SEQUENTIAL CONVEX PROGRAMMING METHODS FOR SOLVING LARGE TOPOLOGY OPTIMIZATION PROBLEMS： IMPLEMENTATION AND COMPUTATIONAL RESULTS

In this paper, we describe a method to solve large-scale structural optimization problems by sequential convex programming （SCP）. A predictor-corrector interior point method is applied to solve the strictly convex subproblems. The SCP algorithm and the topology optimization approach are introduced. Especially, different strategies to solve certain linear systems of equations are analyzed. Numerical results are presented to show the efficiency of the proposed method for solving topology optimization problems and to compare different variants.     

On quasi-weakly almost periodic points

The core problem of dynamical systems is to study the asymptotic behaviors of orbits and their topological structures. It is well known that the orbits with certain recurrence and generating ergodic (or invariant) measures are important, such orbits form a full measure set for all invariant measures of the system, its closure is called the measure center of the system. To investigate this set, Zhou introduced the notions of weakly almost periodic point and quasi-weakly almost periodic point in 1990s, and presented some open problems on complexity of discrete dynamical systems in 2004. One of the open problems is as follows: for a quasi-weakly almost periodic point but not weakly almost periodic, is there an invariant measure generated by its orbit such that the support of this measure is equal to its minimal center of attraction (a closed invariant set which attracts its orbit statistically for every point and has no proper subset with this property)? Up to now, the problem remains open. In this paper, we construct two points in the one-sided shift system of two symbols, each of them generates a sub-shift system. One gives a positive answer to the question above, the other answers in the negative. Thus we solve the open problem completely. More important, the two examples show that a proper quasi-weakly almost periodic orbit behaves very differently with weakly almost periodic orbit.     

Hypercontinuous Posets

The concepts of hypercontinuous posets and generalized completely continuous posets are introduced. It is proved that for a poset P the following three conditions are equivalent:(1) P is hypercontinuous;(2) the dual of P is generalized completely continuous;(3) the normal completion of P is a hypercontinuous lattice. In addition, the relational representation and the intrinsic characterization of hypercontinuous posets are obtained.     

Pre—Separation Axioms in Fuzzifying Topology

1　 IntroductionYing[5,6 ] introduced and elementally developed so called fuzzifying topology with the semanticmethod of continuous valued L ogic.Shen[7] introduced and studied T0 -,T1-,T2 (Hausdorff) -,T3(regularity) -,T4 (normality) -separation axioms in fuzzifying topology.In [3 ]the concepts of thefamily of fuzzifying pre-open sets,fuzzifying pre-neighbourhood structure of a point and fuzzifyingpre-closure are introduced and studied.It is worth to mention that pre-separation axioms are …     

交一致连续偏序集

In this paper, as a generalization of uniform continuous posets, the concept of meet uniform continuous posets via uniform Scott sets is introduced. Properties and characterizations of meet uniform continuous posets are presented. The main results are:(1) A uniform complete poset L is meet uniform continuous iff ↑(U ∩↓ x) is a uniform Scott set for each x ∈ L and each uniform Scott set U;(2) A uniform complete poset L is meet uniform continuous iff for each∨∨x∈ L and each uniform subset S, one has x ∧S ={x ∧ s | s ∈ S}. In particular, a complete lattice L is meet uniform continuous iff L is a complete Heyting algebra;(3) A uniform complete poset is meet uniform continuous iff every principal ideal is meet uniform continuous iff all closed intervals are meet uniform continuous iff all principal filters are meet uniform continuous;(4) A uniform complete poset L is meet uniform continuous if L1 obtained by adjoining a top element1 to L is a complete Heyting algebra;(5) Finite products and images of uniform continuous projections of meet uniform continuous posets are still meet uniform continuous.     

