Nonseparable graphs with a given number of cycles

G. Ringel conjectured that for every positive integer n other than 2, 4, 5, 8, 9, and 16, there exists a nonseparable graph with n cycles. It is proved here that the conjecture is true even with the restriction to planar and hamiltonian graphs.     

Practical asymmetric synthesis of alpha-branched 2-piperazinylbenzylamines by 1,2-additions of organometallic reagents to N-tert-butanesulfinyl imines

[reaction: see text] 2-[4-(tert-Butoxycarbonyl)piperazinyl]benzylidene-tert-butanesulfinamides underwent nucleophilic 1,2-addition with different organometallic reagents to give highly diastereomerically enriched adducts. X-ray crystallography of the resulting alpha-branched N-Boc-2-piperazinylbenzyl-tert-butanesulfinamides confirms different mechanisms depending on the organometallic reagent used. Differential deprotection of the N-Boc and the tert-butanesulfinamides was investigated, and the dehydration byproducts have been identified and characterized. To avoid the formation of byproducts in the acidic deprotection step, the N-tert-butanesulfinamide group was converted to the corresponding N-tert-butanesulfonamide (Bus), which allowed for clean orthogonal deprotection. The efficient synthesis and deprotection of the N-Boc-2-piperazinylbenzyl-tert-butanesulfinamides herein described constitutes an attractive method for extensive structure-activity studies in the search for novel ligands of the human melanocortin 4 receptor.     

Electrophilic cyclization of α-series monoterpene ω-derivatives

New information is discussed concerning the protic and Lewis acid-initiated electrophilic cyclization reaction of -monoterpenols and their acetates; the distinguishing feature of these reactions is their termination by isopropenyl residues in these molecules. The reactions have been found to be general in nature, given additional functionalization of the terminator by chloro-, sulfonyl, sulfonylmethyl, or ester substituents. Cyclization of these linear substrates has also been shown to provide a convenient method for the synthesis of dimethylvinylcyclohexene derivatives and related cyclohexanediols, which are not readily available by other methods.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 6, pp. 1361–1367, June, 1990.     

α-Synuclein overexpression increases dopamine toxicity in BE(2)-M17 cells

Background  

Oxidative stress has been proposed to be involved in the pathogenesis of Parkinson's disease (PD). A plausible source of oxidative stress in nigral dopaminergic neurons is the redox reactions that specifically involve dopamine and produce various toxic molecules, i.e., free radicals and quinone species. α-Synuclein, a protein found in Lewy bodies characteristic of PD, is also thought to be involved in the pathogenesis of PD and point mutations and multiplications in the gene coding for α-synuclein have been found in familial forms of PD.     

Improved density functional theory/electrostatic calculation of the His291 protonation state in cytochrome C oxidase: self-consistent charges for solvation energy calculation

The protonation state of His291 in cytochrome c oxidase (CcO), a ligand to the Cu(B) center of the enzyme, has been recently studied in this group by using combined density functional theory (DFT)/electrostatic (QM/MM) calculations. On the basis of these calculations, a model of the proton pumping mechanism of CcO has been proposed. Due to certain technical difficulties, the procedure used in the previous calculation to find partial atomic charges of the QM system for the solvation energy evaluation was not entirely satisfactory; i.e., it was not self-consistent. Here, we describe a procedure that resolves the problem and report on the improved calculations of the protonation state of the His residue. The new procedure fits the protein and reaction field potentials in the region of the QM system with artificial point charges placed on a surface of a sphere surrounding the QM system and a few charges inside the sphere and allows one to perform DFT calculations that involve an inhomogeneous dielectric environment in a self-consistent way. The procedure improves the accuracy of calculations in comparison with previous work. The improved results show, however, that although the absolute energies change significantly the relative energies of the protonated and deprotonated states of His291 remain close to the previously reported ones and therefore do not change significantly the pK(a) values reported earlier. Therefore, our new improved calculations support for the proposed His291 model of the CcO pump.     

Stress Integration of the Hoek-Brown Material Model Using Incremental Plasticity Theory

This paper presents the formulation of the stress integration procedure for the Hoek-Brown (HB) material model with non-associative yielding condition by using the incremental plasticity method. Main idea of this method is to reach the solution by calculating the plastic matrix according to the method of incremental plasticity (used for elastic constitutive matrix corrections), and with the use of the total strain increment. Computational procedure is implemented within the PAK program package. Results of this procedure were compared with the solutions obtained by other program that contains this material model. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On G-arc-regular dihedrants and regular dihedral maps

A graph Γ is said to be G-arc-regular if a subgroup $G \le\operatorname{\mathsf{Aut}}(\varGamma)$ acts regularly on the arcs of Γ. In this paper connected G-arc-regular graphs are classified in the case when G contains a regular dihedral subgroup D _2n of order 2n whose cyclic subgroup C _n ≤D _2n of index 2 is core-free in G. As an application, all regular Cayley maps over dihedral groups D _2n , n odd, are classified.     

Bound states in continuum: Quantum dots in a quantum well

We report on the existence of a bound state in the continuum (BIC) of quantum rods (QR). QRs are novel elongated InGaAs quantum dot nanostructures embedded in the shallower InGaAs quantum well. BIC appears as an excited confined dot state and energetically above the bottom of a well subband continuum. We prove that high height-to-diameter QR aspect ratio and the presence of a quantum well are indispensable conditions for accommodating the BIC. QRs are unique semiconductor nanostructures, exhibiting this mathematical curiosity predicted 83 years ago by Wigner and von Neumann.     

Exponential Stability in Mean Square for a General Class of Discrete-Time Linear Stochastic Systems

Abstract

The problem of the mean square exponential stability for a class of discrete-time linear stochastic systems subject to independent random perturbations and Markovian switching is investigated. The case of the linear systems whose coefficients depend both to present state and the previous state of the Markov chain is considered. Three different definitions of the concept of exponential stability in mean square are introduced and it is shown that they are not always equivalent. One definition of the concept of mean square exponential stability is done in terms of the exponential stability of the evolution defined by a sequence of linear positive operators on an ordered Hilbert space. The other two definitions are given in terms of different types of exponential behavior of the trajectories of the considered system. In our approach the Markov chain is not prefixed. The only available information about the Markov chain is the sequence of probability transition matrices and the set of its states. In this way one obtains that if the system is affected by Markovian jumping the property of exponential stability is independent of the initial distribution of the Markov chain.

The definition expressed in terms of exponential stability of the evolution generated by a sequence of linear positive operators, allows us to characterize the mean square exponential stability based on the existence of some quadratic Lyapunov functions.

The results developed in this article may be used to derive some procedures for designing stabilizing controllers for the considered class of discrete-time linear stochastic systems in the presence of a delay in the transmission of the data.     

Stochastic analysis of the electromagnetic induction effect on a neuron’s action potential dynamics

Nonlinear Dynamics - The presence of time-varying electromagnetic fields across a neuron cell may cause changes in its electrical characteristics, most notably, in the action potential dynamics....