Equivariant Birch-Swinnerton-Dyer Conjecture for the Base Change of Elliptic Curves: An Example

Let E be an elliptic curve defined over Q and let K/Q be a finite Galois extension with Galois group G. The equivariant Birch-Swinnerton-Dyer conjecture for h(1)(E x(Q) K)(1) viewed as amotive over Q with coefficients in Q[G] relates the twisted L-values associated with E with the arithmetic invariants of the same. In this paper I prescribe an approach to verify this conjecture for a given data. Using this approach, we verify the conjecture for an elliptic curve of conductor 11 and an S-3-extension of Q.

High-temperature superconductivity in La- and Lu-substituted YBa2,Cu3,O7, and related oxides

The perovskites, Y0.75La0.25Ba2Cu3O7 and Y0.75Lu0.25Ba2Cu3O7, show high-Tc superconductivity (with zero resistance at or above 80 K), just as the parent compound YBa2Cu3O7. The Lu-substituted oxide, with the smallest unit-cell parameters, shows the highest Tc besides exhibiting a 100% Meissner effect. Hc1, in these oxides is around 25 mT, but the Hc2, is large. The thermopower of YBa2Cu3O7 shows a sharp transition to zero at the superconducting transition, reinforcing the bulk nature of the superconductivity. Preliminary studies show that ErBa2Cu3O7 and Er0.5Y0.5Ba2Cu3O7 are both high-temperature superconductors with zero resistance in the 82-90 K range.

A Conjecture Concerning Transformation Of A Supercooled Hard-Sphere Liquid To A Metastable Disordered Solid

It is conjectured that the hard sphere system has several distinct solid phases, all but one of which are metastable. The bifurcation theory analysis of freezing is extended to the description of the transition between a supercooled liquid and a disordered solid by defining a restricted phase space for the disordered solid. This approach leads to the prediction of a first order transition between a supercooled hard sphere fluid and a disordered metastable hard sphere solid. The results of the calculation are in qualitative agreement with the results of Woodcock's molecular dynamics computer simulations. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

Curves on threefolds and a conjecture of Griffiths-Harris

We prove that any arithmetically Gorenstein curve on a smooth, general hypersurface of degree at least 6, is a complete intersection. This gives a characterisation of complete intersection curves on general type hypersurfaces in . We also verify that certain 1-cycles on a general quintic hypersurface are non-trivial elements of the Griffiths group.

Hydrothermal phase equilibria in Ln2O3-H2O-CO2 systems for Tm, Yb and Lu

Phase diagrams for Tm2O3-H2O-CO2. Yb2O3-H2O-CO2 and Lu2O3-H2O-CO2 systems at 650 and 1300 bars have been investigated in the temperature range of 100–800°C. The phase diagrams are far more complex than those for the lighter lanthanides. The stable phases are Ln(OH)3, Ln2(CO3)3.3H2O (tengerite phase), orthorhombic-LnOHCO3, hexagonal-Ln2O2CO3. LnOOH and cubic-Ln2O3. Ln(OH)3 is stable only at very low partial pressures of CO2. Additional phases stabilised are Ln2O(OH)2CO3and Ln6(OH)4(CO3)7 which are absent in lighter lanthanide systems. Other phases, isolated in the presence of minor alkali impurities, are Ln6O2(OH)8(CO3)3. Ln4(OH)6(CO3)3 and Ln12O7(OH)10,(CO3)6. The chemical equilibria prevailing in these hydrothermal systems may be best explained on the basis of the four-fold classification of lanthanides.

Modified Lu-Lee cryptosystem

A modified Lu-Lee cryptosystem is proposed which appears to be resistant to the cryptanalytic attacks on the original Lu-Lee scheme. The data expansion due to encryption is moderate, and the size of the public key is also quite small.

Rank-Augmented LU-Algorithm for Computing Generalized Matrix Inverses

A rank-augmnented LU-algorithm is suggested for computing a generalized inverse of a matrix. Initially suitable diagonal corrections are introduced in (the symmetrized form of) the given matrix to facilitate decomposition; a backward-correction scheme then yields a desired generalized inverse.

R3Mn1.5CuV0.5O9 (R = Y, Ho, Er, Tm, Yb and Lu) and Lu3Mn3-3xCu2xVxO9: New noncentro symmetric oxides related to YMnO3

We report formation of new noncentrosymmetric oxides of the formula, R3Mn1.5CuV0.5O9 for R = Y, Ho, Er, Tm, Yb and Lu, possessing the hexagonal RMnO3 (space group P6(3)cm) structure. These oxides could be regarded as the x = 0.5 members of a general series R3Mn3-3xCu2xVxO9. Investigation of the Lu-Mn-Cu-V-O system reveals the existence of isostructural solid solution series, Lu3Mn3-3xCu2xVxO9 for 0 < x <= 0.75. Magnetic and dielectric properties of the oxides are consistent with a random distribution of Mn3+, Cu2+ and V5+ atoms that preserve the noncentrosymmetric RMnO3 structure. (c) 2006 Elsevier Ltd. All rights reserved.

