由向量细分方程生成的高维Riesz小波基

主要研究~$L_{2}(\R^{s})$~中的~Riesz~序列和高维~Riesz~多小波基刻画的问题. 由~Sobolev~空间~$(H^{\mu}(\R^{s}))^{r}~(\mu>0)$~中的紧支集向量细分函数 ~$\varphi=(\varphi^{1},\ldots,\varphi^{r})^{\rm T}$~和~$\tilde{\varphi}=({\tilde\varphi}^{1},\ldots,{\tilde\varphi}^{r})^{\rm T}$~出发, 得到~$L_{2}(\R^{s})$~中的两组~Riesz~多小波基~$\{\psi_{j,k}\}$~和~$\{\tilde{\psi}_{j,k}\}.$~ 在刻画中, 向量函数的方括号积~$[f,g]$~和离散卷积方程组是非常重要的工具.     

一类$L^2(\mathbb{R}^n)$的紧支撑不可分正交小波

本篇文章给出一类$L^{2}(\mathbb{R}^{n})$, $n\geq2$的紧支撑不可分正交小波基的具体构造算法,其中正交小波的伸缩矩阵为$\alpha I_{n}~(\alpha\geq2,\ \alpha \in \mathbb{Z})$, $I_{n}$是$n$阶单位矩阵.最后给出两个不可分正交小波基的构造算例.     

从$L^{\infty}$空间到Bloch型空间一类奇异积分算子的范数

本文研究了单位圆盘上从$L^{\infty}(\mathbb{D})$空间到Bloch型空间 $\mathcal{B}_\alpha$ 一类奇异积分算子$Q_\alpha, \alpha>0$的范数, 该算子可以看成投影算子$P$ 的推广,定义如下$$Q_\alpha f(z)=\alpha \int_{\mathbb{D}}\frac{f(w)}{(1-z\bar{w})^{\alpha+1}}\d A(w),$$ 同时我们也得到了该算子从 $C(\overline{\mathbb{D}})$空间到小Bloch型空间$\mathcal{B}_{\alpha,0}$上的范数.     

强奇异Calder-Zygmund积分及其交换子在 Hardy 型空间上的有界性

给出了局部 Hardy 空间 $h^{p}(\mathbb{R}^{n})$\ $\big(\frac{n}{n+1}相似文献   

弱Morrey空间与Navier-Stokes方程的强解

本文在弱Morrey空间中考虑Navier-Stokes方程的Cauchy问题.首先在Lorentz空间$L_{p,\infty}={L_p}^{*}(\mathbb{R}^{n})$的基础上定义弱Morrey空间$M^*_{p,\lambda}(\mathbb{R}^n)$(特别地, 若$p>1$, 则$M^*_{p,0}(\mathbb{R}^n)=L_{p,\infty}$),进而研究了弱Morrey空间的基本性质. 其次,证明了热算子$U(t)=e^{t\Delta}$和Calder\’{o}n-Zygmund奇异积分算子在弱Morrey空间的有界性,同时建立了弱Morrey空间上的双线性估计. 最后,利用Kato的方法和压缩映射原理, 证明Navier-Stokes方程的Cauchy问题在弱Morrey空间$M^*_{p,\lambda}(\mathbb{R}^n)$($1相似文献   

Zygmund 空间到 Bloch 空间上径向导数算子与积分型算子的乘积

设$H(\mathbb{B})$为单位球上全纯函数类,研究了单位球上 Zygmund 空间到 Bloch 空间上径向导数算子$\Re$与积分型算子$I_\varphi^g$乘积的有界性和紧性, 这里 $$ I_\varphi^g f(z)=\int_0^1 \Re f(\varphi(tz))g(tz)\frac{{\rm d}t}{t},\quad z\in\mathbb{B}, $$ 其中$g\in H(\mathbb{B}),\ g(0)=0$, $\varphi$ 是$\mathbb{B}$上全纯自映射.     

New Sobolev-Weinstein Spaces and Applications

In this paper, we consider the generalized Weinstein operator $\Delta_{W}^{d,\alpha,n}$, we introduce new Sobolev-Weinstein spaces denoted $\mathscr H_{\alpha,d,n}^{s}(\mathbb{R}_{+}^{d+1}),$ $s\in\mathbb{R},$ associated with the generalized Weinstein operator and we investigate their properties. Next, as application, we study the extremal functions on the spaces $\mathscr H_{\alpha,d,n}^{s}(\mathbb{R}_{+}^{d+1})$ using the theory of reproducing kernels.     

