A tail bound for read‐k families of functions

We prove a Chernoff‐like large deviation bound on the sum of non‐independent random variables that have the following dependence structure. The variables are arbitrary [0,1]‐valued functions of independent random variables , modulo a restriction that every X_i influences at most k of the variables . © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 99–108, 2015     

A Simple Synthesis of Stable Heterocyclic Phosphorus Ylides Derived from NH-Acids

Crystalline phosphorus ylides are obtained in excellent yields from the addition reaction between triphenylphosphine, dimethyl acetylenedicarboxylate and strong NH-acids, such as 2-acetylpyrrole, indole, ethyl 3-indolylglyoxalate and N -benzyl-2-pyrrolylglyoxamate. Dynamic NMR effects are observed in the 1 H NMR spectra of stabilized ylides obtained from 2-acetylpyrrole and indole ( j G p = 67.1 and 68.8 kJmol m 1 respectively) and are attributed to restricted rotation around the carbon-carbon partial double bond resulting from conjugation of the ylide moiety with the adjacent carbonyl group.     

Metal−Organic Frameworks toward Electrochemical Sensors: Challenges and Opportunities

Owing to their fascinating characteristics, metal?organic frameworks (MOFs) have attracted great attention and been utilized in a range of applications. The use of MOFs in electrochemical sensors has become an emerging subfield since 2013. However, the poor chemical stability in aqueous solutions and low electrical conductivity of most MOFs become two main concerns that hinder the use of pristine MOFs in electroanalytical systems. In this short review, we aim to focus on these issues and provide perspectives regarding the opportunities and possible strategies in future studies to overcome these challenges in order to design the MOF‐based electrochemical sensors.     

An Adjacency Criterion for the Prime Graph of a Finite Simple Group

For every finite non-Abelian simple group, we give an exhaustive arithmetic criterion for adjacency of vertices in a prime graph of the group. For the prime graph of every finite simple group, this criterion is used to determine an independent set with a maximal number of vertices and an independent set with a maximal number of vertices containing 2, and to define orders on these sets; the information obtained is collected in tables. We consider several applications of these results to various problems in finite group theory, in particular, to the recognition-by-spectra problem for finite groups. Supported by RFBR grant No. 05-01-00797; by the Council for Grants (under RF President) and State Aid of Fundamental Science Schools, project NSh-2069.2003.1; by the RF Ministry of Education Developmental Program for Scientific Potential of the Higher School of Learning, project No. 8294; by FP “Universities of Russia,” grant No. UR.04.01.202; and by Presidium SB RAS grant No. 86-197. __________ Translated from Algebra i Logika, Vol. 44, No. 6, pp. 682–725, November–December, 2005.     

Splitting of liftings in products of probability spaces II

For a probability measure R on a product of two probability spaces that is absolutely continuous with respect to the product measure we prove the existence of liftings subordinated to a regular conditional probability and the existence of a lifting for R with lifted sections which satisfies in addition a rectangle formula. These results improve essentially some of the results from the former work of the authors [W. Strauss, N.D. Macheras, K. Musia?, Splitting of liftings in products of probability spaces, Ann. Probab. 32 (2004) 2389-2408], by weakening considerably the assumptions and by presenting more direct and shorter proofs. In comparison with [W. Strauss, N.D. Macheras, K. Musia?, Splitting of liftings in products of probability spaces, Ann. Probab. 32 (2004) 2389-2408] it is crucial for applications intended that we can now prescribe one of the factor liftings completely freely. We demonstrate the latter by applications to τ-additive measures, transfer of strong liftings, and stochastic processes.     

The mathematics of functional differentiation under conservation constraint

The mathematics of K-conserving functional differentiation, with K being the integral of some invertible function of the functional variable, is clarified. The most general form for constrained functional derivatives is derived from the requirement that two functionals that are equal over a restricted domain have equal derivatives over that domain. It is shown that the K-conserving derivative formula is the one that yields no effect of K-conservation on the differentiation of K-independent functionals, which gives the basis for its generalization for multiple constraints. Connections with the derivative with respect to the shape of the functional variable and with the shape-conserving derivative, together with their use in the density-functional theory of many-electron systems, are discussed. Yielding an intuitive interpretation of K- conserving functional derivatives, it is also shown that K-conserving derivatives emerge as directional derivatives along K-conserving paths, which is achieved via a generalization of the Gateaux derivative for that kind of paths. These results constitute the background for the practical application of K-conserving differentiation.      

N策略工作休假M/M/1排队

考虑策略工作休假M/M/1排队,简记为M/M/1(N-WV)。在休假期间,服务员并未完全停止工作而是以较低的速率为顾客服务。用拟生灭过程和矩阵几何解方法,我们给出了有直观概率意义的稳态队长和稳态条件等待时间的分布。此外,我们也得到了队长和等待时间的条件随机分解结构及附加队长和附加延迟的分布。     

Decycling Number of Some Graphs

1.IntroductionInthispaper,weonlydiscusssimplegraph(withneithermulti-edgenorloop).TheterminologiesnotexplainedcanbeseeninII].Thecyclerankofagraphistheminimumnumberofedgesthatmustberemovedinordertoeliminateallofthecyclesinthegraph.IfGhaspvenices,qedges...     

利用机制设计解决技术定价问题

本研究以机制设计的观点来试图解决技术定价的问题。本研究将实务上常用的创业投资分次筹资的方式视为随着时间的进行，所取得的有关技术定价的讯息逐渐增多，故透过多次的筹资，逐渐的将技术的真实价格逐步反映的一种经济机制。接着，本研究依循机制设计的观点，设计了根据未来某一时点的条件实现与否来重新补偿创业者的持股，以使得创业者的报酬可以达到该项技术真实价格下创业者应有的报酬。特别是（ML〈MT〈MH）形式下的条件选择权机制可以将事前无法确定的技术真实价格在日后加以表明。透过本研究所建议的方法和思路，可以使得过去因技术出价的差距过大，使得新进投资不能进行，而使得社会丧失一次增加社会财富及社会福利的机会的问题得以解决。     

Temporal Behavior of the Conditional and Gibbs’ Entropies

We study the temporal approach to equilibrium of the Gibbs’ and conditional entropies for stochastic systems in the presence of white noise. The conditional entropy will either remain constant or monotonically increase to its maximum of zero. However, the Gibbs’ entropy may have a variety of patterns of approach to its final value ranging from a monotone increase or decrease to an oscillatory approach. We have illustrated all of these behaviors using examples in which both entropy dynamics can be determined analytically.