Surface memory effect in nematics with smectic C short-range order and hydrogen bonded molecules

A surface memory effect (SME) is found in the dimerized nematic with short range smectic C order of 4-n-octyloxybenzoic acid (OOBA) in a cell whose walls have been covered with an obliquely evaporated SiO or ITO layer. The recording and erasure processes are discussed and erasure in the nematic phase is realized. A mechanism for the surface memorization is presented which takes into account the specific character of dimerized nematics preceding cooling into a smectic C phase.     

Optimal Security Liquidation Algorithms

This paper develops trading strategies for liquidation of a financial security, which maximize the expected return. The problem is formulated as a stochastic programming problem that utilizes the scenario representation of possible returns. Two cases are considered, a case with no constraint on risk and a case when the risk of losses associated with trading strategy is constrained by Conditional Value-at-Risk (CVaR) measure. In the first case, two algorithms are proposed; one is based on linear programming techniques, and the other uses dynamic programming to solve the formulated stochastic program. The third proposed algorithm is obtained by adding the risk constraints to the linear program. The algorithms provide path-dependent strategies, i.e., the fraction of security sold depends upon price sample-path of the security up to the current moment. The performance of the considered approaches is tested using a set of historical sample-paths of prices.     

Charge asymmetry in HD+

Expanding the wave functions of the ground and excited states of HD(+) (or pde) in terms of spherically symmetric explicitly correlated Gaussian functions with preexponential multipliers consisting of powers of the internuclear distance, and using the variational method, we performed very accurate nonadiabatic calculations of all bound states of this system corresponding to the zero total angular momentum quantum number (vibrational states; v=0-22). The total and the transition energies obtained agree with the best available calculations. For each state we computed the expectation values of the d-p, d-e, and p-e interparticle distances. This is the first time these quantities were computed for HD(+) using rigorous nonadiabatic wave functions. While up to the v=20 state some asymmetry is showing in the d-e and p-e distances, for v=21 and v=22 we observe a complete breakdown of the Born-Oppenheimer approximation and localization of the electron almost entirely at the deuteron.     

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.     

Synthesis and Properties of Hyperbranched Polyimides Combined with Silica

Summary: The novel hyperbranched polyimide - silica hybrid materials containing theoretically 16 wt% of an inorganic phase were prepared via a sol-gel process. An amine terminated polyimide precursor (hyperbranched polyamic acid) was prepared from commercially available monomers 4,4′,4″-triaminotriphenylmethane and 4,4′-oxydiphthalic anhydride in molar ratio 1:1. Tetramethoxysilane and/or 3-glycidoxypropyltrimethoxysilane (also used as a coupling agent) were used as silica precursors. During thermal exposition the polyimide precursor was transformed to hyperbranched polyimide and hydrolyzed alkoxy groups reacted mutually to form silica. The final products were self-standing films, whose structure was characterized by using IR and ¹³C and ²⁹Si solid state NMR spectroscopy. The influence of the amount of silica and/or coupling agent on their structure and thermal properties was described.     

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...