss some new results which provide strong support for one of the statements of Cosmic Censorship: Strong Cosmic Censorship says that the maximal spacetime development of a set of Cauchy data on a spacelike initial surface (evolved via the vacuum Einstein equations, the Einstein-Maxwell equations, or some other 'reasonable' set) will not be extendible across a Cauchy horizon. (Auth.)

  18. Area theorem and smoothness of compact Cauchy horizons

    CERN Document Server

    Minguzzi, E

    2014-01-01

    We obtain an improved version of the area theorem for not necessarily differentiable horizons which, in conjunction with a recent result on the completeness of generators, allows us to prove that under the null energy condition every compactly generated Cauchy horizon is smooth and compact. We explore the consequences of this result for time machines, topology change, black holes and cosmic censorship. For instance, it is shown that compact Cauchy horizons cannot form in a non-empty spacetime which satisfies the stable dominant energy condition wherever there is some source content.

  19. Area Theorem and Smoothness of Compact Cauchy Horizons

    Science.gov (United States)

    Minguzzi, E.

    2015-10-01

    We obtain an improved version of the area theorem for not necessarily differentiable horizons which, in conjunction with a recent result on the completeness of generators, allows us to prove that under the null energy condition every compactly generated Cauchy horizon is smooth and compact. We explore the consequences of this result for time machines, topology change, black holes and cosmic censorship. For instance, it is shown that compact Cauchy horizons cannot form in a non-empty spacetime which satisfies the stable dominant energy condition wherever there is some source content.

  20. UNCONDITIONAL CAUCHY SERIES AND UNIFORM CONVERGENCE ON MATRICES

    Institute of Scientific and Technical Information of China (English)

    A. AIZPURU; A. GUTIERREZ-DAVILA

    2004-01-01

    The authors obtain new characterizations of unconditional Cauchy series in terms of separation properties of subfamilies of p(N), and a generalization of the Orlicz-Pettis Theorem is also obtained. New results on the uniform convergence on matrices and a new version of the Hahn-Schur summation theorem are proved. For matrices whose rows define unconditional Cauchy series, a better sufficient condition for the basic Matrix Theorem of Antosik and Swartz, new necessary conditions and a new proof of that theorem are given.

  1. First order differential operator associated to the Cauchy-Riemann operator in a Clifford algebra

    International Nuclear Information System (INIS)

    The complex differentiation transforms holomorphic functions into holomorphic functions. Analogously, the conjugate Cauchy-Riemann operator of the Clifford algebra transforms regular functions into regular functions. This paper determines more general first order operator L (matrix-type) for which Lu is regular provided u is regular. For such operator L, the initial value problem ∂u / ∂t = L (t, x, u, ∂u / ∂x) (1) u(0, x) = φ(x) (2) is solvable for an arbitrary regular function φ and the solution is regular in x for each t. (author)

  2. Hamilton-Jacobi Theory in Cauchy Data Space

    Science.gov (United States)

    Campos, CéAdric M.; de Leóan, Manuel; de Diego, David Martín; Vaquero, Miguel

    2015-12-01

    Recently, M. de LeóAn et al. [8] have developed a geometric Hamilton-Jacobi theory for classical fields in the setting of multisymplectic geometry. Our purpose in the current paper is to establish the corresponding Hamilton-Jacobi theory in the Cauchy data space, and relate both approaches.

  3. Multiple elliptic hypergeometric series --An approach from the Cauchy determinant--

    OpenAIRE

    Kajihara, Yasushi; Noumi, Masatoshi

    2003-01-01

    A multiple generalization of elliptic hypergeometric series is investigated and a duality transformation for multiple hypergeometric series is proposed. Our duality transformation obtained from an identity arising from the Cauchy determinant formula for Weierstrass sigma functions, by spcialization of a particular form.

  4. Unit Root Testing in Heteroscedastic Panels Using the Cauchy Estimator

    NARCIS (Netherlands)

    Demetrescu, Matei; Hanck, Christoph

    2012-01-01

    The Cauchy estimator of an autoregressive root uses the sign of the first lag as instrumental variable. The resulting IV t-type statistic follows a standard normal limiting distribution under a unit root case even under unconditional heteroscedasticity, if the series to be tested has no deterministi

  5. Cauchy Tetrahedron Argument Applied to Higher Contact Interactions

    Science.gov (United States)

    dell'Isola, F.; Madeo, A.; Seppecher, P.

    2016-03-01

    Second gradient theories are nowadays used in many studies in order to describe in detail some transition layers which may occur in micro-structured materials and in which physical properties are sharply varying. Sometimes higher order theories are also evoked. Up to now these models have not been based on a construction of stresses similar to the one due to Cauchy, which has been applied only for simple materials. It has been widely recognized that the fundamental assumption by Cauchy that the traction depends only on the normal of the dividing surface cannot be maintained for higher gradient theories. However, this observation did not urge any author, to our knowledge, to revisit the Cauchy construction in order to adapt it to a more general conceptual framework. This is what we do in this paper for a continuum of grade N (also called N-th gradient continuum). Our construction is very similar to the one due to Cauchy; based on the tetrahedron argument, it does not introduce any argument of a different nature. In particular, we avoid invoking the principle of virtual work. As one should expect, the balance assumption and the regularity hypotheses have to be adapted to the new framework and tensorial computations become more complex.

  6. Une remarque sur le problème de Cauchy pour l'opérateur différentiel de partie principale à coefficients polynomiaux II

    OpenAIRE

    Hamada, Yûsaku

    2002-01-01

    In Y. Hamada, Tohoku Math. J., 52 (2000), 79-94, we have given a remark on the domain of holomorphy of the solution of the Cauchy problem for the differential operator with polynomial coefficients. In this article, we give some complements to the results of Y. Hamada, Tohoku Math. J., 52 (2000), 79-94.

  7. Differential operators associated to the Cauchy-Riemann operator in a quaternion algebra

    International Nuclear Information System (INIS)

    This paper deals with the initial value problem of the type φw / φt = L (t, x, w, φw / φxi) (1) w(0, x) = φ(x) (2) where t is the time, L is a linear first order operator (matrix-type) in a Quaternion algebra and φ is a regular function. The article proves necessary and sufficient conditions on the coefficients of operator L under which L is associated to the Cauchy-Riemann operator of Quarternion algebra. This criterion makes it possible to construct the operator L for which the initial problem (1),(2) is solvable for an arbitrary initial regular function φ and the solution is also regular for each t. (author)

  8. Regularity of Cauchy horizons in S{sup 2} x S{sup 1} Gowdy spacetimes

    Energy Technology Data Exchange (ETDEWEB)

    Hennig, Joerg [Max Planck Institute for Gravitational Physics, Am Muehlenberg 1, D-14476 Golm (Germany); Ansorg, Marcus, E-mail: pjh@aei.mpg.d, E-mail: marcus.ansorg@helmholtz-muenchen.d [Institute of Biomathematics and Biometry, Helmholtz Zentrum Muenchen, Ingolstaedter Landstr. 1, D-85764 Neuherberg (Germany)

    2010-03-21

    We study general S{sup 2} x S{sup 1} Gowdy models with a regular past Cauchy horizon and prove that a second (future) Cauchy horizon exists, provided that a particular conserved quantity J is not zero. We derive an explicit expression for the metric form on the future Cauchy horizon in terms of the initial data on the past horizon and conclude the universal relation A{sub p}A{sub f} = (8piJ){sup 2} where A{sub p} and A{sub f} are the areas of past and future Cauchy horizons respectively.

  9. On the generalized Cauchy function and new Conjecture on its exterior singularities

    Institute of Scientific and Technical Information of China (English)

    Theodore Yaotsu Wu

    2011-01-01

    This article studies on Cauchy's function f(z) and its integral, (2πi)J[f(z)] ≡ Φc f(t)dt/(t - z) taken along a closed simple contour C, in regard to their comprehensive properties over the entire z = x + iy plane consisted of the simply connected open domain D+ bounded by C and the open domain D- outside C. ( 1 ) With f(z) assumed to be Cn (n < ∞-times continuously differentiable) (Λ)z ∈ D+ and in a neighborhood of C, f(z) and its derivatives f(n)(z) are proved uniformly continuous in the closed domain D+ = [D+ + C].(2) Cauchy's integral formulas and their derivatives (V)z ∈ D+(or (V)z ∈ D-) are proved to converge uniformly in D+ (or in D- = [D- + C]), respectively, thereby rendering the integral formulas valid over the entire z-plane. (3) The same claims (as for f(z) and J[f(z)]) are shown extended to hold for the complement function F(z), defined to be Cn(V)z ∈ D- and about C. (4) The uniform convergence theorems for f(z) and F(z) shown for arbitrary contour C are adapted to find special domains in the upper or lower half z-planes and those inside and outside the unit circle |z| = 1 such that the four generalized Hilbert-type integral transforms are proved. (5) Further,the singularity distribution of f(z) in D- is elucidated by considering the direct problem exemplified with several typical singularities prescribed in D-. (6) A comparative study is made between generalized integral formulas and Plemelj's formulas on their differing basic properties. (7) Physical significances of these formulas are illustrated with applications to nonlinear airfoil theory. (8) Finally, an unsolved inverse problem to determine all the singularities of Cauchy function f(z) in domain D-, based on the continuous numerical value of f(z)(V)z ∈ D+ = [D+ + C], is presented for resolution as a conjecture.

  10. α-times Integrated Regularized Cosine Functions and Second Order Abstract Cauchy Problens

    Institute of Scientific and Technical Information of China (English)

    张寄洲; 陶有山

    2001-01-01

    In this paper, α -times integrated C-regularized cosine functions and mild α-times integrated C-existence families of second order are introduced. Equivalences are proved among α -times integrated C-regularized cosine function for a linear operator A, C-wellposed of (α + 1)-times abstract Cauchy problem and mild α -times integrated C-existence family of second order for A when the commutable condition is satisfied. In addition, if A = C-1AC, they are also equivalent to A generating the α -times integrated C-regularized cosine finction.The characterization of an exponentially botnded mild α -times integrated C-existence family of second order is given out in terms of a Laplace transform.

  11. Cauchy inequality and uncertainty relations for mixed states

    International Nuclear Information System (INIS)

    Cauchy inequality (CI) relates scalar products of two vectors and their norms. I point out other similar inequalities (SI). Starting with CI Schroedinger derived his uncertainty relation (UR). By using SI other various UR can be obtained. It is shown that they follow from the Schroedinger UR. Two generalizations of CI are obtained for mixed states described by density matrices. Using them two generalizations of UR for mixed states are derived. Both differ from the UR generalization known from the literature. The discussion of these generalizations is given

  12. Implementing Cauchy Reed-Solomon Utilizing OpenCL

    OpenAIRE

    Karlsson, Tim

    2013-01-01

    In this paper the performance of executing Cauchy Reed-Solomon (CRS) coding on the GPU is evaluated and compared with execution on the CPU. Three different prototypes are developed. One is sequential and developed in C++, the other two are developed utilizing C++ and OpenCL. The measurements are done by comparing the execution time of different data block sizes ranging from 16KB up to 256MB with two different encoding ratios, 9/12 and 10/16. The measurements are done on an Intel CPU with 4 co...

  13. Structure of the black hole's Cauchy horizon singularity

    CERN Document Server

    Burko, L M

    1997-01-01

    We study the Cauchy horizon (CH) singularity of a spherical charged black hole perturbed nonlinearly by a self-gravitating massless scalar field. We show numerically that the singularity is weak both at the early and at the late sections of the CH, where the focusing of the area coordinate $r$ is strong. In the early section the metric is almost Reissner-Nordström, and the fields behave according to perturbation analysis. We find exact analytical expressions for the gradients of $r$ and of the scalar field, which are valid at both sections. We then verify these analytical results numerically.

  14. Cauchy, Sturm et les racines des équations

    OpenAIRE

    Benis Sinaceur, Hourya

    1992-01-01

    International audience Relying both on chronological data and textual analysis, this article seeks to determine the mutual influence between A.-L. Cauchy's and Ch.-F. Sturm's research from 1829 to around 1840 on the roots of algebraic equations. The first aim is to specify the elements of a micro-history, strictly limited in time and centered on a well-defined question, yet bound up with the endeavour to build up a mathematical physics at the beginning of the 19th century. The second aim p...

  15. On a Higher Order Cauchy-Pompeiu Formula for Functions with Values in a Universal Clifford Algebra

    OpenAIRE

    Zhongxiang, Zhang

    2007-01-01

    By constructing suitable kernel functions, a higher order Cauchy-Pompeiu formula for functions with values in a universal Clifford algebra is obtained, leading to a higher order Cauchy integral formula.

  16. Hyperelastic bodies under homogeneous Cauchy stress induced by non-homogeneous finite deformations

    CERN Document Server

    Mihai, L Angela

    2016-01-01

    We discuss whether homogeneous Cauchy stress implies homogeneous strain in isotropic nonlinear elasticity. While for linear elasticity the positive answer is clear, we exhibit, through detailed calculations, an example with inhomogeneous continuous deformation but constant Cauchy stress. The example is derived from a non rank-one convex elastic energy. Connections to conforming and non-conforming finite element implementations are drawn.

  17. Gravitational wave extraction based on Cauchy-characteristic extraction and characteristic evolution

    CERN Document Server

    Babiuc, M; Hawke, I; Zlochower, Y; Babiuc, Maria; Szilagyi, Bela; Hawke, Ian; Zlochower, Yosef

    2005-01-01

    We implement a code to find the gravitational news at future null infinity by using data from a Cauchy code as boundary data for a characteristic code. This technique of Cauchy-characteristic Extraction (CCE) allows for the unambiguous extraction of gravitational waves from numerical simulations.

  18. External Field QED on Cauchy Surfaces for Varying Electromagnetic Fields

    Science.gov (United States)

    Deckert, D.-A.; Merkl, F.

    2016-08-01

    The Shale-Stinespring Theorem (J Math Mech 14:315-322, 1965) together with Ruijsenaar's criterion (J Math Phys 18(4):720-737, 1977) provide a necessary and sufficient condition for the implementability of the evolution of external field quantum electrodynamics between constant-time hyperplanes on standard Fock space. The assertion states that an implementation is possible if and only if the spatial components of the external electromagnetic four-vector potential {A_μ} are zero. We generalize this result to smooth, space-like Cauchy surfaces and, for general {A_μ}, show how the second-quantized Dirac evolution can always be implemented as a map between varying Fock spaces. Furthermore, we give equivalence classes of polarizations, including an explicit representative, that give rise to those admissible Fock spaces. We prove that the polarization classes only depend on the tangential components of {A_μ} w.r.t. the particular Cauchy surface, and show that they behave naturally under Lorentz and gauge transformations.

  19. Hybrid particle swarm optimization with Cauchy distribution for solving reentrant flexible flow shop with blocking constraint

    Directory of Open Access Journals (Sweden)

    Chatnugrob Sangsawang

    2016-06-01

    Full Text Available This paper addresses a problem of the two-stage flexible flow shop with reentrant and blocking constraints in Hard Disk Drive Manufacturing. This problem can be formulated as a deterministic FFS|stage=2,rcrc, block|Cmax problem. In this study, adaptive Hybrid Particle Swarm Optimization with Cauchy distribution (HPSO was developed to solve the problem. The objective of this research is to find the sequences in order to minimize the makespan. To show their performances, computational experiments were performed on a number of test problems and the results are reported. Experimental results show that the proposed algorithms give better solutions than the classical Particle Swarm Optimization (PSO for all test problems. Additionally, the relative improvement (RI of the makespan solutions obtained by the proposed algorithms with respect to those of the current practice is performed in order to measure the quality of the makespan solutions generated by the proposed algorithms. The RI results show that the HPSO algorithm can improve the makespan solution by averages of 14.78%.

  20. Moving Heat Source Reconstruction from Cauchy Boundary Data: The Cartesian Coordinates Case

    Directory of Open Access Journals (Sweden)

    Nilson C. Roberty

    2011-01-01

    Full Text Available We consider the problem of reconstruction of an unknown characteristic interval and block transient thermal source inside a domain. By exploring the definition of an Extended Dirichlet to Neumann map in the time space cylinder that has been introduced in Roberty and Rainha (2010a, we can treat the problem with methods similar to that used in the analysis of the stationary source reconstruction problem. Further, the finite difference θ-scheme applied to the transient heat conduction equation leads to a model based on a sequence of modified Helmholtz equation solutions. For each modified Helmholtz equation the characteristic interval and parallelepiped source function may be reconstructed uniquely from the Cauchy boundary data. Using representation formula we establish reciprocity functional mapping functions that are solutions of the modified Helmholtz equation to their integral in the unknown characteristic support. Numerical experiment for capture of an interval and an rectangular parallelepiped characteristic source inside a cubic box domain from boundary data are presented in threedimensional and one-dimensional implementations. The problem of centroid determination is addressed and questions are discussed from an computational points of view.

  1. Noise Kernel for Reissner Nordstrom Metric: Results at Cauchy Horizon

    CERN Document Server

    Satin, Seema

    2015-01-01

    We obtain the Noise Kernel, which defines quantum stress tensor fluctuations for Reissner Nordstrom metric modeled as gravitationally collapsing spacetime, after transforming to coordinates suitable for the evolution.The quantum stress tensor fluctuations at the final stage of collapse namely naked singularity or a black hole are then analysed.The behavior of this entity which is central to semiclassical stochastic gravity at the Cauchy Horizon shows markedly different behaviour from earlier obtained result for self similar Tolman Bondi case showing a very unique divergence. It is known that the quantum stress tensor itself diverges at CH for both Tolman Bondi and Reissner Nordstrom metric. In contrast, it can now be seen that the correlations of the fluctuations of the stress tensor behave differently for the two cases. We give a discussion and further directions of investigations for this interesting behaviour in the two cases (regarding the collapse scenario).

  2. On Cauchy conditions for asymmetric mixed convection boundary layer flows

    Energy Technology Data Exchange (ETDEWEB)

    Amaouche, Mustapha [Laboratoire de Physique Theorique, Universite de Bejaia (Algeria); Kessal, Mohand [Departement Transport et Equipement Petrolier, Faculte des Hydrocarbures et de la Chimie, Universite de Boumerdes, 35000, Boumerdes (Algeria)

    2003-06-01

    The fundamental question of how and where does an asymmetric mixed convection boundary layer flow around a heated horizontal circular cylinder begin to develop is raised. We first transform the classical boundary layer equations by using an integral method of Karman-Pohlhausen type and obtain two coupled equations governing the evolutions of the dynamic and thermal boundary layers. Because of its global character, the implemented method allows to bypass the difficulty of downstream-upstream interactions. Cauchy conditions characterizing the starting of the boundary layers are found; they are obtained in a surprisingly simple manner for the limiting cases corresponding to Pr=1, Pr{yields}0 and Pr{yields}{infinity}. Otherwise, these conditions can be found by using a prediction correction algorithm. Some numerical experiments are finally performed in order to illustrate the theory. (authors)

  3. Completion of a Cauchy space without the T2-restriction on the space

    Directory of Open Access Journals (Sweden)

    Nandita Rath

    2000-08-01

    Full Text Available A completion of a Cauchy space is obtained without the T2 restriction on the space. This completion enjoys the universal property as well. The class of all Cauchy spaces with a special class of morphisms called s-maps form a subcategory CHY' of CHY. A completion functor is defined for this subcategory. The completion subcategory of CHY' turns out to be a bireflective subcategory of CHY'. This theory is applied to obtain a characterization of Cauchy spaces which allow regular completion.

  4. Spectral Cauchy Characteristic Extraction of strain, news and gravitational radiation flux

    CERN Document Server

    Handmer, Casey J; Winicour, Jeffrey

    2016-01-01

    We present a new approach for the Cauchy-characteristic extraction of gravitational radiation strain, news function, and the flux of the energy-momentum, supermomentum and angular momentum associated with the Bondi-Metzner-Sachs asymptotic symmetries. In Cauchy-characteristic extraction, a characteristic evolution code propagates numerical data on an inner worldtube supplied by a Cauchy evolution code to obtain the space-time metric in a neighborhood of null infinity. The metric is first determined in a scrambled form in terms of coordinates determined by the Cauchy formalism. In prior treatments, the waveform is first extracted from this metric and then transformed into an asymptotic inertial coordinate system. This procedure provides the physically proper description of the waveform and the radiated energy but it does not generalize to determine the flux of angular momentum or supermomentum. Here we formulate and implement a new approach which transforms the full metric into an asymptotic inertial frame and...

  5. Analysis of linear waves near the Cauchy horizon of cosmological black holes

    CERN Document Server

    Hintz, Peter

    2015-01-01

    We show that linear scalar waves are bounded and continuous up to the Cauchy horizon of Reissner-Nordstr\\"om-de Sitter and Kerr-de Sitter spacetimes, and in fact decay exponentially fast to a constant along the Cauchy horizon. We obtain our results by modifying the spacetime beyond the Cauchy horizon in a suitable manner, which puts the wave equation into a framework in which a number of standard as well as more recent microlocal regularity and scattering theory results apply. In particular, the conormal regularity of waves at the Cauchy horizon - which yields the boundedness statement - is a consequence of radial point estimates, which are microlocal manifestations of the blue-shift and red-shift effects.

  6. Gravitational wave extraction based on Cauchy-characteristic extraction and characteristic evolution

    OpenAIRE

    Babiuc, M.; Szilagyi, B; Hawke, I.; Zlochower, Y.

    2005-01-01

    We implement a code to find the gravitational news at future null infinity by using data from a Cauchy code as boundary data for a characteristic code. This technique of Cauchy-characteristic extraction (CCE) allows for the unambiguous extraction of gravitational waves from numerical simulations. We first test the technique on non-radiative spacetimes: Minkowski spacetime, perturbations of Minkowski spacetime and static black hole spacetimes in various gauges. We show the convergence and limi...

  7. Cauchy horizon stability in a collapsing spherical dust cloud I: geometric optic approximation and spherically symmetric test fields

    CERN Document Server

    Ortiz, Néstor

    2013-01-01

    A spherical dust cloud which is initially at rest and which has a monotonously decaying density profile collapses and forms a shell-focussing singularity. Provided the density profile is not too flat, meaning that its second radial derivative is negative at the center, this singularity is visible to local, and sometimes even to global observers. According to the strong cosmic censorship conjecture, such naked singularities should be unstable under generic, nonspherical perturbations of the initial data or when more realistic matter models are considered. In an attempt to gain some understanding about this stability issue, in this work we initiate the analysis of a simpler but related problem. We discuss the stability of test fields propagating in the vicinity of the Cauchy horizon associated to the naked central singularity. We first study the high-frequency limit and show that the fields undergo a blueshift as they approach the Cauchy horizon. However, in contrast to what occurs at inner horizons of black ho...

  8. Cauchy graph embedding based diffusion model for salient object detection.

    Science.gov (United States)

    Tan, Yihua; Li, Yansheng; Chen, Chen; Yu, Jin-Gang; Tian, Jinwen

    2016-05-01

    Salient object detection has been a rather hot research topic recently, due to its potential applications in image compression, scene classification, image registration, and so forth. The overwhelming majority of existing computational models are designed based on computer vision techniques by using lots of image cues and priors. Actually, salient object detection is derived from the biological perceptual mechanism, and biological evidence shows that the spread of the spatial attention generates the object attention. Inspired by this, we attempt to utilize the emerging spread mechanism of object attention to construct a new computational model. A novel Cauchy graph embedding based diffusion (CGED) model is proposed to fulfill the spread process. Combining the diffusion model and attention prediction model, a salient object detection approach is presented through perceptually grouping the multiscale diffused attention maps. The effectiveness of the proposed approach is validated on the salient object dataset. The experimental results show that the CGED process can obviously improve the performance of salient object detection compared with the input spatial attention map, and the proposed approach can achieve performance comparable to that of state-of-the-art approaches. PMID:27140886

  9. Who Gave you the Cauchy-Weierstrass Tale? The Dual History of Rigorous Calculus

    CERN Document Server

    Borovik, Alexandre; 10.1007/s10699-011-9235-x

    2011-01-01

    Cauchy's contribution to the foundations of analysis is often viewed through the lens of developments that occurred some decades later, namely the formalisation of analysis on the basis of the epsilon-delta doctrine in the context of an Archimedean continuum. What does one see if one refrains from viewing Cauchy as if he had read Weierstrass already? One sees, with Felix Klein, a parallel thread for the development of analysis, in the context of an infinitesimal-enriched continuum. One sees, with Emile Borel, the seeds of the theory of rates of growth of functions as developed by Paul du Bois-Reymond. One sees, with E. G. Bjorling, an infinitesimal definition of the criterion of uniform convergence. Cauchy's foundational stance is hereby reconsidered.

  10. Cauchy´s stress theorem for stresses represented by measures

    Czech Academy of Sciences Publication Activity Database

    Šilhavý, Miroslav

    2008-01-01

    Roč. 20, č. 2 (2008), s. 75-96. ISSN 0935-1175 Institutional research plan: CEZ:AV0Z10190503 Keywords : Cauchy stress theorem * divergence measure vectorfield * Newton homotopy Subject RIV: BA - General Mathematics Impact factor: 1.552, year: 2008

  11. Convergence and the Cauchy Property of Sequences in the Setting of Actual Infinity

    Science.gov (United States)

    Shipman, Barbara A.

    2013-01-01

    Traditional definitions, language, and visualizations of convergence and the Cauchy property of sequences convey a sense of the sequence as a potentially infinite process rather than an actually infinite object. This has a deep-rooted influence on how we think about and teach concepts on sequences, particularly in undergraduate calculus and…

  12. A note on the derivation of the derivatives of invariants of stretch tensor to the right Cauchy-Green tensor

    Institute of Scientific and Technical Information of China (English)

    TIAN Dongyan; JIN Ming; DUI Guansuo

    2006-01-01

    A new approach for the derivation of the principal invariants of the stretch tensor with respect to the right Cauchy Green tensor is presented in this paper. According to the definition of the derivation of tensor function, the three first-order derivatives for the principal invariants of the stretch tensor are obtained through derivation directly to the right Cauchy-Green tensor by incremental method. Then the three second-order derivatives are yielded by the derivation to the right Cauchy-Green strain tensor directly. Furthermore, an explicit expression of the tangent modulus of the general Varga material is given as an example.

  13. Inner cauchy horizon of axisymmetric and stationary black holes with surrounding matter in einstein-maxwell theory.

    Science.gov (United States)

    Ansorg, Marcus; Hennig, Jörg

    2009-06-01

    We study the interior electrovacuum region of axisymmetric and stationary black holes with surrounding matter and find that there exists always a regular inner Cauchy horizon inside the black hole, provided the angular momentum J and charge Q of the black hole do not vanish simultaneously. In particular, we derive an explicit relation for the metric on the Cauchy horizon in terms of that on the event horizon. Moreover, our analysis reveals the remarkable universal relation (8piJ);{2}+(4piQ;{2});{2}=A;{+}A;{-}, where A+ and A- denote the areas of event and Cauchy horizon, respectively. PMID:19658851

  14. Calculation of Cauchy stress tensor in molecular dynamics system with a generalized Irving-Kirkwood formulism

    CERN Document Server

    Yang, Jerry Zhijian

    2014-01-01

    Irving and Kirkwood formulism (IK formulism) provides a way to compute continuum mechanics quantities at certain location in terms of molecular variables. To make the approach more practical in computer simulation, Hardy proposed to use a spacial kernel function that couples continuum quantities with atomistic information. To reduce irrational fluctuations, Murdoch proposed to use a temporal kernel function to smooth the physical quantities obtained in Hardy's approach. In this paper, we generalize the original IK formulism to systematically incorporate both spacial and temporal average. The Cauchy stress tensor is derived in this generalized IK formulism (g-IK formulism). Analysis is given to illuminate the connection and difference between g-IK formulism and traditional temporal post-process approach. The relationship between Cauchy stress and first Piola-Kirchhoff stress is restudied in the framework of g-IK formulism. Numerical experiments using molecular dynamics are conducted to examine the analysis res...

