In the present note the irrationality measure of Mahler's transcendentalfractions is studied in the general case. The upper and lower bounds for the irrationalityexponent of these fractions are estimated, and the exact values of the irrationalityexponent of certain particular fractions are given.

By introducing the concept of essentially compact subsets of the spaces lp(p ≥ 1), the strongest Orlicz-Pettis topology and the largest mappings family F whichyielded this topology in abstract duality pair (E,F) are obtained. Through usingthese results, the relationship between Dierolf topology F(M*) and Tweddle toplogyT(E, T′) has been shown. It is also proved that both conditionally o(F, E)-sequentiallycompact subsets of F and o(F, E)-countably compact subsets of F belong to the largestmappings family f. Thus, some famous theorems, such as the Graves-Ruess theorem onvector measures, the Thomas theorem on abstract function theory, etc., are improvedsubstantially.

In this paper we investigate the oscillatory properties of solutions of impulsivehyperbolic partial differential equations with fixed moments of impulse effects. Severaloscillation criteria are established for impulsive hyperbolic boundary value problemssubject to two different boundary conditions.

Let p be an odd prime. Let h and ε denote the class number and thefundamental unit of the real qnadratic field Q( p) respectively In this paper, usingsome e1ementary methods, we prove that if p ≡ 3 (mod 4), then 6h εh< (p+α+2)α+2/4(α+2)！, where α = [( p + 1)/2l.

In this paper, the long time behaviors of non-autonomous Navier-Stokesequations on unbounded domains were studied. The ekistence of uniform attractorwas proven when external force terms satisfied suitable conditions. Moreover, theupper bounds of the uniform attractor's dimensions were given.

This paper gives some new fixed point theorems for increasing operatorswithout continuity, which satisfy a compactness condition given by Monch.

In this paper we consider the question: Which classes in the unorientedbordism group of free Z2m-1 actions can be realized as Z2-fixed set of almost free Z2mactions on a closed manifold with Z2-fixed point set having constant codimension k?

In this paper, we give a sufficient and necessary condition of DerL=adL.

A characterization of hereditary algebras is given by means of exact Borelsubalgebras. Moreover, a sufficient and necessary condition,which states when a prin-cipal subalgebra becomes an exact Borel subalgebra, is proved

In this paper, we consider wedst construction question in view of the fixedpoiat of an OPerator. In result, we get a nonlinear operator and investigate somepropoties of this nonlinear opetator.

With the help of continuation theorem in conincidence degree theory andLyapunov funcitonal, we study existence and global attractivity of positive periodicsolution of multispecies ecological competition system with several delays. Some newresults are obtained. Example shows that our results are more general and more easilyverifiable.

In this paper, using some properties of the generalized Lucas sequences,we extend some results of Bender and Herzberg concerning the equation ax2 + by2 =1,2,4Pn, and we obtain a complete answer to the problem of the solvability of theabove equation, and we obtain some applications of the above results to exponentialdiophantine equations.

This paper proved some uniqueness theorems for two meromorphic functionswhich together with their k-th derivatives share the same finite sets of distillct smallfunctions CM or IM.

Let G be a second countale groupoid with Haar system {λu}, A be an abeliangroup which left invariant acts on G, then we have a C*-dynamic system (C*(G), A, β).In this paper we have studied the existence of quasi-invariant measure with certainproperties, using these measures some important results about crossed products andgroupoid C*-algebras have been obtained.

Let X and Y be independent standaxd Brownian motions in Rd1 and Rd2respectively, with X(0) = Y(0) = 0. The process Zd1,d2 = (ztd1,d2,t≥0) given byztd1,d2=X(|Yt|) is called an iterated Brownian motion. In this paper we establish aChung-type law of the iterated logarithm for Zd1,d2.

