Stochastic Arithmetic: s-spaces and Some Applications

It has been recently shown that computation with stochastic numbers as regard to addition and multiplication by scalars can be reduced to computation in familiar vector spaces. In this work we show how this can be used for the algebraic solution of linear systems of equations with stochastic right-hand sides. On several examples we compare the algebraic solution with the simulated solution using the CADNA package.     

The two-step exponential decay reaction network: analysis of the solutions and relation to epidemiological SIR models with logistic and Gompertz type infection contact patterns

Journal of Mathematical Chemistry - We mathematically analyze the solutions to the dynamical system induced by the two-step exponential (growth-)decay (2SED) reaction network involving three...     

Black multi‐crystalline silicon solar cells

A simple method for nano‐scale texturing of silicon surfaces based on local metal‐catalyzed wet chemical etching, which results in an almost complete suppression of reflectivity in a broad spectral range, has been successfully applied to produce black multi‐crystalline silicon solar cells. The performance of the cells is compared to that of reference cells without surface nano‐texturing. A considerable increase of the short circuit current (by 36–42% with respect to the reference cells) without deterioration of other performance parameters is observed under natural sun illumination. Means of further optimization of such black solar cells are discussed. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Valuation of the Extraocular Effective Elastance on the Base of Dynamical Model

This paper makes an attempt to answer the question for the effective (functional) value of extraocular elastance. Here, this question is connected with the problem of rhythmicity mechanism of nystagmus phenomena. A likely dynamical model of the nystagmus horizontal motion is proposed by application of the energy and moment of momentum conservation laws to the extraocular muscle. The model is investigated qualitatively and numerically on the base of existing experimental data in the literature. On the base of analysis of obtained results a hypothesis is formulated that the nystagmus horizontal motions present self-oscillations of the considered system.     

Hamiltonian description and 6D calculations on the ammonia vibrational levels

In this work, a Hamiltonian formalism and a 6D vibrational calculation procedure is described and implemented, designed for the exploration of vibrational motion in ammonia (and any XH₃ molecule). The 6D potential energy surface of ammonia was modelled in simple analytical form (including the inversion potential) at the planar, totally symmetric (D_3h) reference configuration. Using the described method (which is an adaptation of the formalism, previously developed and applied to benzene), 6D calculations were carried out on the vibrational level system of ammonia ¹⁴NH₃, at the lower levels of vibrational excitation. On the basis of the satisfactory agreement between the calculated and the experimentally measured vibrational frequencies, the values of some important harmonic and anharmonic force constants, characterizing the ammonia PES were determined.     

A combined theoretical treatment of T(1)-->S(0) intersystem crossing and intramolecular vibrational redistribution in thiophosgene

We combine our two recent theoretical approaches for electronic relaxation T(1)-->S(0) and vibrational relaxation processes in thiophosgene (SCCl(2)) to provide a more detailed picture of the intersystem crossing (ISC) and phosphorescence from the first triplet T(1). Our analysis shows that ISC is not a true irreversible decay and should lead to violent phosphorescence quantum beats that could be observed experimentally.     

Long zero-free sequences in finite cyclic groups

A sequence in an additively written abelian group is called zero-free if each of its nonempty subsequences has sum different from the zero element of the group. The article determines the structure of the zero-free sequences with lengths greater than n/2 in the additive group Z_n of integers modulo n. The main result states that for each zero-free sequence  of length ?>n/2 in Z_n there is an integer g coprime to n such that if denotes the least positive integer in the congruence class ga_i (modulo n), then . The answers to a number of frequently asked zero-sum questions for cyclic groups follow as immediate consequences. Among other applications, best possible lower bounds are established for the maximum multiplicity of a term in a zero-free sequence with length greater than n/2, as well as for the maximum multiplicity of a generator. The approach is combinatorial and does not appeal to previously known nontrivial facts.     

Amorphous/crystalline silicon heterojunction solar cells with black silicon texture

Excellent passivation of black silicon surfaces by thin amorphous silicon layers deposited with plasma enhanced chemical vapor deposition is demonstrated. Minority charge carrier lifetimes of 1.3 milliseconds, enabling an implied open‐circuit voltage of 714 mV, were achieved. The influence of amorphous silicon parasitic epitaxial growth and thickness, as well as of the texture depth is investigated. Furthermore, quantum efficiency gains for wavelengths above 600 nm, as compared to random textured solar cells, are demonstrated in 17.2% efficient amorphous–crystalline silicon heterojunction solar cells with black silicon texture. (© 2014 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

On the Quasivector Space of Zonotopes in the Plane

In this work we consider centred zonogons represented implicitly as Minkowski sums of centred segments. Using this representation the order relation inclusion (containment) of zonogons has been studied. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Quasivector Spaces of Convex Bodies and Zonotopes

In this work the theory of quasivector spaces has been briefly outlined and applied for computation with zonotopes. An approximation problem for zonotopes in the plane has been formulated and an algorithm for its solution has been proposed.