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## Classical Results (classical + result)
## Selected Abstracts## Linear stability analysis of two-layer rectilinear flow in slot coating AICHE JOURNAL, Issue 10 2010Jaewook NamAbstract Two-layer coating occurs in many products. Ideally, the liquids are deposited onto the substrate simultaneously. In the case of two-layer slot coating, the interlayer between the coating liquids is subjected to enormous shearing. This may lead to flow instabilities that ruin the product. It is important to map the regions of the parameter space at which the flow is unstable. Most of the stability analyses of two-layer rectilinear flow consider the position of the interlayer as an independent parameter. Classical results cannot be applied directly in coating flows. We present a linear stability analysis of two-layer rectilinear flow considering the flow rates as an independent parameter. The predicted neutral-stability curves define the region of stable flow as a function of the operating parameters. The range of coating operating conditions is restricted further, when the condition for the desirable interlayer separation point location are considered together with the stability condition. © 2010 American Institute of Chemical Engineers AIChE J, 2010 [source] ## Undecidable and decidable restrictions of Hilbert's Tenth Problem: images of polynomials vs. images of exponential functions MLQ- MATHEMATICAL LOGIC QUARTERLY, Issue 1 2006Mihai PrunescuAbstract Classical results of additive number theory lead to the undecidability of the existence of solutions for diophantine equations in given special sets of integers. Those sets which are images of polynomials are covered by a more general result in the second section. In contrast, restricting diophantine equations to images of exponential functions with natural bases leads to decidable problems, as proved in the third section. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Averages of characteristic polynomials in random matrix theory COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 2 2006A. BorodinWe compute averages of products and ratios of characteristic polynomials associated with orthogonal, unitary, and symplectic ensembles of random matrix theory. The Pfaffian/determinantal formulae for these averages are obtained, and the bulk scaling asymptotic limits are found for ensembles with Gaussian weights. Classical results for the correlation functions of the random matrix ensembles and their bulk scaling limits are deduced from these formulae by a simple computation. We employ a discrete approximation method: the problem is solved for discrete analogues of random matrix ensembles originating from representation theory, and then a limit transition is performed. Exact Pfaffian/determinantal formulae for the discrete averages are proven using standard tools of linear algebra; no application of orthogonal or skew-orthogonal polynomials is needed. © 2005 Wiley Periodicals, Inc. [source] ## PORTFOLIO OPTIMIZATION WITH JUMPS AND UNOBSERVABLE INTENSITY PROCESS MATHEMATICAL FINANCE, Issue 2 2007Nicole BäuerleWe consider a financial market with one bond and one stock. The dynamics of the stock price process allow jumps which occur according to a Markov-modulated Poisson process. We assume that there is an investor who is only able to observe the stock price process and not the driving Markov chain. The investor's aim is to maximize the expected utility of terminal wealth. Using a classical result from filter theory it is possible to reduce this problem with partial observation to one with complete observation. With the help of a generalized Hamilton,Jacobi,Bellman equation where we replace the derivative by Clarke's generalized gradient, we identify an optimal portfolio strategy. Finally, we discuss some special cases of this model and prove several properties of the optimal portfolio strategy. In particular, we derive bounds and discuss the influence of uncertainty on the optimal portfolio strategy. [source] ## Linear functionals on nonlinear spaces and applications to problems from viscoplasticity theory MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2008Waldemar PompeAbstract A classical result in the theory of monotone operators states that if C is a reflexive Banach space, and an operator A: C,C* is monotone, semicontinuous and coercive, then A is surjective. In this paper, we define the ,dual space' C* of a convex, usually not linear, subset C of some Banach space X (in general, we will have C*,X*) and prove an analogous result. Then, we give an application to problems from viscoplasticity theory, where the natural space to look for solutions is not linear. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Solution of clamped rectangular plate problems INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2004Robert L. TaylorAbstract In this brief note, we present an efficient scheme for determining very accurate solutions to the clamped rectangular plate problem. The method is based upon the classical double cosine series expansion and an exploitation of the Sherman,Morrison,Woodbury formula. If the cosine expansion involves M terms and N terms in the two plate axes directions, then the classical method for this problem involves solving a system of (MN) × (MN) equations. Our proposal reduces the problem down to a system of well-conditioned N × N equations (or M × M when M < N). Numerical solutions for rectangular plates with various side ratios are presented and compared to the solution generated via Hencky's method. Corrections to classical results and additional digits for use in finite-element convergence studies are given. As an application example, these are used to show the rate of convergence for thin plate finite-element solutions computed using the Bogner,Fox,Schmit element. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Utility transversality: a value-based approach JOURNAL OF MULTI CRITERIA DECISION ANALYSIS, Issue 5-6 2005James E. MathesonAbstract We examine multiattribute decision problems where a value function is specified over the attributes of a decision problem, as is typically done in the deterministic phase of a decision analysis. When uncertainty is present, a utility function is assigned over the value function to represent the decision maker's risk attitude towards value, which we refer to as a value-based approach. A fundamental result of using the value-based approach is a closed form expression that relates the risk aversion functions of the individual attributes to the trade-off functions between them. We call this relation utility transversality. The utility transversality relation asserts that once the value function is specified there is only one dimension of risk attitude in multiattribute decision problems. The construction of multiattribute utility functions using the value-based approach provides the flexibility to model more general functional forms that do not require assumptions of utility independence. For example, we derive a new family of multiattribute utility functions that describes richer preference structures than the usual multilinear family. We also show that many classical results of utility theory, such as risk sharing and the notion of a corporate risk tolerance, can be derived simply from the utility transversality relations by appropriate choice of the value function. