Some properties of associated pseudoconnections

Pseudoconnections (or quasi connections) were defined as a generalization of linear connections by Y.-C. Wong in [14], and were developed mainly by Italian and Rumanian mathematicians. The purpose of this paper is to study some properties of a special type of pseudoconnections: the so-called associated pseudoconnections oginirating from linear connections in a very simple manner. In §1 we give a necessary and sufficient condition for a pseudoconnection to be associated, the in §2 we study the geodesics of an associated pseudoconnection. This notion has an immediate application in Finsler geometry, this is the theme of §3. Some questions connecting the curvature of associated pseudoconnections were studied by the author in [7].     

On the Modular Figure and Ford-Spheres

In §1 we study Figure 1 for variable h. In §2 and §3 this is combined with Ford-circles (Figure 2) and the choice h = 0 (Figure 3). In §4 a limit is evaluated. In §5 we treat Figure 5 (“Ford-circles inside the unit-circle”) and a technical application. In §6 contains various modular figures (Figures 7, 8, 9). §7 treats synchronous rotation of Figure 1 and Eoing from R² to R³; the rotating upper half-plane of C corresponds then to the unit-sphere. In §8 a sphere-packing on C is introduced. Finally in §9 a sphere-packing inside the unit-sphere arises.     

Character tables of commutative hecke algebras associated with exceptional weyl groups

The purpose of this paper is to calculate all the character tables of Hecke algebras associated with exceptional Weyl groups and their maximal parabolic subgroups when they are commutative. In the case when Weyl groups are of classical type, they are already known in [D.1] and [D.2]. In §1, we discuss the structure of Hecke algebras and in §2, we calculate all the character tables of these commutative Hecke algebras associated with exceptional Weyl groups.     

概率度量空间与映象的不动点定理

概率度量空间的概念首先由Menger[7]提出,以后许多人对这一空间的理论和应用曾进行过某些讨论(见[1-9])。本文的目的是进一步研究这一空间中映象的不动点定理。在本文的§2中,我们得出了一些新型的不动点定理,这些结果改进和加强了引文[2,3,8]中某些主要结果。     

Duality theorems for a new class of multitime multiobjective variational problems

In this work, we consider a new class of multitime multiobjective variational problems of minimizing a vector of functionals of curvilinear integral type. Based on the normal efficiency conditions for multitime multiobjective variational problems, we study duals of Mond-Weir type, generalized Mond-Weir-Zalmai type and under some assumptions of (??, b)-quasiinvexity, duality theorems are stated. We give weak duality theorems, proving that the value of the objective function of the primal cannot exceed the value of the dual. Moreover, we study the connection between values of the objective functions of the primal and dual programs, in direct and converse duality theorems. While the results in §1 and §2 are introductory in nature, to the best of our knowledge, the results in §3 are new and they have not been reported in literature.     

Tensor product of C-injective modules

The purpose of this paper is to calculate all the character tables of Hecke algebras associated with finite Chevalley groups of exceptional type and their maximal parabolic subgroups when they are commutative. In the case when the groups are of classical type, the character values of Hecke algebras are expressed by using the q-Krawtchouk polynomials and the q-Hahn polynomials (See [10] and [15]). On the other hand, the character tables of commutative Hecke algebras associated with exceptional Weyl groups and their maximal parabolic subgroups are given in [12]. In §1, we discuss the structure of Hecke algebras and in §2, we calculate all the character tables of these commutative Hecke algebras associated with finite Chevalley groups of exceptional type. Although some of them are well known, we include them for completeness     

On the Automorphism Group of a Free Pro-l Meta-abelian Group and an Application to Galois Representations

In § l of this article, we study group-theoretical properties of some automorphism group Ψ^* of the meta-abelian quotient § of a free pro-l group § of rank two, and show that the conjugacy class of some element of order two of Ψ^* is not determined by the action induced on the abelian quotient § of § in the case of § = 2. In § 2 we apply the results to the outer Galois representation § attached to the curve C deleted one point from an elliptic curve E, and give an example that §_c does not factor through the l-adic representation attached to E.     

