CM defect and Hilbert functions of monomial curves

In this article we consider a semigroup ring R = KGamma] of a numerical semigroup Gamma and study the Cohen- Macaulayness of the associated graded ring G(Gamma) := gr(m), (R) := circle plus(n is an element of N) m(n)/m(n+1) and the behaviour of the Hilbert function H-R of R. We define a certain (finite) subset B(Gamma) subset of F and prove that G(Gamma) is Cohen-Macaulay if and only if B(Gamma) = empty set. Therefore the subset B(Gamma) is called the Cohen-Macaulay defect of G(Gamma). Further, we prove that if the degree sequence of elements of the standard basis of is non-decreasing, then B(F) = empty set and hence G(Gamma) is Cohen-Macaulay. We consider a class of numerical semigroups Gamma = Sigma(3)(i=0) Nm(i) generated by 4 elements m(0), m(1), m(2), m(3) such that m(1) + m(2) = mo m3-so called ``balanced semigroups''. We study the structure of the Cohen-Macaulay defect B(Gamma) of Gamma and particularly we give an estimate on the cardinality |B(Gamma, r)| for every r is an element of N. We use these estimates to prove that the Hilbert function of R is non-decreasing. Further, we prove that every balanced ``unitary'' semigroup Gamma is ``2-good'' and is not ``1-good'', in particular, in this case, c(r) is not Cohen-Macaulay. We consider a certain special subclass of balanced semigroups Gamma. For this subclass we try to determine the Cohen-Macaulay defect B(Gamma) using the explicit description of the standard basis of Gamma; in particular, we prove that these balanced semigroups are 2-good and determine when exactly G(Gamma) is Cohen-Macaulay. (C) 2011 Published by Elsevier B.V.

Effect of anchor width on pullout capacity of strip anchors in sand

By incorporating the variation of peak soil friction angle (phi) with mean principal stress (sigma(m)), the effect of anchor width (B) on vertical uplift resistance of a strip anchor plate has been examined. The anchor was embedded horizontally in a granular medium. The analysis was performed using lower bound finite element limit analysis and linear programming. An iterative procedure, proposed recently by the authors, was implemented to incorporate the variation of phi with sigma(m). It is noted that for a given embedment ratio, with a decrease in anchor width (B), (i) the uplift factor (F-gamma) increases continuously and (ii) the average ultimate uplift pressure (q(u)) decreases quite significantly. The scale effect becomes more pronounced at greater embedment ratios.

Reactions of the hexachlorocyclodiphosphazane [MeNPCl3]2 with primary aromatic amines: formation of highly basic bisphosphinimines

Reactions of hexachlorocyclodiphosphazane [MeNPCl3]2 with primary aromatic amines afforded the bisphosphinimine hydrochlorides [(RNH)2(RN)PN(Me)P(NHMe)(NHR)2]+Cl- (R = Ph 1, C6H4Me-4 2 or C6H4OMe-4 3). Dehydrochlorination of 2 and 3 by methanolic KOH yielded highly basic bisphosphinimines [(RNH)2(RN)PN(Me)P(NMe)(NHR)2] (R = C6H4Me-4 4 or C6H4OMe-4 5). Compounds 1-5 have been characterised by elemental analysis and IR and NMR (H-1, C-13, P-31) spectroscopy. The structure of 2 has been confirmed by single-crystal X-ray diffraction. The short P-N bond lengths and the conformations of the PN, units can be explained on the basis of cumulative negative hyperconjugative interactions between nitrogen lone pairs and adjacent P-N sigma* orbitals. Ab initio calculations on the model phosphinimine (H2N)3P=NH and its protonated form suggest that (amino)phosphinimines would be stronger bases compared to many organic bases such as guanidine.

