Decomposition of Quasi-regular Representations Induced from Discrete Subgroups of Nilpotent Lie Groups

We describe the direct integral decomposition of a quasi regular representation of a connected and simply connected nilpotent Lie group G, which is induced from a discrete subgroup Γ. The solution is given explicitly in terms of orbital parameters. That is, the spectrum, multiplicity and spectral measure that constitute the decomposition are described completely in terms of natural objects associated to the co-adjoint orbits of G. We conclude with a study of the multiplicity function in certain cases.      

Nonlinear bending inertia of a vibrating beam

Zusammenfassung Die bei Querschwingungen schlanker Stäbe mit zeitabhängiger Längsbelastung in der Bewegungsdifferentialgleichung auftretenden nichtlinearen Trägheitsterme, herrührend von der Longitudinalbewegung, werden hier im Gegensatz zu früheren Arbeiten mitberücksichtigt. Die sich daraus ergebenden nichtlinearen Korrekturen der Eigenfrequenzen des entsprechenden linearen Systems werden abgeschätzt.     

One Dimensional Behavior of Singular N Dimensional Solutions of Semilinear Heat Equations

We consider u(x,t) a solution of u _t =Δu+|u| ^{p − 1} u that blows up at time T, where u:ℝ ^N ×[0, T)→ℝ, p>1, (N−2)p<N+2 and either u(0)≥ 0 or (3N−4)p<3N+8. We are concerned with the behavior of the solution near a non isolated blow-up point, as T−t→ 0. Under a non-degeneracy condition and assuming that the blow-up set is locally continuous and N−1 dimensional, we escape logarithmic scales of the variable T−t and give a sharper expansion of the solution with the much smaller error term (T−t)^{1, 1/2−η} for any η>0. In particular, if in addition p>3, then the solution is very close to a superposition of one dimensional solutions as functions of the distance to the blow-up set. Finally, we prove that the mere hypothesis that the blow-up set is continuous implies that it is C ^{1, 1/2−η} for any η>0. Received: 20 June 2001 / Accepted: 6 October 2001     

How to improve antifungal bioactivity: POM and DFT study of some chiral amides derivatives of diacetyl-L-tartaric acid and amines

A computational Petra/Osiris/Molinspiration and Density Functional Theory based model has been developed for the identification of physic–chemical parameters governing the bioactivity of chiral amides derivatives of diacetyl-L-tartaric acid and aromatic amines 4–9 containing combined antifungal pharmacophore sites. The six compounds 4–9 analyzed here were previously experimentally and now virtually screened for their antibacterial/antifungal activity. The highest antifungal activity was obtained for compound 6, which exhibited excellent % inhibition, comparable to Terbinafine. Compound 5, represents increased activity as compared to its isomer 6. The increase of bioactivity from 5 to 6 could be attributed to the existence of pi-charge transfer from para-Bromo-phenyl to its amid group (CO^δ?--NH^δ+), which plays a crucial template role in the organization of antifungal O,O-phramacophore sites. Moreover, it is cheap, has fewer side effects, and its possible inclusions in selective fungal/viral media such as Fusarium, HIV, and Hepatitis B/C have to be questioned.     

Some natural aqueous extracts of plants as green inhibitor for carbon steel corrosion in 0.5 M sulfuric acid

The inhibiting impact of natural aqueous extracts of some plants such as curcumin, parsley and cassia bark extracts for the corrosion of carbon steel (C-steel) in 0.5 M H₂SO₄ solution was inspected utilizing some techniques such as galvanostatic and potentiodynamic anodic polarization and weight loss measurements. Outcomes indicated that the percentage inhibition efficiency increases with increasing the concentration of the extract due to its horizontal adsorption on the C-steel surface. The process of adsorption is followed by the Temkin isotherm. These natural extracts acted as pitting corrosion inhibitors by shifting the pitting potential to more noble values. The sequence of inhibition efficiency of the natural extracts decreases in the following order: cassia bark extract > parsley extract > curcumin extract. This arrangement is related to the molecular size of the major components of the three natural extracts used.     

Up–down representations and ergodic theory in nilpotent Lie groups

Let G be a connected and simply connected nilpotent Lie group and A a closed connected subgroup of G. Let Γ be a discrete cocompact subgroup of G. In the first part of this paper we give the direct integral decomposition of the up–down representation . As a consequence, we establish a necessary and sufficient condition for A to act ergodically on G/Γ in the case when Γ is a lattice subgroup of G and A is a one-parameter subgroup of G.     

