Related papers: Towers of function fields with extremal properties
We construct a topology on a given algebraically closed field with a distinguished subfield which is also algebraically closed. This topology is finer than Zariski topology and it captures the sets definable in the pair of algebraically…
In this paper we review many interesting open problems in mathematical physics which may be attacked with the help of tools from constructive field theory. They could give work for future mathematical physicists trained with the…
It is shown that physical fields are formed by physical structures, which in their properties are differential-geometrical structures. These results have been obtained due to using the mathematical apparatus of skew-symmetric differential…
The application of density functional theory to nuclear structure is discussed, highlighting the current status of the effective action approach using effective field theory, and outlining future challenges.
We give a general recipe for explicitly constructing asymptotically optimal towers of modular curves such as {X_0(l^n): n=1,2,3,...}. We illustrate the method by giving equations for eight towers with various geometric features. We conclude…
We establish new conditions that prevent the existence of (weak) normal integral bases in tame Galois extensions of number fields. This leads to the following result: under appropriate technical hypotheses, the existence of a normal…
We classify thick irreducible 3-spherical twin buildings of rank at least 3 in which every panel contains at least 6 chambers. Together with the Main result of [11] we obtain a classification of thick irreducible 3-spherical twin buildings.
We study some properties of the characteristic cycle of a constructible complex on a smooth variety over a perfect field, push-forward and product.
We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a…
In the constructible universe, we construct a co-analytic maximal family of pairwise eventually different functions from $\mathbb{N}$ to $\mathbb{N}$ which remains maximal after adding arbitrarily many Sacks reals (by a countably supported…
We generalize the topological description of the $\mathbb{N}$-graded Proj construction to the multigraded Proj construction for factorially graded rings that are graded by finitely generated abelian groups $D$. However, there is one big…
Any superrosy division ring (i.e. a division ring equipped with an abstract notion of rank) is shown to be centrally finite. Furthermore, division rings satisfying a generalized chain condition on definable subgroups are studied. In…
Density functional theory (DFT) is an incredible success story. The low computational cost, combined with useful (but not yet chemical) accuracy, has made DFT a standard technique in most branches of chemistry and materials science.…
Cyclic number fields of odd prime degree are constructed as ray class fields over the rational number field. They are collected in multiplets sharing a common conductor and discriminant. The algorithms are implemented in Magma and applied…
Let G be the homeomorphism group of a dendrite. We study the normal subgroups of G. For instance, there are uncountably many non-isomorphic such groups G that are simple groups. Moreover, these groups can be chosen so that any isometric…
A hybrid meson is a quark-antiquark pair in which, contrary to ordinary mesons, the gluon field is in an excited state. In the framework of constituent models, the interaction potential is assumed to be the energy of an excited string. An…
We present a simple method to establish the existence of asymptotically good sequences of iso-dual AG-codes. A key advantage of our approach, beyond its simplicity, is its flexibility, allowing it to be applied to a wide range of towers of…
Fourier transform is applied to annular beams of simplified flat two-level geometry: bright outer ring with a darker core. The pattern of focal beam profile (i.e. far field) is calculated and characterized with respect of its intensity…
We prove that, for certain extensions of valued fields which admit a sensible theory of ramification groups, there exist canonical towers that correspond to the break-points of their Herbrand function. In particular, each of the…
For the past few decades, structured light has been gaining popularity across various research fields. Its fascinating properties have been exploited for both previously unforeseen and established applications from new perspectives. Crucial…