In this paper, we prove the self-containning property of Minimal SpanningTree (MST) in nice infinite Euclidean points, from which and the results of AlexanderK. S. in [1] on two-dimensional Poisson continuum percolation, we get a new proof ofAldous D. and Steele's J. M. conjecture in [2] in the two-dimensional case- Actually,we prove it directly while Alexander K. S. prove it by excepting in [3], clearly, ourproof is simpler. For Poisson continuum percolation, we get a description on thetwo-dimensional critical value corresponding to Poisson MST, furthermore, lower andsupper bounds of the critical value related to site percolation are given.

Conditions for the solrability of entire (0, m1,...,mq) interpolationhave been given by Liu Yongping. In this paper, the saturation rate and class of theseoperators is determined in LP(R) Spaces (1≤ p < +∞).

Consider the initial-boundary value problem for the Cahn-Hilliard equation:ut + λ△2u - △f(u)= 0, (f(u) = ∑2p-1 j=1 αjuj with α2p-1 > 0) It is proved that theproblem possesses in H1 - H3 a global attractor Af(α) which is stable with repect toperturbations in the coefficients of f in the sense of Hausdorff semi-distance in H2.

In this article, two classes of nonlinear reaction-diffusion equations arisingin modeling biodegradation in groundwater are investigated. Using the method ofupper and lower solutions, Lp estimates and semigroup we obtain the global ekistence,uniform boundedness, asymptotic behaviour, decay estimates of solution.

In this paper, using the Nevanlinna's value distribution theory, we investigatethe existence problems of admissible solutions of two types of differential equations inthe complex plane and improve some theorems in [1] etc. and obtain some resultswhich are more precise and more general than the previous ones.

Let G be a souble block-transitive automorphism group of 2-(v, 6, 1) design.If G is not flag-transitive, then (1) v = 91 and G = Z91 x Zd, where 3|d|12, or (2)v = Pm and G≤ 5 A L(1,Pm), where p ≠ 2 is a prime and m a positive integer. Whenp = 3, 4|m and m > 4. When p≥ 5, Pm ≡ 1(mod3O).

In this paper, we give some residually finite properties of soluble groups offinite rank, which are the generalizations of the theorems of Smelkin and others.

Let V be a nonnegative potential belonging to the reverse Holder classB2n, λbe any real parameter. The Dirichlet and Neumann problems of Schrodingerequation of form, -△u + Vu + iλu = O in Lipschitz domain D is studied, and ealstence,uniqueness and uniform regularity of the solution for LP boundary data are obtained.

Main results of this paper as follows: Suppose f(t,u): (O, 1) x (0, +∞) →[0,+∞) is continuous, is dereasing on u; there erists real number b > 0 such thatf(t, ru) ≤ r-b f(t,u) for any 0 < r < 1 and (t, u) ∈ (0, 1) x (0, ∞). Then, a necessaryand sufficient conditinn for the Singular second order boundary problemto have positive solutions is 0 < ∫01 G(s,s)f(s, 1)ds < ∞, a necessary and sufficientcondition for that to have C1[0, 1] positive solution is 0 <∫01 f(s,G(s, s))ds < ∞.Where α, β, δ, γ are nonnegative real numbers and αγ +αδ+ βγ > 0, G(t, s) is Green'sfunction of the corresponding boundary value problem.

In this paper, we consider the problem of the existance of non-separablebivariate othonormal compactly supported wavelet basis when the symbol has specialform. We have reached a conclusion, when the symbol has a certain form, non-separablewavelet basis does not exist.

The purpose of the present paper is to study generic minimal submanifold of quaternionic projective space, an integral formula is obtained, and we obtain the sectional curvature's pinching theorem of the compact minimal submanifold.

In this paper, a general univalency criteria for holomorphic on unit ball of Cn is obtained by means subordination chains and many concrete univalancy criteria are given as special cases of the main theorem. Some of them are generalize the well known results of Ahlfors Becher and Krzyz, and others are new.

