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.
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.
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.
The Cauchy problem of f(R) gravity
Lanahan-Tremblay, Nicolas; Faraoni, Valerio
2007-01-01
The initial value problem of metric and Palatini f(R)gravity is studied by using the dynamical equivalence between these theories and Brans-Dicke gravity. The Cauchy problem is well-formulated for metric f(R)gravity in the presence of matter and well-posed in vacuo. For Palatini f(R)gravity, instead, the Cauchy problem is not well-formulated.
Energy Technology Data Exchange (ETDEWEB)
Giovangigli, V.; Graille, B. [Ecole Polytechnique, CMAP, 91 - Palaiseau (France)
2005-01-01
We investigate a system of partial differential equations modeling dissipative plasmas. Transport fluxes are anisotropic linear combinations of gradients and also include zeroth order contributions due to electromagnetic forces. There are also source terms depending on the solution gradient. By using entropic variables, we first recast the system in a partially symmetric form and next in the form of a quasilinear partially symmetric hyperbolic-parabolic system. Using a result of Vol'Pert and Hudjaev, we prove local existence and uniqueness of a bounded smooth solution to the Cauchy problem. (authors)
On the Cauchy Problem Describing an Electron-Phonon Interaction
Institute of Scientific and Technical Information of China (English)
Jo(a)o-Paulo DIAS; Mário FIGUEIRA; Filipe OLIVEIRA
2011-01-01
In this paper, a model is derived to describe a quartic anharmonic interatomic interaction with an external potential involving a pair electron-phonon. The authors study the corresponding Cauchy Problem in the semilinear and quasilinear cases.
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.
THE CAUCHY PROBLEM FOR SOME DISPERSIVE WAVE EQUATIONS
Institute of Scientific and Technical Information of China (English)
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].
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.
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.
CAUCHY PROBLEM FOR GENERAL FIRST ORDER INHOMOGENEOUS QUASILINEAR HYPERBOLIC SYSTEMS
Institute of Scientific and Technical Information of China (English)
李书敏
2002-01-01
In this paper, we consider Cauchy problem for general first order inhomogeneous quasilinear strictly hyperbolic systems. Under the matching condition, we first give an estimate on inhomogeneous terms. By this estimate, we obtain the asymptotic behaviour for the life-span of C1 solutions with "slowly" decaying and small initial data and prove that the formation of singularity is due to the envelope of characteristics of the same family.
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.
Institute of Scientific and Technical Information of China (English)
Chen Guowang; Xue Hongxia
2008-01-01
In this article, the existence, uniqueness and regularities of the global gener-alized solution and global classical solution for the periodic boundary value problem and the Cauchy problem of the general cubic double dispersion equation utt -uxx-auxxtt+bux4 - duxxt= f(u)xx are proved, and the sufficient conditions of blow-up of the solutions for the Cauchy problems in finite time are given.
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.
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.
Cauchy problem in spacetimes with closed timelike curves
International Nuclear Information System (INIS)
The laws of physics might permit the existence, in the real Universe, of closed timelike curves (CTC's). Macroscopic CTC's might be a semiclassical consequence of Planck-scale, quantum gravitational, Lorentzian foam, if such foam exists. If CTC's are permitted, then the semiclassical laws of physics (the laws with gravity classical and other fields quantized or classical) should be augmented by a principle of self-consistency, which states that a local solution to the equations of physics can occur in the real Universe only if it can be extended to be part of a global solution, one which is well defined throughout the (nonsingular regions of) classical spacetime. The consequences of this principle are explored for the Cauchy problem of the evolution of a classical, massless scalar field Φ (satisfying □Φ=0) in several model spacetimes with CTC's
GLOBALLY SMOOTH SOLUTIONS TO CAUCHY PROBLEM OF A QUASILINEAR HYPERBOLIC SYSTEM ARISING IN BIOLOGY
Institute of Scientific and Technical Information of China (English)
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.
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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.
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.
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.
L~p-L~q decay estimates of solutions to Cauchy problems of thermoviscoelastic systems
Institute of Scientific and Technical Information of China (English)
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.
Origins and development of the Cauchy problem in general relativity
Ringström, Hans
2015-06-01
The seminal work of Yvonne Choquet-Bruhat published in 1952 demonstrates that it is possible to formulate Einstein's equations as an initial value problem. The purpose of this article is to describe the background to and impact of this achievement, as well as the result itself. In some respects, the idea of viewing the field equations of general relativity as a system of evolution equations goes back to Einstein himself; in an argument justifying that gravitational waves propagate at the speed of light, Einstein used a special choice of coordinates to derive a system of wave equations for the linear perturbations on a Minkowski background. Over the following decades, Hilbert, de Donder, Lanczos, Darmois and many others worked to put Einstein's ideas on a more solid footing. In fact, the issue of local uniqueness (giving a rigorous justification for the statement that the speed of propagation of the gravitational field is bounded by that of light) was already settled in the 1930s by the work of Stellmacher. However, the first person to demonstrate both local existence and uniqueness in a setting in which the notion of finite speed of propagation makes sense was Yvonne Choquet-Bruhat. In this sense, her work lays the foundation for the formulation of Einstein's equations as an initial value problem. Following a description of the results of Choquet-Bruhat, we discuss the development of three research topics that have their origin in her work. The first one is local existence. One reason for addressing it is that it is at the heart of the original paper. Moreover, it is still an active and important research field, connected to the problem of characterizing the asymptotic behaviour of solutions that blow up in finite time. As a second topic, we turn to the questions of global uniqueness and strong cosmic censorship. These questions are of fundamental importance to anyone interested in justifying that the Cauchy problem makes sense globally. They are also closely
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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.
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 geometric Cauchy problem for surfaces with Lorentzian harmonic Gauss maps
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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 surfac...
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.
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.
Cauchy Problem for Quasilinear Hyperbolic Systems with Higher Order Dissipative Terms
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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.
The Cauchy problem for a model of immiscible gas flow with large data
Energy Technology Data Exchange (ETDEWEB)
Sande, Hilde
2008-12-15
The thesis consists of an introduction and two papers; 1. The solution of the Cauchy problem with large data for a model of a mixture of gases. 2. Front tracking for a model of immiscible gas flow with large data. (AG) refs, figs
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.
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.
ON THE CAUCHY PROBLEM ASSOCIATED TO THE BRINKMAN FLOW IN R^n
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Rafael José Iorio Junior
2012-10-01
Full Text Available In this work we deal with the Cauchy problem associated to the Brinkman flow, which models fluid flow in certain types of porous media. We study local and global well-posedness in Sobolev spaces $H^{s}(mathbb{R}^{n}, s>displaystylefrac{n}{2}+1,$ using Kato's theory for quasilinear equations and parabolic regu-larization.
Cauchy problem and initial traces for a doubly nonlinear degenerate parabolic equation
Institute of Scientific and Technical Information of China (English)
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.
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.
Numerical analysis of Cauchy-type problem arising in electrical engineering
Dücker, Monika
2010-01-01
Inverse problems arise often in physical and technical processes. In this dissertation we consider problems of Cauchy-type based on the application of hybrid insulation. The experimental setup takes place at the NTNU Trondheim which placed at the disposal the measurements for the calculation. In this case we search Dirichlet or Neumann control for given Neumann measurements. After describing the problem of hybrid insulation and introducing the basic principals of functional analysis we analys...
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.
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.
Initial surface disturbance on a shear current: the Cauchy--Poisson problem with a twist
Ellingsen, Simen Å.
2014-01-01
We solve for the first time the classical linear Cauchy--Poisson problem for the time evolution an initial surface disturbance when a uniform shear current is present beneath the surface. The solution is general, including the effects of gravity, surface tension and constant finite depth. The particular case of an initially Gaussian disturbance of width $b$ is studied for different values of three system parameters: a "shear Froude number" $S\\sqrt{b/g}$ ($S$ is the uniform vorticity), the Bon...
Probability representations of Cauchy problem solutions for quantum mechanics equations
International Nuclear Information System (INIS)
Probability representations of quantum mechanics equations in a number of cases allow to see a new interpretation of the generally accepted notions; they also serve as a theoretical basis of the numerical solution of a problems. Probability representations of the solutions of Schroedinger equations and Dirac-Pauli vector equations are presented. In addition, the Heisenberg picture of quantum mechanics equation is considered
Shaldanbayev, Amir; Shomanbayeva, Manat; Kopzhassarova, Asylzat
2016-08-01
This paper proposes a fundamentally new method of investigation of a singularly perturbed Cauchy problem for a linear system of ordinary differential equations based on the spectral theory of equations with deviating argument.
Cauchy problem for some fractional nonlinear ultra-parabolic equations
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Fatma Al-Musalhi
2016-07-01
Full Text Available Blowing-up solutions to nonlocal nonlinear ultra-parabolic equations is presented. The obtained results will contribute in the development of ultra-parabolic equations and enrich the existing non-extensive literature on fractional nonlinear ultra-parabolic problems. Our method of proof relies on a suitable choice of a test function and the weak formulation approach of the sought for solutions.
Efficient numerical method for solving Cauchy problem for the Gamma equation
Koleva, Miglena N.
2011-12-01
In this work we consider Cauchy problem for the so called Gamma equation, derived by transforming the fully nonlinear Black-Scholes equation for option price into a quasilinear parabolic equation for the second derivative (Greek) Γ = VSS of the option price V. We develop an efficient numerical method for solving the model problem concerning different volatility terms. Using suitable change of variables the problem is transformed on finite interval, keeping original behavior of the solution at the infinity. Then we construct Picard-Newton algorithm with adaptive mesh step in time, which can be applied also in the case of non-differentiable functions. Results of numerical simulations are given.
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.
Well-Posedness of the Cauchy Problem for a Space-Dependent Anyon Boltzmann Equation
Arkeryd, Leif; Nouri, Anne
2015-01-01
A fully non-linear kinetic Boltzmann equation for anyons is studied in a periodic 1d setting with large initial data. Strong L 1 solutions are obtained for the Cauchy problem. The main results concern global existence, uniqueness and stabililty. We use the Bony functional, the two-dimensional velocity frame specific for anyons, and an initial layer analysis that moves the solution away from a critical value. 1 Anyons and the Boltzmann equation. Let us first recall the definition of anyon. Con...
On existence of weak solutions to a Cauchy problem for one class of conservation laws
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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.
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.
Two-point boundary value and Cauchy formulations in an axisymmetrical MHD equilibrium problem
International Nuclear Information System (INIS)
In this paper we present two equilibrium solvers for axisymmetrical toroidal configurations, both based on the expansion in poloidal angle method. The first one has been conceived as a two-point boundary value solver in a system of coordinates with straight field lines, while the second one uses a well-conditioned Cauchy formulation of the problem in a general curvilinear coordinate system. In order to check the capability of our moment methods to describe equilibrium accurately, a comparison of the moment solutions with analytical solutions obtained for a Solov'ev equilibrium has been performed. (author)
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.
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.
The Geometric Cauchy Problem for Surfaces With Lorentzian Harmonic Gauss maps
Brander, David
2010-01-01
The geometric Cauchy problem for a class of surfaces in a 3-dimensional pseudo-Riemannian manifold is to find the surface which contains a given curve with a prescribed normal vector field along the curve. We consider this problem for constant negative Gauss surfaces (pseudospherical surfaces) in Euclidean 3-space, and for timelike non-minimal constant mean curvature (CMC) surfaces in the Lorentz-Minkowski 3-space. We prove that there is a unique solution if the prescribed curve is non-characteristic, and for characteristic initial curves (asymptotic curves for pseudospherical surfaces and null curves for timelike CMC) it is necessary and sufficient for similar data to be prescribed along an additional characteristic curve that intersects the first. The proofs also give a method of constructing all solutions using loop group techniques. The method used is the infinite dimensional D'Alembert type representation for surfaces associated to Lorentzian harmonic maps (1-1 wave maps) into symmetric spaces, developed...
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.
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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.
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.
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.
Initial surface disturbance on a shear current: the Cauchy--Poisson problem with a twist
Ellingsen, Simen Å
2014-01-01
We solve for the first time the classical linear Cauchy--Poisson problem for the time evolution an initial surface disturbance when a uniform shear current is present beneath the surface. The solution is general, including the effects of gravity, surface tension and constant finite depth. The particular case of an initially Gaussian disturbance of width $b$ is studied for different values of three system parameters: a "shear Froude number" $S\\sqrt{b/g}$ ($S$ is the uniform vorticity), the Bond number and the depth relative to the initial perturbation width. Different phase and group velocity in different directions yield very different wave patterns in different parameter regimes when the shear is strong, and the well known pattern of diverging ring waves in the absence of shear can take on very different qualitative behaviours. For a given shear Froude number, both finite depth and nonzero capillary effects are found to weaken the influence of the shear on the resulting wave pattern. The various patterns are...
Well-posedness of the Cauchy problem for models of large amplitude internal waves
International Nuclear Information System (INIS)
We consider in this paper the 'shallow-water/shallow-water' asymptotic model obtained in Choi and Camassa (1999 J. Fluid Mech. 396 1–36), Craig et al (2005 Commun. Pure. Appl. Math. 58 1587–641) (one-dimensional interface) and Bona et al (2008 J. Math. Pures Appl. 89 538–66) (two-dimensional interface) from the two-layer system with rigid lid, for the description of large amplitude internal waves at the interface of two layers of immiscible fluids of different densities. For one-dimensional interfaces, this system is of hyperbolic type and its local well-posedness does not raise serious difficulties, although other issues (blow-up, loss of hyperbolicity, etc) turn out to be delicate. For two-dimensional interfaces, the system is nonlocal. Nevertheless, we prove that it conserves some properties of 'hyperbolic type' and show that the associated Cauchy problem is locally well posed in suitable Sobolev classes provided some natural restrictions are imposed on the data. These results are illustrated by numerical simulations with emphasis on the formation of shock waves
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).
Campos Palomino, Juvitsa Milena
2009-01-01
El propósito de este trabajo es abordar la buena colocación en los espacios de Sobolev Hs(T2) para s≥1 del problema de Cauchy asociado a una ecuación del tipo Kuramoto-Sivashisky bidimensional periódica; que modela fenómenos físicos que ocurren en películas delgadas y plasma. / Abstract. The purpose of this work is to establish the well-posedness in the spaces Sobolev spaces Hs(T2) para s≥1 for the Cauchy problem associated for the Kuramoto-Sivashisky two-dimensional equation in the periodica...
KdV－ Burgers方程的 Cauchy问题%The Cauchy Problem of KdV－ Burgers Equation
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方伟中
2001-01-01
In this paper the author gives the existence and uniqueness of the solution for Cauchy′ s problem of mixed type functional differential equation.The uniqueness and stability of solution of the Cauchy problem for KdV－ Burgers′ type equation has been proved in L2 sense.%本文给出了一类混合型泛函微分方程的 Cauchy问题的存在性和唯一性，并在 L2范数的意义下讨论了 KdV－ Burgers方程解的唯一性和稳定性。
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
THE CAUCHY PROBLEM FOR THE GENERALIZED KORTEWEG-DE VRIES-BURGERS EQUATION IN H-s
Institute of Scientific and Technical Information of China (English)
贾月玲
2003-01-01
The Cauchy problem for the generalized Korteweg-de Vries-Burgers equation is considered and the local existence and uniqueness of solutions in Lq (0, T; Lp)∩ L∞(0, T; H-s)(0 ≤ s ＜ 1) are obtained for initial data inH-s. Moreover, the local solutions are global if the initial data are sufficiently small in critical case. Particularly, for s = 0, the generalized Korteweg-de Vries-Burgers equation satisfies the energy equality, so the initial data can be arbitrarily large to obtain the global solution.
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)
MIAO; Changxing(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.
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.
International Nuclear Information System (INIS)
Many-dimensional non-strictly hyperbolic systems of conservation laws with a radially degenerate flux function are considered. For such systems the set of entropies is defined and described, the concept of generalized entropy solution of the Cauchy problem is introduced, and the properties of generalized entropy solutions are studied. The class of strong generalized entropy solutions is distinguished, in which the Cauchy problem in question is uniquely soluble. A condition on the initial data is described that ensures that the generalized entropy solution is strong and therefore unique. Under this condition the convergence of the 'vanishing viscosity' method is established. An example presented in the paper shows that a generalized entropy solution is not necessarily unique in the general case
Lantsman, L
2006-01-01
We show that manifest superfluid properties of the Minkowskian Higgs model with vacuum BPS monopoles quantized by Dirac may be described in the framework of the Cauchy problem to the Gribov ambiguity equation. The latter equation specifies the ambiguity in choosing the covariant Coulomb (transverse) gauge for Yang-Mills fields represented as topological Dirac variables, may be treated as solutions to the Gauss law constraint at the removal of temporal components of these fields. We demonstrate that the above Cauchy problem comes just to fixing the covariant Coulomb gauge for topological Dirac variables in the given initial time instant $t_0$ and finding the solutions to the Gribov ambiguity equation in the shape of vacuum BPS monopoles and excitations over the BPS monopole vacuum referring to the class of multipoles. The next goal of the present study will be specifying the look of Gribov topological multipliers entering Dirac variables in the Minkowskian Higgs model quantized by Dirac, especially at the spat...
Directory of Open Access Journals (Sweden)
Marzena Pytel-Kudela
2006-01-01
Full Text Available The analytical properties of dissolving operators related with the Cauchy problem for a class of nonautonomous partial differential equations in Hilbert spaces are studied using theory of bi-linear forms in respectively rigged Hilbert spaces triples. Theorems specifying the existence of a dissolving operator for a class of adiabatically perturbed nonautonomous partial differential equations are stated. Some applications of the results obtained are discussed.
Symmetry Reduction and Cauchy Problems for a Class of Fourth-Order Evolution Equations
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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.
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.
Institute of Scientific and Technical Information of China (English)
成军祥; 尚海锋
2013-01-01
研究了方程ut－div（｜Dum｜p－2 Dum ）＝t－σuq的Cauchy问题，其中m＞0， p＞1。 此方程为双非线性抛物方程，根据参数m， p的不同取值，方程主部会发生双重退化或双重奇异性。 本文利用先验估计和紧性方法以及对参数m， p作精细划分，得到了测度初值解的最优存在性。%The Cauchy problem of the equation.
On analytic continuability of the missing Cauchy datum for Helmholtz boundary problems
DEFF Research Database (Denmark)
Karamehmedovic, Mirza
2015-01-01
. To this end we identify and characterise a special subspace of the standard pseudodifferential operators with real-analytic symbols. The result is applicable in the estimation of the domain of analytic continuation of solutions across planar pieces of the boundary.......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...
