Determinantal representations of smooth cubic surfaces

For every smooth (irreducible) cubic surface S we give an explicit construction of a representative for each of the 72 equivalence classes of determinantal representations. Equivalence classes (under GL₃ × GL₃ action by left and right multiplication) of determinantal representations are in one to one correspondence with the sets of six mutually skew lines on S and with the 72 (two-dimensional) linear systems of twisted cubic curves on S. Moreover, if a determinantal representation M corresponds to lines (a ₁,...,a ₆) then its transpose M ^t corresponds to lines (b ₁,...,b ₆) which together form a Schläfli’s double-six \(a_1\ldots a_6 \choose b_1\ldots b_6\) . We also discuss the existence of self-adjoint and definite determinantal representation for smooth real cubic surfaces. The number of these representations depends on the Segre type F _i . We show that a surface of type F _i , i = 1,2,3,4 has exactly 2(i?1) nonequivalent self-adjoint determinantal representations none of which is definite, while a surface of type F ₅ has 24 nonequivalent self-adjoint determinantal representations, 16 of which are definite.     

The temperature dependence of dislocation charge in calcium doped single crystals of potassium chloride

Abstract

Using the ultrasonic piezoelectric composite oscillator technique we have measured the temperature dependence of dislocation charge in bent KCl single crystals as a function of Ca impurity concentration. In each case the charge changes sign at an extrinsic isoelectric temperature, T_e , and the shift in Te with impurity concentration allows the calculation of the individual thermodynamic vacancy formation parameters. We obtain h₊ = 1.244±0.014 eV, s₊ = 4.50±0.19 k, h- = 1.346? 0.014 eV and s- = 5.11?0.19K.     

Single-phase Bi2+x(Ca,Sr) n+1 Cu n O2n+4+δ, n = 0, 1, 2, 3 AND ∞, and some substitutional DERIVATIVES

The preparation, structure and properties of five members of the homologous series Bi_2+x(Ca,Sr) _n+1 Cu _n O_2n+4+δ are discussed, namely for n = 0, 1, 2, 3 and ∞. The two end members are insulating phases with a fixed oxygen stoichiometry but the members n = 1, 2 and 3 are superconducting phases with T_c depending on the calcium to strontium ratio and on oxygen stoichiometry as determined by annealing temperature and oxygen partial pressure. Maximum zero resistance T_c 's obtained are n = 1: 76 K, n = 2: 91 K and n = 3: 106 K. The effects of Pb-substitution in n = 2 and n = 3 are discussed with particular reference to the stabilisation of the latter phase. Rare-earth substitution is shown to raise T_c for n = 2 to at least 101 K without the introduction of the n = 3 phase.     

Regenerating a symmetry in asymmetric dark matter

Asymmetric dark matter theories generically allow for mass terms that lead to particle-antiparticle mixing. Over the age of the Universe, dark matter can thus oscillate from a purely asymmetric configuration into a symmetric mix of particles and antiparticles, allowing for pair-annihilation processes. Additionally, requiring efficient depletion of the primordial thermal (symmetric) component generically entails large annihilation rates. We show that unless some symmetry completely forbids dark matter particle-antiparticle mixing, asymmetric dark matter is effectively ruled out for a large range of masses, for almost any oscillation time scale shorter than the age of the Universe.     

Fluctuations of the Increment of the Argument for the Gaussian Entire Function

The Gaussian entire function is a random entire function, characterised by a certain invariance with respect to isometries of the plane. We study the fluctuations of the increment of the argument of the Gaussian entire function along planar curves. We introduce an inner product on finite formal linear combinations of curves (with real coefficients), that we call the signed length, which describes the limiting covariance of the increment. We also establish asymptotic normality of fluctuations.     

Oxygen harvesting from carbon dioxide: simultaneous epoxidation and CO formation

Due to increasing concentrations in the atmosphere, carbon dioxide has, in recent times, been targeted for utilisation (Carbon Capture Utilisation and Storage, CCUS). In particular, the production of CO from CO₂ has been an area of intense interest, particularly since the CO can be utilized in Fischer–Tropsch synthesis. Herein we report that CO₂ can also be used as a source of atomic oxygen that is efficiently harvested and used as a waste-free terminal oxidant for the oxidation of alkenes to epoxides. Simultaneously, the process yields CO. Utilization of the atomic oxygen does not only generate a valuable product, but also prevents the recombination of O and CO, thus increasing the yield of CO for possible application in the synthesis of higher-order hydrocarbons.

Selective formation of atomic oxygen to form epoxides in a waste free process is reported. Simultaneously generating carbon monoxide from carbon dioxide for further use.