Almost Sure Convergence in Extreme Value Theory

Let X₁, …, X_n be independent random variables with common distribution function F. Define and let G(x) be one of the extreme-value distributions. Assume F ∈ D(G), i.e., there exist a_n> 0 and b_n ∈ ? such that . Let l(?∞,x)(·) denote the indicator function of the set (?∞,x) and S(G) =: {x : 0 < G(x) < 1}. Obviously, 1(?∞,x)((M_n?b_n)/a_n) does not converge almost surely for any x ∈ S(G). But we shall prove .     

On a class ofN-dimensional trigonometric series

An analog of Fomin's well-known one-dimensional theorem is proved for trigonometric series of the form

On Cesàro Limit Distribution of a Class of Permutative Cellular Automata

We study Cesàro means (time averages) of the evolution measures of the class of permutative cellular automata over {0, 1} defined by % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiabew% 9aQnaaBaaaleaacaWGcbaabeaakiaadIhacaGGPaWaaSbaaSqaaiaa% d6gaaeqaaOGaeyypa0JaamiEamaaBaaaleaacaWGUbGaaGjcVlaayI% W7cqGHRaWkcaaMi8UaaGjcVlaadkfaaeqaaOGaey4kaSIaeuiOda1a% a0baaSqaaiaadQgacaaMi8UaaGjcVlabg2da9iaayIW7caaMi8UaaG% imaaqaaiaadkfacaaMi8UaaGjcVlabgkHiTiaayIW7caaMi8UaaGym% aaaakiaayIW7caaMi8UaaGjcVlaayIW7caaMi8UaaGjcVlaacIcaca% aIXaGaey4kaSIaamOyamaaBaaaleaacaWGQbaabeaakiabgUcaRiaa% dIhadaWgaaWcbaGaamOBaiaayIW7caaMi8Uaey4kaSIaaGjcVlaayI% W7caWGQbaabeaakiaacMcaaaa!7530! $$(\varphi _B x)_n = x_{n{\kern 1pt} {\kern 1pt} + {\kern 1pt} {\kern 1pt} R} + \Pi _{j{\kern 1pt} {\kern 1pt} = {\kern 1pt} {\kern 1pt} 0}^{R{\kern 1pt} {\kern 1pt} - {\kern 1pt} {\kern 1pt} 1} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} (1 + b_j + x_{n{\kern 1pt} {\kern 1pt} + {\kern 1pt} {\kern 1pt} j} )$$ where B=b ₀ b _R-1is an aperiodic block in {0, 1} ^R and operations are taken mod 2. If the initial measure is Bernoulli, we prove that the limit of the Cesàro mean of the first column distribution exists. When R = 1 and B = 1, _B is the mod 2 sum automaton. For this automaton we show that the limit is the (1/2, 1/2(-Bernoulli measure, and if the initial measure is Markov, we show that the limit of Cesàro mean of the one-site distribution is equidistributed.     

Strong consistency of the mean on randomly deleted sets

Suppose 0t ₁<t ₂<... are fixed points in time. At timet _k , a unit with magnitudeX _k and lifetimeL _k enters a population or is placed into a system. Suppose that theX _k 's are i.i.d. withEX ₁=, theL _k 's are i.i.d., and that theX _k 's andL _k 's are independent. In this paper we find conditions under which the continuous time process Avr{X _k :t _k t<t _k +L _k } is almost surely convergent to . We also demonstrate the sharpness of these conditions.     

AQUEOUS STABLE FREE RADICAL POLYMERIZATION PROCESSES

An overview of aqueous polymerizations, which include emulsion, miniemulsion and suspension polymerizations, under stable free radical polymerization (SFRP) conditions is presented. The success of miniemulsion and suspension SFRP polymerizations is contrasted with the difficulties associated with obtaining a stable emulsion polymerization. A recently developed unique microprecipitation technique is referenced as a means of making submicron sized particles that can be used to achieve a stable emulsion SFRP process.     

用瓦勒布然和逼近周期连续函数

设f(x)是以2π为周期的L可积函数,其Fourier级数为     

Convergence Properties of Two-Stage Stochastic Programming

This paper considers a procedure of two-stage stochastic programming in which the performance function to be optimized is replaced by its empirical mean. This procedure converts a stochastic optimization problem into a deterministic one for which many methods are available. Another strength of the method is that there is essentially no requirement on the distribution of the random variables involved. Exponential convergence for the probability of deviation of the empirical optimum from the true optimum is established using large deviation techniques. Explicit bounds on the convergence rates are obtained for the case of quadratic performance functions. Finally, numerical results are presented for the famous news vendor problem, which lends experimental evidence supporting exponential convergence.     

现代"电子技术基础"课程教学改革的研究与实践

文章分析了高职院校学生普遍存在的现状,指出改革传统教学方式势在必行.提出现代电子技术课程教学改革基本思路,在教学内容、教学模式、教学方法、考试方法等方面进行的一系列改革措施和创新实践.实践证明,这些改革既提高了学生对现代电子技术基础基本理论的掌握,又提高了分析问题和解决问题的能力.     

SO-CPP: Sailfish optimization-based controller placement in IoT-enabled software-defined wireless sensor networks

One of the expanding network topologies that is frequently utilized to improve network development by successfully separating the control plane and data plane is software-defined networking (SDN). In order to function inside complex sensor networks, the SDWSN system frequently relies on centralized controller logic that pulls global network information. In wireless sensor networks (WSNs), using several SDN controllers is known as a promising strategy due to reliability and performance considerations. However, using numerous controllers increases the synchronization overhead between the controllers. Consequently, it is a difficult research challenge to discover the best placement of SDN controllers to enhance the performance of a WSN, subject to the maximum number of controllers calculated based on the synchronization overhead. This research introduces a novel technique to overcome the controller placement problem (CPP) by optimizing multi-constraints within the sensor networks. For selecting the optimal controllers and placing them in an optimal location, a novel sailfish optimization (SO) strategy is introduced that can enhance the search space and maintain optimal global values throughout the iteration. Then, node clustering is performed using the fuzzy-C-means (FCM) clustering technique, which can reduce energy consumption and path delay within the network. The overall latency obtained by the proposed method is about 0.51 and 0.56 ms, and a total run time of 4 ms for both single sink and multi-sink, respectively. The proposed method is implemented in the MATLAB platform, and different performance metrics are analyzed and compared with existing techniques.     

Fixed point properties for nonexpansive representations of topological semigroups

In this paper, we study a fixed point and a nonlinear ergodic properties for an amenable semigroup of nonexpansive mappings on a nonempty subset of a Hilbert space.