Precise Conductance Measurements on Dilute Aqueous Solutions of Sodium and Potassium Hydrogenphosphate and Dihydrogenphosphate

Precise conductance measurements are reported on dilute aqueous solutions of the sodium and potassium salts of orthophosphoric acid at 25 ^∘C. Conductance measurements on solutions of electrolytes such as these phosphate salts that exist in solution as complicated mixtures of ions have previously proved difficult to interpret. To overcome this, a mathematical method has been developed to calculate the concentrations of all the species in the aqueous system M₃PO₄/M₂HPO₄/M₂HPO₄/H₃PO₄ (M = Na or K) over a continuous range of stoichiometries. The Lee–Wheaton conductance equation has been used to interpret the conductance of these multicomponent solutions in terms of the limiting ionic conductances and concentrations of all the ions in the solution. The limiting molar conductances of the ions H₂PO₄ ⁻ and HPO₄ ²⁻ and the ion-pair formation constants of these ions with sodium and potassium ions were determine This work has enabled the accurate determination of solution parameters for the important hydrogenphosphate ions in water and provides an excellent example of the use of an advanced conductance theory in the analysis of the conductance of multicomponent electrolyte systems.     

Hedging mortality/longevity risks of insurance portfolios for life insurer/annuity provider and financial intermediary

In this paper, we propose two risk hedge schemes in which a life insurer (an annuity provider) can transfer mortality (longevity) risk of a portfolio of life (annuity) exposures to a financial intermediary by paying the hedging premium of a mortality-linked security. The optimal units of the mortality-linked security which maximize hedge effectiveness for a life insurer (an annuity provider) can be derived as closed-form formulas under the risk hedge schemes. Numerical illustrations show that the risk hedge schemes can significantly hedge the downside risk of loss due to mortality (longevity) risk for the life insurer (annuity provider) under some stochastic mortality models. Besides, finding an optimal weight of a portfolio of life and annuity business, the financial intermediary can reduce the sensitivity to mortality rates but the model risk; a security loading may be imposed on the hedge premium for a higher probability of gain to compensate the financial intermediary for the inevitable model risk.     

The structure of linear codes of constant weight

In this paper we determine completely the structure of linear codes over of constant weight. Namely, we determine exactly which modules underlie linear codes of constant weight, and we describe the coordinate functionals involved. The weight functions considered are: Hamming weight, Lee weight, two forms of Euclidean weight, and pre-homogeneous weights. We prove a general uniqueness theorem for virtual linear codes of constant weight. Existence is settled on a case by case basis.

     

A Conversation with Lee Alvin DuBridge - Part II

Physicist Lee A. DuBridge became president of the California Institute of Technology in 1946. In this interview he recalls his dealings at Caltech with Linus Pauling; his memories of George W. Beadle, Theodore von Kármán, and J. Robert Oppenheimer; the military Vista Project at Caltech; and the difficulties surrounding the deportation of Hsue-Shen Tsien, Caltech's Goddard Professor of Jet Propulsion.     

On Norden Metrics which Are Locally Conformal to Anti-Kählerian Metrics

We build examples of Norden metrics on × S ¹, where R ^{2 n} _n is either a pseudosphere or a pseudohyperbolic space. These turn out to be locally conformal to flat anti-Kählerian metrics, strongly non anti-Kählerian, and with a parallel Lee form. Conversely, any connected complete anti-Hermitian manifold possessing these properties is shown to be locally analytically homothetic to × S ¹.     

A new numerical approach for single rational soliton solution of Chen‐Lee‐Liu equation with Riesz fractional derivative in optical fibers

In this paper, time‐splitting spectral approximation technique has been proposed for Chen‐Lee‐Liu (CLL) equation involving Riesz fractional derivative. The proposed numerical technique is efficient, unconditionally stable, and of second‐order accuracy in time and of spectral accuracy in space. Moreover, it conserves the total density in the discretized level. In order to examine the results, with the aid of weighted shifted Grünwald‐Letnikov formula for approximating Riesz fractional derivative, Crank‐Nicolson weighted and shifted Grünwald difference (CN‐WSGD) method has been applied for Riesz fractional CLL equation. The comparison of results reveals that the proposed time‐splitting spectral method is very effective and simple for obtaining single soliton numerical solution of Riesz fractional CLL equation.     

Demixing and nematic behaviour of oblate hard spherocylinders and hard spheres mixtures: Monte Carlo simulation and Parsons–Lee theory

Parsons–Lee approach is formulated for the isotropic–nematic transition in a binary mixture of oblate hard spherocylinders and hard spheres. Results for the phase coexistence and for the equation of state in both phases for fluids with different relative size and composition ranges are presented. The predicted behaviour is in agreement with Monte Carlo simulations in a qualitative fashion. The study serves to provide a rational view of how to control key aspects of the behaviour of these binary nematogenic colloidal systems. This behaviour can be tuned with an appropriate choice of the relative size and molar fractions of the depleting particles. In general, the mixture of discotic and spherical particles is stable against demixing up to very high packing fractions. We explore in detail the narrow geometrical range where demixing is predicted to be possible in the isotropic phase. The influence of molecular crowding effects on the stability of the mixture when spherical molecules are added to a system of discotic colloids is also studied.