Related papers: Extensions of real numbers using coset groups
Numerous attempts have been made to replicate the success of complex-valued algebra in engineering and science to other hypercomplex domains such as quaternions, tessarines, biquaternions, and octonions. Perhaps, none have matched the…
We present a new combinatorial approach to the computation of the (real) Fourier expansions of $\cos^n(t)$ and $\sin^n(t)$, where $n\geq 1$ is an integer. As an application, we compute the Fourier expansions of $f(t)=\frac{1}{a-\cos t}$ and…
Genuinely entangled subspaces (GESs) are the class of completely entangled subspaces that contain only genuinely multiparty entangled states. They constitute a particularly useful notion in the theory of entanglement but also have found an…
We show how to use extended word series in the reduction of continuous and discrete dynamical systems to normal form and in the computation of formal invariants of motion in Hamiltonian systems. The manipulations required involve complex…
Complex polynomial optimization has recently gained more and more attention in both theory and practice. In this paper, we study the optimization of a real-valued general conjugate complex form over various popular constraint sets including…
A new sampling methodology based on incomplete cosine expansion series is presented as an alternative to the traditional sinc function approach. Numerical integration shows that this methodology is efficient and practical. Applying the…
We introduce a relaxation of the notion of tensor rank, called s-rank, and show that upper bounds on the s-rank of the matrix multiplication tensor imply upper bounds on the ordinary rank. In particular, if the "s-rank exponent of matrix…
We define a bi-directional embedding between hypersequent calculi and a subclass of systems of rules (2-systems). In addition to showing that the two proof frameworks have the same expressive power, the embedding allows for the recovery of…
We use series expansions to study dynamics of equilibrium and non-equilibrium systems on networks. This analytical method enables us to include detailed non-universal effects of the network structure. We show that even low order…
R-matrix method is used to construct supersymmetric extensions of theta - Euclidean group preserving N = 1/2 supersymmetry and its three- parameter generalization. These quantum symmetry supergroups can be considered as global counterparts…
Decomposition of (finite-dimensional) operators in terms of orthogonal bases of matrices has been a standard method in quantum physics for decades. In recent years, it has become increasingly popular because of various methodologies applied…
A construction of polytopes is given based on integers. These geometries are constructed through a mapping to pure numbers and have multiple applications, including statistical mechanics and computer science. The number form is useful in…
Many groups possess highly symmetric generating sets that are naturally endowed with an underlying combinatorial structure. Such generating sets can prove to be extremely useful both theoretically in providing new existence proofs for…
A new construction of the real number system, that is built directly upon the additive group of integers and has its roots in the definition due to Henri Poincar\'e of the rotation number of an orientation preserving homeomorphism of the…
This work presents the tessellations and polytopes from the perspective of both n-dimensional geometry and abstract symmetry groups. It starts with a brief introduction to the terminology and a short motivation. In the first part, it…
Physical properties of matter are tightly related with the kind of symmetry of the medium. Group theory is a systematic tool, though not always easy to handle, to exploit symmetry properties, for instance to find the eigenvectors and…
Generalized Fourier series with orthogonal polynomial bases have useful applications in several fields, including differential equations, pattern recognition, and image and signal processing. However, computing the generalized Fourier…
Proper classes of extensions of real field was defined and topological properties of these extensions were studied. These extensions can be connected, in this case such set is not closed under binary operations (addition and…
We establish a connection between oriented matroid theory and loop quantum gravity in (2+2) (two time and two space dimensions) and 8-dimensions. We start by observing that supersymmetry implies that the structure constants of the real…
We describe a method for simulating the real time evolution of extended quantum systems in two dimensions. The method combines the benefits of integrability and matrix product states in one dimension to avoid several issues that hinder…