$\mathbb{C}^{n}$中$\mu$-Bergman空间的刻画和微分复合算子

设$p>0$, $\mu$和$\mu_{1}$是$[0,1)$上的正规函数. 本文首先给出了$\mathbb{C}^{n}$中单位球上$\mu$-Bergman空间$A^{p}(\mu)$的几种等价刻画; 然后 分别刻画了$A^{p}(\mu)$到$A^{p}(\mu_{1})$的 微分复合算子$D_{\varphi}$为有界算子以及紧算子的充要条件, 同时给出了当$p>1$时$D_{\varphi}$为 $A^{p}(\mu)$到$A^{p}(\mu_{1})$上紧算子的一种简捷充分条件和必要条件.     

在${\mathbb{R}}^m$中重对数广义律的精确速率

令\{$X$, $X_n$, $n\ge 1$\}是期望为${\mathbb{E}}X=(0,\ldots,0)_{m\times 1}$和协方差阵为${\rm Cov}(X,X)=\sigma^2I_m$的独立同分布的随机向量列, 记$S_n=\sum_{i=1}^{n}X_i$, $n\ge 1$. 对任意$d>0$和$a_n=o((\log\log n)^{-d})$, 本文研究了${{\mathbb{P}}(|S_n|\ge (\varepsilon+a_n)\sigma \sqrt{n}(\log\log n)^d)$的一类加权无穷级数的重对数广义律的精确速率.     

由$q$-积分算子定义的某些亚纯函数类的Fekete-Szeg\"{o}问题

本文首先引入满足如下条件$$-\frac{qzD_{q}f(z)}{f(z)}\prec \varphi (z)$$和$$\frac{-(1-\frac{\alpha }{q})qzD_{q}f(z)+\alpha qzD_{q}[zD_{q}f(z)]}{(1-\frac{\alpha}{q})f(z)-\alpha zD_{q}f(z)}\prec \varphi (z)~(\alpha \in\mathbb{C}\backslash (0,1],\ 0相似文献   

基于模糊FNN-ELECTRE法的国有商业银行竞争力评价

随着金融业全方位开放,国有商业银行已成为国家经济命脉的核心,其竞争力强弱关系着国家经济的繁荣与衰退。本文基于模糊FNN-ELECTRE方法建立国有商业银行竞争力评价模型,以因素神经网络理论(FNN)与ELECTRE融合方法为基础,以现有商业银行竞争力评价指标为着眼,把国有商业银行竞争力的评价体系从现实竞争力和潜在竞争力两个因素抽取为一级指标,以规模、质量、业务结构、效率、成长性五个因素设为二级指标。从实证的角度对银行A、银行B、银行C、银行D、银行E五大国有银行进行分析验证,对其属性值进行和谐性与非和谐性检验得出,银行B竞争能力最强,银行E竞争能力最弱,五大国有银行均有改进空间。     

Formulation of linear problems and solution by a universal machine

Using the predicate language for ordered fields a class of problems referred to aslinear problems is defined. This class contains, for example, all systems of linear equations and inequalities, all linear programming problems, all integer programming problems with bounded variables, all linear complementarity problems, the testing of whether sets that are defined by linear inequalities are semilattices, all satisfiability problems in sentenial logic, the rank-computation of matrices, the computation of row-reduced echelon forms of matrices, and all quadratic programming problems with bounded variables. A single, one, algorithm, to which we refer as theUniversal Linear Machine, is described. It solves any instance of any linear problem. The Universal Linear Machine runs in two phases. Given a linear problem, in the first phase a Compiler running on a Turing Machine generates alinear algorithm for the problem. Then, given an instance of the linear problem, in the second phase the linear algorithm solves the particular instance of the linear problem. The linear algorithm is finite, deterministic, loopless and executes only the five ordered field operations — additions, multiplications, subtractions, divisions and comparisons. Conversely, we show that for each linear algorithm there is a linear problem which the linear algorithm solves uniquely. Finally, it is shown that with a linear algorithm for a linear problem, one can solve certain parametric instances of the linear problem.Research was supported in part by the National Science Foundation Grant DMS 92-07409, by the Department of Energy Grant DE-FG03-87-ER-25028, by the United States—Israel Binational Science Foundation Grant 90-00434 and by ONR Grant N00014-92-J1142.Corresponding author.     

