Approximate first-order and second-order directional derivatives of a marginal function in convex optimization

Given a convex functionf: ^p × ^q (–, +], the marginal function is defined on ^p by (x)=inf{f(x, y)|y ^q }. Our purpose in this paper is to express the approximate first-order and second-order directional derivatives of atx ₀ in terms of those off at (x ₀,y ₀), wherey ₀ is any element for which (x ₀)=f(x ₀,y ₀).The author is indebted to one referee for pointing out an inaccuracy in an earlier version of Theorem 4.1.     

The Padé-Rayleigh-Ritz method for solving large hermitian eigenproblems

We make use of the Padé approximants and the Krylov sequencex, Ax,,...,A ^m–1 x in the projection methods to compute a few Ritz values of a large hermitian matrixA of ordern. This process consists in approaching the poles ofR _x()=((I–A)^–1 x,x), the mean value of the resolvant ofA, by those of [m–1/m]_Rx(), where [m–1/m]_Rx() is the Padé approximant of orderm of the functionR _x(). This is equivalent to approaching some eigenvalues ofA by the roots of the polynomial of degreem of the denominator of [m–1/m]_Rx(). This projection method, called the Padé-Rayleigh-Ritz (PRR) method, provides a simple way to determine the minimum polynomial ofx in the Krylov subspace methods for the symmetrical case. The numerical stability of the PRR method can be ensured if the projection subspacem is sufficiently small. The mainly expensive portion of this method is its projection phase, which is composed of the matrix-vector multiplications and, consequently, is well suited for parallel computing. This is also true when the matrices are sparse, as recently demonstrated, especially on massively parallel machines. This paper points out a relationship between the PRR and Lanczos methods and presents a theoretical comparison between them with regard to stability and parallelism. We then try to justify the use of this method under some assumptions.     

平行光栅对在刻线不平行时的色散研究

 利用三维空间光线追迹法，分析了啁啾脉冲放大系统中的压缩光栅对，在刻线不平行而光栅面平行时光的衍射特性。导出了此时光通过光栅对的群延时，数值计算了系统2阶和3阶色散量，以及这些色散量在光栅对严格平行时的相对误差。得出了中心波长光的接收位置相对于光栅对严格平行时的偏移量，并且分析了它与入射角的变化关系。     

a-convex convergent alternating series

Teaching in a Mathematics Learning Centre requires special skills and knowledge of the theory of teaching and learning. This paper explores those skills and knowledge then considers how they can be applied to help students attain their full academic potential.     

Bilevel convex programming models

Bilevel convex models are studied after being cast into a parametric programming form. This form has a lexicographic inner-outer structure where the optimal value of the outer model is optimized on the set of optimal solutions of the inner model. Optimal solutions are characterized using a Lagrangian saddle-point approach and a marginal value formula is given for the outer model. These are used to formulate a general method for finding an optimal solution by input optimization.     

Prospects of anionic nanolipoplexes in nanotherapy: transmission electron microscopy and light scattering studies

Currently nanosystems composed of polynucleotides and lipid vesicles (nanolipoplexes) are considered to be promising tools for gene therapeutics. Successful in vivo application of these vectors depends on their physicochemical, technological and biological characteristics including morphology, size distribution, molecular interactions and stability. Anionic nanoliposomes (DPPC:DCP:CHOL) were prepared by two different techniques, namely the conventional thin-film hydration method followed by extrusion, and the heating method (HM), in which no volatile solvent or detergent is used. A non-viral and non-cationic gene transfer vector was constructed by incorporating plasmid DNA (pcDNA3.1/His B/lacZ) to the HM-nanoliposomes by the electrostatic mediation of Ca²⁺ ions. Transfection efficiency of the nanolipoplexes was evaluated using a human bronchial epithelial cell line (16HBE14o-) in the presence of serum. Particle characterisation, stability of the formulations and lipid–DNA interaction studies were performed using transmission electron microscopy (TEM) and light scattering. TEM pictures of nanolipoplexes showed presence of two to four closely packed vesicles with signs of fusion. Efficient delivery of plasmid DNA and subsequent β-galactosidase expression was achieved using the anionic nanolipoplexes. Transfection efficiency increased with lipid:DNA ratio up to 7:1 (w/w), where transfection efficiency was 12-fold higher than in untreated cells. Further increase in lipid ratio decreased transfection. These nanolipoplexes appear to be safe, stable and efficient in the protection and delivery of DNA to different cells and tissues.     

