Infinitesimal deformations of restricted simple Lie algebras I

We compute the infinitesimal deformations of two families of restricted simple modular Lie algebras of Cartan-type: the Witt–Jacobson and the Special Lie algebras.     

On the scarcity of contravariant left adjunctions

It is shown that any pair of contravariant mutually left adjoint functors between varieties of algebrasC andD factors through the retractions of these categories onto the complete lattices of epimorphs of their respective initial objects, and is thus fairly degenerate. However, some interesting contravariant left adjoint functors do exist between categories of finitely generated (or otherwise restricted) algebras.This work was done while the author was partly supported by NSF contract DMS 85-02330.Presented by F. E. J. Linton.     

Undirected simple connected graphs with minimum number of spanning trees

We show that for positive integers n, m with n(n−1)/2≥m≥n−1, the graph L_n,m having n vertices and m edges that consists of an (n−k)-clique and k−1 vertices of degree 1 has the fewest spanning trees among all connected graphs on n vertices and m edges. This proves Boesch’s conjecture [F.T. Boesch, A. Satyanarayana, C.L. Suffel, Least reliable networks and reliability domination, IEEE Trans. Commun. 38 (1990) 2004-2009].     

Dimension of complete simple games with minimum

Weighted majority games have the property that players are totally ordered by the desirability relation (introduced by Isbell in [J.R. Isbell, A class of majority games, Quarterly Journal of Mathematics, 7 (1956) 183–187]) because weights induce it. Games for which this relation is total are called complete simple games. Taylor and Zwicker proved in [A.D. Taylor, W.S. Zwicker, Weighted voting, multicameral representation, and power, Games and Economic Behavior 5 (1993) 170–181] that every simple game (or monotonic finite hypergraph) can be represented by an intersection of weighted majority games and consider the dimension of a game as the needed minimum number of them to get it. They provide the existence of non-complete simple games of every dimension and left open the problem for complete simple games.     

A useful ring transformation route to novel thiazepino[7,6-b]indoles from monochloro-β-lactam-fused 1,3-thiazino[6,5-b]indoles,analogues of cyclobrassinin

The Staudinger ketene-imine cycloaddition reactions of cyclobrassinin phytoalexin analogues 2-aryl-4,9-dihydro-1,3-thiazino[6,5-b]indoles with chloroacetyl chloride as a ketene source were investigated under different conditions. Both β-lactam ring formation and the N-chloroacetylation of the indole moiety took place. The indole N-chloroacetyl group can be easily removed by treatment in the presence of silica gel in methanol at reflux temperature. The selective β-lactam formation can be also achieved in certain cases under milder Staudinger conditions. The treatment of azeto[2,1-b]thiazino[6,5-b]indole-1-one derivatives with sodium ethoxide in ethanol provided the novel thiazepino[7,6-b]indole ring systems in a one-step ring transformation. The structures of the new ring systems were determined by means of IR and NMR spectroscopy.     

Effect of Polyethylene glycol methyl ether blend Humic acid on poly (vinylidene fluoride-co-hexafluropropylene) PVDF-HFP membranes: pH responsiveness and antifouling behavior with optimization approach

Flat sheet asymmetric membranes were fabricated with homogeneous solution of poly (vinylidene fluoride-co-hexafluoropropylene) (PVDF-co-HFP) using N-methyl-2-pyrrolidone (NMP) as solvent via phase inversion method. PEGME (Poly ethylene glycol methyl ether) (M_n 5000) blend Humic Acid (HA), of different mole ratio was used as additive. Characterization of the membranes was done by Field emission scanning electron microscope (FESEM), Fourier Transform Infrared (FTIR) spectroscopy, Atomic force microscopy (AFM) and Differential scanning calorimetry (DSC) studies. Liquid-liquid displacement porosimetry (LLDP) study evaluated the morphological parameters, average pore size and pore size distribution. Bovine serum albumin (BSA) (M_W - 68,000 Da) was used to study the antifouling effect and pore blocking mechanism of the membranes. The pure water flux (PWF), solute rejection and flux recovery ratio drastically increases for the PEGME blended HA membranes whereas the water contact angle decreases significantly. The pH responsiveness character of the prepared membranes altered the hydraulic permeability and rejection % at different pH. Finally, optimization of the variables contributing towards the PWF and BSA rejection of the desired membrane was performed using Design expert software 9.0 TRIAL through ANOVA (analysis of variance) using the combination of response surface methodology (RSM) and central composite design (CCD).     

