Abstract In this paper we investigate certain fusion relations associated to an integrable vertex model on the square lattice which is invariant under Sp (4) symmetry. We establish a set of functional include transfer matrix inversion identity. The solution these in thermodynamic limit allows us compute partition function per site fundamental representation model. As byproduct also obtain mixin...

The Klein-Gordon equation of the hydrogen atom has a low-lying eigenstate, called hydrino state, with square integrable wavefunction. The corresponding spinor solution of Dirac’s equation is not square integrable. For this reason the hydrino state has been rejected in the early days of quantum mechanics as being unphysical. Maybe it is time to change opinion.

from the early 1950s, estimating the autocorrelations of polynomials with coefficients on the unit circle has found applications in ising spin systems and in surface acoustic wave designs. in this paper, a technique is introduced that not only estimates the autocorrelations, but for some special types of such polynomials, it locates the frequencies at which maximum autocorrelation occurs.

The ability of the Rigged Hilbert Space formalism to deal with continuous spectrum is demonstrated within the example of the square barrier potential. The non-square integrable solutions of the time-independent Schrödinger equation are used to define Dirac kets, which are (generalized) eigenvectors of the Hamiltonian. These Dirac kets are antilinear functionals over the space of physical wave f...

The ability of the Rigged Hilbert Space formalism to deal with continuous spectrum is demonstrated within the example of the square barrier potential. The non-square integrable solutions of the time-independent Schrödinger equation are used to define Dirac kets, which are (generalized) eigenvectors of the Hamiltonian. These Dirac kets are antilinear functionals over the space of physical wave f...

We use the tridiagonal representation approach to solve radial Schrödinger equation for an inverse-power-law potential of a combined quartic and sextic degrees all angular momenta. The amplitude singularity is larger than that but signs are negative positive, respectively. It turns out system has finite number bound states, which determined by ratio two amplitudes. solution written as series sq...

We obtain a class of exact solutions Bessel-type differential equation, which is six-parameter linear ordinary equation the second order with irregular (essential) singularity at origin. The are obtained using Tridiagonal Representation Approach (TRA) as bounded series square integrable functions written in terms Bessel polynomial on real line. expansion coefficients orthogonal polynomials para...

Several kernel based methods for multi-task learning have been proposed, which leverage relations among tasks as regularization to enhance the overall learning accuracies. These methods assume that the tasks share the same kernel, which could limit their applications because in practice different tasks may need different kernels. The main challenge of introducing multiple kernels into multiple ...