Central Value Of Automorphic <Emphasis Type="Italic">L</Emphasis>-Functions

We prove a generalization to the totally real field case of the Waldspurger’s formula relating the Fourier coefficient of a half integral weight form and the central value of the L-function of an integral weight form. Our proof is based on a new interpretation of Waldspurger’s formula as a combination of two ingredients – an equality between global distributions, and a dichotomy result for theta correspondence. As applications we generalize the Kohnen–Zagier formula for holomorphic forms and prove the equivalence of the Ramanujan conjecture for half integral weight forms and a case of the Lindel?f hypothesis for integral weight forms. We also study the Kohnen space in the adelic setting. The first author was partially supported by NSF grant DMS-0070762. The second author was partially supported by NSF grant DMS-0355285. Received: July 2005 Accepted: August 2005     

Groups with small Dehn functions and bipartite chord diagrams

We introduce a new invariant of bipartite chord diagrams and use it to construct the first examples of groups with Dehn function n²log n. Some of these groups have undecidable conjugacy problem. Our groups are multiple HNN extensions of free groups. We show that n²log n is the smallest Dehn function of a multiple HNN extension of a free group with undecidable conjugacy problem. Both authors were supported in part by the NSF grants DMS 0245600 and DMS 0455881. In addition, the research of the first author was supported in part by the Russian Fund for Basic Research 05-01-00895, the research of the second author was supported in part by the NSF grant DMS 9978802 and the US-Israeli BSF grant 1999298. Received: February 2005; Revision: September 2005; Accepted: September 2005     

Root Decomposition of the Ternary Malcev Algebra <Emphasis Type="Italic">M</Emphasis><Subscript>8</Subscript>

A root decomposition is constructed of the simple eight-dimensional ternary Malcev algebra M ₈. In result, M ₈ is equipped with a structure of a Z ₃-graded ternary algebra.Original Russian Text Copyright © 2005 Pozhidaev A. P.The author was supported by the Russian Science Support Foundation and partially by the Russian Foundation for Basic Research (Grant 05-01-00230).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 901–906, July–August, 2005.     

Extension of Abel's Lemma with <Emphasis Type="Italic">q</Emphasis>-Series Implications

In previous work arising from the study of Ramanujan's Lost Notebook, a new Abel type lemma was proved. In this paper, we discuss extensions of this lemma and use it to prove many q-series identities. The first author was partially supported by NSF grant DMS–0200047. The second author was partially supported by FCT, Portugal, through program POCTI. 2000 Mathematics Subject Classification:Primary—33D15; Secondary—05A30     

The Basis Digraphs of <Emphasis Type="Italic">p</Emphasis>-schemes

It is proved that association schemes with bipartite basis graphs are exactly 2-schemes. This result follows from a characterization of p-schemes for an arbitrary prime p in terms of basis digraphs. Second author work was partially supported by RFFI Grants 07-01-00485, 08-01-00379 and 08-01-00640. First author was visiting the Euler Institute of Mathematics, St. Petersburg, Russia during the time a part of this paper was written and he thanks the Euler Institute for its hospitality     

Averaging Special Values of Dirichlet <Emphasis Type="Italic">L</Emphasis>-Series

In this paper we derive estimates for weighted averages of the special values of Dirichlet L-series which generalize similar estimates of David and Pappalardi [1]. The author is partially supported by NSF grant DMS-0090117. 2000 Mathematics Subject Classification: Primary–11M06; Secondary–11G05     

Trace and Transfer Maps in the Algebraic K -Theory of Spaces

We prove that the composition of the A-theory transfer with the trace map to stable homotopy is weakly homotopic to the Becker–Gottlieb transfer. This shows that the Waldhausen splitting A(*) ≃ Q (S⁰) × Wh(*) of A-theory into stable homotopy and the Whitehead space is natural with respect to transfer maps. (Received: September 2003) Christopher L. Douglas - The author was partially supported by a scholarship from the Rhodes Trust.     

