A Connection Between the Reticulation of a Ring of Quotients and the Localization Lattice of the Reticulation of a Commutative Ring

Through this article, R denotes a commutative ring with identity. The aim of this article is to construct a morphism of lattices between the reticulation of a ring of quotients (of a commutative ring with respect to a Gabriel topology) and the localization lattice of the reticulation of the initial ring. The article is structured as follows: The first section introduces all the necessary notions required to simplify the reading of the article. The second section presents some properties of the topology induced by a Gabriel topology on the reticulation L(R). In the third section the morphism δ, which achieves the intended link, is constructed. The last section studies the defined morphism in some particular cases.     

K-Theory for Triangulated Categories 3 1/2 (B): A Detailed Proof of the Theorem of Homological Functors Dedicated to Daniel Quillen and to the Memory of Robert Thomason

This article is a sequel to K-theory for triangulated categories 3 1/2 (A). In this article, we complete the proof of the main theorem of the previous article.     

Infinite flocks of a quadratic cone

In this article, we construct some infinite analogues of the Fisher flocks. We also consider maximal partial flocks which may be constructed in several ways. In particular, we show that any derivation of a flock inPG(3,K), forK a full field, produces either a flock or a maximal partial flock. We provide constructions which produce maximal partial flocks or maximal partial spreads.In memoriam, Giuseppe TalliniThis article was written while the authors were visiting the Ricco Institute during June of 1994 and was partially supported by Glasgow-Caledonian University. Also, the authors are indebted to Christian Boltanski,D — S, in the writing of this article.The authors also are indebted to the referee for helpful suggestions with regard to this article.     

The sound of music and its link with mathematics

This article discusses a relatively unnoticed application ofmathematics by describing its connection with an aspect of music,in particular, the musical scales. Stemming from a problem foundin a Year 9 mathematics textbook commonly used in Singapore,the article illustrates the role of mathematics in musical scalesby first considering the frequency ratios of consecutive musicalnotes in the ‘just scale’ and secondly explaininghow an anomaly in the ‘just scale’ caused by theuneven frequency ratios is resolved with the help of mathematics,thereby leading to the development of the well-tempered scale.The article ends with an exploration of the frequency ratiosof consecutive musical notes in the well-tempered scale. Notonly does the article aim to broaden the teachers’ horizonswith such an introduction to the mathematical aspect of music,it also hopes to enrich their mathematical experiences as well.     

Invariant Hermitian structures and variational aspects of a family of holomorphic curves on flag manifolds

In this article, we study variational aspects for a special class of holomorphic maps on flag manifolds. We prove stability and non-stability results for such maps with respect to a large number of invariant Hermitian structures on maximal flag manifolds including the (1, 2)-symplectic structures, Einstein metrics, Cartan–Killing metrics, and so on. Some results in this article were announced without proofs in a past article by the first author.     

When Products of Self-Small Modules are Self-Small

A module M is called “self-small” if the functor Hom(M, ?) commutes with direct sums of copies of M. The main goal of the present article is to construct a non-self-small product of self-small modules without nonzero homomorphisms between distinct ones and to correct an error in a claim about products of self-small modules published by Arnold and Murley in a fundamental article on this topic. The second part of the article is devoted to the study of endomorphism rings of self-small modules.     

Fundamentals of a new kind of mathematics based on the Golden Section

The attempt of build up the Fundamentals of a new mathematical direction, which is called Harmony Mathematics, is addressed in the present article. The article has a “strategic” importance for development of computer science and theoretical physics.     

A Note on a Unicity Theorem of N. Terglane

In this article, we prove a unicity theorem of meromorphic functions sharing three values, which is an improvement of the theorem given by Terglane. Some examples show that the result in this article is best possible.     

An Improvement of Normal Approximation of Randomized Orthogonal Array Sampling Designs

This article considers a class of nonlocal stochastic functional differential equations with infinite delay whose coefficients are dependent the pth moment and establishes the existence-and-uniqueness theorem under the conditions that are similar to the classical linear growth condition and the Lipschitz condition. Compared with the existing results, the conditions of this article are easier to test.     

