Linear congruence relations for 2-adic L-series at integers

In the paper we find a further generalization of congruences of the K. Hardy and K. S. Williams [5] type which seems to be a full generalization of congruences of G. Gras [4]. Moreover we extend results of [5], [7], [8], [9] and in part of [6]. We apply ideas and methods of [2], [7] and [9].     

Ingham-Beurling type theorems with weakened gap conditions

Completing a series of works begun by Wiener [34], Paley and Wiener [28] and Ingham [9], a far-reaching generalization of Parseval"s identity was obtained by Beurling [4] for nonharmonic Fourier series whose exponents satisfy a uniform gap condition. Later this gap condition was weakened by Ullrich [33], Castro and Zuazua [5], Jaffard, Tucsnak and Zuazua [11] and then in [2] in some particular cases. In this paper we prove a general theorem which contains all previous results. Furthermore, applying a different method, we prove a variant of this theorem for nonharmonic Fourier series with vector coefficients. This result, partly motivated by control-theoretical applications, extends several earlier results obtained in [15] and [2]. Finally, applying these results we obtain an optimal simultaneous observability theorem concerning a system of vibrating strings. This revised version was published online in June 2006 with corrections to the Cover Date.     

Schensted Algorithms for Dual Graded Graphs

This paper is a sequel to [3]. We keep the notation and terminology and extend the numbering of sections, propositions, and formulae of [3].The main result of this paper is a generalization of the Robinson-Schensted correspondence to the class of dual graded graphs introduced in [3], This class extends the class of Y-graphs, or differential posets [22], for which a generalized Schensted correspondence was constructed earlier in [2].The main construction leads to unified bijective proofs of various identities related to path counting, including those obtained in [3]. It is also applied to permutation enumeration, including rook placements on Ferrers boards and enumeration of involutions.As particular cases of the general construction, we re-derive the classical algorithm of Robinson, Schensted, and Knuth [19, 12], the Sagan-Stanley [18], Sagan-Worley [16, 29] and Haiman's [11] algorithms and the author's algorithm for the Young-Fibonacci graph [2]. Some new applications are suggested.The rim hook correspondence of Stanton and White [23] and Viennot's bijection [28] are also special cases of the general construction of this paper.In [5], the results of this paper and the previous paper [3] were presented in a form of extended abstract.     

On stability of equilibrium of nonholonomic systems : PMM vol. 39, n 6, 1975, pp. 1135–1140

The problem of stability of motion of nonholonomic systems was first considered by Whittaker in [1], and developed in [2–7] et al. The most general results in investigating the stability of equilibrium of conservative nonholonomic systems and in clarifying the influence of the dissipative forces on this stability, were obtained in [5]. In the present paper we give a further generalization of the results obtained in [5].     

A note on linear θ-derivations on JB1-triples

In this paper we prove a generalization of the stability of the functional equation in the spirit of Hyers, Ulam and Rassias. Also we introduce the concept of linear θ-derivations on JB¹-triple, and prove the generalization of the stability of the functional equation in the spirit of Hyers, Ulam and Rassias of linear θ-derivations on JB¹-triple. For resent results see [1], [2], [3].     

A time dependent coupled system related to the tridimensional equations of a nematic liquid crystal

In this paper we prove some results about the existence, uniqueness and regularity of the solutions of a tridimensional variational approximated model for the Leslie's equations of an incompressible nematic liquid crystal (cf. [7]). This model was introduced in [1] where the bidimensional case is studied. Here we use the methods developed in [6], [4] and [8].     

A boolean transfer principle from L*-Algebras to AL*-Algebras

Just as Kaplansky [4] has introduced the notion of an AW*-module as a generalization of a complex Hilbert space, we introduce the notion of an AL*-algebra, which is a generalization of that of an L*-algebra invented by Schue [9, 10]. By using Boolean valued methods developed by Ozawa [6–8], Takeuti [11–13] and others, we establish its basic properties including a fundamental structure theorem. This paper should be regarded as a continuation or our previous paper [5], the familiarity with which is presupposed. MSC: 03C90, 03E40, 17B65, 46L10.     

Convex duality and the Skorokhod Problem. II

In this paper we consider Skorokhod Problems on polyhedral domains with a constant and possibly oblique constraint direction specified on each face of the domain, and with a corresponding cone of constraint directions at the intersection of faces. In part one of this paper we used convex duality to develop new methods for the construction of solutions to such Skorokhod Problems, and for proving Lipschitz continuity of the associated Skorokhod Maps. The main alternative approach to Skorokhod Problems of this type is the reflection mapping technique introduced by Harrison and Reiman [8]. In this part of the paper we apply the theory developed in part one to show that the reflection mapping technique of [8] is restricted to a slight generalization of the class of problems originally considered in [8]. We further illustrate the power of the duality approach by applying it to two other classes of Skorokhod Problems – those with normal directions of constraint, and a new class that arises from a model of processor sharing in communication networks. In particular, we prove existence of solutions to and Lipschitz continuity of the Skorokhod Maps associated with each of these Skorokhod Problems. Received: 17 April 1998 / Revised: 8 January 1999     

A generalization of results of P. Erdös,G. Katona,and D. J. Kleitman concerning Sperner's theorem

A result of Sperner [1] determining the maximal number of subsets of a given set, such that no one is included in the other, has been generalized and strengthened modifying the restrictive condition by Erdös [2], by Katona [3], and Kleitman [7], and by others [4, 5]. A different kind of generalization has been obtained by de Bruijn, Tenbergen, and Kruywijk [6] using the same restrictive condition but for more general entities than sets, namely, for systems in which the elements may occur more than once. That approach is fundamental for number-theoretical considerations since the totality of prime divisors of a given number (each considered with its multiplicity) is of that nature. In this paper we will generalize the results of [2] and [3, 7] in the sense of [6].     