The Order of Hypersubstitutions of Type （2, 2）

Hypersubstitutions are mappings which map operation symbols to terms of the corresponding arities. They were introduced as a way of making precise the concept of a hyperidentity and generalizations to M-hyperidentities. A variety in which every identity is satisfied as a hyperidentity is called solid. If every identity is an M-hyperidentity for a subset M of the set of all hypersubstitutions, the variety is called M-solid. There is a Galois connection between monoids of hypersubstitutions and sublattices of the lattice of all varieties of algebras of a given type. Therefore, it is interesting and useful to know how semigroup or monoid properties of monoids of hypersubstitutions transfer under this Galois connection to properties of the corresponding lattices of M-solid varieties. In this paper, we study the order of each hypersubstitution of type （2, 2）, i.e., the order of the cyclic subsemigroup generated by that hypersubstitution of the monoid of all hypersubstitutions of type （2, 2）. The main result is that the order is 1, 2, 3, 4 or infinite.     

Embeddings of Pure Mendelsohn Triple Systems and Pure Directed Triple Systems

A λ-fold triple system of order v,denoted TS(v,λ),is a pair(V,A)where V is a v-set and A is a collection of 3-subsets(called triples)of V such that each 2-subset of V is contained in exactly λ triples.A triple system is called simple if itcontains no repeated triples. There are two related classes of triple systems,namely,Mendelsohn triple sys-tems and directed triple systems.     

HOPF BIFURCATION ANALYSIS OF A 3D CHAOTIC SYSTEM

In this paper,a 3D chaotic system with multi-parameters is introduced. The dynamical systems of the original ADVP circuit and the modified ADVP model are regarded as special examples to the system.Some basic dynamical behaviors such as the stability of equilibria,the existence of Hopf bifurcation are investigated.We analyse the Hopf bifurcation of the system comprehensively using the first Lyapunov coefficient by precise symbolic computation.As a result,in fact we have studied the further dynamical behaviors.     

Direction monotonicity for a rational Bézier curve

The monotonicity of a rational Bézier curve, usually related to an explicit function,is determined by the used coordinate system. However, the shape of the curve is independent of the coordinate system. To meet the affine invariant property, a kind of generalized monotonicity, called direction monotonicity, is introduced for rational Bézier curves. The direction monotonicity is applied to both planar and space curves and to both Cartesian and affine coordinate systems, and it includes the traditional monotonicity as a subcase. By means of it,proper affine coordinate systems may be chosen to make some rational Bézier curves monotonic.Direction monotonic interpolation may be realized for some of the traditionally nonmonotonic data as well.     

A Notion of Stochastic Input-to-State Stability and Its Application to Stability of Cascaded Stochastic Nonlinear Systems

In this paper, the property of practical input-to-state stability and its application to stability of cascaded nonlinear systems are investigated in the stochastic framework. Firstly, the notion of （practical） stochastic input-to-state stability with respect to a stochastic input is introduced, and then by the method of changing supply functions, （a） an （practical） SISS-Lyapunov function for the overall system is obtained from the corresponding Lyapunov functions for cascaded （practical） SISS subsystems.     

Normal projection: deterministic and probabilistic algorithms

We consider the following problem： for a collection of points in an n-dimensional space, find a linear projection mapping the points to the ground field such that different points are mapped to different values. Such projections are called normal and are useful for making algebraic varieties into normal positions. The points may be given explicitly or implicitly and the coefficients of the projection come from a subset S of the ground field. If the subset S is small, this problem may be hard. This paper deals with relatively large S, a deterministic algorithm is given when the points are given explicitly, and a lower bound for success probability is given for a probabilistic algorithm from in the literature.     

SIGN MATRIX, REGULAR SPLITTINGS AND MONOTONIC ENCLOSURE OF SOLUTIONS FOR NONLINEAR SYSTEM OF EQUATIONS, PARTI

In this paper we introduce the sign matrix of a nonlinear system of equations x = Gx to characterize its hybrid and asynchronous monotonicity as well as convexity. Based on the configuration of the matrix, we define a new type of regular splittings of the system with which the solvability and construction of solutions for the system are transformed to those of the couple systems of the splitting formIt is shown that this couple systems is a general model for developing monotonic enclosure methods of solutions for various types of nonlinear system of equations.     

