Gravity and CP violation

The non-conservation of CP symmetry in the decay of neutralK mesons was discovered almost three decades ago. The origin of this unique phenomenon is still not well understood. There have been attempts to link it with energy splitting of theK and in the earth's gravitational field. In this essay we examine these attempts critically. A more natural way in which a gravitational field can couple asymmetrically to the system is through torsion, which coupling to isospin can, in addition to parity violation, also give rise to a C violation. The magnitude of this effect is estimated in the vicinity of a kaon and found to give a CP-violating parameter of the right value. Moreover, it is predicted that the CP violating parameter for the new system is much smaller 10^–6. Implications for baryogenesis in the early universe is also studied. In this paper we work not with the Newtonian gravitational constantG but with a torsion coupling constant, which is energy-dependent and can be related to the Fermi weak interaction constant.     

Density computations for real quadratic units

In order to study the density of the set of positive integers for which the negative Pell equation is solvable in integers, we compute the norm of the fundamental unit in certain well-chosen families of real quadratic orders. A fast algorithm that computes 2-class groups rather than units is used. It is random polynomial-time in as the factorization of is a natural part of the input for the values of we encounter. The data obtained provide convincing numerical evidence for the density heuristics for the negative Pell equation proposed by the second author. In particular, an irrational proportion of the real quadratic fields without discriminantal prime divisors congruent to 3 mod 4 should have a fundamental unit of norm .

     

Inner shell structure of heavy atoms

The inner-shell structure of some heavy atoms is examined using a self-consistent relativistic local density method. Ar(K), Kr(K) and Xe (K,L ₁,L ₂ andL ₃) binding energies and {ie863-1} (hyper-satellite) energies of Tl, Hg and Tm are calculated. The results are compared with available experimental data. A part of this work was presented byMPD at the Trieste International Symposium on “Core level excitations in atoms, molecules and solids,” 22–26 June 1981, Extended Abstracts (ed.) E Tosatti, ICTP Report No. 89/81 p. 11.     

Tuning of the alpha-terthiophene radical cation coupling reaction using mixed micelles with varying charge density.

The photophysics and photochemistry of alpha-terthiophene (alphaT), compartmentalized in mixed nonionic/anionic micelles, have been investigated with focus on the influence of the micellar surface charge density on the formation of the radical coupling product alpha-hexathiophene (alphaH). By varying the ratio of nonionic-to-anionic surfactants, and assuming ideal mixing, the charge density of the mixed micelles was varied. From Poisson-Boltzmann calculations, performed using the cell model, the electrostatic potential and the counterion activity were estimated as a function of the distance from the micellar surface. Upon excitation, the triplet state of alphaT is formed, from which the alphaT radical cation can be formed by absorption of a second photon. The radical cation can form alphaH if it encounters another alphaT radical cation. Under the experimental conditions used, this implies that the alphaH formation only occurs if the compartmentalized radical cation is able to migrate from its host micelle to another micelle, either via the surrounding bulk or by fusion of two micelles followed by mixing of their contents before micellar fission. The formation yield of the radical cation depends on the charge density of the mixed micelle; a lower charge density, that is, an increased amount of nonionic surfactant, lowers the yield. The yield of the coupling product alphaH, however, does not follow the same trend. A maximum yield of alphaH is found at intermediate nonionic surfactant molar ratios. This behavior is understood in terms of the Poisson-Boltzmann simulation results and by comparing charge-density changes as a function of molar fraction with the changes in counterion activity. The alphaH yield is a result of the balance between an increased possibility of radical cation bulk migration and a lowered electrostatic stabilization of the radical.     

A density functional theory study on the electrocyclization of 1,2,4,6-heptatetraene analogues: converting a pericyclic to a pseudopericyclic reaction

A comprehensive B3LYP/6-31+G* study on the electrocyclization of 1,2,4,6-heptatetraene analogues was conducted. Starting from the cyclization of (2Z)-2,4,5-hexatrienal, a pericyclic disrotatory process favored by the assistance of a electron lone pair, we incorporated small modifications in its molecular structure to obtain a truly pseudopericyclic process. To this purpose electronegative atoms (fluorine and nitrogen) were added to give a more electrophilic character on the carbon atom which is attacked by the electron lone pair of the oxygen atom. The complete pathway for each reaction was determined, and changes in magnetic properties were monitored with a view to estimating the aromatization associated with each process. This information, together with the energetic and structural results, allowed us to classify the reactions as pseudopericyclic or pericyclic. Among all studied reactions only one was a truly pseudopericyclic process and another was a borderline case. The features of this unequivocally pseudopericyclic case were analyzed in depth.     

Solubility of Triethylamine in Tetraethylammonium Chloride Aqueous Solutions from 20 to 35°C

Solubilities of triethylamine in aqueous tetraethylammonium chloride solutions were measured at 20, 25, and 35°C. The molalities in Et₄NCl of the aqueous solvents ranged from 0.03 to 1 mol-kg^–1. The data were evaluated from density measurements using a vibrating-tube densimeter. At each temperature, least-squares method was used to fit experimental density data points to double polynomial equations of various degrees. Triethylamine molalities of the saturated aqueous phases were estimated by extrapolation from those equations. Experimental data were interpreted in terms of hydrophobic and electrostatic perturbed domains in the hydration shells of the noneleceory and of the cation of the salt, as a function of temperature and salt concentration. The conclusions obtained are consistent with previous volumetric studies.     

