相关论文: Flag Paraproducts
This is a brief account of relations between the theory of special functions, on the one side, and superconformal indices and Seiberg dualities of four-dimensional $\mathcal{N}=1$ supersymmetric gauge field theories, on the other side.
Many product formulas are known classically for generalized hypergeometric functions over the complex numbers. In this paper, we establish some analogous formulas for generalized hypergeometric functions over finite fields.
We interpret a formula for meromorphic functions on foliations by Riemann surfaces as an analogue to the product formula of valuations in algebraic number theory.
This note defines a flag vector for $i$-graphs. The construction applies to any finite combinatorial object that can be shelled. Two possible connections to quantum topology are mentioned. Further details appear in the author's "On quantum…
We study generalizations of Schur functors from categories consisting of flags of vector spaces. We give different descriptions of the category of such functors in terms of representations of certain combinatorial categories and infinite…
In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.
The choice of a star product realization for noncommutative field theory can be regarded as a gauge choice in the space of all equivalent star products. With the goal of having a gauge invariant treatment, we develop tools, such as…
We combine continuous and integral logics and found a logical framework for metric measure spaces equipped with a family of continuous relations and operations. We prove the ultraproduct theorem and deduce compactness and other usual…
A conceptual framework for variational formulations of physical theories is proposed. Such a framework is displayed here just for statics, but it is designed to be subsequently adapted to variational formulations of static field theories…
We consider germs of holomorphic vector fields at the origin of $\mathbb{C}^3$, with non-isolated singularities that are tangent to a holomorphic foliation of codimension one. This configuration is known as a $2$-flag of foliations. The…
Supplementary results obtained after the completion of our previous paper are given together with discussing some examples. A quick review of the previous paper is also included.
A paradefinite logic is a logic that can serve as the underlying logic for theories that are inconsistent or incomplete. A well-known paradefinite logic is Belnap-Dunn logic. Various expansions of Belnap-Dunn logic have been studied in the…
We resolve an open problem concerning finite logical implication for path functional dependencies (PFDs).
We develop a Galois theory for systems of linear difference equations with an action of an endomorphism {\sigma}. This provides a technique to test whether solutions of such systems satisfy {\sigma}-polynomial equations and, if yes, then…
Explicit general constructions of paragrassmann calculus with one and many variables are given. Relations of the paragrassmann calculus to quantum groups are outlined and possible physics applications are briefly discussed. This paper is…
It is a basic introduction to differential graded Lie algebras, Maurer-Cartan equation and associated deformation functors.
The work studies some Difference equations, which are connected with Mejer's function.
We give an account, in terms of fibered categories and their fibrewise duals, of aspects of the theory of bundle functors and star-bundle functors in differential geometry.
We construct geometric examples of N-differential graded algebras such as the algebra of differential forms of depth $N$ on an affine manifold, and $N$-flat covariant derivatives.
We use the formal affine Demazure algebra to construct an explicit Leray-Hirsch Theorem for torus equivariant oriented cohomology of flag varieties. We then generalize the Borel model of such theory to partial flag varieties.