A zero-one law for a random subset

We consider first order sentences about two logical structures. First we consider 1,…, n with the successor relation and a random unary relation that points satisfy with probability p(n). We then replace the successor relation with less than. For both structures we characterize those p(n) for which a zero-one law holds.     

END序列强大数律研究

本文研究了END序列的均值强大数律,获得了均值强大数律的充分条件. 作为应用,我们可以立即得到Marcinkiewicz均值和logarithmic均值强大数律.最后我们开展了有关大数定律的数据模拟工     

Asymptotic value distribution of additive functions defined on the symmetric group

We examine the asymptotic value distribution of additive functions defined via the multiplicities of lengths of the cycles comprising a random permutation taken from the symmetric group with equal probability. We establish necessary and sufficient conditions for the weak law of large numbers and for the relative compactness of the sequence of distributions. Considering particular cases, we demonstrate that long cycles play an exceptional role and that, sometimes, in order to obtain a Poisson limit law, their influence must be negligible. The proofs are based on the ideas going back to the seminal papers of I.Z. Ruzsa on the classical additive arithmetic functions.      

The algebraic structure of left semi-trusses

The distributive laws of ring theory are fundamental equalities in algebra. However, recently in the study of the Yang-Baxter equation, many algebraic structures with alternative “distributive” laws were defined. In an effort to study these “left distributive” laws and the interaction they entail on the algebraic structures, Brzeziński introduced skew left trusses and left semi-trusses. In particular the class of left semi-trusses is very wide, since it contains all rings, associative algebras and distributive lattices. In this paper, we investigate the subclass of left semi-trusses that behave like the algebraic structures that came up in the study of the Yang-Baxter equation. We study the interaction of the operations and what this interaction entails on their respective semigroups. In particular, we prove that in the finite case the additive structure is a completely regular semigroup. Secondly, we apply our results on a particular instance of a left semi-truss called an almost left semi-brace, introduced by Miccoli to study its algebraic structure. In particular, we show that one can associate a left semi-brace to any almost left semi-brace. Furthermore, we show that the set-theoretic solutions of the Yang-Baxter equation originating from almost left semi-braces arise from this correspondence.     

Numerical smoothness and error analysis on WENO for the nonlinear conservation laws

In this study, we give an a posteriori error analysis on the weighted essentially nonoscillatory schemes for the nonlinear scalar conservation laws. This analysis is based on the new concept of numerical smoothness, with some new error analysis mechanisms developed for the finite difference and finite volume discretizations. The local error estimate is of optimal order in space and time. The global error estimate grows linearly in time, because of the direct application of the L₁ ‐contraction between entropy solutions in the error propagation analysis. As a beginning, we only deal with smooth solutions in this article. Within the same error propagation framework, when we deal with piecewise smooth solutions later, we only need to work on estimating the local error where smoothness is lost. The smoothness indicators not only serve the purpose of local error estimation, but also serve as a monitor on both the possible numerical instability and the expected solution shapening. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

0–1 laws for maps

A class of finite structures has a 0–1 law with respect to a logic if every property expressible in the logic has a probability approaching a limit of 0 or 1 as the structure size grows. To formulate 0–1 laws for maps (i.e., embeddings of graphs in a surface), it is necessary to represent maps as logical structures. Three such representations are given, the most general being the full cross representation based on Tutte's theory of combinatorial maps. The main result says that if a class of maps has two properties, richness and large representativity, then the corresponding class of full cross representations has a 0–1 law with respect to first‐order logic. As a corollary the following classes of maps on a surface of fixed type have a first‐order 0–1 law: all maps, smooth maps, 2‐connected maps, 3‐connected maps, triangular maps, 2‐connected triangular maps, and 3‐connected triangular maps. ©1999 John Wiley & Sons, Inc. Random Struct. Alg., 14, 215–237, 1999     

