相关论文: A compact formula for the derivative of a 3-D rota…
We introduce a notion of resultant of two meromorphic functions on a compact Riemann surface and demonstrate its usefulness in several respects. For example, we exhibit several integral formulas for the resultant, relate it to potential…
Computation of the spherical harmonic rotation coefficients or elements of Wigner's d-matrix is important in a number of quantum mechanics and mathematical physics applications. Particularly, this is important for the Fast Multipole Methods…
Civan and Sliepcevich [1, 2] suggested that special matrix solver should be developed to further reduce the computing effort in applying the differential quadrature (DQ) method for the Poisson and convection-diffusion equations. Therefore,…
In our previous article [4] an approach to derive Papapetrou equations for constrained electromagnetic field was demonstrated by use of field variational principles. The aim of current work is to present more universal technique of…
Square matrices of the form $\widetilde{\mathbf{A}} =\mathbf{A} + \mathbf{e}D \mathbf{f}^*$ are considered. An explicit expression for the inverse is given, provided $\widetilde{\mathbf{A}}$ and $D$ are invertible with…
In this communication, one shows that there exists in the literature a certain form of deformed derivative that can here be identified as the dual of conformable derivative. The deformed subtraction is used here, together with the duality…
Rotations on the 3-dimensional Euclidean vector-space can be represented by real quaternions, as was shown by Hamilton. Introducing complex quaternions allows us to extend the result to elliptic and hyperbolic rotations on the Minkowski…
This paper presents new approaches for finding the determinant and inverse of a matrix. The choice of pivot selection is kept arbitrary and can be made according to the users need. So the ill conditioned matrices can be handled easily. The…
We show that there are two or more procedures to generalize the known four-dimensional transformation, aiming to generate cylindrically rotating charged exact solutions, to higher dimensional spacetimes . In the one procedure, presented in…
Explicit formulas for the Gauss decomposition of elliptic Cauchy type matrices are derived in a very simple way. The elliptic Cauchy identity is an immediate corollary.
We propose a simple relativistic derivation of the electric and the magnetic fields generated by an electric point charge moving with constant velocity. Our approach is based on the radar detection of the point space coordinates where the…
A novel factorization for the sum of two single-pair matrices is established as product of lower-triangular, tridiagonal, and upper-triangular matrices, leading to semi-closed-form formulas for tridiagonal matrix inversion. Subsequent…
A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector…
We present a theoretical framework for deriving the general $n$-th order Fr\'echet derivatives of singular values in real rectangular matrices, by leveraging reduced resolvent operators from Kato's analytic perturbation theory for…
We give yet another proof for Fa\`{a} di Bruno's formula for higher derivatives of composite functions. Our proof technique relies on reinterpreting the composition of two power series as the generating function for weighted integer…
Starting from the problem of two fixed centres we find a simple derivation of its third integral in terms of the scalar product of the angular momenta about the two fixed centres. This is then generalised to find the general form of the…
The 3-dimensional coherence matrix is interpreted by emphasising its invariance with respect to spatial rotations. Under these transformations, it naturally decomposes into a real symmetric positive definite matrix, interpreted as the…
An exponential representation of the S-matrix provides a natural framework for understanding the semi-classical limit of scattering amplitudes. While sharing some similarities with the eikonal formalism it differs from it in details.…
In this paper we derive a representation of an arbitrary real matrix M as the difference of a real matrix A and the transpose of its inverse. This expression may prove useful for progressing beyond known results for which the appearance of…
An effective estimate for the lattice point discrepancy of ellipsoids of rotation. This paper provides an explicit bound, with numerical constants, for the lattice point discrepancy (= number of integer points minus volume) of an ellipsoid…