Abstract The time-dependent solution of a kind supply chain system with the multi-suppliers and single demander is investigated in this paper. By choosing state space defining operator system, we transfer model into an abstract Cauchy problem. We are devoted to studying unique existence its exponential stability by using theory C 0 -semigroup. prove that generates -semigroup cofinal resolvent p...

The stochastic spectral expansion method offers a simple framework for calculations in de Sitter spacetimes. We show how to extend its reach metastable vacuum states, both the case when potential is bounded from below, and it unbounded below therefore no stable state exists. In cases, decay rate of given by lowest nonzero eigenvalue associated Fokker--Planck equation. corresponding eigenfunctio...

and γ = [ IN + ρH H ]−1 11 , where H is a M × N complex Gaussian matrix with independent entries and M ≥ N . These diagonal entries are related to the “signal to interference and noise ratio” (SINR) in multi-antenna communications. They depend not only on the eigenvalues but also on the corresponding eigenfunction weights, which we are able to evaluate on average constrained on the value of the...

We study the nonlinear eigenvalue problem f(x) = λx for a class of maps f : K → K which are homogeneous of degree one and order-preserving, where K ⊆ X is a closed convex cone in a Banach space X. Solutions are obtained, in part, using a theory of the “cone spectral radius” which we develop. Principal technical tools are the generalized measure of noncompactness and related degree-theoretic tec...

This paper examines the class of generalized Morse wavelets, which are eigenfunction wavelets suitable for use in time-varying spectrum estimation via averaging of time-scale eigenscalograms. Generalized Morse wavelets of order (the corresponding eigenvalue order) depend on a doublet of parameters ( , ); we extend results derived for the special case = = 1 and include a proof of “the resolution...

The use of numerical tools to solve challenging problems in mathematics has exploded in the past several decades. The purpose of this paper is to compare the results of two different types of numerical methods in finding solutions to the eigenvalue problem for a second order elliptic partial differential equations (PDE) with boundary and transmission conditions. Transmission properties result f...

1 Background We begin by recalling the solution of the vibrating string problem and Sturm-Liouville problems. When we solve the problem of the vibrating string using the technique of separation of variables, the differential equation involving the space variable x, and assuming constant mass density, is y (x) + ω 2 c 2 y(x) = 0, (1.1) which we can write as an eigenvalue problem y (x) + λy(x) = ...

xp Xoo„(x")P(x"')dx"dx"'. (10} If we compare these equations with the corresponding equations (19) of Mfffler and Kristensen' in the theory of nonlocal interaction between a local scalar (or pseudoscalar) field and a local spinor field, we notice that the internal eigenfunction x„(r) plays the role of a convergence factor. There is, however, an essential difference between their equations and o...

In this paper, we are interested in the spectral properties of the generalised principal eigenvalue of some nonlocal operator. That is, we look for the existence of some particular solution (λ, φ) of a nonlocal operator. ∫ Ω K(x, y)φ(y)dy + a(x)φ(x) = −λφ(x), where Ω ⊂ Rn is an open bounded connected set, K a nonnegative kernel and a is continuous. We prove that for the generalised principal ei...

We investigate shrinkage priors on power spectral densities for complex-valued circular-symmetric autoregressive processes. construct predictive densities, which asymptotically dominate (i) the Bayesian density based Jeffreys prior and (ii) estimative with maximum likelihood estimator, where Kullback-Leibler divergence from true to a is adopted as risk. Furthermore, we propose general construct...