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.
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.
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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.
Kazeykina, Anna
2011-01-01
In the present paper we are concerned with the Novikov--Veselov equation at negative energy, i.e. with the $(2 + 1)$--dimensional analog of the KdV equation integrable by the method of inverse scattering for the two--dimensional Schr\\"odinger equation at negative energy. We show that the solution of the Cauchy problem for this equation with non--singular scattering data behaves asymptotically as $\\frac{\\const}{t^{3/4}}$ in the uniform norm at large times $t$. We also present some arguments which indicate that this asymptotics is optimal.
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.
On the comparison of Cauchy mean values
Losonczi László
2002-01-01
Suppose that and exist, with , on . Then there is (moreover if ) such that where denotes the divided difference of at the points . This is the Cauchy Mean Value Theorem for divided differences (see e.g. [4]). If the function is invertible then is a mean value of . It is called the Cauchy mean of the numbers and will be denoted by ). Here we completely solve the comparison problem of Cauchy means in the special cases and . In the general case we find necessary conditions (which ar...
Faugeras, Blaise; Blum, Jacques; Boulbe, Cedric
2010-01-01
A numerical method for the computation of the magnetic flux in the vacuum surrounding the plasma in a Tokamak is investigated. It is based on the formulation of a Cauchy problem which is solved through the minimization of a constitutive law error functional. Several numerical experiments are conducted which show the efficiency of the method.
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.
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.
International Nuclear Information System (INIS)
Cosmology is a discipline that encompasses many diverse aspects of physics and astronomy. This is part of its attraction, but also a reason why it is difficult for new researchers to acquire sufficient grounding to enable them to make significant contributions early in their careers. For this reason there are many cosmology textbooks aimed at the advanced undergraduate/beginning postgraduate level. Physical Foundations of Cosmology by Viatcheslav Mukhanov is a worthy new addition to this genre. Like most of its competitors it does not attempt to cover every single aspect of the subject but chooses a particular angle and tries to unify its treatment around that direction. Mukhanov has chosen to focus on the fundamental principles underlying modern cosmological research at the expense of some detail at the frontiers. The book places great emphasis on the particle-astrophysics interface and issues connected with the thermal history of the big-bang model. The treatment of big-bang nucleosynthesis is done in much more detail than in most texts at a similar level, for example. It also contains a very extended and insightful discussion of inflationary models. Mukhanov makes great use of approximate analytical arguments to develop physical intuition rather than concentrating on numerical approaches. The book is quite mathematical, but not in a pedantically formalistic way. There is much use of 'order-of-magnitude' dimensional arguments which undergraduate students often find difficult to get the hang of, but which they would do well to assimilate as early as possible in their research careers. The text is peppered with problems for the reader to solve, some straightforward and some exceedingly difficult. Solutions are not provided. The price to be paid for this foundational approach is that there is not much about observational cosmology in this book, and neither is there much about galaxy formation or large-scale structure. It also neglects some of the trendier recent
THE CAUCHY-KOVALEVSKAYA THEOREM-OLD AND NEW
Institute of Scientific and Technical Information of China (English)
W. Tutschke
2005-01-01
The paper surveys interactions between complex and functional-analytic methods in the Cauchy-Kovalevskaya theory. For instance, the behaviour of the derivative of a bounded holomorphic function led to abstract versions of the Cauchy-Kovalevskaya Theorem.Recent trends in the Cauchy-Kovalevskaya theory are based on the concept of associated differential operators. Since an evolution operator may posses several associated operators, initial data may be decomposed into components belonging to different associated spaces. This technique makes it also possible to solve ill-posed initial value problems.
Institute of Scientific and Technical Information of China (English)
蒋毅; 成和平; 孟宪良; 蒲成林
2006-01-01
For the Cauchy problem for the nonlinear Klein-Gordon equation with potential,we define new stable and unstable sets for the initial data.We prove that if during the evolution enters into the unstable set,the solution blows up in finite time.If during the evolution enters into the stable set,the solution is global.By using scaling argument,we also answer the question of how small the initial data are the global solution of the Cauchy problem exists.%对带势的非线性Klein-Gordon方程柯西问题,我们定义了新的对于初值的稳定和不稳定集.我们证明了如果发展进入了不稳定集,解在有限时间内爆破;如果发展进入了稳定集,解整体存在.运用势并讨论,我们回答了当初值为多少时,柯西问题的整体解存在.
Identifiability of surface sources from Cauchy data
International Nuclear Information System (INIS)
We explore the reconstruction of surface sources from single Cauchy data on the potential. Identifiability is first proven when the location of these sources is known and their density is to be sought. We also investigate the ill-posedness degree to establish that the problem is severely ill-posed, and exhibit the necessary orthogonality conditions fulfilled by exact Cauchy data, for which the process of recovering the density function of the sources succeeds. We later turn to the more difficult reconstruction of the location, the shape and the density function of the sources. Identifiability cannot be obtained for general geometries. Nevertheless, under some acceptable assumptions on the size and the location of these sources, we are able to state identifiability results
Institute of Scientific and Technical Information of China (English)
郝兴文; 王钦
2011-01-01
Kuznetsov方法是估计双曲型方程熵解与它的数值解之间误差的有效方法,文中应用该方法证明一个二阶退化抛物-双曲方程熵解的唯一性,并用双变量方法得到了熵解在初值的L1连续性.%Kuznetsov＇s method is a useful tool to establish the error estimate between numerical solutions and entropy weak solution for hyperbolic equation.This paper uses this method to prove the uniqueness to the Cauchy problem of a special example of second order degenerate parabolic-hyperbolic equation,Meanwhile,the paper obtained that entropy solutions are continuous at t=0 in the sense of L1 norm by the double variable device.
On Bimodal Offset Cauchy Distribution
Directory of Open Access Journals (Sweden)
Girija S.V.S.
2013-05-01
Full Text Available The bivariate Cauchy distribution has received applications in many areas, including biological analyses, clinical trials, stochastic modeling of decreasing failure rate life components, study of labour turnover, queuing theory and reliability (Nayak (1987 and Lee and Gross (1991. In the study of biological analyses, clinical trials and reliability circular distributions will yield suitable results. Circular data arises in a number of different areas such as geological, meteorological, biological and industrial sciences. It is not suggestive to use standard statistical techniques to model circular data, due to the circular geometry of the sample space (p.2 Jammalamadaka and Sen Gupta (2001. It is possible to construct a circular model by transforming a bivariate linear random variate to just its directional component and the resultant model is called ‘offset distribution’. In the literature most of the available circular models were constructed by wrapping a linear model. In recent years some wrapped models were constructed by Dattatreya Rao et al (2007. Here an attempt is made to exploit method of offsetting on Bivariate Cauchy distribution to construct a circular model named by us “OFFSET CAUCHY DISTRIBUTION (OC”. The characteristic function of the Offset Cauchy model is derived and its characteristics are discussed.
Cauchy stress in mass distributions
Koenemann, F. H.
2001-01-01
The thermodynamic definition of pressure P = dU/dV is one form of the principle that in a given state, the mass in V and potential are proportional. Subject of this communication is the significance of this principle for the understanding of Cauchy stress.
Control of Cauchy System for an Elliptic Operator
Institute of Scientific and Technical Information of China (English)
G.MASSENGO MOPHOU; O.NAKOULIMA
2009-01-01
The control of a Cauchy system for an elliptic operator seems to be globally an open problem. In this paper, we analyze this problem using a regularization method which consists in viewing a singular problem as a limit of a family of well-posed problems. Following this analysis and assuming that the interior of considered convex is non-empty, we obtain a singular optimality system (S.O.S.) for the considered control problem.
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
The log-convexity of the poly-Cauchy numbers
Komatsu, Takao; Zhao, Feng-Zhen
2016-01-01
In 2013, Komatsu introduced the poly-Cauchy numbers, which generalize Cauchy numbers. Several generalizations of poly-Cauchy numbers have been considered since then. One particular type of generalizations is that of multiparameter-poly-Cauchy numbers. In this paper, we study the log-convexity of the multiparameter-poly-Cauchy numbers of the first kind and of the second kind. In addition, we also discuss the log-behavior of multiparameter-poly-Cauchy numbers.
Katz, Mikhail G.; Tall, David
2012-01-01
The Dirac delta function has solid roots in 19th century work in Fourier analysis and singular integrals by Cauchy and others, anticipating Dirac's discovery by over a century, and illuminating the nature of Cauchy's infinitesimals and his infinitesimal definition of delta.
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 ...
Pérez, Javier; Aizpuru, Antonio
1999-01-01
En este artículo presentamos un estudio contextualizado de Cours d’Analyse de Cauchy, analizando su significado e importancia. Presentamos especial atención al grado de elaboración teórica de límites, continuidad, series, números reales funciones y series completas, relacionando las aportaciones de Cauchi del nivel conceptual anterior a esta ahora.
Institute of Scientific and Technical Information of China (English)
蒋毅
2011-01-01
For the Cauchy problem of the nonlinear wave equation with linear damping and potential terms, we define new stable and unstable sets for the initial data. We prove that if during the evolution enters into the unstable set, the solution blows up in finite time. If during the evolution enters into the stable set, the solution is global. By using scaling argument, we also answer the question of how small the initial data are, the global solution of the Cauchy oroblem exists.%本文考虑带线性坍塌项和竞争势的非线性波动方程柯西问题．定义了新的稳定集和不稳定集，证明了如果初值进入不稳定集，则解在有限时间爆破；如果初值进入稳定集，则整体解存在．运用势井讨论，回答了当初值在多么小的时候，该柯西问题的整体解存在．
Dirac Equation with External Potential and Initial Data on Cauchy Surfaces
Deckert, D -A
2014-01-01
With this paper we provide a mathematical review on the initial-value problem of the one-particle Dirac equation on space-like Cauchy hypersurfaces for compactly supported external potentials. We, first, discuss the physically relevant spaces of solutions and initial values in position and mass shell representation; second, review the action of the Poincar\\'e group as well as gauge transformations on those spaces; third, introduce generalized Fourier transforms between those spaces and prove convenient Paley-Wiener- and Sobolev-type estimates. These generalized Fourier transforms immediately allow the construction of a unitary evolution operator for the free Dirac equation between the Hilbert spaces of square-integrable wave functions of two respective Cauchy surfaces. With a Picard-Lindel\\"of argument this evolution map is generalized to the Dirac evolution including the external potential. For the latter we introduce a convenient interaction picture on Cauchy surfaces. These tools immediately provide anothe...
Moving Heat Source Reconstruction from the Cauchy Boundary Data
Directory of Open Access Journals (Sweden)
Nilson C. Roberty
2010-01-01
Full Text Available We consider the problem of reconstruction of an unknown characteristic transient thermal source inside a domain. By introducing the definition of an extended dirichlet-to-Neumann map in the time-space cylinder and the adoption of the anisotropic Sobolev-Hilbert spaces, we can treat the problem with methods similar to those used in the analysis of the stationary source reconstruction problem. Further, the finite difference θ scheme applied to the transient heat conduction equation leads to a model based on a sequence of modified Helmholtz equation solutions. For each modified Helmholtz equation the characteristic star-shape source function may be reconstructed uniquely from the Cauchy boundary data. Using representation formula, we establish reciprocity functional mapping functions that are solutions of the modified Helmholtz equation to their integral in the unknown characteristic support.
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.
Quantum Cauchy surfaces in canonical quantum gravity
Lin, Chun-Yen
2016-09-01
For a Dirac theory of quantum gravity obtained from the refined algebraic quantization procedure, we propose a quantum notion of Cauchy surfaces. In such a theory, there is a kernel projector for the quantized scalar and momentum constraints, which maps the kinematic Hilbert space {{K}} into the physical Hilbert space {{H}}. Under this projection, a quantum Cauchy surface isomorphically represents a physical subspace {{D}}\\subset {{H}} with a kinematic subspace {{V}}\\subset {{K}}. The isomorphism induces the complete sets of Dirac observables in {{D}}, which faithfully represent the corresponding complete sets of self-adjoint operators in {{V}}. Due to the constraints, a specific subset of the observables would be ‘frozen’ as number operators, providing a background physical time for the rest of the observables. Therefore, a proper foliation with the quantum Cauchy surfaces may provide an observer frame describing the physical states of spacetimes in a Schrödinger picture, with the evolutions under a specific physical background. A simple model will be supplied as an initiative trial.
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.
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...
An intermediate distribution between Gaussian and Cauchy distributions
Liu, Tong; Dai, Wu-Sheng; Xie, Mi
2012-01-01
In this paper, we construct an intermediate distribution linking the Gaussian and the Cauchy distribution. We provide the probability density function and the corresponding characteristic function of the intermediate distribution. Because many kinds of distributions have no moment, we introduce weighted moments. Specifically, we consider weighted moments under two types of weighted functions: the cut-off function and the exponential function. Through these two types of weighted functions, we can obtain weighted moments for almost all distributions. We consider an application of the probability density function of the intermediate distribution on the spectral line broadening in laser theory. Moreover, we utilize the intermediate distribution to the problem of the stock market return in quantitative finance.
A Cauchy-Davenport theorem for semigroups
Tringali, Salvatore
2012-01-01
We generalize the Davenport transform and use it to prove that, for a (possibly non-commutative) cancellative semigroup $\\mathbb A = (A, +)$ and non-empty subsets $X,Y$ of $A$ such that the subsemigroup generated by $Y$ is commutative, we have $|X + Y| \\ge \\min(\\omega(Y), |X| + |Y| - 1)$, where $\\omega(Y) := \\sup_{y_0 \\in Y \\cap \\mathbb A^{\\times}} \\inf_{y \\in Y \\setminus \\{y_0\\}} ||$. This carries over the Cauchy-Davenport theorem to the broader setting of semigroups, and it implies, in part...
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.
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.
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.
Abstract Description of Internet Traffic of Generalized Cauchy Type
Directory of Open Access Journals (Sweden)
Ming Li
2012-01-01
. Therefore, there is a limitation for fGn to accurately model traffic. Recently, the generalized Cauchy (GC process was introduced to model traffic with the flexibility to separately measure the fractal dimension DGC and the Hurst parameter HGC of traffic. However, there is a fundamental problem whether or not there exists the generality that the GC model is more conformable with real traffic than single parameter models, such as fGn, irrelevant of traffic traces used in experimental verification. The solution to that problem remains unknown but is desired for model evaluation in traffic theory or for model selection against specific issues, such as queuing analysis relating to the autocorrelation function (ACF of arrival traffic. The key contribution of this paper is our solution to that fundamental problem (see Theorem 3.17 with the following features in analysis. (i Set-valued analysis of the traffic of the fGn type. (ii Set-valued analysis of the traffic of the GC type. (iii Revealing the generality previously mentioned by comparing metrics of the traffic of the fGn type to that of the GC type.
Cauchy Based Matched Filter for Retinal Vessels Detection
Zolfagharnasab, Hooshiar; Naghsh-Nilchi, Ahmad Reza
2014-01-01
In this paper, a novel matched filter based on a new kernel function with Cauchy distribution is introduced to improve the accuracy of the automatic retinal vessel detection compared with other available matched filter-based methods, most notably, the methods built on Gaussian distribution function. Several experiments are conducted to pick the best values of the parameters for the new designed filter, including both Cauchy function parameters as well as the matched filter parameters such as ...
Variational approach for restoring blurred images with cauchy noise
DEFF Research Database (Denmark)
Sciacchitano, Federica; Dong, Yiqiu; Zeng, Tieyong
2015-01-01
The restoration of images degraded by blurring and noise is one of the most important tasks in image processing. In this paper, based on the total variation (TV) we propose a new variational method for recovering images degraded by Cauchy noise and blurring. In order to obtain a strictly convex...... and denoising images corrupted by Cauchy noise. Comparison with other existing and well-known methods is provided as well....
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.
Cauchy-Kowalevski and polynomial ordinary differential equations
Directory of Open Access Journals (Sweden)
Roger J. Thelwell
2012-01-01
Full Text Available The Cauchy-Kowalevski Theorem is the foremost result guaranteeing existence and uniqueness of local solutions for analytic quasilinear partial differential equations with Cauchy initial data. The techniques of Cauchy-Kowalevski may also be applied to initial-value ordinary differential equations. These techniques, when applied in the polynomial ordinary differential equation setting, lead one naturally to a method in which coefficients of the series solution are easily computed in a recursive manner, and an explicit majorization admits a clear a priori error bound. The error bound depends only on immediately observable quantities of the polynomial system; coefficients, initial conditions, and polynomial degree. The numerous benefits of the polynomial system are shown for a specific example.
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.
Area Theorem and Smoothness of Compact Cauchy Horizons
Minguzzi, E.
2015-10-01
We obtain an improved version of the area theorem for not necessarily differentiable horizons which, in conjunction with a recent result on the completeness of generators, allows us to prove that under the null energy condition every compactly generated Cauchy horizon is smooth and compact. We explore the consequences of this result for time machines, topology change, black holes and cosmic censorship. For instance, it is shown that compact Cauchy horizons cannot form in a non-empty spacetime which satisfies the stable dominant energy condition wherever there is some source content.
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.
A Cauchy-Davenport theorem for linear maps
Herdade, Simao; Kim, John; Kopparty, Swastik
2015-01-01
We prove a version of the Cauchy-Davenport theorem for general linear maps. For subsets $A,B$ of the finite field $\\mathbb{F}_p$, the classical Cauchy-Davenport theorem gives a lower bound for the size of the sumset $A+B$ in terms of the sizes of the sets $A$ and $B$. Our theorem considers a general linear map $L: \\mathbb{F}_p^n \\to \\mathbb{F}_p^m$, and subsets $A_1, \\ldots, A_n \\subseteq \\mathbb{F}_p$, and gives a lower bound on the size of $L(A_1 \\times A_2 \\times \\ldots \\times A_n)$ in ter...
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].
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...
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
First order differential operator associated to the Cauchy-Riemann operator in a Clifford algebra
International Nuclear Information System (INIS)
The complex differentiation transforms holomorphic functions into holomorphic functions. Analogously, the conjugate Cauchy-Riemann operator of the Clifford algebra transforms regular functions into regular functions. This paper determines more general first order operator L (matrix-type) for which Lu is regular provided u is regular. For such operator L, the initial value problem ∂u / ∂t = L (t, x, u, ∂u / ∂x) (1) u(0, x) = φ(x) (2) is solvable for an arbitrary regular function φ and the solution is regular in x for each t. (author)
Hamilton-Jacobi Theory in Cauchy Data Space
Campos, CéAdric M.; de Leóan, Manuel; de Diego, David Martín; Vaquero, Miguel
2015-12-01
Recently, M. de LeóAn et al. [8] have developed a geometric Hamilton-Jacobi theory for classical fields in the setting of multisymplectic geometry. Our purpose in the current paper is to establish the corresponding Hamilton-Jacobi theory in the Cauchy data space, and relate both approaches.
