In a generalized topological space Tg = (Ω, Tg), ordinary interior and ordinary closure operators intg, clg : P (Ω) −→ P (Ω), respectively, are defined in terms of ordinary sets. In order to let these operators be as general and unified a manner as possible, and so to prove as many generalized forms of some of the most important theorems in generalized topological spaces as possible, thereby attaining desirable and interesting results, the present au- thors have defined the notions of generalized interior and generalized closure operators g-Intg, g-Clg : P (Ω) −→ P (Ω), respectively, in terms of a new class of generalized sets which they studied earlier and studied their essen- tial properties and commutativity. The outstanding result to which the study has led to is: g-Intg : P (Ω) −→ P (Ω) is finer (or, larger, stronger) than intg : P (Ω) −→ P (Ω) and g-Clg : P (Ω) −→ P (Ω) is coarser (or, smal ler, weaker) than clg : P (Ω) −→ P (Ω). The elements supporting this fact are reported therein as a source of inspiration for more generalized operations.

In a generalized topological space T_g = (Ω, T_g) (T_g-space), the g-topology T_g : P (Ω) −→ P (Ω) can be characterized in the generalized sense by specifying the generalized open, generalized closed sets (g-T_g-open, g-T_g-closed sets), generalized interior, generalized closure operators g-Intg, g-Cl_g : P (Ω) −→ P (Ω) (g-T_g-interior, g-T_g-closure operators), or generalized derived, generalized coderived operators g-Der_g, g-Cod_g : P (Ω) −→ P (Ω) (g-T_g-derived, g-T_g-coderived operators), respectively. For very many T_g-spaces, the δ^th-iterates g-Der_g^(δ), g-Cod_g^(δ) : P (Ω) −→ P (Ω) of g-Der_g, g-Cod_g : P (Ω) −→ P (Ω), respectively, defined by transfinite recursion on the class of successor ordinals are also themselves g-T_g-derived, g-T_g-coderived operators for new g-topologies in the generalized sense on Ω. Thus, the use of novel definitions of g-T_g-derived, g-T_g-coderived operators g-Der_g, g-Cod_g : P (Ω) −→ P (Ω), respectively, based on a very clever construction, together with their δ^th-iterates g-T_g-operators g-Der_g^(δ), g-Cod_g^(δ) : P (Ω) −→ P (Ω), defined by transfinite recursion on the class of successor ordinals, will give rise to novel generalized g-topologies on Ω. The present authors have been actively engaged in the study of g-T_g-operators in T_g-spaces. The study of the essential properties and the commutativity of novel definitions of g-T_g-interior and g-T_g-closure operators g-Int_g, g-Cl_g : P (Ω) −→ P (Ω), respectively, in T_g has formed the first part, and the study of the essential properties and sets of consistent, independent axioms of novel definitions of g-T_g-exterior and g-T_g-frontier operators g-Ext_g, g-Fr_g : P (Ω) −→ P (Ω), respectively, has formed the second part. In this work, which forms the last part on the theory of g-T_g-operators in T_g-spaces, the present authors propose to present novel definitions and the study of the essential properties of g-T_g-derived and g-T_g-coderived operators g-Der_g, g-Cod_g : P (Ω) −→ P (Ω), respectively, and their δ^th-iterates, and the notions of g-T_g-open and g-T_g-closed sets of ranks δ in T_g-spaces.

In a generalized topological space Tg = (Ω, Tg), generalized interior and generalized closure operators g-Intg, g-Clg : P (Ω) −→ P (Ω), respectively, are merely two of a number of generalized primitive operators which may be employed to topologize the underlying set Ω in the generalized sense. Generalized exterior and generalized frontier operators g-Extg, g-Frg : P (Ω) −→ P (Ω), respectively, are other generalized primitive operators by means of which characterizations of generalized operations under g-Intg, g-Clg : P (Ω) −→ P (Ω) can be given without even realizing generalized interior and generalized closure operations first in order to topologize Ω in the generalized sense. In a recent work, the present authors have defined novel types of generalized interior and generalized closure operators g-Intg, g-Clg : P (Ω) −→ P (Ω), respectively, in Tg and studied their essential properties and commutativity. In this work, they propose to present novel definitions of generalized exterior and generalized frontier operators g-Extg, g-Frg : P (Ω) −→ P (Ω), respectively, a set of consistent, independent axioms after studying their essential properties, and established further characterizations of generalized operations under g-Intg, g-Clg : P (Ω) −→ P (Ω) in Tg.

This paper consists of two parts. In part I some new relations for a field theory with time intervals are derived. One concept of field theory evaluated is complementarity, another is field operators both defined within a time interval description. Part II includes specific results and commentary. Discussed are time interval dependent wave propagation surfaces for star source emission waves and derived is a metric propagation surface area requirement. The results allow to consider one same field that like gravitation within General Relativity applies to both non zero and zero mass. The associated field energy is space time dependent for non zero mass, and is related to a space time dependent metric tensor for zero mass wave particles. Defined is internal energy transfer where wave particle numbers increase linearly and mass and momentum diminish, decrease inversely with the distance from the wave emission source. The commentary are applications related to cosmological overall volume and temperature dependence.

In this work, an operator superquadratic function (in operator sense) for positive Hilbert space operators is defined. Several examples with some important properties together with some observations which are related to the operator convexity are pointed out. Equivalent statements of a non-commutative version of Jensen's inequality for operator superquadratic function are established. A generalization of the main result to any positive unital linear map is also provided.

In this paper, the transmutation operator method is used to construct an exact solution to the initial boundary value problem for the equation of multidimensional free transverse vibration of a thin elastic plate with a singular Bessel operator acting on geometric variables. We emphasize that multidimensional Erdélyi–Kober operators of fractional order have the property of a transmutation operator, allowing one to transform more complex multidimensional partial differential equations with singular coefficients acting over all variables into simpler ones. If formulas for solutions are known for a simple equation, then we also obtain representations for solutions to the first complex partial differential equation with singular coefficients. In particular, it is successfully applied to the singular differential equations, especially with Bessel-type operators. Using this operator, the considered problem is reduced to a similar problem without the Bessel operator. Based on the solution to the auxiliary problem, an exact solution to the original problem is constructed and analyzed.

There are many criterion to generalize the concept of numerical radius; one of the most recent interesting generalization is what so called the generalized Euclidean operator radius. Simply, it is the numerical radius of multivariable operators. In this work, several new inequalities, refinements and generalizations are established for this kind of numerical radius.

We give an operator solution to an advanced-retarded differential equation. The application of the operators involved produces a solution in terms of Bessel functions.

The theory of fractional calculus extends the order of classical integer calculus from integer to non-integer. As a new engineering application tool, it has made many important research achievements in many fields, including image processing. This paper mainly studies the application of fractional calculus theory in image enhancement and denoising, including the basic theory of fractional calculus and its amplitude frequency characteristics, the application of fractional differential operator in image enhancement, and the application of fractional integral operator in image denoising. The experimental results show that the fractional calculus theory has more special advantages in image enhancement and denoising. Compared with the existing integer order image enhancement operators, the fractional differential operator can more effectively enhance the "weak edge" and "strong texture" details of the image. The fractional order integral image denoising operator can not only improve the signal-to-noise ratio of the image compared to traditional denoising methods, but also better preserve detailed information such as edges and textures of the image.

Motivated from the theory of Hilbert-Schmidt morphisms between Hilbert C*-modules over commutative C*-algebras by Stern and van Suijlekom [J. Funct. Anal., 2021], we introduce the notion of p-absolutely summing morphisms between Hilbert C*-modules over commutative C*-algebras. We show that an adjointable morphism between Hilbert C*-modules over monotone closed commutative C*-algebra is 2-absolutely summing if and only if it is Hilbert-Schmidt. We formulate version of Pietsch factorization problem for p-absolutely summing morphisms and solve partially.

A major task in Functional Time Series Analysis is measuring the dependence within and between processes, for which lagged covariance and cross-covariance operators have proven to be a practical tool in well-established spaces. This article deduces estimators and asymptotic upper bounds of the estimation errors for lagged covariance and cross-covariance operators of processes in Cartesian products of abstract Hilbert spaces for fixed and increasing lag and Cartesian powers. We allow the processes to be non-centered, and to have values in different spaces when investigating the dependence between processes. Also, we discuss features of estimators for the principle components of our covariance operators.

In this paper, we study a co-variational inequality problem involving Yosida approximation operators in real uniformly smooth Banach space and define an iterative method to obtain its solution. We prove some properties of Yosida approximation operator for our purpose, that is strongly accretivity and Lipschitz continuity. An existence as well as convergence result is proved for co-variational inequality problem involving Yosida approximation operators using the concept of nonexpansive sunny retraction.

