Let ηi, i = 1, . . . , n be iid Bernoulli random variables, taking values ±1 with probability 1 2 . Given a multiset V of n elements v1, . . . , vn of an additive group G, we define the concentration probability of V as ρ(V ) := sup v∈G P(η1v1 + . . . ηnvn = v). An old result of Erdős and Moser asserts that if vi are distinct real numbers then ρ(V ) is O(n− 3 2 logn). This bound was then refine...

This note being devoted to some aspects of the inverse problem of representation theory explicates the links between researches on the Sklyanin algebras and the author’s (based on the noncommutative geometry) approach to the setting free of hidden symmetries in terms of ”the quantization of constants”. Namely, the Racah–Wigner algebra for the Sklyanin algebra is constructed. It may be considere...

A general construction for ?nite absolutely continuous invariant measure will be presented. It will be shown that the local bounded distortion of the Radon-Nykodym derivatives of f n () will imply the existence of a ?nite invariant measure for the map f which is absolutely continuous with respect to , a measure on the phase space describing the sets of measure zero. Furthermore we will discuss ...

In this paper, we show that each expanding Thurston map f : S → S has 1 + deg f fixed points, counted with appropriate weight, where deg f denotes the topological degree of the map f . We then prove the equidistribution of preimages and of (pre)periodic points with respect to the unique measure of maximal entropy μf for f . We also show that (S , f, μf ) is a factor of the left shift on the set...

We prove a local variational principle of pressure for any given open cover. More precisely, for a given dynamical system (X,T ), an open cover U of X, and a continuous, realvalued function f on X, we show that the corresponding local pressure P (T, f ;U) satisfies P (T, f ;U) = sup{hμ(T,U) + ∫ X f(x)dμ(x) : μ is a T -invariant measure}, and moreover, the supremum can be attained by a T -invari...

objective: hypoactive sexual desire disorder (hsdd) is a common sexual problem among women. sexual interest and desire inventory –female (sidi-f) has been widely validated and used to measure sexual desire in women. the aim of this study was to determine the psychometric properties of the persian version of sidi-f for iranian population. method: this was a methodological study on the psychometr...

Dirac measure is an important measure in many related branches to mathematics. The current paper characterizes measure-preserving transformations between two Dirac measure spaces or a Dirac measure space and a probability measure space. Also, it studies isomorphic Dirac measure spaces, equivalence Dirac measure algebras, and conjugate of Dirac measure spaces. The equivalence classes of a Dirac ...

To demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the Banach-Zareckitheorem is presented on the basis of the Radon-Nikodym theoremwhich emphasizes on measure-type properties of the Lebesgueintegral. The Banach-Zarecki theorem says that a real-valuedfunction $F$ is absolutely continuous on a finite closed intervalif and only if it is continuo...

In some long term studies, a series of dependent and possibly truncated lifetime data may be observed. Suppose that the lifetimes have a common continuous distribution function F. A popular stochastic measure of the distance between the density function f of the lifetimes and its kernel estimate fn is the integrated square error (ISE). In this paper, we derive a central limit theorem for t...

This paper proposes a method of predicting accuracy of keyword spotting in terms of FA count and spotting score of correct detections. A new measure F for predicting the FA count is calculated by simulation of the keyword spotting for phoneme sequences that phoneme-based language model generates. Another measure C for predicting the spotting score of correct detections is obtained from a produc...