Unit Root Testing in Heteroscedastic Panels Using the Cauchy Estimator
Demetrescu, Matei; Hanck, Christoph
2012-01-01
The Cauchy estimator of an autoregressive root uses the sign of the first lag as instrumental variable. The resulting IV t-type statistic follows a standard normal limiting distribution under a unit root case even under unconditional heteroscedasticity, if the series to be tested has no deterministi
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
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.
Cauchy, Sturm et les racines des équations
Benis Sinaceur, Hourya
1992-01-01
International audience Relying both on chronological data and textual analysis, this article seeks to determine the mutual influence between A.-L. Cauchy's and Ch.-F. Sturm's research from 1829 to around 1840 on the roots of algebraic equations. The first aim is to specify the elements of a micro-history, strictly limited in time and centered on a well-defined question, yet bound up with the endeavour to build up a mathematical physics at the beginning of the 19th century. The second aim p...
External Field QED on Cauchy Surfaces for Varying Electromagnetic Fields
Deckert, D.-A.; Merkl, F.
2016-08-01
The Shale-Stinespring Theorem (J Math Mech 14:315-322, 1965) together with Ruijsenaar's criterion (J Math Phys 18(4):720-737, 1977) provide a necessary and sufficient condition for the implementability of the evolution of external field quantum electrodynamics between constant-time hyperplanes on standard Fock space. The assertion states that an implementation is possible if and only if the spatial components of the external electromagnetic four-vector potential {A_μ} are zero. We generalize this result to smooth, space-like Cauchy surfaces and, for general {A_μ}, show how the second-quantized Dirac evolution can always be implemented as a map between varying Fock spaces. Furthermore, we give equivalence classes of polarizations, including an explicit representative, that give rise to those admissible Fock spaces. We prove that the polarization classes only depend on the tangential components of {A_μ} w.r.t. the particular Cauchy surface, and show that they behave naturally under Lorentz and gauge transformations.
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.
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%.
Moving Heat Source Reconstruction from Cauchy Boundary Data: The Cartesian Coordinates Case
Directory of Open Access Journals (Sweden)
Nilson C. Roberty
2011-01-01
Full Text Available We consider the problem of reconstruction of an unknown characteristic interval and block transient thermal source inside a domain. By exploring the definition of an Extended Dirichlet to Neumann map in the time space cylinder that has been introduced in Roberty and Rainha (2010a, we can treat the problem with methods similar to that used in the analysis of the stationary source reconstruction problem. Further, the finite difference θ-scheme applied to the transient heat conduction equation leads to a model based on a sequence of modified Helmholtz equation solutions. For each modified Helmholtz equation the characteristic interval and parallelepiped source function may be reconstructed uniquely from the Cauchy boundary data. Using representation formula we establish reciprocity functional mapping functions that are solutions of the modified Helmholtz equation to their integral in the unknown characteristic support. Numerical experiment for capture of an interval and an rectangular parallelepiped characteristic source inside a cubic box domain from boundary data are presented in threedimensional and one-dimensional implementations. The problem of centroid determination is addressed and questions are discussed from an computational points of view.
Noise Kernel for Reissner Nordstrom Metric: Results at Cauchy Horizon
Satin, Seema
2015-01-01
We obtain the Noise Kernel, which defines quantum stress tensor fluctuations for Reissner Nordstrom metric modeled as gravitationally collapsing spacetime, after transforming to coordinates suitable for the evolution.The quantum stress tensor fluctuations at the final stage of collapse namely naked singularity or a black hole are then analysed.The behavior of this entity which is central to semiclassical stochastic gravity at the Cauchy Horizon shows markedly different behaviour from earlier obtained result for self similar Tolman Bondi case showing a very unique divergence. It is known that the quantum stress tensor itself diverges at CH for both Tolman Bondi and Reissner Nordstrom metric. In contrast, it can now be seen that the correlations of the fluctuations of the stress tensor behave differently for the two cases. We give a discussion and further directions of investigations for this interesting behaviour in the two cases (regarding the collapse scenario).
On Cauchy conditions for asymmetric mixed convection boundary layer flows
Energy Technology Data Exchange (ETDEWEB)
Amaouche, Mustapha [Laboratoire de Physique Theorique, Universite de Bejaia (Algeria); Kessal, Mohand [Departement Transport et Equipement Petrolier, Faculte des Hydrocarbures et de la Chimie, Universite de Boumerdes, 35000, Boumerdes (Algeria)
2003-06-01
The fundamental question of how and where does an asymmetric mixed convection boundary layer flow around a heated horizontal circular cylinder begin to develop is raised. We first transform the classical boundary layer equations by using an integral method of Karman-Pohlhausen type and obtain two coupled equations governing the evolutions of the dynamic and thermal boundary layers. Because of its global character, the implemented method allows to bypass the difficulty of downstream-upstream interactions. Cauchy conditions characterizing the starting of the boundary layers are found; they are obtained in a surprisingly simple manner for the limiting cases corresponding to Pr=1, Pr{yields}0 and Pr{yields}{infinity}. Otherwise, these conditions can be found by using a prediction correction algorithm. Some numerical experiments are finally performed in order to illustrate the theory. (authors)
Gowdy-symmetric cosmological models with Cauchy horizons ruled by non-closed null generators
Hennig, Jörg
2016-08-01
Smooth Gowdy-symmetric generalized Taub-NUT solutions are a class of inhomogeneous cosmological models with spatial three-sphere topology. They have a past Cauchy horizon with closed null-generators, and they have been shown to develop a second, regular Cauchy horizon in the future, unless in special, well-defined singular cases. Here we generalize these models to allow for past Cauchy horizons ruled by non-closed null generators. In particular, we show local and global existence of such a class of solutions with two functional degrees of freedom. This removes a periodicity condition for the asymptotic data at the past Cauchy horizon that was required before. Moreover, we derive a three-parametric family of exact solutions within that class and study its properties.
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...
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.
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.
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.
Ansorg, Marcus; Hennig, Jörg
2009-06-01
We study the interior electrovacuum region of axisymmetric and stationary black holes with surrounding matter and find that there exists always a regular inner Cauchy horizon inside the black hole, provided the angular momentum J and charge Q of the black hole do not vanish simultaneously. In particular, we derive an explicit relation for the metric on the Cauchy horizon in terms of that on the event horizon. Moreover, our analysis reveals the remarkable universal relation (8piJ);{2}+(4piQ;{2});{2}=A;{+}A;{-}, where A+ and A- denote the areas of event and Cauchy horizon, respectively. PMID:19658851
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.
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.
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.
Jian-Guo Zheng; Chao-Qun Zhang; Yong-Quan Zhou
2015-01-01
Artificial bee colony (ABC) algorithm is a popular swarm intelligence technique inspired by the intelligent foraging behavior of honey bees. However, ABC is good at exploration but poor at exploitation and its convergence speed is also an issue in some cases. To improve the performance of ABC, a novel ABC combined with grenade explosion method (GEM) and Cauchy operator, namely, ABCGC, is proposed. GEM is embedded in the onlooker bees’ phase to enhance the exploitation ability and accelerate c...
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.
Dukkipati, Ambedkar; Murty, Narasimha M; Bhatnagar, Shalabh
2004-01-01
Boltzmann selection is an important selection mechanism in evolutionary algorithms as it has theoretical properties which help in theoretical analysis. However, Boltzmann selection is not used in practice because a good annealing schedule for the `inverse temperature' parameter is lacking. In this paper we propose a Cauchy annealing schedule for Boltzmann selection scheme based on a hypothesis that selection-strength should increase as evolutionary process goes on and distance between two sel...
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
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 tortoise coordinates and the cauchy problem in the stable study of the Schwarzschild black hole
Tian, G; Zhong, S; Tian, Gui-hua; Wang, Shi-kun; Zhong, Shuquan
2006-01-01
Generally, the Schwarzschild black hole was proved stable through two different methods: the mode-decomposition method and the integral method. In the paper, we show the integral method can only apply to the initial data vanishing at both the horizon and the spatial infinity. It can not treat the initial data only vanishing at the spatial infinity. We give an example to show the misleading information caused by the use of the tortoise coordinates in the perturbation equations. Subsequently, the perturbation equation in the Schwarzschild coordinates is shown not sufficient for the stable study.
Approach to a Cauchy Problem in Stability Study of the Schwarzschild Black Hole
Institute of Scientific and Technical Information of China (English)
TIAN Gui-Hua; WANG Shi-Kun; ZHONG Shu-Quan
2007-01-01
Generally, the Schwarzschild black hole is proven to be stable by two different methods: the mode-decomposition method and the integral method. We show that the integral method can only apply to the initial data vanishing at both the horizon and the spatial infinity. It can not treat the initial data only vanishing at the spatial infinity. We give an example to show the misleading information caused by the use of tortoise coordinates in the perturbation equations. Subsequently, the perturbation equations in the Schwarzschild coordinates are shown to be insufficient for the stability study.
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.
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.
Boundedness and decay of scalar waves at the Cauchy horizon of the Kerr spacetime
Hintz, Peter
2015-01-01
Adapting and extending the techniques developed in recent work with Vasy for the study of the Cauchy horizon of cosmological spacetimes, we obtain boundedness, regularity and decay of linear scalar waves on subextremal Reissner-Nordstr\\"om and (slowly rotating) Kerr spacetimes, without any symmetry assumptions; in particular, we provide simple microlocal and scattering theoretic proofs of analogous results by Franzen. We show polynomial decay of linear waves relative to a Sobolev space of order slightly above $1/2$. This complements the generic $H^1_{\\mathrm{loc}}$ blow-up result of Luk and Oh.
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.
Cauchy-Matern Model of Sea Surface Wind Speed at the Lake Worth, Florida
Directory of Open Access Journals (Sweden)
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.
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...
Directory of Open Access Journals (Sweden)
Jian-Guo Zheng
2015-01-01
Full Text Available Artificial bee colony (ABC algorithm is a popular swarm intelligence technique inspired by the intelligent foraging behavior of honey bees. However, ABC is good at exploration but poor at exploitation and its convergence speed is also an issue in some cases. To improve the performance of ABC, a novel ABC combined with grenade explosion method (GEM and Cauchy operator, namely, ABCGC, is proposed. GEM is embedded in the onlooker bees’ phase to enhance the exploitation ability and accelerate convergence of ABCGC; meanwhile, Cauchy operator is introduced into the scout bees’ phase to help ABCGC escape from local optimum and further enhance its exploration ability. Two sets of well-known benchmark functions are used to validate the better performance of ABCGC. The experiments confirm that ABCGC is significantly superior to ABC and other competitors; particularly it converges to the global optimum faster in most cases. These results suggest that ABCGC usually achieves a good balance between exploitation and exploration and can effectively serve as an alternative for global optimization.
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.
$q$-poly-Bernoulli numbers and $q$-poly-Cauchy numbers with a parameter by Jackson's integrals
Komatsu, Takao
2015-01-01
We define $q$-poly-Bernoulli polynomials $B_{n,\\rho,q}^{(k)}(z)$ with a parameter $\\rho$, $q$-poly-Cauchy polynomials of the first kind $c_{n,\\rho,q}^{(k)}(z)$ and of the second kind $\\widehat c_{n,\\rho,q}^{(k)}(z)$ with a parameter $\\rho$ by Jackson's integrals, which generalize the previously known numbers and polynomials, including poly-Bernoulli numbers $B_n^{(k)}$ and the poly-Cauchy numbers of the first kind $c_n^{(k)}$ and of the second kind $\\widehat c_n^{(k)}$. We investigate their p...
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.
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.
Riemann Boundary Value Problems for Koch Curve
Directory of Open Access Journals (Sweden)
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.
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.
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.
Goursat problem for the Yang-Mills-Vlasov system in temporal gauge
Directory of Open Access Journals (Sweden)
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.
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.
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.
A Modified Differential Evolution Algorithm with Cauchy Mutation for Global Optimization
Ali, Musrrat; Pant, Millie; Singh, Ved Pal
Differential Evolution (DE) is a powerful yet simple evolutionary algorithm for optimization of real valued, multi modal functions. DE is generally considered as a reliable, accurate and robust optimization technique. However, the algorithm suffers from premature convergence, slow convergence rate and large computational time for optimizing the computationally expensive objective functions. Therefore, an attempt to speed up DE is considered necessary. This research introduces a modified differential evolution (MDE), a modification to DE that enhances the convergence rate without compromising with the solution quality. In Modified differential evolution (MDE) algorithm, if an individual fails in continuation to improve its performance to a specified number of times then new point is generated using Cauchy mutation. MDE on a test bed of functions is compared with original DE. It is found that MDE requires less computational effort to locate global optimal solution.
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. PMID:23473941
Institute of Scientific and Technical Information of China (English)
时永刚
2005-01-01
信息论测度,特别是Shannon互信息是多模态图像配准的一种重要方法,但除了互信息之外,仍然存在其它的函数来实现这一任务.对互信息、Kullback-Leibler距离和Shannon不等式之间相互关系作了分析,根据这些关系和不等式理论,提出了新的Cauchy-Schwarz距离,并将这一距离测度用于多模态医学图像的配准处理.从计算速度、噪声容忍性、测度函数图形的特点和图像窗口大小影响等几个方面,通过MR和PET医学图像的实验分析,对新的Cauchy-Schwarz距离测度和典型的Shannon信息论测度进行了分析比较.实验结果表明,新的Cauchy-Schwarz距离测度函数同样可以用于多模态图像配准,而且有着更强的噪声容忍性和更为节省的计算量.
N{sup ±}-integrals and boundary values of Cauchy-type integrals of finite measures
Energy Technology Data Exchange (ETDEWEB)
Aliev, R. A., E-mail: aliyevrashid@hotmail.ru, E-mail: alievrashid@box.az [Baku State University (Azerbaijan)
2014-07-31
Let Γ be a simple closed Lyapunov contour with finite complex measure ν, and let G{sup +} be the bounded and G{sup −} the unbounded domains with boundary Γ. Using new notions (so-called N-integration and N{sup +}- and N{sup −}-integrals), we prove that the Cauchy-type integrals F{sup +}(z), z∈G{sup +}, and F{sup −}(z), z∈G{sup −}, of ν are Cauchy N{sup +}- and N{sup −}-integrals, respectively. In the proof of the corresponding results, the additivity property and the validity of the change-of-variable formula for the N{sup +}- and N{sup −}-integrals play an essential role. Bibliography: 21 titles. (paper)
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−.
Energy Technology Data Exchange (ETDEWEB)
Kabal`skii, M.M.
1994-06-05
A method is established for constructing a functional of the variational problem associated with a given nonlinear differential equation of higher order. The Cauchy problem for strongly nonlinear differential equations is solved. The application of this method to the solution of the problem of the resistance of materials is examined. 2 refs.
Multipoint Singular Boundary-Value Problem for Systems of Nonlinear Differential Equations
Directory of Open Access Journals (Sweden)
Zdeněk Šmarda
2009-01-01
Full Text Available A singular Cauchy-Nicoletti problem for a system of nonlinear ordinary differential equations is considered. With the aid of combination of Ważewski's topological method and Schauder's principle, the theorem concerning the existence of a solution of this problem (having the graph in a prescribed domain is proved.
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).
Young, Brent
2010-01-01
Recently, M.K.-H. Kiessling and A.S. Tahvildar-Zadeh proved that a unique global classical solution to the relativistic Vlasov-Poisson system exists whenever the positive, integrable initial datum is spherically symmetric, compactly supported in momentum space, vanishes on characteristics with vanishing angular momentum, and for $\\beta \\ge 3/2$ has $\\mathfrak{L}^{\\beta}$-norm strictly below a positive, critical value $\\mathcal{C}_{\\beta}$. Everything else being equal, data leading to finite t...
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
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.
A unified approach to problems of scattering of surface water waves by vertical barriers
Chakrabarti, A; Banerjea, S; Mandal, BN; Sahoo, T
1997-01-01
A unified analysis involving the solution of multiple integral equations via a simple singular integral equation with a Cauchy type kernel is presented to handle problems of surface water wave scattering by vertical barriers. Some well known results are produced in a simple and systematic manner.
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...
Sedrakian, D M; Khachatrian, A Z
2000-01-01
It is shown that the problem on scattering of an arbitrary polarized plane wave to be incident on the plate of a one-dimensional medium can be formulated as a Cauchy problem for wave equations for s and p waves.
Automorphismes r\\'eels d'un fibr\\'e et op\\'erateurs de Cauchy-Riemann
Crétois, Rémi
2011-01-01
Let $(N,c_N)$ be a complex vector bundle equipped with a real structure over a real curve $(\\Sigma,c_\\Sigma)$ of genus $g \\geq 0$. We compute the sign of the action of the automorphisms of $(N,c_N)$ lifting the identity of $\\Sigma$ on the orientations of the determinant line bundle over the space of real Cauchy-Riemann operators on $(N,c_N)$. This sign can be obtained as the product of two terms. The first one computes the signature of the permutations induced by the automorphisms acting on the $Pin^\\pm$ structures of the real part of $(N,c_N)$. The second one comes from the action of the automorphisms of $(N,c_N)$ on the bordism classes of real Spin structures on $(\\Sigma,c_\\Sigma)$.
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. PMID:7182805
STABILITY OF DISPLACEMENT TO THE SECOND FUNDAMENTAL PROBLEM IN PLANE ELASTICITY
Institute of Scientific and Technical Information of China (English)
Juan LIN; Jinyuan DU
2014-01-01
In this article, by using the stability of Cauchy type integral when the smooth perturbation for integral curve and the Sobolev type perturbation for kernel density hap-pen, we discuss the stability of the second fundamental problem in plane elasticity when the smooth perturbation for the boundary of the elastic domain (unit disk) and the Sobolev type perturbation for the displacement happen. And the error estimate of the displacement between the second fundamental problem and its perturbed problem is obtained.
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.
