A Verified Optimization Technique to Locate Chaotic Regions of Hénon Systems

We present a new verified optimization method to find regions for Hénon systems where the conditions of chaotic behaviour hold. The present paper provides a methodology to verify chaos for certain mappings and regions. We discuss first how to check the set theoretical conditions of a respective theorem in a reliable way by computer programs. Then we introduce optimization problems that provide a model to locate chaotic regions. We prove the correctness of the underlying checking algorithms and the optimization model. We have verified an earlier published chaotic region, and we also give new chaotic places located by the new technique.     

Heuristic Rejection in Interval Global Optimization

Based on the investigation carried out in Ref. 1, this paper incorporates new studies about the properties of inclusion functions on subintervals while a branch-and-bound algorithm is solving global optimization problems. It is found that the relative place of the global minimum value within the inclusion function value of the objective function at the current interval indicates mostly whether the given interval is close to a minimizer point. This information is used in a heuristic interval rejection rule that can save a considerable amount of computation. Illustrative examples are discussed and an extended numerical study shows the advantages of the new approach.     

Isolation of a new member of the ecdysteroid glycoside family: 2-deoxy-20-hydroxyecdysone 22-O-beta-D-glucopyranoside

A new ecdysteroid glycoside, 2-deoxy-20-hydroxyecdysone 22-O-beta-D-glucopyranoside, is isolated from the herb Silene italica ssp. nemoralis (Waldst. and Kit.) Nyman. The compound is purified with multistep chromatography, such as classical column chromatography on alumina and droplet countercurrent distribution. Also, it is expanded using twice low-pressure reversed-phase liquid column chromatography. Chromatography in four steps results in the purified 2-deoxy-20-hydroxyecdysone 22-O-beta-D-glucopyranoside. Two other ecdysteroids have also been separated, including the formerly identified integristerone A and 24(28)-dehydromakisterone A.     

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

The adsorption of -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.     

Functionalization of 2,3,4,5-Tetrahydro-1,5-benzodiazepin-2(1 H)-ones by Electrophilic Aromatic Substitution

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.     

Efficient interval partitioning for constrained global optimization

A new efficient interval partitioning approach to solve constrained global optimization problems is proposed. This involves a new parallel subdivision direction selection method as well as an adaptive tree search. The latter explores nodes (intervals in variable domains) using a restricted hybrid depth-first and best-first branching strategy. This hybrid approach is also used for activating local search to identify feasible stationary points. The new tree search management technique results in improved performance across standard solution and computational indicators when compared to previously proposed techniques. On the other hand, the new parallel subdivision direction selection rule detects infeasible and suboptimal boxes earlier than existing rules, and this contributes to performance by enabling earlier reliable deletion of such subintervals from the search space.     

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.     

Interval method for bounding level sets: Revisited and tested with global optimization problems

An interval method for bounding level sets, modified to increase its efficiency and to get sharper bounding boxes, is presented. The new algorithm was tested with standard global optimization test problems. The test results show that, while the modified method gives a more valuable, guaranteed reliability result set, it is competitive with non-interval methods in terms of CPU time and number of function evaluations.This work was supported by Grant OTKA 1074/1987, and in part by DAAD Fellowship No. 314/108/004/8 during the author's stay at Düsseldorf University.