Some Global Optimization Problems on Stiefel Manifolds

Optimization on Stiefel manifolds was discussed by Rapcsák in earlier papers, and some global optimization methods were considered and tested on Stiefel manifolds. In the paper, test functions are given with known global optimum points and their optimal function values. A restriction, which leads to a discretization of the problem is suggested, which results in a problem equivalent to the well-known assignment problem.     

A Smoothing Newton Method for Semi-Infinite Programming

This paper is concerned with numerical methods for solving a semi-infinite programming problem. We reformulate the equations and nonlinear complementarity conditions of the first order optimality condition of the problem into a system of semismooth equations. By using a perturbed Fischer–Burmeister function, we develop a smoothing Newton method for solving this system of semismooth equations. An advantage of the proposed method is that at each iteration, only a system of linear equations is solved. We prove that under standard assumptions, the iterate sequence generated by the smoothing Newton method converges superlinearly/quadratically.     

Structure and catalytic activity of some soluble polyethylene glycol-peptide conjugates

Soluble catalysts for the Juliá-Colonna asymmetric epoxidation reaction have been constructed in three different ways, using NH₂-PEG-OMe as the support system: suitable solvents have been identified and it is shown that the degree of helicity of the conjugates correlates with the extent of conversion and (to a lesser extent) the enantioselectivity of epoxidation.     

Über 1, 5-Diphenyl-2, 3, 6, 7-tetrahydro-1H, 5H-pyrazolo[1, 2-a]pyrazole(2, 6-Diphenyl-1, 5-diazabicyclo[3, 3, 0]octane)

The synthesis of a 1, 5-diphenyl perhydro-pyrazolo-[1, 2-a] pyrazole (IV) (m. p. = 170–171°) by LiAlH₄-reduction of its 3, 7-dioxo derivative Va, one of the stereoisomers of V, is described. Va was obtained in small yield by the reaction of cinnamic acid with its hydrazide or with hydrazine. It proved to be identical with the compound obtained previously by interaction of cinnamic acid hydrazide with iodine which in the literature erroneously had been described as N, N′-dicinnamoyl hydrazine. This hydrazine now was obtained by bis-acylation of hydrazine with cinnamoyl chloride. In Va the extremely low NMR. absorption of the tertiary protons at ρ = 4,6 ppm is probably due to the spatial grouping with the proton situated in the deshielding region of the carbonyl group. Previously, another tertiary proton with a very low NMR. absorption at ρ = 4,85 ppm has been observed in the «bisimide M», the main criss-cross addition product of one mole benzaldazine and two moles of N-(n-butyl)-maleinimide. A stereostructure for bisimide M is now proposed, which is a hybrid between those of the bisimides L and H.     

Reaction of Isocyanates and Isothiocyanates with Butyraldazine; Formation of 1-Substituted 2-Pyrazolines

Phenyl isothiocyanate reacts with butyraldazine in presence of acidic catalysts to form a 2-pyrazoline (IV) whereas phenyl or benzyl isocyanates under similar conditions yield a mixture of the two isomeric 2-pyrazolines XIa and XII. On reaction with Ac₂O, IV gave the 1-acetyl derivative V. Reduction with LiAlH₄ led to the corresponding pyrazolidines. Reexamination of Kost's three step preparation of a 1-phenylthiocarbamoyl 2-pyrazoline [19] such as X via formic acid cyclization [18] of butyraldazine revealed that his first step product was apparently a mixture of two stereoisomeric 1-formyl-2-pyrazolines VIIIa and VIIIb. A mechanism for the formation of these pyrazolines is proposed.     

Chaotic behavior of confining lattice Gauge field configurations

We analyze the leading Lyapunov exponents of SU(2) Yang-Mills field configurations on the lattice which are initialized by quantum Monte-Carlo simulations. We find that configurations in the strong coupling phase at finite temperature are substantially more chaotic than in deconfinement.     

Spin squeezing and quantum correlations

We discuss the notion of spin squeezing considering two mutually exclusive classes of spin-s states, namely, oriented and non-oriented states. Our analysis shows that the oriented states are not squeezed while non-oriented states exhibit squeezing. We also present a new scheme for construction of spin-s states using 2s spinors oriented along different axes. Taking the case of s=1, we show that the ‘non-oriented’ nature and hence squeezing arise from the intrinsic quantum correlations that exist among the spinors in the coupled state.     

Optimization of Growth Conditions for Test Fungus Cultures used in Direct Bioautographic TLC Detection. 3. Test Fungus: Candida albicans

JPC – Journal of Planar Chromatography – Modern TLC - Optimum conditions have been established for culture of the fungus Candida albicans (ATCC 90028) for microbial detection of zones...     

Limits of parallelism in explicit ODE methods

Numerical methods for ordinary initial value problems that do not depend on special properties of the system are usually found in the class of linear multistage multivalue methods, first formulated by J.C. Butcher. Among these the explicit methods are easiest to implement. For these reasons there has been considerable research activity devoted to generating methods of this class which utilize independent function evaluations that can be performed in parallel. Each such group of concurrent function evaluations can be regarded as a stage of the method. However, it turns out that parallelism affords only limited opportunity for reducing the computing time with such methods. This is most evident for the simple linear homogeneous constant-coefficient test problem, whose solution is essentially a matter of approximating the exponential by an algebraic function. For a given number of stages and a given number of saved values, parallelism offers a somewhat enlarged set of algebraic functions from which to choose. However, there is absolutely no benefit in having the degree of parallelism (number of processors) exceed the number of saved values of the method. Thus, in particular, parallel one-step methods offer no speedup over serial one-step methods for the standard linear test problem. Although the implication of this result for general nonlinear problems is unclear, there are indications that dramatic speedups are not possible in general. Also given are some results relevant to the construction of methods.Work supported in part by National Science Foundation grants DMS 89 11410 and DMS 90 15533 and by US Department of Energy grant DOE DEFG02-87ER25026. Work of the second author was completed while at the University of Illinois.     

Bounded harmonic maps on a class of manifolds

Without imposing any curvature assumptions, we show that bounded harmonic maps with image contained in a regular geodesic ball share similar behaviour at infinity with the bounded harmonic functions on the domain manifold.