A review of statistical models for global optimization

A review of statistical models for global optimization is presented. Rationality of the search for a global minimum is formulated axiomatically and the features of the corresponding algorithm are derived from the axioms. Furthermore the results of some applications of the proposed algorithm are presented and the perspectives of the approach are discussed.     

Study on δ‐form complex in syndiotactic polystyrene–organic molecules systems. IV. Formation of complexes with a mixture of solvents and structural changes during the sorption of solvents by syndiotactic polystyrene mesophase membranes

The syndiotactic polystyrene (sPS) δ form was crystallized from mixtures with different compositions of p‐chlorotoluene–chlorobenzene (p‐CT–CB) and p‐chlorotoluene–1,1,2‐trichloroethane (p‐CT–TCE). The presence of the δ form and TTGG helical conformation was confirmed by Fourier transform infrared and wide‐angle X‐ray diffraction (WAXD) analyses. In sPS/p‐CT–CB and sPS/p‐CT–TCE δ‐form membranes, the relative absorbance (RA) of the p‐chlorotoluene (p‐CT) solvent peak was very high even at very low concentrations of p‐CT in comparison with the RA of higher concentrations of chlorobenzene (CB) or 1,1,2‐trichloroethane (TCE) in the mixtures. However, the RAs of both CB and TCE solvent peaks decreased with decreasing concentrations of CB and TCE in the mixtures. A negligible decrease in the RA of the TTGG helical content was observed with a decreasing concentration of CB or TCE. The WAXD results showed that the 2θ peak positions of the [010] and [ 10] planes of the sPS/p‐CT–CB and sPS/p‐CT–TCE δ‐form membranes appeared in the same position and were almost equal to those of the sPS–p‐CT δ‐form membrane. The mesophases of the sPS–p‐CT [p‐CT (A‐M)] and sPS–TCE [TCE (A‐M)] membranes were used for the sorption studies with different concentrations of various solvents. The sorption amount of aromatic solvents by both p‐CT (A‐M) and TCE (A‐M) mesophase membranes was higher than that of aliphatic solvents, regardless of the size, shape, and nature of the molecular cavity. The 2θ peak of the [010] plane of the sPS membranes slowly approached the original δ‐form value when the sPS mesophase membranes were immersed in various solvents of different concentrations for 48 h. The shifting of the 2θ peak of the [010] plane to the original δ form depended on the nature and concentration of the immersion solvents. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2380–2387, 2005     

Crystal structures of 6-[(2-hydroxy-1,1-bis-hydroxymethyl-ethylamino)-methylene]-4-nitro-cyclohexa-2,4-dienone hydrate and 6-[(2-hydroxy-1,1-bis-hydroxymethyl-ethylamino)-methylene]-4-bromo-cyclohexa-2,4-dienone

Crystal structures of 6-[(2-hydroxy-1,1-bis-hydroxymethyl-ethylamino)-methylene]-4-nitro-cyclohexa-2,4-dienone hydrate (I) and 6-[(2-hydroxy-1,1-bis-hydroxymethyl-ethylamino)-methylene]-4-bromo-cyclohexa-2,4-dienone (II) have been determined. The crystals of I are monoclinic, a = 16.957(1) Å, b = 10.729(2) Å, c = 7.240(3) Å; β = 99.56(3)°, space group P2₁/c, Z = 4, R = 0.0492. The crystals of II are triclinic, a = 10.282(2) Å, b = 7.189(3) Å, c = 16.831(3) Å; α = 90.67(3)°, β = 100.10(3)°, γ = 95.87(3)°; space group P-1, Z = 4, R = 0.0591. The independent part of the unit cell of I contains one unique molecule and water of crystallization, while in II — two unique molecules A and B. C(CH₂OH)₃ fragment of the molecule B manifests the disordering of alcohol oxygen atoms. Both in I and II, the salicylidene fragment of the molecules exists in the quinoid tautomeric form.     

