Accurate non-Born-Oppenheimer calculations of the complete pure vibrational spectrum of D2 with including relativistic corrections

In this work we report very accurate variational calculations of the complete pure vibrational spectrum of the D(2) molecule performed within the framework where the Born-Oppenheimer (BO) approximation is not assumed. After the elimination of the center-of-mass motion, D(2) becomes a three-particle problem in this framework. As the considered states correspond to the zero total angular momentum, their wave functions are expanded in terms of all-particle, one-center, spherically symmetric explicitly correlated Gaussian functions multiplied by even non-negative powers of the internuclear distance. The nonrelativistic energies of the states obtained in the non-BO calculations are corrected for the relativistic effects of the order of α(2) (where α = 1/c is the fine structure constant) calculated as expectation values of the operators representing these effects.     

An algorithm for calculating atomic D states with explicitly correlated gaussian functions

An algorithm for the variational calculation of atomic D states employing n-electron explicitly correlated gaussians is developed and implemented. The algorithm includes formulas for the first derivatives of the hamiltonian and overlap matrix elements determined with respect to the gaussian nonlinear exponential parameters. The derivatives are used to form the energy gradient which is employed in the variational energy minimization. The algorithm is tested in the calculations of the two lowest D states of the lithium and beryllium atoms. For the lowest D state of Li the present result is lower than the best previously reported result.     

Conformational polymorphs of 3‐cyclopropyl‐5‐(3‐methyl‐[1,2,4]triazolo[4,3‐a]pyridin‐7‐yl)‐1,2,4‐oxadiazole

The dipharmacophore compound 3‐cyclopropyl‐5‐(3‐methyl‐[1,2,4]triazolo[4,3‐a]pyridin‐7‐yl)‐1,2,4‐oxadiazole, C₁₂H₁₁N₅O, was studied on the assumption of its potential biological activity. Two polymorphic forms differ in both their molecular and crystal structures. The monoclinic polymorphic form was crystallized from more volatile solvents and contains a conformer with a higher relative energy. The basic molecule forms an abundance of interactions with relatively close energies. The orthorhombic polymorph was crystallized very slowly from isoamyl alcohol and contains a conformer with a much lower energy. The basic molecule forms two strong interactions and a large number of weak interactions. Stacking interactions of the `head‐to‐head' type in the monoclinic structure and of the `head‐to‐tail' type in the orthorhombic structure proved to be the strongest and form stacked columns in the two polymorphs. The main structural motif of the monoclinic structure is a double column where two stacked columns interact through weak C—H…N hydrogen bonds and dispersive interactions. In the orthorhombic structure, a single stacked column is the main structural motif. Periodic calculations confirmed that the orthorhombic structure obtained by slow evaporation has a lower lattice energy (0.97 kcal mol^?1) compared to the monoclinic structure.     

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.     

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.