Abstract Cauchy problems three approaches
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...
Beginnings of the Cauchy problem
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.
Evolution semigroups for nonautonomous Cauchy problems
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Gregor Nickel
1997-01-01
Full Text Available In this paper, we characterize wellposedness of nonautonomous, linear Cauchy problems (NCP {u˙(t=A(tu(tu(s=x∈X on a Banach space X by the existence of certain evolution semigroups.
A Cauchy problem in nonlinear heat conduction
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De Lillo, S [Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, Perugia (Italy); Lupo, G [Dipartimento di Matematica e Informatica, Universita degli Studi di Perugia, Via Vanvitelli, 1, 06123 Perugia (Italy); Sanchini, G [Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, Perugia (Italy)
2006-06-09
A Cauchy problem on the semiline for a nonlinear diffusion equation is considered, with a boundary condition corresponding to a prescribed thermal conductivity at the origin. The problem is mapped into a moving boundary problem for the linear heat equation with a Robin-type boundary condition. Such a problem is then reduced to a linear integral Volterra equation of II type which admits a unique solution.
The Cauchy problem for the Pavlov equation
Grinevich, P. G.; Santini, P. M.; Wu, D.
2015-10-01
Commutation of multidimensional vector fields leads to integrable nonlinear dispersionless PDEs that arise in various problems of mathematical physics and have been intensively studied in recent literature. This report aims to solve the scattering and inverse scattering problem for integrable dispersionless PDEs, recently introduced just at a formal level, concentrating on the prototypical example of the Pavlov equation, and to justify an existence theorem for global bounded solutions of the associated Cauchy problem with small data. An essential part of this work was made during the visit of the three authors to the Centro Internacional de Ciencias in Cuernavaca, Mexico in November-December 2012.
A Parameter Property of Classical Solutions of Cauchy Problems
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Min He
2014-01-01
Full Text Available This work is concerned with the abstract Cauchy problems that depend on parameters. The goal is to study continuity in the parameters of the classical solutions of the Cauchy problems. The situation considered in this work is when the operator of the Cauchy problem is not densely defined. By applying integrated semigroup theory and the results on continuity in the parameters of C0-semigroup and integrated semigroup, we obtain the results on the existence and continuity in parameters of the classical solutions of the Cauchy problems. The application of the obtained abstract results in a parabolic partial differential equation is discussed in the last section of the paper.
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.
On the Cauchy Problem Describing an Electron-Phonon Interaction
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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.
Non-dense domain operator matrices and Cauchy problems
Lalaoui Rhali, S
2002-01-01
In this work, we study Cauchy problems with non-dense domain operator matrices. By assuming that the entries of an unbounded operator matrix are Hille-Yosida operators, we give a necessary and sufficient condition ensuring that the part of this operator matrix generates a semigroup in the closure of its domain. This allows us to prove the well-posedness of the corresponding Cauchy problem. Our results are applied to delay and neutral differential equations.
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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.
Cauchy problem for Laplace equation: An observer based approach
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.
Solving fractional Schrödinger-type spectral problems: Cauchy oscillator and Cauchy well
Żaba, Mariusz; Garbaczewski, Piotr
2014-09-01
This paper is a direct offspring of the work of Garbaczewski and Stephanovich ["Lévy flights and nonlocal quantum dynamics," J. Math. Phys. 54, 072103 (2013)] where basic tenets of the nonlocally induced random and quantum dynamics were analyzed. A number of mentions were made with respect to various inconsistencies and faulty statements omnipresent in the literature devoted to so-called fractional quantum mechanics spectral problems. Presently, we give a decisive computer-assisted proof, for an exemplary finite and ultimately infinite Cauchy well problem, that spectral solutions proposed so far were plainly wrong. As a constructive input, we provide an explicit spectral solution of the finite Cauchy well. The infinite well emerges as a limiting case in a sequence of deepening finite wells. The employed numerical methodology (algorithm based on the Strang splitting method) has been tested for an exemplary Cauchy oscillator problem, whose analytic solution is available. An impact of the inherent spatial nonlocality of motion generators upon computer-assisted outcomes (potentially defective, in view of various cutoffs), i.e., detailed eigenvalues and shapes of eigenfunctions, has been analyzed.
THE CAUCHY PROBLEM FOR SOME DISPERSIVE WAVE EQUATIONS
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Zhang Wenling
2004-01-01
In this paper, we consider the Cauchy problem for some dispersive equations. By means of nonlinear estimate in Besov spaces and fixed point theory, we prove the global well-posedness of the above problem. What's more, we improve the scattering result obtained in [1].
Laplace transform generation theorems and local Cauchy problems
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Claus Müller
2004-01-01
Full Text Available We give new criterions to decide if some vector-valued function is a local Laplace transform and apply this to the theory of local Cauchy problems. This leads to an improvement of known results and new Hille-Yosida-type theorems for local convoluted semigroups.
Uniqueness Result in the Cauchy Dirichlet Problem via Mehler Kernel
Dhungana, Bishnu P.
2014-09-01
Using the Mehler kernel, a uniqueness theorem in the Cauchy Dirichlet problem for the Hermite heat equation with homogeneous Dirichlet boundary conditions on a class P of bounded functions U( x, t) with certain growth on U x ( x, t) is established.
Applications of elliptic Carleman inequalities to Cauchy and inverse problems
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.
The stability for the Cauchy problem for elliptic equations
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.
Application of homotopy analysis method for solving nonlinear Cauchy problem
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V.G. Gupta
2012-11-01
Full Text Available In this paper, by means of the homotopy analysis method (HAM, the solutions of some nonlinear Cauchy problem of parabolic-hyperbolic type are exactly obtained in the form of convergent Taylor series. The HAM contains the auxiliary parameter \\hbar that provides a convenient way of controlling the convergent region of series solutions. This analytical method is employed to solve linear examples to obtain the exact solutions. The results reveal that the proposed method is very effective and simple.
Laneev, E. B.; Mouratov, M. N.; Zhidkov, E. P.
2008-05-01
Cauchy problem for the Laplace equation with inaccurately given Cauchy conditions on an inaccurately defined arbitrary surface is considered. Discretization was performed and proved to obtain a numerical solution. An economic algorithm is proposed.
The Cauchy problem for higher order abstract differential equations
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.
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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.
Oscillatory solutions of the Cauchy problem for linear differential equations
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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.
A formal infinite dimensional Cauchy problem and its relation to integrable hierarchies
Helminck, G.F.; Panasenko, E.A.; Sergeeva, A.O.; Ge, M.L.; Bai, C.; Jing, N.
2012-01-01
In this paper it is shown under mild assumptions that the local solvability of an infinite dimensional formal Cauchy problem is equivalent to a set of zero curvature relations. The role of this type of Cauchy problems plays in integrable systems is illustrated at the hand of lower triangular Toda hi
The Cauchy problem for non-autonomous nonlinear Schr(o)dinger equations
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Peter Y. H. Pang; TANG Hongyan; WANG Youde
2005-01-01
In this paper we study the Cauchy problem for cubic nonlinear Schr(o)dinger equation with space-and time-dependent coefficients on Rm and Tm. By an approximation argument we prove that for suitable initial values, the Cauchy problem admits unique local solutions. Global existence is discussed in the cases of m=1,2.
A NOTE ON "THE CAUCHY PROBLEM FOR COUPLED IMBQ EQUATIONS"
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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.
Estimates for mild solutions to semilinear Cauchy problems
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Kresimir Burazin
2014-09-01
Full Text Available The existence (and uniqueness results on mild solutions of the abstract semilinear Cauchy problems in Banach spaces are well known. Following the results of Tartar (2008 and Burazin (2008 in the case of decoupled hyperbolic systems, we give an alternative proof, which enables us to derive an estimate on the mild solution and its time of existence. The nonlinear term in the equation is allowed to be time-dependent. We discuss the optimality of the derived estimate by testing it on three examples: the linear heat equation, the semilinear heat equation that models dynamic deflection of an elastic membrane, and the semilinear Schrodinger equation with time-dependent nonlinearity, that appear in the modelling of numerous physical phenomena.
The Cauchy problem of scalar-tensor theories of gravity
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Salgado, Marcelo [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apdo. Postal 70-543 Mexico 04510 DF (Mexico)
2006-07-21
The 3 + 1 formulation of scalar-tensor theories of gravity (STT) is obtained in the physical (Jordan) frame departing from the 4 + 0 covariant field equations. Contrary to common belief (folklore), the new system of ADM-like equations shows that the Cauchy problem of STT is well formulated (in the sense that the whole system of evolution equations is of first order in the time derivative). This is the first step towards a full first-order (in time and space) formulation from which a subsequent hyperbolicity analysis (a well-posedness determination) can be performed. Several gauge (lapse and shift) conditions are considered and implemented for STT. In particular, a generalization of the harmonic gauge for STT allows us to prove the well posedness of the STT using a second-order analysis which is very similar to the one employed in general relativity. Several appendices complement the ideas of the main part of the paper.
GLOBALLY SMOOTH SOLUTIONS TO CAUCHY PROBLEM OF A QUASILINEAR HYPERBOLIC SYSTEM ARISING IN BIOLOGY
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郑永树
2001-01-01
This article considers Cauchy problemut- (uv)x = 0,vt- ux =0, (E)v(x,0) = u0(x) ＞ 0, v(x,0) = v0(x). (Ⅰ)A necessary and sufficient condition in guaranteeing that Cauchy problem admits a global G1-solution on t ＞ 0 is obtained.
A Generalized Cauchy Distribution Framework for Problems Requiring Robust Behavior
Carrillo, Rafael E.; Aysal, Tuncer C.; Barner, Kenneth E.
2010-12-01
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.
A Generalized Cauchy Distribution Framework for Problems Requiring Robust Behavior
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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.
Integrated Fractional Resolvent Operator Function and Fractional Abstract Cauchy Problem
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Ya-Ning Li
2014-01-01
Full Text Available We firstly prove that β-times integrated α-resolvent operator function ((α,β-ROF satisfies a functional equation which extends that of β-times integrated semigroup and α-resolvent operator function. Secondly, for the inhomogeneous α-Cauchy problem cDtαu(t=Au(t+f(t, t∈(0,T, u(0=x0, u'(0=x1, if A is the generator of an (α,β-ROF, we give the relation between the function v(t=Sα,β(tx0+(g1*Sα,β(tx1+(gα-1*Sα,β*f(t and mild solution and classical solution of it. Finally, for the problem cDtαv(t=Av(t+gβ+1(tx, t>0, v(k(0=0, k=0,1,…,N-1, where A is a linear closed operator. We show that A generates an exponentially bounded (α,β-ROF on a Banach space X if and only if the problem has a unique exponentially bounded classical solution vx and Avx∈L loc 1(ℝ+,X. Our results extend and generalize some related results in the literature.
THE CAUCHY PROBLEM FOR A CLASS OF DOUBLY DEGENERATE NONLINEAR PARABOLIC EQUATION
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无
2006-01-01
This article studies the Cauchy problem for a class of doubly nonlinear deauthor considers its regularized problem and establishes some estimates. On the basis of the estimates, the existence and uniqueness of the generalized solutions in BV space are proved.
The Cauchy Problem of Scalar Tensor Theories of Gravity
Salgado, M
2006-01-01
The 3+1 formulation of scalar-tensor theories of gravity (STT) is obtained in the physical (Jordan) frame departing from the 4+0 covariant field equations. Contrary to the common believe (folklore), the new system of ADM-like equations shows that the Cauchy problem of STT is well formulated (in the sense that the whole system is of first order in the time-derivative). This is the first step towards a full first order (in time and space) formulation from which a subsequent hyperbolicity analysis (a well-posedness determination) can be performed. Several gauge (lapse and shift) conditions are considered and implemented for STT. In particular, a generalization of the harmonic gauge for STT allows to prove the well posedness of the STT using a second order analysis which is very similar to the one used in general relativity. Some spacetimes of astrophysical and cosmological interest are considered as specific applications. Several appendices complement the ideas of the main part of the paper.
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H. P. Malytska
2014-12-01
Full Text Available The paper found the explicit form of the fundamental solution of Cauchy problem for the equation of Kolmogorov type that has a finite number groups of spatial variables which are degenerate parabolic.
WEAK REGULARIZATION FOR A CLASS OF ILL-POSED CAUCHY PROBLEMS
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无
2006-01-01
This article is concerned with the ill-posed Cauchy problem associated with a densely defined linear operator A in a Banach space. A family of weak regularizing operators is introduced. If the spectrum of A is contained in a sector of right-half complex plane and its resolvent is polynomially bounded, the weak regularization for such ill-posed Cauchy problem can be shown by using the quasi-reversibility method and regularized semigroups. Finally, an example is given.
The Cauchy problem on a characteristic cone for the Einstein equations in arbitrary dimensions
Choquet-Bruhat, Yvonne; Martín-García, José M
2010-01-01
We derive explicit formulae for a set of constraints for the Einstein equations on a null hypersurface, in arbitrary dimensions. We solve these constraints and show that they provide necessary and sufficient conditions so that a spacetime solution of the Cauchy problem on a characteristic cone for the hyperbolic system of the reduced Einstein equations in wave-map gauge also satisfies the full Einstein equations. We prove a geometric uniqueness theorem for this Cauchy problem in the vacuum case.
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Hongwu Zhang
2011-08-01
Full Text Available In this article, we study a Cauchy problem for an elliptic equation with variable coefficients. It is well-known that such a problem is severely ill-posed; i.e., the solution does not depend continuously on the Cauchy data. We propose a modified quasi-boundary value regularization method to solve it. Convergence estimates are established under two a priori assumptions on the exact solution. A numerical example is given to illustrate our proposed method.
L~p-L~q decay estimates of solutions to Cauchy problems of thermoviscoelastic systems
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YANG Lin; HUANG Li-hong; KUANG Feng-lian
2009-01-01
Lp-Lq decay estimate of solution to Cauchy problem of a linear thermoviscoelastic system is studied. By using a diagonalization argument of frequency analysis, the coupled system will be decoupled micrologically. Then with the help of the information of characteristic roots for the coefficient matrix of the system, L~p-L~q decay estimate of parabolic type of solution to the Cauchy problem is obtained.
Cauchy-Riemann方程解的延拓问题%The Extended Problems of Solution for Cauchy-Riemann Equation
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马忠泰; 赵红玲
2005-01-01
This paper, we discuss the solutions' characterize of Cauchy-Riemann equation and the extension phenomenon of Hartogs in Cn and, a series of new extended results of the solutions for Cauchy-Riemann equations is obtained by using the latest developments of the solutions' extension. Furthermore, the case of the extension's limitation for the solutions is also given.
A Fourth-Order Modified Method for the Cauchy Problem of the Modified Helmholtz Equation
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R. Shi; H. H. Qin
2009-01-01
This paper is concerned with the Cauchy problem for the modified Helmholtz equation in an infinite strip domain 0 < x≤ 1, y ∈ R. The Cauchy data at x = 0 is given and the solution is then sought for the interval 0 < x ≤1. This problem is highly ill-posed and the solution (if it exists) does not depend continuously on the given data. In this paper, we propose a fourth-order modified method to solve the Cauchy problem. Convergence estimates are presented under the suitable choices of regularization parameters and the a priori assumption on the bounds of the exact solution. Numerical implementation is considered and the numerical examples show that our proposed method is effective and stable.
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Eva Lowen-Colebunders
1982-01-01
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.
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Danuta Jaruszewska-Walczak
1994-05-01
Full Text Available We formulate a criterion of uniqueness of solutions of a Cauchy problem using the comparison function of the Kamke type. This will be a generalization of classical results concerning first order equations with partial derivatives. We prove that the uniqueness criteria of Perron and Kamke type for differential-function problems are equivalent if given functions are continuous.
Danuta Jaruszewska-Walczak
1994-01-01
We formulate a criterion of uniqueness of solutions of a Cauchy problem using the comparison function of the Kamke type. This will be a generalization of classical results concerning first order equations with partial derivatives. We prove that the uniqueness criteria of Perron and Kamke type for differential-function problems are equivalent if given functions are continuous.
Integral Formula for the Characteristic Cauchy Problem on a curved Background
Joudioux, Jérémie
2009-01-01
We give a local integral formula, valid on general curved space-times, for the characteristic Cauchy problem for the Dirac equation with arbitrary spin using the method developed by Friedlander in his book "the wave equation on a curved spacetime" (1975). The results obtained by Penrose in the flat case in "Null hypersurface initial data for classical fields of arbitrary spin for general relativity" (Gen. Rel. Grav 1980) are recovered directly. It is expected that this method can be used to obtain sharp estimates for the characteristic Cauchy problem for the Dirac equation.
THE CAUCHY PROBLEM FOR THE SYSTEM OF EQUATIONS OF THERMOELASTICITY IN E^n
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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.
An optimal iterative algorithm to solve Cauchy problem for Laplace equation
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.
The Cauchy problem for a model of immiscible gas flow with large data
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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
CAUCHY PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS WITH CHARACTERISTICS WITH CONSTANT MULTIPLICITY
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Wang Libin
2004-01-01
For quasilinear hyperbolic systems with characteristics of constant multiplicity, suppose that characteristics of constant multiplicity(＞1) are linearly degenerate, by means of generalized normalized coordinates we get the global existence and the blow-up phenomenon of the C1 solution to the Cauchy problem under an additional hypothesis.
Cauchy Problem for Quasilinear Hyperbolic Systems with Higher Order Dissipative Terms
Institute of Scientific and Technical Information of China (English)
Wei-guo Zhang
2003-01-01
In this paper, the author studies the global existence, singularities and life span of smooth solutions of the Cauchy problem for a class of quasilinear hyperbolic systems with higher order dissipative terms and gives their applications to nonlinear wave equations with higher order dissipative terms.
Cauchy problem and initial traces for a doubly nonlinear degenerate parabolic equation
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赵俊宁; 徐中海
1996-01-01
The Cauchy problem and initial traces for the doubly degenerate parabolic equationsare studied. Under certain growth condition on the initial datum u0(x) as the existence of solution is proved. The results obtained are optimal in the dass of nonnegative locally bounded solution, for which a Harnack-type inequality holds.
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V. Vijayakumar
2014-09-01
Full Text Available In this article, we study the existence of mild solutions for nonlocal Cauchy problem for fractional neutral evolution equations with infinite delay. The results are obtained by using the Banach contraction principle. Finally, an application is given to illustrate the theory.
POINTWISE ESTIMATES OF SOLUTIONS TO CAUCHY PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS
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WANG WEIKE; YANG XIONGFENG
2003-01-01
This paper considers the pointwise estimate of the solutions to Cauchy problem for quasilin-ear hyperbolic systems, which bases on the existence of the solutions by using the fundamentalsolutions. It gives a sharp pointwise estimates of the solutions on domain under consideration.Specially, the estimate is precise near each characteristic direction.
EXISTENCE AND UNIQUENESS OF THE CAUCHY PROBLEM FOR A GENERALIZED NAVIER-STOKES EQUATIONS
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刘晓风
2003-01-01
We consider the Cauchy problem for a generalized Navier-Stokes equations with hyperdissipation, with the initial data in Lpσ. We follow the theme of [1] but with more complicated analysis on the symbol and obtain the existence and uniqueness results.
Cauchy Problem of Some Doubly Degenerate Parabolic Equations with Initial Datum a Measure
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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.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Presents the iterative method of solving Cauchy problem withreproducing kernel for nonlinear hyperbolic equations, and the application of the computational technique of reproducing kernel space to simplify, the iterative computation and increase the convergence rate and points out that this method is still effective. Even if the initial condition is discrete.
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.
Global existence and decay of solutions of the Cauchy problem in thermoelasticity with second sound
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.
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.
Global solution to the Cauchy problem on a universe fireworks model
Zhenglu Jiang
2008-01-01
We prove existence and uniqueness of the global solution to the Cauchy problem on a universe fireworks model with finite total mass at the initial state when the ratio of the mass surviving the explosion, the probability of the explosion of fragments and the probability function of the velocity change of a surviving particle satisfy the corresponding physical conditions. Although the nonrelativistic Boltzmann-like equation modeling the universe fireworks is mathematically easy, this paper leads rather theoretically to an understanding of how to construct contractive mappings in a Banach space for the proof of the existence and uniqueness by means of methods taken from the famous work by DiPerna & Lions about the Boltzmann equation. We also show both the regularity and the time-asymptotic behavior of solution to the Cauchy problem.
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
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.
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.
Waves attractors in rotating fluids a paradigm for ill-posed Cauchy problems
Rieutord, M; Valdettaro, L
2000-01-01
In the limit of low viscosity, we show that the amplitude of the modes of oscillation of a rotating fluid, namely inertial modes, concentrate along an attractor formed by a periodic orbit of characteristics of the underlying hyperbolic Poincar\\'e equation. The dynamics of characteristics is used to elaborate a scenario for the asymptotic behaviour of the eigenmodes and eigenspectrum in the physically relevant r\\'egime of very low viscosities which are out of reach numerically. This problem offers a canonical ill-posed Cauchy problem which has applications in other fields.
The geometric Cauchy problem for surfaces with Lorentzian harmonic Gauss maps
DEFF Research Database (Denmark)
Brander, David; Svensson, Martin
2013-01-01
The geometric Cauchy problem for a class of surfaces in a pseudo-Riemannian manifold of dimension 3 is to find the surface which contains a given curve with a prescribed tangent bundle along the curve. We consider this problem for constant negative Gauss curvature surfaces (pseudospherical surfaces...... representation for surfaces associated with Lorentzian harmonic maps (1-1 wave maps) into symmetric spaces, developed since the 1990's. Explicit formulae for the potentials in terms of the prescribed data are given, and some applications are considered....
On the Cauchy problem for nonlinear Schrödinger equations with rotation
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.
CAUCHY PROBLEM FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS
Institute of Scientific and Technical Information of China (English)
Lian Ruxu; Liu Jian; Li Hailiang; Xiao Ling
2012-01-01
We consider the Cauchy problem for one-dimensional isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficient.For regular initial data,we show that the unique strong solution exits globally in time and converges to the equilibrium state time asymptotically.When initial density is piecewise regular with jump discontinuity,we show that there exists a unique global piecewise regular solution. In particular,the jump discontinuity of the density decays exponentially and the piecewise regular solution tends to the equilibrium state as t→ +∞.
On existence of weak solutions to a Cauchy problem for one class of conservation laws
Directory of Open Access Journals (Sweden)
P. I. Kogut
2015-02-01
Full Text Available We discuss the existence of weak solutions to the Cauchy problem for one classof hyperbolic conservation laws that models a highly re-entrant production system.The output of the factory is described as a function of the work in progress and theposition of the so-called push-pull point (PPP where we separate the beginning ofthe factory employing a push policy from the end of the factory, which uses a pullpolicy. The main question we discuss in this paper is about the optimal choice ofthe input in-ux, push and pull constituents, and the position of PPP.
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Rubio Gerardo
2011-03-01
Full Text Available We consider the Cauchy problem in ℝd for a class of semilinear parabolic partial differential equations that arises in some stochastic control problems. We assume that the coefficients are unbounded and locally Lipschitz, not necessarily differentiable, with continuous data and local uniform ellipticity. We construct a classical solution by approximation with linear parabolic equations. The linear equations involved can not be solved with the traditional results. Therefore, we construct a classical solution to the linear Cauchy problem under the same hypotheses on the coefficients for the semilinear equation. Our approach is using stochastic differential equations and parabolic differential equations in bounded domains. Finally, we apply the results to a stochastic optimal consumption problem. Nous considérons le problème de Cauchy dans ℝd pour une classe d’équations aux dérivées partielles paraboliques semi linéaires qui se pose dans certains problèmes de contrôle stochastique. Nous supposons que les coefficients ne sont pas bornés et sont localement Lipschitziennes, pas nécessairement différentiables, avec des données continues et ellipticité local uniforme. Nous construisons une solution classique par approximation avec les équations paraboliques linéaires. Les équations linéaires impliquées ne peuvent être résolues avec les résultats traditionnels. Par conséquent, nous construisons une solution classique au problème de Cauchy linéaire sous les mêmes hypothèses sur les coefficients pour l’équation semi-linéaire. Notre approche utilise les équations différentielles stochastiques et les équations différentielles paraboliques dans les domaines bornés. Enfin, nous appliquons les résultats à un problème stochastique de consommation optimale.
The Cauchy Boundary Value Problems on Closed Piecewise Smooth Manifolds in Cn
Institute of Scientific and Technical Information of China (English)
Liang Yu LIN; Chun Hui QIU
2004-01-01
Suppose that D is a bounded domain with a piecewise C1 smooth boundary in Cn. Let ψ∈ C1+α((б)D). By using the Hadamard principal value of the higher order singular integral and solid angle coefficient method of points on the boundary, we give the Plemelj formula of the higher order singular integral with the Bochner-Martinelli kernel, which has integral density ψ. Moreover,by means of the Plemelj formula and methods of complex partial differential equations, we discuss the corresponding Cauchy boundary value problem with the Bochner-Martinelli kernel on a closed piecewise smooth manifold and obtain its unique branch complex harmonic solution.
A Series Solution of the Cauchy Problem for Turing Reaction-diffusion Model
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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.
A dimension decomposition approach based on iterative observer design for an elliptic Cauchy problem
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.
The Cauchy problem for a class of pseudodifferential equations over p-adic field
Chuong, Nguyen Minh; Co, Nguyen Van
2008-04-01
In this paper, some classes much more general than the one in [N.M. Chuong, Yu.V. Egorov, A. Khrennikov, Y. Meyer, D. Mumford (Eds.), Harmonic, Wavelet and p-Adic Analysis, World Scientific, Singapore, 2007] of Cauchy problems for an interesting class of pseudodifferential equations over p-adic fields are studied. The used functions belong to mixed classes of real and p-adic functions. Even for p-adic partial differential equations such problems in such function spaces have not been discussed yet. The established mathematical foundation requires very complicated and very difficult proofs. Days after days, these equations occur increasingly in mathematical physics, quantum mechanics. Explicit solutions of such problems are very needed for specialists on applied mathematics, physics, and engineering.
Essential growth rate for bounded linear perturbation of non-densely defined Cauchy problems
Ducrot, A.; Liu, Z.; Magal, P.
2008-05-01
This paper is devoted to the study of the essential growth rate of some class of semigroup generated by bounded perturbation of some non-densely defined problem. We extend some previous results due to Thieme [H.R. Thieme, Quasi-compact semigroups via bounded perturbation, in: Advances in Mathematical Population Dynamics--Molecules, Cells and Man, Houston, TX, 1995, in: Ser. Math. Biol. Med., vol. 6, World Sci. Publishing, River Edge, NJ, 1997, pp. 691-711] to a class of non-densely defined Cauchy problems in Lp. In particular in the context the integrated semigroup is not operator norm locally Lipschitz continuous. We overcome the lack of Lipschitz continuity of the integrated semigroup by deriving some weaker properties that are sufficient to give information on the essential growth rate.
Institute of Scientific and Technical Information of China (English)
2000-01-01
This article considers Cauchy problem for quasilinear hyperbolic systems in diagonal form.A necessary and sufficient condition in guaranteeing that Cauchy problem admits a unique global classical solution on t 0 is obtained,and a sharp estimate of the life span for the classical solution is given.
Cauchy problem for multiscale conservation laws: Application to structured cell populations
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.
Directory of Open Access Journals (Sweden)
Dhaou Lassoued
2013-04-01
Full Text Available We prove that a family of $q$-periodic continuous matrix valued function ${A(t}_{tin mathbb{R}}$ has an exponential dichotomy with a projector $P$ if and only if $int_0^t e^{imu s}U(t,sPds$ is bounded uniformly with respect to the parameter $mu$ and the solution of the Cauchy operator Problem $$displaylines{ dot{Y}(t=-Y(tA(t+ e^{i mu t}(I-P ,quad tgeq s cr Y(s=0, }$$ has a limit in $mathcal{L}(mathbb{C}^n$ as s tends to $-infty$ which is bounded uniformly with respect to the parameter $mu$. Here, ${ U(t,s: t, sinmathbb{R}}$ is the evolution family generated by ${A(t}_{tin mathbb{R}}$, $mu$ is a real number and q is a fixed positive number.
