spectrophotometric and electrochemical studies were successfully used in quantitative analysis of amitriptyline hydrochloride (ath) and nortriptyline hydrochloride (nth). conductometric titration were carried out in equeous solution using iodide and dopamine and serotonine as titrant. two new methods using spectrophotometry are dascribed for the determination of (ath) and (nth) with potassium b...

We obtain some simple relations between decomposition numbers of quantized Schur algebras at an nth root of unity (over a field of characteristic 0). These relations imply that every decomposition number for such an algebra occurs as a decomposition number for some Hecke algebra of type A. We prove similar relations between coefficients of the canonical basis of the q-deformed Fock space repres...

We prove an analogue of the magnetic nodal theorem on quantum graphs: the number of zeros of the nth eigenfunction of the Schrödinger operator on a quantum graph is related to the stability of the nth eigenvalue of the perturbation of the operator by magnetic potential. More precisely, we consider the nth eigenvalue as a function of the magnetic perturbation and show that its Morse index at zer...

From Nagumo [10], there have been many accomplishments on the study of the existence of solutions for boundary value problems (BVPs) using the theory of differential inequality (cf. [1–9, 11–17]). However, for the nth-order nonlinear differential equations with the nonlinear boundary conditions, results are very few. The authors made some attempts to solve the nth-order Robin problem [14]. Now ...

We use the ultraproduct technique to study local properties of basic quantities of information-based complexity theory – the n-th minimal errors. We consider linear and nonlinear operators in normed spaces, information consists of continuous linear functionals and is assumed to be adaptive. We establish ultrastability and disprove regularity of n-th minimal errors. As a consequence, we answer a...

In this paper we introduce a new order on the set of n-dimensional tuples and prove that this order preserves nestedness in the edge isoperimetric problem for the graph Pn, defined as the nth cartesian power of the well-known Petersen graph. The cutwidth and wirelength of Pn are also derived. These results are then generalized for the cartesian product of Pn and the m-dimensional binary hypercube.

In the theory of random matrices for unitary ensembles associated with Hermitian matrices,m−point correlation functions play an important role. We show that they possess a useful variational principle. Let μ be a measure with support in the real line, and Kn be the nth reproducing kernel for the associated orthonormal polynomials. We prove that for m ≥ 1, det [Kn (μ, xi, xj)]1≤1,j≤m = m! sup P ...

metal pollution has become one of the most serious environmental problems resulting from human activity. phytoremediation utilizes plants to uptake contaminants and can potentially be used to remediate metal-contaminated sites. the present study investigates heavy metal uptake (cd, cr, and ni) from soil by different organs of populus alba and morus alba. for this purpose, cd (40, 80, and 160 m...

Let L = d/dx +u(x) be the one-dimensional Schrödinger operator and H(x, y, t) be the corresponding heat kernel. We prove that the nth Hadamard’s coefficient Hn(x, y) is equal to 0 if and only if there exists a differential operator M of order 2n− 1 such that L = M. Thus, the heat expansion is finite if and only if the potential u(x) is a rational solution of the KdV hierarchy decaying at infini...

Given a bounded sequence of integers {d0,d1,d2, . . .}, 6 ≤ dn ≤M, there is an associated abstract triangulation created by building up layers of vertices so that vertices on the nth layer have degree dn. This triangulation can be realized via a circle packing which fills either the Euclidean or the hyperbolic plane. We give necessary and sufficient conditions to determine the type of the packi...