We study one dimension of program evolution, namely the evolution of the datatypes in a program. Both the object programs subject to datatype transformation, and the meta-programs for transformation are functional programs. We cover (semantics-preserving) refactorings, but also structure-extending and -reducing transformations. A corresponding operator suite is designed, a suitable specificatio...

For anisotropic attenuating media, the albedo operator determines the scattering and the attenuating coefficients up to a gauge transformation. We show that such a determination is stable.

The iterations are studied of the Darboux transformation for the generalized Schrödinger operator. The applications to the Dym and Camassa-Holm equations are considered.

We consider the nonstandard constrained KP (ncKP) hierarchy which is obtained from the multi-constraint KP hierarchy by gauge transformation. The second Hamiltonian structure of the ncKP hierarchy can be simplified by factorizing the Lax operator into multiplication form, thus the generalized Miura transformation is obtained. We also discuss the free field realization of the associated W-algebra.

A transformation of the form x → ±iy ∈ iR; x, y ∈ R, or an equivalent similarity transformation with a metric operator η are shown to map non-Hermitian PT -symmetric Hamiltonians into Hermitian partner Hamiltonians in Hilbert space. Isospectrality and mass signature are also discussed. PACS codes: 03.65.Ge, 03.65.Ca

The work of M. S. Livšic and his collaborators in operator theory associates to a system of commuting nonselfadjoint operators an algebraic curve. Guided by the notion of rational transformation of algebraic curves, we define the notion of a rational transformation of a system of commuting nonselfadjoint operators.

A transformation of the form x → iy; x, y ∈ R, or a Darbouxal-type similarity transformation with a metric operator η are shown to transform non-Hermitian PT -symmetric Hamiltonians (with positive mass m = + |m|) into their Hermitian partner Hamiltonians (with negative mass m = − |m|) in Hilbert space. PACS codes: 03.65.Ge, 03.65.Ca

This paper deals with the boundary value problem involving the differential equation ell y:=-y''+qy=lambda y, subject to the eigenparameter dependent boundary conditions along with the following discontinuity conditions y(d+0)=a y(d-0), y'(d+0)=ay'(d-0)+b y(d-0). In this problem q(x), d, a , b are real, qin L^2(0,pi), din(0,pi) and lambda is a parameter independent of x. By defining a new...

Infinitesimal conformal transformations of IRn are always polynomial and finitely generated when n > 2. Here we prove that the Lie algebra of infinitesimal conformal polynomial transformations over IRn, n ≥ 2, is maximal in the Lie algebra of polynomial vector fields. When n is greater than 2 and p, q are such that p+ q = n, this implies the maximality of an embedding of so(p + 1, q + 1, IR) in...

In this paper is presented a technique for transforming a class of recursive equations called linear equations into iterative equations. Linear equations are characterized by involving at the most one recursive call for any invocation. In contrast to the conventional techniques, the scheme of program transformation presented here involves finding the solution of the given linear equation and tr...