Abanin, A.V.; Khoi, Le Hai
2016-01-01
Let $\\Omega$ be a Carathéodory domain in the complex plane $\\mathbb C$, $A^{-\\infty}(\\Omega)$ the space of functions that are holomorphic in $\\Omega$ with polynomial growth near the boundary $\\partial\\Omega$, and $A^\\infty(\\complement\\Omega)$ the space of holomorphic functions in the interior of $\\complement\\Omega:=\\overline{\\mathbb C}\\setminus\\Omega$, vanishing at infinity and being in $C^\\infty(\\complement\\Omega)$. We prove that the Cauchy transformation of analytic fun...
Pérez Cantor, Edwin Leonardo
2014-01-01
El propósito de este trabajo es estudiar el buen planteamiento en los espacios de Sobolev Hs(T2) para s 1> del problema de Cauchy asociado a una generalización de la ecuación de Kuramoto-Sivashinsky bidimensional periódica, que modela fenómenos físicos que ocurren en películas delgadas
El problema de cauchy asociado a una ecuación del tipo kuramoto-sivashinsky bidimensional periódica
Campos, Juvitsa; Duque, Omar; Rodríguez-Blanco, Guillermo
2012-01-01
El propósito de este trabajo es abordar el buen planteamiento en los espacios de Sobolev $H^{s}(\\mathbb{T}^2)$ para $s\\geq1$ del problema de Cauchy asociado a una ecuación del tipo Kuramoto-Sivashinsky bidimensional periódica, que modela fenómenos físicos que ocurren en películas delgadas.
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.
Energy Technology Data Exchange (ETDEWEB)
Miyata, Y.; Suzuki, T.; Takechi, M.; Urano, H.; Ide, S. [Japan Atomic Energy Agency, Naka, Ibaraki 311-0193 (Japan)
2015-07-15
For the purpose of stable plasma equilibrium control and detailed analysis, it is essential to reconstruct an accurate plasma boundary on the poloidal cross section in tokamak devices. The Cauchy condition surface (CCS) method is a numerical approach for calculating the spatial distribution of the magnetic flux outside a hypothetical surface and reconstructing the plasma boundary from the magnetic measurements located outside the plasma. The accuracy of the plasma shape reconstruction has been assessed by comparing the CCS method and an equilibrium calculation in JT-60SA with a high elongation and triangularity of plasma shape. The CCS, on which both Dirichlet and Neumann conditions are unknown, is defined as a hypothetical surface located inside the real plasma region. The accuracy of the plasma shape reconstruction is sensitive to the CCS free parameters such as the number of unknown parameters and the shape in JT-60SA. It is found that the optimum number of unknown parameters and the size of the CCS that minimizes errors in the reconstructed plasma shape are in proportion to the plasma size. Furthermore, it is shown that the accuracy of the plasma shape reconstruction is greatly improved using the optimum number of unknown parameters and shape of the CCS, and the reachable reconstruction errors in plasma shape and locations of strike points are within the target ranges in JT-60SA.
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.
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
Quantization of area for event and Cauchy horizons of the Kerr-Newman black hole
Visser, Matt
2012-06-01
Based on various string theoretic constructions, and various string-inspired generalizations thereof, there have been repeated suggestions that the areas of black hole event horizons might be quantized in a quite specific manner, in terms of linear combinations of square roots of positive integers. It is important to realise that there are significant physical constraints on such integer-based proposals when one (somewhat speculatively) attempts to extend them outside their original extremal and supersymmetric framework. Specifically, in their most natural and direct physical interpretations, some of the more speculative integer-based proposals for the quantization of 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 compelling Kerr-Newman spacetimes indicate that some caution is called for when assessing the universality of some of the more speculative integer-based string-inspired proposals.
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.
EXPLICIT FORMULATION FOR THE DIRICHLET PROBLEM FOR PARABOLIC-HYPERBOLIC CONSERVATION LAWS
Andreianov, Boris; Karimou Gazibo, Mohamed
2015-01-01
We revisit the Cauchy-Dirichlet problem for degenerate parabolic scalar conservation laws. We suggest a new notion of strong entropy solution. It gives a straightforward explicit characterization of the boundary values of the solution and of the flux, and leads to a concise and natural uniqueness proof, compared to the one of the fundamental work [J. Carrillo, Arch. Ration. Mech. Anal., 1999]. Moreover, general dissipative boundary conditions can be studied in the same framework. The definiti...
Ricciardi, Carlo Alberto; Ricciardi, Elisabetta; Visconti, Luca; Lacquaniti, Antonio; Savica, Vincenzo; Santoro, Domenico; Buemi, Michele; Ricciardi, Biagio
2016-02-01
The Study of urine from the outset has always aroused the interest of scientists and physicians all over the world, from ancient Greeks and Romans to Hindus , Hulcos in Mexico, Australian native etc. The urine in such case was considered not only as a waste product but also as a therapeutic product. In the late XIX century scientific knowledge had already identified the function of substances that favor the increase of urinary output, and physicians over the centuries have always tried to analyze urine in various ways. In Cauchis work in 1933 all chemistry and pathophysiological knowledge of the time was condensed. Cauchi signed the preface as Member of the medical council of Malta. He was a medical doctor of the early20thcentury, He wrote about the physiopathology of urine ranging from chemical and physical behavior, to the analysis of sediments and the special reactions of the urine in various pathologies. In particular Cauchi emphasizes the main diseases of the time combines the behavior of the reaction of urine as a diagnostic and prognostic instrument, stressing the importance of the urine test and describing the method used for analysis at the time. The analyses of the text in the issue seems to belong to archaic medicine, and it is difficult to think today, that what was presented as very up-to-date- science at that time, took place only 80 years ago. Reading the full original text with today experience we are led to consider the increasing importance that scientific community gave in the past, and still gives to urine test. PMID:26913892
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.
Stability of the Cauchy-Jensen Functional Equation in CÃ¢ÂˆÂ—-Algebras: A Fixed Point Approach
Directory of Open Access Journals (Sweden)
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.
International Nuclear Information System (INIS)
The program library IVP++ has been described and tested on the simulation of the hydrodynamics of a one-dimensional channel. Numerical integration methods are briefly reviewed. The calculation-theoretical analysis of the application of implicit high-order integration methods to the simulation of one-dimensional hydro and gas dynamics has been performed
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.
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.
ANALYSIS OF THE SINGULARITY FOR THE VERTICAL CONTACT PROBLEM OF LINE CRACK-INCLUSION
Institute of Scientific and Technical Information of China (English)
沈安; 陶昉敏; 汤任基
2001-01-01
Taking the short-fiber composite materials as engineering back-ground, utilizing the existing basic solutions of single inclusion and single crack, the plane problem of vertical contact interactions between line crack and rigid line inclusion in infinite plane (matrix) from the viewpoint of crack fracture mechanics is studied. According to boundary conditions, a set of standard Cauchy-type singular integral equations of the problem is obtainable. Besides, singular indexes, stresses and stress intensity factors around the contact point are expressed. Numerical examples are given to provide references to engineering.
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
De Lacroix a Cauchy: La fundamentación del cálculo infinitesimal en José Mariano Vallejo (1807-1832
Directory of Open Access Journals (Sweden)
Ausejo, Elena
2015-12-01
Full Text Available This paper studies the foundations of infinitesimal calculus in the work of José Mariano Vallejo (1779-1846, the most influential mathematician in Spanish during the first half of the 19th century. For this purpose, the analytical foundations of his three main works related to infinitesimal calculus are considered: Memoria sobre la curvatura de las líneas en sus diferentes puntos, sobre el radio de curvatura y sobre las evolutas (1807, and the two editions (1813 and 1832 of the volume of his Tratado Elemental de Matemáticas devoted to calculus. The study shows the evolutionary dynamics of Vallejo’s thought, following the European leading references in the development of mathematical analysis in his time, and how Vallejo combines the successive influence of Lagrange, Lacroix, and Cauchy, according to criteria of educational adequacy and mathematical rigor. In particular, the influences and discrepancies on infinitesimal calculus between Vallejo’s Treatise (1813 and Lacroix’ Traité élémentaire de calcul différentiel et de calcul intégral (1802 are determined, as well as the scope of the introduction of Cauchy’s ideas, that were published for the first time in Spain in the second edition of the volume on infinitesimal calculus of Vallejo’s Treatise (1832.Este artículo estudia los aspectos relativos a la fundamentación del cálculo infinitesimal en la obra de José Mariano Vallejo (1779-1846, el matemático de mayor difusión en lengua española de la primera mitad del siglo XIX. Para ello, se consideran los fundamentos analíticos de su Memoria sobre la curvatura de las líneas en sus diferentes puntos, sobre el radio de curvatura y sobre las evolutas (1807 y de las dos ediciones (1813 y 1832 del volumen de su Tratado Elemental de Matemáticas dedicado al cálculo infinitesimal. El estudio muestra la dinámica evolutiva del pensamiento de Vallejo al ritmo de las referencias europeas —especialmente francesas– que encabezan el
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.
基于均匀核的柯西密度估计%Estimation of Cauchy Density Based on Uniform Kernel
Institute of Scientific and Technical Information of China (English)
甘胜进; 陈望学
2012-01-01
Non-parametric kernel density estimation has a good nature and it contains two forms： fixed and variable window width.Their asymptotic convergence rates of the variance are the same,but biases differentiate a lot.Fixed window width and the balloon estimator have the same bias h2,while Ambramson estimator＇s is h4.In this paper,we get a good nature of the fixed window width estimator,and calculate the bias of Cauchy density＇s Ambramson estimator based on uniform kernel,find it exactly unbiased.%非参数核密度估计具有良好的性质,有固定窗宽和变窗宽两种形式,由于渐近方差收敛率相同,而渐近偏度存在差异,固定窗宽和球估计量的偏度为h2,Ambramson估计量为h4,本文提出了固定窗宽核密度估计量的一个性质,并计算基于均匀核的柯西密度Ambramson估计量的期望发现刚好是无偏的。
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.
Edwards, P. J.; Huang, X.; Li, Y. Q. (Editor); Wang, Y. Z. (Editor)
1996-01-01
We briefly review quantum mechanical and semi-classical descriptions of experiments which demonstrate the macroscopic violation of the three Cauchy-Schwarz inequalities: g(sup 2)(sub 11)(0) greater than or equal to 1; g(sup 2)(sub 11)(0) greater than or equal to g(sup 2)(sub 11)(t), (t approaches infinity); (the absolute value of g(sup 2)(sub 11)(0))(exp 2) less than or equal to g(sup 2)(sub 11)(0) g(sup 2)(sub 11)(0). Our measurements demonstrate the violation, at macroscopic intensities, of each of these inequalities. We show that their violation, although weak, can be demonstrated through photodetector current covariance measurements on correlated sub-Poissonian Poissonian, and super Poissonian light beams. Such beams are readily generated by a tandem array of infrared-emitting semiconductor junction diodes. Our measurements utilize an electrically coupled array of one or more infrared-emitting diodes, optically coupled to a detector array. The emitting array is operated in such a way as to generate highly correlated beams of variable photon Fano Factor. Because the measurements are made on time scales long compared with the first order coherence time and with detector areas large compared with the corresponding coherence areas, first order interference effects are negligible. The first and second inequalities are violated, as expected, when a sub-Poissonian light beam is split and the intensity fluctuations of the two split beams are measured by two photodetectors and subsequently cross-correlated. The third inequality is violated by bunched (as well as anti-bunched) beams of equal intensity provided the measured cross correlation coefficient exceeds (F - 1)/F, where F is the measured Fano Factor of each beam. We also investigate the violation for the case of unequal beams.
Numerical solution of random singular integral equation appearing in crack problems
Sambandham, M.; Srivatsan, T. S.; Bharucha-Reid, A. T.
1986-01-01
The solution of several elasticity problems, and particularly crack problems, can be reduced to the solution of one-dimensional singular integral equations with a Cauchy-type kernel or to a system of uncoupled singular integral equations. Here a method for the numerical solution of random singular integral equations of Cauchy type is presented. The solution technique involves a Chebyshev series approximation, the coefficients of which are the solutions of a system of random linear equations. This method is applied to the problem of periodic array of straight cracks inside an infinite isotropic elastic medium and subjected to a nonuniform pressure distribution along the crack edges. The statistical properties of the random solution are evaluated numerically, and the random solution is used to determine the values of the stress-intensity factors at the crack tips. The error, expressed as the difference between the mean of the random solution and the deterministic solution, is established. Values of stress-intensity factors at the crack tip for different random input functions are presented.
... often, it could be a sign of a balance problem. Balance problems can make you feel unsteady or as ... fall-related injuries, such as hip fracture. Some balance problems are due to problems in the inner ...
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.
Astafev, Vladimir; Kasatkin, Andrey
2016-06-01
Prediction of the motion of the oil-water contact boundary has great importance in the problems of design of oilfield development by flooding. In this paper we consider a piston-like model of oil-water displacement, which takes into account differences in viscosity and density of the two fluids. Oil reservoir assumed to be homogeneous and infinite, fixed thickness, with constant values of porosity and permeability coefficients. Filtration of liquids is described by Darcy's law. It is assumed, that both fluids are weakly compressible and the pressure in the reservoir satisfies the quasi-stationary diffusion equation. Piston-like displacement model leads to the discontinuity of the tangential component of the velocity vector at the boundary of oil-water contact. Use the Cauchy integral reduces the problem of finding the current boundaries of oil-water contact to the system of singular integral equations for the tangential and normal components of the velocity vector and the Cauchy problem for the integration of the differential equations of motion of the boundary of oil-water contact. An algorithm for the numerical solution of this problem is developed. The monitoring of oil-water boundary motion for different regular and irregular schemes of flooding is carried out.
$delta$-Quasi Cauchy Sequences
Cakalli, Huseyin
2010-01-01
Recently, a concept of forward continuity and a concept of forward compactness are introduced in the senses that a function $f$ is forward continuous if $\\lim_{n\\to\\infty} \\Delta f(x_{n})=0$ whenever $\\lim_{n\\to\\infty} \\Delta x_{n}=0$,\\; and a subset $E$ of $\\textbf{R}$ is forward compact if any sequence $\\textbf{x}=(x_{n})$ of points in $E$ has a subsequence $\\textbf{z}=(z_{k})=(x_{n_{k}})$ of the sequence $\\textbf{x}$ such that $\\lim_{k\\to \\infty} \\Delta z_{k}=0$ where $\\Delta z_{k}=z_{k+1}...
Institute of Scientific and Technical Information of China (English)
王丽萍; 彭维玲; 肖卓峰
2008-01-01
In the first part of this paper, we discuss the Holder continuity of the cauchy integral operator for regular functions and the relation between ‖T[f] ‖α and ‖f‖α. In the second part of this paper, we introduce the modified cauchy integral operator T for regular functions. Firstly,we prove that the operator T has a unique fixed point by the Banach's Contraction Mapping Principle. Secondly, we give the Mann iterative sequence, and then we show the iterative sequence strongly converges to the fixed point of the operator T.
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.
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.
Explaining the Mind: Problems, Problems
Harnad, Stevan
2001-01-01
The mind/body problem is the feeling/function problem: How and why do feeling systems feel? The problem is not just "hard" but insoluble (unless one is ready to resort to telekinetic dualism). Fortunately, the "easy" problems of cognitive science (such as the how and why of categorization and language) are not insoluble. Five books (by Damasio, Edelman/Tononi...
The Dirichlet problem for the two-dimensional Helmholtz equation for an open boundary
Hayashi, Y.
1973-01-01
Development of a complete theory of the two-dimensional Dirichlet problem for an open boundary. It is shown that the solution of the Dirichlet problem for an open boundary requires the solution of a Fredholm integral equation of the first kind. Although a Fredholm integral equation of the first kind usually has no solution if the kernel is continuous, owing to the logarithmic singularity of the kernel, the equation in this case is converted to a singular integral equation with a Cauchy kernel. It is proven that the homogeneous adjoint equation of the singular integral equation has no nonzero solution. By virtue of this result, and with the aid of an existence theorem known in the theory of singular integral equations, the existence of solutions of the singular integral equation, and then of the unique solution of the Fredholm integral equation of the first kind is proved.
Directory of Open Access Journals (Sweden)
Jordan Hristov
2016-01-01
Full Text Available The article addresses a reappraisal of the famous Ward–Tordai equation describing the equilibrium of surfactants at air/liquid interfaces under diffusion control. The new derivation is entirely developed in the light of fractional calculus. The unified approach demonstrates that this equation can be clearly reformulated as a nonlinear ordinary time-fractional equation of order 1/2. The work formulates versions with different isotherms. A simple solution of the case with the Henry’s isotherm and a discussion of a Cauchy problem involving the Freundlich isotherm are provided.
A problem related to the hall effect in a semiconductor with an electrode of an arbitrary shape
Directory of Open Access Journals (Sweden)
Krutitskii P. A.
1999-01-01
Full Text Available A problem on electric current in a semiconductor film from an electrode of an arbitrary shape is studied in the presence of a magnetic field. This situation describes the Hall effect, which indicates the deflection of electric, current from electric field in a semiconductor. From mathematical standpoint we consider the skew derivative problem for harmonic functions in the exterior of an open arc in a plane. By means of potential theory the problem is reduced to the Cauchy singular integral equation and next to the Fredholm equation of the 2nd kind which is uniquely solvable. The solution of the integral equation can be computed by standard codes by discretization and inversion of the matrix. The uniqueness and existence theorems are formulated.
... in Chinese 繁體中文 ) What Are Knee Problems? (in Korean 한국어 ) What Are Knee Problems? (in Vietnamese bằng ... the knee. Ultrasound. A technique that uses sound waves to produce images of the soft tissue structures ...
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。
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.
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....
Full Text Available ... can have intercourse but experience vaginismus during pelvic exams. Although vaginismus is considered a pain disorder, most ... and are used together to treat a problem. Education is important in understanding the anatomy and physiology ...
Full Text Available ... to a specialist trained in the diagnosis and treatment of sexual problems. This specialist may be a ... in many different ways. Often, multiple types of treatment may be required and are used together to ...
... 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 ...
Full Text Available ... pain disorders. If you are experiencing problems viewing this embedded video, please click here . Transcript Disorders of ... no sexual fantasies and desire for sexual activity. This lack of desire is beyond what normally happens ...
... problems can lead to ED, such as: Poor communication with your partner Feelings of doubt and failure Stress, fear, anxiety, or anger Expecting too much from sex. This can make sex a task instead of ...
Full Text Available ... a problem. Education is important in understanding the anatomy and physiology of sex and in having realistic ... lubricants in that they are absorbed into the skin. Moisturizers are a “maintenance therapy” that is applied ...
