THE BASIC THEORY OF SOLUTIONS OF FUNCTIONAL DIFFERENTIAL EQUATIONS WITH BOUNDED DELAY IN THE SPACE OF INTEGRABLE FUNCTIONS

在可积函数空间中讨论有界滞量泛函微分方程，建立其解的基本理论，包括解的存在性，唯一性及延展性。

Differentiability of Convex Functions in Locally Convex Spaces（Ⅰ）──Continuous Convex Functions and Gateaux Differentiability

The aim of this paper is to investigate the differentiability(Gateaux differentiabllity and subdifferentiability) of continuous convex functions on locally convex spaces and to study the behaviour of some important results for this research area in locally convex spaces.

MULTI-SCALE COHERENT STRUCTURES IN TURBULENT BOUNDARY LAYER DETECTED BY LOCALLY AVERAGED VELOCITY STRUCTURE FUNCTIONS

The time sequence of longitudinal velocity component at different vertical locations in turbulent boundary layer was finely measured in a wind tunnel. The concept of coarse_grained velocity structure functions, which describes the relative motions of straining and compressing for multi_scale eddy structures in turbulent flows, was put forward based on the theory of locally multi_scale average. Based on the consistency between coarse_grained velocity structure function and Harr wavelet transformation,detecting method was presented, by which the coherent structures and their intermittency was identified by multi_scale flatness factor calculated by locally average structure function. Phase_averaged evolution course for multi_scale coherent eddy structures in wall turbulence were extracted by this conditional sampling to educe scheme. The dynamics course of multi_scale coherent eddy structures and their effects on statistics of turbulent flows were studied.

A NOTE ON MEYER-KONIG AND ZELLER OPERATORS FOR FUNCTIONS OF BOUNDED VARIATION

In the present note we give the correct and improved estimate on the rate of convergence of integrated Meyer-Konig and Zetter operators for function of bounded variation.

A Certain Subclass of Analytic Functions with Bounded Positive Real Part

For real numbers α and β such that 0≤α<1<β, we denote by T(α,β) the class of normalized analytic functions which satisfy , where U denotes the open unit disk. We find some relationships involving functions in the class T(α,β). And we estimate the bounds of coefficients and solve Fekete-Szego problem for functions in this class. Furthermore, we investigate the bounds of initial coefficients of inverse functions or bi-univalent functions.

A SHARP ESTIMATE ON THE DEGREE OF APPROXIMATION TO FUNCTIONS OF BOUNDED VARIATION BY CERTAIN OPERATORS

Recently Guo introduced integrated Meyer -Konig and Zeller operators and studied the rate of convergence for function of bounded variation. In this note we give a sharp estimate for these operators.

MEROMORPHIC FUNCTIONS WITH BOUNDED BOUNDARY ROTATION

In this article, we generalize the class of meromorphic functions with bounded boundary rotation and related classes. Characterizations and some properties of these classes of functions are given.

Estimation of Derivatives for Bounded Regular Vanishing Functions

In this paper, we mainly discuss the problem of estimating the n-th derivative for bounded regular vanishing functions. The estimation of the n-th derivative for the function is deduced by the 1-th and 2-th derivative.

α-CARLESON MEASURE AND BLOCH FUNCTIONS ON BOUNDED SYMMETRIC DOMAINS OF C^n

In this paper we defineα-Carleson measure in the Bergman metric on bounded symmetric domains. Some necessary and sufficient conditions about it and Bloch functions on the domains are given.

Design of bounded feedback controls for linear dynamical systems by using common Lyapunov functions

For a linear dynamical system,we address the problem of devising a bounded feedback control,which brings the system to the origin in finite time.The construction is based on the notion of a common Lyapunov function.It is shown that the constructed control remains effective in the presence of small perturbations.

Nemytskii Operator in the Space of Set-Valued Functions of Bounded <i>φ</i>-Variation

In this paper we consider the Nemytskii operator, i.e., the composition operator defined by (Nf)(t)=H(t,f(t)), where H is a given set-valued function. It is shown that if the operator N maps the space of functions bounded φ1-variation in the sense of Riesz with respect to the weight function αinto the space of set-valued functions of bounded φ2-variation in the sense of Riesz with respect to the weight, if it is globally Lipschitzian, then it has to be of the form (Nf)(t)=A(t)f(t)+B(t), where A(t) is a linear continuous set-valued function and B is a set-valued function of bounded φ2-variation in the sense of Riesz with respect to the weight.

Some Results on the Space of Bounded Second Variation Functions in the Sense of Shiba

In this paper, we study the structure of the space of functions of bounded second variation in the sense of Shiba;an integral representation theorem is also proved and necessary conditions are given for that the space be closed under composition of functions. Another significant result is the proof that this space of bounded second variation in the sense of Shiba is a Banach algebra, which is not immediate as it happens in other spaces of generalized bounded variation.

POLYNOMIALLY BOUNDED COSINE FUNCTIONS

We characterize polynomial growth of cosine functions in terms of the resolvent of its generator and give a necessary and sufficient condition for a cosine function with an infinitesimal generator which is polynomially bounded.

Maximally Holomorphic Functions of a Bounded Linear Operator

The maximally holomorphic functions of a bounded linear operator is introduced and applied to representthe spectrum and characterize the single--valued extension property. The well known results of quasi--nilpo-tent equivalent operators follow easily from the relation of their maximally holomorphie functions.

