On quartic half-arc-transitive metacirculants

Following Alspach and Parsons, a metacirculant graph is a graph admitting a transitive group generated by two automorphisms ρ and σ, where ρ is (m,n)-semiregular for some integers m≥1, n≥2, and where σ normalizes ρ, cyclically permuting the orbits of ρ in such a way that σ ^m has at least one fixed vertex. A half-arc-transitive graph is a vertex- and edge- but not arc-transitive graph. In this article quartic half-arc-transitive metacirculants are explored and their connection to the so called tightly attached quartic half-arc-transitive graphs is explored. It is shown that there are three essentially different possibilities for a quartic half-arc-transitive metacirculant which is not tightly attached to exist. These graphs are extensively studied and some infinite families of such graphs are constructed. Both authors were supported in part by “ARRS – Agencija za znanost Republike Slovenije”, program no. P1-0285.     

Stage synthesis of three modified phenols

Conclusions The stepwise synthesis of three modified prenols (t₃ctcOH, t₃c₇tOH and t₈cOH) was realized from sesterterpenol, moraprenol, and solanesol, respectively.For the previous communication, see [1].Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 2, pp. 356–360, February, 1987.     

Infinite horizon disturbance attenuation for discrete-time systems. A Popov-Yakubovich approach

It is proved that for the discrete-time linear systems with time-varying coefficients the existence of a controller which simultaneously stabilizes and provides prescribed disturbance attenuation for the resultant closed-loop system, implies the existence of global solutions to several Kalman-Szegö-Popov-Yakubovich systems. It is also proved that this fact is equivalent to the existence of the positive semidefinite stabilizing solutions to corresponding game-theoretic Riccati equations. The family of all controllers with the above mentioned properties is constructed in terms of the solutions to the cited Kalman-Szegö-Popov-Yakubovich systems. The main tool is the generalized Popov-Yakubovich theory which is essentially developed in an operator-theoretic framework.     

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.     

Diffusion-controlled distribution of solute in Sn-1% Bi specimens solidified by the submerged heater method

Two 1.35 kg, 5.8 cm diameter Sn-1% Bi specimens were solidified using the submerged heater method (SHM). The distribution of solute was found to be uniform axially, indicating that diffusion-controlled steady-state segregation, though to be unattainable on earth because of the gravity induced interference, was achieved.     

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.     

The error bounds of Gauss-Kronrod quadrature formulae for weight functions of Bernstein-Szegő type

We consider the Gauss-Kronrod quadrature formulae for the Bernstein-Szeg? weight functions consisting of any one of the four Chebyshev weights divided by the polynomial \(\rho (t)=1-\frac {4\gamma }{(1+\gamma )^{2}}\,t^{2},\quad t\in (-1,1),\ -1<\gamma \le 0\). For analytic functions, the remainder term of this quadrature formula can be represented as a contour integral with a complex kernel. We study the kernel, on elliptic contours with foci at the points ? 1 and sum of semi-axes ρ > 1, for the given quadrature formula. Starting from the explicit expression of the kernel, we determine the locations on the ellipses where maximum modulus of the kernel is attained. So we derive effective error bounds for this quadrature formula. An alternative approach, which has initiated this research, has been proposed by S. Notaris (Numer. Math. 103, 99–127, 2006).