Let K^ be a singular cardinal of regular uncountable cofinality K. Let {n(£): £, < K} be a continuous increasing sequence with limit rj, and let K^ = ^n^)+^), £ < K, be regular cardinals. Let / be a normal ideal on K, and assume that the reduced product Y\Z.

Let X be a WCG Banach space admitting a Ck-Fréchet smooth norm. Then X admits an equivalent norm which is simultaneously C1-Fréchet smooth, LUR, and a uniform limit of Ck-Fréchet smooth norms. If X = C([0, α]), where α is an ordinal, then the same conclusion holds true with k =∞.

This paper studies four families of polyhedral norms parametrized by a single parameter. The first two families consist of the CVaR norm (which is equivalent to the D-norm, or the largest-k norm) and its dual norm, while the second two families consist of the convex combination of the 1and ∞-norms, referred to as the deltoidal norm, and its dual norm. These families contain the 1and ∞-norms as ...

Let L = K() be an abelian extension of degree n of a number eld K, given by the minimal polynomial of over K. We describe an algorithm for computing the local Artin map associated to the extension L=K at a nite or innnite prime v of K. We apply this algorithm to decide if a nonzero a 2 K is a norm from L, assuming that L=K is cyclic.

This paper studies four families of polyhedral norms parametrized by a single parameter. The first two families consist of the CVaR norm (which is equivalent to the D-norm, or the largest-k norm) and its dual norm, while the second two families consist of the convex combination of the l1and l∞-norms, referred to as the deltoidal norm, and its dual norm. These families contain the l1and l∞-norms...

Abstract One of the main results article Gelfand theory for real Banach algebras , recently published in [Rev R Acad Cienc Exactas Fís Nat Ser A Mat RACSAM 114(4):163, 2020] is Proposition 4.1, which establishes that norm inequality $$\Vert a^{2}\Vert \le \Vert a^{2}+b^{2}\Vert $$ ‖ <mml...

We present a new inversion formula for the classical, finite, and asymptotic Laplace transform f̂ of continuous or generalized functions f . The inversion is given as a limit of a sequence of finite linear combinations of exponential functions whose construction requires only the values of f̂ evaluated on a Müntz set of real numbers. The inversion sequence converges in the strongest possible sens...

We propose a new family of finite element methods for the Naghdi shell model, one method associated with each nonnegative integer k. The methods are based on a nonstandard mixed formulation, and the kth method employs triangular Lagrange finite elements of degree k+2 augmented by bubble functions of degree k+ 3 for both the displacement and rotation variables, and discontinuous piecewise polyno...

Let Ti,T2,...,Td be commuting automorphisms of the probability space (X,n). We call the Zd action (X,T,//) a dynamical system and write Tnx = T^T22...T%d(x) for n G Zd. Denote by X the crossed product of the von Neumann algebra A = L°°(X,M(N,C)) with the dynamical system (X,T,n). The group Zd acts on A by automorphisms / i-> f(Tn) where f(Tn)(x) = f(Tnx) and the algebra X is obtained by complet...

A. Huber and V. Kolmogorov (ISCO 2012) introduced a concept of k-submodular function as a generalization of ordinary submodular (set) functions and bisubmodular functions. They presented a min-max relation for the k-submodular function minimization by considering l1 norm, which requires a non-convex set of feasible solutions associated with the k-submodular function. Our approach overcomes the ...