脉冲Schr(o)dinger方程和最优控制

本文用Fourier变换,得到有界区域上Schroxdinger算iΔ所生成的半群的表达式.并用它引进了受控脉冲型Schrodinger方程的PCι-温和解,证明PCι-温和解的存在唯一性.讨论相应的最优控制问题,证明最优控制的存在性,导出最优化的必要条件.     

方程x~3+1=3py~2有正整数解的必要条件

对于正整数n,设Q(n)是n的无平方因子部分;设p是适合p≡1(mod 6)的奇素数.运用Petr组的性质证明了:如果方程x3+1=3py2有正整数解(x,y),则p≠Q(3s2-2),p≠Q(12s2+1),且3p≠Q(s2+2),其中s是正整数.     

TWO-WEIGHT WEAK-TYPE MAXIMAL INEQUALITIES FOR MARTINGALES

In this article, some necessary and sufficient conditions are shown in order that the inequality of the form Ф1（λ）Pu（f^＊〉λ）≤Ev （Ф2（C｜f∞｜）） holds with some constant C 〉 0 independent of martingale f = （fn）n≥0 and λ 〉 0, where Фl and Ф2 are a pair of Young functions, f^＊=sup n≥0｜fn｜ adn f∞=lim n→∞ fn a.e.     

<Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> integrability of trigonometric series with special varying coefficients

Very recently, Yu, Le and Zhou introduced the so called △B1^＊ and △B2^＊ conditions, which are generalizations of the monotone condition. By applying these two new conditions, the author essentially generalizes the classical results of Chen on the necessary and sufficient conditions of the Lp integrability of trigonometric series. In fact, the present paper gives the first result on the necessary and sufficient conditions of the Lp integrability of trigonometric series, where coefficients may have different signs.     

The spectrum sequences of periodic frame multiresolution analysis

The periodic multiresolution analysis （PMRA） and the periodic frame multiresolution analysis （PFMRA） provide a general recipe for the construction of periodic wavelets and periodic wavelet frames, respectively. This paper addresses PFMRAs by the introduction of the notion of spectrum sequence. In terms of spectrum sequences, the scaling function sequences generating a normalized PFMRA are characterized; a characterization of the spectrum sequences of PFMRAs is obtained, which provides a method to construct PFMRAs since its proof is constructive; a necessary and sufficient condition for a PFMRA to admit a single wavelet frame sequence is obtained; a necessary and sufficient condition for a PFMRA to be contained in a given PMRA is also obtained. What is more, it is proved that an arbitrary PFMRA must be contained in some PMRA. In the meanwhile, some examples are provided to illustrate the general theory.     

A characterization of some weighted inequalities for the vector-valued weighted maximal function

We give in this paper a necessary and sufficient condition of weighted weak and strong type norm inequalities for the vector-valued weighted maximal function.     

再谈充分条件必要条件的本质特征

本文用具体的实例比较详尽地阐述了充分条件、必要条件以及充要条件的本质特征,以方便相关内容的学习。     

开展视力残疾大学生全纳教育的必要条件

视力残疾学生在学习中有一定障碍,有效进行全纳教育必须做到:通过多种途径解决高等教育盲文教材、资料缺乏问题,教师要树立全纳意识,把残疾学生学习障碍减少到最低,残疾学生更要树立信心、加倍努力完成学习任务,这样才能保证全纳教育的实行。全纳教育充分体现了中国大学生具有平等受教育的权利,是世界残疾人教育发展的趋势。     

拟H矩阵的性质及判定

本文首先讨论了拟Ｈ矩阵的若干性质，然后给出了拟Ｈ矩阵的一个必要条件和一种有效的判定方法。     

半群环的主理想升链条件问题

在环为整环、半群为交换无挠可消摹群的条件下对半群环的主理想升链条件进行了研究．得到了半群环满足“主理想升链条件”的必要条件，以及在U(S)=(e)的条件下半群环满足“主理想升链条件”的充要条件．