Mutational analysis a joint framework for Cauchy problems in and beyond vector spaces
Lorenz, Thomas
2010-01-01
Ordinary differential equations play a central role in science and have been extended to evolution equations in Banach spaces. For many applications, however, it is difficult to specify a suitable normed vector space. Shapes without a priori restrictions, for example, do not have an obvious linear structure. This book generalizes ordinary differential equations beyond the borders of vector spaces with a focus on the well-posed Cauchy problem in finite time intervals. Here are some of the examples: - Feedback evolutions of compact subsets of the Euclidean space - Birth-and-growth processes of random sets (not necessarily convex) - Semilinear evolution equations - Nonlocal parabolic differential equations - Nonlinear transport equations for Radon measures - A structured population model - Stochastic differential equations with nonlocal sample dependence and how they can be coupled in systems immediately - due to the joint framework of Mutational Analysis. Finally, the book offers new tools for modelling.
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.
Ill-posedness of the Cauchy problem for totally degenerate system of conservation laws
Directory of Open Access Journals (Sweden)
Wladimir Neves
2005-11-01
Full Text Available In this paper we answer some open questions concerning totally degenerate systems of conservation laws. We study the augmented Born-Infeld system, which is the Born-Infeld model augmented by two additional conservations laws. This system is a nice example of totally degenerate system of conservation laws and, global smooth solutions are conjectured to exist when the initial-data is smooth. We show that this conjecture is false, for the more natural and general condition of initial-data. In fact, first we show that does not exist global smooth solution for any 2X2 totally degenerated system of conservation laws, which the characteristics speeds do not have singular points. Moreover, we sharpen the conjecture in Majda [20]. Under the same hypothesis of initial-data, we show that the Riemann Problem is not well-posed, which follows for weak solutions of the Cauchy Problem. In the end, we prove some results on the direction of well-posedness for the less physically initial-data.
WELL-POSEDNESS FOR THE CAUCHY PROBLEM TO THE HIROTA EQUATION IN SOBOLEV SPACES OF NEGATIVE INDICES
Institute of Scientific and Technical Information of China (English)
HUOZHAOHUI; JIA YUELING
2005-01-01
The local well-posedness of the Cauchy problem for the Hirota equation is established for low regularity data in Sobolev spaces Hs(s ≥ -1-4). Moreover, the global well-posedness for L2 data follows from the local well-posedness and the conserved quantity. For data in Hs(s ＞ 0), the global well-posedness is also proved. The main idea is to use the generalized trilinear estimates, associated with the Fourier restriction norm method.
Institute of Scientific and Technical Information of China (English)
冯玉瑚; 朱凡昌
2004-01-01
Solutions of fuzzy differential equations provide a noteworthy example of time-dependent fuzzy sets. The purpose of this paper is to introduce functions of a suitable Lyapunov-like type and to show the existence and uniqueness theorem for the Cauchy problem of fuzzy differential equations under non-Lipschitz conditions. The comparison principles and the existence and uniqueness theorems of this paper generalize many well-known results up to now.
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).
Diffuse interface methods for inverse problems: case study for an elliptic Cauchy problem
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
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.
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.
Well-posedness of Cauchy problems for Korteweg-de Vries-Benjamin-Ono equation and Hirota equation
Institute of Scientific and Technical Information of China (English)
HUO Zhaohui; GUO Boling
2004-01-01
The well-posedness of the Cauchy problems to the Korteweg-de Vries-Benjamin-Ono equation and Hirota equation is considered. For the Korteweg-de Vries-Benjamin-Ono equation, local result is established for data in Hs(R)(s≥-1/8). Moreover, the global well-posedness for data in L2(R) can be obtained. For Hirota equation, local result is established for initial data in Hs(s≥1/4) .In addition, the local solution is proved to be global in Hs (s≥1) if the initial data are in Hs (s≥1) by energy inequality and the generalization of the trilinear estimates associated with the Fourier restriction norm method.
Thieme, Horst R.; Vosseler, Hauke
2002-01-01
A convolution of Stieltjes type is introduced for operator families of bounded strong variation and vector valued $L_1$-functions. Using this tool, perturbation theorems for integrated semigroups of bounded strong variation are derived, and improved results on $L_p$-solutions to the inhomogeneous Cauchy problem are obtained.
Institute of Scientific and Technical Information of China (English)
2007-01-01
In this paper, we consider the Cauchy problem with initial data given on a semi-bounded axis for inhomogeneous quasilinear hyperbolic systems. Under the assumption that the rightmost (resp. leftmost) eigenvalue is weakly linearly degenerate and the inhomogeneous term satisfies the corresponding matching condition, we obtain the global existence and uniqueness of C1 solution with small and decaying initial data.
Cauchy problem of the generalized Zakharov type system in [Formula: see text].
You, Shujun; Ning, Xiaoqi
2017-01-01
In this paper, we consider the initial value problem for a two-dimensional generalized Zakharov system with quantum effects. We prove the existence and uniqueness of global smooth solutions to the initial value problem in the Sobolev space through making a priori integral estimates and the Galerkin method.
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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.
Cauchy problems for fifth-order KdV equations in weighted Sobolev spaces
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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.
Symmetry Reduction and Cauchy Problems for a Class of Fourth-Order Evolution Equations
Institute of Scientific and Technical Information of China (English)
LI Ji-Na; ZHANG Shun-Li
2008-01-01
We exploit higher-order conditional symmetry to reduce initial-value problems for evolution equations to Cauehy problems for systems of ordinary differential equations (ODEs).We classify a class of fourth-order evolution equations which admit certain higher-order generalized conditional symmetries (GCSs) and give some examples to show the main reduction procedure.These reductions cannot be derived within the framework of the standard Lie approach,which hints that the technique presented here is something essential for the dimensional reduction of evolution equations.
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...
THE CAUCHY PROBLEM OF NONLINEAR SCHR(O)DINGER-BOUSSINESQ EQUATIONS IN Hs(Rd)
Institute of Scientific and Technical Information of China (English)
Han Yongqian
2005-01-01
In this paper, the local well posedness and global well posedness of solutions for the initial value problem (IVP) of nonlinear Schrodinger-Boussinesq equations is considered in Hs(Rd) by resorting Besov spaces, where real number s ≥ 0.
Asymptotic property of solutions to the random cauchy problem for wave equations
Dôku, Isamu
1986-01-01
Based on the existence and uniqueness theorem for random wave equations, we consider asymptotic behaviors of solutions to the random initial value problem. We describe conditions for the equipartition of stochastic energy (or SE for short) by making use of the random spectral theory and, according to Goldstein's semigroup method, we prove the asymptotically equipartitioned SE theorem and the so-called virial theorem of classical mechanics, and also study the probabilistic characterization of the conditions for equipartition. In addition, we show at last the equipartition of SE from a finite time onwards.
The Cauchy problem for the pressureless Euler/isentropic Navier-Stokes equations
Choi, Young-Pil; Kwon, Bongsuk
2016-07-01
We present a new hydrodynamic model consisting of the pressureless Euler equations and the isentropic compressible Navier-Stokes equations where the coupling of two systems is through the drag force. This coupled system can be derived, in the hydrodynamic limit, from the particle-fluid equations that are frequently used to study the medical sprays, aerosols and sedimentation problems. For the proposed system, we first construct the local-in-time classical solutions in an appropriate L2 Sobolev space. We also establish the a priori large-time behavior estimate by constructing a Lyapunov functional measuring the fluctuation of momentum and mass from the averaged quantities, and using this together with the bootstrapping argument, we obtain the global classical solution. The large-time behavior estimate asserts that the velocity functions of the pressureless Euler and the compressible Navier-Stokes equations are aligned exponentially fast as time tends to infinity.
Institute of Scientific and Technical Information of China (English)
无
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.
On the Cauchy problem of a 2 times 2 system of nonstrictly hyperbolic conservation laws
Energy Technology Data Exchange (ETDEWEB)
Kan, P.T.
1989-01-01
Global existence for a 2 {times} 2 system of nonstrictly hyperbolic conservation law is established for data of arbitrary bounded variation. This result is obtained by proving a convergence theorem for the method of artificial viscosity applied to this system of conservation law. For this purpose, the method of compensated compactness and an analysis of the entropy functions are used. This system under consideration is a special case of a canonical class of 2 {times} 2 systems of conservation laws with quadratic flux functions possessing an isolated umbilic point (point of coinciding wave speeds where strict hyperbolicity fails) at the origin of the state space. These systems arise as model equations to equations used in oil reservoir simulations. Their wave curves and Riemann problem solutions are known to exhibit complexities not seen in any strictly hyperbolic systems. In this thesis, besides establishing global existence for a special system in the canonical class, general properties of a subclass are also investigated. The geometry of rarefaction wave curves are analytically studied and Riemann invariants are constructed. An L{sup {infinity}} bound (independent of the viscosity) for the solutions of the corresponding viscous systems are obtained. Also studied is the monotonicity properties of the wave speeds in the Riemann invariant plane.
Institute of Scientific and Technical Information of China (English)
Yan ZHANG
2007-01-01
When a target manifold is complete with a bounded curvature, we prove that there exists a unique global solution which satisfies the Euler-lagrange equation of (τ)(φ,(φ))=fR1+1{(|dφ|2+}dtdx for the given Cauchy data.
Meyer, J C; Needham, D J
2015-03-08
In this paper, we examine a semi-linear parabolic Cauchy problem with non-Lipschitz nonlinearity which arises as a generic form in a significant number of applications. Specifically, we obtain a well-posedness result and examine the qualitative structure of the solution in detail. The standard classical approach to establishing well-posedness is precluded owing to the lack of Lipschitz continuity for the nonlinearity. Here, existence and uniqueness of solutions is established via the recently developed generic approach to this class of problem (Meyer & Needham 2015 The Cauchy problem for non-Lipschitz semi-linear parabolic partial differential equations. London Mathematical Society Lecture Note Series, vol. 419) which examines the difference of the maximal and minimal solutions to the problem. From this uniqueness result, the approach of Meyer & Needham allows for development of a comparison result which is then used to exhibit global continuous dependence of solutions to the problem on a suitable initial dataset. The comparison and continuous dependence results obtained here are novel to this class of problem. This class of problem arises specifically in the study of a one-step autocatalytic reaction, which is schematically given by A→B at rate a(p)b(q) (where a and b are the concentrations of A and B, respectively, with 0
problem has been lacking up to the present.
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.
Energy Technology Data Exchange (ETDEWEB)
Panov, E Yu [Novgorod State University, Novgorod (Russian Federation)
2002-12-31
We construct a theory of locally summable generalized entropy solutions (g.e. solutions) of the Cauchy problem for a first-order non-homogeneous quasilinear equation with continuous flux vector satisfying a linear restriction on its growth. We prove the existence of greatest and least g.e. solutions, suggest sufficient conditions for uniqueness of g.e. solutions, prove several versions of the comparison principle, and obtain estimates for the L{sup p}-norms of solution with respect to the space variables. We establish the uniqueness of g.e. solutions in the case when the input data are periodic functions of the space variables.
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.
Sekerzh-Zen'kovich, S. Ya.
2016-10-01
The problem of Cauchy-Poisson type is considered in the framework of potential tsunami model with impulse cylindical compactly supported source discontinuous with respect to the radial horizontal coordinate under the assumption that the depth of the liquid is constant. An analytical solution of the problem for a special choice of values of the parameters of the source is given. The connection the solution thus obtained with nonstandard characteristics introduced by Maslov is discussed. The graphs of the time history of the free surface elevation are compared with the marigrams, received for the 2011 tsunami from the DART stations 21418, 21413, and 51407, and also with graphs calculated for the well-known model with a "simple" source.
Institute of Scientific and Technical Information of China (English)
刘德朋
2001-01-01
本文就形如 utt＝a2(utt+(2)/(x)ux) 的 Cauchy 问题进行了讨论,得到其相容性条件和古典解的存在性定理,进而对于更一般的一类形如 autt+2butt+cutt+(2)/(x)(aux+bux)=0(a、b、c是常量,且b2-ac＞0)的方程得到类似结果.
Directory of Open Access Journals (Sweden)
El-Bachir Yallaoui
2012-06-01
Full Text Available In this article, we introduce a new class of analytic functions of the unit disc $mathbf{D}$ namely the Exponential Cauchy Transforms $mathbf{{K}_{e}}$ defined by f(z= {displaystyleint_{mathbf{T}}} expleft[ Kleft( xzight ight] dmu(x where $Kleft( zight =left( 1-zight ^{-1}$ is classical Cauchy kernel and $mu(x$ is a complex Borel measures and $x$ belongs to the unit circle $mathbf{T}$ . We use Laguerre polynomials to explore the coefficients of the Taylor expansions of the kernel and Peron's formula to study the asymptotic behavior of the Taylor coefficients. Finally we investigate relationships between our new class $mathbf{{K}_{e}}$, the classical Cauchy space $mathbf{K}$ and the Hardy spaces $H^{p}$.
Dafermos, M
2002-01-01
This talk describes some recent results [16] regarding the problem of uniqueness in the large (also known as strong cosmic censorship) for the initial value problem in general relativity. In order to isolate the essential analytic features of the problem from the complicated setting of gravitational collapse in which it arises, some familiarity with conformal properties of certain celebrated special solutions of the theory of relativity will have to be developed. This talk is an attempt to present precisely these features to an audience of non-specialists, in a way which will hopefully fully motivate a certain characteristic initial value problem for the spherically-symmetric Einstein-Maxwell-Scalar Field system. The considerations outlined here leading to this particular initial value problem are well known in the physics relativity community, where the problem of uniqueness has been studied heuristically [1, 22] and numerically [2, 3]. In [16], the global behavior of solutions to this IVP, in particular, th...
Approximate (m, n)-Cauchy-Jensen Additive Mappings in C*-algebras
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John Michael RASSIAS; Kil Woung JUN; Hark-Mahn KIM
2011-01-01
Concerning the stability problem of functional equations,we introduce a general (m,n)-Cauchy-Jensen functional equation and establish new theorems about the Hyers-Ulam stability of general (m,n)-Cauchy-Jensen additive mappings in C*-algebras,which generalize the results obtained for Cauchy-Jensen type additive mappings.
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钱爱林; 毛建峰; 桂咏新
2011-01-01
Helmholtz方程Cauchy问题是严重不适定问题,本文我们在一个带形区域上考虑了一类Helmholtz方程Cauchy问题:已知Cauchy数据u(0,y)=g(y),在区间0＜x＜1上求解.我们用半离散的中心差分方法得到了这一问题的正则化解,给出了正则化参数的选取规则,得到了误差估计.%The Cauchy problem of Helmholtz equation is severely ill-posed problem. In this paper, we consider the Cauchy problem for the Helmholtz equation where the Cauchy data is given at x = 0 and the solution is sought in the interval 0 ＜ x ＜ 1. A semi-discrete difference schemes together with a choice of regularization parameter is presented and error estimate is obtained.
Santucci, F.; Santini, P. M.
2016-10-01
We study the generalization of the dispersionless Kadomtsev-Petviashvili (dKP) equation in n+1 dimensions and with nonlinearity of degree m+1, a model equation describing the propagation of weakly nonlinear, quasi one-dimensional waves in the absence of dispersion and dissipation, and arising in several physical contexts, like acoustics, plasma physics, hydrodynamics and nonlinear optics. In 2 + 1 dimensions and with quadratic nonlinearity, this equation is integrable through a novel inverse scattering transform, and it has been recently shown to be a prototype model equation in the description of the two-dimensional wave breaking of localized initial data. In higher dimensions and with higher nonlinearity, the generalized dKP equations are not integrable, but their invariance under motions on the paraboloid allows one to construct in this paper a family of exact solutions describing waves constant on their paraboloidal wave front and breaking simultaneously in all points of it, developing after breaking either multivaluedness or single-valued discontinuous profiles (shocks). Then such exact solutions are used to build the longtime behavior of the solutions of the Cauchy problem, for small and localized initial data, showing that wave breaking of small initial data takes place in the longtime regime if and only if m(n-1)≤slant 2. Lastly, the analytic aspects of such wave breaking are investigated in detail in terms of the small initial data, in both cases in which the solution becomes multivalued after breaking or it develops a shock. These results, contained in the 2012 master’s thesis of one of the authors (FS) [1], generalize those obtained in [2] for the dKP equation in n+1 dimensions with quadratic nonlinearity, and are obtained following the same strategy.
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 st...... 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....
THE CAUCHY-KOVALEVSKAYA THEOREM-OLD AND NEW
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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.
p-topological Cauchy completions
Directory of Open Access Journals (Sweden)
J. Wig
1999-01-01
Full Text Available The duality between “regular” and “topological” as convergence space properties extends in a natural way to the more general properties “p-regular” and “p-topological.” Since earlier papers have investigated regular, p-regular, and topological Cauchy completions, we hereby initiate a study of p-topological Cauchy completions. A p-topological Cauchy space has a p-topological completion if and only if it is “cushioned,” meaning that each equivalence class of nonconvergent Cauchy filters contains a smallest filter. For a Cauchy space allowing a p-topological completion, it is shown that a certain class of Reed completions preserve the p-topological property, including the Wyler and Kowalsky completions, which are, respectively, the finest and the coarsest p-topological completions. However, not all p-topological completions are Reed completions. Several extension theorems for p-topological completions are obtained. The most interesting of these states that any Cauchy-continuous map between Cauchy spaces allowing p-topological and p′-topological completions, respectively, can always be extended to a θ-continuous map between any p-topological completion of the first space and any p′-topological completion of the second.
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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.
Demonstration of Cauchy: Understanding Algebraic
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T.L. Costa
2012-11-01
Full Text Available ABSTRACT: In this study we present some considerations about the End of Course Work undergraduate Full Degree in Mathematics / UFMT, drafted in 2011, and by taking title "A story about Cauchy and Euler's theorem on polyhedra" that gave birth to our research project Master of Education, begun in 2012, on the approaches of Euler's theorem on polyhedra in mathematics textbooks. At work in 2011 presented some considerations about the history of Euler's theorem for polyhedra which focus the demonstration presented by Cauchy (1789-1857, who tries to generalize it, relying on assumptions not observable in Euclidean geometry. Therefore, we seek the accessible literature on the history of mathematics; relate some aspects of the demonstration Cauchy with historical events on the development of mathematics in the nineteenth century, which allowed the acceptance of such a demonstration by mathematicians of his time.Keywords: History of Mathematics. Euler's Theorem on Polyhedra. Demonstration of Cauchy.
Carlini, A.; Novikov, I. D.
We consider the action principle to derive the classical, relativistic motion of a selfinteracting particle in a 4D Lorentzian spacetime containing a wormhole and which allows the existence of closed time-like curves. In particular, we study the case of a pointlike particle subject to a “hard-sphere” self-interaction potential and which can traverse the wormhole an arbitrary number of times, and show that the only possible trajectories for which the classical action is stationary are those which are globally self-consistent. Generically, the multiplicity of these trajectories (defined as the number of self-consistent solutions to the equations of motion beginning with given Cauchy data) is finite, and it becomes infinite if certain constraints on the same initial data are satisfied. This confirms the previous conclusions (for a nonrelativistic model) by Echeverria, Klinkhammer and Thorne that the Cauchy initial value problem in the presence of a wormhole “time machine” is classically “ill-posed” (far too many solutions). Our results further extend the recent claim by Novikov et al. that the “principle of self-consistency” is a natural consequence of the “principle of minimal action.”
Carlini, A
1996-01-01
We consider the action principle to derive the classical, relativistic motion of a self-interacting particle in a 4-D Lorentzian spacetime containing a wormhole and which allows the existence of closed time-like curves. In particular, we study the case of a pointlike particle subject to a `hard-sphere' self-interaction potential and which can traverse the wormhole an arbitrary number of times, and show that the only possible trajectories for which the classical action is stationary are those which are globally self-consistent. Generically, the multiplicity of these trajectories (defined as the number of self-consistent solutions to the equations of motion beginning with given Cauchy data) is finite, and it becomes infinite if certain constraints on the same initial data are satisfied. This confirms the previous conclusions (for a non-relativistic model) by Echeverria, Klinkhammer and Thorne that the Cauchy initial value problem in the presence of a wormhole `time machine' is classically `ill-posed' (far too m...
Control of Cauchy System for an Elliptic Operator
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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.
Angular processes related to Cauchy random walks
Cammarota, Valemtina
2011-01-01
We study the angular process related to random walks in the Euclidean and in the non-Euclidean space where steps are Cauchy distributed. This leads to different types of non-linear transformations of Cauchy random variables which preserve the Cauchy density. We give the explicit form of these distributions for all combinations of the scale and the location parameters. Continued fractions involving Cauchy random variables are analyzed. It is shown that the $n$-stage random variables are still Cauchy distributed with parameters related to Fibonacci numbers. This permits us to show the convergence in distribution of the sequence to the golden ratio.
A note on stability and Cauchy time functions
Sánchez, Miguel
2013-01-01
Since the solution of the so-called folk problems of smoothability, there has been a special interest in the properties of classical time and volume functions of spacetimes, among them the recent references arXiv:1108.5120v3 and arXiv:1301.2909v1 . Here we supply some information that completes the one provided in these two papers and discuss some results. As an illustration, we show that any Cauchy temporal function for a globally hyperbolic spacetime remains Cauchy temporal for close metrics - which, in particular, implies stability for global hyperbolicity.
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....
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曾有栋; 陈祖墀
2002-01-01
本文研究奇异半线性抛物方程ut-Δu+V1(x)u=V2(x)up,x∈Rn＼{0},t＞0的Cauchy问题解的存在性.这里,V1(x),V2(x)可以在原点具有奇性.利用Kato类函数和Green tight函数及不动点定理证明了问题存在正的奇异解,它在原点具有奇性.%In this paper we consider the Cauchy problem for the singular semilinear parabolic equation ut-Δu+V1(x)u=V2(x)up,x∈Rn＼{0},t＞0, where V1(x),V2(x) may have singularities at the origin. Using functions of the Kato class and the Green tight functions we got the existence of the positive solution being singular at the origin.
Complex integration and Cauchy's theorem
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
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 ...
Cauchy problem for derivors in finite dimension
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Jean-Francois Couchouron
2001-05-01
Full Text Available In this paper we study the uniqueness of solutions to ordinary differential equations which fail to satisfy both accretivity condition and the uniqueness condition of Nagumo, Osgood and Kamke. The evolution systems considered here are governed by a continuous operators $A$ defined on $mathbb{R}^N$ such that $A$ is a derivor; i.e., $-A$ is quasi-monotone with respect to $(mathbb{R}^{+}^N$.
The origins of Cauchy's rigorous calculus
Grabiner, Judith V
2005-01-01
This text examines the reinterpretation of calculus by Augustin-Louis Cauchy and his peers in the 19th century. These intellectuals created a collection of well-defined theorems about limits, continuity, series, derivatives, and integrals. 1981 edition.
Institute of Scientific and Technical Information of China (English)
刘转转
2011-01-01
在概率论中,求解形如E[φ(X)] -1/(√2πσ)∫-∞+∞φ(x)e-(x-μ)2/(2σ2)ds的积分是很重要的.但即使φ(x)是初等函数如xn,ems,sinmx等,用常规的分部积分法也不易处理.而1维热传导方程初值问题有形如前面的积分解和含有微分算子的级数解,由解的唯一性将把这类期望的积分运算转化为含有微分的级数运算.通过举例说明了该方法在求解数字特征、特征函数等方面的简便实用性,并以公式形式给出了xn,ems,sinmx等解析函数的期望.最后作为补充,给出了n维类似的结论.%In probability theory, the integral such asE [ψ(X) ] =1 -Γ2πσ∫+∞-∞ ψ(x)e-(x-n)2-2σ2 dx is very important,but it is not easy to solve it by using integration by parts, though ψ( x) is the elementary function such asxn, emx , smmx,etc. The solution of the Cauchy problem of one-dimension heat equation has two forms: the integral as E[ψ> (X) ] which was mentioned and the progression with differential operator. Because of the unique of the solution, integral oper-ation can be changed into differential operation. The formulas will be easily given in the form of examples about n-umerical characteristic and characteristic function, etc, when ψ( x) is the elementary function such as xn, emx, sinmx, and the product of them. Finally, the theory of re-dimension heat equation will be given.
Analytic capacity, rectifiability, menger curvature and the Cauchy integral
Pajot, Hervé
2002-01-01
Based on a graduate course given by the author at Yale University this book deals with complex analysis (analytic capacity), geometric measure theory (rectifiable and uniformly rectifiable sets) and harmonic analysis (boundedness of singular integral operators on Ahlfors-regular sets). In particular, these notes contain a description of Peter Jones' geometric traveling salesman theorem, the proof of the equivalence between uniform rectifiability and boundedness of the Cauchy operator on Ahlfors-regular sets, the complete proofs of the Denjoy conjecture and the Vitushkin conjecture (for the latter, only the Ahlfors-regular case) and a discussion of X. Tolsa's solution of the Painlevé problem.
External Field QED on Cauchy Surfaces
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.
Higher-order Laplace equations and hyper-Cauchy distributions
Orsingher, Enzo
2012-01-01
In this paper we introduce new distributions which are solutions of higher-order Laplace equations. It is proved that their densities can be obtained by folding and symmetrizing Cauchy distributions. Another class of probability laws related to higher-order Laplace equations is obtained by composing pseudo-processes with positively-skewed Cauchy distributions which produce asymmetric Cauchy densities in the odd-order case. A special attention is devoted to the third-order Laplace equation where the connection between the Cauchy distribution and the Airy functions is obtained and analyzed.
Homogenization of a Cauchy continuum towards a micromorphic continuum
Hütter, Geralf
2017-02-01
The micromorphic theory of Eringen and Mindlin, including special cases like strain gradient theory or Cosserat theory, is widely used to model size effects and localization phenomena. The heuristic construction of such theories based on thermodynamic considerations is well-established. However, the identification of corresponding constitutive laws and of the large number of respective constitutive parameters limits the practical application of such theories. In the present contribution, a closed procedure for the homogenization of a Cauchy continuum at the microscale towards a fully micromorphic continuum is derived including explicit definitions of all involved generalized macroscopic stress and deformation measures. The boundary value problem to be solved on the microscale is formulated either for using static or kinematic boundary conditions. The procedure is demonstrated with an example.
Cauchy-Schwartz Inequality and Time Entanglement Witness%Cauchy-Schwartz不等式与时间纠缠判据
Institute of Scientific and Technical Information of China (English)
颜辉
2011-01-01
在量子光学中,利用Cauchy-Schwartz不等式可以定义不同性质的光场,从经典光场到量子光场,甚至单光子场;但是Cauchy-Schwartz不等式却不能描述时间纠缠光子对,也就是说并不是违反Cauchy-Sehwartz不等式的双光子态都是时间纠缠态.本文系统介绍Cauchy-Schwartz不等式、时间纠缠判据,以及两者的关系.
Proof of linear instability of the Reissner-Nordstr\\"om Cauchy horizon under scalar perturbations
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...
A generalized Cauchy process and its application to relaxation phenomena
Energy Technology Data Exchange (ETDEWEB)
Lim, S C [Faculty of Engineering, Multimedia University, 63100 Cyberjaya, Selangor (Malaysia); Li Ming [School of Information Science and Technology, East China Normal University, Shanghai 200026 (China)
2006-03-24
We study some of the basic properties of a generalized Cauchy process indexed by two parameters. The application of the Lamperti transformation to the generalized Cauchy process leads to a self-similar process which preserves the long-range dependence. The asymptotic properties of spectral density of the process are derived. Possible application of this process to model relaxation phenomena is considered.