... Inverted nipple; Nipple problems Images Female breast Intraductal papilloma Mammary gland Abnormal discharge from the nipple Normal ... 8. Read More Breast cancer Endocrine glands Intraductal papilloma Update Date 11/16/2014 Updated by: Cynthia ...
Full Text Available ... Smoking Cessation Links to Professional Societies and Organizations Home › Sexual Problems Sexual concern causing distress can be ... Find a Health Care Provider Back to Top Home | About Us | Reproductive Health Topics | News & Publications | Resources ...
Full Text Available ... sexual arousal disorder have little or no genital responsiveness to stimulation and they don’t produce adequate ... problems. This specialist may be a physician, psychologist, social worker, or physical therapist. You may also find ...
... the home Dry mouth during cancer treatment Enteral nutrition - child - managing problems Gastrostomy feeding tube - bolus Jejunostomy feeding tube Mouth and neck radiation - discharge Multiple sclerosis - discharge Stroke - discharge Update Date 5/15/2014 ...
... much higher rates of foot problems. For women, pain in the toes and ball of the foot is much more common than in men, and it gets worse with age. However, pain in the heel tends to decrease as we ...
Full Text Available ... Some women with vaginismus can tolerate a pelvic examination, while some women can have intercourse but experience ... and are used together to treat a problem. Education is important in understanding the anatomy and physiology ...
Galin, Lev Aleksandrovich
2008-01-01
L.A. Galin's book on contact problems is a remarkable work. Actually there are two books: the first, published in 1953 deals with contact problems in the classical theory of elasticity; this is the one that was translated into English in 1961. The second book, published in 1980, included the first, and then had new sections on contact problems for viscoelastic materials, and rough contact problems; this section has not previously been translated into English. In this new translation, the original text and the mathematical analysis have been completely revised, new material has been added, and the material appearing in the 1980 Russian translation has been completely rewritten. In addition there are three essays by students of Galin, bringing the analysis up to date.
Full Text Available ... problems. This specialist may be a physician, psychologist, social worker, or physical therapist. You may also find ... aids include lubricants, moisturizers, and sexual toys. Lubricants work by reducing friction between tissues. Many different types ...
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 ...
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.
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.
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.
... with your sexual partner. Because they are complex, sexual concerns are treated in many different ways. Often, multiple types of treatment may be required and are used together to treat a problem. Education is important in understanding the anatomy and physiology ...
Full Text Available ... important to note that psychological problems such as sexual abuse can be involved as well. Pain caused by lack of lubrication or by vaginismus is not included in this ... woman wants sexual penetration. Women with this condition can still achieve ...
... Home & Community Home › Aging & Health A to Z › Kidney Problems Font size A A A Print Share Glossary Basic Facts & ... The kidneys also help maintain body fluids at normal levels. In addition, the kidneys play important roles in controlling blood pressure and ...
International Nuclear Information System (INIS)
Although there were not reasons to deplore against major activity release from any of the 110 industrial reactors authorized to operate in US, the nuclear incident that occurred at the Three Mile Island Plant in 1979 urged the public conscience toward the necessity of readiness to cope with events of this type. The personnel of the Emergency Planning Office functioning in the frame of US Department of Agriculture has already participated in around 600 intervention drillings on a federal, local or state scale to plan, test or asses radiological emergency plans or to intervene locally. These exercises allowed acquiring a significant experience in elaborating emergency plans, planning the drillings, working out scenarios and evaluation of the potential impact of accidents from the agricultural point of view. We have also taken part in different international drillings among which the most recent are INEX 1 and RADEX 94. We have found on these occasions that the agricultural problems are essential preoccupations in most of the cases no matter if the context is international, national, local or of state level. The paper poses problems specifically related to milk, fruits and vegetables, soils, meat and meat products. Finally the paper discusses issues like drilling planning, alarm and notification, sampling strategy, access authorizations for farmers, removing of contamination wastes. A number of social, political and economical relating problems are also mentioned
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.
The borderlines of the invisibility and visibility for Calderon's inverse problem
Astala, Kari; Paivarinta, Lassi
2011-01-01
We consider the determination of a conductivity function in a two-dimensional domain from the Cauchy data of the solutions of the conductivity equation on the boundary. We prove uniqueness results for this inverse problem, posed by Calderon, for conductivities that are degenerate, that is, they may not be bounded from above or below. In particular, for scalar conductivities we solve the inverse problem in a class which is larger than $L^\\infty$. Also, we give new counterexamples for the uniqueness of the inverse conductivity problem. We say that a conductivity is visible if the inverse problem is solvable so that the inside of the domain can be uniquely determined, up to a change of coordinates, using the boundary measurements. The present counterexamples for the inverse problem have been related to the invisibility cloaking. This means that there are conductivities for which a part of the domain is shielded from detection via boundary measurements. Such conductivities are called invisibility cloaks. In the p...
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.
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.
Use of Lanczos vectors in fluid/structure interaction problems
International Nuclear Information System (INIS)
The goals of any numerical computational technique used for the solution of structural acoustics problems in the exterior infinite domain should be of accuracy with rapid convergence, robustness, and computational efficiency. A computer program has been developed to achieve each of these three goals. Accuracy and robustness in the numerical representation of the integral equations used to represent the infinite fluid was attained through the use of boundary element implementations of the surface Helmholtz integral equations. The computational efficiency was resolved through the use of Lanczos vectors to model the deformation characteristics of the structure. The authors have developed collocation and variational techniques to overcome the difficulties previously encountered in the numerical implementation of the hypersingular integral operator. The Cauchy singularity present in the integral formulation is made numerically amenable through the use of tangential derivatives in both the collocation and variational techniques. The variational approach has the advantage that the resulting added fluid mass term is symmetric and combines efficiently with a finite element approximation of the structural elastic response. Several different strategies making use of the Lanczos vectors have been investigated. The first involved the use of Lanczos vectors solely to characterize the structural response. This reduced form of the structural dynamical matrix was then substituted back into a Burton and Miller formulation of the acoustic problem. The second strategy investigated involved forming the complex Lanzcos vectors of the dynamical matrix formed from the addition of a symmetrical added fluid matrix to the structural mass matrix. The size of resultant matrix equation set solved at each frequency for this strategy is determined by the number of Lanczos vectors used. 19 refs., 10 figs., 2 tabs
Asymptotically flat and regular Cauchy data
Dain, S
2002-01-01
I describe the construction of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of powers of a radial coordinate. I emphasize the motivations and the main ideas behind the proofs.
8. Asymptotically Flat and Regular Cauchy Data
Dain, Sergio
I describe the construction of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of powers of a radial coordinate. I emphasize the motivations and the main ideas behind the proofs.
Generalized Cauchy's Models and Generalized Integrals
Sabra Ramadan
2007-01-01
The space of generalized complex numbers C* has been constructed. The Cachy's model in the space of new generalized functions is well defined. The generalized integral of new generalized function over the compact K has been defined.
Generalized Cauchy's Models and Generalized Integrals
Directory of Open Access Journals (Sweden)
Sabra Ramadan
2007-01-01
Full Text Available The space of generalized complex numbers C* has been constructed. The Cachy's model in the space of new generalized functions is well defined. The generalized integral of new generalized function over the compact K has been defined.
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.
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 $O$.
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
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)
Problem, Problem Solving And Critical Thinking
TÜRNÜKLÜ, Elif B.; YEŞİLDERE, Sibel
2005-01-01
Critical thinking is an essential skill that all people from various sectors should have and need. Problem solving skill which is one of the main purpose of mathematics teaching can be effective in developing critical thinking. The purpose of this study is to emphasize the importance of problem solving in developing critical thinking skills and to expose critical thinking to the pre-service primary mathematics teachers. Aiming these, some mathematical critical thinking problems are prepa...
Blow up of the Solutions of Nonlinear Wave Equation
Svetlin Georgiev Georgiev
2007-01-01
We construct for every fixed the metric , where , , , , are continuous functions, , for which we consider the Cauchy problem , where , ; , , where , , , , , , and are positive constants. When , we prove that the above Cauchy problem has a nontrivial solution in the form for which . When , we prove that the above Cauchy problem has a nontrivial solution in the form for which .
Some geometric constraints and the problem of global regularity for the Navier–Stokes equations
International Nuclear Information System (INIS)
We consider the Cauchy problem for the 3D Navier–Stokes equations and show that weak solutions satisfying suitable geometric conditions are smooth. The first condition we consider requires the vorticity's direction at the point y (near to x) to be within a circular cone of a given small amplitude, with vertex at x and axis along the vorticity's direction at x. The amplitude of the angle at the vertex of the cone depends mainly on the viscosity and on the size of the initial datum. Hence, the vorticity's direction need not be (Hölder) continuous to ensure regularity, as in the results proved in previous studies. Our new results show that a possible singularity deriving from non-trivial collision of strong vortex tubes is depleted if the angle formed by the tubes is small enough. Other conditions regarding the direction of the curl of the vorticity are considered: it is shown that if the direction of curl of the vorticity at point x is 'nearly parallel' to the same quantity at neighbouring points, then weak solutions are smooth
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
... affect desire and function. Psychological causes may include work-related stress and anxiety. They may also include depression or concerns about marriage or relationship problems. For some women, the problem results from past sexual trauma. Occasional ...
... Disease, and Other Dental Problems Diabetic Eye Disease Diabetes and Foot Problems How can diabetes affect my feet? Too much glucose, also called ... you have any of these signs. How can diabetes change the shape of my feet? Nerve damage ...
... Increases in Problem Drinking Join the Fight Against Superbugs Featured Website: Genetic and Rare Diseases Information Center ... Increases in Problem Drinking Join the Fight Against Superbugs Featured Website: Genetic and Rare Diseases Information Center ...
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.
Karrison, Joan; Carroll, Margaret Kelly
1991-01-01
Students with language and learning disabilities may have difficulty solving mathematics word problems. Use of a sequential checklist, identifying clues and keywords, and illustrating a problem can all help the student identify and implement the correct computational process. (DB)
Every pregnancy has some risk of problems. The causes can be conditions you already have or conditions you develop. ... pregnant with more than one baby, previous problem pregnancies, or being over age 35. They can affect ...
Algorithmic Problem Complexity
Burgin, Mark
2008-01-01
People solve different problems and know that some of them are simple, some are complex and some insoluble. The main goal of this work is to develop a mathematical theory of algorithmic complexity for problems. This theory is aimed at determination of computer abilities in solving different problems and estimation of resources that computers need to do this. Here we build the part of this theory related to static measures of algorithms. At first, we consider problems for finite words and stud...
Children with behavorial problem
Cerar, Kristina
2011-01-01
Behavioral problems are becoming more and more common phenomena in children education. When behavioral problems occur it is very important to have the appropriate approach that mitigates or completely removes them. The key to this is to know as much as possible about children development and behavioral problems. The theoretical part contains the features of a child's development and then I focused on behavioral problems and the causes that bring to such results. I described methods to remove...
Frensch, Peter; Funke, Joachim
2005-01-01
Human thinking, and in particular, the human ability to solve complex, real-life problems contributes more than any other human ability to the development of human culture and the growth and development of human life on earth. However, the human ability to solve complex problems is still not well understood, partly because it has for a long time been largely ignored by traditional problem-solving research in the field of psychology. In this article, we present a definition of complex problem ...
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...
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.
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)
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
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.
Semidefinite linear complementarity problems
International Nuclear Information System (INIS)
Semidefinite linear complementarity problems arise by discretization of variational inequalities describing e.g. elastic contact problems, free boundary value problems etc. In the present paper linear complementarity problems are introduced and the theory as well as the numerical treatment of them are described. In the special case of semidefinite linear complementarity problems a numerical method is presented which combines the advantages of elimination and iteration methods without suffering from their drawbacks. This new method has very attractive properties since it has a high degree of invariance with respect to the representation of the set of all feasible solutions of a linear complementarity problem by linear inequalities. By means of some practical applications the properties of the new method are demonstrated. (orig.)
Hidden Symmetry Subgroup Problems
Decker, Thomas; Santha, Miklos; Wocjan, Pawel
2011-01-01
We advocate a new approach of addressing hidden structure problems and finding efficient quantum algorithms. We introduce and investigate the Hidden Symmetry Subgroup Problem (HSSP), which is a generalization of the well-studied Hidden Subgroup Problem (HSP). Given a group acting on a set and an oracle whose level sets define a partition of the set, the task is to recover the subgroup of symmetries of this partition inside the group. The HSSP provides a unifying framework that, besides the HSP, encompasses a wide range of algebraic oracle problems, including quadratic hidden polynomial problems. While the HSSP can have provably exponential quantum query complexity, we obtain efficient quantum algorithms for various interesting cases. To achieve this, we present a general method for reducing the HSSP to the HSP, which works efficiently in several cases related to symmetries of polynomials. The HSSP therefore connects in a rather surprising way certain hidden polynomial problems with the HSP. Using this connect...
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. Finally......, the paper outlines the author’s experiences using creative tools and approaches to: Facilitation of problem solving processes, strategy development in organisations, design of optimisation systems for large scale and complex logistic systems, and creative design of software optimisation for complex non...
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
The Gamification Design Problem
Meder, Michael; Jain, Brijnesh-Johannes
2014-01-01
Under the assumptions that (i) gamification consists of various types of users that experience game design elements differently; and (ii) gamification is deployed in order to achieve some goal in the broadest sense, we pose the gamification problem as that of assigning each user a game design element that maximizes their expected contribution in order to achieve that goal. We show that this problem reduces to a statistical learning problem and suggest matrix factorization as one solution when...
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.......Two of Herbert Simon's best-known papers are 'The Architecture of Complexity' and 'The Structure of Ill-Structured Problems.' We discuss the neglected links between these two papers, highlighting the role of decomposition in the context of problems on which constraints have been imposed...
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
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.
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}
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.
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…
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...
The generalized Tailor Problem
Roerdink, J.B.T.M.; Maragos, P; Schafer, RW; Butt, MA
1996-01-01
The so-called 'Tailor Problem' concerns putting a number of sets within another set by translation, such that the translated sets do not overlap. In this paper we consider a generalization of this problem in which also rotations of the sets are allowed.
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.
MARTONFFY, ANDREA PONTECORVO; AND OTHERS
A CURRICULUM GUIDE IS PRESENTED FOR A 10-WEEK STUDY OF ANCIENT GREEK CIVILIZATION AT THE 10TH-GRADE LEVEL. TEACHING MATERIALS FOR THE UNIT INCLUDE (1) PRIMARY AND SECONDARY SOURCES DEALING WITH THE PERIOD FROM THE BRONZE AGE THROUGH THE HELLENISTIC PERIOD, (2) GEOGRAPHY PROBLEMS, AND (3) CULTURAL MODEL PROBLEM EXERCISES. THOSE CONCEPTS WITH WHICH…
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…
JS Armstrong
2004-01-01
Graffiti is regarded by many as a blight on our cities because it contributes to visual pollution. City governments spend vast sums in an effort to clean the ubiquitous graffiti from urban walls. I suggest that the “cleansing strategy” is an expensive, ineffective way of dealing with the problem; well-known management techniques can solve the problem more efficiently.
Allen, Deborah E.; Donham, Richard S.; Bernhardt, Stephen A.
2011-01-01
In problem-based learning (PBL), students working in collaborative groups learn by resolving complex, realistic problems under the guidance of faculty. There is some evidence of PBL effectiveness in medical school settings where it began, and there are numerous accounts of PBL implementation in various undergraduate contexts, replete with…
... problems that can lead to dislocation of the hip bones. This is also called dysplasia (say: "diss-play-see-uh"). This means that ... problems later in life? Source Screening for Developmental Dysplasia of the Hip by LM French, M.D., and FR Dietz, ...
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…
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…
Medical problems affecting musicians.
Potter, P J; Jones, I C
1995-01-01
The physical demands of performing on musical instruments can cause pain, sensory loss, and lack of coordination. Five cases illustrate common problems. Knowledge of the interaction between the technique of playing the instrument and the particular musician can help physicians diagnose and resolve problems.
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
Routing and scheduling problems
DEFF Research Database (Denmark)
Reinhardt, Line Blander
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...... set cost making the cost of the individual vehicle routes inter-dependant. Depending on the problem type, the size of the problems and time available for solving, different solution methods can be applicable. In this thesis both heuristic methods and several exact methods are investigated depending...... on the problems needed to be solved. The solution methods applied to the problems cover dynamic programming for multi constrained shortest paths, Branch-and-cut for liner shipping, Simulated annealing for transporting assisted passengers in airports, branch-cut-and-price for vehicle routing with time windows...
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.
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.
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.
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.
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...... projects played a major role in this process. First, they acted as a vehicle that assembled planners, politicians and stakeholders to work towards strategic visions across multiple scales. Second and consequently, they stimulated considerable second and third order effects in the form of shared problem...
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.
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.
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.
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.......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...
Eperson, D. B.
1985-01-01
Presents six mathematical problems (with answers) which focus on: (1) chess moves; (2) patterned numbers; (3) quadratics with rational roots; (4) number puzzles; (5) Euclidean geometry; and (6) Carrollian word puzzles. (JN)
... Health Information Basics for You and Your Family Sports Injuries, Handout on Health Health Information Knee Problems Find ... for a long time. This sometimes occurs in sports training. Treatment for tendon injuries and disorders includes: Rest Ice Elevation Medicines such ...
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...
Problems sleeping during pregnancy
... page: //medlineplus.gov/ency/patientinstructions/000559.htm Problems sleeping during pregnancy To use the sharing features on ... time sleeping well. Why is it hard to sleep during pregnancy? Your baby is growing bigger, which ...
Challenging problems in geometry
Posamentier, Alfred S
2012-01-01
Collection of nearly 200 unusual problems dealing with congruence and parallelism, the Pythagorean theorem, circles, area relationships, Ptolemy and the cyclic quadrilateral, collinearity and concurrency and more. Arranged in order of difficulty. Detailed solutions.
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...
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.
... too high. Over time, this can damage your eyes. The most common problem is diabetic retinopathy. It ... light-sensitive tissue at the back of your eye. You need a healthy retina to see clearly. ...
... and rashes clinical tools newsletter | contact Share | Common Foot Problems A A A Trauma, infection, skin disease, ... the sole of the front part of the foot and on the toes. Foot infections include warts; ...
J Gordon Millichap
2008-01-01
The prevalence of sleep problems and their associations with quality of life (QOL), school attendance, and family impacts in children with ADHD were determined in a study at Royal Children's Hospital, University of Melbourne, Australia.
