Synthesis and thermal behaviour of salicylaldimine-based liquid crystalline symmetrical dimers

A series of symmetrical dimers consisting of salicylaldimine moieties connected by flexible alkylene central spacer via ether linkages has been synthesized. In order to validate the empirical rule suggested by Date et al. to account for the smectic behaviour of such dimers, the chain length of the terminal alkoxy chain has been kept constant (C₈) while the number of methylene units in the central spacer was varied from C₃ to C₁₁. Another aim of the present investigation was to understand structure-property relationship in these dimers in which the salicylaldimine mesogenic segment has been used for the first time in dimers. The mesomorphic behaviour of these dimers was evaluated using optical microscopy and differential scanning calorimetry and the structure of some of the mesophases has been further investigated with the help of X-ray diffraction. Our studies reveal that the dimers consisting of 3 to 8 methylene units in the flexible spacer show only smectic (smectic C and smectic A) phases. For the dimers containing 4, 6 and 8 methylene units in the central spacer, a unique filament growth pattern has been observed in the smectic A phase while cooling from the isotropic phase. The dimers containing of C₉ to C₁₁ methylene groups exhibit the nematic phase in addition to smectic modifications. This observation indicates that when the terminal chains are shorter than the spacer, the tendency to form smectic phases is not fully extinguished but is perhaps reduced.     

Highly efficient lens couplers for laser-diodes based on long period grating in special graded-index fiber

A theoretical scheme of a new device consisting of a lensed fiber and a long period grating (LPG) imprinted in a special single mode gradient-index fiber (SSMGIF) is presented. The SSMGIF consists of the single mode uniform core and the graded-index cladding. The performance of the proposed device is based on specific properties of SSMGIF. For high efficiency coupling between number of cladding modes and co-propagating core mode in this special type of the fiber we can use a number of weak LPGs with the same amplitudes of the refractive index modulation and with almost the same lengths. This scheme provides higher coupling efficiency, relaxed longitudinal alignment tolerance, and smaller device size, than an identical scheme with the LPG imprinted in a step-index (SI) fiber. Two different types of fiber lenses (hemispherical and hyperbolic) are presented for comparison.     

Inequivalent quantizations for non-linear σ model

We compute the homotopy groups ₀ and ₁ of the classical configuration space of anO(3) invariant field theory on ×, where is a compact two dimensional manifold for arbitrary genusg and- denotes the time coordinate. We also present the finite dimensional, unitary, irreducible, inequivalent representations of the appropriate fundamental groups and comment on some of their implications.     

Painlevé analysis,conservation laws,and symmetry of perturbed nonlinear equations

We consider the Lie-Backlund symmetries and conservation laws of a perturbed KdV equation and NLS equation. The arbitrary coefficients of the perturbing terms can be related to the condition of existence of nontrivial LB symmetry generator. When the perturbed KdV equation is subjected to Painlevé analysisa la Weiss, it is found that the resonance position changes compared to the unperturbed one. We prove the compatibility of the overdetermined set of equations obtained at the different stages of recursion relations, at least for one branch. All other branches are also indicated and difficulties associated them are discussed considering the perturbation parameter to be small. We determine the Lax pair for the aforesaid branch through the use of Schwarzian derivative. For the perturbed NLS equation we determine the conservation laws following the approach of Chen and Liu. From the recurrence of these conservation laws a Lax pair is constructed. But the Painlevé analysis does not produce a positive answer for the perturbed NLS equation. So here we have two contrasting examples of perturbed nonlinear equations: one passes the Painlevé test and its Lax pair can be found from the analysis itself, but the other equation does not meet the criterion of the Painlevé test, though its Lax pair is found in another way.     

Site-specific cleavage of human telomerase RNA using PNA-neocuproine.Zn(II) derivatives

Here we report the synthesis of a novel PNA based neocuproine.Zn RNA cleaving agent; we demonstrate that such agents sequence specifically cleave a synthetic RNA target and in particular the RNA component of human telomerase.