Finding the Minimal Root of an Equation with the Multiextremal and Nondifferentiable Left-Hand Part

A problem very often arising in applications is presented: finding the minimal root of an equation with the objective function being multiextremal and nondifferentiable. Applications from the field of electronic measurements are given. Three methods based on global optimization ideas are introduced for solving this problem. The first one uses an a priori estimate of the global Lipschitz constant. The second method adaptively estimates the global Lipschitz constant. The third algorithm adaptively estimates local Lipschitz constants during the search. All the methods either find the minimal root or determine the global minimizers (in the case when the equation under consideration has no roots). Sufficient convergence conditions of the new methods to the desired solution are established. Numerical results including wide experiments with test functions, stability study, and a real-life applied problem are also presented.     

Ca3Ni8In4—An Ordered Noncentrosymmetric Variant of the BaLi4 Type

The title compound was synthesized by reacting the elements in an arc-melting apparatus under purified argon and subsequent annealing at 870 K. Ca₃Ni₈In₄ was investigated using X-ray diffraction on both powders and single crystals: P6₃mc, a=898.9(1) pm, c=752.2(2) pm, wR2=0.0591, 327 F² values, and 35 parameters. This structure is an ordered, noncentrosymmetric variant of the BaLi₄ type. The nickel and indium atoms build a complex three-dimensional [Ni₈In₄] polyanion in which the calcium atoms fill distorted hexagonal channels. To a first approximation the formula may be written as (3 Ca²⁺)⁶⁺ [Ni₈In₄]⁶⁻. Within the polyanion the Ni1, Ni3, and Ni4 atoms form one-dimensional cluster units which extend in the c direction while the Ni2 atoms have only indium neighbors in a distorted tetrahedral coordination. The Ni–Ni distances in the cluster range from 241 to 266 pm. The cluster units are surrounded and interconnected by indium atoms. The group– subgroup relation from centrosymmetric BaLi₄ to noncentrosymmetric Ca₃Ni₈In₄ is presented. Chemical bonding in Ca₃Ni₈In₄ and the structural relation with Lu₃Co_7.77Sn₄, Ca₃Au_6.61Ga_4.39, and Co₂Al₅ is briefly discussed.     

Structure and Transformation in Clusters: Computational Experiments

A very brief review of gas-phase electron diffraction and one of its offshoots is given. Parallels are drawn between experimental studies of molecules, including conformational changes, and studies of clusters, including phase changes, calling particular attention to the use of computers as the preferred experimental apparatus. A sketch is presented of what has been learned about matter in transition by the application of computer simulations.     

Encapsulation of Indomethacin in PVP: Solid-State NMR Studies

Summary: ¹³C solid-state NMR and ¹H relaxation time measurements have been used to determine the structure of the crystalline and amorphous forms of the pharmaceutical drug indomethacin. Cross-polarization dynamics parameters were calculated for individual NMR resonances providing an insight into the mobility of functional groups in two forms of indomethacin. The changes of mobility in indomethacin/polyvinylpyrrolidone (PVP) formulation have been investigated via¹H-¹³C solid-state NMR methods. Differences between the amorphous material and its crystalline counterpart have been observed. The γ-amorphous indomethacin rapidly crystallizes with time. It has been shown that encapsulation in the PVP stabilizes the amorphous form of the drug by preventing crystallization due to reduced mobility of the guest in the formulation.     

Early Stages of Interchange Reactions in Polymer Blends

Summary: Simple models are studied for better understanding of the early stages of interchange reactions in polymer blends. For a homogeneous blend of homopolymers A and B, parameters of copolymer AB formed at the reaction beginning are explicitly calculated. It is shown that the analysis of the copolymer composition can help to establish the prevailing interchange mechanism. For a bilayer blend of immiscible homopolymers A and B, the reactive compatibilization through interchange is studied by continual Monte Carlo modeling. The analysis of the local distribution in block length shows that the interdiffusion of blend components may start only after the formation of rather short copolymer blocks in the course of interchange.     

