Duality theory and propagation rules for higher order nets

Higher order nets and sequences are used in quasi-Monte Carlo rules for the approximation of high dimensional integrals over the unit cube. Hence one wants to have higher order nets and sequences of high quality.In this paper we introduce a duality theory for higher order nets whose construction is not necessarily based on linear algebra over finite fields. We use this duality theory to prove propagation rules for such nets. This way we can obtain new higher order nets (sometimes with improved quality) from existing ones. We also extend our approach to the construction of higher order sequences.     

Compact nets,filters, and relations

The notion of compact filter is introduced and compared to related notions of compact nets and compact relations. A characterization of compact nets is given in regular spaces. Several applications in optimization theory and nonlinear analysis are presented.     

基于Euler网的企业流程建模方法研究

本文主要介绍了基于离散事件系统的 Euler网建模方法 ,Euler网方法是在活动周期图方法的基础上 ,以图论和网论为描述语言的一种建模方法 ,它可以较好地支持生命周期 ,能够充分反映企业不断改进和扩展的过程 ,因此本文采用 Euler网方法对企业流程建模进行了重点研究 ,为企业建模提供了新的思路 .     

Studies of lexicography in the generalized network simplex method

This paper introduces an analytical approach for studying lexicography in generalized network problems. The equations obtained can help us to understand and to extend the existing theory. First, it is verified that all nonzero elements have the same sign in each row vector of a basis inverse for a generalized network (GN) problem with positive multipliers. However, this property does not necessarily hold when there exist negative multipliers. Second, we developed a strategy to select the dropping arc in the GN simplex algorithm when addressing GN problems with positive andnegative multipliers. This strategy is also based on lexicography and requires performing some comparisons. However, the values to be compared are already known since they can be obtained as a by-product of the calculations necessary to compute the basis representation of the entering arc. Consequently, the computational effort per pivot step isO(n) in the worst case. This worst case effort is the same as that required by the strongly convergent rules for selecting the dropping arc in the method of strong convergence.     

A combinatorial characterization of (t,m,s)-nets in base b

We consider (t,m,s)-nets in base b, which were introduced by Niederreiter in 1987. These nets are highly uniform point distributions in s-dimensional unit cubes and have applications in the theory of numerical integration and pseudorandom number generation. A central question in their study is the determination of the parameter values for which these nets exist. Niederreiter has given several methods for their construction, all of which are based on a general construction principle from his 1987 paper. We define a new family of combinatorial objects, the so-called “generalized orthogonal arrays,” and then discuss a combinatorial characterization of (t.m.s)-nets in base b in terms of these generalized orthogonal arrays. Using this characterization, we describe a new method for constructing (t.m.s)-nets in base b that is not based on the aforementioned construction principle. This method gives rise to some very general conditions on the parameters (involving a link with the theory of orthogonal arrays) that are sufficient to ensure the existence of a (t.m.s)-net in base b. In this way we construct many nets that are new. © 1996 John Wiley & Sons, Inc.     

Local conformal nets arising from framed vertex operator algebras

We apply an idea of framed vertex operator algebras to a construction of local conformal nets of (injective type III₁) factors on the circle corresponding to various lattice vertex operator algebras and their twisted orbifolds. In particular, we give a local conformal net corresponding to the moonshine vertex operator algebras of Frenkel-Lepowsky-Meurman. Its central charge is 24, it has a trivial representation theory in the sense that the vacuum sector is the only irreducible DHR sector, its vacuum character is the modular invariant J-function and its automorphism group (the gauge group) is the Monster group. We use our previous tools such as α-induction and complete rationality to study extensions of local conformal nets.     

