161 resultados para Laguerre H-atom Polynomial


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Empirical potential energy calculations have been carried out to determine the preferred conformations of penicillins and penicillin sulphones and their 1-oxa-1-dethia and 1-carba-1-dethia analogues. With the exception of 1-oxa-1-dethia penicillins, all the other compounds favour C2 and the C3 puckered conformations of their five-membered rings. Replacement of C2 methyl groups by hydrogen atoms as in bisnorpenicillin V or oxidation of sulphur in position 1 as in sulphones, makes the C3 puckered form much less favourable. Addition of an amino-acyl group at the C6 atom, however, makes the C3 puckered form more favoured in penicillin G or V and in 1-carba-1-dethia penicillins. Through the replacement of the sulphur atom at position 1 by an oxygen atom or by a -CH2 group increases the non-planarity of the lactam peptide bond, it significantly affects the relative disposition of the C3 carboxyl group with respect to the β-lactam ring. These conformational differences have been correlated with the biological activities of these compounds. The present study suggests that the conformation of the bicyclic ring system may be more important for initial binding with the crosslinking enzyme(s) involved in the biosynthesis of bacterial cell-wall peptidoglycan and that the mode of binding is influenced by the nature of the side-group at the C6 atom. These studies predict, in agreement with experimental results, that the 1-oxa-1-dethia penicillin nulceus is an inhibitor of penicillianses. The study also suggests that the stereospecificities of the crosslinking enzyme(s) and penicillinases are very similar with regard to the nature of the side-group at the 6 atom and the confirmation of the bicyclic ring system. However, the confirmational requirement for the bicyclic ring system appears to be more specific in the former enzyme than in the latter.

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CsHaN205, PL a = 6.438 (2), b = 7.486 (3), c = 8.048 (4)A, a = 72.2(1), fl = 80.8(1), y = 76.4 (1) °, D m = 1.65 (1) (flotation), D c = 1.64 Mg m -3, Z = 2. Final R = 0.095 for 1205 observed reflections. The molecule assumes the sterically least favourable conformation with the side chain carboxyl group staggered between the a-carboxyl group and the N atom attached to C '~. The ureido group takes part in two specific interactions involving two nearly parallel hydrogen bonds in one and two convergent hydrogen bonds in the other.

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In this paper a method of solving certain third-order non-linear systems by using themethod of ultraspherical polynomial approximation is proposed. By using the method of variation of parameters the third-order equation is reduced to three partial differential equations. Instead of being averaged over a cycle, the non-linear functions are expanded in ultraspherical polynomials and with only the constant term retained, the equations are solved. The results of the procedure are compared with the numerical solutions obtained on a digital computer. A degenerate third-order system is also considered and results obtained for the above system are compared with numerical results obtained on the digital computer. There is good agreement between the results obtained by the proposed method and the numerical solution obtained on digital computer.

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ABSTRACT: Infrared studies of synthetic alamethicin fragments and model peptides containing a-aminoisobutyric acid (Aib) have been carried out in solution. Tripeptides and larger fragments exhibit a strong tendency to form /3 turns, stabilized by 4 - 1 10-atom hydrogen bonds. Dipeptides show less well-defined structures, though C5 and C7 conformations are detectable. Conformational restrictions imposed by Aib residues result in these peptides populating a limited range of states. Integrated intensities of the hydrogen-bonded N-H stretching band can be used to quantitate the number of intramolecular hydrogen bonds. Predictions made from infrared data are in excellent agreement with nuclear magnetic resonance and X-ray diffraction studies. Assignments of the urethane and tertiary amide carbonyl groups in the free state have been made in model peptides. Shifts to lower frequency on hydrogen bonding are observed for the carbonyl groups. The 1-6 segment of alamethicin is shown to adopt a 310 helical structure stabilized by four intramolecular hydrogen bonds. The fragments Boc-Leu-Aib-Pro-Val-Aib-OMe (1 2-1 6) and Boc-Gly-Leu-Aib-Pro-Val-Aib-OMe (1 1-1 6) possess structures involving 4 - 1 and 5 - 1 hydrogen bonds. Supporting evidence for these structures is obtained from proton nuclear magnetic resonance studies.

