Related papers: An ordered structure of rank two related to Dulac'…
If F is a family of mod 2 flat k-cycles in the unit n-ball, we lower bound the maximal volume of any cycle in F in terms of the homology class of F in the space of all cycles. We give examples to show that these lower bounds are fairly…
It has been common wisdom among mathematicians that Extended Topological Field Theory in dimensions higher than two is naturally formulated in terms of n-categories with n> 1. Recently the physical meaning of these higher categorical…
We consider the 1-parameter family of planar quintic systems, $\dot x= y^3-x^3$, $\dot y= -x+my^5$, introduced by A. Bacciotti in 1985. It is known that it has at most one limit cycle and that it can exist only when the parameter $m$ is in…
We consider the enumeration problem of first-order queries over structures of bounded degree. It was shown that this problem is in the Constant-Delaylin class. An enumeration problem belongs to Constant-Delaylin if for an input of size n it…
We established the existence, uniqueness and stability of subsonic flows past an airfoil with a vortex line at the trailing edge. Such a flow pattern is governed by the two dimensional steady compressible Euler equations. The vortex line…
We introduce and study a natural class of fields in which certain first-order definable sets are existentially definable, and characterise this class by a number of equivalent conditions. We show that global fields belong to this class, and…
We study the model theory of vector spaces with a bilinear form over a fixed field. For finite fields this can be, and has been, done in the classical framework of full first-order logic. For infinite fields we need different logical…
We find that second order quantification is problematic when a quantified concept variable is supposed to function predicatively. This issue is analyzed and it is shown that a constructive interpretation of the falling under relation…
We consider the two-variable fragment of first-order logic with one distinguished binary predicate constrained to be interpreted as a transitive relation. The finite satisfiability problem for this logic is shown to be decidable, in triply…
We present an algebraic framework which simultaneously generalizes the notion of linear subspaces, matroids, valuated matroids, and oriented matroids. We call the resulting objects matroids over hyperfields. In fact, there are (at least)…
In this work, we consider optimal control problems for mechanical systems on vector spaces with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an…
Motivated by some computations of Feynman integrals and certain conjectures on mixed Tate motives, Bejleri and Marcolli posed questions about the $\mathbb{F}_1$-structure (in the sense of torification) on the complement of a hyperplane…
We perform the canonical and path integral quantizations of a lower-order derivatives model describing Podolsky's generalized electrodynamics. The physical content of the model shows an auxiliary massive vector field coupled to the usual…
The paper has a form of a survey and consists of three parts. It is focused on the relationship between the many-sorted theory, which leads to logical geometry and one-sorted theory, which is based on the important model-theoretic concepts.…
Preference cycles are prevalent in problems of decision-making, and are contradictory when preferences are assumed to be transitive. This contradiction underlies Condorcet's Paradox, a pioneering result of Social Choice Theory, wherein…
We consider weighted double Hurwitz numbers, with the weight given by arbitrary rational function times an exponent of the completed cycles. Both special singularities are arbitrary, with the lengths of cycles controlled by formal…
In this paper, we study the structure of the set of tilings produced by any given tile-set. For better understanding this structure, we address the set of finite patterns that each tiling contains. This set of patterns can be analyzed in…
We prove that if a smooth vector field $F$ of $S^3$ generates a sufficiently complicated heteroclinic knot, the flow also generates infinitely many periodic orbits, which persist under smooth perturbations which preserve the heteroclinic…
We theoretically and numerically investigate a two-dimensional O(2) model where an order parameter is convected by shear flow. We show that a long-range phase order emerges in two dimensions as a result of anomalous suppression of phase…
Second order systems whose drift is defined by the gradient of a given potential are considered, and minimization of the $L^1$-norm of the control is addressed. An analysis of the extremal flow emphasizes the role of singular trajectories…