Viscosity approximation methods for resolvents of accretive operators in Banach spaces

In this paper, we first prove a strong convergence theorem for resolvents of accretive operators in a Banach space by the viscosity approximation method, which is a generalization of the results of Reich [J. Math. Anal. Appl. 75 (1980), 287–292], and Takahashi and Ueda [J. Math. Anal. Appl. 104 (1984), 546–553]. Further using this result, we consider the proximal point algorithm in a Banach space by the viscosity approximation method, and obtain a strong convergence theorem which is a generalization of the result of Kamimura and Takahashi [Set-Valued Anal. 8 (2000), 361–374]. Dedicated to the memory of Jean Leray     

Certain Results Concerning the Iterative Function System

Invention of wavelets and fractals have revolutionized several areas of emerging technologies, especially image processing and scientific computing. The iterated function system [2-4,13,17,18,20,25,26,29], inverse problem of images [5,14-16] and wavelet-based numerical methods [6,7,10,19,22,23] are basic in-gredients of these exciting developments. The iterated function system and the collage theorem are among the basic mathematical tools which are consequences of the Banach contraction fixed point theorem. In one of the sections of this paper we have generalized these two theorems applying a generalization of the Banach contraction fixed point theorem due to Edelstein [11]. In the other section we have studied the inverse problem of images by the iterative function system with grey-level in the context of Besov space, extending a result of Forte and Vrscay [16].     

On the E-unitary covers for a Bruck semigroup

We give a characterization of theE-unitary covers for a Bruck semigroup, which is a generalization of Theorem 3 given in [1]. In a recent paper [1] we gave a characterization of theE-unitary covers for a Bruck semigroupB(T,α) whereT is a finite chain of groups, and now we give a characterization forB(T,α) whereT is any inverse semigroup. We use here the notations and the terminology of Petrich's book [2]. First we prove a Theorem which is more general than [[1], Theorem 2]. I wish to express my thanks to Dr. G. Pollák for his valuable advice.     

Combinatorial obstructions to the lifting of weaving diagrams

This paper deals with various connections of oriented matroids [3] and weaving diagrams of lines in space [9], [16], [27]. We encode the litability problem of a particular weaving diagramD onn lines by the realizability problem of a partial oriented matroid χ _D with2n elements in rank 4. We prove that the occurrence of a certain substructure inD implies that χD is noneuclidean in the sense of Edmonds, Fukuda, and Mandel [12], [14]. Using this criterion we construct an infinite class of minor-minimal noneuclidean oriented matroids in rank 4. Finally, we give an easy algebraic proof for the nonliftability of the alternating weaving diagram on a bipartite grid of 4×4 lines [16].     

Uniqueness results of meromorphic functions whose derivatives share four small functions

We prove an oscillation theorem of two meromorphic functions whose derivatives share four values IM. From this we obtain some uniqueness theorems, which improve the corresponding results given by Yang [16] and Qiu [10], and supplement results given by Nevanlinna [9] and Gundersen [3, 4]. Some examples are provided to show that the results in this paper are best possible.     

Multiplicity results for a class of quasilinear eigenvalue problems on unbounded domains

Using a recent result of Ricceri [10] we prove a multiplicity result for a class of quasilinear eigenvalue problems with nonlinear boundary conditions on an unbounded domain. Our paper completes previous results obtained by Carstea and Rădulescu [4], Chabrowski [1], [2], Kandilakis and Lyberopoulos [6] and Pflüger [7]. Received: 17 April 2007     

On maximally saturated graphs

Motivated by a well known theorem of Turán in [7], we prove a partition theorem. We also point out that each of the family of maximally saturated graphs is chromatically unique which is a generalization of a result in [5].     

On Standard Ideals

In the paper,we study a class of standard ideals which are more general than the m-primary standared ideals discussed in[2].We will prove an important equality concerning I-weak sequences;thus a generalization of the equality of [2] is established.     

亚纯函数微分多项式f~kQ[f]+P[f]的零点分布

文[4]对简单形式的微分多项式fkf’+a的零点分布进行了讨论,文[1]对一般形式的微分多项式fkQ[f]+P[f]的零点分布进行了讨论.但由于极点给证明带来的困难,这些工作主要是对整函数来做的.本文证明了任一满足δ(∞,f)>k+2ΓQ+3ΓP+2/2k+2ΓQ+1的超越亚纯函数f,微分多项式fkQ[f]+P[f]在不含f,Q[f]极点和P[f]零、极点的可数个圆盘并集之外有无穷多个零点,其中k≥3Γp+2,而ΓQ,ΓP分别是f的微分多项式Q[f],P[f]的权.文[1]和[2,4,6]中的结论是本文结论的特殊情况.     

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].     

Haruspicy 2: The anisotropic generating function of self-avoiding polygons is not D-finite

We prove that the anisotropic generating function of self-avoiding polygons is not a D-finite function—proving a conjecture of Guttmann [Discrete Math. 217 (2000) 167-189] and Guttman and Enting [Phys. Rev. Lett. 76 (1996) 344-347]. This result is also generalised to self-avoiding polygons on hypercubic lattices. Using the haruspicy techniques developed in an earlier paper [Rechnitzer, Adv. Appl. Math. 30 (2003) 228-257], we are also able to prove the form of the coefficients of the anisotropic generating function, which was first conjectured in Guttman and Enting [Phys. Rev. Lett. 76 (1996) 344-347].