Rubinstein, J Hyam
2009-01-01
This is a personal view of some problems on minimal surfaces, Ricci flow, polyhedral geometric structures, Haken 4-manifolds, contact structures and Heegaard splittings, singular incompressible surfaces after the Hamilton-Perelman revolution.
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.
... nonsurgical ways to obtain symptom relief? • What are Kegel exercises? • Can surgery correct pelvic support problems? • Glossary ... your overall health and possibly your prolapse symptoms. • Kegel exercises—These exercises strengthen the muscles that surround ...
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.
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.
Directory of Open Access Journals (Sweden)
J Gordon Millichap
2008-05-01
Full Text Available The prevalence of sleep problems and their associations with quality of life (QOL, school attendance, and family impacts in children with ADHD were determined in a study at Royal Children's Hospital, University of Melbourne, Australia.
Helfgott, Harald Andrés
2015-01-01
The ternary Goldbach conjecture, or three-primes problem, states that every odd number $n$ greater than $5$ can be written as the sum of three primes. The conjecture, posed in 1742, remained unsolved until now, in spite of great progress in the twentieth century. In 2013 -- following a line of research pioneered and developed by Hardy, Littlewood and Vinogradov, among others -- the author proved the conjecture. In this, as in many other additive problems, what is at issue is really the proper...
Trahtman, A. N.
2007-01-01
The synchronizing word of deterministic automaton is a word in the alphabet of colors (considered as letters) of its edges that maps the automaton to a single state. A coloring of edges of a directed graph is synchronizing if the coloring turns the graph into deterministic finite automaton possessing a synchronizing word. The road coloring problem is a problem of synchronizing coloring of directed finite strongly connected graph with constant outdegree of all its vertices if the greatest comm...
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.
Hubble, Douglas
1982-01-01
Adolescence is a period of active growth and development-physical, sexual, social and emotional. There are wide normal variations between the time of onset and the attainment of full maturity. Many adolescents present few if any problems during this potentially turbulent period, and make the necessary adjustments without undue stress to themselves, their family or their friends. Problems in growth and hormonal balance, presenting as short and tall teenagers, menstrual irregularities, obesity ...
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...
Steiner Forest Orientation Problems
Cygan, Marek; Nutov, Zeev
2011-01-01
We consider connectivity problems with orientation constraints. Given a directed graph $D$ and a collection of ordered node pairs $P$ let $P[D]={(u,v) \\in P: D contains a uv-paths}$. In the Steiner Forest Orientation problem we are given an undirected graph $G=(V,E)$ with edge-costs and a set $P \\subseteq V \\times V$ of ordered node pairs. The goal is to find a minimum-cost subgraph $H$ of $G$ and an orientation $D$ of $H$ such that $P[D]=P$. We give a 4-approximation algorithm for this problem. In the Maximum Pairs Orientation problem we are given a graph $G$ and a multi-collection of ordered node pairs $P$ on $V$. The goal is to find an orientation $D$ of $G$ such that $|P[D]|$ is maximum. Generalizing the result of Arkin and Hassin for $|P|=2$, we will show that for a mixed graph $G$ (that may have both directed an undirected edges), one can decide in $n^{O(|P|)}$ time whether $G$ has an orientation $D$ with $P[D]=P$ (for undirected graphs this problem admits a polynomial time algorithm for any $P$, but it...
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.
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.
Sperling, J
2009-01-01
In 1927 the great physicist Paul A. M. Dirac failed to provide a consistent quantum description of the phase of a radiation field. Only one year later, he developed the famous Dirac theory of the electron, which led to the anti-particle -- the positron. We show that the reason for Dirac's failure with the phase problem bears a striking resemblance to his ingenious insight into the nature of the electron. For a correct quantum description of the phase of a radiation field it is necessary to take the polarisation into account. Similarly to the introduction of the anti-particle of the electron, the inclusion of the second polarisation resolves the inconsistency of the quantum phase problem. This also leads to new insight into the quantum measurement problem of time.
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.
DEFF Research Database (Denmark)
de Graaff, Erik; Guerra, Aida
Problem-Based Learning (PBL) is an innovative method to organize the learning process in such a way that the students actively engage in finding answers by themselves. During the past 40 years PBL has evolved and diversified resulting in a multitude in variations in models and practices. However...... model and in general problem based and project based learning. We apply the principle of teach as you preach. The poster aims to outline the visitors’ workshop programme showing the results of some recent evaluations......., the key principles remain the same everywhere. Graaff & Kolmos (2003) identify the main PBL principles as follows: 1. Problem orientation 2. Project organization through teams or group work 3. Participant-directed 4. Experiental learning 5. Activity-based learning 6. Interdisciplinary learning and 7...
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.
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.
Zinser, Brian
We present two distinct mathematical models where high-order integral equations are applied to electromagnetic problems. The first problem is to find the electric potential in and around ion channels and Janus particles. The second problem is to find the electromagnetic scattering caused by a set of simple geometric objects. In biology, we consider two types of inhomogeneities: the first one is a simple model of an ion channel which consists of a finite height cylindrical cavity embedded in a layered electrolytes/membrane environment, and the second one is a Janus particle made of two different semi-spherical dielectric materials. A boundary element method (BEM) for the Poisson-Boltzmann equation based on Muller's hyper-singular second kind integral equation formulation is used to accurately compute electrostatic potentials. The proposed BEM gives O(1) condition numbers and we show that the second order basis converges faster and is more accurate than the first order basis. For solar cells, we develop a Nystrom volume integral equation (VIE) method for calculating the electromagnetic scattering according to the Maxwell equations. The Cauchy principal values (CPVs) that arise from the VIE are computed using a finite size exclusion volume with explicit correction integrals. Outside the exclusion, the hyper-singular integrals are computed using an interpolated quadrature formulae with tensor-product quadrature nodes. We considered cubes, rectangles, cylinders, spheres, and ellipsoids. As the new quadrature weights are pre-calculated and tabulated, the integrals are calculated efficiently at runtime. Simulations with many scatterers demonstrate the efficiency of the interpolated quadrature formulae. We also demonstrate that the resulting VIE has high accuracy and p-convergence.
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.
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.
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
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
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
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.
Solving Environmental Problems
DEFF Research Database (Denmark)
Grimpe, Christoph; Ørding Olsen, Anders; Sofka, Wolfgang
dispersed. As a result, firms frequently collaborate with international partners. We shed new light on collaborative search strategies led by firms in general and for solving environmental problems in particular. Both topics are largely absent in the extant open innovation literature. Using data from...... the European Seventh Framework Programme for research and technological development, our results indicate that the problem solving potential of a search strategy increases with the diversity of existing knowledge of the partners in a consortium and with the experience of the partners involved. Moreover, we...
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
Electrical problems committee report
International Nuclear Information System (INIS)
This document is the report of the committee appointed to review the experience of the MFE Program with electrical equipment and to suggest actions to minimize future problems. The committee observed that the electrical problems that have occurred could be traced not to misapplication of project and engineering technical principles, but to lack of application of project and engineering management principles. The report is structured so that the first four sections: Introduction, Findings, Recommendations, and Immediate Recommended Actions, can be used as an executive summary. The discussion section and attachments contain further detail
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
The Quantum Falsifiability Problem
Dall'Arno, Michele; Brandsen, Sarah; Buscemi, Francesco
2016-01-01
A hypothesis about a physical device is falsified as soon as an experiment collects data that is not compatible with it. Here we construct a general framework to study the quantum falsifiability problem, namely, the problem of deciding whether a given input-output probability distribution (i.e., the data) can be obtained from a given candidate quantum channel (i.e., the hypothesis) or not. Our approach is completely device-independent, as the piece of experimental evidence -- the input-output...
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
Assessing the Quality of Problems in Problem-Based Learning
Sockalingam, Nachamma; Rotgans, Jerome; Schmidt, Henk
2012-01-01
This study evaluated the construct validity and reliability of a newly devised 32-item problem quality rating scale intended to measure the quality of problems in problem-based learning. The rating scale measured the following five characteristics of problems: the extent to which the problem (1) leads to learning objectives, (2) is familiar, (3)…
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…
International Nuclear Information System (INIS)
The risks of accidents and the safety actions concerning the components and the staff protection at Vivitron are analyzed. The risks induced by the utilization of SF6 is mainly asphyxia. The sealing defects on the gas storage devices and gas leaking inside Vivitron are considered. The safety actions and devices are summarized. Radiation protection problems are also discussed
International Nuclear Information System (INIS)
The meeting of the Radiation Energy Spectra Unfolding Workshop organized by the Radiation Shielding Information Center is discussed. The plans of the unfolding code benchmarking effort to establish methods of standardization for both the few channel neutron and many channel gamma-ray and neutron spectroscopy problems are presented
Nelson, Norman N.; Fisch, Forest N.
1973-01-01
Discussed are techniques of presentation and solution of the Classical Cake Problem. A frosted cake with a square base is to be cut into n pieces with the volume of cake and frosting the same for each piece. Needed are minimal geometric concepts and the formula for the volume of a prism. (JP)
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.
... of a lack of health-care providers, an absence of insurance, or transportation problems. The American Academy of Pediatrics believes that all children deserve a "medical home" and supports the implementation of school-based clinics, especially in areas where children do ...
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.
Environmental Health Problems.
Environmental Health Service (DHEW/PHS), Rockville, MD.
Aimed at a society which is forced to make decisions relative to their total environment, this pamphlet discusses a few of the problems associated with restoring and maintaining an environmental relationship conducive to the health and well-being of man. The topics covered include: air pollution, noise, solid waste, the urban environment, drinking…
... of time in their own world—even for teenagers—but they’re often lonely and want to make friends. The problem is, they’re not sure how to act in social settings. Between that and their eccentricities, they may become victims of teasing and bullying . Parents of a child with AS, or any ...
... a clinical breast exam done? • What is breast self-awareness? • How is breast self-awareness different from the traditional breast self-exam? •Glossary ... problems includes mammography , clinical breast exams, and breast self-awareness. What is mammography? Mammography is an X-ray ...
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.
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,
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…
Nervous System Problems and Dementia
... Language: Fact Sheet 505 Nervous System Problems and Dementia WHAT ARE NERVOUS SYSTEM PROBLEMS? WHAT ARE THE ... of AIDS these were all called “HIV-Associated Dementia.” However, a broader range of problems is showing ...
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.
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.
Directory of Open Access Journals (Sweden)
Michael Segal
2004-11-01
Full Text Available Abstract: Ad-hoc networks of sensor nodes are in general semi-permanently deployed. However, the topology of such networks continuously changes over time, due to the power of some sensors wearing out to new sensors being inserted into the network, or even due to designers moving sensors around during a network re-design phase (for example, in response to a change in the requirements of the network. In this paper, we address the problem of covering a given path by a limited number of sensors Ã¢Â€Â” in our case to two, and show its relation to the well-studied matrix multiplication problem.
Energy Technology Data Exchange (ETDEWEB)
McAllindon, D. [Atomic Energy of Canada Limited, Darlington NGD, Bowmanville, ON (Canada); Sloan, D. [Ontario Hydro Nuclear, Darlington NGD, Bowmanville, ON (Canada); Mayer, P. [Ontario Hydro Technologies, Toronto, ON (Canada)
1997-07-01
Resistance Temperature Detectors (RTDs) and their measurement circuit components have been a significant maintenance item at Darlington. Analysis of the problems has shown that RTDs and electrical penetrations (EPs) have been the largest sources of faults. A failure mechanism in which the RTD electrical resistance shifts upward was identified as a major source of RTD failures, which prompted a detailed failure investigation by Ontario Hydro Technologies (OHT). The investigation concluded that the root cause failure mechanism is chlorine contamination of the platinum wire during manufacture which resulted in surface damage to the wire and flaking of the wire surface during operation. Electrical penetrations in Darlington are of a pre-built modular design with two crimps internal to the EP. Spurious resistance in poor quality crimps in the EPs lead to errors in resistance measurement. The problem led to a complex and costly job to insert new modules in existing spare EPs. (author)
MCNP: Photon benchmark problems
Energy Technology Data Exchange (ETDEWEB)
Whalen, D.J.; Hollowell, D.E.; Hendricks, J.S.
1991-09-01
The recent widespread, markedly increased use of radiation transport codes has produced greater user and institutional demand for assurance that such codes give correct results. Responding to these pressing requirements for code validation, the general purpose Monte Carlo transport code MCNP has been tested on six different photon problem families. MCNP was used to simulate these six sets numerically. Results for each were compared to the set's analytical or experimental data. MCNP successfully predicted the analytical or experimental results of all six families within the statistical uncertainty inherent in the Monte Carlo method. From this we conclude that MCNP can accurately model a broad spectrum of photon transport problems. 8 refs., 30 figs., 5 tabs.
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.
DEFF Research Database (Denmark)
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 research project was carried out as a co-creation process with close cooperation between researcher...... 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...
Directory of Open Access Journals (Sweden)
Tjandra Y. Aditama
2002-03-01
Full Text Available Smoking is an important public health probLem in Indonesia. Up to 60% of male adult population as well as about 4% of female adult population are smokers. In fact, some of Indonesian kretek cigarettes have quite high tar and nicotine content. Besides health effect, smoking habit also influence economic status of the individuals as well as the family. In health point of view, even though reliable nation wide morbidity and mortality data are scarce, report from various cities showed smoking related diseases, such as Lung cancer, COPD, effect of pregnancy, etc. Other problem is a fact that smoking habit start quite in early age in Indonesia. This article also describe factors complicate smoking control program as well as several things to be done to strengthen smoking control program in Indonesia. (Med J Indones 2002; 11: 56-65Keywords : smoking, Indonesia, impact
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.
Europeanisation: Solution or problem?
Directory of Open Access Journals (Sweden)
Claudio M. Radaelli
2004-10-01
Full Text Available Is there something new in recent research on Europeanisation? Or should we go back to what we already know about political integration in Europe and avoid the term? This article reviews recent work in four steps: the identification of the specific domain of Europeanisation; the relationship between Europeanisation, on the one hand, and governance, institutions, and discourse, on the other; the methodological problems and the models emerging in this new field of research; and an assessment of the results arising out of theoretical and empirical research. One theme throughout the article is that, in order to develop a progressive agenda, Europeanisation should be seen as a problem, not as a solution. It is neither a new theory, nor an ad-hoc approach. Rather, it is a way of orchestrating existing concepts and to contribute to cumulative research in political science. Europeanisation does not provide any simple fix to theoretical or empirical problems. Quite the opposite, it can deliver if approached as a set of puzzles. A problem in search of explanation not the explanation itself (Gualini 2003. The conclusion is that Europeanisation has contributed to the emergence of new insights, original explanations, and interesting questions on three important issues: the understanding and analysis of 'impact', how to endogeneise international governance in models of domestic politics, and the relationship between agency and change. These three issues are prominent in the research agendas of international relations, theoretical policy analysis, and comparative politics. To contribute to major issues at the core of political science is a valuable result for a relatively new field of inquiry.
International Nuclear Information System (INIS)
The collection comprises the materials of working meeting 'The Development of Technologies of the 'Ukrytie' Radioactive Waste Management', held on May 20-21, 1997 in Chernobyl. The results of research work of the experts of Ukraine and other countries directed on solving problems, concerning removal of fuel containing materials and other radioactive waste from destroyed Unit 4 of Chernobyl NPP are given. The data on waste quantities, their location and classification, strategy of waste management and some technologies are described
Santos, Emilio
1992-10-01
The problem of hidden variables in quantum mechanics is formalized as follows. A general or contextual (noncontextual) hidden-variables theory is defined as a mapping f: Q×M → C (f: Q→C) where Q is the set of projection operators in the appropriate (quantum) Hilbert space, M is the set of maximal Boolean subalgebras of Q and C is a (classical) Boolean algebra. It is shown that contextual (noncontextual) hidden-variables always exist (do not exist).
Tjandra Y Aditama
2002-01-01
Smoking is an important public health probLem in Indonesia. Up to 60% of male adult population as well as about 4% of female adult population are smokers. In fact, some of Indonesian kretek cigarettes have quite high tar and nicotine content. Besides health effect, smoking habit also influence economic status of the individuals as well as the family. In health point of view, even though reliable nation wide morbidity and mortality data are scarce, report from various cities showed smoking rel...
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.
Lau, August; Yin, Chuan
2012-01-01
Classical approach of solvability problem has shed much light on what we can solve and what we cannot solve mathematically. Starting with quadratic equation, we know that we can solve it by the quadratic formula which uses square root. Polynomial is a generalization of quadratic equation. If we define solvability by using only square roots, cube roots etc, then polynomials are not solvable by radicals (square root, cube root etc). We can classify polynomials into simple (solvable by radicals)...
Kulturwissenschaftliche Probleme internationaler Managementforschung
Janzer, Alexander
2007-01-01
Diplom-Kulturwirt Alexander Janzer untersucht kulturwissenschaftliche Probleme der internationalen Managementforschung, die ihrerseits methodisch besonders häufig auf kulturvergleichende Umfrageforschung zurückgreift. This paper presents the most common errors of cross-cultural management research. Research in this field is based primarily on the concepts and methods of cross-cultural psychology (e.g. Hofstede 1980, Schwartz 1994, Triandis 1980). It is shown how current research from the C...
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.
Medical problems of musicians.
Lockwood, A H
1989-01-26
Surveys of performing musicians indicate that almost half of them experience playing-related medical problems, some of which threaten or end their careers. Overuse injuries involving the muscle--tendon unit are the most common problem, with symptoms ranging from mild pain while the musician is playing to pain severe enough to preclude any use of the affected hand. String players are the most commonly affected, and percussionists the least. The most important predisposing characteristic is the use of repetitive movements during long hours of practice, but awkward body positions mandated by the shape and weight of the instrument, the technical difficulty of the repertoire, and unfamiliar instruments may also play a part. Women are more commonly affected than men. Rest is the cornerstone of therapy. Neural impingement syndromes affecting the median or ulnar nerves or the thoracic outlet affect many musicians. Focal dystonias may involve part or all of a hand or the muscles forming the embouchure (the position of the lips in wind players). These are very resistant to therapy and may terminate or drastically alter a career. Stress, especially performance anxiety, may impede performance. Beta-adrenergic blocking agents prevent the symptoms of performance anxiety and are frequently used by musicians without medical supervision. A recognition of the unique problems of musician-patients has led to the formation of successful specialty clinics in a number of cities. PMID:2643048
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
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.
