Shell Partition and Metric Semispaces: Minkowski Norms, Root Scalar Products, Distances and Cosines of Arbitrary Order

Vector semispaces are studied from a realistic way with the intention to define a natural metric, adapted to their peculiar structure, which reside on the essential positive definiteness of their elements. From this point of view, Minkowski norms allow classifying semispaces in shells, that is: subsets where all the vector elements possess the same norm values. Shell structure appears to be a possible disjoint partition of any semispace and so shells become equivalence classes Then, the unit shell appears to be the core of the semispace homothetic construction as well as the origin of the semispace metrics. Minkowski or root scalar products permit to connect two or more semispace elements and conduct towards generalized definitions of Pth order root distances and cosines. Finally, the unit shell of a given semispace, in company of both Boolean tagged sets, inward matrix products and with the aid of the matrix signatures as well, it is seen as the seed to construct any arbitrary element of the semispace connected vector space. Finite and infinite dimensional vector spaces application examples are provided along the work discussion.     

Mutations of links in genus 2 handlebodies

A short proof is given to show that a link in the 3-sphere and any link related to it by genus 2 mutation have the same Alexander polynomial. This verifies a deduction from the solution to the Melvin-Morton conjecture. The proof here extends to show that the link signatures are likewise the same and that these results extend to links in a homology 3-sphere.

     

基于扩展混沌映射的认证密钥协商协议

近年来,基于混沌映射和智能卡的认证密钥协商协议被相继提出.然而,防篡改读卡器使得这类协议的实现成本较高并且很难在实际中广泛应用.另外,基于混沌映射的数字签名方案需要很高的计算资源,这使得依赖签名方案的公钥发布存在安全问题.据此,本文基于扩展混沌映射提出一种新的无智能卡的认证密钥协商协议.新协议消除了公钥发布过程.安全和性能分析表明,新协议能抵抗各类攻击并且计算复杂度较低.因此,新协议更适合在实际环境中应用.     

Cohomology Complex Projective Space with Actions of G_5

§1. Introduction A cohomology complex projective nspace is a smooth, closed, orientable 2nmanifold M2n such that there is a class x∈H2(M; Z) with the property that H*(M; Z)=z［x］/(xn+1). Let i: K2n-1M2n be the inclusion map of a closed, connected, orientable submanifold and d is an integer; we say that the degree of K2n-2 is d, if i*［K］ is the Poincaré dual of dx. We always assume that the orientation of K2n-2 is chosen in such a way that d is nonnegative. Let p be a prime number…     

Crystal → nematic phase transition in the liquid crystalline system 1‐isothiocyanato‐4‐(trans‐4‐propylcyclohexyl) benzene (3CHBT) probed by temperature‐dependent micro‐Raman study and DFT calculations

Raman spectra of 3CHBT in unoriented form were recorded at 14 different temperature measurements in the range 25–55 °C, which covers the crystal → nematic (N) phase transition, and the Raman signatures of the phase transition were identified. The wavenumber shifts and linewidth changes of Raman marker bands with varying temperature were determined. The assignments of important vibrational modes of 3CHBT were also made using the experimentally observed Raman and infrared spectra, calculated wavenumbers, and potential energy distribution. The DFT calculations using the B3LYP method employing 6‐31G functional were performed for geometry optimization and vibrational spectra of monomer and dimer of 3CHBT. The analysis of the vibrational bands, especially the variation of their peak position as a function of temperature in two different spectral regions, 1150–1275 cm⁻¹ and 1950–2300 cm⁻¹, is discussed in detail. Both the linewidth and peak position of the ( C H ) in‐plane bending and ν(NCS) modes, which give Raman signatures of the crystal → N phase transition, are discussed in detail. The molecular dynamics of this transition has also been discussed. We propose the co‐existence of two types of dimers, one in parallel and the other in antiparallel arrangement, while going to the nematic phase. The structure of the nematic phase in bulk has also been proposed in terms of these dimers. The red shift of the ν(NCS) band and blue shift of almost all other ring modes show increased intermolecular interaction between the aromatic rings and decreased intermolecular interaction between two  NCS groups in the nematic phase. Copyright © 2009 John Wiley & Sons, Ltd.     

Study of the ‘Raman spectroscopic signature of life’ in mitochondria isolated from budding yeast

The ‘Raman spectroscopic signature of life’ is a Raman band at 1602 cm⁻¹ that sharply reflects the metabolic activity of cell mitochondria. Here we report the study of thissignature in isolated yeast mitochondria. The existence and behaviour of the 1602 cm⁻¹ band in isolated mitochondria have been confirmed to be the same as in living yeast cells: the intensity of the band decreases with timewhen a respiration inhibitor, sodium azide, is added. The present study shows the significance of isolated mitochondria in elucidating the origin of this still unassigned Raman band. Copyright © 2009 John Wiley & Sons, Ltd.     

Birkhoff‐Frink representations as functors

In an earlier article we characterized, from the viewpoint of set theory, those closure operators for which the classical result of Birkhoff and Frink, stating the equivalence between algebraic closure spaces, subalgebra lattices and algebraic lattices, holds in a many‐sorted setting. In the present article we investigate, from the standpoint of category theory, the form these equivalences take when the adequate morphisms of the several different species of structures implicated in them are also taken into account. Specifically, our main aim is to provide a functorial rendering of the Birkhoff‐Frink representation theorems for both single‐sorted algebras and many‐sorted algebras, by defining the appropriate categories and functors, covariant and contravariant, involved in the process (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Performance enhancement and validation of the open-source software for modeling of ship infrared signatures (OSMOSIS)

Designing stealth technologies for modern warships requires methods for signatures reduction (radar, infrared, etc). First, we have to model these signatures. In Lapierre et al. (2006), Lapierre et al. (2007) [3] and [4], we proposed an infrared (IR) ship signature simulation software (OSMOSIS) that can manage parametric emissivity. OSMOSIS comprises a smart computation time and memory management. Evaluating the effectiveness of an IR signature reduction method implies simulating the evolution of the IR signature with time. This requires a huge computation time. In this paper, we propose a novel hierarchical meshing strategy leading to an important reduction of the computation time. The time complexity of the algorithm is shown to be , where N is the requested number of facets of the mesh of the ship’s surface. Then, we validate OSMOSIS on temperature measurements performed on an “L-shape” object.     

Some results on information properties of coherent systems

This paper considers information properties of coherent systems when component lifetimes are independent and identically distributed. Some results on the entropy of coherent systems in terms of ordering properties of component distributions are proposed. Moreover, various sufficient conditions are given under which the entropy order among systems as well as the corresponding dual systems hold. Specifically, it is proved that under some conditions, the entropy order among component lifetimes is preserved under coherent system formations. The findings are based on system signatures as a useful measure from comparison purposes. Furthermore, some results on the system's entropy are derived when lifetimes of components are dependent and identically distributed. Several illustrative examples are also given.     

基于辫群的代理签名方案

Artin辫群是可以有限表示的无限非交换群。近年来被认为是公钥加密的一种重要来源；代理签名[1]是一种具有特殊功能的数字签名．本文，我们首次提出基于辫群（主要利用辫群中的难解问题；共轭问题，多共轭问题，求根的问题）的代理签名方案．