Abstract: The goal of sparse linear hyperspectral unmixing is to determine a scanty subset of spectral signatures of materials contained in each mixed pixel and to estimate their fractional abundances. This turns into an `0-norm minimization, which is an NP-hard problem. In this paper, we propose a new iterative method, which starts as an `1-norm optimization that is convex, has a unique soluti...

This paper is concerned with a general existence and continuous dependence of mild solutions to semilinear functional differential equations with infinite delay in Banach spaces. In particular, our results are applicable to the equations whose Co-semigroups and nonlinear operators, defined on an open set, are noncompact. Introduction. Let £ be a Banach space over the real field R with norm | | ...

We present a systematic study of the thermodynamic properties of a polydisperse fluid mixture. The size of the particles, σ , is assumed to be distributed according to a continuous distribution function fΣ(σ) , for which we have chosen a Γ -distribution. The interatomic potentials are given by a hard core repulsion plus an adjacent attractive tail in the form of a squarewell or a Yukawa potenti...

We consider the singular nonlinear integral equation u(x)= ∫RN g(x, y,u(y))dy/|y− x|σ for all x ∈ RN , where σ is a given positive constant and the given function g(x, y,u) is continuous and g(x, y,u) ≥M|x|β1|y|β(1 + |x|)−γ1 (1 + |y|)−γuα for all x, y ∈ RN , u ≥ 0, with some constants α,β,β1,γ,γ1 ≥ 0 and M > 0. We prove in an elementary way that if 0 ≤ α ≤ (N + β− γ)/(σ + γ1 − β1), (1/2)(N + β ...

Let f be a function on a bounded domain Ω ⊆ R and δ be a positive function on Ω such that B(x, δ(x)) ⊆ Ω. Let σ(f)(x) be the average of f over the ball B(x, δ(x)). The restricted mean-value theorems discuss the conditions on f, δ, and Ω under which σ(f) = f implies that f is harmonic. In this paper, we study the stability of harmonic functions with respect to the map σ. One expects that, in gen...

Let {ξj ; j ≥ 1} be a centered strictly stationary random sequence defined by S0 = 0, Sn = ∑n j=1 ξj and σ(n) = √ ES2 n, where σ(t), t > 0, is a nondecreasing continuous regularly varying function. Suppose that there exists n0 ≥ 1 such that, for any n ≥ n0 and 0 ≤ ε < 1, there exist positive constants c1 and c2 such that c1 e−(1+ε)x 2/2 ≤ P { |Sn| σ(n) ≥ x } ≤ c2 e −(1−ε)x2/2, x ≥ 1. Under some...

The datum σ yields a measure dσ on the boundary ∂P—on each edge E we take dσ to be a constant multiple of the standard Lebesgue measure with the constant normalised so that the mass of the edge is σ(E). Equally, the datum σ specifies an affine-linear defining function λE for each edge E, i.e. the edge lies in the hyperplane λ E (0). We choose an inward-pointing normal vector v at a point of E w...

Let (M, g) be a compact Riemannian manifold without boundary, with dimM ≥ 3, and f : R→ R a continuous function which is sublinear at infinity. By various variational approaches, existence of multiple solutions of the eigenvalue problem −∆gω + α(σ)ω = K̃(λ, σ)f(ω), σ ∈M, ω ∈ H 1 (M), is established for certain eigenvalues λ > 0, depending on further properties of f and on explicit forms of the f...

We offer conditions on semipositone function f t, u0, u1, . . . , un−2 such that the boundary value problem, uΔ n t f t, u σn−1 t , uΔ σn−2 t , . . . , uΔ n−2 σ t 0, t ∈ 0, 1 ∩ T, n ≥ 2, uΔi 0 0, i 0, 1, . . . , n − 3, αuΔ 0 − βuΔ 0 0, γuΔ σ 1 δuΔ σ 1 0, has at least one positive solution, where T is a time scale and f t, u0, u1, . . . , un−2 ∈ C 0, 1 × R 0,∞ n−1,R −∞,∞ is continuous with f t, ...

Let σ : Σ → Σ be the left shift acting on Σ, a one-sided Markov subshift on a countable alphabet. Our intention is to guarantee the existence of σinvariant Borel probabilities that maximize the integral of a given locally Hölder continuous potential A : Σ → R. Under certain conditions, we are able to show not only that A-maximizing probabilities do exist, but also that they are characterized by...