On Spacetime, Points, and Bare Particulars

In his paper Bare Particulars, T. Sider claims that one of the most plausible candidates for bare particulars are spacetime points. The aim of this paper is to shed light on Sider’s reasoning and its consequences. There are three concepts of spacetime points that allow their identification with bare particulars. One of them, Moderate structural realism, is considered to be the most adequate due its appropriate approach to spacetime metric and moderate view of mereological simples. However, it pushes the Substratum theory to dismiss primitive thisness as the only identity condition for bare particulars, but the paper argues that such elimination is a legitimate step.     

范德蒙德行列式与多项式的不动点

以范德蒙德行列式为工具,得到关于多项式不动点的两个新结论,以及线性代数中某已知结论的一个新证明,另外提供实例说明多项式不动点的应用．     

Permutation Diagrams, Fixed Points and Kazhdan-Lusztig R-Polynomials

In this paper, we give an algorithm for computing the Kazhdan-Lusztig R-polynomials in the symmetric group. The algorithm is described in terms of permutation diagrams. In particular we focus on how the computation of the polynomial is affected by certain fixed points. As a consequence of our methods, we obtain explicit formulas for the R-polynomials associated with some general classes of intervals, generalizing results of Brenti and Pagliacci. Received May 13, 2005     

关于Orlicz空间LM*(0,1)中函数的LO点、LB点与MLO点

Some relationships among LO, LB and MLO points of Functions in L_M^*(0,L) have been investigated in more detail in this paper, thus improving the corresponding principal results of Salehov's.     

Equiangular Points

Apoint T is an equiangular point of a collection of localized vectors if all of them are seen from T at an equal oriented angle. It is proved that almost each planar triple of vectors with fixed origins (not all of which coincide) has an equiangular point. As a consequence, it is proved that if a planar triple of vectors has no equiangular points, then their projections to a certain axis are equal. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 299, 2003, pp. 162–168.     

Lattice Points, Dedekind Sums, and Ehrhart Polynomials of Lattice Polyhedra

Abstract. Let σ be a simplex of R ^N with vertices in the integral lattice Z ^N . The number of lattice points of mσ (={mα : α ∈ σ}) is a polynomial function L(σ,m) of m ≥ 0 . In this paper we present: (i) a formula for the coefficients of the polynomial L(σ,t) in terms of the elementary symmetric functions; (ii) a hyperbolic cotangent expression for the generating functions of the sequence L(σ,m) , m ≥ 0 ; (iii) an explicit formula for the coefficients of the polynomial L(σ,t) in terms of torsion. As an application of (i), the coefficient for the lattice n -simplex of R ⁿ with the vertices (0,. . ., 0, a _j , 0,. . . ,0) (1≤ j≤ n) plus the origin is explicitly expressed in terms of Dedekind sums; and when n=2 , it reduces to the reciprocity law about Dedekind sums. The whole exposition is elementary and self-contained.     

Lattice Points, Dedekind Sums, and Ehrhart Polynomials of Lattice Polyhedra

   Abstract. Let σ be a simplex of R ^N with vertices in the integral lattice Z ^N . The number of lattice points of mσ (={mα : α ∈ σ}) is a polynomial function L(σ,m) of m ≥ 0 . In this paper we present: (i) a formula for the coefficients of the polynomial L(σ,t) in terms of the elementary symmetric functions; (ii) a hyperbolic cotangent expression for the generating functions of the sequence L(σ,m) , m ≥ 0 ; (iii) an explicit formula for the coefficients of the polynomial L(σ,t) in terms of torsion. As an application of (i), the coefficient for the lattice n -simplex of R ⁿ with the vertices (0,. . ., 0, a _j , 0,. . . ,0) (1≤ j≤ n) plus the origin is explicitly expressed in terms of Dedekind sums; and when n=2 , it reduces to the reciprocity law about Dedekind sums. The whole exposition is elementary and self-contained.     

Fixed Points,Continuous Selections,and Existence of Solution of Optimization-Related Problems

We propose a definition of a generalized type of Knaster–Kuratowski–Mazurkiewicz (KKM) mappings, called a weak T-KKM mapping, and a corresponding weak KKM property. A new extension of the Fan–Glicksberg fixed-point theorem is established. Sufficient conditions for the existence of a continuous selection, a fixed point of a composition, and a coincidence point are also provided. Then, we use the obtained results to study the existence of solutions to various optimization-related problems. Discussions and detailed examples are included as well to compare our results with existing ones and to explain their advantages in many situations.     

