Two equations whose variables take values in the Pauli algebra of complex quaternions are shown to be equivalent to the standard Dirac equation and its Hermitian conjugate taken together. They are transformed one into the other by an outer automorphi...
In this paper, we prove that the isospectral flows associated with both the x-part and the n-part of the Lax pair of the semi-discrete lattice potential Korteweg–de Vries equation are symmetries of the equation. Furthermore, we show that these...
The eigenfunction approach used for discrete symmetries is deduced from the concept of quantum numbers. We show that the irreducible representations (irreps) associated with the eigenfunctions are indeed a shorthand notation for the set of eigenvalue...
Discrete symmetries govern the motion and real axis crossings of interference zeros in the meromorphic continuation of a wave field, thereby determining the singular structure of its logarithmic derivatives. We considered two counter-propagating seco...
We consider the discrete
A direct approach is proposed for constructing conservation laws of discrete evolution equations, regardless of the existence of a Lagrangian. The approach utilizes pairs of symmetries and adjoint symmetries, in which adjoint symmetries make up for t...
This article explains how discrete symmetry groups can be directly applied to obtain the particular solutions of nonlinear ordinary differential equations (ODEs). The particular solutions of some nonlinear ordinary differential equations have been ge...
The symmetry group of a (discrete) Painlevé equation provides crucial information on the properties of the equation. In this paper, we argue against the commonly held belief that the symmetry group of a given equation is solely determined by i...
Positivity of a linear control system is interpreted as a symmetry with respect to transformations preserving the nonnegative cone of the state space. We study systems on arbitrary time scales and compare positivity criteria for different time scales...
A new type of discrete soliton, which we call zigzag solitons, is founded in two-component discrete Rabi lattices with long-range hopping. The spontaneous symmetry breaking (SSB) of zigzag solitons is also studied. Through numerical simulation, we fo...
This study presents the detailed experimental results of fine structures and dynamics in a stratified flow past a sphere, which is towed with constant velocity in a transparent basin. We developed experimental procedures based on the complete solutio...
We have investigated a new type of redirection waveguides for concentration solar-cell systems. The solar cell units are to be placed in the peripheral region of the waveguide. The redirection waveguide converts three-dimensionally propagating (3D) p...
The neutral kaon system is a very peculiar system that offers unique possibilities to perform precise tests of the CPT symmetry. The entanglement of neutral kaon pairs that are produced at a
Controllers designed on the basis of an approximate discrete time model can fail when they are applied to the real processes. This is a problem of interest in adaptive symmetry control system theory. In this paper, we introduce the certain polynomial...
We demonstrate that the celebrated Stückelberg formalism is modified in the case of a massive four (3 + 1)-dimensional (4D) Abelian 2-form theory due to the presence of a self-duality discrete symmetry in the theory. The latter symmetry entails...
In the paper, we describe a method for deriving generalized symmetries for a generic discrete quadrilateral equation that allows a Lax pair. Its symmetry can be interpreted as a flow along the tangent direction of its solution evolving with a Lie gro...
Symmetries in the Physical Laws of Nature lead to observable effects. Beyond the regularities and conserved magnitudes, the last few decades in particle physics have seen the identification of symmetries, and their well-defined breaking, as the guidi...
The FitzHugh–Nagumo model has been used empirically to model certain types of neuronal activities. It is also a non-linear dynamical system applicable to chemical kinetics, population dynamics, epidemiology and pattern formation. In the literat...
It is shown that replacing the sinusoidal chip in Golay complementary code pairs by special classes of waveforms that satisfy two conditions, symmetry/anti-symmetry and quazi-orthogonality in the convolution sense, renders the complementary codes imm...
In this paper, we propose the symmetric structure of the reconstructed points discretization model to partition and order the subsets of Ordered Subset Expectation Maximum (OSEM) algorithms for image reconstruction and then simplify the calculation o...
Study of certain angular correlations in the three-photon annihilations of the triplet state of positronium, the electron–positron bound state, may be used as a probe of potential CP and CPT-violating effects in the leptonic sector. We present...
This paper investigates the Discrete Targets Search Problem, (DTSP), which aims to quickly search for discrete objects scattered in a vast symmetry region. Different from continuous function extremal value search, the discrete points search cannot ma...
In certain established approaches to quantum gravity, such as causal set theory and causal dynamical triangulations, discrete spacetime structure is taken to be a primary feature, not a secondary effect of “quantizing” a pre-existing clas...
A natural example of evolution can be described by a time-dependent two degrees-of-freedom Hamiltonian. We choose the case where initially the Hamiltonian derives from a general cubic potential, the linearised system has frequencies 1 and
The current paper studies the global shell layer of the Finite Ring Continuum framework in the symmetry-complete regime realized here by framed finite fields,
To examine the development of pattern formation from the viewpoint of symmetry, we applied a two-dimensional discrete Walsh analysis to a one-dimensional cellular automata model under two types of regular initial conditions. The amount of symmetropy...
