This paper is devoted to the applications of classical topological degrees to nonlinear problems involving various classes of operators acting between ordered Banach spaces.In this framework,the Leray-Schauder,Browder-Petryshyn,and Amann-Weiss degree theories are considered,and several existence results are obtained.The non-Archimedean case is also discussed.
In this paper,we shall define the renormalization of the multiple q-zeta values (MqZV) which are special values of multiple q-zeta functions ζq(s1,...,sd) when the arguments are all positive integers or all non-positive integers.This generalizes the work of Guo and Zhang (Renormalization of Multiple Zeta Values,arxiv:math/0606076v3).We show that our renormalization process produces the same values if the MqZVs are well-defined originally and that these renormalizations of MqZV satisfy the q-stuffle relations if we use shifted-renormalizations for all divergent ζq(s1,...,sd) (i.e.,s1≤1).Moreover,when q↑1 our renormalizations agree with those of Guo and Zhang.
This paper is devoted to a class of inverse problems for a nonlinear parabolic differential equation.The unknown coefficient of the equation depends on the gradient of the solution and belongs to a set of admissible coefficients.It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence.Based on this result the existence of a quasisolution of the inverse problem is obtained in the appropriate class of admissible coefficients.
In this paper,we prove the persistence of hyperbolic lower dimensional invariant tori for Gevrey-smooth perturbations of partially integrable Hamiltonian systems under Rüssmann's nondegeneracy condition by an improved KAM iteration,and the persisting invariant tori are Gevrey smooth,with the same Gevrey index as the Hamiltonian.
Problems of the simultaneous optimal estimates and the optimal tests in general mixed models are considered.A necessary and sufficient condition is presented for the least squares estimate of the fixed effects and the analysis of variance (Hendreson Ⅲ's) estimate of variance components being uniformly minimum variance unbiased estimates simultaneously.This result can be applied to the problems of finding uniformly optimal unbiased tests and uniformly most accurate unbiased confidential interval on parameters of interest,and for finding equivalences of several common estimates of variance components.
We show the close connection between apparently different Galois theories for comodules introduced recently in [J.Gómez-Torrecillas and J.Vercruysse,Comatrix corings and Galois Comodules over firm rings,Algebr.Represent.Theory,10 (2007),271-306] and [Wisbauer,On Galois comodules,Comm.Algebra 34 (2006),2683-2711].Furthermore we study equivalences between categories of comodules over a coring and modules over a firm ring.We show that these equivalences are related to Galois theory for comodules.
In this paper we discuss the K-groups of Wiener algebra
.For the 1-shift space XGM2,we obtain a characterization of Fredholm operators on XGM2n for all n∈N.We also calculate the K-groups of operator algebra on the 1-shift space XGM2.
In the present paper we describe a specialization of prinjective Ringel-Hall algebra to 1,for prinjective modules over incidence algebras of posets of finite prinjective type,by generators and relations.This gives us a generalisation of Serre relations for semisimple Lie algebras.Connections of prinjective Ringel-Hall algebras with classical Lie algebras are also discussed.
In this paper we discuss the Einstein-Kähler metric on the third Cartan-Hartogs domain YⅢ(n,q;K).Firstly we get the complete Einstein-Kähler metric with explicit form on YⅢ(n,q;K) in the case of K=q/2+1/q-1.Secondly we obtain the holomorphic sectional curvature under this metric and get the sharp estimate for this holomorphic curvature.Finally we prove that the complete Einstein-Kähler metric is equivalent to the Bergman metric on YⅢ(n,q;K) in case of K=q/2+1/q-1.
This paper deals with asymptotic behavior of solutions to a parabolic system,where two heat equations with inner absorptions are multi-coupled via inner sources and boundary flux.We determine four kinds of simultaneous blow-up rates under different dominations of nonlinearities in the model.Two characteristic algebraic systems associated with the problem are introduced to get very simple descriptions for the four simultaneous blow-up rates as well as the known critical exponents,respectively.It is observed that the blow-up rates are independent of the nonlinear inner absorptions.
In this paper,we introduce the pre-frame operator Q for the g-frame in a complex Hilbert space,which will play a key role in studying g-frames and g-Riesz bases etc.Using the pre-frame operator Q,we give some necessary and sufficient conditions for a g-Bessel sequence,a g-frame,and a g-Riesz basis in a complex Hilbert space,which have properties similar to those of the Bessel sequence,frame,and Riesz basis respectively.We also obtain the relation between a g-frame and a g-Riesz basis,and the relation of bounds between a g-frame and a g-Riesz basis.Lastly,we consider the stability of a g-frame or a g-Riesz basis for a Hilbert space under perturbation.
In this paper,using the matrix skills and operator theory techniques we characterize the commutant of analytic Toeplitz operators on Bergman space.For f(z)=zng(z)(n≥1),g(z)=b0+b1zp1+b2zp2+…,bk≠0(k=0,1,2,…),our main result is (Mf)=(Mzn)∩ (Mg)=(Mzs),where s=g.c.d.(n,p1,p2,...).In the last section,we study the relation between strongly irreducible curve and the winding number W(f,f(α)),α∈D.
In this paper,we prove the following theorem:Let p be a prime number,P a Sylow psubgroup of a group G and π=π(G)\{p}.If P is seminormal in G,then the following statements hold:1) G is a p-soluble group and P'≤Op(G); 2) lp(G)≤2 and lπ(G)≤2; 3) if a π-Hall subgroup of G is q-supersoluble for some q∈π,then G is q-supersoluble.
.For the 1-shift space XGM2,we obtain a characterization of Fredholm operators on XGM2n for all n∈N.We also calculate the K-groups of operator algebra on the 1-shift space XGM2.
