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Coulomb wave functions are difficult to compute numerically for extremely low energies, even with direct numerical integration. Hence, it is more convenient to use asymptotic formulas in this region. It is the object of this paper to derive…
Variational calculations using Gaussian wave functionals combined with an approximate projection on gauge invariant states are presented. We find that the energy exhibits a minimum for a wave functional centered around a non vanishing…
We establish derivative estimates of solution of elliptic system in narrow regions.
We give an algorithm to compute the series expansion for the inverse of a given function. The algorithm is extremely easy to implement and gives the first $N$ terms of the series. We show several examples of its application in calculating…
High accuracy helium wave functions based on exponentials with random coefficients are transformed into momentum space. The utility of the wave functions is demonstrated through calculation of the expectation value of various operators…
We develop closed-form expansions for the implied volatility of VIX options within the class of forward variance models. Our approach builds on weak-approximation techniques for VIX option prices and yields explicit implied volatility…
The evaluation of vacuum expectation values (VEVs) in massive integrable quantum field theory (QFT) is a nontrivial renormalization-group "connection problem" -- relating large and short distance asymptotics -- and is in general unsolved.…
While analytic calculations may give access to complex-valued electromagnetic field data which allow trivial access to envelope and phase information, the majority of numeric codes uses a real-valued represantation. This typically increases…
The learning and evaluation of energy-based latent variable models (EBLVMs) without any structural assumptions are highly challenging, because the true posteriors and the partition functions in such models are generally intractable. This…
We obtain cubature formulas of volume potentials over bounded domains combining the basis functions introduced in the theory of approximate approximations with their integration over the tangential-halfspace. Then the computation is reduced…
We extend the $L^4$-square function estimates for the parabola and the half-cone to quadratic manifolds in higher dimensions and their conical extensions. To this end, we require transversality for the tangent spaces of the quadratic…
Vacuum expectation values of local fields for all dual pairs of non-simply laced affine Toda field theories recently proposed are checked against perturbative analysis. The computations based on Feynman diagram expansion are performed upto…
This paper presents a comprehensive review of the wave-function approach for derivation of the number-resolved Master equations, used for description of transport and measurement in mesoscopic systems. The review contains important…
We present a simple formalism for the calculation of the derivatives of the electronic density matrix at any order, within density functional theory. Our approach, contrary to previous ones, is not based on the perturbative expansion of the…
We recommended consequent discrete combinatorial research in mathematical physics. Here we show an example how discretization of partial differential equations can be done and that quickly unexpected new findings can result from research in…
We study Whitney-type estimates for approximation of convex functions in the uniform norm on various convex multivariate domains while paying a particular attention to the dependence of the involved constants on the dimension and the…
We present the mathematical and numerical theory for evanescent waves in subwavelength band gap materials. We begin in the one-dimensional case, whereby fully explicit formulas for the complex band structure, in terms of the capacitance…
A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of extensor fields is present using algebraic and analytical tools developed in previous papers. Several important formulas are derived.
The derivative expansion of the effective action is considered in the model with two interacting real scalar fields in curved spacetime. Using the functional approach and local momentum representation, the coefficient of the derivative term…
In this article, we are concerned with a multidimensional degenerate parabolic-hyperbolic equation driven by Levy processes. Using bounded variation (BV) estimates for vanishing viscosity approximations, we derive an explicit continuous…