A nonconvex quadratic optimization approach to the maximum edge weight clique problem

The maximum edge weight clique (MEWC) problem, defined on a simple edge-weighted graph, is to find a subset of vertices inducing a complete subgraph with the maximum total sum of edge weights. We propose a quadratic optimization formulation for the MEWC problem and study characteristics of this formulation in terms of local and global optimality. We establish the correspondence between local maxima of the proposed formulation and maximal cliques of the underlying graph, implying that the characteristic vector of a MEWC in the graph is a global optimizer of the continuous problem. In addition, we present an exact algorithm to solve the MEWC problem. The algorithm is a combinatorial branch-and-bound procedure that takes advantage of a new upper bound as well as an efficient construction heuristic based on the proposed quadratic formulation. Results of computational experiments on some benchmark instances are also presented.     

A short proof of the Arendt-Chernoff-Kato theorem

We give a short new proof of the Arendt-Chernoff-Kato theorem, which characterizes generators of positive C ₀ semigroups in order unit spaces. The proof avoids half-norms and subdifferentials and is based on a sufficient condition for an operator to have positive inverse, which is new even for matrices.     

Experience with using counterexamples in an introductory calculus class

The paper describes a personal experience with using counterexamples as a pedagogical strategy in the teaching and learning of an introductory calculus course at a university of technology.     

Microstructure evolution during severe plastic deformation

Radiotracer diffusion studies of severely deformed, ultra-fine grained materials have revealed the presence of ultra-fast transport paths, which include “non-equilibrium” grain boundaries and free volume. Under some experimental conditions, percolating porosity is produced even in pure copper. Micro-cracks may form in metals, if the local maximum shear stress exceeds the shear yield stress. However, their growth and propagation is postponed till late in the deformation process owing to the ductility of metals, the hydrostatic component of the stress system and/or dynamic recovery/recrystallization. In other words, crack growth and propagation is present only when the scope for further deformation is highly restricted. Using this approach, the load required for equal channel angular pressing, the change in the slope of the Hall–Petch plot with decreasing grain size and the theoretical limit for the smallest grain size attainable in a metal in a severe plastic deformation process are predicted and validated by experimental results. Experimentally successful prevention of percolated crack formation by the superposition of a hydrostatic pressure is also accounted for using this model.     

Magnetic resonance in systems with equivalent spin-1/2 nuclides. Part 2: energy values and spin states

In an earlier paper (Part 1), featuring group-theoretical analysis, it was shown that the isotropic EPR spectra of free radical (S=1/2) species XL(n), where the n equivalent nuclei also have spin 1/2, have a more complicated form than anticipated from the usual (first-order) oversimplified analysis. The nucleus of X is taken to be spin-less. The latter predicts n+1 lines with intensity ratios given by the coefficients of the binomial expansion; for systems with n=3, the EPR spectrum in fact consists of 6 lines. Analogous considerations hold for NMR spectroscopy of XL(n) non-radicals. For n > or = 3 systems, the degeneracy of the energy levels cannot be completely removed by the Zeeman electronic and nuclear interactions. Explicit solutions for n=3 (analytic, as well as computational) of the spin-hamiltonian for the energies and spin states have been obtained and are given in the present work. Discussion of the underlying theory, invoking exchange degeneracy, is included herein in some detail, focusing on line positions and relative spectral intensities.     

The Products of Suzuki Reaction of Ethyl 4-Chloro-5-Methylthieno[2,3-d]Pyrimidine-6-Carboxylate with Potassium Allyltrifluoroborate and Transformations Thereof

Chemistry of Heterocyclic Compounds - 5-Methylthieno[2,3-d]pyrimidine-6-carboxylates substituted with prop-1-en-1-yl and hexa-1,5-dien-3-yl fragments in the C-4 position of the heterocycle were...     