The authors intend to establish new oscillation criteria for a class of generalized third order functional difference equation of the form \begin{equation}{\label{eq01}} \Delta_{\ell}\left(a_2(n)\left[\Delta_{\ell}\left(a_1(n)\left[\Delta_{\ell}z(n)\right]^{\beta_1}\right)\right]^{\beta_2}\right)+q(n)f(x(g(n)))=0, ~~n\geq n_0, \end{equation} where $z(n)=x(n)+p(n)x(\tau(n))$. We also present sufficient conditions for the solutions to converges to zero. Suitable examples are presented to validate our main results.

This paper derives measurement and identical principles, then makes the two principles into measurement and identical theorems of quantum mechanics, plus the three theorems derived earlier, we deduce the axiom system of current quantum mechanics, the general quantum theory no axiom presumptions not only solves the crisis to understand in current quantum mechanics, but also obtains new discoveries, e.g., discovers the velocities of quantum collapse and entanglement are instantaneously infinitely large. We deduce the general Schrȍdinger equation of any n particles from two aspects, and the wave function not only has particle properties of the complex square root state vector of the classical probability density of any n particles, but also has the plane wave properties of any n particles. Thus, the current crisis of the dispute about the origin of wave- particle duality of any n microscopic particles is solved. We display the classical locality and quantum non-locality for any n particle system, show entanglement origins, and discover not only any n-particle wave function system has the original, superposition and across entanglements, but also the entanglements are of interactions preserving conservation or correlation, three kinds of entanglements directly give lots of entanglement sources. This paper discovers, one of two pillars of modern physics, quantum mechanics of any n particle system is a generalization ( mechanics ) theory of the complex square root ( of real density function ) of classical statistical mechanics, any n particle system’s quantum mechanics of being just a generalization theory of the complex square root of classical statistical mechanics is both a revolutionary discovery and key new physics, which are influencing people’s philosophical thinking for modern physics, solve all the crisises in current quantum theories, quantum information and so on, and make quantum theory have scientific solid foundations checked, no basic axiom presumption and no all quantum strange incomprehensible properties, because classical statistical mechanics and its complex square root have scientific solid foundations checked. Thus, all current studies on various entanglements and their uses to quantum computer, quantum information and so on must be further updated and classified by the new entanglements. This and our early papers derive quantum physics, solve all crisises of basses of quantum mechanics, e.g., wave-particle duality & the first quantization origins, quantum nonlocality, entanglement origins & classifications, wave collapse and so on.Key words: quantum mechanics, operator, basic presumptions, wave-particle duality, principle of measurement, identical principle, superposition principle of states, entanglement origin, quantum communication, wave collapse, classical statistical mechanics, classical mechanics

The multivariate Gaussian random fields with matrix-based scaling laws are widely used for inference in statistics and many applied areas. In such contexts interests are often in symmetry and in the rates of change of spatial surfaces in any given direction. This article analyzes the almost sure sample function behavior for operator fractional Brownian motion, including multivariate fractional Brownian motion. We obtain the estimations of small ball probability and the strongly locally nondeterministic for operator fractional Brownian motion in any given direction. Applying these estimates we obtain Chung's laws of the iterated logarithm for spatial surfaces of operator fractional Brownian motion. Our results show that the precise rates of change of spatial surfaces are completely determined by the self-similarity exponent.

In this paper we introduce the hypo-q-norms on a Cartesian product of algebras of bounded linear operators on Hilbert spaces. A representation of these norms in terms of inner products, the equivalence with the q-norms on a Cartesian product and some reverse inequalities obtained via the scalar reverses of Cauchy-Buniakowski-Schwarz inequality are also given. Several bounds for the norms δ_p, ϑ_p and the real norms η_r,p and θ_r,p are provided as well.

This work aims to introduce a novel concept: the Riesz-Dunkl fractional derivatives, within the context of Dunkl type operators. A particularly noteworthy revelation is that when a specific parameter $\kappa$ equals zero, the Riesz-Dunkl fractional derivative smoothly reduces to both the well-known Riesz fractional derivative and the fractional second-order derivative. Furthermore, we introduce a new concept: the fractional Sobolev space. This space is defined and characterized using the versatile framework of the Dunkl transform.

In this paper, a generic fractional derivative is defined as a set of the linear operators left-inverse to the Riemann-Liouville fractional integral. Then the theory of the left-invertible operators developed by Przeworska-Rolewicz is applied for derivation of its properties. In particular, we characterize its domain, null-space, and projector operator, establish the interrelations between its different realisations, and present a generalized fractional Taylor formula involving the generic fractional derivative. Then we consider the fractional relaxation equation containing the generic fractional derivative, derive a closed form formula for its unique solution, and study its complete monotonicity.

The evolution of even and odd Schrödinger cat states of the inverted oscillator is obtained in the center-of-mass tomographic probability description of the two-mode oscillator.The notion of entangled probability distribution is reviewed. Evolution equations describing the time-dependence of probability distributions identified with quantum system states are discussed.The connection with the Schrödinger equation and the von Neumann equation is clarified.

The primary objective of this paper is to establish connections between two well-known but previously independently developed theories: the theory of violator spaces and the theory of greedoids. Violator spaces were introduced by Matoušek et al. in 2008 as a generalization of linear programming problems. Greedoids were introduced by Korte and Lovász in 1981 in an effort to characterize combinatorial structures where greedy algorithms yield optimal solutions. In this work, we explore the relationships between violator spaces and greedoids, demonstrating that greedoids can be defined using a variant of a violator operator. These interrelations provide a new characterization of antimatroids.

This paper puts forward an alteration for Tensor Calculus utliized in a coordinate system which is under a dynamic distortion drawing inspiration from similar fields such as the Calculus of Moving Surfaces (CMS). The paper establishes transformation laws for Tensors within these regions and establishes Operators such as the Tensorial Field Derivative which enforce a Tensorial Transformation on Tensors defined within a Dynamically Moving coordinate system. This variation of Tensor Calculus can be utilized to observe how disciplines such as QFT and Continuum Mechanics would change to accomodate for a distorting coordinate system and can be utliized to develop new theoretical models which account for this temporal distortion particularly within Biological Settings.

Spatio-Temporal Dynamic Mode Decomposition (STDMD) is an extension of Dynamic Mode Decomposition (DMD) designed to handle spatio-temporal datasets. It extends the framework so that it can analyze data that has both spatial and temporal variations, allowing for the extraction of spatial structures and their temporal evolution. The STDMD method extracts temporal and spatial development information simultaneously, including wavenumber, frequencies and growth rates, which is essential in complex dynamic systems. We provide a comprehensive mathematical framework for sequential and parallel STDMD approaches. We also introduce delay coordinates generalization to the presented algorithms to extend the scope of their application. The extension, labeled delay embedding STDMD allows the use of delayed data, which can be both time-delayed and space-delayed. An explicit expression of the presented algorithms in matrix form is also provided, which facilitates theoretical analysis and provides a solid foundation for further research and development. The novel approach is demonstrated using some illustrative model dynamics.

he Grassmann variables are used to formally transform a system with constraints into an unconstraint system. As a result, the Schr\"{o}dinger equation arises instead of the Wheeler-DeWitt one. The Schrodinger equation describes a system's evolution, but a definition of the scalar product is needed to calculate the mean values of the operators. We suggest an explicit formula for the scalar product related to the Klein-Gordon scalar product. The calculation of the mean values is compared with an etalon method, in which a redundant degree of freedom is excluded. Nevertheless, we could note that a complete correspondence with the etalon picture is not found. Apparently, the picture with the Grassmann variables requires a further understanding of the underlying Hilbert space.

n our previous paper, we showed that the so-called quantum entanglement also exists in classical mechanics. The inability to measure this classical entanglement was rationalized with the definition of a classical observer which collapses all entanglement into distinguishable states. It was shown that evidence for this primary coherence is Newton’s third law. However, in reformulating a "classical entanglement theory" we assumed the existence of Newton’s second law as an operator form where a force operator was introduced through a Hilbert space of force states. In this paper, we derive all related physical quantities and laws from basic quantum principles. We not only define a force operator but also derive the classical mechanic's laws and prove the necessity of entanglement to obtain Newton’s third law.

We compute explicitly trace of one-dimensional diffusion process which can be regarded as a Dirichlet form on graphs and we study its conservativeness property. Finally, we give an example of a discretization of one dimensional diffusion of Bessel's process with order $\nu$.

