Average boundary conditions in Cauchy problems

We consider the general Cauchy problem with initial data in a Hilbert space and with a formal dissipative linear generator. A complete parametrization is known of the (abstract) boundary conditions which make this problem well set. We exhibit a distinguished subset $\text{B}$_E of the set $\text{B}$ of boundary conditions and demonstrate explicitly that the evolution associated with each B in $\text{B}$ can be represented as a (time independent) average over the evolutions associated with B′ in $\text{B}$_E. Applications are discussed to Schrödinger equations in bounded regions or with singular potentials.     

Book review

Demand Functions and the Slutsky Matrix by S.N. Afriat, Princeton University Press, New Jersey 1980 (xii + 269pp.).     

Temperature dependence of the thermal conductivity for tellurium dioxide

The thermal conductivity of tellurium dioxide is reported as a function of temperature. At 77K, the thermal conductivity is 0.09 W/cm-K and it decreases approximately as the inverse of the temperature to a value of 0.02 W/cm-K at 300K. The anisotropy between the a- and c-axes is less than 20% over the entire experimental temperature range, with the a-axis more conductive than the c-axis. By making some simplifying assumptions, the phonon mean free paths and relaxation times are deduced.     

On the nature of the low-lying states of TiO

A series of CAS SCF calculations are used to describe the lowest states of TiO. TiO is described as having polarized double bonds involving the Ti 3d orbitals. The nature of the excited states is discussed.     

Effect of temperature on ionic volumes and heat capacities in methanol

A flow densimeter and flow heat capacity calorimeter have been employed to measure precision densities and specific heats of selected electrolytes and nonelectrolytes in methanol at 20, 25, and 40°C. Apparent molar volumes and heat capacities have been calculated and the corresponding standard state functions, V ^o and C _p, ^o , evaluated. The data have been used, along with known volumes and heat capacity data at 25°C for numerous alkanes, to generate volumes and heat capacities of model compounds for organic electrolytes. Comparison of the thermodynamic functions for the model compounds with those of the corresponding electrolytes at the respective temperatures has made it possible to assign single ion values and to establish the temperature effects of ionic charges on the volumes and heat capacities of solutes.     

Computational investigation of rules governing selective adsorption intensities

Rules previously derived by Wolfe and Weare governing selective adsorption scattering intensities are investigated computationally via the attractive corrugated wall (ACW) model of Harvie and Weare. These rules, which correlate features of the scattering intensity with the form of the atom surface potential, correctly predict intensity features seen in the ACW calculation.     

A radical diophantine equation

All solutions in positive integers x, yz of the diophantine equation $\text{x}{}^{\mathrm{<mtext>1</mtext><mtext>m</mtext>}}\text{+ y}{}^{\mathrm{<mtext>1</mtext><mtext>n</mtext>}}\text{= z}{}^{\mathrm{<mtext>1</mtext><mtext>r</mtext>}}$ are determined, where m, n, r are given positive integers. The proof makes use of a simple criterion for the irreducibility of the polynomial xⁿ ? a over the rationals, where a is a positive rational.     

Preliminary studies on the recovery of oil from chattanooga shale

Three exploratory investigations have been performed to examine the recovery of oil from the Chattanooga black shale formation. Thermogravimetric data were analyzed to yield an average activation energy of 57.1 kcal mol^?1 for the conversion process; positive deviations from a reaction order of 3.7 were observed suggesting the presence of autocatalytic effects at low conversion levels. Thermal chromatographic analysis indicated that the maximum organic product release occurred at approximately 435°C and resulted in an oil of relatively low distillation range. A packed bed of shale was retorted in the self-sustained combustion mode thus suggesting the feasibility of this mode for in situ oil recovery. Comparisons with oil shale from Colorado's Green River formation have been made throughout.