Nonmonotone curvilinear line search methods for unconstrained optimization

We present a new algorithmic framework for solving unconstrained minimization problems that incorporates a curvilinear linesearch. The search direction used in our framework is a combination of an approximate Newton direction and a direction of negative curvature. Global convergence to a stationary point where the Hessian matrix is positive semidefinite is exhibited for this class of algorithms by means of a nonmonotone stabilization strategy. An implementation using the Bunch-Parlett decomposition is shown to outperform several other techniques on a large class of test problems.The work of this author was based on research supported by the National Science Foundation Grant CCR-9157632, the Air Force Office of Scientific Research Grant F49620-94-1-0036 and the Department of Energy Grant DE-FG03-94ER61915.These authors were partially supported by Agenzia Spaziale Italiana, Roma, Italy.     

Reduced-size polarized basis sets for calculations of molecular electric properties. II. Simulation of the Raman spectra

The accuracies of the calculated vibrational frequencies and Raman intensities given by two new, highly compact Pol-type basis sets, Z2PolX and Z3PolX, have been determined and compared to the 6-31G(d), PolX, and aug-cc-pVTZ basis sets. Calculation of accurate Raman intensities has previously required large basis sets, but the ZmPolX basis sets are smaller even than PolX, which are the most compact basis sets able to calculate accurate Raman intensities. For the largest compound studied, C5H10O2, Z3PolX required more than an order of magnitude less CPU time than PolX, which has been shown to be 10 times faster than aug-cc-pVTZ. Two sets of test molecules were studied: one was a series of small molecules for which experimental values for absolute Raman activities were available; the second was a series of medium-sized molecules (mainly common organic solvents) where only relative Raman band intensities were available. The accuracies of the Raman intensities given by both of the ZmPolX basis sets were good compared to those of the PolX and aug-cc-pVTZ sets, and much better than the 6-31G(d) values. The errors in even unscaled frequency values <2000 cm(-1) were also acceptable and were slightly lower for Z3PolX than Z2PolX (30 cm(-1) vs. 48 cm(-1)). The combination of good intensity and frequency data meant that for the medium-sized organic molecules there was a close correspondence between the simulated Raman spectra and experimental data, and that the observed bands could easily be assigned on the basis of these calculations. Achieving this level of accuracy in the simulations at modest computational cost should now allow computational methods to be combined with experimental Raman studies much more widely than is currently the case.     

On some examples of obstructed irregular surfaces

We determine the base space of the Kuranishi family of some complete intersections in the product of an abelian variety and a projective space.As a consequence,we obtain new examples of obstructed irregular surfaces with ample canonical bundle and maximal Albanese dimension.     

Semiempirical model for adsorption of polyatomics

Multisite-occupancy adsorption is described by using a new formalism based on the occupation balance approximation (Roma, F.; Ramirez-Pastor, A. J.; Riccardo, J. L. J. Chem. Phys. 2001, 114, 10932). In this framework, the adsorption isotherm is characterized by a correction function C, which relates to the conditional probability of finding the ith empty site to a lattice with i - 1 already vacant sites. A simple semiempirical adsorption isotherm is proposed by approximating C as a combination of the correction functions corresponding to exact 1-D calculations and the Guggenheim-DiMarzio approximation, with adequate weights. Results are compared with corresponding ones from Monte Carlo simulations.     

Some 2-(dialkylamino) substituted chromenylium salts

The reaction of 2-(dialkylamino)-7-methoxychromones with malononitrile in the presence of acetic anhydride afforded [2-(dialkylamino)-7-methoxy-4H-chromen-4-ylidene]malononitriles. When these compounds were refluxed with concentrated hydrochloric (or hydroiodic) acid, 2-(dialkylamino)-7-methoxy(or hydroxy)-4-methylchromenylium salts were obtained. The use of concentrated sulfuric acid or polyphosphoric acid in the hydrolysis was also investigated. The preparation of ethyl [2-(dialkylamino)-7-methoxy-4H-chromen-4-ylidene]cyanoacetates and their behavior when treated with acids are also described, as well as the synthesis of some 3-(dialkylamino)-1-methylnaphtho[2,1-b]pyrylium salts.     

