A finite difference approach to the equations of age-dependent population dynamics

We establish the convergence of the finite difference scheme for the nonlinear equations of population dynamics proposed by Guertin and MacCamy. The applicability of the discrete equations to establish qualitative properties of the solution to the continuous problem is also illustrated.     

Chvátal closures for mixed integer programming problems

Chvátal introduced the idea of viewing cutting planes as a system for proving that every integral solution of a given set of linear inequalities satisfies another given linear inequality. This viewpoint has proven to be very useful in many studies of combinatorial and integer programming problems. The basic ingredient in these cutting-plane proofs is that for a polyhedronP and integral vectorw, if max(wx|x P, wx integer} =t, thenwx t is valid for all integral vectors inP. We consider the variant of this step where the requirement thatwx be integer may be replaced by the requirement that be integer for some other integral vector . The cutting-plane proofs thus obtained may be seen either as an abstraction of Gomory's mixed integer cutting-plane technique or as a proof version of a simple class of the disjunctive cutting planes studied by Balas and Jeroslow. Our main result is that for a given polyhedronP, the set of vectors that satisfy every cutting plane forP with respect to a specified subset of integer variables is again a polyhedron. This allows us to obtain a finite recursive procedure for generating the mixed integer hull of a polyhedron, analogous to the process of repeatedly taking Chvátal closures in the integer programming case. These results are illustrated with a number of examples from combinatorial optimization. Our work can be seen as a continuation of that of Nemhauser and Wolsey on mixed integer cutting planes.Supported by Sonderforschungsbereich 303 (DFG) and by NSF Grant Number ECS-8611841.Supported by NSF Grant Number ECS-8418392 and Sonderforschungsbereich 303 (DFG), Institut für Ökonometrie und Operations Research, Universität Bonn, FR Germany.     

Synthesis and characterization of liquid‐crystalline polyphosphonates containing disubstituted ferrocene esters as mesogens

A series of ferrocene‐containing liquid‐crystalline polyphosphonates with an even number of methylene groups are reported. All the polymers gave birefringent melts. The mesophase was identified as transparent with an increase in the spacer. The effects of pendant substitution and the spacer were studied with thermogravimetric analysis and differential scanning calorimetry. The effects of the phosphonate group in the spacer and the ferrocene ester group in the mesogen were examined. The presence of a steplike mesogenic structure and a pendant phenyl group in the spacer led to reductions in the glass‐transition and melting temperatures. The ferrocene moiety in the mesogen might be one of the reasons for the increased thermal stability and decreased liquid crystallinity. An energy‐minimized structure for the mesogenic and spacer segments was created with computer‐modeling programs, and it suggested the reason for the reductions in the glass‐transition and melting temperatures. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2256–2263, 2002     

A semi-discrete convergent scheme for a quasilinear hyperbolic equation

We establish here the convergence (thereby proving the existence) of a semi-discrete scheme for the quasilinear hyperbolic equation where x ∈ Rⁿ, t ∈ [0,T], and ? ∈ L^∞ (Rⁿ). It is well known that the above problem does not necessarily have global classical solutions and the usual concepts of weak solution. do not lead to a unique solution The existence of a unique solution to the above problem in a suitable sense was established in [3], where a parabolic problem obtained by introducing the term ??Δu was studied and then the behavior as ? → 0 was discussed. A difference scheme approach to a problem of the above type where ?_i does not depend on x and t and Ψ does not depend on u was also studied in [2]. The aim of this paper is to present a proof for the case when ? depends on x, Ψ depends on u, and the technical complications in this case are nontrivial. The discussions in this paper my be considered as continuation of the ideas in the above papers.     

