Symbolic Interval Inference Approach for Subdivision Direction Selection in Interval Partitioning Algorithms

In bound constrained global optimization problems, partitioning methods utilizing Interval Arithmetic are powerful techniques that produce reliable results. Subdivision direction selection is a major component of partitioning algorithms and it plays an important role in convergence speed. Here, we propose a new subdivision direction selection scheme that uses symbolic computing in interpreting interval arithmetic operations. We call this approach symbolic interval inference approach (SIIA). SIIA targets the reduction of interval bounds of pending boxes directly by identifying the major impact variables and re-partitioning them in the next iteration. This approach speeds up the interval partitioning algorithm (IPA) because it targets the pending status of sibling boxes produced. The proposed SIIA enables multi-section of two major impact variables at a time. The efficiency of SIIA is illustrated on well-known bound constrained test functions and compared with established subdivision direction selection methods from the literature.     

Nonlinear coordinate transformations for unconstrained optimization II. Theoretical background

In this two-part article, nonlinear coordinate transformations are discussed in order to simplify global unconstrained optimization problems and to test their unimodality on the basis of the analytical structure of the objective functions. If the transformed problems can be quadratic in some or all the variables, then the optimum can be calculated directly, without an iterative procedure, or the number of variables to be optimized can be reduced. Otherwise, the analysis of the structure can serve as a first phase for solving global unconstrained optimization problems.The first part treats real-life problems where the presented technique is applied and the transformation steps are constructed. The second part of the article deals with the differential geometrical background and the conditions of the existence of such transformations.The paper was presented at the II. IIASA Workshop on Global Optimization, Sopron (Hungary), December 9–14, 1990.     

Nonlinear coordinate transformations for unconstrained optimization I. Basic transformations

In this two-part article, nonlinear coordinate transformations are discussed to simplify unconstrained global optimization problems and to test their unimodality on the basis of the analytical structure of the objective functions. If the transformed problems are quadratic in some or all the variables, then the optimum can be calculated directly, without an iterative procedure, or the number of variables to be optimized can be reduced. Otherwise the analysis of the structure can serve as a first phase for solving unconstrained global optimization problems.The first part treats real-life problems where the presented technique is applied and the transformation steps are constructed. The second part of the article deals with the differential geometrical background and the conditions of the existence of such transformations.The paper was presented at the II. IIASA Workshop on Global Optimization, Sopron (Hungary), December 9–14, 1990.     

Functionalization of 2,3,4,5-Tetrahydro-1,5-benzodiazepin-2(1<Emphasis Type="Italic">H</Emphasis>)-ones by Electrophilic Aromatic Substitution

Summary. Highly substituted, novel, 8- and 9-nitro-2,3,4,5-tetrahydro-1,5-benzodiazepin-2(1H)-ones were obtained by direct nitration of the 7-bromo-5-trifluoroacetyl (or formyl)-substituted tetrahydrobenzodiazepinones. Alkaline and acidic hydrolysis of the novel mononitro derivatives was examined. Semiempirical AM1 calculations of aromatic substituents orientation in the nitration products are presented.     

Adsorption of l-histidine on copper surface as evidenced by surface-enhanced Raman scattering spectroscopy

The adsorption of l-histidine on a copper electrode from H₂O- and D₂O-based solutions is studied by means of surface-enhanced Raman scattering (SERS) spectroscopy. Different adsorption states of histidine are observed depending upon pH, potential, and the presence of the SO²⁻₄ and Cl⁻ ions. In acidic solutions of pH 1.2 the imidazole ring of the adsorbed histidine remains protonated and is not involved in the chemical coordination with the surface. The SO²⁻₄ and Cl⁻ ions compete with histidine for the adsorption sites. In solutions of pH 3.1 three different adsorption states of histidine are observed depending on the potential. Histidine adsorbs with the protonated imidazole ring oriented mainly perpendicularly to the surface at potentials more positive than −0.2 V. Transformation of that adsorption state occurs at more negative potentials. As this takes place, histidine adsorbs through the α-NH₂ group and the neutral imidazole ring. The Cl⁻ ions cause the protonation and detachment of the α-NH₂ group from the surface and the formation of the ion pair NH⁺₃ … Cl⁻ can be observed. In the neutral solution of pH 7.0 histidine adsorbs through the deprotonated nitrogen atom of the imidazole ring and the α-COO⁻ group at E ≥ −0.2 V. However, this adsorption state is transformed into the adsorption state in which the α-NH₂ group and/or neutral imidazole ring participate in the anchoring of histidine to the surface, once the potential becomes more negative. In alkaline solutions of pH 11.9 histidine is adsorbed on the copper surface through the neutral imidazole ring.     

Towards a computer-assisted proof for chaos in a forced damped pendulum equation

We report on the first steps made towards the computational proof of the chaotic behaviour of the forced damped pendulum. Although, chaos for this pendulum was being conjectured for long, and it has been plausible on the basis of numerical simulations, there is no rigorous proof for it. In the present paper we provide computational details on a fitting model and on a verified method of solution. We also give guaranteed reliability solutions showing some trajectory properties necessary for complicate chaotic behaviour.     

A Heuristic Rejection Criterion in Internal Global Optimization Algorithms

This paper investigates the properties of the inclusion functions on subintervals while a Branch-and-Bound algorithm is solving global optimization problems. It has been found that the relative place of the global minimum value within the inclusion interval of the inclusion function of the objective function at the actual interval mostly indicates whether the given interval is close to minimizer point. This information is used in a heuristic interval rejection rule that can save a big amount of computation. Illustrative examples are discussed and a numerical study completes the investigation.This revised version was published online in October 2005 with corrections to the Cover Date.     

Ein einfacher Syntheseweg zu Naturstoffen mit 5-H-Furan-2-on-Struktur

Starting from an aldehyde, γ-Yliden-α, β-butenolides were synthesised simply by the use of 2,5-dihydro-2,5-dimethoxyfuran in the presence of trimethylchlorosilane.     

Synthesis, crystal structure and antiradical effect of copper(II) Schiff base complexes containing five-, six- and unusual seven-membered rings

The synthesis and solid-state structure of mononuclear copper(II) complexes [Cu(SAIB)(H(2)O)(2)] (1), [Cu(SBAIB)(H(2)O)(2)]·H(2)O (2) and [Cu(SGABA)(H(2)O)(2)] (3) are described. Schiff base ligands H(2)SAIB, H(2)SBAIB and H(2)SGABA chelate the copper(II) ion in an O,N,O tridentate fashion. The square-pyramidal geometry of the final complexes is completed by two water ligands. The formation of an unusual seven-membered ring in the set of copper(II) N-salicylidene-aminoacidates is reported. Compounds 1-3 were evaluated by the antiradical activity assay.