Bioactive constituents of Iris hybrida (Iridaceae): Processing effect

Iris genus plants are a valuable source of bioactive compounds, which are an important component for pharmaceutical development. The present article shows the potential for mineral nutrition with application of magnesium sulfate, iron chelates and potassium oxide affecting the phenolic compound contents in Iris hybrida ‘Tsikavynka’, I. hybrida ‘Tambo’ and I. hybridа ‘Widecombe Fire’. The effect of mineral processing was specific to plant organs and varied in the component composition. The Iris rhizomes had an increased total phenolic compound content after treatment (up to 10% of the total isoflavonoid content, up to 8% of phenolic acids, up to 5% of γ-pyrones and up to 13% of flavonoids), determined using UV–vis spectroscopy. A positive effect of nutrition on the biosynthesis and content of individual isoflavonoids (tectoridin, nigricin d -glucoside, genistin, iristectorigenin B, nigricin, irigenin and irisolidone) and xanthone mangiferin in Iris rhizomes by HPLC was established. In addition, an increase in the chlorogenic acid amount in Iris leaves was noted. The results demonstrate the sensitivity of Iris phenylpropanoid metabolism to mineral nutrition and can be used to predict medical plant cultivation with increased content of bioactive constituents.     

Synthesis of 4-polyfluoroalkyl-1,3-dithiolanes via [3+2] cycloaddition of thiocarbonyl ylide to polyfluoroalkanethioamides

Chemistry of Heterocyclic Compounds - New 4-polyfluoroalkyl-1,3-dithiolanes were synthesized by reaction of polyfluoroalkanethioamides with thiocarbonyl ylide that was generated in situ by...     

Computational study of the aminolysis of anhydrides: effect of the catalysis to the reaction of succinic anhydride with methylamine in gas phase and nonpolar solution

Different possible pathways of the aminolysis reaction of succinic anhydride were investigated by applying high level electronic structure theory, examining the general base catalysis by amine and the general acid catalysis by acetic acid, and studying the effect of solvent. The density functional theory at the B3LYP/6-31G(d) and B3LYP/6-311++G(d,p) levels was employed to investigate the reaction pathways for the aminolysis reaction between succinic anhydride and methylamine. The single point ab initio calculations were based on the second-order M?ller-Plesset perturbation theory (MP2) with 6-31G(d) and 6-311++G(d,p) basis sets and CCSD(T)/6-31G(d) level calculations for geometries optimized at the B3LYP/6-311++G(d,p) level of theory. A detailed analysis of the atomic movements during the process of concerted aminolysis was further obtained by intrinsic reaction coordinate calculations. Solvent effects were assessed by the polarized continuum model method. The results show that the concerted mechanism of noncatalyzed aminolysis has distinctly lower activation energy compared with the addition/elimination stepwise mechanism. In the case of the process catalyzed by a second methylamine molecule, asynchronous proton transfer takes place, while the transition vectors of the acid-catalyzed transition states correspond to the simultaneous motion of protons. The most favorable pathway of the reaction was found through the bifunctional acid catalyzed stepwise mechanism that involves formation of eight-membered rings in the transition state structures. The difference between the activation barriers for the two mechanisms averages 2 kcal/mol at various levels of theory.     

Single nanoparticle plasmonic devices by the "grafting to" method

Hierarchically organized single-nanoparticle structures synthesized in this work consisted of a 200 nm silica core and a pH-responsive poly(2-vinylpyridine) shell decorated with 15 nm gold nanoparticles. pH changes in the range of 3-6 back and forth results in a swelling-shrinking polymer brush shell and, thus, in the tuning distance between noble nanoparticles. A change in the interparticle distance is accompanied by a very pronounced shift in the maximum wavelength of the surface plasmon absorption peak. The dispersion of the resulting composite nanoparticles reversibly changed color from red to purple-blue as the pH changed from 2.5 to 6. Such hierarchically assembled nanostructures can be used as free-standing single-particle sensors in various miniaturized analytical systems.