Approximation algorithms for nonnegative polynomial optimization problems over unit spheres

We consider approximation algorithms for nonnegative polynomial optimization problems over unit spheres. These optimization problems have wide applications e.g., in signal and image processing, high order statistics, and computer vision. Since these problems are NP-hard, we are interested in studying on approximation algorithms. In particular, we propose some polynomial-time approximation algorithms with new approximation bounds. In addition, based on these approximation algorithms, some efficient algorithms are presented and numerical results are reported to show the efficiency of our proposed algorithms.     

Sorbitol-based supramolecular organogelators with effective phase-selective gelation and significant self-healing property

Several effective phase-selective gelators (PSGs) have been developed from a series of cheap and easy-to-make sorbitol-based compounds for the removal of many oils from their biphasic mixtures with water. The dominant factors that drive gelation have been studied using FTIR and temperature-dependent ¹H NMR spectra. Additionally, the case of PSGs exhibit significant self-healing properties that can recover the gelatin block and hence provide a more flexible approach for oil-spill recovery. The highly effective phase-selective performance and self-healing properties of these organogelators indicate the potential and promising applicability in oil-spill recovery.     

克山病病区低硒儿童血小板血栓素、聚集性和超微结构改变

对比研究了克山病病区和非病区儿童的硒状态，血浆血栓素和前列环素水平，血小板血栓素形成、聚集性和超微结构，发现：1．全血和红细胞硒水平低的病医儿童血小板谷胱甘肽过氧化物酶活性也显著低于非病区；2．病区儿童血浆血栓素显著高于非病区，而前列环素却无显著差异；3．用花生四烯酸刺激血小板时，病区儿童血小板聚集反应和血栓素形成均显著高于非病区；4．血栓素与聚集性基显著正相关，两者分别与全血或红细胞硒水平呈明显负相关；5．病区儿童血小板形态明显异常，出现变形和团聚血小板，α-颗粒显著减少，结果提示病区儿童血小板处于活化状态，可能是克山病发病的一个危险因素。     

Banach空间中对偶规划的存在性定理

本文利用无穷下降方向，在Ｂａｎａｃｈ空间中建立了若干非凸对偶规划的存在性定理。作为特例，给出了半无限对偶规划和有限对偶规划的存在性定理。     

仿衣壳结构的巨大中空超分子纳米容器的多组分自组装构筑及其功能

在自然界病毒衣壳及笼状蛋白质大分子结构的启发下,运用V型双齿桥连吡啶配体和具有平面四方构型的Pd²⁺离子的溶液配位自组装,一系列具有M_nL_2n经验分子式的多组分巨大中空“纳米容器”型超分子结构被成功构筑。通过在配体内外引入官能团的策略,可以简单地实现衣壳骨架结构的内外功能化。内功能化后的“纳米容器”具有特殊的高密度相,不仅可以实现对不同类型客体分子的包裹,而且可以作为“纳米反应器”实现尺寸均一可控纳米粒子的原位合成以及小分子的催化转化。外功能化的核壳结构则可以对寡肽、DNA等生物分子具有特定的识别作用。本文对此类“纳米容器”型超分子的设计原理、自组装合成与表征、以及功能化应用等方面进行了综述。     

Spectral theory of nonnegative tensors

Higher-order tensors are natural extensions of matrices;matrices are order-2 tensors.However,higher-order tensors represent multilinear maps,which are nonlinear,unlike matrices.The spectral theory of matrices plays a fundamental role in many branches of mathematics as well as a multitude of applied sciences.In contrast to the well robust theory of matrices,the development of the spectral theory for tensors is still at its early stages.In recent years,with the rapid flow of massive data in this digital world,the demand for effective and etficient data-processing and data-managing algorithms finds its way in connection with the spectral theory of tensors.In particular,such key concepts as rank and eigenvalues-eigenvectors of a given tensor are getting more intriguing and challenging to researchers today.     

Efficient algorithms for computing the largest eigenvalue of a nonnegative tensor

Consider the problem of computing the largest eigenvalue for nonnegative tensors. In this paper, we establish the Q-linear convergence of a power type algorithm for this problem under a weak irreducibility condition. Moreover, we present a convergent algorithm for calculating the largest eigenvalue for any nonnegative tensors.     

Preface

Preface

Preface