*Correspondence: [email protected] Department of Mathematics, Inner Mongolia University, Hohhot, 010021, China Abstract The present paper deals with the dependence of eigenvalues of 2nth order boundary value transmission problems on the problem. The eigenvalues depend not only continuously but also smoothly on the problem. Some new differential expressions of eigenvalues with respect to an endpoi...

In this short note, we present a fast and reliable algorithm for evaluating special nth-order pentadiagonal Toeplitz determinants in linear time. The algorithm is suited for implementation using Computer Algebra Systems (CAS) such as MACSYMA and MAPLE. Two illustrative examples are given. 2007 Elsevier Inc. All rights reserved.

In this paper, we prove the existence of at least three positive solutions of boundary value problems for nth order nonlinear impulsive integrodifferential equations of mixed type on infinite interval with infinite number of impulsive times. Our results are obtained by applying a new fixed point theorem introduced by Avery and Peterson.

New integrability properties of a family sequences ordinary differential equations, which contains the Riccati and Abel chains as most simple sequences, are studied. The determination n generalized symmetries nth-order equation in each chain provides, without any kind integration, n-1 functionally independent first integrals equation. A remaining integral arises by quadrature using Jacobi last ...

We consider a self-convolutive recurrence whose solution is the sequence of coefficients in the asymptotic expansion of the logarithmic derivative of the confluent hypergeometic function U(a, b, z). By application of the Hilbert transform we convert this expression into an explicit, non-recursive solution in which the nth coefficient is expressed as the (n− 1)th moment of a measure, and also as...

≤ n− 1 n . Equality only occurs for p(z) = a1z + anz n with arbitrary a1, an ∈ C \ {0}. Here a proof will be given by a variational method which recently has been used in a similar way to prove Sendov’s conjecture (s. [2]). Former results and the backgrounds of both conjectures can be found in the survey article of Schmeisser [4]. Let n > 1 be fixed and define Fn as the class of nth degree moni...

Potential field methods such as gravity and magnetic methods are among the most applied geophysical methods in mineral exploration. A high-resolution technique is developed to image geologic boundaries such as contacts and faults. Potential field derivatives are the basis of many interpretation techniques. In boundary detection, the analytic signal quantity is d...