Functional Monomers and Polymers. 145. Synthetic Application Based on the Tautomerism of Polymer-Bound Purine and Pyrimidine Bases

Polymer-bound alkylthiopurine and -pyrimidine bases were prepared and used as the polymeric reagents for the reactions of nitrile, olefin, and enone formation. The corresponding low molecular weight compounds were also prepared for comparison. Differences in the reactivity of these reagents were related to the change in tautomerism of the purine and pyrimidine moieties.     

Synthesis,characterization, photo‐induced alignment,and surface orientation of poly(9,9‐dioctylfluorene‐alt‐azobenzene)s

Three types of bi‐functionalized copolymers ( P1FAz , P2FAz , and P3FAz ) with different numbers of fluorene units and an azobenzene unit were synthesized and characterized using UV–vis and polarized absorption spectroanalysis. The trans‐cis photoisomerization was conformed under 400 nm light irradiation for all copolymers in chloroform. However, in the film state, only the trans‐cis photoisomerization occurred by mono‐fluorene attached copolymer poly[(9,9‐di‐n‐octylfluorenyl‐2,7‐diyl)‐alt‐4,4′‐azobenzene)] ( P1FAz ). Photo‐induced alignment was achieved using the P1FAz film after irradiation with linear polarized 400 nm light and subsequent annealing at 60 °C. Surface orientation of a spin‐coating film of poly(9,9‐didodecylfluorene) ( F12 ) was achieved using the photo‐induced alignment layer of the P1FAz film after annealing at 90 °C. The photo‐induced alignment layer of P1FAz has potential application to the surface orientation technique for appropriate polymers, which will be useful for the fabrication of optoelectronics devices. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Solitons and Fractal Kerr Response

Optical solitary waves that propagate in a Kerr medium exhibiting a power-law nonlocal response are studied analytically. The first-principles stability analysis based on quantum field theory shows that within the whole range of the exponent (the fractal dimension) the solitary wave can be stabilized.     

Design and modeling of microwave photonic devices

Different types of finite element methods (FEMs) for microwave and optical waveguides are reviewed and are utilized for modeling of a traveling-wave (TW) optical modulator, as one of the typical microwave photonic devices. Using the quasi-TEM and the full-wave vector FEM solvers for microwave waveguides and the scalar FEM solver for optical waveguides, the behaviour of a TW Z-cut Ti:LiNbO3 Mach–Zehnder optical modulator with a ridge structure is investigated.     

Applicability of classical optical fiber theories to holey fibers

We discuss the applicability of well-established classical optical fiber theories to holey fibers. By appropriately defining the V parameter, we can easily estimate the fundamental properties of holey fibers, such as effective index, group-velocity dispersion, mode field diameter, beam divergence, and splice loss, through simple empirical expressions without the need for heavy numerical computations. We confirm the validity of the V parameter defined here by comparing the calculated results with the earlier experimental and numerical results.     

Algebraically Decaying Modes in Many Dimensions: Application of Fubini’s Identity to Guided-Wave Optics

We show analytically that application of an identity in conformal invariant field theories to multidimensional guided-wave optics predicts a generic family of modes with algebraic (power-law) tails in the evanescent field.     

Low-density attack revisited

The low-density attack proposed by Lagarias and Odlyzko is a powerful algorithm against the subset sum problem. The improvement algorithm due to Coster et al. would solve almost all the problems of density <0.9408... in the asymptotical sense. On the other hand, the subset sum problem itself is known as an NP-hard problem, and a lot of efforts have been paid to establish public-key cryptosystems based on the problem. In these cryptosystems, densities of the subset sum problems should be higher than 0.9408... in order to avoid the low-density attack. For example, the Chor-Rivest cryptosystem adopted subset sum problems with relatively high densities. In this paper, we further improve the low-density attack by incorporating an idea that integral lattice points can be covered with polynomially many spheres of shorter radius and of lower dimension. As a result, the success probability of our attack can be higher than that of Coster et al.’s attack for fixed dimensions. The density bound is also improved for fixed dimensions. Moreover, we numerically show that our improved low-density attack makes the success probability higher in case of low Hamming weight solution, such as the Chor-Rivest cryptosystem, if we assume SVP oracle calls.      

Stability of Multidimensional Solitary Waves for Cubic-Quintic Nonlinearity

We show analytically that in the presence of cubic and quintic nonlinearities above a certain critical power, multidimensional optical solitary waves could propagate stably in bulk media. To investigate the stability an analytical expression for the solitary-wave fields with an arbitrary transverse dimension is derived through the combined use of Galerkin’s method and self-consistent-field approximation.