ON THE ISOMORPHISMS OF COMPLETE INTERSECTION VARIETIES

ＯＮ　ＴＨＥ　ＩＳＯＭＯＲＰＨＩＳＭＳ　ＯＦ　ＣＯＭＰＬＥＴＥＩＮＴＥＲＳＥＣＴＩＯＮ　ＶＡＲＩＥＴＩＥＳＤＵＨｏｎｇ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈｉｎａ）Ａｂｓｔ...     

ON THE FOUNDATION OF ALGEBRAIC DIFFERENTIAL GEOMETRY

An algebraic differential variety is defined as the zero-set of a differentialpolynomial set,and algebraic differential geometry is devoted to the study of such varieties.We give various decomposition formulas for the structures of such zero-sets which imply inparticular,the unique decomposition of an algebraic differential variety into its irreduciblecomponents.These formulas will find applications in various directions including mechanicaltheorem-proving of differential geometries.     

ON THE EXISTENCE OF MEROMORPHIC SOLUTIONS OF ALGEBRAIC DIFFERENTIAL EQUATIONS

ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＯＦＭＥＲＯＭＯＲＰＨＩＣＳＯＬＵＴＩＯＮＳＯＦＡＬＧＥＢＲＡＩＣＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ￥ＹＵＡＮＷｅｎｊｕｎ（ＤｅｐａｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉｎｊｉａｎｇＮｏｏｒｍａｌＵｎｉｖｅｒｓ...     

ON THE ALGEBRAIC VARIETY DECOMPOSITION

ＯＮＴＨＥＡＬＧＥＢＲＡＩＣＶＡＲＩＥＴＹＤＥＣＯＭＰＯＳＩＴＩＯＮＷＵＪｉｎｚｈａｏ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈｉｎａ）ＯＮＴＨＥＡＬＧＥＢＲＡＩＣＶＡＲＩＥＴ...     

THE ALGEBRAIC CRITERIA FOR THE ASYMPTOTIC BEHAVIOR OF COOPERATIVE SYSTEMS WITH CONCAVE NONLINEARITIES

For the discrete dynamical system on the nonnegative orthant generated bya cooperative and concave map T, we present an algebraic criterion of its asymptoticbehavior. The global behavior of such a system is completely determined by the sign of allprincipal minors of the matrix I-DT(0). This criterion applies to the cooperative systemwhich is concave, time-dependent and periodic in t. We give the sufficient conditions thatthe zero solution of such a system is globally asymptotically stable and that it possesses anonzero periodic solution which attracts all initial conditions in the nonnegative orthant.except at the origin. The results of Smith under weaker conditions and some applicationsare included.     

ON THE LEAST EIGENVALUE OF A GRAPH

Let G be a simple graph with n vertices and λ_n(G) be the least eigenvalue of G.In this paper, we show that, if G is connected but not complete, then λ_n(G)≤λ_n(K_(n-1)~1)and the equality holds if and only if G K_(n-1)~1, where K_(n-1)~1, is the graph obtained by thecoalescence of a complete graph K_(n-1) of n-1 vertices with a path P_2 of length one of itsvertices.     

A NOTE ON THE PAPER "ON THE CONNECTIVITY OF CAYLEY COLOR GRAPHS

ＡＮＯＴＥＯＮＴＨＥＰＡＰＥＲ＂ＯＮＴＨＥＣＯＮＮＥＣＴＩＶＩＴＹＯＦＣＡＹＬＥＹＣＯＬＯＲＧＲＡＰＨＳ＂￥ＭＥＮＧＪｉｘｉａｎｇ；ＨＵＡＮＧＱｉｏｎｇｘｉａｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉｎｉｉａｎｇＵｎｉｖｅｒｓｉｔｙ，...     

ON THE CONNECTIVITY OF CAYLEY COLOR GRAPHS

In this paper we obtain the necessary and sufficient condition for the connec-tivity of the Cayley color graphs or the Cayley graphs to be equal to their minimum degree.The sharp lower bounds of connectivity of Cayley color graphs and the Cayley graphs arealso obtained. Our results generalize the previous results obtained in [1] to [3].     

BLOW-UP CRITERION OF SMOOTH SOLUTIONS TO THE MHD EQUATIONS IN BESOV SPACES

In this paper we discuss the logarithmic Sobolev inequalities in Besov spaces,and show their applications to the blow-up criterion of smooth solutions to the incompressible magneto-hydrodynamics equations.     

ON THE CONSTRUCTION OF GROEBNER BASIS OF A POLYNOMIAL IDEAL BASED ON RIQUIER-JANET THEORY

As a consequence of a previons study of algebraic differential geometry(see [WU1]) theremay be associated to certain special kinds of differential ideals some well-behaved basis enjoyingsome well-behaved properties.If the differential ideals are further specialized so that theycorrespond to ordinary polynomial ideals then such a well-behaved basis will become the usualGroebner basis of the polynomial ideals while the latter is not known for differential ideals.     

