Temperature dependence features of the photoluminescence spectral distribution of Li2B4O7 and Li2B4O7:Cu

The temperature dependence of the photoluminescence (PhL) spectral distributions has been reported for the lithium tetraborate Li₂B₄O₇ (LTB) and Li₂B₄O₇:Cu (LTB:Cu) single crystals and for glassy LTB:Cu. It was found that the emission peaks of the LTB and LTB:Cu single crystals are non-elementary and splittable by temperature increase into several elementary peaks. By the sample heating the temperature quenching of PhL as well as the redistribution of the PhL intensity among elementary peaks was observed. Heating of the LTB:Cu single crystal samples caused no shift of the spectral maxima of the individual PhL peaks. The curve describing the temperature dependency of individual PhL peaks for the LTB:Cu single crystal is characterized by maxima resulting from combination of PhL and thermostimulated luminescence (TSL). The PhL intensity for glassy LTB:Cu is significantly lower than that for LTB:Cu single crystal with the equivalent copper dopant content. As compared to the LTB:Cu single crystal, the PhL spectral maximum for glassy LTB:Cu is wider and shifted to the lower energy range. Heating of the glassy LTB:Cu sample results in the PhL temperature quenching without any shift of the spectral maximum.     

Algebraic Method for Group Classification of (1+1)-Dimensional Linear Schrödinger Equations

In the present paper, we study the existence of solutions for some nonlocal problems involving the \(p(x)\)-Laplacian operator. The approach is based on a new sub-supersolution method.     

Effective desynchronization by nonlinear delayed feedback

We show that nonlinear delayed feedback opens up novel means for the control of synchronization. In particular, we propose a demand-controlled method for powerful desynchronization, which does not require any time-consuming calibration. Our technique distinguishes itself by its robustness against variations of system parameters, even in strongly coupled ensembles of oscillators. We suggest our method for mild and effective deep brain stimulation in neurological diseases characterized by pathological cerebral synchronization.     

Elements of high order in finite fields of the form Fq[x]/Φr(x)

We obtain explicit lower bounds on multiplicative orders of finite field elements that have more general form than Gauss periods of a special type. This bound improves in a partial case of Gauss period the previous bound of Ahmadi, Shparlinski and Voloch (2010) [2].     

Multi-dimensional quasi-simple waves in weakly dissipative flows

A multi-dimensional simple wave formalism is employed to formulate a multi-dimensional quasi-simple wave for a weakly dissipative fluid. This is a natural but nontrivial generalization of the so-called unidirectional quasi-simple wave. The method is more close to multi-orders analysis which is different from the standard perturbation method. Detailed solving up to the second order is presented for a 2D sound simple wave. A new 2D Burgers equation is derived for the wave phase. It essentially differs from the known 2D generalizations of the Burgers equation, e.g., from the Zabolotskaya-Khokhlov equation. The derived equation is investigated in the framework of group analysis of differential equations. Multi-parameter families of its exact solutions are constructed. Simplest solutions are chosen for analysis of their physical relevance in the initial variables.     

Symmetry Analysis of Barotropic Potential Vorticity Equation

Recently F. Huang [Commun. Theor. Phys. 42 (2004) 903] and X. Tang and P.K. Shukla [Commun. Theor. Phys. 49 (2008) 229] investigated symmetry properties of the barotropic potential vorticity equation without forcing anddissipation on the beta-plane. This equation is governed by two dimensionless parameters, F and β, representing the ratio of the characteristic length scale to the Rossby radius of deformation and the variation of earth' angular rotation, respectively. In the present paper it is shown that in the case F≠ 0 there exists a well-defined point transformation to set β= 0. Theclassification of one- and two-dimensional Lie subalgebras of the Lie symmetry algebra of the potential vorticity equation is given for the parameter combination F≠0 and β = 0. Based upon this classification, distinct classes of group-invariant solutions are obtained and extended to the case β≠ 0.