Related papers: Classification of real nodal orders

We describe an online database of number fields which accompanies this paper The database centers on complete lists of number fields with prescribed invariants. Our description here focuses on summarizing tables and connections to…

We identify a number of decidable and undecidable fragments of first-order concatenation theory. We also give a purely universal axiomatization which is complete for the fragments we identify. Furthermore, we prove some normal-form results.

The present work is dedicated to searching parameters, alternative to entropy, applicable for description of highly organized systems. The general concept has been offered, in which the system complexity and order are functions of the order…

We characterize the order of principal congruences of a bounded lattice (also of a complete lattice and of a lattice of length 5) as a bounded ordered set. We also state a number of open problems in this new field.

In this paper we study random orderings of the integers with a certain invariance property. We describe all such orders in a simple way. We define and represent random shuffles of a countable set of labels and then give an interpretation of…

In this paper we study the distribution of orders of bounded discriminants in number fields. We give an asymptotic formula for the number of orders contained in the ring of integers of a quintic number field.

We study d-minimal expansions of ordered fields, and dense pairs thereof. We also consider other generalizations of o-minimality.

A method based on order completion for solving general equations is presented. In particular, this method can be used for solving large classes of nonlinear systems of PDEs, with possibly associated initial and/or boundary value problems.

We classify crossed product gradings for arbitrary groups and fields up to several equivalence relations in terms of group actions and their orbits.

We determine the set of catenary degrees, the set of distances, and the unions of sets of lengths of the monoid of nonzero ideals and of the monoid of invertible ideals of orders in quadratic number fields.

We study degree two unirational parameterizations of geometrically rational surfaces over the real field.

For every natural number $m$, the existentially closed models of the theory of fields with $m$ commuting derivations can be given a first-order geometric characterization in several ways. In particular, the theory of these differential…

In this paper, we give a new approach for the study of Weyl-type theorems. Precisely we introduce the concepts of spectral valued and spectral partitioning functions. Using two natural order relations on the set of spectral valued…

We classify up to equivalence the gradings on Hurwitz superalgebras and on symmetric composition superalgebras, over any field. Also, classifications up to isomorphism are given in case the field is algebraically closed. By grading, here we…

We study semi-isolation as a binary relation on the locus of a complete type and prove that under some additional assumptions it induces the strict order property.

This thesis studies arithmetic of linear algebraic groups. It involves studying the properties of linear algebraic groups defined over global fields, local fields and finite fields, or more generally the study of the linear algebraic groups…

In this paper we study grouplike monoids, these are monoids that contain a group to which we add an ordered set of idempotents. We classify finite categories with two objects having grouplike endomorphism monoids, and we give a count of…

When dealing with large graphs, such as those that arise in the context of online social networks, a subset of nodes may be labeled. These labels can indicate demographic values, interest, beliefs or other characteristics of the nodes…

We determine the most general group of equivalence transformations for a family of differential equations defined by an arbitrary vector field on a manifold. We also find all invariants and differential invariants for this group up to the…

The graded Lie algebra associated with the Nottingham group over a field of prime characteristic serves as a fundamental example of Nottingham algebras, a class of infinite-dimensional, positively graded thin algebras. This paper completes…