Relative energy of organic compounds IV. Radicals,carbocations, and carbanions

The structure-dependent energies of organic radicals, cations, and anions are deduced from their calculated relative enthalpies and are compared to the relative enthalpies of their parent compounds. The use of relative enthalpies to express the relative energies of organic radicals, cations, and anions proved to be as fruitful as in the case of their parent organic compounds. The same energy-determining structural factors may have stronger, weaker, or even opposite effects in the radicals, cations, or anions than those in their parent molecules.     

Affine Reductive Spaces of Small Dimension and Left A-Loops

In this paper we determine the at least 4-dimensional affine reductive homogeneous manifolds for an at most 9-dimensional simple Lie group or an at most 6-dimensional semi-simple Lie group. Those reductive spaces among them which admit a sharply transitive differentiable section yield local almost differentiable left A-loops. Using this we classify all global almost differentiable left A-loops L having either a 6-dimensional semi-simple Lie group or the group as the group topologically generated by their left translations. Moreover, we determine all at most 5-dimensional left A-loops L with as the group topologically generated by their left translations.     

Monotonicity properties of operations on generalized topologies

Summary In the paper [5], several operations on generalized topologies are considered. They are not monotone in general, but an old result on monotonicity may be sharpened.     

On Dupin Hypersurfaces in R5 Parametrized by Lines of Curvature

We provide a complete local characterization of Dupin hypersurfaces in R⁵, with four distinct principal curvatures, parametrized by lines of curvature. Such hypersurfaces are given in terms of the principal curvatures and vector valued functions that describe plane curves. We include explicit examples of such Dupin hypersurfaces which are irreducible and have nonconstant Lie curvature.     

A stochastic bi-objective location model for strategic reverse logistics

In this paper we propose a comprehensive model for reverse logistics planning where many real-world features are considered such as the existence of several facility echelons, multiple commodities, choice of technology and stochasticity associated with transportation costs and waste generation. Moreover, we adopt a bi-objective model for the problem. First, the cost for building and operating the network is to be minimized. Second, the obnoxious effect caused by the reverse network facilities is also to be minimized. A two-stage stochastic bi-objective mixed-integer programming formulation is proposed, in which the strategic decisions are considered in the first stage and the tactical/operational decisions in the second one. A set of different scenarios is considered, and the extensive form of the deterministic equivalent problem is presented. This model is tested with a case study based on some data from the Spanish province of Cordoba. Nondominated solutions are obtained by combining the two different objectives and by using a general solver.     

On differential properties for bivariate orthogonal polynomials

In this paper, we consider bivariate orthogonal polynomials associated with a quasi-definite moment functional which satisfies a Pearson-type partial differential equation. For these polynomials differential properties are obtained. In particular, we deduce some structure and orthogonality relations for the successive partial derivatives of the polynomials.      

Bounds for the generalized Marcum function of the second kind

The Ramanujan Journal - This paper provides elementary proofs for several types of congruences involving multipartitions and self-convolutions of the divisor function. Our computations use...     

Spectral Criteria for Design of an Optical Modulator Based on Frustrated Total Internal Reflection

The spectral study of an optical modulator based on the frustrated total internal reflection is presented under static and dynamic conditions. An optical modulator based on macroscopic moving parts makes spectrometers voluminous and has low compactness. The use of static or quasi-static optical modulators, such as the one proposed in this paper, avoids these problems. The study under static conditions reveals that the modulator equalises the spectral emittance of a black body. The modulation efficiency is defined by comparing the modulator with an ideal square chopper. Study under dynamic conditions reveals spectral criteria that must be met in the design of the mechanical system of the modulator to shift the maximum value of the modulation efficiency to the desired wavelength.