In this paper we first present some conditions on Banach lattice E such that the space Lr(E,F) is a Riesz space even if Banach lattice F is not Dedekind a-complete, then we deduce some characterizations on Banach lattice F such that each continuous operator from a Lp-space into F is regular. Some related results are also provided.

In this paper, AS property is introduced, and a problem in [1] is discussed. First, the paper shows that the Scott topology on a distributive complete lattice L has a basis of open filters if and only if L is a KS. frame for some ordinal number a, i.e., KS frame. By the result, one can judge whether the Scott topology and the Scott open filter topology on a distributive complete lattice are coincide. Then some KS frames are constructed in the paper, which are not continuous.

For positive integer n = a 10kn + + a0, we say that a, a0 are the digits of n, and denote s(n) = a + + a0 ), sm(n) = (a) m + + (a))m. We call 1m2m3m4m5m6m7m8m9m 1m0m1m1m1m2m1m3m1m4m the m-order sequence of digits, and define the function fm (x) = 1m + 2mx1 + + 9mx8 + 1mx9 + 0x10 + 1mx11 + 1mx12+ . Two theorems on fm(x) are given.

Let E be a Cantor-type set on real line and let Ea = E+a = { } for . Let Go = { ; dimH(E E) = dimB(Ea E) = pdimH E}, 0 < p < 1, where E - E = {x - y: x,y E}. The fractal dimensions of Ea E and Gp are determined under some conditions.

This paper is concerned with nonexistence of positive solution of a class of nonlinear delay partial difference equation. Sufficient conditions are obtained for the nonexistence of positive solutions of this equation.

In this paper, we first give the concept of a Cartan embedding of a homogeneous space, then using the theory of automorphisms of Lie groups and Lie algebras, we determine the compact Riemannian 4-symmetric spaces whose Cartan embedings are minimal.

In this paper, we give the following results: (1) A class of planar n-polynomial system with at least [n2] weak focus of order 1. (2) A class of planar n-polynomial system with at least [n2] family limit cycles.

In this paper, some construction theorems of pluriharmonic maps into complex Grassmann manifolds are obtained. These generalize the results of Mo Xiaohuan, Burstall F. E., Wood J. C. and Udagawa S.

In this paper, we discus the growth of meromorphic functions with a deficient value, and prove that. Suppose that f(z) is a transcendental meromorphic function of lower order with a deficient value, let =fnP[f] + P(f), where, P[f] and Q[f] are differential polynomials of f(z), and all of the orders of the coefficients of Q[f] and P[f] are less than , furthermore, the weight of P(f) is at most n - 3. If there exist finite number of rays satisfy with a positive number , for any small positive number , then max1 where, is the order of f(z).

In this paper, we consider the non-stationary MDP average model with countable state space and arb.iotrary action space : Using the (f, B)-generated policies of Feinberg E. A. for reference. We put forward the (G, B)-generated policies which are the generalization of Markov policies and (f, B)-generated policies of Feinberg E. A.. By probability and analysics method, we prove the existence of persistently optimal (G, B)-generated policies. under weaker ergodict conditions.

In this paper, we give the strongest admissible polar topology F(Us) for which it has the same s-multiplier convergent sequence as weak topology in the locally convex space. Also we obtain the sufficient condition and necessary condition for Thus, we prove that c0 (or lp, 0 < p < )- multiplier convergence is invariants with respect to all admissible polar topology.

The author establishes the connection between the modulusμ(γ) of the plane Grtzsch ring and its generalizationμa(γ), which appears in Ramanujan's generalized modular equation, and extends several well-known results forμ(γ) toμa(γ), thus providing a method for the study of the modular equations.

Let l(y) = be a symmetric differential expression defined on interval [a). In L2 , we give the complete characterization for all maximal accretive operators associated with l(y) via explicit boundary conditions, and we obtain the complete analytic description for all nonnegative self-adjoint extensions of the minimal operator generated by l(y).