Liquid Crystalline Phases in 4-Acetyl-4′-n-Alkanoyloxy-Azobenzenes

Abstract

The preparation and melting behaviour of the homologous series of 4-acetyl-4′-n-alkanoylox-azobenzenes, CH₃-CO-C₆H₄-N?N-C₆H₄-O-CO-(CH₂) _n -CH₃, (with n ranging from zero to 16) is reported. The melting behaviour has been investigated by means of thermal microscopy and differential scanning calorimetry. The experimental results indicate for almost all the compounds the presence of solid state polymorphism and a type A smectic; for one compound a type B smectic phase is also present. Some homologs present, in addition, a nematic phase.     

Reflecting diffusions and hyperbolic Brownian motions in multidimensional spheres

We consider diffusion processes $ {{\left( {{{{\underline{\mathrm{X}}}}_d}(t)} \right)}_{{t\geqslant 0}}} $ moving inside spheres $ S_R^d $ ? ? ^d and reflecting orthogonally on their surfaces. We present stochastic differential equations governing the reflecting diffusions and explicitly derive their kernels and distributions. Reflection is obtained by means of the inversion with respect to the sphere $ S_R^d $ . The particular cases of Ornstein–Uhlenbeck process and Brownian motion are examined in detail. The hyperbolic Brownian motion on the Poincaré half-space ? _d is examined in the last part of the paper, and its reflecting counterpart within hyperbolic spheres is studied. Finally, a section is devoted to reflecting hyperbolic Brownian motion in the Poincaré disc D within spheres concentric with D.     

A simple and efficient approach to the synthesis of β-N-methylamino-l-alanine (BMAA)

A novel, efficient, and straightforward synthesis of β-N-methylamino-l-alanine (BMAA) in two steps starting from l-N,N-dibenzylserine benzyl ester is described. This method, in the light of other syntheses of BMAA, provides benefits such as mild reaction conditions, a simple work-up procedure, good yields, and the retention of the serine stereochemistry.     

Highly shifted LIPOCEST agents based on the encapsulation of neutral polynuclear paramagnetic shift reagents

Improved LIPOCEST MRI contrast agents with highly shifted intraliposomal water protons were prepared by entrapping neutral polynuclear Tm(III)-based paramagnetic shift reagents in phospholipidic vesicles.     

Representation Formulae for Solutions to Some Classes of Higher Order Systems and Related Liouville Theorems

Let m ≥ 1 be an integer and N > 2m. Let μ be a positive Radon measure on . We study necessary and sufficient conditions on possible distributional solutions of , that guarantee the validity of the representation formula a.e. on , where and c(2m) is a positive constant depending on m and N. Several consequences are derived. In particular we prove Liouville theorems for systems of higher order elliptic inequalities and weighted form of Hardy-Littlewood-Sobolev systems of integral equations. Received: March 2008     

Development of a CZE method for the determination of mizolastine and its impurities in pharmaceutical preparations using response surface methodology

A fast and selective CZE method for the determination of mizolastine and related impurities is described. Response surface methodology was applied to study the influence of phosphate/triethanolamine (TEA) buffer concentration, heptakis(2,3,6-tri-O-methyl)-beta-CD (TMbetaCD) concentration, voltage and temperature. The optimum conditions were: 105 mM phosphate/TEA buffer (pH 3.0) containing 10 mM TMbetaCD, temperature 19 degrees C and voltage 30 kV. Validation of the method was performed in drug substance and drug product. Robustness was evaluated using a Plackett-Burman design, including pH among the considered factors. Applying the optimal conditions, the nine peaks were baseline separated in about 10 min. The method was applied to the quality control of mizolastine in controlled-release tablets.     

Monitoring the traceability of the pH of a primary tetraborate buffer: comparison of results from primary and secondary apparatus

This paper reports evaluation of the behaviour of different combined glass electrodes applied to measurement of the pH of a primary, 0.01 mol kg⁻¹, tetraborate buffer. Measurements were first performed by use of a primary Harned cell (at 15, 25, and 37 °C); these results were then compared with those obtained for the same solution by use of three combined glass electrodes (25 °C) with different membranes and liquid-junction designs, calibrated by use of commercial pH-metric buffers. The pH of the same solution was also measured in terms of the molal concentration of hydrogen ions, using acid–base titration to evaluate the formal potential difference K of each cell at fixed ionic strength, I, adjusted by addition of KCl or Et₄NI (tetraethylammonium iodide). The reference value from primary measurement, paH = 9.171, was slightly closer to the mean value obtained by determination of concentration, rather than that obtained by direct measurement of activity; the differences were smaller than the extended uncertainty characteristics of the secondary measurements. The importance of evaluation of the ionic strength of the solution under study is emphasised. We verified that for tetraborate buffer slight modification of the value of I used to calculate γ _i (the activity coefficient of a single ion) in the calculation of paH from the acidity function at zero molality of chloride can significantly affect the reference value of the calibrator tool. This is true, in general, for low values of the ionic strength, such as those considered in this work; an approximate value of I can then cause distortions along the pH traceability chain. Application of the concepts of thermodynamics to this traceability chain is discussed.     

A multifunctional nanoassembly of mesogen-bearing amphiphiles and porphyrins for the simultaneous photodelivery of nitric oxide and singlet oxygen

We report a molecular nanoassembly able to supply simultaneously, in the same region of space and under the exclusive control of visible light, nitric oxide and singlet oxygen, two species playing a key role in the therapy of cancer; the considerable fluorescence of this nanoaggregate and its reduced size (ca. 40 nm) represent additional advantages that make this photoactive vehicle an appealing candidate to be tested in biological systems.     

Global Nonexistence Theorems for a Class of Evolution Equations with Dissipation

We study abstract evolution equations with nonlinear damping terms and source terms, including as a particular case a nonlinear wave equation of the type $ \ba{cl} u_{tt}-\Delta u+ b|u_t|^{m-2}u_t=c|u|^{p-2}u, &;(t,x)\in [0,T)\times\Omega,\\[6pt] u(t,x)=0, &;(t,x)\in [0,T)\times\partial \Omega,\\[6pt] u(0,\cdot)=u_0\in H_0^1(\Omega), \quad u_t(0,\cdot)=v_0\in L^2(\Omega),\es&; \ea $ \ba{cl} u_{tt}-\Delta u+ b|u_t|^{m-2}u_t=c|u|^{p-2}u, &;(t,x)\in [0,T)\times\Omega,\\[6pt] u(t,x)=0, &;(t,x)\in [0,T)\times\partial \Omega,\\[6pt] u(0,\cdot)=u_0\in H_0^1(\Omega), \quad u_t(0,\cdot)=v_0\in L^2(\Omega),\es&; \ea where 0 < T ￡ ￥0\Omega is a bounded regular open subset of \mathbbRⁿ\mathbb{R}^n, n 3 1n\ge 1, b,c > 0b,c>0, p > 2p>2, m > 1m>1. We prove a global nonexistence theorem for positive initial value of the energy when 1 < m < p,    2 < p ￡ \frac2nn-2. 1-Laplacian operator, q > 1q>1.     

Iterated processes and their applications to higher order differential equations

In this paper we construct models obtained by suitably combining Brownian motions and telegraphs in such a way that their transition functions satisfy higher-order parabolic or hyperbolic equations of different types. Equations with time-varying coefficients are also derived by considering processes endowed either with drift or with suitable modifications of their structure. Finally the distribution of the maximum of the iterated Brownian motion (along with some other properties) is presented. This work is partially supported by the Natural Science Foundation of Guangdong Province, National Natural Science Foundation of China grant No. 19501026 and the Alexander von Humbodlt Foundation