Autonomous marine vessels are expected to avoid intervessel collisions and comply with the international regulations for safe voyages. This article presents a stepwise path planning method using stream functions. The dynamic flow of fluids is used as guidance model, where collision avoidance in static environments achieved by applying circular theorem sink flow. We extend this adding vortex flo...

In this paper we study triangularization of collections of matrices whose entries come from a finite-dimensional division ring. First, we give a generalization of Guralnick's theorem to the case of finite-dimensional division rings and then we show that in this case the reduced trace function is a suitable alternative for trace function by presenting two triangularization results. The first one...

Algebraic attacks on stream ciphers [9] recover the key by solving an overdefined system of multivariate equations. Such attacks can break several interesting cases of LFSR-based stream ciphers, when the output is obtained by a Boolean function, see [9– 11]. Recently this approach has been successfully extended also to combiners with memory, provided the number of memory bits is small, see [1, ...

We address a problem of sampling and reconstructing periodic piecewise polynomials based on the theory for signals with a finite rate of innovation (FRI signals) from samples acquired by a sinc kernel. This problem was discussed in a previous paper. There was, however, an error in a condition about the sinc kernel. Further, even though the signal is represented by parameters, these explicit val...

Hermite’s theorem states that there are only finitely many number fields with bounded discriminant. In this work, we investigate an analog of Hermite’s theorem for function fields: there are only finitely many separable function fields with bounded degree and discriminant. We prove this in the case that the function fields are unramified at ∞. Although Hermite’s theorem for function fields is k...

A key derivation function is used to generate one or more cryptographic keys from a private (secret) input value. This paper proposes a new method for constructing a generic stream cipher based key derivation function. We show that our proposed key derivation function based on stream ciphers is secure if the underlying stream cipher is secure. We simulate instances of this stream cipher based k...

The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining p...