Generation and amplification of dual-color femtosecond pulses by a noncollinear optical parametric up-conversion process

Noncollinear optical parametric up-conversion generation and amplification are realized in a thick β-barium borate (BBO) crystal, and a couple of visible femtosecond up-conversion laser pulses can be achieved by a femtosecond pulse at 800 nm as the pump sources. The theoretical and experimental results indicate that there exist phase-matching conditions for dual-color noncollinear parametric up-conversion generation and amplification, and their wavelengths can be tuned by rotating the BBO crystal. This parametric up-conversion generation and amplification can be attributed to three and five-wave mixing in a thick BBO crystal, and it shows the potential application on optical parametric chirped pulse amplification (OPCPA) to generate multi-color ultraviolet or visible femtosecond laser pulses pumped directly by femtosecond fundamental laser pulses without frequency-doubling or tripling.     

Electron-TO-phonon interaction in polar crystals

In the present work, the interaction between electrons and long-wavelength transverse optical (TO) vibrations in a polar insulator is considered. The crystal model employed for the theoretical analysis includes classical potentials and electronic polarizabilities. A significant enhancement of the strength of the electron-TO-phonon interaction in ferroelectrics has been found. A microscopic justification of this effect is given. A bridge that relates the interaction of electrons with the polar long-wavelength TO modes of lattice vibrations to the long-range dipole-dipole interaction is established. As an application of our analysis, a novel method for quantitative predictions of the electron-TO-phonon interaction constants in polar crystals via the data of experimental studies is suggested.     

Parametric model of the BAW resonator phase-noise

Excepted for the very short terms the frequency stability of ultra-stable oscillators is mainly limited by the resonator noise. In this work we proposed a parametric model of the bulk acoustic wave (BAW) resonator phase noise based on an equivalent circuit. This model explains phase noise generated by a BAW crystal from a point of view of parametric fluctuations and proves the f⁻¹ dependences of the crystal noise. The model performance is verified with simulation. Simulation results are compared to experimental data and discussed. Comparison of three existing models is made.     

Approximating Pareto curves using semidefinite relaxations

We approximate as closely as desired the Pareto curve associated with bicriteria polynomial optimization problems. We use three formulations (including the weighted sum approach and the Chebyshev approximation) and each of them is viewed as a parametric polynomial optimization problem. For each case is associated a hierarchy of semidefinite relaxations and from an optimal solution of each relaxation one approximates the Pareto curve by solving an inverse problem (first two cases) or by building a polynomial underestimator (third case).     

Optimizing fuzzy p-hub center problem with generalized value-at-risk criterion

In this study, we reduce the uncertainty embedded in secondary possibility distribution of a type-2 fuzzy variable by fuzzy integral, and apply the proposed reduction method to p-hub center problem, which is a nonlinear optimization problem due to the existence of integer decision variables. In order to optimize p-hub center problem, this paper develops a robust optimization method to describe travel times by employing parametric possibility distributions. We first derive the parametric possibility distributions of reduced fuzzy variables. After that, we apply the reduction methods to p-hub center problem and develop a new generalized value-at-risk (VaR) p-hub center problem, in which the travel times are characterized by parametric possibility distributions. Under mild assumptions, we turn the original fuzzy p-hub center problem into its equivalent parametric mixed-integer programming problems. So, we can solve the equivalent parametric mixed-integer programming problems by general-purpose optimization software. Finally, some numerical experiments are performed to demonstrate the new modeling idea and the efficiency of the proposed solution methods.     

Lower semicontinuity of solution mapping to parametric generalized strong vector equilibrium problems

In this paper, the lower semicontinuity of solution mapping to parametric generalized strong vector equilibrium problems without the assumptions of monotonicity and compactness is established by using a new proof method which is different from the ones used in the literature.     

Harmonic Force Field and Mean Amplitudes for Gallium Tribromide and Triiodide Dimers

Harmonic force fields are developed for the Ga₂Br₆ and Ga₂I₆ molecules. The analysis confirms previous assignments of experimental frequencies. Mean amplitudes of vibration are calculated.     

A refined integro-surface energy-based model for vibration of magnetically actuated double-nanowire-systems carrying electric current

A novel surface energy-based model is developed to examine more precisely vibrations of current-carrying double-nanowire-systems immersed in a longitudinal magnetic field. Using Biot-Savart and Lorentz laws, a more refined version of interwire interactional magnetic forces is presented. By employing Rayleigh beam theory, the equations of motion are derived. In fact, these are coupled integro-differential equations which are more accurate with respect to those of the previously developed models. For simply supported and clamped nanosystems, governing equations are analyzed via assumed mode method. The effects of interwire distance, slenderness ratio, electric current, magnetic field strength, and surface effect on the fundamental frequency are addressed carefully. The obtained results display the importance of exploiting the refined model for vibration analysis of nanosystems with low interwire distance, high electric current, and high magnetic field strength.     

Analyzing the Sensitivity of Generalized Linear Models to Incomplete Outcomes via the IDE Algorithm

Incomplete data models typically involve strong untestable assumptions about the missing data distribution. As inference may critically depend on them, the importance of sensitivity analysis is well recognized. Molenberghs, Kenward, and Goetghebeur proposed a formal frequentist approach to sensitivity analysis which distinguishes ignorance due to unintended incompleteness from imprecision due to finite sampling by design. They combine both sources of variation into uncertainty. This article develops estimation tools for ignorance and uncertainty concerning regression coefficients in a complete data model when some of the intended outcome values are missing. Exhaustive enumeration of all possible imputations for the missing data requires enormous computational resources. In contrast, when the boundary of the occupied region is of greatest interest, reasonable computational efficiency may be achieved via the imputation towards directional extremes (IDE) algorithm. This is a special imputation method designed to mark the boundary of the region by maximizing the direction of change of the complete data estimator caused by perturbations to the imputed outcomes. For multi-dimensional parameters, a dimension reduction approach is considered. Additional insights are obtained by considering structures within the region, and by introducing external knowledge to narrow the boundary to useful proportions. Special properties hold for the generalized linear model. Examples from a Kenyan HIV study will illustrate the points.     

Closedness of the solution map for parametric weak vector equilibrium problems

In this paper we introduced a new definition of vector topological pseudomonotonicity to study the parametric weak vector equilibrium problems. The main result gives sufficient conditions for closedness of the solution map defined on the set of parameters.