Moment information for probability distributions,without solving the moment problem,II: Main-mass,tails and shape approximation

How much information does a small number of moments carry about the unknown distribution function? Is it possible to explicitly obtain from these moments some useful information, e.g., about the support, the modality, the general shape, or the tails of a distribution, without going into a detailed numerical solution of the moment problem? In this, previous and subsequent papers, clear and easy to implement answers will be given to some questions of this type. First, the question of how to distinguish between the main-mass interval and the tail regions, in the case we know only a number of moments of the target distribution function, will be addressed. The answer to this question is based on a version of the Chebyshev–Stieltjes–Markov inequality, which provides us with upper and lower, moment-based, bounds for the target distribution. Then, exploiting existing asymptotic results in the main-mass region, an explicit, moment-based approximation of the target probability density function is provided. Although the latter cannot be considered, in general, as a satisfactory solution, it can always serve as an initial approximation in any iterative scheme for the numerical solution of the moment problem. Numerical results illustrating all the theoretical statements are also presented.     

城市老旧居住小区交通环境评价指标与评价方法

定量的评判城市老旧居住小区整体交通环境质量并进而科学有效的提出老旧小区交通环境更新与改善措施,对城市老旧居住小区交通环境进行了调查,明确了老旧居住小区存在的突出交通问题,并提出了城市老旧居住小区交通环境评价的指标体系,包括行人跨路出行指数、无人行道路段长度占比、停车泊位供需比、路内非法停车占比、平均停车步行距离、泊位数量户数比、人均步行空间、无障碍通道、盲道设置比例、非机动车泊位供需比、地面停放车辆数小区面积比、外部穿行交通周转量小区面积比等。并给出了具体指标的计算方法与获得办法。以长沙市四个典型老旧居住小区为例,对评价方法进行了论证,并得到城市老旧居住小区存在的一般问题,包括人车混杂、人车交织现象严重,停车泊位短缺、车辆乱停乱放,交通设施、特别是弱势群体交通设施缺乏。给出的评价指标、评价方法与结论可为城市老旧小区改造更新,特别是其中很重要的交通环境更新提供决策依据。     

A double-stage piecewise recursive filter for real-time applications

This paper examines the basic problem of estimating the state of a system described by a set of dynamical equations. The state estimation is performed by means of optimal filtering techniques in which the state observation is given by a set of nonlinear equations.The basic issue encountered in most engineering problems is the availability of more observable information than the processor can effectively process in real-time, while performing full optimal filtering on all available observable data. To alleviate this deficiency, an algorithm is developed in which the rate of information processing is kept at a high value, while the system statistics are evaluated at a much slower rate.The method utilizes a combination of fast and slow filtering loops, in which the observable data are processed at a high rate during the fast loop, while the system error covariance, gain computations, and all other system statistics are processed at a lower rate in the slow loop. Methods are provided to resolve any incompatibility in the system statistics resulting from this fast-loop/slow-loop processing combination.Applications describing problems pertaining to aircraft navigation are presented. Specifically, applications to aircraft navigation through a satellite network are studied. Appropriate simulation results from the above studies are shown.This work was performed under contract with the Department of the Air Force, Space and Missile Organization (SAMSO), Los Angeles, California, Contract No. F04-701-75-C-0180.The authors are indebted to Dr. C. Johnson, GPS System Engineer, Mr. G. Consolver, GPS Software Manager, and Mr. W. Riley, Communications/Navigation Department, Texas Instruments for their continuous encouragement in the course of this work. Also, they are indebted to Major M. Birnbaum, SAMSO, for his constructive criticism on the conceptual design of this work, and to Mr. A. Bierman, Aerospace Corporation, for kindly providing simulation data of aircraft trajectories. Finally, the authors would like to express their gratitude to Dr. N. Carlson, Intermetrics, for valuable consultation during the progress of this work.Portions of this paper were presented by the senior author at the GSP Conference, Plan 76, IEEE Position, Location, and Navigation Symposium, San Diego, California, 1976.     

