Asymptotics for the number of n-quasigroups of order 4

The asymptotic form of the number of n-quasigroups of order 4 is $3^{n+1} 2^{2^n +1} (1+o(1))$. Keywords: n-quasigroups, MDS codes, decomposability, reducibility.Comment: 15 p., 3 fi

Algorithms for solving inverse geophysical problems on parallel computing systems

For solving inverse gravimetry problems, efficient stable parallel algorithms based on iterative gradient methods are proposed. For solving systems of linear algebraic equations with block-tridiagonal matrices arising in geoelectrics problems, a parallel matrix sweep algorithm, a square root method, and a conjugate gradient method with preconditioner are proposed. The algorithms are implemented numerically on a parallel computing system of the Institute of Mathematics and Mechanics (PCS-IMM), NVIDIA graphics processors, and an Intel multi-core CPU with some new computing technologies. The parallel algorithms are incorporated into a system of remote computations entitled "Specialized Web-Portal for Solving Geophysical Problems on Multiprocessor Computers." Some problems with "quasi-model" and real data are solved. © 2013 Pleiades Publishing, Ltd

Representations of (2,n)(2,n)-semigroups by multiplace functions

We describe the representations of $(2,n)$-semigroups, i.e. groupoids with $n$ binary associative operations, by partial $n$-place functions and prove that any such representation is a union of some family of representations induced by Schein's determining pairs.Comment: 17 page

A mathematical model of the controlled axial flow divider for mobile machines

The authors give a mathematical model of the axial adjustable flow divider allowing one to define the parameters of the feed pump and the hydraulic motor-wheels in the multi-circuit hydrostatic transmission of mobile machines, as well as for example built features that allows to clearly evaluate the mutual influence of the values of pressure and flow on all input and output circuits of the system

Josephson array of mesoscopic objects. Modulation of system properties through the chemical potential

The phase diagram of a two-dimensional Josephson array of mesoscopic objects is examined. Quantum fluctuations in both the modulus and phase of the superconducting order parameter are taken into account within a lattice boson Hubbard model. Modulating the average occupation number $n_0$ of the sites in the system leads to changes in the state of the array, and the character of these changes depends significantly on the region of the phase diagram being examined. In the region where there are large quantum fluctuations in the phase of the superconducting order parameter, variation of the chemical potential causes oscillations with alternating superconducting (superfluid) and normal states of the array. On the other hand, in the region where the bosons interact weakly, the properties of the system depend monotonically on $n_0$. Lowering the temperature and increasing the particle interaction force lead to a reduction in the width of the region of variation in $n_0$ within which the system properties depend weakly on the average occupation number. The phase diagram of the array is obtained by mapping this quantum system onto a classical two-dimensional XY model with a renormalized Josephson coupling constant and is consistent with our quantum Path-Integral Monte Carlo calculations.Comment: 12 pages, 8 Postscript figure

Simulation of parameters of hydraulic drive with volumetric type controller

© Published under licence by IOP Publishing Ltd. The article presents a mathematical model of volumetric type hydraulic drive controller that allows to calculate the parameters of forward and reverse motion. According to the results of simulation static characteristics of rod's speed and the force of the hydraulic cylinder rod were built and the influence of the angle of swash plate of the controller at the characteristics profile is shown. The results analysis showed that the proposed controller allows steplessly adjust the speed□ of hydraulic cylinder's rod motion and the force developed on the rod without the use of flow throttling

Death of Neurons following Injury Requires Conductive Neuronal Gap Junction Channels but Not a Specific Connexin

A grant from the One-University Open Access Fund at the University of Kansas was used to defray the author's publication fees in this Open Access journal. The Open Access Fund, administered by librarians from the KU, KU Law, and KUMC libraries, is made possible by contributions from the offices of KU Provost, KU Vice Chancellor for Research & Graduate Studies, and KUMC Vice Chancellor for Research. For more information about the Open Access Fund, please see http://library.kumc.edu/authors-fund.xml.Pharmacological blockade or genetic knockout of neuronal connexin 36 (Cx36)-containing gap junctions reduces neuronal death caused by ischemia, traumatic brain injury and NMDA receptor (NMDAR)-mediated excitotoxicity. However, whether Cx36 gap junctions contribute to neuronal death via channel-dependent or channel-independent mechanism remains an open question. To address this, we manipulated connexin protein expression via lentiviral transduction of mouse neuronal cortical cultures and analyzed neuronal death twenty-four hours following administration of NMDA (a model of NMDAR excitotoxicity) or oxygen-glucose deprivation (a model of ischemic injury). In cultures prepared from wild-type mice, over-expression and knockdown of Cx36-containing gap junctions augmented and prevented, respectively, neuronal death from NMDAR-mediated excitotoxicity and ischemia. In cultures obtained form from Cx36 knockout mice, re-expression of functional gap junction channels, containing either neuronal Cx36 or non-neuronal Cx43 or Cx31, resulted in increased neuronal death following insult. In contrast, the expression of communication-deficient gap junctions (containing mutated connexins) did not have this effect. Finally, the absence of ethidium bromide uptake in non-transduced wild-type neurons two hours following NMDAR excitotoxicity or ischemia suggested the absence of active endogenous hemichannels in those neurons. Taken together, these results suggest a role for neuronal gap junctions in cell death via a connexin type-independent mechanism that likely relies on channel activities of gap junctional complexes among neurons. A possible contribution of gap junction channel-permeable death signals in neuronal death is discussed.National Institutes of Health (NIH) (R21 NS076925)University of Kansas Medical Center funds to A. B. B.NIH P20 GM104936, P30 AG035982UL1 TR000001NIH HD00252

Quantum orientational melting of mesoscopic clusters

By path integral Monte Carlo simulations we study the phase diagram of two - dimensional mesoscopic clusters formed by electrons in a semiconductor quantum dot or by indirect magnetoexcitons in double quantum dots. At zero (or sufficiently small) temperature, as quantum fluctuations of particles increase, two types of quantum disordering phenomena take place: first, at small values of quantum de Boer parameter q < 0.01 one can observe a transition from a completely ordered state to that in which different shells of the cluster, being internally ordered, are orientationally disordered relative to each other. At much greater strengths of quantum fluctuations, at q=0.1, the transition to a disordered (superfluid for the boson system) state takes place.Comment: 4 pages, 6 Postscript figure

Representations of Menger (2,n)(2,n)-semigroups by multiplace functions

Investigation of partial multiplace functions by algebraic methods plays an important role in modern mathematics were we consider various operations on sets of functions, which are naturally defined. The basic operation for $n$-place functions is an $(n+1)$-ary superposition $[ ]$, but there are some other naturally defined operations, which are also worth of consideration. In this paper we consider binary Mann's compositions \op{1},...,\op{n} for partial $n$-place functions, which have many important applications for the study of binary and $n$-ary operations. We present methods of representations of such algebras by $n$-place functions and find an abstract characterization of the set of $n$-place functions closed with respect to the set-theoretic inclusion