DSC study on the effect of isocyanates and catalysts on the HTPB cure reaction

The urethane forming cure reactions of hydroxyl terminated polybutadiene (HTPB) binder with three different isocyanate curatives, viz., toluene diisocyanate (TDI), isophorone diisocyanate (IPDI) and 4,4-methylene bis(cyclohexyl isocyanate) (MCHI), were investigated by differential scanning calorimetry (DSC). The effect of two cure catalysts, viz., dibutyl tin dilaurate (DBTDL) and ferrric tris-acetylacetonate (FeAA) on the cure reactions was also studied. Cure kinetics was evaluated using the multiple heating rate Ozawa method. The reactivities of the three isocyanates and catalytic efficiencies were compared based on the DSC reaction temperatures, activation energies and rate constants. Viscosity build-up in these systems at isothermal temperature was also studied and compared with the results from DSC.     

Frobenius distributions of elliptic curves in short intervals on average

The Ramanujan Journal - For an elliptic curve $$E/{\mathbb {Q}}$$ , let $$a_p$$ denote the trace of its Frobenius endomorphism over $${\mathbb {F}}_p$$ , where p is a prime of good reduction for E....     

Versatile new uranyl(VI) dihalide complexes supported by tunable organic amide ligands

A series of uranyl(VI) dihalide complexes UO2X2L2 (X = Cl, Br) supported by organic amide ligands (L = R'C(O)NR2; R' = i-Pr; R = i-Pr, i-Bu, s-Bu) offers the versatile combination of facile synthesis using benchtop methods, air-stable crystalline solids obtained in high yield, high solubility in common organic solvents and tunable steric/electronic properties.     

Macromolecular crystallography research at Trombay

Neutron diffraction studies of hydrogen positions in small molecules of biological interest at Trombay have provided valuable information that has been used in protein and enzyme structure model-building and in developing hydrogen bond potential functions. The new R-5 reactor is expected to provide higher neutron fluxes and also make possible smallangle neutron scattering studies of large biomolecules and bio-aggregates. In the last few years infrastructure facilities have also been established for macromolecular x-ray crystallography research. Meanwhile, the refinement of carbonic hydrases’ and lysozyme structures have been carried out and interesting results obtained on protein dynamics and structure-function relationships. Some interesting presynaptic toxin phospholipases have also been taken up for study.     

Synthesis,spectral, thermal,and flammability studies of phenolphthalein polyphosphate esters

Polyphosphate esters were synthesized from phenolphthalein and aryl phosphorodichloridates by interfacial polycondensation using a phase transfer catalyst. The polymers were characterized by IR, ¹H-, ¹³C-, and ³¹P-NMR spectroscopy. The molecular weights were calculated by end group analysis using ³¹P-NMR spectral data. The thermal stability of the polymers was studied by thermogravimetry and the flammability was investigated by measuring limiting oxygen index values.     

High-temperature transformations of Cu-rich hydrotalcites

CuM(II)Al ternary hydrotalcites (M(II) = Ni, Co and Mg) with a (Cu+M(II))/Al atomic ratio of 3.0 and Cu/M(II) atomic ratio of 5.0 were synthesized by coprecipitation under low supersaturation. Powder X-ray diffraction of the as-synthesized samples showed a pattern characteristic of hydrotalcite-like (HT-like) structure (JCPDS: 41-1428). Thermal analyses of these samples showed four stages of weight loss/heat change when recorded in nitrogen. Analysis of the evolved gases characterized the nature of these transformations. The thermoanalytical effects differed significantly especially for the high-temperature transformations, when the treatment was performed in oxygen. In situ powder X-ray diffraction of the samples was carried out to elucidate the phase evolution of these compounds. Surprisingly formation of CuO was noted at temperatures around 200°C well below the destruction of the layered network. The nature of the resulting phases varied with both the nature of the co-bivalent metal ion and the heating atmosphere. FT-IR spectroscopy confirmed the retention of carbonate ions at higher temperatures (above 700°C), although the concentration of carbonate anion (most likely unidentate) varied with the calcination temperature. The crystallinity of CuO increased significantly above 600°C, probably through dissociation of copper oxycarbonate. Significant differences in the thermal transformation temperatures (for the third and the fourth transformations) of these samples containing different co-bivalent metal ions were not observed. This suggests that an association of the co-bivalent metal ions and/or trivalent metal ion in this phase is unlikely. A plausible thermal evolution scheme of these hydrotalcites is proposed.