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The concept of orbital compatibility is used to explain the relative energies of different macropolyhedral structural patterns such as closo-closo, closo-nido, and nido-nido. A large polyhedral borane condenses preferentially with a smaller polyhedron owing to orbital compatibility. Calculations carried out at the B3LYP/6-31G* level show that the macropolyhedron closo(12)-closo(6) is the most preferred structural pattern among the face-sharing closo-closo systems. The relative stabilities of four-shared-atom closo-closo, three-shared-atom closo-closo, three-shared-atom closo-nido, edge-sharing closo-nido, and edge-sharing nido-nido structures are in accordance with the difference in the number of vertices of the individual polyhedra of the macropolyhedra. When the difference in the number of vertices of the individual polyhedra is large, the stability of the macropolyhedra is also large. Calculations further show that the orbital compatibility plays an important role in deciding the stability of the macropolyhedral boranes with more than two polyhedral units. The dependence of the orbital compatibility on the relative stability of the macropolyhedron varies with other factors such as inherent stability of the individual polyhedron and steric factors.

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The parametric resonance in a system having two modes of the same frequency is studied. The simultaneous occurence of the instabilities of the first and second kind is examined, by using a generalized perturbation procedure. The region of instability in the first approximation is obtained by using the Sturm's theorem for the roots of a polynomial equation.

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Self-tuning is applied to the control of nonlinear systems represented by the Hammerstein model wherein the nonlinearity is any odd-order polynomial. But control costing is not feasible in general. Initial relay control is employed to contain the deviations.

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C14Ht0F3NO2, P2.Jc, a = 12.523 (4), b = 7.868(6), c = 12.874 (3)A, fl = 95.2 (2) ° , O,,, = 1.47 (4), D e = 1.47 Mg m -3, Z = 4. Final R = 0.074 for 2255 observed reflections. The carboxyl group and the phenyl ring bearing the carboxyl group are nearly coplanar whereas the two phenyl rings are inclined with respect to each other at 52.8 ° . The difference between the two polymorphs of flufenamic acid lies in the geometrical disposition of the [3-(trifluoromethyl)- phenyl]amino moiety with respect to the benzoic acid moiety. As in other fenamate structures, the carboxyl group and the imino N atom are connected through an intramolecular hydrogen bond; also, pairs of centrosymmetrically related molecules are connected through hydrogen bonds involving carboxyl groups.

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In this paper the method of ultraspherical polynomial approximation is applied to study the steady-state response in forced oscillations of a third-order non-linear system. The non-linear function is expanded in ultraspherical polynomials and the expansion is restricted to the linear term. The equation for the response curve is obtained by using the linearized equation and the results are presented graphically. The agreement between the approximate solution and the analog computer solution is satisfactory. The problem of stability is not dealt with in this paper.

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Photodimerization of acenaphthylene and 5,6-dichloroacenaphthylene solubilized in sodium dodecylsulphate (SDS), cetyltrimethylammonium chloride (CTAC), dodecyltrimethylammonium chloride (DTAC), cetyltrimethylammonium bromide (CTAB) and Triton X-100 micelles gives a mixture of cis and trans dimers. The magnitude of the cis:trans ratio is sensitive to the type of micelle used. In CTAB micelles the heavy atom effect of the bromide counter-ions leads to an increased triplet-derived trans dimer yield, whereas in micelles with light atom counter-ions (CTAC, DTAC and SDS) the singlet-derived cis dimer predominates.

