Related papers: Wilson Theorems for Double-, Hyper-, Sub- and Supe…
Contents: Generalities, Chiral supermultiplets, Super Yang-Mills theory, Superspace Feynman graphs, Renormalization, Supercurrent, Finite theories.
In this note we prove that the factorization theorem for dominated polynomials previously proved by the authors is equivalent to an alternative factorization scheme that uses classical linear techniques and a linearization process. However,…
We calculate Wilson loops on boundaries of Lifshitz-like dual backgrounds with different scaling parameters, assuming existence of a field theory dual to string theory in the bulk. We consider scaling parameters to be variable quantities…
We apply a general approach for distributions of binary isolating and semi-isolating formulas to the class of strongly minimal theories.
We study a generalization of the classical Pentagonal Number Theorem and its applications. We derive new identities for certain infinite series, recurrence relations and convolution sums for certain restricted partitions and divisor sums.…
We present a summary of the applications of duality to Donaldson-Witten theory and its generalizations. Special emphasis is made on the computation of Donaldson invariants in terms of Seiberg-Witten invariants using recent results in N=2…
The aim of this paper is to present an extension theorem for the functions separately holomorphic on generalized (N,k)-crosses with pluripolar singularities.
In the research, with aid of the Fa\`a di Bruno formula, be virtue of several identities for the Bell polynomials of the second kind, with help of two combinatorial identities, by means of the (logarithmically) complete monotonicity of…
Binomial Theorem for (N+n)^r is described with non-commuting variables N and n.
We generalize Romanoff's theorem. Also, we obtain a result on sums related to Euler's totient function.
We use generalized Taylor formulae in order to give some simple constructions in the real closure of an \ovfz. We deduce a new, simple quantifier elimination algorithm for \rcvfs and some theorems about constructible subsets of real…
We prove a generalization of classical Montel's theorem for the mixed differences case, for polynomials and exponential polynomial functions, in commutative setting.
We provide a geometric condition that guarantees strong Wilf equivalence in the generalized factor order. This provides a powerful tool for proving specific and general Wilf equivalence results, and several such examples are given.
We derive exact formulas for circular Wilson loops in the $\mathcal{N}=4$ and $\mathcal{N}=2^{* }$ theories with gauge groups $U(N)$ and $SU(N)$ in the $k$-fold symmetrized product representation. The formulas apply in the limit of large…
We generalize generating functions for hypergeometric orthogonal polynomials, namely Jacobi, Gegenbauer, Laguerre, and Wilson polynomials. These generalizations of generating functions are accomplished through series rearrangement using…
For positive integers m and n, denote S(m,n) as the associated Stirling number of the second kind and let z be a complex variable. In this paper, we introduce the Stirling functions S(m,n,z) which satisfy S(m,n,z) = S(m,n) for any z which…
A simple definition of torsion theory is presented, as a factorization system with both classes satisfying the 3--for--2 property. Comparisons with the traditional notion are given, as well as connections with the notions of fibration and…
Generalized dualities had an intriguing incursion into Double Field Theory (DFT) in terms of local $O(d,d)$ transformations. We review this idea and use the higher derivative formulation of DFT to compute the first order corrections to…
We develop a method to construct algebraic invariants for hypermatrices. We then construct hyperdeterminants and exhibit a generalization of the Cayley-Hamilton theorem for hypermatrices.
These notes give an exposition of Deligne's theorem on the existense of super fiber functor.