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Article A boundary value problem for second-order nonlinear difference equations on the integers(Cambridge Univ Press, 2005) Dal, F; Guseinov, GSIn this study, we are concerned with a boundary value problem (BVP) for nonlinear difference equations on the set of all integers Z, under the assumption that the left-hand side is a second-order linear difference expression which belongs to the so-called Weyl-Hamburger limit-circle case. The BVP is considered in the Hilbert space l(2) and includes boundary conditions at infinity. Existence and uniqueness results for solution of the considered BVP are established.Article On the Resolvent of the Laplace-Beltrami Operator in Hyperbolic Space(Cambridge Univ Press, 2015) Guseinov, Gusein Sh.In this paper, a detailed description of the resolvent of the Laplace-Beltrami operator in n-dimensional hyperbolic space is given. The resolvent is an integral operator with the kernel (Green's function) being a solution of a hypergeometric differential equation. Asymptotic analysis of the solution of this equation is carried out.Article Citation - WoS: 6Citation - Scopus: 5Distortion in the Finite Determination Result for Embeddings of Locally Finite Metric Spaces Into Banach Spaces(Cambridge Univ Press, 2019) Ostrovska, S.; Ostrovskii, M. I.Given a Banach space X and a real number alpha >= 1, we write: (1) D(X) <= alpha if, for any locally finite metric space A, all finite subsets of which admit bilipschitz embeddings into X with distortions <= C, the space A itself admits a bilipschitz embedding into X with distortion <= alpha . C; (2) D(X) = alpha(+) if, for every epsilon > 0, the condition D(X) <= alpha + epsilon holds, while D(X) <= alpha does not; (3) D(X) <= alpha(+) if D(X) = alpha(+) or D(X) <= alpha. It is known that D(X) is bounded by a universal constant, but the available estimates for this constant are rather large. The following results have been proved in this work: (1) D((circle plus(infinity)(n= 1) X-n)(p)) <= 1(+) for every nested family of finite-dimensional Banach spaces {X-n}(n=1)(infinity) and every 1 <= p <= 8 infinity. (2) D((circle plus 8(n=1)(infinity)l(infinity)(n) )(p)) = 1(+) for 1 < p < infinity. (3) D(X) <= 4(+) for every Banach space X with no nontrivial cotype. Statement (3) is a strengthening of the Baudier-Lancien result (2008).Article Citation - WoS: 5Citation - Scopus: 8Discrete Scan Statistics Generated by Exchangeable Binary Trials(Cambridge Univ Press, 2010) Eryilmaz, SerkanLet {X-i}(i=1)(n) be a sequence of random variables with two possible outcomes, denoted 0 and 1. Define a random variable S-n,S-m to be the maximum number of Is within any m consecutive trials in {X-i}(i=1)(n). The random variable S-n,S-m is called a discrete scan statistic and has applications in many areas. In this paper we evaluate the distribution of discrete scan statistics when {X-i}(i=1)(n) consists of exchangeable binary trials. We provide simple closed-form expressions for both conditional and unconditional distributions of S-n,S-m for 2m >= n. These results are also new for independent, identically distributed Bernoulli trials, which are a special case of exchangeable trials.
