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In this paper, we derive the asymptotic expansions of the moments of normalized partial maxima for general error distribution. A byproduct is to deduce the convergence rates of the moments of normalized maxima to the moments of the corresponding extreme value distribution. [ABSTRACT FROM AUTHOR]

Abstract: Impulse radio sequences (IRSs) were introduced by Chu and Colbourn to study sequence or signal design for ultrawideband radio with unmodulated time-hopping. The central researches on IRSs lie in the determination of the value , i.e., the largest possible number of sequences in an -IRS. When , Chang and Wang have determined the value of . As far as the authors know, there has been no study on the case of . So we in this paper focus on this case with . We will determine the exact value of for any positive integers and . We also calculate the exact value of for and . [Copyright &y& Elsevier]

□ We calculate the asymptotics of the moments as well as the limiting distribution (after the appropriate normalization) of the maximum of independent, not identically distributed, geometric random variables. In many cases, the limit distribution turns out to be the standard Gumbel. The motivation comes from a variant of the genomic evolutionary model proposed by Wilf and Ewens[15]as an answer to the criticism of the Darwinian theory of evolution stating that the time required for the appropriate mutations is huge. A byproduct of our analysis is the asymptotics of the moments as well as the limiting distribution (after the appropriate normalization) of the maximum of independent, not identically distributed, exponential random variables. [ABSTRACT FROM AUTHOR]

Abstract: Let be a simple twofold triple system of order . For every , , the pair is contained in exactly two different triples, say, and . Any two blocks satisfying form a matched pair. Suppose that there is a partition of into matched pairs. If we replace the double edge with its corresponding single edge from a matched pair , , we have a . Let be the collection of s obtained by replacing the double edge of each matched pair of with its corresponding single edge, and be the collection of the deleted edges. If can be reassembled into a collection of s, then is a maximum twofold -packing of order . We call a metamorphosis of the simple twofold triple system . In this paper, we show that there exists a metamorphosis of a simple twofold triple system of order into a maximum twofold -packing of order if and only if and with two exceptions of and one possible exception of . [Copyright &y& Elsevier]

Abstract: Let denote the partial maximum of an independent and identically distributed lognormal random sequence. In this paper, we derive the exact uniform convergence rate of the distribution of the normalized maximum to its extreme value distribution, where the constants and are chosen by an optimal way. [Copyright &y& Elsevier]

Let (Xn) denote an independent and identically distributed random sequence. Let $S_n = \sum_{k = 1}^{n}X_{k}$ and Mn = max{X1, ..., Xn} be its partial sum and maximum. Suppose that some of the random variables of X1, X2,... can be observed and denote by $\widetilde{M}_n$ the maximum of observed random variables from the set {X1, ..., Xn}. In this paper, we consider the joint limiting distribution of $(\widetilde{M}_n, M_n, S_n)$ and the almost sure central limit theorems related to the random vector $( \widetilde{M}_n, M_n, S_n)$. Furthermore, we extend related results to weakly dependent stationary Gaussian sequences. [ABSTRACT FROM AUTHOR]

Abstract: The coherence of a random matrix, which is defined to be the largest magnitude of the Pearson correlation coefficients between the columns of the random matrix, is an important quantity for a wide range of applications including high-dimensional statistics and signal processing. Inspired by these applications, this paper studies the limiting laws of the coherence of random matrices for a full range of the dimension with a special focus on the ultra high-dimensional setting. Assuming the columns of the random matrix are independent random vectors with a common spherical distribution, we give a complete characterization of the behavior of the limiting distributions of the coherence. More specifically, the limiting distributions of the coherence are derived separately for three regimes: , , and . The results show that the limiting behavior of the coherence differs significantly in different regimes and exhibits interesting phase transition phenomena as the dimension grows as a function of . Applications to statistics and compressed sensing in the ultra high-dimensional setting are also discussed. [Copyright &y& Elsevier]

Motivated by time series analysis, we consider the problem of solving the recurrence relation un+1 = vn+1 + un ⊗ vn for n ≠ 0 and un, given the sequence vn. A solution is given as a Bell polynomial. When vn can be written as a weighted sum of nth powers, then the solution un also takes this form. [ABSTRACT FROM AUTHOR]

In risk theory we often encounter stochastic models containing randomly weighted sums. In these sums, each primary real-valued random variable, interpreted as the net loss during a reference period, is associated with a nonnegative random weight, interpreted as the corresponding stochastic discount factor to the origin. Therefore, a weighted sum of m terms, denoted as , represents the stochastic present value of aggregate net losses during the first m periods. Suppose that the primary random variables are independent of each other with long-tailed distributions and are independent of the random weights. We show conditions on the random weights under which the tail probability of —the maximum of the first n weighted sums—is asymptotically equivalent to that of —the last weighted sum. [ABSTRACT FROM PUBLISHER]

