We study strong solutions u : R → X, a Banach space X, of the nth-order evolution equation u(n) −Au(n−1) = f , an infinitesimal generator of a strongly continuous group A : D(A) ⊆ X → X, and a given forcing term f : R → X. It is shown that if X is reflexive, u and u(n−1) are Stepanov-bounded, and f is Stepanov almost periodic, then u and all derivatives u′, . . . ,u(n−1) are strongly almost per...

over high levels u. For a large class of such random fields we compute the u → ∞ asymptotic joint distribution of the numbers of critical points, of various types, of X in Au, conditional on Au being non-empty. This allows us, for example, to obtain the asymptotic conditional distribution of the Euler characteristic of the excursion set. In a significant departure from the Gaussian situation, t...

In this paper we are interested in abstract problems of Barenblatt’s type. In a first part, we investigate the problem f (∂t u)+Au = g where f and A are maximal monotone operators and by assuming that A derives from a potential J . With general assumptions on the operators, we prove the existence of a solution. In the second part of the paper, we examine a stochastic version of the above proble...

Let a compact group U act by automorphisms of a commutative regular and Wiener Banach algebra A. We study representations Ru of U on quotient spaces A/I(üj), where u> is an orbit of U in the Gelfand space X of A and L(uj) is the minimal closed ideal with hull w C X. The main result of the paper is: if A = AP(X) is a weighted Fourier algebra on a LCA group X = A with a subpolynomial weight p on ...

∀ ` σ` ∈ R, σ` ≥ 0 (2) ∀ `, `′ 〈u`, u`′〉 = 〈v`, v`′〉 = δ(`, `′) (3) To prove this consider the matrix AA ∈ Rm×m. Set u` to be the `’th eigenvector of AA . By definition we have that AAu` = λ`u`. Since AA T is positive semidefinite we have λ` ≥ 0. Since AA is symmetric we have that ∀ `, `′ 〈u`, u`′〉 = δ(`, `′). Set σ` = √ λ` and v` = 1 σ` Au`. Now we can compute the following: 〈v`, v`′〉 = 1 σ2 `...

A commutative power-associative algebra A of characteristic >5 with an idempotent u may be written1 as the supplementary sum ^=^4„(l)+4u(l/2)+^4u(0) where 4U(X) is the set of all xx in A with the property xx« =Xxx. The subspaces Au(l) and .4K(0) are orthogonal subalgebras, [AU(1/2)]2QAU(1)+AU(0) andAu(K)Au(l/2) C4„(l/2)+^4u(l—X) forX=0, 1. The algebra A is called w-stable if 4u(X)-4„(l/2)C.4u(l...

Class II-restricted T cell clones specific for myelin basic protein (MBP) have been generated from PL/J and (PL/J X SJL/J)F1 [((PLSJ)F1] mice following sensitization to rat MBP. Of 17 T cell clones generated from (PLSJ)F1 mice, 5 are I-Au(A alpha uA beta u) restricted, one is restricted to I-As(A alpha sA beta s), 10 are restricted to hybrid I-A(u X s)F1 (A alpha sA beta u) determinants, and on...

Answer set programming (ASP) approach is an efficient approach for solving the maximum quartet consistency problem. We distinguish two factors that affect the efficiency of a recent ASP approach for solving maximum quartet consistency problem; answer set programming itself and a variety of preprocessing steps. In this paper, we propose a method for applying one of the preprocessing steps used i...

where A(t), B(t), C(t) Î C[0,1], f(t, u) : [0,1] × [0, ∞) ® [0. ∞) is continuous. In recent years, BVPs for sixth-order ordinary differential equations have been studied extensively, see [1-7] and the references therein. For example, Tersian and Chaparova [1] have studied the existence of positive solutions for the following systems (1.2): { u(6) + Au(4) + Bu′′ + Cu − f (t, u) = 0. 0 < x < L, u...