ON THE EMBEDDING OF TOP IN THE CATEGORY OF STRATIFIED L-TOPOLOGICAL SPACES

§1. Introduction and PreliminariesLet L be a complete lattice. An L-topology on a set X is a subset τ of LX closed withrespect to ?nite meets and arbitrary joins. (X,τ) is called an L-topological space. The L-topology τ is called strati?ed if it contains all the constant maps from X to L, and in this case(X,τ) is called a strati?ed L-topological space. A continuous map between two L-topologicalspaces (X,τX) and (Y,τY ) is a function f : X ?→ Y such that f←(λ) = λ ? f ∈ τX…     

ON THE REALIZATION THEORY OF IMPULSE RESPONSE SEQUENCES

In the practical physics and engineering systems, the informations that we can acquire are only the input-output data. It is an lmportant problem how obtain internal structure of system by this informations, namely, the realization problem of systems. The existing realization theory are all to construct the realization from the transfer function of systems. However, for a practical system,     

CHEBYSHEV METHODS WITH DISCRETE NOISE： THE τ-ROCK METHODS

Stabilized or Chebyshev explicit methods have been widely used in the past to solve stiff ordinary differential equations. Making use of special properties of Chebyshev-like polynomials, these methods have favorable stability properties compared to standard explicit methods while remaining explicit. A new class of such methods, called ROCK, introduced in [Numer. Math., 90, 1-18, 2001] has recently been extended to stiff stochastic differential equations under the name S-ROCK [C. R. Acad. Sci. Paris, 345（10）, 2007 and Commun. Math. Sci, 6（4）, 2008]. In this paper we discuss the extension of the S-ROCK methods to systems with discrete noise and propose a new class of methods for such problems, the τ-ROCK methods. One motivation for such methods is the simulation of multi-scale or stiff chemical kinetic systems and such systems are the focus of this paper, but our new methods could potentially be interesting for other stiff systems with discrete noise. Two versions of the τ-ROCK methods are discussed and their stability behavior is analyzed on a test problem. Compared to the τ-leaping method, a significant speed-up can be achieved for some stiff kinetic systems. The behavior of the proposed methods are tested on several numerical experiments.     

Two new types of bounded waves of CH-γ equation

In this paper, the bifurcation method of dynamical systems and numerical approach of differential equations are employed to study CH-γ equation. Two new types of bounded waves are found. One of them is called the compacton. The other is called the generalized kink wave. Their planar graphs are simulated and their implicit expressions are given. The identity of theoretical derivation and numerical simulation is displayed.     

Sober拓扑分子格

A topological molecular lattice (TML) is a pair (L, T), where L is a completely distributive lattice and r is a subframe of L. There is an obvious forgetful functor from the category TML of TML‘s to the category Loc of locales. In this note,it is showed that this forgetful functor has a right adjoint. Then, by this adjunction,a special kind of topological molecular lattices called sober topological molecular lattices is introduced and investigated.     

Generalized isochronous centers for complex systems

In this paper, the definition of generalized isochronous center is given in order to study unitedly real isochronous center and linearizability of polynomial differential systems. An algorithm to compute generalized period constants is obtained, which is a good method to find the necessary conditions of generalized isochronous center for any rational resonance ratio. Its two linear recursive formulas are symbolic and easy to realize with computer algebraic system. The function of time-angle difference is introduced to prove the sufficient conditions. As the application, a class of real cubic Kolmogorov system is investigated and the generalized isochronous center conditions of the origin are obtained.     

闭排队网络中性能势与无穷小实现因子之间的关系

In this paper,the concept of the infinitesimal realization factor is extended to the parameter-dependent performance functions in closed queueing networks. Then the concepts of realization matrix (its elements are called realization factors) and performance potential are introduced,and the relations between infinitesimal realization factors and these two quantities are discussed. This provides a united framework for both IPA and non IPA approaches. Finally,another physical meaning of the service rate is given.