In this paper, the(0,1)-heat form of B￣n is constructed.As an application of the(0,1)-heat form of B￣n,the integral reprentation of the solution of the-equation on B￣n is given。
This paper study the problem for the chaxacteriztions of the minus partial order ofmorphism set in a category, its main results are: 1. prove fourteen characterizations of the minuspartial order in a general category ; 2. the results that using inclusion relation of (1)-inverse,(1,2)-inverse and parallel sum characterized the minus partial order of a complex matrix by category; 3.give the inverse example for proposition 1(ix) of [5], then negate the Hartwig's this characterization.
In this paper we investigate the relationship between a module and a comodule. LetA be a algebra and M be a right A-module,we show that M°={f ∈M￣*; there be some idealI of A such that f(MI)= 0 and dim A/I finite}is a right A°-comodule. We use the result togive a H-module algebra A,with its dual there be some ideal I of A such thatF(I)=0 and dim A/I finite } is not a H°-comodule coalgebra.
A class of l-groups is called a sub-product class,if it is closed under taking convexl-subgroups and forming completely subdirect products.Let U be a sub-product class and G beis called a sub-product radical of G.In this paper we proved that a sub-product class U is determined by the sub-product radical mapping G→U(G).And we also proved that in thethe meet is determined by the sub-product radical mapping G→whilethe join is determined by the sub-product radical mapping G→ this is beautiful result.
Let R be a G-graded ring,HG, be a subgroup of G; By constructing two Moritacontexts, we give some sufficient and necessary conditions for R{H}to be Morita equivalent toR_H, and for R#G￣* to be equivalent to R_H#H￣*.
In this paper, the(0,1)-heat form of B￣n is constructed.As an application of the(0,1)-heat form of B￣n,the integral reprentation of the solution of the-equation on B￣n is given。
This paper studies the average sum of partial quotients of a class of the finitecontinued frartions.A accurate asymptotic formula is given out. It improves upon a well-knownresult due H. Yao and D.Knuth.
In this paper, using the first standard imbedding of CP￣m into an (m￣2 + 2m)-dimentional Euclide an space, we define a Gauss map for a submanifold in CP￣m. We obtainsome conditions which ensure that the Gauss map is harmonic or relatively affine.
In the theory of the universal phenomenon obtained in the numerical research aboutinterval maps and circle maps,a key role is played by the renormalization group hinctionalequations and their solutions.This paper studies the functional equations connecting the twomaps The existence of its infinite C￣∞ solutions is shown by constructing method.The scope ofparameter is larger than D in[9]. Finaly, some further problems which need to be studied areposed.
In this paper, our main result is as follows.Theorem Suppose thatλ_1,…,λ_q are non-zero real numbers not all in rational ratio, and k=4,5…,11.Then,for 0<σ<σ_k,the inequality has infinitely many solutions in integers. Where K is any real number,
Let G be a graph and g,j be two integer-valued hinctions defined on the vertexset of G and (g,f)-factor of a graph G is a spanning subgraph F of G such thatfor each vertex x of F Inthis paper some sumcient conditions for a graphto be (g,f)-factorable and a necessary and sufficient condition for a grah to be a (g,f)-deleted guaph are given Some applications of these conditions are discussed .
In this paper we give an asympotic estimate for the lifetunes of conditfoned diffusionprocesses in bounded Lipschitz domains D. From this we obtain the spectral conditions for thefiniteness or infiniteness of gauge and conditional gauge, gauge theorem and conditional gaugetheorem are obtained here too.
In this paper,some aufficient conditions of existence of periodic orbits of the typeBC* L￣∞in unimodal functions with kneading sequences BC are given. Then the existence ofeventually periodic orbits in a general ununodal function f discussed. It is proved that if ak-th eventually n-periodic admissible sequence AB￣∞ satisfies certain requirements then f hasa k-th eventually n-periodic orbit of type AB￣∞ For an ext ensive class of unimodal functions,the condition of the main theorem in Part II.3 of Ref. [1] is weakened and simplified adn its conslusion is strengthened.For general continuous functions,the conalusion of Theorem 2 in Ref.[8] is also replenished.
In this paper we give a computation formula for orthogonal groups of the sum oftwo quadric modules over commutative rings.For the quadric modules over polynomial ring,wegive a local-golbal theorem for some subgroups of the quardic modules.