Synthesis of new spiro‐[isothiochromene‐3,5′‐isoxazolidin]‐4(1H)‐ones

A series of seven new 2′,3′,4′‐substituted spiro[isothiochromene‐3,5′‐isoxazolidin]‐4(1H)‐ones ( 7‐13 ) has been prepared in the reaction of benzylidene(phenyl)azane oxide ( 5 ) or benzylidene(methyl)azane oxide ( 6 ) with (3Z)‐3‐(4‐substituted‐benzylidene)‐1H‐isothio‐ chromen‐4(3H)‐one ( 1‐4 ). The reaction occurs by a 1,3‐dipolar cycloaddition mechanism that leads to the regiospecific formation of various spiroisoxazolidines ( 7‐13 ).     

Densities and volumetric properties of (N-(2-hydroxyethyl)morpholine + ethanol, + 1-propanol, + 2-propanol, + 1-butanol,and + 2-butanol) at (293.15, 298.15, 303.15, 313.15, and 323.15) K

Densities of binary mixtures of N-(2-hydroxyethyl)morpholine with ethanol, 1-propanol, 2-propanol, 1-butanol, and 2-butanol were measured over the entire composition range at temperatures from (293.15 to 323.15) K and atmospheric pressure using a vibrating-tube densimeter. The excess molar volumes, V^E were calculated from density data and fitted to the Redlich–Kister polynomial equation. Apparent molar volumes, partial molar volume at infinite dilution and the thermal expansion coefficient of the mixtures were also calculated. The V^E values were found to be negative over the entire composition range and at all temperatures studied and become less negative with increasing carbon chain length of the alkanols.     

On the mechanism of the unwanted acetylation of polysaccharides by 1,3-dialkylimidazolium acetate ionic liquids: part 2—the impact of lignin on the kinetics of cellulose acetylation

Cellulose acetylation has been reported as a side reaction of cellulose treatment with the ionic liquid 1-ethyl-3-methylimidazolium acetate ([EMIm][OAc]) (Karatzos et al. in Cellulose 19:307–312, 2012) and other 1,3-dialkylimidazolium acetate ionic liquids. 1-Acetylimidazole (AcIm), an [EMIm][OAc] impurity, has been found to be the actual acetylating agent (Zweckmair et al. in Cellulose 22:3583–3596, 2015), and the degree of acetylation was relatively low, below a DS of approx. 0.1%. Higher degrees of cellulose acetylation (DS > 10%) have been observed when the entire wood was mixed with [EMIm][OAc] instead of cellulosic pulp only (Abushammala et al. in Carbohydr Polym 134:609–616, 2015). In this paper, we explore the impact of wood constituents, mainly lignin, on cellulose acetylation using AcIm. The results demonstrate that lignin itself can be readily acetylated upon mixing with AcIm, and—noteworthy—that lignin presence significantly accelerates cellulose acetylation. The initial rate of cellulose acetylation by AcIm increased from 1.8 to 4.7%/h when only 1% of lignin, based on cellulose mass, was added. A mechanistic study employing cellulose and lignin model compounds showed lignin to be more susceptible to acetylation than cellulose and to act as an intermediate acetyl group source for further cellulose acetylation in a catalytic scenario.     

Effect of pressure on mass absorption in an ammonia–water absorption system

Absorption phenomenon of ammonia vapor into ammonia water solution has been investigated experimentally, by inserting superheated ammonia vapor into a test cell containing a stagnant pool of ammonia water solution. Before commencing the experiment, the pressure in the test cell corresponds to the equilibrium vapor of the ammonia–water system at room temperature. When the valve is opened, mechanical equilibrium is established quickly and the pressure in the test cell becomes equal to that of the ammonia vapor cylinder. The difference between the initial pressure in the vapor cylinder and the initial pressure in the test cell is found to have a major influence on the absorption rate. The main objective of this study is to investigate the effect of this initial pressure difference on the absorption rate of ammonia vapor. A correlation which gives the total absorbed mass of ammonia as a function of the initial concentration, the initial pressure difference and time is derived. In addition the absorbed mass at no pressure difference could be estimated from the absorbed mass at initial pressure difference.