Log-linear modeling using conditional log-linear structures

Analysis of large dimensional contingency tables is rather difficult. Fienberg and Kim (1999, Journal of American Statistical Association, 94, 229–239) studied the problem of combining conditional (on single variable) log-linear structures for graphical models to obtain partial information about the full graphical log-linear model. In this paper, we consider the general log-linear models and obtain explicit representation for the log-linear parameters of the full model based on that of conditional structures. As a consequence, we give conditions under which a particular log-linear parameter is present or not in the full model. Some of the main results of Fienberg and Kim follow from our results. The explicit relationships between full model and the conditional structures are also presented. The connections between conditional structures and the layer structures are pointed out. We investigate also the hierarchical nature of the full model, based on conditional structures. Kim (2006, Computational Statistics and Data Analysis, 50, 2044–2064) analyzed graphical log-linear models based on conditional log-linear structures, when a set of variables is conditioned. For this case, we employ the Möbius inversion technique to obtain the interaction parameters of the full log-linear model, and discuss their properties. The hierarchical nature of the full model is also studied based on conditional structures. This result could be effectively used for the model selection also. As applications of our results, we have discussed several typical examples, including a real-life example.     

Strong convergence on weakly logarithmic combinatorial assemblies

We deal with the random combinatorial structures called assemblies. Instead of the traditional logarithmic condition which assures asymptotic regularity of the number of components of a given order, we assume only lower and upper bounds of this number. Using the author’s analytic approach, we generalize the independent process approximation in the total variation distance of the component structure of an assembly. To evaluate the influence of strongly dependent large components, we obtain estimates of the appropriate conditional probabilities by unconditioned ones. The estimates are applied to examine additive functions defined on a new class of structures, called weakly logarithmic. Some analogs of Major’s and Feller’s theorems which concern almost sure behavior of sums of independent random variables are proved.     

A new convergence proof of the Adomian decomposition method for a mixed hyperbolic elliptic system of conservation laws

In this paper, we propose a new convergence proof of the Adomian’s decomposition method (ADM), applied to the generalized nonlinear system of partial differential equations (PDE’s) based on new formula for Adomian polynomials. The decomposition scheme obtained from the ADM yields an analytical solution in the form of a rapidly convergent series for a system of conservation laws. Systems of conservation laws is presented, we obtain the stability of the approximate solution when the system changes type. We show with an explicit example that the latter property is true for general Cauchy problem satisfying convergence hypothesis. The results indicate that the ADM is effective and promising.     

李代数的Poisson代数结构Ⅱ

本文研究民具有无限维中心的Toroidal李代数.通过利用其明确的生成元,确定了其上所有的非交换Poisson代数结构,从而推广了有限维中心的情形.     

非平稳NA随机变量满足迭对数律及大数定律的充分条件

本文应用Shao所提供的极大值矩不等式及概率不等式,给出了不具有平稳分布的NA随机变量列满足迭对数律和大数定律的充分条件.     

Multi-exchange neighborhood structures for the capacitated minimum spanning tree problem

The capacitated minimum spanning tree (CMST) problem is to find a minimum cost spanning tree with an additional cardinality constraint on the sizes of the subtrees incident to a given root node. The CMST problem is an NP-complete problem, and existing exact algorithms can solve only small size problems. Currently, the best available heuristic procedures for the CMST problem are tabu search algorithms due to Amberg et al. and Sharaiha et al. These algorithms use two-exchange neighborhood structures that are based on exchanging a single node or a set of nodes between two subtrees. In this paper, we generalize their neighborhood structures to allow exchanges of nodes among multiple subtrees simultaneously; we refer to such neighborhood structures as multi-exchange neighborhood structures. Our first multi-exchange neighborhood structure allows exchanges of single nodes among several subtrees. Our second multi-exchange neighborhood structure allows exchanges that involve multiple subtrees. The size of each of these neighborhood structures grows exponentially with the problem size without any substantial increase in the computational times needed to find improved neighbors. Our approach, which is based on the cyclic transfer neighborhood structure due to Thompson and Psaraftis and Thompson and Orlin transforms a profitable exchange into a negative cost subset-disjoint cycle in a graph, called an improvement graph, and identifies these cycles using variants of shortest path label-correcting algorithms. Our computational results with GRASP and tabu search algorithms based on these neighborhood structures reveal that (i) for the unit demand case our algorithms obtained the best available solutions for all benchmark instances and improved some; and (ii) for the heterogeneous demand case our algorithms improved the best available solutions for most of the benchmark instances with improvements by as much as 18%. The running times our multi-exchange neighborhood search algorithms are comparable to those taken by two-exchange neighborhood search algorithms. Received: September 1998 / Accepted: March 2001?Published online May 18, 2001     