Moving finite element methods by use of space–time elements: I. Scalar problems

This article deals with moving finite element methods by use of the time-discontinuous Galerkin formulation in combination with oriented space–time meshes. A principle for mesh orientation in space–time based on minimization of the residual, related to adaptive error control via an a posteriori error estimate, is presented. The relation to Miller's moving finite element method is discussed. The article deals with scalar problems; systems will be treated in a companion article. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:251–262, 1998     

Oscillation of membranes in an incompressible fluid

This article considers the problem of natural oscillations of membranes in an unbounded incompressible fluid. The article contains a qualitative analysis of the equations used and upper and lower bounds are obtained for the natural frequencies of the membrane. Translated fromDinamicheskic Sistemy. Vol. 12. pp. 23–29, 1993.     

Statistical testing of optimality conditions in multiresponse simulation-based optimization

This article studies simulation-based optimization with multiple outputs. It assumes that the simulation model has one random objective function and must satisfy given constraints on the other random outputs. It presents a statistical procedure for testing whether a specific input combination (proposed by some optimization heuristic) satisfies the Karush–Kuhn–Tucker (KKT) first-order optimality conditions. The article focuses on “expensive” simulations, which have small sample sizes. The article applies the classic t test to check whether the specific input combination is feasible, and whether any constraints are binding; next, it applies bootstrapping (resampling) to test the estimated gradients in the KKT conditions. The new methodology is applied to three examples, which gives encouraging empirical results.     

New Characterizations of Dualizing Modules

Let R be a commutative Noetherian ring. In this article, we provide some new criteria for a semidualizing module to be dualizing in terms of special homological properties of module categories. The purpose of this article is twofold: first, it aims at improving Christensen's and Takahashi et al.'s characterizations of dualizing modules; secondly, while applying these criteria to the ring itself, we not only recover some results of Jenda and Xu, respectively, but also obtain a new characterization of Gorenstein rings.     

基于灰色关联度理论的飞机顶层设计方案优选决策模型

探讨了飞机方案设计阶段应用决策方法的重要性;建立了飞机顶层设计方案优选的层次结构和评价指标体系;应用灰色关联度理论和方法建立了方案优选的灰色层次决策模型,并利用该模型对某飞机设计方案进行优选评价和敏感性分析,得到了满意的结果     

Some design-theoretic properties of buekenhout unitals

The purpose of this article is to discuss some questions about parabolic Buekenhout unitals, considered as designs. In this article, we define a parabolic Buekenhout unital to be a unital in any two-dimensional translation plane obtained from the cone over any ovoid. In particular, we discuss resolutions of these designs, inversive plane residuals obtainable from these designs, and also some issues about disjoint Steiner systems. © 1996 John Wiley & Sons, Inc.     

Generalized André planes of order p tthat admit a homology group of order (p t−1)/2

In this article, a classification is given of finite generalized André planes of odd order K that admit an affine homology group of order (k–1)/2.Dedicated to A. Wagner on the occasion of his 60th birthdayThis article was written when the first author was visiting the University of Iowa during 1990–91.     

Extension to BV functions of the large deformation diffeomorphisms matching approach

The image matching within the framework of large deformations via diffeomorphisms is extended to the space of bounded variation functions. Thanks to a semi-differentiation lemma, which is the central new result of this article, we derive the geodesic equations for a general penalty term and we describe the associated momentum. To cite this article: F.-X. Vialard, F. Santambrogio, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Positive and unbounded solution of stochastic delayed evolution equations

This article is concerned with the blowup phenomenon of stochastic delayed evolution equations. We first establish the sufficient condition to ensure the existence of a unique nonnegative solution of stochastic parabolic equations. Then the problem of blow-up solutions in mean L^q-norm, q ? 1, in a finite time is considered. The main aim in this article is to investigate the effect of time delay and stochastic term. A new result shows that the stochastic delayed term can induce singularities.