Global optimization problems and domain reduction strategies

In this paper we discuss domain reduction strategies for global optimization problems with a nonconvex objective function over a bounded convex feasible region. After introducing a standard domain reduction and its iterated version, we will introduce a new reduction strategy. Under mild assumptions, we will prove the equivalence between the new domain reduction and the iterated version of the standard one, allowing a new interpretation of the latter and a new way of computing it. Finally, we prove that any “reasonable” domain reduction strategy is independent of the order by which variables are processed.     

An intuitionistic fixed point theory

In this article we prove that a certain intuitionistic version of the well-known fixed point theory is conservative over for almost negative formulas. Received October 24, 1995     

A HEAT KERNEL VERSION OF HARDY’S THEOREM FOR THE LAGUERRE HYPERGROUP

In this article, we prove a heat kernel version of Hardy’s theorem for the Laguerre hypergroup.     

A version of Brauer’s theorem for integer central functions

In this article we prove an effective version of the classical Brauer’s Theorem for integer class functions on finite groups.      

On a kähler version of cheeger-gromoll-perelman's soul theorem

In this note, we will prove a Kähler version of Cheeger-Gromoll-Perelman's soul theorem, only assuming the sectional curvature is nonnegative and bisectional curvature is positive at one point.     

The Core of a Locally Extended Affine Lie Algebra

Locally extended affine Lie algebras are a general version of extended affine Lie algebras. In this article, we completely describe the structure of the core of a locally extended affine Lie algebra. We prove that the core of a locally extended affine Lie algebra is a direct limit of Lie tori.     

Graded decomposition numbers for cyclotomic Hecke algebras

In recent joint work with Wang, we have constructed graded Specht modules for cyclotomic Hecke algebras. In this article, we prove a graded version of the Lascoux-Leclerc-Thibon conjecture, describing the decomposition numbers of graded Specht modules over a field of characteristic zero.     

Finitary isomorphism of some renewal processes to Bernoulli schemes

Using the marker and filler methods of Keane and Smorodinsky, we prove that entropy is a complete finitary isomorphism invariant for r-processes. It is conjectured that entropy is a complete finitary isomorphism invariant for finitary factors of Bernoulli schemes. We present a weaker version of this conjecture with hope that its proof is more attainable with present methods. In doing so, we define a one-way finitary isomorphism and prove one-way finitary results for random walks. We will also extend the marker and filler methods of Keane and Smorodinsky to a class of countable state processes.     

Finiteness of real quadratic fields which admit positive integral diagonal septanary universal forms

In this paper, we will prove if D is large enough, there are no positive integral diagonal septanary universal quadratic forms over . Received: 13 November 1997 / Revised version: 17 November 1998     

Canonical Euler-Lagrange equations and Jacobi's theorem on regular surfaces

In this article we establish conditions under which canonical variables can be defined for a variational problem defined on a geometric (compact) surface. Also, we show the form the corresponding Euler-Lagrange equations assume once we rewrite them in terms of such canonical variables. Furthermore, we prove a version of Jacobi's theorem generalizing the univariate standard version of this theorem. The main results are applied to the conformal Gauss curvature functional.     

Stochastic Monge–Kantorovich problem and its duality

In this article, we prove the existence of a stochastic optimal transference plan for a stochastic Monge–Kantorovich problem by measurable selection theorem. A stochastic version of Kantorovich duality and the characterization of stochastic optimal transference plan are also established. Moreover, Wasserstein distance between two probability kernels is also discussed.     

A note on envelopes of homotopies

In this article, we deal with the notion of the envelopes of homotopies which is the generalized version of functional envelopes in discrete dynamical systems. We prove the stability for envelopes of homotopies in complete normed algebra and we get the stabilities of the derivation and the extended derivation for the notion in the spaces.     

Degeneration of weight spectral sequences

 A notion of morphism of semi-stable type is a higher dimensional analogue of semi-stable degeneration over the unit disc. For a proper surjective morphism of semi-stable type, the author constructed a cohomological mixed Hodge complex which gives a candidate of the limit of Hodge structures. In this article we define finite increasing filtrations on the cohomological mixed Hodge complex above and prove the E ₂ -degeneracy of the spectral sequences obtained from these filtrations. Received: 5 December 2000 / Revised version: 29 January 2002     

No minimally reasonable collective-choice process can be strategy-proof

In this paper I will prove that every collective-choice process fulfilling certain mild requirements - notably a version of Nondictatorship and a very weak unanimity-reduction condition - is manipulable: none is strategy-proof. Gibbard and Satterthwaite have each proved a similar result just for resolute processes - ones yielding only single-member choice sets. My theorem does not assume resoluteness, which I criticize as an unreasonable requirement.     

Superconvergence and a posteriori error estimation for triangular mixed finite elements

Summary. In this paper,we prove superconvergence results for the vector variable when lowest order triangular mixed finite elements of Raviart-Thomas type [17] on uniform triangulations are used, i.e., that the -distance between the approximate solution and a suitable projection of the real solution is of higher order than the -error. We prove results for both Dirichlet and Neumann boundary conditions. Recently, Duran [9] proved similar results for rectangular mixed finite elements, and superconvergence along the Gauss-lines for rectangular mixed finite elements was considered by Douglas, Ewing, Lazarov and Wang in [11], [8] and [18]. The triangular case however needs some extra effort. Using the superconvergence results, a simple postprocessing of the approximate solution will give an asymptotically exact a posteriori error estimator for the -error in the approximation of the vector variable. Received December 6, 1992 / Revised version received October 2, 1993     

广义凸性的几个问题

本文讨论在可微条件下严格伪凸和Ortega-Rheinbold伪凸和拟凸的关系。     

A new one-step iterative scheme for approximating common fixed points of two multivalued nonexpansive mappings

In this paper, we introduce a new one-step iterative process to approximate the common fixed points of two multivalued nonexpansive mappings. We will also prove a strong convergence theorem in a uniformly convex Banach space under the multivalued version of so-called Condition (A′).     

Logarithmic Vanishing Theorems and Arakelov–Parshin Boundedness for Singular Varieties

This article can be divided into two loosely connected parts. The first part is devoted to proving a singular version of the logarithmic Kodaira–Akizuki–Nakano vanishing theorem of Esnault and Viehweg in the style of Navarro-Aznar et al. This in turn is used to prove other vanishing theorems. In the second part, these vanishing theorems are used to prove an Arakelov–Parshin type boundedness result for families of canonically polarized varieties with rational Gorenstein singularities.     

An algebraic construction of the ring of¶piecewise polynomial functions

In this note we will prove an algebraic characterization of the piecewiese polynomial functions of a real ℚ-algebra A. This characterization is related to the realm of investigations concerning the Pierce–Birkhoff conjecture. Received: 23 June 1997 / Revised version: 26 May 1998