It is shown that if a non-constant meromorphic function f(z) is of finite order and shares certain values with its shifts/difference operators then f(z) coincides with that particular shift/difference operator.

Increasing distributed generation and intermittency, along with the increasing frequency of extreme weather events, impose a serious challenge for the electric power supply security. Understanding the costs of interruption is vital in terms of enhancing the power system infrastructure and planning the distribution grid. On the other hand, customer rights and demand response techniques are further reasons to study the worth of power reliability. In this paper, the authors make use of directional distance function and shadow pricing method for a case study from Finland. The aim is to calculate the cost of one minute of power interruption from the distribution network operator perspective. The sample consists of 78 distribution network operators from Finland with cost and network information between 2013 and 2015.

The article presents extremely current issues concerning imaging and measurements carried out using coordinate optical systems in which the result of scanning spatial objects is a point cloud. What is important, the entire accuracy assessment of the conducted fast, effective coordinate measurement nowadays takes place in the computational area, beyond direct sensory percep-tion, and depends increasingly on its power and the computational algorithms used. Further-more, we are getting closer and closer to recognising virtual standards in coordinate metrology as a direction that allows for an increase in measurement accuracy. Especially in recent years, the importance of the problem has been confirmed by the activities of the most significant scientific and research centres. They focus on improving the accuracy of the data obtained in the form of point clouds, using more precise scanning methods for this purpose, and developing filtering algorithms to remove noise, including methods using artificial intelligence. Based on many years of research, the authors identified a problem regarding the difficulty in developing data obtained from optical systems, such as laser triangulation head systems, systems operating on the principle of structural light, photogrammetric systems, as well as computer tomographs, and the impact of these systems on the assessment of measurement accuracy. Therefore, the optical measurement process was analysed in terms of the quality of the acquired point clouds. The authors presented the division of factors, which, in coordinate optical meas-urements, generate errors in data acquisition and development. The authors also indicated which of these factors generate the most significant errors and, above all, emphasised the impact of the software used, the measurement operator, and the methods of cloud filtration applied by the operator. Therefore, the accuracy assessment of the optical measurement has been noted as a critical problem, and so far, it has not been solved effectively. In the article, as a solution to this problem, the authors proposed the OPTI-U method of estimating uncertainty for optical meas-urements. The method, what is very important, was developed and verified under the conditions of an accredited calibration laboratory. The summary also gives directions for further work on developing and disseminating the developed method, particularly introducing virtual standards.

Discussing quantum theory foundations, von Neumann noted that the measurement process should not be regarded in terms of a temporal evolution. A reason for his claim is insurmountability of the gap between reversible and irreversible processes. The time operator formalism that goes beyond such a gap is adequate framework for elaboration of the measurement problem. It considers signals to be stochastic processes, whether they correspond to variables or distribution densities. Signal processing like that utilizes statistical properties to perform its tasks, which is the definition of statistical signal processing. A hierarchy of the measurement process is indicated by crossing between states and devices, which implies an evolution in the temporal domain. The concept has generalized to an open system by the use of duality in frame theory.

In this article, rst we are going to review the concept of ordinary frames , in more general case in measure spaces, namely, gc-frames. We try to develop the use of measure space in describing frames. Then by means of the gc-frames, we shall introduce gn-operators, which we shall show that each trace class operator has a vector-valued integral representation and vice-versa.

In the past two decades, metaheuristic optimization algorithms (MOAs) have been increasingly popular, particularly in logistic, science, and engineering problems. The fundamental characteristics of such algorithms are that they are dependent on a parameter or a strategy. Some online and offline strategies are employed in order to obtain optimal configurations of the algorithms. Adaptive operator selection is one of them, and it determines whether or not to update a strategy from the strategy pool during the search process. In the filed of machine learning, Reinforcement Learning (RL) refers to goal-oriented algorithms, which learn from the environment how to achieve a goal. On MOAs, reinforcement learning has been utilised to control the operator selection process. Existing research, however, fails to show that learned information may be transferred from one problem-solving procedure to another. The primary goal of the proposed research is to determine the impact of transfer learning on RL and MOAs. As a test problem, a set union knapsack problem with 30 separate benchmark problem instances is used. The results are statistically compared in depth. The learning process, according to the findings, improved the convergence speed while significantly reducing the CPU time.

This document introduces a new cryptosystem mixing two improvement standards generally used for text encryption, in order to give birth a new color image encryption algorithm capable of dealing with known attacks. Firstly, two substitution matrixes attached to a strong replacement function will be generated for advanced Vigenere technique application. At the end of this first round, the output vector is subdivided into size blocks according to the used chaotic map, for acting a single enhanced Hill circuit insured by a large inversible matrix. A detailed description of such a large involutive matrix constructed using Kronecker products will be given. accompanied by a dynamic translation vector to eliminate any linearity. A solid chaining is established between the encrypted block and the next clear block to avoid any differential attack. Simulations carried out on a large volume of images of different sizes and formats ensure that our approach is not exposed to any known attacks.

The necessary and sufficient conditions of existence of the nonlinear operator equations' branches of solutions in the neighbourhood of branching points are derived. The approach is based on reduction of the nonlinear operator equations to finite-dimensional problems. Methods of nonlinear functional analysis, integral equations, spectral theory based on index of Kronecker-Poincare, Morse-Conley index, power geometry and other methods are employed. Proposed methodology enables justification of the theorems on existence of bifurcation points and bifurcation sets in the nonstandard models. Formulated theorems are constructive. For a certain smoothness of the nonlinear operator, the asymptotic behaviour of the solutions is analysed in the neighbourhood of the branch points and uniformly converging iterative schemes with a choice of the uniformization parameter enables the comprehensive analysis of the problems details. General theorems are illustrated on the nonlinear integral equations.

The concept of neutrosophic number is a significant mathematical tool to deal with real scientific problems because it can tackle indeterminate and incomplete information which exists generally in real problems. In this article, we use neutrosophic numbers (a + bI), where a and bI denote determinate component and indeterminate component respectively. We explore the situations in which the input information is needed to express in terms of neutrosophic numbers. We define score functions and accuracy functions for ranking neutrosophic numbers. We then define a cosine function to determine unknown criteria weights. We define neutrosophic number harmonic mean operators and proved their basic properties. Then, we develop two novel MCGDM strategies using the proposed aggregation operators. We solve a numerical example to demonstrate the feasibility and effectiveness of the proposed two strategies. Sensitivity analysis with variation of “I” on neutrosophic numbers is performed to demonstrate how the preference ranking order of alternatives is sensitive to the change of “I”. The efficiency of the developed strategies is ascertained by comparing the obtained results from the proposed strategies with the existing strategies in the literature.

This paper discusses two major applications of SU(3) theory, the first being the question of quantum brachistochrones and problems in time optimal control theory, the second being the use of spherical tensor decompositions of the special functions which are associated to SU(3) via the isotropic oscillator. We discuss the derivation of the quantum brachistochrone problem more generally from the perspective of von Neumann equations and matrix mechanics, arriving at an equivalent formulation to the Lagrangian method. Discussion is given to the application of such advanced methods in quantum computation, and some future directions that may be amenable to a similar sort of an

We consider a new model of a branching random walk on a multidimensional lattice with continuous time and one source of particle reproduction and death, as well as an infinite number of sources in which, in addition to the walk, only absorption of particles can occur. The asymptotic behavior of the integer moments of both the total number of particles and the number of particles at a lattice point is studied depending on the relationship between the model parameters. In the case of the existence of an isolated positive eigenvalue of the evolution operator of the average number of particles, a limit theorem is obtained on the exponential growth of both the total number of particles and the number of particles at a lattice point.

We present set-theoretical solutions of the Yang-Baxter equation in BCK–algebras. Some solutions in BCK−algebras are not solutions in other structures (such as MV −algebras). Related to our investigations we also consider some new structures: Boolean coalgebras and a unified braid condition – quantum Yang-Baxter equation. Finally, we will see how poetry has accompanied the development / history of the Yang–Baxter equation.

This paper presents Chebyshev Type inequalities for the Riemann-Liouville variable-order fractional integral operator using two synchronous functions on the set of real numbers. It is the first result of its kind in the current literature using variable-order Riemann-Liouville fractional integral operator. Some special cases for the result obtained in the paper are discussed.