A failure of a class of K-BKZ equations based on principal stretches

The invariants in the K-BKZ constitutive equation for an incompressible viscoelastic fluid are usually taken to be the trace of the Finger strain tensor and its inverse. The basis for this choice of invariants is not derived from the K-BKZ theory, but rather is due to the perception that this is the most natural choice. Research into using other sets of invariants in the K-BKZ equation, such as the principal stretches or the eigenvalues of the Finger strain tensor (i.e., the squares of the principal stretches) is relatively new. We attempt here to derive a K-BKZ equation based on the squares of the principal stretches that models the behavior of a low-density polyethylene melt in simple shear and uniaxial elongational deformation. In doing so, two assumptions are made as to the form of the strain-dependent energy function: first, that there is a function f(q) such that the energy function can be written as the sum of f(q _i ),i = 1, 2, 3, where the q _i 'sare the squares of the principal stretches, and second that f is a power law. We find that the K-BKZ equation resulting from these two assumptions is inadequate to describe both the shear and elongational behavior of our material and we conclude that the second of the above assumptions is not valid. Further investigation, including predictions of the second normal stress difference and some finite element calculations reveals that the first assumption is also invalid for our material.     

Optimization of a novel method based on solidification of floating organic droplet by high-performance liquid chromatography for evaluation of antifungal drugs in biological samples

In this study, a simple, rapid, and highly efficient liquid-phase microextraction method based on solidification of floating organic droplet was coupled with high performance liquid chromatography-photo diode array detection (HPLC-PDA) for determination of ketoconazole, clotrimazole, and miconazole as antifungal drugs. Central composite design (CCD) was used for optimization of several factors affecting the extraction efficiency. The optimized conditions were established to be 550 rpm for stirring rate, 35 min for extraction time, 57 °C for extraction temperature, 8.5 for solution pH, 10 μl for organic solvent volume, and 7% (w/v) of NaCl for ionic strength. Limit of detections (LODs) of the extraction method ranged from 0.01 to 0.1 μg L⁻¹ and the linear dynamic ranges (LDRs) ranged from 0.1 to 300 μg L⁻¹ for the three antifungal drugs. Relative standard deviations (RSDs) of the proposed method were 5-11%. Preconcentration factors in the range of 306-1350 were obtained at extraction time of 35 min. Finally, performance of the proposed method was evaluated for the extraction and determination of the drugs’ levels in microgram per liter in samples and satisfactory results were obtained.     

Pressurised hot water extraction followed by simultaneous derivatization and headspace solid-phase microextraction and gas chromatography-tandem mass spectrometry for the determination of aliphatic primary amines in sewage sludge

In this paper we describe an environmentally friendly and sensitive method for the determination of ten primary amines in sewage sludge. The method is based on pressurised hot water extraction (PHWE) followed by simultaneous derivatization with pentafluorobenzaldehyde (PFBAY) and headspace solid-phase microextraction (HS-SPME) and subsequent gas-chromatography ion-trap tandem mass spectrometry (GC-IT-MS-MS) analysis. The influence of the main factors on the PHWE of sludge was optimized by a central composite design. For all species the optimal conditions were water at pH 4 as the extracting solvent, an extraction temperature of 100 °C and an extraction time of 15 min. The separation and detection of the ten amines by GC-IT-MS-MS took just 10 min and the entire process took approximately 1 h. Repeatability and reproducibility between days, expressed as RSD (%) (n = 5), were less than 19 and 24%, respectively. The average limit of detection (LOD) was of 65 μg kg⁻¹ s (range found 9-135) and the average limit of quantification (LOQ) was of 230 μg kg⁻¹ (range found 50-450) of dry weight (d.w.). Under optimized conditions we used this method to determine the compounds in industrial and municipal sewage sludge samples and in sludge from a potable water treatment plant. Methylamine and isobutylamine showed the highest levels in one of the industrial sewage sludge samples (404 and 543 mg kg⁻¹ (d.w.), respectively). To our knowledge, this paper presents for the first time the determination of ten primary amines in sewage sludge samples using PHWE.     

双生成元$A_n$型拟遗传代数的拟遗传序

本文讨论双生成元$A_n$型代数的拟遗传序的性质,给出了该类代数的单模序是拟遗传序的充分必要条件,并利用组合技巧得出了该类代数拟遗传序的数目.