Neural nets in a group decision process

In recent years there has been some interest in applying Artificial Adaptive Agents (AAA) to the study of complex adaptive systems, especially economic systems. Neural networks are frequently employed as AAA. Artificial neural nets mimic certain aspects of the physical structure and information processing of the human brain and their most attractive characteristic is their ability to learn a pattern from a given set of examples. In this study, we investigated the ability of neural nets to model human behavior in a group decision process. The context was a market entry game with a linear payoff function and binary decisions. The players had to decide, for each trial, whether or not to enter a market whose capacity is public knowledge. Human behavior in this situation has been modeled and empirically validated by the Nash equilibrium for noncooperative n-person games. A simulation of the game was performed with neural nets instead of human subjects. The nets were trained using the results of the games in which they participated. The simulation with groups of neural nets exhibits phenomena very similar to those observed in groups of human players. Received February 2000     

Some covering properties in topological and uniform spaces

Recent progress in selection principles theory is discussed and is illustrated mainly by the Hurewicz covering property and its strong version, the Gerlits-Nagy property GN(*). Some results that have not been published elsewhere are given with proofs.     

A comprehensive approach of planning and scheduling based on petri nets

The main results available on the use of black-and-white Petri nets for modelling, planning and scheduling manufacturing systems are presented. In the first part of the paper, the basics of Petri nets necessary to understand the subsequent presentation are introduced. Particular attention is paid to event graphs, a particular type of Petri nets used for modelling and evaluating ratio-driven systems. The second part of the paper is devoted to ratio-driven systems, their modelling and their scheduling. Job-shops, assembly systems, and KANBAN systems are used to illustrate this section. Finally, the general case is investigated of manufacturing systems subject to changing demands. An approach based on conflict-free Petri nets with input and output transitions is proposed for planning and scheduling this type of system.     

Extracting embedded generalized networks from linear programming problems

If a linear program (LP) possesses a large generalized network (GN) submatrix, this structure can be exploited to decrease solution time. The problems of finding maximum sets of GN constraints and finding maximum embedded GN submatrices are shown to be NP-complete, indicating that reliable, efficient solution of these problems is difficult. Therefore, efficient heuristic algorithms are developed for identifying such structure and are tested on a selection of twenty-three real-world problems. The best of four algorithms for identifying GN constraint sets finds a set which is maximum in twelve cases and averages 99.1% of maximum. On average, the GN constraints identified comprise more than 62.3% of the total constraints in these problems. The algorithm for identifying embedded GN submatrices finds submatrices whose sizes, rows plus columns, average 96.8% of an LP upper bound. Over 91.3% of the total constraint matrix was identified as a GN submatrix in these problems, on average.The act of being wise is the act of knowing what to overlook.William James (ca. 1890)     

Translations and construction of generalised nets

A theory of certain types of translations for generalised nets is developed, and the structure of nets constructed by a special method is analysed, especially with regard to subsets and extensions. This enables nonisomorphism results to be established, along with theorems that the number of nonisomorphic solutions of a certain type (for example, complete or maximal) tends to infinity with k.     

Completeness in quasi-uniform spaces

We introduce a theory of completeness (the π-completeness) for quasi-uniform spaces which extends the theories of bicompleteness and half-completeness and prove that every quasi-uniform space has a π-completion. This theory is based on a new notion of a Cauchy pair of nets which makes use of couples of nets. We call them cuts of nets and our inspiration is due to the construction of the τ-cut on a quasi-uniform space (cf. [1], [20]). This new version of completeness coincides with bicompletion, half-completion and D-completion in extended subclasses of the class of quasi-uniform spaces.     

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.     

Steady solution of solitary wave and linear shear current interaction

The steady solution of a solitary wave propagating in the presence of a linear shear background current is investigated by the Green–Naghdi (GN) equations. The steady solution is obtained by use of the Newton–Raphson method. Three aspects are investigated; they are the wave speed, wave profile and velocity field. The converged GN results are compared with results from the literature. It is found that for the opposing-current case of the solitary wave with a small amplitude, the results of the GN equations match results from the literature well, while for the solitary wave with a large amplitude, results from the literature are seen to be not as accurate. In the following-current case, though the amplitude of the solitary wave is small, the GN results are shown to be accurate. The velocity along the water column at the wave crest and the velocity field for different cases are calculated by the GN equations. The results of the GN equations show obvious differences when compared with the results obtained by superposing the no-current results and linear shear current linearly. We find that for the same current strength, the vortex is stronger for the steep solitary-wave case than that for the small solitary-wave case.     