Concentration-dependent NMR and conductivity studies of (PEG)(x)NH4ClO4

Films of (PEG)(x)NH4ClO4 (x = 5 to 1000) were prepared and characterized. The physical properties are observed to be a sensitive function of concentration. Hygroscopicity increases as salt content increases. Conductivity peaks (sigma = 2.7 x 10(-6) S/cm) at x = 46. The H-1 NMR line width has a minimum at x = 46, while that of Cl-35 monotonically increases with salt concentration, indicating that the complex is essentially a protonic conductor.

Electrical transport studies in alkali borovanadate glasses

The ac conductivity and dielectric behaviors of sodium borovanadate glasses have been studied over wide ranges of composition and frequency. The de activation energies calculated from the complex impedance plots decrease linearly with the Na2O concentration, indicating that ionic conductivity dominates in these glasses. The possible origin of low-temperature departures of conductivity curves (from linearity) of vanadium-rich glasses in log sigma versus 1/T plots is discussed. The ac conductivities have been fitted to the Almond-West type power law expression with use of a single value of s. It is found that in most of the glasses s exhibits a temperature-dependent minimum. The dielectric data are converted into moduli (M*) and are analyzed using the Kohlrausch-William-Watts stretched exponential function, The activation barriers, W, calculated from the temperature-dependent dielectric loss peaks compare well with the activation barriers calculated from the de conductivity plots. The stretching exponent beta is found to be temperature independent and is not likely to be related as in the equation beta = 1 - s, An attempt is made to elucidate the origin of the stretching phenomena. It appears that either a model of the increased contribution of polarization energy (caused by the increased modifier concentration) and hence the increased monopole-induced dipole interactions or a model based on increased intercationic interactions can explain the slowing down of the primitive relaxation in ionically conducting glasses.

Electron donor-acceptor complex of ICl with diethyl ether - He I photoelectron spectroscopy and ab initio molecular orbital study

The He I photoelectron spectrum of the diethyl ether-ICl complex has been obtained. The oxygen orbitals are shifted to higher binding energies and that of ICl to lower binding energies owing to complex formation. Ab initio molecular orbital (MO) calculations of the complex molecule showed that the bonding is between the sigma-type lone pair of oxygen and the I atom and that the complex has C-2v symmetry. The binding energy of the complex is computed to be 8.06 kcal mol(-1) at the MP2/3-21G* level. The orbital energies obtained from the photoelectron spectra of the complex are compared and assigned with orbital energies obtained by MO calculations. Natural bond orbital analysis (NBO) shows that charge transfer is from the sigma-type oxygen lone pair to the iodine atom and the magnitude of charge transfer is 0.0744 e.

Helix termination and chain reversal: Crystal and molecular structure of the alpha,beta-dehydrooctapeptide Boc-Val Delta Phe-Phe-Ala-Leu-Ala-Delta Phe-Leu-OH

The crystal structure of the dehydro octapeptide Boc-Val-Delta Phe-Phe-Ala-Leu-Ala-Delta Phe-Leu-OH has been determined to atomic resolution by X-ray crystallographic methods. The crystals grown by slow evaporation of peptide solution in methanol/water are orthorhombic, space group P2(1)2(1)2(1). The unit cell parameters are a = 8.404(3), b = 25.598(2) and c = 27.946(3) Angstrom, Z = 4. The agreement factor is R = 7.58% for 3636 reflections having (\F-o\) greater than or equal to 3 sigma (\F-o\). The peptide molecule is characterised by a 3(10)-helix at the N-terminus and a pi-turn at the C-terminus. This conformation is exactly similar to the helix termination features observed in proteins. The pi-turn conformation observed in the octapeptide is in good agreement with the conformational features of pi-turns seen in some proteins. The alpha(L)-position in the pi-turn of the octapeptide is occupied by Delta Phe(7), which shows that even bulky residues can be accommodated in this position of the pi-turns. In proteins, it is generally seen that alpha(L)-position is occupied by glycine residue. No intermolecular head-to-tail hydrogen bonds are observed in solid state structure of the octapeptide. A water molecule located in the unit cell of the peptide molecule is mainly used to hold the peptide molecule together in the crystal. The conformation observed for the octapeptide might be useful to understand the helix termination and chain reversal in proteins and to construct helix terminators for denovo protein design.

