We use an interactive epistemology framework to provide a systematic analysis of some solution concepts for games with asymmetric information. We characterize solution concepts using expressible epistemic assumptions, represented as events in the canonical space generated by primitive uncertainty about the payoff relevant state, payoff irrelevant information, and actions. In most of the paper, ...

We announce a proof of an asymptotic formula for the ground{state energy of a large atom. The early work of Thomas{Fermi, Hartree{Fock, Dirac and Scott predicted

Let F be a distribution and let f be a locally summable function. The distribution F( f ) is defined as the neutrix limit of the sequence {Fn( f )}, where Fn(x) = F(x)∗δn(x) and {δn(x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function δ(x). The composition of the distributions x−sIn|x| and |x| is evaluated for s= 1,2, . . . ,μ > 0 and μs = 1,2,...

Let f be a real arithmetic function and ∆(n, f) := sup u2R, 06v61 ���� X d|n eu<d6eu+v f(d) ���� denote the corresponding generalization of Hooley’s Delta-function. We investigate weighted moments of ∆(n; f) for oscillating functions f , typical cases being those of a non principal Dirichlet character or of the Möbius function. We obtain, in particular, sharp bounds up to factors (log x)o(1) fo...

Let F be a distribution in D′ and let f be a locally summable function. The composition F f x of F and f is said to exist and be equal to the distribution h x if the limit of the sequence {Fn f x } is equal to h x , where Fn x F x ∗ δn x for n 1, 2, . . . and {δn x } is a certain regular sequence converging to the Dirac delta function. It is proved that the neutrix composition δ rs−1 tanhx 1/r ...

We describe some new families of quasimodes for the Laplacian perturbed by the addition of a potential formally described by a Dirac delta function. As an application we find, under some additional hypotheses on the spectrum, subsequences of eigenfunctions of Šeba billiards that localise around a pair of unperturbed eigenfunctions.

The delta-function potential model and its application to the calculations of bond region as well as nonbond region electron contributions to the parallel component and bond perpendicular component are briefly surveyed. The L E W I S L A N G M U I R octet rule modified by LINNETT as a doublequartet of electrons is employed. The calculations of bond and molecular polarizabilities have been made ...

This paper is devoted to the study of delta shockwaves for a hyperbolic systemof conservation laws of Keyfitz-Kranzer typewith two linearly degenerate characteristics.TheRiemannproblem is solved constructively.TheRiemann solutions include exactly two kinds. One consists of two (or just one) contact discontinuities, while the other contains a delta shock wave. Under suitable generalized Rankine-...