An approximation scheme for the two-stage,two-dimensional knapsack problem

We present an approximation scheme for the two-dimensional version of the knapsack problem which requires packing a maximum-area set of rectangles in a unit square bin, with the further restrictions that packing must be orthogonal without rotations and done in two stages. Achieving a solution which is close to the optimum modulo a small additive constant can be done by taking wide inspiration from an existing asymptotic approximation scheme for two-stage two-dimensional bin packing. On the other hand, getting rid of the additive constant to achieve a canonical approximation scheme appears to be widely nontrivial.     

First-principles study of aqueous hydroxide solutions

Car-Parrinello molecular dynamics simulations have been carried out for aqueous NaOH and KOH solutions under ambient conditions over a wide range of concentrations. From these simulations, we have observed a continuous change of the water structure with added hydroxide, characterized by a significant shift of the second peak of the OO radial distribution functions to shorter distances. At the highest concentration investigated, the normal tetrahedral coordination of pure water is completely missing, a result that is consistent with a recent neutron diffraction experiment. The added hydroxide also gives rise to some unique spectroscopic features, including a "free" O-H stretch, a broadening of the normal water OH stretching band, and a large blue shift of both the librational band and the low-frequency translation. These results are in good agreement with the experimental data. Finally, it was demonstrated that the structural and dynamical behavior is inextricably linked to the formation of compact hydroxide-water complexes.     

Lack of self-averaging in neutral evolution of proteins

We simulate neutral evolution of proteins imposing conservation of the thermodynamic stability of the native state in the framework of an effective model of folding thermodynamics. This procedure generates evolutionary trajectories in sequence space which share two universal features for all of the examined proteins. First, the number of neutral mutations fluctuates broadly from one sequence to another, leading to a non-Poissonian substitution process. Second, the number of neutral mutations displays strong correlations along the trajectory, thus causing the breakdown of self-averaging of the resulting evolutionary substitution process.     

Restrictions and expansions of holomorphic representations

We compute tensor products of representations of the holomorphic discrete series of a Lie group G, or restrictions to some subgroup G′. A detailed study is done for the case of the conformal group O(4, 2).     

Principio di entropia e restrizioni termodinamiche per fluidi con memoria

Riassunto In questo lavoro si affrontano i problemi relativi alle restrizioni termodinamiche, imposte dal principio di entropia nella formulazione di Müller [1], per fluidi con memoria, mediante il metodo dei moltiplicatori di Lagrange.

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Summary In this work Author deals with the problems pertinent to the thermodynamic restrictions, which are due to principle of entropy in the formulation of Müller [1], for fluids with a memory, through the Lagrange multipliers.

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Lavoro eseguito nell'ambito del G.N.F.M. del C.N.R.     

Reciprocal and variational theorems for nonlocal theory of viscoelastic materials

Summary We study some variational and reciprocal problems for viscoelastic materials with nonlocal constitutive equations and in particular with dissipative boundary conditions.

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Riassunto Si determinano alcuni teoremi variazionali e di reciprocitá per materiali viscoelastici con una dipendenza anche spaziale e con condizioni al contorno dissippative.

     

Research on heterocyclic compounds. XIII. Synthesis of 4,5-dihydro-5-oxo-3-isoxazoleacetic acid and related compounds

Some new 4,5-dihydro-5-oxoisoxazole derivatives were synthesized as part of a study to prepare potential antiinflammatory agents. The reaction of the diethyl ester of 3-oxopentanedioic acid with hydroxylamine afforded the 3-hydroxyimino derivative, which was then cyclized to the title compound. This reacted with diazomethane to give a couple of isomeric methyl derivatives, namely methyl 2,5-dihydro-2-methyl-5-oxo-3-isoxazoleacetate and methyl 5-methoxy-3-isoxazoleacetate. Reaction of these compounds with ammonia gave the corresponding acetamides. All compounds were characterized by elemental analysis, uv, ir, and ¹H-nmr spectra.     

Chemical modification of chitosan under high-intensity ultrasound

Chitosan (CTS), a biocompatible, biodegradable, non-toxic polymer, dissolves in water only if pH is lowered under 6.5, when a substantial fraction of the amino groups is protonated. Its range of application has been much extended by partially depolymerising it or converting it to water-soluble derivatives. Working under high-intensity ultrasound at 17.8-18.5 kHz, using either a simple horn or a cup horn, we achieved a controlled depolymerization of CTS, also prepared in high yields several derivatives that can be useful intermediates for further chemical modification, as well as several water-soluble derivatives that lend themselves to a host of industrial applications. Compared to conventional methods, all these reactions went to completion in considerably shorter times at lower temperatures.