Structural Variability of R2C Adducts of 3a,6a‐Diaza‐1,4‐diphosphapentalene: Tuning the N→P Bonding

3a,6a‐Diaza‐1,4‐diphosphapentalene (DDP) reacts with hexachlorocyclopentadiene to form a stable adduct (ClC)₄C=DDP ( 4 ). The phosphorus atom involved into coordination has a pyramidal arrangement but retains partial double bonding with carbon [1.752(3) Å]. At the same time, the P–N bond remains covalent [1.824(3) Å]. The adduct 4 is better described as a zwitterionic compound with strongly delocalized positive and negative charges. A similar zwitterionic adduct DDP=C(CN)₂ was prepared by the reactions of dichloro‐DDP ( 7 ) with malononitrile in the presence of Et₃N. DFT calculations showed that related structures are formed in the case of the substituents (ClC)₄C=, (HC)₄C=, (NC)₂C=, and (MeCO)₂C=, possessing electron‐delocalizing properties. Compounds with other R₂C groups (R = Ph, Me, C₆F₅, Cl), possessing electronegative properties as well, but insufficient e‐delocalization, demonstrate the noncovalent P–N bonding and a little shorter R₂C–P bond lengths (ca. 1.70 Å).     

Spin Seebeck coefficient of a molecular spin pump

Within a generalized version of previously considered model of a molecular spin pump controlled by an external electric field [J. Fransson and M. Galperin, Phys. Rev. B, 2010, 81, 075311] we discuss thermal properties of such spintronic devices. The spin Seebeck coefficient of a molecular spin pump is introduced, and several possible definitions of a nonequilibrium Seebeck coefficient are discussed. The influence of inelastic effects in spin transport on its thermospintronic characteristics are demonstrated within numerical examples.     

Pareto Analysis vis-à-vis Balance Space Approach in Multiobjective Global Optimization

There is much controversy about the balance space approach, introduced first in Ref. 1, pp. 138–140, with the consideration of the balance number and balance vectors, and then further developed in Ref. 2, with the consideration of balance points and balance sets. There were attempts to identify the balance space approach with some other methods of multiobjective optimization, notably the method proposed in Ref. 3 and most recently Pareto analysis, as presented in Ref. 4. In this paper, we compare Pareto analysis with the balance space approach on several examples to demonstrate the interrelation and the differences of the two methods. As a byproduct, it is shown that, in some cases, the entire Pareto sets, proper and adjoint, can be determined very simply, without any special investigation of the (nonscalarized, nonconvex) multiobjective global optimization problem. The method of parameter introduction is presented in application to determining the Pareto sets and balance set. The use of computer graphics software complemented with the Gauss–Jordan matrix reduction algorithm is proposed for a class of otherwise intractable problems with nonconvex constraint sets.     

Magnetization of a diffusive ring: Beyond the perturbation theory

Average persistent current over a set of diffusive metallic rings with fixed number of electrons is considered. We study the case in which the phase breaking time is much greater than an inverse average interlevel distance. In such a case, many return events for an electron must be taken into account. As a result, one arrives at a nonperturbative problem for a cooperon mode fixed by an external magnetic field. This multi-cooperon problem has been considered previously by Altland et al., [Europhys. Lett. 20, 155 (1992)] and in several following papers within the framework of supersymmetric approach. Such an approach involves very tedious calculations which were performed using a computer algebraic package. Here we solve the problem in question with the help of a replica trick. It is demonstrated that the replica trick in combination with a proper analytical continuation in the replica space allows one to obtain the result in much more explicit way. Zh. éksp. Teor. Fiz. 111, 1057–1070 (March 1997) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Switching in molecular transport junctions: polarization response

We discuss several proposed explanations for the switching and negative differential resistance (NDR) behavior seen in some molecular junctions. Several theoretical models are discussed, and we present results of electronic structure calculations on a series of substituted oligo(phenylene ethynylene) molecules. It is shown that a previously proposed polaron model is successful in predicting NDR behavior, and the model is elaborated with image charge effects and parameters from electronic structure calculations. This model now incorporates substituent effects and includes the effects of conformational change, charging, and image charge stabilization.     

Mathematical modeling and numerical simulation of metal nanoparticles electrooxidation

A mathematical model is proposed that describes the processes of electrooxidation of metal nanoparticles localized on the surface of an indifferent macroelectrode. In contrast to previously proposed models based on geometric factors (shapes of particles and diffusion zones), the proposed model has introduced thermodynamic considerations which take into account the energy differences between the nanoparticle ensembles from microparticles and macroparticles. A series of voltammograms was obtained as a result of calculations and characteristic relationships between the different parameters were found. An analysis of the findings, on the one hand, predicts the shape and characteristic features of the experimental voltammograms and, on the other hand, provides information regarding energetic properties of the nanoparticles.     

Radial Solutions and Orthogonal Trajectories in Multiobjective Global Optimization

This paper presents a new, ray-oriented method for the global solution of nonscalarized vector optimization problems and a framework for the application of the Karush–Kuhn–Tucker theorem to such problems. Properties of nonlinear multiobjective problems implied by the Karush–Kuhn–Tucker necessary conditions are investigated. The regular case specific to nonscalarized MOPs is singled out when a nonlinear MOP with nonlinearities only in the constraints reduces to a nondegenerate linear system. It is shown that the trajectories of the Lagrange multipliers corresponding to the components of the vector cost function are orthogonal to the corresponding trajectories of the vector deviations in the balance space (to the balance set for Pareto solutions). Illustrative examples are presented.     

Instability and refinement of models in long term planning of large scale projects

Instability of models used in long term planning of large scale industrial projects is demonstrated. The uncertainty band around the balance set is introduced to account for unpredictable variations of important parameters or utilities created by instability in multi-objective optimization of large scale projects. Then, instability of dynamic models of growth is considered including population dynamics with saturation and long term optimal planning in social and economic spheres. A method of successive refinement in a synthetic multi-model system is proposed, and application of the sequence of refined models is illustrated on a real-life example of construction of a dam with yearly refinements of the initial model, based on past history of project realization.     

On pseudoinverses of operator products

The analytical structure of the Moore-Penrose pseudoinverse of the product ab of any two operators over finite-dimensional unitary spaces is studied. The existence of the unique representation of the form (ab)⁺=b⁺(h+g)a⁺ is proved. Here h:= (a⁺abb⁺)⁺ is an (oblique) projector and g is an operator with a number of special properties. In particular, h+g is a projector, g is orthogonal to h in some metric, and g³=0. A necessary and sufficient condition for the case (ab)⁺=b⁺ha⁺ is established. This case contains the classical one (ab)⁺=b⁺a⁺ (the reverse-order law). For the latter a new necessary and sufficient condition is given.