In this abstract, we develop a solid theoretical foundation for a bottom-up program specialisation technique, capable of specialising a logic program w.r.t. a set of unit clauses. Extending a well-known operator, originally introduced for composing logic programs, we deene a bottom-up partial deduction operator and prove correctness of the transformation with respect to the S-semantics.

High order finite difference methods obeying a summation-by-parts (SBP) rule are developed for equidistant grids. With curvilinear grids, a coordinate transformation operator that does not destroy the SBP property must be used. We show that it is impossible to construct such an operator without decreasing the order of accuracy of the method.

We apply an analogue of the Zakharov-Shabat dressing method to obtain infinite matrix solutions to the Toda lattice hierarchy. Using an operator transformation we convert some of these into solutions in terms of integral operators and Fredholm determinants. Others are converted into a class of operator solutions to the l-periodic Toda hierarchy.

In this paper we used the finite Fourier transformation to obtain the polar decomposition of the q-deformed boson algebra with q a root of unity. Since the q-deformed boson algebra was known [1,2], much work has been accomplished in this direction [3-8]. It is well known that this algebra has an infinite dimensional representation when the deformation parameter q is real, while it has a finite ...

We define a family of integral operators using multiplier transformation on the space of normalized meromorphic functions and introduce several new subclasses using this operator. We investigate various inclusion relations for these subclasses and some interesting applications involving a certain class of the integral operator are also considered.

We introduce a new domain wall operator that represents a full (real) Möbius transformation of a given non-chiral Dirac kernel. Shamir's and Boriçi's domain wall fermions are special cases of this new class. By tuning the parameters of the Möbius operator and by introducing a new Red/Black preconditioning, we are able to reduce the computational effort substantially.

We study the rapid stabilization of heat equation on 1-dimensional torus using backstepping method with a Fredholm transformation. This classical framework allows us to present transformations for Laplace operator in sharp functional setting, which is main objective this work. first prove that, under some assumptions control operator, two scalar controls are necessary and sufficient get control...