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Full-Text Articles in Algebra
Regular Functions On The Scaled Hypercomplex Numbers, Daniel Alpay, Ilwoo Cho
Regular Functions On The Scaled Hypercomplex Numbers, Daniel Alpay, Ilwoo Cho
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper, we study the regularity of R-differentiable functions on open connected subsets of the scaled hypercomplex numbers {Ht}t∈R by studying the kernels of suitable differential operators {∇t}t∈R, up to scales in the real field R.
Spacetime Geometry Of Acoustics And Electromagnetism, Lucas Burns, Tatsuya Daniel, Stephon Alexander, Justin Dressel
Spacetime Geometry Of Acoustics And Electromagnetism, Lucas Burns, Tatsuya Daniel, Stephon Alexander, Justin Dressel
Mathematics, Physics, and Computer Science Faculty Articles and Research
Both acoustics and electromagnetism represent measurable fields in terms of dynamical potential fields. Electromagnetic force-fields form a spacetime bivector that is represented by a dynamical energy–momentum 4-vector potential field. Acoustic pressure and velocity fields form an energy–momentum density 4-vector field that is represented by a dynamical action scalar potential field. Surprisingly, standard field theory analyses of spin angular momentum based on these traditional potential representations contradict recent experiments, which motivates a careful reassessment of both theories. We analyze extensions of both theories that use the full geometric structure of spacetime to respect essential symmetries enforced by vacuum wave propagation. The …
A Little More On Ideals Associated With Sublocales, Oghenetega Ighedo, Grace Wakesho Kivunga, Dorca Nyamusi Stephen
A Little More On Ideals Associated With Sublocales, Oghenetega Ighedo, Grace Wakesho Kivunga, Dorca Nyamusi Stephen
Mathematics, Physics, and Computer Science Faculty Articles and Research
As usual, let RL denote the ring of real-valued continuous functions on a completely regular frame L. Let βL and λL denote the Stone- Čech compactification of L and the Lindelöf coreflection of L, respectively. There is a natural way of associating with each sublocale of βL two ideals of RL, motivated by a similar situation in C(X). In [12], the authors go one step further and associate with each sublocale of λL an ideal of RL in a manner similar to one of the ways one does it for sublocales of βL. The intent in this paper …