Degree-regular triangulations of torus and Klein bottle

A triangulation of a connected closed surface is called weakly regular if the action of its automorphism group on its vertices is transitive. A triangulation of a connected closed surface is called degree-regular if each of its vertices have the same degree. Clearly, a weakly regular triangulation is degree-regular. In [8], Lutz has classified all the weakly regular triangulations on at most 15 vertices. In [5], Datta and Nilakantan have classified all the degree-regular triangulations of closed surfaces on at most 11 vertices. In this article, we have proved that any degree-regular triangulation of the torus is weakly regular. We have shown that there exists ann-vertex degree-regular triangulation of the Klein bottle if and only if n is a composite number ≥ 9. We have constructed two distinctn-vertex weakly regular triangulations of the torus for eachn ≥ 12 and a (4m + 2)-vertex weakly regular triangulation of the Klein bottle for eachm ≥ 2. For 12 ≤n ≤ 15, we have classified all then-vertex degree-regular triangulations of the torus and the Klein bottle. There are exactly 19 such triangulations, 12 of which are triangulations of the torus and remaining 7 are triangulations of the Klein bottle. Among the last 7, only one is weakly regular.     

Dielectric properties of KDP-type ferroelectric crystals in the presence of external electric field

Considering external electric field as well as third- and fourth-order phonon anharmonic interaction terms in the pseudospin-lattice coupled mode (PLCM) model Hamiltonian for KDP-type ferroelectrics, expressions for field-dependent shift, width, renormalized soft mode frequency, Curie temperature, dielectric constant and dielectric loss are evaluated. For the calculation, method of statistical double-time temperature-dependent Green’s function has been used. By fitting model values of physical quantities, temperature and electric field dependences of soft mode frequency, dielectric constant and loss have been calculated which compare well with experimental results of Baumgartner [8] and Choi and Lockwood [9]. Both dielectric constant and loss decrease with electric field.     

Pollution-error in the h-version of the finite-element method and the local quality of a-posteriori error estimators

In this paper we study the pollution-error in the h-version of the finite element method and its effect on the local quality of a-posteriori error estimators. We show that the pollution-effect in an interior subdomain depends on the relationship between the mesh inside and outside the subdomain and the smoothness of the exact solution. We also demonstrate that it is possible to guarantee the quality of local error estimators in any mesh-patch in the interior of a finite-element mesh by employing meshes which are sufficiently refined outside the patch.     

Why chaos is rarely observed in natural populations

An attempt has been made to understand why chaotic dynamics have received poor evidential support from field studies. Our study opens up the possibility that the cause of failure might not be poor quality of data, as pointed out by earlier authors, but an ecological reality. We have designed two model food chains to examine whether there is a biological basis for the crisis. This investigation is effected with the help of a new method which we introduce at an appropriate place in the text. The fact that chaos exists in a narrow range of parametric values in both the model systems suggests that the crisis indeed has a biological origin.     

Thin layer chromatographic studies of anils II. Separation,identification and determination

Thin layer chromatographic behaviour of ten anils was studied on silica gel adsorbent mixed with starch binder with ten solvent systems. Simultaneous separation, identification and determination of ternary mixtures of isomers was stressed. TheR _F increasing order was found to be dependent on the solvent and independent of the degree of saturation of the chamber. The correlations ofR _F with _max and (C=O) of isomers were established and used in their identification. Six anils were separated in methanol—benzene (11).     

Kinetics and mechanism of the ruthenium(III)-catalyzed oxidation of hydroxy-acids byN-bromosuccinimide

Summary The kinetics of the Ru^III-catalyzed oxidation of the hydroxy acids; lactic, tartaric, malic and citric acids byN-bromosuccinimide in HClO₄ and in the presence of Hg(OAc)₂ have been studied. The reactions exhibit a first order rate dependence with respect to the oxidant and zeroth order rate dependence with respect to substrate. The rate is retarded by [H⁺], accelerated at law Ru^III concentrations but independent of [Ru^III] at higher Ru^III concentrations. A mechanism consistent with the observed kinetic data is proposed.     

Palladium(II) complexes of aliphatic amines and their oxidation by chloramine‐T in perchloric acid medium

The formation of palladium(II) complexes with aliphatic amines and their oxidation by chloramine‐T in perchloric acid medium has been studied. The spectrophotometric studies showed the formation of 1:1 and 1:2 complexes between palladium(II) and amine in absence of HClO₄. An increase in [HClO₄] in reaction mixture suppresses the complex formation and in presence of [HClO₄] ～10^?3 mol dm^?3 only a 1:1 complex between palladium(II) and amine has been observed. The effect of Cl^? on the complex formation has also been studied. Palladium(II)‐catalyzed oxidation of these amines by chloramine‐T showed a first‐order dependence of rate with respect to each—oxidant, substrate, catalyst, and H⁺. The mechanism consistent with kinetic data for the oxidation process has been proposed in absence as well as in presence of initial [Cl^?]. © 2002 Wiley Periodicals, Inc. Int J Chem Kinet 34: 603–612, 2002     

Studies on electroosmotic and electrophoretic behavior of cholesterol in aqueous solutions

Electrical properties of cholesterol interfaces have been investigated. For this purpose electroosmotic and hydrodynamic permeation of water, sodium chloride, barium chloride, aluminum chloride, and urea solutions across a cholesterol plug have been investigated. Dependence of electroosmotic permeability on concentration of electrolytes has also been studied. Electrophoretic mobility of cholesterol particles of known size distribution and dispersed in solutions of varying concentrations of electrolytes and urea has also been studied. The data have been used to estimate ζ potentials in order to have a plausible picture of the electrical double layer at the cholesterol/ solution interfaces.     

NMR spectroscopic study of the inclusion complex of desloratadine with β-cyclodextrin in solution

Desloratadine (DES) is an antihistamine used in the treatment of allergies and chronic urticaria. ¹H NMR spectroscopic study of varying ratios of DES and β-Cyclodextrin (β-CD) in D₂O suggests the formation of a 1:1 inclusion complex formed by the penetration of Cl-substituted aromatic ring into the β-CD cavity. The stoichiometry and binding constant of the complex were determined by Scott’s method.     

Complexation of Fluvastatin Sodium with β-Cyclodextrin: NMR Spectroscopic Study in Solution

¹H NMR spectroscopic study of fluvastatin sodium (FLU), β-Cyclodextrin (β-CD) and their mixtures confirmed the formation of FLU/β-CD inclusion complex in solution. The stoichiometry of the complex was determined to be 1:1 and the overall binding constant (K _s) was calculated to be 340 M⁻¹. Two dimensional COSY, ROESY and DEPTO experiments were performed for the unambiguous assignment of aromatic proton resonances and it was found that two isomeric forms of FLU are present in solution. It was confirmed with the help of ROESY spectral data that only F-substituted aromatic ring penetrates the β-CD cavity and there is chiral differentiation by the β-CD as one of the isomer binds more strongly, which is indicated by the intensity of correlation peaks. The mode of penetration of the guest into the β-CD cavity was also established and structure of the complex has been proposed.