Analysis of Anti-Cancer and Anti-Inflammatory Properties of 25 High-THC Cannabis Extracts

Cannabis sativa is one of the oldest cultivated plants. Many of the medicinal properties of cannabis are known, although very few cannabis-based formulations became prescribed drugs. Previous research demonstrated that cannabis varieties are very different in their medicinal properties, likely due to the entourage effect—the synergistic or antagonistic effect of various cannabinoids and terpenes. In this work, we analyzed 25 cannabis extracts containing high levels of delta-9-tetrahydrocannabinol (THC). We used HCC1806 squamous cell carcinoma and demonstrated various degrees of efficiency of the tested extracts, from 66% to 92% of growth inhibition of cancer cells. Inflammation was tested by induction of inflammation with TNF-α/IFN-γ in WI38 human lung fibroblasts. The efficiency of the extracts was tested by analyzing the expression of COX2 and IL6; while some extracts aggravated inflammation by increasing the expression of COX2/IL6 by 2-fold, other extracts decreased inflammation, reducing expression of cytokines by over 5-fold. We next analyzed the level of THC, CBD, CBG and CBN and twenty major terpenes and performed clustering and association analysis between the chemical composition of the extracts and their efficiency in inhibiting cancer growth and curbing inflammation. A positive correlation was found between the presence of terpinene (pval = 0.002) and anti-cancer property; eucalyptol came second, with pval of 0.094. p-cymene and β-myrcene positively correlated with the inhibition of IL6 expression, while camphor correlated negatively. No significant correlation was found for COX2. We then performed a correlation analysis between cannabinoids and terpenes and found a positive correlation for the following pairs: α-pinene vs. CBD, p-cymene vs. CBGA, terpenolene vs. CBGA and isopulegol vs. CBGA. Our work, thus, showed that most of high-THC extracts demonstrate anti-cancer activity, while only certain selected extracts showed anti-inflammatory activity. Presence of certain terpenes, such as terpinene, eucalyptol, cymene, myrcene and camphor, appear to have modulating effects on the activity of cannabinoids.     

Abnormally slow reaction of oppositely charged ions: The kinetics of dopamine hydrochloride oxidation by ammonium peroxydisulfate

The kinetic curves for oxidation of dopamine hydrochloride in aqueous solution in the presence of ammonium peroxydisulfate were obtained by UV–vis spectroscopy and potentiometry. It was shown that the reaction follows the first-order kinetic equation and proceeds at a low rate. The values for the activation energy and the preexponential factor were determined as 75 kJ × mol⁻¹ and 4 × 10⁸ s⁻¹, respectively. The activation entropy was found having a negative value of −89 J × mol⁻¹ × K⁻¹. The first reaction order, the low preexponential factor and the negative activation entropy value for the reaction between the 2-(3,4-dihydroxyphenyl)ethanammonium cation and the peroxydisulfate anion were explained by the formation of ionic associates, which slowly enter into the internal redox reaction.     

A one-dimensional local tuning algorithm for solving GO problems with partially defined constraints

Lipschitz one-dimensional constrained global optimization (GO) problems where both the objective function and constraints can be multiextremal and non-differentiable are considered in this paper. Problems, where the constraints are verified in a priori given order fixed by the nature of the problem are studied. Moreover, if a constraint is not satisfied at a point, then the remaining constraints and the objective function can be undefined at this point. The constrained problem is reduced to a discontinuous unconstrained problem by the index scheme without introducing additional parameters or variables. A new geometric method using adaptive estimates of local Lipschitz constants is introduced. The estimates are calculated by using the local tuning technique proposed recently. Numerical experiments show quite a satisfactory performance of the new method in comparison with the penalty approach and a method using a priori given Lipschitz constants.This research was supported by the following grants: FIRB RBNE01WBBB, FIRB RBAU01JYPN, PRIN 2005017083-002, and RFBR 04-01-00455-a. The authors would like to thank anonymous referees for their subtle suggestions.     

An algorithm for solving global optimization problems with nonlinear constraints

In this paper we propose an algorithm using only the values of the objective function and constraints for solving one-dimensional global optimization problems where both the objective function and constraints are Lipschitzean and nonlinear. The constrained problem is reduced to an unconstrained one by the index scheme. To solve the reduced problem a new method with local tuning on the behavior of the objective function and constraints over different sectors of the search region is proposed. Sufficient conditions of global convergence are established. We also present results of some numerical experiments.     

Three‐Component Gallium(III)‐Promoted Addition of Halide Anions and Acetylenes to Donor–Acceptor Cyclopropanes

A new strategy for the three‐component addition of halide anions and acetylenes to donor–acceptor cyclopropanes (DACs) is presented. This reaction, which occurs with high E selectivity, is promoted by gallium(III) salts and based on the 1,2‐zwitterionic reactivity of DACs. It opens up a new group of processes involving DACs. The reaction occurs readily with a broad range of substrates and is tolerant of various functional groups. This methodology makes it possible to assemble highly functionalized vinyl halides, which are very convenient building blocks in organic synthesis. A possible mechanism of this reaction and its stereochemical aspects are discussed in detail.