Saddle Points and Pareto Points in Multiple Objective Programming

In this paper relationships between Pareto points and saddle points are studied in convex and nonconvex multiple objective programming. The analysis is based on partitioning the index sets of objectives and constraints and splitting the original problem into subproblems having a special structure. The results are based on scalarizations of multiple objective programs and related linear and augmented Lagrangian functions. In the nonconvex case, a saddle point characterization of Pareto points is possible under assumptions that guarantee existence of Pareto points and stability conditions of single objective problems. Essentially, these conditions are not stronger than those in analogous results for single objective programming.This research was partially supported by ONR Grant N00014-97-1-784AMS Subject Classification: 90C29, 90C26     

局部FC-空间上的几乎不动点和不动点

利用古典的KKM原理的开[闭]形式得到FC-空间上的KKM型定理并给出局部FC-空间上的上[下]半连续映射的几乎不动点定理,最后给出在局部FC-空间上具有闭值且其值为FC-子空间的上半连续映射的不动点定理.     

Points of local nonconvexity,clear visibility,and starshaped sets in Rd

Let S be a compact, connected, locally starshaped set in R^d, S not convex. For every point of local nonconvexity q of S, define A_q to be the subset of S from which q is clearly visible via S. Then ker S = {conv A_q: q lnc S}. Furthermore, if every d+1 points of local nonconvexity of S are clearly visible from a common d-dimensional subset of S, then dim ker S = d.     

Stochastic Breakeven Points

When the probability of a negative unit contribution is non-negligible, desirable and undesirable data configurations may map into the same breakeven point. In the general case, the decision relevance of a breakeven point probability distribution is rather obscure. Assuming bivariate normality, with a "small" probability of a negative denominator, then an approximation procedure based on the Geary-Hinkley transformation is a convenient and powerful means of obtaining information about the breakeven point probability distribution. Hence, for practical purposes it may be unnecessary to resort to computer simulation or to numerical integration of the complex exact density function of the breakeven point.     

多目标规划的ak—较多有效点与ak—较多最优点

在[1]中,作引入了多目标规划的较多有效点及较多最优点的概念,并讨论了它们的性质,本首次提出了ak-较多有效点与ak-较多最优点的概念,并讨论了ak-较多有效点,ak-较多最优点、ak-较多有效解,ak-较多最优解的相关性质。     

Gyration Numbers, Fixed Points and K2

We give a formula for the Boyle-Krieger gyration numbers ofan involution in the symmetry group Aut (_A) of an even subshiftof finite type _A in terms of the number of fixed points of in the periodic orbits of _A. A relationship between gyrationnumbers, the algebraic K-theory group K₂, and the tame symbolis also discussed.     

不动点在讨论驻点存在性问题中的应用

本文通过建立不动点与驻点之间的关系，从而利用不动点的存在性来确定函数驻点的存在性。     

The Density of Rational Points on Non-Singular Hypersurfaces, I

For any n 3, let F Z[X₀, ..., X_n] be a form of degree d 5that defines a non-singular hypersurface X Pⁿ. The main resultin this paper is a proof of the fact that the number N(F; B)of Q-rational points on X which have height at most B satisfies , for any > 0. The implied constantin this estimate depends at most upon d, and n. New estimatesare also obtained for the number of representations of a positiveinteger as the sum of three dth powers, and for the paucityof integer solutions to equal sums of like polynomials. 2000Mathematics Subject Classification 11G35 (primary), 11P05, 14G05(secondary).     

Images,Fixed Points and Vector Extremum Problems

Based on recent results on image space analysis, the paper aims at describing a fixed point approach to vector optimization problems. Possible extensions to the bi-level vector optimization are discussed.     

一类解析函数族的极值点与支撑点

设Ω={f(z):f(z)在|z|<1内解析，f(z)=z+∑^{+∞}_{n=2}{a_n z^n}, a_n是实数,∑^{+∞}_{n=2}{n|a_n|≤1}}.该文找出了函数族Ω的极值点与支撑点.       

Extreme Points and Strongly Extreme Points of Musielak-Orlicz Sequences Spaces

Criteria for extreme points and strongly extreme points in Musielak-Orlicz sequence spaces, equipped with both the Luxemburg norm and the Orlicz norm, are given.     

Lattice Points in Convex Bodies with Planar Points on the Boundary

 An asymptotic formula is proved for the number of lattice points in large threedimensional convex bodies. In contrast to the usual assumption the Gaussian curvature of the boundary may vanish at non-isolated points. It is only assumed that the second fundamental form vanishes at isolated points where the tangent plane is rational and some ellipticity condition holds.