A curvature theory for discrete surfaces based on mesh parallelity

We consider a general theory of curvatures of discrete surfaces equipped with edgewise parallel Gauss images, and where mean and Gaussian curvatures of faces are derived from the faces’ areas and mixed areas. Remarkably these notions are capable of unifying notable previously defined classes of surfaces, such as discrete isothermic minimal surfaces and surfaces of constant mean curvature. We discuss various types of natural Gauss images, the existence of principal curvatures, constant curvature surfaces, Christoffel duality, Koenigs nets, contact element nets, s-isothermic nets, and interesting special cases such as discrete Delaunay surfaces derived from elliptic billiards.     

Rate of convergence of the generalized newton algorithm using the fixed-point approach

This paper shows that the generalized Newton algorithm [GN(r)], developed by Kalaba and Tishler (Ref. 1), can be described as a fixed-point algorithm. In addition to specifying sufficient conditions for convergence of the GN(r), we show that, forr=1, 2, 3, its rate of convergence increases with the order of the derivatives which are used.The authors are indebted to I. Zang for drawing their attention to an error in an earlier draft of this paper. Suggestions and comments by N. Levin and D. Trietsch are also gratefully acknowledged.     

A Theory of Nets for Polyhedra and Polytopes Related to Incidence Geometries

Our purpose is to elaborate a theory of planar nets or unfoldings for polyhedra, its generalization and extension to polytopes and to combinatorial polytopes, in terms of morphisms of geometries and the adjacency graph of facets.     

Epistemic irrelevance in credal nets: The case of imprecise Markov trees

We focus on credal nets, which are graphical models that generalise Bayesian nets to imprecise probability. We replace the notion of strong independence commonly used in credal nets with the weaker notion of epistemic irrelevance, which is arguably more suited for a behavioural theory of probability. Focusing on directed trees, we show how to combine the given local uncertainty models in the nodes of the graph into a global model, and we use this to construct and justify an exact message-passing algorithm that computes updated beliefs for a variable in the tree. The algorithm, which is linear in the number of nodes, is formulated entirely in terms of coherent lower previsions, and is shown to satisfy a number of rationality requirements. We supply examples of the algorithm’s operation, and report an application to on-line character recognition that illustrates the advantages of our approach for prediction. We comment on the perspectives, opened by the availability, for the first time, of a truly efficient algorithm based on epistemic irrelevance.     

Parallel permit grammars and some graph representations of Petri nets

The graph of a set grammar is introduced in such a way that each set rule of the grammar is represented by a cartesian subgraph of it. The correspondence between cartesian subgraphs and transitions of Petri nets (which satisfy the axiom of extensionality) is established. The set grammars with input (initial) and output (terminal) elements are studied in an analogy to Chomsky's string grammars and their strong equivalence. Permit rules and parallel permit rules are introduced in such a way that parallel permit grammars are more general tools than Petri nets themselves, because the equivalence between homogeneous parallel permit grammars and set grammars (and Petri nets) is proved.     

Application of a hybrid meshless technique for natural frequencies analysis in functionally graded thick hollow cylinder subjected to suddenly thermal loading

A hybrid meshless technique based on composition of meshless local Petrov–Galerkin method (for spatial variables) and Newmark finite difference method (for time domain) is developed for natural frequencies analysis of thick cylinder made of functionally graded materials (FGMs). The FG cylinder is assumed to be under suddenly thermal loading, axisymmetric and plane strain conditions. The dynamic behaviors and time history of displacements are obtained in time domain using Green–Naghdi (GN) theory of coupled thermo-elasticity (without energy dissipation). Using fast Fourier transform (FFT) technique, the displacements are transferred to frequency domain and all natural frequencies are illustrated for various grading patterns of FGMs. The variations of mechanical properties in FG thick hollow cylinder are considered to be in nonlinear volume fraction law through radial direction. The presented hybrid meshless technique furnishes a ground to analyze the effects of various grading patterns of FGMs on natural frequencies, which are obtained employing GN coupled thermo-elasticity governing equations. Also, the frequency history and natural frequencies are illustrated for various grading patterns at several points across thickness of cylinder.