Solving nonlinear equations is a problem that needs to be dealt with in the practical engineering application. This paper uses Block–Broyden method for solving large-scale nonlinear systems, and two preconditioners are applied for solving the underlying linear systems, including SSOR preconditioner as well as ASSOR method, which is based on SSOR. It discusses their implementation processes and ...

In this manuscript, we consider the inverse problem for non self-adjoint Sturm--Liouville operator $-D^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. We prove by defining a new Hilbert space and using spectral data of a kind, the potential function can be uniquely determined by a set of value of eigenfunctions at an interior point and p...

Assembling a gene from candidate exons is an important problem in computational biology. Among the most successful approaches to this problem is spliced alignment, proposed by Gelfand et al., which scores different candidate exon chains within a DNA sequence of length m by comparing them to a known related gene sequence of length n, m = Θ(n). Gelfand et al. gave an algorithm for spliced alignme...

A causal Poisson bracket algebra for Liouville exponentials on a cylinder is derived using an exchange algebra for free fields describing the in and out asymptotics. The causal algebra involves an even number of space-time points with a minimum of four. A quantum realisation of the algebra is obtained which preserves causality and the local form of non-equal time brackets. Following Polyakov’s ...

The zeros of the eigenfunctions of self-adjoint Sturm–Liouville eigenvalue problems interlace. For these problems interlacing is crucial for completeness. For the complex Sturm–Liouville problem associated with the Schrödinger equation for a non-Hermitian PT-symmetric Hamiltonian, completeness and interlacing of zeros have never been examined. This paper reports a numerical study of the Sturm– ...