In this paper, we revisit the two theoretical approaches for the formulation of the tachyonic Dirac equation. The first approach works within the theory of restricted relativity, starting from a Lorentz invariant Lagrangian consistent with a spacelike four-momentum. The second approach uses the theory of relativity extended to superluminal motions and works directly on the ordinary Dirac equation through superluminal Lorentz transformations. The equations resulting from the two approaches show mostly different, if not opposite, properties. In particular, the first equation violates the invariance under the action of the parity and charge conjugation operations. Although it is a good mathematical tool to describe the dynamics of a space-like particle, it also shows that the mean particle velocity is subluminal. In contrast, the second equation is invariant under the action of parity and charge conjugation symmetries, but the particle it describes is consistent with the classical dynamics of a tachyon. This study shows that it is not possible with the currently available theories to formulate a covariant equation that coherently describes the neutrino in the framework of the physics of tachyons, and depending on the experiment, one equation rather than the other should be used.

In this article, we establish the existence of and then compare smallest eigenvalues for nabla fractional boundary value problems involving a fractional difference boundary condition, using the theory of u0-positive operators with respect to a cone in a Banach space.

The identification of linear dynamic systems with static nonlinearities in the delta domain has been presented in this paper applying a firefly based hybrid meta-heuristic algorithm integrating Firefly algorithm (FA) and Gray wolf optimizer (GWO). FA diversifies the search space globally while GWO intensifies the solutions through its local search abilities. A test system with continuous polynomial nonlinearities has been considered for hammerstein and wiener system identification in continuous, discrete and delta domain. Delta operator modelling unifies system identification of continuous-time systems with discrete domain at higher sampling frequency. Pseudo random binary sequence, contaminated with white noise, has been taken up as the input signal to estimate the unknown model parameters as well as static nonlinear coefficients. The hybrid algorithm not only outperforms the parent heuristics of which they are constituted but also proves better as compared to some standard and latest heuristic approaches reported in the literature.

Purpose: Decomposition analysis of forecasting errors relating to time series generated by a 3PL logistics operator for ten distribution channels operated by the logistics operator. Design / methodology / approach: The studies were focused on the analysis of 10 distribution channels operated by the 3PL logistics operator who used a forecasting tool based on a modified ARIMA algorithm to prepare forecasts. In this paper, R environment was used. The studies focused on the visual analysis of forecasting error series, on the analysis of the basic parameters of the error time series distributions, on the analysis of STL decomposition and statistical tests relating to trend and seasonality. Findings: The forecasting error analysis indicates that there are different patterns and characteristics of errors for individual channels. The statistical test results for various channels display significant differences between forecast groups in some cases. This suggests that the forecasting tool can be more accurate for some than for other channels. Research limitations: Logistic operations are usually based on numerous variables which may influence forecast quality. Moreover, the absence of any information on the forecasting models and input data used may prevent complete understanding of error sources. Value of the paper: The studies described in this paper emphasized valuable conclusions which can be drawn from the analysis of time series forecasting errors in the context of logistic operations. The findings indicated the need for an adapted approach to forecasting for each and every channel, the importance of improving the forecasting tool and the potential to optimize the forecast accuracy by focusing on the trend and seasonality. For this reason, the analysis is an important input into the theory and practice relating to demand forecasting by logistics operators in distribution networks. The studies contribute to the works related to demand forecasting by logistics operators.

Quantum nonlocality represents correlation properties between subsystems of a composite quantum system, usually including the four types: Bell nonlocality, steerability, entanglement, and quantum correlation (quantum discord). Given a basis $e_{AB}=\{|e_{ij}\>\}_{i\in[d_A],j\in[d_B]}$ for the Hilbert space $\H_A\otimes \H_B$ of a bipartite system $AB$, a density operator $\rho^{AB}$ (quantum state) of $AB$ can be represented as a $d_Ad_B\times d_Ad_B$ matrix $\hat{\rho}_{e_{AB}}=[\]$, called the density matrix of a density operator $\rho^{AB}$. A natural question is what is the relationship between the quantum nonlocality of a density operator $\rho^{AB}$ and its corresponding density matrix $\hat{\rho}_{e_{AB}}$? In this work, we discuss the relationships between quantum locality and basis, and prove that one type of quantum locality of density operators and that of their density matrices under a basis are the same if and only if the chosen basis is the tensor product of the bases of subsystems. Consequently, different bases define different quantum nonlocality density operators.

This work presents a novel approach for the study of the movement of droplets on inclined surfaces under the influence of gravity and chemical heterogeneities. The developed numerical methodology uses data-driven modeling to extend the applicability limits of an analytically derived reduced-order model for the contact line velocity. More specifically, while the reduced-order model is able to capture the effects of the chemical heterogeneities to a satisfactory degree, it does not account for gravity. To alleviate this shortcoming, datasets generated from direct numerical simulations are used to train a data-driven model for the contact line velocity, which is based on the Fourier neural operator and corrects the reduced-order model predictions to match the reference solutions. This hybrid surrogate model, which comprises of both analytical and data-driven components, is then integrated in time to simulate the droplet movement, offering a speedup of five orders of magnitude compared to direct numerical simulations. The performance of this hybrid model is quantified and assessed in different wetting scenarios, by considering various inclination angles and values for the Bond number, demonstrating the accuracy of the predictions as long as the adopted parameters lie within the ranges considered in the training dataset.

This work is devoted to the construction and study of commutative gates for a two-qubit quantum system. Using four-dimensional algebra developed by the Kazakh mathematician Abenov M.M. all groups of commutative gates have been constructed, and among all states of a two-qubit quantum system, unitary states with which a specific gate is connected have been identified. An explicit type of gate is described that transfers a quantum system from one unitary state to another unitary state. The proposed approach opens up new possibilities for the design of quantum algorithms not only for two-qubit quantum systems, but also for $n$-qubit quantum systems.

In this paper, we study a differential operator of parabolic type with a variable and unbounded coefficient, defined on an infinite strip. Sufficient conditions for the existence and compactness of the resolvent are established, and an estimate for the maximum regularity of solutions of the equation Lu=f∈L_2(Ω) is obtained. Two-sided estimates for the distribution function of approximation numbers are obtained. As is known, estimates of approximation numbers show the rate of best approximation of the resolvent of an operator by finite-dimensional operators. The paper proves the assertion about the existence of positive eigenvalues among the eigenvalues of the given operator and finds two-sided estimates for them.

This work deals with finding out whether the heart rate values of operators of forwarding machines during the work shift are influenced by the individual activities that the operator has to perform during timber skidding, or by the operators themselves. Furthermore, the work deals with determining the difficulty of individual activities in terms of physical load. For this purpose, the work shift of operators carrying out timber skidding was divided into individual activities: Driving, Maintenance, Forwarding, Break. During these work activities, the heart rate of each operator was taken for subsequent evaluation. The results show that the highest pulse rates of the operators were achieved during the Maintenance of the entrusted machine, while the highest pulse fluctuations in the operators were recorded during Forwarding. As part of this activity, the highest heart rate of the entire measurement process was recorded (132.0000 bpm), but also the lowest (42.0000 bpm). Furthermore, it was proven that both the operator and the activity he performs affect the pulse rate. The activities themselves did not differ from each other in only one of the six cases of comparison. Specifically, it was Driving and Forwarding.

This paper is related to the fractional view analysis of Helmholtz equations, using innovative analytical techniques. The fractional analysis of the proposed problems has been done in terms of Caputo-operator sense. In the current methodology, first, we applied the r-Laplace transform to the targeted problem. The iterative method is then implemented to obtain the series form solution. After using the inverse transform of the r-Laplace, the desire analytical solution is achieved. The suggested procedure is verified through specific examples of the fractional Helmholtz equations. The present method is found to be an effective technique having a closed resemblance with the actual solutions. The proposed technique has less computational cost and a higher rate of convergence. The suggested methods are therefore very useful to solve other systems of fractional order problems.

In this paper, we introduce two subclasses of analytic and Spirallike functions and investigate convolution properties, the necessary and sufficient condition, coefficient estimates and inclusion properties for these classes .

In this paper, we investigate a new subclass of univalent functions defined by a generalized differential operator, and obtain some interesting properties of functions belonging to the class R^m λµ ( α, β, γ, υ ).

In the present research, we will develop some integral inequalities of Hermite Hadamard type for differentiable η-convex function. Moreover, our results include several new and known results as special cases.

This work intends to present a study on relations between a Lie algebra called dispersion operators algebra, linear canonical transformation and a phase space representation of quantum mechanics that we have introduced and studied in previous works. The paper begins with a brief recall of our previous works followed by the description of the dispersion operators algebra which is performed in the framework of the phase space representation. Then, linear canonical transformations are introduced and linked with this algebra. A multidimensional generalization of the obtained results is given.

