algebra has many classical and new open problems. Much research now focuses on the interface between algebra and other fields. See http://www.openproblemgarden.org/category/algebra http://www.openproblemgarden.org/category/group theory and https://en.wikipedia.org/wiki/List of unsolved problems in mathematics. For a fuller, yet still brief, description, see https://en.wikipedia.org/wiki/Abstrac...

The paper is concerned with the optimistic formulation of a bilevel optimization problem with multiobjective lower-level problem. Considering the scalarization approach for the multiobjective program, we transform our problem into a scalar-objective optimization problem with inequality constraints by means of the well-known optimal value reformulation. Completely detailed first-order necessary ...

Using the recent formulation of Noether’s theorem for the problems of the calculus of variations with fractional derivatives, the Lagrange multiplier technique, and the fractional Euler-Lagrange equations, we prove a Noetherlike theorem to the more general context of the fractional optimal control. As a corollary, it follows that in the fractional case the autonomous Hamiltonian does not define...

In some modern complex industrial communication systems, a core network with meshed topology is used to connect large amount of heterogeneous local networks and devices. It should be able to support real-time requirements of the related traffic, as many industrial processes are either mission or safe critical. In this paper, the problem of offering hard and soft real-time as well as best effort...

This paper reports on the multi-scale modelling of an intestinal crypt cellular structure coupled with Wnt signalling. Using formal modelling techniques based on the stochastic π-calculus, which supports ambients needed for compartments, we develop a collection of cell and molecular level models. The focus of our study is the role of Wnt in the control of cell division and differentiation. Usin...

An L2 theory of differential forms is proposed for the Banach manifold of continuous paths on Riemannian manifolds M furnished with its Brownian motion measure. Differentiation must be restricted to certain Hilbert space directions, the H-tangent vectors. To obtain a closed exterior differential operator the relevant spaces of differential forms, the H-forms, are perturbed by the curvature of M...

Fractional calculus (differentiation and integration of arbitrary order) arise naturally in various areas of applied science and engineering such as mechanics, electricity, chemistry, biology, economics, control theory, signal and image processing, polymer rheology, regular variation in thermodynamics, biophysics, blood flow phenomena, aerodynamics, electro-dynamics of complex medium, viscoelas...

Part I. Classical Mechanics 9 0. Intro 9 0.1. Mechanical systems 9 0.2. Lagrangian and Hamiltonian formulation 9 1. Lagrangian approach 10 1.1. Manifolds 10 1.2. Differentiation 11 1.3. Calculus of Variations on an interval 11 1.4. Lagrangian reformulation of Newton‘s equation 13 2. Hamiltonian approach 14 2.1. Metrics: linear algebra 14 2.2. The passage to the cotangent vector bundle via the k...

In a recent paper, published at arXiv:0910.2381, we started a discussion on the new possibilities arising from the use of fractional differential calculus in image processing. We have seen that the fractional calculation is able to enhance the quality of images, with interesting possibilities in edge detection and image restoration. Here, we want to discuss more deeply its role as a tool for th...