提高维吾尔文搜索质量的一些关键技术研究

维吾尔语和土耳其语、乌兹别克语、哈萨克语等同属于阿尔泰语系突厥语分支,是一种粘着型语言,具有丰富的构词合构形附加成分.主要分布于中国新疆维吾尔自治区,以及中西亚地区的维吾尔族使用.目前使用基于阿拉伯文字母的维吾尔文.当前用google,bing等搜索引擎搜索维吾尔文时搜索结果不包括该词语的构词合构形附加成分等其它形式.严重影响了搜索结果的准确性.通过词干提取和词缀附加生成词语组合的方法以解决提高维吾尔文搜索质量的问题.此问题解决,将在大幅度提高维吾尔文搜索的准确性,并针对提高其它突厥语族语言(土耳其语、乌兹别克语、哈萨克语等)的搜索质量、数据挖掘、数据分析、数据安全、自然语言理解等研究领域有一定的参考价值.     

绿色产品定价与市场入侵研究:基于市场权力结构的视角

为研究绿色产品定价与市场入侵问题,针对由两个制造商和一个零售商组成的系统,构建了制造商主导、零售商主导以及供需双方均势等三种权力结构模型,分析了权力结构、消费者绿色偏好等因素对绿色产品定价和市场入侵的影响。研究发现:绿色产品入侵市场存在可行条件,并且绿色产品市场入侵会导致普通产品制造商的利润损失;市场入侵对零售商有利,说明零售商会有动机引入绿色产品;绿色产品入侵市场和市场权力结构均会影响各个企业最优定价策略,其中拥有主导权的企业会选择高价策略;权力结构会影响供需双方的利润分配,以及导致系统利润的损失。     

金融风险在股票市场的传染效应及联动行为分析

近年来金融危机频发并表现出了易传染性,引起了众多学者的高度关注。以动态条件相关模型研究美欧股市与中、日、韩股市间的时变相关性,并结合内生多重结构突变模型划分危机传染阶段,选用溢出指数模型分析股市间的风险溢出特性;随后,定义股市间相互影响的联动模式并构建不同传染阶段的加权有向网络图分析股市间的联动行为。研究表明:美欧股市对中日韩股市有明显的传染效应,被传染的速度和持续时间均不相同;金融传染和风险溢出展现出一定的不一致性,危机期间日股的风险溢出效应强于美股;传染效应在联动网络中表现为联动模式的高聚类性和高联动性,相比欧债危机,次贷危机时期股市间展现出更强的联动行为;日股与美欧股市在两次危机中均表现出最强的联动性,其所受影响也最大。     

Personae at play. ‘Men of Mathematics’ in commentary

Mathematical writers, above all, Euclid, tend to present their theorems as decontextualized, abstract propositions, which has become the standard modus of textual presentation in theoretical mathematics. Mathematical commentators, however, provide their readers with personal names and historical facts in order to elucidate problems, provide contexts of discovery, or construct doxographies, among other things. Modern readers have used such information for the construction of histories of science. When we look at these passages, however, we see that personal names and information about mathematicians of the past can serve quite a range of different objectives, such as the strategic self-positioning of the commentator vis-à-vis the past or present of mathematics, the education of the reader, mathematical or moral, the construction of the history of the field, etc. Not only does the commentator present a persona of himself to the reader, he can also turn colleagues and predecessors into personae. This paper attempts to elucidate the practice, by offering four examples of such plays of and with personae, in Pappus, Eutocius, al-Nayrīzī, and Proclus.     

On the mechanical and thermomechanical properties of low-density polyethylene/ethylene-α-octene copolymer blends

Blends of low-density polyethylene (LDPE) and ethylene-octene copolymer (EOC) were obtained. The effect of EOC content and absorbed radiation dose on the mechanical and thermomechanical properties of LDPE/EOC blends are investigated. Particular attention is given to a tensile stress-strain analysis and the “form-memory” effect of the blends. With growing LDPE content, the elastic modulus, the yield stress, and the thermorelaxation and residual stresses of the blends increase, but the ultimate elongation at break decreases, which is caused by the higher crystallinity of polyethylene. As a result of radiation-induced cross-linking, the elastic modulus, the yield stress (at a 1% strain), the ultimate yield strength, and the thermorelaxation and residual stresses increase, while the ultimate elongation at break and the melt flow-behavior index decrease, which is confirmed by the growing gel fraction in the blend. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 279–286, March–April, 2008.