THE COLLOCATION METHODS FOR SINGULAR INTEGRAL EQUATIONS WITH CAUCHY KERNELS
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
This paper applies the singular integral operators,singular quadrature operators and discretization matrices associated withsingular integral equations with Cauchy kernels, which are established in [1],to give a unified framework for various collocation methods of numericalsolutions of singular integral equations with Cauchy kernels. Under theframework, the coincidence of the direct quadrature method and the indirectquadrature method is very simple and obvious.
Application of geometric algebra to electromagnetic scattering the Clifford-Cauchy-Dirac technique
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...
Self-accelerating Massive Gravity: Superluminality, Cauchy Surfaces and Strong Coupling
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...
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.
On resolution to Wu's conjecture on Cauchy function's exterior singularities
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Theodore Yaotsu Wu
2011-01-01
This is a series of studies on Wu's conjecture and on its resolution to be presented herein. Both are devoted to expound all the comprehensive properties of Cauchy's function f(z) (z = x + iy) and its integral J[∫(z)] = (2πi)-1 φ f(t)(t - z)-1dt taken along the unit circle as contour C, inside which (the open domain D+)f(z) is regular but has singularities distributed in open domain Doutside C. Resolution is given to the inverse problem that the singularities of f(z) can be determined in analytical form in terms of the values f(t) of f(z) numerically prescribed on C (｜t｜ = 1), as so enunciated by Wu's conjecture. The case of a single singularity is solved using complex algebra and analysis to acquire the solution structure for a standard reference. Multiple singularities are resolved by reducing them to a single one by elimination in principle, for which purpose a general asymptotic method is developed here for resolution to the conjecture by induction, and essential singularities aretreated with employing the generalized Hilbert transforms.These new methods are applicable to relevant problems in mathematics, engineering and technology in analogy with resolving the inverse problem presented here.
Radiative transfer in plane-parallel media and Cauchy integral equations III. The finite case
Rutily, Bernard; Chevallier, Loïc
2006-01-01
We come back to the Cauchy integral equations occurring in radiative transfer problems posed in finite, plane-parallel media with light scattering taken as monochromatic and isotropic. Their solution is calculated following the classical scheme where a Cauchy integral equation is reduced to a couple of Fredholm integral equations. It is expressed in terms of two auxiliary functions $\\zeta_+$ and $\\zeta_-$ we introduce in this paper. These functions show remarkable analytical properties in the complex plane. They satisfy a simple algebraic relation which generalizes the factorization relation of semi-infinite media. They are regular in the domain of the Fredholm integral equations they satisfy, and thus can be computed accurately. As an illustration, the X- and Y-functions are calculated in the whole complex plane, together with the extension in this plane of the so-called Sobouti's functions.
Estimation and Control for Linear Systems with Additive Cauchy Noise
2013-12-17
1 0 −1 0 −5 −10 1 0.5 0 −0.5 −1 1 0 −1 0.2 0 −0.2 20 0 −20 −40 −60 0 20 40 60 80 100 Time Steps (k) (a) Cauchy N oise ...Simulation 1 0 −1 0 20 40 60 80 100 Time Steps (k) (b) Gaussian N oise Simulation Figure 1: Cauchy and Kalman Estimators for a stable system
Construction of Involution Cauchy-Hadamard Type MDS Matrices%对合Cauchy-Hadamard型MDS矩阵的构造
Institute of Scientific and Technical Information of China (English)
崔霆; 金晨辉
2010-01-01
MDS矩阵和对合MDS矩阵在分组密码中有广泛应用.该文将考察同时是Hadamard矩阵和Cauchy矩阵的那些MDS矩阵,给出了这类矩阵的结构、构造方法和个数,从而得到了MDS矩阵一种新的构造方法.该文还证明了Cauchy-Hadamard型MDS矩阵都等效于对合的Cauchy-Hadamard型MDS矩阵,并给出了由Cauchy-Hadamard型MDS矩阵构造对合的Cauchy-Hadamard型MDS矩阵的方法.
Robinson manifolds and Cauchy-Riemann spaces
Trautman, A
2002-01-01
A Robinson manifold is defined as a Lorentz manifold (M, g) of dimension 2n >= 4 with a bundle N subset of C centre dot TM such that the fibres of N are maximal totally null and there holds the integrability condition [Sec N, Sec N] subset of Sec N. The real part of N intersection N-bar is a bundle of null directions tangent to a congruence of null geodesics. This generalizes the notion of a shear-free congruence of null geodesics (SNG) in dimension 4. Under a natural regularity assumption, the set M of all these geodesics has the structure of a Cauchy-Riemann manifold of dimension 2n - 1. Conversely, every such CR manifold lifts to many Robinson manifolds. Three definitions of a CR manifold are described here in considerable detail; they are equivalent under the assumption of real analyticity, but not in the smooth category. The distinctions between these definitions have a bearing on the validity of the Robinson theorem on the existence of null Maxwell fields associated with SNGs. This paper is largely a re...
Fast multi-swarm optimization based-on Cauchy mutation and crossover operation
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
The standard particle swarm optimization (PSO) algorithm is a novel evolutionary algorithm in which each particle studies its own previous best solution and the group's previous best solutions to optimization problems. One problem in PSO is its tendency of trapping into local optima. In this paper, a multi-swarm technique based on fast particle swarm optimization (FPSO) algorithm is proposed by introducing crossover operation. FPSO is global search algorithm which can prevent PSO from trapping into local optima in light of Cauchy mutation. Though it can get high optimizing precision, the convergence rate is not satisfactory. FMSO can not only find satisfying solutions, but also speed up the search.
Parameters Identification for an Abstract Cauchy Problem by Quasilinearization
1989-10-01
if in addition ’ is of bounded variation on (-r,01, then DF(q) satisfies (1111). -12- Proof: Let A = max lakI and IhI = max IhkI Then we obtain the...zero as q 4 q* and (H8) holds. If ’ is of bounded variation on I-r,0, then y and ; are of bounded variation on {-r,TI. By 115, Theorem 2.1.7(b)] this...4.5) satisfies (1110). Moreover, if in addition u is of bounded variation on [0,T], then DG(q) satisfies (H13). Proof: Using (4.5) in place of (4.4
Lectures on Cauchy's problem in linear partial differential equations
Hadamard, Jacques
2003-01-01
Would well repay study by most theoretical physicists."" - Physics Today""An overwhelming influence on subsequent work on the wave equation."" - Science Progress""One of the classical treatises on hyperbolic equations."" - Royal Naval Scientific ServiceDelivered at Columbia University and the Universities of Rome and Zürich, these lectures represent a pioneering investigation. Jacques Hadamard based his research on prior studies by Riemann, Kirchhoff, and Volterra. He extended and improved Volterra's work, applying its theories relating to spherical and cylindrical waves to all normal hyperbol
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.
Cauchy problem as a two-surface based `geometrodynamics'
Rácz, István
2014-01-01
Four-dimensional spacetimes foliated by a two-parameter family of homologous two-surfaces are considered in Einstein's theory of gravity. By combining a 1+(1+2) decomposition, the canonical form of the spacetime metric and a suitable specification of the conformal structure of the foliating two-surfaces a gauge fixing is introduced. It is shown that, in terms of the chosen geometrically distinguished variables, the 1+3 Hamiltonian and momentum constraints can be recast into the form of a parabolic equation and a first order symmetric hyperbolic system, respectively. Initial data to this system can be given on one of the two-surfaces foliating the three-dimensional initial data surface. The 1+3 reduced Einstein's equations are also determined. By combining the 1+3 momentum constraint with the reduced system of the secondary 1+2 decomposition a mixed hyperbolic-hyperbolic system is formed. It is shown that solutions to this mixed hyperbolic-hyperbolic system are also solutions to the full set of Einstein's equa...
Area theorem and smoothness of compact Cauchy horizons
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.
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.
Can a particle detector cross a Cauchy horizon?
Juárez-Aubry, Benito A
2015-01-01
Cauchy horizons are well known to exhibit instabilities in classical spacetime dynamics and singularities in quantum field theory. We analyse the response of an Unruh-DeWitt particle detector that falls towards a Cauchy horizon, in terms of the specifics of the horizon, the choice of the quantum state and the specifics of the detector's trajectory. As a prototype, we study in detail the case for the $1+1$ Reissner-Nordstr\\"om black hole with a scalar field in the Hartle-Hawking state. Comparisons are made with the response of a detector that falls into a Schwarzschild-like singularity.
ON CAUCHY-POMPEIU FORMULA FOR FUNCTIONS WITH VALUES IN A UNIVERSAL CLIFFORD ALGEBRA
Institute of Scientific and Technical Information of China (English)
无
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].
Institute of Scientific and Technical Information of China (English)
刘柏鑫; 任婷婷
2016-01-01
研究三维不可压双流体MHD方程Cauchy问题，给出该问题在小初值条件下解的整体存在性结果。%This paper deals with the Cauchy pronlems of 3D two-fluid MHD model. The global well-posedness is obtained under the two-fluid MHD model.
Nested iterations and strengthened Cauchy-Bunyakowski-Schwarz inequalities.
J.H. Brandts; S. Korotov; M. Krizek
2004-01-01
ABSTRACT: It is known that in one, two, and three spatial dimensions, the optimal constant in the strengthened Cauchy-Bunyakowski-Schwarz (CBS) inequality for the Laplacian for red-refined linear finite element spaces, takes values zero, $\\half\\sqrt{2}$ and $\\half\\sqrt{3}$, respectively. In this pap
Modified Mixed Lagrangian-Eulerian Method Based on Numerical Framework of MT3DMS on Cauchy Boundary.
Suk, Heejun
2016-07-01
MT3DMS, a modular three-dimensional multispecies transport model, has long been a popular model in the groundwater field for simulating solute transport in the saturated zone. However, the method of characteristics (MOC), modified MOC (MMOC), and hybrid MOC (HMOC) included in MT3DMS did not treat Cauchy boundary conditions in a straightforward or rigorous manner, from a mathematical point of view. The MOC, MMOC, and HMOC regard the Cauchy boundary as a source condition. For the source, MOC, MMOC, and HMOC calculate the Lagrangian concentration by setting it equal to the cell concentration at an old time level. However, the above calculation is an approximate method because it does not involve backward tracking in MMOC and HMOC or allow performing forward tracking at the source cell in MOC. To circumvent this problem, a new scheme is proposed that avoids direct calculation of the Lagrangian concentration on the Cauchy boundary. The proposed method combines the numerical formulations of two different schemes, the finite element method (FEM) and the Eulerian-Lagrangian method (ELM), into one global matrix equation. This study demonstrates the limitation of all MT3DMS schemes, including MOC, MMOC, HMOC, and a third-order total-variation-diminishing (TVD) scheme under Cauchy boundary conditions. By contrast, the proposed method always shows good agreement with the exact solution, regardless of the flow conditions. Finally, the successful application of the proposed method sheds light on the possible flexibility and capability of the MT3DMS to deal with the mass transport problems of all flow regimes.
Prestack AVA inversion of exact Zoeppritz equations based on modified Trivariate Cauchy distribution
Zhou, Lin; Li, Jingye; Chen, Xiaohong; Liu, Xingye; Chen, Li
2017-03-01
Obtaining interlayer weak reflection information that helps identify properties and accurate density information from complex and elusive reservoirs is particularly important for reservoir characterization and detection. However, conventional prestack amplitude variation with incidence angle inversion method is strongly influenced by the accuracy of the approximate Zoeppritz equations, which suppresses weak reflections coming from the commonly used prior distribution. In this paper, we address these problems by using exact Zoeppritz equations. First, the objective function of the inverse problem was constructed and the modified Cauchy distribution was introduced as the prior information by utilizing Bayes' theorem. In the complicated objective function, the forward operators are the sophisticated and nonlinear Zoeppritz equations with respect to estimate parameters. We then combined the idea of generalized linear inversion with iterative reweighed least-squares algorithm in order to solve the problem. Generalized linear inversion was used to solve the objective function, from which a nonlinear solution of the model parameters' perturbations can be calculated. The iterative reweighed least-squares algorithm was applied to solve the nonlinear expression in an attempt to obtain an updated iterative formula of the model parameters. Therefore the prestack amplitude variation with incidence angle inversion was able to be performed in order to better characterize a reservoir. Both synthetic and field data examples show that the new method can not only directly inverse P-wave velocity, S-wave velocity and density, but also provides accurate estimation results, particularly for density. The introduction of the modified Trivariate Cauchy prior constraints effectively estimated and inverted elastic parameters of weak reflections. Both examples demonstrated the feasibility and effectiveness of the proposed method.
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.
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.
Cauchy-perturbative matching and outer boundary conditions computational studies
Rezzolla, L; Matzner, R A; Rupright, M E; Shapiro, S L; Rezzolla, Luciano; Abrahams, Andrew M; Matzner, Richard A.; Rupright, Mark E.; Shapiro, Stuart L.
1999-01-01
We present results from a new technique which allows extraction of gravitational radiation information from a generic three-dimensional numerical relativity code and provides stable outer boundary conditions. In our approach we match the solution of a Cauchy evolution of the nonlinear Einstein field equations to a set of one-dimensional linear equations obtained through perturbation techniques over a curved background. We discuss the validity of this approach in the case of linear and mildly nonlinear gravitational waves and show how a numerical module developed for this purpose is able to provide an accurate and numerically convergent description of the gravitational wave propagation and a stable numerical evolution.
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%.
Cauchy pdf modelling and its application to SAR image despeckling
Institute of Scientific and Technical Information of China (English)
Chen Guozhong; Liu Xingzhao
2008-01-01
Synthetic aperture radar(SAR)imagery is a kind of coherent system that produces a random pattern,named speckle,which degrades the merit of SAR images and affects their further application seriously.Therefore,how to restore SAR image from the speckle has become a necessary step in post-processing of image.A new despeckling method is putforth on the basis of wavelet.First.a new approach on the basis of"second kind statistics"is used to estimate the dispersion parameter of the Cauchy distribution.Then,this Cauchy prior is applied to model the distribution of the wavelet coefficients for the log-transformed reflectance of SAR image.Based on the above ideas,a new homomorphic wavelet-based maximum a posterior(MAP)despeckling method is proposed.Finally,the simulated speckled image and the real SAR image are used to verify our proposed method and the results show that it outperforms the other methods in terms of the speckle reduction and the feature retention.
Cauchy-perturbative matching revisited: tests in spherical symmetry
Zink, B L; Pazos, E; Tiglio, M; Diener, Peter; Pazos, Enrique; Tiglio, Manuel; Zink, Burkhard
2006-01-01
During the last few years progress has been made on several fronts making it possible to revisit Cauchy-perturbative matching (CPM) in numerical relativity in a more robust and accurate way. This paper is the first in a series where we plan to analyze CPM in the light of these new results. Here we start by testing high-order summation-by-parts operators, penalty boundaries and contraint-preserving boundary conditions applied to CPM in a setting that is simple enough to study all the ingredients in great detail: Einstein's equations in spherical symmetry, describing a black hole coupled to a massless scalar field. We show that with the techniques described above, the errors introduced by Cauchy-perturbative matching are very small, and that very long term and accurate CPM evolutions can be achieved. Our tests include the accretion and ring-down phase of a Schwarzschild black hole with CPM, where we find that the discrete evolution introduces, with a low spatial resolution of \\Delta r = M/10, an error of 0.3% a...
MATCHING PURSUITS AMONG SHIFTED CAUCHY KERNELS IN HIGHER-DIMENSIONAL SPACES
Institute of Scientific and Technical Information of China (English)
钱涛; 王晋勋; 杨燕
2014-01-01
Appealing to the Clifford analysis and matching pursuits, we study the adaptive decompositions of functions of several variables of finite energy under the dictionaries con-sisting of shifted Cauchy kernels. This is a realization of matching pursuits among shifted Cauchy kernels in higher-dimensional spaces. It offers a method to process signals in arbitrary dimensions.
Hyperelastic bodies under homogeneous Cauchy stress induced by non-homogeneous finite deformations
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.
Signaling, Entanglement, and Quantum Evolution Beyond Cauchy Horizons
Yurtsever, U; Yurtsever, Ulvi; Hockney, George
2005-01-01
Consider a bipartite entangled system half of which falls through the event horizon of an evaporating black hole, while the other half remains coherently accessible to experiments in the exterior region. Beyond complete evaporation, the evolution of the quantum state past the Cauchy horizon cannot remain unitary, raising the questions: How can this evolution be described as a quantum map, and how is causality preserved? What are the possible effects of such nonstandard quantum evolution maps on the behavior of the entangled laboratory partner? More generally, the laws of quantum evolution under extreme conditions in remote regions (not just in evaporating black-hole interiors, but possibly near other naked singularities and regions of extreme spacetime structure) remain untested by observation, and might conceivably be non-unitary or even nonlinear, raising the same questions about the evolution of entangled states. The answers to these questions are subtle, and are linked in unexpected ways to the fundamenta...
Differential geometric formulation of the Cauchy Navier equations
Schadt, Frank
2011-01-01
The paper presents a reformulation of some of the most basic entities and equations of linear elasticity - the stress and strain tensor, the Cauchy Navier equilibrium equations, material equations for linear isotropic bodies - in a modern differential geometric language using differential forms and lie derivatives. Similar steps have been done successfully in general relativity, quantum physics and electrodynamics and are of great use in those fields. In Elasticity Theory, however, such a modern differential geometric approach is much less common. Furthermore, existing reformulations demand a vast knowledge of differential geometry, including nonstandard entities such as vector valued differential forms and the like. This paper presents a less general but more easily accessible approach to using modern differential geometry in elasticity theory than those published up to now.
Spectral Cauchy Characteristic Extraction of strain, news and gravitational radiation flux
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...
Energy Technology Data Exchange (ETDEWEB)
Philipp, M; Vergnat, C; Mueller, U; Sanctuary, R; Baller, J; Krueger, J K [Laboratoire de Physique des Materiaux, Universite du Luxembourg, 162A, avenue de la Faiencerie, L-1511 Luxembourg (Luxembourg); Possart, W [Fachbereich Werkstoffwissenschaften, Universitaet des Saarlandes, D-66123 Saarbruecken (Germany); Alnot, P [LPMI, Universite Nancy (France)], E-mail: martine.philipp@uni.lu
2009-01-21
The non-equilibrium process of polymerization of reactive polymers can be accompanied by transition phenomena like gelation or the chemical glass transition. The sensitivity of the mechanical properties at hypersonic frequencies-including the generalized Cauchy relation-to these transition phenomena is studied for three different polyurethanes using Brillouin spectroscopy. As for epoxies, the generalized Cauchy relation surprisingly holds true for the non-equilibrium polymerization process and for the temperature dependence of polyurethanes. Neither the sol-gel transition nor the chemical and thermal glass transitions are visible in the representation of the generalized Cauchy relation. Taking into account the new results and combining them with general considerations about the elastic properties of the isotropic state, an improved physical foundation of the generalized Cauchy relation is proposed.
Analysis of linear waves near the Cauchy horizon of cosmological black holes
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.
Philipp, M; Vergnat, C; Müller, U; Sanctuary, R; Baller, J; Possart, W; Alnot, P; Krüger, J K
2009-01-21
The non-equilibrium process of polymerization of reactive polymers can be accompanied by transition phenomena like gelation or the chemical glass transition. The sensitivity of the mechanical properties at hypersonic frequencies-including the generalized Cauchy relation-to these transition phenomena is studied for three different polyurethanes using Brillouin spectroscopy. As for epoxies, the generalized Cauchy relation surprisingly holds true for the non-equilibrium polymerization process and for the temperature dependence of polyurethanes. Neither the sol-gel transition nor the chemical and thermal glass transitions are visible in the representation of the generalized Cauchy relation. Taking into account the new results and combining them with general considerations about the elastic properties of the isotropic state, an improved physical foundation of the generalized Cauchy relation is proposed.
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...
Who Gave you the Cauchy-Weierstrass Tale? The Dual History of Rigorous Calculus
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.
Institute of Scientific and Technical Information of China (English)
PING Yun-Xia; LIU Lie; ZHANG Chao-Min; CHENG Ze
2011-01-01
Violations of Bell inequality, Cauchy-Schwarz inequality and entanglement in a two-mode three-level atomic system are investigated. It is shown that there are some states, which are entangled but do not violate Bell inequality in this system. Moreover, the relations of violations of Bell inequality, Cauchy-Schwarz inequality, and entanglement are discussed in detail.
Fixed Points of Non-expansive Operators on Weakly Cauchy Normed Spaces
Directory of Open Access Journals (Sweden)
Sahar M. Ali
2007-01-01
Full Text Available We proved the existence of fixed points of non-expansive operators defined on weakly Cauchy spaces in which parallelogram law holds, the given normed space is not necessarily be uniformly convex Banach space or Hilbert space, we reduced the completeness and the uniform convexity assumptions which imposed on the given normed space.
Elcoro, Luis; Etxebarria, Jesus
2011-01-01
The requirement of rotational invariance for lattice potential energies is investigated. Starting from this condition, it is shown that the Cauchy relations for the elastic constants are fulfilled if the lattice potential is built from pair interactions or when the first-neighbour approximation is adopted. This is seldom recognized in widely used…
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.
Riemann boundary value problem for hyperanalytic functions
Directory of Open Access Journals (Sweden)
Ricardo Abreu Blaya
2005-01-01
Full Text Available We deal with Riemann boundary value problem for hyperanalytic functions. Furthermore, necessary and sufficient conditions for solvability of the problem are derived. At the end the explicit form of general solution for singular integral equations with a hypercomplex Cauchy kernel in the Douglis sense is established.
Cn中Cauchy-Stieltjes积分及其乘子的性质%Properties of Cauchy-Stieltjes Integrals and Their Multipliers
Institute of Scientific and Technical Information of China (English)
罗太元; 董新汉
2005-01-01
讨论了n维复空间Cn中Cauchy-Stieltjes积分Fnp及其乘子Mnp的一些性质.通过对Mnp中函数f的径向导数Rf(z)的积分平均估计,证明了Mnp中的函数f是有界的.讨论了同一测度在不同乘子空间的积分之间的联系,从而得到Fnp的一个遗传性质.利用Cn中Dirichlet空间Dnq范数的积分表示证明了Fnp与Dnq的包含关系.
Smith, H. V.
2008-01-01
A method is derived for the numerical evaluation of the error term arising in some Gauss-type formulae modified so as to approximate Cauchy Principal Value integrals. The method uses Chebyshev polynomials of the first kind. (Contains 1 table.)
Energy Technology Data Exchange (ETDEWEB)
Philipp, M; Mueller, U; Jimenez Rioboo, R J; Baller, J; Sanctuary, R; Krueger, J K [Laboratoire de Physique des Materiaux, University of Luxembourg, 162A avenue de la Faiencerie, L-1511 Luxembourg (Luxembourg); Possart, W [Fachbereich Werkstoffwissenschaften, Universitaet des Saarlandes, D-66123 Saarbruecken (Germany)], E-mail: martine.philipp@uni.lu
2009-02-15
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.
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...
Efficient video sequence matching using the Cauchy function and the modified Hausdorff distance
Kim, Sang Hyun; Park, Rae-Hong
2001-12-01
To manipulate large video databases, effective video indexing and retrieval are required. While most algorithms for video retrieval can be commonly used for frame-wise user query or video content query, video sequence matching has not been investigated much. In this paper, we propose an efficient algorithm to match the video sequences using the Cauchy function of histograms between successive frames and the modified Hausdorff distance. To effectively match the video sequences and to reduce the computational complexity, we use the key frames extracted by the cumulative measure, and compare the set of key frames using the modified Hausdorff distance. Experimental results show that the proposed video sequence matching algorithms using the Cauchy function and the modified Hausdorff distance yield the high accuracy and performances compared with conventional algorithms such as histogram difference and directed divergence methods.
Generalized Radar 4-COORDINATES and Equal-Time Cauchy Surfaces for Arbitrary Accelerated Observers
Alba, David; Lusanna, Luca
All existing 4-coordinate systems centered on the world-line of an accelerated observer are only locally defined, as for Fermi coordinates both in special and general relativity. As a consequence, it is not known how non-inertial observers can build equal-time surfaces which (a) correspond to a conventional observer-dependent definition of synchronization of distant clocks, and (b) are good Cauchy surfaces for Maxwell equations. Another type of coordinate singularities generating the same problems are those connected to the relativistic rotating coordinate systems used in the treatment of the rotating disk and the Sagnac effect. We show that the use of Hamiltonian methods based on 3+1 splittings of space-time allows one to define as many observer-dependent globally defined radar 4-coordinate systems as nice foliations of space-time with space-like hyper-surfaces admissible according to Møller (for instance, only the differentially rotating relativistic coordinate system, but not the rigidly rotating ones of non-relativistic physics, are allowed). All these conventional notions of an instantaneous 3-space for an arbitrary observer can be empirically defined by introducing generalizations of the Einstein ½ convention for clock synchronization in inertial frames. Each admissible 3+1 splitting has two naturally associated congruences of time-like observers: as a consequence every 3+1 splitting gives rise to non-rigid non-inertial frames centered on any one of these observers. Only for Eulerian observers are the simultaneity leaves orthogonal to the observer world-line. When there is a Lagrangian description of an isolated relativistic system, its reformulation as a parametrized Minkowski theory allows one to show that all the admissible synchronization conventions are gauge equivalent, as also happens in the canonical metric and tetrad gravity, where, however, the chrono-geometrical structure of space-time is dynamically determined. The framework developed in this
Codomains for the Cauchy-Riemann and Laplace operators in ℝ2
Directory of Open Access Journals (Sweden)
Lloyd Edgar S. Moyo
2008-01-01
Full Text Available A codomain for a nonzero constant-coefficient linear partial differential operator P(∂ with fundamental solution E is a space of distributions T for which it is possible to define the convolution E*T and thus solving the equation P(∂S=T. We identify codomains for the Cauchy-Riemann operator in ℝ2 and Laplace operator in ℝ2 . The convolution is understood in the sense of the S′-convolution.
On the Existence of a Maximal Cauchy Development for the Einstein Equations - a Dezornification
Sbierski, Jan
2013-01-01
In 1969, Choquet-Bruhat and Geroch established the existence of a unique maximal globally hyperbolic Cauchy development of given initial data for the Einstein equations. Their proof, however, has the unsatisfactory feature that it relies crucially on the axiom of choice in the form of Zorn's lemma. In this paper we present a proof that avoids the use of Zorn's lemma. In particular, we provide an explicit construction of this maximal globally hyperbolic development.
A Subspace Embedding Method in L2 Norm via Fast Cauchy Transform
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Xu Xiang
2013-01-01
Full Text Available We propose a subspace embedding method via Fast Cauchy Transform (FCT in L2 norm. It is motivated by and complements the work of the subspace embedding method in Lp norm, for all p∈[1,∞] except p = 2, by K. L. Clarkson (ACM-SIAM, 2013. Unlike the traditionally used orthogonal basis in Johnson-Lindenstrauss (JL embedding, we employ the well-conditioned basis in L2 norm to obtain concentration property of FCT in L2 norm.
Local stability of the Pexiderized Cauchy and Jensen's equations in fuzzy spaces
Directory of Open Access Journals (Sweden)
Kang Jung Im
2011-01-01
Full Text Available Abstract Lex X be a normed space and Y be a Banach fuzzy space. Let D = {(x, y ∈ X × X : ||x|| + ||y|| ≥ d} where d > 0. We prove that the Pexiderized Jensen functional equation is stable in the fuzzy norm for functions defined on D and taking values in Y. We consider also the Pexiderized Cauchy functional equation. 2000 Mathematics Subject Classification: 39B22; 39B82; 46S10.