  15. Interphases, gelation, vitrification, porous glasses and the generalized Cauchy relation: epoxy/silica nanocomposites

    International Nuclear Information System (INIS)

    The generalized Cauchy relation (gCR) of epoxy/silica nano-composites does not show either the chemically induced sol-gel transition or the chemically induced glass transition in the course of polymerization. Astonishingly, by varying the silica nanoparticles' concentration between 0 and 25 vol% in the composites, the Cauchy parameter A of the gCR remains universal and can be determined from the pure epoxy's elastic moduli. Air-filled porous silica glasses are considered as models for percolated silica particles. A longitudinal modulus versus density representation evidences the aforementioned transition phenomena during polymerization of the epoxy/silica nanocomposites. The existence of optically and mechanically relevant interphases is discussed.

  16. Sobre la equivalencia entre sucesiones con límite finito y sucesiones de Cauchy

    OpenAIRE

    Claros, Francisco Javier; Sánchez, María Teresa; Coriat, Moisés

    2009-01-01

    Estudiamos, desde perspectivas simbólica y fenomenológica, diferencias y analogías existentes entre dos definiciones: la de límite finito de una sucesión y la de sucesión de Cauchy. Las diferencias entre una y otra definición parecen acentuarse en el aspecto fenomenológico, ya que observamos fenómenos distintos en cada una de ellas.

  17. Artificial Bee Colony Algorithm Combined with Grenade Explosion Method and Cauchy Operator for Global Optimization

    OpenAIRE

    Jian-Guo Zheng; Chao-Qun Zhang; Yong-Quan Zhou

    2015-01-01

    Artificial bee colony (ABC) algorithm is a popular swarm intelligence technique inspired by the intelligent foraging behavior of honey bees. However, ABC is good at exploration but poor at exploitation and its convergence speed is also an issue in some cases. To improve the performance of ABC, a novel ABC combined with grenade explosion method (GEM) and Cauchy operator, namely, ABCGC, is proposed. GEM is embedded in the onlooker bees’ phase to enhance the exploitation ability and accelerate c...

  18. Cauchy Annealing Schedule: An Annealing Schedule for Boltzmann Selection Scheme in Evolutionary Algorithms

    OpenAIRE

    Dukkipati, Ambedkar; Murty, Narasimha M; Bhatnagar, Shalabh

    2004-01-01

    Boltzmann selection is an important selection mechanism in evolutionary algorithms as it has theoretical properties which help in theoretical analysis. However, Boltzmann selection is not used in practice because a good annealing schedule for the `inverse temperature' parameter is lacking. In this paper we propose a Cauchy annealing schedule for Boltzmann selection scheme based on a hypothesis that selection-strength should increase as evolutionary process goes on and distance between two sel...

  19. The tortoise coordinates and the cauchy problem in the stable study of the Schwarzschild black hole

    CERN Document Server

    Tian, G; Zhong, S; Tian, Gui-hua; Wang, Shi-kun; Zhong, Shuquan

    2006-01-01

    Generally, the Schwarzschild black hole was proved stable through two different methods: the mode-decomposition method and the integral method. In the paper, we show the integral method can only apply to the initial data vanishing at both the horizon and the spatial infinity. It can not treat the initial data only vanishing at the spatial infinity. We give an example to show the misleading information caused by the use of the tortoise coordinates in the perturbation equations. Subsequently, the perturbation equation in the Schwarzschild coordinates is shown not sufficient for the stable study.

  20. Approach to a Cauchy Problem in Stability Study of the Schwarzschild Black Hole

    Institute of Scientific and Technical Information of China (English)

    TIAN Gui-Hua; WANG Shi-Kun; ZHONG Shu-Quan

    2007-01-01

    Generally, the Schwarzschild black hole is proven to be stable by two different methods: the mode-decomposition method and the integral method. We show that the integral method can only apply to the initial data vanishing at both the horizon and the spatial infinity. It can not treat the initial data only vanishing at the spatial infinity. We give an example to show the misleading information caused by the use of tortoise coordinates in the perturbation equations. Subsequently, the perturbation equations in the Schwarzschild coordinates are shown to be insufficient for the stability study.

  1. The Cauchy Problem for the p-Laplacian Equation with a Nonlinear Source

    Institute of Scientific and Technical Information of China (English)

    LEI Pei-dong

    2001-01-01

    In this paper we study the existence and uniqueness of positive solutions for the p-Laplacian equation with nonlinear sourceu/ t = div(| Du |p-2Du) + u-q, p > 2, 0 < q < ∞ in the class of functions with some prescribed growth rate as | x |→ ∞. We also give a description of thelarge time behaviour and show that it is determined by the competition between the diffusion and the source.

  2. MAXIMAL SUBSPACES FOR SOLUTIONS OF THE SECOND ORDER ABSTRACT CAUCHY PROBLEM

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    For a continuous, increasing function ω: R+ → R+\\{0} of finite exponential type, this paper introduces the set Z(A, ω) of all x in a Banach space X for which the second order abstract differential equation (2) has a mild solution such that [ω(t)]-1u(t,x) is uniformly continues on R+, and show that Z(A, ω) is a maximal Banach subspace continuously embedded in X, where A ∈ B(X) is closed. Moreover, A|z(A,ω) generates an O(ω(t))strongly continuous cosine operator function family.

  3. Global smooth solution of the Cauchy problem for a model of a radiative flow

    Czech Academy of Sciences Publication Activity Database

    Ducomet, B.; Nečasová, Šárka

    2015-01-01

    Roč. 14, č. 1 (2015), s. 1-36. ISSN 0391-173X R&D Projects: GA ČR GA201/08/0012 Institutional support: RVO:67985840 Keywords : Navier-Stokes-Fourier system * radiative equilibrium Subject RIV: BA - General Mathematics Impact factor: 0.921, year: 2014 http://annaliscienze.sns.it/index.php?page=Article&id=332

  4. On the Cauchy Problem of Evolution p-Laplacian Equation with Nonlinear Gradient Term

    Institute of Scientific and Technical Information of China (English)

    Mingyu CHEN; Junning ZHAO

    2009-01-01

    The authors study the existence of solution to p-Laplacian equation with non-linear forcing term under optimal assumptions on the initial data,which are assumed to be measures.The existence of local solution is obtained.

  5. Cauchy problem for a generalized weakly dissipative periodic two-component Camassa-Holm system

    Directory of Open Access Journals (Sweden)

    Wenxia Chen

    2014-05-01

    Full Text Available In this article, we study a generalized weakly dissipative periodic two-component Camassa-Holm system. We show that this system can exhibit the wave-breaking phenomenon and determine the exact blow-up rate of strong solution to the system. In addition, we establish a sufficient condition for having a global solution.

  6. 100 great problems of elementary mathematics their history and solution

    CERN Document Server

    Dorrie, Heinrich

    2013-01-01

    Problems that beset Archimedes, Newton, Euler, Cauchy, Gauss, Monge and other greats, ready to challenge today's would-be problem solvers. Among them: How is a sundial constructed? How can you calculate the logarithm of a given number without the use of logarithm table? No advanced math is required. Includes 100 problems with proofs.

  7. Symmetries of 2-lattices and second order accuracy of the Cauchy--Born Model

    CERN Document Server

    Van Koten, Brian

    2012-01-01

    We show that the Cauchy--Born model of a single-species 2-lattice is second order if the atomistic and continuum kinematics are connected in a novel way. Our proof uses a generalization to 2-lattices of the point symmetry of Bravais lattices. Moreover, by identifying similar symmetries in multi-species pair interaction models, we construct a new stored energy density, using shift-gradients but not strain gradients, that is also second order accurate. These results can be used to develop highly accurate continuum models and atomistic/continuum coupling methods for materials such as graphene, hcp metals, and shape memory alloys.

  8. Initial Value Problems for Wave Equations on Manifolds

    International Nuclear Information System (INIS)

    We study the global theory of linear wave equations for sections of vector bundles over globally hyperbolic Lorentz manifolds. We introduce spaces of finite energy sections and show well-posedness of the Cauchy problem in those spaces. These spaces depend in general on the choice of a time function but it turns out that certain spaces of finite energy solutions are independent of this choice and hence invariantly defined. We also show existence and uniqueness of solutions for the Goursat problem where one prescribes initial data on a characteristic partial Cauchy hypersurface. This extends classical results due to Hörmander

  9. Initial Value Problems for Wave Equations on Manifolds

    Energy Technology Data Exchange (ETDEWEB)

    Bär, Christian, E-mail: baer@math.uni-potsdam.de [Universität Potsdam, Institut für Mathematik (Germany); Wafo, Roger Tagne, E-mail: rtagnewafo@yahoo.com [University of Douala, Faculty of Science, Department of Mathematics and Computer Science (Cameroon)

    2015-12-15

    We study the global theory of linear wave equations for sections of vector bundles over globally hyperbolic Lorentz manifolds. We introduce spaces of finite energy sections and show well-posedness of the Cauchy problem in those spaces. These spaces depend in general on the choice of a time function but it turns out that certain spaces of finite energy solutions are independent of this choice and hence invariantly defined. We also show existence and uniqueness of solutions for the Goursat problem where one prescribes initial data on a characteristic partial Cauchy hypersurface. This extends classical results due to Hörmander.

  10. Navier-Stokes Equations—Millennium Prize Problems

    OpenAIRE

    Asset A. Durmagambetov; Leyla S. Fazilova

    2015-01-01

    In this work, we present final solving Millennium Prize Problems formulated by Clay Math. Inst., Cambridge. A new uniform time estimation of the Cauchy problem solution for the Navier-Stokes equations is provided. We also describe the loss of smoothness of classical solutions for the Navier-Stokes equations.

  11. $q$-poly-Bernoulli numbers and $q$-poly-Cauchy numbers with a parameter by Jackson's integrals

    OpenAIRE

    Komatsu, Takao

    2015-01-01

    We define $q$-poly-Bernoulli polynomials $B_{n,\\rho,q}^{(k)}(z)$ with a parameter $\\rho$, $q$-poly-Cauchy polynomials of the first kind $c_{n,\\rho,q}^{(k)}(z)$ and of the second kind $\\widehat c_{n,\\rho,q}^{(k)}(z)$ with a parameter $\\rho$ by Jackson's integrals, which generalize the previously known numbers and polynomials, including poly-Bernoulli numbers $B_n^{(k)}$ and the poly-Cauchy numbers of the first kind $c_n^{(k)}$ and of the second kind $\\widehat c_n^{(k)}$. We investigate their p...

  12. Artificial Bee Colony Algorithm Combined with Grenade Explosion Method and Cauchy Operator for Global Optimization

    Directory of Open Access Journals (Sweden)

    Jian-Guo Zheng

    2015-01-01

    Full Text Available Artificial bee colony (ABC algorithm is a popular swarm intelligence technique inspired by the intelligent foraging behavior of honey bees. However, ABC is good at exploration but poor at exploitation and its convergence speed is also an issue in some cases. To improve the performance of ABC, a novel ABC combined with grenade explosion method (GEM and Cauchy operator, namely, ABCGC, is proposed. GEM is embedded in the onlooker bees’ phase to enhance the exploitation ability and accelerate convergence of ABCGC; meanwhile, Cauchy operator is introduced into the scout bees’ phase to help ABCGC escape from local optimum and further enhance its exploration ability. Two sets of well-known benchmark functions are used to validate the better performance of ABCGC. The experiments confirm that ABCGC is significantly superior to ABC and other competitors; particularly it converges to the global optimum faster in most cases. These results suggest that ABCGC usually achieves a good balance between exploitation and exploration and can effectively serve as an alternative for global optimization.

  13. The Cauchy-Lagrangian method for numerical analysis of Euler flow

    CERN Document Server

    Podvigina, O; Frisch, U

    2015-01-01

    A novel semi-Lagrangian method is introduced to solve numerically the Euler equation for ideal incompressible flow in arbitrary space dimension. It exploits the time-analyticity of fluid particle trajectories and requires, in principle, only limited spatial smoothness of the initial data. Efficient generation of high-order time-Taylor coefficients is made possible by simple recurrence relations that follow from the Cauchy invariants formulation of the Euler equations (Zheligovsky & Frisch, J. Fluid Mech. 2014, 749, 404-430). Truncated time-Taylor series of very high order allow the use of time steps vastly exceeding the Courant-Friedrichs-Lewy limit, without compromising the accuracy of the solution. Tests performed on the two-dimensional Euler equation indicate that the Cauchy-Lagrangian method is more --- and occasionally much more --- efficient and less prone to instability than Eulerian Runge-Kutta methods and less prone to rapid growth of rounding errors than the high-order Eulerian time-Taylor algor...

  14. Formulation of the Problem of Sonic Boom by a Maneuvering Aerofoil as a One-Parameter Family of Cauchy Problems

    Indian Academy of Sciences (India)

    S Baskar; Phoolan Prasad

    2006-02-01

    For the structure of a sonic boom produced by a simple aerofoil at a large distance from its source we take a physical model which consists of a leading shock (LS), a trailing shock (TS) and a one-parameter family of nonlinear wavefronts in between the two shocks. Then we develop a mathematical model and show that according to this model the LS is governed by a hyperbolic system of equations in conservation form and the system of equations governing the TS has a pair of complex eigenvalues. Similarly, we show that a nonlinear wavefront originating from a point on the front part of the aerofoil is governed by a hyperbolic system of conservation laws and that originating from a point on the rear part is governed by a system of conservation laws, which is elliptic. Consequently, we expect the geometry of the TS to be kink-free and topologically different from the geometry of the LS. In the last section we point out an evidence of kinks on the LS and kink-free TS from the numerical solution of the Euler’s equations by Inoue, Sakai and Nishida [5].

  15. Completeness in the sense of Cauchy principal value of the eigenfunction systems of infinite dimensional Hamiltonian operator

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    The properties of eigenvalues and eigenfunctions of the infinite dimensional Hamiltonian operators are studied, and the suffcient conditions of the completeness in the sense of Cauchy principal value of the eigenfunction systems of the infinite dimensional Hamiltonian operators are given. In the end, concrete examples are constructed to justify the effectiveness of the criterion.

  16. Completeness in the sense of Cauchy principal value of the eigenfunction systems of infinite dimensional Hamiltonian operator

    Institute of Scientific and Technical Information of China (English)

    Alatancang; WU DeYu

    2009-01-01

    The properties of eigenvalues and eigenfunctions of the infinite dimensional Hamiltonian operators are studied,and the sufficient conditions of the completeness in the sense of Cauchy principal value of the eigenfunction systems of the infinite dimensional Hamiltonian operators are given.In the end,concrete examples are constructed to justify the effectiveness of the criterion.

  17. Comparing Gravitational Waveform Extrapolation to Cauchy-Characteristic Extraction in Binary Black Hole Simulations

    CERN Document Server

    Taylor, Nicholas W; Reisswig, Christian; Scheel, Mark A; Chu, Tony; Kidder, Lawrence E; Szilagyi, Bela

    2013-01-01

    We extract gravitational waveforms from numerical simulations of black hole binaries computed using the Spectral Einstein Code. We compare two extraction methods: direct construction of the Newman-Penrose (NP) scalar $\\Psi_4$ at a finite distance from the source and Cauchy-characteristic extraction (CCE). The direct NP approach is simpler than CCE, but NP waveforms can be contaminated by near-zone effects---unless the waves are extracted at several distances from the source and extrapolated to infinity. Even then, the resulting waveforms can in principle be contaminated by gauge effects. In contrast, CCE directly provides, by construction, gauge-invariant waveforms at future null infinity. We verify the gauge invariance of CCE by running the same physical simulation using two different gauge conditions. We find that these two gauge conditions produce the same CCE waveforms but show differences in extrapolated-$\\Psi_4$ waveforms. We examine data from several different binary configurations and measure the domi...

  18. Newton`s iteration for inversion of Cauchy-like and other structured matrices

    Energy Technology Data Exchange (ETDEWEB)

    Pan, V.Y. [Lehman College, Bronx, NY (United States); Zheng, Ailong; Huang, Xiaohan; Dias, O. [CUNY, New York, NY (United States)

    1996-12-31

    We specify some initial assumptions that guarantee rapid refinement of a rough initial approximation to the inverse of a Cauchy-like matrix, by mean of our new modification of Newton`s iteration, where the input, output, and all the auxiliary matrices are represented with their short generators defined by the associated scaling operators. The computations are performed fast since they are confined to operations with short generators of the given and computed matrices. Because of the known correlations among various structured matrices, the algorithm is immediately extended to rapid refinement of rough initial approximations to the inverses of Vandermonde-like, Chebyshev-Vandermonde-like and Toeplitz-like matrices, where again, the computations are confined to operations with short generators of the involved matrices.

  19. A Modified Differential Evolution Algorithm with Cauchy Mutation for Global Optimization

    Science.gov (United States)

    Ali, Musrrat; Pant, Millie; Singh, Ved Pal

    Differential Evolution (DE) is a powerful yet simple evolutionary algorithm for optimization of real valued, multi modal functions. DE is generally considered as a reliable, accurate and robust optimization technique. However, the algorithm suffers from premature convergence, slow convergence rate and large computational time for optimizing the computationally expensive objective functions. Therefore, an attempt to speed up DE is considered necessary. This research introduces a modified differential evolution (MDE), a modification to DE that enhances the convergence rate without compromising with the solution quality. In Modified differential evolution (MDE) algorithm, if an individual fails in continuation to improve its performance to a specified number of times then new point is generated using Cauchy mutation. MDE on a test bed of functions is compared with original DE. It is found that MDE requires less computational effort to locate global optimal solution.

  20. Modelling mortality of a stored grain insect pest with fumigation: probit, logistic or Cauchy model?

    Science.gov (United States)

    Shi, Mingren; Renton, Michael

    2013-06-01

    Computer simulation models can provide a relatively fast, safe and inexpensive means to judge and weigh the merits of various pest control management options. However, the usefulness of such simulation models relies on the accurate estimation of important model parameters, such as the pest mortality under different treatments and conditions. Recently, an individual-based simulation model of population dynamics and resistance evolution has been developed for the stored grain insect pest Rhyzopertha dominica, based on experimental results showing that alleles at two different loci are involved in resistance to the grain fumigant phosphine. In this paper, we describe how we used three generalized linear models, probit, logistic and Cauchy models, each employing two- and four-parameter sub-models, to fit experimental data sets for five genotypes for which detailed mortality data was already available. Instead of the usual statistical iterative maximum likelihood estimation, a direct algebraic approach, generalized inverse matrix technique, was used to estimate the mortality model parameters. As this technique needs to perturb the observed mortality proportions if the proportions include 0 or 1, a golden section search approach was used to find the optimal perturbation in terms of minimum least squares (L2) error. The results show that the estimates using the probit model were the most accurate in terms of L2 errors between observed and predicted mortality values. These errors with the probit model ranged from 0.049% to 5.3%, from 0.381% to 8.1% with the logistic model and from 8.3% to 48.2% with the Cauchy model. Meanwhile, the generalized inverse matrix technique achieved similar results to the maximum likelihood estimation ones, but is less time consuming and computationally demanding. We also describe how we constructed a two-parameter model to estimate the mortalities for each of the remaining four genotypes based on realistic genetic assumptions. PMID:23473941

  1. On an inverse problem for scalar conservation laws

    International Nuclear Information System (INIS)

    We study in what sense one can determine the flux functions k = k(x) and f = f(u), k piecewise constant, in the scalar hyperbolic conservation law ut + (k(x)f(u))x = 0 by observing the solution u(t, ·) of the Cauchy problem with suitable piecewise constant initial data u|t=0 = uo. (paper)

  2. N{sup ±}-integrals and boundary values of Cauchy-type integrals of finite measures

    Energy Technology Data Exchange (ETDEWEB)

    Aliev, R. A., E-mail: aliyevrashid@hotmail.ru, E-mail: alievrashid@box.az [Baku State University (Azerbaijan)

    2014-07-31

    Let Γ be a simple closed Lyapunov contour with finite complex measure ν, and let G{sup +} be the bounded and G{sup −} the unbounded domains with boundary Γ. Using new notions (so-called N-integration and N{sup +}- and N{sup −}-integrals), we prove that the Cauchy-type integrals F{sup +}(z), z∈G{sup +}, and F{sup −}(z), z∈G{sup −}, of ν are Cauchy N{sup +}- and N{sup −}-integrals, respectively. In the proof of the corresponding results, the additivity property and the validity of the change-of-variable formula for the N{sup +}- and N{sup −}-integrals play an essential role. Bibliography: 21 titles. (paper)

  3. Comparing gravitational waveform extrapolation to Cauchy-characteristic extraction in binary black hole simulations

    Science.gov (United States)

    Taylor, Nicholas W.; Boyle, Michael; Reisswig, Christian; Scheel, Mark A.; Chu, Tony; Kidder, Lawrence E.; Szilágyi, Béla

    2013-12-01

    We extract gravitational waveforms from numerical simulations of black hole binaries computed using the Spectral Einstein Code. We compare two extraction methods: direct construction of the Newman-Penrose (NP) scalar Ψ4 at a finite distance from the source and Cauchy-characteristic extraction (CCE). The direct NP approach is simpler than CCE, but NP waveforms can be contaminated by near-zone effects—unless the waves are extracted at several distances from the source and extrapolated to infinity. Even then, the resulting waveforms can in principle be contaminated by gauge effects. In contrast, CCE directly provides, by construction, gauge-invariant waveforms at future null infinity. We verify the gauge invariance of CCE by running the same physical simulation using two different gauge conditions. We find that these two gauge conditions produce the same CCE waveforms but show differences in extrapolated-Ψ4 waveforms. We examine data from several different binary configurations and measure the dominant sources of error in the extrapolated-Ψ4 and CCE waveforms. In some cases, we find that NP waveforms extrapolated to infinity agree with the corresponding CCE waveforms to within the estimated error bars. However, we find that in other cases extrapolated and CCE waveforms disagree, most notably for m=0 “memory” modes.

  4. Grid-size dependence of Cauchy boundary conditions used to simulate stream-aquifer interactions

    Science.gov (United States)

    Mehl, S.; Hill, M.C.

    2010-01-01

    This work examines the simulation of stream–aquifer interactions as grids are refined vertically and horizontally and suggests that traditional methods for calculating conductance can produce inappropriate values when the grid size is changed. Instead, different grid resolutions require different estimated values. Grid refinement strategies considered include global refinement of the entire model and local refinement of part of the stream. Three methods of calculating the conductance of the Cauchy boundary conditions are investigated. Single- and multi-layer models with narrow and wide streams produced stream leakages that differ by as much as 122% as the grid is refined. Similar results occur for globally and locally refined grids, but the latter required as little as one-quarter the computer execution time and memory and thus are useful for addressing some scale issues of stream–aquifer interactions. Results suggest that existing grid-size criteria for simulating stream–aquifer interactions are useful for one-layer models, but inadequate for three-dimensional models. The grid dependence of the conductance terms suggests that values for refined models using, for example, finite difference or finite-element methods, cannot be determined from previous coarse-grid models or field measurements. Our examples demonstrate the need for a method of obtaining conductances that can be translated to different grid resolutions and provide definitive test cases for investigating alternative conductance formulations.

  5. The inverse problem for variational computation and its application to the integration of nonlinear ordinary differential equations of higher order

    Energy Technology Data Exchange (ETDEWEB)

    Kabal`skii, M.M.

    1994-06-05

    A method is established for constructing a functional of the variational problem associated with a given nonlinear differential equation of higher order. The Cauchy problem for strongly nonlinear differential equations is solved. The application of this method to the solution of the problem of the resistance of materials is examined. 2 refs.

  6. THE INTERACTION PROBLEM BETWEEN THE ELASTIC LINE INCLUSIONS

    Institute of Scientific and Technical Information of China (English)

    陶昉敏; 张明焕; 汤任基

    2002-01-01

    Using the engineering model of elastic line inclusion and the basic solutions of a single inclusion, the interaction problem between line inclusions in an elastic solid was investigated. A set of standard Cauchy-type singular equations of the problem was presented. The stress intensity factors at points of inclusions and the interface stresses of two sides of the inclusion were calculated. Several numerical examples were given. The results could be regarded as a reference to engineering.

  7. Criterion of positivity for semilinear problems with applications in biology

    OpenAIRE

    Duprez, Michel; Perasso, Antoine

    2016-01-01

    The goal of this article is to provide an useful criterion of positivity and well-posedness for a wide range of infinite dimensional semilinear abstract Cauchy problems. This criterion is based on some weak assumptions on the non-linear part of the semilinear problem and on the existence of a strongly continuous semigroup generated by the differential operator. To illustrate a large variety of applications, we exhibit the feasibility of this criterion through three examples in mathematical bi...

  8. Global classical solution to the Cauchy problem of 2D baratropic compressible Navier-Stokes system with large initial data

    OpenAIRE

    Huang, Jingchi; Wang, Chao

    2014-01-01

    For periodic initial data with initial density, we establish the global existence and uniqueness of strong and classical solutions for the two-dimensional compressible Navier-Stokes equations with no restrictions on the size of initial data provided the shear viscosity is a positive constant and the bulk one is $\\lam=\\rho^{\\b}$ with $\\b>1.$

  9. Asymptotic behavior of the solution to the Cauchy problem for the Timoshenko system in thermoelasticity of type III

    KAUST Repository

    Rahali, Radouane

    2013-03-01

    In this paper, we investigate the decay property of a Timoshenko system in thermoelasticity of type III in the whole space where the heat conduction is given by the Green and Naghdi theory. Surprisingly, we show that the coupling of the Timoshenko system with the heat conduction of Green and Naghdi\\'s theory slows down the decay of the solution. In fact we show that the L-2-norm of the solution decays like (1 + t)(-1/8), while in the case of the coupling of the Timoshenko system with the Fourier or Cattaneo heat conduction, the decay rate is of the form (1 + t)(-1/4) [25]. We point out that the decay rate of (1 + t)(-1/8) has been obtained provided that the initial data are in L-1 (R) boolean AND H-s (R); (s >= 2). If the wave speeds of the fi rst two equations are di ff erent, then the decay rate of the solution is of regularity-loss type, that is in this case the previous decay rate can be obtained only under an additional regularity assumption on the initial data. In addition, by restricting the initial data to be in H-s (R) boolean AND L-1,L-gamma (R) with gamma is an element of [0; 1], we can derive faster decay estimates with the decay rate improvement by a factor of t(-gamma/4).

  10. Optimal $\\mathfrak{L}^{\\beta}$-Control for the Global Cauchy Problem of the Relativistic Vlasov-Poisson System

    OpenAIRE

    Young, Brent

    2010-01-01

    Recently, M.K.-H. Kiessling and A.S. Tahvildar-Zadeh proved that a unique global classical solution to the relativistic Vlasov-Poisson system exists whenever the positive, integrable initial datum is spherically symmetric, compactly supported in momentum space, vanishes on characteristics with vanishing angular momentum, and for $\\beta \\ge 3/2$ has $\\mathfrak{L}^{\\beta}$-norm strictly below a positive, critical value $\\mathcal{C}_{\\beta}$. Everything else being equal, data leading to finite t...

  11. LogCauchy, log-sech and lognormal distributions of species abundances in forest communities

    Science.gov (United States)

    Yin, Z.-Y.; Peng, S.-L.; Ren, H.; Guo, Q.; Chen, Z.-H.

