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Hypergraph Horn functions were introduced as a subclass of Horn functions that can be represented by a collection of circular implication rules. These functions possess distinguished structural and computational properties. In particular,…
Most of the special functions of mathematical physics are connected with the representation of Lie groups. The action of elements $D$ of the associated Lie algebras as linear differential operators gives relations among the functions in a…
The cell complex structure is one of the most fundamental structures in topology and combinatorics, the Morse decomposition of a dynamical system analyzes the global gradient behavior, and the Reeb graph of a function is an elementary tool…
We introduce an operad of formal fractions, abstracted from the Mould operads and containing both the Dendriform and the Tridendriform operads. We consider the smallest set-operad contained in this operad and containing four specific…
New families of $E$-functions are described in the context of the compact simple Lie groups O(5) and G(2). These functions of two real variables generalize the common exponential functions and for each group, only one family is currently…
We obtain explicit expressions for genus 2 degenerate sigma-function in terms of genus $1$ sigma-function and elementary functions as solutions of a system of linear PDEs satisfied by the sigma-function. By way of application we derive a…
This paper describes a part of the factorization theory of the family of all the entire functions with non vanishing derivatives. In particular it proves that this family of mappings contains primes. This assures that this family of entire…
We define a ring whose elements are rational functions, whose addition is polynomial multiplication, and whose multiplication is a convolution operation. It is then show that this ring's endomorphisms exhibit a strong classification.…
We show that any multiple-valued function can be represented by a linear lambda term typed in a second-order polymorphic type system, using two distinct styles. The first is a circuit style, which mimics combinational circuits in switching…
Consider a_1,a_2,...,a_n, arbitrary elements of R. We characterize those real functions f that decompose into the sum of a_j-periodic functions, i.e., f=f_1+...+f_n with D_{a_j}f(x):=f(x+a_j)-f(x)=0. We show that f has such a decomposition…
Dualities are mathematical mappings that reveal unexpected links between apparently unrelated systems or quantities in virtually every branch of physics. Systems that are mapped onto themselves by a duality transformation are called…
We prove a generalised Yuan--Hunt--Ma\~n\'e Conjecture: if $\mathcal{F}$ is the Banach space of $\alpha$-H\"older functions, and $\mathcal{T}$ is either a space of Lipschitz expanding maps, or of Anosov diffeomorphisms, or the family of…
We exhibit an adjunction between a category of abstract algebras of partial functions and a category of set quotients. The algebras are those atomic algebras representable as a collection of partial functions closed under relative…
Binomial Cayley graphs are obtained by considering the binomial coefficient of the weight function of a given Cayley graph and a natural number. We introduce these objects and study two families: one associated with symmetric groups and the…
Let $A$ be a rational function. For any decomposition of $A$ into a composition of rational functions $A=U\circ V$ the rational function $\widetilde A=V\circ U$ is called an elementary transformation of $A$, and rational functions $A$ and…
Structural stability of holomorphic functions has been the subject of much research in the last fifty years. Due to various technicalities, however, most of that work has focused on so-called finite-type functions (functions whose set of…
We classify small binary bibraces, using the correspondence with alternating algebras over the field F2, up to dimension eight, also determining their isomorphism classes. These finite-dimensional algebras, defined by an alternating…
In this paper, we give a geometric interpretation of optimal functionals in the context of intersection of symmetry planes and cyclic polytopes. For 1D CFTs, we demonstrate that at given derivative order, the functional is given by a…
Most of the special functions of mathematical physics are connected with the representation of Lie groups. The action of elements $D$ of the associated Lie algebras as linear differential operators gives relations among the functions in a…
Binary embeddings provide efficient and powerful ways to perform operations on large scale data. However binary embedding typically requires long codes in order to preserve the discriminative power of the input space. Thus binary coding…