Sebil Kaplan

• Vrije Universiteit Amsterdam

The notion of Bezout matrix is an essential tool in studying broad variety of subjects: zeroes of polynomials, stability of differential equations, rational transformations of algebraic curves, systems of commuting nonselfadjoint operators, boundaries of quadrature domains etc. We present a survey of several properties of Bezout matrices and their...

We generalize the Moishezon Teicher algorithm that was suggested for the computation of the braid monodromy of an almost real curve. The new algorithm suits a larger family of curves, and enables the computation of braid monodromy not only of caspidal curves, but of general algebraic curves, with some non simple singularities. Moreover, it works al...

The word problem of a group is an important question. The word problem in the braid group is of particular interest for topologists, algebraists and geometers. In [7] we have looked at the braid group from a topological point of view, and thus using a new computerized representation of some elements of the fundamental group we gave a solution for i...

In this paper we give an algorithm for solving a main case of the conjugacy problem in the braid groups. We also prove that half-twists satisfy a special root property which allows us to reduce the solution for the conjugacy problem in half-twists into the free group. Using this algorithm one is able to check conjugacy of a given braid to one of E....

Since the braid group was discovered by E. Artin, the question of its conjugacy problem has been solved by Garside and Birman, Ko and Lee. However, the solutions given thus far are difficult to compute with a computer, since the number of operations needed is extremely large. Meanwhile, random algorithms used to solve difficult problems such as pri...

The word problem of a group is a very important question. The word problem in the braid group is of particular interest for topologists, algebraists and geometers. In previouse article we have looked at the braid group from a topological point of view, and thus using a new computerized representation of some elements of the fundamental group we gav...

Xenon feedback can produce spatial oscillations in large power reactors. ; Depending on the reactor size, materials inventory, power, and temperature ; coefficient, these oscillations may be either transient or persistent. This ; phenomenon is treated by a modal analysis in which nonlinear terms are retained. ; The nonlinear effects are shown to li...

An exploration is made into a method for using reciprocal variational problems to develop figures of merit for approximate solutions of diffusion problems. The theory of the reciprocal problems is described in both a continuous and discrete context. Connections with the method of Slobodyansky are discussed. A strategem is presented for extending th...

The method of flux synthesis is extended in a systematic way to allow the possibility of using different sets of trial functions in different axial zones. The necessary equations are derived in some detail and numerical examples are presented. The results of these examples are very satisfactory and suggest, therefore, that the synthesis procedure c...

The physical question of the spatial stability of a reactor with respect to xenon oscillations corresponds to a mathematical question regarding the location in the complex plane of the roots of a certain eigenvalue problem. The introduction of feedback controllers corresponds to the imposition of constraints on the eigenvalue problem. The effect of...

ABS>Lightly damped core power oscillations with a frequency characterized by the reciprocal of the core transport time have been observed in boiling reactors. The oscillations are attributed to regenerative feedback through the "inner" reactivity feedback loop in which the feedback path consists of heat generation in the fuel, heat transfer to...

The delayed neutron effects in flux tilt transients were examined in a ; simple model of an initially uniform bare core with energy group and one group of ; delayed precursors. Transient behavior of the flux shape was examined by a first-; order perturbation theory and a modal expansion. (C.J.G.);