Temperature Stresses in a Piecewise-Homogeneous Cylindrical Shell Caused by the Presence of a Longitudinal Crack

By using the method of generalized conjugation problems, we propose a numerical scheme for investigation of the redistribution of temperature stresses in a piecewise-homogeneous cylindrical shell caused by a longitudinal crack. This scheme is based on systems of integral equations (some of them are singular) to determine the unknown jumps of integral characteristics of the disturbed temperature field and displacements and their derivatives on the line of a crack and on the interface as well as the derivatives of these integral characteristics with respect to the longitudinal coordinate at the interface.     

Controlling an oscillating Jackson-type network having state-dependent service rates

We consider a Jackson-type network comprised of two queues having state-dependent service rates, in which the queue lengths evolve periodically, exhibiting noisy cycles. To reduce this noise a certain heuristic, utilizing regions in the phase space in which the system behaves almost deterministically, is applied. Using this heuristic, we show that in order to decrease the probability of a customers overflow in one of the queues in the network, the server in that same queue – contrary to intuition – should be shut down for a short period of time. Further noise reduction is obtained if the server in the second queue is briefly shut down as well, when certain conditions hold.     

Property (<Emphasis Type="Italic">T</Emphasis>) and rigidity for actions on Banach spaces

We study property (T) and the fixed-point property for actions on L ^p and other Banach spaces. We show that property (T) holds when L ² is replaced by L ^p (and even a subspace/quotient of L ^p ), and that in fact it is independent of 1≤p<∞. We show that the fixed-point property for L ^p follows from property (T) when 1<p< 2+ε. For simple Lie groups and their lattices, we prove that the fixed-point property for L ^p holds for any 1< p<∞ if and only if the rank is at least two. Finally, we obtain a superrigidity result for actions of irreducible lattices in products of general groups on superreflexive spaces. Bader partially supported by ISF grant 100146; Furman partially supported by NSF grants DMS-0094245 and DMS-0604611; Gelander partially supported by NSF grant DMS-0404557 and BSF grant 2004010; Monod partially supported by FNS (CH) and NSF (US).     

Temperature-dependent behavior of birefringence and rotation of the optical indicatrix in crystals of deuterated triglycinesulfate

On the basis of a complex null-polarimetric method, the natural birefringence and the rotation of the optical indicatrix in crystals of deuterated triglycinesulfate are measured in the temperature range of 300–340 K. The temperature-dependent behavior of the optical parameters is shown to be close to that observed previously in triglycinesulfate crystals. Changes in them upon the ferroelectric phase transition can be accounted for by the spontaneous quadratic electro-optic effect, with the values of the electro-optic coefficients being larger by a factor of 1.4 than in triglycinesulfate crystals.     

Considerations on modelling the market for softwood lumber in the United States

The analysis in this paper looks at two important elements in modelling the market for timber in the United States. First, the issue of directional causality between price and quantity and its implications in a modelling effort is investigated. Second, the extent of the geographic market for timber is discussed and a method of detecting it is suggested. The method for detecting the extent of the geographical market is tractable and can be applied in a straightforward way. Both considerations are applied to the softwood lumber market in the United States.     

The synthesis of malonimide derivatives as potential penicillin analogs

Malonimidoacetic acid derivatives (VIII, XIII) were synthesized as a potential penicillin analogs, hut they failed to inhibit the growth of bacteria when tested in vitro against a range of Gram-positive and Gram-negative microorganisms.     

Finding the αn-th largest element

We describe an algorithm for selecting the n-th largest element (where 0<<1), from a totally ordered set ofn elements, using at most (1+(1+o(1))H())·n comparisons whereH() is the binary entropy function and theo(1) stands for a function that tends to 0 as tends to 0. For small values of this is almost the best possible as there is a lower bound of about (1+H())·n comparisons. The algorithm obtained beats the global 3n upper bound of Schönhage, Paterson and Pippenger for <1/3.     

RMS dipole moments of the valence excited states of linear polyenes

Asymmetrical vibrations induce small oscillating dipole moments in the ground states of linear all-trans polyenes. Upon vertical excitation into one of the two low-lying valence excited states the induced in-plane dipole moments are increased 3 times and more. The rms dipole moments increase with the chain length. The inducing modes are the CCC skeletal bending and the CC stretching vibrations. CH stretching vibrations are also found to contribute non-negligible polarization.     

Derivation of class II force fields. VIII. Derivation of a general quantum mechanical force field for organic compounds

A class II valence force field covering a broad range of organic molecules has been derived employing ab initio quantum mechanical "observables." The procedure includes selecting representative molecules and molecular structures, and systematically sampling their energy surfaces as described by energies and energy first and second derivatives with respect to molecular deformations. In this article the procedure for fitting the force field parameters to these energies and energy derivatives is briefly reviewed. The application of the methodology to the derivation of a class II quantum mechanical force field (QMFF) for 32 organic functional groups is then described. A training set of 400 molecules spanning the 32 functional groups was used to parameterize the force field. The molecular families comprising the functional groups and, within each family, the torsional angles used to sample different conformers, are described. The number of stationary points (equilibria and transition states) for these molecules is given for each functional group. This set contains 1324 stationary structures, with 718 minimum energy structures and 606 transition states. The quality of the fit to the quantum data is gauged based on the deviations between the ab initio and force field energies and energy derivatives. The accuracy with which the QMFF reproduces the ab initio molecular bond lengths, bond angles, torsional angles, vibrational frequencies, and conformational energies is then given for each functional group. Consistently good accuracy is found for these computed properties for the various types of molecules. This demonstrates that the methodology is broadly applicable for the derivation of force field parameters across widely differing types of molecular structures. Copyright 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1782-1800, 2001