    2005-01-01

    Species-abundance (SA) pattern is one of the most fundamental aspects of biological community structure, providing important information regarding species richness, species-area relation and succession. To better describe the SA distribution (SAD) in a community, based on the widely used lognormal (LN) distribution model with exp(-x2) roll-off on Preston's octave scale, this study proposed two additional models, logCauchy (LC) and log-sech (LS), respectively with roll-offs of simple x-2 and e-x. The estimation of the theoretical total number of species in the whole community, S*, including very rare species not yet collected in sample, was derived from the left-truncation of each distribution. We fitted these three models by Levenberg-Marquardt nonlinear regression and measured the model fit to the data using coefficient of determination of regression, parameters' t-test and distribution's Kolmogorov-Smirnov (KS) test. Examining the SA data from six forest communities (five in lower subtropics and one in tropics), we found that: (1) on a log scale, all three models that are bell-shaped and left-truncated statistically adequately fitted the observed SADs, and the LC and LS did better than the LN; (2) from each model and for each community the S* values estimated by the integral and summation methods were almost equal, allowing us to estimate S* using a simple integral formula and to estimate its asymptotic confidence internals by regression of a transformed model containing it; (3) following the order of LC, LS, and LN, the fitted distributions became lower in the peak, less concave in the side, and shorter in the tail, and overall the LC tended to overestimate, the LN tended to underestimate, while the LS was intermediate but slightly tended to underestimate, the observed SADs (particularly the number of common species in the right tail); (4) the six communities had some similar structural properties such as following similar distribution models, having a common

  12. Generalized Moisil-Théodoresco Systems and Cauchy Integral Decompositions

    Directory of Open Access Journals (Sweden)

    Ricardo Abreu Blaya

    2008-05-01

    Full Text Available Let ℝ0,m+1(s be the space of s-vectors (0≤s≤m+1 in the Clifford algebra ℝ0,m+1 constructed over the quadratic vector space ℝ0,m+1, let r,p,q∈ℕ with 0≤r≤m+1, 0≤p≤q, and r+2q≤m+1, and let ℝ0,m+1(r,p,q=∑j=pq⨁ ℝ0,m+1(r+2j. Then, an ℝ0,m+1(r,p,q-valued smooth function W defined in an open subset Ω⊂ℝm+1 is said to satisfy the generalized Moisil-Théodoresco system of type (r,p,q if ∂xW=0 in Ω, where ∂x is the Dirac operator in ℝm+1. A structure theorem is proved for such functions, based on the construction of conjugate harmonic pairs. Furthermore, if Ω is bounded with boundary Γ, where Γ is an Ahlfors-David regular surface, and if W is a ℝ0,m+1(r,p,q-valued Hölder continuous function on Γ, then necessary and sufficient conditions are given under which W admits on Γ a Cauchy integral decomposition W=W++W−.

  13. A unified approach to problems of scattering of surface water waves by vertical barriers

    OpenAIRE

    Chakrabarti, A; Banerjea, S; Mandal, BN; Sahoo, T

    1997-01-01

    A unified analysis involving the solution of multiple integral equations via a simple singular integral equation with a Cauchy type kernel is presented to handle problems of surface water wave scattering by vertical barriers. Some well known results are produced in a simple and systematic manner.

  14. Some improperly posed problems of mathematical physics

    CERN Document Server

    Lavrentiev, M M

    1967-01-01

    This monograph deals with the problems of mathematical physics which are improperly posed in the sense of Hadamard. The first part covers various approaches to the formulation of improperly posed problems. These approaches are illustrated by the example of the classical improperly posed Cauchy problem for the Laplace equation. The second part deals with a number of problems of analytic continuations of analytic and harmonic functions. The third part is concerned with the investigation of the so-called inverse problems for differential equations in which it is required to determine a dif­ ferential equation from a certain family of its solutions. Novosibirsk June, 1967 M. M. LAVRENTIEV Table of Contents Chapter I Formu1ation of some Improperly Posed Problems of Mathematic:al Physics § 1 Improperly Posed Problems in Metric Spaces. . . . . . . . . § 2 A Probability Approach to Improperly Posed Problems. . . 8 Chapter II Analytic Continuation § 1 Analytic Continuation of a Function of One Complex Variable fro...

  15. On the problem of scattering of a plane electromagnetic wave on the one-dimensional dielectric plate with an arbitrary refractive index

    CERN Document Server

    Sedrakian, D M; Khachatrian, A Z

    2000-01-01

    It is shown that the problem on scattering of an arbitrary polarized plane wave to be incident on the plate of a one-dimensional medium can be formulated as a Cauchy problem for wave equations for s and p waves.

  16. STABILITY OF DISPLACEMENT TO THE SECOND FUNDAMENTAL PROBLEM IN PLANE ELASTICITY

    Institute of Scientific and Technical Information of China (English)

    Juan LIN; Jinyuan DU

    2014-01-01

    In this article, by using the stability of Cauchy type integral when the smooth perturbation for integral curve and the Sobolev type perturbation for kernel density hap-pen, we discuss the stability of the second fundamental problem in plane elasticity when the smooth perturbation for the boundary of the elastic domain (unit disk) and the Sobolev type perturbation for the displacement happen. And the error estimate of the displacement between the second fundamental problem and its perturbed problem is obtained.

  17. The borderlines of the invisibility and visibility for Calderon's inverse problem

    OpenAIRE

    Astala, Kari; Lassas, Matti; Paivarinta, Lassi

    2011-01-01

    We consider the determination of a conductivity function in a two-dimensional domain from the Cauchy data of the solutions of the conductivity equation on the boundary. We prove uniqueness results for this inverse problem, posed by Calderon, for conductivities that are degenerate, that is, they may not be bounded from above or below. In particular, for scalar conductivities we solve the inverse problem in a class which is larger than $L^\\infty$. Also, we give new counterexamples for the uniqu...

  18. Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations

    Directory of Open Access Journals (Sweden)

    M. G. Crandall

    1999-07-01

    Full Text Available We study existence of continuous weak (viscosity solutions of Dirichlet and Cauchy-Dirichlet problems for fully nonlinear uniformly elliptic and parabolic equations. Two types of results are obtained in contexts where uniqueness of solutions fails or is unknown. For equations with merely measurable coefficients we prove solvability of the problem, while in the continuous case we construct maximal and minimal solutions. Necessary barriers on external cones are also constructed.

  19. El problema de cauchy asociado a una generalización de la ecuación de Kuramoto-Sivashinsky bidimensional periódica

    OpenAIRE

    Pérez Cantor, Edwin Leonardo

    2014-01-01

    El propósito de este trabajo es estudiar el buen planteamiento en los espacios de Sobolev Hs(T2) para s 1> del problema de Cauchy asociado a una generalización de la ecuación de Kuramoto-Sivashinsky bidimensional periódica, que modela fenómenos físicos que ocurren en películas delgadas

  20. El problema de cauchy asociado a una ecuación del tipo kuramoto-sivashinsky bidimensional periódica

    OpenAIRE

    Campos, Juvitsa; Duque, Omar; Rodríguez-Blanco, Guillermo

    2012-01-01

    El propósito de este trabajo es abordar el buen planteamiento en los espacios de Sobolev $H^{s}(\\mathbb{T}^2)$ para $s\\geq1$ del problema de Cauchy asociado a una ecuación del tipo Kuramoto-Sivashinsky bidimensional periódica, que modela fenómenos físicos que ocurren en películas delgadas.

  1. Cauchy transformation and mutual dualities between $A^{-\\infty}(\\Omega)$ and $A^\\infty(\\complement\\Omega)$ for Carathéodory domains

    OpenAIRE

    Abanin, A.V.; Khoi, Le Hai

    2016-01-01

    Let $\\Omega$ be a Carathéodory domain in the complex plane $\\mathbb C$, $A^{-\\infty}(\\Omega)$ the space of functions that are holomorphic in $\\Omega$ with polynomial growth near the boundary $\\partial\\Omega$, and $A^\\infty(\\complement\\Omega)$ the space of holomorphic functions in the interior of $\\complement\\Omega:=\\overline{\\mathbb C}\\setminus\\Omega$, vanishing at infinity and being in $C^\\infty(\\complement\\Omega)$. We prove that the Cauchy transformation of analytic fun...

  2. Finding Solutions to the Picard Boundary Value Problem via Homotopy Method%用同伦方法求Picard边值问题的解

    Institute of Scientific and Technical Information of China (English)

    李兰; 徐旭

    2008-01-01

    This paper deals with the problem of finding solutions to the Picard boundary problem. In our approach, by means of the homotopy method, the equation considered is linked to a simpler equation by introducing a parameter. We first find the solutions of the simpler equation, and give a priori estimates of" the equa tion we considered, and then one can obtain the solutions of Picard boundary problem by following the path of solutions of Cauchy problem.

  3. Assessment of the accuracy of plasma shape reconstruction by the Cauchy condition surface method in JT-60SA

    Energy Technology Data Exchange (ETDEWEB)

    Miyata, Y.; Suzuki, T.; Takechi, M.; Urano, H.; Ide, S. [Japan Atomic Energy Agency, Naka, Ibaraki 311-0193 (Japan)

    2015-07-15

    For the purpose of stable plasma equilibrium control and detailed analysis, it is essential to reconstruct an accurate plasma boundary on the poloidal cross section in tokamak devices. The Cauchy condition surface (CCS) method is a numerical approach for calculating the spatial distribution of the magnetic flux outside a hypothetical surface and reconstructing the plasma boundary from the magnetic measurements located outside the plasma. The accuracy of the plasma shape reconstruction has been assessed by comparing the CCS method and an equilibrium calculation in JT-60SA with a high elongation and triangularity of plasma shape. The CCS, on which both Dirichlet and Neumann conditions are unknown, is defined as a hypothetical surface located inside the real plasma region. The accuracy of the plasma shape reconstruction is sensitive to the CCS free parameters such as the number of unknown parameters and the shape in JT-60SA. It is found that the optimum number of unknown parameters and the size of the CCS that minimizes errors in the reconstructed plasma shape are in proportion to the plasma size. Furthermore, it is shown that the accuracy of the plasma shape reconstruction is greatly improved using the optimum number of unknown parameters and shape of the CCS, and the reachable reconstruction errors in plasma shape and locations of strike points are within the target ranges in JT-60SA.

  4. Existence and regularity of solutions for hyperbolic functional differential problems

    Directory of Open Access Journals (Sweden)

    Zdzisław Kamont

    2014-01-01

    Full Text Available A generalized Cauchy problem for quasilinear hyperbolic functional differential systems is considered. A theorem on the local existence of weak solutions is proved. The initial problem is transformed into a system of functional integral equations for an unknown function and for their partial derivatives with respect to spatial variables. The existence of solutions for this system is proved by using a method of successive approximations. We show a theorem on the differentiability of solutions with respect to initial functions which is the main result of the paper.

  5. Validity of the Cauchy-Born rule applied to discrete cellular-scale models of biological tissues

    KAUST Repository

    Davit, Y.

    2013-04-30

    The development of new models of biological tissues that consider cells in a discrete manner is becoming increasingly popular as an alternative to continuum methods based on partial differential equations, although formal relationships between the discrete and continuum frameworks remain to be established. For crystal mechanics, the discrete-to-continuum bridge is often made by assuming that local atom displacements can be mapped homogeneously from the mesoscale deformation gradient, an assumption known as the Cauchy-Born rule (CBR). Although the CBR does not hold exactly for noncrystalline materials, it may still be used as a first-order approximation for analytic calculations of effective stresses or strain energies. In this work, our goal is to investigate numerically the applicability of the CBR to two-dimensional cellular-scale models by assessing the mechanical behavior of model biological tissues, including crystalline (honeycomb) and noncrystalline reference states. The numerical procedure involves applying an affine deformation to the boundary cells and computing the quasistatic position of internal cells. The position of internal cells is then compared with the prediction of the CBR and an average deviation is calculated in the strain domain. For center-based cell models, we show that the CBR holds exactly when the deformation gradient is relatively small and the reference stress-free configuration is defined by a honeycomb lattice. We show further that the CBR may be used approximately when the reference state is perturbed from the honeycomb configuration. By contrast, for vertex-based cell models, a similar analysis reveals that the CBR does not provide a good representation of the tissue mechanics, even when the reference configuration is defined by a honeycomb lattice. The paper concludes with a discussion of the implications of these results for concurrent discrete and continuous modeling, adaptation of atom-to-continuum techniques to biological

  6. Maximum Principles and Boundary Value Problems for First-Order Neutral Functional Differential Equations

    Directory of Open Access Journals (Sweden)

    Domoshnitsky Alexander

    2009-01-01

    Full Text Available We obtain the maximum principles for the first-order neutral functional differential equation where , and are linear continuous operators, and are positive operators, is the space of continuous functions, and is the space of essentially bounded functions defined on . New tests on positivity of the Cauchy function and its derivative are proposed. Results on existence and uniqueness of solutions for various boundary value problems are obtained on the basis of the maximum principles.

  7. EXPLICIT FORMULATION FOR THE DIRICHLET PROBLEM FOR PARABOLIC-HYPERBOLIC CONSERVATION LAWS

    OpenAIRE

    Andreianov, Boris; Karimou Gazibo, Mohamed

    2015-01-01

    We revisit the Cauchy-Dirichlet problem for degenerate parabolic scalar conservation laws. We suggest a new notion of strong entropy solution. It gives a straightforward explicit characterization of the boundary values of the solution and of the flux, and leads to a concise and natural uniqueness proof, compared to the one of the fundamental work [J. Carrillo, Arch. Ration. Mech. Anal., 1999]. Moreover, general dissipative boundary conditions can be studied in the same framework. The definiti...

  8. The concept of the urine test and specific reaction of the urine in various diseases according to Enrico Cauchi - member of the medical council of Malta (1933).

    Science.gov (United States)

    Ricciardi, Carlo Alberto; Ricciardi, Elisabetta; Visconti, Luca; Lacquaniti, Antonio; Savica, Vincenzo; Santoro, Domenico; Buemi, Michele; Ricciardi, Biagio

    2016-02-01

    The Study of urine from the outset has always aroused the interest of scientists and physicians all over the world, from ancient Greeks and Romans to Hindus , Hulcos in Mexico, Australian native etc. The urine in such case was considered not only as a waste product but also as a therapeutic product. In the late XIX century scientific knowledge had already identified the function of substances that favor the increase of urinary output, and physicians over the centuries have always tried to analyze urine in various ways. In Cauchis work in 1933 all chemistry and pathophysiological knowledge of the time was condensed. Cauchi signed the preface as Member of the medical council of Malta. He was a medical doctor of the early20thcentury, He wrote about the physiopathology of urine ranging from chemical and physical behavior, to the analysis of sediments and the special reactions of the urine in various pathologies. In particular Cauchi emphasizes the main diseases of the time combines the behavior of the reaction of urine as a diagnostic and prognostic instrument, stressing the importance of the urine test and describing the method used for analysis at the time. The analyses of the text in the issue seems to belong to archaic medicine, and it is difficult to think today, that what was presented as very up-to-date- science at that time, took place only 80 years ago. Reading the full original text with today experience we are led to consider the increasing importance that scientific community gave in the past, and still gives to urine test. PMID:26913892

  9. Deriving a complete set of eigendistributions for a gravitational wave equation describing the quantized interaction of gravity with a Yang-Mills field in case the Cauchy hypersurface is non-compact

    CERN Document Server

    Gerhardt, Claus

    2016-01-01

    In a recent paper we quantized the interaction of gravity with a Yang-Mills and Higgs field and obtained as a result a gravitational wave equation in a globally hyperbolic spacetime. Assuming that the Cauchy hypersurfaces are compact we proved a spectral resolution for the wave equation by applying the method of separation of variables. In this paper we extend the results to the case when the Cauchy hypersurfaces are non-compact by considering a Gelfand triplet and applying the nuclear spectral theorem.

  10. Solution of the generalized Saint Venant problem

    International Nuclear Information System (INIS)

    A well-known problem in the mathematical theory of elasticity about the torsional rigidity P(Ω) of a bar whose cross-section is an arbitrary simply connected domain Ω is considered. It is shown that P(Ω) is equivalent to the moment of inertia of the domain relative to its boundary. Thus, a new interpretation of the well-known Coulomb's formula is suggested, and on this basis the following problem, which has its origins in works of Cauchy and Saint Venant, is solved: find a geometric parameter equivalent to the torsional rigidity coefficient of elastic bars with simply connected cross-sections. The proof is based on the definition of the torsional rigidity as the norm of a certain embedding operator in a Sobolev space and on the theory of conformal maps. In particular, some conformally invariant inequalities are established

  11. An existence theorem for the Cauchy problem on the light-cone for the vacuum Einstein equations with near-round analytic data

    OpenAIRE

    Choquet-Bruhat, Yvonne; Chrusciel, Piotr; Martin-garcia, Jose

    2010-01-01

    Представлен класс характеристических релятивистски обобщенных исходных данных, удовлетворяющих условию почти закругленности на вершине светового конуса. Показано, что для любых подобных аналитических данных существует соответствующее решение для вакуумных уравнений Эйнштейна, определенное в окрестности вершины в световом конусе будущего.A class of characteristic general relativistic initial data satisfying a near-roundness condition at the tip of a light-cone is introduced. It is shown that f...

  12. Library IVP++ of algorithms for the integration of Cauchy problems for the simulation of the hydrodynamics of one-dimensional channels

    International Nuclear Information System (INIS)

    The program library IVP++ has been described and tested on the simulation of the hydrodynamics of a one-dimensional channel. Numerical integration methods are briefly reviewed. The calculation-theoretical analysis of the application of implicit high-order integration methods to the simulation of one-dimensional hydro and gas dynamics has been performed

  13. ANALYSIS OF THE SINGULARITY FOR THE VERTICAL CONTACT PROBLEM OF LINE CRACK-INCLUSION

    Institute of Scientific and Technical Information of China (English)

    沈安; 陶昉敏; 汤任基

    2001-01-01

    Taking the short-fiber composite materials as engineering back-ground, utilizing the existing basic solutions of single inclusion and single crack, the plane problem of vertical contact interactions between line crack and rigid line inclusion in infinite plane (matrix) from the viewpoint of crack fracture mechanics is studied. According to boundary conditions, a set of standard Cauchy-type singular integral equations of the problem is obtainable. Besides, singular indexes, stresses and stress intensity factors around the contact point are expressed. Numerical examples are given to provide references to engineering.

  14. De Lacroix a Cauchy: La fundamentación del cálculo infinitesimal en José Mariano Vallejo (1807-1832

    Directory of Open Access Journals (Sweden)

    Ausejo, Elena

    2015-12-01

    Full Text Available This paper studies the foundations of infinitesimal calculus in the work of José Mariano Vallejo (1779-1846, the most influential mathematician in Spanish during the first half of the 19th century. For this purpose, the analytical foundations of his three main works related to infinitesimal calculus are considered: Memoria sobre la curvatura de las líneas en sus diferentes puntos, sobre el radio de curvatura y sobre las evolutas (1807, and the two editions (1813 and 1832 of the volume of his Tratado Elemental de Matemáticas devoted to calculus. The study shows the evolutionary dynamics of Vallejo’s thought, following the European leading references in the development of mathematical analysis in his time, and how Vallejo combines the successive influence of Lagrange, Lacroix, and Cauchy, according to criteria of educational adequacy and mathematical rigor. In particular, the influences and discrepancies on infinitesimal calculus between Vallejo’s Treatise (1813 and Lacroix’ Traité élémentaire de calcul différentiel et de calcul intégral (1802 are determined, as well as the scope of the introduction of Cauchy’s ideas, that were published for the first time in Spain in the second edition of the volume on infinitesimal calculus of Vallejo’s Treatise (1832.Este artículo estudia los aspectos relativos a la fundamentación del cálculo infinitesimal en la obra de José Mariano Vallejo (1779-1846, el matemático de mayor difusión en lengua española de la primera mitad del siglo XIX. Para ello, se consideran los fundamentos analíticos de su Memoria sobre la curvatura de las líneas en sus diferentes puntos, sobre el radio de curvatura y sobre las evolutas (1807 y de las dos ediciones (1813 y 1832 del volumen de su Tratado Elemental de Matemáticas dedicado al cálculo infinitesimal. El estudio muestra la dinámica evolutiva del pensamiento de Vallejo al ritmo de las referencias europeas —especialmente francesas– que encabezan el

  15. The Scattering Problem for a Noncommutative Nonlinear Schrödinger Equation

    Directory of Open Access Journals (Sweden)

    Bergfinnur Durhuus

    2010-06-01

    Full Text Available We investigate scattering properties of a Moyal deformed version of the nonlinear Schrödinger equation in an even number of space dimensions. With rather weak conditions on the degree of nonlinearity, the Cauchy problem for general initial data has a unique globally defined solution, and also has solitary wave solutions if the interaction potential is suitably chosen. We demonstrate how to set up a scattering framework for equations of this type, including appropriate decay estimates of the free time evolution and the construction of wave operators defined for small scattering data in the general case and for arbitrary scattering data in the rotationally symmetric case.

  16. Macroscopic Violation of Three Cauchy-Schwarz Inequalities Using Correlated Light Beams From an Infra-Red Emitting Semiconductor Diode Array

    Science.gov (United States)

    Edwards, P. J.; Huang, X.; Li, Y. Q. (Editor); Wang, Y. Z. (Editor)

    1996-01-01

    We briefly review quantum mechanical and semi-classical descriptions of experiments which demonstrate the macroscopic violation of the three Cauchy-Schwarz inequalities: g(sup 2)(sub 11)(0) greater than or equal to 1; g(sup 2)(sub 11)(0) greater than or equal to g(sup 2)(sub 11)(t), (t approaches infinity); (the absolute value of g(sup 2)(sub 11)(0))(exp 2) less than or equal to g(sup 2)(sub 11)(0) g(sup 2)(sub 11)(0). Our measurements demonstrate the violation, at macroscopic intensities, of each of these inequalities. We show that their violation, although weak, can be demonstrated through photodetector current covariance measurements on correlated sub-Poissonian Poissonian, and super Poissonian light beams. Such beams are readily generated by a tandem array of infrared-emitting semiconductor junction diodes. Our measurements utilize an electrically coupled array of one or more infrared-emitting diodes, optically coupled to a detector array. The emitting array is operated in such a way as to generate highly correlated beams of variable photon Fano Factor. Because the measurements are made on time scales long compared with the first order coherence time and with detector areas large compared with the corresponding coherence areas, first order interference effects are negligible. The first and second inequalities are violated, as expected, when a sub-Poissonian light beam is split and the intensity fluctuations of the two split beams are measured by two photodetectors and subsequently cross-correlated. The third inequality is violated by bunched (as well as anti-bunched) beams of equal intensity provided the measured cross correlation coefficient exceeds (F - 1)/F, where F is the measured Fano Factor of each beam. We also investigate the violation for the case of unequal beams.

  17. [Population problem, comprehension problem].

    Science.gov (United States)

    Tallon, F

    1993-08-01

    Overpopulation of developing countries in general, and Rwanda in particular, is not just their problem but a problem for developed countries as well. Rapid population growth is a key factor in the increase of poverty in sub-Saharan Africa. Population growth outstrips food production. Africa receives more and more foreign food, economic, and family planning aid each year. The Government of Rwanda encourages reduced population growth. Some people criticize it, but this criticism results in mortality and suffering. One must combat this ignorance, but attitudes change slowly. Some of these same people find the government's acceptance of family planning an invasion of their privacy. Others complain that rich countries do not have campaigns to reduce births, so why should Rwanda do so? The rate of schooling does not increase in Africa, even though the number of children in school increases, because of rapid population growth. Education is key to improvements in Africa's socioeconomic growth. Thus, Africa, is underpopulated in terms of potentiality but overpopulated in terms of reality, current conditions, and possibilities of overexploitation. Africa needs to invest in human resources. Families need to save, and to so, they must refrain from having many children. Africa should resist the temptation to waste, as rich countries do, and denounce it. Africa needs to become more independent of these countries, but structural adjustment plans, growing debt, and rapid population growth limit national independence. Food aid is a means for developed countries to dominate developing countries. Modernization through foreign aid has had some positive effects on developing countries (e.g., improved hygiene, mortality reduction), but these also sparked rapid population growth. Rwandan society is no longer traditional, but it is also not yet modern. A change in mentality to fewer births, better quality of life for living infants, better education, and less burden for women must occur

  18. Mathematical Model of a pH-gradient Creation at Isoelectrofocusing. Part II. Numerical Solution of the Stationary Problem

    CERN Document Server

    Sakharova, L V; Zhukov, M Yu

    2013-01-01

    The mathematical model describing the natural textrm{pH}-gradient arising under the action of an electric field in an aqueous solution of ampholytes (amino acids) is constructed and investigated. This paper is the second part of the series papers \\cite{Part1,Part3,Part4} that are devoted to pH-gradient creation problem. We present the numerical solution of the stationary problem. The equations system has a small parameter at higher derivatives and the turning points, so called stiff problem. To solve this problem numerically we use the shooting method: transformation of the boundary value problem to the Cauchy problem. At large voltage or electric current density we compare the numerical solution with weak solution presented in Part 1.

  19. Stability analysis of the inverse transmembrane potential problem in electrocardiography

    Science.gov (United States)

    Burger, Martin; Mardal, Kent-André; Nielsen, Bjørn Fredrik

    2010-10-01

    In this paper we study some mathematical properties of an inverse problem arising in connection with electrocardiograms (ECGs). More specifically, we analyze the possibility for recovering the transmembrane potential in the heart from ECG recordings, a challenge currently investigated by a growing number of groups. Our approach is based on the bidomain model for the electrical activity in the myocardium, and leads to a parameter identification problem for elliptic partial differential equations (PDEs). It turns out that this challenge can be split into two subproblems: the task of recovering the potential at the heart surface from body surface recordings; the problem of computing the transmembrane potential inside the heart from the potential determined at the heart surface. Problem (1), which can be formulated as the Cauchy problem for an elliptic PDE, has been extensively studied and is well known to be severely ill-posed. The main purpose of this paper is to prove that problem (2) is stable and well posed if a suitable prior is available. Moreover, our theoretical findings are illuminated by a series of numerical experiments. Finally, we discuss some aspects of uniqueness related to the anisotropy in the heart.

  20. The Fixed Point Theorem and the Iterative Approximation of Modified Cauchy Integral Operator of Regular Functions%正则函数的修正的Cauchy型积分算子的不动点定理及迭代构造

    Institute of Scientific and Technical Information of China (English)

    王丽萍; 彭维玲; 肖卓峰

    2008-01-01

    In the first part of this paper, we discuss the Holder continuity of the cauchy integral operator for regular functions and the relation between ‖T[f] ‖α and ‖f‖α. In the second part of this paper, we introduce the modified cauchy integral operator T for regular functions. Firstly,we prove that the operator T has a unique fixed point by the Banach's Contraction Mapping Principle. Secondly, we give the Mann iterative sequence, and then we show the iterative sequence strongly converges to the fixed point of the operator T.

  1. $delta$-Quasi Cauchy Sequences

    OpenAIRE

    Cakalli, Huseyin

    2010-01-01

    Recently, a concept of forward continuity and a concept of forward compactness are introduced in the senses that a function $f$ is forward continuous if $\\lim_{n\\to\\infty} \\Delta f(x_{n})=0$ whenever $\\lim_{n\\to\\infty} \\Delta x_{n}=0$,\\; and a subset $E$ of $\\textbf{R}$ is forward compact if any sequence $\\textbf{x}=(x_{n})$ of points in $E$ has a subsequence $\\textbf{z}=(z_{k})=(x_{n_{k}})$ of the sequence $\\textbf{x}$ such that $\\lim_{k\\to \\infty} \\Delta z_{k}=0$ where $\\Delta z_{k}=z_{k+1}...

  2. Interactions between discontinuities for binary mixture separation problem and hodograph method

    CERN Document Server

    Elaeva, M S; Yu, Zhukov M

    2016-01-01

    The Cauchy problem for first-order PDE with the initial data which have a piecewise discontinuities localized in different spatial points is completely solved. The interactions between discontinuities arising after breakup of initial discontinuities are studied with the help of the hodograph method. The solution is constructed in analytical implicit form. To recovery the explicit form of solution we propose the transformation of the PDEs into some ODEs on the level lines (isochrones) of implicit solution. In particular, this method allows us to solve the Goursat problem with initial data on characteristics. The paper describes a specific problem for zone electrophoresis (method of the mixture separation). However, the method proposed allows to solve any system of two first-order quasilinear PDEs for which the second order linear PDE, arising after the hodograph transformation, has the Riemann-Green function in explicit form.

  3. Explaining the Mind: Problems, Problems

    OpenAIRE

    Harnad, Stevan

    2001-01-01

    The mind/body problem is the feeling/function problem: How and why do feeling systems feel? The problem is not just "hard" but insoluble (unless one is ready to resort to telekinetic dualism). Fortunately, the "easy" problems of cognitive science (such as the how and why of categorization and language) are not insoluble. Five books (by Damasio, Edelman/Tononi...

