Related papers: When is a Bol loop Moufang?
The explainability of a robot's actions is crucial to its acceptance in social spaces. Explaining why a robot fails to complete a given task is particularly important for non-expert users to be aware of the robot's capabilities and…
It is shown how integrability of the generalized Lie equations of a local analytic Moufang loop is related to the reductivity conditions and Sagle-Yamaguti identity.
We consider voting rules in settings where voters' identities are difficult to verify. Voters can manipulate the process by casting multiple votes under different identities or abstaining from voting. Immunities to such manipulations are…
Qubit Models which aim to resolve the information paradox must not redefine entanglement entropy as a redefinition does not address the correct issue of the information paradox. The purpose of this letter is to understand why any…
Our paper deals about identities involving Bell polynomials. Some identities on Bell polynomials derived using generating function and successive derivatives of binomial type sequences. We give some relations between Bell polynomials and…
Mathematics has been used in the exploration and enumeration of juggling patterns. In the case when we catch and throw one ball at a time the number of possible juggling patterns is well-known. When we are allowed to catch and throw any…
A combinatorial construction proves an identity for the product of the Pfaffian of a skew-symmetric matrix by the Pfaffian of one of its submatrices. Several applications of this identity are followed by a brief history of Pfaffians.
The paper defines the notion of alternative loop algebra F[Q] for any nonassociative Moufang loop Q as being any non-zero homomorphic image of the loop algebra FQ of a loop Q over a field F. For the class M of all nonassociative alternative…
We discuss the problem of determining whether the state of several quantum mechanical subsystems is entangled. As in previous work on two subsystems we introduce a procedure for checking separability that is based on finding state…
The purpose of this paper is to characterize several classes of functional identities involving inverses with related mappings from a unital Banach algebra $\mathcal{A}$ over the complex field into a unital $\mathcal{A}$-bimodule…
Although they differ in the functionality they offer, low-level systems exhibit certain patterns of design and utilization of computing resources. In this paper, we argue the position that modalities, in the sense of modal logic, should be…
Existing protocols for multilateral negotiation require a full consensus among the negotiating parties. In contrast, we propose a protocol for multilateral negotiation that allows partial consensus, wherein only a subset of the negotiating…
In multipartite entanglement theory, the partial separability properties have an elegant, yet complicated structure, which boils down in the case when multipartite correlations are considered. In this work, we elaborate this, by giving…
Left Cheban loops are loops that satisfy the identity x(xy.z) = yx.xz. Right Cheban loops satisfy the mirror identity {(z.yx)x = zx.xy}. Loops that are both left and right Cheban are called Cheban loops. Cheban loops can also be…
A probability method is provided to prove three classes of combinatorial identities. The method is extremely simple, only one step after the proper probability setup.
We prove that the integral closedness of any ideal of height at least two is compatible with specialization by a generic element. This opens the possibility for proofs using induction on the height of an ideal. Also, with additional…
Multimodal learning has seen remarkable progress, particularly with the emergence of large-scale pre-training across various modalities. However, most current approaches are built on the assumption of a deterministic, one-to-one alignment…
The Hamiltonian cycle polynomial can be evaluated to count the number of Hamiltonian cycles in a graph. It can also be viewed as a list of all spanning cycles of length $n$. We adopt the latter perspective and present a pair of original…
We classify Bol loops of order $27$, using a combination of theoretical results and computer search. There are $15$ Bol loops of order $27$, including five groups. New constructions for the ten nonassociative Bol loops of order $27$ are…
We propose a classification of group properties according to whether they can be deduced from the assumption that a group's subgroup lattice contains an interval isomorphic to some lattice. We are able to classify a few group properties as…