Let X be a K3 surface which is intersection of three (i.e. a net P) of quadrics in P. The curve of degenerate quadrics has degree 6 and defines a natural double covering Y of P ramified in this curve which is again a K3. This is a classical example of a correspondence between K3 surfaces which is related with moduli of sheaves on K3’s studied by Mukai. When general (for fixed Picard lattices) X...

Although the equation of motion, recently proposed for the classical radiating electron, is of non-local character in proper time, the Newtonian initial data (position and velocity) are sufficient to guarantee existence and uniqueness of the solutions. The corresponding existence proof is accomplished by the Picard-Lindelöf method of successive approximations. This method indicates the possibil...

We address the usefulness of the unstable manifold correction (UMC) in a Picard iteration for the solution of the velocity field in higher-order ice-flow models. We explain underand overshooting and how one can remedy them. We then discuss the rationale behind the UMC, initially developed to remedy overshooting, and how it was previously introduced in a Picard iteration to calculate the velocit...

The goal of this lecture is to explain in detail the statement that a Picard groupoid is “the same thing as” an Ω-spectrum E with πi(E) = 0 for i 6= 0, 1. Along the way we introduce the notion of a (very special) Γ-space, which provides one of the possible ways of formalising the concept of an “abelian group structure defined up to all the higher homotopies”, and we present an approach to K-the...

This paper 1 introduces a new line of research which ensures soundness and completeness in Natural Language text planners on top of an efficient control strategy. The work builds on the HUNTER-GATItERER analysis system (Beale. 96; Beale & Nirenburg, 96). That system employs constraint satisfaction, branch-and-bound and solution synthesis techniques to produce near linear-time processing for kno...

This paper presents Differential Transformation Method (DTM) and Picard‟s Iterative Method (PIM) as computational techniques in solving linear and nonlinear differential equations. For numerical analysis of the methods, three examples are considered. The results obtained are compared with their corresponding exact solutions. A link between successive terms of the solutions using the two methods...

and for the sake of simplicity we will assume that the coefficients p and q are, throughout the finite interval a = x = b, continuous real functions of the real variable x. We shall find it convenient to lay down the following definition : The equation (1) is said to be oscillatory or non-oscillatory in the interval a~x~b according as it does or does not have at least one solution (not identica...

In this paper we generalize the well known converse to the contraction principle due to C. Bessaga, dropping the uniqueness of the fixed point from its hypotheses. Some properties of weakly Picard mappings are given.

In this paper, we establish weak and strong convergence theorems for mean nonexpansive maps in Banach spaces under the Picard–Mann hybrid iteration process. We also construct an example of mappings show that it exceeds class mappings. To numerical accuracy our main outcome, process is more effective than all Picard, Mann, Ishikawa iterative processes.