T0-SEPARATION IN TOPOLOGICAL CATEGORIES

R.-E. Hoffmann [5,6] has introduced the notion of an (E,M)-universally topological functor, which provides a categorical characterization of the T₀-separation axiom of general topology. In this paper, we characterise these functors in terms of the unique extension of structure functors defined on the subcategory of “separated” objects (of the domain category). This, in turn, leads to a solution of some problems due to G.C.L. Brümmer [1,2]. Other results include a generalization of L. Skula's characterization of the bireflective subcategories of Top [10].     

Synchronized and desynchronized E0L forms

In this paper we investigate some basic properties of synchronized and desynchronized E0L forms. Several open problems concerning those forms (and their connection to grammar forms) are solved.     

Extension of two theorems of Payne to some nonlinear Dirichlet problems

In this paper we prove that under certain convexity and symmetry assumptions on a domain in the plane any positive solutionu, of Δu+λf(u)=0, in,D,u=0 on ?D has only one interior critical point. This extends results of L. E. Payne [1].     

On ϵ productions for terminals in E0L forms

When working with E0L forms, equality of languages and of language families has traditionally been considered modulo the empty word ? to avoid trivial but cumbersome distinctions of cases. Despite this fact, the role of ?-productions is often significant in L form theory particular, it has previously been shown that vomplete forms must have ?-productions We strengthen this result by proving that vomplete forms must even have ?-productions for nonterminals. Based on this theorem we establish that there are E0L forms with the property that any form equivalent E0L form must generate the empty word. Thus, despite the fact that we define equality of languages modulo ?, we are still unable to ignore the presence of the empty word in languages when studying L forms. The proof of our main theorem is based on a number of lemmas which allow to show that certain E0L forms are not form equivalent. In view of the difficulty of proving or disproving form equivalence of arbitrary E0L forms (conjectured to be undecidable) these lemmas may well be of independent interest.     

Centered forms for functions in several variables

R. E. Moore [3] has introduced the centered form of a rational function f for obtaining good and easily computable approximations which include the exact range of f over an interval X. Moore's definition is implicit, while explicit formulas for the centered form are given in [8] and [9]. In [9], centered forms of higher order for functions of one variable are developed which lead to better estimations than the centered forms defined originally. In this paper, centered forms of higher order for rational functions in several variables are explicitly defined. They also give better approximations than the centered forms defined originally.     

非退化扩散过程的极性与相交性

本文讨论非退化扩散过程的极性，得到了几个较好的充分条件，它可看作[1]的进一步深化，此外，我们将这些结果用来研究两个独立的非退化扩散过程的相交性，得到了一些有意思的结果。     

Hypervarieties of a given type

In this paper we consider the notions of hyperidentities and hypervarieties of a given type , without nullary operations, originated by J. Aczel [1], V. D. Belousov [2], W. D. Neumann [12] and W. Taylor [21]. Solid varieties are defined. Their equations correspond to hyperidentities and they form a complete sublattice of the lattice L() of all varieties of type . A completeness theorem for hyperidentities is formulated in analogue to G. Birkhoff [3]. The technique of weak isomorphisms, introduced by E. Marczewski and A. Goetz [7] assists us in partially answering a problem of W. Taylor (Problem 4, [21]).Presented by Ivo Rosenberg.This work was done while the first author was visiting the University of Kaiserslautern, under the auspices of the Alexander von Humboldt Foundation.As a part of this paper was done during the second author's visit to La Trobe University, the financial assistance by ARGS grant B 85154851 and by the DFG is gratefully acknowledged.     

Compact and precompact sets in asymmetric locally convex spaces

The aim of the present paper is to study precompactness and compactness within the framework of asymmetric locally convex spaces, defined and studied by the author in [S. Cobza?, Asymmetric locally convex spaces, Int. J. Math. Math. Sci. 2005 (16) (2005) 2585-2608]. The obtained results extend some results on compactness in asymmetric normed spaces proved by [L.M. García-Raffi, Compactness and finite dimension in asymmetric normed linear spaces, Topology Appl. 153 (2005) 844-853], and [C. Alegre, I. Ferrando, L.M. García-Raffi, E.A. Sánchez-Pérez, Compactness in asymmetric normed spaces, Topology Appl. 155 (6) (2008) 527-539].     

A note on Weak-Type Interpolation and Function Spaces

This paper is concerned with an interpolation theorem for operatorsof generalized weak-type on rearrangement invariant spaces.As a tool, generalized average operators of D. W. Boyd, P. L.Butzer and F. Fehér, and L. Maligranda are employed.The theorem contains a result of D. W. Boyd [1] for Lebesguespaces and fills in a gap left by papers of E. M. Semenov [6]and M. Zippin [9].     

Estimates for generalized derivatives of quasipolynomials from Muntz system

L. Schwartz has obtained estimates for coefficients of quasipolynomials from Muntz system. In this paper we obtain exact estimates for generalized derivatives of such quasipolynomials on the interval [0, 1].     

Ein Homomorphiesatz und verwandte Operatoren in topologischen Vektorräumen

The following homomorphism theorem is proved: Let E be a sequentially complete topological vector space and let SL(E) be a certain bounded endomorphism on E. (I-S)L(E) is an open map if and only if (I-S)(E) is closed in E. The proof is based on the method of verwandte Operatoren introduced by Pietsch [6].     

