Related papers: Gales Suffice for Constructive Dimension
In this paper, we provide new applications of Fibonacci and Lucas numbers. In some circumstances, we find algebraic structures on some sets defined with these numbers, we generalize Fibonacci and Lucas numbers by using an arbitrary binary…
Canonical extension of finitary ordered structures such as lattices, posets, proximity lattices, etc., is a certain completion which entirely describes the topological dual of the ordered structure and it does so in a purely algebraic and…
We introduce and investigate binary $(k,k)$-designs -- combinatorial structures which are related to binary orthogonal arrays. We derive general linear programming bound and propose as a consequence a universal bound on the minimum possible…
We define a class of associative algebras generalizing 'clannish algebras', as introduced by the second author, but also incorporating semilinear structure, like a skew polynomial ring. Clannish algebras generalize the well known 'string…
We introduce appropriate definitions of dimensions in order to characterize the fractal properties of complex networks. We compute these dimensions in a hierarchically structured network of particular interest. In spite of the nontrivial…
Graphs, and sequences of growing graphs, can be used to specify the architecture of mathematical models in many fields including machine learning and computational science. Here we define structured graph "lineages" (ordered by level…
Recent work in percolation has led to exact solutions for the site and bond critical thresholds of many new lattices. Here we show how these results can be extended to other classes of graphs, significantly increasing the number and variety…
We study and simulate N=2 supersymmetric Wess-Zumino models in one and two dimensions. For any choice of the lattice derivative, the theories can be made manifestly supersymmetric by adding appropriate improvement terms corresponding to…
A rapidly growing body of research on compositional generalization investigates the ability of a semantic parser to dynamically recombine linguistic elements seen in training into unseen sequences. We present a systematic comparison of…
We study the N=2 four-dimensional superconformal index in various interesting limits, such that only states annihilated by more than one supercharge contribute. Extrapolating from the SU(2) generalized quivers, which have a Lagrangian…
We give upper-bounds for the dimension of some linear systems. The theorem improves the differential Horace method introduced by Alexander-Hirschowitz, and was conjectured by Simpson. Possible applications are the calculus of the dimension…
A parametrization of gauge fields on complex projective spaces of arbitrary dimension is given as a generalization of the two-dimensional case. Gauge transformations act homogeneously on the fields, facilitating a manifestly gauge-invariant…
We explore the interlacing between model category structures attained to classes of modules of finite $\mathcal{X}$-dimension, for certain classes of modules $\mathcal{X}$. As an application we give a model structure approach to the…
In this paper several examples of gaps (lacunes) between dimensions of maximal and submaximal symmetric models are considered, which include investigation of number of independent linear and quadratic integrals of metrics and counting the…
There is now compelling evidence in favour of the hierarchical structure formation paradigm. Semi-analytic modelling is a powerful tool which allows the formation and evolution of galaxies to be followed in a hierarchical framework. We…
A new algebraic Cayley graph is constructed using finite fields. Its connectedness and diameter bound are studied via Weil's estimate for character sums. These graphs provide a new source of expander graphs, extending classical results of…
In this paper we look into the structure of finite-dimensional graded superalgebras of various types such as associative, Lie and Jordan over an algebraically closed field of characteristic zero.
Conference matrices are used to define complex structures on real vector spaces. Certain lattices in these spaces become modules for rings of quadratic integers. Multiplication of these lattices by non-principal ideals yields simple…
We prove that the martingale dimensions for canonical diffusion processes on a class of self-similar sets including nested fractals are always one. This provides an affirmative answer to the conjecture of S. Kusuoka [Publ. Res. Inst. Math.…
It is shown that the expansion methods developed in refs. arXiv:hep-th/0212347 and arXiv:hep-th/0401033v2 can be generalized so that they permit to study the expansion of algebras of loops, both when the compact finite-dimensional algebra…