基于碳水化合物的阳离子聚合物载体在基因释放中的应用

在基因治疗中,基因释放载体是不可缺少的重要组成部分.近几年来聚合物基因释放载体的研究主要旨在开发低毒或无毒的阳离子聚合物用于安全有效的基因释放.作为一类天然化合物,基于碳水化合物的阳离子聚合物载体由于其良好的生物相容性和低毒性被广泛地研究并应用于基因释放.本文阐述了聚合物基因释放的机理,并对近几年来一些典型的含碳水化合物的阳离子聚合物基因释放载体作一综述.     

Effect of Cationic Lipid Nanoparticle Loaded siRNA with Stearylamine against Chikungunya Virus

Chikungunya is an infectious disease caused by mosquito-transmitted chikungunya virus (CHIKV). It was reported that NS1 and E2 siRNAs administration demonstrated CHIKV inhibition in in vitro as well as in vivo systems. Cationic lipids are promising for designing safe non-viral vectors and are beneficial in treating chikungunya. In this study, nanodelivery systems (hybrid polymeric/solid lipid nanoparticles) using cationic lipids (stearylamine, C9 lipid, and dioctadecylamine) and polymers (branched PEI-g-PEG -PEG) were prepared, characterized, and complexed with siRNA. The four developed delivery systems (F1, F2, F3, and F4) were assessed for stability and potential toxicities against CHIKV. In comparison to the other nanodelivery systems, F4 containing stearylamine (Octadecylamine; ODA), with an induced optimum cationic charge of 45.7 mV in the range of 152.1 nm, allowed maximum siRNA complexation, better stability, and higher transfection, with strong inhibition against the E2 and NS1 genes of CHIKV. The study concludes that cationic lipid-like ODA with ease of synthesis and characterization showed maximum complexation by structural condensation of siRNA owing to high transfection alone. Synergistic inhibition of CHIKV along with siRNA was demonstrated in both in vitro and in vivo models. Therefore, ODA-based cationic lipid nanoparticles can be explored as safe, potent, and efficient nonviral vectors overcoming siRNA in vivo complexities against chikungunya.     

Palindromic Vectors,Symmetropy and Symmentropy as Symmetry Descriptors of Binary Data

Today, the palindromic analysis of biological sequences, based exclusively on the study of “mirror” symmetry properties, is almost unavoidable. However, other types of symmetry, such as those present in friezes, could allow us to analyze binary sequences from another point of view. New tools, such as symmetropy and symmentropy, based on new types of palindromes allow us to discriminate binarized 1/f noise sequences better than Lempel–Ziv complexity. These new palindromes with new types of symmetry also allow for better discrimination of binarized DNA sequences. A relative error of 6% of symmetropy is obtained from the HUMHBB and YEAST1 DNA sequences. A factor of 4 between the slopes obtained from the linear fits of the local symmentropies for the two DNA sequences shows the discriminative capacity of the local symmentropy. Moreover, it is highlighted that a certain number of these new palindromes of sizes greater than 30 bits are more discriminating than those of smaller sizes assimilated to those from an independent and identically distributed random variable.     

动态环境约束下企业的资本积累

本文讨论动态环境约束下企业的动态投资行为,拓广了文献[4]的结果.为了使讨论的问题更符合实际情况,本文假设政府设定的污染排放上限是与企业的规模大小有关,即假设污染排放上限是生产资本的函数,讨论动态环境约束下企业的最佳动态投资行为,并为政府制定污染排放政策提供依据.