Characteristics of Problems in Problem-based Learning
Sockalingam, Nachamma
2010-01-01
textabstractThis thesis focuses on characteristics of problems in Problem-based Learning (PBL). Problems initiate the students’ learning process in PBL. Several studies have shown that the quality of problems has a positive influence on students’ academic achievement and interest. In addition, the quality of problems has been shown to have a higher influence than the tutor’s performance and students’ prior knowledge on students’ learning. The implication of these findings is that designing go...
Space Power Engineering Problems
Senkevich, V. P.
2002-01-01
Development of space power engineering in the first half of XXI century shall be aimed at preventing the forthcoming energy crisis and ecological catastrophes. The problem can be solved through using solar energy being perpetual, endless, and ecologically safe. As of now, issues on the development and employment of solar power stations and its beaming to the ground stations in the SHF band are put on the agenda. The most pressing problem is to develop orbital solar reflectors to illuminate towns in the polar regions, agricultural regions, and areas of processing sea products. Space-based technologies can be used to deal with typhoons, green house effects, and "ozone holes". Recently, large, frameless film structures formed by centrifugal forces offer the promise of structures for orbital power plants, reflectors, and solar sails. A big success is achieved in the development of power generating solar array elements of amorphous silicon. These innovations would make the development of orbital solar power plants dozens of times cheaper. Such solar arrays shall be used in the nearest future on heavy communication satellites and the Earth remote sensing platforms for generation of 140-160 kW at a specific power beyond 300 W/kg. The cargo traffic needed to develop and maintain the orbital power plants and reflector systems could be equipped with solar sails as the future low thrust propulsion. In 2000, the mankind witnessed an unexpected beginning of energy crisis along with strong hydro- meteorological events (typhoons, floods) that shocked the USA, the Western Europe, England, Japan, and other countries. The total damage is estimated as 90 billions of dollars. The mankind is approaching a boundary beyond which its further existence would depend on how people would learn to control weather and use ecologically safe power sources. Space technology base on the research potential accumulated in the previous century could serve for the solution of this problem.
Sperling, J.; Vogel, W
2009-01-01
In 1927 the great physicist Paul A. M. Dirac failed to provide a consistent quantum description of the phase of a radiation field. Only one year later, he developed the famous Dirac theory of the electron, which led to the anti-particle -- the positron. We show that the reason for Dirac's failure with the phase problem bears a striking resemblance to his ingenious insight into the nature of the electron. For a correct quantum description of the phase of a radiation field it is necessary to ta...
Mechanics: Ideas, problems, applications
Ishlinskii, A. Iu.
The book contains the published articles and reports by academician Ishlinskii which deal with the concepts and ideas of modern mechanics, its role in providing a general understanding of the natural phenomena, and its applications to various problems in science and engineering. Attention is given to the methodological aspects of mechanics, to the history of the theories of plasticity, friction, gyroscopic and inertial systems, and inertial navigation, and to mathematical methods in mechanics. The book also contains essays on some famous scientists and engineers.
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.
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
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...
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...
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.
Drevenšek, Sanja
2016-01-01
Korupcija je kompleksen pojav in vse večji problem v vseh državah tudi v Sloveniji. Pojavlja se v različnih oblikah, njene posledice pa so uničujoče za širšo družbo, državo kakor tudi za vsakega posameznika. Problematika je sicer v Sloveniji urejena z zakonodajo, ki je primerljiva z evropsko zakonodajo o preprečevanju korupcije. Ustanovljeno imamo tudi Komisijo za preprečevanje korupcije kot samostojen in neodvisen državni organ, katerega temeljno poslanstvo je doseči ničelno toleranco do kor...
Schistosomiasis: progress and problems
Institute of Scientific and Technical Information of China (English)
George Y. Wu; Mohab H. Halim
2000-01-01
@@ INTRODUCTION Schistosomiasis, also commonly known as bilharziasis, is one of the most significant parasitic diseases of humans. A report of World Health Organization in 1996 estimated that over 200 million people were infested worldwide, mainly in rural agricultural and periurban areas. Of these, 20 million suffer severe consequences from the disease and 120 million are symptomatic. Symptoms range from fever, headache and lethargy, to severe sequelae including ascites, hepatosplenomegaly and even death[1]. More than 600 million people in the tropics are at risk for developing schistosomiasis.Schistosomiasis is the major public health problem in rural Egypt, with almost six million Egyptians are infested[2].
Gao, Keyue
2012-01-01
This paper deals with a problem in which two players share a previously sliced pizza and try to eat as much amount of pizza as they can. It takes time to eat each piece of pizza and both players eat pizza at the same rate. One is allowed to take a next piece only after the person has finished eating the piece on hand. Also, after the first piece is taken, one can only take a piece which is adjacent to already-taken piece. This paper shows that, in this real time setting, the starting player c...
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.
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…
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.
Decomposition Approaches for Optimization Problems
Kinable, Joris
2014-01-01
This dissertation encompasses the development of decomposition approaches for a variety of both real-world and fundamental optimization problems. Many optimization problems comprise of multiple interconnected subproblems, often rendering them too large or too complicated to solve as a single integral problem. Decomposition approaches are required to deal with these problems efficiently. By decomposing a problem into multiple subproblems, efficient dedicated procedures can be employed to solve...
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
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.
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…
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.
Edmondson, Amy C
2016-06-01
Companies today increasingly rely on teams that span many industries for radical innovation, especially to solve "wicked problems." So leaders have to understand how to promote collaboration when roles are uncertain, goals are shifting, expertise and organizational cultures are varied, and participants have clashing or even antagonistic perspectives. HBS professor Amy Edmondson has studied more than a dozen cross-industry innovation projects, among them the creation of a new city, a mango supply-chain transformation, and the design and construction of leading-edge buildings. She has identified the leadership practices that make successful cross-industry teams work: fostering an adaptable vision, promoting psychological safety, enabling knowledge sharing, and encouraging collaborative innovation. Though these practices are broadly familiar, their application within cross-industry teams calls for unique leadership approaches that combine flexibility, open-mindedness, humility, and fierce resolve. PMID:27491195
International Nuclear Information System (INIS)
This collection comprises the materials of the VI International Conference 'Shelter' Object', 15 years: today and future'. The topics of this issue's works cover the results of 15-year operation of the Shelter Object and investigations of conditions of its nuclear-, radiation- and general technical safety, procedures of monitoring of fuel-containing material conditions, building structures, problems of object's conversion into an ecologically safe system, preparation of technologies for radwaste (RW) management, working out of procedures using the remotely controlled facilities for diagnostics, prospecting of complicated in access Shelter Object premises, RW retrieval and management, etc. A very important role play the works aimed at the upgrade of radiation safety, protection of public and environment
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)
H. Williams
1952-07-01
Full Text Available It will help delegates to realize something of the range and magnitude of Service equipment problems if I touch on a few of the many important items which concern the Corps of Engineers in their preparations for war. The Engineers' role in battle is to assist our own forces to maintain their mobility by the passage of obstacles of every, description, the construction of roads and tracks and by meeting the Air Force's requirements airfields and air-strips. Secondly, to deny mobility to the enemy's forces by creating obstacles by demolitions and the destruction of materials, and by the construction of weapon positions and shelters. And lastly to support the administrative machine by supplying water, bulk fuel, power and Engineer stores where required, by meeting the Army's Transportation needs and in numerous other ways dependent on Engineering.
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.
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.
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.
Lau, August
2012-01-01
Classical approach of solvability problem has shed much light on what we can solve and what we cannot solve mathematically. Starting with quadratic equation, we know that we can solve it by the quadratic formula which uses square root. Polynomial is a generalization of quadratic equation. If we define solvability by using only square roots, cube roots etc, then polynomials are not solvable by radicals (square root, cube root etc). We can classify polynomials into simple (solvable by radicals) and complex (not solvable by radicals). We will use the same metaphor to separate what is solvable (simple part) and what is not solvable (complex part). This paper is a result of our presentation at a University of Houston seminar. In this paper, we will study seismic complexity through the eyes of solvability. We will investigate model complexity, data complexity and operator complexity. Model complexity is demonstrated by multiple scattering in a complex model like Cantor layers. Data complexity is studied through Bet...
DEFF Research Database (Denmark)
Görlich, Anne; Katznelson, Noemi; Stentoft, Mette
Uddannelsessystemet rummer i dag en stor del af de sårbare og udsatte unge, der tidligere havde ufaglærte jobs eller var på kontanthjælp. Det skaber udfordringer i forhold til den politiske målsætning om, at 95 procent af en ungdomsårgang skal gennemføre en ungdomsuddannelse. Disse udfordringer har...... været omdrejningspunktet i Skive Kommunes projekt ’Fra problemer til mirakler’, hvor man har søgt at styrke sårbare unges selvtillid, motivation for og deltagelse i en kompetencegivende uddannelse og dermed holde dem ude af kontanthjælpssystemet....
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
International Nuclear Information System (INIS)
Members of the Institute have worked on a number of problems including the following: acceleration algorithms for the Monte Carlo analysis of lattice field, and gauge and spin theories, based on changes of variables specific to lattices of dimension 2ell; construction of quaternionic generalizations of complex quantum mechanics and field theory; wave functions for paired Hall states; black hole quantum mechanics; generalized target-space duality in curved string backgrounds; gauge symnmetry algebra of the N = 2 string; two-dimensional quantum gravity and associated string theories; organizing principles from which the signal processing of neural networks in the retina and cortex can be deduced; integrable systems of KdV type; and a theory for Kondo insulators
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.
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.
Radiological problems in Kazakhstan
International Nuclear Information System (INIS)
Kazakhstan historical development and available mineral resources have pre-determined a scale of radiological problems in the state. Kazakhstan keeps leading positions in the world in explored uranium resources and hydrocarbon raw. More than five hundred nuclear explosions were performed in various regions of Kazakhstan. There is necessity to carry out remediation actions at the former test sites of Kazakhstan, especially at the Semipalatinsk test-site (STS). But because of the high cost of such actions it should be expedient to carry out them only in case of emergency and inclusion of the former test sites lands to the national economic activity, as in general, under conditions of competent policy of inhabitants, STS doesn't represent a hazard. At the same time, we ought not to lose an invaluable scientific material of test-sites. It is necessary to keep some areas of Semipalatinsk test-site as a rarities, reflected the important stages of the human evolution. Test-sites should be considered as world laboratory for studies of artificial radionuclides behaviour in natural medium. Illustrations of radiation-hazardous objects, of used technologies and procedures, under the Kazakhstan Republic instance, show that main power industries lead to the common increase of radioactivity materials in human environment. Mankind certainly will become aware of fact that industrial activities, under the current level of science and technologies development, will lead to the common increase of radioactivity materials in human environment. Solving of radioecological problems is possible only when people review their approach to a radioactivity, as a whole. Not only specialists involved in this field, but also all local population have to know rules of radiation safety and how reasonable manage with radioactive materials
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.
The worldwide "wildfire" problem.
Gill, A Malcolm; Stephens, Scott L; Cary, Geoffrey J
2013-03-01
The worldwide "wildfire" problem is headlined by the loss of human lives and homes, but it applies generally to any adverse effects of unplanned fires, as events or regimes, on a wide range of environmental, social, and economic assets. The problem is complex and contingent, requiring continual attention to the changing circumstances of stakeholders, landscapes, and ecosystems; it occurs at a variety of temporal and spatial scales. Minimizing adverse outcomes involves controlling fires and fire regimes, increasing the resistance of assets to fires, locating or relocating assets away from the path of fires, and, as a probability of adverse impacts often remains, assisting recovery in the short-term while promoting the adaptation of societies in the long-term. There are short- and long-term aspects to each aspect of minimization. Controlling fires and fire regimes may involve fire suppression and fuel treatments such as prescribed burning or non-fire treatments but also addresses issues associated with unwanted fire starts like arson. Increasing the resistance of assets can mean addressing the design and construction materials of a house or the use of personal protective equipment. Locating or relocating assets can mean leaving an area about to be impacted by fire or choosing a suitable place to live; it can also mean the planning of land use. Assisting recovery and promoting adaptation can involve insuring assets and sharing responsibility for preparedness for an event. There is no single, simple, solution. Perverse outcomes can occur. The number of minimizing techniques used, and the breadth and depth of their application, depends on the geographic mix of asset types. Premises for policy consideration are presented. PMID:23634593
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.
Kolkata Restaurant Problem as a Generalised El Farol Bar Problem
Chakrabarti, Bikas K.
Generalisation of the El Farol bar problem to that of many bars here leads to the Kolkata restaurant problem, where the decision to go to any restaurant or not is much simpler (depending on the previous experience of course, as in the El Farol bar problem). This generalised problem can be exactly analysed in some limiting cases discussed here. The fluctuation in the restaurant service can be shown to have precisely an inverse cubic behavior, as widely seen in the stock market fluctuations.
Addressing problems of employee performance.
McConnell, Charles R
2011-01-01
Employee performance problems are essentially of 2 kinds: those that are motivational in origin and those resulting from skill deficiencies. Both kinds of problems are the province of the department manager. Performance problems differ from problems of conduct in that traditional disciplinary processes ordinarily do not apply. Rather, performance problems are addressed through educational and remedial processes. The manager has a basic responsibility in ensuring that everything reasonable is done to help each employee succeed. There are a number of steps the manager can take to address employee performance problems.
Problem Solvers: Problem--How Long Can You Stand?
Teaching Children Mathematics, 2010
2010-01-01
Healthy lifestyles are increasingly emphasized these days. This month the authors begin a series of mathematical problems that also address physical activity. They hope that these problems offer opportunities to investigate mathematics and also reinforce the desire to lead a healthy life. In their first problem of the academic year, students…
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…
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
Dental Health and Orthodontic Problems
... Text Size Email Print Share Dental Health and Orthodontic Problems Page Content Article Body Dental Health Twin ... color can be tinted to match the teeth. Orthodontic Problems Crooked teeth, overbites and underbites are best ...
Feder, Tomás
2009-06-01
Results on graph turnpike problem without distinctness, including its NP-completeness, and an O(m+n log n) algorithm, is presented. The usual turnpike problem has all pairwise distances given, but does not specify which pair of vertices w e corresponds to. There are two other problems that can be viewed as special cases of the graph turnpike problem, including the bandwidth problem and the low-distortion graph embedding problem. The aim for the turnpike problem in the NP-complete is to orient the edges with weights w i in either direction so that when the whole cycle is transversed in the real line, it returns to a chosen starting point for the cycle. An instance of the turnpike problem with or without distinctness is uniquely mappable if there exists at most one solution up to translation and choice of orientation.
Sherlock Holmes, Master Problem Solver.
Ballew, Hunter
1994-01-01
Shows the connections between Sherlock Holmes's investigative methods and mathematical problem solving, including observations, characteristics of the problem solver, importance of data, questioning the obvious, learning from experience, learning from errors, and indirect proof. (MKR)
Dementia - behavior and sleep problems
... this page: //medlineplus.gov/ency/patientinstructions/000029.htm Dementia - behavior and sleep problems To use the sharing ... on this page, please enable JavaScript. People with dementia often have certain problems when it gets dark ...
ON VECTOR NETWORK EQUILIBRIUM PROBLEMS
Institute of Scientific and Technical Information of China (English)
Guangya CHEN
2005-01-01
In this paper we define a concept of weak equilibrium for vector network equilibrium problems.We obtain sufficient conditions of weak equilibrium points and establish relation with vector network equilibrium problems and vector variational inequalities.
Eldercare at Home: Communication Problems
... improving it. It is never just one person's responsibility. Communication problems may require adjusting to new limitations and possibly ... lead to further loss of communication skills and social isolation. ... with communication problems but pay attention to the way they communicate ...
Eldercare at Home: Mobility Problems
... dementia, poor eyesight, or need for medication review. Obvious problems with gait and balance (such as a ... condition such as emphysema or infection, a stroke, depression, circulatory problems, or over-medication with sedatives or ...
Direct Problems and Inverse Problems in Biometric Systems
Directory of Open Access Journals (Sweden)
Mihailescu Marius Iulian
2013-10-01
Full Text Available The article purpose is to describe the two sides of biometrics technologies, direct problems and inverse problems. The advance that we face today in field of Information Technology makes Information Security an inseparable part. The authentication has a huge role when we deal about security. The problems that can appear in implementing and developing biometrics systems is raising many problems, and one of the goal of this article is to focus on direct and inverse problems which is a new and challenging branch in biometrics technologies.
Terrorism and identity problem
Directory of Open Access Journals (Sweden)
Šijaković Ivan
2002-01-01
Full Text Available Terrorism is phenomenon of modern society, which became expressive especially in second half of twentieth century. There is a real danger that it could increase in growing number of terrorist groups, their aims, arms and ways of work, and that it could effect also in twentieth first century. Terrorism endangers the most important product of modern times: democracy, freedom, and human rights. There are different causes and reasons for existing of terrorist organizations and their cruel terrorist actions. This text analyzes a question of identity as a possible reason for existing of different terrorist groups and organizations and for their actions. Search for identity and question how to defend it create different problems and difficulties for individuals and groups. That identity is one-sided, disported, based on a false faith and so called salvation, but, to defend it somebody is prepared to sacrifice everything, his own life if that is necessary (but frequently somebody else's. That way, terrorism can be understood as a way of defending that identity.
The Classical Electron Problem
Gill, T L; Lindesay, J
2001-01-01
In this paper, we construct a parallel image of the conventional Maxwell theory by replacing the observer-time by the proper-time of the source. This formulation is mathematically, but not physically, equivalent to the conventional form. The change induces a new symmetry group which is distinct from, but closely related to the Lorentz group, and fixes the clock of the source for all observers. The new wave equation contains an additional term (dissipative), which arises instantaneously with acceleration. This shows that the origin of radiation reaction is not the action of a "charge" on itself but arises from inertial resistance to changes in motion. This dissipative term is equivalent to an effective mass so that classical radiation has both a massless and a massive part. Hence, at the local level the theory is one of particles and fields but there is no self-energy divergence (nor any of the other problems). We also show that, for any closed system of particles, there is a global inertial frame and unique (...
Karpowicz, Anna
2011-01-01
The considered model will be formulated as related to "the fishing problem" even if the other applications of it are much more obvious. The angler goes fishing. He uses various techniques and he has at most two fishing rods. He buys a fishing ticket for a fixed time. The fishes are caught with the use of different methods according to the renewal processes. The fishes' value and the inter arrival times are given by the sequences of independent, identically distributed (i.i.d.) random variables with the known distribution functions. It forms the marked renewal--reward process. The angler's measure of satisfaction is given by the difference between the utility function, depending on the value of the fishes caught, and the cost function connected with the time of fishing. In this way, the angler's relative opinion about the methods of fishing is modelled. The angler's aim is to have as much satisfaction as possible and additionally he has to leave the lake before a fixed moment. Therefore his goal is to find two...
