Orientational dynamics in the isotropic phase of a calamitic liquid-crystal model

We report a molecular dynamics simulation study on the isotropic phase of an idealized calamitic liquid crystal model with a length-to-width ratio of approximately 5-6. The study focuses on the characterization of single-particle and collective orientational dynamics on approaching the phase transition to the nematic phase. Recent experimental and simulation works have suggested that a power law behavior exists at relatively short times in the decay of the time derivative of the orientational correlation functions. Qualitatively, our simulation data are consistent with these findings. Both single-particle and collective time correlation function derivatives possess, in their respective log-log plots, a linear region at very short times, whose slope is essentially independent from the thermodynamic state. Nevertheless, the single-particle orientational correlation functions are better described by a function which is the sum of a fast exponential, an intermediate stretched-exponential and a slow exponential, while the collective orientational correlation functions are satisfactorily described by a sum of two exponentials, at higher density, or by just one exponential, at lower density.     

Enthalpies of Solution of Organic Compounds inWater/Octan-1-ol Mixtures. A Rationale Based ona Model of Structural Organization of the SolventMedium

Limiting enthalpies of solution _solnH°(oct/w) of several monofunctionalcompounds (tetrahydropyran, diethylamine, pyrrolidine, piperidine,1-methylpiperidine) in water–octan-1-ol mixtures with water content ranging from zero tosaturation have been determined at 25°C. The observed phenomenology hasbeen interpreted by supposing that the solvent medium undergoes a microphasetransition at water mole fraction of about 0.08. In the water-poor region theexperimental behavior is consistent with the presence of water molecules inprevailingly monodispersed form, while in the water-rich region the formationof organized pseudomicellar water aggregates is suggested. Two different simplemodels have also been proposed to describe quantitatively the observed trendsof _solnH°(oct/w) vs. mole fraction of water.Deceased while this research was in progress. The coauthors wish to dedicate this work to his memory     

Perfect fibonacci and lucas numbers

In this note, we show that the classical Fibonacci and Lucas sequence do not contain any perfect number.     

Base-promoted cyclization of 1-nitrohydrazones bearing a thioether function

Functionalized 1-nitrohydrazones 5 react with sodium hydride in boiling benzene to afford different types of ring-closed products. The formation of the latter can be ascribed to competitive modes of evolution of first-formed nitrile imines.     

The stability of the solutions of a class of integrodifferential systems with infinite delays

Various stability types, analogous to those in the theory of ordinary differential equations, are defined for some classes of integrodifferential systems of equations with infinite delays. Then, on the basis of a variation of constants formula and some results in functional analysis and Laplace transform theory, some necessary conditions and necessary and sufficient conditions are established in order that the trivial solution of a class of systems may be classified as one of the stability types considered in the definitions.     

Disidein,a pentacyclic sesterterpene condensed with an hydroxyhydroquinone moiety,from the sponge Disidea pallescens

A novel pentacyclic saturated sesterpene condensed with hydroxyhydroquinone moiety, which we named disidein (1), has been isolated from the marine sponge Disidea pallescens as disulfate sodium calcium salt. A minor accompaining compound, which seems a likely precursor of disidein, has been identified as 2-pentaprenylbenzoquinone (7).     

Mercury(II) derivatives of azoles

The reaction between mercury(II) chloride and azoles(pyrazole, 3,5-dimethylpyrazole, benzotriazole, 1,2,4-triazole) afforded mainly N-chloro mercury derivatives, although other reactions, such as the well known ring mercuration or the formation of a complex, were observed simultaneously. Therefore, no simple generalization explains the observed reactivity of azoles towards mercury(II) chloride, each reaction investigated being a different case.     

Spherical means and the restriction phenomenon

Let Γ be a smooth compact convex planar curve with arc length dm and let dσ=ψ dm where ψ is a cutoff function. For Θ∈SO (2) set σ_Θ(E) = σ(ΘE) for any measurable planar set E. Then, for suitable functions f in ℝ², the inequality.

Rounding Procedures for the Discrete Version of the Capacitated Economic Order Quantity Problem

The capacitated Economic Order Quantity problem (capacitated EOQ) is a well-known problem where products have to be shipped between two points with a vehicle of given capacity. Each shipment has a fixed cost, independent of the shipped quantity, and an inventory cost is generated in the two points. The problem consists in finding the optimal time between consecutive shipments, which minimizes the total cost. The problem is a capacitated variant of the EOQ problem and has a closed form solution. Since such solution is often irrational, it is often rounded to an integer value. In this paper we investigate the errors which are generated by rounding procedures to integer and powers-of-two values. We show that, although in the worst case a tight general relative error of 2 is generated by all the considered rounding procedures, the procedure which rounds to the best between the lower and upper values (integer or powers-of-two) has a performance of $\frac{1}{2}$ ( $\sqrt 2 + 1/\sqrt 2 $ )≈1.06 on classes of instances of high practical relevance.