Energy gaps in a spacetime crystal

This Letter presents an analysis of the band structure of a spacetime potential lattice created by a standing electromagnetic wave. We show that there are energy band gaps. We estimate the effect, and propose a measurement that could confirm the existence of such phenomena.     

Synthesis of copper nanoparticles catalyzed by pre-formed silver nanoparticles

Synthesis of well dispersed copper nanoparticles was achieved by reduction of copper nitrate in aqueous solution using hydrazine monohydrate as a reducer in the presence of preformed silver nanoparticles as catalysts. It has been demonstrated that addition of silver nanoparticles to the reaction mixture leads to formation of aqueous dispersion of copper nanoparticles and also results in a drastic reduction in reaction time compared to procedures reported in the literature. The absorption spectrum of the dispersions, HR-TEM and STEM images and XRD pattern indicate the formation of copper nanoparticles with particle size in the range of 5–50 nm.     

The small quantum group as a quantum double

We prove that the quantum double of the quasi-Hopf algebra of dimension attached in [P. Etingof, S. Gelaki, On radically graded finite-dimensional quasi-Hopf algebras, Mosc. Math. J. 5 (2) (2005) 371–378] to a simple complex Lie algebra and a primitive root of unity q of order n² is equivalent to Lusztig's small quantum group (under some conditions on n). We also give a conceptual construction of using the notion of de-equivariantization of tensor categories.     

Optimization of Fabry-Perot ring resonator embedding a grating based mirror

We study a triangular arrangement of two flat mirrors and a grating mirror for coupling a \(-1{\mathrm{st}}\) diffracted order light beam into a traveling-wave intra-cavity light recirculation and out-of-cavity output, combining the \(0\,{\mathrm{th}}\) and the repeatedly diffracted secondary \(+1{\mathrm{st}}\) order beams. The thus designed and then optimized grating Fabry-Perot ring cavity demonstrates high output contrast and detection resolution for wavelength, cavity length and incidence angle.     

On the {{\mathcal{N}}=2} Superconformal Index and Eigenfunctions of the Elliptic RS Model

We define an infinite sequence of superconformal indices, ${{\mathcal{I}}_n}$ , generalizing the Schur index for ${{\mathcal{N}}=2}$ theories. For theories of class ${{\mathcal{S}}}$ we then suggest a recursive technique to completely determine ${{\mathcal{I}}_n}$ . The information encoded in the sequence of indices is equivalent to the ${{\mathcal{N}}=2}$ superconformal index depending on a maximal set of fugacities. Mathematically, the procedure suggested in this note provides a perturbative algorithm for computing a set of eigenfunctions of the elliptic Ruijsenaars–Schneider model.     

Pyridine•BrF3, the missing link for clean fluorinations of aromatic derivatives

This work demonstrates the unique features of the never used before Py?BrF(3) complex in the field of aromatic organic fluorinations. The main disadvantage of the noncomplexed BrF(3) is the fact that usually, in addition to the desired fluorination, a parallel electrophilic aromatic bromination takes place as well. Use of the Py?BrF(3) complex reduces this electrophilic bromination, which is observed with most reagents based on fluorine and bromine [BrF].     

Doping silver nanoparticles in AOT lyotropic lamellar phases

The organic lyotropic liquid crystal with long-range structural order is used as template to assemble inorganic/organic hybrid by doping pre-fabricated Ag nanoparticles. The lamellar hybrid with both hydrophilic and hydrophobic particles doped simultaneously is realized for the first time. The change of template structure after doping and the stability origin of dual-doped system are characterized by small angle X-ray scattering and polarized optical microscopy. Results show that the interaction and space matching between surfactant bilayers and doped particles are key factors to obtain stable hybrid.     

A note on conjugate gradient convergence – Part III

Summary. In this paper we again consider the rate of convergence of the conjugate gradient method. We start with a general analysis of the conjugate gradient method for uniformly bounded solutions vectors and matrices whose eigenvalues are uniformly bounded and positive. We show that in such cases a fixed finite number of iterations of the method gives some fixed amount of improvement as the the size of the matrix tends to infinity. Then we specialize to the finite element (or finite difference) scheme for the problem . We show that for some classes of function we see this same effect. For other functions we show that the gain made by performing a fixed number of iterations of the method tends to zero as the size of the matrix tends to infinity. Received July 9, 1998 / Published online March 16, 2000