A New View on Fuzzy Hypermodules

We describe the relationship between the fuzzy sets and the algebraic hyperstructures. In fact, this paper is a continuation of the ideas presented by Davvaz in （Fuzzy Sets Syst., 117： 477- 484, 2001） and Bhakat and Das in （Fuzzy Sets Syst., 80： 359-368, 1996）. The concept of the quasicoincidence of a fuzzy interval value with an interval-valued fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of a fuzzy point in fuzzy sets. By using this new idea, the concept of interval-valued （α,β）-fuzzy sub-hypermodules of a hypermodule is defined. This newly defined interval-valued （α,β）-fuzzy sub-hypermodule is a We shall study such fuzzy sub-hypermodules and sub-hypermodules of a hypermodule. generalization of the usual fuzzy sub-hypermodule. consider the implication-based interval-valued fuzzy     

On the first homology of automorphism groups of manifolds with geometric structures

Hermann and Thurston proved that the group of diffeomorphisms with compact support of a smooth manifold M which are isotopic to the identity is a perfect group. We consider the case where M has a geometric structure. In this paper we shall survey on the recent results of the first homology of the diffeomorphism groups which preserve a smooth G-action or a foliated structure on M. We also work in Lipschitz category. This research was partially supported by Grant-in-Aid for Scientific Research (No. 16540058), Japan Society for the Promotion of Science. This research was partially supported by Grant-in-Aid for Scientific Research (No. 14540093), Japan Society for the Promotion of Science.     

Banaschewski’s theorem for generalized <Emphasis Type="Italic">MV</Emphasis>-algebras

A generalized MV-algebra A is called representable if it is a subdirect product of linearly ordered generalized MV-algebras. Let S be the system of all congruence relations ϱ on A such that the quotient algebra A/ϱ is representable. In the present paper we prove that the system S has a least element. This work was supported by Science and Technology Assistance Agency under Contract No AVPT-51-032002. The work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information (grant I/2/2005).     

Collapsing to Riemannian manifolds with boundary and the convergence of the eigenvalues of the Laplacian

We prove that the eigenvalues of the Laplacian acting on functions converge to those of the limit manifold for a special collapsing family of closed Riemannian manifolds without curvature bounds. The proof uses L ²-analysis.Dedicated to Professor Hajime Urakawa on his sixtieth birthday.The author is partially supported by the Grant-in-Aid for Scientific Research No. 16740026 of the Japan Society for the Promotion of Science.     

Normal generation of line bundles of high degrees on smooth algebraic curves

We give necessary and sufficient conditions for non-special line bundles of degree2g — 2 and 2g — 3 being not normally generated. We also provide criteria for special line bundles of degreed > 2g — 6 being normally generated. This work was done under JSPS-KOSEF joint research program 1997. The first named author was partially supported by Grant-in-Aid for Scientific Research, the Ministry of Education, #10440051. The second named author was partially supported by BSRI(1998-015-D00023) and SNU(99-5-l-031). During the period when this paper was prepared for publication, the second named author was enjoying the hospitality of ICTP. The third named author was partially supported by Grant-in-Aid for Scientific Research, the Ministry of Education, #09640043.     

Hybrid Steepest Descent Methods for Zeros of Nonlinear Operators with Applications to Variational Inequalities

In this paper, the hybrid steepest descent methods are extended to develop new iterative schemes for finding the zeros of bounded, demicontinuous and φ-strongly accretive mappings in uniformly smooth Banach spaces. Two iterative schemes are proposed. Strong convergence results are established and applications to variational inequalities are given. In this research, the first author was partially supported by the National Science Foundation of China (10771141), Ph.D. Program Foundation of Ministry of Education of China (20070270004), and Science and Technology Commission of Shanghai Municipality (075105118). The third author was partially supported by Grant NSC 96-2628-E-110-014-MY3.     

