Improved spatial decay bounds in generalized heat conduction

This paper deals with heat conduction in a semi-infinite cylinder using the generalized Maxwell-Cattaneo equations. Spatial decay bounds for the temperature and heat flux under two different types of boundary conditions are derived. For fixed time it is shown that in each case the solutions decay in appropriate measure like the exponential of a quadratic function of the distance from the base of the cylinder, whereas in previous work they had been shown to decay only at least as fast as the exponential of a linear function.Received: January 13, 2004     

Improved spatial decay bounds in generalized heat conduction

This paper deals with heat conduction in a semi-infinite cylinder using the generalized Maxwell-Cattaneo equations. Spatial decay bounds for the temperature and heat flux under two different types of boundary conditions are derived. For fixed time it is shown that in each case the solutions decay in appropriate measure like the exponential of a quadratic function of the distance from the base of the cylinder, whereas in previous work they had been shown to decay only at least as fast as the exponential of a linear function.     

Improved bounds for some nonstandard problems in generalized heat conduction

We consider the Maxwell-Cattaneo system of equations for generalized heat conduction where the temperature and heat flux satisfy a nonstandard auxiliary condition which prescribes a combination of their values initially and at a later time. We obtain L₂ bounds for the temperature and heat flux by means of Lagrange identities. These bounds extend the range of validity for the parameter in the nonstandard condition under a constraint on the coefficients in the differential equations.     

Explicit decay bounds in some quasilinear one‐dimensional parabolic problems

In the first part of this paper we study a thermal diffusion process described by a semilinear parabolic problem and we introduce a new maximum principle in order to obtain explicit decay bounds for the temperature and its gradient. In the second part we find analogous bounds for the so‐called ground water equation in a more general form. Copyright © 1999 John Wiley & Sons, Ltd.     

矩阵广义逆新的扰动上界

利用矩阵的奇异值分解方法,研究了矩阵广义逆的扰动上界,得到了在F-范数下矩阵广义逆的扰动上界定理,所得定理推广并彻底改进了近期的相关结果.相应的数值算例验证了定理的有效性.     

Exponential bounds for generalized poisson distributions

Exponential estimates are constructed for the probabilities of large deviations of Poisson random sums. Supported by the Russian Foundation for Fundamental Research (grant No. 97-01-00271) and the Russian Humanitarian Science Foundation (grant No. 97-02-02235). Proceedings of the Seminar on Stability Problems for Stochastic Models. Moscow, Russia, 1996, Part II.     

Some nonstandard problems in generalized heat conduction

The Maxwell-Cattaneo system of equations for generalized heat conduction is considered where the temperature and heat flux, respectively, are subject to auxiliary conditions which prescribe a combination of their values initially and at a later time. By means of differential inequalities, L₂ exponential decay bounds for the temperature and heat flux are determined in terms of data for a range of values of the parameter in the nonstandard auxiliary condition. Decay bounds are also obtained in two related problems.     

Some nonstandard problems in generalized heat conduction

The Maxwell-Cattaneo system of equations for generalized heat conduction is considered where the temperature and heat flux, respectively, are subject to auxiliary conditions which prescribe a combination of their values initially and at a later time. By means of differential inequalities, L₂ exponential decay bounds for the temperature and heat flux are determined in terms of data for a range of values of the parameter in the nonstandard auxiliary condition. Decay bounds are also obtained in two related problems. Received: July 14, 2003     

Residual error bounds of generalized eigenvalue systems

A backward error analysis of approximate deflation pair systems of generalized eigenvalue problem is presented. The perturbation matrices obtained can be expressed by the residuals of the approximate deflation pair systems. Therefore, the corresponding error bounds with respect to the Frobenius norm and the spectral norm are computable.     

Effective bounds for generalized linear global relations

This paper puts forward new effective lower bounds for the values of linear forms from certain series in non-Archimedian fields. The results obtained are related to the generalization of Siegel–Shidlovski’s method.     

