Related papers: Towers of function fields with extremal properties
After a historical review, I present the progress in the field of realistic NN potentials that we have seen in recent years. A new generation of very quantitative (high-quality/high-precision) NN potentials has emerged. These potentials…
We define various height functions for motives over number fields. We compare these height functions with classical height functions on algebraic varieties, and also with analogous height functions for variations of Hodge structures on…
The physics potential of low-performance and high-performance neutrino factories is briefly reviewed..
For a finite field of odd number of elements we construct families of permutation binomials and permutation trinomials with one fixed-point (namely zero) and remaining elements being permuted as disjoint cycles of same length. Binomials and…
Generalized topological spaces in the sense of Cs\'{a}sz\'{a}r have two main features which distinguish them from typical topologies. First, these families of subsets are not closed under intersections. Second, we allow for the possibility…
Rigorous mathematical foundations of density functional theory are revisited, with some use of infinitesimal (nonstandard) methods. A thorough treatment is given of basic properties of internal energy and ground-state energy functionals…
We construct a fully faithful functor from the category of graphs to the category of fields. Using this functor, we resolve a longstanding open problem in computable model theory, by showing that for every nontrivial countable structure S,…
Various methods have been used to construct rational points and rational curves on rationally connected algebraic varieties. We survey recent advances in two of them, the descent and the fibration method, in a number-theoretical context…
There are limit groups having non-conjugate elements whose images are conjugate in every free quotient. Towers over free groups are freely conjugacy separable.
We show that reasonably well behaved 3d and 4D TQFts must contain certain algebraic structures. In 4D, we find both Hopf categories and trialgebras.
Complex systems have motivated continuing interest from the scientific community, leading to new concepts and methods. Growing systems represent a case of particular interest, as their topological, geometrical, and also dynamical properties…
We use the notion of an Etesi $C^*$-algebra to prove that the real class field towers are always finite.
We show that one can use model categories to construct rational orthogonal calculus. That is, given a continuous functor from vector spaces to based spaces one can construct a tower of approximations to this functor depending only on the…
The first examples of formations which are arboreous (and therefore Hall) but not freely indexed (and therefore not locally extensible) are found. Likewise, the first examples of solvable formations which are freely indexed and arboreous…
Skew idempotent functionals of ordered semirings are studied. Different associative and non-associative semirings are considered. Theorems about properties of skew idempotent functionals are proved. Examples are given.
System of alternatively orthogonalized rational functions of Jacobi type on the half line $[1, \infty)$ is defined and its properties are established. Three subsystems of proper and mixed systems of rational functions with nice properties…
Rationals are known to form interesting and computationally rich structures, such as Farey sequences and infinite trees. Little attention is being paid to more general, systematic exposition of the basic properties of fractions as a set.…
We describe the construction of the genus-zero parts of conformal field theories in the sense of G. Segal from representations of vertex operator algebras satisfying certain conditions. The construction is divided into four steps and each…
We introduce in this section an Algebraic and Combinatorial approach to the theory of Numbers. The approach rests on the observation that numbers can be identified with familiar combinatorial objects namely rooted trees, which we shall here…
We construct and study fields F with the property that F has infinitely many extensions of some fixed degree, but E*/(E*)^n is finite for every finite extension E of F and every n>0.