Cross-polarized wave generation in the UV region

We demonstrate experimentally the generation of cross-polarized femtosecond pulses in BaF2 crystal in the UV region. We show that unsaturated cross-polarized wave generation in the UV is six times more efficient than in the visible region, and we deduce the corresponding wavelength dispersion of the third-order nonlinearity.     

Temperature-dependent lasing and spectroscopy of Yb:Y2O3 and Yb:Sc2O3

Spectroscopic and laser properties of Yb³⁺ in ceramic Y₂O₃ have been studied at room and cryogenic temperatures. Laser performance is very substantially improved by cooling to liquid nitrogen temperature, primarily due to the great reduction in ground state absorption that permits laser operation on the much stronger 1030-nm emission line rather than the 1077-nm line. The 976-nm “zero line” is observed to become much weaker as the temperature is reduced. Several models for this behavior are considered, but none adequately explains this surprising result. Spectroscopy of Yb:Sc₂O₃ indicates that it is likely to be an even better cryogenic gain material, given samples of comparable optical quality.     

Ionic equilibrium in mixtures of protophobic and protophilic polar non‐hydrogen bond donor solvents: acids,salts, and indicators in acetone containing 5 mol% DMSO

Properties of a protophobic polar non‐HBD solvent can be strongly modified by introduction of a small amount of a protophilic polar non‐HBD solvent. In this paper, acetone (AC) with 5 mol% additive of DMSO, a solvent with , was considered as a media for acid–base reactions. Conductance was used for determination of dissociation constants of a set of salts, hydrogen chloride, and picric acid. The last‐named was also studied by UV‐vis spectroscopy. The introduction of 5 mol% of DMSO results in suppressing, to some extent, the homoconjugation processes in AC media as well as of proton hydration by (possible) traces of water. The dissociation of salicylic acid and 2,4‐dinitrophenol was examined utilizing quinhydrone electrodes in a cell with liquid junction. The pK_a values of buffer acids and values of buffer solutions were calculated by taking into account the incomplete dissociation of salts. The response of the glass electrode appeared to be satisfactory, which allowed the estimation of the pK_a value of benzoic acid. The apparent ionization constants of 22 acid–base indicators in buffer mixtures and perchloric acid solutions were determined in (AC + 5 mol% DMSO) using the spectrophotometric procedure. Copyright © 2009 John Wiley & Sons, Ltd.     

Higher borides and oxygen-enriched Mg–B–O inclusions as possible pinning centers in nanostructural magnesium diboride and the influence of additives on their formation

The study of high pressure (2 GPa) synthesized MgB₂-based materials allows us to conclude that higher borides (with near MgB₁₂ stoichiometry) and oxygen-enriched Mg–B–O inclusions can be pinning centers in nanostructural magnesium diboride matrix (with average grain sizes of 15–37 nm). It has been established that additions of Ti or SiC as well as manufacturing temperature can affect the size, amount and distribution of these inclusions in the material structure and thus, influence critical current density. The superconducting behavior of materials with near MgB₁₂ stoichiometry of matrix is discussed.     

Non-iterative Rauscher method for 1-DOF system: a new approach to studying non-autonomous system via equivalent autonomous one

Rauscher method becomes the matter of interest because in combination with the method of nonlinear normal vibration modes it allows to calculate steady forced vibrations in the system with multiple degrees of freedom (DOF) via reduction in the number of DOFs. However, modern realizations of that approach have drawbacks such as iterative nature and the need to have initial approximation for the solution. The primary principle of Rauscher method is in obtaining periodic solutions of a non-autonomous system via studying some equivalent autonomous one. In the paper, a new non-iterative variant of Rauscher method is considered. In its current statement, the method can be used in analysis of forced harmonic oscillations in a nonlinear system with one degree of freedom. The primary goals of the study were to find out what kind of equivalent autonomous systems could be built for a given non-autonomous one and how they can be used for the construction of periodic solutions and/or periodic phase plane orbits of the initial system. It is shown that three different types of equivalent autonomous dynamical systems can be built for a given 1-DOF non-autonomous one. The system of 1st type is a fourth-order dynamical system. Technically it can be considered as a 2-DOF system where additional “DOF” is explicitly “responsible” for forced oscillations. The system of 2nd type is a third-order dynamical system. Its periodic orbits are exactly the same as in the initial system. Using the invariant manifold of the system of 1st type, the system of 2nd type can be reduced to the form \(W(x,x')=0\) (which is called here the equivalent system of the 3rd type). It is important that the function \(W(x,x')\) can be built a priori. Once \(W(x,x')\) is found: (i) one can obtain different periodical orbits corresponding to forced oscillations in the initial system; (ii) one can estimate amplitudes of vibrations for these regimes; (iii) one can track bifurcations of periodical regimes of the initial system with respect to change in amplitude of external excitation f. As shown in the paper, periodical orbits of the initial non-autonomous system can be obtained via two different approaches: (i) as set of points on phase plane satisfying the condition \(W(x,x')=0\); (ii) via the application of harmonic balance method to the equivalent system of 1st type using system’s energy level as a continuation parameter. This approach has advantage over application of harmonic balance method to initial system because the latter requires good initial guess for expansion coefficients, while the new approach does not and always starts from zero initial guess.     

