Related papers: A binary operation on the class of coherently diag…
Using a binary representation for basis elements of an algebra combined with a framework of multiplier and index functions, a connection has been established between the structure of a large class of algebras and the XOR componentwise…
This paper presents a graded hierarchy or chain of binary operations on the reals and the complex numbers. The operations are related distributively in the sense that any one of them distributes over the next lower operation in the chain.…
We suggest that the canonical parallel operation of processes is composition in a well-supported compact closed category of spans of reflexive graphs. We present the parallel operations of classical process algebras as derived operations…
In previous work "Betweenness algebras" we introduced and examined the class of betweenness algebras. In the current paper we study a larger class of algebras with binary operators of possibility and sufficiency, the weak mixed algebras.…
The present paper is devoted to the study of dimonoids, algebraic structures with two associative binary operations that satisfy a prescribed system of axioms. We investigate the properties of dual dimonoids. In the class of noncommutative…
Although algebraic structures are frequently analyzed using unary and binary operations, they can also be effectively defined and unified through ternary operations. In this context, we introduce structures that contain two constants and a…
We explain how the simplicial higher-order unstable homotopy operations defined in [BBS2] may be composed and inserted one in another, thus forming a coherent if complicated algebraic structure.
Associated to each simplicial complex is a binary hierarchical model. We classify the simplicial complexes that yield unimodular binary hierarchical models. Our main theorem provides both a construction of all unimodular binary hierarchical…
In this paper, continuous binary operations of a topological space are studied and a criterion of their invertibility is proved. The classification problem of groups of invertible continuous binary operations of locally compact and locally…
We construct two combinatorially equivalent line arrangements in the complex projective plane such that the fundamental groups of their complements are not isomorphic. The proof uses a new invariant of the fundamental group of the…
We develop a compositional framework for formal synthesis of hybrid systems using the language of category theory. More specifically, we provide mutually compatible tools for hierarchical, sequential, and independent parallel composition.…
Binary operations on algebras of observables are studied in the quantum as well as in the classical case. It is shown that certain natural compatibility conditions with the associative product imply the properties which usually are…
In the context of Higman embeddings of recursive groups into finitely presented groups we suggest an algorithm which uses Higman operations to explicitly constructs the specific recursively enumerable sets of integer sequences arising…
Multiple binomial sums form a large class of multi-indexed sequences, closed under partial summation, which contains most of the sequences obtained by multiple summation of products of binomial coefficients and also all the sequences with…
We introduce a structure termed ``connected cyclic diagonal'' on a chain complex, which induces stable power operations in its cohomology with the property that negative power operations consistently vanish. This chain level structure is…
In this paper we present a recurrent relation for counting meaningful compositions of the higher-order differential operations on the space $R^{n}$ (n=3,4,...) and extract the non-trivial compositions of order higher than two.
A diagram of algebras is a functor valued in a category of associative algebras. I construct an operad acting on the Hochschild bicomplex of a diagram of algebras. Using this operad, I give a direct proof that the Hochschild cohomology of a…
Binary idempotent semirings govern classical path algebras. Their multiplicative structure is dyadic. We examine whether this restriction is structural or accidental. We define ternary idempotent $\Gamma$-semirings as higher-arity ordered…
This paper provides a class of complex symmetric weighted composition operators on $H^2(\mathbb{D})$ to includes the unitary subclass, the Hermitian subclass and the normal subclass obtained by Bourdon and Noor. A characterization of…
We study generalized sums of linear orders. These are binary operations that, given linear orders $A$ and $B$, return an order $A \oplus B$ that can be decomposed as an isomorphic copy of $A$ interleaved with a copy of $B$. We show that…