Reactivity Of Pph3 Toward Ru2cl(O2cme)4 - Synthesis And X-Ray Crystal-Structure Of [Ru(O2cme)(Mecn)2(Pph3)2](Clo4)

A new ruthenium(II) complex of the type [Ru(O2CMe)(MeCN)2(PPh3)2](CiO4) (1) has been isolated from a reaction between Ru2Cl(O2CMe), and PPh3 in MeCN followed by the addition of NaClO4. The structure of 1 is determined by single crystal X-ray studies. The crystal belongs to the monoclinic space group C2/m with the following unit cell dimensions for the C42H39N2O6P2ClRu(M = 866.15): a = 23.295(1)angstrom, b = 23.080(1)angstrom, c = 9.159(1)angstrom, beta = 107.32(1)-degrees, V = 4701(1)angstrom3, Z = 4, D(c) = 1.224 gcm-3, lambda(Mo - K-alpha) = 0.7107 angstrom, mu(Mo - K-alpha) = 4.09 cm-1, T = 293K, R = 0.081 (R(w) = 0.094) for 2860 reflections with I greater-than-or-equal-to 3-sigma(I) and g = 0.015853. In the complex cation, the symmetry about the metal centre is essentially octahedral showing the presence of a chelating acetato, two cis-oriented MeCN and two trans-disposed PPh3 ligands. The mechanistic aspects of the core cleavage reaction are discussed.

The crystal structure of hydrated barium copper oxalate

BaCu(C2O4)(2) . 6H2O is triclinic, P (1) over bar, with a = 6.5405(9), b = 9.202(3), c = 10.939(1) Angstrom, alpha = 85.46(2), beta = 79.22(1), gamma = 80.45(2), V = 636.99(1) Angstrom(3), Z = 2, D-0 = 2.14, D-c = 2.465 g . cm(-3), R = 0.074, wR = 0.0746 for 2219 significant reflections \F-0\ greater than or equal to 6.0 sigma F-0. The barium has eleven coordinations and the coordination polyhedra is a capped antiprism. Six water oxygen atoms are coordinated whereas the other five are coming from the oxalate group. In the unit cell the molecule's form a polymeric network. One lattice water molecule belongs to the coordinating water. The barium oxygen distances vary from 2.75 Angstrom to 3.15 Angstrom.

Structure of 7-ethylamino-6-methyl-4-trifluoromethylcoumarin

C13H12F3NO2, M(r) = 271.2, triclinic, P1BAR, a = 5.029 (2), b = 7.479 (2), c = 17.073 (5) angstrom, alpha = 97.98 (2), beta = 95.54 (3), gamma = 103.62 (3)-degrees, V = 612.4 (4) angstrom 3, Z = 2, D(m) = 1.463, D(x) = 1.471 g cm-3, lambda(Mo K-alpha) = 0.71069 angstrom, mu = 1.23 cm-1, F(000) = 280, T = 298 K, final R value is 0.041 for 2047 observed reflections with \F(omicron)\ greater-than-or-equal-to 6-sigma(\F(omicron)\). The N-C(sp2) bond length is 1.356 (2) angstrom. The N and C atoms of the ethylamino group deviate by < 0.15 angstrom from the plane of the aromatic ring. Short intramolecular contacts, C(3)...F(17) 2.668 (3) angstrom [H(3)...F(17) 2.39 (2) angstrom, C(3)-H(C3)...F(17) 98 (1)-degrees], C(5)...F(18) 3.074 (3) and C(5)...F(19) 3.077 (3) angstrom exist in the structure. The crystal structure is stabilized by intermolecular N-H...O hydrogen bonds with N(12)-H(N12) 0.79 (3), H(N12)...O(11)' 2.36 (3), N(12)...O(11)' (x - 1, y + 1, z) 3.105 (3) angstrom and N(12)-H(N12)...O(11)' 155 (2)-degrees.

