Highly fluorescent crystalline and liquid crystalline columnar phases of pyrene-based structures

A concept for highly ordered solid-state structures with bright fluorescence is proposed: liquid crystals based on tetraethynylpyrene chromophores, where the rigid core is functionalized with flexible, promesogenic alkoxy chains. The synthesis of this novel material is presented. The thermotropic properties are studied by means of differential scanning calorimetry (DSC), cross-polarized optical microscopy (POM), and X-ray diffraction. The mesogen possesses an enantiotropic Col(h) phase over a large temperature range before clearing. The material is highly fluorescent in solution and, most remarkably, in the condensed state, with a broad, strongly red shifted emission. Fluorescence quantum yields (Phi(F)) have been determined to be 70% in dichloromethane solution and 62% in the solid state. Concentration- and temperature-dependent absorption and emission studies as well as quantum-chemical calculations on isolated molecules and dimers are used to clarify the type of intermolecular interactions present as well as their influence on the fluorescence quantum yield and spectral properties of the material. The high luminescence efficiency in the solid state is ascribed to rotated chromophores, leading to an optically allowed lowest optical transition.     

PAMAM dendrimers for efficient siRNA delivery and potent gene silencing

Genuine, nondegraded PAMAM dendrimers self-assemble with siRNA into nanoscale particles that are efficient for siRNA delivery and induce potent endogenous gene silencing.     

Vibrational spectra and structures of H2O-NO, HDO-NO, and D2O-NO complexes. An IR matrix isolation and DFT study

The IR spectra of H2O+NO, HDO+NO, and D2O+NO, isolated in solid neon at low temperature have been investigated. Concentration effects and detailed vibrational analysis of deuterated and partially deuterated species allowed identification of three 1:1 HDO-NO species, two 1:1 D2O-NO species, and only one 1:1 H2O-NO complex. From comparison between the experimental spectra and the results of DFT calculations, it appeared that two different types of weakly bound complexes between water and nitric oxide can be formed in a neon matrix. The first species is a 1:1 complex where bonding occurs between water hydrogen and nitric oxide nitrogen, in which OH-N and OD-N intermolecular bonds are engaged. For this complex only DOD-NO, HOD-NO, and DOH-NO isotopic species have been experimentally detected and no IR bands of HOH-NO were observed. This result could be explained by the fact that the dissociation energy of HOH-NO is lower than those of DOD-NO, HOD-NO and DOH-NO. For the second detected 1:1 H2O-NO complex and its isotopic variants, the H2O-NO potential surface was explored systematically at the B3LYP level, but no stable species corresponding to the complex could be calculated. The structure of the second observed 1:1 H2O-NO complex results from columbic attractions between water and nitric oxide and could be stabilized only in matrix, probably by interaction between NO, water and (Ne)n.     

Variational inequality formulation for the games with random payoffs

We consider an n-player non-cooperative game with random payoffs and continuous strategy set for each player. The random payoffs of each player are defined using a finite dimensional random vector. We formulate this problem as a chance-constrained game by defining the payoff function of each player using a chance constraint. We first consider the case where the continuous strategy set of each player does not depend on the strategies of other players. If a random vector defining the payoffs of each player follows a multivariate elliptically symmetric distribution, we show that there exists a Nash equilibrium. We characterize the set of Nash equilibria using the solution set of a variational inequality (VI) problem. Next, we consider the case where the continuous strategy set of each player is defined by a shared constraint set. In this case, we show that there exists a generalized Nash equilibrium for elliptically symmetric distributed payoffs. Under certain conditions, we characterize the set of a generalized Nash equilibria using the solution set of a VI problem. As an application, the random payoff games arising from electricity market are studied under chance-constrained game framework.     

