Quotient probabilistic normed spaces and completeness results

We introduce the concept of quotient in PN spaces and give some examples. We prove some theorems with regard to the completeness of a quotient.     

Bodies of constant width in arbitrary dimension

We give a number of characterizations of bodies of constant width in arbitrary dimension. As an application, we describe a way to construct a body of constant width in dimension n, one of its (n – 1)‐dimensional projection being given. We give a number of examples, like a four‐dimensional body of constant width whose 3D‐projection is the classical Meissner's body. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Directed triangles in directed graphs

We show that each directed graph (with no parallel arcs) on n vertices, each with indegree and outdegree at least n/twhere t=2.888997… contains a directed circuit of length at most 3.     

Differential FBG sensor for temperature-compensated high-pressure (or displacement) measurement

A differential fiber Bragg grating (FBG) sensor with a free active element bulk-modulus for high-pressure (or displacement) measurement is presented. Based on the differential measurement method and an isosceles triangle cantilever structure, problems of cross-sensitivity and chirped signal in FBG sensor are improved both theoretically and experimentally. Preliminary experiments indicate that temperature-compensated measurement results agree well with the theoretical analysis. Displacement measurement sensitivity is 1.75 pm/μm, and the estimated pressure measurement resolution can reach 0.27 MPa in case the wavelength shift measurement resolution is 0.01 nm.     

Gap exponents for percolation processes with triangle condition

A study is made of the gap exponents for percolation processes with the triangle condition in the subcritical region. It is show that the gaps are given by _t =2 fort=2, 3,. Scaling theory predicts thatP _p (¦C ₀¦S(p))–(p _c –p) andE _p (1/¦C ₀¦; ¦C ₀¦S(p))–(p _c –p)³, whereS(p) is the typical cluster size. It is found that (p _c –p)P _p (|C ₀S(p) ^1–)(p _c –p)^1–2 and (p _c –p)³E _p (1/|C ₀|;|C ₀|S(p) ^1–))(p _c –p)^3–4.     

Alternating Sign Matrices and Some Deformations of Weyl's Denominator Formulas

An alternating sign matrix is a square matrix whose entries are 1, 0, or –1, and which satisfies certain conditions. Permutation matrices are alternating sign matrices. In this paper, we use the (generalized) Littlewood's formulas to expand the products and 2 as sums indexed by sets of alternating sign matrices invariant under a 180° rotation. If we put t = 1, these expansion formulas reduce to the Weyl's denominator formulas for the root systems of type B _n and C _n. A similar deformation of the denominator formula for type D _n is also given.     

A fast parallel clustering algorithm for molecular simulation trajectories

We implemented a GPU‐powered parallel k‐centers algorithm to perform clustering on the conformations of molecular dynamics (MD) simulations. The algorithm is up to two orders of magnitude faster than the CPU implementation. We tested our algorithm on four protein MD simulation datasets ranging from the small Alanine Dipeptide to a 370‐residue Maltose Binding Protein (MBP). It is capable of grouping 250,000 conformations of the MBP into 4000 clusters within 40 seconds. To achieve this, we effectively parallelized the code on the GPU and utilize the triangle inequality of metric spaces. Furthermore, the algorithm's running time is linear with respect to the number of cluster centers. In addition, we found the triangle inequality to be less effective in higher dimensions and provide a mathematical rationale. Finally, using Alanine Dipeptide as an example, we show a strong correlation between cluster populations resulting from the k‐centers algorithm and the underlying density. © 2012 Wiley Periodicals, Inc.     

三角形Au@TiO2介孔催化剂可见光降解亚甲蓝

利用溶胶凝胶法制备出一种三角形Au@TiO₂核壳材料。经过水热晶化,该材料膨胀至300 nm,壳层TiO₂晶化为介孔锐钛矿相,但核心三角形Au颗粒的形貌保持不变。采用粉末X射线衍射(PXRD)、ζ电位、高分辨透射电子显微镜(HRTEM)、热重分析(TGA)、光致发光(PL)光谱、光电流(i-t)以及光催化降解技术,对样品的结构和性能进行了系统、详细的检测与分析。经过晶化处理的Au@TiO₂在可见光波段的光降解亚甲蓝性能比未晶化时有了显著的提升, 1 mg·mL^-1 Au@c-TiO₂可以在可见光照射1 h后实现对60 mg·L^-1亚甲蓝全降解。电子顺磁共振(EPR)测试表明·O₂^-和·OH两种自由基对光降解起到了很大作用。通过综合分析实验结果和时域有限差分(FDTD)分析,探究了催化反应的机理。     

Fabrication of Pascal-triangle Lattice of Proteins by Inducing Ligand Strategy

A protein Pascal triangle has been constructed as new type of supramolecular architecture by using the inducing ligand strategy that we previously developed for protein assemblies. Although mathematical studies on this famous geometry have a long history, no work on such Pascal triangles fabricated from native proteins has been reported so far due to their structural complexity. In this work, by carefully tuning the specific interactions between the native protein building block WGA and the inducing ligand R-SL , a 2D Pascal-triangle lattice with three types of triangular voids has been assembled. Moreover, a 3D crystal structure was obtained based on the 2D Pascal triangles. The distinctive carbohydrate binding sites of WGA and the intralayer as well as interlayer dimerization of RhB was the key to facilitate nanofabrication in solution. This strategy may be applied to prepare and explore various sophisticated assemblies based on native proteins.     

形式三角矩阵环上的有限表示模

形式三角矩阵环,又称广义三角矩阵环,这类环及其上的模在环模理论中扮演着重要的角色.本文对形式三角矩阵环上的有限表示模进行了一些探讨.