Some results on the isometries and equivalences of quantum codes are pre- sented,one of which generalizes one of the results of Bogart et al.,by these results, we construct an isometry of quantum codes which is not an equivalent mapping but preserves the symplectic inner product,i.e.,a theorem of MacWilliams cannot be gen- eralized to the quantum codes.

In this paper,strong convergence theorems for approximation of common fixed points of a finite family of asymptotically demicontractive mappings are proved in an arbitrary Banach space using an implicit iteration scheme with random errors. Our results of this paper improve and extend the corresponding results.

We study the extension of isometries between the unit spheres of normed space E and l~1(F).We obtain that any surjective isometry between the unit spheres of normed space E and l~1(F)can be extended to be a linear isometry on the whole space E,and give an affirmative answer to the corresponding Tingley's problem.

In this note,the norm attainability of elementary operators and generalized derivations is established.We prove that if an elementary operator and a generalized derivation defined on B(H)are norm-attinable,then the restrictions on the unitary group of B(H)of the elementary operator and the generalized derivation are also norm-attainable,respectively,where B(H)denotes the set of all bounded linear op- erators on a Hilbert space H.

The main purpose of this paper is to construct a new Hopf algebra denoted by R(?)K#_σH arising from two important structures,crossed product algebra structure and twisted Smahs coprodcuct structure,and discuss under what condition it will be a self-dual Hopf algebra.We recover the results of[7]by trivializing the right coaction.

We study the boundedness and compactness of the composition operators between Hardy spaces on the unit ball for the case q

In this paper,the second-order differential equation involving iterates of the unknown function x″(z)=G(z,x(z),x~2(z),...,x~m(z))is investigated in the com- plex field C for the existence of analytic solutions.By reducing the equation with the Schr(?)der transformation,x(z)=y(αy~(-1)(z)),to another functional differential equation without iteration of the unknown functionα~2y″(αz)y′(z)-αy′(αz)y″(z)= (y′(z))~3G(y(z),y(αz),...,y(α~mz)),we give the existence of its local invertible analytic solutions.We discuss not only thoseαgiven in Schr(?)der transformation in the hyper- bolic case 0<|α|<1 and resonance,i.e.,at a root of the unity,but also thoseαnear resonance(i.e.,near a root of the unity)under Brjuno condition.

In this paper,the multiplication and convolution of functions in theω- ultradifferentiable function spaces ε_*(R~N)andω-test function spaces D*(R~N)are dis- cussed,and it is obtained that D(R~N)is the multiplier space of D*(R~N),D(R~N)is the multiplier space of ε_*(R~N)in the sense of convolution,and the Parseval equation holds in the spaces of D*(R~N).

We discuss the boundary structure of lattice self-affine Tiles,and obtain a sufficient condition for the boundary of a plane lattice self-affine Tile to be a simple closed curve.And as a particular application of this condition,we will provide a new proof for a Bandt-Wang theorem.

For a pair of dual frame multiresolution analyses,we construct a pair of dual frame wavelets and a pair of quasi-biorthogonal frame wavelets with the help of filter banks.Furthermore,we show necessary and sufficient conditions satisfied by filter bands of a pair of dual frame wavelets and a pair of quasi-biorthogonal frame wavelets.

There have been many studies on interpolation by neural networks in Eu- clidean spaces.However,there are plentiful concrete problems which must be measured by using non-Euclidean metrics.This paper deals with the interpolation and approx- imation of neural networks in general non-Euclidean spaces.That is,first construct interpolation networks in general spaces,and then construct approximate interpolation networks,finally,study the approximation of continuous functional with approximating network.

Let E be a real Banach space with a uniformly Gteaux differentiable norm, D be a nonempty closed convex subset of E and T:D→D be an asymptotically nonexpansive mapping with a squence{k_n}[1,∞,k_n→1.It is shown that under some suitable conditions,the sequence with errors{x_n}defined by(1.3)and(1.5) converges strongly to some fixed points of T.The results presented in this paper also extend and improve some recent results.

Using the relation between a matroid and its erections,especially the relation dealing with a special map f,this paper makes a concrete analysis of the concrete conditions for the erection of Vámos matroid.Afterwards,it obtains that except for the trivial case,Vámos matroid has no erections,thereby answering an open problem raised by Welsh"Does the Vámos matroid have an erection?".

The lower bound of the first eigenvalue of Laplacian on closed manifolds is always a very interesting problem.We study this subject in this paper under the assumption of small global curvature pinching.Finally,we derive a lower bound of the first eigenvalue of Laplacian according to the geometry of the manifolds.

We introduce the modified Ishikawa iteration for asymptotically nonexpan- sive mappings by the CQ method,and prove the strong convergence theorems of the modified Ishikawa iteration process.These results extend and improve the correspond- ing ones now existing.

Let R be a 2-torsion free commutative ring with unity,and M_n(R)(n≥2) be the algebra of all n×n matrices over R.In this paper we prove that every mapΦ:M_n(R)→M_n(R)satisfyingΦ(ABA)=Φ(A)BA+AΦ(B)A+ABΦ(A)for all A,B∈M_n(R)is of the form:There exist T∈M_n(R)and an additive derivationφof R such thatΦ(A)=AT-TA+A_φfor all A=(a_(ij))∈M_n(R),where A_φ=(φ(a_(ij))).

In this paper,a kind of multivariate linear operators,q-Stancu operators, are defined on a simplex,which generalize the famous Bernstein operators and Stancu operators.By establishing the upper and lower bound estimations of approximation order,the optimal approximation order(saturation order)and the characteristics of these operators approximating the continuous functions are characterized.Moreover, the saturation class of approximation is confirmed.

On the basis of fundamental Nevanlinna theory the problem of normality of meromorphic functions that share three finite complex values with their k-th derivatives (k is any positive integer)is discussed and some examples are provided to show the result is sharp.

Using the energy estimates and bootstrap arguments,the global existence of classical solutions for the competitor-competitor-mutualist model with cross-diffusion is proved when the space dimensions is at most 5.Under certain conditions of the coefficients of the reaction functions,the convergence of the solutions is established for the system by Lyapunov functions.

This paper deals with a class of nonlinear Schrdinger equations-ε~2△v+ V(x)v=K(x)v~p,x∈R~N,v∈W~(1,2)(R~N),v(x)>0,with potential V(x)having a positive lower bound or vanishing at infinity,respectively.By the strong maximum principle we show that the ground states concentrate uniformly in smallε>0.

We study the Riemann-Hilbert boundary value problems for some classes of hyperbolic equations in commutative quaternion algebra space with basis elements 1,i,j,k satisfying the relationship i~2=j~2=-1,ij=ji=k,and obtain the general solutions and the solvable conditions of the problems respectively in different cases.

We introduce a concept of well-formed normal forms in intermediate logics, and put forward a general method to investigate them.By applying this method,we show that HT is the weakest intermediate logic with general implicational normal form and that CPL is the only intermediate logic with restricted implicational normal form.

This paper gives a characterization of first order lattice-valued logic with the lattice being finite,inverse and having a strong character formula,that is,if L is a regular logical system stronger than L_1 and L has compactness property and LS property,then L～L_1.

For sequences of R~d-valued random vectors with operator stable distribu- tion(without Gaussian component)with an exponent A,an invertible linear operator, this paper obtians the limiting results for the partial sums and weighted sums(inculd- ing some classical summable methods,such as Cesàro's method,delayed sum,Euler's method,Borel's method and geometrical weighted sum,etc.)via integer test.As appli- cations,we obtain Chover-type laws of iterated logarithm for them under the spectral decomposition of A,which is related to the eigenvalues of A.