Distinguished Completion of a Direct Product of Lattice Ordered Groups

The distinguished completion E(G) of a lattice ordered group G was investigated by Ball [1], [2], [3]. An analogous notion for MV-algebras was dealt with by the author [7]. In the present paper we prove that if a lattice ordered group G is a direct product of lattice ordered groups G _i (i I), then E(G) is a direct product of the lattice ordered groups E(G _i). From this we obtain a generalization of a result of Ball [3].     

Inclusion of the roots of a polynomial based on Gerschgorin's theorem

Summary In this note a new companion matrix is presented which can be interpreted as a product of Werner's companion matrices [13]. Gerschgorin's theorem yields an inclusion of the roots of a polynomial which is best in the sense of [4] and generalizes a result of L. Elsner [5]. This inclusion is better than the one due to W. Börsch-Supan in [1].Dedicated to Professor E. Stein on the occasion of his 60th birthday.     

赋β-范空间中单位球面间的等距算子的线性延拓

本文得到了等距映射的线性延拓的一般结果:设E,F是赋范(或β-严格凸赋β-范)线性空间,若V_0:S_1(E)→S_1(F)是等距,且对任意的x,y∈S_1(E),有‖V_0x-|(?)|V_0y‖≤‖x-|(?)|y‖,(?)∈R,则V_0必可延拓到全空间上等距算子(或线性等距算子)。特别,当E,F是赋范线性空间,V_0是满射或F为严格凸空间时,则V_0必可延拓为全空间的线性等距算子,从而推广了文[3～5]中的相应结果。     

Concentration factors for functions with harmonic bounded mean variation

We discuss determination of jumps for functions with generalized bounded variation. The questions are motivated by A. Gelb and E. Tadmor [1], F. Móricz [5] and [6] and Q. L. Shi and X. L. Shi [7]. Corollary 1 improves the results proved in B. I. Golubov [2] and G. Kvernadze [3]. Supported by NSFC 10671062.     

Classification of Casorati ideal Lagrangian submanifolds in complex space forms

In this paper, using optimization methods on Riemannian submanifolds, we establish two improved inequalities for generalized normalized δ-Casorati curvatures of Lagrangian submanifolds in complex space forms. We provide examples showing that these inequalities are the best possible and classify all Casorati ideal Lagrangian submanifolds (in the sense of B.-Y. Chen) in a complex space form. In particular, we generalize the recent results obtained in G.E. Vîlcu (2018) [34].     

权为任意正实数的Poincare级数（II）解析的情形

设ｒ为一个正实数，１＜ｒ＜２，是一个Ｈ－群，υ：Γ→Ｃ是一个乘子系（定义见文［８］）．本文在［８］的基础上讨论了Ｐｏｉｎｃａｒｅ级数的存在性．令Ｐ＿（ｎｒ）（ｚ，υ，Ａ＿ｊ，Γ，ｋ＿ｊ）＝Ｐ＿（ｎｒ）（ｚ，０，υ，Γ，ｋ＿ｊ）．这里Ｐ＿（ｎｒ）（ｚ，ｓ，Ａ＿ｊ，Γ，ｋ＿ｊ）如文［８］中定义．我们有：定理｛Ｐ＿（ｎｒ）（ｚ，υ，Ａ＿ｊ，Γ，ｋ＿ｊ）｝ｎ＋ｋ＿Ｋ＞０是群Γ的，权为ｒ的具有乘子系υ的全纯歧点型模形式，且它们张成歧点型模形式所成的空间．应用这个结果，我们证明了一些模形式的性质并推导出一个重要的恒等式．该恒等式在半整权模形式的Ｆｏｕｒｉｅｒ系数估计中有极重要的地位．     

<Emphasis Type="Italic">G</Emphasis>-projectable and Λ-projectable binary linear block codes

The binary [24,12,8] Golay code has projection O onto the quaternary [6,3,4] hexacode [9] and the [32,16,8] Reed-Muller code has projection E onto the quaternary self-dual [8,4,4] code [6]. Projection E was extended to projection G in [8]. In this paper we introduce a projection, to be called projection Λ, that covers projections O, E and G. We characterise G-projectable self-dual codes and Λ-projectable codes. Explicit methods for constructing codes having G and Λ projections are given and several so constructed codes that have best known optimal parameters are introduced.      

Natural operations with projectable tangent valued forms on a fibred manifold

Summary Let p: EB be a fibred manifold. Then, we consider the sheaf (E)=(B)P(E) of (local) projectable tangent valued forms on E, where (B) is the sheaf of (local) differential forms on B andP(E) is the sheaf of (local) projectable vector fields on E. The Frölicher-Nijenhuis bracket makes (E) to be a sheaf of graded Lie algebras [18]. In this paper we study all natural R -bilinear operations on (E) which are of Frölicher-Nijenhuis type. By using the analytical method of [16], we prove that there is a three-parameter family of such operators on (E). As a consequence, we obtain a result on the unicity of the covariant differential of tangent valued forms and of the curvature associated with a given connection on E. All manifolds and mappings are assumed to be infinitely differentiable.This paper has been written during the author's visit at the Institute of Applied Mathematics «Giovanni Sansone». Florence, Italy. The author would like to thank ProfessorMarco Modugno for his kind hospitality and for stimulating discussions.     

Basic formulas and languages Part I. The theory

A general mathematical framework to deal with (the decidability status of) properties of derivations in E0L systems (forms) is developed. It is based on the theory of well-quasi-orders. This paper (the first of two parts) deals with the mathematical theory of the proposed approach.