  4. Breathing Problems

    Science.gov (United States)

    ... you're not getting enough air. Sometimes mild breathing problems are from a stuffy nose or hard ... conditions such as asthma, emphysema or pneumonia cause breathing difficulties. So can problems with your trachea or ...

  5. The Dirichlet problem for the two-dimensional Helmholtz equation for an open boundary

    Science.gov (United States)

    Hayashi, Y.

    1973-01-01

    Development of a complete theory of the two-dimensional Dirichlet problem for an open boundary. It is shown that the solution of the Dirichlet problem for an open boundary requires the solution of a Fredholm integral equation of the first kind. Although a Fredholm integral equation of the first kind usually has no solution if the kernel is continuous, owing to the logarithmic singularity of the kernel, the equation in this case is converted to a singular integral equation with a Cauchy kernel. It is proven that the homogeneous adjoint equation of the singular integral equation has no nonzero solution. By virtue of this result, and with the aid of an existence theorem known in the theory of singular integral equations, the existence of solutions of the singular integral equation, and then of the unique solution of the Fredholm integral equation of the first kind is proved.

  6. A unified nonlinear fractional equation of the diffusion-controlled surfactant adsorption: Reappraisal and new solution of the Ward–Tordai problem

    Directory of Open Access Journals (Sweden)

    Jordan Hristov

    2016-01-01

    Full Text Available The article addresses a reappraisal of the famous Ward–Tordai equation describing the equilibrium of surfactants at air/liquid interfaces under diffusion control. The new derivation is entirely developed in the light of fractional calculus. The unified approach demonstrates that this equation can be clearly reformulated as a nonlinear ordinary time-fractional equation of order 1/2. The work formulates versions with different isotherms. A simple solution of the case with the Henry’s isotherm and a discussion of a Cauchy problem involving the Freundlich isotherm are provided.

  7. Sociale problemer

    DEFF Research Database (Denmark)

    Christensen, Anders Bøggild; Rasmussen, Tove; Bundesen, Peter;

    Sociale problemer kan betragtes som selve udgangspunktet for socialt arbejde, hvor ambitionen er at råde bod på problemerne og sikre, at udsatte borgere får en bedre tilværelse. Det betyder også, at diskussionen af sociale problemer er afgørende for den sociale grundfaglighed. I denne bog sætter en...... række fagfolk på tværs af det danske socialfaglige felt fokus på sociale problemer. Det diskuteres, hvad vi overhovedet forstår ved sociale problemer, hvordan de opstår, hvilke konsekvenser de har, og ikke mindst hvordan man som fagprofessionel håndterer sociale problemer i det daglige arbejde. Bogen er...... skrevet som lærebog til professionsuddannelser, hvor sociale problemer udgør en dimension, bl.a. socialrådgiver-, pædagog- og sygeplejerskeuddannelserne....

  8. Popular Problems

    DEFF Research Database (Denmark)

    Skovhus, Randi Boelskifte; Thomsen, Rie

    2016-01-01

    This article introduces a method to critical reviews and explores the ways in which problems have been formulated in knowledge production on career guidance in Denmark over a 10-year period from 2004 to 2014. The method draws upon the work of Bacchi focussing on the ‘What's the problem represented...... provides a constructive basis for a critical analysis and discussion of the collective empirical knowledge production on career guidance, stimulating awareness of problems and potential solutions among the career guidance community....

  9. Solution of 3D inverse scattering problems by combined inverse equivalent current and finite element methods

    International Nuclear Information System (INIS)

    An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained

  10. Knee Problems

    Science.gov (United States)

    ... in Chinese 繁體中文 ) What Are Knee Problems? (in Korean 한국어 ) What Are Knee Problems? (in Vietnamese bằng ... the knee. Ultrasound. A technique that uses sound waves to produce images of the soft tissue structures ...

  11. On explicit and numerical solvability of parabolic initial-boundary value problems

    Directory of Open Access Journals (Sweden)

    Olga Lepsky

    2006-05-01

    Full Text Available A homogeneous boundary condition is constructed for the parabolic equation (∂t+I−Δu=f in an arbitrary cylindrical domain Ω×ℝ (Ω⊂ℝn being a bounded domain, I and Δ being the identity operator and the Laplacian which generates an initial-boundary value problem with an explicit formula of the solution u. In the paper, the result is obtained not just for the operator ∂t+I−Δ, but also for an arbitrary parabolic differential operator ∂t+A, where A is an elliptic operator in ℝn of an even order with constant coefficients. As an application, the usual Cauchy-Dirichlet boundary value problem for the homogeneous equation (∂t+I−Δu=0 in Ω×ℝ is reduced to an integral equation in a thin lateral boundary layer. An approximate solution to the integral equation generates a rather simple numerical algorithm called boundary layer element method which solves the 3D Cauchy-Dirichlet problem (with three spatial variables.

  12. Sexual Problems

    Medline Plus

    Full Text Available ... can have intercourse but experience vaginismus during pelvic exams. Although vaginismus is considered a pain disorder, most ... and are used together to treat a problem. Education is important in understanding the anatomy and physiology ...

  13. Sexual Problems

    Medline Plus

    Full Text Available ... sexual problems. This specialist may be a physician, psychologist, social worker, or physical therapist. You may also ... see” their actions. In addition to improving sexual function, pelvic floor muscle rehabilitation can improve pelvic pain ...

  14. Sexual Problems

    Medline Plus

    Full Text Available ... Smoking Cessation Links to Professional Societies and Organizations Home › Sexual Problems Sexual concern causing distress can be ... Find a Health Care Provider Back to Top Home | About Us | Reproductive Health Topics | News & Publications | Resources ...

  15. Sexual Problems

    Medline Plus

    Full Text Available ... common problem that may be due to many factors, including physical, psychological, medical conditions, or medications. Men ... or as deep pain. Both psychological and physical factors can contribute to the condition. Current thinking is ...

  16. Sleep Problems

    Science.gov (United States)

    ... For Consumers Consumer Information by Audience For Women Sleep Problems Share Tweet Linkedin Pin it More sharing ... PDF 474KB) En Español Medicines to Help You Sleep Tips for Better Sleep Basic Facts about Sleep ...

  17. Sexual Problems

    Medline Plus

    Full Text Available ... pain disorders. If you are experiencing problems viewing this embedded video, please click here . Transcript Disorders of ... no sexual fantasies and desire for sexual activity. This lack of desire is beyond what normally happens ...

  18. Erection problems

    Science.gov (United States)

    ... problems can lead to ED, such as: Poor communication with your partner Feelings of doubt and failure Stress, fear, anxiety, or anger Expecting too much from sex. This can make sex a task instead of ...

  19. Sexual Problems

    Medline Plus

    Full Text Available ... Some women with vaginismus can tolerate a pelvic examination, while some women can have intercourse but experience ... and are used together to treat a problem. Education is important in understanding the anatomy and physiology ...

  20. Sexual Problems

    Medline Plus

    Full Text Available ... such as chronic testicular pain, and 4) other causes of sexual pain that include conditions of the ... should be taken seriously. When a sexual problem causes you distress, don’t be afraid to talk ...

  1. Swallowing problems

    Science.gov (United States)

    ... the home Dry mouth during cancer treatment Enteral nutrition - child - managing problems Gastrostomy feeding tube - bolus Jejunostomy feeding tube Mouth and neck radiation - discharge Multiple sclerosis - discharge Stroke - discharge Update Date 5/15/2014 ...

  2. Sexual Problems

    Medline Plus

    Full Text Available ... and Smoking Cessation Links to Professional Societies and Organizations Home › Sexual Problems Sexual concern causing distress can ... Site Terms & Conditions of Use | Web Design and Development by The Berndt Group

  3. Foot Problems

    Science.gov (United States)

    ... much higher rates of foot problems. For women, pain in the toes and ball of the foot is much more common than in men, and it gets worse with age. However, pain in the heel tends to decrease as we ...

  4. Sexual Problems

    Medline Plus

    Full Text Available ... to a specialist trained in the diagnosis and treatment of sexual problems. This specialist may be a ... in many different ways. Often, multiple types of treatment may be required and are used together to ...

  5. Sexual Problems

    Medline Plus

    Full Text Available ... problems. This specialist may be a physician, psychologist, social worker, or physical therapist. You may also find ... aids include lubricants, moisturizers, and sexual toys. Lubricants work by reducing friction between tissues. Many different types ...

  6. Sexual Problems

    Medline Plus

    Full Text Available ... and are used together to treat a problem. Education is important in understanding the anatomy and physiology ... counselors are mental health providers who have specialized training in working with people with sexual concerns. Cognitive ...

  7. Sexual Problems

    Medline Plus

    Full Text Available ... sexual arousal disorder have little or no genital responsiveness to stimulation and they don’t produce adequate ... problems. This specialist may be a physician, psychologist, social worker, or physical therapist. You may also find ...

  8. Sexual Problems

    Medline Plus

    Full Text Available ... a problem. Education is important in understanding the anatomy and physiology of sex and in having realistic ... lubricants in that they are absorbed into the skin. Moisturizers are a “maintenance therapy” that is applied ...

  9. Contact problems

    CERN Document Server

    Galin, Lev Aleksandrovich

    2008-01-01

    L.A. Galin's book on contact problems is a remarkable work. Actually there are two books: the first, published in 1953 deals with contact problems in the classical theory of elasticity; this is the one that was translated into English in 1961. The second book, published in 1980, included the first, and then had new sections on contact problems for viscoelastic materials, and rough contact problems; this section has not previously been translated into English. In this new translation, the original text and the mathematical analysis have been completely revised, new material has been added, and the material appearing in the 1980 Russian translation has been completely rewritten. In addition there are three essays by students of Galin, bringing the analysis up to date.

  10. Sexual Problems

    Medline Plus

    Full Text Available ... and Smoking Cessation Links to Professional Societies and Organizations Home › Sexual Problems Sexual concern causing distress can ... such as sexual abuse can be involved as well. Pain caused by lack of lubrication or by ...

  11. Sexual Problems

    Medline Plus

    Full Text Available ... concerns with your sexual partner. Because they are complex, sexual concerns are treated in many different ways. ... a healthcare professional. Although sexual problems can be complex, there are a variety of treatments that can ...

  12. Nipple problems

    Science.gov (United States)

    ... Inverted nipple; Nipple problems Images Female breast Intraductal papilloma Mammary gland Abnormal discharge from the nipple Normal ... 8. Read More Breast cancer Endocrine glands Intraductal papilloma Update Date 11/16/2014 Updated by: Cynthia ...

  13. Knapsack problems

    CERN Document Server

    Kellerer, Hans; Pisinger, David

    2004-01-01

    Thirteen years have passed since the seminal book on knapsack problems by Martello and Toth appeared. On this occasion a former colleague exclaimed back in 1990: "How can you write 250 pages on the knapsack problem?" Indeed, the definition of the knapsack problem is easily understood even by a non-expert who will not suspect the presence of challenging research topics in this area at the first glance. However, in the last decade a large number of research publications contributed new results for the knapsack problem in all areas of interest such as exact algorithms, heuristics and approximation schemes. Moreover, the extension of the knapsack problem to higher dimensions both in the number of constraints and in the num­ ber of knapsacks, as well as the modification of the problem structure concerning the available item set and the objective function, leads to a number of interesting variations of practical relevance which were the subject of intensive research during the last few years. Hence, two years ago ...

  14. On the existence and uniqueness of solutions of optimal control problems of linear distributed systems which are not solved with respect to the time derivative

    International Nuclear Information System (INIS)

    We investigate optimal control problems for linear distributed systems which are not solved with respect to the time derivative and whose homogeneous part admits a degenerate strongly continuous solution semigroup. To this end, we first obtain theorems on the existence of a unique strong solution of the Cauchy problem. This enables us to formulate sufficient conditions for the solubility of the optimal control problems under consideration. In contrast to earlier papers on a similar topic, we substantially weaken the conditions on the quality functional with respect to the state function. The abstract results thus obtained are illustrated by an example of an optimal control problem for the linearized system of Navier-Stokes equations.

  15. Sexual Problems

    Medline Plus

    Full Text Available ... and Smoking Cessation Links to Professional Societies and Organizations Home › Sexual Problems Sexual concern causing distress can ... You can optimize the sexual setting by enhancing communication with your partner, promoting non-sexual intimacy, and ...

  16. Kidney Problems

    Science.gov (United States)

    ... Home & Community Home › Aging & Health A to Z › Kidney Problems Font size A A A Print Share Glossary Basic Facts & ... The kidneys also help maintain body fluids at normal levels. In addition, the kidneys play important roles in controlling blood pressure and ...

  17. Sexual Problems

    Medline Plus

    Full Text Available ... with your sexual partner. Because they are complex, sexual concerns are treated in many different ways. Often, multiple types of treatment may be required and are used together to treat a problem. Education is important in understanding the anatomy and physiology ...

  18. Dewey's Problem.

    Science.gov (United States)

    Cohen, David K.

    1998-01-01

    Maintains that Dewey tried to solve social problems related to the growth of industrialism, increasing economic inequality, and political inequality. Argues that Dewey aspired to create a counterculture to correct the human and social devastation of industrial capitalism through a curriculum and instruction that rooted academic learning in…

  19. Sexual Problems

    Medline Plus

    Full Text Available ... focuses on how one’s thinking influences feelings and behavior. Sensate focus exercises are structured “touching” activities that ... concerns should be taken seriously. When a sexual problem causes you distress, don’t be afraid to ...

  20. Sexual Problems

    Medline Plus

    Full Text Available ... important to note that psychological problems such as sexual abuse can be involved as well. Pain caused by lack of lubrication or by vaginismus is not included in this ... woman wants sexual penetration. Women with this condition can still achieve ...

  1. Mouth Problems

    Science.gov (United States)

    ... Here 1. Is the person an infant or child? Yes See "Mouth Problems in Infants and Children." No 2. Do you have pain in your ... usually heal on their own. To relieve discomfort, rinse with salt water or diluted hydrogen peroxide, or apply an over-the-counter oral gel. You may also use an analgesic such ...

  2. Agricultural problems

    International Nuclear Information System (INIS)

    Although there were not reasons to deplore against major activity release from any of the 110 industrial reactors authorized to operate in US, the nuclear incident that occurred at the Three Mile Island Plant in 1979 urged the public conscience toward the necessity of readiness to cope with events of this type. The personnel of the Emergency Planning Office functioning in the frame of US Department of Agriculture has already participated in around 600 intervention drillings on a federal, local or state scale to plan, test or asses radiological emergency plans or to intervene locally. These exercises allowed acquiring a significant experience in elaborating emergency plans, planning the drillings, working out scenarios and evaluation of the potential impact of accidents from the agricultural point of view. We have also taken part in different international drillings among which the most recent are INEX 1 and RADEX 94. We have found on these occasions that the agricultural problems are essential preoccupations in most of the cases no matter if the context is international, national, local or of state level. The paper poses problems specifically related to milk, fruits and vegetables, soils, meat and meat products. Finally the paper discusses issues like drilling planning, alarm and notification, sampling strategy, access authorizations for farmers, removing of contamination wastes. A number of social, political and economical relating problems are also mentioned

  3. Method of independent timesteps in the numerical solution of initial value problems

    Energy Technology Data Exchange (ETDEWEB)

    Porter, A.P.

    1976-07-21

    In the numerical solution of initial-value problems in several independent variables, the timestep is controlled, especially in the presence of shocks, by a small portion of the logical mesh, what one may call the crisis zone. One is frustrated by the necessity of doing in the whole mesh frequent calculations required by only a small part of the mesh. It is shown that it is possible to choose different timesteps natural to different parts of the mesh and to advance each zone in time only as often as is appropriate to that zone's own natural timestep. Prior work is reviewed and for the first time an investigation of the conditions for well-posedness, consistency and stability in independent timesteps is presented; a new method results. The prochronic and parachronic Cauchy surfaces are identified; and the reasons (well-posedness) for constraining the Cauchy surfaces to be prochronic (as distinct from the method of Grandey), that is, to lie prior to the time of the crisis zone (the zone of least timestep), are indicated. Stability (in the maximum norm) of parabolic equations and (in the L2 norm) of hyperbolic equations is reviewed, without restricting the treatment to linear equations or constant coefficients, and stability of the new method is proven in this framework. The details of the method of independent timesteps, the rules for choosing timesteps and for deciding when to update and when to skip zones, and the method of joining adjacent regions of differing timestep are described. The stability of independent timestep difference schemes is analyzed and exhibited. The economic advantages of the method, which often amount to an order-of-magnitude decrease in running time relative to conventional or implicit difference methods, are noted.

  4. Method of independent timesteps in the numerical solution of initial value problems

    International Nuclear Information System (INIS)

    In the numerical solution of initial-value problems in several independent variables, the timestep is controlled, especially in the presence of shocks, by a small portion of the logical mesh, what one may call the crisis zone. One is frustrated by the necessity of doing in the whole mesh frequent calculations required by only a small part of the mesh. It is shown that it is possible to choose different timesteps natural to different parts of the mesh and to advance each zone in time only as often as is appropriate to that zone's own natural timestep. Prior work is reviewed and for the first time an investigation of the conditions for well-posedness, consistency and stability in independent timesteps is presented; a new method results. The prochronic and parachronic Cauchy surfaces are identified; and the reasons (well-posedness) for constraining the Cauchy surfaces to be prochronic (as distinct from the method of Grandey), that is, to lie prior to the time of the crisis zone (the zone of least timestep), are indicated. Stability (in the maximum norm) of parabolic equations and (in the L2 norm) of hyperbolic equations is reviewed, without restricting the treatment to linear equations or constant coefficients, and stability of the new method is proven in this framework. The details of the method of independent timesteps, the rules for choosing timesteps and for deciding when to update and when to skip zones, and the method of joining adjacent regions of differing timestep are described. The stability of independent timestep difference schemes is analyzed and exhibited. The economic advantages of the method, which often amount to an order-of-magnitude decrease in running time relative to conventional or implicit difference methods, are noted

  5. The borderlines of the invisibility and visibility for Calderon's inverse problem

    CERN Document Server

    Astala, Kari; Paivarinta, Lassi

    2011-01-01

    We consider the determination of a conductivity function in a two-dimensional domain from the Cauchy data of the solutions of the conductivity equation on the boundary. We prove uniqueness results for this inverse problem, posed by Calderon, for conductivities that are degenerate, that is, they may not be bounded from above or below. In particular, for scalar conductivities we solve the inverse problem in a class which is larger than $L^\\infty$. Also, we give new counterexamples for the uniqueness of the inverse conductivity problem. We say that a conductivity is visible if the inverse problem is solvable so that the inside of the domain can be uniquely determined, up to a change of coordinates, using the boundary measurements. The present counterexamples for the inverse problem have been related to the invisibility cloaking. This means that there are conductivities for which a part of the domain is shielded from detection via boundary measurements. Such conductivities are called invisibility cloaks. In the p...

  6. Kramers problem: numerical Wiener-Hopf-like model characteristics.

    Science.gov (United States)

    Ezin, A N; Samgin, A L

    2010-11-01

    Since the Kramers problem cannot be, in general, solved in terms of elementary functions, various numerical techniques or approximate methods must be employed. We present a study of characteristics for a particle in a damped well, which can be considered as a discretized version of the Melnikov [Phys. Rev. E 48, 3271 (1993)] turnover theory. The main goal is to justify the direct computational scheme to the basic Wiener-Hopf model. In contrast to the Melnikov approach, which implements factorization through a Cauchy-theorem-based formulation, we employ the Wiener-Levy theorem to reduce the Kramers problem to a Wiener-Hopf sum equation written in terms of Toeplitz matrices. This latter can provide a stringent test for the reliability of analytic approximations for energy distribution functions occurring in the Kramers problems at arbitrary damping. For certain conditions, the simulated characteristics are compared well with those determined using the conventional Fourier-integral formulas, but sometimes may differ slightly depending on the value of a dissipation parameter. Another important feature is that, with our method, we can avoid some complications inherent to the Melnikov method. The calculational technique reported in the present paper may gain particular importance in situations where the energy losses of the particle to the bath are a complex-shaped function of the particle energy and analytic solutions of desired accuracy are not at hand. In order to appreciate more readily the significance and scope of the present numerical approach, we also discuss concrete aspects relating to the field of superionic conductors. PMID:21230615

  7. Use of Lanczos vectors in fluid/structure interaction problems

    International Nuclear Information System (INIS)

    The goals of any numerical computational technique used for the solution of structural acoustics problems in the exterior infinite domain should be of accuracy with rapid convergence, robustness, and computational efficiency. A computer program has been developed to achieve each of these three goals. Accuracy and robustness in the numerical representation of the integral equations used to represent the infinite fluid was attained through the use of boundary element implementations of the surface Helmholtz integral equations. The computational efficiency was resolved through the use of Lanczos vectors to model the deformation characteristics of the structure. The authors have developed collocation and variational techniques to overcome the difficulties previously encountered in the numerical implementation of the hypersingular integral operator. The Cauchy singularity present in the integral formulation is made numerically amenable through the use of tangential derivatives in both the collocation and variational techniques. The variational approach has the advantage that the resulting added fluid mass term is symmetric and combines efficiently with a finite element approximation of the structural elastic response. Several different strategies making use of the Lanczos vectors have been investigated. The first involved the use of Lanczos vectors solely to characterize the structural response. This reduced form of the structural dynamical matrix was then substituted back into a Burton and Miller formulation of the acoustic problem. The second strategy investigated involved forming the complex Lanzcos vectors of the dynamical matrix formed from the addition of a symmetrical added fluid matrix to the structural mass matrix. The size of resultant matrix equation set solved at each frequency for this strategy is determined by the number of Lanczos vectors used. 19 refs., 10 figs., 2 tabs

  8. Inverse Boundary Problems for Systems in Two Dimensions

    CERN Document Server

    Albin, Pierre; Tzou, Leo; Uhlmann, Gunther

    2011-01-01

    We prove identification of coefficients up to gauge by Cauchy data at the boundary for elliptic systems on oriented compact surfaces with boundary or domains of $\\mathbb{C}$. In the geometric setting, we fix a Riemann surface with boundary, and consider both a Dirac-type operator plus potential acting on sections of a Clifford bundle and a connection Laplacian plus potential (i.e. Schr\\"odinger Laplacian with external Yang-Mills field) acting on sections of a Hermitian bundle. In either case we show that the Cauchy data determines both the connection and the potential up to a natural gauge transformation: conjugation by an endomorphism of the bundle which is the identity at the boundary. For domains of $\\mathbb{C}$, we recover zeroth order terms up to gauge from Cauchy data at the boundary in first order elliptic systems.

  9. Generalized Cauchy's Models and Generalized Integrals

    OpenAIRE

    Sabra Ramadan

    2007-01-01

    The space of generalized complex numbers C* has been constructed. The Cachy's model in the space of new generalized functions is well defined. The generalized integral of new generalized function over the compact K has been defined.

  10. Generalized Cauchy's Models and Generalized Integrals

    Directory of Open Access Journals (Sweden)

    Sabra Ramadan

    2007-01-01

    Full Text Available The space of generalized complex numbers C* has been constructed. The Cachy's model in the space of new generalized functions is well defined. The generalized integral of new generalized function over the compact K has been defined.

  11. Cauchy-characteristic extraction in numerical relativity

    OpenAIRE

    Bishop, N.; Gomez, R.; Lehner, L.; Winicour, J.

    1997-01-01

    We treat the calculation of gravitational radiation using the mixed timelike-null initial value formulation of general relativity. The determination of an exterior radiative solution is based on boundary values on a timelike worldtube $\\Gamma$ and on characteristic data on an outgoing null cone emanating from an initial cross-section of $\\Gamma$. We present the details of a 3-dimensional computational algorithm which evolves this initial data on a numerical grid, which is compactified to incl...

  12. Geometry of Cauchy-Riemann submanifolds

    CERN Document Server

    Shahid, Mohammad; Al-Solamy, Falleh

    2016-01-01

    This book gathers contributions by respected experts on the theory of isometric immersions between Riemannian manifolds, and focuses on the geometry of CR structures on submanifolds in Hermitian manifolds. CR structures are a bundle theoretic recast of the tangential Cauchy–Riemann equations in complex analysis involving several complex variables. The book covers a wide range of topics such as Sasakian geometry, Kaehler and locally conformal Kaehler geometry, the tangential CR equations, Lorentzian geometry, holomorphic statistical manifolds, and paraquaternionic CR submanifolds. Intended as a tribute to Professor Aurel Bejancu, who discovered the notion of a CR submanifold of a Hermitian manifold in 1978, the book provides an up-to-date overview of several topics in the geometry of CR submanifolds. Presenting detailed information on the most recent advances in the area, it represents a useful resource for mathematicians and physicists alike.

  13. Asymptotically flat and regular Cauchy data

    CERN Document Server

    Dain, S

    2002-01-01

    I describe the construction of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of powers of a radial coordinate. I emphasize the motivations and the main ideas behind the proofs.

  14. 8. Asymptotically Flat and Regular Cauchy Data

    Science.gov (United States)

    Dain, Sergio

    I describe the construction of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of powers of a radial coordinate. I emphasize the motivations and the main ideas behind the proofs.

  15. The Chicken Problem.

    Science.gov (United States)

    Reeves, Charles A.

    2000-01-01

    Uses the chicken problem for sixth grade students to scratch the surface of systems of equations using intuitive approaches. Provides students responses to the problem and suggests similar problems for extensions. (ASK)

  16. Problem, Problem Solving And Critical Thinking

    OpenAIRE

    TÜRNÜKLÜ, Elif B.; YEŞİLDERE, Sibel

    2005-01-01

    Critical thinking is an essential skill that all people from various sectors should have and need. Problem solving skill which is one of the main purpose of mathematics teaching can be effective in developing critical thinking. The purpose of this study is to emphasize the importance of problem solving in developing critical thinking skills and to expose critical thinking to the pre-service primary mathematics teachers. Aiming these, some mathematical critical thinking problems are prepa...

  17. PROBLEMS OF MIGRANT LABOR.

    Science.gov (United States)

    WALLS, FOREST

    PRESENT MIGRANT LABOR PROBLEMS AND SOLUTIONS WHICH HAVE BEEN PROPOSED ARE PRESENTED. THE FIRST PROBLEM AREA IS PROVIDING EDUCATION FOR MIGRANT CHILDREN. THIS IS HINDERED BY THE PROBLEM OF SECURING COMPLIANCE WITH MINIMUM EDUCATION LAWS AND BY LAWS PROHIBITING EMPLOYMENT OF CHILDREN DURING SCHOOL HOURS. A SECOND PROBLEM AREA IS THAT OF CHILD LABOR.…

  18. Blow up of the Solutions of Nonlinear Wave Equation

    OpenAIRE

    Svetlin Georgiev Georgiev

    2007-01-01

    We construct for every fixed the metric , where , , , , are continuous functions, , for which we consider the Cauchy problem , where , ; , , where , , , , , , and are positive constants. When , we prove that the above Cauchy problem has a nontrivial solution in the form for which . When , we prove that the above Cauchy problem has a nontrivial solution in the form for which .

  19. Some geometric constraints and the problem of global regularity for the Navier–Stokes equations

    International Nuclear Information System (INIS)

    We consider the Cauchy problem for the 3D Navier–Stokes equations and show that weak solutions satisfying suitable geometric conditions are smooth. The first condition we consider requires the vorticity's direction at the point y (near to x) to be within a circular cone of a given small amplitude, with vertex at x and axis along the vorticity's direction at x. The amplitude of the angle at the vertex of the cone depends mainly on the viscosity and on the size of the initial datum. Hence, the vorticity's direction need not be (Hölder) continuous to ensure regularity, as in the results proved in previous studies. Our new results show that a possible singularity deriving from non-trivial collision of strong vortex tubes is depleted if the angle formed by the tubes is small enough. Other conditions regarding the direction of the curl of the vorticity are considered: it is shown that if the direction of curl of the vorticity at point x is 'nearly parallel' to the same quantity at neighbouring points, then weak solutions are smooth

  20. Differential equations problem solver

    CERN Document Server

    Arterburn, David R

    2012-01-01

    REA's Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Differential Equations Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Differential Equations problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. They're perfect for undergraduate and graduate studies.The Differential Equations Problem Solver is the perfect resource for any class, any exam, and

  1. [The mind -- body problem].

