Related papers: Dimension expanders via quiver representations
We find generators for the algebra of rational differential invariants for general and degenerate Kundt spacetimes and relate this to other approaches to the equivalence problem for Lorentzian metrics. Special attention is given to…
Humans are able to conceive physical reality by jointly learning different facets thereof. To every pair of notions related to a perceived reality may correspond a mutual relation, which is a notion on its own, but one-level higher. Thus,…
In this paper we give a characterisation of trivial extension algebras in terms of quivers with relations. This result is based on a explicit description of the ideal of relations of the trivial extension of an algebra, given by the first…
Associated to the two types of finite dimensional simple superalgebras, there are the general linear Lie superalgebra and the queer Lie superalgebra. The universal enveloping algebras of these Lie superalgebras act on the tensor spaces of…
This paper offers an approach to extensible knowledge representation and reasoning for a family of formalisms known as Description Logics. The approach is based on the notion of adding new concept constructors, and includes a heuristic…
In this paper, we consider a generalized strong vector quasi-equilibrium problem and we prove the existence of its solutions by using some suxiliary results. One of the established theorems is proved by using an approximation method.
We study several classes of indecomposable representations of quivers on infinite-dimensional Hilbert spaces and their relation. Many examples are constructed using strongly irreducible operators. Some problems in operator theory are…
Theories defined in higher than four dimensions have been used in various frameworks and have a long and interesting history. Here we review certain attempts, developed over the last years, towards the construction of unified particle…
We derive a piecewise-linear formula for the rigid representation of a Dynkin quiver of a given dimension vector, and illustrate the formula in several examples.
We study multiplicative Diophantine approximation property of vectors and compute Diophantine exponents of hyperplanes via dynamics.
A Hilbert space in M dimensions is shown explicitly to accommodate representations that reflect the prime numbers decomposition of M. Representations that exhibit the factorization of M into two relatively prime numbers: the kq…
The issues of quintessence and cosmic acceleration can be discussed in the framework of higher order theories of gravity. We can define effective pressure and energy density directly connected to the Ricci scalar of curvature of a generic…
A conjecture regarding the structure of expander graphs is discussed.
The evolution of the extra dimension is investigated in the context of brane world cosmology. New cosmological solutions are found. In particular, solutions in the form of waves travelling along the extra dimension are identified.
For a linear difference equation with the coefficients being computable sequences, we establish algorithmic undecidability of the problem of determining the dimension of the solution space including the case when some additional prior…
The manifold hypothesis suggests that high-dimensional data often lie on or near a low-dimensional manifold. Estimating the dimension of this manifold is essential for leveraging its structure, yet existing work on dimension estimation is…
Significant research has been carried out in the past half-century on defining generalised determinants for transformations between (typically real) vector spaces of different dimensions. We review three different generalisations of the…
The theory of operads (May, cyclic, modular, PROPs, etc) is extended to include higher dimensional phenomena, i.e. operations between operations, mimicking the algebraic structure on varieties of arbitrary dimensions, having marked…
We give a criterion when an expansion of the ordered set of real numbers defines the image of the expansion of the real field by the set of natural numbers under a semialgebraic injection. In particular, we show that for a non-quadratic…
We prove addition and subspace theorems for asymptotic large inductive dimension. We investigate a transfinite extension of this dimension and show that it is trivial.