Heat of Formation of O2–

A series of Born–Mayer-type calculations are used to calculate the lattice energies of simple oxides (MgO, BeO, CaO, and ZnO). Repulsion and other non-Coulombic contributions to the lattice energy are obtained using thermodynamic and recent ultrasonic data for the bulk moduli and the isothermal pressure and temperature derivatives of the elastic constants. Using thermochemical data for the heat of formation of MgO, CaO, and BeO and their cations, the heat of formation of O2–, DeltaHf°(O2–), is calculated to be 197 ± 5 kcal/mole. Using the largest value of DeltaHf°(O2–), obtained for MgO, presumably the most ionic of the crystals treated, a value of 202.3 kcal/mole is obtained. These values are believed to be more accurate than earlier values given by Morris and by Huggins and Sakamoto who obtained 210 ± 6 and 221 ± 15 kcal/mole. The anomalously low value calculated for DeltaHf°(O2–) for ZnO is believed to result from a substantial covalent contribution in the Zn[Single Bond]O bond in this oxide

Social Security Reform: Legal Analysis of Social Security Benefit Entitlement Issues

[Excerpt] Calculations indicating that in the long run the Social Security program will not be financially sustainable under the present statutory scheme have fueled the current debate regarding Social Security reform. This report addresses selected legal issues which may be raised regarding entitlement to Social Security benefits as Congress considers possible changes to the Social Security program, and in view of projected long-range shortfalls in the Social Security Trust Funds

Markovian acyclic directed mixed graphs for discrete data

Acyclic directed mixed graphs (ADMGs) are graphs that contain directed ($\rightarrow$) and bidirected ($\leftrightarrow$) edges, subject to the constraint that there are no cycles of directed edges. Such graphs may be used to represent the conditional independence structure induced by a DAG model containing hidden variables on its observed margin. The Markovian model associated with an ADMG is simply the set of distributions obeying the global Markov property, given via a simple path criterion (m-separation). We first present a factorization criterion characterizing the Markovian model that generalizes the well-known recursive factorization for DAGs. For the case of finite discrete random variables, we also provide a parameterization of the model in terms of simple conditional probabilities, and characterize its variation dependence. We show that the induced models are smooth. Consequently, Markovian ADMG models for discrete variables are curved exponential families of distributions.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1206 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Inferring the Rate-Length Law of Protein Folding

We investigate the rate-length scaling law of protein folding, a key undetermined scaling law in the analytical theory of protein folding. We demonstrate that chain length is a dominant factor determining folding times, and that the unambiguous determination of the way chain length corre- lates with folding times could provide key mechanistic insight into the folding process. Four specific proposed laws (power law, exponential, and two stretched exponentials) are tested against one an- other, and it is found that the power law best explains the data. At the same time, the fit power law results in rates that are very fast, nearly unreasonably so in a biological context. We show that any of the proposed forms are viable, conclude that more data is necessary to unequivocally infer the rate-length law, and that such data could be obtained through a small number of protein folding experiments on large protein domains

Melting and Freezing Lines for a Mixture of Charged Colloidal Spheres with Spindle-Type Phase Diagram

We have measured the phase behavior of a binary mixture of like-charged colloidal spheres with a size ratio of 0.9 and a charge ratio of 0.96 as a function of particle number density n and composition p. Under exhaustively deionized conditions the aqueous suspension forms solid solutions of body centered cubic structure for all compositions. The freezing and melting lines as a function of composition show opposite behavior and open a wide, spindle shaped coexistence region. Lacking more sophisticated treatments, we model the interaction in our mixtures as an effective one-component pair energy accounting for number weighted effective charge and screening constant. Using this description, we find that within experimental error the location of the experimental melting points meets the range of melting points predicted for monodisperse, one component Yukawa systems made in several theoretical approaches. We further discuss that a detailed understanding of the exact phase diagram shape including the composition dependent width of the coexistence region will need an extended theoretical treatment.Comment: 25 pages, 4 figure

A Coupled Quantum Otto Cycle

We study the 1-d isotropic Heisenberg model of two spin-1/2 systems as a quantum heat engine. The engine undergoes a four-step Otto cycle where the two adiabatic branches involve changing the external magnetic field at a fixed value of the coupling constant. We find conditions for the engine efficiency to be higher than the uncoupled model; in particular, we find an upper bound which is tighter than the Carnot bound. A new domain of parameter values is pointed out which was not feasible in the interaction-free model. Locally, each spin seems to effect the flow of heat in a direction opposite to the global temperature gradient. This seeming contradiction to the second law can be resolved in terms of local effective temperature of the spins

Graded Lie algebras with finite polydepth

If A is a graded connected algebra then we define a new invariant, polydepth A, which is finite if $Ext_A^*(M,A) \neq 0$ for some A-module M of at most polynomial growth. Theorem 1: If f : X \to Y is a continuous map of finite category, and if the orbits of H_*(\Omega Y) acting in the homology of the homotopy fibre grow at most polynomially, then H_*(\Omega Y) has finite polydepth. Theorem 2: If L is a graded Lie algebra and polydepth UL is finite then either L is solvable and UL grows at most polynomially or else for some integer d and all r, $\sum_{i=k+1}^{k+d} {dim} L_i \geq k^r$, $k\geq$ some $k(r)$