Abstract: Let be a stationary Gaussian sequence with mean 0 and variance 1. Let and . Suppose that some of the random variables of can be observed and let denote the partial maximum of the observed variables. In this note, we study the limiting distribution of random vector for the strongly dependent case where is convex with and is monotone with . [ABSTRACT FROM AUTHOR]

Consider a difference equation whose evolution rule is defined as the maximum of several first-order equations. It is shown that if the first-order equations are individually contractive, then the aggregated max-type equation converges to a fixed point. A corresponding result holds for local convergence. [ABSTRACT FROM AUTHOR]

Abstract: The palmprint is one of the most reliable physiological characteristics that can be used to distinguish between individuals. In this paper, we propose a palmprint recognition method based on multifractal spectrum technology using statistical moment approaches. The multifractal spectrum of palmprint is calculated by developing an algorithm for extracting palmprint characteristics. The three parameters proposed as the distinguishing palmprint features include the width spread and maximum of multifractal spectrum, and a parameter which describes the asymmetry of the spectrum curve. The identification process can be divided into the following main steps: (1) capturing palmprint image, extracting and normalizing the subimages; (2) defining a coordinate system and calculating partition function; (3) estimating multifractal spectrum; (4) extracting the three parameters and, finally, (5) the feature matching and palmprint identification. The experimental results demonstrate the feasibility of the proposed method. [Copyright &y& Elsevier]

Abstract: The so-called comonotonic-★-property for Sugeno integral is introduced and investigated, where is a binary operation. Under the assumption that and , we prove that Sugeno integral possesses comonotonic-★-property if and only if ★ equals to one of the four operators: minimum, maximum, PF (the first projection) and PL (the last projection). We also discuss comonotonic-★-property when this assumption does not hold. [Copyright &y& Elsevier]

Abstract: The concept of upper and lower semicontinuity of fuzzy mappings introduced by Bao and Wu [Y.E. Bao, C.X. Wu, Convexity and semicontinuity of fuzzy mappings, Comput. Math. Appl., 51 (2006) 1809–1816] is redefined by using the concept of parameterized triples of fuzzy numbers. On the basis of the linear ordering of fuzzy numbers proposed by Goetschel and Voxman [R. Goetschel, W. Voxman, Elementary fuzzy calculus, Fuzzy Sets and Systems 18], we prove that an upper semicontinuous fuzzy mapping attains a maximum (with respect to this linear ordering) on a nonempty closed and bounded subset of the -dimensional Euclidean space , and that a lower semicontinuous fuzzy mapping attains a minimum (with respect to this linear ordering) on a nonempty closed and bounded subset of . [Copyright &y& Elsevier]

Cohen and Sackrowitz (1989) derive a uniformly minimum variance conditionally unbiased estimator (UMVCUE) for the mean of a selected population for the univariate normal case with variance known and unknown as well as for the gamma case in a two-stage design. We extend this methodology to the bivariate normal case where the covariance matrix is assumed to be known. The population with the largest sample mean of the first dimension is selected for additional observations in a second stage. The goal of the analysis is to find an unbiased estimate of the mean of the second dimension with all of the data. [ABSTRACT FROM AUTHOR]

Abstract: Given a bounded domain , we prove that if is a function whose gradient is Lipschitzian in and non-zero at 0, then, for each small enough, the restriction of the integral functional to the sphere has a unique global minimum and a unique global maximum. [Copyright &y& Elsevier]

Let (Xn)n ≥0 be a real random walk starting at 0, with centered increments bounded by a constant K. The main result of this study is: ∣P(Sn/√ x) - P(σsup0≤1 Bu ≥ x)∣ ≤ C (n, K) ㌚ln n/nm where x ≥ 0, σ² is the variance of the increments, Sn is the supremum at time n of the random walk, (Bu, u ≥ 0) is a standard linear Brownian motion and C(n, K) is an explicit constant. We also prove that in the previous inequality Sn can be replaced by the local score and sup0≤u≤1 Bu by sup0≤u≤1 ∣Bu∣. [ABSTRACT FROM AUTHOR]

The definition of a Detour–Harary index is ω H (G) = 1 2 ∑ u , v ∈ V (G) 1 l (u , v | G) , where G is a simple and connected graph, and l (u , v | G) is equal to the length of the longest path between vertices u and v. In this paper, we obtained the maximum Detour–Harary index about unicyclic graphs, bicyclic graphs, and cacti, respectively. [ABSTRACT FROM AUTHOR]