Cauchy's almost forgotten Lagrangian formulation of the Euler equation for 3D incompressible flow
Frisch, Uriel
2014-01-01
Two prized papers, one by Augustin Cauchy in 1815, presented to the French Academy and the other by Hermann Hankel in 1861, presented to G\\"ottingen University, contain major discoveries on vorticity dynamics whose impact is now quickly increasing. Cauchy found a Lagrangian formulation of 3D ideal incompressible flow in terms of three invariants that generalize to three dimensions the now well-known law of conservation of vorticity along fluid particle trajectories for two-dimensional flow. This has very recently been used to prove analyticity in time of fluid particle trajectories for 3D incompressible Euler flow and can be extended to compressible flow, in particular to cosmological dark matter. Hankel showed that Cauchy's formulation gives a very simple Lagrangian derivation of the Helmholtz vorticity-flux invariants and, in the middle of the proof, derived an intermediate result which is the conservation of the circulation of the velocity around a closed contour moving with the fluid. This circulation the...
Directory of Open Access Journals (Sweden)
Schümann Kerstin
2016-09-01
Full Text Available Thermoplastic polymers exhibit non-isochoric behaviour during tensile and compression testing as well as particular deformations like local necking (tension or buckling (compression. A method for the determination of Cauchy stresses from tensile and compression tests is presented, that considers the actual deformations of the test specimens. The exact geometry of the specimens in the respective present configuration is determined in photographs, which are taken continuously throughout the test. The engineering stresses at several time points are converted into Cauchy stresses using newly developed formulas in consideration of the actual specimen geometry. For validation finite element analyses of the tensile and compression tests are performed using the identified stress-strain curves. The numerical results show good agreement with the experiments for the tested polymers. Thus a method for conversion of engineering to Cauchy stresses in tensile and compression tests could be established considering the non-isochoric deformation in plasticity. With this method “true” stress-strain curves as input for finite element material models can be identified for arbitrary materials.
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.
The Cauchy problem for the 3-D Vlasov-Poisson system with point charges
Marchioro, Carlo; Pulvirenti, Mario
2010-01-01
In this paper we establish global existence and uniqueness of the solution to the three-dimensional Vlasov-Poisson system in presence of point charges in case of repulsive interaction. The present analysis extends an analogeous two-dimensional result by Caprino and Marchioro [On the plasma-charge model, to appear in Kinetic and Related Models (2010)].
MAXIMAL SUBSPACES FOR SOLUTIONS OF THE SECOND ORDER ABSTRACT CAUCHY PROBLEM
Institute of Scientific and Technical Information of China (English)
无
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.
Directory of Open Access Journals (Sweden)
Andrei Perjan
2009-07-01
Full Text Available We study the behavior of solutions to perturbed second order abstract evolution equations in Hilbert spaces, when the small parameter, multiplying the second order time derivative, converges to zero.
THE CAUCHY PROBLEM FOR A CLASS OF COUPLED SYSTEMS CONTAINING A CONVOLUTION OPERATOR
Institute of Scientific and Technical Information of China (English)
杨成荣; 伍卓群
2003-01-01
Some results on the invariant regions ,existence and uniqueness of solutions to a class of integrodifferential systems are established. Applying these results to integrodifferential systems with a small parameter e ＞ 0, we obtain,in particular, some estimates of solutions uniform in ε＞ 0.
Directory of Open Access Journals (Sweden)
K. Balachandran
2006-09-01
Full Text Available In this paper we prove the existence of mild and strong solutions of nonlinear time varying delay integrodifferential equations of Sobolev type with nonlocal conditions in Banach spaces. The results are obtained by using the theory of compact semigroups and Schaefer's fixed point theorem.
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.
The Cauchy Problem for the 3-D Vlasov-Poisson System with Point Charges
Marchioro, Carlo; Miot, Evelyne; Pulvirenti, Mario
2011-07-01
In this paper we establish global existence and uniqueness of the solution to the three-dimensional Vlasov-Poisson system in the presence of point charges with repulsive interaction. The present analysis extends an analogous two-dimensional result (Caprino and Marchioro in Kinet. Relat. Models 3(2):241-254, 2010).
100 great problems of elementary mathematics their history and solution
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.
Directory of Open Access Journals (Sweden)
Yekini Shehu
2010-01-01
real Banach space which is also uniformly smooth using the properties of generalized f-projection operator. Using this result, we discuss strong convergence theorem concerning general H-monotone mappings and system of generalized mixed equilibrium problems in Banach spaces. Our results extend many known recent results in the literature.
Symmetries of 2-lattices and second order accuracy of the Cauchy--Born Model
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.
Cauchy-Matern Model of Sea Surface Wind Speed at the Lake Worth, Florida
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Ming Li
2012-01-01
Full Text Available We study the Cauchy-Matern (CM process with long-range dependence (LRD. The closed form of its power spectrum density (PSD function is given. We apply it to model the autocovariance function (ACF and the PSD of the sea surface wind speed (wind speed for short observed in the Lake Worth, Florida, over the 1984–2006 period. The present results exhibit that the wind speed at the Lake Worth over 1984–2006 is of LRD. The present results exhibit that the CM process may yet be a novel model to fit the wind speed there.
On the Direct Cauchy Theorem in Widom Domains: Positive and Negative Examples
Yuditskii, Peter
2010-01-01
We discuss several questions which remained open in our joint work with M. Sodin "Almost periodic Jacobi matrices with homogeneous spectrum, infinite-dimensional Jacobi inversion, and Hardy spaces of character--automorphic functions". In particular, we show that there exists a non-homogeneous set $E$ such that the Direct Cauchy Theorem (DCT) holds in the Widom domain $\\bbC\\setminus E$. On the other hand we demonstrate that the weak homogeneity condition on $E$ (introduced recently by Poltoratski and Remling) does not ensure that DCT holds in the corresponding Widom domain.
Otra demostración de la desigualdad de Cauchy- Schwarz
Directory of Open Access Journals (Sweden)
Javier MARTÍN LALANDA
2009-12-01
Full Text Available En todo espacio euclideo E, en el que se haya definido una norma se verifica la siguiente desigualdad, conocida con el nombre Desigualdad de Cauchy-Schwarz. Para el modo usual en que se suele demostrar esta desigualdad, se parte de uno de los axiomas asociados a la definición de producto interno, aquel que dice que el producto interno de todo vector por sí mismo es siempre un número real, mayor o igual que cero
A boundary value problem for hypermonogenic functions in Clifford analysis
Institute of Scientific and Technical Information of China (English)
QIAO; Yuying
2005-01-01
This paper deals with a boundary value problem for hypermonogenic functions in Clifford analysis. Firstly we discuss integrals of quasi-Cauchy's type and get the Plemelj formula for hypermonogenic functions in Clifford analysis, and then we address Riemman boundary value problem for hypermonogenic functions.
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.
Riemann Boundary Value Problems for Koch Curve
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Zhengshun Ruanand
2012-11-01
Full Text Available In this study, when L is substituted for Koch curve, Riemann boundary value problems was defined, but generally speaking, Cauchy-type integral is meaningless on Koch curve. When some analytic conditions are attached to functions G (z and g (z, through the limit function of a sequence of Cauchytype integrals, the homogeneous and non-homogeneous Riemann boundary problems on Koch curve are introduced, some similar results was attained like the classical boundary value problems for analytic functions.
The Cauchy-Lagrangian method for numerical analysis of Euler flow
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...
Application of Cauchy wavelet transformation to identify time-variant modal parameters of structures
Huang, C. S.; Liu, C. Y.; Su, W. C.
2016-12-01
This work proposes a procedure for accurately identifying instantaneous modal parameters of a linear time-varying system using a time-varying autoregressive with exogenous input (TVARX) model with the continuous Cauchy wavelet transform (CCWT). An appropriate TVARX model is established using the velocity and displacement responses of the system under consideration. The time-varying coefficients of the TVARX are expanded as piecewise polynomial functions. CCWTs with various scale parameters are then applied to the TVARX model to evaluate the instantaneous modal parameters of different modes. The CCWTs of the velocity and displacement responses are analytically obtained from the CCWT of the measured acceleration responses. The effectiveness and accuracy of the proposed procedure are validated by numerical simulations of single and multiple degrees of freedom systems that have periodically varying and sharply varying stiffness and damping coefficients. The effects of noise, the Cauchy wavelet function and the order of the polynomial on the evaluation of the modal parameters are explored in processing the numerically simulated acceleration responses of systems with a single degree of freedom subjected to base excitation. Finally, the proposed procedure is adopted to determine the modal parameters of a five-story symmetric steel frame from its measured acceleration responses in a shaking table test. The measured strains reveal the yielding of columns in the first story. The variations of the identified instantaneous natural frequencies and modal damping ratios with time are consistent with the physical phenomena that are observed from the measured strains and base excitation acceleration.
一个广义的Cauchy型的Taylor公式%A Taylor's Formula of Generalized Cauchy Type
Institute of Scientific and Technical Information of China (English)
苏翃; 赵振华; 董建
2009-01-01
给出了一个高阶导数形式的、广义的Cauchy型的Taylor公式,它将数学分析中一阶微分形式的Cauchy中值定理推广到高阶导数形式,同时它也是Taylor中值定理的推广.%Taylor's formula of having the form of higher order derivative and generalized Cauchy type is obtained, which extends Cauchy's mean-value theorem of differential form of first order in mathematical analysis to the form of higher order derivative, and is the spread of Taylor's mean-value theorem.
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].
Giorgio, Ivan
2016-08-01
In order to design the microstructure of metamaterials showing high toughness in extension (property to be shared with muscles), it has been recently proposed (Dell'Isola et al. in Z Angew Math Phys 66(6):3473-3498, 2015) to consider pantographic structures. It is possible to model such structures at a suitably small length scale (resolving in detail the interconnecting pivots/cylinders) using a standard Cauchy first gradient theory. However, the computational costs for such modelling choice are not allowing for the study of more complex mechanical systems including for instance many pantographic substructures. The microscopic model considered here is a quadratic isotropic Saint-Venant first gradient continuum including geometric nonlinearities and characterized by two Lamé parameters. The introduced macroscopic two-dimensional model for pantographic sheets is characterized by a deformation energy quadratic both in the first and second gradient of placement. However, as underlined in Dell'Isola et al. (Proc R Soc Lond A 472(2185):20150790, 2016), it is needed that the second gradient stiffness depends on the first gradient of placement if large deformations and large displacements configurations must be described. The numerical identification procedure presented in this paper consists in fitting the macro-constitutive parameters using several numerical simulations performed with the micro-model. The parameters obtained by the best fit identification in few deformation problems fit very well also in many others, showing that the reduced proposed model is suitable to get an effective model at relevantly lower computational effort. The presented numerical evidences suggest that a rigorous mathematical homogenization result most likely holds.
Goursat problem for the Yang-Mills-Vlasov system in temporal gauge
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Marcel Dossa
2011-12-01
Full Text Available This article studies the characteristic Cauchy problem for the Yang-Mills-Vlasov (YMV system in temporal gauge, where the initial data are specified on two intersecting smooth characteristic hypersurfaces of Minkowski spacetime $(mathbb{R}^{4},eta $. Under a $mathcal{C}^{infty }$ hypothesis on the data, we solve the initial constraint problem and the evolution problem. Local in time existence and uniqueness results are established thanks to a suitable combination of the method of characteristics, Leray's Theory of hyperbolic systems and techniques developed by Choquet-Bruhat for ordinary spatial Cauchy problems related to (YMV systems.
Institute of Scientific and Technical Information of China (English)
无
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.
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.
Different glassy states, as indicated by a violation of the generalized Cauchy relation
Energy Technology Data Exchange (ETDEWEB)
Krueger, J K [Laboratoire Europeen de Recherche Universitaire Saarland-Lorraine (LERUSL), Universitaet des Saarlandes, Fakultaet fuer Physik und Elektrotechnik 7.2, Gebaeude 38, D-66041 Saarbruecken (Germany); Britz, T [Laboratoire Europeen de Recherche Universitaire Saarland-Lorraine (LERUSL), Universitaet des Saarlandes, Fakultaet fuer Physik und Elektrotechnik 7.2, Gebaeude 38, D-66041 Saarbruecken (Germany); Coutre, A le [Laboratoire Europeen de Recherche Universitaire Saarland-Lorraine (LERUSL), Universitaet des Saarlandes, Fakultaet fuer Physik und Elektrotechnik 7.2, Gebaeude 38, D-66041 Saarbruecken (Germany); Baller, J [Laboratoire Europeen de Recherche Universitaire Saarland-Lorraine (LERUSL), Universitaet des Saarlandes, Fakultaet fuer Physik und Elektrotechnik 7.2, Gebaeude 38, D-66041 Saarbruecken (Germany); Possart, W [Universitaet des Saarlandes, Fakultaet fuer Chemie, Pharmazie und Werkstoffwissenschaften 8.15, Gebaeude 22, D-66041 Saarbruecken (Germany); Alnot, P [Laboratoire Europeen de Recherche Universitaire Saarland-Lorraine (LERUSL), Universitaet des Saarlandes, Fakultaet fuer Physik und Elektrotechnik 7.2, Gebaeude 38, D-66041 Saarbruecken (Germany); Sanctuary, R [Centre Universitaire de Luxembourg, Departement des Sciences, Laboratoire 1.19, 162a Avenue de la Faiencerie, L-1511, Luxembourg (Luxembourg)
2003-07-01
Using Brillouin spectroscopy as a probe for high-frequency clamped acoustic properties, a shear modulus c{sub 44}{sup {infinity}} can be measured in addition to the longitudinal modulus c{sub 11}{sup {infinity}} already well above the thermal glass transition. On slow cooling of the liquid through the thermal glass transition temperature T{sub g}, both moduli show a kink-like behaviour and the function c{sub 11}{sup {infinity}} = c{sub 11}{sup {infinity}}(c{sub 44}{sup {infinity}}) follows a generalized Cauchy relation (gCR) defined by the linear relation c{sub 11}{sup {infinity}} = 3c{sub 44}{sup {infinity}} + constant, which completely hides the glass transition. In this work we show experimentally that on fast cooling this linear transformation becomes violated within the glassy state, but that thermal ageing drives the elastic coefficients towards the gCR, i.e. towards a unique glassy state.
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.
Explicit solutions of generalized Cauchy-Riemann systems using the transplant operator
Kravchenko, Vladislav V
2009-01-01
In [8] it was shown that the transplant operator transforms solutions of one Vekua equation into solutions of another Vekua equation, related to the first via a Schr\\"odinger equation. In this paper we demonstrate a fundamental property of this operator: it transforms formal powers of the first Vekua equation into formal powers of the same order for the second Vekua equation. This property allows us to obtain positive formal powers and a generating sequence of a "complicated" Vekua equation from positive formal powers and a generating sequence of "simpler" Vekua equation. Similar results is obtained regarding construction of Cauchy kernels. Elliptic and hyperbolic pseudoanalytic function theory are considered and examples are given to illustrate the procedure.
Dechoum, K; Khoury, A Z; 10.1103/PhysRevA.83.063843
2011-01-01
We analyze the three-mode correlation properties of the electromagnetic field in a optical parametric oscillator below threshold. We employ a perturbative expansion of the It\\^o equations derived from the positive-P representation of the density matrix. Using the generalized Cauchy-Schwarz inequality, we investigate the genuine quantum nature of the triple correlations between the interacting fields, since in this case continuous variable entanglement is not detected by the van Loock-Furusawa criterion [Phys. Rev. A {\\bf 67}, 052315 (2003)]. Although not being a necessary condition, these triple correlations are a sufficient evidence of tripartite entanglement. Of course, our characterization of the quantum correlations is applicable to non-Gaussian states, which we show to be the case of the optical parametric oscillator below threshold, provided nonlinear quantum fluctuations are properly taken into account.
Institute of Scientific and Technical Information of China (English)
时统业; 周本虎
2006-01-01
设f(x),g(x)均在[a,b]上可积,则Cauchy-Schwarz不等式可加强为:[∫baf(x)g(x)dx]2 ≤∫baf2(x)dx∫ba g2(x)dx + 2/b-a∫ba f(x)g(x)dx∫ba f(x)d(x)∫ba g(x)dx - 1/b-a∫ba f2(x)dx ·[∫ba g(x)dx]2-1/b-a∫ba g2(x)dx[∫ba f(x)dx]2.由此推广了文[1]结果
An Analysis of Surface Relaxation in the Surface Cauchy--Born Model
Jayawardana, K; Ortner, C; Park, H S
2011-01-01
The Surface Cauchy-Born (SCB) method is a computational multi-scale method for the simulation of surface-dominated crystalline materials. We present an error analysis of the SCB method, focused on the role of surface relaxation. In a linearized 1D model we show that the error committed by the SCB method is O(1) in the mesh size; however, we are able to identify an alternative "approximation parameter" - the stiffness of the interaction potential - with respect to which the error in the mean strain is exponentially small. Our analysis naturally suggests an improvement of the SCB model by enforcing atomistic mesh spacing in the normal direction at the free boundary.
Modelling mortality of a stored grain insect pest with fumigation: probit, logistic or Cauchy model?
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.
THE NONLOCAL INITIAL PROBLEMS OF A SEMILINEAR EVOLUTION EQUATION
Institute of Scientific and Technical Information of China (English)
王远弟; 冉启康
2004-01-01
The purpose of this paper is to investigate the existence of solutions to a nonlocal Cauchy problem for an evolution equation. The methods used here include the abstract semigroup methods in proper spaces and Schauder's theorem.And the abstract results are applied to a system of nonlinear partial differential equations with nonlinear boundary conditions.
N{sup ±}-integrals and boundary values of Cauchy-type integrals of finite measures
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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)
Poisson kernel and Cauchy formula of a non-symmetric transitive domain
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In 1965, Lu Yu-Qian discovered that the Poisson kernel of the homogenous domain S m,p,q={Z∈Cm×m, Z1∈Cm×p,Z2 ∈Cq×m|2i1( Z-Z+)-Z1Z1′-Z2′Z2>0} does not satisfy the Laplace-Beltrami equation associated with the Bergman metric when S m,p,q is not symmetric. However the map T0:Z→Z, Z1→Z1 , Z2→Z2 transforms S m,p,q into a domain S I (m, m + p + q) which can be mapped by the Cayley transformation into the classical domains R I (m, m + p + q). The pull back of the Bergman metric of R I (m, m + p + q) to S m,p,q is a Riemann metric ds 2 which is not a Khler metric and even not a Hermitian metric in general. It is proved that the Laplace-Beltrami operator associated with the metric ds 2 when it acts on the Poisson kernel of S m,p,q equals 0. Consequently, the Cauchy formula of S m,p,q can be obtained from the Poisson formula.
Generalized Moisil-Théodoresco Systems and Cauchy Integral Decompositions
Directory of Open Access Journals (Sweden)
Ricardo Abreu Blaya
2008-01-01
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−.
Institute of Scientific and Technical Information of China (English)
高浩; 吴冬梅; 丁洁
2012-01-01
Comparing with the other optimization algorithms, particle swarm optimization (PSO)has the merits of fast convergence rata and easy application, but the results of research have shown that the PSO has the shortcoming that it is easily be trapped into local optimum. A quantum-behaved particle swarm optimization with Cauchy mutation (CQPSO) is presented. The results of experiment show that the new algorithm not only accelerate the global search ability but also accelerate the convergence rate of the PSO, so it can be applied in engineering optimization problems.%和其他优化算法相比，粒子群算法有着简单易实现以及寻优结果快的优点，但研究结果表明标准粒子群算法在优化过程中存在着易于陷入最小的缺陷。文章提出了一种基于Cauchy策略的量子-粒子群算法。标准测试函数的仿真结果表明，新的算法不仅能够提高算法的全局搜索能力，而且能够加快算法的寻优速度，能够应用在实际工程中的函数优化问题。
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.
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).
Cavalcanti, Marcelo M.; Corrêa, Wellington J.; Domingos Cavalcanti, Valéria N.; Tebou, Louis
2017-02-01
In this paper, we study the existence at the H1-level as well as the stability for the damped defocusing Schrödinger equation in Rd. The considered damping coefficient is time-dependent and may vanish at infinity. To prove the existence, we employ the method devised by Özsarı, Kalantarov and Lasiecka [27], which is based on monotone operators theory. In particular, when d = 1 or d = 2, we obtain the uniqueness. Decay estimates for the L2-level and (H1 ∩L p + 2)-level energies are established with the help of direct multipliers method, coupled with refined energy estimates and a lower semi-continuity argument.
基于高阶Cauchy-Born准则的单壁碳纳米管本构模型%A higher order Cauchy-Born rule based constitutive model of SWNT
Institute of Scientific and Technical Information of China (English)
郭旭; 王晋宝; 张洪武
2005-01-01
提出了一种基于高阶Cauchy-Born准则建立单壁碳纳米管本构模型的方法.通过引入高阶变形梯度,合理地修正了传统Cauchy-Born准则在描述纳米管变形几何关系时所存在的缺陷.利用原子间相互作用势以及能量等效原理,得到了基于广义连续介质模型的单壁碳纳米管的本构关系.由此得到的本构参数不仅与变形梯度张量F,而且与其梯度 F相关,因此是一种广义连续介质模型.利用这样的本构模型,本文还对单壁碳纳米管的杨氏模量进行了预测,并与采用其他方法得到的结果进行了对比,从而证实了所提出方法的有效性.
LogCauchy, log-sech and lognormal distributions of species abundances in forest communities
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
Elementary proof of Cauchy integral theorem%柯西积分定理的初等证明
Institute of Scientific and Technical Information of China (English)
王信松; 张节松
2011-01-01
利用数学分析的知识构造一个简单的恒同逼近函数,由此用分析中的逼近思想,成功地用满足柯西-黎曼条件的连续可微的函数逼近一般的可微函数,给出了柯西积分定理的一个初等证明,克服了复变函数论中这一关键性定理证明繁琐或者超纲的困难.%In this paper, a simple identity approximation function was constructed by using the knowledge of mathematic analysis, thereby, applying the approximation idea in analysis, we successfully obtained that ordinary differential functions were well approximated by continuously differentiable functions satisfying the Cauchy-Riemann equations, and an elementary proof of Cauchy integral theorem was presented, which overcame some troublesome or over-syllabus difficulties in the proof of the theorem in the text of complex variable functions, and was also beneficial to the teaching.
Institute of Scientific and Technical Information of China (English)
A.Kanoune; N.Mehidi
2008-01-01
We analyze the exponential decay property of solutions of the semilinear wave equation in bounded domain Q of RN with a damping term which is effective on the exterior of a ball and boundary conditions of the Cauchy-ventcel type.Under suitable and natural assumptions on the nonlinearity,we prove that the exponential decay holds locally uniformly for finite energy solutions provided the nonlinearity is subcritical at infinity.Subcriticality means,roughly speaking,that the nonlinearity grows at infinity at most as a power P＜5.The results obtained in R3 and RN by B.Dehman,G.Lebeau and E.Zuazua on the inequalities of the classical energv(which estimate the total energy of solutions in terms of the energy localized in the exterior of a ball)and on Strichartz's estimates,allow us to give an application to the stabilization controllability of the semilinear wave equation in a bounded domain of RN with a subcritical nonlinearity on the domain and its boundary,and conditions on the boundary of Cauchy-Vlentcel type.
Some improperly posed problems of mathematical physics
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...
Uniqueness of Bounded Variation Solutions of Cauchy Systems Involving Parameter%含参量Cauchy系统有界变差解的唯一性
Institute of Scientific and Technical Information of China (English)
马学敏; 李宝麟; 林长伟
2013-01-01
By using Henstock-Kurzweil integral, uniqueness of bounded variation solutions of Cauchy systems involving parameter is discussed in the condition of generalization of ω.%利用Henstock-Kurzweil积分，在ω较弱的条件下，讨论了含参量Cauchy系统有界变差解的唯一性。
On $L^1$ extremal problem for entire functions
Yuditskii, Peter
2012-01-01
We generalized the Korkin-Zolotarev theorem to the case of entire functions having the smallest $L^1$ norm on a system of intervals $E$. If $\\bbC\\setminus E$ is a domain of Widom type with the Direct Cauchy Theorem we give an explicit formula for the minimal deviation. Important relations between the problem and the theory of canonical systems with reflectionless resolvent functions are shown.
Gerr, S
1982-01-01
An attempt is made to draw an analogy between contour drawing and a particular mathematical theorem. The analogy is seen to depend on the fact that both methods use definite values along a contour to imply a totality of values within the contour; thus, the use of a part to suggest the whole, by way of a hypothetical 'gestalt-like integration' in the case of the art contour, and the usual process of mathematical integration in the case of Cauchy's formula. Examples illustrating the analogy are drawn from a wide range of artistic work: a modern American drawing, a Cro-Magnon cave painting, and two Chinese works. The traditional Chinese philosophy of painting is invoked in support of the analogy because of its explicit emphasis on the primacy of outline drawing in Chinese painting. Some speculations are offered on further development and application of the analogy.
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.
Sucesión convergente y sucesión de Cauchy : equivalencia matemática y equivalencia fenomenológica
Claros Mellado, Francisco Javier; Sánchez Compaña, María Teresa; Coriat Benarroch, Moisés
2013-01-01
Esta investigación está enmarcada por la Fenomenología, el Pensamiento Matemático Avanzado y los Sistemas de Representación; en ella estudiamos una equivalencia fenomenológica, junto a la conocida equivalencia matemática, entre sucesión convergente y sucesión de Cauchy. Enunciamos dos fenómenos organizados por definiciones de límite finito de una sucesión y de sucesión de Cauchy; con el apoyo de libros de texto de secundaria, reconocemos en los libros de texto españoles dos fenómenos organiza...
Nal, P L
2002-01-01
We consider the asymptotic stability and the boundedness with probability one of solutions of linear lto stochastic differential equations not reduced to the Cauchy form and give some numerical examples to show that our sufficient conditions for the asymptotic stability with probability one of solutions are more general and more effective than those of Korenevskij and Mitropoloshij. Moreover, our results can also be applied to the case when the unperturbed linear deterministic system is not assumed to be stable.
On explicit and numerical solvability of parabolic initial-boundary value problems
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Lepsky Olga
2006-01-01
Full Text Available A homogeneous boundary condition is constructed for the parabolic equation in an arbitrary cylindrical domain ( being a bounded domain, and being the identity operator and the Laplacian which generates an initial-boundary value problem with an explicit formula of the solution . In the paper, the result is obtained not just for the operator , but also for an arbitrary parabolic differential operator , where is an elliptic operator in of an even order with constant coefficients. As an application, the usual Cauchy-Dirichlet boundary value problem for the homogeneous equation in 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.
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.
Zhang, L. W.; Ademiloye, A. S.; Liew, K. M.
In normal physiological and healthy conditions, red blood cells (RBCs) deform readily as they pass through the microcapillaries and the spleen, however, upon invasion by the malaria parasite, the host RBC membrane begins to lose their deformability. In spite of the progress in understanding malaria pathogenesis, the primary mechanism responsible for the loss of deformability remains unclear. In this paper, we examine the effects of Plasmodium falciparum infection and maturation on the deformability of parasitized or infected red blood cells (iRBCs) by means of a three-dimensional (3D) multiscale red blood cell (RBC) framework. This multiscale framework is developed based on the Cauchy-Born rule and the meshfree IMLS-Ritz method. The atomistic scale strain energy density function of the RBC membrane was computed using a selected representative cell based on the membrane spectrin network. The results obtained from our numerical simulations affirm that the presence of malaria infection significantly increases the rigidity of RBC membrane. It was observed that in the trophozoite and schizont infection stages, biconcave cell geometry leads to better prediction than nearly spherical geometry in comparison with experimental studies. Furthermore, we confirm that increase in temperature also results to increased stiffening of the cell membrane. Lastly, the observed decrease in the deformability of iRBC membrane may be primarily due to the structural remodeling and changes in the microstructure of the membrane rather than the change in cell shape.
