Matrix algebras with Multiplicative Decomposition Property

We consider the Multiplicative Decomposition Property (the multiplicative analogue of the Riesz Decomposition Property) for entry-wise ordered matrix algebras over the reals. We characterize for which matrix pairs such a decomposition exists and use this result to present necessary and sufficient conditions for a matrix algebra to enjoy the decomposition property by all its positive matrix pairs. Thus we describe all matrix algebras with the decomposition property.     

On the stability of a domain-wall brane model

We establish stability and nonstability results for a domain-wall brane model arising in classical field theory. In particular, we show the nonexistence of nontrivial bounded solutions on the real line for a coupled pair of parameter dependent linear second order ordinary differential equations for an open set of those parameters. Moreover, we establish the existence of nontrivial solutions for a hypersurface of the parameters. We use Fredholm theory for compact linear operators combined with the Lyapunov-Schmidt method to prove our results. The model is stable, respectively unstable, for those parameters for which the coupled system does not, respectively does, have nontrivial solutions.     

Optimization of the derivatization reaction and the solid-phase microextraction conditions using a D-optimal design and three-way calibration in the determination of non-steroidal anti-inflammatory drugs in bovine milk by gas chromatography-mass spectrometry

An experimental design optimization is reported of an analytical procedure used in the simultaneous determination of seven non-steroidal anti-inflammatory drugs (NSAIDs) in bovine milk by gas chromatography with mass spectrometry detection (GC-MS). This analytical procedure involves a solid-phase microextraction (SPME) step and an aqueous derivatization procedure of the NSAIDs to ethyl esters in bovine milk. The following NSAIDs are studied: ibuprofen (IBP), naproxen (NPX), ketoprofen (KPF), diclofenac (DCF), flufenamic acid (FLF), tolfenamic acid (TLF) and meclofenamic acid (MCL). Three kinds of SPME fibers - polyacrylate (PA), polydimethylsiloxane/divinylbenzene (PDMS/DVB) and polydimethylsiloxane (PDMS) - are compared to identify the most suitable one for the extraction process, on the basis of two steps: to determine the equilibrium time of each fiber and to select the fiber that provides the best figures-of-merit values calculated with three-way PARAFAC-based calibration models at the equilibrium time. The best results were obtained with the PDMS fiber. Subsequently, 8 experimental factors (related to the derivatization reaction and the SPME) were optimized by means of a D-optimal design that involves only 14 rather than 512 experiments in the complete factorial design. The responses used in the design are the sample mode loadings of the PARAFAC decomposition which are related to the quantity of each NSAID that is extracted in the experiment. Owing to the fact that each analyte is unequivocally identified in the PARAFAC decomposition, a calibration model is not needed for each experimental condition. The procedure fulfils the performance requirements for a confirmatory method established in European Commission Decision 2002/657/EC.     

Classification of the centers and their isochronicity for a class of polynomial differential systems of arbitrary degree

In this paper we classify the centers localized at the origin of coordinates, and their isochronicity for the polynomial differential systems in R² of degree d that in complex notation z=x+iy can be written as where j is either 0 or 1. If j=0 then d?5 is an odd integer and n is an even integer satisfying 2?n?(d+1)/2. If j=1 then d?3 is an integer and n is an integer with converse parity with d and satisfying 0<n?[(d+1)/3] where [⋅] denotes the integer part function. Furthermore λ∈R and A,B,C,D∈C. Note that if d=3 and j=0, we are obtaining the generalization of the polynomial differential systems with cubic homogeneous nonlinearities studied in K.E. Malkin (1964) [17], N.I. Vulpe and K.S. Sibirskii (1988) [25], J. Llibre and C. Valls (2009) [15], and if d=2, j=1 and C=0, we are also obtaining as a particular case the quadratic polynomial differential systems studied in N.N. Bautin (1952) [2], H. Zoladek (1994) [26]. So the class of polynomial differential systems here studied is very general having arbitrary degree and containing the two more relevant subclasses in the history of the center problem for polynomial differential equations.     