Diastereoselective 1,3‐Dipolar Cycloadditions of Chiral Derivatives of 2‐Oxoethanenitrile Oxide to Noncyclic Conjugated Symmetrical Alkenes

Asymmetric 1,3‐dipolar cycloadditions of chiral derivatives of the nitrile oxides 3a – 3c derived from (2R)‐bornane‐10,2‐sultam, (2R)‐10‐(dicyclohexylsulfamoyl)isoborneol, and (1R)‐8‐phenylmenthol, to either (E)‐stilbene 4 or dimethyl fumarate 5 , leading to the corresponding 4,5‐dihydroisoxazoles 6a – 6c and 7a – 7c in both moderate yields and diastereoselectivities, are presented. All cycloadducts were converted into the corresponding methyl esters 8 and 9 , which were used for determination of their enantiomeric purities via chiral HPLC analyses. In the case of both stilbene cycloadducts 6a and 6b , their absolute configurations were determined by X‐ray crystal‐structure analyses. These [3+2] cycloadditions suggest the participation of the thermodynamically less stable SO₂/CO syn‐conformer in the π_y approach along the C?O bond of the linear nitrile oxide 3a .     

Reduced–size polarized basis sets for calculations of molecular electric properties. III. Second–row atoms

Reduced–size polarized (ZmPolX) basis sets are developed for the second–row atoms X = Si, P, S, and Cl. The generation of these basis sets follows from a simple physical model of the polarization effect of the external electric field which leads to highly compact polarization functions to be added to the chosen initial basis set. The performance of the ZmPolX sets has been investigated in calculations of molecular dipole moments and polarizabilities. Only a small deterioration of the quality of the calculated molecular electric properties has been found. Simultaneously the size of the present reduced–size ZmPolX basis sets is about one-third smaller than that of the usual polarized (PolX) sets. This reduction considerably widens the range of applications of the ZmPolX sets in calculations of molecular dipole moments, dipole polarizabilities, and related properties.     

Fire- and heat-resistant matrix resins based on ethynyl-substituted aromatic cyclotriphosphazenes

A novel class of fire- and heat-resistant matrix resins has been synthesized by thermal polymerization of ethynyl-substituted aromatic cyclotriphosphazenes. Thermal polymerization of new tris[4-(4′-ethynylbenzanilido)phenoxy]tris(phenoxy) cyclotriphosphazene ( III ) and tris[4-(4′-ethynylphthalimido)phenoxy]tris(phenoxy)cyclotriphosphazene ( VII ) at 250°C for 1–1.5 h gave tough polymers. The thermal stabilities of the polymers were evaluated in nitrogen and in air by thermogravimetric analysis (TGA). The synthesised polymers were stable to 400–410°C and showed char yield of 78–65% at 800°C in nitrogen and of 78–69% at 700°C in air. The ethynyl-substituted polymer precursor ( III ) was synthesised by the reaction of tris(4-aminophenoxy)tris(phenoxy)cyclotriphosphazene ( I ) with 4-ethynylbenzoyl chloride. The polymer precursor ( VII ) was synthesised by a solution condensation of I with 4-ethynylphthalic anhydride followed by in situ thermal cyclodehydration at 150°C. The structure of polymer precursors was characterized using proton nuclear magnetic resonance (¹H-NMR), infrared (IR) spectroscopy, and elemental analysis. The curing of polymer precursors was monitored by differential scanning calorimetery (DSC) and IR spectroscopy. The synthesised matrix resins are potential candidates for the development of heat- and fire-resistant fiber-reinforced composites. © 1993 John Wiley & Sons, Inc.     

Induction of phr gene expression in E. coli strain KY706/pPL-1 by He–Ne laser (632.8 nm) irradiation

We have observed that He–Ne laser irradiation of E. coli strain KY706/pPL-1 leads to induction of photolyase gene, phr. The magnitude of induction was found to depend on the He–Ne laser fluence, fluence rate and post-irradiation incubation period in the nutrient medium. The optimum values for fluence and fluence rate were 7×10³ J/m² and 100 W/m², respectively, and the induction of phr gene was observed to saturate beyond an incubation period of 2 h. Experiments carried out with singlet oxygen quenchers and with D₂O suggest that the effect is mediated via singlet oxygen. Photoreactivation studies carried out after UVC exposure of both the He–Ne laser-exposed as well as unexposed cells showed a larger surviving fraction in the He–Ne laser pre-irradiated cells. This can be attributed to He–Ne laser irradiation-induced induction of phr expression. However, since even without photoreactivating light He–Ne laser pre-irradiated cells show higher survival against UVC radiation it appears that He–Ne laser irradiation induces both light-dependent as well as dark DNA repair processes.