Quantization of area for event and Cauchy horizons of the Kerr-Newman black hole
Visser, Matt
2012-01-01
Based on various string theoretic constructions, there have been repeated suggestions that the areas of black hole event horizons should be quantized in a quite specific manner, involving linear combinations of square roots of natural numbers. It is important to realise the significant physical limitations of such proposals when one attempts to extend them outside their original framework. Specifically, in their most natural and direct physical interpretations, these specific proposals for horizon areas fail for the ordinary Kerr-Newman black holes in (3+1) dimensions, essentially because the fine structure constant is not an integer. A more baroque interpretation involves asserting the fine structure constant is the square root of a rational number; but such a proposal has its own problems. Insofar as one takes (3+1) general relativity (plus the usual quantization of angular momentum and electric charge) as being paramount, the known explicitly calculable spectra of horizon areas for the physically compellin...
Validity of the Cauchy-Born rule applied to discrete cellular-scale models of biological tissues
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
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.
Initial data problems for the two-component Camassa-Holm system
Directory of Open Access Journals (Sweden)
Xiaohuan Wang
2014-06-01
Full Text Available This article concerns the study of some properties of the two-component Camassa-Holm system. By constructing two sequences of solutions of the two-component Camassa-Holm system, we prove that the solution map of the Cauchy problem of the two-component Camassa-Holm system is not uniformly continuous in $H^s(\\mathbb{R}$, $s>5/2$.
Approximations of the operator exponential in a periodic diffusion problem with drift
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Pastukhova, Svetlana E [Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University), Moscow (Russian Federation)
2013-02-28
A Cauchy problem for a parabolic diffusion equation with 1-periodic coefficients containing first order terms is studied. For the corresponding semigroup we construct approximations in the L{sup 2}-operator norm on sections t=const of order O(t{sup -m/2}) as t{yields}{infinity} for m=1 or m=2. The spectral method based on the Bloch representation of an operator with periodic coefficients is used. Bibliography: 25 titles.
Energy Technology Data Exchange (ETDEWEB)
Mehta, Sheetal, E-mail: smehta-29@yahoo.com; Das, Kallol, E-mail: smehta-29@yahoo.com; Keller, Jag Mohan, E-mail: smehta-29@yahoo.com [Department of Physics, St. Aloysius College (Autonomous), Jabalpur-482001, Madhya Pradesh, India and Department of Physics and Electronics, Rani Durgawati University, Jabalpur-482001, Madhya Pradesh (India)
2014-04-24
Poly (methyl methacrylate) / Polystyrene and iodine / selenium hybrid matrixes have been prepared and characterized. Refractive index measurements were done at 390, 535, 590, 635 nm wavelengths. Abbe's number and Cauchy's constants of the iodine / selenium doped poly (methylmethacrylate) and polystyrene samples are being reported. The results also showed that the refractive index of the composite varies non-monotonically with the doping concentration at low iodine concentration or in the region of nanoparticles formation and is also dependent on thermal annealing.
关于柯西sn-对称空间的一个注记%A Note on Cauchy sn-Symmetric Spaces
Institute of Scientific and Technical Information of China (English)
陈内萍
2013-01-01
It is proved that a space is a Cauchy sn-symmetric space if and only if it has a sn-devel-opment consisting of cs-covers ( or sn-covers) if and only if it is a sequence-covering π-image of a metric space .%证明了一个空间是柯西sn-对称空间当且仅当它有一个由cs-复盖或sn-复盖组成sn-展开当且仅当它是度量空间的序列复盖π映射。
Stability of the Cauchy-Jensen Functional Equation in CÃ¢ÂˆÂ—-Algebras: A Fixed Point Approach
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Jong Su An
2008-06-01
Full Text Available we prove the Hyers-Ulam-Rassias stability of CÃ¢ÂˆÂ—-algebra homomorphisms and of generalized derivations on CÃ¢ÂˆÂ—-algebras for the following Cauchy-Jensen functional equation 2f((x+y/2+z=f(x+f(y+2f(z, which was introduced and investigated by Baak (2006. The concept of Hyers-Ulam-Rassias stability originated from the stability theorem of Th. M. Rassias that appeared in (1978.
关于Cauchy型积分与Fourier积分的研究%On the Investigation with Cauchy Type Integral and Fourier Integral
Institute of Scientific and Technical Information of China (English)
李平润
2014-01-01
利用复分析中推广的Cauchy留数定理与奇异积分方程中的Plemelj 公式，首次给出了 Cauchy型积分与 Fourier积分之间的关系，并得出了单侧的 Fourier积分的性质，然后给予证明。%In this paper,by using the Residue theorem and Plemelj formula,the relation of Cauchy type integral and Fourier integral is given,and the properties of the one-sided Fourier integral are proved.
Computational experiment on the numerical solution of some inverse problems of mathematical physics
Vasil'ev, V. I.; Kardashevsky, A. M.; Sivtsev, PV
2016-11-01
In this article the computational experiment on the numerical solution of the most popular linear inverse problems for equations of mathematical physics are presented. The discretization of retrospective inverse problem for parabolic equation is performed using difference scheme with non-positive weight multiplier. Similar difference scheme is also used for the numerical solution of Cauchy problem for two-dimensional Laplace equation. The results of computational experiment, performed on model problems with exact solution, including ones with randomly perturbed input data are presented and discussed.
Multidimensional integral representations problems of analytic continuation
Kytmanov, Alexander M
2015-01-01
The monograph is devoted to integral representations for holomorphic functions in several complex variables, such as Bochner-Martinelli, Cauchy-Fantappiè, Koppelman, multidimensional logarithmic residue etc., and their boundary properties. The applications considered are problems of analytic continuation of functions from the boundary of a bounded domain in C^n. In contrast to the well-known Hartogs-Bochner theorem, this book investigates functions with the one-dimensional property of holomorphic extension along complex lines, and includes the problems of receiving multidimensional boundary analogs of the Morera theorem. This book is a valuable resource for specialists in complex analysis, theoretical physics, as well as graduate and postgraduate students with an understanding of standard university courses in complex, real and functional analysis, as well as algebra and geometry.
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.
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Wei Sun
2013-01-01
problem in Sobolev spaces is developed firstly. The solution is represented in the form of the combined angular potential and single-layer potential. The final integral equations do not contain hypersingular integrals. Uniqueness and existence of the solution to the equations are proved. The weakly singular and Cauchy singular integral arising in these equations can be computed directly by truncated series of Chebyshev polynomials with their weighting function without approximation. The numerical simulation showing the high accuracy of the scheme is presented.
广义可压缩弹性杆方程的柯西问题%On the Cauchy problem for a generalized compressible elastic rods equation
Institute of Scientific and Technical Information of China (English)
易婷
2014-01-01
A class of nonlinear dispersive equation with Hamiltonian structure is investigated .The equa-tion have the characteristics of Camassa-Holm equation and compressible elastic rod wave equation . Through a priori estimation ,two conservation laws are given .By further studying the properties of strong solutions ,it show s that strong solution blow s up in finite time .%研究一类具有哈密顿结构的非线性扩散方程，此类方程具有Camassa-Holm方程和可压缩弹性杆波动方程的特点。通过对此方程进行先验估计，得到两个守恒量。进一步研究此类方程强解的性质，可知强解在有限的时间内爆破。
Choquet-Bruhat, Yvonne; Martín-García, José M
2010-01-01
We prove that analytic initial data on a light cone arising from a metric satisfying a "near-roundness" condition near the vertex lead to a solution of the vacuum Einstein equations to the future of the light-cone.
一类积微分方程(组)的Cauchy问题%The Cauchy Problem for a Class of Intergrodifferential Equations
Institute of Scientific and Technical Information of China (English)
杨成荣
2000-01-01
The existence, uniqueness of bounded and continuous solutions of a class of integrodifferential equations and some estimates of solutions are established. Applying these results to integrodifferential systems with a small parameter ε>0, we obtain, in particular, some estimates of solutions uniform in ε.
Problems in classical potential theory with applications to mathematical physics
Lundberg, Erik
In this thesis we are interested in some problems regarding harmonic functions. The topics are divided into three chapters. Chapter 2 concerns singularities developed by solutions of the Cauchy problem for a holomorphic elliptic equation, especially Laplace's equation. The principal motivation is to locate the singularities of the Schwarz potential. The results have direct applications to Laplacian growth (or the Hele-Shaw problem). Chapter 3 concerns the Dirichlet problem when the boundary is an algebraic set and the data is a polynomial or a real-analytic function. We pursue some questions related to the Khavinson-Shapiro conjecture. A main topic of interest is analytic continuability of the solution outside its natural domain. Chapter 4 concerns certain complex-valued harmonic functions and their zeros. The special cases we consider apply directly in astrophysics to the study of multiple-image gravitational lenses.
Chang, Chien-Chieh; Chen, Chia-Shyun
2002-06-01
A flowing partially penetrating well with infinitesimal well skin is a mixed boundary because a Cauchy condition is prescribed along the screen length and a Neumann condition of no flux is stipulated over the remaining unscreened part. An analytical approach based on the integral transform technique is developed to determine the Laplace domain solution for such a mixed boundary problem in a confined aquifer of finite thickness. First, the mixed boundary is changed into a homogeneous Neumann boundary by substituting the Cauchy condition with a Neumann condition in terms of well bore flux that varies along the screen length and is time dependent. Despite the well bore flux being unknown a priori, the modified model containing this homogeneous Neumann boundary can be solved with the Laplace and the finite Fourier cosine transforms. To determine well bore flux, screen length is discretized into a finite number of segments, to which the Cauchy condition is reinstated. This reinstatement also restores the relation between the original model and the solutions obtained. For a given time, the numerical inversion of the Laplace domain solution yields the drawdown distributions, well bore flux, and the well discharge. This analytical approach provides an alternative for dealing with the mixed boundary problems, especially when aquifer thickness is assumed to be finite.
Muskhelishvili, N I
2011-01-01
Singular integral equations play important roles in physics and theoretical mechanics, particularly in the areas of elasticity, aerodynamics, and unsteady aerofoil theory. They are highly effective in solving boundary problems occurring in the theory of functions of a complex variable, potential theory, the theory of elasticity, and the theory of fluid mechanics.This high-level treatment by a noted mathematician considers one-dimensional singular integral equations involving Cauchy principal values. Its coverage includes such topics as the Hölder condition, Hilbert and Riemann-Hilbert problem
On a nonlinear elliptic problem with critical potential in R2
Institute of Scientific and Technical Information of China (English)
SHEN; Yaotian; YAO; Yangxin; HEN; Zhihui
2004-01-01
Consider the existence of nontrivial solutions of homogeneous Dirichlet problem for a nonlinear elliptic equation with the critical potential in R2. By establishing a weighted inequality with the best constant, determine the critical potential in R2, and study the eigenvalues of Laplace equation with the critical potential. By the Pohozaev identity of a solution with a singular point and the Cauchy-Kovalevskaya theorem, obtain the nonexistence result of solutions with singular points to the nonlinear elliptic equation. Moreover, for the same problem, the existence results of multiple solutions are proved by the mountain pass theorem.
球面区域上buckling特征值的万有估计%UNIVERSAL BOUNDS ON EIGENVALUES OF THE BUCKLING PROBLEM ON SPHERICAL DOMAINS
Institute of Scientific and Technical Information of China (English)
黄广月; 李兴校; 曹林芬
2011-01-01
We study the eigenvalues of buckling problem on domains in the unit sphere.By introducing a new parameter and using Cauchy inequality,we optimize the inequality obtained by Wang and Xia in[12].%本文研究了球面域上的buckling特征值问题.通过引入新的参数和使用Cauchy不等式,优化了Wang-Xia在文献[1 2]中的不等式.
A solution to Lov\\'asz's Seventeenth problem
Hatami, Hamed
2010-01-01
Many fundamental theorems in extremal graph theory can be expressed as linear inequalities between homomorphism densities. In the language of quantum graphs the validity of a linear inequality between homomorphism densities is equivalent to the positivity of a corresponding quantum graph. Lov\\'asz composed a collection of open problems in this area, and in Problem 17 he asks whether every positive quantum graph can be represented as a sum of squares of labeled quantum graphs. A related question by Razborov asks whether every true linear inequality between homomorphism densities can be proven using certain applications of the Cauchy-Schwarz inequality. We answer both questions in the negative by introducing explicit valid inequalities that do not satisfy the required conditions. Razborov's question and Lov\\'asz's seventeenth problem are both precise instances of a general question of Razborov whether every true linear inequality between homomorphism densities can be proven using a finite amount of manipulation...
De Lacroix a Cauchy: La fundamentación del cálculo infinitesimal en José Mariano Vallejo (1807-1832
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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
Institute of Scientific and Technical Information of China (English)
WANG; Baoxiang(
2001-01-01
［1］Ablowitz, M. J., Haberman, R., Nonlinear evolution equations in two and three dimensions, Phys. Rev. Lett., 1975, 35:1185-1188.［2］Davey, A., Stewartson, K., On three dimensional packets of surface waves, Proc. Roy. Soc. Ser. A, 1974, 338: 101-110.［3］Ghidaglia, J. M., Saut, J. C., On the initial value problem for the Davey-Stewartson systems, Nonlinearity, 1990, 3:475-506.［4］Hayashi, N., Saut, J. C., Global existence of small solutions to the Davey-Stewartson and the Ishimori systems, Diff. Integ.Equation, 1995, 8: 1657-1675.［5］Ohta, M. , Stability of standing waves for the generalized Davey-Stewartson systems, J. Dyn. Diff. Eqs. , 1994, 6: 325-334.［6］Ohta, M., Instability of standing waves for the generalized Davey-Stewartson systems, Ann. Inst. Henri. Poncare Phys. The-or., 1995, 63: 69-80.［7］Ozawa, T., Exact blow-up solutions to the Cauchy problem for the Davey-Stewartson systems, Proc. Roy. Soc. London A,1992, 436: 345-349.［8］Sung, L. Y., Long time decay of the solutions of the Davey-Stewartson Ⅱ equations, J. Nonlinear Sci., 1995, 5: 433-452.［9］Guo, B. L. , Wang, B. X. , The Cauchy problem for the Davey-Stewartson system, Comm. on Pure Appl. Math. , 1999,LII: 1477-1490.［10］Cazenave, T. , Weissler, F. B. , The Cauchy problem for critical nonlinear Schrodinger equations in H ', Nonlinear Anal.TMA, 1990, 14: 807-836.［11］Wang, B. X. , Bessel (Riesz) potentials on Banach function spaces and their applications (Ⅰ) Theory, Acta Math. Sinica,1998, 14: 327-340.［12］Bergh, J., Lofstrom, J., Interpolation Spaces, Berlin: Springer-Verlag, 1976.［13］Triebel, H., Function Space Theory, Basel: Birkhauser-Verlag, 1983.［14］Ginibre, J. , Velo, G. , On the global Cauchy problem for nonlinear Klein-Gordon equations, Math. Z, 1985, 189: 487-505.［15］Wang, B. X. , On existence and scattering for critical and subcritical nonlinear Klein-Gordon equations in H s, Nonlinear .Anal. TMA, 1998, 31: 573-587.
NOVEL REGULARIZED BOUNDARY INTEGRAL EQUATIONS FOR POTENTIAL PLANE PROBLEMS
Institute of Scientific and Technical Information of China (English)
ZHANG Yao-ming; L(U) He-xiang; WANG Li-min
2006-01-01
The universal practices have been centralizing on the research of regularization to the direct boundary integal equations (DBIEs). The character is elimination of singularities by using the simple solutions. However, up to now the research of regularization to the first kind integral equations for plane potential problems has never been found in previous literatures. The presentation is mainly devoted to the research on the regularization of the singular boundaryintegral equations with indirect unknowns. A novel view and idea is presented herein, in which the regularized boundary integral equations with indirect unknowns without including the Cauchy principal value (CPV) and Hadamard-finite-part (HFP) integrals are established for the plane potential problems.With some numerical results, it is shown that the better accuracy and higher efficiency,especially on the boundary, can be achieved by the present system.
Kinsella, John J.
1970-01-01
Discussed are the nature of a mathematical problem, problem solving in the traditional and modern mathematics programs, problem solving and psychology, research related to problem solving, and teaching problem solving in algebra and geometry. (CT)
The Scattering Problem for a Noncommutative Nonlinear Schrödinger Equation
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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.
General theory of spherically symmetric boundary-value problems of the linear transport theory.
Kanal, M.
1972-01-01
A general theory of spherically symmetric boundary-value problems of the one-speed neutron transport theory is presented. The formulation is also applicable to the 'gray' problems of radiative transfer. The Green's function for the purely absorbing medium is utilized in obtaining the normal mode expansion of the angular densities for both interior and exterior problems. As the integral equations for unknown coefficients are regular, a general class of reduction operators is introduced to reduce such regular integral equations to singular ones with a Cauchy-type kernel. Such operators then permit one to solve the singular integral equations by the standard techniques due to Muskhelishvili. We discuss several spherically symmetric problems. However, the treatment is kept sufficiently general to deal with problems lacking azimuthal symmetry. In particular the procedure seems to work for regions whose boundary coincides with one of the coordinate surfaces for which the Helmholtz equation is separable.
Nourazar, S. S.; Nazari-Golshan, A.
2015-01-01
A hybrid of Fourier transform and new modified homotopy perturbation method based on the Adomian method is developed to solve linear and nonlinear partial differential equations. The Taylor series expansion is used to expand nonlinear term of partial differential equation and the Adomian polynomial incorporated into homotopy perturbation method combined with Fourier transform, is used to solve partial differential equations. Three case study problems, partial differential equations, are handled using homotopy perturbation method and Fourier transform modified homotopy perturbation method (FTMHPM). Results obtained are compared with exact solution. The comparison reveals that for same components of recursive sequences, errors associated with Fourier transform modified method are much less than the other and are valid for a large range of x-axis coordinates.
Moment theory and some inverse problems in potential theory and heat conduction
Ang, Dang Dinh; Le, Vy Khoi; Trong, Dang Duc
2002-01-01
Moment Theory is not a new subject; however, in classical treatments, the ill-posedness of the problem is not taken into account - hence this monograph. Assuming a "true" solution to be uniquely determined by a sequence of moments (given as integrals) of which only finitely many are inaccurately given, the authors describe and analyze several regularization methods and derive stability estimates. Mathematically, the task often consists in the reconstruction of an analytic or harmonic function, as is natural from concrete applications discussed (e.g. inverse heat conduction problems, Cauchy's problem for the Laplace equation, gravimetry). The book can be used in a graduate or upper undergraduate course in Inverse Problems, or as supplementary reading for a course on Applied Partial Differential Equations.
An application of the Nash-Moser theorem to the vacuum boundary problem of gaseous stars
Makino, Tetu
2017-01-01
We have been studying spherically symmetric motions of gaseous stars with physical vacuum boundary governed either by the Euler-Poisson equations in the non-relativistic theory or by the Einstein-Euler equations in the relativistic theory. The problems are to construct solutions whose first approximations are small time-periodic solutions to the linearized problem at an equilibrium and to construct solutions to the Cauchy problem near an equilibrium. These problems can be solved when 1 / (γ - 1) is an integer, where γ is the adiabatic exponent of the gas near the vacuum, by the formulation by R. Hamilton of the Nash-Moser theorem. We discuss on an application of the formulation by J.T. Schwartz of the Nash-Moser theorem to the case in which 1 / (γ - 1) is not an integer but sufficiently large.
Institute of Scientific and Technical Information of China (English)
杨宏
2014-01-01
用一种修正的非局部边值问题方法,研究严重不适定修正的Helmholtz方程柯西问题.在对精确解的先验假设和正则化参数的选取下,得到相应的收敛性估计,数值结果表明该方法是稳定可行的.
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.
... you are having balance problems, see your doctor. Balance disorders can be signs of other health problems, such ... cases, treating the illness that is causing the disorder will help with the balance problem. Exercises, a change in diet, and some ...
Directory of Open Access Journals (Sweden)
Muhammad Aslam Noor
2004-01-01
Full Text Available We consider a new class of equilibrium problems, known as hemiequilibrium problems. Using the auxiliary principle technique, we suggest and analyze a class of iterative algorithms for solving hemiequilibrium problems, the convergence of which requires either pseudomonotonicity or partially relaxed strong monotonicity. As a special case, we obtain a new method for hemivariational inequalities. Since hemiequilibrium problems include hemivariational inequalities and equilibrium problems as special cases, the results proved in this paper still hold for these problems.
Stability analysis of the inverse transmembrane potential problem in electrocardiography
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.
Application of a new method of nonlinear dynamical system identification to biochemical problems.
Karnaukhov, A V; Karnaukhova, E V
2003-03-01
The system identification method for a variety of nonlinear dynamic models is elaborated. The problem of identification of an original nonlinear model presented as a system of ordinary differential equations in the Cauchy explicit form with a polynomial right part reduces to the solution of the system of linear equations for the constants of the dynamical model. In other words, to construct an integral model of the complex system (phenomenon), it is enough to collect some data array characterizing the time-course of dynamical parameters of the system. Collection of such a data array has always been a problem. However difficulties emerging are, as a rule, not principal and may be overcome almost without exception. The potentialities of the method under discussion are demonstrated by the example of the test problem of multiparametric nonlinear oscillator identification. The identification method proposed may be applied to the study of different biological systems and in particular the enzyme kinetics of complex biochemical reactions.
Interactions between discontinuities for binary mixture separation problem and hodograph method
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.
An inverse time-dependent source problem for a time-fractional diffusion equation
Wei, T.; Li, X. L.; Li, Y. S.
2016-08-01
This paper is devoted to identifying a time-dependent source term in a multi-dimensional time-fractional diffusion equation from boundary Cauchy data. The existence and uniqueness of a strong solution for the corresponding direct problem with homogeneous Neumann boundary condition are firstly proved. We provide the uniqueness and a stability estimate for the inverse time-dependent source problem. Then we use the Tikhonov regularization method to solve the inverse source problem and propose a conjugate gradient algorithm to find a good approximation to the minimizer of the Tikhonov regularization functional. Numerical examples in one-dimensional and two-dimensional cases are provided to show the effectiveness of the proposed method. This paper was supported by the NSF of China (11371181) and the Fundamental Research Funds for the Central Universities (lzujbky-2013-k02).
Koch曲线上的齐次Riemann边值问题%Homogeneous Riemann Boundary Value Problems for Koch Curve
Institute of Scientific and Technical Information of China (English)
阮正顺; 罗艾花
2012-01-01
当L为典型的分形曲线-Koch曲线时,提出了Riemann边值问题,但在一般情况下,在Koch曲线上所做的Cauchy型积分无意义.当对已知函数G(z),g(z)增加一定的解析条件,同时利用一列Cauchy型积分的极限函数,对定义在Koch曲线上的齐次Riemann边值问题进行了讨论,并得到与经典解析函数边值问题相类似的结果.%In this paper, when Lis substituted for Koch curve, Riemann boundary value problems was defined, but generally speaking, Cauchy-type integral is meaningless on Koch curve. When some analytic conditions are attached to functions G(z)and g(z), through the limit function of a sequence of Cauchy-type integrals, the homogeneous Riemann boundary problems on Koch curve are introduced, some similar results was attained with the classical boundary value problems for analytic functions.
... your legs or feet Movement disorders such as Parkinson's disease Diseases such as arthritis or multiple sclerosis Vision or balance problems Treatment of walking problems depends on the cause. Physical therapy, surgery, or mobility aids may help.
... know the exact cause of your prostate problem. Prostatitis The cause of prostatitis depends on whether you ... prostate problem in men older than age 50. Prostatitis If you have a UTI, you may be ...
The initial value problem of scalar-tensor theories of gravity
Energy Technology Data Exchange (ETDEWEB)
Salgado, Marcelo; Martinez del Rio, David [Instituto de Ciencias Nucleares Universidad Nacional Autonoma de Mexico Apdo. Postal 70-543 Mexico 04510 D.F. (Mexico)
2007-11-15
The initial value problem of scalar-tensor theories of gravity (STT) is analyzed in the physical (Jordan) frame using a 3+1 decomposition of spacetime. A first order strongly hyperbolic system is obtained for which the well posedness of the Cauchy problem can be established. We provide two simple applications of the 3+1 system of equations: one for static and spherically symmetric spacetimes which allows the construction of unstable initial data (compact objects) for which a further black hole formation and scalar gravitational wave emission can be analyzed, and another application is for homogeneous and isotropic spacetimes that permits to study the dynamics of the Universe in the framework of STT.
Directory of Open Access Journals (Sweden)
Terent'eva Elena Olegovna
2013-09-01
Full Text Available Inner and outer Lamb problems are of extreme importance for various applications in geophysics, as these problems are often used for simulation of wave fields accompanying earthquakes. Solutions of the outer Lamb problem of concentrated force impact applied to the free surface of an elastic half-plane are analyzed in this article. Two solutions are compared: the analytical solution obtained in 1984 and the solution obtained in a modern FEM complex Abaqus.
Terent'eva Elena Olegovna
2013-01-01
Inner and outer Lamb problems are of extreme importance for various applications in geophysics, as these problems are often used for simulation of wave fields accompanying earthquakes. Solutions of the outer Lamb problem of concentrated force impact applied to the free surface of an elastic half-plane are analyzed in this article. Two solutions are compared: the analytical solution obtained in 1984 and the solution obtained in a modern FEM complex Abaqus.
Timergaliev, S. N.; Kharasova, L. S.
2016-11-01
Solvability of one system of nonlinear second order partial differential equations with given initial conditions is considered in an arbitrary field. Reduction of the initial system of equations to one nonlinear operator equation is used to study the problem. The solvability is established with the use of the principle of contracting mappings. The method used in these studies is based on the integral representations for the displacements. These representations are constructed with the use of general solutions to the inhomogeneous Cauchy-Riemann equation.
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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.
Energy Technology Data Exchange (ETDEWEB)
Kılıç, Emre, E-mail: emre.kilic@tum.de; Eibert, Thomas F.
2015-05-01
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.
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Skovhus, Randi Boelskifte; Thomsen, Rie
2017-01-01
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 to be" (WPR) approach. Forty-nine…
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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...... to be’ (WPR) approach. Forty-nine empirical studies on Danish youth career guidance were included in the study. An analysis of the issues in focus resulted in nine problem categories. One of these, ‘targeting’, is analysed using the WPR approach. Finally, the article concludes that the WPR approach...... 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....
... 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 ...
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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 (Ã¢ÂˆÂ‚t+IÃ¢ÂˆÂ’ÃŽÂ”u=f in an arbitrary cylindrical domain ÃŽÂ©ÃƒÂ—Ã¢Â„Â (ÃŽÂ©Ã¢ÂŠÂ‚Ã¢Â„Ân being a bounded domain, I and ÃŽÂ” 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 Ã¢ÂˆÂ‚t+IÃ¢ÂˆÂ’ÃŽÂ”, but also for an arbitrary parabolic differential operator Ã¢ÂˆÂ‚t+A, where A is an elliptic operator in Ã¢Â„Ân of an even order with constant coefficients. As an application, the usual Cauchy-Dirichlet boundary value problem for the homogeneous equation (Ã¢ÂˆÂ‚t+IÃ¢ÂˆÂ’ÃŽÂ”u=0 in ÃŽÂ©ÃƒÂ—Ã¢Â„Â 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.
A Problem on the Addition of Residue Classes by Sark?zy%Sark?zy的一个加法剩余类问题
Institute of Scientific and Technical Information of China (English)
杨仕椿; 汤建钢
2013-01-01
The characteristic of the A+B and A+^B,is a difficult topic in number theory and combinatorics,and plays an important and profound role. In this paper,we first noted that under normal circumstances,the answer of a problem on the addition of residue classes by Sark?zy is negative. Secondly,for the mode even number m of irreducible residue system, using Cauchy-Davenport theorem,we give the problem in two preliminary results when m=2 p,2k p(k≥2),where p is a prime number. Finally,we presented some problems and conjectures to be studied.%关于A+B以及A+^B的性质问题,一直是数论与组合数学中的困难课题和重要问题。本文首先指出,在一般情况下,关于Sark?zy的一个加法剩余类猜想的答案是否定的。其次,对于模偶数 m的既约剩余系,利用Cauchy-Davenport定理,给出当m=2p,2kp(k≥2)时该问题的两个初步的结果,这里p为素数。最后,提出一些待研究的问题和猜想。
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...