    Science.gov (United States)

    Pérez, Diana I

    2005-01-01

    In this paper I present, in the first place, two of the main problems in the philosophy of mind: 1) the problem of the criteria of the mental, and 2) the problem of the relationship between the mental and the physical. In the last part, I mention two problems highly discussed nowadays which, in my view, will produce the most important advance in the knowledge of our minds in the next decades: the problem of consciousness and its neural basis, and the problem of the origin and development of a theory of mind. PMID:16220149

  2. Locating Problems with Quality Circles.

    Science.gov (United States)

    White, Donald D.; Bednar, David A.

    1985-01-01

    Five categories of common quality circles problems are identified to help firms anticipate difficulties and avert circle failures. These categories include encountered internal problems, encountered external problems, created internal problems, created external problems, and interface problems. Solutions are suggested. (CT)

  3. Increases in Problem Drinking

    Science.gov (United States)

    ... Increases in Problem Drinking Join the Fight Against Superbugs Featured Website: Genetic and Rare Diseases Information Center ... Increases in Problem Drinking Join the Fight Against Superbugs Featured Website: Genetic and Rare Diseases Information Center ...

  4. Recognition of Problem Drinkers

    OpenAIRE

    Cornel, Michiel; van Zutphen, Wim M.

    1989-01-01

    General practitioners often see patients with problems related to drinking behaviour, but recognize only a small proportion of these problem drinkers. The authors discuss some mechanisms of this non-recognition phenomenon and suggest ways to enhance early recognition.

  5. Diabetes and Foot Problems

    Science.gov (United States)

    ... Disease, and Other Dental Problems Diabetic Eye Disease Diabetes and Foot Problems How can diabetes affect my feet? Too much glucose, also called ... you have any of these signs. How can diabetes change the shape of my feet? Nerve damage ...

  6. Solving Word Problems.

    Science.gov (United States)

    Karrison, Joan; Carroll, Margaret Kelly

    1991-01-01

    Students with language and learning disabilities may have difficulty solving mathematics word problems. Use of a sequential checklist, identifying clues and keywords, and illustrating a problem can all help the student identify and implement the correct computational process. (DB)

  7. Traveling with breathing problems

    Science.gov (United States)

    If you have breathing problems and you: Are short of breath most of the time Get short of breath when you walk 150 ... or less Have been in the hospital for breathing problems recently Use oxygen at home, even if ...

  8. Creativity for Problem Solvers

    DEFF Research Database (Denmark)

    Vidal, Rene Victor Valqui

    2009-01-01

    This paper presents some modern and interdisciplinary concepts about creativity and creative processes specially related to problem solving. Central publications related to the theme are briefly reviewed. Creative tools and approaches suitable to support problem solving are also presented. Finall...

  9. Health Problems in Pregnancy

    Science.gov (United States)

    Every pregnancy has some risk of problems. The causes can be conditions you already have or conditions you develop. ... pregnant with more than one baby, previous problem pregnancies, or being over age 35. They can affect ...

  10. Challenging problems in algebra

    CERN Document Server

    Posamentier, Alfred S

    2012-01-01

    Over 300 unusual problems, ranging from easy to difficult, involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms, more. Detailed solutions, as well as brief answers, for all problems are provided.

  11. Algorithmic Problem Complexity

    OpenAIRE

    Burgin, Mark

    2008-01-01

    People solve different problems and know that some of them are simple, some are complex and some insoluble. The main goal of this work is to develop a mathematical theory of algorithmic complexity for problems. This theory is aimed at determination of computer abilities in solving different problems and estimation of resources that computers need to do this. Here we build the part of this theory related to static measures of algorithms. At first, we consider problems for finite words and stud...

  12. Children with behavorial problem

    OpenAIRE

    Cerar, Kristina

    2011-01-01

    Behavioral problems are becoming more and more common phenomena in children education. When behavioral problems occur it is very important to have the appropriate approach that mitigates or completely removes them. The key to this is to know as much as possible about children development and behavioral problems. The theoretical part contains the features of a child's development and then I focused on behavioral problems and the causes that bring to such results. I described methods to remove...

  13. Thinking and problem solving

    OpenAIRE

    Frensch, Peter; Funke, Joachim

    2005-01-01

    Human thinking, and in particular, the human ability to solve complex, real-life problems contributes more than any other human ability to the development of human culture and the growth and development of human life on earth. However, the human ability to solve complex problems is still not well understood, partly because it has for a long time been largely ignored by traditional problem-solving research in the field of psychology. In this article, we present a definition of complex problem ...

  14. Mathematics as Problem Solving.

    Science.gov (United States)

    Soifer, Alexander

    This book contains about 200 problems. It is suggested that it be used by students, teachers or anyone interested in exploring mathematics. In addition to a general discussion on problem solving, there are problems concerned with number theory, algebra, geometry, and combinatorics. (PK)

  15. Optimal obstacle control problem

    Institute of Scientific and Technical Information of China (English)

    ZHU Li; LI Xiu-hua; GUO Xing-ming

    2008-01-01

    In the paper we discuss some properties of the state operators of the optimal obstacle control problem for elliptic variational inequality. Existence, uniqueness and regularity of the optimal control problem are established. In addition, the approximation of the optimal obstacle problem is also studied.

  16. Inverse problems of geophysics

    International Nuclear Information System (INIS)

    This report gives an overview and the mathematical formulation of geophysical inverse problems. General principles of statistical estimation are explained. The maximum likelihood and least square fit methods, the Backus-Gilbert method and general approaches for solving inverse problems are discussed. General formulations of linearized inverse problems, singular value decomposition and properties of pseudo-inverse solutions are given

  17. Melamine: problems in obstetrics.

    Science.gov (United States)

    Wiwanitkit, Viroj

    2009-09-01

    Emerging problem of melamine contamination in milk and dairy products from Asia is a global problem. There are emerging questions on the adverse effect and toxicity of melamine. Acute renal failure due to acute melamine intoxication is reported. In this paper, the author will briefly discuss on the problem of melamine in obstetrics. PMID:19148659

  18. The problem of simultaneity

    Science.gov (United States)

    Marx, G.

    Drake's formula for the possible number of independent civilizations in the Galaxy is discussed in the light of several new hypotheses (e.g., Lovelock's Gaia hypothesis). Emphasis is placed on ways to overcome the time problem, i.e., the problem of how to communicate with civilizations that may arise in the future. Electronic, nucleonic, and bionic approaches to this problem are discussed.

  19. [Doctors' alcohol problems].

    Science.gov (United States)

    Florkowski, Antoni; Gruszczyński, Wojciech; Gałecki, Piotr; Szubert, Sławomir; Klus, Marek; Zboralski, Krzysztof

    2008-01-01

    An overusing and an addiction to alcoholic drinks are important problems in a medical society. The studies made in the United States had documented that about 8-12% doctors were addicted to alcohol. In many cases the doctors are able to keep their problem as a secret and their activity is satisfied up to the moment when a decrease is noticed. Some factors--such as a high level of stress--predispose doctors to alcoholic problems especially surgeons. Alcohol problems should be identified as early as possible, and therapy ought to be given as well. There is no reason to hide the problem. PMID:19025048

  20. Path Problems in Networks

    CERN Document Server

    Baras, John

    2010-01-01

    The algebraic path problem is a generalization of the shortest path problem in graphs. Various instances of this abstract problem have appeared in the literature, and similar solutions have been independently discovered and rediscovered. The repeated appearance of a problem is evidence of its relevance. This book aims to help current and future researchers add this powerful tool to their arsenal, so that they can easily identify and use it in their own work. Path problems in networks can be conceptually divided into two parts: A distillation of the extensive theory behind the algebraic path pr

  1. Internal Percolation Problem

    OpenAIRE

    Bezsudnov, I.; Snarskii, A.

    2008-01-01

    Introduced and investigated new kind of percolation problem - so called internal percolation problem (IP). In usual percolation problem current flows from top to bottom of the system and here it can be called as external percolation problem (EP) despite of the IP case when voltage is applied to the system through bars which are inside of the hole in system. EP problem has two major parameters: M size of system and a0 size of inclusion, lattice size etc. IP holds one more parameter the size of...

  2. CSNI LOCA standard problems

    International Nuclear Information System (INIS)

    In the 3. meeting of the CSNI Working Group on ECCS (August 1976), several countries expressed views on the scope of the Standard Problem programme and how often Standard Problems should be performed. Based on discussions expressed during the meeting and on some opinions, several recommendations have been made. They are presented here, divided into five sections: Objectives of CSNI Standard Problems; Proposals for New CSNI Standard Problems; Specifications for Standard Problem Analysis; Reporting of Results from CSNI Standard Problem Exercises; Calculated Results and Experimental Data Comparison Report. Section I discusses the purpose for doing Standard Problems, and the other four sections discuss the different documents that should be prepared in support of the programme. Each of these four sections attempts to outline specifications for the content of the documents

  3. Matrix interdiction problem

    Energy Technology Data Exchange (ETDEWEB)

    Pan, Feng [Los Alamos National Laboratory; Kasiviswanathan, Shiva [Los Alamos National Laboratory

    2010-01-01

    In the matrix interdiction problem, a real-valued matrix and an integer k is given. The objective is to remove k columns such that the sum over all rows of the maximum entry in each row is minimized. This combinatorial problem is closely related to bipartite network interdiction problem which can be applied to prioritize the border checkpoints in order to minimize the probability that an adversary can successfully cross the border. After introducing the matrix interdiction problem, we will prove the problem is NP-hard, and even NP-hard to approximate with an additive n{gamma} factor for a fixed constant {gamma}. We also present an algorithm for this problem that achieves a factor of (n-k) mUltiplicative approximation ratio.

  4. Semidefinite linear complementarity problems

    International Nuclear Information System (INIS)

    Semidefinite linear complementarity problems arise by discretization of variational inequalities describing e.g. elastic contact problems, free boundary value problems etc. In the present paper linear complementarity problems are introduced and the theory as well as the numerical treatment of them are described. In the special case of semidefinite linear complementarity problems a numerical method is presented which combines the advantages of elimination and iteration methods without suffering from their drawbacks. This new method has very attractive properties since it has a high degree of invariance with respect to the representation of the set of all feasible solutions of a linear complementarity problem by linear inequalities. By means of some practical applications the properties of the new method are demonstrated. (orig.)

  5. Convergence of Optimization Problems

    Directory of Open Access Journals (Sweden)

    K. Jeyalakshmi

    2012-03-01

    Full Text Available In this paper we consider a general optimization problem (OP and study the convergence and approximation of optimal values and optimal solutions to changes in the cost function and the set of feasible solutions. We consider the convergence optimization problems under the familiar notion of uniform convergence. We do not assume the convexity of the functions involved. Instead we consider a class of functions whose directional derivatives are convex. They are known as locally convex functions or following Craven and Mond nearly convex functions. We given necessary preliminaries and we prove that a sequence of locally convex optimization problems converge to a locally convex problem. We also prove that uniform convergence of locally convex optimization problems implies epi-graph convergence of the problems. Even though for simplicity we have taken locally convex functions, the results given here can be proved for locally Lipchitz functions also.

  6. Hidden Symmetry Subgroup Problems

    CERN Document Server

    Decker, Thomas; Santha, Miklos; Wocjan, Pawel

    2011-01-01

    We advocate a new approach of addressing hidden structure problems and finding efficient quantum algorithms. We introduce and investigate the Hidden Symmetry Subgroup Problem (HSSP), which is a generalization of the well-studied Hidden Subgroup Problem (HSP). Given a group acting on a set and an oracle whose level sets define a partition of the set, the task is to recover the subgroup of symmetries of this partition inside the group. The HSSP provides a unifying framework that, besides the HSP, encompasses a wide range of algebraic oracle problems, including quadratic hidden polynomial problems. While the HSSP can have provably exponential quantum query complexity, we obtain efficient quantum algorithms for various interesting cases. To achieve this, we present a general method for reducing the HSSP to the HSP, which works efficiently in several cases related to symmetries of polynomials. The HSSP therefore connects in a rather surprising way certain hidden polynomial problems with the HSP. Using this connect...

  7. Group Problem Solving

    CERN Document Server

    Laughlin, Patrick R

    2011-01-01

    Experimental research by social and cognitive psychologists has established that cooperative groups solve a wide range of problems better than individuals. Cooperative problem solving groups of scientific researchers, auditors, financial analysts, air crash investigators, and forensic art experts are increasingly important in our complex and interdependent society. This comprehensive textbook--the first of its kind in decades--presents important theories and experimental research about group problem solving. The book focuses on tasks that have demonstrably correct solutions within mathematical

  8. Inverse Quadratic Transportation Problem

    OpenAIRE

    Jalilzadeh, Afrooz; Hamedani, Erfan Yazdandoost

    2014-01-01

    Many research has been conducted about quadratic programming and inverse optimization. In this paper we present the combination aspect of these subjects, applying on transportation problem. First, we obtain the inverse form of quadratic tranportation problem under $L_1$ norm by using duality as well as introducing the optimal value. Then, we do the same process for inverse quadratic transportation problem (IQTP) under $L_\\infty$ norm.

  9. The Gamification Design Problem

    OpenAIRE

    Meder, Michael; Jain, Brijnesh-Johannes

    2014-01-01

    Under the assumptions that (i) gamification consists of various types of users that experience game design elements differently; and (ii) gamification is deployed in order to achieve some goal in the broadest sense, we pose the gamification problem as that of assigning each user a game design element that maximizes their expected contribution in order to achieve that goal. We show that this problem reduces to a statistical learning problem and suggest matrix factorization as one solution when...

  10. Numerical problems in physics

    CERN Document Server

    Singh, Devraj

    2015-01-01

    Numerical Problems in Physics, Volume 1 is intended to serve the need of the students pursuing graduate and post graduate courses in universities with Physics and Materials Science as subject including those appearing in engineering, medical, and civil services entrance examinations. KEY FEATURES: * 29 chapters on Optics, Wave & Oscillations, Electromagnetic Field Theory, Solid State Physics & Modern Physics * 540 solved numerical problems of various universities and ompetitive examinations * 523 multiple choice questions for quick and clear understanding of subject matter * 567 unsolved numerical problems for grasping concepts of the various topic in Physics * 49 Figures for understanding problems and concept

  11. Shielding benchmark problems, (2)

    International Nuclear Information System (INIS)

    Shielding benchmark problems prepared by Working Group of Assessment of Shielding Experiments in the Research Committee on Shielding Design in the Atomic Energy Society of Japan were compiled by Shielding Laboratory in Japan Atomic Energy Research Institute. Fourteen shielding benchmark problems are presented newly in addition to twenty-one problems proposed already, for evaluating the calculational algorithm and accuracy of computer codes based on discrete ordinates method and Monte Carlo method and for evaluating the nuclear data used in codes. The present benchmark problems are principally for investigating the backscattering and the streaming of neutrons and gamma rays in two- and three-dimensional configurations. (author)

  12. The Target Visitation Problem

    OpenAIRE

    Hildenbrandt, Achim

    2015-01-01

    The thesis considers the target visitation problem, a combinatorial optimization problem, which merges the classical traveling salesman problem with the linear ordering problem. In more detail, we are looking for a tour which visits a set of targets and which is optimal with respect to two different aspects: On the one hand, we have given a travel cost from each target to every other. On the other hand, we have preference values which tell us how much we would like to visit one target before ...

  13. A Stochastic Employment Problem

    Science.gov (United States)

    Wu, Teng

    2013-01-01

    The Stochastic Employment Problem(SEP) is a variation of the Stochastic Assignment Problem which analyzes the scenario that one assigns balls into boxes. Balls arrive sequentially with each one having a binary vector X = (X[subscript 1], X[subscript 2],...,X[subscript n]) attached, with the interpretation being that if X[subscript i] = 1 the ball…

  14. Hip Problems in Infants

    Science.gov (United States)

    ... problems that can lead to dislocation of the hip bones. This is also called dysplasia (say: "diss-play-see-uh"). This means that ... problems later in life? Source Screening for Developmental Dysplasia of the Hip by LM French, M.D., and FR Dietz, ...

  15. Heat exchangers: operation problems

    International Nuclear Information System (INIS)

    The main operation problems for heat exchangers are fouling, corrosion, vibrations and mechanical resistance. Fouling and corrosion lead to an over dimensioning, energy consumption increase, corroded pieces change, shutdown costs. Vibrations are taken in account during the dimensioning phase of the heat exchangers. Mechanical resistance problems are, for the classical ones, described in regulation texts. (A.B.). 5 figs., 4 tabs

  16. Convex Congestion Network Problems

    OpenAIRE

    2004-01-01

    This paper analyzes convex congestion network problems.It is shown that for network problems with convex congestion costs, an algorithm based on a shortest path algorithm, can be used to find an optimal network for any coalition. Furthermore an easy way of determining if a given network is optimal is provided.

  17. Reconfigurable layout problem

    NARCIS (Netherlands)

    Meng, G.; Heragu, S.S.; Zijm, H.

    2004-01-01

    This paper addresses the reconfigurable layout problem, which differs from traditional, robust and dynamic layout problems mainly in two aspects: first, it assumes that production data are available only for the current and upcoming production period. Second, it considers queuing performance measure

  18. Simon on problem solving

    DEFF Research Database (Denmark)

    Foss, Kirsten; Foss, Nicolai Juul

    2006-01-01

    general approach to problem solving. We apply these Simonian ideas to organisational issues, specifically new organisational forms. Specifically, Simonian ideas allow us to develop a morphology of new organisational forms and to point to some design problems that characterise these forms....

  19. The Graffiti Problem

    OpenAIRE

    JS Armstrong

    2004-01-01

    Graffiti is regarded by many as a blight on our cities because it contributes to visual pollution. City governments spend vast sums in an effort to clean the ubiquitous graffiti from urban walls. I suggest that the “cleansing strategy” is an expensive, ineffective way of dealing with the problem; well-known management techniques can solve the problem more efficiently.

  20. Teaching through Problem Solving

    Science.gov (United States)

    Fi, Cos D.; Degner, Katherine M.

    2012-01-01

    Teaching through Problem Solving (TtPS) is an effective way to teach mathematics "for" understanding. It also provides students with a way to learn mathematics "with" understanding. In this article, the authors present a definition of what it means to teach through problem solving. They also describe a professional development vignette that…

  1. Mathematical Problem Solving.

    Science.gov (United States)

    Mayer, Richard E.

    This chapter examines research on the cognitive processes involved in mathematical problem solving. The introduction includes definitions of key terms and a summary of four cognitive processes used in mathematical problem solving: (1) translating; (2) integrating; (3) planning; and (4) executing. Examples are then provided and exemplary research…

  2. The generalized Tailor Problem

    NARCIS (Netherlands)

    Roerdink, J.B.T.M.; Maragos, P; Schafer, RW; Butt, MA

    1996-01-01

    The so-called 'Tailor Problem' concerns putting a number of sets within another set by translation, such that the translated sets do not overlap. In this paper we consider a generalization of this problem in which also rotations of the sets are allowed.

  3. Problems in baryon spectroscopy

    Energy Technology Data Exchange (ETDEWEB)

    Capstick, S. [Florida State Univ., Tallahassee, FL (United States)

    1994-04-01

    Current issues and problems in the physics of ground- and excited-state baryons are considered, and are classified into those which should be resolved by CEBAF in its present form, and those which may require CEBAF to undergo an energy upgrade to 8 GeV or more. Recent theoretical developments designed to address these problems are outlined.

  4. Dynamical inverse problems

    CERN Document Server

    Gladwell, Graham ML

    2011-01-01

    The papers in this volume present an overview of the general aspects and practical applications of dynamic inverse methods, through the interaction of several topics, ranging from classical and advanced inverse problems in vibration, isospectral systems, dynamic methods for structural identification, active vibration control and damage detection, imaging shear stiffness in biological tissues, wave propagation, to computational and experimental aspects relevant for engineering problems.

  5. Medical problems affecting musicians.

    OpenAIRE

    Potter, P J; Jones, I C

    1995-01-01

    The physical demands of performing on musical instruments can cause pain, sensory loss, and lack of coordination. Five cases illustrate common problems. Knowledge of the interaction between the technique of playing the instrument and the particular musician can help physicians diagnose and resolve problems.

  6. Problem-Based Learning

    Science.gov (United States)

    Allen, Deborah E.; Donham, Richard S.; Bernhardt, Stephen A.

    2011-01-01

    In problem-based learning (PBL), students working in collaborative groups learn by resolving complex, realistic problems under the guidance of faculty. There is some evidence of PBL effectiveness in medical school settings where it began, and there are numerous accounts of PBL implementation in various undergraduate contexts, replete with…

  7. GREECE--SELECTED PROBLEMS.

    Science.gov (United States)

    MARTONFFY, ANDREA PONTECORVO; AND OTHERS

    A CURRICULUM GUIDE IS PRESENTED FOR A 10-WEEK STUDY OF ANCIENT GREEK CIVILIZATION AT THE 10TH-GRADE LEVEL. TEACHING MATERIALS FOR THE UNIT INCLUDE (1) PRIMARY AND SECONDARY SOURCES DEALING WITH THE PERIOD FROM THE BRONZE AGE THROUGH THE HELLENISTIC PERIOD, (2) GEOGRAPHY PROBLEMS, AND (3) CULTURAL MODEL PROBLEM EXERCISES. THOSE CONCEPTS WITH WHICH…

  8. Problems in equilibrium theory

    CERN Document Server

    Aliprantis, Charalambos D

    1996-01-01

    In studying General Equilibrium Theory the student must master first the theory and then apply it to solve problems. At the graduate level there is no book devoted exclusively to teaching problem solving. This book teaches for the first time the basic methods of proof and problem solving in General Equilibrium Theory. The problems cover the entire spectrum of difficulty; some are routine, some require a good grasp of the material involved, and some are exceptionally challenging. The book presents complete solutions to two hundred problems. In searching for the basic required techniques, the student will find a wealth of new material incorporated into the solutions. The student is challenged to produce solutions which are different from the ones presented in the book.

  9. The Guderley problem revisited

    Energy Technology Data Exchange (ETDEWEB)

    Ramsey, Scott D [Los Alamos National Laboratory; Kamm, James R [Los Alamos National Laboratory; Bolstad, John H [NON LANL

    2009-01-01

    The self-similar converging-diverging shock wave problem introduced by Guderley in 1942 has been the source of numerous investigations since its publication. In this paper, we review the simplifications and group invariance properties that lead to a self-similar formulation of this problem from the compressible flow equations for a polytropic gas. The complete solution to the self-similar problem reduces to two coupled nonlinear eigenvalue problems: the eigenvalue of the first is the so-called similarity exponent for the converging flow, and that of the second is a trajectory multiplier for the diverging regime. We provide a clear exposition concerning the reflected shock configuration. Additionally, we introduce a new approximation for the similarity exponent, which we compare with other estimates and numerically computed values. Lastly, we use the Guderley problem as the basis of a quantitative verification analysis of a cell-centered, finite volume, Eulerian compressible flow algorithm.

  10. Structural Identification Problem

    Directory of Open Access Journals (Sweden)

    Suvorov Aleksei

    2016-01-01

    Full Text Available The identification problem of the existing structures though the Quasi-Newton and its modification, Trust region algorithms is discussed. For the structural problems, which could be represented by means of the mathematical modelling of the finite element code discussed method is extremely useful. The nonlinear minimization problem of the L2 norm for the structures with linear elastic behaviour is solved by using of the Optimization Toolbox of Matlab. The direct and inverse procedures for the composition of the desired function to minimize are illustrated for the spatial 3D truss structure as well as for the problem of plane finite elements. The truss identification problem is solved with 2 and 3 unknown parameters in order to compare the computational efforts and for the graphical purposes. The particular commands of the Matlab codes are present in this paper.

  11. The interval ordering problem

    CERN Document Server

    Dürr, Christoph; Spieksma, Frits C R; Nobibon, Fabrice Talla; Woeginger, Gerhard J

    2011-01-01

    For a given set of intervals on the real line, we consider the problem of ordering the intervals with the goal of minimizing an objective function that depends on the exposed interval pieces (that is, the pieces that are not covered by earlier intervals in the ordering). This problem is motivated by an application in molecular biology that concerns the determination of the structure of the backbone of a protein. We present polynomial-time algorithms for several natural special cases of the problem that cover the situation where the interval boundaries are agreeably ordered and the situation where the interval set is laminar. Also the bottleneck variant of the problem is shown to be solvable in polynomial time. Finally we prove that the general problem is NP-hard, and that the existence of a constant-factor-approximation algorithm is unlikely.

  12. Problem Solving and Learning

    CERN Document Server

    Singh, Chandralekha

    2016-01-01

    One finding of cognitive research is that people do not automatically acquire usable knowledge by spending lots of time on task. Because students' knowledge hierarchy is more fragmented, "knowledge chunks" are smaller than those of experts. The limited capacity of short term memory makes the cognitive load high during problem solving tasks, leaving few cognitive resources available for metacognition. The abstract nature of the laws of physics and the chain of reasoning required to draw meaningful inferences makes these issues critical. In order to help students, it is crucial to consider the difficulty of a problem from the perspective of students. We are developing and evaluating interactive problem-solving tutorials to help students in the introductory physics courses learn effective problem-solving strategies while solidifying physics concepts. The self-paced tutorials can provide guidance and support for a variety of problem solving techniques, and opportunity for knowledge and skill acquisition.

  13. The Interaction Programming Problem

    Institute of Scientific and Technical Information of China (English)

    LI Rong-sheng; CHENG Ying

    2001-01-01

    Based upon the research to the economic equilibrium problems, we present a kind of new mathematical programming problem-interaction programming problem (abbreviated by IPP). The IPP is composed of two or multiple parametric programming problems which is interrelated with each other. The IPP reflects the equality and mutual benefit relationship between two (or among multiple) economic planners in an economic system. In essence, the IPP is similar to the generalized Nash equilibria (GNE) game which has been given several names in the literature: social equilibria games, pseudo-Nash equilibria games, and equilibrium programming problems. In this paper, we establish the mathematical model and some basic concepts to the IPP. We investigate the structure and the properties of the IPP. We also give a necessary and sufficient conditions for the existence of the equilibrium points to a kind of linear IPP.

  14. Problems of energy supply. Probleme der Energieversorgung

    Energy Technology Data Exchange (ETDEWEB)

    Frank, W.

    1983-01-01

    Political education is to enable judgement of present-day questions. This requires knowledge of the essential facts in the field of energy supply. The brochure on hand is meant to make it easier for the reader to put forward his own arguments. The reader is to see that it is due to the many motives determining energy policy which aggravate an understanding about ways of solving problems of energy supply. This brochure is designed to enhance political education by giving a survey of tasks in energy policy to be solved on an international level and in Austria.

  15. Puzzles, Pastimes, Problems.

    Science.gov (United States)

    Eperson, D. B.

    1985-01-01

    Presents six mathematical problems (with answers) which focus on: (1) chess moves; (2) patterned numbers; (3) quadratics with rational roots; (4) number puzzles; (5) Euclidean geometry; and (6) Carrollian word puzzles. (JN)

  16. What Are Knee Problems?

    Science.gov (United States)

    ... Health Information Basics for You and Your Family Sports Injuries, Handout on Health Health Information Knee Problems Find ... for a long time. This sometimes occurs in sports training. Treatment for tendon injuries and disorders includes: Rest Ice Elevation Medicines such ...

  17. Pelvic Support Problems

    Science.gov (United States)

    ... nonsurgical ways to obtain symptom relief? • What are Kegel exercises? • Can surgery correct pelvic support problems? • Glossary ... your overall health and possibly your prolapse symptoms. • Kegel exercises—These exercises strengthen the muscles that surround ...