ON MANAGERIAL DECISION PROBLEM OF THE AUCTION SITES

This paper studies one managerial decision problem of the auction sites： how to combine penalties with commissions？ It is shown that when there exists secondary auction market, the auction whose penalty is a linear function of the seller＇s commission will be more efficient than the auction with only commissions but no penalties. It has also been proven that using this strategy can maximize the expected revenue for the seller, the auction site and their total expected revenues.     

ON THE DEDEKIND COMPLETION OF ~*R

The Dedekind Completion ~*R of a nonstandard real field R is studied.Topological andalgebraic properties of two subsets of ~*R consisting of additive universal numbers and multiplicativeuniversal numbers respectively are exhibited.From this,we introduce a kind of new non-Archimedeanfields,generalizing A.Robinson's ~ρR.We prove that these fields are real closed fields,and study theinteger rings,rational fields,fields of algebraic numbers and rings of algebraic integers subordinate tothese fields.     

ON THE FREQUENCY STABILITY OF MODERN ELECTRONIC EQUIPMENTS

Frequency stability is one of the key problems and important specifications of modern electronicequipments (including aeronautical, navigational and communication equipments; CW and pulseradar; interferometer and VLBI; electronic measurement and modern physical experiment, etc).More and more scientists take increasing interest to it following the rapid development of modernelectronic technique. This monography is the first overall treatment of this subject. Many new concepts and app-roaches are proposed for the first time. It presents the fundamental concapts of statistical oscilla-     

ON THE NUMBER OF FIXED POINTS OF NONLINEAR OPERATORS AND APPLICATIONS

In this paper, the famous Amann three-solution theorem is generalized. Multiplicity question of fixed points for nonlinear operators via two coupled parallel sub-super solutions is studied. Under suitable conditions, the existence of at least six distinct fixed points of nonlinear operators is proved. The theoretical results are then applied to nonlinear system of Hammerstein integral equations.     

ON THE DESIGN OF A NEURO-FUZZY CONTROLLER–APPLICATION TO THE CONTROL OF A BIOREACTOR

1. Introduction Fuzzy controllers have interesting characteristics, principally concerning their robustness and their ability to integrate human knowledge in the design of control systems, allowing to a human operator to interpret, at every time, the action of the control system. However, the synthesis of a fuzzy controller, giving the controlled process a specified behaviour, is not an evident thing. Indeed, tuning the parameters of a fuzzy controller is often achieved by a succession of tria…     

ON THE CONDITION FOR CONSISTENCY OF RESAMPLING ESTIMATORS OF VARIANCE OF TRIMMED L-STATISTICS

1.IntroductionLetXI,X2,''tX.beani.i.d.randomsamplewithcommondistributionfunction(c.d.f.)F(unknown),andFibetheempiricaldistributionfunction(e.d.f.)basedonthesample.ConsiderthefollowingfunctionalofFwhereF--'(t)ginf{x:F(x)2t}istheinversefunctionofF(inversef…     

ON THE COMPLETION TIME AND THE INTERRUPTION TIME OF A JOB PROCESSED ON AN UNRELIABLE MACHINE

This paper considers the completion time and the interruption time of a job processed on an unreliable machine. By using the general theory of stochastic orderings, we obtain the closure properties of the distribution of the completion time and the interruption time on L^ and PH life distribution classes. We get an exponential bound for the tail probability of the interruption time.     

ON THE EXISTENCE OF FIXED POINTS FOR MAPPINGS OF ASYMPTOTICALLY NONEXPANSIVE TYPE

Let C be a nonempty weakly compact convex subset of a Banach space X, and T : C →C a mapping of asymptotically nonexpansive type. Then there hold the following conclusions: (i) if X has uniform normal structure and limsup |||TjN||| < N(X)~1/(N(X)) , where|||TjN||| is the exact Lipschitz constant of TjN , N is some positive integer, and N(X) is the normal structure coefficient of X, then T has a fixed point; (ii) if X is uniformly convex in every direction and has weak uniform normal structure, then T has a fixed point.     

ON THE BEST UNIFORM CONVERGENCE RATE OF EB ESTIMATORS

ＯＮＴＨＥＢＥＳＴＵＮＩＦＯＲＭＣＯＮＶＥＲＧＥＮＣＥＲＡＴＥＯＦＥＢＥＳＴＩＭＡＴＯＲＳＬＩＡＮＧＨｕａ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈｉｎａ）ＹＵＡＮＹａｈｕａ（...     

A NOTE ON THE STOCHASTIC ROOTS OF STOCHASTIC MATRICES

In this paper, we study the stochastic root matrices of stochastic matrices. All stochastic roots of2×2 stochastic matrices are found explicitly.A method based on characteristic polynomial of matrix isdeveloped to find all real root matrices that are functions of the original 3×3 matrix, including allpossible(function)stochastic root matrices. In addition, we comment on some numerical methods forcomputing stochastic root matrices of stochastic matrices.