Geometric modules and Quinn homology theory

LetR be a ring with unit and invariant basis property. In [1], the authors define a functorK(_;R):TOP/LIP _c-LPEP by combining the open cone construction of [7] with a geometric module construction and show this functor is a homology theory. This paper shows that if attention is restricted to objects TOP/LIP _c with a homotopy colimit structure, then the functorK(_;R) is a Quinn homology theory, In particular, for each having a homotopy colimit structure,K(;R) is a homotopy colimit in the category of -spectra. Furthermore, the constituent spectra of this homotopy colimit are obtained naturally from the fibres of .Partially supported by the National Science Foundation under grant number DMS88-03148.Partially supported by the SNF (Denmark) under grant number 11-7792.     

Conformational dependence of the intrinsic acidity of the aspartic acid residue sidechain in N-acetyl- -aspartic acid-N′-methylamide

The sidechain conformational potential energy hypersurfaces (PEHS) for the γ_L, β_L, α_L, and α_D backbone conformations of N-acetyl- -aspartate-N′-methylamide were generated. Of the 81 possible conformers initially expected for the aspartate residue, only seven were found after geometric optimizations at the B3LYP/6-31G(d) level of theory. No stable conformers could be located in the δ_L, _L, γ_D, δ_D, and _D backbone conformations. The ‘adiabatic’ deprotonation energies for the endo and exo forms of N-acetyl- -aspartic acid-N′-methylamide were calculated by comparing their optimized relative energies against those found for the seven stable conformers of N-acetyl- -aspartate-N′-methylamide. Sidechain conformational PEHSs were also generated for the estimation of ‘vertical’ deprotonation energies for both endo and exo forms of N-acetyl- -aspartic acid-N′-methylamide. All backbone–sidechain (N–H⁻O–C) and backbone–backbone (N–HO=C) hydrogen bond interactions were analyzed. A total of two backbone–backbone and four backbone–sidechain interactions were found for N-acetyl- -aspartate-N′-methylamide. The deprotonated sidechain of N-acetyl- -aspartate-N′-methylamide may allow the aspartyl residue to form strong hydrogen bond interactions (since it is negatively charged) which may be significant in such processes as protein–ligand recognition and ligand binding. As a primary example, the molecular geometry of the aspartyl residue may be important in peptide folding, such as that in the RGD tripeptide.     

N,N'-ethylenebis(pyridoxylideneiminato) and N,N'-ethylenebis(pyridoxylaminato): synthesis, characterization, potentiometric, spectroscopic, and DFT studies of their vanadium(IV) and vanadium(V) complexes

The Schiff base N,N'-ethylenebis(pyridoxylideneiminato) (H(2)pyr(2)en, 1) was synthesized by reaction of pyridoxal with ethylenediamine; reduction of H(2)pyr(2)en with NaBH(4) yielded the reduced Schiff base N,N'-ethylenebis(pyridoxylaminato) (H(2)Rpyr(2)en, 2); their crystal structures were determined by X-ray diffraction. The totally protonated forms of 1 and 2 correspond to H(6)L(4+), and all protonation constants were determined by pH-potentiometric and (1)H NMR titrations. Several vanadium(IV) and vanadium(V) complexes of these and other related ligands were prepared and characterized in solution and in the solid state. The X-ray crystal structure of [V(V)O(2)(HRpyr(2)en)] shows the metal in a distorted octahedral geometry, with the ligand coordinated through the N-amine and O-phenolato moieties, with one of the pyridine-N atoms protonated. Crystals of [(V(V)O(2))(2)(pyren)(2)].2 H(2)O were obtained from solutions containing H(2)pyr(2)en and oxovanadium(IV), where Hpyren is the "half" Schiff base of pyridoxal and ethylenediamine. The complexation of V(IV)O(2+) and V(V)O(2) (+) with H(2)pyr(2)en, H(2)Rpyr(2)en and pyridoxamine in aqueous solution were studied by pH-potentiometry, UV/Vis absorption spectrophotometry, as well as by EPR spectroscopy for the V(IV)O systems and (1)H and (51)V NMR spectroscopy for the V(V)O(2) systems. Very significant differences in the metal-binding abilities of the ligands were found. Both 1 and 2 act as tetradentate ligands. H(2)Rpyr(2)en is stable to hydrolysis and several isomers form in solution, namely cis-trans type complexes with V(IV)O, and alpha-cis- and beta-cis-type complexes with V(V)O(2). The pyridinium-N atoms of the pyridoxal rings do not take part in the coordination but are involved in acid-base reactions that affect the number, type, and relative amount of the isomers of the V(IV)O-H(2)Rpyr(2)en and V(V)O(2)-H(2)Rpyr(2)en complexes present in solution. DFT calculations were carried out and support the formation and identification of the isomers detected by EPR or NMR spectroscopy, and the strong equatorial and axial binding of the O-phenolato in V(IV)O and V(V)O(2) complexes. Moreover, the DFT calculations done for the [V(IV)O(H(2)Rpyr(2)en)] system indicate that for almost all complexes the presence of a sixth equatorial or axial H(2)O ligand leads to much more stable compounds.     