In this paper, we define the cohomology of a modified $\lambda$-differential left-symmetric algebra with coefficients in a suitable representation. We also introduce the notion of modified $\lambda$-differential left-symmetric 2-algebra. We classify linear deformations and abelian extensions of modified $\lambda$-differential left-symmetric algebras using the second cohomology group and classify skeletal modified $\lambda$-differential left-symmetric 2-algebra using the third cohomology group as our propose cohomology applications. Moreover, we prove that strict modified $\lambda$-differential left-symmetric 2-algebras are equivalent to crossed modules of modified $\lambda$-differential left-symmetric algebras.

The purpose of this paper is to summarize and share the field experiment results of KEPCO's project consortium to create a TSO-DSO-DERA interaction scheme. The field experiment was conducted based on the prequalification algorithm proposed in the previous research from the same consortium and was designed to verify the validity of the algorithm under realistic grid conditions. In addition, during the course of the field experiment, it was found that points that were missed or not given much importance in the existing prequalification algorithm could affect the completeness of the overall system, and then practical improvements were made to improve it. The demonstration results confirm that the proposed algorithm is effective in real-world grid environments and can help DSOs ensure the reliability of the distribution system while supporting DERA's participation in the wholesale market using the proposed prequalification scheme.

Real-world optimization problems are often gov- erned by one or more constraints. Over the last few decades, extensive research has been performed in Constrained Opti- mization Problems (COPs) fueled by advances in computational power. In particular, Evolutionary Algorithms (EAs) are a preferred tool for practitioners for solving these COPs within practicable time limits. We propose a novel hybrid Evolutionary Algorithm based on the Differential Evolution algorithm and Adaptive Parameter Gaining Sharing Knowledge-based algo- rithm to solve global real-world constrained parameter space. The proposed CHAGSKODE algorithm leverages the power of multiple adaptation strategies concerning the control parameters, search mechanisms, as well as uses knowledge sharing between junior and senior phases. We test our method on the benchmark functions taken from the CEC2020 special session & competition on real-world constrained optimization. Experimental results indicate that CHAGSKODE is able to achieve state-of-the- art performance on real-world constrained global optimization when compared against other well-known real-world constrained optimizers.

Real-world optimization problems are often governed by one or more constraints. Over the last few decades, extensive research has been performed in Constrained Optimization Problems (COPs) fueled by advances in computational intelligence. In particular, Evolutionary Algorithms (EAs) are a preferred tool for practitioners for solving these COPs within practicable time limits. We propose an ensemble of multi- method hybrid EA framework with four mutation operators, two crossover operators, multi-search [Differential Evolution (DE) & Gaining Sharing Knowledge (GSK)] optimization algorithm, and ensemble of constraint handling techniques to solve global real- world constrained optimization problem. The proposed frame- work FEPEA has an ascendancy of multiple adaptation strategies concerning the control parameters, search mechanisms, two sub-populations as well as uses knowledge sharing mechanism between junior and senior phases. The algorithm also combines the power of four popular constraint handling techniques (CHT) and uses a voting mechanism to select any particular CHT. On top of that, this algorithm also uses both linear and non- linear population size reduction in every step of the evolutionary process. We test our method on 57 real-world problems provided as part of the CEC 2020 special session & competition on real- world constrained optimization benchmark suite. Experimental results indicate that FEPEA is able to achieve state-of-the- art performance on real-world constrained global optimization when compared against other well-known real-world constrained optimizers.

This paper presents an optimized feature-centered reflection symmetry axis detection and localization framework for object perception. The proposed framework is formed to obtain an improved reflection symmetry axis based on the salient symmetry feature. It starts with a refined Multi-scale Saliency Symmetry Model (MSSM), which is realized by applying isotropic symmetry operator on salient points in scale-space rather than all pixels. In each scale, salient points are initially extracted as local extremal from an image, and they are further refined by a multi-scale implementation for generating salient symmetry feature maps. A Symmetric Transformation Matrix is then computed using the optimal feature matching pairs, which can be explicitly used as an abstract representation of the constraint regions of symmetry objects in an image to optimize the performance of the potential symmetry axis detection. The framework has been investigated experimentally both on the classical dataset from a symmetry detection challenge and the latest dataset. It has shown that the framework can get a better or comparative result and also can be further adapted into terminated human--computer equipment for reflection symmetry object perception and tracking.

This paper aims to investigate the criteria of behaviour of certain type of third order neutral generalized difference equations with distributed delay. With the technique of generalized Riccati transformation and Philos-type method, some oscillation criteria are obtained to ensure convergence and oscillatory solution of suitable example is listed to illustrate the main result.

In the present paper, we introduced and study a new class of harmonic univalent functions on unit disc U. also we obtain coefficient conditions, extreme points, convolution condition for the above class of harmonic univalent functions.

We consider rotational hypersurface in the four dimensional Euclidean space. We calculate the mean curvature and the Gaussian curvature, and some relations of the rotational hypersurface. Moreover, we define the third Laplace-Beltrami operator and apply it to the rotational hypersurface.

Uchino first initiated the study of generalized Reynolds operators on associative algebras. Recently, related research has become a hot topic. In this paper, we first introduce the notion of generalized Reynolds operators on Hom-Lie triple systems associated to a representation and a 3-cocycle. Then, we develop cohomology of generalized Reynolds operators on Hom-Lie triple systems with coefficients in a suitable representation. As applications, we use the first cohomology group to classify linear deformations and we study the obstruction class of an extendable order $n$ deformation. Finally, we introduce and investigate Hom-NS-Lie triple system as the underlying structure of generalized Reynolds operators on Hom-Lie triple systems.

We consider a Cauchy problem for differential equations in a Hilbert space $X$. The problem is stated in a time interval $I$, which can be finite or infinite. Weuse a fixed point argument for history-dependent operators to prove the unique solvability of the problem. Then, we state and prove convergence criteria for both a general fixed point problem and thecorresponding Cauchy problem. These criteria provide necessary and sufficient conditions on a sequence $\{u_n\}$ which guarantee its convergence to the solution of the corresponding problem, in the space of both continuous and continuously differentiable functions. We then specify our results in the study of a particular differential equation governed by two nonlinear operators. Finally, we provide an application in viscoelasticity and give a mechanical interpretation of the corresponding convergence result.

A data-driven analysis method known as dynamic mode decomposition (DMD) approximates the linear Koopman operator on projected space. In the spirit of Johnson-Lindenstrauss Lemma, we will use random projection to estimate the DMD modes in reduced dimensional space. In practical applications, snapshots are in high dimensional observable space and the DMD operator matrix is massive. Hence, computing DMD with the full spectrum is infeasible, so our main computational goal is estimating the eigenvalue and eigenvectors of the DMD operator in a projected domain. We will generalize the current algorithm to estimate a projected DMD operator. We focus on a powerful and simple random projection algorithm that will reduce the computational and storage cost. While clearly, a random projection simplifies the algorithmic complexity of a detailed optimal projection, as we will show, generally the results can be excellent nonetheless, and quality understood through a well-developed theory of random projections. We will demonstrate that modes can be calculated for a low cost by the projected data with sufficient dimension.

Splines and quasi-interpolation operators are important both in approximation theory and applications. In this paper, we construct a family of quasi-interpolation operators for the bivariate quintic spline spaces S₅³ (∆_mn⁽²⁾). Moreover, the properties of the proposed quasi-interpolation operators are studied, as well as its applications for solving two-dimensional Burgers’ equation and image reconstruction. Some numerical examples show that these methods, which are easy to implement, provide accurate results.

Graph query languages such as Cypher are widely adopted to match and retrieve data in a graph representation, due to their ability of retrieving and transforming information. Despite the most natural way to match and transform information is through rewriting rules, those are scarcely or partially adopted in graph query languages. Their inability of doing so has a major impact on the subsequent way the information is structured, as it might then appear more natural to provide major constraint over the data representation so to consequently constraint the way the information should be represented. On the other hand, recent works are starting to move towards an opposite direction, as the provision of a truly general semistructured model (GSM) allows to both represent all the available data formats (Network-Based, Relational, and Semistructured) as well as support an holistic query language expressing all major queries in such languages. In this paper, we show that the usage of GSM enables the definition of a general rewriting mechanism which can be expressed in current graph query languages only at the cost of adhering the query to the specificity of the underlying data representation. We formalise the proposed query language in terms graph rewriting mechanisms described as a set of production rules $L\to R$ while providing restriction to the characterization of L, while extending it to support structural graph nesting operations, useful to aggregate similar information around an entry-point of interest. We discuss how GSM, by fully supporting index-based data representation, allows for a better physical model implementation leveraging the benefits of columnar database storages. Preliminary benchmarks shows the scalability of this proposed implementation in comparison with state-of-the-art implementations.

