116 resultados para SQUARES


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The chemical-shift of the X-ray K-absorption edge of Co was studied in a large number of compounds, complexes (spinels) and minerals of Co in its different oxidation states having widely different crystal structures and containing different types of bonding and various types of ligands, and were reported collectively, for the first time, in a single paper. A quadratic relationship was established on the basis of least-squares regression analysis to hold between the chemical-shift and the effective charge on the absorbing atom, but the dominance of the linear term was shown. This relation was utilized in evaluating the charge on the Co-ion in a number of minerals. The effect on chemical-shift of oxidation states of the absorbing atom, of the bond length, crystal structure and higher shell atoms of the molecule, and of electronegativity, atomic number and ionic radius of the ligand was discussed.

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The ternary metal nucleotide complexes [Ni(en)1.3(H2O)1.4(H2O)2][Ni(5?-dGMP)2(en)0.7-(H2O)0.6(H2O)2]·7H2O (1) and [Ni(en)2(H2O)2][Ni(5?-GMP)2(H2O)4]·6H2O (2)(en = ethylenediamine, 5?-dGMP = 2?-deoxyguanosine 5?-monophosphate, 5?-GMP = guanosine 5?-monophosphate) have been prepared and their structures analyzed by X-ray diffraction methods. Both compounds crystallise in the space group C2221 with a= 8.810(1), b= 25.090(4), c= 21.084(1)Å, and Z= 4 for (1) and a= 8.730(1), b= 25.691(4), c= 21.313(5)Å, and Z= 4 for (2). The structures were deduced from the analogous CoIII complexes and refined by full-matrix least-squares methods to final R values of 0.087 and 0.131 for 1 211 and 954 reflections for (1) and (2) respectively. An interesting feature of the deoxyribonucleotide complex (1) is that en is not totally labilized from the metal centre on nucleotide co-ordination, as observed in corresponding ribonucleotide complexes. Apart from extensive intra- and inter-molecular hydrogen bonding, the structures are stabilized by significant intracomplex base�base and base�sugar interactions. The nucleotides in both complexes have an anti base, C(2?)-endo sugar pucker, and gauche�gauche conformation about the C(4?)�C(5?) bond.

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The method of least squares could be used to refine an imperfectly related trial structure by adoption of one of the following two procedures: (i) using all the observed at one time or (ii) successive refinement in stages with data of increasing resolution. While the former procedure is successful in the case of trial structures which are sufficiently accurate, only the latter has been found to be successful when the mean positional error (i.e.<|[Delta]r|>) for the atoms in the trial structure is large. This paper makes a theoretical study of the variation of the R index, mean phase-angle error, etc. as a function of <|[Delta]r|> for data corresponding to different esolutions in order to find the best refinement procedure [i.e. (i) or (ii)] which could be successfully employed for refining trial structures in which <|[Delta]r|> has large, medium and low values. It is found that a trial structure for which the mean positional error is large could be refined only by the method of successive refinement with data of increasing resolution.

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C9H10ClNO2, Mol · wt = 199.69, monoclinic, C2/c, Z = 8, a = 15.782(2) Å, b = 3.958(1) Å, c = 29.448(2) Å, β = 92.08°, ν = 1838.35 Å3, ϱc = 1.443 g cm−3, ϱ0 = 1.438(2) g cm−3. The structure of (4-chloro-2-methylphenoxy) acetamide (2M4ClPA) was determined by direct methods and refined by full-matrix least-squares methods to R = 0.079. The molecules dimerize about a centre of symmetry and the N – H⋯O distance is = 2.909(3) Å.

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Promethazine picrate (C23H23N5O7S) crystallises in the triclinic space group P[unk] with a = 8.137(1), b = 8.144(3), c = 19.224(6) Å, α = 87.78(3), β = 79.97(2), γ = 70.57(2)° and two molecules per unit cell. The structure was solved by direct methods (MULTAN 80) using 2438 observed reflections [I > 2.5 σ(I)]. Refinement was carried out by block-diagonal least-squares methods to a final R = 0.052. The picrate group is planar and is almost perpendicular to the promethazine plane. The two groups are joined by a hydrogen bond. The pairs of molecules related by a centre of symmetry make a molecular arrangement where promethazine and picrate groups are packed in sheets in three dimensions.

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l-Valyl-l-lysine hydrochloride, C11N3O3H23 HCl, rystallizes in the monoclinic space group P2, with a = 5.438(5), b = 14.188(5), c = 9.521(5) Å, β= 95.38(2)° and Z = 2. The crystal structure, solved by direct methods, refined to R = 0.036, using full matrix least-squares method. The peptide exists in a zwitterionic form, with the N atom of the lysine side-chain protonated. The two γ-carbons of the valine side-chain have positional disorder, giving rise to two conformations, χ111= -67.3 and 65.9°, one of which (65.9°) is sterically less favourable and has been found to be less popular amongst residues branching at β-C. The lysine side-chain has the geometry of g− tgt, not seen in crystal structures of the dipeptides reported so far. Interestingly, χ32 (63.6°) of lysine side-chain has a gauche+ conformation unlike in most of the other tructures, where it is trans. The neighbouring peptide molecules are hydrogen bonded in a head-to-tail fashion, a rather uncommon interaction in lysine peptide structures. The structure shows considerable similarity with that of l-Lys-l-Val HO in conformational angles and H-bond interactions [4].

