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].     

Quasi 3D imaging of DNA-gold nanoparticle tetrahedral structures

Verification by imaging of the structure of 3D DNA constructs, both bare and conjugated to metal nanoparticles, is challenging. We demonstrate here two transmission electron microscopy (TEM) based methods to distinguish between fully formed tetrahedra, synthesized from DNA conjugated with gold nanoparticles (GNPs) at their vertices, and structures which are only partially formed. When deposited on a surface, fully formed tetrahedra are expected to retain their 3D pyramidal structure, while partially formed structures are expected to form a 2D structure. The first method by which 3D and 2D structures were distinguished was imaging them at different defocusing values. While for 2D structures all the four GNPs acquire Fresnel fringes at the same defocusing value, for 3D structures at least one particle is at a different plane with respect to the others, and so it acquires Fresnel fringes at a different defocusing value. The second method we show is imaging of the structures at different angles. While a single TEM image gives only a 2D projection of the structure, by combining information achieved from imaging at several tilting angles one may verify the structural construct.     

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     

Surface modification. I. Polyacrolein microspheres covalently bonded onto polyethylene

The synthesis and characterization of novel surfaces composed of polyacrolein microspheres covalently bonded onto polyethylene films are described. These surfaces were prepared through a sequence of reactions carried out onto polyethylene films in order to form primary amine groups at the w position. Polyacrolein microspheres in water were then covalently bonded to these modified polyethylene surfaces. The binding between the microspheres and the modified surfaces is due to the interaction between the aldehyde groups of the microspheres and the amine groups of the modified surfaces to form the polyvalent Schiff base bonds. Fourier transform-infrared/attenuated total reflection, electron spectroscopy for chemical analysis, contact angle measurements, and scanning electron microscopy have been used for the characterization of the modified polyethylene surfaces.     

Uniform limit theorems for Harris recurrent Markov chains

Summary We study uniform limit theorems for regenerative processes and get strong law of large numbers and central limit theorem of this type. Then we apply those results to Harris recurrent Markov chains based on some ideas of K. Athreya, P. Ney and E. Nummelin.     

Few nucleon transfer versus fragmentation in the production of projectile-like fragments in the40Ar+68Zn reaction at 27.6 MeV/nucleon

The isotope distributions, momentum width distributions, and velocities of the projectile-like fragments in the⁴⁰Ar on⁶⁸Zn reaction have been measured at 27.6 MeV/nucleon incident energy. The results show the existence of a fragmentation process well described in the framework of the high energy fragmentation model. However, important contributions from direct nucleon transfer and damped collisions are present.