Occupation games on graphs in which the second player takes almost all vertices

Given a connected graph G=(V,E), two players take turns occupying vertices v∈V by placing black and white tokens so that the current vertex sets B,W⊆V are disjoint, B∩W=0?, and the corresponding induced subgraphs G[B] and G[W] are connected any time. A player must pass whenever (s)he has no legal move. (Obviously, after this, the opponent will take all remaining vertices, since G is assumed connected.) The game is over when all vertices are taken, V=B^∗∪W^∗. Then, Black and White get b=|B^∗|/|V| and w=|W^∗|/|V|, respectively. Thus, the occupation game is one-sum, b+w=1, and we could easily reduce it to a zero-sum game by simply shifting the payoffs, b^′=b−1/2,w^′=w−1/2. Let us also notice that b≥0 and w≥0; moreover, b>0 and w>0 whenever |V|>1.[Let us remark that the so-called Chinese rules define similar payoffs for the classic game of GO, yet, the legal moves are defined in GO differently.]Like in GO, we assume that Black begins. It is easy to construct graphs in which Black can take almost all vertices, more precisely, for each ε>0 there is a graph G for which b>1−ε. In this paper we show that, somewhat surprisingly, there are also graphs in which White can take almost all vertices.     

Physicochemical studies of molecular hyperpolarizability of imidazole derivatives

A series of substituted imidazoles have been synthesized in very good yield under solvent free condition by grinding 1,2-diketone, arylaldehyde, arylamine and ammonium acetate in the presence of molecular iodine as the catalyst. The short reaction time, good yield and easy workup make this protocol practically and economically attractive and the imidazoles are characterized by NMR spectra, X-ray, mass and CHN analysis. The push-pull character of series of imidazoles have been analyzed by the quotient of the occupations of the bonding (π) and anti-bonding (π*) orbitals of the central linking -N=C-C=C- unit. Excellent correlation of the push-pull parameter with the corresponding bond lengths d(CN) and d(CC) strongly recommend both the occupation quotients (π*/π) and the corresponding bond lengths are reasonable sensors for quantifying the push-pull character and for the molecular hyperpolarizability ?(0) of these compounds. To support the experimental results, theoretical calculations (heat of formation, NLO, NBO and vibrational analysis) were also made. Within this context, reasonable conclusions concerning the steric hindrance in the chromospheres, push-pull character, hyperpolarizability of the imidazoles and their application as NLO materials will be drawn.     

Stochastic differential games: Occupation measure based approach

A new approach based on occupation measures is introduced for studying stochastic differential games. For two-person zero-sum games, the existence of values and optimal strategies for both players is established for various payoff criteria. ForN-person games, the existence of equilibria in Markov strategies is established for various cases.     

Occupation times for the finite buffer fluid queue with phase-type ON-times

In this short communication we study a fluid queue with a finite buffer. The performance measure we are interested in is the occupation time over a finite time period, i.e., the fraction of time the workload process is below some fixed target level. Using an alternating renewal sequence, we determine the double transform of the occupation time; the occupation time for the finite buffer M/G/1 queue with phase-type jumps follows as a limiting case.     

A one-dimensional version of the random interlacements

We base ourselves on the construction of the two-dimensional random interlacements (Comets et al., 2016) to define the one-dimensional version of the process. For this, we consider simple random walks conditioned on never hitting the origin. We compare this process to the conditional random walk on the ring graph. Our results are the convergence of the vacant set on the ring graph to the vacant set of one-dimensional random interlacements, a central limit theorem for the interlacements’ local time and the convergence in law of the local times of the conditional walk on the ring graph to the interlacements’ local times.     

Estimation error for occupation time functionals of stationary Markov processes

The approximation of integral functionals with respect to a stationary Markov process by a Riemann sum estimator is studied. Stationarity and the functional calculus of the infinitesimal generator of the process are used to explicitly calculate the estimation error and to prove a general finite sample error bound. The presented approach admits general integrands and gives a unifying explanation for different rates obtained in the literature. Several examples demonstrate how the general bound can be related to well-known function spaces.     

On uniform closeness of local times of Markov chains and i.i.d. sequences

In this paper we consider the field of local times of a discrete-time Markov chain on a general state space, and obtain uniform (in time) upper bounds on the total variation distance between this field and the one of a sequence of $n$ i.i.d. random variables with law given by the invariant measure of that Markov chain. The proof of this result uses a refinement of the soft local time method of Popov and Teixeira (2015).     

以道德品质为引领,促创新人才之培养

为培养高素质的创新人才,加快中国特色社会主义强国的建设步伐,提出了以道德品质为引领,促进创新人才之培养的方法,分析了该方法的缘由、重要性及必要性,叙述了以道德品质为引领培养创新人才的模式、方法、实践及效果,实际结果表明:该方法是可操作的、可行的,确实对创新人才的培养从根本上起到了促进作用,是培养创新人才、高素质人才的好方法。     

道德风险影响下的保险最优投资研究

在考虑道德风险的情况下,以均值方差准则为目标研究保险人最优投资问题.假设保险盈余过程服从C-L模型,金融市场上存在一种无风险资产和一种风险资产可供投资,其中风险资产的价格过程服从几何布朗运动.在纯道德风险保险契约设计中,借鉴相关研究对努力水平和效用化努力成本的假设,量化道德风险对盈余过程的影响.在均值方差目标下,建立保险人最优投资问题的广义Hamilton-Jacobi-Bellman(HJB)方程,给出保险人时间一致的均衡投资策略和价值函数.结果显示累计索赔比例参数越大,公司对最优努力水平越敏感,采取措施降低道德风险有利于公司收益提升;努力成本参数越大,公司会降低努力水平减少支出,避免损失.     

P2P保险的道德风险问题研究

伴随信息产业的快速发展和互联网保险的广泛运用,近几年来国际上出现了一种新型保险模式――P2P保险(Peer to Peer Insurance)。该模式基于互联网,通过聚集若干风险类型相似的投保人组建风险共担互助小组,风险互助小组成员间一般是亲戚、朋友等熟人关系。P2P保险形成的相互监督机制和声誉机制,可以较好地解决传统保险市场中存在的道德风险问题。本文利用经济学中的比较静态分析方法,研究了P2P保险的道德风险问题,并从理论上证明了在P2P保险模式下,投保人会倾向于更加努力防范风险以降低出险概率,道德风险问题可以得到有效缓解。