Left dihedral codes over finite chain rings

Let R be a finite commutative chain ring, $D_{2n}$ be the dihedral group of size 2n and $R[D_{2n}]$ be the dihedral group ring. In this paper, we completely characterize left ideals of $R[D_{2n}]$ (called left $D_{2n}$-codes) when $\gcd (char(R),n)=1$. In this way, we explore the structure of some skew-cyclic codes of length 2 over R and also over $R\times S$, where S is an isomorphic copy of R. As a particular result, we give the structure of cyclic codes of length 2 over R. In the case where $R={\mathbb{F}}_{p^m}$ is a Galois field, we give a classification for left $D_{2N}$-codes over ${\mathbb{F}}_{p^m}$, for any positive integer N. In both cases we determine dual codes and identify self-dual ones.     

A mathematical model for the 3d location estimation of 2D echocardiography data

The recovery of 3D left ventricle(LV) shape using 2D echocardiography is very attractable topic in the field of ultrasound imaging. In this paper, we propose a mathematical model to determine the 3D position of LV contours extracted from multiple 2D echocardiography images. We formulate the proposed model as a non-convex constrained minimization problem. To solve it, we propose a proximal alternating minimization algorithm with a solver OPTI for quadratically constrained quadratic program. For validating the proposed model, numerical experiments are performed with real ultrasound data. The experimental results show that the proposed model is promising and available for real echocardiography data.     

含各向异性左手材料的一维Thue-Mores准周期结构的反射带隙

采用传输矩阵法,研究了由各向同性右手材料和各向异性左手材料组成的Thue-Morse准周期结构的反射带隙,分析了入射角、偏振和晶格比例缩放因子对反射带隙的影响.结果表明该结构存在一个全方向反射带隙,该带隙的宽度由TE模的低频带边缘和TM模的高频带边缘决定.当在该结构中插入一层缺陷时,在全方向带隙中出现一条缺陷模.对TE模,缺陷模的位置受入射角的影响很弱,而对TM模,缺陷模的位置随入射角的增大,向高频方向移动.     

三维斑点追踪成像评价甲状腺功能亢进患者左心室收缩功能改变的应用价值

目的 探讨三维斑点追踪成像（3D-STI）技术在评价甲状腺功能亢进(甲亢)患者左心室整体收缩功能中的应用价 值。方法 选择50 例甲状腺功能亢进患者与45 例健康志愿者,获取心尖四腔心切面动态图像,存储左心室三维全容积动态图像后,运用3D-STI 软件进行脱机分析,得到两组收缩期左心室整体纵向峰值应变（GLS）、圆周峰值应变（GCS）、左心室扭转度角度峰值(LV-tw)、左心室扭力（LV-tor）、左心室心底水平旋转角度峰值（Prot-B）、左心室心尖水平旋转角度峰值（Prot-A）及左心室射血分数（LVEF）等,比较两组三维应变（3DS）指标之间的差异。结果 与正常对照组比较,甲亢组的左心室收缩功能增强,GLS、GCS 分别为（-20.47±3.08）% vs.（-18.52±4.77）%、（-28.98±3.00）% vs.（-25.88±2.12）%,两组差异均有统计学意义（均P＜0.05）;甲亢组LV-tw、LV-tor、LVProt-A、LVProt-B 均较正常对照组略有增加,但差异均无统计学意义（均P＞0.05）。结论 3D-STI 可无 创、敏感检测甲亢患者左心室三维应变,为临床客观评估甲亢左心室收缩功能提供一种新方法。     

左C-半群的左交错积结构

给出了左C-半群的另一种结构,所谓左交错积结构,并刻画了它的特殊情形.这种结构为左C-半群在广义正则半群类中的再推广奠定了基础.     

Left inverses of matrices with polynomial decay

It is known that the algebra of Schur operators on ?² (namely operators bounded on both ?¹ and ?^∞) is not inverse-closed. When ?²=?²(X) where X is a metric space, one can consider elements of the Schur algebra with certain decay at infinity. For instance if X has the doubling property, then Q. Sun has proved that the weighted Schur algebra Aω(X) for a strictly polynomial weight ω is inverse-closed. In this paper, we prove a sharp result on left-invertibility of the these operators. Namely, if an operator A∈Aω(X) satisfies ‖Afp_‖?‖fp_‖, for some 1?p?∞, then it admits a left-inverse in Aω(X). The main difficulty here is to obtain the above inequality in ?². The author was both motivated and inspired by a previous work of Aldroubi, Baskarov and Krishtal (2008) [1], where similar results were obtained through different methods for X=Zd, under additional conditions on the decay.     

Fixed point properties for semigroup of nonexpansive mappings on Fréchet spaces

In this paper, we shall establish a fixed point property on Fréchet spaces for left reversible semitopological semigroups generalizing some classical results.     

Hochschild and ordinary cohomology rings of small categories

Let C be a small category and k a field. There are two interesting mathematical subjects: the category algebra kC and the classifying space |C|=BC. We study the ring homomorphism HH^∗(kC)→H^∗(|C|,k) and prove it is split surjective, using the factorization category of Quillen [D. Quillen, Higher algebraic K-theory I, in: Lecture Notes in Math., vol. 341, Springer-Verlag, Berlin, 1973, pp. 85-147] and certain techniques from functor cohomology theory. This generalizes the well-known theorems for groups and posets. Based on this result, we construct a seven-dimensional category algebra whose Hochschild cohomology ring modulo nilpotents is not finitely generated, disproving a conjecture of Snashall and Solberg [N. Snashall, Ø. Solberg, Support varieties and Hochschild cohomology rings, Proc. London Math. Soc. 88 (3) (2004) 705-732].     

Spectral theory of left definite difference operators

This paper is concerned with the spectral theory for the second-order left definite difference boundary value problems. Existence of eigenvalues of boundary value problems is proved, numbers of their eigenvalues are calculated and fundamental spectral results are obtained.     

Modeling of aortic valve dynamics in a lumped parameter model of left ventricular-arterial coupling

A lumped parameter model of the sub-system of left ventricle, aortic valve, systemic arteries, systemic capillaries and systemic veins was considered during systole. A model of aortic valve dynamics based solely on geometrical and kinematical consideration is defined. The model is described by two geometrical parameters of aortic valve and a few kinematical relationships. The proposed model mimics the incisures in the aortic flow and aortic pressure very well. We showed that the dicrotic notch could be explained by aortic valve closing in terms of a lumped parameter model, without a need for any wave reflection theory. According to the proposed model the effects of aortic valve dynamics on the aortic flow and pressure are mainly limited to the valve opening and closing periods. The model offers a new paradigm for defining a more realistic left ventricle model.