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M r=670.02, monoclinic, C2/c, a= 31.003(4), b=11.037(2), c=21.183(3)A, fl= 143.7 (1) °, V= 4291.2/k 3, D,n = 2.06, D x = 2.07Mgm -3, Z=8, MoKa, 2=0.7107/k, /~=7.45 mm -1, F(000) = 2560, T= 293 K, R = 0.061 for 1697 observed reflections. The bromphenol blue molecule consists essentially of three planar groupings: the sulfonphthalein ring system and two dibromophenol rings attached to the tetrahedral C atom of the five-membered ring of the sulfonphthalein system. The dibromophenol rings are inclined with resPect to each other at 73 ° whereas they make angles of 85 and 68 ° with respect to the sulfonphthalein system. The molecules aggregate into helical columns with the non-polar regions of the molecules in the interior and the polar regions on the surface. The columns are held together by a network of hydrogen bonds.

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The conformational analysis of d-pantothenic acid using classical semiempirical methods has been carried out. The pantothenic acid molecule can exist in the neutral form (I) or in the ionised form (II) with a deprotonated negatively charged carboxyl group. The neutral molecule as well as the anion is highly flexible and has an ensemble of several allowed conformations rather than one or two unique conformations. The distribution of allowed conformations indicate that the β-alanine as well as the pantoic acid part of the molecule prefers partially folded conformations. The conformation of the former is greatly affected by the ionisation state of the carboxyl group whereas that of the latter is not. Possibility of intramolecular hydrogen bonding in different allowed conformations has also been explored. A bifurcated hydrogen bond involving a carboxyl (or carboxylate) oxygen atom and a hydroxyl oxygen atom, as acceptors, and the amide nitrogen atom as the donor occurs frequently in both I and II. Amongst the two crystal structures containing pantothenic acid reported so far, the conformation of the molecule in l-lysine d-pantothenate lies in the allowed region and is stabilised by a bifurcated intramolecular hydrogen bond, whereas that in the calcium bromide salt falls in a disallowed region, presumably due to the requirement of tridentate metal coordination.

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The synthesis of 4,4,N,N-tetramethyl-NN-dinitroso-2,2-methylenedianiline (1) by the route p-MeC6H4NH2+ HCHO + OH–(p-MeC6H4NMe)2CH2(7b); (7b)+ acid at 70 °C 4,N-dimethyl-6-(N-methyl-p-toluidinomethyl)aniline (4b); (4b)+ acid at 130 °C 4,4,NN-tetramethyl-2,2-methylenedianiline (3b); (3b)+ HNO2(1), is described. Aspects of the 1H n.m.r. spectra of the above and related compounds are discussed. A crystal-structure analysis of compound (1) shows one of the N-nitroso-groups to be disordered with the endo-form being in preponderance (4 : 1) over the exo-form. The other N-nitroso-group is exclusively exo in the solid state. There is little or no resonance between the benzene ring and the nitroso-group attached to the ring, the two groups being almost perpendicular to each other. In one of the N-nitroso-groups, the nitrogen atom deviates significantly from the plane of the benzene ring to which it is attached. Both amide nitrogen atoms show some pyramidal character.

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allo-4-Hydroxy-L-proline crystallizes from an aqueous solution as the dihydrate. The crystals are orthorhombic, space group P212121, with a=7.08 (2), b=22.13 (3), c= 5"20 (2) A,. The structure was solved by direct methods and refined by block-diagonal least squares. The final R for 733 observed reflexions is 0.054. The molecule exists as a zwitterion with hydroxyl and carboxyl groups cis to the pyrrolidine ring. The latter is puckered at the fl-carbon atom, which deviates by -0.54 A, from the best plane formed by the four remaining atoms. The molecules are held together by a network of hydrogen bonds, the water molecules playing a dominant role in the stability of the structure.

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The crystal and molecular structure of the title compound (1) has been determined by the heavy-atom method from 1038 observed three-dimensional photographic data. Crystals are orthorhombic, with a = 20.07 ± 0.02, b= 10.05 ± 0.02, c= 7.31 ± 0.01 Å, space group P212121, with Z= 4. The structure was refined by block diagonal leastsquares to R 0.099. The conformation of the norbornane moiety is discussed. The seven-membered ring portion of the molecule adopts an approximate chair conformation. The packing of the molecules in the crystal is mainly a consequence of van der Waals interactions.