We study a class of not-finitely graded Lie algebras related to generalized Heisenberg-Virasoro algebras HV,and we determine the concrete structures of the derivations of HV.To compute the derivations Der HV of HV,we can decompose them into a sum of the inner derivations ad HV and the derivations (Der HV)0 whose degree is zero.
We construct indecomposable quadratic lattices of rank 3,4,5 and 6 over a suitable Hasse domain of the rational function field F19(x),which,in particular,solves the problem proposed by Gerstein about the existence of indecomposable quadratic lattices of rank 5 over global function fields.
Let F be the familiar class of normalized univalent functions in the unit disk.Fekete and Szegö proved the well-known result maxf∈F|a3-λa22|=1+2e-2λ/1-λ for λ∈[0,1].We investigate the corresponding problem for the class of starlike mappings defined on the bounded starlike circular domain in Cn.The proofs of these results use some restrictive assumptions,which in the case of one complex variable are automatically satisfied.
The main purpose of this paper is using the analytic methods and the properties of Gauss sums to study the computational problem of one kind hybrid power mean of two-term exponential sums and two-term character sums,and give an exact expression for it.As its applications,we obtained an asymptotic formula for the hybrid power mean and a sharp asymptotic formula for the mean value of Dirichlet L-functions weighted by the two-term exponential sums and two-term character sums.
Let Tσ be the bilinear Fourier multiplier operator associated with multiplier σ satisfying the Sobolev regularity that supk∈Z ||σk||Ws (R2n)<∞ for some s∈(n,2n].We give the boundedness of Tσ and the commutators Tσ,b generated by Tσ and b=(b1,b2)∈(BMO (Rn))2,as well as the compactness of Tσ,b (if b1,b2∈CMO (Rn),the BMO-closure of Cc∞ (Rn)) from Lp1,λ(ω1)×Lp2,λ(ω2) to Lp,λ(νw) for appropriate indices p1,p2,p∈(1,∞)(1/p=1/p1+1/p2) and multiple weights ω=(ω1,ω2)∈Ap/t (R2n).The main ingredient is to establish the multiple weighted estimates for the variants of certain multi (sub) linear maximal operators on the weighted Morrey spaces,and a sufficient condition for a subset in the weighted Morrey spaces to be a strongly precompact set,which are in themselves interesting.
Applying I-convergence and I*-convergence of sequences in Banach space X,this paper first present a sufficient and neccessary condition for an ideal I has the additive property,then establish the relation between w-I-convergence,w-I*-convergnence and uni-w-I*-convergence,also the connection between w-I-convergence and convergence,finally we define I-A-statistical convergence which is the generalization of I-λ-statistical convergence,and by using subdifferential mapping to define a set of finite additive measures,we show the equivalent description of I-A-statistical convergence,this is an application of finite additive measures.
The definitions of partially weakly increasing property of a pair of random mappings (F,G) with respect to g and partially weakly increasing property of (F,G) are introduced and the existence of common coupled random coincidence points and common coupled random fixed points for a sequence of mappings Fk:Ω×X×X→X,k=1,2,...and g:Ω×X→X and h:Ω×X→X under various contractive conditions in complete and separable partially ordered metric spaces are studied.Many new results are obtained,which generalize some results in the corresponding literatures.
The paper studied the deficiency and value distribution of meromorphic functions concerning difference.We mainly proved:let c be a nonzero finite complex number,let f(z) be a transcendental entire function in C,and let n be a positive integer.If Δcnf(z)≠0,then either f(z) takes on every complex value infinitely often,or Δcnf(z) takes on every non-zero complex value infinitely often.
Many authors discussed the problem of existence and growth of complex difference equations,and obtained some intererting results.Using Nevanlinna theory of the value distribution of meromorphic functions,we investigate the expression of meromorphic solutions of a type of system of comples difference equations,and extend some results of solutions of complex difference equations to systems of complex difference equations.
We using the technique of space decompositions,the representation of the Drazin inverse for multiplicative combination aP+bQ+cPQ+dQP+ePQP associated with two idempotents P and Q is obtained under the condition PQP=QPQ.
We focus on symmetric partially balanced incomplete block designs with automorphism group M12 acting on 396 points.To begin with,we proved that there is no non-trivial 2-(396,k,λ) symmetric design admitting M12 be an automorphism group.Then up to isomorphism,we obtained three SPBIB designs with v=396 and k=80.Finally,we gave the complete classification of SPBIB designs with v=396 and automorphism group M12.
We use the Schauder fixed point theorem and the upper and lower solutions method to investigate the existence and uniqueness of positive solutions for a class of fractional p-Laplacian boundary value problems,and establish the iterative sequences for the unique solution.
Let M2 be the algebra of all 2×2 complex matrices and Φ:M2→M2 be a linear map.A 1-1 correspondence between the set of 3×3 complex orthogonal matrices and the set of similarity transformations of M2 is established,which then is applied to show that Φ preserves the determinant (resp.the spectrum,the peripheral spectrum) of Lie products if and only if there exist a scalar c∈{±1,±i},matrices S,T∈M2 with T invertible,such that Φ(A)=cTAT-1+tr(SA) I for all A∈M2.
The crossing numbers of Km-□Pn were successively determined for 4 ≤ m ≤ 6 by Kleš? et al.In this paper,the crossing numbers of Km--2K2 are obtained by the construction method for 4 ≤ m ≤ 12 and m≠10,12.On the basis,the crossing numbers of Km-□Pn for 4 ≤ m ≤ 9 and m≠8 can be determined.The method that we use is more general relatively.
Let H be an infinite dimensional separable complex Hilbert space and B(H) the algebra of all bounded linear operators on H.T∈B(H) satisfies Property (ω) if σa(T)\σea(T)=π00(T),where σa(T) and σea(T) denote the approximate point spectrum and essential approximate point spectrum of T respectively,π00(T)={λ∈iso σ(T):0N (T-λI)<∞}.T∈B(H) is said to have the perturbation of Property (ω) if T+K satisfies Property (ω) for all compact operator K∈B(H).We prove the equivalence of the perturbation of Property (ω) for anti-diagonal operator matrix and its square.
In this note,the spectrum of Jordan products of positive contractions are discussed.We shall establish characterizations of the minimum and maximum spectrum points of Jordan products of positive contractions.And a characterization of minimum spectral points of Jordan products of orthogonal projections is given.
