An integer programming model for two- and three-stage two-dimensional cutting stock problems

In this paper, an integer programming model for two-dimensional cutting stock problems is proposed. In the problems addressed, it is intended to cut a set of small rectangular items of given sizes from a set of larger rectangular plates in such a way that the total number of used plates is minimized.     

A Halogen‐Bond Donor Catalyst for Templated Macrocyclization

A halogen‐bond templated 1:1 macrocyclization in solution is reported. Tetra(iodoperfluorophenyl) ethers were used as halogen‐bonded exotemplates in a substoichiometric amount (5 mol %). Pyridine‐containing macrocyclic architectures were formed by ruthenium‐catalyzed tandem metathesis/transfer hydrogenation sequence using sodium borohydride and methanol as non‐dihydrogen hydrogen source. The halogen‐bonded stabilization energies were analyzed relying on density functional theory.     

Kinetics of N-glutaryl-L-phenylalanine p-nitroanilide hydrolysis catalyzed by alpha-chymotrypsin in aqueous solutions of dodecyltrimethylammonium bromide

The rate of hydrolysis of N-glutaryl-L-phenylalanine p-nitroanilide (GPNA) catalyzed by alpha-chymotrypsin (alpha-CT) has been measured in aqueous solutions of dodecyltrimethylammonium bromide (DTAB) at concentrations below and above the critical micelle concentration, as well as in the absence of surfactant. Under all the conditions employed, the reaction follows a Michaelis-Menten mechanism. The presence of the surfactant leads to superactivity below and above the critical micelle concentration (CMC), with a maximum reaction rate taking place near the CMC when the results are treated in terms of the analytical concentration of the substrate. A similar behavior was observed by working with the enzyme partially deactivated in the presence of 4 M urea. After correction to take into account the partitioning of the substrate between the micelles and the external media, the activity of the enzyme tends to remain almost constant above the corresponding CMCs. This results from a compensation of a decrease in the catalytic constant (k(cat)) and a decrease in the Michaelis constant (K(M)). The behavior of alpha-CT in the hydrolysis of GPNA in DTAB solutions is at variance with that previously reported for the hydrolysis of 2-naphthyl acetate in solutions of the same surfactant (E. Abuin, E. Lissi, R. Duarte, Langmuir 19 (2003) 5374). An explanation of the different effects of the surfactant on the behavior of the enzyme with both substrates is advanced, taking into account the complexity of the mechanism of the alpha-CT-mediated reaction, more specifically, in terms of different rate-limiting steps for the formation of the measured products.     

Aperture-Angle Optimization Problems in Three Dimensions

Let [a,b] be a line segment with end points a, b and a point at which a viewer is located, all in R ³. The aperture angle of [a,b] from point , denoted by (), is the interior angle at of the triangle (a,b,). Given a convex polyhedron P not intersecting a given segment [a,b] we consider the problem of computing _max() and _min(), the maximum and minimum values of () as varies over all points in P. We obtain two characterizations of _max(). Along the way we solve several interesting special cases of the above problems and establish linear upper and lower bounds on their complexity under several models of computation.     

Jacobians and differents of projective varieties

Let X be a reduced and irreducible projective variety of dimension d. Let π:X→Y be a separable noetherian normalization of X and ? the canonical morphism Ω^d _X/k→Ω^d _L/k. From our main result: $$J_X \varphi (\pi ^* \Omega ^d _{Y/k} ) = \theta _k (X/Y)\varphi (\Omega ^d _{X/k} )$$ we deduce relations among: complementary module C(X/Y), Kähler different θ_k(X/Y), Dedekind different θ_D(X/Y), jacobian ideal J_K and ω-jacobian ideal \(\tilde J_X\) .     

A SEARCH FOR LUMINESCENT FREE RADICAL RECOMBINATION

Abstract— Radical recombinations producing a single bond are potentially chemiluminescent reactions. The probability that a radical recombination leads to an excited state will depend on the relative shape of the ground and excited surfaces. This information can be obtained from the rate constants of the ground state and excited states dissociation, and the energy differences between the states. From the available data it was concluded that acyl radicals are among the most promising radicals regarding the probability of recombination leading to excited triplet states. Experimental efforts to detect luminescence following the recombination of acyl radicals will be discussed.     

Synthesis of enantiomerically pure,highly functionalized,medium-sized carbocycles from carbohydrates: formal total synthesis of (+)-calystegine b(2)

The free radical cyclization (FR) and the ring-closing metathesis (RCM) reaction have been analyzed in order to develop new and original synthetic protocols for the synthesis of enantiomerically pure, highly functionalized, medium-sized carbocycles from carbohydrates. As a result, we report here for the first time examples of the 7-exo FR cyclization of acyclic radical precursors derived from sugars. This process appears to be extremely sensitive to the conformational mobility of the radical species in the transition state. The use of two isopropylidene groups blocking four of the total present hydroxyl groups and a good radical acceptor (as an alpha,beta-unsaturated ester) are mandatory conditions for a successful ring closure protocol. The RCM reaction by using Grubbs' catalyst on selected carbohydrate-derived precursors has afforded variable yields of the expected unsaturated cycloheptane or cycloctane derivatives. The synthesis of the cycloheptitols has been carried out in good yields, regardless of the absolute configuration at the different stereocenters and the nature of the O-functional groups bound in allylic positions to one of the double bonds implicated in the metathesis reaction. Conversely, in the cyclooctane synthesis, we have observed that the success of the reaction depends not only on the absolute configuration at the different stereocenters close to the double bonds but also on the nature of the O-protecting groups on these stereocenters. Finally, the RCM strategy has been used in an attempt to prepare natural (+)-calystegine B(2) from D-glucose. The synthesis of compound 92 from D-glucose constitutes a formal total synthesis of (+)-calystegine B(2), showing the importance of the steric hindrance in allylic positions for a successful RCM reaction.     

Time domain approach to semiclassical dynamics: Breaking the log time barrier

The presence of chaos in the classical dynamics is not necessarily the destructive element it was thought to be for semiclassical approximations in the time domain. The method of calculating the semiclassical propagation of initial states and correlation functions for nonlinear and chaotic dynamics is shown, and the excellent accuracy is noted for rather long times. The breakdown timescale is much longer than the infamous "log time" for the cases investigated here.