Simple Equations Method and Non-Linear Differential Equations with Non-Polynomial Non-Linearity

We discuss the application of the Simple Equations Method (SEsM) for obtaining exact solutions of non-linear differential equations to several cases of equations containing non-polynomial non-linearity. The main idea of the study is to use an appropriate transformation at Step (1.) of SEsM. This transformation has to convert the non-polynomial non- linearity to polynomial non-linearity. Then, an appropriate solution is constructed. This solution is a composite function of solutions of more simple equations. The application of the solution reduces the differential equation to a system of non-linear algebraic equations. We list 10 possible appropriate transformations. Two examples for the application of the methodology are presented. In the first example, we obtain kink and anti- kink solutions of the solved equation. The second example illustrates another point of the study. The point is as follows. In some cases, the simple equations used in SEsM do not have solutions expressed by elementary functions or by the frequently used special functions. In such cases, we can use a special function, which is the solution of an appropriate ordinary differential equation, containing polynomial non-linearity. Specific cases of the use of this function are presented in the second example.     

Einige Bemerkungen über inhomogene diophantische Approximationen

Archiv der Mathematik - We discuss some easy statements dealing with linear inhomogeneous Diophantine approximation. Surprisingly, we did not find some of them in the literature. In particular, we...     

New organic supports for metallocene catalysts applied in olefin polymerizations

Nano-sized latex particles as organic supports for metallocenes applied in olefin polymerizations are introduced. The particles are functionalized with nucleophilic surfaces such as polyethylenoxide (PEO), polypropyleneoxide (PPO) or pyridine units allowing an immobilization of the metallocene catalysts via a non-covalent immobilization process. The latices are obtained by emulsion or miniemulsion polymerization with styrene, divinylbenzene as the crosslinker, and either PEO or PPO functionalized styrene or 4-vinylpyridine for surface functionalization. The supported catalysts, e.g. [Me₂Si(2MeBenzInd)₂ZrCl₂/MAO] on PPO containing latices or Cp₂ZrMe₂/([Ph₃C][B(C₆F₅)₄]) on pyridine functionalized materials were tested in ethylene polymerizations. Remarkably, high activities and excellent product morphologies were obtained. The influence of the degree of surface functionalization on activity and productivity was investigated. Furthermore, the fragmentation of the catalyst was studied by electron microscopy using bismuth-labeled latex particles or by fluorescence and confocal fluorescence microscopy using dye-labeled supports. Finally, a self-immobilizing catalyst/monomer system is presented. It is demonstrated that by using PEO-functionalized olefins, the metallocenes were immobilized on the monomers. Subjecting these mixtures to an ethylene copolymerization, again high activities and productivities as well as polyolefin beads with high bulk densities are observed, indicating that an extra supporting process for controlling the product size and shape of the polyolefins is not necessary for these monomers.     

Interplay of chemical and physical factors in reacting polymer blends. Theoretical considerations

Various effects produced by copolymers in polymer blends are discussed, with an emphasis on the role of interchain interactions. Simple theoretical models are considered to study the following problems: the interplay of diffusion and macromolecular reaction in compatible and incompatible blends, the stabilizing effect of premade diblock copolymer on the system of minor phase particles in incompatible blends, the kinetics of transesterification in a homogeneous blend. The effect of diblock copolymer on the Ostwald ripening in a polymer blend is stated in more details; the possibility of narrowing the size distribution of minor phase particles is predicted.