Spatial decay bounds for double diffusive convection in Brinkman flow

This paper examines the time-dependent double diffusive convection in Brinkman flow in a semi-infinite cylinder. Under appropriate initial and boundary conditions the authors establish exponential decay of solutions in “energy” norm with distance from the finite end of the cylinder.     

Spatial decay bounds for time dependent magnetohydrodynamic geophysical flow

This article is concerned with spatial decay bounds for the time dependent magnetohydrodynamic geophysical flow in an infinite pipe when homogeneous lateral surface boundary conditions are applied. Assuming that the entrance velocity and magnetic field data are small enough and the fluid flow converges to laminar flow as the distance down the pipe tends to infinity, we derive a second order differential inequality that leads to an exponential decay estimate for the “energy” associated with the velocity and magnetic field represented by the difference between the entrance flow and fully developed laminar flow. We also show how to establish the explicit decay bounds for the total energy.     

Inequalities and bounds for generalized complete elliptic integrals

Computable bounds for the generalized complete elliptic integrals of the first and second kind are obtained. Also, bounds for some combinations and products for integrals under discussion are established. It has been proven that both families of integrals are logarithmically convex as functions of the first parameter. This property has been employed to obtain several inequalities involving integrals in question.     

Pertubation bounds for the definite generalized eigenvalue problem

Let A and B be Hermitian matrices, and let c(A, B) = inf{|x^H(A + iB)x|:6 = 1}. The eigenvalue problem Ax = λBx is called definite if c(A, B)>0. It is shown that a definite problem has a complete system of eigenvectors and that its eigenvalues are real. Under pertubations of A and B, the eigenvalues behave like the eigenvalues of a Hermitian matrix in the sense that there is a 1-1 pairing of the eigenvalues with the perturbed eigenvalues and a uniform bound for their differences (in this case in the chordal metric). Pertubation bounds are also developed for eigenvectors and eigenspaces.     

On a generalized vector equilibrium problem with bounds

We prove the existence of a solution to the generalized vector equilibrium problem with bounds. We show that several known theorems from the literature can be considered as particular cases of our results, and we provide examples of applications related to best approximations in normed spaces and variational inequalities.     

Hedging under generalized good-deal bounds and model uncertainty

We study a notion of good-deal hedging, that corresponds to good-deal valuation and is described by a uniform supermartingale property for the tracking errors of hedging strategies. For generalized good-deal constraints, defined in terms of correspondences for the Girsanov kernels of pricing measures, constructive results on good-deal hedges and valuations are derived from backward stochastic differential equations, including new examples with explicit formulas. Under model uncertainty about the market prices of risk of hedging assets, a robust approach leads to a reduction or even elimination of a speculative component in good-deal hedging, which is shown to be equivalent to a global risk minimization in the sense of Föllmer and Sondermann (1986) if uncertainty is sufficiently large.     

Improved bounds on the generalized acyclic chromatic number

An r-acyclic edge chromatic number of a graph G, denoted by a _r ^′ r(G), is the minimum number of colors used to produce an edge coloring of the graph such that adjacent edges receive different colors and every cycle C has at least min {|C|, r} colors. We prove that a _r ^′ r(G) ≤ (4r + 1)Δ(G), when the girth of the graph G equals to max{50, Δ(G)} and 4 ≤ r ≤ 7. If we relax the restriction of the girth to max {220, Δ(G)}, the upper bound of a _r ^′ r(G) is not larger than (2r + 5)Δ(G) with 4 ≤ r ≤ 10.     

Implicit representation of generalized variable upper bounds in linear programming

In certain linear programs, especially those derived from integer programs, large numbers of constraints may have very simple form. Examples are:x _ij 1 (simple upper bounds [SUB]), _i x _ij = 1 (generalized upper bounds [GUB]) andx _ij y _i (variable upper bounds [VUB]). A class of constraints called generalized VUB [GVUB] is introduced which includes GUB and VUB as special cases. Also introduced is a method for representing GVUB constraints implicitly within the mechanics of the simplex method.Research supported in part by the Mobil Oil Corporation.