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The reactions of the complexes [MI2(CO)3-(NCMe)2] (M = Mo, W) with the diphosphazane ligands RN{P(OPh)2}2 (R = Me, Ph) in CH2Cl2 at room temperature afford new seven-coordinated complexes of the type [MI2(CO)3{P(OPh)2}2NR]. The molybdenum complexes are sensitive to air oxidation even in the solid state, whereas the tungsten complexes are more stable in the solid state and in solution. The structure of the tungsten complex [WI2(CO)3{P(OPh)2}2NPh] has been determined by single-crystal X-ray diffraction. It crystallizes in the orthorhombic system with the space group Pna 2(1), a = 19.372 (2) angstrom, b = 11.511 (1) angstrom, c = 15.581 (1) angstrom, and Z = 4. Full-matrix least-squares refinement with 3548 reflections (I > 2.5-sigma-(I)) led to final R and R(w) values of 0.036 and 0.034, respectively. The complex adopts a slightly distorted pentagonal-bypyramidal geometry rarely observed for such a type of complexes; two phosphorus atoms of the diphosphazane ligand, two iodine atoms, and a carbonyl group occupy the equatorial plane, and the other two carbonyl groups, the apical positions.

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Hydrazinium metal chlorides, (N2H5)2MCl4·2H2O (where M = Fe, Co, Ni and Cu), have been prepared from the aqueous solutions of the respective metal chlorides and hydrazine hydrochloride (N2H4·HCl or N2H4·2HCl) and investigated by spectral and thermal analyses. The crystal structure of the iron complex has been determined by direct methods and refined by full-matrix least-squares to an R of 0.023 and Rw of 0.031 for 1495 independent reflections. The structure shows ferrous ion in an octahedral environment bonded by two hydrazinium cations, two chloride anions and two water molecules. In the complex cation [Fe(N2H5)2(H2O)2Cl2]2+, the coordinated groups are in trans positions.

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The structure of bovine prothrombin fragment 1 has been refined at 2.25 Å resolution using high resolution measurements made with the synchrotron beam at CHESS. The synchrotron data were collected photographically by oscillation methods (R-merge = 0.08). These were combined with lower order diffractometer data for refinement purposes. The structure was refined using restrained least-squares methods with the program PROLSQ to a crystallographic R-value of 0.175. The structure includes 105 water molecules with occupancies of >0·6. The first 35 residues (Ala1-Leu35) of the N-terminal ?-carboxy glutamic acid-domain (Ala1-Cys48) of fragment 1 are disordered as are two carbohydrate chains of Mr ? 5000; the latter two combine to render 40% of the structure disordered. The folding of the kringle of fragment 1 is related to the close intramolecular contact between the inner loop disulfide groups. Half of the conserved sequence of the kringle forms an inner core surrounding these disulfide groups. The remainder of the sequence conservation is associated with the many turns of the main chain. The Pro95 residue of the kringle has a cis conformation and Tyr74 is ordered in fragment 1, although nuclear magnetic resonance studies indicate that the comparable residue of plasminogen kringle 4 has two positions. Surface accessibility calculations indicate that none of the disulfide groups of fragment 1 is accessible to solvent.

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A Schiff base metal complex, [Cu(II)(PLP-DL-tyrosinato)(H2O)].4H2O (PLP = pyridoxal phosphate), with the molecular formula CuC17O13N2H27P has been prepared and characterized by magnetic, spectral, and X-ray structural studies. The compound crystallizes in the triclinic space group P1BAR with a = 8.616 (2) angstrom, b = 11.843 (3) angstrom, c = 12.177 (3) angstrom, alpha = 103.40 (2)degrees, beta = 112.32 (2)degrees, gamma = 76.50 (1)degrees, and Z = 2. The structure was solved by the heavy-atom method and refined by least-squares techniques to a final R value of 0.057 for 3132 independent reflections. The coordination geometry around Cu(II) is distorted square pyramidal with phenolic oxygen, imino nitrogen, and carboxylate oxygen from the Schiff base ligand and water oxygen as basal donor atoms. The axial site is occupied by a phosphate oxygen from a neighboring molecule, thus resulting in a one-dimensional polymer. The structure reveals pi-pi interaction of the aromatic side chain of the amino acid with the pyridoxal pi system. A comparative study is made of this complex with similar Schiff base complexes. The variable-temperature magnetic behavior of this compound shows a weak antiferromagnetic interaction.

