Relative Discrete Spectrum and Joinings

 A joining characterization of ergodic isometric extensions is given. We also give a simple joining proof of a relative version of the Halmos-von Neumann theorem.     

Crossing Numbers of Periodic Graphs

A graph is periodic if it can be obtained by joining identical pieces in a cyclic fashion. It is shown that the limit crossing number of a periodic graph is computable. This answers a question of Richter [1, Problem 4.2].     

Bounce trajectories with one Bounce point

Summary In this paper we study the existence of bounce trajectories, under the action of a potential field, having only one bounce point and joining two prescribed points in a bounded regular domain ofR ^N.Work supported by M.P.I. and G.N.A.F.A.     

Asymptotically exact joining conditions at the junction of plates with very different characteristics

The phenomenon of the boundary layer which occurs when plates are joined is studied A procedure for deriving the asymptotically exact joining (transmission) conditions which associate the two-dimensional equations for the deformation of the plates along the joining line Γ is developed using the method of matched asymptotic expansions. Two situations are discussed in which these conditions turn out to be non-standard: the bending moment in Γ must disappear and the deflection can undergo a jump (for real values of the physical parameters, the longitudinal displacements and forces as well as the bending and the shearing force always remain continuous). One of the situations (the joining of “thick, soft” and a “thin, rigid” shells) is characteristic of a moving loudspeaker system. The results of a numerical experiment, which confirm the asymptotic analysis of the problem, are presented.     

Heavy fans, cycles and paths in weighted graphs of large connectivity

A set of paths joining a vertex y and a vertex set L is called (y,L)-fan if any two of the paths have only y in common, and its width is the number of paths forming it. In weighted graphs, it is known that the existence of heavy fan is useful to find a heavy cycle containing some specified vertices.In this paper, we show the existence of heavy fans with large width containing some specified vertices in weighted graphs of large connectivity, which is a weighted analogue of Perfect's theorem. Using this, in 3-connected weighted graphs, we can find heavy cycles containing three specified vertices, and also heavy paths joining two specified vertices containing two more specified vertices. These results extend the previous results in 2-connected weighted graphs to 3-connected weighted graphs.     

Solution of the Helmholtz equation in unbounded stepped regions

The article considers the determination of the acoustic field excited by a point source in two-dimensional unbounded stepped regions. A method is proposed for solving the corresponding boundary-value problems for the nonhomogeneous Helmholtz equation by joining numerical and analytical solutions.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 56, pp. 17–21, 1985     

Quasifactors of ergodic systems with positive entropy

The relation between the two notions, quasifactors and joinings, is investigated and the notion of a joining quasifactor is introduced. We clarify the close connection between quasifactors and symmetric infinite selfjoinings which arises from de Finetti-Hewitt-Savage theorem. Unlike the zero-entropy case where quasifactors seems to preserve some properties of their parent system, it is shown that any ergodic system of positive entropy admits all ergodic systems of positive entropy as quasifactors. A restricted version of this result is obtained for joining quasifactors.     

超市模型的实时动态控制及其数值分析

超市模型是针对大型并行排队网络所进行的 实时动态控制的随机负载平衡策略, 它在计算机网络、云计算、制造系统、交通网络等领域有着重要的实际应用价值. 本文考虑了超市模型中的若干重要问题: 实时动态控制模式; 效率比较; 平均场黑洞; 马氏变动环境; 稳定性; 固定点; 系统性能评价等等. 同时, 本文也通过数值算例研究了上述重要问题, 包括对顾客加入最短队列的超市模型与服务台服务最长队列的超市模型进行了性能比较, 给出了他们效率的优劣分析; 在超市模型中对控制到达过程机制进行了三种情况的对比; 对马氏变动环境下的超市模型进行了性能评价.     

Zur Darstellung der Unterräume von Kettengeometrien

A subspace of a chain geometry in the sense of W. Benz [1] is defined as a subset S of points such that the chain joining any three pairwise non-parallel points of S is contained in S. In this note we are concerned with the problem of determining those subspaces that can be represented by subalgebras.     

Stability of discontinuity structures described by a generalized KdV–Burgers equation

The stability of discontinuities representing solutions of a model generalized KdV–Burgers equation with a nonmonotone potential of the form φ(u) = u⁴–u² is analyzed. Among these solutions, there are ones corresponding to special discontinuities. A discontinuity is called special if its structure represents a heteroclinic phase curve joining two saddle-type special points (of which one is the state ahead of the discontinuity and the other is the state behind the discontinuity).The spectral (linear) stability of the structure of special discontinuities was previously studied. It was shown that only a special discontinuity with a monotone structure is stable, whereas special discontinuities with a nonmonotone structure are unstable. In this paper, the spectral stability of nonspecial discontinuities is investigated. The structure of a nonspecial discontinuity represents a phase curve joining two special points: a saddle (the state ahead of the discontinuity) and a focus or node (the state behind the discontinuity). The set of nonspecial discontinuities is examined depending on the dispersion and dissipation parameters. A set of stable nonspecial discontinuities is found.     

