The Banach-Stone theorem states that any surjective, linear mapping T between spaces of continuous functions that satisfies ‖T (f)− T (g)‖ = ‖f − g‖, where ‖ · ‖ denotes the uniform norm, is a weighted composition operator. We study a multiplicative analogue, and demonstrate that a surjective mapping T , not necessarily linear, between algebras of continuous functions with ‖T (f)T (g)‖ = ‖fg‖ m...

We give a simple proof of central limit theorem for linear statistics the circular $\beta $-ensembles which is valid at almost microscopic scales functions class $C^{3}$. Using coupling introduced by Valko and Virag [48], we deduce Sine$_{\beta }$ processes. also discuss connections between our result theory Gaussian Multiplicative Chaos. Based on results [37], show that exponential logarithm r...

‎We extend the notion of approximately multiplicative to approximately n-multiplicative maps between locally multiplicatively convex algebras and study some properties of these maps‎. ‎‎W‎e prove that every approximately n-multiplicative linear functional on a functionally continuous locally multiplicatively convex algebra is continuous‎. ‎We also study the relationship between approximately mu...

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Complex numerals (e.g., four hundred) have a multiplicative structure (four hundred = 4 x 100). This paper investigates whether children are sensitive to the meaning of the multiplicative structure. We designed a novel word learning paradigm and taught 4to 6-year-old children the meaning of a novel numeral phrase (e.g., ‘one gobi houses’ to mean a group of three houses). We then asked whether t...

In this paper, we study a coupled system of nonlinear fractional differential equations with multi-point boundary condi- tions. The differential operator is taken in the Riemann-Liouville sense. Applying the Schauder fixed-point theorem and the contrac- tion mapping principle, two existence results are obtained for the following system D^{alpha}_{0+}x(t)=fleft(t,y(t),D^{p}_{0+}y(t)right), t in (0,...

There are several kinds of hyperrings, for example, Krasnerhyperrings, multiplicative hyperring, general hyperrings and$H_v$-rings. In a multiplicative hyperring, the multiplication isa hyperoperation, while the addition is a binary operation. In this paper, the notion of derivation on multiplicative hyperrings is introduced and some related properties are investigated. {bf Keywords:} multiplic...

We derive strong laws of large numbers and central limit theorems for Bajraktarević, Gini exponential- (also called Beta-type) logarithmic Cauchy quotient means independent identically distributed (i.i.d.) random variables. The a sequence i.i.d. variables behave asymptotically normal with the usual square root scaling just like geometric given Somewhat surprisingly, multiplicative in rather dif...

the sarcoglycanopathies (sgps) are a subgroup of autosomal recessive limb girdle muscular dystrophies (lgmds). they are caused by mutations in gamma, alpha, beta, and delta sarcoglycans (sgs) genes. alpha-sgps are the most frequent form of sgps. muscle biopsy studies in patients with sarcoglycanopathies have indicated that loss of one sg subunit leads to instability of whole sg complex.  autozy...

| To each number > 1 correspond abelian groups in R d , of the form = P d i=1 Z e i , which obey. The set Z of beta-integers is a countable set of numbers : it is precisely the set of real numbers which are polynomial in when they are written in \basis ", and Z = Zwhen 2 N. We prove here a list of arithmetic properties of Z : addition, multiplication, relation with integers, when is a quadratic...