Semenov-Tian-Shansky has introduced the modified classical Yang-Baxter equation, which is called the modified $r$-matrix. Relevant studies have been extensive in recent times. This paper is devoted to study cohomology theory of modified Rota-Baxter pre-Lie algebras and its applications. First we introduce the concept and representations of modified Rota-Baxter pre-Lie algebras. We then develop the cohomology of modified Rota-Baxter pre-Lie algebras with coefficients in a suitable representation. As applications, we consider the infinitesimal deformations, abelian extensions and skeletal modified Rota-Baxter pre-Lie 2-algebra in terms of lower degree cohomology groups.

This study focuses on the formulation and analysis of a numerical method to compute singularly perturbed functional differential equations (SP-FDEs) involving large mixed shifts. SP-FDEs are a class of differential equations with both shifts and small perturbation parameter. Such equations arise in various scientific fields to model phenomena with memory effects and perturbed dynamics. In this particular study, the considered SP-FDEs involve large negative shift (delay) and large positive shift (advance). Dealing with large mixed shifts in SP-FDEs gives rise to challenges in terms of stability analysis, numerical methods, and convergence of a solution. In this paper, the influence of the large mixed shifts is treated by choosing a uniform mesh discretized in such a way that the term with the shifts lie on the nodal points. Then, using the Numerov’s finite difference method, the continuous problem is transformed into a finite difference scheme and the influence of the perturbation parameter is handled by introducing a fitting factor in the difference scheme. Stability estimate and convergence analysis of the developed scheme are investigated and proved. Numerical experiments are carried out to demonstrate the validity and applicability of the developed scheme. It is shown that the numerical scheme obtained in this work is parameter-robust of second order convergence rate.

Modeling and assessing the sustainability of machining systems has been considered to be a crucial approach to improving the environmental performance of the machining processes. As the most common machining system, the computer numerical control (CNC) milling system is a typical man-machine cooperative system where the activities of the machine tool and operator generate material and energy consumption. However, the energy consumption of the operator in the CNC milling system has often been ignored in most existing research. Therefore, existing methods fail to provide a comprehensive understanding of the sustainability of the CNC milling system. To fill this gap, an exergy loss assessment method is proposed to investigate the sustainability of the CNC milling system, where the energy consumption of the operator, the energy consumption of the machine tool, and material consumption are taken into consideration. The key performance indexes of the energy consumption of the operator, the energy consumption of the machine tool, the exergy loss, and the specific exergy loss (SEL) are analyzed and modeled. To demonstrate the feasibility of the proposed method, a case study was carried out on a three-axis machining center (XH714D), in which SEL was found to be 88.04J/mm3. The proposed method is effective to assess the sustainability of the CNC milling system, and the established exergy loss models build a good basis for exergy efficiency optimization.

Drugs-drugs interactions(DDI) are entities composed of different chemical substructures (functional groups). In existing methods that predict drug–drug interactions based on the usage of substructures, each node is considered the center of a substructure, and adjacent nodes eventually become centers of similar substructures, resulting in redundancy. Furthermore, the significant differ- ences in structure and properties among compounds can lead to unrelated pairings, making it difficult to integrate information. This heterogeneity negatively affects the prediction results. To address these issues, we propose a drug–drug interaction prediction method based on substructure signature learning (DDI-SSL). This method extracts useful information from local subgraphs surrounding drugs and effectively utilizes substructures to assist in predicting drug side effects. Additionally, a deep clustering algorithm is used to aggregate similar substructures, allowing any individual subgraph to be reconstructed using this set of global signatures. Furthermore, we developed a layer-independent collaborative attention mechanism to model the mutual influence between drugs, generating signal strength scores for each class of drugs to mitigate noise caused by heterogeneity. Finally, we evaluated DDI-SSL on a comprehensive dataset and demonstrated improved performance in DDI prediction compared to state-of-the-art methods.

Vectorial optical fields have sparked considerable interest with potential applications such as optical nano-fabrication, optical micromachining, quantum information processing, optical imaging, and so on. Traditional compact vectorial optical generators with amplitude modulation perform poorly in terms of diffraction effect reduction. In order to address this issue, the refractive 4f system in amplitude modulation is longitudinally aligned using an optimization approach presented in this research. The phase images used for longitudinal alignment are loaded into the liquid crystal spatial light modulator (SLM), and the distance between the lens and the mirror in the reflective 4f system is adjusted for longitudinal alignment by compensating for the neglected phase in the integrated module of the compact vectorial optical field generator. The spot images collected by the CCD are processed using the improved eight-direction Sobel operator, and the longitudinal alignment in the reflective 4f system is determined by the sharpness of the image. The sharpness of the lines' edges and the overall image are both enhanced after optimization compared to before optimization. The results show that the proposed method can significantly reduce the longitudinal alignment error of the reflective 4f system in the amplitude modulation of the compact vectorial optical field generator, lessen the diffraction effect, and improve the performance of the system.

We introduce the notion of p-adic magic contraction on p-adic Hilbert space. We derive p-adic Halmos dilation, p-adic Egervary N-dilation, p-adic von Neumann inequality and p-adic Sz.-Nagy dilation for p-adic magic contraction.

The high dimensions and governing non linear dynamics in wind farm systems make the design of numerical optimal controllers computationally expensive. A possible pathway to circumvent this challenge lies in finding reduced order models which can accurately embed the existing non linearities. The work here presented applies the ideas motivated by non linear dynamical systems theory - the Koopman Operator - to an innovative algorithm in the context of wind farm systems - Input Output Dynamic Mode Decomposition - to improve on the ability to model the aerodynamic interaction between wind turbines in a wind farm and uncover insights into the existing dynamics. It is shown that a reduced order linear state space model can reproduce the downstream turbine generator power dynamics and reconstruct the upstream turbine wake. It is further shown that the fit can be improved by judiciously choosing the Koopman observables used in the IODMD algorithm without jeopardizing the models ability to rebuild the turbine wake. The extensions to the IODMD algorithm provide an important step towards the design of linear reduced order models which can accurately reproduce the dynamics in a wind farm.

Fractional differential mathematical model unfolding the dynamics of the COVID-19 pandemic in India is presented and explored in this paper. The purpose of this study is to estimate the future outbreak of disease and potential control strategies using mathematical models in India as a whole country as well as in some of the states of the country. This model is calibrated based on reported cases of infections over the month of April 2020 in India. We have used iterative fractional complex transform method to find approximate solutions of the model having modified Riemann Liouville fractional differential operator. We have also carried out a comparative analysis between actual and estimated cumulative cases graphically, moreover, most sensitive parameters for basic reproduction number$(R_0)$ are computed and their effect on transmission dynamics of COVID-19 pandemic is investigated in detail.

In this paper, we study the third order semilocal convergence of the Newton-like method for finding the approximate solution of nonlinear operator equations in the setting of Banach spaces. First, we discuss the convergence analysis under ω-continuity condition, which is weaker than the Lipschitz and Hölder continuity conditions. Second, we apply our approach to solve Fredholm integral equations, where the first derivative of involved operator not necessarily satisfy the Hölder and Lipschitz continuity conditions. Finally, we also prove that the R-order of the method is 2p + 1 for any p $\in$ (0,1].

Properties of time domain parameters of the vibration signal have been extensively studied for the fault diagnosis of rolling element bearings (REB). Parameters like kurtosis and Envelope Harmonic-to-Noise Ratio are most widely applied in this field and some important progress has been made. However, since only one-sided information is contained in these parameters respectively, problems still exist in practice when the signals collected are of complicated structure and/or contaminated by strong background noises. A new parameter, named Shock pulse index (SPI), is proposed in this paper. It integrates the mutual advantage of both parameters above and can help effectively identify fault related impulse components under the interference of strong background noises, unrelated harmonic components and random impulses. The SPI optimizes the parameters of Maximum Correlated Kurtosis Deconvolution (MCKD), which is used to filter the signals under consideration. Finally, the interested transient information contained in the filtered signal can be highlighted through demodulation with Teager Energy Operator (TEO). Fault related impulse components can therefore be extracted accurately. Simulations and experiment analyses verify the effectiveness and correctness of the SPI.

We investigate the existence and representation of the generalized core-EP inverse of some triangular matrices over a Banach algebra. Further, the general representations of the generalized core-EP inverse of a triangular matrix over a $C^*$-algebra are presented. As applications, the generalized core-EP inverses of some block operator matrices over Hilbert spaces are given.

