Two integrable lattice hierarchies associated with two discrete matrix spectral problems are derived, and the infinitely many conservation laws of the first integrable model is obtained. Moreover, the Darboux transformations based on different Darboux matrixes (2.3.4) and (3.2.4) for the above-mentioned integrable hierarchies are established with the help of two different gauge transformations ...

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...

We establish the asymptotic behavior of solution to generalized Wiener–Hopf equation whose kernel is a probability distribution, whereas inhomogeneous term directly Riemann integrable function. To this end, we prove that convolution finite measure and function also

When a class of fuzzy value functions constitute a metric space, the completeness and separability is an important problem that must be considered to discuss the approximation of fuzzy systems. In this paper, Firstly, a new tK-integral norm is defined by introducing two induced operators, and prove that the class of tK-integrable fuzzy value functions is a metric space. And then, the integral t...

For a (classically) integrable quantum-mechanical system with two degrees of freedom, the functional dependence H=HQ(J1,J2) of the Hamiltonian operator on the action operators is analyzed and compared with the corresponding functional relationship H(p1,q1;p2,q2)=HC(J1,J2) in the classical limit of that system. The former converges toward the latter in some asymptotic regime associated with the ...

In this paper, integrability conditions and an integrating algorithm of fully rheonomous affine constraints (FRACs) for the partially integrable case are studied. First, some preliminaries on the FRACs are illustrated. Next, necessary and sufficient conditions on the partially integrable case for the FRACs are derived. Then, an integrating algorithm to calculate independent first integrals of t...

and Applied Analysis 3 Let L2 Λ be a square integrable function space with inner product and norm as follows:

The six-vertex model on an N × N square lattice with domain wall boundary conditions is considered. A Fredholm determinant representation for the partition function of the model is given. The kernel of the corresponding integral operator is of the so-called integrable type, and involves classical orthogonal polynomials. From this representation, a " reconstruction " formula is proposed, which e...

The six-vertex model on an N × N square lattice with domain wall boundary conditions is considered. A Fredholm determinant representation for the partition function of the model is given. The kernel of the corresponding integral operator is of the so-called integrable type, and involves classical orthogonal polynomials. From this representation, a " reconstruction " formula is proposed, which e...