Structure of diaquadichlorobis(hydrazinium)iron(II) dichloride

[Fe(N2H5)2(H2O)2Cl2].Cl2, M(r) = 299.65, monoclinic, P2(1)/c, a = 8.027 (1), b = 5.725 (2), c = 11.430 (2) angstrom, beta = 97.08 (1)-degrees, V = 521.3 (2) angstrom 3, Z = 2, D(m) = 1.92, D(x) = 1.910 g cm-3, lambda(Mo K-alpha) = 0.71069 angstrom, mu = 24.5 cm-1, F(000) = 304, T = 295 K, final R = 0.0242 and wR = 0.0292 for 1411 significant [F(o) > 5.0-sigma(F(o))] reflections. The crystal contains discrete Cl- ions and complex [Fe(N2H5)2(H2O)2Cl2]2+ cations. In the complex cation, the Fe atom is bonded to two hydrazinium cations, two Cl atoms and two water molecules. The coordinated atoms are trans to each other. The ions are connected by both N-H...Cl and O-H...Cl type hydrogen bonds.

Structure of N-nitroso-r-2,c-7-diphenylhexahydro-1,4-diazepin-5-one

C17H17N3O2, M(r) = 295.34, orthorhombic, P2(1)2(1)2(1), a = 7.659 (1), b = 12.741 (1), c = 15.095 (1) angstrom, V = 1473.19 (2) angstrom 3, Z = 4, D(m) = 1.33, D(x) = 1.32 Mg m-3, lambda(Cu K-alpha) = 1.5418 angstrom, mu = 0.68 mm-1, F(000) = 624, T = 295 K, R = 0.031 for 1549 unique observed reflections with I > 2.5-sigma(I). The seven-membered heterocyclic ring adopts a boat conformation flattened at the nitroso end of the ring. The substituent phenyl rings occupy pseudo-axial positions and the nitroso group is coplanar with the C(2), N(1), C(7) plane of the central ring. The crystal structure is stabilized by intermolecular N-H...O and weak C-H...O hydrogen bonds.

The Gaussian Toeplitz matrix

An analytical expression for the LL(T) decomposition for the Gaussian Toeplitz matrix with elements T(ij) = [1/(2-pi)1/2-sigma] exp[-(i - j)2/2-sigma-2] is derived. An exact expression for the determinant and bounds on the eigenvalues follows. An analytical expression for the inverse T-1 is also derived.

Organometallic Chemistry of Diphosphazanes. 11. Reactions of fac-[Mo(CO)3(MeCN){.eta.2-Ph2PN(Pri)PPh(DMP)}] (DMP = 3,5-Dimethyl-1-Pyrazolyl) with Diphosphazanes and Diphosphinoalkanes and Oxidative Addition with Iodine