Chaotic maps have simple structures but can display complex behavior. In this paper, we apply discrete memristance and a nonlinear term in order to design new memristive maps. A general model for constructing memristive maps has been presented, in wh...
We discuss mathematical and physical arguments contrasting continuous and discrete, limitless discretization as arbitrary granularity. In this regard, we focus on Incomputable (lacking an algorithm that computes in finite time) Real Numbers (IRNs). W...
Symmetry preserving difference schemes approximating equations of Hamiltonian systems are presented in this paper. For holonomic systems in the Hamiltonian framework, the symmetrical operators are obtained by solving the determining equations of Lie...
According to recent research, discrete-time fractional-order models have greater potential to investigate behaviors, and chaotic maps with fractional derivative values exhibit rich dynamics. This manuscript studies the dynamics of a new fractional ch...
Vector arithmetic is a base of (coordinate) geometry, physics and various other disciplines. The usual method is based on Cartesian coordinate-system which fits both to continuous plane/space and digital rectangular-grids. The triangular grid is also...
The conventional Hoek–Brown (H–B) failure criterion does not explicitly account for the combined effects of anisotropy and high confining pressure on rock strength. In bedded rocks, anisotropic mechanical behavior arises from the orientat...
In this article, an invariantized finite difference scheme to find the solution of the heat equation, is developed. The scheme is based on a discrete symmetry transformation. A comparison of the results obtained by the proposed scheme and the Crank N...
The discrete system serves an important role in mimicking collective dynamics found in continuous dynamical systems, which are relevant to many realistic natural and artificial systems. To investigate the dynamical transition of a discrete system, we...
This paper is devoted to comparing the asymptotics of a solution, describing the wave motion of a discrete lattice and its continuous approximations. The transition from a discrete medium to a continuous one changes the symmetry of the system. The in...
The calculation of symmetry in amputee gait is a valuable tool to assess the functional aspects of lower limb prostheses and how it impacts the overall gait mechanics. This paper analyzes the vertical trajectory of the body center of mass (CoM) of a...
Memristives provide a high degree of non-linearity to the model. This property has led to many studies focusing on developing memristive models to provide more non-linearity. This article studies a novel fractional discrete memristive system with inc...
This paper presents a modeling and simulation approach in order to perform a generative analysis of folktales aimed at validating Claude Lévi-Strauss’ theory and method. To this aim, a discrete-event simulation is proposed. The simulation is based on...
In recent years, artificial intelligence techniques have become fundamental parts of various engineering research activities and practical realizations. The advantages of the neural networks, as one of the main artificial intelligence methods, make t...
We present a formal reconstruction of the conventional number systems, including integers, rationals, reals, and complex numbers, based on the principle of relational finitude over a finite field
It is known that in Lorentz-violating effective field theory, there is a classical equivalence between certain coefficients (c and f), in spite of the fact that the operators of the two types of coefficients described appear to have opposite behavior...
The defact standard of a solar cell is that electric power generation is made at the same place as photoharvesting is performed, i.e., the function of photoharvesting/photoreception is spatially degenerated with that of electric power generation (pho...
In this paper, we propose two new two-dimensional chaotic maps with closed curve fixed points. The chaotic behavior of the two maps is analyzed by the 0–1 test, and explored numerically using Lyapunov exponents and bifurcation diagrams. It has...
We organize a table of regular graphs with minimal diameters and minimal mean path lengths, large bisection widths and high degrees of symmetries, obtained by enumerations on supercomputers. These optimal graphs, many of which are newly discovered, m...
Pseudoscalars appear frequently in particle spectra. They can be light if they appear as pseudo-Goldstone bosons from some spontaneously broken global symmetries with the decay constant f. Since any global symmetry is broken at least by quantum gravi...
We have developed a quantum field theory of spinors based on the algebra of canonical anticommutation relations (CAR algebra). The proposed approach is based on the use of Grassmann densities in the momentum space and their derivatives with respect t...
In this paper, the D3 dihedral logistic map of fractional order is introduced. The map presents a dihedral symmetry D3. It is numerically shown that the construction and interpretation of the bifurcation diagram versus the fractional order requires s...
We have developed a quantum field theory of spinors based on the algebra of canonical anticommutation relations (CAR algebra) of Grassmann densities in the momentum space. We have proven the existence of two spinor vacua. Operators C and T transform...
In this short note, we describe the symmetry responsible for absolute, nonperturbative proton stability in the Standard Model. The SM with
A review of the landscape of CPT symmetry tests is presented, centered around the Standard-Model Extension and focusing on tests in the neutral meson system. A discussion of the relevant theories summarizes original ideas. It is followed by a short t...
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