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The crystal and molecular structure of the title compound has been determined by direct methods from diffractometer data. Crystals are orthorhombic, with Z= 4 in a unit cell of dimensions : a= 13.811 (10), b= 5.095(5), c= 12.914(10)Å, space group P212121. The structure was refined by least-squares to R 3.31% for 868 observed reflections. There is significant non-planarity of the peptide group and its nitrogen atom is significantly pyramidal. There is no correlation between the double-bond character and reactivity of the C–N bond of the terminal amide group in glutamine and acetamide

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The crystal and molecular structures of the Tris salt of adenosine 5'-diphosphate were determined from X-ray diffraction data. The crystals are monoclinic, space P21, and Z = 2 with a=9.198 (2) A, b=6.894 (1) A, c=18.440 (4) A, and beta = 92.55 (2) degrees. Intensity data were collected on an automated diffractometer. The structure was solved by the heavy-atom technique and refined by least squares to R = 0.047. The ADP molecule adopts a folded conformation. The conformation about the glycosidic bond is anti. The conformation of the ribose ring is close to a perfect C(2')-endo-C-(3')-exo puckering. The conformation about C(4')-C(5') is gauche-gauche, similar to other nucleotide structures. The pyrophosphate chain displays a nearly eclipsed geometry when viewed down the P-P vector, unlike the staggered conformation observed in crystal structures of other pyrophosphates. The less favorable eclipsed conformation probably results from the observed association of Tris molecules with the polar diphosphate chain through electrostatic interactions and hydrogen bonds. Such interactions may play an important role in Tris-buffered aqueous solutions of nucleotides and metal ions.

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A model comprising several servers, each equipped with its own queue and with possibly different service speeds, is considered. Each server receives a dedicated arrival stream of jobs; there is also a stream of generic jobs that arrive to a job scheduler and can be individually allocated to any of the servers. It is shown that if the arrival streams are all Poisson and all jobs have the same exponentially distributed service requirements, the probabilistic splitting of the generic stream that minimizes the average job response time is such that it balances the server idle times in a weighted least-squares sense, where the weighting coefficients are related to the service speeds of the servers. The corresponding result holds for nonexponentially distributed service times if the service speeds are all equal. This result is used to develop adaptive quasi-static algorithms for allocating jobs in the generic arrival stream when the load parameters are unknown. The algorithms utilize server idle-time measurements which are sent periodically to the central job scheduler. A model is developed for these measurements, and the result mentioned is used to cast the problem into one of finding a projection of the root of an affine function, when only noisy values of the function can be observed

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This paper may be considered as a sequel to one of our earlier works pertaining to the development of an upwind algorithm for meshless solvers. While the earlier work dealt with the development of an inviscid solution procedure, the present work focuses on its extension to viscous flows. A robust viscous discretization strategy is chosen based on positivity of a discrete Laplacian. This work projects meshless solver as a viable cartesian grid methodology. The point distribution required for the meshless solver is obtained from a hybrid cartesian gridding strategy. Particularly considering the importance of an hybrid cartesian mesh for RANS computations, the difficulties encountered in a conventional least squares based discretization strategy are highlighted. In this context, importance of discretization strategies which exploit the local structure in the grid is presented, along with a suitable point sorting strategy. Of particular interest is the proposed discretization strategies (both inviscid and viscous) within the structured grid block; a rotated update for the inviscid part and a Green-Gauss procedure based positive update for the viscous part. Both these procedures conveniently avoid the ill-conditioning associated with a conventional least squares procedure in the critical region of structured grid block. The robustness and accuracy of such a strategy is demonstrated on a number of standard test cases including a case of a multi-element airfoil. The computational efficiency of the proposed meshless solver is also demonstrated. (C) 2010 Elsevier Ltd. All rights reserved.

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Three different complexes of copper (I) with bridging 1, 2-bis(diphenylphosphino)ethane (dppe), namely [Cu2 (mu-dppe) (CH3CN)6] (ClO4)2 (1), [Cu2 (mu-dppe)2 (CH3 CN)2] (ClO4)2 (2), and [Cu2 (mu-dppe) (dppe)2 (CH3CN)2] (ClO4)2 (3) have been prepared. The structure of [Cu2 (mu-dppe) (dPPe)2 (CH3CH)2] (ClO4)2 has been determined by X-ray crystallography. It crystallizes in the space group PT with a=12.984(6) angstrom, b=13.180(6) angstrom, c=14.001(3) angstrom, alpha=105.23(3), beta=105.60(2), gamma=112.53 (4), V=1944 (3) angstrom3, and Z=1. The structure was refined by least-squares method with R=0.0365; R(w)=0.0451 for 6321 reflections with F0 greater-than-or-equal-to 3 sigma (F0). The CP/MAS P-31 and IR spectra of the complexes have been analysed in the light of available crystallographic data. IR spectroscopy is particularly helpful in identifying the presence of chelating dppe. P-31 chemical shifts observed in solid state are very different from those observed in solution, and change significantly with slight changes in structure. In solution, complex 1 remains undissociated but complexes 2 and 3 undergo extensive dissociation. With a combination of room temperature H-1, Cu-63, and variable temperature P-31 NMR spectra, it is possible to understand the various processes occurring in solution.