The use of fac-[Mo(CO)(3)(MeCN)(eta(2)-L(1))] (1a) {L(1) = Ph(2)PN(Pr-i)PPh(DMP)}(2) as a precursor to metalloligands and bimetallic, heterotrimetallic, and heptacoordinated complexes is reported. The reaction of 1a with diphosphazane, dppa, or a diphosphinoalkane such as dppm or dppe yields the fac-eta(1)-diphosphine substituted metalloligands, fac-[Mo(CO)(3)(eta(2)-L(1))(eta(1)-PXP)] {PXP = dppa (2), dppm (3), and dppe (4)}. These undergo isomerization to yield the corresponding mer-diphosphine complexes (5-7). Oxidation of the uncoordinated phosphorus atom of the mer-eta(1)-dppm-substituted complex eventually provides mer-[Mo(CO)(3)-(eta(2)-L(1)){eta(1)-Ph(2)PCH(2)P(O)Ph(2)}](8). The structure of the latter complex has been confirmed by single crystal X-ray diffraction {triclinic system, P ($) over bar 1; a = 11.994(3), b = 14.807(2), c = 15.855(3) Angstrom; alpha = 114.24(1), beta = 91.35(2), and gamma = 98.95(1)degrees; Z = 2, 4014 data (F-0 > 5 sigma(F-0)), R = 0.066, R(W) = 0.069}. Treatment of the dppe metalloligand 7 with [PtCl2(COD)] yields the heterotrimetallic complex cis-[PtCl2{mer-[Mo(CO)(3)(eta(2)-L(1))(eta(1)-dppe]}(2)] (9). Attempts to prepare a related trimetallic complex with the dppm-containing metalloligand were unsuccessful; only the tetracarbonyl complex cis-[Mo(CO)(4)(eta(2)-L(1))] (1b) and cis-[PtCl2(eta(2)-dppm)] were obtained. Reaction of la with dppe in the ratio 2:1 yields the mer-mer dinuclear complex [{mer-[Mo(CO)(3)(eta(2)-L(1))]}(2)(mu-dppe)] (10) bridged by dppe. Oxidation of 1a with iodine yields the Mo(II) heptacoordinated complex [MoI2(CO)(2)(eta(3)-L(1))] (11) with tridentate PPN coordination. The same Mo(II) complex 11 is also obtained by the direct oxidation of the tetracarbonyl complex cis-[Mo(CO)(4)(eta(2)-L(1))] (1b) with iodine. The structure of 11 has been confirmed by X-ray diffraction studies {monoclinic system, Cc; a = 10.471(2), b = 19.305(3), c = 17.325(3) Angstrom; beta = 95.47(2)degrees; Z = 4, 3153 data (F-0 > 5 sigma(F-0)), R = 0.049, R(W) = 0.051}. This complex exhibits an unusual capped-trigonal prismatic geometry around the metal. A similar heptacoordinated complex 12 with a chiral diphosphazane ligand {L(3) = (S,R)-P(h)2PN-(*CHMePh)*PPh(DMP)} has also been synthesized.

Charge-ordering in manganates

Ordering of Mn3+ and Mn4+ ions occurs in the rare earth manganates of the general composition Ln(1-x)A(x)MnO(3) (Ln rare earth, A = Ca, Sr). Such charge-ordering is associated with antiferromagnetic and insulating properties. This phenomenon is to be contrasted with the ferromagnetic metallic behavior that occurs when double-exchange between the Mn3+ and Mn4+ ions predominates. Two distinct types of charge-ordering can be delineated. In one, a ferromagnetic metallic (FMM) state transforms to the charge-ordered (CO) state on cooling. In the other scenario, the CO state is found in the paramagnetic ground stale and there is no ferromagnetism down to the lowest temperatures. Magnetic fields transform the CO state to the FMM state, when the average radius of the A-site cations is sufficiently large ([r(A)] > 1.17 Angstrom). Chemical melting of the CO state by Cr3+ substitution in the Mn site is also found only when [r(A)] greater than or similar to 1.17 Angstrom. The effect of the size of the A-cations on the Mn-O-Mn angle is not enough to explain the observed variations of the charge-ordering temperature as well as the ferromagnetic Curie temperature T-c. An explanation based on a competition between the Mn and A-cation orbitals for sigma-bonding with the oxygen rho(sigma) orbitals is considered to account for the large changes in T-c and hence the true bandwidth, with [r(A]). Effects of radiation, electric field, and other factors on the CO state are discussed along with charge-ordering in other manganate systems. Complex phase transitions, accompanied by changes in electronic and magnetic properties, occur in manganates with critical values of(rA) Or bandwidth. Charge-ordering is found in layered manganates, BixCa1-xMnO3 and CaMnO3-delta.