SOME SMALL DEVIATION THEOREMS FOR ARBITRARY CONTINUOUS RANDOM SEQUENCE

Let （Xn）n∈EN be a sequence of arbitrary continuous random variables, by the notion of relative entropy hμ^μ（w） as a measure of dissimilarity between probability measure # and reference measure μ, the explicit, general bounds for the partial sums of arbitrary continuous random variables under suitable conditions are developed. The argument uses the known and elementary lcmma of convergence for likelihood ratio.

Inversion formula and Parseval theorem for complex continuous wavelet transforms studied by entangled state representation

In a preceding letter （2007 Opt. Lett. 32 554） we propose complex continuous wavelet transforms and found Laguerre-Gaussian mother wavelets family. In this work we present the inversion formula and Parseval theorem for complex continuous wavelet transform by virtue of the entangled state representation, which makes the complex continuous wavelet transform theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.

APPROXIMATE SAMPLING THEOREM FOR BIVARIATE CONTINUOUS FUNCTION

An approximate solution of the refinement equation was given by its mask, and the approximate sampling theorem for bivariate continuous function was proved by applying the approximate solution . The approximate sampling function defined uniquely by the mask of the refinement equation is the approximate solution of the equation , a piece-wise linear function , and posseses an explicit computation formula . Therefore the mask of the refinement equation is selected according to one' s requirement, so that one may controll the decay speed of the approximate sampling function .

Caputo-Hadamard型分数阶隐式微分方程周期边值问题解的存在性

用连续性定理讨论一类Caputo-Hadamard型分数阶隐式微分方程周期边值问题,得出了解的存在性结果,并给出具体实例进行说明.

Banach空间中均匀连续映射的一个扩张定理

把定义在Banach空间中闭球上的均匀连续映射扩张到全空间。

ON THE EXISTENCE OF ZERO POINTS OF A CONTINUOUS FUNCTION

A sufficient condition is given to assert that a continuous mapping between Rm and Rn has a zero. The constructive proof of the result is based upon continuation methods and supplies the existence of a path leading to the zero point.

ARBITRARILY LONG ARITHMETIC PROGRESSIONS FOR CONTINUED FRACTIONS OF LAURENT SERIES

A famous theorem of Szemer＇edi asserts that any subset of integers with posi- tive upper density contains arbitrarily arithmetic progressions. Let Fq be a finite field with q elements and Fq（（X^-1）） be the power field of formal series with coefficients lying in Fq. In this paper, we concern with the analogous Szemeredi problem for continued fractions of Laurent series： we will show that the set of points x ∈ Fq（（X-1）） of whose sequence of degrees of partial quotients is strictly increasing and contain arbitrarily long arithmetic progressions is of Hausdorff dimension 1/2.

INTERSECTION THEOREMS CONCERNING NONCOMPACT SETS WITH H-CONVEX SECTIONS AND THEIR APPLICATIONS

In this paper, we prove some intersection theorems concerning noncompact sets with H-convex sections which generalize the corresponding results of Ma, Fan, Tarafdar, Lassonde and Shin-Tan to H-spaces without the linear structure and to noncompact setting. An application to von Neumann type minimax theorems is given.

ON THE CONDITIONAL VERSION OFKOLMOGOROV'S THREE-SERIES THEOREM

This paper studies the conditional version of Kolmogorov’s three-series theorem, and gets a new extention form of the conditional version. The results here present us an answer to the question when (or where) the conditional version also provide necessary conditions for convergence in dependent cases. Furthermore, some new sufficient conditions are obtained.

Hlder continuity of two types of bidirectionally coupled generalised synchronisation manifold

This paper studies the existence of HSlder continuity of bidireetionally coupled generalised synchronisation （GS）. Based on the slaving principle of synergetics and the modified system approach, it classifies the GS into several types. The existences of two main types of HSlder continuous bidirectionally coupled CS inertial manifolds are theoretically analysed and proved by using the Schauder fixed point theorem. Numerical simulations illustrate the theoretical results.

SYSTEM OF COINCIDENCE THEOREMS IN PRODUCT TOPOLOGICAL SPACES AND APPLICATIONS (Ⅰ)

A new notion of finite continuous topological space（in short, FC-space） with out convexity structure was introduced. A new continuous selection theorem was established in FC-spaces. By applying the continuous selection theorem, some new coincidence theorems for two families of set-valued mappings defined on product space of noncompact FC-spaces are proved under much weak assumptions. These results generalize many known results in recent literature. Some applications will be given in a follow-up paper.

NASH EQUILIBRIA WITHOUT CONTINUITY OF THE CHOICE RULES

The proposal in Alcantud and Alo′s-Ferrer [1], where players that express their tastes according to choice rules facing a competitive situation, is further exploited here. We prove that, under lack of continuity of the choice rules it is also possible to ensure the existence of equilibrium. We shall appeal to general situations that are fulfilled by well-established models, where players have non-transitive preferences of various types.

A SPECIAL MODULUS OF CONTINUITY AND THE K-FUNCTIONAL

We consider the questions connected with the approximation of a real continuous 1-periodic functions and give a new proof of the equivalence of the special Boman-Shapiro modulus of continuity with Peetre’s K-functional. We also prove Jackson’s inequality for the approximation by trigonometric polynomials.

Some embedding theorems for W～(1,p)(Ω, H～n)

For the maps on the Heisenberg group target, we prove a Poincare type inequality. Applying this Poincare type inequality, we obtain the corresponding versions of Sobolev and Rellich embedding theorems.

PIECEWISE CONTINUOUS SOLUTIONS OF INITIAL VALUE PROBLEMS OF SINGULAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH IMPULSE EFFECTS

Results on the existence of piecewise continuous solutions for two classes of initial value problems of impulsive singular fractional differential equations are obtained.

ON THE SPECTRAL CHARACTERIZATION OF A STRONGLY CONTINUOUS PERTURBED SEMIGROUP

In this paper, we get a sufficient condition to estimate the essential type of a strongly continuous sendgroup in a Banach space, using oh condition we prove that the essential type of the strongly continuous semigroup don't increase under the A-smoothing perturbation and establish the spectral mapping theorem for the asymptotic parts of the spectrum of generator and semgroup.

Framing Noether’s Theorem

We discuss Noether’s theorem from a new perspective and show that the spatial continuous symmetries of a system are on one hand symmetries of the space and on the other hand are dictated by the system’s potential energy. The Noether’s charges arising from an infinitesimal motion, or a Killing vector field, of the space, are conserved if the Lie derivative of the potential energy by this vector field vanishes. The possible spatial symmetries of a mechanical system are listed according to the potential energy of the external forces.

NEW FIXED POINT THEOREMS FOR P_1-COMPACT MAPPINGS IN BANACH SPACES

E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder＇s theorem, Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem, etc.

Common Fixed Point Theorem in Intuitionistic Fuzzy Metric Space Using <i>R</i>-Weakly Commuting Mappings

In this paper, we prove a common fixed point theorem in Intuitionistic fuzzy metric space by using pointwise R-weak commutativity and reciprocal continuity of mappings satisfying contractive conditions.