Linear and Nonlinear Finite Element Analysis of Active Composite Laminates

The paper presents a finite element concept for analysis of thin-walled active structures featuring fiber reinforced composite laminate as a passive structural material. The structure is rendered active by embedding piezoelectric material as a multifunctional material. A 9-node degenerated shell element based on the first order shear deformation theory is developed as a modelling tool capable of predicting the general behavior of the structure for controlling purposes. The von-Kármán type nonlinearities are considered. The solution strategy of the geometrical nonlinear analysis is based on the incremental approach using the updated Lagrangian formulation. Some numerical results are given to demonstrate the behavior of the element. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Half‐transitive graphs of valency 4 with prescribed attachment numbers

A graph X is said to be ½‐transitive if its automorphism group Aut X acts vertex‐ and edge‐, but not arc‐transitively on X. Then Aut X induces an orientation of the edges of X. If X has valency 4, then this orientation gives rise to so‐called alternating cycles, that is even length cycles in X whose every other vertex is the head and every other vertex is the tail of its two incident edges in the above orientation. All alternating cycles have the same length 2r(X), where r(X) is the radius of X, and any two adjacent alternating cycles intersect in the same number of vertices, called the attachment number a(X) of X. All known examples of ½‐transitive graphs have attachment number 1, r or 2r, where r is the radius of the graph. In this article, we construct ½‐transitive graphs with all other possible attachment numbers. The case of attachment number 2 is dealt with in more detail. © 2000 John Wiley & Sons, Inc. J Graph Theory 34: 89–99, 2000     

Characterizations of normal, hyponormal and EP operators

In this paper normal and hyponormal operators with closed ranges, as well as EP operators, are characterized in arbitrary Hilbert spaces. All characterizations involve generalized inverses. Thus, recent results of S. Cheng and Y. Tian [S. Cheng, Y. Tian, Two sets of new characterizations for normal and EP matrices, Linear Algebra Appl. 375 (2003) 181-195] are extended to infinite-dimensional settings.     

Ion‐exchange resins. III. Functionalization–morphology correlations in the synthesis of some macroporous,strong basic anion exchangers and uranium‐sorption properties evaluation

The synthesis and characterization of a series of macroporous, strong basic anion exchangers (SBAEs), with an average pore radius higher than 50 nm, and the evaluation of their sorption properties for uranyl chlorocomplexes from HCl solutions are reported. Finely divided macroporous styrene–divinylbenzene (S–DVB) copolymers with a narrow distribution of beads sizes, diameters within the range of 90–200 μm, were prepared for this purpose with 2‐ethyl‐1‐hexanol as a porogen, at a high dilution of monomers (D ≥ 0.55 mL/mL). Chloromethyl groups were introduced with (CH₂O)_n/Me₃SiCl as a chloromethylation agent in the presence of a Lewis acid as a catalyst (TiCl₄, SnCl₄, and FeCl₃) in CHCl₃ as a reaction medium. SnCl₄ and FeCl₃ gave comparable chloromethylation degrees in the same reaction conditions. TiCl₄ was not efficient as a catalyst in the chloromethylation with this reagent. Diethyl‐2‐hydroxyethylamine was used as a tertiary amine to prepare SBAEs. Structural and morphological characteristics were determined after every functionalization step of the macroporous network. Both the chloromethylation, in the presence of FeCl₃ as a catalyst, and the amination reactions determined a significant decrease of the pore volume, in the whole range of the nominal crosslinking degree, comparative with the starting copolymer. The specific surface area and the average pore radius varied in a different way as a function of the nominal crosslinking degree. Thus, the specific surface area increased and the average pore radius decreased after chloromethylation and amination for copolymers with a DVB content lower than 10 wt %. Small decreases of the specific surface area and the average pore radius were observed after chloromethylation and amination reactions for copolymers with a DVB content higher than 10 wt %. SBAEs were also characterized by thermogravimetric analysis and sorption capacity for uranyl chlorocomplexes. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2451–2461, 2004     

Least‐squares problems for Michaelis–Menten kinetics

The Michaelis–Menten kinetics is fundamental in chemical and physiological reaction theory. The problem of parameter identification, which is not well posed for arbitrary data, is shown to be closely related to the Chebyshev sum inequality. This inequality yields sufficient conditions for existence of feasible solutions both for nonlinear and for linear least‐squares problems. The conditions are natural and practical as they are satisfied if the data show the expected monotone and concave behaviour. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

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.