Related papers: Dimension quotients as boundary limits
The main result of this paper concerns the behavior of a free boundary arising from a minimization problem, close to the fixed boundary in two dimensions.
We give bounds on the global dimension of a finite length, piecewise hereditary category in terms of quantitative connectivity properties of its graph of indecomposables. We use this to show that the global dimension of a finite…
Limits and colimits of diagrams, defined by maps between sets, are universal constructions fundamental in different mathematical domains and key concepts in theoretical computer science. Its importance in semantic modeling is described by…
Dimension is a standard and well-studied measure of complexity of posets. Recent research has provided many new upper bounds on the dimension for various structurally restricted classes of posets. Bounded dimension gives a succinct…
A parity is a rule to assign labels to the crossings of knot diagrams in a way compatible with Reidemeister moves. Parity functors can be viewed as parities which provide to each knot diagram its own coefficient group that contains parities…
The new model for the free solvable groups of level two is given; this helps to calculate the Poisson-Furstenberg boundary of the group.
A dimension group is a partially ordered countable group such that (1) every finite subset is contained in an ordered subgroup which is a finite direct power of Z and (2) the group has an order unit i.e. a positive element u such that every…
We consider the behaviour of holomorphic functions on a bounded open subset of the plane, satisfying a Lipschitz condition with exponent $\alpha$, with $0<\alpha<1$, in the vicinity of an exceptional boundary point where all such functions…
In this note, we find a sharp bound for the minimal number (or in general, indexing set) of subspaces of a fixed (finite) codimension needed to cover any vector space V over any field. If V is a finite set, this is related to the problem of…
De Finetti theorems tell us that if we expect the likelihood of outcomes to be independent of their order, then these sequences of outcomes could be equivalently generated by drawing an experiment at random from a distribution, and…
We define a notion of free product for coarse spaces that generalizes the corresponding notion of a free product for groups. We show that free products preserve coarse properties such as coarse property C, finite coarse decomposition…
A quantum frame is defined by a material object subject to the laws of quantum mechanics. The present paper studies the relations between quantum frames, which in the classical case are described by elements of the Poincare' group. The…
We have computed by a Monte Carlo method the fourth virial coefficient of free anyons, as a function of the statistics angle theta. It can be fitted by a four term Fourier series, in which two coefficients are fixed by the known…
One could begin a study like the present one by simply postulating that our universe is four-dimensional. There are ample reasons for doing this. Experience, observation and experiment all point to the fact that we inhabit a…
Convertible bonds give rise to the so-called free boundary; i.e., an unknown boundary between continuation and conversion regions of the bond. The characteristic feature of such a bond, with an extra call feature, is that the free boundary…
We discuss the notion of essential dimension of a finite group and explain its relation with birational algebraic geometry. We show how this leads to a (partial) classification of simple finite groups of essential dimension less than or…
We study properties of a category after quotienting out a suitable chosen group of isomorphisms on each object. Coproducts in the original category are described in its quotient by our new weaker notion of a 'phased coproduct'. We examine…
This short introductory category theory textbook is for readers with relatively little mathematical background (e.g. the first half of an undergraduate mathematics degree). At its heart is the concept of a universal property, important…
Starting with a quaternion difference equation with boundary conditions, a parameterized sequence which is complete in finite dimensional quaternion Hilbert space is derived. By employing the parameterized sequence as the kernel of discrete…
We have previously shown how to construct a deformation quantization of any locally compact space on which a vector group acts. Within this framework we show here that, for a natural class of Hamiltonians, the quantum evolutions will have…