A generalization of Filliman duality

Filliman duality expresses (the characteristic measure of) a convex polytope containing the origin as an alternating sum of simplices that share supporting hyperplanes with . The terms in the alternating sum are given by a triangulation of the polar body . The duality can lead to useful formulas for the volume of . A limiting case called Lawrence's algorithm can be used to compute the Fourier transform of .

In this note we extend Filliman duality to an involution on the space of polytopal measures on a finite-dimensional vector space, excluding polytopes that have a supporting hyperplane coplanar with the origin. As a special case, if is a convex polytope containing the origin, any realization of as a linear combination of simplices leads to a dual realization of .

     

移动WiMAX竞技于边缘市场

经过多年的酝酿,移动WiMAX终于成为一种为网络运营商提供高速数据传输服务的可行方式。近几个月来,一些运营商开始部署这种技术,但是语音服务的欠缺很可能会降低移动WiMAX短期内对客户的吸引力。另外,一些长期性问题依旧悬而未决。例如,运营商将怎样在移动语音技术环境下提供基于移动WiMAX的数据服务?发展     

Non-treeability for product group actions

A product of two lcsc non-compact groups G ₁ × G ₂ acting freely by measure preserving transformation on a standard Borel probability space gives rise to a non-treeable equivalence relation unless both groups are amenable. Partially supported by NSF grant DMS 0140503     

To breathe or not to breathe—That is the question: An investigation of speech breathing kinematics in world class Shakespearean actors

Anteroposterior diameter changes of the rib cage and abdomen were recorded during respiratory and speaking activities in four adult subjects, three men and one woman, all of whom had extensive dramatic training and experience and were earning their livelihood as professional actors. Data were charted to solve for lung volume, and volume displacements of the rib cage and abdomen. The more vigorous and louder monologue performances by the professional actor subjects differed from other speaking and reading activities in the following parameters of lung volume, separate volumes, relative volume contributions, and the frequent use of respiratory phase transitions. Novice actor subjects' monologue performances are compared to the monologue performances of the professional actor subjects.     

Positive solutions to periodic boundary value problems involving nonlinear operators of Meir-Keeler-type

We establish fixed point theorems for mixed monotone operators of Meir-Keeler type on ordered Banach spaces through projective metric. As applications, we use the fixed point theorems obtained in this paper to study the existence and uniqueness of positive solutions for different classes of nonlinear problems which include two-order two-point boundary value problems and fourth-order two-point boundary value problems for elastic beam equations.     

Kinetics of hydrolysis of some new heterocyclic azomethines

Kinetics of base hydrolysis of new heterocyclic azomethines derived from active methyl quaternary salts and aromatic nitroso compounds were investigated in the presence of 70% (wt/wt) water-methanol. The base hydrolysis of these compounds is strictly first-order with respect to OH^– and azomethine. The rate determining step is suggested to be the attack of the hydroxide ion on the free base. Effects of water content and nature of organic hydroxylic solvent have been studied. It is concluded that specific solute-solvent interactions through dispersion forces play a major role in the base hydrolysis rate of the azomethines investigated. The effect of pH (2.98 – 12.24) on hydrolysis rates of compounds having a diethylamino substituent in the presence of 30% methanol has been studied. In acidic media, the rate determining step is probably the water attack on the protonated substrate.     

Displacement affinity chromatography of protein phosphatase one (PP1) complexes

Background  

Protein phosphatase one (PP1) is a ubiquitously expressed, highly conserved protein phosphatase that dephosphorylates target protein serine and threonine residues. PP1 is localized to its site of action by interacting with targeting or regulatory proteins, a majority of which contains a primary docking site referred to as the RVXF/W motif.