Comparative study of liquid-crystalline ordering in a monomer,linear polymer,and graft copolymer by the photon transmission technique

The photon transmission technique was used to study the phase transitions of a liquid crystalline acrylate monomer, 6-(4-cyanobiphenyl-4′oxy)hexyl acrylate (LC6), its homopolymer (PLC6) and its graft copolymer (GLC6) with polytetrahydrofuran grafts. The phase transitions were also confirmed by DSC and polarizing microscopy. We observed the phase transition sequence isotropic–nematic–smectic A–smectic C in the LC6 monomer. In PLC6 and GLC6 polymers, the nematic and smectic A phases appear dominant. The apparent nematic–smectic A transition is of first order in PLC6 and of second order in GLC6, with the transition temperature remaining the same. The effects of quenched random constraints introduced in GLC6 are consistent with the theory of quenched random interactions. The critical exponents were also evaluated.     

Twenty-third MAX-lab User Meeting

The 23^rd Annual User Meeting for MAX-lab users was held at Scandic Star Hotel in Lund, Sweden, on November 8-10, 2010. The meeting was, as in previous years, jointly organized by MAX-lab and the MAX-lab Association for Synchrotron Radiation Users (FASM). From the start in the late 1980s these meetings have grown with the user community of MAX-lab, and with increasing interest in the development of MAX IV, the coming synchrotron radiation facility in Sweden (http://www.maxlab.lu.se/maxlab/max4/index.html.), this growth has accelerated. The last four meetings have hosted around 300 participants, with a new record number of 342 registered participants and 26 commercial exhibitors at this meeting!     

Critical Exponents of Kappa Carrageenan in the Coil-Helix and Helix-Coil Hysteresis Loops

The steady-state fluorescence technique was used to study coil-helix (sol-gel) and helix-coil (gel-sol) transitions of the kappa carrageenan-water system with various carrageenan contents. Fluorescence (I) and scattered light (I_sc ) intensities were measured against temperature to determine critical phase transition temperatures and exponents. It was observed that the coil-helix transition temperatures, T_ch were much lower than the helix-coil (T_hc ) transition temperatures due to the hysteresis of the phase transition loops. The gel fraction exponent (β) was measured and found to be in accord with the classical Flory-Stockmayer model.     

Establishing strong connectivity using optimal radius half-disk antennas

Given a set S of points in the plane representing wireless devices, each point equipped with a directional antenna of radius r and aperture angle $\alpha ?180\mathrm{°}$, our goal is to find orientations and a minimum r for these antennas such that the induced communication graph is strongly connected. We show that $r=\sqrt{3}$ if $\alpha \in [180\mathrm{°},240\mathrm{°})$, $r=\sqrt{2}$ if $\alpha \in [240\mathrm{°},270\mathrm{°})$, $r=2\sin (36\mathrm{°})$ if $\alpha \in [270\mathrm{°},288\mathrm{°})$, and $r=1$ if $\alpha ?288\mathrm{°}$ suffices to establish strong connectivity, assuming that the longest edge in the Euclidean minimum spanning tree of S is 1. These results are worst-case optimal and match the lower bounds presented in [I. Caragiannis, C. Kaklamanis, E. Kranakis, D. Krizanc, A. Wiese, Communication in wireless networks with directional antennae, in: Proc. of the 20th Symp. on Parallelism in Algorithms and Architectures, 2008, pp. 344–351]. In contrast, $r=2$ is sometimes necessary when $\alpha <180\mathrm{°}$.     

Analysis and improvement of a novel image fusion encryption algorithm based on DNA sequence operation and hyper-chaotic system

Recently, a novel image encryption algorithm based on DNA operation and hyper-chaotic system has been proposed by Zhang et al. The encryption algorithm first shuffles the image pixels using Chen chaotic system. After shuffling process, the proposed encryption algorithm changes the gray levels of the image pixels using DNA operation. In this study, we give out complete break for the proposed cryptosystem using a chosen plaintext attack. Both mathematical proofs and experimental results are presented to support the proposed attacks. Main motivation behind this study was to analyze whether proposed image encryption algorithm is suitable for secure communication or not. Based on the results of our analysis, we also discussed the potential improvements for the algorithm and proposed a modified new encryption algorithm accordingly. Essential elements of designing secure image encryption algorithms and potential application areas are also stated.     

Local well-posedness of the higher-order nonlinear Schrödinger equation on the half-line: Single-boundary condition case

We establish local well-posedness in the sense of Hadamard for a certain third-order nonlinear Schrödinger equation with a multiterm linear part and a general power nonlinearity, known as higher-order nonlinear Schrödinger equation, formulated on the half-line $\{x>0\}$. We consider the scenario of associated coefficients such that only one boundary condition is required and hence assume a general nonhomogeneous boundary datum of Dirichlet type at $x=0$. Our functional framework centers around fractional Sobolev spaces $H_x^s({\mathbb{R}}_{+})$ with respect to the spatial variable. We treat both high regularity ( $s>\frac{1}{2}$) and low regularity ( ) solutions: in the former setting, the relevant nonlinearity can be handled via the Banach algebra property; in the latter setting, however, this is no longer the case and, instead, delicate Strichartz estimates must be established. This task is especially challenging in the framework of nonhomogeneous initial-boundary value problems, as it involves proving boundary-type Strichartz estimates that are not common in the study of Cauchy (initial value) problems. The linear analysis, which forms the core of this work, crucially relies on a weak solution formulation defined through the novel solution formulae obtained via the Fokas method (also known as the unified transform) for the associated forced linear problem. In this connection, we note that the higher-order Schrödinger equation comes with an increased level of difficulty due to the presence of more than one spatial derivatives in the linear part of the equation. This feature manifests itself via several complications throughout the analysis, including (i) analyticity issues related to complex square roots, which require careful treatment of branch cuts and deformations of integration contours; (ii) singularities that emerge upon changes of variables in the Fourier analysis arguments; and (iii) complicated oscillatory kernels in the weak solution formula for the linear initial-boundary value problem, which require a subtle analysis of the dispersion in terms of the regularity of the boundary data. The present work provides a first, complete treatment via the Fokas method of a nonhomogeneous initial-boundary value problem for a partial differential equation associated with a multiterm linear differential operator.     

On multiplicative and Volterra minimization methods

Theory and applications of multiplicative and Volterra calculi have been evolving rapidly over the recent years. As numerical minimization methods have a wide range of applications in science and engineering, the idea of the design of minimization methods based on multiplicative and Volterra calculi is self-evident. In this paper, the well-known Newton minimization method for one and two variables is developed in the frameworks of multiplicative and Volterra calculi. The efficiency of these proposed minimization methods is exposed by examples, and the results are compared with the original minimization method. One of the striking results of the proposed method is that the rate of convergence and the range of initial values are considerably larger compared to the original method.     

Generalized limits and sequence of matrices

Positivity - Banach has proved that there exist positive linear regular functionals on m such that they are invariant under shift operator where m is the space of all bounded real sequences. It has...     

Characterization of essential oil from Matricaria sevanensis by microwave-assisted distillation

Journal of Thermal Analysis and Calorimetry - Matricaria sevanensis is a widespread plant species grown in Central Anatolian and helps to prevent sleep disorders, influenza and stomach upsets when...