On the Asymmetry for Convex Domains of Constant Width

The extremal convex bodies of constant width for the Minkowski measure of asymmetry are discussed. A result, similar to that of H. Groemer＇s and of H. Lu＇s, is obtained, which states that, for the Minkowski measure of asymmetry, the most asymmetric convex domains of constant width in R2 are Reuleaux triangles.

A Sort of Gray-scale Morphological Dilations and Erosions

We introduce first a sort of gray-scale morphological dilations and erosions, which might have some further applications in image analysis. Then we show that the dilation and the erosion defined here form adjunctive pairs. The duality between the dilation and the erosion and some other properties, such as homothety, of these operators are discussed the Commuting property with translation and as well.

SEPARABLE CONDITIONS AND SCALARIZATION OF BENSON PROPER EFFICIENCY

Under the assumption that the ordering cone has a nonempty interior and is separable （or the feasible set has a nonempty interior and is separable）, we give scalarization theorems on Benson proper effciency. Applying the results to vector optimization problems with nearly cone-subconvexlike set-valued maps, we obtain scalarization theorems and Lagrange multiplier theorems for Benson proper effcient solutions.

Investigation for parametric vibration of rolling mill

The vibration unsteady condition of rolling mill caused by flexural vibration of strip has been investigated. The parametric flexural vibration equation of rolled strip has been established. The parametric flexural vibration stability of rolled strip has been studied and the regions of stability and unstability have been determined based on Floquet theory and perturbation method. The flexural vibration of strip is unstable when the frequency of variable tension is two times as the natural frequency of flexural vibration strip. The characteristic of current in a temp driving motor’s main loop has been studied and tested, it has been proved that there are 6 harmonic component and 12 harmonic component in main loop of driving motor electricity. The vertical vibration of working roller has been tested, the test result approves that the running unsteady is caused by parametric vibration. It attaches importance to the parametric vibration of rolling mill.

Measures of Asymmetry Dual to Mean Minkowski Measures of Asymmetry for Convex Bodies

Khovanov type homology is a generalization of Khovanov homology.The main result of this paper is to give a recursive formula for Khovanov type homology of pretzel knots P（-n,-m, m）. The computations reveal that the rank of the homology of pretzel knots is an invariant of n. The proof is based on a ＂shortcut＂ and two lemmas that recursively reduce the computational complexity of Khovanov type homology.

CHARACTERIZATION OF SOLID CONES

The author gives a dual characterization of solid cones in locally convex spaces. From this the author obtains some criteria for judging convex cones to be solid in various kinds of locally convex spaces. Using a general expression of the interior of a solid cone, the author obtains a number of necessary and sufficient conditions for convex cones to be solid in the framework of Banach spaces. In particular, the author gives a dual relationship between solid cones and generalized sharp cones. The related known results are improved and extended.

A NUMERICAL METHOD OF K-S ENTROPY CALCULATION FOR A STRANGE ATTRACTOR

Based directly on the original definition of K-S entropy, a new algorithm for calculating K-S entropy from chaotic time series is developed by using some techniques of coding and code operation.

On Properties of p-critical Points of Convex Bodies

Properties of the p-measures of asymmetry and the corresponding affine equivariant p-critical points, defined recently by the second author, for convex bodies are discussed in this article. In particular, the continuity of p-critical points with respect to p on （1, ＋∞） is confirmed, and the connections between general p-critical points and the Minkowski-critical points （∞-critical points） are investigated. The behavior of p-critical points of convex bodies approximating a convex bodies is studied as well.

Theorems of Helly's Type for Partially-closed Half-spaces

In this article, under quite weaker conditions, theorems of Helly’s type for(not necessarily finite) family of partially closed half-spaces are presented in both analytic and geometric forms. Examples are also provided to show that these conditions cannot be omitted in general.