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 ...
Baronti, Marco; van der Putten, Robertus; Venturi, Irene
2016-01-01
This book, intended as a practical working guide for students in Engineering, Mathematics, Physics, or any other field where rigorous calculus is needed, includes 450 exercises. Each chapter starts with a summary of the main definitions and results, which is followed by a selection of solved exercises accompanied by brief, illustrative comments. A selection of problems with indicated solutions rounds out each chapter. A final chapter explores problems that are not designed with a single issue in mind but instead call for the combination of a variety of techniques, rounding out the book’s coverage. Though the book’s primary focus is on functions of one real variable, basic ordinary differential equations (separation of variables, linear first order and constant coefficients ODEs) are also discussed. The material is taken from actual written tests that have been delivered at the Engineering School of the University of Genoa. Literally thousands of students have worked on these problems, ensuring their real-...
Energy Technology Data Exchange (ETDEWEB)
Plekhanova, Marina V; Fedorov, Vladimir E
2011-04-30
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.
Study of the Navier-Stokes regularity problem with critical norms
Ohkitani, Koji
2016-04-01
We study the basic problems of regularity of the Navier-Stokes equations. The blowup criteria on the basis of the critical {H}1/2-norm, is bounded from above by a logarithmic function, (Robinson et al 2012 J. Math. Phys. 53 115618). Assuming that the Cauchy-Schwarz inequality for the {H}1/2-norm is not an overestimate, we replace it by a square-root of a product of the energy and the enstrophy. We carry out a simple asymptotic analysis to determine the time evolution of the energy. This generalises the (already ruled-out) self-similar blowup ansatz. Some numerical results are also presented, which support the above-mentioned replacement. We carry out a similar analysis for the four-dimensional Navier-Stokes equations.
INVESTIGATION OF STURM-LIOUVILLE PROBLEM SOLVABILITY IN THE PROCESS OF ASYMPTOTIC SERIES CREATION
Directory of Open Access Journals (Sweden)
A. I. Popov
2015-09-01
Full Text Available Subject of Research. Creation of asymptotic expansions for solutions of partial differential equations with small parameter reduces, usually, to consequent solving of the Sturm-Liouville problems chain. To find some term of the series, the non-homogeneous Sturm-Liouville problem with the inhomogeneity depending on the previous term needs to be solved. At the same time, the corresponding homogeneous problem has a non-trivial solution. Hence, the solvability problem occures for the non-homogeneous Sturm-Liouville problem for functions or formal power series. The paper deals with creation of such asymptotic expansions. Method. To prove the necessary condition, we use conventional integration technique of the whole equation and boundary conditions. To prove the sufficient condition, we create an appropriate Cauchy problem (which is always solvable and analyze its solution. We deal with the general case of power series and make no hypotheses about the series convergence. Main Result. Necessary and sufficient conditions of solvability for the non-homogeneous Sturm-Liouville problem in general case for formal power series are proved in the paper. As a particular case, the result is valid for functions instead of formal power series. Practical Relevance. The result is usable at creation of the solutions for partial differential equation in the form of power series. The result is general and is applicable to particular cases of such solutions, e.g., to asymptotic series or to functions (convergent power series.
Institute of Scientific and Technical Information of China (English)
陈淑琴; 詹华税
2011-01-01
考虑抛物-双曲方程:uz+a(x,t)/2.▽xu2=△u+,t＞0,其中α是向量值函数,div α≤0,且u+= max{u,0}.该方程在[u＜0]上是双曲方程,在[u＞0]上是抛物方程.证明了若该方程的熵解在x→∞时不超过线性增长,那么它在加权的空间中解具有稳定性.同时,说明了线性增长条件对于它的解的唯一性成立时已经是最优化的条件了.
Institute of Scientific and Technical Information of China (English)
林建忠; 叶中行
2000-01-01
在金融数学中,用跳跃-扩散型随机微分方程模型描述证券价格过程更为符合实际,讨论了由高维Poisson过程和Brown运动共同驱动的随机微分方程的Feynman-Kac定理.首先建立了高维Poisson过程的两个基本性质,在此基础上,导出了推广的向后热传导方程Cauchy问题解的Feynman-Kac定理.其次,利用Burkholder不等式建立了跳跃-扩散型随机过程的矩不等式,并由此建立了推广的二阶线性抛物型方程Cauchy问题解的Feynman-Kac定理.
Directory of Open Access Journals (Sweden)
Yaping Hu
2015-01-01
the nonsmooth convex optimization problem. First, by using Moreau-Yosida regularization, we convert the original objective function to a continuously differentiable function; then we use approximate function and gradient values of the Moreau-Yosida regularization to substitute the corresponding exact values in the algorithm. The global convergence is proved under suitable assumptions. Numerical experiments are presented to show the effectiveness of this algorithm.
Directory of Open Access Journals (Sweden)
Xin-He Miao
2012-01-01
Full Text Available This paper investigates the Lipschitz continuity of the solution mapping of symmetric cone (linear or nonlinear complementarity problems (SCLCP or SCCP, resp. over Euclidean Jordan algebras. We show that if the transformation has uniform Cartesian P-property, then the solution mapping of the SCCP is Lipschitz continuous. Moreover, we establish that the monotonicity of mapping and the Lipschitz continuity of solutions of the SCLCP imply ultra P-property, which is a concept recently developed for linear transformations on Euclidean Jordan algebra. For a Lyapunov transformation, we prove that the strong monotonicity property, the ultra P-property, the Cartesian P-property, and the Lipschitz continuity of the solutions are all equivalent to each other.
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.
Pikichyan, H. V.
2016-06-01
It is shown that for the nonlinear boundary value problem of determining the radiation field inside a one-dimensional anisotropic medium illuminated from outside at its boundaries on both sides, the formulas for adding layers in semilinear systems of differential equations for radiative transfer, invariant embedding, and total Ambartsumyan invariance can be used to reduce the equations for the problem to separable equations with initial conditions. The fields travelling to the left and right are thereby found independently of one another. In addition, when one of them has been determined, the other can be found directly using an explicit expression. A general equivalence property of operators with respect to a certain mathematical form, expression, or functional is formulated mathematically. New equations, referred to as kinetic equations of equivalency, are derived from the mutual equivalence of the differential operators of the Boltzmann kinetic equation (the equations of radiative transfer) and the functional equation of the Ambartsumian's complete invariance. Besides separability, these new equations also have the property of linearity. Formulas are also introduced for special problems of single sided illumination of a medium that in this case serve as supplementary information in the initial conditions for formulating Cauchy problems.
On the singularities of 3-D Protter's problem for the wave equation
Directory of Open Access Journals (Sweden)
Myron K. Grammatikopoulos
2001-01-01
Full Text Available In this paper we study boundary-value problems for the wave equation, which are three-dimensional analogue of Darboux-problems (or of Cauchy-Goursat problems on the plane. It is shown that for $n$ in $mathbb{N}$ there exists a right hand side smooth function from $C^n(ar{Omega}_{0}$, for which the corresponding unique generalized solution belongs to $C^n(ar{Omega}_{0}ackslash O$, and it has a strong power-type singularity at the point $O$. This singularity is isolated at the vertex $O$ of the characteristic cone and does not propagate along the cone. In this paper we investigate the behavior of the singular solutions at the point $O$. Also, we study more general boundary-value problems and find that there exist an infinite number of smooth right-hand side functions for which the corresponding unique generalized solutions are singular. Some a priori estimates are also stated.
Initial-boundary value problems for second order systems of partial differential equations
Kreiss, Heinz-Otto; Petersson, N Anders
2010-01-01
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of n equations as a larger first order system. Unfortunately, the resulting first order system consists, in general, of more than 2n equations which leads to many complications, such as side conditions which must be satisfied by the solution of the larger first order system. Here we will use the theory of pseudo-differential operators combined with mode analysis. There are many desirable properties of this approach: 1) The reduction to first order systems of pseudo-differential equations poses no difficulty and always gives a system of 2n equations. 2) We can localize the problem, i.e., it is only necessary to study the Cauchy problem and halfplane problems with constant coefficients. 3) The class of problems we can treat is much larger than previous approaches based on "integ...
Milne, a routine for the numerical solution of Milne's problem
Rawat, Ajay; Mohankumar, N.
2010-11-01
The routine Milne provides accurate numerical values for the classical Milne's problem of neutron transport for the planar one speed and isotropic scattering case. The solution is based on the Case eigen-function formalism. The relevant X functions are evaluated accurately by the Double Exponential quadrature. The calculated quantities are the extrapolation distance and the scalar and the angular fluxes. Also, the H function needed in astrophysical calculations is evaluated as a byproduct. Program summaryProgram title: Milne Catalogue identifier: AEGS_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGS_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 701 No. of bytes in distributed program, including test data, etc.: 6845 Distribution format: tar.gz Programming language: Fortran 77 Computer: PC under Linux or Windows Operating system: Ubuntu 8.04 (Kernel version 2.6.24-16-generic), Windows-XP Classification: 4.11, 21.1, 21.2 Nature of problem: The X functions are integral expressions. The convergence of these regular and Cauchy Principal Value integrals are impaired by the singularities of the integrand in the complex plane. The DE quadrature scheme tackles these singularities in a robust manner compared to the standard Gauss quadrature. Running time: The test included in the distribution takes a few seconds to run.
FUNDAMENTAL MATRIX OF LINEAR CONTINUOUS SYSTEM IN THE PROBLEM OF ESTIMATING ITS TRANSPORT DELAY
Directory of Open Access Journals (Sweden)
N. A. Dudarenko
2014-09-01
Full Text Available The paper deals with the problem of quantitative estimation for transport delay of linear continuous systems. The main result is received by means of fundamental matrix of linear differential equations solutions specified in the normal Cauchy form for the cases of SISO and MIMO systems. Fundamental matrix has the dual property. It means that the weight function of the system can be formed as a free motion of systems. Last one is generated by the vector of initial system conditions, which coincides with the matrix input of the system being researched. Thus, using the properties of the system- solving for fundamental matrix has given the possibility to solve the problem of estimating transport linear continuous system delay without the use of derivation procedure in hardware environment and without formation of exogenous Dirac delta function. The paper is illustrated by examples. The obtained results make it possible to solve the problem of modeling the pure delay links using consecutive chain of aperiodic links of the first order with the equal time constants. Modeling results have proved the correctness of obtained computations. Knowledge of transport delay can be used when configuring multi- component technological complexes and in the diagnosis of their possible functional degeneration.
Inverse Boundary Problems for Systems in Two Dimensions
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.
Institute of Scientific and Technical Information of China (English)
房艳峰; 高华喜
2013-01-01
Cauchy-inequality is utilized to analyze and evaluate the variance of the simulation result of the Monte Carlo method with importance sampling technique involved. The concept of medium probability is introduced and the relationship between medium probability and simulation result variance is deduced. And based on this conclusion, the sampling function which will minimum the simulation result variance is figured, and cirque and semi-cirque intercepting tail importance sampling methods, as importance sampling techniques, are built. Especially, the ratio between the sampling function to the original distribution function is constant in the methods and the sampling points distribute in a spherical space, which take the origin as a center and the distance from the origin to the limit state surface as a radius. Furthermore, the quantitative description for the reduction of variance of simulation results can be obtained. The results of example and analysis indicate that the variance of simulation results by cirque and semi-cirque intercepting tail importance sampling methods can be reduced to one tenth and one twentieth of that by a direct method.%该文采用柯西不等式对结构可靠度计算中Monte Carlo重要抽样法的模拟方差进行了分析与评价,提出了中间概率的概念并推导出其与模拟方差的函数关系.在此基础上得出使方差达到极小值的抽样函数具体形式,并建立了属于重要抽样技术的圆环和半圆环取尾抽样方法.与其他方法不同的是其抽样函数与原变量分布函数的比值是一常数,其分布区域是以原点为中心以原点到极限状态面距离为半径的圆形外部空间,模拟结果的方差可以定量描述.理论分析和例题模拟结果都表明:圆环取尾抽样方法可使模拟结果的方差缩减到直接模拟的1/10,而半圆环取尾抽样方法能缩减到1/20.
Singular solutions to Protter's problem for the 3-D wave equation involving lower order terms
Directory of Open Access Journals (Sweden)
Myron K. Grammatikopoulos
2003-01-01
Full Text Available In 1952, at a conference in New York, Protter formulated some boundary value problems for the wave equation, which are three-dimensional analogues of the Darboux problems (or Cauchy-Goursat problems on the plane. Protter studied these problems in a 3-D domain $Omega_0$, bounded by two characteristic cones $Sigma_1$ and $Sigma_{2,0}$, and by a plane region $Sigma_0$. It is well known that, for an infinite number of smooth functions in the right-hand side, these problems do not have classical solutions. Popivanov and Schneider (1995 discovered the reason of this fact for the case of Dirichlet's and Neumann's conditions on $Sigma_0$: the strong power-type singularity appears in the generalized solution on the characteristic cone $Sigma_{2,0}$. In the present paper we consider the case of third boundary-value problem on $Sigma_0$ and obtain the existence of many singular solutions for the wave equation involving lower order terms. Especifica ally, for Protter's problems in $mathbb{R}^{3}$ it is shown here that for any $nin N$ there exists a $C^{n}({Omega}_0$-function, for which the corresponding unique generalized solution belongs to $C^{n}({Omega}_0slash O$ and has a strong power type singularity at the point $O$. This singularity is isolated at the vertex $O$ of the characteristic cone $Sigma_{2,0}$ and does not propagate along the cone. For the wave equation without lower order terms, we presented the exact behavior of the singular solutions at the point $O$.
Variations on strongly lacunary quasi Cauchy sequences
Kaplan, Huseyin; Cakalli, Huseyin
2016-08-01
We introduce a new function space, namely the space of Nθ (p)-ward continuous functions, which turns out to be a closed subspace of the space of continuous functions for each positive integer p. Nθα(p ) -ward continuity is also introduced and investigated for any fixed 0 kr-1, kr], and θ = (kr) is a lacunary sequence, i.e. an increasing sequence of positive integers such that k0 ≠ 0, and hr: kr-kr-1 →∞.
Geometry of Cauchy-Riemann submanifolds
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.
Class and Home Problems: Optimization Problems
Anderson, Brian J.; Hissam, Robin S.; Shaeiwitz, Joseph A.; Turton, Richard
2011-01-01
Optimization problems suitable for all levels of chemical engineering students are available. These problems do not require advanced mathematical techniques, since they can be solved using typical software used by students and practitioners. The method used to solve these problems forces students to understand the trends for the different terms…
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)
Institute of Scientific and Technical Information of China (English)
杨少兵; 吴命利
2014-01-01
从波动量法的基本理论入手，研究波动量比值符号的概率统计特征，通过理论分析提出当谐波源受到多种随机因素影响时波动量比值的实部和虚部的概率密度服从广义柯西分布，并选取Pearson VII公式对此进行描述。然后，给出利用概率统计和非线性曲线拟合估计谐波阻抗的具体方法及步骤。进而分析影响波动量法误差的各种因素，推导理论误差表达式并提出修正误差的措施。与各类依赖判据进行数据过滤的方法相比，概率法的数据处理过程更为简便，具有较好的通用性、可靠性及抗干扰性，同时，概率法能更全面地分析波动量比值的概率统计特征，避免数据的误处理。蒙特卡洛仿真及实例应用分析验证了所提方法的有效性和实用性。%Starting from the basic theory of fluctuation method, this paper studied probability characteristics of the ratio of harmonic voltage fluctuation to harmonic current fluctuation. Through theoretical analysis, it was proved that the probability density of both real and imaginary part of the ratio follow the generalized Cauchy distribution if the harmonic source is affected by many random factors. So the Pearson VII formula was selected to describe the above distributions. An approach and its specific steps of using probability statistics and nonlinear curve-fitting were proposed to be used for estimation of power system harmonic impedances. Furthermore, this paper analyzed the factors affecting the estimated error of fluctuation method, and then gave out a set of error formulas and measured to reduce the error. Compared with the methods depending on data filtering strategies, the probability approach is more simple and convenient in data processing. And it has more advantages such as universality, reliability and noise immunity. Meanwhile, it can reduce failure rate of data processing by considering the probability characteristics in a
Constipation and Defecation Problems
... Home / Digestive Health Topic / Constipation and Defecation Problems Constipation and Defecation Problems Basics Resources Overview Constipation is one of the most frequent gastrointestinal complaints ...
Quadratic eigenvalue problems.
Energy Technology Data Exchange (ETDEWEB)
Walsh, Timothy Francis; Day, David Minot
2007-04-01
In this report we will describe some nonlinear eigenvalue problems that arise in the areas of solid mechanics, acoustics, and coupled structural acoustics. We will focus mostly on quadratic eigenvalue problems, which are a special case of nonlinear eigenvalue problems. Algorithms for solving the quadratic eigenvalue problem will be presented, along with some example calculations.
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.…
Karnaukhov, A V; Karnaukhova, E V
2004-01-01
A wide range of biophysical systems are described by nonlinear dynamic models mathematically presented as a set of ordinary differential equations in the Cauchy explicit form: [formula: see text] Fij(X1(t),..,XN(t),t), (i = 1,...,N, j = 1,...,M), where Fij (X1(t), ..., XN(t), t) is a set of basis functions satisfying the Lipschitz condition. We investigate the problem of evaluation of model constants aij (the system identification) using experimental data about the time dependence of the dynamic parameters of the system Xi(t). A new method of system identification for the class of similar nonlinear dynamic models is proposed. It is shown that the problem of identifying an initial nonlinear model can be reduced to the solution of a system of linear equations for the matrix of the dynamic model constants [aj]i. It is proposed to determine the set of dynamic model constants aij using the criterion of minimal quadratic discrepancy for the time dependence of the set of dynamic parameters Xi(t). An important special case of the nonlinear model, the quadratic model, is considered. Test problems of identification using this method are presented for two nonlinear systems: the Van der Pol type multiparametric nonlinear oscillator and the strange attractor of Ressler, a widely known example of dynamic systems showing the stochastic behavior.
Problem solving III: factors influencing classroom problem
Directory of Open Access Journals (Sweden)
Sayonara Salvador Cabral da Costa
1997-05-01
Full Text Available This paper presents a review of the literature in the area of problem solving, particularly in physics, focusing only on factors that influence classroom problem solving. Fifty-seven papers have been analyzed in terms of theoretical basis, investigated factors/methodology and findings/relevant factors, which were organized in a table that served as support for a synthesis made by the authors. It is the third of a four-paper series reviewing different aspects of the problem solving subject.
Differential equations problem solver
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
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...
... Ear Nose & Throat Emotional Problems Eyes Fever From Insects or Animals Genitals and Urinary Tract Glands & Growth ... important distinction is that this is not a vision problem ; rather, the brain is reversing, inverting or ...
Challenging problems in algebra
Posamentier, Alfred S
1996-01-01
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.
Mathematics as Problem Solving.
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)
Vehicle Routing Problem Models
Directory of Open Access Journals (Sweden)
Tonči Carić
2004-01-01
Full Text Available The Vehicle Routing Problem cannot always be solved exactly,so that in actual application this problem is solved heuristically.The work describes the concept of several concrete VRPmodels with simplified initial conditions (all vehicles are ofequal capacity and start from a single warehouse, suitable tosolve problems in cases with up to 50 users.
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.
Classifying IS Project Problems
DEFF Research Database (Denmark)
Munk-Madsen, Andreas
2006-01-01
The literature contains many lists of IS project problems, often in the form of risk factors. The problems sometimes appear unordered and overlapping, which reduces their usefulness to practitioners as well as theoreticians. This paper proposes a list of criteria for formulating project problems...
Directory of Open Access Journals (Sweden)
Marie Pelleau
2009-10-01
Full Text Available This paper presents a new method and a constraint-based objective function to solve two problems related to the design of optical telecommunication networks, namely the Synchronous Optical Network Ring Assignment Problem (SRAP and the Intra-ring Synchronous Optical Network Design Problem (IDP. These network topology problems can be represented as a graph partitioning with capacity constraints as shown in previous works. We present here a new objective function and a new local search algorithm to solve these problems. Experiments conducted in Comet allow us to compare our method to previous ones and show that we obtain better results.
Pelleau, Marie; Truchet, Charlotte
2009-01-01
This paper presents a new method and a constraint-based objective function to solve two problems related to the design of optical telecommunication networks, namely the Synchronous Optical Network Ring Assignment Problem (SRAP) and the Intra-ring Synchronous Optical Network Design Problem (IDP). These network topology problems can be represented as a graph partitioning with capacity constraints as shown in previous works. We present here a new objective function and a new local search algorithm to solve these problems. Experiments conducted in Comet allow us to compare our method to previous ones and show that we obtain better results.
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
The Accelerated Kepler Problem
Namouni, Fathi
2007-01-01
The accelerated Kepler problem is obtained by adding a constant acceleration to the classical two-body Kepler problem. This setting models the dynamics of a jet-sustaining accretion disk and its content of forming planets as the disk loses linear momentum through the asymmetric jet-counterjet system it powers. The dynamics of the accelerated Kepler problem is analyzed using physical as well as parabolic coordinates. The latter naturally separate the problem's Hamiltonian into two unidimensional Hamiltonians. In particular, we identify the origin of the secular resonance in the accelerated Kepler problem and determine analytically the radius of stability boundary of initially circular orbits that are of particular interest to the problem of radial migration in binary systems as well as to the truncation of accretion disks through stellar jet acceleration.
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.
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
Rǎdulescu, Teodora-Liliana T.; Andreescu, Titu; Rǎdulescu, Vicenţiu
2015-01-01
This book ontains a collection of challenging problems in elementary mathematical analysis, uses competition-inspired problems as a platform for training typical inventive skills, develops basic valuable techniques for solving problems in mathematical analysis on the real axis, assumes only a basic knowledge of the topic but opens the path to competitive research in the field, includes interesting and valuable historical accounts of ideas and methods in analysis, presents a connection between...
Energy Technology Data Exchange (ETDEWEB)
Laporte, G.
1987-01-01
Location-routing problems involve simultaneously locating a number of facilities among candidate sites and establishing delivery routes to a set of users in such a way that the total system cost is minimized. This paper presents a survey of such problems. It includes some applications and examples of location-routing problems, a description of the main heuristics that have been developed for such problems, and reviews of various formulations and algorithms used in solving these problems. A more detailed review is given of exact algorithms for the vehicle routing problem, three-index vehicle flow formulations, and two-index vehicle flow formulations and algorithms for symmetrical and non-symmetrical problems. It is concluded that location-routing problem research is a fast-growing area, with most developments occurring over the past few years; however, research is relatively fragmented, often addresses problems which are too specific and contains several voids which have yet to be filled. A number of promising research areas are identified. 137 refs., 3 figs.
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
Known TCP Implementation Problems
Paxson, Vern (Editor); Allman, Mark; Dawson, Scott; Fenner, William; Griner, Jim; Heavens, Ian; Lahey, K.; Semke, J.; Volz, B.
1999-01-01
This memo catalogs a number of known TCP implementation problems. The goal in doing so is to improve conditions in the existing Internet by enhancing the quality of current TCP/IP implementations. It is hoped that both performance and correctness issues can be resolved by making implementors aware of the problems and their solutions. In the long term, it is hoped that this will provide a reduction in unnecessary traffic on the network, the rate of connection failures due to protocol errors, and load on network servers due to time spent processing both unsuccessful connections and retransmitted data. This will help to ensure the stability of the global Internet. Each problem is defined as follows: Name of Problem The name associated with the problem. In this memo, the name is given as a subsection heading. Classification one or more problem categories for which the problem is classified: "congestion control", "performance", "reliability", "resource management". Description A definition of the problem, succinct but including necessary background material. Significance A brief summary of the sorts of environments for which the problem is significant.
Goldman, Iosif Ilich; Geilikman, B T
2006-01-01
This challenging book contains a comprehensive collection of problems in nonrelativistic quantum mechanics of varying degrees of difficulty. It features answers and completely worked-out solutions to each problem. Geared toward advanced undergraduates and graduate students, it provides an ideal adjunct to any textbook in quantum mechanics.
DEFF Research Database (Denmark)
Foss, Kirsten; Foss, Nicolai Juul
2006-01-01
as a 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....
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.
Problem Solving Techniques Seminar.
Massachusetts Career Development Inst., Springfield.
This booklet is one of six texts from a workplace literacy curriculum designed to assist learners in facing the increased demands of the workplace. Six problem-solving techniques are developed in the booklet to assist individuals and groups in making better decisions: problem identification, data gathering, data analysis, solution analysis,…
A Stochastic Employment Problem
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…
DEFF Research Database (Denmark)
Ovesen, Nis
2015-01-01
Problem-based learning (PBL) is becoming increasingly popular in design educations, but how is it taught and practiced? This paper presents a case study of a three-day workshop that has the purpose of introducing PBL to design students. A theoretical background on PBL and problems in design is es...
Wicked Problems: Inescapable Wickedity
Jordan, Michelle E.; Kleinsasser, Robert C.; Roe, Mary F.
2014-01-01
The article explores the concept of wicked problems and proposes a reinvigorated application of this concept for wider educational use. This recommendation stems from the contributions of a number of scholars who frame some of the most contentious and recalcitrant educational issues as wicked problems. The present authors build upon these previous…
STONE, EDWARD
THE REPORT POINTS OUT THAT, IN GENERAL, CHRONIC PROBLEM PARENTS GREW UP IN ENVIRONMENTS OF EMOTIONAL IMPOVERISHMENT, INCONSISTENCY, CONFUSION, AND DISORDER, OFTEN WITH DEPRIVATION OF FOOD, CLOTHING, AND SHELTER. THESE PARENTS CATEGORIZE PEOPLE AS THOSE WHO GIVE AND THOSE WHO TAKE. THEY BLAME THEIR PROBLEMS ON EXTERNAL CIRCUMSTANCES NOT UNDER THEIR…
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.
PROBLEMS OF TURKISH LEXICOGRAPHY.
TIETZE, ANDREAS
THE LEXICOGRAPHICAL PROBLEMS IN THE TURKISH LANGUAGE WERE DISCUSSED. HISTORICAL REVIEW OF THE LANGUAGE WAS PRESENTED WITH PROBLEMS OF LEXICOGRAPHY THAT EXISTED IN THE PAST COMPARED WITH THOSE OF THE PRESENT. DISCUSSION TOPICS OF THE REPORT INCLUDED (1) NAME OF THE LANGUAGE, (2) DELIMITATION COMPARED WITH RELATED LANGUAGES, (3) DELIMINATION…
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
Current Social Problem Novels.
Kenney, Donald J.
This review of social problem novels for young adults opens with a brief background of the genre, then lists the dominant themes of social problem fiction and nonfiction novels that have been published in the last two years, such as alcoholism, alienation, death, growing up and self-awarness, drugs, and divorce. Other themes mentioned are…
Harper, Kathleen A.; Etkina, Eugenia
2002-10-01
As part of weekly reports,1 structured journals in which students answer three standard questions each week, they respond to the prompt, If I were the instructor, what questions would I ask or problems assign to determine if my students understood the material? An initial analysis of the results shows that some student-generated problems indicate fundamental misunderstandings of basic physical concepts. A further investigation explores the relevance of the problems to the week's material, whether the problems are solvable, and the type of problems (conceptual or calculation-based) written. Also, possible links between various characteristics of the problems and conceptual achievement are being explored. The results of this study spark many more questions for further work. A summary of current findings will be presented, along with its relationship to previous work concerning problem posing.2 1Etkina, E. Weekly Reports;A Two-Way Feedback Tool, Science Education, 84, 594-605 (2000). 2Mestre, J.P., Probing Adults Conceptual Understanding and Transfer of Learning Via Problem Posing, Journal of Applied Developmental Psychology, 23, 9-50 (2002).
