Theoretical calculations of the substituent effect on molecular properties of the RCN⋯HF hydrogen-bonded complexes with R = NH2, CH3O,CH3, OH,SH, H,Cl, F,CF3, CN and NO2

DFT calculations with B3LYP and PBE1PBE functionals and 6–311++G(d,p) basis set have been performed in order to obtain molecular geometries, binding energies and vibrational properties of the RCN?HF H-bonded complexes with R = NH₂, CH₃O, CH₃, OH, SH, H, Cl, F, CF₃, CN and NO₂. As expected, it has been verified as a red-shift of the HF stretching frequency (ν_HF), in conformity with the elongation of the bond after complexation. On the other hand, the CN stretching frequency (ν_CN) is blue-shifted and corresponds to a shortening of the bond. The binding energies (ΔE_c), including BSSE and ZPVE corrections, show a linear correlation with several structural, electronic and vibrational properties. In particular, an important linear dependence between the binding energy and the calculated dipole moment of the free RCN molecule (μ_RCN) has been found. This result suggests that μ_RCN can be a useful quantity in order to predict the ability of this fragment to form a hydrogen-bond. The IR intensities of stretching and bending modes of complexed HF acid fragment are adequately interpreted through the atomic polar tensor of the hydrogen atom in HF using the modified CCFO model for infrared intensities. The new vibrational modes arising from complexation show several interesting features.     

Multi-parametric disaggregation technique for global optimization of polynomial programming problems

This paper discusses a power-based transformation technique that is especially useful when solving polynomial optimization problems, frequently occurring in science and engineering. The polynomial nonlinear problem is primarily transformed into a suitable reformulated problem containing new sets of discrete and continuous variables. By applying a term-wise disaggregation scheme combined with multi-parametric elements, an upper/lower bounding mixed-integer linear program can be derived for minimization/maximization problems. It can then be solved to global optimality through standard methods, with the original problem being approximated to a certain precision level, which can be as tight as desired. Furthermore, this technique can also be applied to signomial problems with rational exponents, after a few effortless algebraic transformations. Numerical examples taken from the literature are used to illustrate the effectiveness of the proposed approach.     

Defect numbers of singular integral operators with Carleman shift and almost periodic coefficients

This paper is devoted to the study of properties of the kernel and the cokernel of singular integral operators with almost periodic coefficients and a Carleman shift. In particular, the dimensions of their kernels and cokernels are obtained. This is done by considering appropriate properties of the related almost periodic elements and, in special, the partial indices of some of their relevant factorizations.     

Existence of seven solutions for an asymptotically linear Dirichlet problem without symmetries

In this paper, we establish sufficient conditions for an asymptotically linear elliptic boundary value problem to have at least seven solutions. We use the mountain pass theorem, Lyapunov–Schmidt reduction arguments, existence of solutions that change sign exactly once, and bifurcation properties. No symmetry is assumed on the domain or the non-linearity.     

Divisibility of exponential sums via elementary methods

We present an elementary method for evaluating the order of p-divisibility of exponential sums over a prime field. This method unifies and sometimes improves previously known results of Ax-Katz, Moreno-Moreno, Adolphson-Sperber, and Cao-Sun.     

Optimal operation of hydrothermal systems with Hydrological Scenario Generation through Bootstrap and Periodic Autoregressive Models

In electrical power systems with strong hydro generation, the use of adequate techniques to generate synthetic hydrological scenarios is extremely important for the evaluation of the ways the system behaves in order to meet the forecast energy demand. This paper proposes a new model to generate natural inflow energy scenarios in the long-term operation planning of large-sized hydrothermal systems. This model is based on the Periodic Autoregressive Model, PAR (p), where the identification of the p orders is based on the significance of the Partial Autocorrelation Function (PACF) estimated via Bootstrap, an intensive computational technique. The scenarios generated through this new technique were applied to the operation planning of the Brazilian Electrical System (BES), using the previously developed methodology of Stochastic Dynamic Programming based on Convex Hull algorithm (SDP-CHull). The results show that identification via Bootstrap is considerably more parsimonious, leading to the identification of lower orders models in most cases which retains the statistical characteristics of the original series. Additionally it presents a closer total mean operation cost when compared to the cost obtained via historic series.     

Spinning rigid bodies driven by orbital forcing: the role of dry friction

Nonlinear Dynamics - A “circular orbital forcing” makes a chosen point on a rigid body follow a circular motion while the body spins freely around that point. We investigate this...     

Inhibition of the oxygen evolution reaction during titanium passivation in aqueous phosphoric acid solution

Journal of Solid State Electrochemistry - The anodic oxide on titanium can be thickened by anodization, with the consequent corrosion properties of this oxide depending on many variables, including...