Dedicated to Alan George on the occasion of his 60th birthday Abstract. The splitting lemma is one of the two main tools of support theory, a framework for bounding the condition number of definite and semidefinite preconditioned linear systems. The splitting lemma allows the analysis of a complicated system to be partitioned into analyses of simpler systems. The other tool is the symmetric-pro...

We use the algebraic nested Bethe ansatz to solve the eigenvalue and eigenvector problem of the supersymmetric SUq(n|m) model with open boundary conditions. Under an additional condition that model is related to a multicomponent supersymmetric t-J model. We also prove that the transfer matrix with open boundary condition is SUq(n|m) invariant. PACS: 7510J, 0520,0530

We begin by defining an apppropriate linear point boundary condition. Given 1 ≤ j ≤ n−1 and 1 ≤ k ≤ n− j, positive integers m1, . . ., mk such that m1 + · · ·+mk = n− j, points a < x1 < · · · < xk < xk+1 < · · · < xk+j < b, real numbers yil, 1 ≤ i ≤ ml, 1 ≤ l ≤ k, and real numbers yn−j+l, 1 ≤ l ≤ j, a boundary condition of the form y(xl) = yil, 1 ≤ i ≤ m, 1 ≤ l ≤ k, y(xk+l) = yn−j+l, 1 ≤ l ≤ j,...

In this paper, under some appropriate conditions, we prove some $Delta$ and strong convergence theorems of endpoints for multi-valued nonexpansive mappings using modified Agarwal-O'Regan-Sahu iterative process in the general setting of 2-uniformly convex hyperbolic spaces. Our results extend and unify some recent results of the current literature.

soil salinity poses considerable and increasing problems for agriculture, and is receiving much attention from plant breeders. the identification of genes whose expression enables plants to adapt to and/or tolerate salt stress is essential for breeding programs, but little is known about the genetic mechanisms of traits in saline conditions. the data obtained from 75 families produced by crossi...

Under a minimum of assumptions, we develop in generality the basic theory of universal algebra in a symmetric monoidal closed category V with respect to a specified system of arities j : J ↪→ V . Lawvere’s notion of algebraic theory generalizes to this context, resulting in the notion of single-sorted V -enriched J -cotensor theory, or J -theory for short. For suitable choices of V and J , such...