Thermodynamic Parameters for the Association of Fluorinated Benzenesulfonamides with Bovine Carbonic Anhydrase II

This paper describes a calorimetric study of the association of a series of seven fluorinated benzenesulfonamide ligands (C₆H_nF_5?nSO₂NH₂) with bovine carbonic anhydrase II (BCA). Quantitative structure–activity relationships between the free energy, enthalpy, and entropy of binding and pK_a and log P of the ligands allowed the evaluation of the thermodynamic parameters in terms of the two independent effects of fluorination on the ligand: its electrostatic potential and its hydrophobicity. The parameters were partitioned to the three different structural interactions between the ligand and BCA: the Zn^II cofactor–sulfonamide bond (≈65 % of the free energy of binding), the hydrogen bonds between the ligand and BCA (≈10 %), and the contacts between the phenyl ring of the ligand and BCA (≈25 %). Calorimetry revealed that all of the ligands studied bind in a 1:1 stoichiometry with BCA; this result was confirmed by ¹⁹F NMR spectroscopy and X‐ray crystallography (for complexes with human carbonic anhydrase II).     

LOCALIZED PATTERNS OF THE CUBIC-QUINTIC SWIFT-HOHENBERG EQUATIONS WITH TWO SYMMETRY-BREAKING TERMS

Homoclinic snake always refers to the branches of homoclinic orbits \mbox{near} a heteroclinic cycle connecting a hyperbolic or non-hyperbolic equilibrium and a periodic orbit in a reversible variational system. In this paper, the normal form of a Swift-Hohenberg equation with two different symmetry-breaking terms (non-reversible term and non-k-symmetry term) are investigated by using multiple scale method, and their bifurcation diagrams are initially studied by numerical simulations. Typically, we predict numerically the existence of so-called round-snakes and round-isolas upon particular two symmetric-breaking perturbations.     

Optical switching and alignment of antiferroelectric liquid crystals containing an azo group

The optical properties of two kinds of photochromic antiferroelectric liquid crystal (AFLC) containing an azo group have been examined. Depending on the substituting group at the chiral centre, these AFLCs showed different photoinduced phase transitions by Ar⁺ laser light irradiation. This phase transition has led to a new form of optical switching controlled by a bias voltage. In addition, it was found that these AFLCs caused an azimuthal photoalignment effect regulated by linearly polarized Ar⁺ laser light irradiation. These phenomena were applied to image storage.     

Classroom note: Using the binomial series to prove the arithmetic mean–geometric mean inequality

In 1968, Leon Gerber compared (1 + x) ^a to its kth partial sum as a binomial series. His result is stated and, as an application of this result, a proof of the arithmetic mean–geometric mean inequality is presented.     

On the usage of NURBS as interface representation in free‐surface flows

When simulating free‐surface flows using the finite element method, there are many cases where the governing equations require information which must be derived from the available discretized geometry. Examples are curvature or normal vectors. The accurate computation of this information directly from the finite element mesh often requires a high degree of refinement—which is not necessarily required to obtain an accurate flow solution. As a remedy and an option to be able to use coarser meshes, the representation of the free surface using non‐uniform rational B‐splines (NURBS) curves or surfaces is investigated in this work. The advantages of a NURBS parameterization in comparison with the standard approach are discussed. In addition, it is explored how the pressure jump resulting from surface tension effects can be handled using doubled interface nodes. Numerical examples include the computation of surface tension in a two‐phase flow as well as the computation of normal vectors as a basis for mesh deformation methods. For these examples, the improvement of the numerical solution compared with the standard approaches on identical meshes is shown. Copyright © 2011 John Wiley & Sons, Ltd.     

On a family of highly regular graphs by Brouwer,Ivanov, and Klin

Highly regular graphs for which not all regularities are explainable by symmetries are fascinating creatures. Some of them like, e.g., the line graph of W. Kantor’s non-classical $GQ(5^2,5)$, are stumbling stones for existing implementations of graph isomorphism tests. They appear to be extremely rare and even once constructed it is difficult to prove their high regularity. Yet some of them, like the McLaughlin graph on 275 vertices and Ivanov’s graph on 256 vertices are of profound beauty. This alone makes it an attractive goal to strive for their complete classification or, failing this, at least to get a deep understanding of them. Recently, one of the authors discovered new methods for proving high regularity of graphs. Using these techniques, in this paper we study a classical family of strongly regular graphs, originally discovered by A.E. Brouwer, A.V. Ivanov, and M.H. Klin in the late 80s. We analyse their symmetries and show that they are $(3,5)$-regular but not 2-homogeneous. Thus we promote these graphs to the distinguished club of highly regular graphs with few symmetries.     

Models of information aggregation in financial markets: a review

This article reviews static and dynamic models of information aggregation in the literature. It highlights the key assumptions these models make, the results they obtain and the issues that still need to be explored to further our understanding of information aggregation in financial markets.