The k-server problem, introduced by Manasse, McGeoch and Sleator [29, 30] is a fundamental online problem where k mobile servers are required to serve a sequence of requests on a metric space, with the minimum possible movement cost. Despite the conjectured existence of a Θ(log k)-competitive randomized algorithm, the best known upper bound for arbitrary metric spaces is 2k − 1. Even for one of...

Stieltjes moment problem is considered to recover a probability density function from the knowledge of its infinite sequence of ordinary moments. The approximate density is obtained through maximum entropy technique, under the constraint of few fractional moments. The latter are numerically obtained from the infinite sequence of ordinary moments and are chosen in such a way as to convey the max...

The Evans wave equation [1] of general relativity is expressed in spinor form, thus producing the Dirac equation in general relativity. The Dirac equation in special relativity is recovered in the limit of Euclidean or flat spacetime. By deriving the Dirac equation from the Evans equation it is demonstrated that the former originates in a novel metric compatibility condition, a geometrical cons...

The 2D incompressible Boussinesq system with partial or fractional dissipation have recently attracted considerable attention. In this paper, we study the Cauchy problem for the 2D Boussinesq system in a periodic domain with fractional vertical dissipation in the subcritical case, and we prove the global well-posedness of strong solutions. Based on this, we also discuss the existence of the glo...

Automatic presentations, also called FA-presentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of fundamental decision problems. This paper studies FA-presentable algebras. First, an example is given to show that the class of finitely generated FA-presentable algebras is not closed under forming finitely generated subalgebras, even wi...

The chromatic number of the plane is the chromatic number of the uncountably infinite graph that has as its vertices the points of the plane and has an edge between two points if their distance is 1. This chromatic number is denoted χ(R). The problem was introduced in 1950, and shortly thereafter it was proved that 4 ≤ χ(R) ≤ 7. These bounds are both easy to prove, but after more than 60 years ...

In our earlier work, we introduced a definition for the electric charge "fractional-order" multipoles using the concept of fractional derivatives and integrals [l]. Here, we utilize that definition to introduce a detailed image theory for the two-dimensional (2-D) electrostatic potential distributions in front of a perfectly conducting wedge with arbitrary wedge angles, and for the three-dimens...

In this note we treat the equations of fractional elasticity. After establishing well-posedness, we show a compactness result related to the theory of homog-enization. For this, a previous result in (abstract) homogenization theory of evolutionary equations has to be improved. The approach also permits the consideration of non-local operators (in time and space).

In the present paper, we are concerned with a minimax fractional programming problem containing arbitrary norms and establish duality theorems for a dual model related to minimax fractional programming problem under the assumptions of second order (Φ, ρ)-invexity.

Lifting, tilting and fractional programming, though seemingly different, reduce to a common optimization problem. This connection allows us to revisit key properties of these three problems on mixed integer linear sets. We introduce a simple common framework for these problems, and extend known results from each to the other two.