Finite element simulation for material accumulation and welding processes including a free melt surface

A modeling and simulation approach for problems with solid-liquid-solid phase transitions and a free surface, feasible for material accumulation processes based on laser-based free form heading and welding processes for joining different metallic materials is presented. Both named processes are modeled within the framework of continuum mechanics by coupling the Stefan problem with the Navier-Stokes equations including a free capillary surface. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Menger-type theorems with restrictions on path lengths

If the paths of length s, joining two non-adjacent vertices u, υ of a graph cannot be destroyed by deleting less than t vertices, then there are at least t internally vertex-disjoint paths joining u and υ, each having length less than . Some constructions show that using paths of length at least s/t−1^t might be necessary.     

Network Splines

A multivariate interpolant to scattered data is developed by generalizing (weighted) bivariate network splines to an n-dimensional setting. A graph joining the data points serves to define a set of edges over which an interpolating curve network is constructed subject to smoothness and minimal energy constraints. A subsequent extension of the curve network to the convex hull of the data points defines a smooth interpolating surface. The problems of existence and uniqueness are investigated and some examples of interpolants to rapidly varying data in ?³ and ?⁴ are presented.     

Implicit-degrees and circumferences

In this paper, we introduce a new concept — implicit-degrees of vertices of graphs. Related to this concept, a new definition for the closure of a graph is introduced. This closure is obtained by recursively joining pairs of nonadjacent vertices whose implicit-degree sum is at least the order of the graph. A criterion for deciding whether a graph is hamiltonian from its closure is obtained. Two other important results concerning the implicit-degrees of vertices and circumferences of graphs are presented.     

Disjoint shortest paths in graphs

It is an interesting problem that how much connectivity ensures the existence ofn disjoint paths joining givenn pairs of vertices, but to get a sharp bound seems to be very difficult. In this paper, we study how muchgeodetic connectivity ensures the existence ofn disjointgeodesics joining givenn pairs of vertices, where a graph is calledk-geodetically connected if the removal of anyk−1 vertices does not change the distance between any remaining vertices.     

Latin square and intersection of surface

A technique is developed here to estimate an unknown curve joining two points in a three dimensional Euclidean space. A special application presented here is a computer procedure to determine the intersection of two arbitrary given smooth surfaces. The method used is to assume that y is a function of x and the set (x,y(x)) lies on the projection of the intersection of two surfaces. The function y is determined by least square curve fitting on a Latin square of experimental values. The procedure is written in APL (A Programming Language). A set of preliminary results is presented. The results indicate that this is a successful procedure for some simple surfaces, including some conic surfaces.     

Finding shortest paths in a sequence of triangles in 3D by the method of orienting curves

We present an efficient algorithm for finding the shortest path joining two points in a sequence of triangles in three-dimensional space without planar unfolding. The concept of a funnel associated with a common edge along a sequence of triangles is introduced, that is similar to Lee and Preparata’s one in a simple polygon. The sequence of funnels associated with all common edges of the sequence is constructed and then the shortest path is determined by cusps of these funnels. Such funnels are determined iteratively to their associated edges by the Method of Orienting Curves, which was introduced by Phu [Ein konstruktives Lösungsverfahren für das Problem des Inpolygons kleinsten Umfangs von J. Steiner. Optimization. 1987;18:349–359]. The method consists of the concepts of final curves and orienting curves (the special cases of straightest geodesics). We then show that the shortest path from the cusp of a given funnel to the direct destination in the processed region of the funnel is determined by parts of orienting curves and a final curve. A numerical example for finding the shortest path joining two points in the sequence of triangles is presented and visualized by JavaView software.     

Blowing up: application to $G^2$-continuous 8-sided filling patch

Summary. We propose a method for filling a n-sided hole, , that interpolates n connected boundary curves of a given net of patches. This method allows the joining with patches defined in many different ways. A new class of blowing up pole-functions is introduced in order to build a G-continuous n-sided filling surface. This filling surface is in one piece, image of . Received February 21, 2000 / Revised version received January 2, 2001 / Published online December 18, 2001     

On geodesics in asymptotic Teichm��ller spaces

Let R be a Riemann surface of infinite analytic type, T(R) and AT(R) be the Teichmüller space and asymptotic Teichmüller space on R respectively. The purpose of this paper is to discuss some problems related to geodesics in AT(R). It is proved that uniqueness of geodesics joining two given points [??] and [??] in T (R) dose not imply uniqueness of geodesics joining?[[??]] and [[??]] in AT(R). Furthermore, a Beltrami differential??? is constructed such that there are infinitely many geodesics joining [[0]] and?[[??]] in AT(R), and a sufficient condition to determine the difference of the geodesics [[t?? ₁]] and [[t?? ₂]] (0??? t??? 1) joining [[0]] and?[[??]] in AT(??) is given.