Discussion on the Geometrie Structure of Strange Attractor

We discuss the tr&nsversal heteroclinic cycle formed by hyperbolic periodic points of diffeomorphism on the differential manifold.We point out that every possible kind of transversal heteroclinic cycle has the Smsdehorse property and the unstable manifolds of hyperbolic periodic points have the closure relation mutually.Therefore the strange attractor may be the closure of unstable manifolds of a countable number of hyperbolic periodic points.The Henon mapping is used as an example to show that the conclusion is reasonable.

A conjecture on the norm of Lyapunov mapping

A conjecture that the norm of Lyapunov mapping LA equals to its restriction to the symmetric set, S, i.e., ｜｜LA｜｜ =｜｜LA｜s｜｜ was proposed in [1]. In this paper, a method for numerical testing is provided first. Then, some recent progress on this conjecture is presented.

Upper semi-continuity of attractors for multivalued semi-flow under random perturbation

In this paper the upper semi-continuity of global attractors for multivalued semi-flows under random perturbation was studied. First, the existence of random attractors for multivalued random semi-flows was considered, then it was proved that the global attractors for multivalue semi-flows are the upper semi-continuity under random perturbation. This result can be used in the numerical approximation of multivalued semi-flows and non-autonomous perturbation of multivalued semi-flows.

THE RELATION OF DIMENSION, ENTROPY AND LYAPUNOV EXPONENT IN RANDOM CASE

We consider random systems generated by two-sided compositions of random surface diffeomorphisms, together with an ergodic Borel probability measure μ. Let D（μω） be its dimension of the sample measure, then we prove a formula relating D（μω） to the entropy and Lyapunov exponents of the random system, where D （μω） is dimHμω, dimBμm, or dimBμm.

EXISTENCE OF OPTIMAL STRONG PARTIALLY BALANCED DESIGNS

A strong partially balanced design SPBD（v, b, k; λ,0） whose b is the maximum number of blocks in all SPBD（v, b, k; λ, 0）, as an optimal strong partially balanced design, briefly OSPBD（v, k, λ） is studied. In investigation of authentication codes it has been found that the strong partially balanced design can be used to construct authentication codes. This note investigates the existence of optimal strong partially balanced design OSPBD（v, k, 1） for k = 3 and 4, and shows that there exists an OSPBD（v, k, 1） for any v ≥ k.

The Artinianness of Local Cohomology Modules

In this paper, let （R, m） be a Noetherian local ring, I lohtain in R an ideal, M and N be two finitely generated modules. Firstly, we study the properties of HI^t（M）, t = f-depth（I, M） and discuss the relationship between the Artinianness of HI^i（M, N） and the Artinianness of HI^i（N）. Then, we get that HI^d（M, N） is I-cofinite, if （R, m） is a d-dimensional Gorenstein local ring.

A THEOREM ON THE CONVEXITY OF PLANAR PARAMETRIC CURVES OF DEGREE N

The main result of this paper is a theorem about the convexity of curves of degree n on a plane. As its application ,we obtained a sufficient condition that a space curve of degree n in R^3 has no singularity points and staying points.

A SUBCLASS OF M1 -SPACES

In this paper,We defined M1^#-space,in some meaning,it is a dual concept of M1^#-space. We proved that Metrizable→M1^#→M1.

ON A QUESTION OF LASNEV SPACE

In this note we give a new characterization of Lasnev spaces in terms of g-functions, which answers a question about lasnev spaces raised by J.Nagata.

A NOTE ON ASSOCIATED GRADED RINGS OF IDEALS HAVING HIGHER ANALYTIC DEVIATION

In this note,we will generalize some results about the Cohen-Macaulaymess and Goronsteinness of Rees rings and associated graded rings of ideals having higher analytic deviation.

The Zero-divisor Graphs of Abelian Regular Rings

We introduce the zero-divisor graph for an abelian regular ring and show that if R,S are abelian regular, then (K0(R),[R])≌(K0(S),[S]) if and only if they have isomorphic reduced zero-divisor graphs. It is shown that the maximal right quotient ring of a potent semiprimitive normal ring is abelian regular, moreover, the zero-divisor graph of such a ring is studied.