相关论文: Recurrence relations for relativistic two centre m…
In the literature on quantum reference frames, the internal (relative) properties of a system are defined as those which are preserved under an arbitrary change of reference frame. For a system of quantum spins, these are all properties…
This note provides formula for determinant and inverse of r-circulant matrices with general sequences of third order. In other words, the study combines many papers in the literature.
By definition, reciprocal matrices are tridiagonal $n$-by-$n$ matrices $A$ with constant main diagonal and such that $a_{i,i+1}a_{i+1,i}=1$ for $i=1,\ldots,n-1$. For $n\leq 6$, we establish criteria under which the numerical range…
Calculations of two-particle correlations usually assume particles interact only pair-wise after their final collisions with third bodies. By considering classical trajectories, we show that interactions with the mean field can alter the…
In this paper, we develop an approach to recursively estimate the quadratic risk for matrix recovery problems regularized with spectral functions. Toward this end, in the spirit of the SURE theory, a key step is to compute the (weak)…
A simple recurrence relation for the even order moments of the Fabius function is proven. Also, a very similar formula for the odd order moments in terms of the even order moments is proved. The matrices corresponding to these formulas (and…
The general scheme for the treatment of relaxation processes and temporal autocorrelations of dynamical variables for many particle systems is presented in framework of the recurrence relations approach. The time autocorrelation functions…
The ensemble inter-relations to be considered are special features of classical cases, where the joint eigenvalue probability density can be computed explicitly. Attention will be focussed too on the consequences of these inter-relations,…
This study presents the derivation of a recursive formula for integrals of products of $N$ Hermite polynomials, establishing a numerically stable scheme for their accurate evaluation in computer codes. The derivation is notably simple and…
In this paper, we have applied a three-dimensional approach for calculation of the relativistic nucleon-nucleon potential. The quadratic operator relation between the non-relativistic and the relativistic nucleon-nucleon interactions is…
If $A$ is a tridiagonal matrix, then the equations $AX=I$ and $XA=I$ defining the inverse $X$ of $A$ are in fact the second order recurrence relations for the elements in each row and column of $X$. Thus, the recursive algorithms should be…
Formal definition of the reference frame is given. This definition is valid for nonrelativistic and relativistic cases. Proposed definition allows using wide classes of reference frames without restriction to inertial, uniformly accelerated…
The variational calculation of the two-electron reduced density matrix (2-RDM) is extended to periodic molecular systems. If the 2-RDM theory is extended to the periodic case without consideration of time-reversal symmetry, however, it can…
We revisit the relative perturbation theory for invariant subspaces of positive definite matrix pairs. As a prototype model problem for our results we consider parameter dependent families of eigenvalue problems. We show that new estimates…
Reciprocal transformations mix the role of the dependent and independent variables of (nonlinear partial) differential equations to achieve simpler versions or even linearized versions of them. These transformations help in the…
In this paper, we outline a method to determine all recursive relations for a subnormal 2-variable weighted shift, up to total degree $k$, entirely from the representing measure. This allows us to show that the densities of the atoms do not…
We introduce the concept of reflexive moment functional in two variables and the definition of reflexive orthogonal polynomial system. Also reverse matrices and their interesting algebraic properties are studied. Reverse matrices and…
We set up a method for a recursive calculation of the effective potential which is applied to a cubic potential with imaginary coupling. The result is resummed using variational perturbation theory (VPT), yielding an exponentially fast…
We present a proof of the generalized Kramers-Pasternack relation using the hyper-radial equation approach. Following Kramers' method, we manipulate the radial equation by multiplying it with an expression closely related to terms in the…
We consider a certain linear recursive relation with integer parameters and study some of its algebraic and geometric properties, with the purpose of estimating the number of chains of valences in the Farey series.