Aim of this note is to provide a brief outline of the theory of shift-differentials, introduced in [2], and show how their construction can be extended to the case of vector valued functions. In the following, we consider the space BV of scalar integrable functions having bounded variation, endowed with the L norm. We recall that, given a map Φ : X 7→ Y between normed linear spaces, its differe...

Multiple-scale homogenization problems are treated in the space BV of functions of bounded variation, using the notion of multiple-scale convergence developed in [35]. In the case of one microscale Amar’s result [3] is recovered under more general conditions; for two or more microscales new results are obtained. AMS Classification Numbers (2010): 49J45, 35B27, 26A45

We present a very short derivation of the integral representation of the two-sided Skorokhod reflection Z of a continuous function X of bounded variation, which is a generalization of the integral representation of the one-sided map featured in [1, 4]. We also show that Z satisfies a simpler integral representation when additional conditions are imposed on X.

We study the asymptotics of subset counts for the uniformly random partition of the set [n]. It is known that typically most of the subsets of the random partition are of size r, with re=n. Confirming a conjecture formulated by Arratia and Tavare , we prove that the counts of other subsets are close, in terms of the total variation distance, to the corresponding segments of a sequence [Zj] of i...

It is obvious that lp (/> 2:1) or any Hubert space satisfies (A). In §3 it is shown that Lp (p>l) does likewise. The method of proof is entirely different from that of Clarkson. In §4 it is shown that if X is any Banach space having the property that every function on a linear interval to X, which satisfies a Lipschitz condition, is differentiable almost everywhere, then also every function of ...

the object of this paper is to introduce the notion of intuitionisticfuzzy continuous mappings and intuitionistic fuzzy bounded linear operatorsfrom one intuitionistic fuzzy n-normed linear space to another. relation betweenintuitionistic fuzzy continuity and intuitionistic fuzzy bounded linearoperators are studied and some interesting results are obtained.

We address the problem of computing the dimension of the space of plane curves of fixed degree and general multiple base points. A conjecture of Harbourne and Hirschowitz gives geometric meaning to when this dimension is larger than the expected dimension obtained from Riemann-Roch; specifically, the dimension is larger than expected if and only if the system has a multiple (−1)-curve in its ba...

Let [Formula: see text] be the maximal order of a number field. Belcher showed in the 1970s that every algebraic integer in [Formula: see text] is the sum of pairwise distinct units, if the unit equation [Formula: see text] has a non-trivial solution [Formula: see text]. We generalize this result and give applications to signed double-base digit expansions.