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.     

Crystal structure and magnetic properties of dinuclear iron(III) complex with ONNO-donor ligand

A new dinuclear Fe(III) complex, [Fe(5-MeOL1)(OH)_0.86(CH₃O)_0.14]₂?2(CH₃OH), [H₂-5-MeOL1 = N,N′-bis(5-methoxy-2-hydroxybenzylidene)-2,2-dimethylpropane-1,3-diamine], 1 has been synthesized and characterized by single crystal structure analysis. The structure of 1 consists of two Fe(III) centers with one tetradentate schiff base ligand (N₂O₂) which are bridged by dihydroxo/dimethoxo groups to yield a Fe₂O₂ core. Complex 1 exhibits weak antiferromagnetic exchange interaction between Fe(III) ions with J = ?0.21 cm^–1.     

Novel and Stereospecific Synthesis of (2S)‐3‐(2,4,5‐Trifluorophenyl)propane‐1,2‐diol from D‐Mannitol

A stereospecific synthesis of (2S)‐3‐(2,4,5‐trifluorophenyl)propane‐1,2‐diol from D ‐mannitol has been developed. The reaction of 2,3‐O‐isopropylidene‐D ‐glyceraldehyde with 2,4,5‐trifluorophenylmagnesium bromide gave [(4R)‐2,2‐dimethyl‐1,3‐dioxolan‐4‐yl](2,4,5‐trifluorophenyl)methanol in 65% yield as a mixture of diastereoisomers (1 : 1). The Ph₃P catalyzed reaction of the latter with C₂Cl₆ followed by reduction with Pd/C‐catalyzed hydrogenation gave (2S)‐3‐(2,4,5‐trifluorophenyl)propane‐1,2‐diol with >99% ee and 65% yield.     

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.     

On the inheritance of the strongly π-extending property

In this article, we focus on modules with the property that every projection invariant submodule is essential in a fully invariant direct summand. In contrast to π-extending condition, it is shown that the former property is inherited by direct summands and Morita invariant. An application of our results yields that the endomorphism ring of a free module enjoys the property. Moreover, we characterize generalized triangular matrix rings with the aforementioned property and apply to somewhat special cases.     

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.     

The proapoptotic G41S mutation to human cytochrome c alters the heme electronic structure and increases the electron self-exchange rate

The naturally occurring G41S mutation to human (Hs) cytochrome (cyt) c enhances apoptotic activity based upon previous in vitro and in vivo studies, but the molecular mechanism underlying this enhancement remains unknown. Here, X-ray crystallography, nuclear magnetic resonance (NMR) spectroscopy, and density functional theory (DFT) calculations have been used to identify the structural and electronic differences between wild-type (WT) and G41S Hs cyt c. S41 is part of the hydrogen bonding network for propionate 7 of heme pyrrole ring A in the X-ray structure of G41S Hs cyt c and, compared to WT, G41S Hs cyt c has increased spin density on pyrrole ring C and a faster electron self-exchange rate. DFT calculations illustrate an electronic mechanism where structural changes near ring A can result in electronic changes at ring C. Since ring C is part of the solvent-exposed protein surface, we propose that this heme electronic structure change may ultimately be responsible for the enhanced proapoptotic activity of G41S Hs cyt c.