多品种容量运输问题的位势法

运输问题有很广泛的应用,其解法也很多.做为多品种物资容量运输问题,尽管在现实中有极为广泛的应用,但对其算法讨论的却很少.从计算数学角度来看,用线性规划分解原则来处理它,明显是不适宜的;用图论方法解它,也有困难.为此,我们把位势法推广到多品种物资容量运输问题上,并相应地做了必要的理论讨论.     

Seminearrings,seminearfields and their semigroup-theoretical background

In this paper we deal with some basic properties of seminearrings (S,+,·), in particular with respect to multiplicative cancellativity (§2) and to seminearfields (§3, §4). All seminearrings of order 2 are listed in §5. In general, we do not assume that (S,+) is associative. Moreover, we present most of our results as consequences of corresponding statements on semigroups (S,·). Clearly, all results apply to semirings and nearrings, particularly to those with associative addition, and some of them will be new also in this context. Dedicated to Professor L. M. Gluskin on his 60th birthday     

方型锥上第一类Siegel域

<正> 记V为R~n中不包含直线的仿射齐性开凸锥(简称齐性锥),则C~n中点集■(V)={z∈C~n|Im(z)∈V}称为齐性锥V上第一类Siegel域,它仿射齐性.熟知齐性锥V上第一类Siegel域在解析等价下的分类即齐性锥在仿射等价下的分类.这方面已有结果为Vinberg关于仿射齐性自共轭锥的分类. 本文考虑方型锥,即这种齐性锥,它仿射等价于适合条件     

On pure uniform holomorphy in spaces of holomorphic germs

If E is a complex (DFC)-space (see § 2), we show that E leads to pure uniform holomorphy (see §2) if and only if its Fréchet dual space E′ is separable (see Theorem 1, where these two conditions have other eight equivalent ones). By using a theorem of Mujica (see §4), we consider the (DFC)-space K(K) of germs around K of holomorphic C-valued functions where K is a nonvoid compact subset of a complex metrizable locally convex space E, and ?(K) is endowed with the topology ?₀ obtained as an inductive limit of compact-open topologies (see §4). Not only Theorem 1 applies to ?(K), with E replaced by ?(K) in its statement, but also ?(K) leads to pure uniform holomorphy if and only if E is separable (see Theorem 2).     

Left ideals of polynomial rings in several indeterminates

We consider maximal left ideals L of the polynomial ring R[λ₁, …, λ_n], for R noncommutative. In §1 we reprove and generalize Resco's result that any maximal left ideal L is generated by ≤ n elements whenever R is simple Artinian, and obtain more precise information about the generators when R satisfies a PI. In many instances, fewer than n generators suffice; this is considered in §3, by means of various examples. In §2 we see by a straightforward argument that L has bounded height as a prime left ideal whenever R is a simple Pl-ring, but this does not- hold in general for R simple Artinian.     

关于“K类”准线性双曲型守恒律组整体解的研究

<正> 关于准线性双曲型守恒律组整体解的研究,其意义是许多人所熟知的.Diperna R.J.在文[1]中,利用Glimm J.格式证明了“K类”守恒律组之具有界变差初值的初值问题存在整体广义解.关于研究这类方程的意义,该文已经说明. 我们知道,对于方程式的情形,曾经用多种方法研究存在性问题,这不是为了改善证明方法,而是不同方法各自有不同实际意义.但是,迄今对于方程组,用Glimm J.格式几乎成了唯一的方法,其他只有对初值用阶梯函数逼近的方法有一些结果.     

