Extending lagrange interpolation to develop a 4-node quadrilateral element

Today finite element method is a well established tool in engineering analysis and design. Though there axe many two and three dimensional finite elements available, it is rare that a single element performs satisfactorily in majority of practical problems. The present work deals with the development of 4-node quadrilateral element using extended Lagrange interpolation functions. The classical univariate Lagrange interpolation is well developed for 1-D and is used for obtaining shape functions. We propose a new approach to extend the Lagrange interpolation to several variables. When variables axe more than one the method also gives the set of feasible bubble functions. We use the two to generate shape function for the 4-node arbitrary quadrilateral. It will require the incorporation of the condition of rigid body motion, constant strain and Navier equation by imposing necessary constraints. The procedure obviates the need for isoparametric transformation since interpolation functions are generated for arbitrary quadrilateral shapes. While generating the element stiffness matrix, integration can be carried out to the accuracy desired by dividing the quadrilateral into triangles. To validate the performance of the element which we call EXLQUAD4, we conduct several pathological tests available in the literature. EXLQUAD4 predicts both stresses and displacements accurately at every point in the element in all the constant stress fields. In tests involving higher order stress fields the element is assured to converge in the limit of discretisation. A method thus becomes available to generate shape functions directly for arbitrary quadrilateral. The method is applicable also for hexahedra. The approach should find use for development of finite elements for use with other field equations also.

4,4′-Bipyridyl complexes of iron: Magnetic, Mössbauer and other spectroscopic studies

4,4prime-Bipyridyl (4,4prime-bipy) complexes of ferrous salts of the Fe(4,4prime-bipy)x(anion)y type (where x or y=1 or 2) and of ferric salts of the Fe(4,4prime-bipy)m(anion)n type (where m=1 or 2 and n=3) have been synthesised. Elemental analyses, i.r. and electronic spectra, magnetic and Mössbauer studies have been performed to characterize the complexes. 4,4prime-Bipy and some anions are inferred to act as bridging ligands. The magnetic moments, electronic and Mössbauer spectra suggest that the complexes are of high spin type with distorted octahedral structures. The value of the isomer shift and quadrupole splitting are discussed in terms of bonding of the ligand and anions.

Open manifolds, Ozsvath-Szabo invariants and exotic R-4 ` S

We construct an invariant of certain open four-manifolds using the Heegaard Floer theory of Ozsvath and Szabo. We show that there is a manifold X homeomorphic to R-4 for which the invariant is non-trivial,showing that X is an exotic R-4. This is the first invariant that detects exotic R-4' s. (C) 2009 Published by Elsevier GmbH.

Synthesis of Poly(1,4-Divinylbenzene Peroxide)

Polymeric peroxides have received renewed attention in the recent past, in view of some significant explorations of their physical and chemical properties. The potential of polymeric peroxides as a class, as specialized fuel, and the need to synthesize such new materials have been reported in the literature. So far, this class of polymers is constituted only by a dozen or so polyperoxides. From the point of view of their use in propellant applications, the importance lies in making materials which are easy to handle etc., unlike the earlier reported poly(styrene peroxide) (PSP), a sticky semi-solid mass. However, judging from the better combustion characteristics, exploring aromatic monomers was thought worthwhile. In this preliminary communication, the synthesis of a new polymeric peroxide made from 1,4-divinylbenzene is reported. The polymer obtained was in powder form and had an exothermic heat of degradation approximately equal to that of PSP. 4 ref.--AA

Non-periodic tilings in 2-dimensions with 4, 6, 8, 10 and 12-fold symmetries

The two dimensional plane can be filled with rhombuses, so as to generate non-periodic tilings with 4, 6, 8, 10 and 12-fold symmetries. Some representative tilings constructed using the rule of inflation are shown. The numerically computed diffraction patterns for the corresponding tilings are also shown to facilitate a comparison with possible X-ray or electron diffraction pictures.

Novel organic porous solids with channel and layered structures from 1,3,5-triazine-2,4,6-triaminehexaacetic acid and its calcium salt

Single crystals of a symmetrically substituted molecule, 1,3,5-triazine-2,4,6-triaminehexaacetic acid, (TTHA) and its Ca2+ salt have been synthesized, the analysis of which reveals the existence of novel channel type cavities and helical packing organizations in the crystals.

