Related papers: A Generalization of the "Raboter" Operation
We prove a relationship between certain integer expressions involving operators similar to the binary exclusive or. This gives a proof and generalization of a result conjectured about sequence A178729 in Sloane's Online Encyclopedia of…
A classical method for partition generating functions is developed into a tool with wide applications. New expansions of well-known theorems are derived, and new results for partitions with n copies of n are presented.
We generalize to arbitrary categories of algebras the notion of an NS-algebra. We do this by using a bimodule property, as we did for defining the general notions of a dendriform and tridendriform algebra. We show that several types of…
Inspired by the fundamental results obtained by P. Halmos and A. Monteiro, concerning equivalence relations and monadic Boolean algebras, we recall the `concrete' Rauszer Boolean algebra pointed out by C. Rauszer (1971), via un preorder R.…
We extend the notion of generalized unitarity cuts to accommodate loop integrals with higher powers of propagators. Such integrals frequently arise in for example integration-by-parts identities, Schwinger parametrizations and Mellin-Barnes…
In the present article we define and investigate relative Rota--Baxter operators and relative averaging operators on racks and rack algebras. Also, if B is a Rota--Baxter or averaging operator on a rack X, then we can extend B by linearity…
In this paper we present equivalence results for several types of unbounded operator functions. A generalization of the concept equivalence after extension is introduced and used to prove equivalence and linearization for classes of…
In this article, for modelling numeral systems, the operator approach, which is introduced in [25], is generalized for a certain case. An example of such numeral systems is introduced and considered.
This work aims at the precise and efficient computation of the x-ray projection of an image represented by a linear combination of general shifted basis functions that typically overlap. We achieve this with a suitable adaptation of ray…
In this paper we define a new transform on (generalized) Boolean functions, which generalizes the Walsh-Hadamard, nega-Hadamard, $2^k$-Hadamard, consta-Hadamard and all $HN$-transforms. We describe the behavior of what we call the root-…
In this short note, we present certain generalized versions of the commutator formulas of some natural operators on manifolds, and give some applications.
We present a base class of automata that induce a numeration system and we give an algorithm to give the n-th word in the language of the automaton when the expansion of n in the induced numeration system is feeded to the automaton.…
There are major advantages in a newer version of Grover's quantum algorithm utilizing a general unitary transformation in the search of a single object in a large unsorted database. In this paper, we generalize this algorithm to multiobject…
We study the notion of recurrence and some of its variations for linear operators acting on Banach spaces. We characterize recurrence for several classes of linear operators such as weighted shifts, composition operators and multiplication…
We present a combinatorial method of constructing solutions to the normal ordering of boson operators. Generalizations of standard combinatorial notions - the Stirling and Bell numbers, Bell polynomials and Dobinski relations - lead to…
In a 1976 landmark paper, Gordon James defined the regularisation maps on integer partition, yielding certain decomposition numbers for modular representations of $\mathfrak{S}_n$. We describe a generalisation of James's regularisation map…
General approach to the multiplication or adjoint operation of $2\times 2$ block operator matrices with unbounded entries are founded. Furthermore, criteria for self-adjointness of block operator matrices based on their entry operators are…
We survey current term-wise techniques for quadratizing high-degree pseudo-Boolean functions and introduce a new one, which allows multiple splits of terms. We also introduce the first aggregative approach, which splits a collection of…
Machine learning for robot manipulation promises to unlock generalization to novel tasks and environments. But how should we measure the progress of these policies towards generalization? Evaluating and quantifying generalization is the…
This paper proposes new factorizations for computing the Neumann series. The factorizations are based on fast algorithms for small prime sizes series and the splitting of large sizes into several smaller ones. We propose a different basis…