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We present some new results on heavy-element nuclear-structure properties calculated on the basis of the finite-range droplet model and folded-Yukawa single-particle potential. Specifically, we discuss calculations of nuclear ground-state…
A new method for approximating fractional derivatives of the Gaussian function and Dawson's integral are presented. Unlike previous approaches, which are dominantly based on some discretization of Riemann-Liouville integral using polynomial…
We prove a fractional Pohozaev type identity in a generalized framework and discuss its applications. Specifically, we shall consider applications to nonexistence of solutions in the case of supercritical semilinear Dirichlet problems and…
We present a simple method to decompose the Green forms corresponding to a large class of interesting symmetric Dirichlet forms into integrals over symmetric positive semi-definite and finite range (properly supported) forms that are…
We present a heavy quark fragmentation mechanism based on a modified version of the standard model of quark fragmentation, taking into account peculiarities of the Regge trajectories of quarkonia containing heavy quarks. The modified model…
The Dicke model describes an ensemble of N identical two-level atoms (qubits) coupled to a single mode of a bosonic field. The fermion Dicke model should be obtained by changing the atomic pseudo-spin operators by a linear combination of…
By using coupling method, a Bismut type derivative formula is established for the Markov semigroup associated to a class of hyperdissipative stochastic Navier-Stokes/Burgers equations. As applications, gradient estimates, dimension-free…
The application of functional integral methods and the Hubbard--Stratonovich transformation to the Hubbard model is discussed. For the attractive case, using a simple gauge transformation of the superconducting order parameter field, the…
We consider a quasi-regular Dirichlet form. We show that a bounded signed measure charges no set of zero capacity associated with the form if and only if the measure can be decomposed into the sum of an integrable function and a bounded…
Miura-type transformations (MTs) are an essential tool in the theory of integrable nonlinear partial differential and difference equations. We present a geometric method to construct MTs for differential-difference (lattice) equations from…
The solution of pseudo initial value differential equations, either ordinary or partial (including those of fractional nature), requires the development of adequate analytical methods, complementing those well established in the ordinary…
A thorough account is given of the derivation of uniform semiclassical approximations to the particle and kinetic energy densities of N noninteracting bounded fermions in one dimension. The employed methodology allows the inclusion of…
Quasi-classical quantization of crystal dislocations field is considered in terms of functional integral. The generalized zeta-function is used to evaluate the functional integral and quantum corrections to mass in quasi-classical…
In our preceding paper, we have proposed an algorithm for obtaining finite-norm solutions of higher-order linear ordinary differential equations of the Fuchsian type [\sum_m p_m (x) (d/dx)^m] f(x) = 0 (where p_m is a polynomial with…
In this paper, we first establish decay estimates for the fractional and higher-order fractional H\'enon-Lane-Emden systems by using a nonlocal average and integral estimates, which deduce a result of non-existence. Next, we apply the…
We survey approaches to nonrelativistic density functional theory (DFT) for nuclei using progress toward ab initio DFT for Coulomb systems as a guide. Ab initio DFT starts with a microscopic Hamiltonian and is naturally formulated using…
Solution of fractional differential equations is an emerging area of present day research because such equations arise in various applied fields. In this paper we have developed analytical method to solve the system of fractional…
This paper deals with some special integral transforms of Bargmann-Fock type in the setting of quaternionic valued slice hyperholomorphic and Cauchy-Fueter regular functions. The construction is based on the well-known Fueter mapping…
In this work, we propose an efficient finite element method for solving fractional Sturm-Liouville problems involving either the Caputo or Riemann-Liouville derivative of order $\alpha\in(1,2)$ on the unit interval $(0,1)$. It is based on…
In this paper we discuss a new approach to the quasinormal-mode problem in general relativity. By combining a characteristic formulation of the perturbation equations with the integration of a suitable phase-function for a complex valued…