Phase relations in the systems Cu–O–R2O3(R = Tm, Lu) and Gibbs energies of formation of Cu2R2O5 compounds

The phase relations in the systems Cu–O–R2O3(R = Tm, Lu) have been determined at 1273 K by X-ray diffraction, optical microscopy and electron probe microanalysis of samples equilibrated in evacuated quartz ampules and in pure oxygen. Only ternary compounds of the type Cu2R2O5 were found to be stable. The standard Gibbs energies of formation of the compounds have been measured using solid-state galvanic cells of the type, Pt|Cu2O + Cu2R2O5+ R2O3‖(Y2O3)ZrO2‖CuO + Cu2O‖Pt in the temperature range 950–1325 K. The standard Gibbs energy changes associated with the formation of Cu2R2O5 compounds from their binary component oxides are: 2CuO(s)+ Tm2O3(s)→Cu2Tm2O5(s), ΔG°=(10400 – 14.0 T/K)± 100 J mol–1, 2CuO(s)+ Lu2O3(s)→Cu2Lu2O5(s), ΔG°=(10210 – 14.4 T/K)± 100 J mol–1 Since the formation is endothermic, the compounds become thermodynamically unstable with respect to component oxides at low temperatures, Cu2Tm2O5 below 743 K and Cu2Lu2O5 below 709 K. When the chemical potential of oxygen over the Cu2R2O5 compounds is lowered, they decompose according to the reaction, 2Cu2R2O5(s)→2R2O3(s)+ 2Cu2O(s)+ O2(g) The equilibrium oxygen potential corresponding to this reaction is obtained from the emf. Oxygen potential diagrams for the Cu–O–R2O3 systems at 1273 K are presented.

(Ba3MTiMO9)-Ti-III-O-V (M-III = Fe, Ga, Y, Lu, M-V = Nb, Ta, Sb) perovskite oxides Synthesis, structure and dielectric properties

We describe the synthesis structures and dielectric properties of new perovskite oxides of the formula (Ba3MTiMO9)-Ti-III-O-V for M-III = Fe Ga Y Lu and M-V = Nb Ta Sb While M-V = Nb and Ta oxides adopt disordered/partially ordered 3C perovskite structures where M-III/Ti/M-V metal-oxygen octahedra are corner connected the M-V = Sb oxides show a distinct preference for the 6H structure where Sb-V/Ti-IV metal-oxygen octahedra share a common face forming (Sb Ti)O-9 dimers that are corner-connected to the (MO6)-O-III octahedra The preference of antimony oxides (Sb-V 4d(10)) for the 6H structure which arises from a special Sb-V-O chemical bonding that tends to avoid linear Sb-O-Sb linkages unlike Nb-V/Ta-V d(0) atoms which prefer similar to 180 degrees Nb/Ta-O-Nb/Ta linkages - is consistent with the crystal chemistry of M-V-O oxides in general The dielectric properties reveal a significant difference among Mill members All the oxides with the 3C structure excepting those with Mill = Fe show a normal low loss dielectric behaviour with epsilon = 20-60 in the temperature range 50-400 degrees C the M-III = Fe members with this structure (M-V = Nb Ta) display a relaxor-like ferroelectric behaviour with large E values at frequencies <= 1 MHz (50-500 degrees C) (C) 2010 Elsevier Masson SAS All rights reserved

Proof of a conjecture of Frankl and Furedi

We give a simple linear algebraic proof of the following conjecture of Frankl and Furedi [7, 9, 13]. (Frankl-Furedi Conjecture) if F is a hypergraph on X = {1, 2, 3,..., n} such that 1 less than or equal to /E boolean AND F/ less than or equal to k For All E, F is an element of F, E not equal F, then /F/ less than or equal to (i=0)Sigma(k) ((i) (n-1)). We generalise a method of Palisse and our proof-technique can be viewed as a variant of the technique used by Tverberg to prove a result of Graham and Pollak [10, 11, 14]. Our proof-technique is easily described. First, we derive an identity satisfied by a hypergraph F using its intersection properties. From this identity, we obtain a set of homogeneous linear equations. We then show that this defines the zero subspace of R-/F/. Finally, the desired bound on /F/ is obtained from the bound on the number of linearly independent equations. This proof-technique can also be used to prove a more general theorem (Theorem 2). We conclude by indicating how this technique can be generalised to uniform hypergraphs by proving the uniform Ray-Chaudhuri-Wilson theorem. (C) 1997 Academic Press.

The Herzog-Vasconcelos conjecture for affine semigroup rings

Let S be a simplicial affine semigroup such that its semigroup ring A = k[S] is Buchsbaum. We prove for such A the Herzog-Vasconcelos conjecture: If the A-module Der(k)A of k-linear derivations of A has finite projective dimension then it is free and hence A is a polynomial ring by the well known graded case of the Zariski-Lipman conjecture.

2-Halooxyethylene ethers of cholesterol as novel single component, room temperature cholesteric LC materials

A series of 2-haloethoxyethyl cholesteryl ethers has been synthesized. Each material shows attractive liquid-crystalline properties as revealed by differential scanning calorimetry, polarizing microscopy, and temperature-dependence of selective reflection characteristic of the cholesteric mesophase. These are interesting examples of simple, nonpolymeric, single component systems that show the cholesteric mesophase at room temperature.

Decomposition temperatures of Cu2Ln2O5 (Ln = Tb, Dy, Ho, Er, Tm, Yb, and Lu) compounds

The equilibrium decomposition temperatures of Cu2Ln2O5 (Ln = Tb, Dy, Ho, Er, Tm, Yb, and Lu) compounds have been measured using a combined DTA-TGA apparatus under a flowing Ar + O2 gas mixture, in which the partial pressure of oxygen was controlled at 5.0 × 103 Pa. The Cu2Ln2O5 compounds yield Ln2O3 and Cu2O on decomposition. The decomposition temperature increases monotonically with the atomic number of the lanthanide element. This suggests that the stability of the Cu2Ln2O5 compounds with respect to the component binary oxides increases with decreasing radius of the Ln3+ ion.