An Adjoint Equivalence of the Category IS of Inverse-sheaves

We have obtained the category IS of r(r≥0)-dimensional inverse-sheaves of open setsof R~n and the followingTheorem1 Let U:C~r→IS be the forgetful functor.Then there is an adjoint equivalence:IS—C~r.Corollary1 C~r-manifolds(X,(?))and(Y,(?))are diffeomorphic iff U(X,(?))and U(Y,(?))are isomorphic.     

On the Quotient Compact Images of Metric Spaces

This paper gives an internal characterization of the quotient compact images of metric spaces, which answers a question posed by Arhangel'skii; and an example is constructed to show that the quotient compact images of metric spaces are not preserved by perfect maps.     

The Quotient Category of a Graded Morita-Takeuchi Context

In this paper, we offer a graded equivalence between the quotient categories defined by any graded Morita-Takeuchi context via certain modifications of the graded cotensor functors. As a consequence, we show a commutative diagram that establish the relation between the closed objects of the categories gr^c and M^C, where C is a graded coalgebra.     

On the Left Classical Quotient Rings of the Superprime Rings

ＯｎｔｈｅＬｅｆｔＣｌａｓｓｉｃａｌＱｕｏｔｉｅｎｔＲｉｎｇｓｏｆｔｈｅＳｕｐｅｒｐｒｉｍｅＲｉｎｇｓＣｈｅｎＰｅｉｃｉ（陈培慈）（Ｄｅｐｔ．ｏｆＭａｔｈ．ＪｉａｎｇｘｉＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｎａｎｃｈａｎｇ，ＪｉａｎｇｘｉＰｏｒｖｉｎｃ...     

On the Decomposition of Hopf Module Coalgebra

In1969,Sweedler[1]giventhedecompositiontheoreyofcoalgebraswhicharecocommu-tative.In1975,Kaplansky[2]showedthatanycoalgebracanbeuniquelydecomposedintoadirectsumofitsindecomposablesubcoalgebras.From1978to1992,Shudo[3]andXu[4]consructuredtheindecomposabledirectsumcomponentsofacoalggebra,viadefineequivalenceralationforthesetofsimplesubcoalgebras.Asweknow,themodolecoalgebraisthennaturalgeneralizationofcoalgebra.AndittakesplayanimportentroleintheDrinfelddouble.Inthispaper,wediscussthedecompositio…     

On the Denominator of the Poincaré Series for Monomial Quotient Rings

Let S = 𝕜 [x ₁,…, x _n ] be a polynomial ring over a field 𝕜 and I a monomial ideal of S. It is well known that the Poincaré series of 𝕜 over S/I is rational. We describe the coefficients of the denominator of the series and study the multigraded homotopy Lie algebra of S/I.     

On the Structure of the B—cocleft Module Coalgebra

§１．　ＴｈｅＥｑｕｉｖａｌｅｎｔＴｈｅｏｒｅｍｏｆｔｈｅＣｒｏｓｓｅｄＣｏｐｒｏｄｕｃｔＬｅｔＣｂｅａｌｅｆｔＨ－ｗｅａｋｌｙｃｏｍｏｄｕｌｅｃｏａｌｇｅｂｒａ［４］ｗｉｔｈｔｈｅｓｔｒｕｃｔｕｒｅρ－Ｃ（ｃ）＝∑ｃ（１）ｃ（２）．ＤｂｅｌｅｆｔＨ－ｍｏｄｕｌｅｃｏａｌｇｅｂｒａ［２］ｗｉｔｈｔｈｅｓｔｒｕｃｔｕｒｅ“”．Ｆｏｒα∈Ｈｏｍκ（Ｃ，ＨＨ）ｄｅｎｏｔｅα（ｃ）＝∑α１（ｃ）α２（ｃ）．Ｄｅｆｉｎｅ△－：ＣＤ→（ＣＤ）（ＣＤ）ａｎｄε－：ＣＤ→κａｓｆｏｌｌｏｗ－ｉ…     

On the Equivalence and Generalized of Weyl Theorem Weyl Theorem

We know that an operator T acting on a Banach space satisfying generalized Weyl＇s theorem also satisfies Weyl＇s theorem. Conversely we show that if all isolated eigenvalues of T are poles of its resolvent and if T satisfies Weyl＇s theorem, then it also satisfies generalized Weyl＇s theorem. We give also a sinlilar result for the equivalence of a-Weyl＇s theorem and generalized a-Weyl＇s theorem. Using these results, we study the case of polaroid operators, and in particular paranormal operators.     

On the invariants of Möbius groupsM(R n )

Suppose that $$\operatorname{Re} (a + d^ * ) \in \left\{ {\begin{array}{*{20}c} {( - 2,2),if g(x) is f.p.f. or elliptic,} \\ {\left[ { - 2,2} \right], if g(x) is parabolic,} \\ {( - \infty ,\infty ), if g(x) is loxodromic.} \\ \end{array} } \right.$$ is a Clifford matrix of dimensionn, g(x)=(ax+b)(cx+d) ^?1. We study the invariant balls and the more careful classifications of the loxodromic and parabolic elements inM(R ⁿ ), prove that the loxodromic elements inM(R ^2k+1 ) certainly have an invariant ball, expound the geometric meaning of Ahlfors' hyperbolic elements, and introduce the uniformly hyperbolic and parabolic elements and give their identifications. We prove that $$\operatorname{Re} (a + d^ * ) \in \left\{ {\begin{array}{*{20}c} {( - 2,2),if g(x) is f.p.f. or elliptic,} \\ {\left[ { - 2,2} \right], if g(x) is parabolic,} \\ {( - \infty ,\infty ), if g(x) is loxodromic.} \\ \end{array} } \right.$$ These results are fundamental in the higher dimensional Möbius groups, especially in Fuchs groups.     

