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Examples of unbounded homogeneous domains in complex space

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Science China mathematics 2005年第z1期48卷 248-261页

作者： Michael Eastwood Alexander Isaev department of pure mathematics university of adelaide South Australia 5005AustraliaDepartment of Mathematics The Australian National UniversityCanberraACT 0200Australia

We present several examples of homogeneous domains in complex space that do not have bounded realisations. The domains are equivalent to tubes over affinely homogeneous domains in real space.

关键词： homogeneous unbounded domains.

On the Same n-Types for the Wedges of the Eilenberg-Maclane Spaces

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Chinese Annals of mathematics,Series B 2016年第6期37卷 951-962页

作者： Dae-Woong LEE department of mathematics Institute of Pure and Applied Mathematics Chonbuk National University

Given a connected CW-space X, SNT（X） denotes the set of all homotopy types [X＇] such that the Postnikov approximations X（n） and X＇^（n） are homotopy equivalent for all n. The main purpose of this paper is to show that the set of all the same homotopy n- types of the suspension of the wedges of the Eilenberg-MacLane spaces is the one element set consisting of a single homotopy type of itself, i.e., SNT（Σ（K（Z, 2a1） ∨ K（Z, 2a2）∨… ∨ K（Z,2ak））） = ＊ for a1 〈 a2 〈 … 〈 ak, as a far more general conjecture than the original one of the same n-type posed by McGibbon and Moller （in [McGibbon, C. A. and Moller, J. M., On infinite dimensional spaces that are rationally equivalent to a bouquet of spheres, Proceedings of the 1990 Barcelona Conference on Algebraic Topology, Lecture Notes in Math., 1509, 1992, 285-293].）

关键词： Same n-type Aut Basic Whitehead product Samelson product Bott-Samelson theorem Tensor algebra Cartan-Serre theorem Hopf-Thom theorem

A class of singular integrals on the n-complex unit sphere

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Science China mathematics 1999年第12期42卷 1233-1245页

作者： Michael Cowling 钱涛 department of pure mathematics University of New South Walse

The operaton on the n-complex unit sphere under study have three forms: the singular integrals with holomorphic kernels, the bounded and holomorphic Fourier multipliers, and the Cauchy-Dunford bounded and holomorphic functional calculus of the radial Dirac operator $D = \sum\nolimits_{k = 1}^n {z_k \frac{\partial }{{\partial _{z_k } }}} $ . The equivalence between the three fom and the strong-type (p,p), 1

关键词： singular integral Fourier multiplier the unit sphere in C n lunetional calculus

Twisted analytic torsion

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Science China mathematics 2010年第3期53卷 555-563页

作者： MATHAI Varghese department of mathematics University of Adelaide

We review the Reidemeister, Ray-Singer’s analytic torsion and the Cheeger-Mller theorem. We describe the analytic torsion of the de Rham complex twisted by a flux form introduced by the current authors and recall its properties. We define a new twisted analytic torsion for the complex of invariant differential forms on the total space of a principal circle bundle twisted by an invariant flux form. We show that when the dimension is even, such a torsion is invariant under certain deformation of the metric and the flux form. Under T-duality which exchanges the topology of the bundle and the flux form and the radius of the circular fiber with its inverse, the twisted torsion of invariant forms are inverse to each other for any dimension.

关键词： analytic torsion circle bundles T-duality

FINITE ELEMENT APPROXIMATION FOR A CLASS OF PARAMETER ESTIMATION PROBLEMS

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Journal of Systems Science & Complexity 2014年第5期27卷 866-882页

作者： CHANG Yanzhen YANG Danping department of mathematics Beijing University of Chemical Technology department of mathematics Shanghai Key Laboratory of Pure Mathematics and Mathematical PracticeEast China Normal University

This paper investigates the finite element approximation of a class of parameter estimation problems which is the form of performance as the optimal control problems governed by bilinear parabolic equations,where the state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant *** authors derive some a priori error estimates for both the control and state ***,the numerical experiments verify the theoretical results.

关键词： A priori error estimate finite element approximation optimal control problems

ALGORITHMS FOR A SYSTEM OF GENERALIZED MIXED EQUILIBRIUM PROBLEMS AND A COUNTABLE FAMILY OF SOME NONLINEAR MULTI-VALUED NONEXPANSIVE-TYPE MAPS

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Acta Mathematica Scientia 2018年第6期38卷 1805-1820页

作者： Ogonnaya Michael ROMANUS Ukamaka Victoria NNYABA Monday Ogudu NNAKWE department of pure and Applied mathematics African University of Science and Technology

In this paper, relaxed iterative algorithms of Krasnoselskii-type and Halpern-type that approximate a solution of a system of a generalized mixed equilibrium problem anda common fixed point of a countable family of totally quasi-C-asymptotically nonexpansivemulti-valued maps are constructed. Strong convergence of the sequence generated by thesealgorithms is proved in uniformly smooth and strictly convex real Banach spaces with Kadec-Klee property. Furthermore, several applications of our theorems are also presented. Finally,our theorems are significant improvements on several important recent results for this classof nonlinear problems.

关键词： Halpern-type algorithm Krasnoselskii-type algorithm system of generalizedmixed equilibrium problems totally quasi-C-asymptotically nonexpansive multi-valued maps equally continuous maps

Reconstruction of Singular Second-order Differential Equations From Spectral Characteristics

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Acta Mathematicae Applicatae Sinica 2019年第3期35卷 645-654页

作者： Seyfollah MOSAZADEH department of pure mathematics Faculty of Mathematical Sciences University of Kashan

In this work,we study boundary value problems for second-order differential equations with singularities of second kind inside an ***,we investigate properties of the spectrum,then prove a theorem on completeness of eigenfunctions,and study the inverse problem of reconstructing the differential equation from spectral characteristics.

关键词： singularity spectral characteristics inverse problem completeness Weyl function

PRODUCTS OF RESOLVENTS AND MULTIVALUED HYBRID MAPPINGS IN C AT(0) SPACES

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Acta Mathematica Scientia 2018年第3期38卷 791-804页

作者： Gholamreza ZAMANI ESKANDANI Soheila AZARMI Masoumeh RAEISI department of pure mathematics Faculty of Mathematical Sciences university of Tabriz department of pure mathematics Faculty of Mathematical SciencesUniversity of Tabriz

In this article, we introduce and investigate the concept of multivalued hybrid mappings in C AT（0） spaces by using the concept of quasilinearization. Also, we present a new iterative algorithm involving products of Moreau-Yosida resolvents for finding a common element of the set of minimizers of a finite family of convex functions and a common fixed point of two multivalued hybrid mappings in C AT（0） spaces.

关键词： Multivalued hybrid mappings convex optimization C AT(0) spaces

LR-normal orthogroups

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Science China mathematics 2006年第3期49卷 330-341页

作者： SHUM K. P. SEN M. K. Faculty of Science department of pure mathematics

A new kind of regular orthogroups, namely, the LR-normal orthogroups is introduced and investigated. In particular, we will introduce the gearing techniques for fitting semigroup components on a semilattice in the con... 详细信息

关键词： LR-regular orthogroups, LR-normal orthogroups, gearing of semigroups.