Some modifications of the Dudley metric

Upper and lower bounds are obtained for the modified Dudley metric in terms of the Levy-Prokhorov metric.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 61, pp. 17–24, 1976.In conclusion, we want to thank V. M. Zolotarev for suggesting the problem and for his constant interest in this work.     

On the Irrationality of Certain Series

In this note we consider the irrationality of certain series of the form . A conjecture of P. Erds in [Sur lirrationalité dune certaine série, C. R. Acad. Sci., Paris, Sér I 292(1981), 765-768] is confirmed, and the theorem of the same paper is generalized.     

Some modifications of the theorem of Beltrami

The two main topics of this text are as follows: Firstly, three modifications of the theorem of Beltrami will be presented for diffeomorphisms between Riemannian manifolds and a space form which preserve the geodesic circles, the geodesic hyperspheres, or the minimal surfaces, respectively. Secondly, it is defined what it means for an infinitesimal deformation of a metric to preserve the geodesics up to first order, and a corresponding infinitesimal version of Beltrami’s theorem is given.     

Certain Diophantine Properties of the Mahler Measure

It is proved that a polynomial in several Mahler measures with positive rational coefficients is equal to an integer if and only if all these Mahler measures are integers. An estimate for the distance between a metric Mahler measure and an integer is obtained. Finally, it is proved that the ratio of two distinct Mahler measures of algebraic units is irrational.     

On Certain Subcovers of the Hermitian Curve

We present a simple construction that gives explicit equations for certain subcovers of the Hermitian curve. We show that maximal curves with a certain type of defining equations are covered by the Hermitian curve.     

Certain geometric properties of the Mittag-Leffler functions

In the present investigation, the Mittag-Leffler functions with their normalization are considered. Several sufficient conditions are obtained so that the Mittag-Leffler functions have certain geometric properties including univalency, starlikeness, convexity and close-to-convexity in the open unit disk. Partial sums of Mittag-Leffler functions are also studied. The results obtained are new and their usefulness is depicted by deducing several interesting corollaries and examples.     

On the Uniform Distribution of Certain Sequences

We investigate the uniform distribution of the sequence n as n ranges over the natural numbers and is a fixed positive real number which is not an integer. We then apply this in conjunction with the Linnik-Vaughan method to study the uniform distribution of the sequence p as p ranges over the prime numbers.     

On the Positive Definiteness of Certain Functions

For a coinmutative senugoup (S, +, *) with involution and a function f : S → [0, ∞), the set S(f) of those p ≥ 0 such that f^P is a positive definite function on S is a closed subsemigroup of [0, ∞) containing 0. For S = (IR, +, x* = -x) it may happen that S(f) = { kd : k ∈ N₀ } for some d > 0, and it may happen that S(f) = {0} ? [d, ∞) for some d > O. If α > 2 and if S = (?, +, n* = -n) and f(n) = e^?[n]α or S = (IN₀, +, n* = n) and f(n) = e^nα, then S(f) ∪ (0, c) = ? and [d, ∞) ? S(f) for some d ≥; c > 0. Although (with c maximal and d minimal) we have not been able to show c = d in all cases, this equality does hold if S = ? and α ≥ 3.4. In the last section we give sinipler proofs of previously known results concerning the positive definiteness of x → e^?||x||α on normed spaces.     

Certain Cuntz Semigroup Properties of Certain Crossed Product C*-algebras

We show that the following properties of the C^*-algebras in a class Ω are inherited by simple unital C-algebras in the class TAΩ:(1)(m,n)-decomposable,(2) weakly(m,n)-divisible,(3) weak Riesz interpolation.As an application,let A be an infinite dimensional simple unital C-algebra such that A has one of the above-listed properties.Suppose that α:G→Aut(A) is an action of a finite group G on A which has the tracial Rokhlin property.Then the crossed product C^*-algebra C^*(G,A,α) also has the property under consideration.     

某些级数的无理性

本文证明了某些与二阶线性递推数列有关的无穷级数的和的无理性．特别，推广了某些与Ｆｉｂｏｎａｃｃｉ和Ｌｕｃａｓ数列有关的无理性结果     

某些空间的等距算子

In this paper , We give some representation theorems of isometrics of (L^p₁∩L^p₂(012<+∞), and aslo, obtain some representations of some isometries of L^p(μ,E)(0相似文献   

Certain properties of bicompactifications

Let P be some topological property. A space X is said to be P-situated in the bicompactification bX if in bX, X has a basis of open neighborhoods each of which possesses property P. In the class of normal and in the class of extremally disconnected spaces we give the intrinsic characteristics of spaces weakly paracompactly situated in their own Stone-Cech bicompactifications. We consider other applications of the concept of the P-situation of spaces in their bicompactifications.Translated from Matematicheskie Zametki, Vol. 17, No. 3, pp. 467–473, March, 1975.     

Certain embedding theorems

We obtain necessary and sufficient conditions such that, for f(x) from LP(0, 1), the integral ₀ ¹ ¦f (x)¦qdx (0<p<1,p<q<p(1 –p)^–1) is convergent, or for f LP[0, 1] for all p 1, the integral ₀ ¹ e¦f(x)¦dx is convergent.Translated from Matematicheskie Zametki, Vol. 19, No. 2, pp. 187–200, February, 1976.     

Certain Liouville series

Abstract The main results of this paper give two criteria for certain infinite series of rational numbers to be Liouville. Some examples are also included. Keywords: Liouville numbers, Infinite series Mathematics Subject Classification (2000): 11J82     

Fuzzy logic modifications of the Analytic Hierarchy Process

The Analytic Hierarchy Process (AHP) is a measurement methodology based on pair-wise comparisons that relies on judgment to derive priority scales. During its implementation, one constructs hierarchies, then makes judgments or performs measurements on pairs of elements with respect to a criterion to derive preference scales, which are then synthesized throughout the structure to select the preferred alternative.One of the areas where the AHP finds application is in the subjective phases of risk assessment (RA), where it is used to structure and prioritize diverse risk factors, including the judgments of experts. Since fuzzy logic (FL) has been shown to be an effective tool for accommodating human experts and their communication of linguistic variables, there has been research aimed at modeling the fuzziness in the AHP (FAHP), and recently the focus of some of that modeling has been with respect to RA.The literature discusses more than one FAHP model, which raises the question as to which are the prominent models and what are their characteristics. In response to this question, we examine three of the most influential FAHP models. The article proceeds as follows. It begins with a brief overview of the AHP and its limitations when confronted with a fuzzy environment. This is followed by a discussion of FL modifications of the AHP. A RA-based likelihood score example is used throughout. The article ends with a commentary on the findings.