Normal cirulant graphs with noncyclic regular subroups

We prove that any circulant graph of order n with connection set S such that n and the order of ?(S), the subgroup of ? that fixes S set‐wise, are relatively prime, is also a Cayley graph on some noncyclic group, and shows that the converse does not hold in general. In the special case of normal circulants whose order is not divisible by 4, we classify all such graphs that are also Cayley graphs of a noncyclic group, and show that the noncyclic group must be metacyclic, generated by two cyclic groups whose orders are relatively prime. We construct an infinite family of normal circulants whose order is divisible by 4 that are also normal Cayley graphs on dihedral and noncyclic abelian groups. © 2005 Wiley Periodicals, Inc. J Graph Theory     

Chirality of toroidal molecular graphs

Symmetry properties of a class of toroidal molecular graphs, arising as covers of certain bipartite cubic Cayley graphs of dihedral groups, are studied. Although these symmetries make all vertices and all edges indistinguishable, they imply intrinsic chirality.     

Sakurai addition and ring annulation of allylsilanes with alpha, beta-unsaturated esters. Experimental results and ab initio theoretical predictions examining allylsilane reactivity

Trimethylallylsilane has been shown to add to methyl acrylate in good yield when catalyzed by TiCl(4) at room-temperature despite literature reporting to the contrary. Further, even with these small alkyl ligands on the metal, ring annulation occurs to a large extent, in addition to simple allylation (Sakurai addition). The kinetic product is the ((trimethylsilyl)methyl)cyclobutane derivative which can be isomerized to cyclopentanoid, the thermodynamic product, if left in the presence of the catalyst. Consistent with other literature in this area, increasing the size of the ligands on silicon increases both the rate of product formation and the proportion of ring annulation relative to allylation. To develop a predictive model for allylsilane reactivity, ab initio gas-phase calculations have been made on the parent allylsilane with different ligands on the metal and on the reaction between these allylsilanes and acrolein, acrylic acid, and methyl acrylate. Predictions indicate that as the length of n-alkyl ligands on silicon increase, so does the apparent ability of the Si-Calpha bond of the allylsilane to hyperconjugate with developing vacant p orbital on Cbeta as the allylsilane begins to attack an electrophile. This is corroborated by a gradually increasing HOMO in the ground-state allylsilane as the ligands are changed from methyl through to n-hexyl and an increasing Si-Calpha bond length and decreasing Si-Calpha-Cbeta bond angle in the protonated species. These results in the gas phase mirror the reactivity of these n-alkyl-substituted allylsilanes in experiment; i.e., as the length of the alkyl chain increases, reactivity increases significantly. Triisopropylallylsilane, a very reactive silane, appears to anomalous in charge distribution and geometrical features compared with other substituted allylsilane systems which is due, presumably, to steric effects. The calculations on the protonated species would indicate that almost no hyperconjugative stabilization can occur on the basis of the bond lengths and angles necessary to promote good orbital overlap between the Si-Calpha bond and the empty p orbital on Cbeta. However, the gas-phase reaction of the triisopropylallylsilane with acrolein and methyl acrylate led to comparatively low energy barriers of 13.1 and 24.5, respectively, which is consistent with its high experimental reactivity. Together, this computational analysis has produced a useful model for predicting allylsilane reactivity and some possible explanations for this reactivity.     

Cationic polyelectrolytes. IV. Kinetic study of the reaction of acrylic polymers containing tertiary amine groups with halogenated compounds in dipolar aprotic solvents

The reaction kinetics of halogenated compounds with tertiary amine groups attached at an acrylic macromolecular chain have ben studied. Three acrylic polymers were used. Two of them have mainly a structural unit of N, N-dimethylaminopropylacrylamide and the third is poly(N,N-dimethylaminoethylmethacrylate). Dimethylformamide, dimethylacetamide, and dimethylsulfoxide (DMSO) were used as dipolar aprotic solvents. Benzyl chloride and allyl chloride were considered as halogenated compounds with increased reactivity. The reaction kinetics depend on the polymer and halogenated-compound structures as well as the nature of the solvent. In the most of the cases the reactions carried out on polymers are accompanied by self-accelerating processes, with the exception of DMSO, which obviously has normal second-order kinetics. The reaction of polymers containing units of N,N-dimethylaminopropylacrylamide are compared with one having a low molecular weight, for instance N,N′-bis(3-dimethylaminopropyl)glutaramide.     

Electrophilic cyclization of α-monoterpenols as a model for the biosynthesis of tri- and tetracyclic diterpenes

Low temperature electrophilic cyclization of -geraniol, -nerol, and -linalool initiated by BF₃ ^.etherate leads to the formation of dimethylvinylcyclohexenes and bicyclo[3.2.1]octyl fluoride, which have monoterpene skeletons. The -monoterpenol starting materials may be regarded as close models to labdadienols, and their transformation as mimicking the biosynthesis of diterpenes in the pimarane and gibbane series according to Wenkert.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 6, pp. 1368–1372, June, 1990.     

Total syntheses of (±)-β-irone

The conversion of the product of the ene reaction of PhSOCl with geranyl acetate into racemic -irone has been accomplished in seven steps, using highpressure techniques for the olefination of -methylcyclocitral.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 11, pp. 2607–2610, November, 1989.     

Characterization of the distribution of the sintering activator boron in powder metallurgical steels with SIMS

Powder metallurgy is a well-established method for manufacturing ferrous precision parts. A very important step is sintering, which can be strongly enhanced by the formation of a liquid phase during the sintering process. Boron activates this process by forming such a liquid phase at about 1200 °C. In this work, the sintering of Fe–B was performed under the protective atmospheres of hydrogen, argon or nitrogen. Using different grain sizes of the added ferroboron leads to different formations of pores and to the formation of secondary pores. The effect of boron was investigated by means of Secondary Ion Mass Spectrometry (SIMS) supported by Scanning Electron Microscopy (SEM) and Light Microscopy (LM). To verify the influence of the process parameters on the mechanical properties, the microstructure (pore shape) was examined and impact energy measurements were performed.The concentrations of B in different samples were varied from 0.03–0.6 weight percent (wt%). Higher boron concentrations are detectable by EPMA, whereas the distributions of boron in the samples with interesting overall concentration in the low wt% range are only detectable by means of SIMS.This work shows that the distribution of boron strongly depends on its concentration and the sintering atmosphere used. At low concentration (up to 0.1 wt%) there are boride precipitations; at higher concentration there is a eutectic iron–boron grain boundary network. There is a decrease of the impact energy observed that correlates with the amount of eutectic phase.     

A Note on the Range of Toeplitz Operators

A well known lemma attributed to Coburn states that a Toeplitz operator with non-trivial kernel acting on the Hardy space must have dense range. We show that the range of a non-zero Toeplitz operator with non-trivial kernel must contain all polynomials and state this in a precise form.     

Is the low-l microwave background cosmic?

The large-angle (low-l) correlations of the cosmic microwave background exhibit several statistically significant anomalies compared to the standard inflationary cosmology. We show that the quadrupole plane and the three octopole planes are far more aligned than previously thought (99.9% C.L.). Three of these planes are orthogonal to the ecliptic at 99.1% C.L., and the normals to these planes are aligned at 99.6% C.L. with the direction of the cosmological dipole and with the equinoxes. The remaining octopole plane is orthogonal to the supergalactic plane at 99.6% C.L.