We adapt the Faddeev-LeVerrier algorithm for computation of characteristic polynomials to Pfaffian a skew-symmetric matrix. This yields very simple, easy implement and parallelize computational cost O(n?+1) where n is size matrix O(n?) multiplying n×n-matrices, ??[2,2.37286). compare its performance that other algorithms show how it can be used compute Euler form Riemannian manifold using compu...

Introduction: Cretan matrices – orthogonal matrices, consisting of the elements 1 and –b (real number), are an ideal object for visual application finite-dimensional mathematics. These include, in particular, Hadamard and, with expansion number elements, conference matrices. The most convenient research apparatus is to use field theory multiplicative Galois groups, which especially important ne...

Following footsteps of Gauss, Euler, Riemann, Hurwitz, Smith, Hardy, Littlewood, Hedlund, Khinchin and Chebyshev, we visit some topics in elementary number theory. For matrices defined by Gaussian primes we observe a circular spectral law for the eigenvalues. We experiment then with various Goldbach conjectures for Gaussian primes, Eisenstein primes, Hurwitz primes or Octavian primes. These con...

Motivated by Harish-Chandra theory, we construct, starting from a simple CDD-pole S-matrix, a hierarchy of new S-matrices involving ever “higher” (in the sense of Barnes) gamma functions. These new S-matrices correspond to scattering of excitations in ever more complex integrable models. From each of these models, new ones are obtained either by “q-deformation”, or by considering the Selberg-ty...

In this paper we give an explicit parametrization for all two-qubit density matrices. This is important for calculations involving entanglement and many other types of quantum information processing. To accomplish this we present a generalized Euler angle parametrization for SU(4) and all possible two-qubit density matrices. The important group-theoretical properties of such a description are t...

Using coherent-state techniques, we prove a sampling theorem for Majorana's (holomor-phic) functions on the Riemann sphere and we provide an exact reconstruction formula as a convolution product of N samples and a given reconstruction kernel (a sinc-type function). We also discuss the effect of over-and under-sampling. Sample points are roots of unity, a fact which allows explicit inversion for...

A methodology for the formulation of dynamic equations of motion of a serial flexible-link manipulator using the decoupled natural orthogonal complement (DeNOC) matrices, introduced elsewhere for rigid links, is presented in this paper. First, the Euler Lagrange (EL) equations of motion of the system at hand are written. Then, using the DeNOC matrices associated with the velocity constraints of...

The effect of the nonlocal parameter on free vibration analysis nano scaled trusses and frames is examined. Accordingly, firstly, axial bending vibrations longitudinal element are formulated. Simple rod Euler-Bernoulli assumptions considered for vibrations, respectively. Finite matrices obtained by applying average weighted residue to equation motion vibration. These combined according freedoms...

Abel's quadratures for integrable Hamiltonian systems are defined up to a group law of the corresponding Abelian variety $A$. If $A$ is isogenous direct product varieties $A\cong A_1\times\cdots\times A_k$, can be used construct various Lax matrices on factors $A_1,\ldots,A_k$. As an example, we discuss 2-dimensional reducible $A=E_+\times E_-$, which 1-dimensional $E_\pm$ obtained by Euler in ...

We consider a linearized Euler–Maxwell model for the propagation and absorption of electromagnetic waves in magnetized plasma. present derivation model, we show its well-posedeness, strong polynomial stability under suitable fairly general assumptions, exponential same conditions as Maxwell system, finally convergence to time-harmonic regime. No homogeneity assumption is made, topological geome...