New Linear Codes Over \mathbb{F}_3 and \mathbb{F}_5 and Improvements on Bounds

One of the most important problems of coding theory is to constructcodes with best possible minimum distances. In this paper, we generalize the method introduced by [8] and obtain new codes which improve the best known minimum distance bounds of some linear codes. We have found a new linear ternary code and 8 new linear codes over with improved minimumdistances. First we introduce a generalized version of Gray map,then we give definition of quasi cyclic codes and introduce nearlyquasi cyclic codes. Next, we give the parameters of new codeswith their generator matrices. Finally, we have included twotables which give Hamming weight enumerators of these new codes.     

Minimal Modules Over Serial Rings

We investigate several model theoretic minimalities in the framework of modules over a given serial ring R.     

Multiple Eigenvalues in Spectral Analysis for Solving QBD Processes

A number of authors have recently suggested solving quasi birth-and-death (QBD) processes through the use of eigenvalue-based methods. These methods take on a special form when there are multiple eigenvalues present. We investigate this problem in a general setting as well as in the context of a specific preemptive priority queueing model.      

准静态离散元方法和线性粘弹性问题的模拟

离散元方法是近年发展起来的一种新数值方法,但原则上只能用于动态问题。从静力平衡条件出发建立了离散元系统的准静态演化方程并证明了系数矩阵具有对称正定、稀疏、带状分布等特点,适用于“有效列”方法求解,该解法比高斯消去法节省更多的内存和机时。通过引入广义Maxwell体的元间作用模型建立起线性粘弹性材料准静态响应的离散元模拟方法。该方法独立于传统动态离散元方法,是传统动态离散元方法的拓展,可望在更多领域获得应用。     

Semilinear elliptic problems near resonance with a nonprincipal eigenvalue

We consider the Dirichlet problem for the equation −Δu=λu±f(x,u)+h(x) in a bounded domain, where f has a sublinear growth and h∈L². We find suitable conditions on f and h in order to have at least two solutions for λ near to an eigenvalue of −Δ. A typical example to which our results apply is when f(x,u) behaves at infinity like a(x)|u|^q−2u, with M>a(x)>δ>0, and 1<q<2.     

Tandem mass spectrometric analysis of novel diquaternary ammonium gemini surfactants and their bromide adducts in electrospray-positive ion mode ionization

Gemini surfactants are cationic lipids which are utilized for both in vitro and in vivo gene delivery. Structurally, they are comprised of two hydrophobic tail regions with polar head termini that are attached to one another through a spacer region. Structural elucidation and characterization of 29 novel diquaternary ammonium gemini surfactant molecules were achieved using a quadrupole time-of-flight mass spectrometer (QqToF-MS) and a quadrupole-hexapole-quadrupole mass spectrometer (QhQ-MS). The tested compounds were categorized into four distinct structural families based upon the composition of the spacer region. Single stage (MS), tandem stage (MS/MS) and quasimulti-stage (quasi MS(3)) mass spectrometric analysis allowed for confirmation of each gemini surfactant's molecular composition and structure through the identification of common and unique product ions. Identification of similarities in the gemini surfactants' fragmentation behaviour resulted in the production of a universal fragmentation pathway that can assist in the future MS/MS analysis of novel quaternary ammonium gemini surfactants, with unique product ions being indicative of specific structural elements. Furthermore, evidence for the association of agemini surfactant with bromine counter ion was confirmed during MS analysis of tested gemini surfactants regardless of their chemical composition; previously, evidence for bromine and gemini surfactant association was only observed with compounds bearing short alkyl spacer regions. MS/MS analysis of the bromine adducts was also confirmatory to the molecular structure.Understanding the ionization and fragmentation behaviour of gemini surfactants, including bromine adducts, will allow for future qualitative and quantitative identification of these novel drug delivery agents within biological samples.     

Center problem and bifurcation behavior for a class of quasi analytic systems

Results about the study of nonanalytic systems’ center-focus and bifurcations of limit cycles are hardly seen in published references up till now. In this paper, we investigated the problems of determining center or focus and bifurcations for a class of planar quasi cubic analytic systems. The recursive formula to figure out generalized focal values is given, ulteriorly the conditions for four limit cycles from the origin or the point at infinity are obtained and center problems are considered. What is worth pointing out is that we offer a kind of interesting phenomenon that the exponent parameter λ control the non-analyticity of studied system (3.8) in this paper. In terms of nonanalytic differential systems, our work is new.     

Complex affine distributions

Geometry of affine immersions is the study of hypersurfaces that are invariant under affine transformations. As with the hypersurface theory on the Euclidean space, an affine immersion can induce a torsion-free affine connection and a (pseudo)-Riemannian metric on the hypersurface. Moreover, an affine immersion can induce a statistical manifold, which plays a central role in information geometry. Recently, a statistical manifold with a complex structure is actively studied since it connects information geometry and Kähler geometry. However, a holomorphic complex affine immersion cannot induce such a statistical manifold with a Kähler structure. In this paper, we introduce complex affine distributions, which are non-integrable generalizations of complex affine immersions. We then present the fundamental theorem for a complex affine distribution, and show that a complex affine distribution can induce a statistical manifold with a Kähler structure.