Influence of Cycle Temperatures on the Thermochemical Heat Storage Densities in the Systems Water/Microporous and Water/Mesoporous Adsorbents

The adsorption equilibrium of water on microporous adsorbents (zeolites of NaA-, NaY- and NaX-type as well as their ion exchanged forms) and on mesoporous adsorbents (different silica gels and composite material i.e. silica gel + salt hydrate) has been studied experimentally and theoretically. Using the Dubinin theory of pore filling the characteristic curves of the adsorption systems and other relevant dependences such as isotherms, isobars, isosteres and the curve of the differential heat of adsorption were calculated. For all systems investigated the adsorption were calculated. A_ads and the desorption potential A_des of the closed heat storage system were estimated. These values define the working range of the adsorption/desorption cycle and allow to calculate the specific heat storage density Δ h_sp. On the basis of Δ h_sp the different adsorbents were compared in order to select the optimal porous storage material for a given application. The presented experimental and theoretical investigations show that the adsorption systems water-zeolite and water-composites are promising working pairs for thermochemical heat storage processes for hot tap water supply and space heating of single family dwellings. The advantage of the water-composite system is the low desorption temperature (solar energy) the main shortcoming the low temperature lift. The advantage of the water zeolite system is the high temperature lift, the shortcoming are the relative high desorption temperatures.     

Optimal convergence properties of kernel density estimators without differentiability conditions

Let X ₁, X ₂, ..., X _n be independent observations from an (unknown) absolutely continuous univariate distribution with density f and let % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% GabmOzayaajaGaaiikaiaadIhacaGGPaGaeyypa0Jaaiikaiaad6ga% caWGObGaaiykamaaCaaaleqabaGaeyOeI0IaaGymaaaakmaaqadaba% Gaam4saiaacUfadaWcgaqaaiaacIcacaWG4bGaeyOeI0Iaamiwamaa% BaaaleaacaWGPbaabeaakiaacMcaaeaacaWGObGaaiyxaaaaaSqaai% aadMgacqGH9aqpcaaIXaaabaGaamOBaaqdcqGHris5aaaa!5356!\[\hat f(x) = (nh)^{ - 1} \sum\nolimits_{i = 1}^n {K[{{(x - X_i )} \mathord{\left/ {\vphantom {{(x - X_i )} {h]}}} \right. \kern-\nulldelimiterspace} {h]}}} \] be a kernel estimator of f(x) at the point x, \s-<x<, with h=h _n (h _n O and nh _n , as n) the bandwidth and K a kernel function of order r. Optimal rates of convergence to zero for the bias and mean square error of such estimators have been studied and established by several authors under varying conditions on K and f. These conditions, however, have invariably included the assumption of existence of the r-th order derivative for f at the point x. It is shown in this paper that these rates of convergence remain valid without any differentiability assumptions on f at x. Instead some simple regularity conditions are imposed on the density f at the point of interest. Our methods are based on certain results in the theory of semi-groups of linear operators and the notions and relations of calculus of finite differences.This research was supported in part by grants from the Natural Sciences and Engineering Research Council of Canada and the University of Alberta Central Research Fund.     

Phenomenology of nonlocal cellular automata

Dynamical systems with nonlocal connections have potential applications to economic and biological systems. This paper studies the dynamics of nonlocal cellular automata. In particular, all two-state, three-input nonlocal cellular automata are classified according to the dynamical behavior starting from random initial configurations and random wirings, although it is observed that sometimes a rule can have different dynamical behaviors with different wirings. The nonlocal cellular automata rule space is studied using a mean-field parametrization which is ideal for the situation of random wiring. Nonlocal cellular automata can be considered as computers carrying out computation at the level of each component. Their computational abilities are studied from the point of view of whether they contain many basic logical gates. In particular, I ask the question of whether a three-input cellular automaton rule contains the three fundamental logical gates: two-input rules AND and OR, and one-input rule NOT. A particularly interesting edge-of-chaos nonlocal cellular automaton, the rule 184, is studied in detail. It is a system of coupled selectors or multiplexers. It is also part of the Fredkin's gate—a proposed fundamental gate for conservative computations. This rule exhibits irregular fluctuations of density, large coherent structures, and long transient times.     

Partial molal volumes of ions in organic solvents from ultrasonic vibration potential and density measurements. III. Dimethylsulfoxide

The partial molal volumes of Li⁺, Na⁺, K⁺, Rb⁺, Cs⁺, Cl^–, Br^–, I^–, and NO ₃ ^- in DMSO at 25°C have been determined from ultrasonic vibration potential data and density data for solutions of uni-univalent electrolytes. Hepler's semiemprirical equation has been used to split ionic partial molal volumes into geometric and electrostrictive contributions. The results obtained in this work confirm the conclusion of our previous studies, namely, that the contribution of electrostriction is essentially determined by the properties of that layer of atoms, 0.3 to 0.4 nm thick, in contact with the ion and by the degree of steric hindrance of the poles of the dipole of the solvent molecule. On the other hand, the geometric contribution depends on the size of the solvent molecule and also on the arrangement of the solvent molecules about the ions. It is shown that the geometric contribution to the partial molal volume of ions is largely increased when ions cannot come close enough to the poles of the solvent-molecule dipole, owing to steric hindrance.