In logic and algebra,the researches on some logical algebraic structures are important topics at all times.BL algebras,R0 algebras and MTL algebras which are proposed recently are representative results in this area.The present paper discusses properties and algebraic structures of MTL algebras.Several characteristic properties of MTL algebras are revealed,and relationships among MTL algebras and the related algebraic structures are clarified.Moreover,characteristic properties of residual impli- cations induced by left continuous t-norms are investisgated in this paper since they are closely related to MTL algebras.
In this paper,we define"exterior boundary ball accessible domain"and make use of the modulus of curves family to obtain the following result:Let D be a bounded quasiconvex domain in Rn,f is a K-quasiconformal mapping which maps D onto B~n,if D is an exterior boundary ball accessible domain,then f∈Lip_α(D),whereα=K(1/1-n),
In this paper,it is shown that if f be a nonconstant entire function such that the hyper orderσ2(f)<(1/2),k being a positive integer,and if f and f(k)share z CM,then f(k)(z)-z=c(f(z)-z)where c is a nonzero constant.
In this paper,with the aid of iterative method for the mixed monotone operators,we study the existence of positive almost periodic solutions for some neutral integral equation,through which some known results are extended.
In this paper,the authors analyse some properties of the linear difference operator M:[Mx](t)=x(t)-Cx(t-r),and then,by employing the continuation theorem of coincidence degree principle developed by Mawhin,a class of neutral func- tional differential systems with deviating arguments is studied.Some new results on the existence of periodic solutions are obtained.The significance of this paper is that the matrix C is not required to be symmetric.Therefore,the results of this paper im- prove and extend some known results in the recent literature.Moreover,the methods to estimate a priori bounds of periodic solutions are different from the corresponding ones of the past.
This paper sets up regularity on lattice-valued logic,proves that the first or- der lattice-valued logic with the lattice being finite,inverse and having strong character formula is regular and that Fraise theorem holds on it.
We investigate the characteristic boundary value problems for first and second order complex hyperbolic equations.For the two kinds of linear equations obtain the general solutions and the solvable conditions of the problems respectively in different cases,and for the quasilinear second order complex hyperbolic equation,the prove the existence and uniqueness of its solution.
We study simultaneous approximation for the linear combination of Baskakov and Szász-Mirakian operators.Here we give a Voronovskaja type asymptotic formula and an error estimate in simultaneous approximation for these operators.
We study the Drazin invertibility of the sum of two Drazin invertible linear operators on Hilbert spaces.Moreover,the Drazin invertibility of the upper triangular operator matrix is also discussed.
We prove the corresponding rank axioms of a matroid of arbitrary cardinality defined by Betten and Wenzel in 2003.This is applied to investigate the single element extensions of matroids of arbitrary cardinality.
For the Lq-norm approximation,we determine the weakly asymptoticl order for the p-average errors of the Lagrange interpolation sequence and the Hermite-Fejér interpolation sequence based on the Chebyshev nodes on the Wiener space.By these results we know that for 2(?)q<∞,1(?)p<∞,the p-average errors of Lagrange interpolation sequence and Hermite-Fejér interpolation sequence based on the Cheby- shev nodes are weakly equivalent to the p-average errors of the corresponding best polynomial approximation sequence.In the sense of Information-Based Complexity,if permissible information functionals are function evaluations at fixed points,then the p-average errors of Lagrange interpolation sequence and Hermite-Fejér interpolation sequence based on the Chebyshev nodes are weakly equivalent to the corresponding sequence of minimal p-average radii of nonadaptive information.
In this paper,by using the infinity order type function of Xiong Qinglai's and a sufficient and necessary condition for infinity order Borel direction which was established by Chuang Chitai,the angular distribution of the solutions of differential equations with entire coefficients is discussed,the connection of location of zeros of the solution of second order or higher order differential equation et al.the Borel direction is established,which can be regarded as an alternatiue version of Wu Shengjian et al.
Necessary and sufficient conditions for uniform monotonicity,upper(lower) locally uniform monotonicity and strict monotonicity of Orlicz-Sobolev spaces with Orlicz norm are given.The monotone coefficients of the spaces are computed.Some applications to the best approximation are presented,which improve the results in [2-3].
