The present work concerns the algebra of semi-magic square matrices. These can be decomposed into matrices of specific rotational symmetry types, where the square of a matrix of pure type always has a particular type. We examine the converse problem of categorising the square roots of such matrices, observing that roots of either type occur, but only one type is generated by the functional calc...

Baxter’s Q-operator for the quantum transfer matrix of the XXZ spin-chain is constructed employing the representation theory of quantum groups. The spectrum of this Q-operator is discussed and novel functional relations which describe the finite temperature regime of the XXZ spin-chain are derived. For non-vanishing magnetic field the previously known Bethe ansatz equations can be replaced by a...

Abstract This study aims to describe the hydroponic vegetable agribusiness at Cv. Hydroponic Roots, Moncongloe District, Maros Regency. Identifying and analyzing factors that must be considered in development of strategies developing also recommending alternative product for businesses. The research method used data collection methods, namely observation, questionnaires interviews were analyzed...

We develop the derivation we proposed in hep-th/0703177 of the dressing phase of the S-matrix in the AdS/CFT correspondence in the framework of the underlying bare integrable model. We elaborate the configuration of the Bethe roots describing the physical vacuum, which consists of a long Bethe string stretched along the imaginary axis and stacks distributed along the real axis. We determine the...

We present a constructive existence proof that every real skew-Hamiltonian matrix W has a real Hamiltonian square root. The key step in this construction shows how one may bring any such W into a real quasi-Jordan canonical form via symplectic similarity. We show further that every W has infinitely many real Hamiltonian square roots, and give a lower bound on the dimension of the set of all suc...

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 for several random matrix ensembles. When compared with the corresponding formulae for characteristic polynomials, our results show both striking similarities...

Bacillus subtilis is a plant-beneficial Gram-positive bacterium widely used as a biofertilizer. However, relatively little is known regarding the molecular processes underlying this bacterium's ability to colonize roots. In contrast, much is known about how this bacterium forms matrix-enclosed multicellular communities (biofilms) in vitro. Here, we show that, when B. subtilis colonizes Arabidop...

Unitary matrices have a rich mathematicalstructure which is closely analogous to real symmetric matrices. For real symmetric matrices this structure can be exploited to develop very eecient numerical algorithms and for some of these algorithms unitary analogues are known. Here we present a unitary analogue of the bisection method for symmetric tridiagonal matrices. Recently Delsarte and Genin i...

We analyze the solutions of one-sided matrix equations over algebraically closed fields characteristic zero in a certain transcendental extension main field that are generated by set invertible matrices. establish conditions under which roots corresponding to different matrices from this coincide.