On the Category of Koszul Modules of Complexity One of an Exterior Algebra

In this paper, we prove that there is a natural equivalence between the category F1（x） of Koszul modules of complexity 1 with filtration of given cyclic modules as the factor modules of an exterior algebra A = ∧V of an m-dimensional vector space, and the category of the finite-dimensional locally nilpotent modules of the polynomial algebra of m - 1 variables.     

On Unitary Equivalence of Analytic Toeplitz Operators

ＯｎＵｎｉｔａｒｙＥｑｕｉｖａｌｅｎｃｅｏｆＡｎａｌｙｔｉｃＴｏｅｐｌｉｔｚＯｐｅｒａｔｏｒｓＤｉｎｇＸｕａｎｈａｏ（丁宣浩）（ＤａｘｉａｎＴｅａｃｈｅｒ＇ｓＣｏｌｅｇｅ，Ｄａｘｉａｎ，Ｓｉｃｈｕａｎ，６３５０００）ＡｂｓｔｒａｃｔＩｎｔｈｉｓｐａｐ...     

On Lie Algebras in the Category of Yetter—Drinfeld Modules

The category of Yetter—Drinfeld modules over a Hopf algebra K (with bijective antipode over a field k) is a braided monoidal category. If H is a Hopf algebra in this category then the primitive elements of H do not form an ordinary Lie algebra anymore. We introduce the notion of a (generalized) Lie algebra in such that the set of primitive elements P(H) is a Lie algebra in this sense. Also the Yetter—Drinfeld module of derivations of an algebra A in is a Lie algebra. Furthermore for each Lie algebra in there is a universal enveloping algebra which turns out to be a Hopf algebra in .     

Equivalence Relation on the Set of Subsets of Z_v and Enumeration of the Equivalence Classes

Motivated by the concept of equivalent cyclic difference sets on Z_v (the residue ring modulo v), we introduce a similar equivalence relation on the set of subsets of Z_v as follows. Difinition Let D_1 and D_2 be two subsets of Z_v. If D_1=tD_2+s for some t, s∈Z_v(ged(t,v)=1), then D_1 and D_2 are said to be equivalent, denoted by D_～D_2.     

On Subgroups and Quotient Groups of L-fuzzy Topological Groups

In paper [1], it gave the concept and basic properties of L-fuzzy topological groups. This paper will enter the concept of quotient groups of L-fuzzy topological groups and will prove some properties of subgroups and quotient groups. The persent work is the continuation of [1] and hence all the conventions in [1] still hold good in the present paper.     

On ℓ p -summability of the characteristic values of intergral operators onL(R N )

LetB _p (L ₂) (0<p<) denote the space of all compact linear operatorsK onL(R ^N ) with the following property: the sum ofp-th powers of all positive eigenvalues (repeated according to their multiplicity) of the nonnegative compact operator (K ^* K)^1/2 converges. We prove aB _p -criterion for an integral operatorK onL(R ^N ), for 0<p2. We require that its kernel have sufficient fractional smoothness and decay at infinity. Our proof is based on a suitable factorization of the operatorK which involves fractional powers (H+I)^– 0, 0<1, of the resolvent of the selfadjoint elliptic operatorH=(–) ^m +M _q ^2m onL(R ^N ).     

On the Integral Curvature of Curve-(III)

In this paper we prove the following theorem.It is a generalization of Tenchel's theorem on theintegral curvature of curve.Theorem.If 1 is the length of a curve C=AB and φ is the angle between the tangent vectors ofC at A,B,then the integral curvature of C     

On the Equivalence of the Mizoguchi-Takahashi Locally Contractive Map and the Nadler’s Locally Contractive Map

Abstract

In this paper, the equivalence between multi-valued maps satisfying the Mizoguchi-Takahashi’s uniformly locally contractive condition and multi-valued maps satisfying the Nadler’s uniformly locally contractive condition is obtained on metrically convex space. We have provided examples to illustrate that this equivalence need not be true on any arbitrary metric space.     

On a problem connected with zeros of ζ(s) on the critical line

The existence of zeros ofZ ^(k)(t) in short intervals of the type [T, T+H] is established, whereHT ^a(k)logT, . Hitherto the sharpest bounds for the constanta(k) are obtained by employing a certain exponential averaging technique and the estimation of the relevant exponential sums. Bounds for are also derived, under the assumption that orZ(t) does not vanish in certain short intervals.     

On Contact Equivalence of Monge-Ampère Equations to Linear Equations with Constant Coefficients

We solve a problem of local contact equivalence of hyperbolic and elliptic Monge-Ampère equations to linear equations with constant coefficients. We find normal forms for such equations: the telegraph equation and the Helmholtz equation.