Postdatism -- a perinatal problem?
Chhabra, S; Sood, S
1990-01-01
It has been traditionally accepted that maternal and fetal complications are at their lowest levels 37-42 weeks into gestation. 20% of pregnancies completed after 42 weeks gestation are thought to be affected by the postmaturity syndrome of uteroplacental insufficiency resulting in oligohydramnios, meconium passage, loss of fetal subcutaneous tissue, fetal asphyxia, and fetal death. Some workers, however, have also found that pregnancies completed between 40 and 42 weeks carry significant risk. The authors explored this question in a case-control study of 464 women seen at the Mahatma Gandhi Institute of Medical Sciences in Maharashtra, India. The cases of postdatism occurred in the absence of any other medical or obstetric problem. The operative delivery rate increased significantly among these patients compared to deliveries between 39 and 40 weeks. There was neither significant asphyxia nor perinatal loss in term completed normal patients. Asphyxia and perinatal mortality did, however, occur with postdatism. The authors note the likely role of oligohydramnios combined with placental dysfunction.
Bronchiectasis: still a problem
Institute of Scientific and Technical Information of China (English)
Wang Zengli
2014-01-01
Objective The purpose of this descriptive review was to delineate the current knowledge of bronchiectasis in terms of prevalence,burden of disease,pathophysiology,and management.Data sources The National Library of Medicines MEDLINE and PubMed database (2005-2013) were used to conduct a search using the keyword term "bronchiectasis".The references for articles being considered for inclusion were searched from additional sources such as conference proceedings.Study selection Criteria for inclusion of articles included data outlining epidemiology,pathogenesis,diagnosis,and evidence-based guidelines for management of bronchiectasis.In assessing the quality of the articles,factors such as size of the population studied,clinical setting of the study,and whether or not the studies were prospective or retrospective were taken into consideration.Review articles were also included in our data collection.Results Despite many advances in modem medicine,bronchiectasis still remains a significant public health problem in developed countries and the developing world.It carries a significant burden worldwide in terms of morbidity and mortality,as well as financially to the affected population.In addition,bronchiectasis may associate with chronic airflow obstruction,regardless of smoking status.Conclusions Bronchiectasis is a debilitating illness responsible for significant morbidity with a poor health-related quality of life.The condition has a substantial socioeconomic cost because both primary and secondary healthcare resources are frequently used and periods of sick leave are common.
Sharp regularity properties for the non-cutoff spatially homogeneous Boltzmann equation
Glangetas, Leo; Li, Hao-Guang; Xu, Chao-Jiang
2014-01-01
Accepted to publish by "Kinetic and Related Models" In this work, we study the Cauchy problem for the spatially homogeneous non-cutoff Boltzamnn equation with Maxwellian molecules. We prove that this Cauchy problem enjoys Gelfand-Shilov regularizing effect, that means the smoothing properties is same as the Cauchy problem defined by the evolution equation associated to a fractional harmonic oscillator. The power of this fractional is exactly the singular index of non-cutoff collisional ker...
Smoothing of mixed complementarity problems
Energy Technology Data Exchange (ETDEWEB)
Gabriel, S.A.; More, J.J. [Argonne National Lab., IL (United States). Mathematics and Computer Science Div.
1995-09-01
The authors introduce a smoothing approach to the mixed complementarity problem, and study the limiting behavior of a path defined by approximate minimizers of a nonlinear least squares problem. The main result guarantees that, under a mild regularity condition, limit points of the iterates are solutions to the mixed complementarity problem. The analysis is applicable to a wide variety of algorithms suitable for large-scale mixed complementarity problems.
Heuristic methods for messenger problem
Kobzareva, Maria
2011-01-01
This work describes static and dynamic problems with one messenger or multiple number of messengers and suggests a possibility of solving such problems with modified heuristic methods. To solve messenger problem, modified nearest neighbor heuristic, modified insertion heuristic and modified exchange heuristic are used. The main contribution of this work are applications, developed in MS Excel, programmed with Visual Basic for Application, that can solve static and dynamic problems with one me...
Dimensions of problem based learning
DEFF Research Database (Denmark)
Nielsen, Jørgen Lerche; Andreasen, Lars Birch
2013-01-01
The article contributes to the literature on problem based learning and problem-oriented project work, building on and reflecting the experiences of the authors through decades of work with problem-oriented project pedagogy. The article explores different dimensions of problem based learning...... and Learning (MIL). We discuss changes in the roles of the teachers as supervisors within this learning environment, and we explore the involvement of students as active participants and co-designers of how course and project activities unfold....
The Split Variational Inequality Problem
Censor, Yair; Reich, Simeon
2010-01-01
We propose a new variational problem which we call the Split Variational Inequality Problem (SVIP). It entails finding a solution of one Variational Inequality Problem (VIP), the image of which under a given bounded linear transformation is a solution of another VIP. We construct iterative algorithms that solve such problems, under reasonable conditions, in Hilbert space and then discuss special cases, some of which are new even in Euclidean space.
About an optimal visiting problem
Bagagiolo, Fabio; Benetton, Michela
2010-01-01
In this paper we are concerned with the optimal control problem consisting in minimizing the time for reaching (visiting) a fixed number of target sets, in particular more than one target. Such a problem is of course reminiscent of the famous "Traveling Salesman Problem" and brings all its computational diculties. Our aim is to apply the dynamic programming technique in order to characterize the value function of the problem as the unique viscosity solution of a suitable Hamilton-Jacobi equat...
Wild, Walter J.
1980-01-01
Discusses the simplest three-body problem, known as Euler's problem. The article, intended for students in the undergraduate mathematics and physics curricula, shows how the complex equations for a specific three-body problem can be solved on a small calculator. (HM)
Problem children or harassed childhood?
DEFF Research Database (Denmark)
Warming, Hanne
instition as stressed andnoisy, and thus it is the children they try to change (re-socialize) to solve the problems. The paper concludes that the discoruses tend to individualize structural problems with the result that a large group of children are identified as problem children rather than given better...
Solving complex fisheries management problems
DEFF Research Database (Denmark)
Petter Johnsen, Jahn; Eliasen, Søren Qvist
2011-01-01
A crucial issue for the new EU common fisheries policy is how to solve the discard problem. Through a study of the institutional set up and the arrangements for solving the discard problem in Denmark, the Faroe Islands, Iceland and Norway, the article identifies the discard problem as related...
International Nuclear Information System (INIS)
The report contains data on operational and emergency staff of the Chernobyl nuclear power plant who were exposed to radiation as a consequence of the reactor accident, the size of the doses received and consequences for health. 203 persons were found to have acute radiation sickness. Of the 22 patients suffering from an extremely severe degree of acute radiation sickness, 19 died. Of the 23 patients with severe bone marrow syndrome, 7 died. For the majority of patients, clinical recovery occurred toward the end of the second month following the accident. The main harmful factor for all victims was the relatively uniform gamma- and beta-radiation effect in a dosage exceeding 1 Gy and, in the case of 35 people exceeding 4 Gy. Radiation damage to wide areas of the skin was one of the main factors contributing to the overall severe condition of the patients, and was a determining factor in the main fatal complications. A preliminary evaluation of the use of some biochemical and immunological tests in the event of accidental exposure to radiation and the methods of treatment and preliminary assessment of their effectiveness are presented. Another part of the report contains data on the doses from radiation exposure to the population of the town of Pripyat' until the time of evacuation and to the population in the 30 km zone around Chernobyl' nuclear power plant and radiation consequences of the accident for the population of different regions in the European part of the USSR, especially the problems related to the contamination of food products. The last part of the report gives some data on the organization of medical examinations of the population from the region around the Chernobyl' plant and on the long-term programmes for the medical and biological monitoring of the population and personnel
International Nuclear Information System (INIS)
The resonant frequencies of solar acoustic-gravity waves are considered as probes of the sun's internal structure and dynamics. A perturbation method for calculating the effects of slow rotation and weak magnetic fields on p-mode frequencies is presented. Distortion of the equilibrium state of the star is taken into account. The method is applied to various hypothetical magnetic field geometries and rotation laws. Asymptotic estimates are developed and compared with the numerical results. The combined effect of rotation and magnetic fields is discussed. Current observations are reviewed in the light of the present results. A simple model is used to investigate the frequencies of high-degree acoustic modes which may be confined to the solar chromosphere. Such modes may be detected in observations from space. It is argued that they could provide a means of determining the mean sound speed in the chromosphere and the location of the transition zone between chromosphere and corona. It has been suggested that the sun could contain in its core quark nuggets which may constitute the ''missing mass''. Solar oscillations provide an extra set of constraints that any solar model must satisfy. Non-standard solar models containing a central black hole and a quark nugget core are constructed. The effect on a combination of resonant p-frequencies sensitive to conditions in the core is calculated by an asymptotic method. A black hole tends to make agreement between theoretical eigenfrequencies and observation worse. A quark nugget core may improve the agreement but tends to make the neutrino problem more acute. (author)
DEFF Research Database (Denmark)
Foss, Kirsten; Foss, Nicolai
as a general approach to problem solving. We apply these Simonian ideas to organizational issues, specifically new organizational forms. Specifically, Simonian ideas allow us to develop a morphology of new organizational forms and to point to some design problems that characterize these forms.Keywords: Herbert...... Simon, problem-solving, new organizational forms. JEL Code: D23, D83......Two of Herbert Simon's best-known papers are "The Architecture of Complexity" and "The Structure of Ill-Structured Problems." We discuss the neglected links between these two papers, highlighting the role of decomposition in the context of problems on which constraints have been imposed...
About an Optimal Visiting Problem
Energy Technology Data Exchange (ETDEWEB)
Bagagiolo, Fabio, E-mail: bagagiol@science.unitn.it; Benetton, Michela [Unversita di Trento, Dipartimento di Matematica (Italy)
2012-02-15
In this paper we are concerned with the optimal control problem consisting in minimizing the time for reaching (visiting) a fixed number of target sets, in particular more than one target. Such a problem is of course reminiscent of the famous 'Traveling Salesman Problem' and brings all its computational difficulties. Our aim is to apply the dynamic programming technique in order to characterize the value function of the problem as the unique viscosity solution of a suitable Hamilton-Jacobi equation. We introduce some 'external' variables, one per target, which keep in memory whether the corresponding target is already visited or not, and we transform the visiting problem in a suitable Mayer problem. This fact allows us to overcome the lacking of the Dynamic Programming Principle for the originary problem. The external variables evolve with a hysteresis law and the Hamilton-Jacobi equation turns out to be discontinuous.
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......) and may be defined in any number of dimensions. Solution methods are based on theory from both computational geometry and operations research. The scientific contributions of this thesis are presented in the form of six papers and a section which introduces the many problem types and recent solution...... of items. The heuristic was developed in collaboration with an industrial partner and is now being used to solve hundreds of problems every day as part of their planning process. A simple heuristic for optimizing a placement of items with respect to balance and moment of inertia is presented in the fifth...
A taxonomy of inductive problems.
Kemp, Charles; Jern, Alan
2014-02-01
Inductive inferences about objects, features, categories, and relations have been studied for many years, but there are few attempts to chart the range of inductive problems that humans are able to solve. We present a taxonomy of inductive problems that helps to clarify the relationships between familiar inductive problems such as generalization, categorization, and identification, and that introduces new inductive problems for psychological investigation. Our taxonomy is founded on the idea that semantic knowledge is organized into systems of objects, features, categories, and relations, and we attempt to characterize all of the inductive problems that can arise when these systems are partially observed. Recent studies have begun to address some of the new problems in our taxonomy, and future work should aim to develop unified theories of inductive reasoning that explain how people solve all of the problems in the taxonomy.
Yip, Vania T.; Ang, Rebecca P.; Ooi, Yoon Phaik; Fung, Daniel S. S.; Mehrotra, Kala; Sung, Min; Lim, Choon Guan
2013-01-01
Background: The high prevalence of attention problems in children warrants concern, as it is a risk factor for internalizing and externalizing problems. There lies a need to understand possible factors that may mediate this link so that interventions may be targeted to alleviate these mediators and interrupt the link between attention problems and…
Problem based teaching with other focuses than problem solving
Hansson, Per-Olof; Jansson, Per; Wihlborg, Elin
2015-01-01
Problem based teaching has been on the agenda in higher education for at least the last twenty years and is embedded in professional educations often to prepare students for real life problem solving. However, in when higher education rather aim to provide deeper theoretical and reflective competences promoting the students capacities to address unpredictable challenges in different contexts, there might be other ways of applying and using problem based educational tools. In this paper we des...
The problem of time and the problem of quantum measurement
Singh, Tejinder P
2012-01-01
Quantum theory depends on an external classical time, and there ought to exist an equivalent reformulation of the theory which does not depend on such a time. The demand for the existence of such a reformulation suggests that quantum theory is an approximation to a stochastic non-linear theory. The stochastic non-linearity provides a dynamical explanation for the collapse of the wave-function during a quantum measurement. Hence the problem of time and the measurement problem are related to each other: the search for a solution for the former problem naturally implies a solution for the latter problem.
Dimensions of problem based learning
DEFF Research Database (Denmark)
Nielsen, Jørgen Lerche; Andreasen, Lars Birch
2013-01-01
The article contributes to the literature on problem based learning and problem-oriented project work, building on and reflecting the experiences of the authors through decades of work with problem-oriented project pedagogy. The article explores different dimensions of problem based learning such...... as the exploration of problems, the project method, online collaboration, and the dialogic nature of students’ working together. A special attention is given to the historical development and theoretical roots of problem-oriented project work in Denmark. The case to be explored will be the Masters...... programme in ICT and Learning (MIL). We discuss changes in the roles of the teachers as supervisors within this learning environment, and we explore the involvement of students as active participants and co-designers of how course and project activities unfold....
Problem Prioritization in Usability Evaluation:
DEFF Research Database (Denmark)
Hertzum, Morten
2006-01-01
Severity assessments enable prioritization of problems encountered during usability evaluations and thereby provide a device for guiding the utilization of design resources. However, designers' response to usability evaluations is also influenced by other factors, which may overshadow severity...... problems, emphasizing that to be effective severity assessments must be reliable, valid, and sufficiently persuasive to justify the cost of fixing problems. For the usability inspections, evaluators' ratings of problem impact and persistence were weakly correlated with the number of evaluators reporting...... a problem, indicating that different evaluators represent different subgroups of users or alternatively that evaluator-made severity assessments are of questionable reliability. To call designers' attention to the severe problems, the halving of the severity sum is proposed as a means of visualizing...
Problem Solving and Complex Systems
Guinand, Frédéric
2008-01-01
The observation and modeling of natural Complex Systems (CSs) like the human nervous system, the evolution or the weather, allows the definition of special abilities and models reusable to solve other problems. For instance, Genetic Algorithms or Ant Colony Optimizations are inspired from natural CSs to solve optimization problems. This paper proposes the use of ant-based systems to solve various problems with a non assessing approach. This means that solutions to some problem are not evaluated. They appear as resultant structures from the activity of the system. Problems are modeled with graphs and such structures are observed directly on these graphs. Problems of Multiple Sequences Alignment and Natural Language Processing are addressed with this approach.
Inverse problem in hydrogeology
Carrera, Jesús; Alcolea, Andrés; Medina, Agustín; Hidalgo, Juan; Slooten, Luit J.
2005-03-01
The state of the groundwater inverse problem is synthesized. Emphasis is placed on aquifer characterization, where modelers have to deal with conceptual model uncertainty (notably spatial and temporal variability), scale dependence, many types of unknown parameters (transmissivity, recharge, boundary conditions, etc.), nonlinearity, and often low sensitivity of state variables (typically heads and concentrations) to aquifer properties. Because of these difficulties, calibration cannot be separated from the modeling process, as it is sometimes done in other fields. Instead, it should be viewed as one step in the process of understanding aquifer behavior. In fact, it is shown that actual parameter estimation methods do not differ from each other in the essence, though they may differ in the computational details. It is argued that there is ample room for improvement in groundwater inversion: development of user-friendly codes, accommodation of variability through geostatistics, incorporation of geological information and different types of data (temperature, occurrence and concentration of isotopes, age, etc.), proper accounting of uncertainty, etc. Despite this, even with existing codes, automatic calibration facilitates enormously the task of modeling. Therefore, it is contended that its use should become standard practice. L'état du problème inverse des eaux souterraines est synthétisé. L'accent est placé sur la caractérisation de l'aquifère, où les modélisateurs doivent jouer avec l'incertitude des modèles conceptuels (notamment la variabilité spatiale et temporelle), les facteurs d'échelle, plusieurs inconnues sur différents paramètres (transmissivité, recharge, conditions aux limites, etc.), la non linéarité, et souvent la sensibilité de plusieurs variables d'état (charges hydrauliques, concentrations) des propriétés de l'aquifère. A cause de ces difficultés, le calibrage ne peut êtreséparé du processus de modélisation, comme c'est le
Active Learning for Matching Problems
Charlin, Laurent; Zemel, Rich; Boutilier, Craig
2012-01-01
Effective learning of user preferences is critical to easing user burden in various types of matching problems. Equally important is active query selection to further reduce the amount of preference information users must provide. We address the problem of active learning of user preferences for matching problems, introducing a novel method for determining probabilistic matchings, and developing several new active learning strategies that are sensitive to the specific matching objective. Expe...
Solving Public Transit Scheduling Problems
Mesquita, Marta; Moz, Margarida; Paias, Ana; Paixão, José; Pato, Margarida Vaz; Respício, Ana
2008-01-01
Operational planning within public transit companies has been extensively tackled but still remains a challenging area for operations research models and techniques. This phase of the planning process comprises vehicle scheduling, crew scheduling and rostering problems. In this paper, a new integer mathematical formulation to describe the integrated vehicle-crew-rostering problem is presented. The method proposed to solve this multi-objective problem is a sequential algorithm considered withi...
Mathematical problems for chemistry students
Pota, Gyorgy
2006-01-01
Mathematical Problems for Chemistry Students has been compiled and written (a) to help chemistry students in their mathematical studies by providing them with mathematical problems really occurring in chemistry (b) to help practising chemists to activate their applied mathematical skills and (c) to introduce students and specialists of the chemistry-related fields (physicists, mathematicians, biologists, etc.) into the world of the chemical applications. Some problems of the collection are mathematical reformulations of those in the standard textbooks of chemistry, other