We consider a stationary inclusion in a real Hilbert space X, governed by a set of constraints K, a nonlinear operator A and an element f∈X. Under appropriate assumptions on the data the inclusion has a unique solution, denoted by u. We state and prove a covergence criterion, i.e., we provide necessary and sufficient conditions on a sequence {un}⊂X which guarantee its convergence to the solution u. We then present several applications which provide the continuous dependence of the solution with respect to the data K, A and f, on one hand, and the convergence of an associate penalty problem, on the other hand. We use these abstract results in the study of a frictional contact problem with elastic materials which, in a weak formulation, leads to a stationary inclusion for the deformation field. Finally, we apply the abstract penalty method in the anlysis of two nonlinear elastic constitutive laws.

Fractional calculus is defined by expanded integer order integration and differentiation. In this paper, multiple mathematical models of a nonlinear dual tank device are precisely formulated by fractional calculus. Using the accurate model, multivariable Fractional-Order Controller is designed for the nonlinear device. The merits of the fractional-order design include: 1) Control of multivariable nonlinearities, 2) Compensation of uncertainties, 3) Elimination of coupling effects. Simulations and experiments are conducted to verify the precision of the fractional order models and the effectiveness of the multivariable fractional-order control design.

This study examines the impact of chainsaw chain type and tree species on the concen-tration of inhalable wood dust generated during motor-manual harvesting in forested areas. The chainsaw chain is a critical component, contributing not only to productivity but also to the oper-ator's health and safety. Wood dust creation during harvesting operations poses significant risks and necessitates careful attention due to its potential health effects. We investigated the effects by conducting real-world measurements of inhalable dust within the operator's breathing zone during forestry work. Two different chain types were evaluated: the commonly used 3/8" pitch chain (conventional chain) and the 0.325" pitch chain. Additionally, measurements were taken for three tree species: beech, oak, and pine (including both live and standing dead trees after a fire). Results showed that, overall, using the conventional 3/8" chain type yielded the highest concentration of wood dust for all three tree species. Notably, the highest wood dust concentration was observed in the burned Pinus brutia cluster, also with the 3/8" chain pitch. These findings emphasize the im-portance of understanding how chain type and tree species contribute to wood dust levels and provide valuable insights for enhancing operator health and safety during motor-manual har-vesting operations

The Pythagorean fuzzy set (PFS), which is characterized by a membership and a non-membership degree and the square sum of them is less or equal to one, can act as an effective tool to express decision makers’ fuzziness and uncertainty. Considering that the Heronian mean (HM) is a powerful aggregation operator which can take the interrelationship between any two arguments, we study the HM in Pythagorean fuzzy environment and propose new operators for aggregating interval-valued Pythagorean fuzzy information. First, we investigate the HM and geometric HM (GHM) under interval-valued intuitionistic fuzzy environment and develop a series of aggregation operators for interval-valued intuitionistic fuzzy numbers (IVIFNs) including interval-valued intuitionistic fuzzy Heronian mean (IVIFHM), interval-valued intuitionistic fuzzy geometric Heronian mean (IVIFGHM), interval-valued intuitionistic fuzzy weighted Heronian mean (IVIFWHM) and interval-valued intuitionistic fuzzy weighted geometric Heronian mean (IVIFWGHM). Second, some desirable and important properties of these aggregation operators are discussed. Third, based on these aggregation operators, a novel approach to multi-attribute decision making (MADM) is proposed. Finally, to demonstrate the validity of the approach, a numerical example is provided and discussed. Moreover, we discuss several real-world applications of these operators within policy-making contexts.

This study explores the properties and behavior of bi-close-to-convex functions, introducing new subclasses defined by their relationship with fractional differential operator and bi-univalent functions. Using the Faber polynomial technique, we derive upper bounds for the n^{th} coefficient of functions in these classes. We also investigate the erratic behavior of initial coefficients in bi-close-to-convex functions, as characterized by the (λ,q)-fractional differintegral operator. Furthermore, we address Fekete-Szegö problems and present notable findings from our investigation, contributing to the continued growth and refinement of geometric function theory, yielding new insights and practical uses.

The goal of the current study is to analyse several nonlinear two-dimensional time-fractional Rosenau Hymanequations. The two-dimensional fractional Rosenau-Hyman equation has extensive use in engineering and applied sciences. The fractional view analysis of two-dimensional time-fractional Rosenau-Hyman equations is discussed using the homotopy perturbation approach, adomian decomposition method, and Yang transformation. Some examples involving two-dimensional time-fractional Rosenau-Hyman equations are provided in order to better understand the suggested approaches. The solutions appear as infinite series. We offer a comparison between the accurate solutions and those that are generated employing the proposed approaches in order to demonstrate the effectiveness and applicability of the proposed techniques. The results are graphically illustrated using 2D and 3D graphs. It has been noted that the obtained results and the targeted problems real solutions are quite similar. Calculated solutions at various fractional levels describe some of the problems useful dynamics. Other fractional problems that arise in other fields of science and engineering can be solved using a modified version of the current techniques.

Jellyfish search (JS) algorithm impersonates the foraging behavior of jellyfish in the ocean. It is a new developed meta-heuristic algorithm that solves complex and real world optimization problems. The global explore capability and robustness of JS are strong, but JS still has great development space in solving complex optimization problems with high dimensions and multiple local optima. Therefore, an enhanced jellyfish search (EJS) algorithm is developed in this study, and three improvements are made: (i) By adding sine and cosine learning factors, the jellyfish can learn from both random individual and best individual during Type B motion in swarm to enhance the optimization capability and convergence speed; (ii) Adding local escape operator can skip local optimal trap and boost the exploitation ability of JS; (iii) Opposition-based learning operator and quasi-opposition learning operator can increase and strengthen the population distribution more diversified, and better individuals are selected from present and new opposition-solution to participates in the next iteration, which can boost the solution’s quality, meanwhile convergence speed is fasted and its precision is increased. In addition, the performance contrast of the developed EJS and some previous outstanding and advanced methods are evaluated on CEC2017, CEC2019 test suite and six real engineering example of case. It is demonstrated that EJS algorithm escaped the trap of local optimum, enhanced the solution’s quality and the calculation speed. What’s more, the practical engineering applications of EJS algorithm also verify its superiority and effectiveness in solving both constrained and unconstrained optimization problems, and it stretched one’s mind for solving such optimization problems.

In this paper we investigate analytic automorphisms of complex topological vector spaces and their applications to linear and nonlinear transitive operators. We constructed some examples of polynomial automorphisms which show that a natural analogue of the Jacobian Conjecture for infinite dimensional spaces is not true. Also, we prove that any separable Fréchet space supports a transitive analytic operator which is not a polynomial. We found some connections of analytic automorphisms and algebraic bases of symmetric polynomials and applications to hypercyclisity of composition operators.

Purpose of this article is to introduce a modification of Phillips operators on the interval $\left[ \frac{1}{2},\infty \right) $ via Dunkl generalization. This type of modification enables a better error estimation on the interval $\left[ \frac{1}{2},\infty \right) $ rather than the classical Dunkl Phillips operators on $\left[ 0,\infty \right) $. We discuss the convergence results and obtain the degrees of approximations. Furthermore, we calculate the rate of convergence by means of modulus of continuity, Lipschitz type maximal functions, Peetre's $K$-functional and second order modulus of continuity.

In this paper, we provide some enlightening examples of the application of Clifford algebra in geometry, which show the concise representation, simple calculation and profound insight of this algebra. The definition of Clifford algebra implies geometric concepts such as vector, length, angle, area and volume, and unifies the calculus of scalar, spinor, vector and tensor, so that it is able to naturally describe all variables and calculus in geometry and physics. Clifford algebra unifies and generalizes real number, complex, quaternion and vector algebra, converts complicated relations and operations into intuitive matrix algebra independent of coordinate systems. By localizing the basis or frame of space-time and introducing differential and connection operators, Clifford algebra also contains Riemann geometry. Clifford algebra provides a unified, standard, elegant and open language and tools for numerous complicated mathematical and physical theories. Clifford algebra calculus is an arithmetic-like operation that can be well understood by everyone. This feature is very useful for teaching purposes, and popularizing Clifford algebra in high schools and universities will greatly improve the efficiency of students to learn fundamental knowledge of mathematics and physics. So Clifford algebra can be expected to complete a new big synthesis of scientific knowledge.

Purpose of this article is to introduce a modification of Phillips operators on the interval $\left[ \frac{1}{2}% ,\infty \right) $ via Dunkl generalization. This type of modification enables a better error estimation on the interval $\left[ \frac{1}{2},\infty \right) $ rather than the classical Dunkl Phillips operators on $\left[ 0,\infty \right) $. We discuss the convergence results and obtain the degrees of approximations. Furthermore, we calculate the rate of convergence by means of modulus of continuity, Lipschitz type maximal functions, Peetre's $K$-functional and second order modulus of continuity.

