Related papers: On Rotations as Spin Matrix Polynomials
The `classical' model for a massive spinning particle, which was recently proposed, is derived from the isotropic rotator model. Through this derivation, we note that the spin can be understood as the relativistic extension of the isotropic…
Matrices of the irreducible representations of double crystallographic point groups O, Td, Ox{1,I} and Tdx{1,I} are derived. The characteristic polynomials (spinor bases) up to the sixth power are obtained. The method for the derivation of…
We investigate the construction of circulant matrices derived from primitive roots over finite fields. Our approach reduces exponential sums to Jacobi sums, thereby establishing explicit connections between character theory and matrix…
Schur's transforms of a polynomial are used to count its roots in the unit disk. These are generalized them by introducing the sequence of symmetric sub-resultants of two polynomials. Although they do have a determinantal definition, we…
The twenty-one-vertex model, the spin $1$ analogue of the eight-vertex model is considered on the basis of free field representations of vertex operators in the $2\times 2$-fold fusion SOS model and vertex-face transformation. The tail…
Combinatorial formulas expressing cyclic rook polynomials and cyclic permanents of rectangular matrices in terms of expansions along rows are presented
Properties of partial integrals such as real and complex-valued polynomial, multiple polynomial, exponential, and conditional for ordinary differential systems are studied. The possibilities of constructing first integrals and last…
We utilize generalized unitarity and recursion relations combined with effective field theory(EFT) techniques to compute spin dependent interaction terms for inspiralling binary systems in the post newtonian(PN) approximation. Using these…
The 8 $\times$ 8 matrix representation of SO(8) Symmetry has been defined by using the direct product of Pauli matrices and Gamma matrices. These 8 $\times$ 8 matrices are being used to describe the rotations in SO(8) symmetry. The…
This paper proposes a new factor rotation for the context of functional principal components analysis. This rotation seeks to re-represent a functional subspace in terms of directions of decreasing smoothness as represented by a generalized…
Bilinear systems of equations are defined, motivated and analyzed for solvability. Elementary structure is mentioned and it is shown that all solutions may be obtained as rank one completions of a linear matrix polynomial derived from…
We use the fermionic construction of two-matrix model partition functions to evaluate integrals over rational symmetric functions. This approach is complementary to the one used in the paper ``Integrals of Rational Symmetric Functions,…
There are two kinds of polynomial functions on matrix algebras over commutative rings: those induced by polynomials with coefficients in the algebra itself and those induced by polynomials with scalar coefficients. In the case of algebras…
We study multiple orthogonal polynomials exploiting their explicit determinantal representation in terms of moments. Our reasoning follows that applied to solve the Hermite-Pad\'{e} approximation and interpolation problems. We study also…
In this note we consider several kind of partition functions of one-dimensional models with nearest - neighbor interactions $I_n, n\in \mathbf{Z}$ and spin values $\pm 1$. We derive systems of recursive equations for each kind of such…
The paper addresses the calculation of correlation functions of permanental polynomials of matrices with random entries. By exploiting a convenient contour integral representation of the matrix permanent some explicit results are provided…
We propose an alternative approach for the construction of the unitary matrix which performs generalized unitary rotations of the system consisting of independent identical subsystems (for example spin system). This matrix, when applied to…
General revision. In particular the parts concerning involutive bases over rings have been significantly changed. In addition some proofs have been improved.
We consider binomial and inverse binomial sums at infinity and rewrite them in terms of a small set of constants, such as powers of $\pi$ or $\log(2)$. In order to perform these simplifications, we view the series as specializations of…
We consider the set of $n\times n$ matrices with rational entries having numerator and denominator of size at most $H$ and obtain upper and lower bounds on the number of such matrices of a given rank and then apply them to count such…