In this paper,some sufficient conditions are given for an operator T= (?)T)_n to be bounded on H_B~p and BMO_(p,B)~-,where T_n(n∈P)are operators with property A.As applications,with the help of operator-valued martingale transforms, the strong(p,p)type,weak(1,1)type inequalities and the boundedness on BMO~-_(p,B) for maximal operators of matrix type are obtained.The results are counterparts for maximal operators in classical martingale H~p theory.
Schur type polynomial which the research base for the real symmetric form is constructed.Schur subspace which is consisted of the real symmetric polynomial vanishing at(1,1,...,1)is also studied.And constructive theory of Suchur subspace is built.As an application,we use them to determine the definition of symmetric forms and to solve some kind of the 17th Problem of Hilbert.
In this paper,we prove that if m>0 is an integer,and(a,c,δ)=(m,m+ 1,-1),(m,m+2,-2),(m,m+4,-4),or(m+2,m,2),then simultaneous Pell equations ax~2-cy~2=δ,y~2-bz~2=1 possess at most one positive integer solution(x,y,z).
A class of singular second-order periodic boundary value problems is con- sidered where the nonlinear term f(t,u)is a local Caratheódory function.Main tools are the height functions that describe the growth feature of nonlinear term f(t,u)on bounded set.Several sufficient conditions to guarantee the existence of single or multi- ple positive solutions are obtained by considering the integrations of height functions. Our work shows that the existence is independent of the properties of nonlinear term f(t,u)near u=0.
A class of Finsler metrics in the following form F=α+εβ+(kβ~2/α)+(k~2β~4/3α~3)-(k~3β~6/5α~5),are discussed,whereα=(a_(ij)y~iy~j)is a Riemann metric,β=b_iy_i is a 1-form,εand k≠0 are constants.The properties of flag curvature for these metrics are studied,and the sufficient and necessary condition of locally projectively fiat for F is obtained.
We prove the existence of invariant curves of planar reversible mapping which is quasi-periodic in one of the spatial variables,when the reversible mapping is C~l smooth.Moreover,we give the relation between l and smoothness of invariant curves and the exponent in the Diophantine condition.
We investigate the sharper threshold phenomena associated with the non- linear SchrSdinger equation with a harmonic potential,where the answer to questions of global existence vs.finite time blowup depends on the initial data.By construct- ing two types of constrained variational problems and establishing the invariant local semi-flows,we derive two different thresholds of blowup and global existence for the supercritical case of the system in two different spaces by applying the potential well argument and the concavity method.
In this paper,we prove that every a-biderivation of T(N)is an innerσ- biderivation if dim 0_+≠1 or dim H(?)≠1.As an application,we describe the form of linear map f:T(N)→T(N)satisfying f(X)X=σ(X)f(X)for all X∈T(N).
We will derive the plane isoperimetric inequality and the Bonnesen's isoperi- metric inequality by the method of integral geometry.We give simplified proofs of some geometric inequalities about the area,the length,the in-radius and the out-radius of a plane domain D.
In this paper,by using the topological degree theory and the fixed point index theory,the existence of four kinds of solutions(i.e.,zero solution,positive solu- tion,negative solution and sign-changing solution)for asymptotically linear operator equations is discussed,and the abstract results are applied to two-point boundary value problems for differential equations.
The main purpose of this paper is to use the generalized Bernoulli numbers, Gauss sums and the mean value theorems of Dirichlet L-functions to study the asymp- totic property of the difference between an r-th residue and its inverse modulo p(a prime),and give some interesting hybrid mean value formulae involving the general Kloosterman sums.
For p>0,Lutwak,Yang and Zhang introduced a star bodyΓ_(-p)K of a convex body K.In this paper we consider the question of whetherΓ_(-p)KΓ_(-p)L implies vol_n(K)(?)vol_n(L).Our results are dual forms for the studies ofΓ_p by Lutwak in the case p=1 and by Grinberg and Zhang in the case p>1.
This paper investigates a class of fourth order singular sublinear bound- ary value problems.A necessary and sufficient condition for the existence of C~2[0,1] positive solutions as well as C~3 [0,1] positive solutions is given by using fixed point the- orem of cone expansion of norm type.We also obtaied the incomparability of C~2 [0,1] positive solutions.