Directory of Open Access Journals (Sweden)
Dan Ophir
2011-12-01
Full Text Available The process of making complex and controversial decisions, that is, dealing with moral or ethical dilemmas, have intrigued people and inspired writers from time immemorial. Dilemmas give both color and depth to characters in good literary works. But beyond literary fiction, dilemmas occupy society in every day issues such as in introducing legislation or solving current political problems. One example of a current political dilemma is how to deal with Iran’s quest for nuclear weapons. If it were possible to assess and quantify each of the alternative solutions for a given problem, the process of decision making would be much easier. If a problem involves only two optional solutions, game theory techniques can be used. However, real life problems are usually multi-unit, multi-optional problems, as in Iran
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.
Boots, Byron
2011-01-01
Recently, there has been much interest in spectral approaches to learning manifolds---so-called kernel eigenmap methods. These methods have had some successes, but their applicability is limited because they are not robust to noise. To address this limitation, we look at two-manifold problems, in which we simultaneously reconstruct two related manifolds, each representing a different view of the same data. By solving these interconnected learning problems together and allowing information to flow between them, two-manifold algorithms are able to succeed where a non-integrated approach would fail: each view allows us to suppress noise in the other, reducing bias in the same way that an instrumental variable allows us to remove bias in a {linear} dimensionality reduction problem. We propose a class of algorithms for two-manifold problems, based on spectral decomposition of cross-covariance operators in Hilbert space. Finally, we discuss situations where two-manifold problems are useful, and demonstrate that sol...
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.
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.
Problems in equilibrium theory
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.
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 common divisor of lengths of all its cycles is one. The problem was posed by Adler, Goodwyn and Weiss over 30 years ago and evoked a noticeable interest among the specialists in theory of graphs, deterministic automata and symbolic dynamics. The problem is described even in "Vikipedia" - the popular Internet Encyclopedia. The positive solution of the road coloring problem is presented.
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.
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.
X-Ray Diffractometry of Thin Layers - Possibilities and Problems
Directory of Open Access Journals (Sweden)
Vladimir Zucha
2005-01-01
Full Text Available Efficieney of two deconvolution methods used in X-ray powder diffraction analysis is compared for thin films of Pd and Pt. The first method is the classical Stokes method and the second one is method of indirect deconvolution. But calculated integral breadth of Gauss and Cauchy components of Voigt function which describe the physical broadening are different. The analysis of the all found pheromones show that the method of indirect deconvolution gives more accurate results.
Nonlocal Problems for Fractional Differential Equations via Resolvent Operators
Directory of Open Access Journals (Sweden)
Zhenbin Fan
2013-01-01
Full Text Available We discuss the continuity of analytic resolvent in the uniform operator topology and then obtain the compactness of Cauchy operator by means of the analytic resolvent method. Based on this result, we derive the existence of mild solutions for nonlocal fractional differential equations when the nonlocal item is assumed to be Lipschitz continuous and neither Lipschitz nor compact, respectively. An example is also given to illustrate our theory.
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.
Variational methods for a resonant problem with the p-Laplacian in $R^N$
Directory of Open Access Journals (Sweden)
Benedicte Alziary
2004-05-01
Full Text Available The solvability of the resonant Cauchy problem $$ - Delta_p u = lambda_1 m(|x| |u|^{p-2} u + f(x quadhbox{in } mathbb{R}^N ;quad uin D^{1,p}(mathbb{R}^N, $$ in the entire Euclidean space $mathbb{R}^N$ ($Ngeq 1$ is investigated as a part of the Fredholm alternative at the first (smallest eigenvalue $lambda_1$ of the positive $p$-Laplacian $-Delta_p$ on $D^{1,p}(mathbb{R}^N$ relative to the weight $m(|x|$. Here, $Delta_p$ stands for the $p$-Laplacian, $mcolon mathbb{R}_+o mathbb{R}_+$ is a weight function assumed to be radially symmetric, $m otequiv 0$ in $mathbb{R}_+$, and $fcolon mathbb{R}^No mathbb{R}$ is a given function satisfying a suitable integrability condition. The weight $m(r$ is assumed to be bounded and to decay fast enough as $ro +infty$. Let $varphi_1$ denote the (positive eigenfunction associated with the (simple eigenvalue $lambda_1$ of $-Delta_p$. If $int_{mathbb{R}^N} fvarphi_1 ,{ m d}x =0$, we show that problem has at least one solution $u$ in the completion $D^{1,p}(mathbb{R}^N$ of $C_{mathrm{c}}^1(mathbb{R}^N$ endowed with the norm $(int_{mathbb{R}^N} | abla u|^p ,{ m d}x^{1/p}$. To establish this existence result, we employ a saddle point method if $1 < p < 2$, and an improved Poincar'e inequality if $2leq p< N$. We use weighted Lebesgue and Sobolev spaces with weights depending on $varphi_1$. The asymptotic behavior of $varphi_1(x= varphi_1(|x|$ as $|x|o infty$ plays a crucial role. end{abstract}
Generalized emissivity inverse problem.
Ming, DengMing; Wen, Tao; Dai, XianXi; Dai, JiXin; Evenson, William E
2002-04-01
Inverse problems have recently drawn considerable attention from the physics community due to of potential widespread applications [K. Chadan and P. C. Sabatier, Inverse Problems in Quantum Scattering Theory, 2nd ed. (Springer Verlag, Berlin, 1989)]. An inverse emissivity problem that determines the emissivity g(nu) from measurements of only the total radiated power J(T) has recently been studied [Tao Wen, DengMing Ming, Xianxi Dai, Jixin Dai, and William E. Evenson, Phys. Rev. E 63, 045601(R) (2001)]. In this paper, a new type of generalized emissivity and transmissivity inverse (GETI) problem is proposed. The present problem differs from our previous work on inverse problems by allowing the unknown (emissivity) function g(nu) to be temperature dependent as well as frequency dependent. Based on published experimental information, we have developed an exact solution formula for this GETI problem. A universal function set suggested for numerical calculation is shown to be robust, making this inversion method practical and convenient for realistic calculations.
Cumulative Vehicle Routing Problems
Kara, &#;mdat; Kara, Bahar Yeti&#;; Yeti&#;, M. Kadri
2008-01-01
This paper proposes a new objective function and corresponding formulations for the vehicle routing problem. The new cost function defined as the product of the distance of the arc and the flow on that arc. We call a vehicle routing problem with this new objective function as the Cumulative Vehicle Routing Problem (CumVRP). Integer programming formulations with O(n2) binary variables and O(n2) constraints are developed for both collection and delivery cases. We show that the CumVRP is a gener...
DEFF Research Database (Denmark)
Tietjen, Anne; Jørgensen, Gertrud
2016-01-01
In a time of increasing globalisation and urbanisation, shrinking peripheral rural areas have become a truly wicked planning problem in many European countries. Although a problem can be easily perceived and measured by various indicators, the precise definition of the problem is problematic. Based......, place-based and project-oriented process directed at concrete physical outcomes. We frame strategic planning as a translation process where the interaction between human and non-human actors translates a unique, complex and contested situation into an innovated situation. We find that local physical...
Problems Digesting Dairy Products?
... Consumers Home For Consumers Consumer Updates Problems Digesting Dairy Products? Share Tweet Linkedin Pin it More sharing ... the natural sugar found in milk and other dairy products. People who cannot digest lactose have a ...
Wilson, James Q.; And Others
1972-01-01
Argues that most of the underlying assumptions of presently recommended solutions to the problem of heroin addiction are unreasonable, unwarranted, or at least open to more than one interpretation. (DM)
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)
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...
... 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 ...
Institute of Scientific and Technical Information of China (English)
岳科来
2016-01-01
There have considerable number of design philosophies and design methods in this world,but today I’d like to intorduce a new design problem solving system which comes from Chinese traditonal religion Dao.
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.
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.
Menstruation and Menstrual Problems
... and Menstrual Problems: Condition Information Skip sharing on social media links Share this: Page Content What is menstruation? What is the menstrual cycle? When happens when a pregnancy occurs? What is menstruation? Menstruation (pronounced men-stroo- ...
DEFF Research Database (Denmark)
Tietjen, Anne; Jørgensen, Gertrud
2016-01-01
In a time of increasing globalisation and urbanisation, shrinking peripheral rural areas have become a truly wicked planning problem in many European countries. Although a problem can be easily perceived and measured by various indicators, the precise definition of the problem is problematic. Based...... on the case of a Danish planning process which was carried out in collaboration with a charitable trust, this paper discusses an emerging strategic planning approach at the municipal level. We use the concept of wicked problems, strategic planning theory and Actor-Network-Theory to study a collaborative......, place-based and project-oriented process directed at concrete physical outcomes. We frame strategic planning as a translation process where the interaction between human and non-human actors translates a unique, complex and contested situation into an innovated situation. We find that local physical...
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.
Heggie, D C
2000-01-01
This didactic paper is motivated by the problem of understanding how stars escape from globular star clusters. One formulation of this problem is known, in dynamical astronomy, as Hill's problem. Originally intended as a model for the motion of the moon around the earth with perturbations by the sun, with simple modifications it also serves as a model for the motion of a star in a star cluster with perturbations by the galaxy. The paper includes introductory sections on the derivation of the equations of motion of Hill's problem, their elementary properties, and extensions to deal with non-point masses and non-circular orbits. We then show how the rate of escape may be calculated numerically and estimated theoretically, and discuss how this simple picture is modified if the stars in a cluster are also undergoing two-body relaxation. Finally we introduce some established ideas for obtaining the distribution of escape times.
Directory of Open Access Journals (Sweden)
Dr Jane Gregory
2016-11-01
Full Text Available Framing ‘science and society’ as a conflict has diverted us from more important problems. Our economic environment urges the commercialisation and social acceptance of new technologies, and science communicators and their publics contribute work to these ends. These activities neglect existing, uncontroversial technologies that, in a collaboration between responsible scientists and their publics, could be deployed to address global problems.
Dubois, Swan; Zhu, Nini
2012-01-01
We investigate the hardness of establishing as many stable marriages (that is, marriages that last forever) in a population whose memory is placed in some arbitrary state with respect to the considered problem, and where traitors try to jeopardize the whole process by behaving in a harmful manner. On the negative side, we demonstrate that no solution that is completely insensitive to traitors can exist, and we propose a protocol for the problem that is optimal with respect to the traitor containment radius.
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.
Distributed Storage Allocation Problems
Leong, Derek; Dimakis, Alexandros G.; Ho, Tracey
2009-01-01
We investigate the problem of using several storage nodes to store a data object, subject to an aggregate storage budget or redundancy constraint. It is challenging to find the optimal allocation that maximizes the probability of successful recovery by the data collector because of the large space of possible symmetric and nonsymmetric allocations, and the nonconvexity of the problem. For the special case of probability-l recovery, we show that the optimal allocatio...
Colored Traveling Salesman Problem.
Li, Jun; Zhou, MengChu; Sun, Qirui; Dai, Xianzhong; Yu, Xiaolong
2015-11-01
The multiple traveling salesman problem (MTSP) is an important combinatorial optimization problem. It has been widely and successfully applied to the practical cases in which multiple traveling individuals (salesmen) share the common workspace (city set). However, it cannot represent some application problems where multiple traveling individuals not only have their own exclusive tasks but also share a group of tasks with each other. This work proposes a new MTSP called colored traveling salesman problem (CTSP) for handling such cases. Two types of city groups are defined, i.e., each group of exclusive cities of a single color for a salesman to visit and a group of shared cities of multiple colors allowing all salesmen to visit. Evidences show that CTSP is NP-hard and a multidepot MTSP and multiple single traveling salesman problems are its special cases. We present a genetic algorithm (GA) with dual-chromosome coding for CTSP and analyze the corresponding solution space. Then, GA is improved by incorporating greedy, hill-climbing (HC), and simulated annealing (SA) operations to achieve better performance. By experiments, the limitation of the exact solution method is revealed and the performance of the presented GAs is compared. The results suggest that SAGA can achieve the best quality of solutions and HCGA should be the choice making good tradeoff between the solution quality and computing time.
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...
Bicriteria network design problems
Energy Technology Data Exchange (ETDEWEB)
Marathe, M.V. [Los Alamos National Lab., NM (United States); Ravi, R. [Princeton Univ., NJ (United States); Sundaram, R. [Massachusetts Inst. of Tech., Cambridge, MA (United States); Ravi, S.S.; Rosenkrantz, D.J.; Hunt, H.B. III [State Univ. of New York, Albany, NY (United States). Dept. of Computer Science
1997-11-20
The authors study a general class of bicriteria network design problems. A generic problem in this class is as follows: Given an undirected graph and two minimization objectives (under different cost functions), with a budget specified on the first, find a subgraph from a given subgraph class that minimizes the second objective subject to the budget on the first. They consider three different criteria -- the total edge cost, the diameter and the maximum degree of the network. Here, they present the first polynomial-time approximation algorithms for a large class of bicriteria network design problems for the above mentioned criteria. The following general types of results are presented. First, they develop a framework for bicriteria problems and their approximations. Second, when the two criteria are the same they present a black box parametric search technique. This black box takes in as input an (approximation) algorithm for the criterion situation and generates an approximation algorithm for the bicriteria case with only a constant factor loss in the performance guarantee. Third, when the two criteria are the diameter and the total edge costs they use a cluster based approach to devise approximation algorithms. The solutions violate both the criteria by a logarithmic factor. Finally, for the class of treewidth-bounded graphs, they provide pseudopolynomial-time algorithms for a number of bicriteria problems using dynamic programming. The authors show how these pseudopolynomial-time algorithms can be converted to fully polynomial-time approximation schemes using a scaling technique.
Computational problems in engineering
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.
[Halitosis. A common problem].
Laine, M L; Slot, D E; Danser, M M
2011-12-01
Halitosis is a frequently occurring problem, the cause of which is generally to be found in the mouth. The challenge for oral health care providers is to diagnose it correctly and treat it effectively. Differential diagnosis is of great importance in making a distinction between halitosis which originates in the mouth and which does not originate in the mouth. Oral halitosis can be treated effectively by good oral health care. Plaque accumulation on the tongue is the most common cause of oral halitosis. Tongue cleansing, possibly in combination with a specific mouth wash, is consequently recommended as an element of oral hygiene care. Other oral health problems, such as periodontal disease, caries and ill-fitting removable dentures should be treated adequately to eliminate these problems as potential causes of halitosis.
Solved problems in electromagnetics
Salazar Bloise, Félix; Bayón Rojo, Ana; Gascón Latasa, Francisco
2017-01-01
This book presents the fundamental concepts of electromagnetism through problems with a brief theoretical introduction at the beginning of each chapter. The present book has a strong didactic character. It explains all the mathematical steps and the theoretical concepts connected with the development of the problem. It guides the reader to understand the employed procedures to learn to solve the exercises independently. The exercises are structured in a similar way: The chapters begin with easy problems increasing progressively in the level of difficulty. This book is written for students of physics and engineering in the framework of the new European Plans of Study for Bachelor and Master and also for tutors and lecturers. .
Revisiting the Lambert's Problem
Izzo, Dario
2014-01-01
The orbital boundary value problem, also known as Lambert Problem, is revisited. Building upon Lancaster and Blanchard approach, new relations are revealed and a new variable representing all problem classes, under L-similarity, is used to express the time of flight equation. In the new variable, the time of flight curves have two oblique asymptotes and they mostly appear to be conveniently approximated by piecewise continuous lines. We use and invert such a simple approximation to provide an efficient initial guess to an Householder iterative method that is then able to converge, for the single revoltuion case, in only two iterations. The resulting algorithm is compared to Gooding's procedure revealing to be numerically as accurate, while having a smaller computational complexity.
Energy Technology Data Exchange (ETDEWEB)
Sivertsen, B.
1995-09-01
This document focuses on the specific problems of urban air pollution related to emissions, urban climate, meteorology, smog potential, specific locations, air pollution measurements and trends. Examples are given with cases from European cities in particular. The north south differences, coastal and inland problems and data from various parts of Europe are presented. Global trends and results from the UNEP programme are used to illustrate the magnitude of the problem. Special emphasis is placed on the impact of different sources and their importance in selected cities. Different types of atmospheric dispersion models, their development and use, is outlined. The importance of local and regional meteorological data for explanation purposes and for estimating and forecasting urban air quality is presented. Finally, monitoring programmes, mapping, impact assessment and optimum abatement strategy planning are illustrated with examples from different areas in the world. 9 refs., 56 figs., 1 table
DEFF Research Database (Denmark)
de Graaff, Erik; Guerra, Aida
, 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......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...... in Engineering Education. In answer to the requests for visits the Aalborg Centre for Problem Based Learning in Engineering Science and Sustainability under the auspices of UNESCO (UCPBL) a two days programme for visitors is offered two times a year. The workshop is an introduction workshop to the Aalborg PBL...
Chou, Kai-Seng
2001-01-01
Although research in curve shortening flow has been very active for nearly 20 years, the results of those efforts have remained scattered throughout the literature. For the first time, The Curve Shortening Problem collects and illuminates those results in a comprehensive, rigorous, and self-contained account of the fundamental results.The authors present a complete treatment of the Gage-Hamilton theorem, a clear, detailed exposition of Grayson''s convexity theorem, a systematic discussion of invariant solutions, applications to the existence of simple closed geodesics on a surface, and a new, almost convexity theorem for the generalized curve shortening problem.Many questions regarding curve shortening remain outstanding. With its careful exposition and complete guide to the literature, The Curve Shortening Problem provides not only an outstanding starting point for graduate students and new investigations, but a superb reference that presents intriguing new results for those already active in the field.
A Survey of Transportation Problems
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...
Problems over Information Systems
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.
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
Calculus problems and solutions
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
Advanced calculus problem solver
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
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The pricing of electricity trasmission requires determining how much use each generator is making of a transmission line and what is each generator's contribution to the system losses. Such problems cannot be solved by only using Kirchoff's laws. This paper proposes two current decomposition axioms based on which the theories and models are established for the current trace problem. To create an efficient algorithm the graph theory is employed. It is proved that there is no directed circuit in a directed current distribution graph. According to this theorem a very simple and efficient algorithm based on recursive elimination process is suggested. A simple example is used to explain the algorithm.
Matrices in Engineering Problems
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
Problems in classical mechanics
Katkar, L N
2014-01-01
Problems in classical mechanics presents a lucid treatment of the formulations of Lagrangian, Hamiltonian, and the Principles of Calculus of Variations etc. important for the study of modern physics. The study of classical mechanics prepares students to apply the principles and the mathematical tools to solve real life problems. The book also incorporates and discusses in detail topics such as Central Force Motion, Rigid Body Motion and Canonical Transformations. KEY FEATURES: Around 200 solved examples with complete mathematical theory Around 70 examples given as an exercise to test and develop students understanding The physical interpretation of the Hamiltonian is highlighted
Classic Problems of Probability
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
Minimal Controllability Problems
Olshevsky, Alex
2013-01-01
Given a linear system, we consider the problem of finding a small set of variables to affect with an input so that the resulting system is controllable. We show that this problem is NP-hard; indeed, we show that even approximating the minimum number of variables that need to be affected within a multiplicative factor of $c \\log n$ is NP-hard for some positive $c$. On the positive side, we show it is possible to find sets of variables matching this inapproximability barrier in polynomial time....
Electric circuits problem solver
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
DEFF Research Database (Denmark)
Ovesen, Nis
2015-01-01
Problem-based learning (PBL) is becoming increasingly popular in design educations, but how is it taught and practiced? This paper presents a case study of a three-day workshop that has the purpose of introducing PBL to design students. A theoretical background on PBL and problems in design...... is established and is backing up the case study. The study shows that design engineering and architectural students without experience in PBL in general finds the approach to be beneficial when working on a design challenge in a student team....
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....
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…
The information recovery problem
Baccetti, Valentina; Terno, Daniel R
2016-01-01
The problem of rescuing unitary matter evolution on a black hole spacetime remains unresolved. We argue that some prominent cures are more troubling than the disease, demonstrate that their central element --- forming of the event horizon before the evaporation begins --- is not necessarily true, and describe a fully coupled matter-gravity system which is manifestly unitary.
Pratelli, Aldo
2016-01-01
This book presents a series of lectures on three of the best known examples of free discontinuity problems: the Mumford-Shah model for image segmentation, a variational model for the epitaxial growth of thin films, and the sharp interface limit of the Ohta-Kawasaki model for pattern formation in dyblock copolymers.
Managing soil remediation problems.
Okx, J P; Hordijk, L; Stein, A
1996-12-01
Soil remediation has only a short history but the problem addressed is a significant one. Cost estimates for the clean-up of contaminated sites in the European Union and the United States are in the order of magnitude of 1,400 billion ECU. Such an enormous operation deserves the best management it can get. Reliable cost estimations per contaminated site are an important prerequisite. This paper addresses the problems related to site-wise estimations.When solving soil remediation problems, we have to deal with a large number of scientific disciplines. Too often solutions are presented from the viewpoint of only one discipline. In order to benefit from the combined disciplinary knowledge and experience, we think that it is necessary to describe the interrelations between these disciplines. This can be realized by developing an adequate model of the desired process which enables to consider and evaluate the essential factors as interdependent components of the total system.The resulting model provides a binding paradigm to the contributing disciplines which will result in improved efficiency and effectivity of the decision and the cost estimation process. In the near future, we will release the "Biosparging and Bioventing Expert Support System", an expert support system for problem owners, consultants and authorities dealing with the design and operation of a biosparging and/or a bioventing system.
The Vehicle Rescheduling Problem
R. Spliet (Remy); A.F. Gabor (Adriana); R. Dekker (Rommert)
2009-01-01
textabstractThe capacitated vehicle routing problem is to find a routing schedule describing the order in which geographically dispersed customers are visited to satisfy demand by supplying goods stored at the depot, such that the traveling costs are minimized. In many practical applications, a long
Aeroelastic problems in turbomachines
Bendiksen, Oddvar O.
1993-01-01
An overview is given of aeroelastic problems in turbomachines, emphasizing recent research. Unsteady flow in cascade and turbomachinery rotors is discussed, including supersonic and transonic linearized potential flow and nonlinear flow models. Computational and modeling aspects of the flutter of fan and compressor blades are examined. The correlation of the findings with experimental data is considered. Future directions in turbomachinery aeroelasticity are addressed.
Olson, Alton T.
1993-01-01
Presents a series of solution methods to the Eight Queens Problem of placing eight queens on a chess board so that no one queen can capture another. Solution methods progress from empirical approaches to the use of computer algorithms. Geometric transformations are used to find other solutions. (MDH)
1981-05-18
obstacles that were not encountered previously in puzzle-like problems. Basically, the exact operators to be used are usually not given, the goal state...same height on other side 5. IF something goes down frictionless surface THEN can find acceleration of gravity on the incline using trigonometry 6
Institute of Scientific and Technical Information of China (English)
刘香情; 钱丹
2002-01-01
With the population growing, a lot of problems have come out, Nowadays a lot of tall buildings have been built, but the houses are still very short; A lot of cars and buses have increased, but they are still crowded with people; A lot of schools have been built,
Solving Problems through Circles
Grahamslaw, Laura; Henson, Lisa H.
2015-01-01
Several problem-solving interventions that utilise a "circle" approach have been applied within the field of educational psychology, for example, Circle Time, Circle of Friends, Sharing Circles, Circle of Adults and Solution Circles. This research explored two interventions, Solution Circles and Circle of Adults, and used thematic…
De Bono, Edward
A group of children were presented with several tasks, including the invention of a sleep machine and a machine to weigh elephants. The tasks were chosen to involve the children in coping with problems of a distinct character. A study of the children's drawings and interpretations shows that children's thinking ability is not very different from…
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…
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.
Team Learning on Messy Problems
Rouwette, E.A.J.A.; Vennix, J.A.M.
2007-01-01
Concentrates on procedures used to foster group learning for a particular type of problem, the so-called messy problem. The distinctive feature of messy problems is that the people involved have different ideas on what the problem is or whether there even is a problem. Nevertheless, those involved i
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.
A model for routing problem in quay management problem
Zirour, Mourad; Oughalime, Ahmed; Liong, Choong-Yeun; Ismail, Wan Rosmanira; Omar, Khairuddin
2014-06-01
Quadratic Assignment Problem (QAP), like Vehicle Routing Problem, is one of those optimization problems that interests many researchers in the last decades. The Quay Management Problem is a specific problem which could be presented as a QAP which involves a double assignment of customers and products toward loading positions using lifting trucks. This study focuses on the routing problem while delivering the customers' demands. In this problem, lifting trucks will route around the storage sections to collect the products then deliver to the customers who are assigned to specific loading positions. The objective of minimizing the residence time for each customer is sought. This paper presents the problem and the proposed model.
Heuristics for Multidimensional Packing Problems
DEFF Research Database (Denmark)
Egeblad, Jens
In this thesis we consider solution methods for packing problems. Packing problems occur in many different situations both directly in the industry and as sub-problems of other problems. High-quality solutions for problems in the industrial sector may be able to reduce transportation and production...... costs significantly. For packing problems in general are given a set of items and one of more containers. The items must be placed within the container such that some objective is optimized and the items do not overlap. Items and container may be rectangular or irregular (e.g. polygons and polyhedra...... methods. Two important problem variants are the knapsack packing problem and the strip-packing problem. In the knapsack packing problem, each item is given a profit value, and the problem asks for the subset with maximal profit that can be placed within one container. The strip-packing problem asks...
How to solve mathematical problems
Wickelgren, Wayne A
1995-01-01
Seven problem-solving techniques include inference, classification of action sequences, subgoals, contradiction, working backward, relations between problems, and mathematical representation. Also, problems from mathematics, science, and engineering with complete solutions.
Common Sleep Problems (For Teens)
... Surgery? A Week of Healthy Breakfasts Shyness Common Sleep Problems KidsHealth > For Teens > Common Sleep Problems Print ... have emotional problems, like depression. What Happens During Sleep? You don't notice it, of course, but ...
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.
Scattering problems in elastodynamics
Diatta, Andre; Kadic, Muamer; Wegener, Martin; Guenneau, Sebastien
2016-09-01
In electromagnetism, acoustics, and quantum mechanics, scattering problems can routinely be solved numerically by virtue of perfectly matched layers (PMLs) at simulation domain boundaries. Unfortunately, the same has not been possible for general elastodynamic wave problems in continuum mechanics. In this Rapid Communication, we introduce a corresponding scattered-field formulation for the Navier equation. We derive PMLs based on complex-valued coordinate transformations leading to Cosserat elasticity-tensor distributions not obeying the minor symmetries. These layers are shown to work in two dimensions, for all polarizations, and all directions. By adaptative choice of the decay length, the deep subwavelength PMLs can be used all the way to the quasistatic regime. As demanding examples, we study the effectiveness of cylindrical elastodynamic cloaks of the Cosserat type and approximations thereof.
Scattering problems in elastodynamics
Diatta, Andre; Wegener, Martin; Guenneau, Sebastien
2016-01-01
In electromagnetism, acoustics, and quantum mechanics, scattering problems can routinely be solved numerically by virtue of perfectly matched layers (PMLs) at simulation domain boundaries. Unfortunately, the same has not been possible for general elastodynamic wave problems in continuum mechanics. In this paper, we introduce a corresponding scattered-field formulation for the Navier equation. We derive PMLs based on complex-valued coordinate transformations leading to Cosserat elasticity-tensor distributions not obeying the minor symmetries. These layers are shown to work in two dimensions, for all polarizations, and all directions. By adaptative choice of the decay length, the deep subwavelength PMLs can be used all the way to the quasi-static regime. As demanding examples, we study the effectiveness of cylindrical elastodynamic cloaks of the Cosserat type and approximations thereof.