Radical classes and weak radical mappings of GMV-algebras

We use the concept of generalized MV-algebra (GMV-algebra, in short) in the sense of Galatos and Tsinakis; the main tool in their investigation was a truncation construction. The relations between radical classes of GMV-algebras and radical classes of lattice ordered groups are investigated in the present paper. Further, we apply the truncation construction for dealing with weak retract mappings of GMV-algebras. This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence — Physics of Information (Grant I/2/2005).     

Robust game theory

We present a distribution-free model of incomplete-information games, both with and without private information, in which the players use a robust optimization approach to contend with payoff uncertainty. Our ``robust game' model relaxes the assumptions of Harsanyi's Bayesian game model, and provides an alternative distribution-free equilibrium concept, which we call ``robust-optimization equilibrium,' to that of the ex post equilibrium. We prove that the robust-optimization equilibria of an incomplete-information game subsume the ex post equilibria of the game and are, unlike the latter, guaranteed to exist when the game is finite and has bounded payoff uncertainty set. For arbitrary robust finite games with bounded polyhedral payoff uncertainty sets, we show that we can compute a robust-optimization equilibrium by methods analogous to those for identifying a Nash equilibrium of a finite game with complete information. In addition, we present computational results. The research of the author was partially supported by a National Science Foundation Graduate Research Fellowship and by the Singapore-MIT Alliance. The research of the author was partially supported by the Singapore-MIT Alliance.     

Harmonic Functions,Entropy, and a Characterization of the Hyperbolic Space

Let (M ⁿ ,g) be a compact Riemannian manifold with Ric ≥−(n−1). It is well known that the bottom of spectrum λ ₀ of its universal covering satisfies λ ₀≤(n−1)²/4. We prove that equality holds iff M is hyperbolic. This follows from a sharp estimate for the Kaimanovich entropy. The author was partially supported by NSF Grant 0505645.     

Visible surgery, four-dimensionals-cobordisms and related questions in geometric topology

The visible surgery theory of M. Weiss is used to complete the topological classification of four-dimensionals-cobordisms between three-dimensional spherical spaceforms. Applications to various questions concerning pseudo-isotopies of 3-manifolds, computations of the simple Wall groups of finite periodic groups, and inductive detection of self-homeomorphisms of manifolds are also discussed.The first named author was partially supported by a grant from the Louisiana Board of Regents and National Science Foundation Grants DMS 89-01583 and 91-01575, and the second named author was partially supported by National Science Foundation Grants DMS 86-02543, 89-02622 and 91-02711.     

Irreducibility of the Igusa tower

We shall give a simple （basically） the Igusa tower over Shimura varieties of PEL purely in characteristic p proof of the irreducibility of type. Our result covers Shimura variety of type A and type C classical groups, in particular, the Siegel modular varieties, the Hilbert-Siegel modular varieties, Picard surfaces and Shimura varieties of inner forms of unitary and symplectic groups over totally real fields.     

On the equivalence of nonlinear complementarity problems and least-element problems

Strictly pseudomonotoneZ-maps operating on Banach lattices are considered. Equivalence of complementarity problems and least-element problems is established under certain regularity and growth conditions. This extends a recent result by Riddell (1981) for strictly monotoneZ-maps to the pseudomonotone case. Some other problems equivalent to the above are discussed as well.This work was partially supported by the National Science Council under grant NSC 82-0208-M-110-023.Corresponding author.     

On a cancellation rule for subdirect products of lattice ordered groups and of <Emphasis Type="Italic">GMV</Emphasis>-algebras

The notion of internal subdirect decomposition can be defined in each variety of algebras. In the present note we prove the validity of a cancellation rule concerning such decompositions for lattice ordered groups and for GMV-algebras. For the case of groups, this cancellation rule fails to be valid. This work was partially supported by the Slovak Academy of Sciences via the project Center of Excellence — Physics of Information, Grant I/2/2005.