On using the modified variational iteration method for solving the nonlinear coupled equations in the mathematical physics

This paper applied the modified variational iteration method to the nonlinear coupled partial differential equations via the generalized nonlinear Hirota Satsuma coupled KdV equations, the nonlinear coupled Kortewge–de Vries KdV equations and the nonlinear shallow water equations together with the initial conditions. The proposed modification is made by introducing Adomian’s polynomials in the correct functional. The suggested algorithm is quite efficient and is practically well suited for use in such problems. The proposed iterative scheme finds the solution without any discritization, liberalization, perturbation, or restrictive assumptions.     

A semi-oriented radial measure for measuring the efficiency of decision making units with negative data,using DEA

Data Envelopment Analysis (DEA) is a nonparametric method for measuring the efficiency of a set of decision making units such as firms or public sector agencies, first introduced into the operational research and management science literature by Charnes, Cooper, and Rhodes (CCR) [Charnes, A., Cooper, W.W., Rhodes, E., 1978. Measuring the efficiency of decision making units. European Journal of Operational Research 2, 429–444]. The original DEA models were applicable only to technologies characterized by positive inputs/outputs. In subsequent literature there have been various approaches to enable DEA to deal with negative data.     

Frequency polygons for continuous random fields

We study the frequency polygon investigated by Scott (J Am Stat Assoc 80: 348–354, 1985) as a nonparametric density estimate for a continuous and stationary real random field \({\left( X_{\mathbf{t}},\mathbf{t}\in\mathbb{R}^{N}\right)}\). We establish the asymptotic expressions for the integrated pointwise squared bias and the integrated pointwise squared variance of the estimate when the field is observed over a rectangular domain of \({\mathbb{R}^{N}}\). Under mild mixing conditions, we show that the estimate achieves the same rate of convergence to zero of the integrated mean squared error as kernel estimators and it can also attain the optimal uniform strong rate of convergence \({\left(\widehat{\mathbf{T}}^{-1} \log \widehat{\mathbf{T}}\right)^{1/3}}\) for appropriate choices of the bin widths.     

Isometric Equivalence of Integration Operators

We are interested in the isometric equivalence problem for the Cesàro operator C(f) (z) = \frac1z ò₀^zf(x) \frac11-xd x{C(f) (z) =\frac{1}{z} \int_{0}^{z}f(\xi) \frac{1}{1-\xi}d \xi} and an operator T_g(f)(z)=\frac1zò₀^zf(x) g^￠(x) d x{T_{g}(f)(z)=\frac{1}{z}\int_{0}^{z}f(\xi) g^{\prime}(\xi) d \xi}, where g is an analytic function on the disc, on the Hardy and Bergman spaces. Then we generalize this to the isometric equivalence problem of two operators T_g1{T_{g_{1}}} and T_g2{T_{g_{2}}} on the Hardy space and Bergman space. We show that the operators T_g1{T_{g_{1}}} and T_g2{T_{g_{2}}} satisfy T_g1U₁=U₂T_g2{T_{g_{1}}U_{1}=U_{2}T_{g_{2}}} on H ^p , 1 ≤ p < ∞, p ≠ 2 if and only if g₂(z) = lg₁(e^iqz){g_{2}(z) =\lambda g_{1}(e^{i\theta}z) }, where λ is a modulus one constant and U _i , i = 1, 2 are surjective isometries of the Hardy Space. This is analogous to the Campbell-Wright result on isometrically equivalence of composition operators on the Hardy space.     

Bounded-degree polyhedronization of point sets

In 1994 Grünbaum showed that, given a point set S in ${\mathbb{R}}^3$, it is always possible to construct a polyhedron whose vertices are exactly S. Such a polyhedron is called a polyhedronization of S. Agarwal et al. extended this work in 2008 by showing that there always exists a polyhedronization that can be decomposed into a union of tetrahedra (tetrahedralizable). In the same work they introduced the notion of a serpentine polyhedronization for which the dual of its tetrahedralization is a chain. In this work we present a randomized algorithm running in $O(n{\log }^{6}n)$ expected time which constructs a serpentine polyhedronization that has vertices with degree at most 7, answering an open question by Agarwal et al.