  18. Problems sleeping during pregnancy

    Science.gov (United States)

    ... page: //medlineplus.gov/ency/patientinstructions/000559.htm Problems sleeping during pregnancy To use the sharing features on ... time sleeping well. Why is it hard to sleep during pregnancy? Your baby is growing bigger, which ...

  19. Challenging problems in geometry

    CERN Document Server

    Posamentier, Alfred S

    2012-01-01

    Collection of nearly 200 unusual problems dealing with congruence and parallelism, the Pythagorean theorem, circles, area relationships, Ptolemy and the cyclic quadrilateral, collinearity and concurrency and more. Arranged in order of difficulty. Detailed solutions.

  20. Overcoming breastfeeding problems

    Science.gov (United States)

    Plugged milk ducts; Nipple soreness when breastfeeding; Breastfeeding - overcoming problems; Let-down reflex ... Breastfeeding (nursing) your baby can be a good experience for both the mother and the baby. It ...

  1. The problem of pain.

    Science.gov (United States)

    Nicholson, Keith; Martelli, Michael F

    2004-01-01

    Pain problems, especially posttraumatic headache, are very common following head trauma. Pain may be the most significant problem, more disabling than any brain or other injuries, and interfering with aspects of cognition or other function. However, posttraumatic headache and most other chronic posttraumatic pain problems remain poorly understood. This article reviews fundamental issues that should be considered in understanding the nature of chronic pain including the distinction between acute and chronic pain; neurobiological distinctions between the lateral and medial pain system; nociceptive versus neuropathic or other central pain; sensitization effects; the widely accepted view of chronic pain as a multidimensional subjective experience involving sensory, motivational-affective and cognitive-behavioral components; the problem of mind-body dualism; the role of psychosocial factors in the onset, maintenance, exacerbation or severity of pain; plus issues of response bias and malingering. PMID:14732827

  2. Our Accountability Problems

    Science.gov (United States)

    Cunningham, Luvern L.

    1969-01-01

    Evaluation of school administrators to determine whether they are truly performing their functions adequately has presented a problem of long standing since most administrators find excuses to avoid appraisal of their performance. (CK)

  3. Diabetic Eye Problems

    Science.gov (United States)

    ... damage your eyes. The most common problem is diabetic retinopathy. It is a leading cause of blindness ... You need a healthy retina to see clearly. Diabetic retinopathy damages the tiny blood vessels inside your ...

  4. Enuresis: A Social Problem.

    Science.gov (United States)

    McDonald, James E.

    1978-01-01

    Several theories and treatments of enuresis are described. The authors conclude that enuresis is a social problem (perhaps due to maturational lag, developmental delay or faulty learning) which requires teacher and parental tolerance and understanding. (SE)

  5. Problems in optics

    CERN Document Server

    Rousseau, Madeleine; Ter Haar, D

    1973-01-01

    This collection of problems and accompanying solutions provide the reader with a full introduction to physical optics. The subject coverage is fairly traditional, with chapters on interference and diffraction, and there is a general emphasis on spectroscopy.

  6. Problems of Chernobyl

    International Nuclear Information System (INIS)

    The collection contains scientific articles which theme is mainly directed on the solving of the problems of 'Ukryttia' safe exploitation ensuring and transformation in into an ecologically safe system and report materials of ISTC 'Shelter' works during 2000 year

  7. Common Foot Problems

    Science.gov (United States)

    ... and rashes clinical tools newsletter | contact Share | Common Foot Problems A A A Trauma, infection, skin disease, ... the sole of the front part of the foot and on the toes. Foot infections include warts; ...

  8. Creativity and Problem Solving

    DEFF Research Database (Denmark)

    Vidal, Rene Victor Valqui

    2004-01-01

    This paper presents some modern and interdisciplinary concepts about creativity and creative processes of special relevance for Operational Research workers. Central publications in the area Creativity-Operational Research are shortly reviewed. Some creative tools and the Creative Problem Solving...

  9. Micronutrient problems in Korea

    International Nuclear Information System (INIS)

    Background information on the extent of micronutrient problems in connection with the low productivity paddy soils in Korea is given. Areas of research on micronutrients in which isotopes might suitably be employed are outlined

  10. Menstrual Cycle Problems

    Science.gov (United States)

    ... problem with the lining of the uterus, or OVARIAN CYSTS. See your doctor. *5. Are your periods heavier ... fullness or nausea? Yes You may have an OVARIAN CYST, or you may be PREGNANT. If you could ...

  11. [Oral problems in divers].

    Science.gov (United States)

    Scheper, W A; Lobbezoo, F; Eijkman, M A J

    2005-05-01

    Divers can have several oral problems. Firstly, problems caused by pressure changes. These are barodontalgia and odontocrexis. Barodontalgia is toothache by barotrauma. Odontocrexis is restorations coming lose or breaking or tooth fractures by expansion of air beneath restorations. Other problems can occur by cements used to fix casted restorations, by inflammations in the orofacial region, and by not yet fully healed oral wounds. Secondly, there are problems related to the diver's mouthpiece. To keep the mouthpiece in place, the mandible has to be forced in a forward position. Holding this position often and for long periods of time, may develop or aggravate temporomandibular dysfunction. Insufficient fit of the mouthpiece may induce oral mucosal lesions. Therefore, it is recommended to produce individual diver mouthpieces. It is also recommended to produce individual diver mouthpieces for complete dentures wearing divers and for divers with fixed orthodontic appliances. PMID:15932043

  12. Sleep Problems and ADHD

    OpenAIRE

    J Gordon Millichap

    2008-01-01

    The prevalence of sleep problems and their associations with quality of life (QOL), school attendance, and family impacts in children with ADHD were determined in a study at Royal Children's Hospital, University of Melbourne, Australia.

  13. Problems around 3-manifolds

    OpenAIRE

    Rubinstein, J Hyam

    2009-01-01

    This is a personal view of some problems on minimal surfaces, Ricci flow, polyhedral geometric structures, Haken 4-manifolds, contact structures and Heegaard splittings, singular incompressible surfaces after the Hamilton-Perelman revolution.

  14. The Congruence Subgroup Problem

    Indian Academy of Sciences (India)

    M S Raghunathan

    2004-11-01

    This is a short survey of the progress on the congruence subgroup problem since the sixties when the first major results on the integral unimodular groups appeared. It is aimed at the non-specialists and avoids technical details.

  15. 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...

  16. Solving Tommy's Writing Problems.

    Science.gov (United States)

    Burdman, Debra

    1986-01-01

    The article describes an approach by which word processing helps to solve some of the writing problems of learning disabled students. Aspects considered include prewriting, drafting, revising, and completing the story. (CL)

  17. The ternary Goldbach problem

    OpenAIRE

    Helfgott, Harald Andrés

    2015-01-01

    The ternary Goldbach conjecture, or three-primes problem, states that every odd number $n$ greater than $5$ can be written as the sum of three primes. The conjecture, posed in 1742, remained unsolved until now, in spite of great progress in the twentieth century. In 2013 -- following a line of research pioneered and developed by Hardy, Littlewood and Vinogradov, among others -- the author proved the conjecture. In this, as in many other additive problems, what is at issue is really the proper...

  18. Problems encountered by tourists

    OpenAIRE

    C. Madhavi; A. Auroubindo Ganesh

    2010-01-01

    Tourism is an upcoming and fast growing industry in developing countries like India. Due to its newness in nature, there are some hurdles that the tourists face. This will affect the national economy and the growth of this industry may get affected. This paper focuses on identifying such problems and their intensity level. This also attempts to study whether there is any significant difference in the problem faced by respondents based on demographic factors. Convenient samples of 150 res...

  19. Accelerator shielding benchmark problems

    International Nuclear Information System (INIS)

    Accelerator shielding benchmark problems prepared by Working Group of Accelerator Shielding in the Research Committee on Radiation Behavior in the Atomic Energy Society of Japan were compiled by Radiation Safety Control Center of National Laboratory for High Energy Physics. Twenty-five accelerator shielding benchmark problems are presented for evaluating the calculational algorithm, the accuracy of computer codes and the nuclear data used in codes. (author)

  20. The decentralized implementability problem

    OpenAIRE

    Fiaz, Shaik; Trentelman, H.L.

    2010-01-01

    This paper deals with the problems of decentralized implementability and decentralized regular implementability in the context of finite-dimensional linear differential system behaviors. Given a plant behavior with a pre-specified partition of the system variable and a desired behavior, the problem of decentralized implementability is to find a controller which is decentralized with respect to the given partition and implements (regularly) the desired behavior with respect to the plant. In th...

  1. Accelerator shielding benchmark problems

    Energy Technology Data Exchange (ETDEWEB)

    Hirayama, H.; Ban, S.; Nakamura, T. [and others

    1993-01-01

    Accelerator shielding benchmark problems prepared by Working Group of Accelerator Shielding in the Research Committee on Radiation Behavior in the Atomic Energy Society of Japan were compiled by Radiation Safety Control Center of National Laboratory for High Energy Physics. Twenty-five accelerator shielding benchmark problems are presented for evaluating the calculational algorithm, the accuracy of computer codes and the nuclear data used in codes. (author).

  2. The road coloring problem

    OpenAIRE

    Trahtman, A. N.

    2007-01-01

    The synchronizing word of deterministic automaton is a word in the alphabet of colors (considered as letters) of its edges that maps the automaton to a single state. A coloring of edges of a directed graph is synchronizing if the coloring turns the graph into deterministic finite automaton possessing a synchronizing word. The road coloring problem is a problem of synchronizing coloring of directed finite strongly connected graph with constant outdegree of all its vertices if the greatest comm...

  3. PROBLEMS OF ADOLESCENCE

    OpenAIRE

    Hubble, Douglas

    1982-01-01

    Adolescence is a period of active growth and development-physical, sexual, social and emotional. There are wide normal variations between the time of onset and the attainment of full maturity. Many adolescents present few if any problems during this potentially turbulent period, and make the necessary adjustments without undue stress to themselves, their family or their friends. Problems in growth and hormonal balance, presenting as short and tall teenagers, menstrual irregularities, obesity ...

  4. The basketball problem

    Science.gov (United States)

    Schröer, H.

    In basketball there is the problem of hitting a basket at a determined distance and a determined height. The quantities that can be changed during the inclined throw are the initial velocity and the angle of throw. At first we neglect the air resistance. Then we treat the same problem in a medium (liquid, gas) with constant density. We obtain two differential equations. Then we view special cases of the retarding force. There is an english and a german edition.

  5. Problem Based Learnig

    OpenAIRE

    Kolmos, Anette; Kuru, Selahattin; Hansen, Hans; Eskil, Taner; Podesta, Luca; Fink, Flemming; Graaff, Erik de; Uwe Wolff, Jan; Soylu, Ahmet

    2007-01-01

    This report discuss Problem-Based and Project-Based Learning (PBL) as an approach to meeting the demand for the educational requirements of the next generation engineering graduates. The report is prepared as the final report of the Special Interest Group (SIG) B5 of the Erasmus Thematic Network Project TREE (Teaching and Research in Engineering Education) on Problem- Based and Project-Based Learning. In engineering education there is a shift in emphasis from professional skill...

  6. Steiner Forest Orientation Problems

    CERN Document Server

    Cygan, Marek; Nutov, Zeev

    2011-01-01

    We consider connectivity problems with orientation constraints. Given a directed graph $D$ and a collection of ordered node pairs $P$ let $P[D]={(u,v) \\in P: D contains a uv-paths}$. In the Steiner Forest Orientation problem we are given an undirected graph $G=(V,E)$ with edge-costs and a set $P \\subseteq V \\times V$ of ordered node pairs. The goal is to find a minimum-cost subgraph $H$ of $G$ and an orientation $D$ of $H$ such that $P[D]=P$. We give a 4-approximation algorithm for this problem. In the Maximum Pairs Orientation problem we are given a graph $G$ and a multi-collection of ordered node pairs $P$ on $V$. The goal is to find an orientation $D$ of $G$ such that $|P[D]|$ is maximum. Generalizing the result of Arkin and Hassin for $|P|=2$, we will show that for a mixed graph $G$ (that may have both directed an undirected edges), one can decide in $n^{O(|P|)}$ time whether $G$ has an orientation $D$ with $P[D]=P$ (for undirected graphs this problem admits a polynomial time algorithm for any $P$, but it...

  7. The Steiner tree problem

    CERN Document Server

    Hwang, FK; Winter, P

    1992-01-01

    The Steiner problem asks for a shortest network which spans a given set of points. Minimum spanning networks have been well-studied when all connections are required to be between the given points. The novelty of the Steiner tree problem is that new auxiliary points can be introduced between the original points so that a spanning network of all the points will be shorter than otherwise possible. These new points are called Steiner points - locating them has proved problematic and research has diverged along many different avenues. This volume is devoted to the assimilation of the rich field of intriguing analyses and the consolidation of the fragments. A section has been given to each of the three major areas of interest which have emerged. The first concerns the Euclidean Steiner Problem, historically the original Steiner tree problem proposed by Jarník and Kössler in 1934. The second deals with the Steiner Problem in Networks, which was propounded independently by Hakimi and Levin and has enjoyed the most...

  8. Computational problems in engineering

    CERN Document Server

    Mladenov, Valeri

    2014-01-01

    This book provides readers with modern computational techniques for solving variety of problems from electrical, mechanical, civil and chemical engineering. Mathematical methods are presented in a unified manner, so they can be applied consistently to problems in applied electromagnetics, strength of materials, fluid mechanics, heat and mass transfer, environmental engineering, biomedical engineering, signal processing, automatic control and more.   • Features contributions from distinguished researchers on significant aspects of current numerical methods and computational mathematics; • Presents actual results and innovative methods that provide numerical solutions, while minimizing computing times; • Includes new and advanced methods and modern variations of known techniques that can solve difficult scientific problems efficiently.  

  9. Dirac's Quantum Phase Problem

    CERN Document Server

    Sperling, J

    2009-01-01

    In 1927 the great physicist Paul A. M. Dirac failed to provide a consistent quantum description of the phase of a radiation field. Only one year later, he developed the famous Dirac theory of the electron, which led to the anti-particle -- the positron. We show that the reason for Dirac's failure with the phase problem bears a striking resemblance to his ingenious insight into the nature of the electron. For a correct quantum description of the phase of a radiation field it is necessary to take the polarisation into account. Similarly to the introduction of the anti-particle of the electron, the inclusion of the second polarisation resolves the inconsistency of the quantum phase problem. This also leads to new insight into the quantum measurement problem of time.

  10. Problem Based Learning

    DEFF Research Database (Denmark)

    de Graaff, Erik; Guerra, Aida

    Problem-Based Learning (PBL) is an innovative method to organize the learning process in such a way that the students actively engage in finding answers by themselves. During the past 40 years PBL has evolved and diversified resulting in a multitude in variations in models and practices. However...... model and in general problem based and project based learning. We apply the principle of teach as you preach. The poster aims to outline the visitors’ workshop programme showing the results of some recent evaluations......., the key principles remain the same everywhere. Graaff & Kolmos (2003) identify the main PBL principles as follows: 1. Problem orientation 2. Project organization through teams or group work 3. Participant-directed 4. Experiental learning 5. Activity-based learning 6. Interdisciplinary learning and 7...

  11. Problems in quantum mechanics

    CERN Document Server

    Kogan, VI; Gersch, Harold

    2011-01-01

    Written by a pair of distinguished Soviet mathematicians, this compilation presents 160 lucidly expressed problems in nonrelativistic quantum mechanics plus completely worked-out solutions. Some were drawn from the authors' courses at the Moscow Institute of Engineering, but most were prepared especially for this book. A high-level supplement rather than a primary text, it constitutes a masterful complement to advanced undergraduate and graduate texts and courses in quantum mechanics.The mathematics employed in the proofs of the problems-asymptotic expansions of functions, Green's functions, u

  12. Problem Based Game Design

    DEFF Research Database (Denmark)

    Reng, Lars; Schoenau-Fog, Henrik

    2011-01-01

    At Aalborg University’s department of Medialogy, we are utilizing the Problem Based Learning method to encourage students to solve game design problems by pushing the boundaries and designing innovative games. This paper is concerned with describing this method, how students employ it in various...... projects and how they learn to analyse, design, and develop for innovation by using it. We will present various cases to exemplify the approach and focus on how the method engages students and aspires for innovation in digital entertainment and games....

  13. Another thorny problem

    Directory of Open Access Journals (Sweden)

    Calvert Watkins

    2015-09-01

    Full Text Available Students of Indo-European are beset by thorns, from the third letter of the Runic alphabet through the Hieroglyphic Luvian excrescent +ra/i to Brugmann's 'Notbehelf' *kp of such cognate sets as the word for 'bear'; see J. Schindler, "A thorny problem," Die Sprache 23 (1977 25ff. Our problem is simpler, however sticky; it is a pleasure to offer a suggestion for its solution to Professor Bojan Čop, who has so enriched Hittite studies over so many years.

  14. Problems encountered by tourists

    Directory of Open Access Journals (Sweden)

    C. Madhavi

    2010-10-01

    Full Text Available Tourism is an upcoming and fast growing industry in developing countries like India. Due to its newness in nature, there are some hurdles that the tourists face. This will affect the national economy and the growth of this industry may get affected. This paper focuses on identifying such problems and their intensity level. This also attempts to study whether there is any significant difference in the problem faced by respondents based on demographic factors. Convenient samples of 150 respondents have been selected for this study. Suitable statistical tools such as Cluster analysis, Chi-square test and multiple regression are used.

  15. Calculus problems and solutions

    CERN Document Server

    Ginzburg, A

    2011-01-01

    Ideal for self-instruction as well as for classroom use, this text helps students improve their understanding and problem-solving skills in analysis, analytic geometry, and higher algebra. More than 1,200 problems appear in the text, with concise explanations of the basic notions and theorems to be used in their solution. Many are followed by complete answers; solutions for the others appear at the end of the book. Topics include sequences, functions of a single variable, limit of a function, differential calculus for functions of a single variable, fundamental theorems and applications of dif

  16. Electric circuits problem solver

    CERN Document Server

    REA, Editors of

    2012-01-01

    Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. All your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. Nothing remotely as comprehensive or as helpful exists in their subject anywhere. Perfect for undergraduate and graduate studies.Here in this highly useful reference is the finest overview of electric circuits currently av

  17. Electrical problems committee report

    International Nuclear Information System (INIS)

    This document is the report of the committee appointed to review the experience of the MFE Program with electrical equipment and to suggest actions to minimize future problems. The committee observed that the electrical problems that have occurred could be traced not to misapplication of project and engineering technical principles, but to lack of application of project and engineering management principles. The report is structured so that the first four sections: Introduction, Findings, Recommendations, and Immediate Recommended Actions, can be used as an executive summary. The discussion section and attachments contain further detail

  18. Matrices in Engineering Problems

    CERN Document Server

    Tobias, Marvin

    2011-01-01

    This book is intended as an undergraduate text introducing matrix methods as they relate to engineering problems. It begins with the fundamentals of mathematics of matrices and determinants. Matrix inversion is discussed, with an introduction of the well known reduction methods. Equation sets are viewed as vector transformations, and the conditions of their solvability are explored. Orthogonal matrices are introduced with examples showing application to many problems requiring three dimensional thinking. The angular velocity matrix is shown to emerge from the differentiation of the 3-D orthogo

  19. The Quantum Falsifiability Problem

    OpenAIRE

    Dall'Arno, Michele; Brandsen, Sarah; Buscemi, Francesco

    2016-01-01

    A hypothesis about a physical device is falsified as soon as an experiment collects data that is not compatible with it. Here we construct a general framework to study the quantum falsifiability problem, namely, the problem of deciding whether a given input-output probability distribution (i.e., the data) can be obtained from a given candidate quantum channel (i.e., the hypothesis) or not. Our approach is completely device-independent, as the piece of experimental evidence -- the input-output...

  20. Advanced calculus problem solver

    CERN Document Server

    REA, Editors of

    2012-01-01

    Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. All your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. Nothing remotely as comprehensive or as helpful exists in their subject anywhere. Perfect for undergraduate and graduate studies.Here in this highly useful reference is the finest overview of advanced calculus currently av

  1. Classic Problems of Probability

    CERN Document Server

    Gorroochurn, Prakash

    2012-01-01

    "A great book, one that I will certainly add to my personal library."—Paul J. Nahin, Professor Emeritus of Electrical Engineering, University of New Hampshire Classic Problems of Probability presents a lively account of the most intriguing aspects of statistics. The book features a large collection of more than thirty classic probability problems which have been carefully selected for their interesting history, the way they have shaped the field, and their counterintuitive nature. From Cardano's 1564 Games of Chance to Jacob Bernoulli's 1713 Golden Theorem to Parrondo's 1996 Perplexin

  2. Problems over Information Systems

    KAUST Repository

    Chikalov, Igor

    2011-01-01

    The problems of estimation of the minimum average time complexity of decision trees and design of efficient algorithms are complex in general case. The upper bounds described in Chap. 2.4.3 can not be applied directly due to large computational complexity of the parameter M(z). Under reasonable assumptions about the relation of P and NP, there are no polynomial time algorithms with good approximation ratio [12, 32]. One of the possible solutions is to consider particular classes of problems and improve the existing results using characteristics of the considered classes. © Springer-Verlag Berlin Heidelberg 2011.

  3. The Urinal Problem

    Science.gov (United States)

    Kranakis, Evangelos; Krizanc, Danny

    A man walks into a men's room and observes n empty urinals. Which urinal should he pick so as to maximize his chances of maintaining privacy, i.e., minimize the chance that someone will occupy a urinal beside him? In this paper, we attempt to answer this question under a variety of models for standard men's room behavior. Our results suggest that for the most part one should probably choose the urinal furthest from the door (with some interesting exceptions). We also suggest a number of variations on the problem that lead to many open problems.

  4. Assessing the Quality of Problems in Problem-Based Learning

    Science.gov (United States)

    Sockalingam, Nachamma; Rotgans, Jerome; Schmidt, Henk

    2012-01-01

    This study evaluated the construct validity and reliability of a newly devised 32-item problem quality rating scale intended to measure the quality of problems in problem-based learning. The rating scale measured the following five characteristics of problems: the extent to which the problem (1) leads to learning objectives, (2) is familiar, (3)…

  5. Additivity in bankruptcy problems and in allocation problems

    OpenAIRE

    Gustavo Bergantiños; Luciano Méndez-Naya

    2001-01-01

    We study the property of additivity in bankruptcy problems and in allocation problems. In bankruptcy problems we use this property to characterize the Talmudic rule proposed by Rabbi Ibn Ezra. Moreover we generalize this rule to every bankruptcy problem. Again, using additivity we characterize the rights egalitarian solution in allocation problems.

  6. A Survey of Transportation Problems

    OpenAIRE

    2014-01-01

    This paper aims at being a guide to understand the different types of transportation problems by presenting a survey of mathematical models and algorithms used to solve different types of transportation modes (ship, plane, train, bus, truck, Motorcycle, Cars, and others) by air, water, space, cables, tubes, and road. Some problems are as follows: bus scheduling problem, delivery problem, combining truck trip problem, open vehicle routing problem, helicopter routing problem, truck loading p...

  7. Local and Global Analytic Solutions for a Class of Characteristic Problems of the Einstein Vacuum Equations in the "Double Null Foliation Gauge"

    CERN Document Server

    Caciotta, Giulio

    2011-01-01

    The main goal of this work consists in showing that the analytic solutions for a class of characteristic problems for the Einstein vacuum equations have an existence region larger than the one provided by the Cauchy-Kowalevski theorem due to the intrinsic hyperbolicity of the Einstein equations. To prove this result we first describe a geometric way of writing the vacuum Einstein equations for the characteristic problems we are considering, in a gauge characterized by the introduction of a double null cone foliation of the spacetime. Then we prove that the existence region for the analytic solutions can be extended to a larger region which depends only on the validity of the apriori estimates for the Weyl equations, associated to the "Bel-Robinson norms". In particular if the initial data are sufficiently small we show that the analytic solution is global. Before showing how to extend the existence region we describe the same result in the case of the Burger equation, which, even if much simpler, nevertheless...

  8. Stokes-Leibenson problem for Hele-Shaw flow: a critical set in the space of contours

    Science.gov (United States)

    Demidov, A. S.; Lohéac, J.-P.; Runge, V.

    2016-01-01

    The Stokes-Leibenson problem for Hele-Shaw flow is reformulated as a Cauchy problem of a nonlinear integro-differential equation with respect to functions a and b, linked by the Hilbert transform. The function a expresses the evolution of the coefficient longitudinal strain of the free boundary and b is the evolution of the tangent tilt of this contour. These functions directly reflect changes of geometric characteristics of the free boundary of higher order than the evolution of the contour point obtained by the classical Galin-Kochina equation. That is why we managed to uncover the reason of the absence of solutions in the sink-case if the initial contour is not analytic at at least one point, to prove existence and uniqueness theorems, and also to reveal a certain critical set in the space of contours. This set contains one attractive point in the source-case corresponding to a circular contour centered at the source-point. The main object of this work is the analysis of the discrete model of the problem. This model, called quasi-contour, is formulated in terms of functions corresponding to a and b of our integro-differential equation. This quasi-contour model provides numerical experiments which confirm the theoretical properties mentioned above, especially the existence of a critical subset of co-dimension 1 in space of quasi-contours. This subset contains one attractive point in the source-case corresponding to a regular quasi-contour centered at the source-point. The main contribution of our quasi-contour model concerns the sink-case: numerical experiments show that the above subset is attractive. Furthermore, this discrete model allows to extend previous results obtained by using complex analysis. We also provide numerical experiments linked to fingering effects.

  9. Problems with Smell

    Science.gov (United States)

    ... types of accidents in order of frequency involve cooking eating or drinking spoiled foods or toxic substances failing to detect gas leaks or fires If you think you have a problem with your sense of smell, see your doctor. home | health topics A-Z | videos A-Z | training | ...

  10. Microbiological problems in radiosterilization

    International Nuclear Information System (INIS)

    Criteria for medical materials sterilization from the view point of sanitary-hygiene aspects have been broadly discussed. More important problems have been pointed out as follows: assurance of proper hygienic conditions in production, pharmacopoeia rules and regulations compliance, physico-chemical and biological investigations of each new material and product. 19 refs, 4 figs, 3 tabs

  11. Human Population Problems

    Science.gov (United States)

    Emmel, Thomas C.; Sligh, Michael M.

    1970-01-01

    Asserts that overpopulation is the most pressing world problem. Topics discussed include population control in primitive societies, population growth and control in modern societies, methods of motivational population control, consequences of no population control, and mass famines during the 1970's in underdeveloped countries. Cities 33…

  12. Symmetries of Spectral Problems

    Science.gov (United States)

    Shabat, A.

    Deriving abelian KdV and NLS hierarchies, we describe non-abelian symmetries and "pre-Lax" elementary approach to Lax pairs. Discrete symmetries of spectral problems are considered in Sect. 4.2. Here we prove Darboux classical theorem and discuss a modern theory of dressing chains.

  13. Problem Solving with Patents

    Science.gov (United States)

    Moore, Jerilou; Sumrall, William J.

    2008-01-01

    Exploring our patent system is a great way to engage students in creative problem solving. As a result, the authors designed a teaching unit that uses the study of patents to explore one avenue in which scientists and engineers do science. Specifically, through the development of an idea, students learn how science and technology are connected.…

  14. Types of Learning Problems

    Science.gov (United States)

    ... of time in their own world—even for teenagers—but they’re often lonely and want to make friends. The problem is, they’re not sure how to act in social settings. Between that and their eccentricities, they may become victims of teasing and bullying . Parents of a child with AS, or any ...

  15. The CP Violation Problem

    CERN Document Server

    Naboulsi, R

    2003-01-01

    A review on CP violation in the B and K mesons systems is given, which, we hope may familiarize new Belle members in the basic ingredients of this topic, which is one of the most challenging problems of experimental high energy physics.

  16. Health Problems at School

    Science.gov (United States)

    ... of a lack of health-care providers, an absence of insurance, or transportation problems. The American Academy of Pediatrics believes that all children deserve a "medical home" and supports the implementation of school-based clinics, especially in areas where children do ...