The existence of sensitive optimal policies in two multi-dimensional queueing models

Recently Dekker and Hordijk [3,4] introduced conditions for the existence of deterministic Blackwell optimal policies in denumerable Markov decision chains with unbounded rewards. These conditions include- uniform geometric recurrence.The-uniform geometric recurrence property also implies the existence of average optimal policies, a solution to the average optimality equation with explicit formula's and convergence of the value iteration algorithm for average rewards. For this reason, the verification of-uniform geometric convergence is also useful in cases where average and-discounted rewards are considered.On the other hand,-uniform geometric recurrence is a heavy condition on the Markov decision chain structure for negative dynamic programming problems. The verification of-uniform geometric recurrence for the Markov chain induced by some deterministic policy together with results by Sennott [14] yields the existence of a deterministic policy that minimizes the expected average cost for non-negative immediate cost functions.In this paper-uniform geometric recurrence will be proved for two queueing models: theK competing queues and the two centre open Jackson network with control of the service rates.The research of the author is supported by the Netherlands Organization for Scientific Research N.W.O.     

A fast iterative method to find the matrix geometric mean of two HPD matrices

The purpose of this research is to present a novel scheme based on a quick iterative scheme for calculating the matrix geometric mean of two Hermitian positive definite (HPD) matrices. To do this, an iterative scheme with global convergence is constructed for the sign function using a novel three‐step root‐solver. It is proved that the new scheme is convergent and shown to have global convergence behavior for this target, when square matrices having no pure imaginary eigenvalues. Next, the constructed scheme is used and extended through a well‐known identity for the calculation of the matrix geometric mean of two HPD matrices. Ultimately, several experiments are collected to show its usefulness.     

Mean curvature flow with free boundary – Type 2 singularities

In this paper we give sufficient conditions that guarantee the mean curvature flow with free boundary on a pinched cylinder develops a Type 2 curvature singularity. We additionally prove that Type 0 singularities may only occur at infinity.     

实现均匀照度光伏聚光镜设计

为满足聚光光伏系统的聚光需求,解决传统点聚焦式聚光光伏系统中聚焦光斑不均匀、径长比过大和聚光比较小的缺点,在不增加二次匀光器件的前提下,设计了径长比小、聚焦光斑相对均匀、聚光比高的聚光光伏系统。根据几何光学柯勒照明原理、等光程原理和反射定律,通过数值求解等光程方程组获得聚光镜各个面型的轮廓曲线。利用TracePro软件对所设计的聚光系统进行光线追迹模拟,结果表明:在聚光比为725的情况下,聚焦光斑最大照度仅为太阳照度的2300倍,是点聚焦情况下的1/10左右,系统的径长比为0.3,接收角为0.72°。系统设计实现了结构紧凑,聚光性能高的设计目标,为高倍聚光光伏系统的小型化,简单化提供了一种有效的解决途径。     

Crystal planes and reciprocal space in Clifford geometric algebra

This paper discusses the geometry of kD crystal cells given by (k+ 1) points in a projective space ?^{n+ 1}. We show how the concepts of barycentric and fractional (crystallographic) coordinates, reciprocal vectors and dual representation are related (and geometrically interpreted) in the projective geometric algebra Cl(?^{n+ 1}) (see (Die Ausdehnungslehre von 1844 und die Geom. Anal. Teubner: Leipzig, 1894)) and in the conformal algebra Cl(?^{n+ 1, 1}). The crystallographic notions of d‐spacing, phase angle, structure factors, conditions for Bragg reflections, and the interfacial angles of crystal planes are obtained in the same context. Copyright © 2011 John Wiley & Sons, Ltd.