相关论文: A compact formula for the derivative of a 3-D rota…
For any real diagonalizable matrix with complex eigenvalues we provide a real, coordinate free decomposition with a clear geometric interpretation.
In this paper we derive the fourth-order asymptotic expansions of the trapezoidal approximation for the fractional integral and the $L1$ approximation for the Caputo derivative. We use the expansion of the $L1$ approximation to obtain the…
Estimates of the approximate factor model are increasingly used in empirical work. Their theoretical properties, studied some twenty years ago, also laid the ground work for analysis on large dimensional panel data models with cross-section…
In the field of radial basis functions mathematicians have been endeavouring to find infinitely differentiable and compactly supported radial functions. This kind of functions is extremely important. One of the reasons is that its error…
We introduce a way to express compact quantum electrodynamics with dynamical matter on two- and three-dimensional spatial lattices in a gauge redundancy-free manner while preserving translational invariance. By transforming to a rotating…
Objects' rigid motions in 3D space are described by rotations and translations of a highly-correlated set of points, each with associated $x,y,z$ coordinates that real-valued networks consider as separate entities, losing information.…
The exponential of the triangular matrix whose entries in the diagonal at distance $n$ from the principal diagonal are all equal to the sum of the inverse of the divisors of $n$ is the triangular matrix whose entries in the diagonal at…
We present a very simple expression and a Fortran code for the fast and precise calculation of three-dimensional harmonic-oscillator transformation brackets. The complete system of symmetries for the brackets along with analytical…
Higher-order tensors appear in various areas of mechanics as well as physics, medicine or earth sciences. As these tensors are highly complex, most are not well understood. Thus, the analysis and the visualization process form a highly…
A discrete rotation algorithm can be apprehended as a parametric application $f\_\alpha$ from $\ZZ[i]$ to $\ZZ[i]$, whose resulting permutation ``looks like'' the map induced by an Euclidean rotation. For this kind of algorithm, to be…
In the field of radial basis functions mathematicians have been endeavouring to find infinitely differentiable and compactly supported radial functions. This kind of functions are extremely important for some reasons. First, its…
In this paper an exponential multiplicative formula for the R-matrix is provided for the twisted affine quantum algebras.
The transformation of the partial fractional derivatives under spatial rotation in $R^2$ are derived for the Riemann-Liouville and Caputo definitions. These transformation properties link the observation of physical quantities, expressed…
We derive and prove an explicit formula for the sum of the fractional parts of certain geometric series. Although the proof is straightforward, we have been unable to locate any reference to this result. This summation formula allows us to…
A procedure to obtain differentiation matrices is extended straightforwardly to yield new differentiation matrices useful to obtain derivatives of complex rational functions. Such matrices can be used to obtain numerical solutions of some…
We derive a closed-form expression for the kth power of semicirculant matrices by using the determinant of certain matrices. As an application, a closed-form expression for the kth power of r-circulant matrices is also povided.
The logarithmic corotational derivative is a key concept in rate-type constitutive relations in continuum mechanics. The derivative is defined in terms of the logarithmic spin tensor, which is a skew-symmetric tensor/matrix given by a…
Computing multivariate derivatives of matrix-like expressions in the compact, coordinate free fashion is very important for both theory and applied computations (e.g. optimization and machine learning). The critical components of such…
This paper presents a new derivative parsing algorithm for parsing expression grammars; this new algorithm is both simpler and faster than the existing parsing expression derivative algorithm presented by Moss. This new algorithm improves…
We obtain exact solutions to the class of parabolic partial differential equations of arbitrary dimensionality and with arbitrary potentials. The solutions are presented in a compact-form: as explicit mathematical expressions consisting of…