Chip-Firing Games on Directed Graphs

We consider the following (solitary) game: each node of a directed graph contains a pile of chips. A move consists of selecting a node with at least as many chips as its outdegree, and sending one chip along each outgoing edge to its neighbors. We extend to directed graphs several results on the undirected version obtained earlier by the authors, P. Shor, and G. Tardos, and we discuss some new topics such as periodicity, reachability, and probabilistic aspects.Among the new results specifically concerning digraphs, we relate the length of the shortest period of an infinite game to the length of the longest terminating game, and also to the access time of random walks on the same graph. These questions involve a study of the Laplace operator for directed graphs. We show that for many graphs, in particular for undirected graphs, the problem whether a given position of the chips can be reached from the initial position is polynomial time solvable.Finally, we show how the basic properties of the probabilistic abacus can be derived from our results.     

人工神经网络用于锕系离子An3+水解常数pK1预测研究

０引言水解常数是金属离子水溶液化学的基础数据，对于研究水溶液中离子的状态以及进一步研究其在水溶液中的其它化学行为是必不可少的。一般金属离子（包括镧系金属离子）的水解常数数据相对较为完善，对它们水解的规律性也有不少研究，但锕系金属离子的水解常数数据迄今较缺乏，特别是重锕系的水解常数数据基本空缺犤１～５犦。这主要是因为锕系多为放射性元素，重锕系则基本是人工元素，被发现或合成较晚，即使通过核反应合成，量也往往极少（常以多少个原子个数计算），且半衰期大多很短，因而从获取样品到进行有关化学研究都相当困难。…     

A Sharp Condition for the Ground State of Difference Equation

This note is concerned with a novel inequality condition for the existence of ground states of partial difference systems. Our result is potentially applicable to the estimation of eigenvalues of the loaded strings and nets.     

Two coordination polymers based on 2,2′-biimidazoles and d10 metal ions: syntheses,structures, and luminescence

Two d¹⁰ metal coordination polymers, [Zn(µ-Me₂biim)Cl₂] _n (1) and [Cd₃(MeHbiim)₂(1,4-BDC)₃] _n (2) (Me₂biim?=?N,N′-dimethyl-2,2′-biimidazole, MeHbiim?=?N-methyl-2,2′-biimidazole, 1,4-BDC?=?1,4-benzenedicarboxylate), were synthesized under hydrothermal conditions and characterized by elemental analysis, infrared spectroscopy, thermogravimetric analysis, and single-crystal X-ray crystallography. Complex 1 features an infinite neutral zigzag 1-D chain. Interchain hydrogen-bonding interactions further extend the 1-D arrangement to generate a 2-D supramolecular architecture. Complex 2 features a 3-D coordination polymer with α-Po net topology, based on linear trinuclear {Cd₃O₁₄N₄} clusters. Both complexes have high thermal stability and exhibit strong luminescence at room temperature.     

Comment on “Extending Hirshfeld‐I to bulk and periodic materials”

In recent years, several methods have been developed that partition the electron density among atoms using spherically symmetric atomic weights. D. E. P. Vanpoucke, P. Bultinck, and I. Van Driessche (J. Comput. Chem. 2012, doi: 10.1002/jcc.23088) recently reported a periodic implementation of the Hirshfeld‐I method that uses a combination of Becke‐style and uniform integration grids and modified atomic reference densities to compute net atomic charges in periodic materials. Herein, this method is discussed in the context of earlier periodic implementations of the Hirshfeld‐I method, the Iterated Stockholder Atoms method, and the density derived electrostatic and chemical method.     

Metal ions Directed Self-assembly based on Mixed Ligands: From 2D hcb Net to 3D cds Framework

Two coordination polymers (CPs), namely, [Zn(BPDC)(3-bpdb)_0.5(H₂O)₂]_n ( 1 ), and [Ni(BPDC)(3-bpdb)(H₂O)₂]_n ( 2 ) (where H₂BPDC = 4,4'-biphenyldicarboxylic acid, 3-bpdb = 1,4-bis(3-pyridyl)-2,3-diaza-1,3-butadiene) have been solvothermally synthesized and characterized by single-crystal X-ray diffraction, IR, elemental analyses, PXRD, and SEM. CP 1 possesses a 2D 3-connected hcb net, and weak hydrogen bonding and π ··· π stacking contacts further link the 2D networks to form 3D supramolecular structure. The structure of 2 presents a 4-connected threefold interpenetrated cds framework. Through structural analysis, it is found that the coordination geometry of metal ions significantly affects the binding behaviors of the ligands and the resultant extended networks of the CPs. Besides, the Hirshfeld surface analyses detailed the surface characteristics of the two CPs. In addition, the thermal stabilities and photoluminescent properties were also investigated.     

The Conjugate Nets, Cartan Submanifolds, and Laplace Transformations in Space Forms

In this paper we establish the geometric theory of conjugate nets, Cartan submanifolds, and Laplace transformations in sphere and pseudo-sphere spaces. The corresponding theory in cases of projective and Euclidean spaces has been established by Chern, Kamran and Tenenblat.     

A Theorem Concerning Nets Arising from Generalized Quadrangles with a Regular Point

Suppose is a generalized quadrangle (GQ) of order , with a regular point. Then there is a net which arises from this regular point. We prove that if such a net has a proper subnet with the same degree as the net, then it must be an affine plane of order t. Also, this affine plane induces a proper subquadrangle of order t containing the regular point, and we necessarily have that . This result has many applications, of which we give one example. Suppose is an elation generalized quadrangle (EGQ) of order , with elation point p. Then is called a skew translation generalized quadrangle (STGQ) with base-point p if there is a full group of symmetries about p of order t which is contained in the elation group. We show that a GQ of order s is an STGQ with base-point p if and only if p is an elation point which is regular.     

一种时序逻辑网络的快速设计方法

引用1984年尹克震提出的“开关函数的反演公式”,采用伪随机序列技术的思想,提出移位寄存器型时序逻辑网络的一种快速设计方法。     

一种嵌入式关系模型的形式化描述

在 Ｎ Ｒ／ Ｔ 网的基础上,对基于嵌入式关系模型的数据库信息系统的行为,给出了一种形式化的描述方法,并设计了一个变迁点火执行算法