Molecular and crystal structure of 4-ethynylcyanobenzene. An example of Csingle bondHcdots, three dots, centeredN hydrogen bonding

The molecular and crystal structures of 4-ethynylcyanobenzene arereported. The packing of molecules in the crystal is found to be homologous with the crystal structures of HCN, cyanoacetylene and 4-cyano-4'-ethynylbiphenyl. Alternatively, these four crystals could be said to constitute a structural homologous series. The influence of C-H center dot center dot center dot N hydrogen bonding in directing a linear supramolecular arrangement of molecules with ethynyl and cyano groups at opposite ends, is illustrated. (C) 2010 Elsevier B.V. All rights reserved.

Synthesis and Antileukemic Activity of 1-((S)-2-Amino-4,5,6,7-tetrahydrobenzo[d]thiazol-6-yl)-3-(substituted phenyl)urea Derivatives

Heterocyclic urea derivatives play an important role as anticancer agents because of their good inhibitory activity against receptor tyrosine kinases (RTKs), raf kinases, protein tyrosine kinases (PTKs), and NADH oxidase, which play critical roles in many aspects of tumorigenesis. Benzothiazole moiety constitutes an important scaffold of drugs, possessing several pharmacological functions, mainly the anticancer activity. Based on these interesting properties of benzothiazoles and urea moiety to obtain new biologically active agents, we synthesized a series of novel 1-((S)-2-amino-4,5,6.7-tetrahydrobenzo[d]thiazol-6-yl)-3-(substituted phenyl)urea derivatives and evaluated for their efficacy as antileukemic agents against two human leukemic cell lines (K562 and Reh). These compounds showed good and moderate cytotoxic effect to cancer cell lines tested. Compounds with electron-withdrawing chloro and fluoro substituents on phenyl ring showed good activity and compounds with electron-donating methoxy group showed moderate activity. Compound with electron-withdrawing dichloro substitution on phenyl ring of aryl urea showed good activity. Further, lactate dehydrogenase (LDH) assay, flow cytometric analysis of annexin V-FITC/propidium iodide (PI) double staining and DNA fragmentation studies showed that compound with dichloro substitution on phenyl ring of aryl urea can induce apoptosis.

Selective para metalation of unprotected 3-methoxy and 3,5-dimethoxy benzoic acids with n-butyl lithium-potassium tert-butoxide (LIC-KOR): synthesis of 3,5-dimethoxy-4-methyl benzoic acid

The potassium salt of 3-methoxy and 3,5-dimethoxy benzoic acids undergoes deprotonation at the position para to the carboxylate group selectively when treated with LIC-KOR in THF at -78 degrees C and it has been extended to the synthesis of 3,5-dimethoxy-4-methyl benzoic acid. (C) 2000 Elsevier Science Ltd. All rights reserved.

Plasticity in the primary binding site of galactose/N-acetylgalactosamine-specific lectins - Implication of the C-H center dot center dot center dot O hydrogen bond at the specificity-determining C-4 locus of the saccharide in 4-methoxygalactose recognition by jacalin and winged bean (basic) agglutinin I

It is currently believed that an unsubstituted axial hydroxyl at the specificity-determining C-4 locus of galactose is indispensable for recognition by galactose/N-acetylgalactosamine-specific lectins. Titration calorimetry demonstrates that 4-methoxygalactose retains binding allegiance to the Moraceae lectin jacalin and the Leguminosae lectin, winged bean (basic) agglutinin (WBA I). The binding reactions were driven by dominant favorable enthalpic contributions and exhibited significant enthalpy-entropy compensation. Proton NMR titration of C-methoxygalactose with jacalin and WBA I resulted in broadening of the sugar resonances without any change in chemical shift. The alpha-and beta-anomers of 4-methoxygalactose were found to be in slow exchange with free and lectin-bound states. Both the anomers experience magnetically equivalent environments at the respective binding sites. The binding constants derived from the dependence of NMR line widths on 4-methoxygalactose concentration agreed well with those obtained from titration calorimetry. The results unequivocally demonstrate that the loci corresponding to the axially oriented C-4 hydroxyl group of galactose within the primary binding site of these lectins exhibit plasticity. These analyses suggest, for the first time, the existence of C-H ... O-type hydrogen-bond(s) in protein-carbohydrate interactions in general and between the C-4 locus of galactose derivative and the lectins jacalin and WBA I in particular.