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In this paper we study the local solvability of the initial-boundary problem for the modified Kawahara equation on the half line.By setting up some Strichartz-type estimates of the Duhamel forcing terms for a corresponding forced initial value problem, we prove that the initial-boundary problem of the modified Kawahaxa equation on the half line is locally solvable if the initial function belongs to H~8 (R_x~+) and the boundary function belongs to g~(x+2/5)(R_t~+) with 1/4■s＜2.

Let P_k denote any integer with no more than k prime factors,counted according to multiplicity.It is proved that for almost all sufficiently large even integers n■2 (mod 6),the equation n=P_1+P_2 has a solution in prime variables P_1,P_2 such that P_2+2=P_3.For every sufficiently large odd integer N■1 (mod 6),the equation N=p_1+p_2+p_3 has a solution in prime variables P_1,P_2,P_3 such that p_2+2=P_3,P_3+2=P_2.

In this paper,we study the convergence of solutions of a class of delay differ- ential equations.These equations have important practical applications and generalize those on which Bernfeld and Haddock conjectured that each solution of the equations tends.to a constant.We first give an example to point out the errors in several existing works on the convergence of solutions of the equations as well as their generalizations. Then we confirm the Bernfeld-Haddock conjecture under weaker conditions.Our re- sult corrects and improves the existing ones.An appendix by Professor Tongren Ding is also given to correct the mistakes in one of his works.

In this paper,we discuss the natural action of symmetric group on the moduli space of n-marked Riemannian spheres.We calculated out all the fixed points of this action and all the symmetric types of n-marked Riemannian sphere.We also discussed the dynamic property of the action of SL(2,C) on Riemannian sphere,so as to give a description of the periodic property of this action.Basing on this,we give a description of the singularity of the moduli space of n-punctured Riemannian sphere.

In this paper,we show that the lattice of invariant subspaces for a class of subdecomposable operators is rich.Moreover,we provide a counter-examples on a Hilbert space in which the operator T has infinitely many invariant subspaces while the invariant subspace lattice Lat(T) for T is not rich.

In this paper,a feasible sequential equality constrained quadratic program- ming algorithm is proposed to solve the nonlinear inequality constrained optimization. Per single iteration,it is only neccessary to sovle three equality constrained quadratic programmings with the same scale(or in addition,a linear programming),so the com- putational effort is reduced.The theoretical analysis shows that the algorithm is global and superlinear convergence under some suitable conditions.Numerical results show that the method in this paper is effective.

In this paper,we introduce and study a new system of generalized mixed vector quasi-equilibrium problems in product FC-spaces.By using the maximal element theorem,some existence results of solutions for the system of generalized mixed vector quasi-equilibrium problems in product FC-spaces are given.The results presented in this paper improve and extend some known results in the literature.

The aim of this note is to study the local regularity of solutions in Morrey spaces to the elliptic equation in divergence form-(a_(ij)u_(x_i))_(x_j)+b_iu_(x_i)-(d_ju)_(x_j)+cu= (f_j)_(x_j),a.e.x∈Ω.Where a_(ij)∈VMO∩L~∞(Ω),and the lower order terms belong to suitable Morrey spaces.

In this paper,we introduce T_0-,T_1-,T_2-,T_3-,T_4-separation axioms in the framework of I-fuzzy topology,and give some of their equivalents as well as the relations with one another of these axioms.

Let A be a unital complex Banach algebra,Ωbe a region andγbe a rectifiable closed curve such that ins(γ)Ω.It is proved that the Riesz functional calculus f:x)f(x) is a Lipschitz operator from some A_δ~γinto A,i.e.,f∈L~1(A_δ~γ,A) and has the Lipschitz constant L_1 (f)■(M_f(γ)Γ)/(2πδ~2)As an application,Lipschitz propertites of the operator valued root-function TT 1/m and the absolute value function T|T| are disccussed.Lastly,it is proved that f∈L~1 (E,A) holds for every nonempty bounded subset E of A.

In this paper,we show that the only complete spacelike hypersurfaces with constant mean curvature in Lorentz-Minkowski space which are bounded be- tween two concentric hyperbolic cylinders are the hyperbolic cylinders,i.e.,the product R~k×H~(n-k).In the case of constant higher mean curvature,if the sectional curvature is bounded from below,then the only complete spacelike hypersurfaces in Lorentz- Minkowski space which are bounded between two concentric hyperbolic spaces are the hyperbolic spaces.

Let p be a prime,n be any positive integer.We define the Smarandache primitive function S_p(n) as the smallest positive integer such that S_p(n)! is divisible by p~n.In this paper,we use the elementary methods to study the solvability of the equation S_p(1)+S_p(2)+…+S_p(n)=S_p((n(n+1)/2)),and give all its solutions.