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.
Problems in Cybersemiotic Modelling
DEFF Research Database (Denmark)
Brier, Søren
2014-01-01
the Peircean theory of the observer as the phaneroscopic foundation. 4. Cobley points out that both models, as they are combined in Cybersemiotics lacks to integrate a theory of interest and power. They are too consensual in their view on communication. This is a general problem in both theories. Still Luhmann......Going from an empirical to an informational paradigm of cognition and communication, does not really help us to analyze, how the living systems manage to make a meaningful interpretation of environment that is useful for their survival and procreation. Other models are needed. 1. There is von...... Uexküll’s cybernetic-behavioral model, which has the problem of being placed in a Platonic, static worldview. The Umwelt of an animal is a construction limited of its functional realism of survival. It is connected to the species. 2. Ture von Uexküll and Søren Brier both realized that Maturana and Varela...
Medical problems in pregnancy.
Narayan, Bhaskar; Nelson-Piercy, Catherine
2016-12-01
The prevalence of medical problems in pregnancy is increasing because of a complex interplay between demographic and lifestyle factors, and developments in modern medicine. Maternal mortality and morbidity resulting from treatable medical conditions, such as venous thromboembolism, epilepsy and autoimmune disease, have not decreased in recent years. This is despite a marked decrease in overall maternal mortality. It is vital that all physicians acquire a basic knowledge and understanding of medical problems in pregnancy. This includes prepregnancy measures such as counselling and optimisation of medical therapy, as well as multidisciplinary management throughout pregnancy and the postpartum period. Prompt recognition and treatment of acute and chronic illness is of clear benefit, and most drugs and many radiological investigations may be used in pregnancy.
1979-01-01
The corrosion problem, it turned out, stemmed from the process called electrolysis. When two different metals are in contact, an electrical potential is set up between them; when the metals are surrounded by an electrolyte, or a conducting medium, the resulting reaction causes corrosion, often very rapid corrosion. In this case the different metals were the copper grounding system and the ferry's aluminum hull; the dockside salt water in which the hull was resting served as the electrolyte. After identifying the source of the trouble, the Ames engineer provided a solution: a new wire-and-rod grounding system made of aluminum like the ferry's hull so there would no longer be dissimilar metals in contact. Ames research on the matter disclosed that the problem was not unique to the Golden Gate ferries. It is being experienced by many pleasure boat operators who are probably as puzzled about it as was the Golden Gate Transit Authority.
Institute of Scientific and Technical Information of China (English)
王锡凡; 王秀丽
2000-01-01
The pricing of electricity trasmission requires determining how much use each generator is making of a transmission line and what is each generator’s contribution to the system losses. Such problems cannot be solved by only using Kirchoff’s laws. This paper proposes two current decomposition axioms based on which the theories and models are established for the current trace problem. To create an efficient algorithm the graph theory is employed. It is proved that there is no directed circuit in a directed current distribution graph. According to this theorem a very simple and efficient algorithm based on recursive elimination process is suggested. A simple example is used to explain the algorithm .
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.
The Boolean Isomorphism problem
Energy Technology Data Exchange (ETDEWEB)
Agrawal, M. [Indian Institute of Technology, Kanpur (India); Thierauf, T. [Universitaet Ulm (Germany)
1996-12-31
We investigate the computational complexity of the Boolean Isomorphism problem (BI): on input of two Boolean formulas F and G decide whether there exists a permutation of the variables of G such that F and G become equivalent. Our main result is a one-round interactive proof for BI, where the verifier has access to an NP oracle. To obtain this, we use a recent result from learning theory by Bshouty et.al. that Boolean formulas can be learned probabilistically with equivalence queries and access to an NP oracle. As a consequence, BI cannot be {sigma}{sup p}{sub 2} complete unless the Polynomial Hierarchy collapses. This solves an open problem posed in [BRS95]. Further properties of BI are shown: BI has And- and Or-functions, the counting version, No. BI, can be computed in polynomial time relative to BI, and BI is self-reducible.
DEFF Research Database (Denmark)
Hansen, David
2012-01-01
employee strengths in continuou simprovements of the work system. The research question was: “How can Lean problem solving and Appreciative Inquiry be combined for optimized work system innovation?” The research project was carried out as a co-creation process with close cooperation between researcher......Many industrial production work systems have increased in complexity, and their new business model scompete on innovation, rather than low cost.At a medical device production facility committed to Lean Production, a research project was carried out to use Appreciative Inquiry to better engage...... and participants and was documented by qualitative methods. This paper presents an academic literature review on Appreciative Inquiry and problem solving for continuous improvements that did not reveal successful attempts in combining the two.Both the literature and the empirical study showed one of the main...
Hansen, David
2012-01-01
Many industrial production work systems have increased in complexity, and their new business model scompete on innovation, rather than low cost.At a medical device production facility committed to Lean Production, a research project was carried out to use Appreciative Inquiry to better engage employee strengths in continuou simprovements of the work system. The research question was: “How can Lean problem solving and Appreciative Inquiry be combined for optimized work system innovation?”The r...
Gol'dman, I I
2010-01-01
A comprehensive collection of problems of varying degrees of difficulty in nonrelativistic quantum mechanics, with answers and completely worked-out solutions. Among the topics: one-dimensional motion, transmission through a potential barrier, commutation relations, angular momentum and spin, and motion of a particle in a magnetic field. An ideal adjunct to any textbook in quantum mechanics, useful in courses in atomic and nuclear physics, mathematical methods in physics, quantum statistics and applied differential equations. 1961 edition.
Martinez-Camara, Marta; Dokmanic, Ivan; Ranieri, Juri; Scheibler, Robin; Vetterli, Martin; STOHL Andreas
2013-01-01
Knowing what amount of radioactive material was released from Fukushima in March 2011 and at what time instants is crucial to assess the risk, the pollution, and to understand the scope of the consequences. Moreover, it could be used in forward simulations to obtain accurate maps of deposition. But these data are often not publicly available. We propose to estimate the emission waveforms by solving an inverse problem. Previous approaches have relied on a detailed expert guess of how the relea...
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.
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....
CHIH HSUN HSIEH
2011-01-01
The work presented in this paper has been motivated primarily by Zadeh's idea of linguistic variables intended to provide rigorous mathematical modeling of natural language and CWW, Computing With Words. This paper reports some modeling of the linguistic inventory problems where CWW have been implemented: linguistic production inventory, linguistic inventory models under linguistic demand and linguistic lead time, linguistic production inventory models based on the preference of a decision ma...
Localized Geometric Query Problems
Augustine, John; Maheshwari, Anil; Nandy, Subhas C; Roy, Sasanka; Sarvattomananda, Swami
2011-01-01
A new class of geometric query problems are studied in this paper. We are required to preprocess a set of geometric objects $P$ in the plane, so that for any arbitrary query point $q$, the largest circle that contains $q$ but does not contain any member of $P$, can be reported efficiently. The geometric sets that we consider are point sets and boundaries of simple polygons.
2016-07-22
problem in 2-D networks. We then develop two polynomial-time approximation algorithms that offer and approximation ratios for general directed hypergraphs...for both 1-Dand1.5-Dnetworks.This algorithmdoes not require the knowledge of eavesdropper locations and achieves the best performance offered by any...received October 22, 2013; revised February 28, 2014; accepted April 12, 2014; approved by IEEE/ACM TRANSACTIONS ON NETWORKING Ed- itor G. Xue. Date of
Wang, Mao-Che; Liu, Chia-Yu; Shiao, An-Suey; Wang, Tyrone
2005-08-01
Acute diffuse otitis externa (swimmer's ear), otomycosis, exostoses, traumatic eardrum perforation, middle ear infection, and barotraumas of the inner ear are common problems in swimmers and people engaged in aqua activities. The most common ear problem in swimmers is acute diffuse otitis externa, with Pseudomonas aeruginosa being the most common pathogen. The symptoms are itching, otalgia, otorrhea, and conductive hearing loss. The treatment includes frequent cleansing of the ear canal, pain control, oral or topical medications, acidification of the ear canal, and control of predisposing factors. Swimming in polluted waters and ear-canal cleaning with cotton-tip applicators should be avoided. Exostoses are usually seen in people who swim in cold water and present with symptoms of accumulated debris, otorrhea and conductive hearing loss. The treatment for exostoses is transmeatal surgical removal of the tumors. Traumatic eardrum perforations may occur during water skiing or scuba diving and present with symptoms of hearing loss, otalgia, otorrhea, tinnitus and vertigo. Tympanoplasty might be needed if the perforations do not heal spontaneously. Patients with chronic otitis media with active drainage should avoid swimming, while patients who have undergone mastoidectomy and who have no cavity problems may swim. For children with ventilation tubes, surface swimming is safe in a clean, chlorinated swimming pool. Sudden sensorineural hearing loss and some degree of vertigo may occur after diving because of rupture of the round or oval window membrane.
Quantum Counterfeit Coin Problems
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.
Ruskey, Frank; Williams, Aaron
In the classic Josephus problem, elements 1, 2,...,n are placed in order around a circle and a skip value k is chosen. The problem proceeds in n rounds, where each round consists of traveling around the circle from the current position, and selecting the kth remaining element to be eliminated from the circle. After n rounds, every element is eliminated. Special attention is given to the last surviving element, denote it by j. We generalize this popular problem by introducing a uniform number of lives ℓ, so that elements are not eliminated until they have been selected for the ℓth time. We prove two main results: 1) When n and k are fixed, then j is constant for all values of ℓ larger than the nth Fibonacci number. In other words, the last surviving element stabilizes with respect to increasing the number of lives. 2) When n and j are fixed, then there exists a value of k that allows j to be the last survivor simultaneously for all values of ℓ. In other words, certain skip values ensure that a given position is the last survivor, regardless of the number of lives. For the first result we give an algorithm for determining j (and the entire sequence of selections) that uses O(n 2) arithmetic operations.
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.
Characteristics of Problems in Problem-based Learning
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
Thinking Process of Naive Problem Solvers to Solve Mathematical Problems
Mairing, Jackson Pasini
2017-01-01
Solving problems is not only a goal of mathematical learning. Students acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations by learning to solve problems. In fact, there were students who had difficulty in solving problems. The students were naive problem solvers. This research aimed to describe…
Obstacle problems in mathematical physics
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.
Institute of Scientific and Technical Information of China (English)
詹华税; 赵俊宁
2005-01-01
本文证明了拟线性退化抛物方程 (e)u/(e)t=n∑i=1 (e)/(e)xi(aij(u)(e)u/(e)xi)+n∑i=1 (e)bi(u)/(e)xi -c(u), u(x,0)=u0(x),aij(u)ξiξj≥0,(A)ξ∈Rn 的Cauchy问题BV解的唯一性和稳定性.
Problem Order Implications for Learning
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…
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.
Creating Games from Mathematical Problems
Pinter, Klara
2011-01-01
The emphasis on problem solving and problem solving courses has become a standard staple of most teacher preparation programs in mathematics. While opinions differ on whether problem solving should be integrated throughout the preparatory courses or teachers should also have a dedicated course for it, everybody agrees that problem solving skills…
Extended Mixed Vector Equilibrium Problems
Directory of Open Access Journals (Sweden)
Mijanur Rahaman
2014-01-01
Full Text Available We study extended mixed vector equilibrium problems, namely, extended weak mixed vector equilibrium problem and extended strong mixed vector equilibrium problem in Hausdorff topological vector spaces. Using generalized KKM-Fan theorem (Ben-El-Mechaiekh et al.; 2005, some existence results for both problems are proved in noncompact domain.
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
Elementary topology problem textbook
Viro, O Ya; Netsvetaev, N Yu; Kharlamov, V M
2008-01-01
This textbook on elementary topology contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment centered at the notions of fundamental group and covering space. The book is tailored for the reader who is determined to work actively. The proofs of theorems are separated from their formulations and are gathered at the end of each chapter. This makes the book look like a pure problem book and encourages the reader to think through each formulation. A reader who prefers a more traditional style can either find the pr
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.
1982-10-01
Artificial Intelig ~ence (Vol. III, edited by Paul R. Cohen and’ Edward A.. Feigenbaum)’, The chapter was written B’ Paul Cohen, with contributions... Artificial Intelligence (Vol. III, edited by Paul R. Cohen and EdWard A. Feigenbaum). The chapter was written by Paul R. Cohen, with contributions by Stephen...Wheevoats"EntermdI’ Planning and Problem ’Solving by Paul R. Cohen Chaptb-rXV-of Volumec III’of the Handbook of Artificial Intelligence edited by Paul R
The Gilbert Arborescence Problem
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.
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...
DEFF Research Database (Denmark)
Janstrup, Kira
2010-01-01
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...
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.
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)
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…
Abstraction and Problem Reformulation
Giunchiglia, Fausto
1992-01-01
In work done jointly with Toby Walsh, the author has provided a sound theoretical foundation to the process of reasoning with abstraction (GW90c, GWS9, GW9Ob, GW90a). The notion of abstraction formalized in this work can be informally described as: (property 1), the process of mapping a representation of a problem, called (following historical convention (Sac74)) the 'ground' representation, onto a new representation, called the 'abstract' representation, which, (property 2) helps deal with the problem in the original search space by preserving certain desirable properties and (property 3) is simpler to handle as it is constructed from the ground representation by "throwing away details". One desirable property preserved by an abstraction is provability; often there is a relationship between provability in the ground representation and provability in the abstract representation. Another can be deduction or, possibly inconsistency. By 'throwing away details' we usually mean that the problem is described in a language with a smaller search space (for instance a propositional language or a language without variables) in which formulae of the abstract representation are obtained from the formulae of the ground representation by the use of some terminating rewriting technique. Often we require that the use of abstraction results in more efficient .reasoning. However, it might simply increase the number of facts asserted (eg. by allowing, in practice, the exploration of deeper search spaces or by implementing some form of learning). Among all abstractions, three very important classes have been identified. They relate the set of facts provable in the ground space to those provable in the abstract space. We call: TI abstractions all those abstractions where the abstractions of all the provable facts of the ground space are provable in the abstract space; TD abstractions all those abstractions wllere the 'unabstractions' of all the provable facts of the abstract space are
Muna, Demitri; Allen, Alice; Ashley, Richard; Asmus, Daniel; Azzollini, Ruyman; Bannister, Michele; Beaton, Rachael; Benson, Andrew; Berriman, G Bruce; Bilicki, Maciej; Boyce, Peter; Bridge, Joanna; Cami, Jan; Cangi, Eryn; Chen, Xian; Christiny, Nicholas; Clark, Christopher; Collins, Michelle; Comparat, Johan; Cook, Neil; Croton, Darren; Davids, Isak Delberth; Depagne, Éric; Donor, John; Santos, Leonardo A dos; Douglas, Stephanie; Du, Alan; Durbin, Meredith; Erb, Dawn; Faes, Daniel; Fernández-Trincado, J G; Foley, Anthony; Fotopoulou, Sotiria; Frimann, Søren; Frinchaboy, Peter; Garcia-Dias, Rafael; Gawryszczak, Artur; George, Elizabeth; Gonzalez, Sebastian; Gordon, Karl; Gorgone, Nicholas; Gosmeyer, Catherine; Grasha, Katie; Greenfield, Perry; Grellmann, Rebekka; Guillochon, James; Gurwell, Mark; Haas, Marcel; Hagen, Alex; Haggard, Daryl; Haines, Tim; Hall, Patrick; Hellwing, Wojciech; Herenz, Edmund Christian; Hinton, Samuel; Hlozek, Renee; Hoffman, John; Holman, Derek; Holwerda, Benne Willem; Horton, Anthony; Hummels, Cameron; Jacobs, Daniel; Jensen, Jens Juel; Jones, David; Karick, Arna; Kelley, Luke; Kenworthy, Matthew; Kitchener, Ben; Klaes, Dominik; Kohn, Saul; Konorski, Piotr; Krawczyk, Coleman; Kuehn, Kyler; Kuutma, Teet; Lam, Michael T; Lane, Richard; Liske, Jochen; Lopez-Camara, Diego; Mack, Katherine; Mangham, Sam; Mao, Qingqing; Marsh, David J E; Mateu, Cecilia; Maurin, Loïc; McCormac, James; Momcheva, Ivelina; Monteiro, Hektor; Mueller, Michael; Munoz, Roberto; Naidu, Rohan; Nelson, Nicholas; Nitschelm, Christian; North, Chris; Nunez-Iglesias, Juan; Ogaz, Sara; Owen, Russell; Parejko, John; Patrício, Vera; Pepper, Joshua; Perrin, Marshall; Pickering, Timothy; Piscionere, Jennifer; Pogge, Richard; Poleski, Radek; Pourtsidou, Alkistis; Price-Whelan, Adrian M; Rawls, Meredith L; Read, Shaun; Rees, Glen; Rein, Hanno; Rice, Thomas; Riemer-Sørensen, Signe; Rusomarov, Naum; Sanchez, Sebastian F; Santander-García, Miguel; Sarid, Gal; Schoenell, William; Scholz, Aleks; Schuhmann, Robert L; Schuster, William; Scicluna, Peter; Seidel, Marja; Shao, Lijing; Sharma, Pranav; Shulevski, Aleksandar; Shupe, David; Sifón, Cristóbal; Simmons, Brooke; Sinha, Manodeep; Skillen, Ian; Soergel, Bjoern; Spriggs, Thomas; Srinivasan, Sundar; Stevens, Abigail; Streicher, Ole; Suchyta, Eric; Tan, Joshua; Telford, O Grace; Thomas, Romain; Tonini, Chiara; Tremblay, Grant; Tuttle, Sarah; Urrutia, Tanya; Vaughan, Sam; Verdugo, Miguel; Wagner, Alexander; Walawender, Josh; Wetzel, Andrew; Willett, Kyle; Williams, Peter K G; Yang, Guang; Zhu, Guangtun; Zonca, Andrea
2016-01-01
The Astropy Project (http://astropy.org) is, in its own words, "a community effort to develop a single core package for Astronomy in Python and foster interoperability between Python astronomy packages." For five years this project has been managed, written, and operated as a grassroots, self-organized, almost entirely volunteer effort while the software is used by the majority of the astronomical community. Despite this, the project has always been and remains to this day effectively unfunded. Further, contributors receive little or no formal recognition for creating and supporting what is now critical software. This paper explores the problem in detail, outlines possible solutions to correct this, and presents a few suggestions on how to address the sustainability of general purpose astronomical software.
Baweja, R; Calhoun, S; Baweja, R; Singareddy, R
2013-10-01
Sleep complaints and sleep disorders are common during childhood and adolescence. The impact of not getting enough sleep may affect children's' physical health as well emotional, cognitive and social development. Insomnia, sleep-disordered breathing, parasomnias and sleep disturbances associated with medical and psychiatric disorders are some of the commonly encountered sleep disorders in this age group. Changes in sleep architecture and the amount of sleep requirement associated with each stage of development should be considered during an evaluation of sleep disorders in children. Behavioral treatments should be used initially wherever possible especially considering that most pharmacologic agents used to treat pediatric sleep disorders are off-label. In this review we address the most common sleep problems in children/adolescents as they relate to prevalence, presentation and symptoms, evaluation and management.
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.
The supersymmetric flavor problem
Dimopoulos, Savas K; Dimopoulos, Savas; Sutter, Dave
1995-01-01
The supersymmetric SU(3)\\times SU(2)\\times U(1) theory with minimal particle content and general soft supersymmetry breaking terms has 110 physical parameters in its flavor sector: 30 masses, 39 real mixing angles and 41 phases. The absence of an experimental indication for the plethora of new parameters places severe constraints on theories posessing Planck or GUT-mass particles and suggests that theories of flavor conflict with naturalness. We illustrate the problem by studying the processes \\mu \\rightarrow e + \\gamma and K^0 - \\bar{K}^0 mixing which are very sensitive probes of Planckian physics: a single Planck mass particle coupled to the electron or the muon with a Yukawa coupling comparable to the gauge coupling typically leads to a rate for \\mu \\rightarrow e + \\gamma exceeding the present experimental limits. A possible solution is that the messengers which transmit supersymmetry breaking to the ordinary particles are much lighter than M_{\\rm Planck}.
Benson, Brian
2007-01-01
In this paper we study the Three Hat Problem which appeared in Puzzle Corner of the Technology Review magazine. This puzzle gives a scenario in which three players wearing hats are sitting together and each hat can be seen by everyone except the player that is wearing that hat. Each player is told that all of the hats contain a positive integer and that two of the integers add to the third. In an ordered, turn-wise, modular fashion, each player truthfully states whether or not he knows his integer. We give a strategy which allows for one of the players to solve for his integer for all possible integer configurations of the puzzle and prove it is the optimal such strategy.
Mauroy, Alexandre; Taslakian, Perouz; Langerman, Stefan; Jungers, Raphaël
2016-09-01
A four-bar linkage is a mechanism consisting of four rigid bars which are joined by their endpoints in a polygonal chain and which can rotate freely at the joints (or vertices). We assume that the linkage lies in the 2-dimensional plane so that one of the bars is held horizontally fixed. In this paper we consider the problem of reconfiguring a four-bar linkage using an operation called a pop. Given a four-bar linkage, a pop reflects a vertex across the line defined by its two adjacent vertices along the polygonal chain. Our main result shows that for certain conditions on the lengths of the bars, the neighborhood of any configuration that can be reached by smooth motion can also be reached by pops. The proof relies on the fact that pops are described by a map on the circle with an irrational number of rotation.
Directory of Open Access Journals (Sweden)
Erik af Edholm
1975-01-01
Full Text Available The myth of the recurrence of the golden age after a period of accelerating miseries ("messianic woes" in the near future is of course not peculiar to the chiliasm of the European later middle ages. On the contrary, it belongs to the basic eschatological themes of millenarism in general. These themes are found also in Hindu tradition. To determine those general characteristics of traditional Hindu society which can contribute to an explanation of the relative unimportance of peasant rebellions and the lack of chiliastic mass movements, is not a problem to be solved within the field of the history of religions. For example, the egalitarian message of the bhakti saints, disputing the hierarchy, did not preclude that the salvationist sects did adapt to the caste system. The religious movements contributed to and gave ideological form to adjustments within the existing social structure. Obviously there was little need for millenarism in this process.
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
Gaussian quantum marginal problem
Eisert, J; Sanders, B C; Tyc, T
2007-01-01
The quantum marginal problem asks what local spectra are consistent with a given state of a composite quantum system. This setting, also referred to as the question of the compatibility of local spectra, has several applications in quantum information theory. Here, we introduce the analogue of this statement for Gaussian states for any number of modes, and solve it in generality, for pure and mixed states, both concerning necessary and sufficient conditions. Formally, our result can be viewed as an analogue of the Sing-Thompson Theorem (respectively Horn's Lemma), characterizing the relationship between main diagonal elements and singular values of a complex matrix: We find necessary and sufficient conditions for vectors (d1, ..., dn) and (c1, ..., cn) to be the symplectic eigenvalues and symplectic main diagonal elements of a strictly positive real matrix, respectively. More physically speaking, this result determines what local temperatures or entropies are consistent with a pure or mixed Gaussian state of ...
Routing and scheduling problems
DEFF Research Database (Denmark)
Reinhardt, Line Blander
be that the objects routed have an availability time window and a delivery time window or that locations on the path have a service time window. When routing moving transportation objects such as vehicles and vessels schedules are made in connection with the routing. Such schedules represent the time for the presence...... to a destination on a predefined network, the routing and scheduling of vessels in a liner shipping network given a demand forecast to be covered, the routing of manpower and vehicles transporting disabled passengers in an airport and the vehicle routing with time windows where one version studied includes edge...... of a connection between two locations. This could be an urban bus schedule where busses are routed and this routing creates a bus schedule which the passengers between locations use. In this thesis various routing and scheduling problems will be presented. The topics covered will be routing from an origin...
Instrumentation problems for physicians.
Turner, G O
1980-01-01
The physician has, for whatever reasons, diminished his or her level of involvement on the team dedicated to developing, refining, and evaluating medical technology. As a result, the challenge confronting the physician and the technology development team today is to orchestrate a team structure that will ensure the greatest input and commitment from physicians and other professionals during current and future technology development. The charges of cost escalation and dehumanization in our system of health care delivery will also be discussed, as will the lack of, or confusion about, access to data concerning cost of a given instrument, and fuzzy semantics and perspectives on technology and instrumentation. The author suggests answers to, or means to ameliorate, the problems.
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.
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.
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.
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.
Fostering Information Problem Solving Skills Through Completion Problems and Prompts
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.
Fostering information problem solving skills through completion problems and prompts
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.
Mechanics problems in undergraduate physics
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
Energy Technology Data Exchange (ETDEWEB)
Ullrich, Peter [Institut fuer Informatik, TU Muenchen, Boltzmannstrasse 3, D-85748 Garching (Germany); Werner, Ernst [Institut fuer Physik, Universitaet Regensburg, Universitaetsstrasse 31, D-93040 Regensburg (Germany)
2006-05-19
We investigate the generally assumed inconsistency in light cone quantum field theory that the restriction of a massive, real scalar free field to the nullplane {sigma} = {l_brace}x{sup 0} + x{sup 3} = 0{r_brace} is independent of mass (Leutwyler, Klauder and Streit 1970 Nuovo Cimento A 66 536), but the restriction of the two-point function is mass dependent (see, e.g., Nakanishi and Yamawaki 1977 Nucl. Phys. B 122 15; Yamawaki K 1997 Proc. Int. Workshop New Nonperturbative Methods and Quantization on the Light Cone (Les Houches, France) Preprint hep-th/9707141). We resolve this inconsistency by showing that the two-point function has no canonical restriction to {sigma} in the sense of distribution theory. Only the so-called tame restriction of the two-point function, which we have introduced in (Ullrich P 2004 Uniqueness in the characteristic Cauchy problem of the Klein-Gordon equation and tame restrictions of generalized functions Preprint math-ph/0408022 (submitted)) exists. Furthermore, we show that this tame restriction is indeed independent of the mass. Hence the inconsistency is induced by the erroneous assumption that the two-point function has a (canonical) restriction to {sigma}.
The Skill of Problem by The Method of Structural Function%利用构造函数法解题技巧
Institute of Scientific and Technical Information of China (English)
翟延慧
2001-01-01
数学分析作为经典数学的重要基础知识的一个分支，其思想、内容和方法的内涵极为丰富。对初学者来说，做习题是很困难的事，但有些习惯的解法是有规律可循的。其中构造函数法就是常用的一个方法，例如拉格朗日中值定理和柯西中值定理等许多定理和命题都是用构造函数法来证明的。%Mathematics Analytic is branch of important basic knowledge for classical mathematics. The intention is so rich for the idea,content and method. For beginning man,Solving problem is very diffcult thing. In fact,it is regular to find right answer for the exercises. Usually,people apply the method of structural function. For example,Lagrange mid-valve theorem and Cauchy mid-valve proposition was proved by the method of structural function
Problem effectiveness in a course using problem-based learning
D.H.J.M. Dolmans (Diana); W.H. Gijselaers (Wim); H.G. Schmidt (Henk); S.B. van der Meer
1993-01-01
textabstractBackground. Problem-based learning (PBL) emphasizes active generation of learning issues by students. Both students and reachers, however, tend to worry that not all important knowledge will be acquired. To explore this question, problem effectiveness (i.e., for each problem, the degree
Problem Solving through an Optimization Problem in Geometry
Poon, Kin Keung; Wong, Hang-Chi
2011-01-01
This article adapts the problem-solving model developed by Polya to investigate and give an innovative approach to discuss and solve an optimization problem in geometry: the Regiomontanus Problem and its application to football. Various mathematical tools, such as calculus, inequality and the properties of circles, are used to explore and reflect…