  17. LEXICOGRAPHICAL PROBLEMS IN PASHTO.

    Science.gov (United States)

    CHAVARRIS-AGUILAR, O.L.; PENZL, HERBERT

    PROBLEMS IN DEVELOPING SUITABLE DICTIONARIES OF PASHTO WERE REPORTED. PASHTO WAS DESCRIBED AS A MEMBER OF THE IRANIAN BRANCH OF THE INDO-EUROPEAN LANGUAGES SPOKEN IN EASTERN AND SOUTHERN AFGHANISTAN AND IN NORTHEASTERN PAKISTAN. FIVE TOPICS DEALING WITH THE PASHTO LANGUAGE WERE DISCUSSED--(1) STATISTICS, (2) WRITTEN CORPUS AND LEXICAL STUDIES, (3)…

  18. Thermodynamics with Design Problems.

    Science.gov (United States)

    Cilento, E. V.; Sears, J. T.

    1983-01-01

    Discusses how basic thermodynamics concepts are integrated with design problems. Includes course goals, instructional strategies, and major advantages/disadvantages of the integrated design approach. Advantages include making subject more concrete, emphasizing interrelation of variables, and reinforcing concepts by use in design analysis; whereas…

  19. Benchmark problem proposal

    International Nuclear Information System (INIS)

    The meeting of the Radiation Energy Spectra Unfolding Workshop organized by the Radiation Shielding Information Center is discussed. The plans of the unfolding code benchmarking effort to establish methods of standardization for both the few channel neutron and many channel gamma-ray and neutron spectroscopy problems are presented

  20. Security problems at Vivitron

    International Nuclear Information System (INIS)

    The risks of accidents and the safety actions concerning the components and the staff protection at Vivitron are analyzed. The risks induced by the utilization of SF6 is mainly asphyxia. The sealing defects on the gas storage devices and gas leaking inside Vivitron are considered. The safety actions and devices are summarized. Radiation protection problems are also discussed

  1. Environmental Health Problems.

    Science.gov (United States)

    Environmental Health Service (DHEW/PHS), Rockville, MD.

    Aimed at a society which is forced to make decisions relative to their total environment, this pamphlet discusses a few of the problems associated with restoring and maintaining an environmental relationship conducive to the health and well-being of man. The topics covered include: air pollution, noise, solid waste, the urban environment, drinking…

  2. The passive polymer problem

    CERN Document Server

    Wiese, K J

    1999-01-01

    In this article, we introduce a generalization of the diffusive motion of point-particles in a turbulent convective flow with given correlations to a polymer or membrane. In analogy to the passive scalar problem we call this the passive polymer or membrane problem. We shall focus on the expansion about the marginal limit of velocity-velocity correlations which are uncorrelated in time and grow with the distance x as |x|^epsilon, and epsilon small. This relation gets modified for polymers and membranes (the marginal advecting flow has correlations which are shorter ranged.) The construction is done in three steps: First, we reconsider the treatment of the passive scalar problem using the most convenient treatment via field theory and renormalization group. We explicitly show why IR-divergences and thus the system-size appear in physical observables. In a second step, we reformulate the problem in terms of a Langevin equation. This is not only interesting in its own, but also gives an efficient algorithm to det...

  3. Screening for Breast Problems

    Science.gov (United States)

    ... a clinical breast exam done? • What is breast self-awareness? • How is breast self-awareness different from the traditional breast self-exam? •Glossary ... problems includes mammography , clinical breast exams, and breast self-awareness. What is mammography? Mammography is an X-ray ...

  4. Universal Design Problem Solving

    Science.gov (United States)

    Sterling, Mary C.

    2004-01-01

    Universal design is made up of four elements: accessibility, adaptability, aesthetics, and affordability. This article addresses the concept of universal design problem solving through experiential learning for an interior design studio course in postsecondary education. Students' experiences with clients over age 55 promoted an understanding of…

  5. Dynamical impurity problems

    International Nuclear Information System (INIS)

    In the past few years there has been a resurgence of interest in dynamical impurity problems, as a result of developments in the theory of correlated electron systems. The general dynamical impurity problem is a set of conduction electrons interacting with an impurity which has internal degrees of freedom. The simplest and earliest example, the Kondo problem, has attracted interest since the mid-sixties not only because of its physical importance but also as an example of a model displaying logarithmic divergences order by order in perturbation theory. It provided one of the earliest applications of the renormalization group method, which is designed to deal with just such a situation. As we shall see, the antiferromagnetic Kondo model is controlled by a strong-coupling fixed point, and the essence of the renormalization group solution is to carry out the global renormalization numerically starting from the original (weak-coupling) Hamiltonian. In these lectures, we shall describe an alternative route in which we identify an exactly solvable model which renormalizes to the same fixed point as the original dynamical impurity problem. This approach is akin to determining the critical behavior at a second order phase transition point by solving any model in a given universality class

  6. Microbiological problems in radiosterilization

    International Nuclear Information System (INIS)

    Microbiological problems connected with radiosterilization of medical materials, pharmaceuticals and cosmetics have been discussed in detail. Dose-response relationship for different bacteria has been shown. Recommended sterilization and postirradiation control procedures have been described. 24 refs, 6 figs, 5 tabs

  7. Unfolding a Problem

    Science.gov (United States)

    Currier, Sarah Cox

    2015-01-01

    In this article, Sarah Currier, a math specialist at Elizabeth Hall International School in Minnesota, describes how she used origami in a deliberate manner to teach content. She shares how she uses paper folding to teach mathematical concepts, reinforce vocabulary, and as a problem-solving model. She also offers ideas for using origami in other…

  8. Catastrophes control problem

    International Nuclear Information System (INIS)

    The problem of catastrophe control is discussed. Catastrophe control aims to withdraw responsible engineering constructions out of the catastrophe. The mathematical framework of catastrophes control systems is constructed. It determines the principles of systems filling by the concrete physical contents and, simultaneously, permits to employ modern control methods for the synthesis of optimal withdrawal strategy for protected objects

  9. The Classical Cake Problem

    Science.gov (United States)

    Nelson, Norman N.; Fisch, Forest N.

    1973-01-01

    Discussed are techniques of presentation and solution of the Classical Cake Problem. A frosted cake with a square base is to be cut into n pieces with the volume of cake and frosting the same for each piece. Needed are minimal geometric concepts and the formula for the volume of a prism. (JP)

  10. Resolução de equações diferenciais por redes neurais artificiais: problemas com gradientes elevados e domínios arbitrários = Resolution of differential equations with artificial neural networks: high gradients and arbitrary domains problems

    Directory of Open Access Journals (Sweden)

    Luiz Henry Monken e Silva

    2005-01-01

    Full Text Available Neste artigo a habilidade das redes neurais perceptron multicamada eminterpolar foi utilizada para analisar duas classes de problemas de contorno. A primeira classe é formada por equações diferenciais em que a solução pode apresentar gradientes elevados e a segunda classe é formada de equações diferenciais definidas em domínios arbitrários. As metodologias propostas por Lagaris et al. (1998 foram estendidas para casos de equações diferenciais sujeitas às condições de Cauchy e condições de contorno mistas. Os resultados fornecidos pelo método da rede neural se apresentam precisos quando comparados com os resultados analíticos ou por métodos numéricos de resolução deequações diferenciais. A precisão alcançada nos resultados e a facilidade no manuseio do método para resolver estes problemas de contorno encorajaram a continuidade da pesquisa, particularmente no tocante à convergência e estabilidade numérica.In this paper, the ability of the multilayer perceptron neural network (MLP in interpolation was used to analyze two classes of boundary value problems. The first class is formed by differential equations, with solutions which can have high gradients and the second are partial differential equations, defined on arbitrary shaped domain. Also, the methodologies proposed by Lagaris et al. (1998 were enlarged for differential equations subjected to Cauchy and mix boundary conditions type. The results of the artificial neural network method are very precise when comparison to the analytical ones or those of classical numerical methods to solve differential equations. The precision achieved in the results and the ability to handle the method, to solve those boundary value problems, were encouraging to keep the research, particularly on an important direction, concerning convergence and numerical stability.

  11. Nervous System Problems and Dementia

    Science.gov (United States)

    ... Language: Fact Sheet 505 Nervous System Problems and Dementia WHAT ARE NERVOUS SYSTEM PROBLEMS? WHAT ARE THE ... of AIDS these were all called “HIV-Associated Dementia.” However, a broader range of problems is showing ...

  12. How to solve mathematical problems

    CERN Document Server

    Wickelgren, Wayne A

    2012-01-01

    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.

  13. No Problem? No Research, Little Learning ... Big Problem!

    Directory of Open Access Journals (Sweden)

    Fernando Ornelas Marques

    2012-06-01

    Full Text Available The motivation to carry out this study stemmed from the generalized perception that nowadays youth lacks the skills for the 21st century. Especially the high-level competences like critical thinking, problem solving and autonomy. Several tools can help to improve these competences (e.g. the SCRATCH programming language, but, as researchers and educators, we are mostly concerned with the skill to recognize problems. What if we do not find problems to solve? What if we do not even feel the need to find or solve problems? The problem is to recognize the problem; the next step is to equate the problem; finally we have to feel the need to solve it. No need? No invention. Recognizing a problem is probably the biggest problem of everyday life, because we are permanently faced with problems (many ill-defined problems, which we need to identify, equate and solve.

  14. The Potluck Problem

    CERN Document Server

    Enumula, Prabodh K

    2008-01-01

    This paper proposes the Potluck Problem as a model for the behavior of independent producers and consumers under standard economic assumptions. We model this by using resource allocation in a multi-agent system in which there is no explicit communication among the agents. The model proposed has many applications in modeling systems like electrical power grids with many consumers and producers, service-on-demand in grid computing and peer-to-peer computing environments, maintaining a good ratio between demand and inventory in supply chain management, etc. It is observed that a rational learning approach is unable to achieve equilibrium or near-equilibrium in the Potluck Problem. Instead, a weighted majority learning algorithm is applied, which does much better in maintaining parity of supply and demand in varying-demand situations.

  15. MCNP: Photon benchmark problems

    International Nuclear Information System (INIS)

    The recent widespread, markedly increased use of radiation transport codes has produced greater user and institutional demand for assurance that such codes give correct results. Responding to these pressing requirements for code validation, the general purpose Monte Carlo transport code MCNP has been tested on six different photon problem families. MCNP was used to simulate these six sets numerically. Results for each were compared to the set's analytical or experimental data. MCNP successfully predicted the analytical or experimental results of all six families within the statistical uncertainty inherent in the Monte Carlo method. From this we conclude that MCNP can accurately model a broad spectrum of photon transport problems. 8 refs., 30 figs., 5 tabs

  16. Problem discourse of textbook

    Directory of Open Access Journals (Sweden)

    Pešić Jelena M.

    2005-01-01

    Full Text Available This paper deals with various reasons for treating the problematisation of textbook discourse as an important aspect of its educational design. These reasons are derived from: the nature of learning process, the nature of scientific knowledge and both motivational and cognitive saint achieved through a problematisation of learning material. Implications drawn from these considerations, along with textbook genre possibilities and constrains, lead us to define some basic strategies of textbook discourse problematisation. They refer to: way of presenting knowledge (problem structuring of text, presenting the history of knowledge and different perspectives; use of specific questions and tasks; metacognitive support of the learning process and specific type of textbook language (dialogical problem focused, language of thinking.

  17. Problems of Chernobyl

    International Nuclear Information System (INIS)

    The digest comprises the scientific articles whose topics are streamlined to solving the problems of safe operation provision of the Ukryttia Object and its conversion into an ecologically safe systems, as well as the reporting materials on ISTC Shelters works in keeping with the Section 2.5 'ISCT Shelter's Works of nationwide significance' of 'Complex program of works at Ukryttia Object for the year of 2002'

  18. Creativity and Problem Solving

    DEFF Research Database (Denmark)

    Vidal, Rene Victor Valqui

    2004-01-01

    This paper presents some modern and interdisciplinary concepts about creativity and creative processes of special relevance for Operational Research workers. Central publications in the area Creativity-Operational Research are shortly reviewed. Some creative tools and the Creative Problem Solving...... approach are also discussed. Finally, some applications of these concepts and tools are outlined. Some central references are presented for further study of themes related to creativity or creative tools....

  19. Creativity and problem Solving

    Directory of Open Access Journals (Sweden)

    René Victor Valqui Vidal

    2004-12-01

    Full Text Available This paper presents some modern and interdisciplinary concepts about creativity and creative processes of special relevance for Operational Research workers. Central publications in the area Creativity-Operational Research are shortly reviewed. Some creative tools and the Creative Problem Solving approach are also discussed. Finally, some applications of these concepts and tools are outlined. Some central references are presented for further study of themes related to creativity or creative tools.

  20. CULTURAL DOMAINS: TRANSLATION PROBLEMS

    OpenAIRE

    Isabel Negro Alousque

    2009-01-01

    Much of the lexis of a language has a cultural referent and is thus specific to a speech community. The meaning of culturally marked words is often difficult to grasp without some cultural knowledge and poses translation problems, particularly when the words are associated with cultural domains (Nida, 2001). In the present paper we focus on the French cultural domain of cooking. After outlining the elements of the domain, we analyse the difficulties in translating the lexical units from the d...

  1. Seismic Solvability Problems

    OpenAIRE

    Lau, August; Yin, Chuan

    2012-01-01

    Classical approach of solvability problem has shed much light on what we can solve and what we cannot solve mathematically. Starting with quadratic equation, we know that we can solve it by the quadratic formula which uses square root. Polynomial is a generalization of quadratic equation. If we define solvability by using only square roots, cube roots etc, then polynomials are not solvable by radicals (square root, cube root etc). We can classify polynomials into simple (solvable by radicals)...

  2. Kulturwissenschaftliche Probleme internationaler Managementforschung

    OpenAIRE

    Janzer, Alexander

    2007-01-01

    Diplom-Kulturwirt Alexander Janzer untersucht kulturwissenschaftliche Probleme der internationalen Managementforschung, die ihrerseits methodisch besonders häufig auf kulturvergleichende Umfrageforschung zurückgreift. This paper presents the most common errors of cross-cultural management research. Research in this field is based primarily on the concepts and methods of cross-cultural psychology (e.g. Hofstede 1980, Schwartz 1994, Triandis 1980). It is shown how current research from the C...

  3. Problems of adolescents sexuality.

    OpenAIRE

    Whatley, J.; Thin, N; B. Reynolds; Blackwell, A

    1989-01-01

    Recent discussions highlighted adolescents' sexual behaviour, but published studies concentrate on specific problems or subgroups of patients without addressing factors related to sexuality. To obtain a broad picture we studied two groups of adolescents attending genito-urinary medicine/sexually transmitted disease (STD) clinics in contrasting areas of Britain, inner London and Swansea. These were evaluated for referral pattern, sexual partner, contraception, obstetric history, sexually trans...

  4. Consumers and Agency Problems

    OpenAIRE

    Canice J. Prendergast

    2001-01-01

    Consumers solve many agency problems, by pointing out when they believe that agents have made mistakes. This paper considers the role that consumers play in inducing efficient behavior by agents. I distinguish between two case: those where consumers have similar preferences to the principal, and those where consumer preferences diverge from those of the principal. In the former case, allowing consumer feedback improves allocations, and increasing consumer information is unambiguously benefici...

  5. Problems of Chernobyl

    International Nuclear Information System (INIS)

    The collection comprises the materials of working meeting 'The Development of Technologies of the 'Ukrytie' Radioactive Waste Management', held on May 20-21, 1997 in Chernobyl. The results of research work of the experts of Ukraine and other countries directed on solving problems, concerning removal of fuel containing materials and other radioactive waste from destroyed Unit 4 of Chernobyl NPP are given. The data on waste quantities, their location and classification, strategy of waste management and some technologies are described

  6. Problem of hidden variables

    Science.gov (United States)

    Santos, Emilio

    1992-10-01

    The problem of hidden variables in quantum mechanics is formalized as follows. A general or contextual (noncontextual) hidden-variables theory is defined as a mapping f: Q×M → C (f: Q→C) where Q is the set of projection operators in the appropriate (quantum) Hilbert space, M is the set of maximal Boolean subalgebras of Q and C is a (classical) Boolean algebra. It is shown that contextual (noncontextual) hidden-variables always exist (do not exist).

  7. Smoking problem in Indonesia

    OpenAIRE

    Tjandra Y Aditama

    2002-01-01

    Smoking is an important public health probLem in Indonesia. Up to 60% of male adult population as well as about 4% of female adult population are smokers. In fact, some of Indonesian kretek cigarettes have quite high tar and nicotine content. Besides health effect, smoking habit also influence economic status of the individuals as well as the family. In health point of view, even though reliable nation wide morbidity and mortality data are scarce, report from various cities showed smoking rel...

  8. Europeanisation: Solution or problem?

    Directory of Open Access Journals (Sweden)

    Claudio M. Radaelli

    2004-10-01

    Full Text Available Is there something new in recent research on Europeanisation? Or should we go back to what we already know about political integration in Europe and avoid the term? This article reviews recent work in four steps: the identification of the specific domain of Europeanisation; the relationship between Europeanisation, on the one hand, and governance, institutions, and discourse, on the other; the methodological problems and the models emerging in this new field of research; and an assessment of the results arising out of theoretical and empirical research. One theme throughout the article is that, in order to develop a progressive agenda, Europeanisation should be seen as a problem, not as a solution. It is neither a new theory, nor an ad-hoc approach. Rather, it is a way of orchestrating existing concepts and to contribute to cumulative research in political science. Europeanisation does not provide any simple fix to theoretical or empirical problems. Quite the opposite, it can deliver if approached as a set of puzzles. A problem in search of explanation not the explanation itself (Gualini 2003. The conclusion is that Europeanisation has contributed to the emergence of new insights, original explanations, and interesting questions on three important issues: the understanding and analysis of 'impact', how to endogeneise international governance in models of domestic politics, and the relationship between agency and change. These three issues are prominent in the research agendas of international relations, theoretical policy analysis, and comparative politics. To contribute to major issues at the core of political science is a valuable result for a relatively new field of inquiry.

  9. Random eigenvalue problems revisited

    Indian Academy of Sciences (India)

    S Adhikari

    2006-08-01

    The description of real-life engineering structural systems is associated with some amount of uncertainty in specifying material properties, geometric parameters, boundary conditions and applied loads. In the context of structural dynamics it is necessary to consider random eigenvalue problems in order to account for these uncertainties. Within the engineering literature, current methods to deal with such problems are dominated by approximate perturbation methods. Some exact methods to obtain joint distribution of the natural frequencies are reviewed and their applicability in the context of real-life engineering problems is discussed. A new approach based on an asymptotic approximation of multi-dimensional integrals is proposed. A closed-form expression for general order joint moments of arbitrary numbers of natural frequencies of linear stochastic systems is derived. The proposed method does not employ the ‘small randomness’ assumption usually used in perturbation based methods. Joint distributions of the natural frequencies are investigated using numerical examples and the results are compared with Monte Carlo simulation.

  10. Quantum Counterfeit Coin Problems

    CERN Document Server

    Iwama, Kazuo; Raymond, Rudy; Teruyama, Junichi

    2010-01-01

    The counterfeit coin problem requires us to find all false coins from a given bunch of coins using a balance scale. We assume that the balance scale gives us only ``balanced'' or ``tilted'' information and that we know the number k of false coins in advance. The balance scale can be modeled by a certain type of oracle and its query complexity is a measure for the cost of weighing algorithms (the number of weighings). In this paper, we study the quantum query complexity for this problem. Let Q(k,N) be the quantum query complexity of finding all k false coins from the N given coins. We show that for any k and N such that k < N/2, Q(k,N)=O(k^{1/4}), contrasting with the classical query complexity, \\Omega(k\\log(N/k)), that depends on N. So our quantum algorithm achieves a quartic speed-up for this problem. We do not have a matching lower bound, but we show some evidence that the upper bound is tight: any algorithm, including our algorithm, that satisfies certain properties needs \\Omega(k^{1/4}) queries.

  11. Medical problems of musicians.

    Science.gov (United States)

    Lockwood, A H

    1989-01-26

    Surveys of performing musicians indicate that almost half of them experience playing-related medical problems, some of which threaten or end their careers. Overuse injuries involving the muscle--tendon unit are the most common problem, with symptoms ranging from mild pain while the musician is playing to pain severe enough to preclude any use of the affected hand. String players are the most commonly affected, and percussionists the least. The most important predisposing characteristic is the use of repetitive movements during long hours of practice, but awkward body positions mandated by the shape and weight of the instrument, the technical difficulty of the repertoire, and unfamiliar instruments may also play a part. Women are more commonly affected than men. Rest is the cornerstone of therapy. Neural impingement syndromes affecting the median or ulnar nerves or the thoracic outlet affect many musicians. Focal dystonias may involve part or all of a hand or the muscles forming the embouchure (the position of the lips in wind players). These are very resistant to therapy and may terminate or drastically alter a career. Stress, especially performance anxiety, may impede performance. Beta-adrenergic blocking agents prevent the symptoms of performance anxiety and are frequently used by musicians without medical supervision. A recognition of the unique problems of musician-patients has led to the formation of successful specialty clinics in a number of cities. PMID:2643048

  12. Characteristics of Problems in Problem-based Learning

    NARCIS (Netherlands)

    N. Sockalingam (Nachamma)

    2010-01-01

    textabstractThis thesis focuses on characteristics of problems in Problem-based Learning (PBL). Problems initiate the students’ learning process in PBL. Several studies have shown that the quality of problems has a positive influence on students’ academic achievement and interest. In addition, the q

  13. Obstacle problems in mathematical physics

    CERN Document Server

    Rodrigues, J-F

    1987-01-01

    The aim of this research monograph is to present a general account of the applicability of elliptic variational inequalities to the important class of free boundary problems of obstacle type from a unifying point of view of classical Mathematical Physics.The first part of the volume introduces some obstacle type problems which can be reduced to variational inequalities. Part II presents some of the main aspects of the theory of elliptic variational inequalities, from the abstract hilbertian framework to the smoothness of the variational solution, discussing in general the properties of the free boundary and including some results on the obstacle Plateau problem. The last part examines the application to free boundary problems, namely the lubrication-cavitation problem, the elastoplastic problem, the Signorini (or the boundary obstacle) problem, the dam problem, the continuous casting problem, the electrochemical machining problem and the problem of the flow with wake in a channel past a profile.

  14. Direct Problems and Inverse Problems in Biometric Systems

    OpenAIRE

    Mihailescu Marius Iulian

    2013-01-01

    The article purpose is to describe the two sides of biometrics technologies, direct problems and inverse problems. The advance that we face today in field of Information Technology makes Information Security an inseparable part. The authentication has a huge role when we deal about security. The problems that can appear in implementing and developing biometrics systems is raising many problems, and one of the goal of this article is to focus on direct and inverse problems which is a new and c...

  15. Characteristics of Problems in Problem-based Learning

    OpenAIRE

    Sockalingam, Nachamma

    2010-01-01

    textabstractThis thesis focuses on characteristics of problems in Problem-based Learning (PBL). Problems initiate the students’ learning process in PBL. Several studies have shown that the quality of problems has a positive influence on students’ academic achievement and interest. In addition, the quality of problems has been shown to have a higher influence than the tutor’s performance and students’ prior knowledge on students’ learning. The implication of these findings is that designing go...

  16. The world food problem

    International Nuclear Information System (INIS)

    Argument continues in the world press as to the urgency of the food problem. Some economists in equating world food production statistics with population figures have convinced themselves there is more than enough food per capita and, accordingly, no problem. Looking in greater depth than these gross averages, however, we find that there is indeed a prospective problem, and of such a nature and magnitude as to tax all of mankind's talents and resources in its resolution. It is true that certain of the developed countries of the world in the last generation acquired agricultural production capabilities that notably exceeded the resident population's capacity to consume. 'Surplus' in these areas became an ugly word during this period of a generally favorable weather cycle, and restrictions on the amount of and that could be devoted to graincrops were imposed to curb this tremendous capacity. A fickle Mother Nature, however, has turned things around during the early 1970's by one or another of her many vacillations in the form of local drought, excess moisture, shortened growing season, or other means, in some of the major producing areas. Inconsequence, the food grain surpluses are now gone and the world is looking at a three to four week reserve at any given moment. The cost of food products available from exporting countries has doubled and trebled in price during the past two years. The potential for famine exceeds in magnitude anything the world has ever known. It is against this background that the World Food Conference will be held in Rome during November of this year. (author)

  17. PROBLEM KORUPCIJE V ZDRAVSTVU

    OpenAIRE

    Drevenšek, Sanja

    2016-01-01

    Korupcija je kompleksen pojav in vse večji problem v vseh državah tudi v Sloveniji. Pojavlja se v različnih oblikah, njene posledice pa so uničujoče za širšo družbo, državo kakor tudi za vsakega posameznika. Problematika je sicer v Sloveniji urejena z zakonodajo, ki je primerljiva z evropsko zakonodajo o preprečevanju korupcije. Ustanovljeno imamo tudi Komisijo za preprečevanje korupcije kot samostojen in neodvisen državni organ, katerega temeljno poslanstvo je doseči ničelno toleranco do kor...

  18. Conway's napkin problem

    OpenAIRE

    Claesson, Anders; Petersen, T. Kyle

    2005-01-01

    The napkin problem was first posed by John H. Conway, and written up as a `toughie' in "Mathematical Puzzles: A Connoisseur's Collection," by Peter Winkler. To paraphrase Winkler's book, there is a banquet dinner to be served at a mathematics conference. At a particular table, $n$ men are to be seated around a circular table. There are $n$ napkins, exactly one between each of the place settings. Being doubly cursed as both men and mathematicians, they are all assumed to be ignorant of table e...

  19. The Container Stowage Problem

    DEFF Research Database (Denmark)

    Janstrup, Kira; Rose, Trine Høyer; Andersen, Kent Høj;

    The main purpose of this project is to use integer programming to create a model that minimizes the costs for container transportation by ship. To make the model as realistic as possible it will be based on information from a large shipping company about the vessel layout and container types. In...... addition to our project two other projects are made where an optimal solution to the container stowage problem also is tried to be found, but by using constraint programming and local search instead respectively. We will therefore in the end compare these three methods and the achieved results on fastness...

  20. XML problem, design, solution

    CERN Document Server

    Amiano, Mitch; Ethier, Kay; Thomas, Michael D

    2006-01-01

    Offering a unique approach to learning XML, this book walks readers through the process of building a complete, functional, end-to-end XML solutionFeatured case study is an online business product catalog that includes reports, data input/output, workflow, stylesheet formatting, RSS feeds, and integration with external services like Google, eBay, and AmazonThe format of presenting a problem and working through the design to come up with a solution enables readers to understand how XML markup allows a business to share data across applications internally or with partners or customers even thoug

  1. Dirac's Quantum Phase Problem

    OpenAIRE

    Sperling, J.; Vogel, W

    2009-01-01

    In 1927 the great physicist Paul A. M. Dirac failed to provide a consistent quantum description of the phase of a radiation field. Only one year later, he developed the famous Dirac theory of the electron, which led to the anti-particle -- the positron. We show that the reason for Dirac's failure with the phase problem bears a striking resemblance to his ingenious insight into the nature of the electron. For a correct quantum description of the phase of a radiation field it is necessary to ta...

  2. Mechanics: Ideas, problems, applications

    Science.gov (United States)

    Ishlinskii, A. Iu.

    The book contains the published articles and reports by academician Ishlinskii which deal with the concepts and ideas of modern mechanics, its role in providing a general understanding of the natural phenomena, and its applications to various problems in science and engineering. Attention is given to the methodological aspects of mechanics, to the history of the theories of plasticity, friction, gyroscopic and inertial systems, and inertial navigation, and to mathematical methods in mechanics. The book also contains essays on some famous scientists and engineers.

  3. The Gilbert Arborescence Problem

    CERN Document Server

    Volz, M G; Ras, C J; Swanepoel, K J; Thomas, D A

    2009-01-01

    We investigate the problem of designing a minimum cost flow network interconnecting n sources and a single sink, each with known locations and flows. The network may contain other unprescribed nodes, known as Steiner points. For concave increasing cost functions, a minimum cost network of this sort has a tree topology, and hence can be called a Minimum Gilbert Arborescence (MGA). We characterise the local topological structure of Steiner points in MGAs, showing, in particular, that for a wide range of metrics and cost-functions the degree of each Steiner point is 3.