Spin-Spin Relaxation Process of 23Na-NMR in Na-Loaded NaY

Abstract

Spin-spin relaxation of ²³Na-NMR is observed by the spin echo method at room temperature for Y-type zeolite loaded with Na metal without hydration. For saturated and no levels of loading, the echo decay is well fitted by single exponential function. T ₂ decreases to be 0.25 times smaller by loading. This decrease of T ₂ is explained semiquantitatively with assuming nuclear dipole-dipole interaction between neighboring Na.     

热致液晶乙基纤维素与尼龙－1010共混物的研究

在自制单螺杆小型挤出机上通过熔融共混的办法，制备了不同配比（５／９５—２５／７５）的ＥＣ／Ｎｙｌｏｎ—１０１０共混物．用ＷＡＸＤ、ＤＳＣ、毛细管流变仪、力学性能测试等方法对共混物进行了研究．发现共混后尼龙－１０１０的形态结构有明显改变，其强度、模量都有提高，在高剪切速率下，共混物粘度大大降低．配比为１５８５时，这些性能的改进尤为明显．     

Hyperbolic elements in negatively curved groups

We show that in a negatively curved groupG the conjugacy class of any infinite cyclic subgroup contains a straight element, an elementg with |g ⁿ |=n|g|, and thus the translation number of an element in a negatively curved group is rational with uniformly bounded denominator. We also find an upper bound on the cardinality of a finite normal subgroup.     

Order-unit quantum Gromov-Hausdorff distance

We introduce a new distance dist_oq between compact quantum metric spaces. We show that dist_oq is Lipschitz equivalent to Rieffel's distance dist_q, and give criteria for when a parameterized family of compact quantum metric spaces is continuous with respect to dist_oq. As applications, we show that the continuity of a parameterized family of quantum metric spaces induced by ergodic actions of a fixed compact group is determined by the multiplicities of the actions, generalizing Rieffel's work on noncommutative tori and integral coadjoint orbits of semisimple compact connected Lie groups; we also show that the θ-deformations of Connes and Landi are continuous in the parameter θ.     

NaCl interaction with interfacially polymerized polyamide films of reverse osmosis membranes: A solid-state Na NMR study

²³Na nuclear magnetic resonance (NMR) spectroscopy of NaCl-exchanged polyamide (PA) films comparable to those of the active skin layer of many reverse osmosis (RO) membranes provides novel insight into the structural environments and dynamical behavior of Na⁺ in such films. Unsupported PA films were synthesized via interfacial polymerization of trimesoyl chloride in hexane and m-phenylenediamine in aqueous solution, and SEM, FT-IR, and ¹³C NMR data demonstrate successful thin film polymerization. Compositional data confirm this conclusion and demonstrate equal Na and Cl incorporation during NaCl exchange from aqueous solution. The ²³Na NMR spectra for freshly made polymer samples exchanged in 1 M NaCl solution show significant relative humidity (RH) dependence. At near 0% RH, there are resonances for crystalline NaCl and rigidly held Na⁺ in the PA. With increasing RH, a resonance for solution-like dynamically averaged Na⁺ appears and above 51% RH is the only signal observed. The slightly negative chemical shift of this resonance suggests a dominantly hydrous environment with some atomic-scale coordination by atoms of the polymer. The greatly reduced ²³Na T₁ relaxation rates for this resonance relative to bulk solution and crystalline NaCl confirm close association with the polymer. Variable temperature ²³Na NMR spectra for a sample equilibrated at 97% RH obtained from −80 to 20 °C show the presence of rigidly held Na⁺ in a hydrated environment at low temperatures and replacement of this resonance by the dynamically averaged signal at temperatures above about −20 °C. The results provide support for the solution–diffusion model for RO membranes transport and demonstrate the capabilities of multi-nuclear NMR methods to investigate molecular-scale structure and dynamics of the interactions between dissolved species and RO membranes.