Under some conditions, we prove the existence of H 1(R 3) solutions for the 3 D incompressible Euler equations with axisymmetric initial data.

This note is devoted to study the exponential convergence rate in the total variation for reversible Markov processes by comparing it with the spectral gap. It is proved that in a quite general setup, with a suitable restriction on the initial distributions, the rate is bounded from below by the spectral gap. Furthermore, in the compact case or for birth death processes or half line diffusions, the rate is shown to be equal to the spectral gap.

Suppose G is a finite group, R is a graded ring of type G with identity and S is a multiplicatively closed subset of the set consisting of all homogeneous elements of R. Let =x∈Gae(gx,x)a∈S, Deg (a)=g∈G] and S==x∈ G ae (gx,xh)a ∈S, Deg (a)=g∈ G, h∈ G. M G(R) denotes the matrices over R with the rows columns indexed by elements of G. In this paper, we prove that R satisfies the left Ore condition with S if and only if R# G satisfies the left Ore condition with  if and only if M G(R) satisfies the left Ore condition with S=. Inaddition, we obtained the following results:  -1 (R# G) is isomorphic to (S -1 R)# G and S=, -1 (M G(R)) is isomorphic to M G(S -1 R) as rings.

This paper provides a “independent identically copy” way to establish the strong approximation theorems for strongly mixing random variables by using a special result of Sakhanenko(1984) for independent random variables. Application to increments of partial sums isdiscussed.

In this paper the authors prove that the strongly singular integral operators are bounded from the homogeneous weighted Herz type Hardy spaces to the homogeneous weighted Herz spaces.

The series of convex functions on a Banach space is studied. The generalizations of the Moreau Rockafellar theorem are given. As an application, the partial generalization of the Kuhn Tucker theorem is obtained.

In this paper, the problem on limit cycles of Type I equation of quadratic differential systems dx/dt=-y+δx+lx 2+mxy+ny 2,dy/dt=x has been researched. It obtained the existential condition of limit cycles on large range when l=0 .Furthermore, the paper also discussed the existence problem of boundary line cycles (strange limit cycles) and bifurcation curve.

In this paper we determine all basic connected, finite dimensional algebras with finite representation type over an algebraically closed field which have normed multiplicative bases with 1 relations.

In this paper, we prove that the modulus of convexity for Banach spaces X and L p(X) satisfy the following inequalities: aδ X(bε p/2 )δ L p(X) (ε)δ X (ε), p2); cδ X(dε)δ L p(X) (ε)δ X (ε),(1

In this paper, we investigate finite rank operators in ideals of nest algebras.And then we use properties of finite rank operators to characterize such ideals.

In this paper, we investigate initial bound ary value problem of a class of quasilinear parabolic equation. The quenching phenomenon is obtained, and the asymptotic behavior of quenching solution is analyzed. The results which we obtain include the correspond conclusions of .

In this paper, strictly real Hilbert rings are further investigated. In order to characterize strictly real Hilbert rings, we prove the following results: Let A be a commutative ring with 1, and let A be the polynomial ring over A in one variable X . Then (1) A is a strictly real Hilbert ring if and only if every real maximal ideal of A contracts in A to a maximal ideal;(2) A is a strictly real Hilbert ring if and only if A is a real Hilbert ring, and every real maximal ideal of A is maximal.

In this paper, several existence theorems on multiple positive solutions of some nonlinear operator equations are obtained. The results are applied to nonlinear Hammerstein integral equations and Sturm Liouville two point boundary value problems, moreover, some new conclusions are given.

In this paper, by thinking of the complex analysis in several variables, we prove the Poincaré-Bertrand transformation formulae of the singular integrals in Clifford analysis.

In this paper, by establishing Littlewood-Paley theory associated with the generalized Sublaplacian L, we obtain the spectral multipliers theorem for L. As a consequence, the multipliers for a certain kind of Laguerre expansions are given.

In this paper, by the method of majorant to give some existence theorems of the analytic solutions of a class second order iterative functional differential equations x″(z)=mj=0 p j x j(z) (where z∈ C, m 2 is a positive integer, and x j(z) denotes the m-th iterate of the unknown function x(z)).

This paper discusses the isometric approximation problem from a finite dimensional normed space X into an infinite dimensional space C( Ω ). And it shows that the answer of the problem is negative if and only if X is not a subspace of any l ∞ n (n∈N) and Ω has infinite isolated points.

In this paper, we give some rigidity theorems which concern with 3-dim compact minimal submanifolds in a hight-dim sphere. Under a global pinching condition, the pinching constant on the scalar curvature is improved. We also study the problem of rigidity of Ricci curvature.

In the present paper we consider the small random perturbations of one-dimensional diffusion processes. By virtue of stochastic analysis methods, we investigate the asymptotics of the mean exit times and probabilistical estimates of the exit times as the perturbations tend to zero.

The defined lower type and proximate lower order for the analytic function defined by Laplace-Stieltjes transform in the half plane σ>0; we establish the relations between the proximate lower order and lower type of the transform and “coefficients” and “exponent”. It is the lower type′s sufficient and necessary conditions, extending the corresponding results of Dirichlet series.

Consider the impulsive neutral delay differential equation [y(t)+Py(t-τ)]′ +Q(t) y(t-σ)=0,t 0, t≠ t k, k=1,2,…, y(t + k) -y(t - k)=b k y(t k), k=1,2,…, (E)where τ,σ and P are constants, τ>0, σ>0, Q(t)∈ C([0,∞), R +), b k >-1, k=1,2,…. Sufficient conditions are given to insure that all solutions of Eq. (E) are oscillatory for the respective cases P -1, -1

<0 and P>0.

This paper deals with a class of nonlinear boundary value problems which appears in the study of models of flows through porous media. Existence results of asymptotic bifurcation and continua are reported both for operator equations and for boundary value problems.

This paper divides Z automata into pairs of ω automata, develops the L(MP) theory of Z . Using the technique of Z automata, it proves that the L (MP) theory of Z is decidable. As an application it also proves that the correctness problem for the finite state process is decidable.

This paper studies a class of stationary impulse control models, not only proves the existence of optimal impulse control but also constructs an optimal control.

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