The globally hyperbolic metric splitting for non-smooth wave-type space-times

We investigate a generalization of the so-called metric splitting of globally hyperbolic space-times to non-smooth Lorentzian manifolds and show the existence of this metric splitting for a class of wave-type space-times. The approach used is based on smooth approximations of non-smooth space-times by families (or sequences) of globally hyperbolic space-times. In the same setting we indicate as an application the extension of a previous result on the Cauchy problem for the wave equation.     

关于矩阵族稳定的(J)条件及其与Buchanan准则的关系

本文注意到矩阵族稳定的Kreiss定理和Buchanan准则不便于实际应用。文中(§2,§3)从Kreiss定理的豫解条件出发得到了至少对于四阶以下矩阵族较为实用的判别稳定性的(J)条件;并证明了对于其特征值赋套的上三角矩阵族,(J)条件与Buchanan准则的等价性。§4作为(J)条件的应用讨论了逼近于二维、三维波动方程的显式差分方程(其增长矩阵分别是三、四阶矩阵族),得到了稳定的充要条件。     

Geodesic connectedness in Gödel type space-times

In this paper we use a variational approach in order to prove the geodesic connectedness of some Gödel type space-times; moreover direct methods allow to prove the geodesic connectedness of the Gödel Universe. At last a result of geodesic completeness is given.     

Modal Meinongianism for Fictional Objects

Drawing on different suggestions from the literature, we outline a unified metaphysical framework, labeled as Modal Meinongian Metaphysics (MMM), combining Meinongian themes with a non-standard modal ontology. The MMM approach is based on (1) a comprehension principle (CP) for objects in unrestricted, but qualified form, and (2) the employment of an ontology of impossible worlds, besides possible ones. In §§1–2, we introduce the classical Meinongian metaphysics and consider two famous Russellian criticisms, namely (a) the charge of inconsistency and (b) the claim that naïve Meinongianism allows one to prove that anything exists. In §3, we have impossible worlds enter the stage and provide independent justification for their use. In §4, we introduce our revised comprehension principle: our CP has no restriction on the (sets of) properties that can characterize objects, but parameterizes them to worlds, therefore having modality explicitly built into it. In §5, we propose an application of the MMM apparatus to fictional objects and defend the naturalness of our treatment against alternative approaches. Finally, in §6, we consider David Lewis’ notorious objection to impossibilia, and provide a reply to it by resorting to an ersatz account of worlds.     

论G?del不完备性定理

The object of this expository paper is to disclose the real essential idea involved in G?del's imcompleteness theorem through a detailed analysis of the proof presented in Arbib's booklet. In §1 very extensive definitions have been given of the potential infinite and the real infinite, respectively. In §2 the general concept concerning types of infinite extension processes as well as the principle of relatively complete exhaustion have been expounded. In§3 a deeper analysis has been made of the well-known proof of G?del's imcompleteness theorem, thus leading to the conclusion that G?del's theorem is actually implied by the most general principle that any infinite process of lower type cannot exhaust and exhibit the whole content of the corresponding process with relatively higher type, where the words "exhaust" and "exhibit" may be given precise meanings in certain special cases including the case for G?del's arithmetic logic.     

e~(ax+bx~2)(a,b∈R)参数平面上的骚动区域

本文将参数（ａ，ｂ）平面分为七个区域，然后讨论在每一个区域中ｅａｘ＋ｂｘ２的不动点分布（§１）．在§２中，我们得到一个定理：在Ｄ∞１∪Ｄ∞Ｃ中ｅａｘ＋ｂｘ２是骚动的（在扩充意义下）．     

Vive la différence II. The Ax-Kochen isomorphism theorem

We show in §1 that the Ax-Kochen isomorphism theorem [AK] requires the continuum hypothesis. Most of the applications of this theorem are insensitive to set theoretic considerations. (A probable exception is the work of Moloney [Mo].) In §2 we give an unrelated result on cuts in models of Peano arithmetic which answers a question on the ideal structure of countable ultraproducts of ℤ posed in [LLS]. In §1 we also answer a question of Keisler regarding Scott complete ultrapowers of ℝ (see 1.18).