This is an expository article the aim of which is to introduce interested students and researchers to the topic of tensor rank, in particular to the construction of explicit tensors of high rank. We try to keep the mathematical concepts and language used as simple as possible to address a broad audience. This article is thought to be an appetizer and does not provide by any means a complete cov...

Algebras of generalized functions offer possibilities beyond the purely distributional approach in modelling singular quantities in non-smooth differential geometry. This article presents an introductory survey of recent developments in this field and highlights some applications in mathematical physics. Mathematics Subject Classification (2000): Primary: 46F30; secondary: 46T30, 53B20.

In this paper, first we extend the known definition of cross-ratio of collinear points to whole Moufang plane. Later we introduce the cross-ratios for lines and the known results about the cross-ratios of points which are adapted to crossratios of lines without using the principle of duality. Finally, we give a theorem which describes the relation between the cross-ratios of points and lines. M...

We are concerned with a 2D time harmonic wave propagation problem in a medium including a thin slot whose thickness ε is small with respect to the wavelength. In a previous article, we derived formally an asymptotic expansion of the solution with respect to ε using the method of matched asymptotic expansions. We also proved the existence and uniqueness of the terms of the asymptotics. In this p...

Given a fixed set of voter preferences, different candidates may win outright given different scoring rules. We investigate how many voters are able to allow all n candidates to win for some scoring rule. We will say that these voters impose a disordering on these candidates. The minimum number of voters it takes to impose a disordering on 3 candidates is 9. For 4 candidates, 6 voters are neces...

We use branched surfaces to define an equivalence relation on C1 codimension one foliations of any closed orientable 3-manifold that are transverse to some fixed nonsingular flow. There is a discrete metric on the set of equivalence classes with the property that foliations that are sufficiently close (up to equivalence) share important topological properties. ____________________ Date: January...

In this paper, a solution method for classical fair division problem utilizing cut-and-choose protocol has been examined and a new method has been suggested in order to eliminate the deficiencies of that method. Furthermore, the problem has been generalized and mathematical models have been written according to oddness or evenness of the number of persons and solution techniques have been given...

• Mathematics Subject Classification: 60E15, 90C40, 49N15 •

Under reasonable assumptions on the data u, v and the function f , we show that the nonlinear periodic Goursat problem ∂u ∂x∂y (x, y) = f(x, y, u(x, y)); u(x, 0) = v(x); u(0, y) = w(y) which cannot be posed in the general theory of distributions, may be studied and solved in a differential algebra of periodic new generalized functions on R2. This algebra contains, in a canonical way, the space ...

We show that for 5-gonal curves of odd genus g ≥ 13 and even genus g ≥ 28 the ⌈ g−1 2 ⌉-th syzygy module of the curve is not determined by the syzygies of the scroll swept out by the special pencil of degree 5. 2010 Mathematics Subject Classification: 13D02,14H51