An error analysis of projection methods for solving linear integral equations of the second kind is presented. The relationships between several direct methods for solving integral equations are examined. It is shown that the error analysis given is applicable to other methods, including a modified Nyström method and certain degenerate kernel methods.

We derive sampleepaths continuity results for some sto-chastic Volterra integrals with degenerate kernel under integrability assumptions on the integrand. Some applications to processes arising in the analysis of the fractional Brownian motion are given. Embeddings of Besov spaces into sets of HHlder continuous functions are the key elements. RRSUMM. Nous montrons la continuitt trajectorielle d...

This paper describes a distributed hybrid architecture that imparts autonomous intelligence capabilities of “perception-decision-action” to an ALV (Autonomous Landing Vehicle) control unit. This architecture is investigated by performance metrics of an adaptive inference system based grammar. The system is shown to degenerate to a remote thread execution mechanism of a Real-Time Operating Syste...

In this paper we present an explicit (rank one) function transform which contains several Jacobi-type function transforms and Hankel-type transforms as degenerate cases. The kernel of the transform, which is given explicitly in terms of basic hypergeometric series, thus generalizes the Jacobi function as well as the Bessel function. The kernel is named the Askey-Wilson function, since it provid...

We show that for any fixed i, j ≥ 1, the k-Dominating Set problem restricted to graphs that do not have Ki,j as a subgraph is fixed parameter tractable (FPT) and has a polynomial kernel. This result implies that this problem restricted to bounded-degenerate graphs has a polynomial kernel, solving an open problem posed by Alon and Gutner in [3]. Our result extends the class of graphs for which t...

Degenerate primers-based polymerase chain reaction (PCR) are commonly used for isolation of unidentified gene sequences in related organisms. For designing the degenerate primers, we propose the use of local alignment search method for searching the conserved regions long enough to design an acceptable primer pair. To test this method, a WD40 repeat-containing domain protein from Beauveria bass...

It is well known that in operations research‎, ‎degeneracy can cause a cycle in a network‎ ‎simplex algorithm which can be prevented by maintaining strong‎ ‎feasible bases in each pivot‎. ‎Also‎, ‎in a network consists of n arcs‎ ‎and m nodes‎, ‎not considering any new conditions on the entering‎ ‎variable‎, ‎the upper bound of consecutive degenerate pivots is equal‎ $left( ‎begin{array}{c}‎ ‎n...

In this paper we consider the null controllability for a population model depending on time, space and age. Moreover, diffusion coefficient degenerate at boundary of domain. The novelty is that first time presence memory term, which makes computations more difficult. However, under suitable condition kernel deduce result original problem via new Carleman estimates adjoint associated to nonhomog...