The associativity problem for the class of finite multiplication tables is known to be undecidable, even for quite narrow infinite subclasses of tables. We present criteria which can be used to decide associativity in many cases, although any effective method based on such criteria must eventually fail on a table of some size (as otherwise decidability for the general class would follow). By me...

We show that several standard associative quantizations can be expressed as cochain module twists in the spirit of Moyal products, at least to O(~), but where the twist element is not a cocycle. This puts such quantisations induced by covariance groups into the setting of our previous work on semiclassicalisation of differential structures where we showed that that noncommutative geometry force...

Asymptotic near-tip fields are analyzed for a plane strain Mode I crack propagating dynamically in non-associative elastic–plastic solids of the Drucker–Prager type with an isotropic linear strain hardening response. Eigen solutions are obtained over a range of material parameters and crack speeds, based on the assumption that asymptotic solutions are variable-separable and fully continuous. A ...

Starting from a thermomechanical description of elastoplasticity, a stress-based variational principle is derived. The principle, which generalizes von Mises’s principle of maximum plastic dissipation, reproduces the conventional elastic/hardening-plastic framework applicable to metals as a special case and further proves to be suitable for developing constitutive models for frictional material...

Before we dive into the accessibility stream of nowadays indicatory applications of octonions to computer and other sciences and to quantum physics let us focus for a while on the crucially relevant events for today's revival on interest to nonassociativity. Our reflections keep wandering back to the Brahmagupta-Fibonacci Two-Square Identity and then via the Euler Four-Square Identity up to the...

We present a new algorithm recognizing general context-free languages in O(BM(n)) time, where BM(n) is the time to multiply two n by n boolean matrices. The only known algorithm for this problem with the same asymptotic complexity is the Valiant's algorithm [Va75], which is quite sofisticated. The probem related to texts is reduced to arithmetics of matrices whose elements are in a semiring of ...

We construct spherical harmonics for fuzzy spheres of even and odd dimensions, generalizing the correspondence between finite matrix algebras and fuzzy two-spheres. The finite matrix algebras associated with the various fuzzy spheres have a natural basis which falls in correspondence with tensor constructions of irreducible representations of orthogonal groups SO(n). This basis is useful in des...

During the last few decades, nonassociative structures have been employed in various fields of modern physics. Among others, one may mention the rise of nonassociative objects such as 3-cocycles, which are linked with violations of the Jacobi identity in anomalous quantum field theory, and quantum mechanics with the Dirac monopole, the appearance of Lie groupoids and algebroids in the context o...

We define reproducibility to mean getting bitwise identical results from multiple runs of the same program, perhaps with different hardware resources or other changes that should ideally not change the answer. Many users depend on reproducibility for debugging or correctness [1]. However, dynamic scheduling of parallel computing resources, combined with nonassociativity of floating point additi...