In this paper, we give the white noise calculus for the Fermion system and prove the Fock expansion for any continuous linear operators from the space of test functionals to the space of generalized functionals. As an application of the Fock expansion, we give a necessary and sufficient condition for implementability of Bogoliubov automorphisms on Z2-invariant subalgebra of canonical anti-commu...

Popular modern generalized gradient approximations are biased toward the description of free-atom energies. Restoration of the first-principles gradient expansion for exchange over a wide range of density gradients eliminates this bias. We introduce a revised Perdew-Burke-Ernzerhof generalized gradient approximation that improves equilibrium properties of densely packed solids and their surfaces.

The paper studies some properties of the ring of integer-valued quasi-polynomials. On this ring, theory of generalized Euclidean division and generalized greatest common divisor are presented. Applications to finite simple continued fraction expansion of rational numbers and Smith normal form of integral matrices with an integer parameter are also given.

In this paper we study the properties of coefficients appearing in the series expansions for zeros of generalized Rogers-Ramanujan series. Our primary purpose is to address several conjectures made by M. E. H Ismail and C. Zhang. We prove that the coefficients in the series expansion of each zero approach rational multiples of π and π as q → 1−. We also show that certain polynomials arising in ...

We present the theory of weak gravitational lensing in cosmologies with generalized gravity, described in the Lagrangian by a generic function depending on the Ricci scalar and a non-minimally coupled scalar field. We work out the generalized Poisson equations relating the dynamics of the fluctuating components to the two gauge invariant scalar gravitational potentials, fixing the new contribut...

An asymptotic expansion is obtained for an incomplete beta-type integral, which arises in the study of probabilities of large deviations. The expansion obtained yields large deviation results for binomial, quantile, and related probabilities. Our approach is based on a generalized version of Laplace's method.

We develop an operator formulation for the Drell-Yan production of lepton pair in hadron-hadron collisions. We employ the generalized Wilson operator expansion where the main ingredients are the Keldysh formalism and the gauge-invariant nonlocal operators. Compared to conventional approaches based on the collinear expansion of the relevant diagrams, our approach has an advantage of preserving e...