Related papers: On Systems of Linear Quaternion Functions
The main properties of hypercomplex generalization of quaternion system as antiquaternion are presented in this article. Definitions and studied of antiquaternions conjugation are introduced, their norm and zero divisor, and how to perform…
This paper provides an alternative description for the fixed points of the fractal operator associated with a mixed possibly infinite iterated function system via a canonical projection type function. Some visual aspects of our results are…
The article deals with the subject of solving the problem of canonical-map synthesis for Hamiltonian systems. For this purpose, the controlling-function method has been developed that allows appropriate changes of the variables in terms of…
Most of theoretical physics is based on the mathematics of functions of a real or a complex variable; yet we frequently are drawn to try extending our reach to include quaternions. The non-commutativity of the quaternion algebra poses…
The low-rank quaternion matrix approximation has been successfully applied in many applications involving signal processing and color image processing. However, the cost of quaternion models for generating low-rank quaternion matrix…
Complete analysis of quantum wave functions of linear systems in an arbitrary number of dimensions is given. It is shown how one can construct a complete set of stationary quantum states of an arbitrary linear system from purely classical…
It is well known that there is an integral theorem for quaternion-valued functions analogous to Cauchys Theorem for complex-valued functions, namely Fueters Theorem. The class of quaternionic functions for which this applies are generally…
The canonical partition function approach was designed to avoid the overlap problem that affects the lattice simulations of nuclear matter at high density. The method employs the projections of the quark determinant on a fix quark number…
The fractional quantization of singular systems with second order Lagrangian is examined. The fractional singular Lagrangian is presented. The equations of motion are written as total differential equations within fractional calculus. Also,…
We consider a constructive modification of quantum-mechanical formalism. Replacement of a general unitary group by unitary representations of finite groups makes it possible to reproduce quantum formalism without loss of its empirical…
With a view towards models of quantum computation and/or the interpretation of linear logic, we define a functional language where all functions are linear operators by construction. A small step operational semantic (and hence an…
An irreducible canonical approach to second-class constraints reducible of an arbitrary order is given. This method generalizes our previous results from [Europhys. Lett. 50 (2000) 169, J. Phys. A: Math. Theor. 40 (2007) 14537] for first-…
Linear algebra is usually defined over a field such as the reals or complex numbers. It is possible to extend this to skew fields such as the quaternions. However, to the authors' knowledge there is no commonly accepted notation of linear…
The paper develops a method for discrete computational Fourier analysis of functions defined on quasicrystals and other almost periodic sets. A key point is to build the analysis around the emerging theory of quasicrystals and diffraction…
In this paper, we introduce the generalized Fibonacci-Lucas quaternions and we prove that the set of these elements is an order,in the sense of ring theory, of a quaternion algebra. Moreover, we investigate some properties of these…
Quantum hamiltonian reduction is a fundamental tool of conformal field theory and vertex algebra representation theory. It has traditionally been applied to study highest-weight modules. On the other hand, inverse quantum hamiltonian…
We give details of a formerly known relation between ternary quadratic forms and quaternion orders through the even Clifford algebra. Based on this and classifications of ternary quadratic forms we give a completely explicit classification…
In the note, all indecomposable canonical forms of linear systems with dimension less than or equal to $4$ are determined based on Belitskii's algorithm. As an application, an effective way to calculate dimensions of equivalence classes of…
The decomposition of the polynomials on the quaternionic unit sphere in $\Hd$ into irreducible modules under the action of the quaternionic unitary (symplectic) group and quaternionic scalar multiplication has been studied by several…
The representation of the resolvent as an integral operator, the $m$ function, and the associated spectral representation are fundamental topics in the spectral theory of self-adjoint ordinary differential operators. Versions of these are…