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Local solvability is analyzed for natural families of partial differential operators having double characteristics. In some families the set of all operators that are not locally solvable is shown to have both infinite dimension and…
Starting from arbitrary Hilbert spaces, we reduce the problem to verify entanglement of any bipartite quantum state to finite dimensional subspaces. Hence, entanglement is a finite dimensional property. A generalization for multipartite…
Given a nonempty set $\mathcal{L}$ of linear orders, we say that the linear order $L$ is $\mathcal{L}$-convex embeddable into the linear order $L'$ if it is possible to partition $L$ into convex sets indexed by some element of $\mathcal{L}$…
We give a short proof of polynomial recurrence with large intersection for additive actions of finite-dimensional vector spaces over countable fields on probability spaces, improving upon the known size and structure of the set of strong…
In this article we consider the action of affine group and time rescaling on planar quadratic differential systems. We construct a system of representatives of the orbits of systems with at least five invariant lines, including the line at…
This article highlights historical achievements in the partition theory of countable homogeneous relational structures, and presents recent work, current trends, and open problems. Exciting recent developments include new methods involving…
The partition function with boundary conditions for various two-dimensional Ising models is examined and previously unobserved properties of conformal invariance and universality are established numerically.
We give divisibility results for the (global) characteristic varieties of hypersurface complements expressed in terms of the local characteristic varieties at points along one of the irreducible components of the hypersurface. As an…
We consider rationally connected complex projective manifolds M and show that their loop spaces--infinite dimensional complex manifolds--have properties similar to those of M. Furthermore, we give a finite dimensional application concerning…
In this paper the notion of Dirac structure in finite dimension is extended to the convenient setting. In particular, we introduce the notion of partial Dirac structure on convenient Lie algebroids and manifolds. We then look for those…
Numerous properties of vector addition systems with states amount to checking the (un)boundedness of some selective feature (e.g., number of reversals, run length). Some of these features can be checked in exponential space by using…
We consider random fields admitting a spectral representation with infinitely divisible integrator and prove some of their properties.
Differential algebraic geometry seeks to extend the results of its algebraic counterpart to objects defined by differential equations. Many notions, such as that of a projective algebraic variety, have close differential analogues but their…
Over the past twenty years, lecture hall partitions have emerged as fundamental combinatorial structures, leading to new generalizations and interpretations of classical theorems and new results. In recent years, geometric approaches to…
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 introduce a notion of relative primeness for equivalence relations, strengthening the notion of non-reducibility, and show for many standard benchmark equivalence relations that non-reducibility may be strengthened to relative primeness.…
We classify the three-dimensional representations of the modular group that are reducible but indecomposable, and their associated spaces of holomorphic vector-valued modular forms. We then demonstrate how such representations may be…
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…
We characterize the downsets of integer partitions (ordered by containment of Ferrers diagrams) and compositions (ordered by the generalized subword order) which have finite dimension in the sense of Dushnik and Miller. In the case of…
A classical method for partition generating functions is developed into a tool with wide applications. New expansions of well-known theorems are derived, and new results for partitions with n copies of n are presented.