A smooth surface interpolation scheme for positive and convex data has been developed. This scheme has been extended from the rational quadratic spline function of Sarfraz [11] to a rational bi-quadratic spline function. Simple data dependent constraints are derived on the free parameters in the description of rational bi-quadratic spline function to preserve the shape of 3D positive and convex...

We give a new proof that the El-Mistikawy and Werle finite-difference scheme is uniformly second-order accurate for a nonselfadjoint singularly perturbed boundary value problem. To do this, we use exponential finite elements and a discretized Green's function. The proof is direct, gives the nodal errors explicitly in integral form, and involves much less computation than in previous proofs of t...

We give a new and hopefully more easily understandable structural proof for the decomposition of a k-valued transducer into k unambiguous functional transducers, a result established by A. Weber. The number of states of the transducers given by our construction outperforms Weber’s one by one exponential. Moreover, we solve a problem left open by Weber, the decomposition of a bounded length-degr...

The profinite topology is used in rational languages classification. In particular, several important decidability problems, related to the Malcev product, reduce to the computation of the closure of a rational language in the profinite topology. It is known that given a rational language by a deterministic automaton, computing a deterministic automaton accepting its profinite closure can be do...

The possibility of using elliptic curves over the rational field non-zero ranks in cryptographic schemes is studied. For first time, construction cryptosystems proposed security which based on complexity solving knapsack problem numbers ranks. A new approach to use for proposed. few experiments have been carried out estimate heights characteristic points infinite order. model a cryptosystem res...

In this paper, the typical exponential method, diamond difference and modified time discrete scheme is researched for self adaptive time step. The second-order time evolution scheme is applied to time-dependent spherical neutron transport equation by discrete ordinates method. The numerical results show that second-order time evolution scheme associated exponential method has some good properti...