In this letter, the numerical scheme of nonlinear Volterra-Fredholm integro-differential equations is proposed in a reproducing kernel Hilbert space (RKHS). The method is constructed based on the reproducing kernel properties in which the initial condition of the problem is satised. The nonlinear terms are replaced by its Taylor series. In this technique, the nonlinear Volterra-Fredholm integro...

The main attempt of this article is extension the method so that it generallywould be able to consider the classical solution of the systems and moreover,produces the optimal trajectory and control directly at the same time. There-fore we consider a control system governed by a bone marrow cancer equation.Next, by extending the underlying space, the existence of the solution is con-sidered and ...

The solution-space structure of the three-satisfiability problem (3-SAT) is studied as a function of the control parameter α (ratio of the number of clauses to the number of variables) using numerical simulations. For this purpose one has to sample the solution space with uniform weight. It is shown here that standard stochastic local-search (SLS) algorithms like average satisfiability (ASAT) e...

Many simulations in science and engineering give rise to sparse linear systems of equations. It is a well known fact that the cost of the simulation process is almost always governed by the solution of the linear systems especially for largescale problems. The emergence of extreme-scale parallel platforms, along with the increasing number of processing cores available on a single chip pose sign...

With current Network Mobility (NEMO) Basic Support, all communications to and from Mobile Network Nodes must go through the Mobile Router and Home Agent (MRHA) tunnel when the mobile network is away. This results in increased length of packet route and increased packet delay in most cases. To overcome these limitations, one might have to turn to Route Optimization (RO) for NEMO. This memo docum...

Most geophysical problem require some type of regularization. Unfortunately most regularization schemes produce “smeared” results that are often undesirable when applying other criteria (such as geologic feasibility). By forming regularization operators in terms of recursive steering filters, built from a priori information sources, we can efficiently guide the solution towards a more appealing...

In [23], Todorcevic gives a survey of basis problems in combinatorial set theory, listing nine theorems and six working conjectures — all in the presence of PFA — including the following three of interest to us here: Conjecture 1 (Todorcevic; [23]). If R is a binary relation, then either R ≤ א0 ·ω1 or [ω1]0 ≤ R. Conjecture 2 (Hajnal, Juhasz; [5]). If X is a regular Hausdorff space, then the fol...

In comparative genomics, algorithms that sort permutations by reversals are often used to propose evolutionary scenarios of large scale genomic mutations between species. One of the main problems of such methods is that they give one solution while the number of optimal solutions is huge, with no criteria to discriminate among them. Bergeron et al. [4] started to give some structure to the set ...

In this paper we propose a generalisation of the k-nearest neighbour (k-NN) retrieval method based on an error function using distance metrics in the solution and problem space. It is an interpolate method which is proposed to be effective for sparse case bases. The method applies equally to nominal, continuous and mixed domains, and does not depend upon an embedding n-dimensional space. In con...