On using lens-assisted hologram interferometry to investigate semiconductor device behaviour

The paper analyses some of the causes that limit the performance of the hologram interferometry method when used for the study of the behaviour of semiconductors devices. Then some results are shown obtained by the authors using a method of lens-assisted microscope hologram interferometry for studying such structures. The method allows detection of defects and, besides, it renders quantitatively the structure local non-uniformities during the normal operation of the semiconductor devices.     

Structural reinvestigation of ammonium hypophosphite: was dihydrogen bonding observed long ago?

The past decade has seen the explosive emergence of "dihydrogen bonds", interactions between the electrons of M-H sigma-bonds, where M is less electronegative than H (M = Al, B, Ga, Ir, Mo, Mn, Os, Re, Ru, W) and traditional proton donors. But 70 years ago, such an interaction was proposed by Zachariasen and Mooney [J. Chem. Phys. 1934, 2, 34-37] on the basis of their single-crystal X-ray diffraction structure (heavy atoms positions only) of ammonium hypophosphite (NH(4)H(2)PO(2)). We redetermined this structure at high resolution with a focus on the hydrogen atoms, using a modern diffractometer equipped with a CCD detector. Molecular orbital calculations were performed to investigate the charge density and the bond polarity of the P-H bonds and to assess their potential for participation in dihydrogen bonds. Neither the theory nor the X-ray structure supports the original claim of H...H interactions in this salt.     

Multistep reaction analysis. A numerical approach based on relaxation theory

A general numerical method and program for simulation of the kinetics of multistep reactions is described, with details for collation of data, construction of a mechanistic model, and simulation of reciprocal relaxation times and calculation of individual rate constants. The working scheme of the program includes an initial approximate simulation by adjustment of the rate constants followed by their optimization with a Powell minimization subroutine. The procedure is applied to aromatic nucleophilic addition.     

Towards sympathetic cooling of trapped ions with laser-cooled Mg + ions for mass spectrometry and laser spectroscopy

Sympathetic cooling by laser cooled Mg ions has been proposed as a method for fast cooling of highly charged ions to a very low temperature. The paper describes the construction of the solid state laser system at 279.63 nm required for laser cooling of the Mg ions. The laser system is composed of a fiber laser at 1,118.54 nm and two successive second harmonic generation (SHG) ring cavities for frequency quadrupling. In the first SHG cavity, non-critical phase matching of a lithium triborate (LBO) crystal is used for doubling from 1,118.54 to 559.27 nm. The second SHG cavity uses critical phase matching of a β-barium borate (BBO) crystal for doubling from 559.27 to 279.63 nm. With the aid of Boyd–Kleinmann theory, optimum experimental parameters are calculated and used for an efficient SHG. Besides this, the paper intends to be a shortcut for practical applications of the Boyd–Kleinmann theory for SHG.     

Convergence rates for forward–backward dynamical systems associated with strongly monotone inclusions

We investigate the convergence rates of the trajectories generated by implicit first and second-order dynamical systems associated to the determination of the zeros of the sum of a maximally monotone operator and a monotone and Lipschitz continuous one in a real Hilbert space. We show that these trajectories strongly converge with exponential rate to a zero of the sum, provided the latter is strongly monotone. We derive from here convergence rates for the trajectories generated by dynamical systems associated to the minimization of the sum of a proper, convex and lower semicontinuous function with a smooth convex one provided the objective function fulfills a strong convexity assumption. In the particular case of minimizing a smooth and strongly convex function, we prove that its values converge along the trajectory to its minimum value with exponential rate, too.     

A new algorithm that generates the image of the attractor of a generalized iterated function system

Numerical Algorithms - We provide a new algorithm (called the grid algorithm) designed to generate the image of the attractor of a generalized iterated function system on a finite dimensional space...     

A Bound of the Finslerian Ricci Scalar

In the Riemannian as well as in the Finslerian geometry, certain conditions on the Ricci scalar or the Ricci tensor provide obstructions on the topology of the base manifold and so on the configuration of cut points by limitations of the injectivity radius, see the Bonnet–Myers theorem and its variants and generalizations. In this paper, we show that conversely, prescribing the injectivity radius of a Finsler manifold, some limitations of the Ricci scalar are obtained. Some consequences of the condition that the Ricci tensor is h-parallel with respect to the Chern–Rund connection are found. In addition, some classes of examples are provided.     

Gradient-type penalty method with inertial effects for solving constrained convex optimization problems with smooth data

We consider the problem of minimizing a smooth convex objective function subject to the set of minima of another differentiable convex function. In order to solve this problem, we propose an algorithm which combines the gradient method with a penalization technique. Moreover, we insert in our algorithm an inertial term, which is able to take advantage of the history of the iterates. We show weak convergence of the generated sequence of iterates to an optimal solution of the optimization problem, provided a condition expressed via the Fenchel conjugate of the constraint function is fulfilled. We also prove convergence for the objective function values to the optimal objective value. The convergence analysis carried out in this paper relies on the celebrated Opial Lemma and generalized Fejér monotonicity techniques. We illustrate the functionality of the method via a numerical experiment addressing image classification via support vector machines.     

Theory and computation for multiple positive solutions of non-local problems at resonance

Resonance non-positone and non-isotone problems for first order differential systems subjected to non-local boundary conditions are reduced to the non-resonance positone and isotone case by changes of variables. This allows us to prove the existence of multiple positive solutions. The theory is illustrated by two examples for which three positive numerical solutions are obtained using the Mathematica shooting program.