Optical limiters and diffraction elements based on a COANP-fullerene system: Nonlinear optical properties and quantum-chemical simulation

The results of optical study and quantum-chemical simulation of a conjugated organic system, 2-cyclooctylamino-5-nitropyridine (COANP)-fullerene, performed to determine its potential for application as a limiter of visible and near-IR laser radiation and as a material for diffraction elements in systems for reversible recording of optical information, are presented. Complexation between a COANP molecule and fullerene is considered as one of the main mechanisms responsible for the corresponding properties of this system. For the first time, nonlinear optical characteristics of COANP-C₆₀ and COANP-C₇₀ systems are comparatively studied and the intermolecular interaction between a COANP molecule and fullerene is analyzed on the quantum-chemical level.     

Recording dynamic holograms in a semiconductor crystal CdF<Subscript>2</Subscript>:In

The kinetics of decay of a phase hologram in a semiconductor CdF₂ crystal with bistable In centers is studied. Kinetic constants of the hologram decay are found, and the potential relief of the bistable center is plotted. The resolving power of the crystal is evaluated and recording of a transparency is demonstrated.     

Effect of maltodextrins on the surface activity of small-molecule surfactants

We report on the effect of commercially important polysaccharides (maltodextrins with variable dextrose equivalent (Paselli SA-2, MD-6 and MD-10) on the surface activity at the air–water interface of small-molecule surfactants (sms), possessing different hydrophobic–lipophilic balance ((SSL (Na⁺), the main component is a sodium salt of stearol–lactoyl lactic acid, and PGE (080), polyglycerol ester of C18 fatty acid), and widely used in food products. A marked change of the surface activity of sms was found in the presence of maltodextrins by tensiometry. The combined data of laser multiangle light scattering and mixing calorimetry have suggested that this result is governed by specific complex formation between maltodextrins and sms in aqueous medium. Measurements have been made of the molar mass, the second virial coefficient and the enthalpy of intermolecular interactions in aqueous solutions. The implication of a degree of polymerization of maltodextrins in this phenomenon was shown. The interrelation between the molecular parameters of the formed complexes and their surface activity at the air–water interface has been revealed and discussed.     

L2 -cohomology of manifolds with flat ends

Geometric and Functional Analysis - We give a topological interpretation of the spaces of L2 -harmonic forms on manifolds with flat ends. We also prove a Chern-Gauss-Bonnet formula for the L2...     

Integral Newton-Type Polynomials with Continual Nodes

We construct an integral Newton-type interpolation polynomial with a continual set of nodes. This interpolant is unique and preserves an operator polynomial of the corresponding degree.     

Crack path instabilities in DCDC experiments in the low speed regime

We studied the low speed fracture regime (10⁻⁴-10⁻⁹ m s⁻¹) in different glassy materials (soda-lime glass, glass ceramics) with variable but controlled length scale of heterogeneity. The chosen mechanical system enabled us to work in pure mode I (tensile) and at a fixed load on double cleavage drilled compression specimen. The internal residual stresses of studied samples were carefully relaxed by appropriate thermal treatment. By means of optical and atomic force microscopy techniques fracture surfaces have been examined. We have shown for the first time that the crack front line underwent an out-of-plane oscillating behavior as a result of a reproducible sequence of instabilities. The wavelength of such a phenomenon is in the micrometer range and its amplitude in the nanometer range. These features were observed for different glassy materials providing that a typical length scale characterizing internal heterogeneities was lower than a threshold limit estimated to few nanometers. This effect is the first clear experimental evidence of crack path instabilities in the low speed regime in a uniaxial loading experiment. This phenomenon has been interpreted by referring to the stability criterion for a straight crack propagation as presented by Adda-Bedia et al. [Phys. Rev. Lett. 76 (1996) 1497].     

20-relative neighborhood graphs are hamiltonian

For any two points p and q in the Euclidean plane, define LUN_pq = { v | v ∈ R², d_pv < d_pq and d_qv < d_pq}, where d_uv is the Euclidean distance between two points u and v . Given a set of points V in the plane, let LUN_pq(V) = V ∩ LUN_pq. Toussaint defined the relative neighborhood graph of V, denoted by RNG(V) or simply RNG, to be the undirected graph with vertices V such that for each pair p,q ∈ V, (p,q) is an edge of RNG(V) if and only if LUN_pq (V) = ?. The relative neighborhood graph has several applications in pattern recognition that have been studied by Toussaint. We shall generalize the idea of RNG to define the k-relative neighborhood graph of V, denoted by kRNG(V) or simply kRNG, to be the undirected graph with vertices V such that for each pair p,q ∈ V, (p,q) is an edge of kRNG(V) if and only if | LUN_pq(V) | < k, for some fixed positive number k. It can be shown that the number of edges of a kRNG is less than O(kn). Also, a kRNG can be constructed in O(kn₂) time. Let E_c = {e_pq| p ∈ V and q ∈ V}. Then G_c = (V,E_c) is a complete graph. For any subset F of E_c, define the maximum distance of F as max_epq∈Fd_pq. A Euclidean bottleneck Hamiltonian cycle is a Hamiltonian cycle in graph G_c whose maximum distance is the minimum among all Hamiltonian cycles in graph G_c. We shall prove that there exists a Euclidean bottleneck Hamiltonian cycle which is a subgraph of 20RNG(V). Hence, 20RNGs are Hamiltonian.