The Phase Transition in Statistical Models Defined on Farey Fractions

We consider several statistical models defined on the Farey fractions. Two of these models may be regarded as spin chains, with long-range interactions, while another arises in the study of multifractals associated with chaotic maps exhibiting intermittency. We prove that these models all have the same free energy. Their thermodynamic behavior is determined by the spectrum of the transfer operator (Ruelle–Perron–Frobenius operator), which is defined using the maps (presentation functions) generating the Farey tree. The spectrum of this operator was completely determined by Prellberg. It follows that these models have a second-order phase transition with a specific heat divergence of the form C [ ln² ]^–1. The spin chain models are also rigorously known to have a discontinuity in the magnetization at the phase transition.     

Calculation of Two-Center Nuclear Attraction Integrals over Integer and Noninteger n-Slater Type Orbitals in Nonlined-Up Coordinate Systems

Two-center nuclear attraction integrals over Slater type orbitals with integer and noninteger principal quantum numbers in nonlined up coordinate systems have been calculated by means of formulas in our previous work (T. Özdoan and M. Orbay, Int. J. Quant. Chem. 87 (2002) 15). The computer results for integer case are in best agreement with the prior literature. On the other hand, the results for noninteger case are not compared with the literature due to the scarcity of the literature, but also compared with the limit of integer case and good agreements are obtained. The proposed algorithm for the calculation of two-center nuclear attraction integrals over Slater type orbitals with noninteger principal quantum numbers in nonlined-up coordinate systems permits to avoid the interpolation procedure used to overcome the difficulty introduced by the presence of noninteger principal quantum numbers. Finally, numerical aspects of the presented formulae are analyzed under wide range of quantum numbers, orbital exponents and internuclear distances.     

Equivalence Groups for First-Order Balance Equations and Applications to Electromagnetism

We investigate the groups of equivalence transformations for first-order balance equations involving an arbitrary number of dependent and independent variables. We obtain the determining equations and find their explicit solutions. The approach to this problem is based on a geometric method that depends on Cartan's exterior differential forms. The general solutions of the determining equations for equivalence transformations for first-order systems are applied to a class of the Maxwell equations of electrodynamics.     

Improved Bounds for Ternary Linear Codes of Dimension 8 Using Tabu Search

In this paper, new codes of dimension 8 are presented which give improved bounds on the maximum possible minimum distance of ternary linear codes. These codes belong to the class of quasi-twisted (QT) codes, and have been constructed using a stochastic optimization algorithm, tabu search. Twenty three codes are given which improve or establish the bounds for ternary codes. In addition, a table of upper and lower bounds for d ₃(n, 8) is presented for n 200.     

On the embedding of some linear spaces in finite projective planes

The problem of embedding of linear spaces in finite projective planes has been examined by several authors ([1], [2], [3], [4], [5], [6]). In particular, it has been proved in [1] that a linear space which is the complement of a projective or affine subplane of order m is embeddable in a unique way in a projective plane of order n. In this article, we give a generalization of this result by embedding linear spaces in a finite projective plane of order n, which are complements of certain regularA-affine linear spaces with respect to a finite projective plane.     

Structure–reactivity relationships of alkyl α‐hydroxymethacrylate derivatives

A series of alkyl α‐hydroxymethacrylate derivatives with various secondary functionalities (ether, ester, carbonate, and carbamate) and terminal groups (alkyl, cyano, oxetane, cyclic carbonate, phenyl and morpholine) were synthesized to investigate the effect of intermolecular interactions, H‐bonding, π–π interactions, and dipole moment on monomer reactivity. All of the monomers except one ester and one ether derivative are novel. The polymerization rates, determined by using photo‐DSC, showed the average trend (aromatic carbamate > hydroxyl > ester > carbonate ～ aliphatic carbamate ～ ether), with several exceptions due to the differences in terminal groups. There is a correlation between the chemical shift differences of the double bond carbons, the calculated dipole moments, and the reactivities only for nonhydrogen bonded monomers. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Soluble alkyl substituted poly(3,4‐propylenedioxyselenophene)s: A new platform for optoelectronic materials

Optical and electrochemical properties of regiosymmetric and soluble alkylenedioxyselenophene‐based electrochromic polymers, namely poly(3,3‐dibutyl‐3,4‐dihydro‐2H‐selenopheno[3,4‐b][1,4]dioxephine) (PProDOS‐C₄), poly(3,3‐dihexyl‐3,4‐dihydro‐2H‐selenopheno[3,4‐b][1,4]dioxephine) (PProDOS‐C₆), and poly(3,3‐didecyl‐3,4‐dihydro‐2H‐selenopheno[3,4‐b][1,4]dioxephine) (PProDOS‐C₁₀), are highlighted. It is noted that these unique polymers have low bandgaps (1.57–1.65 eV), and they are exceptionally stable under ambient atmospheric conditions. Polymer films retained 82–97% of their electroactivity after 5000 cycles. The percent transmittance of PProDOS‐C_n (n = 4, 6, 10) films found to be between 55 and 59%. Furthermore, these novel soluble PProDOS‐C_n polymers showed electrochromic behavior: a color change form pure blue to highly transparent state in a low switching time (1.0 s) during oxidation with high coloration efficiencies (328–864 cm² C^?1) when compared to their thiophene analogues. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011