Differentiability of Convex Functions in Locally Convex Spaces(Ⅱ)──Frechet

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Uniformly Bounded Set-Valued Composition Operators in the Spaces of Functions of Bounded Variation in the Sense of Riesz

We show that the lateral regularizations of the generator of any uniformly bounded set-valued composition Nemytskij operator acting in the spaces of functions of bounded variation in the sense of Riesz, with nonempty bounded closed and convex values, are an affine function.

Cortico-striatal gamma oscillations are modulated by dopamine D3 receptors in dyskinetic rats

Long-term levodopa administration can lead to the development of levodopa-induced dyskinesia.Gamma oscillations are a widely recognized hallmark of abnormal neural electrical activity in levodopa-induced dyskinesia.Currently,studies have reported increased oscillation power in cases of levodopa-induced dyskinesia.However,little is known about how the other electrophysiological parameters of gamma oscillations are altered in levodopa-induced dyskinesia.Furthermore,the role of the dopamine D3 receptor,which is implicated in levodopa-induced dyskinesia,in movement disorder-related changes in neural oscillations is unclear.We found that the cortico-striatal functional connectivity of beta oscillations was enhanced in a model of Parkinson’s disease.Furthermore,levodopa application enhanced cortical gamma oscillations in cortico-striatal projections and cortical gamma aperiodic components,as well as bidirectional primary motor cortex(M1)↔dorsolateral striatum gamma flow.Administration of PD128907(a selective dopamine D3 receptor agonist)induced dyskinesia and excessive gamma oscillations with a bidirectional M1↔dorsolateral striatum flow.However,administration of PG01037(a selective dopamine D3 receptor antagonist)attenuated dyskinesia,suppressed gamma oscillations and cortical gamma aperiodic components,and decreased gamma causality in the M1→dorsolateral striatum direction.These findings suggest that the dopamine D3 receptor plays a role in dyskinesia-related oscillatory activity,and that it has potential as a therapeutic target for levodopa-induced dyskinesia.

SOME PROPERTIES OF BOUNDED SETS IN INDUCTIVE LIMITS

Let (E,ξ）=indlim (En,ξn） be an inductive limit of a sequence of locally convex spaces,For brevity,denote by (DS) each set Bbounded in (E,ξ） is contained in some En； and (DST) each set B bounded in (E,ξ） is contained and bounded in some (En,ξn）. Theovem 1.(DS) holds provided that (i) for each n∈N,there is a neighborhood Un of o in (En,ξn） and m(n)∈ such that -↑Un^E包含于Em(n),and (ii) for any neighborhood V n of o in (En,ξn）,∞↑Un=1 Vn absorbs every bounded set in (E,ξ）. theorem 2 Let all (En,ξn） be metrizable and (DS) hold,then for each bounded set B IN (E,ξ）and each n ∈N thcrc is a neighborhood U k of o in (Ek,ξk）, 1≤k≤n ,and m(n)∈N such that ——↑(B+U1+U2+…+Un)^E包含于 Em(n). theorem 3. Let all (En,ξn） be Frechet spaces.Then (DST) holds if and only if (i) for each n ∈N,there is u neighborhood U n of in (En,ξn） and m(n)∈N such that 0↑Un^E包含于Em(n),and (ii) for each each closed ,absosed,absolutely conuex,bounded set B in (E,ξ）,∞↑Un=1(（εnB)∩Un）absorbs B,where U n is any neighborhood of o in (En,ξn） and εn is any positive number for every n ∈N。

基于功能影像学探讨百会治疗失眠的中枢机制

百会为治疗失眠的效穴,临床使用频率高。功能影像学,广义上包括多种成像技术,狭义主要指功能性磁共振成像(fMRI),数据分析方法分为功能分离和功能整合两类,试验设计方案包括任务态(Tb-fMRI)与静息态(Rs-fMRI),静息态因操作简便且能直观反映针刺持续和累积效应而被广泛应用。多项fMRI研究表明,失眠患者在视觉区、感觉运动区、情绪相关脑区等存在局部功能异常,针刺百会单穴或组穴可引起特定脑区如顶叶、额叶、颞叶等的改变,从而改善睡眠。针刺单穴百会主要集中在Rs-fMRI局部一致性(ReHo)、比率低频振幅(fALFF)研究,而针刺百会组穴研究从Rs-fMRI局部一致性(ReHo)、度中心度(DC)、种子连接(FC),以及Tb-fMRI比率低频振幅(fALFF)等方面展开,研究发现不同研究方法和穴位组合下的脑区激活改变存在差异,且针刺百会组穴所调控脑区多于单穴针刺,体现了百会对失眠、认知和情绪的调节作用以及腧穴间的协同作用。然而,针刺百会引起的中枢信号改变复杂,功能影像作为评估失眠的中枢指标虽有潜力,但仍需更规范、深入的研究。

ON CERTAIN CLASS OF ANALYTIC FUNCTIONS DEFINED BY DIFFERENTIAL SUBORDINATION

In this paper, the new subclass B-n(lambda,alpha,A,B) of analytic functions is introduced. Its subordination relations, inclusion relations, the inequality properties and convering theorem are discussed. The results obtained in this paper are sharp, which generalize the related works of some authors and some other new results are obtained.