A note on a symmetry analysis and exact solutions of a nonlinear fin equation

A similarity analysis of a nonlinear fin equation has been carried out by M. Pakdemirli and A.Z. Sahin [Similarity analysis of a nonlinear fin equation, Appl. Math. Lett. (2005) (in press)]. Here, we consider a further group theoretic analysis that leads to an alternative set of exact solutions or reduced equations with an emphasis on travelling wave solutions, steady state type solutions and solutions not appearing elsewhere.     

Noether-Type Symmetries and Conservation Laws Via Partial Lagrangians

We show how one can construct conservation laws of Euler-Lagrange-type equations via Noether-type symmetry operators associated with what we term partial Lagrangians. This is even in the case when a system does not directly have a usual Lagrangian, e.g. scalar evolution equations. These Noether-type symmetry operators do not form a Lie algebra in general. We specify the conditions under which they do form an algebra. Furthermore, the conditions under which they are symmetries of the Euler-Lagrange-type equations are derived. Examples are given including those that admit a standard Lagrangian such as the Maxwellian tail equation, and equations that do not such as the heat and nonlinear heat equations. We also obtain new conservation laws from Noether-type symmetry operators for a class of nonlinear heat equations in more than two independent variables.     

Theoretical investigation of triazine based a star shape pyrrole monomer

In this work, we report a comprehensive theoretical investigation of electroactive star shaped pyrrole functionalized triazine monomer with two main goals. First goal of this work is to explore the physical and chemical properties of the monomer, then to investigate correlation between the experimental and the theoretical properties of monomer. The scale factor which is calculated from B3LYP/cc-pVDZ was determined as 0.985 for FT-IR and it is an important and reliable contribution to the literature. It is determined that the most appropriate basis set for this molecule. The other novel objective of this research is to investigate temperature effect on displacement of chlorine atoms in 2,4,6-trichloro-1,3,5-triazine. This method applied for the first time in the literature for triazines is especially crucial to the synthesis of unsymmetrical triazines.     

Exact solutions of some general nonlinear wave equations in elasticity

A similarity analysis of a nonlinear wave equation in elasticity is studied; in particular, one with anharmonic corrections. The symmetry transformation give rise to exact solutions via the method of invariants. In some cases, graphical figure of the solutions are presented. Furthermore, we consider some cases wherein the velocities of the longitudinal and transversal plane waves are variable. Finally, a brief discussion on how a symmetry analysis on a perturbation of the elasticity equation can be pursued.     

Synthesis of benzyl bromides with hexabromoacetone: an alternative path to drug intermediates

A series of benzyl bromides were efficiently prepared from the corresponding alcohols with Br₃CCOCBr₃/PPh₃ at low temperatures and under neutral conditions. The present protocol was applied to the heterocyclic analogues and to the successful synthesis of the precursor of the antiulcer drug omeprazole, thus furnishing an alternate, mild method for the preparation of these drug intermediates. A significant steric factor was observed throughout both series supporting a S_N2 mechanism.     

Circadian variations in biologically closed electrochemical circuits in Aloe vera and Mimosa pudica

The circadian clock regulates a wide range of electrophysiological and developmental processes in plants. This paper presents, for the first time, the direct influence of a circadian clock on biologically closed electrochemical circuits in vivo. Here we show circadian variation of the plant responses to electrical stimulation. The biologically closed electrochemical circuits in the leaves of Aloe vera and Mimosa pudica, which regulate their physiology, were analyzed using the charge stimulation method. The electrostimulation was provided with different timing and different voltages. Resistance between Ag/AgCl electrodes in the leaf of Aloe vera was higher during the day than at night. Discharge of the capacitor in Aloe vera at night was faster than during the day. Discharge of the capacitor in a pulvinus of Mimosa pudica was faster during the day. The biologically closed electrical circuits with voltage gated ion channels in Mimosa pudica are also activated the next day, even in the darkness. These results show that the circadian clock can be maintained endogenously and has electrochemical oscillators, which can activate ion channels in biologically closed electrochemical circuits. We present the equivalent electrical circuits in both plants and their circadian variation to explain the experimental data.     

On symmetries,reductions, conservation laws and conserved quantities of optical solitons with inter-modal dispersion

This paper studies the compressional dispersive Alfvén (CDA) waves where Noether symmetries will be calculated from which the corresponding conservation laws will be obtained via Noether's theorem. Furthermore, one case of double reduction is performed via the association of a conserved vector with a Noether symmetry (with zero gauge). The conserved quantities of optical solitons in the presence of intermodal dispersion that is governed by the perturbed nonlinear Schrödinger's equation with Kerr law nonlinearity. The invariance-multiplier method is adopted to carry out the analysis, from which the conserved densities are then retrieved. Finally, the conserved quantities are obtained using the 1-soliton solution of the governing equation.     

Toward artificial developmental regulators

A polyamide-peptide conjugate is designed which recruits sequence specifically the developmental regulator Exd to a cognate DNA site. In particular, an eight-ring hairpin polyamide (Im-Im-Py(C3H6NHR)-Py-gamma-Im-Py-Py-Py-beta-Dp) with a heptapeptide (R = Ac-Phe-Tyr-Pro-Trp-Met-Lys-Gly-) attached on a central ring was shown to induce cooperative binding of the Drosophila Hox protein cofactor Exd with a Kd of 4.4 nM in vitro, an order of magnitude more efficient than the natural Hox protein partner Ubx. The conjugate joins two sequence specific domains, one for DNA and one for the protein. This small molecule thus serves as a cooperative protein-DNA dimerizer, which mimics the natural Hox family of developmental regulators.     

Microprobe analysis of low alloyed sintered steels

Homogenization of Mo, W and Cr in alloyed P/M carbon steels during sintering with a transient liquid phase has been investigated by microscopic and microanalytical means. The reaction was found to start with carburization of the VIa metal, continues with the formation of different carbides, and generation of a liquid phase between the carbide and -Fe. The steady state equilibrium remains stable until all VIa metal has been consumed. Microprobe analysis was found to yield optimum results if selected model samples, in which homogenization should not proceed too fast, are investigated.Dedicated to Professor Günther Tölg on the occasion of his 60th birthday