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## On a non-uniqueness in fragmentation models MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2002J. BanasiakAbstract Equations of fragmentation describing e.g. the polymer degradation, despite their apparent simplicity, have numerous non-typical features. One of them is the existence of multiple solutions. In this paper, applying classical results of Hille and Phillips, we explain their occurrence and prove that nevertheless the uniqueness holds for a large class of physically reasonable solutions. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## Equilibrium problem for thermoelectroconductive body with the Signorini condition on the boundary MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 4 2001D. HömbergAbstract We investigate a boundary value problem for a thermoelectroconductive body with the Signorini condition on the boundary, related to resistance welding. The mathematical model consists of an energy-balance equation coupled with an elliptic equation for the electric potential and a quasistatic momentum balance with a viscoelastic material law. We prove the existence of a weak solution to the model by using the Schauder fixed point theorem and classical results on pseudomonotone operators. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## Locally compact (2, 2)-transformation groups MATHEMATISCHE NACHRICHTEN, Issue 7 2010Alfonso Di BartoloAbstract We determine all locally compact imprimitive transformation groups acting sharply 2-transitively on a non-totally disconnected quotient space of blocks inducing on any block a sharply 2-transitive group and satisfying the following condition: if ,1, ,2 are two distinct blocks and Pi, Qi , ,i (i = 1, 2), then there is just one element in the inertia subgroup which maps Pi onto Qi. These groups are natural generalizations of the group of affine mappings of the line over the algebra of dual numbers over the field of real or complex numbers or over the skew-field of quaternions. For imprimitive locally compact groups, our results correspond to the classical results of Kalscheuer for primitive locally compact groups (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## ON AXISYMMETRIC TRAVELING WAVES AND RADIAL SOLUTIONS OF SEMI-LINEAR ELLIPTIC EQUATIONS NATURAL RESOURCE MODELING, Issue 3 2000THOMAS P. WITELSKIABSTRACT. Combining analytical techniques from perturbation methods and dynamical systems theory, we present an elementaryapproach to the detailed construction of axisymmetric diffusive interfaces in semi-linear elliptic equations. Solutions of the resulting non-autonomous radial differential equations can be expressed in terms of a slowlyvarying phase plane system. Special analytical results for the phase plane system are used to produce closed-form solutions for the asymptotic forms of the curved front solutions. These axisym-metric solutions are fundamental examples of more general curved fronts that arise in a wide variety of scientific fields, and we extensivelydiscuss a number of them, with a particular emphasis on connections to geometric models for the motion of interfaces. Related classical results for traveling waves in one-dimensional problems are also reviewed briefly. Manyof the results contained in this article are known, and in presenting known results, it is intended that this article be expositoryin nature, providing elementarydemonstrations of some of the central dynamical phenomena and mathematical techniques. It is hoped that the article serves as one possible avenue of entree to the literature on radiallysymmetric solutions of semilinear elliptic problems, especiallyto those articles in which more advanced mathematical theoryis developed. [source] ## Random trees and general branching processes RANDOM STRUCTURES AND ALGORITHMS, Issue 2 2007Anna RudasAbstract We consider a tree that grows randomly in time. Each time a new vertex appears, it chooses exactly one of the existing vertices and attaches to it. The probability that the new vertex chooses vertex x is proportional to w(deg(x)), a weight function of the actual degree of x. The weight function w : , , ,+ is the parameter of the model. In 4 and 11 the authors derive the asymptotic degree distribution for a model that is equivalent to the special case, when the weight function is linear. The proof therein strongly relies on the linear choice of w. Using well-established results from the theory of general branching processes we give the asymptotical degree distribution for a wide range of weight functions. Moreover, we provide the asymptotic distribution of the tree itself as seen from a randomly selected vertex. The latter approach gives greater insight to the limiting structure of the tree. Our proof is robust and we believe that the method may be used to answer several other questions related to the model. It relies on the fact that considering the evolution of the random tree in continuous time, the process may be viewed as a general branching process, this way classical results can be applied. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007 [source] ## A risk model driven by Lévy processes APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 2 2003Manuel MoralesAbstract We present a general risk model where the aggregate claims, as well as the premium function, evolve by jumps. This is achieved by incorporating a Lévy process into the model. This seeks to account for the discrete nature of claims and asset prices. We give several explicit examples of Lévy processes that can be used to drive a risk model. This allows us to incorporate aggregate claims and premium fluctuations in the same process. We discuss important features of such processes and their relevance to risk modeling. We also extend classical results on ruin probabilities to this model. Copyright © 2003 John Wiley & Sons, Ltd. [source] |