Estimations for the characteristic values of a Sturm-Liouville problem

We consider a particular Sturm-Liouville problem, with boundary conditions containing the characteristic values. This problem governs the stability of the interfaces in oil recovery, by using the Hele-Shaw model of a homogeneous porous medium. We obtain estimations of the approximative characteristic values, by using a finite-difference approximation and the Gerschgorin's localization theorem. We obtain estimations of the exact characteristic values by using the Rayleigh's quotient of the initial problem. The upper limit of the approximative characteristic values is (in general) greater than the lower limit of the exact characteristic values. The same upper limit is given by the two methods, for a particular value of a parameter of the problem. This value gives us a large improvement of the stability. A previous convergence result is confirmed.     

Estimations for the characteristic values of a Sturm-Liouville problem

Zeitschrift für angewandte Mathematik und Physik - We consider a particular Sturm-Liouville problem, with boundary conditions containing the characteristic values. This problem governs the...     

Extreme values and a Gaussian central limit theorem

Summary We examine the central limit theorem with Gaussian limit law for a sequence of independent, identically distributed, vector valued random variables whose partial sums can be centered and normalized to be tight with non-degenerate limit laws. These results apply to the situation when the sequence is in the domain of attraction of a non-degenerate stable law of indexp(0,2], and are achieved by eliminating the extreme values from the partial sums.Supported in part by NSF Grant MCS-8219742Work done while visiting the University of Wisconsin, Madison, with partial support by NSF Grant MCS-8219742     

Extreme values of a portfolio of Gaussian processes and a trend

We consider the extreme values of a portfolio of independent continuous Gaussian processes ( ) which are asymptotically locally stationary, with expectations and variances , and a trend for some constants with . We derive the probability for , which may be interpreted as ruin probability. AMS 2000 Subject Classifications Primary—60G15, 62G32, 91B28     

Extreme values of Markov population processes

In contrast to the classical theory of partial sums of independent and identically distributed random variables, the maximum value taken by a component of a Markov population process x_N is typically largely determined by the variation in its mean, rather than by stochastic fluctuation. A closer approximation to its distribution is found by considering the supremum of V(t) ? N^{$\text{1}\text{2}$}c(t) for a suitable centred Gaussian process V, where c incorporates the effect of the variation in the mean of x_N. Under appropriate conditions, it is shown that this has a distribution which is normally distributed, to within an error of order N^{?$\text{1}\text{2}$} log N, and expressions for the mean and variance of the approximating distribution are derived.     

Extreme values of exponentially autocorrelated sequences

The statistics of extreme values of autocorrelated sequences often forms an important aspect of the analysis of numerous physical phenomena. This study examines the statistical behavior of the extreme values of three different types of sequences, each of which has an exponential-type autocorrelation function. Computer experiments are used to investigate the distribution function and the moments of the maximum value of each of these sequences. The effects of varying degrees of autocorrelation, and other parameters such as the length of the underlying sequence, are also studied and quantified.     

On a class of nonlinear problems on characteristic values

For a class of problems on characteristic values where the spectral parameter enters in a polynomial form we establish the fact that proximity of the operator-coefficients of the corresponding operator-functions implies proximity of the n-th characteristic values.     

Extreme values of the resurgence for homogeneous ideals in polynomial rings

We show that two ostensibly different versions of the asymptotic resurgence introduced by E. Guardo, B. Harbourne and A. Van Tuyl in 2013 are the same. We also show that the resurgence and asymptotic resurgence attain their maximal values simultaneously, if at all, which we apply to a conjecture of E. Grifo. For radical ideals of points, we show that the resurgence and asymptotic resurgence attain their minimal values simultaneously. In addition, we introduce an integral closure version of the resurgence and relate it to the other versions of the resurgence. In closing we provide various examples and raise some related questions, and we finish with some remarks about computing the resurgence.     

Identities for sums of characteristic values of entire matrix pencils

The paper deals with an entire matrix-valued function of a complex argument (an entire matrix pencil) f of order ρ(f)<∞. Identities for the following sums of the characteristic values of f are established:

     

Extreme values and the law of the iterated logarithm

Summary IfX takes values in a Banach spaceB and is in the domain of attraction of a Gaussian law onB, thenX satisfies the compact law of the iterated logarithm (LIL) with respect to a regular normalizing sequence { _n } iffX satisfies a certain integrability condition. The integrability condition is equivalent to the fact that the maximal term of the sample {X ₁, X ₂,..., X _n} does not dominate the partial sums {S _n}, and here we examine the precise influence of these maximal terms and its relation to the compactLIL. In particular, it is shown that if one deletes enough of the maximal terms there is always a compactLIL with non-trivial limit set.Supported in part by NSF Grant MCS-8219742Work done while visiting the University of Wisconsin, Madison, with partial support by NSF Grant MCS-8219742     

Inequality for second characteristic values of positive operators of certain classes

A homogeneous additive operator A, positive on a cone K of a Banach space E partially ordered by K, is investigated. It is assumed that K is a reproducing cone in E and that A has a characteristic vector u₀: Au₀ = ₀u₀ in K. It is proved that if for some 1, then any other characteristic value of A satisfies the inequality ||<(-1)/(+1) ₀. This is the best possible upper bound in the class of operators considered.Translated from Matematicheskie Zametki, Vol. 19,No. 1, pp. 27–33, January, 1971.The author takes this opportunity to thank M. A. Krasnosel'skii for his interest in this work.     

Weighted shapley values for games in generalized characteristic function form

We study the family of weighted Shapley values for games in generalized characteristic function form. These values are defined and characterized.     

Admissible estimation of linear functions of characteristic values of a finite population

The problem on admissibility of estimators is considered based on the point of view of the superpopulation model. The necessary and sufficient conditions for linear estimators of an arbitrary linear function of characteristic values of a finite population to be admissible in the class of linear or all estimators are obtained respectively. Project supported by the National Natural Science Foundation of China.     

Stability of characteristic values of singular integral equations

A study is made of the problem concerning existence of nontrivial solutions of the equation (A+C)f=f for all compact (or small in norm) operators.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 165, pp. 136–142, 1987.     

Extreme values of operator norms in spaces with equivalent norms

The paper is concerned with various characteristics of spaces (L, ‖·‖) with equivalent norms and of operators on these spaces. In particular, the notion of distance between equivalent norms in the space L is introduced and the relationship between norms of the space and norms of operators in L is studied. Bibliography: 4 titles. Translated fromObchyslyuval'na ta Prykladna Matematyka, No. 80, 1996, pp. 25–32.