Compression and the origins of Zipf's law for word frequencies

Here we sketch a new derivation of Zipf's law for word frequencies based on optimal coding. The structure of the derivation is reminiscent of Mandelbrot's random typing model but it has multiple advantages over random typing: (1) it starts from realistic cognitive pressures, (2) it does not require fine tuning of parameters, and (3) it sheds light on the origins of other statistical laws of language and thus can lead to a compact theory of linguistic laws. Our findings suggest that the recurrence of Zipf's law in human languages could originate from pressure for easy and fast communication. © 2016 Wiley Periodicals, Inc. Complexity 21: 409–411, 2016     

Contract design and supply chain coordination in the electricity industry

In this article we propose a model of the supply chain in electricity markets with multiple generators and retailers and considering several market structures. We analyze how market design interacts with the different types of contract and market structure to affect the coordination between the different firms and the performance of the supply chain as a whole. We compare the implications on supply chain coordination and on the players’ profitability of two different market structures: a pool based market vs. bilateral contracts, taking into consideration the relationship between futures and spot markets. Furthermore, we analyze the use of contracts for differences and two-part-tariffs as tools for supply chain coordination. We have concluded that there are multiple equilibria in the supply chain contracts and structure and that the two-part tariff is the best contract to reduce double marginalization and increase efficiency in the management of the supply chain.     

Super Jaulent-Miodek hierarchy and its super Hamiltonian structure,conservation laws and its self-consistent sources

A super Jaulent-Miodek hierarchy and its super Hamiltonian structures are constructed by means of a kind of Lie super algebras and super trace identity. Moreover, the self-consistent sources of the super Jaulent-Miodek hierarchy is presented based on the theory of self-consistent sources. Further- more, the infinite conservation laws of the super Jaulent-Miodek hierarchy are also obtained. It is worth noting that as even variables are boson variables, odd variables are fermi variables in the spectral problem, the commutator is different from the ordinary one.     

Structures preserved by the QR-algorithm

In this paper we investigate some classes of structures that are preserved by applying a (shifted) QR-step on a matrix A. We will handle two classes of such structures: the first we call polynomial structures, for example a matrix being Hermitian or Hermitian up to a rank one correction, and the second we call rank structures, which are encountered for example in all kinds of what we could call Hessenberg-like and lower semiseparable-like matrices. An advantage of our approach is that we define a structure by decomposing it as a collection of ‘building stones’ which we call structure blocks. This allows us to state the results in their natural, most general context.     

Witt代数和Virasoro代数上的Poisson代数结构

Poisson代数是指同时具有结合代数结构和李代数结构的一类代数,其结合代数结构和李代数结构满足Leibniz法则.确定了特征为0和特征为p>0的基域上的Witt代数和Virasoro代数上的Poisson代数结构.     

A Method of Representing Rough Sets System Determined by Quasi Orders

In this paper, we study about the ordered structure of rough sets determined by a quasi order. A characterization theorem for rough sets of an approximation space (U, R) based on a quasi order R is given in Nagarajan and Umadevi (2010). Then using the characterization of rough sets determined by a quasi order, its rough sets system is represented by a new construction. This construction is generalized and abstracted into a new method of constructing Kleene based algebraic structures from dually isomorphic distributive lattices. Then by using different varieties of distributive lattices, we obtain various Kleene based algebraic structures. By this construction, we give various algebraic structures to the rough sets system determined by a quasi order R.     

Restricted dynamic programming based neighborhoods for the hop-constrained minimum spanning tree problem

In this paper we develop, study and test new neighborhood structures for the Hop-constrained Minimum Spanning Tree Problem (HMSTP). These neighborhoods are defined by restricted versions of a new dynamic programming formulation for the problem and provide a systematic way of searching neighborhood structures based on node-level exchanges. We have also developed several local search methods that are based on the new neighborhoods. Computational experiments for a set of benchmark instances with up to 80 nodes show that the more elaborate methods produce in a quite fast way, heuristic solutions that are, for all cases, within 2% of the optimum.