Luminescence of yttrium–aluminum garnet crystals with Eu<Superscript>2+</Superscript> impurity ions

Luminescence of yttrium-aluminum garnet Y₃Al₅O₁₂: Eu,Si samples is studied. It is found that luminescence is associated with Eu²⁺ ions, but does not correspond to intracenter 4f ⁶5d ¹–4f ⁷ transitions. Measurements of the excited state lifetime point to the luminescence mechanism involving charge-transfer states.     

Polynomial mixing for the complex Ginzburg–Landau equation perturbed by a random force at random times

In this paper we study the problem of ergodicity for the complex Ginzburg–Landau (CGL) equation perturbed by an unbounded random kick-force. Randomness is introduced both through the kicks and through the times between the kicks. We show that the Markov process associated with the equation in question possesses a unique stationary distribution and satisfies a property of polynomial mixing.      

On a new property of <Emphasis Type="Italic">n</Emphasis>-poised and <Emphasis Type="Italic">G</Emphasis><Emphasis Type="Italic">C</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> sets

In this paper we consider n-poised planar node sets, as well as more special ones, called G C _n sets. For the latter sets each n-fundamental polynomial is a product of n linear factors as it always holds in the univariate case. A line ? is called k-node line for a node set \(\mathcal X\) if it passes through exactly k nodes. An (n + 1)-node line is called maximal line. In 1982 M. Gasca and J. I. Maeztu conjectured that every G C _n set possesses necessarily a maximal line. Till now the conjecture is confirmed to be true for n ≤ 5. It is well-known that any maximal line M of \(\mathcal X\) is used by each node in \(\mathcal X\setminus M, \)meaning that it is a factor of the fundamental polynomial. In this paper we prove, in particular, that if the Gasca-Maeztu conjecture is true then any n-node line of G C _n set \(\mathcal {X}\) is used either by exactly \(\binom {n}{2}\) nodes or by exactly \(\binom {n-1}{2}\) nodes. We prove also similar statements concerning n-node or (n ? 1)-node lines in more general n-poised sets. This is a new phenomenon in n-poised and G C _n sets. At the end we present a conjecture concerning any k-node line.     

Functional equations and their related operads

Using functional equations, we define functors that generalize standard examples from calculus of one variable. Examples of such functors are discussed, and their Taylor towers are computed. We also show that these functors factor through objects enriched over the homology of little -cubes operads and discuss the relationship between functors defined via functional equations and operads. In addition, we compute the differentials of the forgetful functor from the category of -Poisson algebras in terms of the homology of configuration spaces.

     

Growth of profiled single crystals of lithium iodate using a shaper from polymer nanoparticles

A possibility of growth of profiled single crystals of α-LiIO₃ with a hollow channel using a shaper from polymer nanoparticles is showed. A method of creating the nanoparticles of polystyrene is described.     

Wideband EPR Spectroscopy of Mo3+ Ions in Yttrium–Aluminum Garnet

Physics of the Solid State - The crystals of yttrium–aluminum garnet with an admixture of iron and cerium have been studied by the method of wideband EPR spectroscopy. Resonance absorption of...     

Semi-global weak stabilization of bilinear Schrödinger equations

We consider a linear Schrödinger equation, on a bounded domain, with bilinear control, representing a quantum particle in an electric field (the control). Recently, Nersesyan proposed explicit feedback laws and proved the existence of a sequence of times ${(t_n)}_{n\in \mathbb{N}}$ for which the values of the solution of the closed loop system converge weakly in $H^2$ to the ground state. Here, we prove the convergence of the whole solution, as $t\to +\infty$. The proof relies on control Lyapunov functions and an adaptation of the LaSalle invariance principle to PDEs.     

Experimental constraints on polarizability corrections to hydrogen hyperfine structure

We present a state-of-the-art evaluation of the polarizability corrections--the inelastic nucleon corrections--to the hydrogen ground-state hyperfine splitting using analytic fits to the most recent data. We find a value Delta(pol)=1.3+/-0.3 ppm. This is 1-2 ppm smaller than the value of Delta(pol) deduced using hyperfine splitting data and elastic nucleon corrections obtained from modern form factor fits.     

Nonlinear optical activity and spectroscopy of L-nitrohistidine monohydrate

Comparative investigation of vibrational (IR and Raman) and NMR spectra of L-nitrohistidine monohydrate (L-NH·H₂O) and L-histidine (L-His) has been performed with allowance for structural data. Nonlinear-optical activity and the range of transparency of L-NH·H₂O are determined. Influence of nitrogroup on structural, spectral, and nonlinear-optical properties is emphasized.