  4. Pizza Race Problem

    OpenAIRE

    Gao, Keyue

    2012-01-01

    This paper deals with a problem in which two players share a previously sliced pizza and try to eat as much amount of pizza as they can. It takes time to eat each piece of pizza and both players eat pizza at the same rate. One is allowed to take a next piece only after the person has finished eating the piece on hand. Also, after the first piece is taken, one can only take a piece which is adjacent to already-taken piece. This paper shows that, in this real time setting, the starting player c...

  5. Problems of Massive Gravities

    CERN Document Server

    Deser, S; Ong, Y C; Waldron, A

    2014-01-01

    The method of characteristics is a key tool for studying consistency of equations of motion; it allows issues such as predictability, maximal propagation speed, superluminality, unitarity and acausality to be addressed without requiring explicit solutions. We review this method and its application to massive gravity theories to show the limitations of these models' physical viability: Among their problems are loss of unique evolution, superluminal signals, matter coupling inconsistencies and micro-acausality (propagation of signals around local closed timelike/causal curves). We extend previous no-go results to the entire three-parameter range of massive gravity theories. It is also argued that bimetric models suffer a similar fate.

  6. The leap year problem

    OpenAIRE

    Deursen, van, A

    1998-01-01

    A significant number of programs incorrectly treats the year 2000 as a non-leap year. We list 21 real life code fragments illustrating the large variety of ways that are used to determine whether a given year is a leap year or not. Some of these fragments are correct; others will fail in the year 2000. The fragments are written in C, Pascal, COBOL, and assembly language. We discuss the consequences for automated tool support, as well as the organizational implications of the leap year problem.

  7. Embedded Plateau Problem

    OpenAIRE

    Coşkunuzer, Barış

    2010-01-01

    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 364, Number 3, March 2012, Pages 1211–1224 S 0002-9947(2011)05486-3 Article electronically published on October 19, 2011 EMBEDDED PLATEAU PROBLEM BARIS COSKUNUZER Abstract. We show that if Γ is a simple closed curve bounding an embedded disk in a closed 3-manifold M, then there exists a disk Σ in M with boundary Γ such that Σ minimizes the area among the embedded disks with boundary Γ. Moreover, Σ is smooth...

  8. Problem Order Implications for Learning

    Science.gov (United States)

    Li, Nan; Cohen, William W.; Koedinger, Kenneth R.

    2013-01-01

    The order of problems presented to students is an important variable that affects learning effectiveness. Previous studies have shown that solving problems in a blocked order, in which all problems of one type are completed before the student is switched to the next problem type, results in less effective performance than does solving the problems…

  9. Analysis of the tracing problem

    Institute of Scientific and Technical Information of China (English)

    Nanfeng Jie; Hui Wang; YunqingSun

    2005-01-01

    Here the tracing problems are researched from two thoroughly different approaches: calculus method and numerical analysis. Generally speaking, the calculus method give a universal qualitative way to deal with such kind of problem, but the numerical analysis method can offer more further quantitative result for such kind of problem. Our research shows the detail results of application of these two methods in tracing problem.

  10. Double pendulum contact problem

    Directory of Open Access Journals (Sweden)

    Špička J.

    2014-06-01

    Full Text Available The work concerns contact problems focused on biomechanical systems modelled by a multibody approach. The example is modelling of impact between a body and an infrastructure. The paper firstly presents algorithm for minimum distance calculation. An analytical approach using a tangential plain perpendicular to an initial one is applied. Contact force generated during impact is compared by three different continuous force models, namely the Hertz’s model, the spring-dashpot model and the non-linear damping model. In order to identify contact parameters of these particular models, the method of numerical optimization is used. Purpose of this method is to find the most corresponding results of numerical simulation to the original experiment. Numerical optimization principle is put upon a bouncing ball example for the purpose of evaluation of desirable contact force parameters. The contact modelling is applied to a double pendulum problem. The equation of motion of the double pendulum system is derived using Lagrange equation of the second kind with multipliers, respecting the contact phenomena. Applications in biomechanical research are hinted at arm gravity motion and a double pendulum impact example.

  11. Decomposition Approaches for Optimization Problems

    OpenAIRE

    Kinable, Joris

    2014-01-01

    This dissertation encompasses the development of decomposition approaches for a variety of both real-world and fundamental optimization problems. Many optimization problems comprise of multiple interconnected subproblems, often rendering them too large or too complicated to solve as a single integral problem. Decomposition approaches are required to deal with these problems efficiently. By decomposing a problem into multiple subproblems, efficient dedicated procedures can be employed to solve...

  12. Combinatorial problems in mathematical competitions

    CERN Document Server

    Yao, Zhang

    2011-01-01

    This book focuses on combinatorial problems in mathematical competitions. It provides basic knowledge on how to solve combinatorial problems in mathematical competitions, and also introduces important solutions to combinatorial problems and some typical problems with often-used solutions. Some enlightening and novel examples and exercises are well chosen in this book. With this book, readers can explore, analyze and summarize the ideas and methods of solving combinatorial problems. Their mathematical culture and ability will be improved remarkably after reading this book.

  13. Some Undecidable Problems on Approximability of NP Optimization Problems

    Institute of Scientific and Technical Information of China (English)

    黄雄

    1996-01-01

    In this paper some undecidable problems on approximability of NP optimization problems are investigated.In particular,the following problems are all undecidable:(1) Given an NP optimization problem,is it approximable in polynomial time?(2)For any polynomial-time computable function r(n),given a polynomial time approximable NP optimization problem,has it a polynomial-time approximation algorithm with approximation performance ratio r(n) (r(n)-approximable)?(3)For any polynomial-time computable functions r(n),r'(n),where r'(n)problem,is it r'(n)-approximable?

  14. Understanding the Problem. Problem Solving and Communication Activity Series. The Math Forum: Problems of the Week

    Science.gov (United States)

    Math Forum @ Drexel, 2009

    2009-01-01

    Different techniques for understanding a problem can lead to ideas for never-used-before solutions. Good problem-solvers use a problem-solving strategy and may come back to it frequently while they are working on the problem to refine their strategy, see if they can find better solutions, or find other questions. Writing is an integral part of…

  15. The landslide problem

    Institute of Scientific and Technical Information of China (English)

    G. Shanmugam

    2015-01-01

    The synonymous use of the general term“landslide”, with a built-in reference to a sliding motion, for all varieties of mass-transport deposits (MTD), which include slides, slumps, debrites, topples, creeps, debris avalanches etc. in subaerial, sublacustrine, sub-marine, and extraterrestrial environments has created a multitude of conceptual and nomen-clatural problems. In addition, concepts of triggers and long-runout mechanisms of mass movements are loosely applied without rigor. These problems have enormous implications for studies in process sedimentology, sequence stratigraphy, palaeogeography, petroleum geol-ogy, and engineering geology. Therefore, the objective of this critical review is to identify key problems and to provide conceptual clarity and possible solutions. Speciifc issues are the fol-lowing:(1) According to“limit equilibrium analyses”in soil mechanics, sediment failure with a sliding motion is initiated over a shear surface when the factor of safety for slope stability (F) is less than 1. However, the term landslide is not meaningful for debris lfows with a lfowing mo-tion. (2) Sliding motion can be measured in oriented core and outcrop, but such measurement is not practical on seismic proifles or radar images. (3) Although 79 MTD types exist in the geological and engineering literature, only slides, slumps, and debrites are viable depositional facies for interpreting ancient stratigraphic records. (4) The use of the term landslide for high-velocity debris avalanches is inappropriate because velocities of mass-transport processes cannot be determined in the rock record. (5) Of the 21 potential triggering mechanisms of sediment failures, frequent short-term events that last for only a few minutes to several hours or days (e.g., earthquakes, meteorite impacts, tsunamis, tropical cyclones, etc.) are more relevant in controlling deposition of deep-water sands than sporadic long-term events that last for thousands to millions of years (e

  16. Problems of Chernobyl

    International Nuclear Information System (INIS)

    This collection comprises the materials of the VI International Conference 'Shelter' Object', 15 years: today and future'. The topics of this issue's works cover the results of 15-year operation of the Shelter Object and investigations of conditions of its nuclear-, radiation- and general technical safety, procedures of monitoring of fuel-containing material conditions, building structures, problems of object's conversion into an ecologically safe system, preparation of technologies for radwaste (RW) management, working out of procedures using the remotely controlled facilities for diagnostics, prospecting of complicated in access Shelter Object premises, RW retrieval and management, etc. A very important role play the works aimed at the upgrade of radiation safety, protection of public and environment

  17. Financing and insurance problems

    International Nuclear Information System (INIS)

    The author analyses the papers presented at the Paris Conference on the maturity of nuclear energy. It is evident that financing possibilities will be a determinant factor in the rate of development of nuclear power during the years to come. After having evaluated the capital requirements necessitated for the development of nuclear programmes, the parties intervening have examined the means at the disposal of electricity manufacturers to meet these needs (self-financing, recourse to external financing, regrouping, on an international scale of the electricity manufacturers of the setting up of high capacity plants). As concerns the insurance problems, they are becoming more and more involved as nuclear applications, are further diversified and intensified. The parties intervening have discussed new tarification techniques likely to be applied and pointed out the possibilities offered by regrouping or pooling of insurers (Market Pool) which allow for a maximum of risks to be covered without exceeding the means proper to each company concerned

  18. Problems in risk comparisons

    International Nuclear Information System (INIS)

    Risk comparisons are usually made for some specific purpose (to help communicating the message that a situation is either acceptable or not acceptable). However, the communication should be fair and, as the author of the next Chapter says: relevant, adequate, understandable and credible. Since ''risk'' has many attributes, the characterization of risks to be compared must involve appropriately compared attributes. The author of this Chapter begins by discussing the difficult task of risk characterization before he deals with the problems involved in risk comparison. He finally refers to the principle of ceteris paribus, which means that, in risk comparisons, all factors, circumstances and assumptions which are not explicitly presented in the risk characterization and quantification must be mutually equivalent. (author). 14 refs, 1 tab

  19. A stochastic control problem

    Directory of Open Access Journals (Sweden)

    William Margulies

    2004-11-01

    Full Text Available In this paper, we study a specific stochastic differential equation depending on a parameter and obtain a representation of its probability density function in terms of Jacobi Functions. The equation arose in a control problem with a quadratic performance criteria. The quadratic performance is used to eliminate the control in the standard Hamilton-Jacobi variational technique. The resulting stochastic differential equation has a noise amplitude which complicates the solution. We then solve Kolmogorov's partial differential equation for the probability density function by using Jacobi Functions. A particular value of the parameter makes the solution a Martingale and in this case we prove that the solution goes to zero almost surely as time tends to infinity.

  20. Some engineering problems

    Directory of Open Access Journals (Sweden)

    H. Williams

    1952-07-01

    Full Text Available It will help delegates to realize something of the range and magnitude of Service equipment problems if I touch on a few of the many important items which concern the Corps of Engineers in their preparations for war. The Engineers' role in battle is to assist our own forces to maintain their mobility by the passage of obstacles of every, description, the construction of roads and tracks and by meeting the Air Force's requirements airfields and air-strips. Secondly, to deny mobility to the enemy's forces by creating obstacles by demolitions and the destruction of materials, and by the construction of weapon positions and shelters. And lastly to support the administrative machine by supplying water, bulk fuel, power and Engineer stores where required, by meeting the Army's Transportation needs and in numerous other ways dependent on Engineering.

  1. The Password Problem

    Energy Technology Data Exchange (ETDEWEB)

    Walkup, Elizabeth [Stanford Univ., CA (United States)

    2016-06-01

    Passwords are an ubiquitous, established part of the Internet today, but they are also a huge security headache. Single sign-on, OAuth, and password managers are some of the solutions to this problem. OAuth is a new, popular method that allows people to use large, common authentication providers for many web applications. However, it comes at the expense of some privacy: OAuth makes users easy to track across websites, applications, and devices. Password managers put the power in the hands of the users, but this vulnerability survey reveals that you have to be extremely careful which program you choose. All in all, password managers are the solution of choice for home users and small organizations, but large companies will probably want to invest in their own SSO solutions.

  2. The global warming problem

    International Nuclear Information System (INIS)

    In this chapter, a discussion is presented of the global warming problem and activities contributing to the formation of acid rain, urban smog and to the depletion of the ozone layer. Globally, about two-thirds of anthropogenic carbon dioxide emissions arise from fossil-fuel burning; the rest arise primarily from deforestation. Chlorofluorocarbons are the second largest contributor to global warming, accounting for about 20% of the total. The third largest contributor is methane, followed by ozone and nitrous oxide. A study of current activities in the US that contribute to global warming shows the following: electric power plants account for about 33% of carbon dioxide emissions; motor vehicles, planes and ships (31%); industrial plants (24%); commercial and residential buildings (11%)

  3. Seismic Solvability Problems

    CERN Document Server

    Lau, August

    2012-01-01

    Classical approach of solvability problem has shed much light on what we can solve and what we cannot solve mathematically. Starting with quadratic equation, we know that we can solve it by the quadratic formula which uses square root. Polynomial is a generalization of quadratic equation. If we define solvability by using only square roots, cube roots etc, then polynomials are not solvable by radicals (square root, cube root etc). We can classify polynomials into simple (solvable by radicals) and complex (not solvable by radicals). We will use the same metaphor to separate what is solvable (simple part) and what is not solvable (complex part). This paper is a result of our presentation at a University of Houston seminar. In this paper, we will study seismic complexity through the eyes of solvability. We will investigate model complexity, data complexity and operator complexity. Model complexity is demonstrated by multiple scattering in a complex model like Cantor layers. Data complexity is studied through Bet...

  4. Problems of massive gravities

    Science.gov (United States)

    Deser, S.; Izumi, K.; Ong, Y. C.; Waldron, A.

    2015-01-01

    The method of characteristics is a key tool for studying consistency of equations of motion; it allows issues such as predictability, maximal propagation speed, superluminality, unitarity and acausality to be addressed without requiring explicit solutions. We review this method and its application to massive gravity (mGR) theories to show the limitations of these models' physical viability: Among their problems are loss of unique evolution, superluminal signals, matter coupling inconsistencies and micro-acausality (propagation of signals around local closed time-like curves (CTCs)/closed causal curves (CCCs)). We extend previous no-go results to the entire three-parameter range of mGR theories. It is also argued that bimetric models suffer a similar fate.

  5. Problems in particle theory

    International Nuclear Information System (INIS)

    Members of the Institute have worked on a number of problems including the following: acceleration algorithms for the Monte Carlo analysis of lattice field, and gauge and spin theories, based on changes of variables specific to lattices of dimension 2ell; construction of quaternionic generalizations of complex quantum mechanics and field theory; wave functions for paired Hall states; black hole quantum mechanics; generalized target-space duality in curved string backgrounds; gauge symnmetry algebra of the N = 2 string; two-dimensional quantum gravity and associated string theories; organizing principles from which the signal processing of neural networks in the retina and cortex can be deduced; integrable systems of KdV type; and a theory for Kondo insulators

  6. Problems of nuclear waste

    International Nuclear Information System (INIS)

    An enormous stockpile of nuclear weapons was reduced during the Cold War as a result of frantic Soviet-US competition, accompanied by considerable radioactive pollution of the environment. This pollution was inevitable. Former adversaries began to sober only recently. As a result, areas of weapons complexes both in the USA (Hanford, Savannah, Oak Ridge) and in Russia (Chelyabinsk-65, Tomsk-7, Krasnoyarsk-25) look like battlefields of the Cold War. A Nuclear weapon-free world will only be achieved (if at all) after reaching changes in the principles that guide state policies and actions. A nuclear-waste-free world implies that the environment's radioactive pollution of a military nature would be eliminated and all potential dangers from civil nuclear energy prevented. This can be attained after solution of some economic, political and social problems

  7. Wicked Problem Solvers.

    Science.gov (United States)

    Edmondson, Amy C

    2016-06-01

    Companies today increasingly rely on teams that span many industries for radical innovation, especially to solve "wicked problems." So leaders have to understand how to promote collaboration when roles are uncertain, goals are shifting, expertise and organizational cultures are varied, and participants have clashing or even antagonistic perspectives. HBS professor Amy Edmondson has studied more than a dozen cross-industry innovation projects, among them the creation of a new city, a mango supply-chain transformation, and the design and construction of leading-edge buildings. She has identified the leadership practices that make successful cross-industry teams work: fostering an adaptable vision, promoting psychological safety, enabling knowledge sharing, and encouraging collaborative innovation. Though these practices are broadly familiar, their application within cross-industry teams calls for unique leadership approaches that combine flexibility, open-mindedness, humility, and fierce resolve. PMID:27491195

  8. Fra problemer til mirakler

    DEFF Research Database (Denmark)

    Görlich, Anne; Katznelson, Noemi; Stentoft, Mette

    Uddannelsessystemet rummer i dag en stor del af de sårbare og udsatte unge, der tidligere havde ufaglærte jobs eller var på kontanthjælp. Det skaber udfordringer i forhold til den politiske målsætning om, at 95 procent af en ungdomsårgang skal gennemføre en ungdomsuddannelse. Disse udfordringer har...... været omdrejningspunktet i Skive Kommunes projekt ’Fra problemer til mirakler’, hvor man har søgt at styrke sårbare unges selvtillid, motivation for og deltagelse i en kompetencegivende uddannelse og dermed holde dem ude af kontanthjælpssystemet....

  9. The solar neutrino problem

    International Nuclear Information System (INIS)

    The problem of missing solar neutrinos is reviewed and discussed. The experiments of the 70s show a solar neutrino flux to be 4 times lower than the flux predicted by the standard model of the Sun. The three possible origins of this contradiction are analysed: the cross sections of nuclear reactions going on in the internal region of the Sun must be remeasured; the unknown properties of neutrino, like neutrino oscillation or decay, must be investigated theoretically and experimentally; or the standard model of the Sun must be changed, e.g. by a periodically pulsating star model or by a model describing periodic admixtures of He-3 to the central region of the Sun. Some new models and newly proposed experiments are described. The importance of new electronic detection methods of neutrinos is underlined. (D.Gy.)

  10. 一种求解Robin反问题的边界型无网格方法%A boundary-type meshless method for the Robin inverse problem

    Institute of Scientific and Technical Information of China (English)

    董超峰

    2013-01-01

    给出一种求解非齐次稳态热传导方程Robin反问题的边界型无网格方法.该方法首先利用Newton法则将Robin反问题转化为Cauchy问题,然后用边界粒子法处理非齐次项以避免区域内部的离散节点,并结合基本解方法分别求得近似特解以及相应齐次问题的近似解.鉴于所考虑问题的不适定性,引入截断奇异值分解和L-曲线准则来求解离散后得到的高度病态的线性方程组.最后给出数值例子说明该方法的稳定性和有效性.%A boundary-type meshless method is proposed to solve the Robin inverse problem associated with inhomogeneous steady-state heat conduction.In the present method,the problem is transformed into the inverse Cauchy problem by Newton's law of convective heat transfer; the boundary particle method is used to handle the inhomogeneous term in order to avoid the requirement of inner nodes; a method of fundamental solutions is then employed to evaluate the particular solution and the corresponding homogenous solution.Since the inverse problem is ill-posed,the truncated singular value decomposition with the regularization parameter given by the L-curve method is introduced to solve the resultant highly ill-conditioned system of linear equations.Numerical results are presented to verify the reliability and efficiency of the proposed method.

  11. The worldwide "wildfire" problem.

    Science.gov (United States)

    Gill, A Malcolm; Stephens, Scott L; Cary, Geoffrey J

    2013-03-01

    The worldwide "wildfire" problem is headlined by the loss of human lives and homes, but it applies generally to any adverse effects of unplanned fires, as events or regimes, on a wide range of environmental, social, and economic assets. The problem is complex and contingent, requiring continual attention to the changing circumstances of stakeholders, landscapes, and ecosystems; it occurs at a variety of temporal and spatial scales. Minimizing adverse outcomes involves controlling fires and fire regimes, increasing the resistance of assets to fires, locating or relocating assets away from the path of fires, and, as a probability of adverse impacts often remains, assisting recovery in the short-term while promoting the adaptation of societies in the long-term. There are short- and long-term aspects to each aspect of minimization. Controlling fires and fire regimes may involve fire suppression and fuel treatments such as prescribed burning or non-fire treatments but also addresses issues associated with unwanted fire starts like arson. Increasing the resistance of assets can mean addressing the design and construction materials of a house or the use of personal protective equipment. Locating or relocating assets can mean leaving an area about to be impacted by fire or choosing a suitable place to live; it can also mean the planning of land use. Assisting recovery and promoting adaptation can involve insuring assets and sharing responsibility for preparedness for an event. There is no single, simple, solution. Perverse outcomes can occur. The number of minimizing techniques used, and the breadth and depth of their application, depends on the geographic mix of asset types. Premises for policy consideration are presented. PMID:23634593

  12. Radiological problems in Kazakhstan

    International Nuclear Information System (INIS)

    Kazakhstan historical development and available mineral resources have pre-determined a scale of radiological problems in the state. Kazakhstan keeps leading positions in the world in explored uranium resources and hydrocarbon raw. More than five hundred nuclear explosions were performed in various regions of Kazakhstan. There is necessity to carry out remediation actions at the former test sites of Kazakhstan, especially at the Semipalatinsk test-site (STS). But because of the high cost of such actions it should be expedient to carry out them only in case of emergency and inclusion of the former test sites lands to the national economic activity, as in general, under conditions of competent policy of inhabitants, STS doesn't represent a hazard. At the same time, we ought not to lose an invaluable scientific material of test-sites. It is necessary to keep some areas of Semipalatinsk test-site as a rarities, reflected the important stages of the human evolution. Test-sites should be considered as world laboratory for studies of artificial radionuclides behaviour in natural medium. Illustrations of radiation-hazardous objects, of used technologies and procedures, under the Kazakhstan Republic instance, show that main power industries lead to the common increase of radioactivity materials in human environment. Mankind certainly will become aware of fact that industrial activities, under the current level of science and technologies development, will lead to the common increase of radioactivity materials in human environment. Solving of radioecological problems is possible only when people review their approach to a radioactivity, as a whole. Not only specialists involved in this field, but also all local population have to know rules of radiation safety and how reasonable manage with radioactive materials

  13. International safeguards problem

    International Nuclear Information System (INIS)

    To recognize the limitations of safeguards as a barrier to nuclear proliferation is not to deny their essential role in the effort to contain that problem. Without a safeguards system, international nuclear commerce and development would not, indeed could not, be what they are today. The problems evoked in the discussion of the spread of sensitive nuclear technology underscore the importance of ensuring that activities do not outpace our ability to control them. To sustain a global nuclear economy requires a readiness to live within the constraints that such an economy requires. Enhanced safeguards and strengthened national commitments to facilitate their application are key elements of those constraints. So also may be a prepardness by many nations to forego explicitly national control over all facets of the nuclear fuel cycle while still sharing fully and equally in the benefits of the peaceful atom. The challenge of the coming years will be to craft mechanisms and institutions enabling the continued growth of peaceful nuclear activity without further impairing international security. The constraints that such an outcome entails are not limited to nations lacking sophisticated nuclear technology; they apply to the most advanced nuclear nations as well--partly through adherence to the safeguards system that these countries call upon others to adopt, and partly through greater willingness to entertain solutions that may involve greater international involvement in, and control over, their own peaceful nuclear productive activities. With time, the relative incompatibility of nuclear energy with full national sovereignty, and the far-sighted wisdom of the Baruch Plan, are becoming increasingly clear. 1 table, 10 references

  14. On Brauer's problem 21

    Institute of Scientific and Technical Information of China (English)

    ZENG; Jiwen(

    2001-01-01

    [1]Brauer, R., Representations of finite groups, in Lectures in Mathematics, Vol. 1, New York: Wiley, 1963, 133-175.[2]Feit, W. , The Representation Theory of Finite Groups, Amsterdam: North-Holland, 1982.[3]Külshammer, B., Landau's theorem for p-blocks of p-solvable groups, J. Reine Angew. Math., 1990, 404: 189-191.[4]Külshammer B., Robinson, G. R., Alperin-Mckey implies Brauer's problem 21, J. Algebra, 1996, 180: 208-210.[5]Zeng Jiwen, An inequality of block invariants, J. Algebra, 1997, 193: 724-727.[6]Nagao, N., Tsushima, Y., Representations of Finite Groups, New York: Academic Press, Inc., 1989.[7]Robinson, G. R., On Brauer's k(B) problem, J. Algebra, 1992, 147: 450-455.[8]Zhang Jiping, p-regular orbits and p-blocks of defect zero, Comm. Algebra, 1993, 21(1): 299-307.[9]Xu Minyao, Huang ,Jianhua, An Introduction to Finite Groups (in Chinese), Vol. 2, Beijing: Science Press, 1999.[10]Alperin, ,J. L. , Weights for finite group, Proc. Sympos. Pure Math. , 1987, 47: 369-379.[11]Puig, L., Usami, Y., Perfect isometrics for blocks with Abelian defect groups and cyclic four inertial quotients, J. Algebra,1996.[12]Dade, E. C., Counting characters in blocks, I, Invent. Math., 1992, 109: 187-210.

  15. Fostering Information Problem Solving Skills Through Completion Problems and Prompts

    OpenAIRE

    Frerejean, Jimmy; Brand-Gruwel, Saskia; Kirschner, Paul A.

    2012-01-01

    Frerejean, J., Brand-Gruwel, S., & Kirschner, P. A. (2012, September). Fostering Information Problem Solving Skills Through Completion Problems and Prompts. Poster presented at the EARLI SIG 6 & 7 "Instructional Design" and "Learning and Instruction with Computers", Bari, Italy.

  16. Fostering information problem solving skills through completion problems and prompts

    OpenAIRE

    Frerejean, Jimmy; Brand-Gruwel, Saskia; Kirschner, Paul A.

    2012-01-01

    Frerejean, J., Brand-Gruwel, S., & Kirschner, P. A. (2012, November). Fostering information problem solving skills through completion problems and prompts. Poster presented at the ICO Fall School 2012, Girona, Spain.

  17. Kolkata Restaurant Problem as a Generalised El Farol Bar Problem

    Science.gov (United States)

    Chakrabarti, Bikas K.

    Generalisation of the El Farol bar problem to that of many bars here leads to the Kolkata restaurant problem, where the decision to go to any restaurant or not is much simpler (depending on the previous experience of course, as in the El Farol bar problem). This generalised problem can be exactly analysed in some limiting cases discussed here. The fluctuation in the restaurant service can be shown to have precisely an inverse cubic behavior, as widely seen in the stock market fluctuations.

  18. Mechanics problems in undergraduate physics

    CERN Document Server

    Strelkov, S P

    2013-01-01

    Problems in Undergraduate Physics, Volume I: Mechanics focuses on solutions to problems in physics. The book first discusses the fundamental problems in physics. Topics include laws of conservation of momentum and energy; dynamics of a point particle in circular motion; dynamics of a rotating rigid body; hydrostatics and aerostatics; and acoustics. The text also offers information on solutions to problems in physics. Answers to problems in kinematics, statics, gravity, elastic deformations, vibrations, and hydrostatics and aerostatics are discussed. Solutions to problems related to the laws of

  19. Sherlock Holmes, Master Problem Solver.

    Science.gov (United States)

    Ballew, Hunter

    1994-01-01

    Shows the connections between Sherlock Holmes's investigative methods and mathematical problem solving, including observations, characteristics of the problem solver, importance of data, questioning the obvious, learning from experience, learning from errors, and indirect proof. (MKR)

  20. Dementia - behavior and sleep problems

    Science.gov (United States)

    ... this page: //medlineplus.gov/ency/patientinstructions/000029.htm Dementia - behavior and sleep problems To use the sharing ... on this page, please enable JavaScript. People with dementia often have certain problems when it gets dark ...