Distribution System Operators (DSOs) are adapting to changing energy demands and the shift toward renewable and decentralized energy. Circularity is increasingly relevant for DSOs as their distribution systems age and need replacing. Taking circular action, however, is generally regarded as challenging as the current circular economy (CE) landscape is highly fragmented and rarely touches the implementation level. A longitudinal case study at Dutch DSO Liander on the circu-larity of distribution transformers was used to understand empirical success factors for taking circular action and to generate prescriptive knowledge on the operationalization of circularity. Six design propositions for circular action were formulated that suggest to 1) initiate small-scale cir-cularity experiments, 2) involve technical and strategic experts, 3) synergize circularity with more urgent, primary goals 4) translate circular initiatives bottom-up and top-down, 5) collaborate with other DSOs, and 6) create multidisciplinary teams. At DSO Liander, selecting the right interventions depending on the changing context contributed to operationalizing circularity for distribution transformers and achieving circularity targets. The generalizable design propositions could assist other DSOs in optimizing their strategy toward circular action.

The introduction of Maritime Autonomous Surface Ship (MASS) through the development of autonomous navigation technologies is expected to bring about new technologies, new vessel types, and new job roles such as remote operation center (ROC) and remote operator (RO). The MASS Code are currently being discussed through Maritime Safety Committee (MSC) of International Maritime Organization (IMO). This code is expected to be adopted in the form of non-mandatory guidelines until 2025, with the goal of establishing mandatory requirements by 2028. Additionally, revisions to the International Convention on Standards of Training, Certification and Watchkeeping for Seafarers (STCW) related to crew training and qualifications are planned for adoption by 2027, which will include requirements for MASS operators. This paper aims to examine the fundamental competencies required for safe MASS operation by remote operators using the Analytic Hierarchy Process (AHP) method, considering the emergence of the new profession of RO. Building upon the 66 Knowledge, Understanding & Proficiencies (KUPs) outlined for marine officer in the STCW Convention, the study seeks to identify the additional competencies necessary for RO and contribute to the development of a training model for the future.

We show how the Poincar\'e--Riemann--Hilbert boundary-value problem enables us to construct effective estimates of the potential in the Schr\"odinger equation. The apparatus of the three-dimensional inverse problem of quantum scattering theory is developed for this. It is shown that the unitary scattering operator can be studied as a solution of the Poincar\'e--Riemann--Hilbert boundary-value problem. This allows us to go on to study the potential in the Schr\"odinger equation

We introduce the lower chaos grade of a real-valued function F defined on the Markov triple (E,μ,Γ), where μ is a probability measure and Γ is the carré du champ operator. As an application of this concept, we obtain the better estimate of the four moments theorem for Markov diffusion generators worked by Bourguin et al (2019). For our purpose, we need to find the largest number except zero in the set of eigenvalues corresponding to its eigenfunction in the case where the square of a random variable F, coming from a Markov triple structure, can be expressed as a sum of eigenfunctions, We give some examples of eigenfunctions of the diffusion generators such as Ornstein-Uhlenbeck, Jacobi and Romanovski-Routh. In particular, two bounds, called the four moments theorem and fourth moment theorem respectively, will be provided for the normal approximation of the case where a random variable F comes from eigenfunctions of a Jacobi generator.

In this work the existence and nonexistence of stationary radial solutions to the elliptic partial differential equation arising in the molecular beam epitaxy are studied. Since we are interested in radial solutions we arrive at the following fourth-order differential equation

The properties of iterative splitting methods with serial versions have been analyzed since recent years, see [1] and [3]. We extend the iterative splitting methods to a class of parallel versions, which allow to reduce the computational time and keep the benet of the higher accuracy with each iterative step. Parallel splitting methods are nowadays important to solve large problems, which can be splitted in subproblems and computed independently with the dierent processors. We present a novel parallel iterative splitting method, which is based on the multi-splitting methods, see [2], [10] and [15]. Such a exibilisation with multisplitting methods allow to decompose large iterative splitting methods and recover the benet of their underlying waveform-relaxation (WR) methods. We discuss the convergence results of the parallel iterative splitting methods, while we could reformulate such an error to a summation of the individual WR methods. We discuss the numerical convergence of the serial and parallel iterative splitting methods and present dierent numerical applications to validate the benet of the parallel versions.

Here, we propose a prescriptive simulation model of a process operator’s decision-making assisted by artificial intelligence (AI) algorithm in a technical system control loop. We analyze situations fraught with a catastrophic threat that may cause unacceptable damage. Operators’ decision-making is interpreted in terms of a subjectively admissible probability of disaster and subjectively necessary reliability of its assessment. We distinguish four extreme decision-making strategies corresponding to different ratios between the above variables. An experiment simulating a process facility, an AI algorithm and operator's decision-making strategy was held. It showed that depending on the properties of a controlled process (the speed of hazard onset) and the AI algorithm characteristics (Type I and II error rate), each of such strategies or some intermediate strategy may prove to be more beneficial than others. The same approach is applicable to the identification and analysis of sustainability of strategies applied in real-life operating conditions, as well as to the development of a computer simulator to train operators to control hazardous technological processes using AI-generated advice.

Market dynamics is based on classical electrodynamics and uses quantum electrodynamics as a reference model framework. Its construction is always based on Bourbaki structuralism. Market dynamics studies the interaction between price, demand and supply. Quantum electrodynamics studies the interaction between photons, electrons and positrons. Both belong to the category of single charge dynamics and share a symmetry group. Market dynamics introduces market charge and defines demand and supply respectively. By examining the market hesitation phenomenon, spin is introduced as the intrinsic property of demand and supply. Therefore, demand and supply can be defined by Dirac spinors. By introducing the coin cone and valence shell, virtual prices are defined; demand and supply interact by exchanging virtual prices. These interactions can be described by Feynman diagrams. The cognitive field has the function of polarizing decision-making and is described by the magnetic field. Market dynamics believes that the social economy itself is an experiment and every market participant is an observer. We established the non-commutative relationship of market observation and the market version of the uncertainty principle of observation information, and defined the quantum version of the invisible hand. On the basis of classical electrodynamics, the relationship between price field and Maxwell field is discussed, and the concept of gauge potential is introduced. Market fluctuations (including mesoscopic and quantum fluctuations) caused by high-order cognition (including gaming, decision-making and reasoning). The fluctuation phenomena inherent in various markets are the basis for understanding both the cognition of market participants and the phase transition of the market. Six components of the market wave function are defined, namely the global phase factor, global gauge potential and global gauge field strength, as well as the local phase factor, local gauge potential and local gauge field strength. Gauge transformation is a integral part of quantum electrodynamics and market dynamics. The gauge principle is then given to show that global symmetry is a necessary condition for local symmetry. Four operators are introduced, namely the Newton mean operator, the Einstein cone operator, the Schrödinger evolution operator and the Dirac field theory operator. These four operators are applied to the market wave function respectively, presenting four operator phases of the market wave function. The change of operator state is called the phase transition of the market wave function.

In this paper, the connections between quantum non-locality and permutation symmetries are explored. This includes two types of symmetries: permutation across a superposition and permutation of qubits in a quantum system. An algorithm is proposed for nding the separability class of a quantum state using a method based on factorizing an arbitrary multipartite state into possible partitions, cyclically permuting qubits of the vectors in a superposition to check which separability class it falls into and thereafter using a reduced density-matrix analysis of the system is proposed. For the case of mixed quantum states, conditions for separability are found in terms of the partial transposition of the density matrices of the quantum system. One of these conditions turns out to be the Partial Positive Transpose (PPT) condition. A graphical method for analyzing separability is also proposed. The concept of permutation of qubits is shown to be useful in dening a new entanglement measure in the `engle'.

Intuitionistic fuzzy set, which can be represented using the triangular intuitionistic fuzzy number (TIFN), is a more generalized platform for expressing imprecise, incomplete and inconsistent information when solving multi-criteria decision-making problems, as well as for reflecting the evaluation information exactly in different dimensions. In this paper, the TIFN has been applied for solving some multi-criteria decision-making problems by developing a new triangular intuitionistic fuzzy geometric aggregation operator, that is the generalized triangular intuitionistic fuzzy ordered weighted geometric averaging (GTIFOWGA) operator, and defining some triangular intuitionistic fuzzy geometric aggregation operators including the triangular intuitionistic fuzzy weighted geometric averaging (TIFWGA) operator, the ordered weighted geometric averaging (TIFOWGA) operator and the hybrid geometric averaging (TIFHWGA) operator. Based on these operators, a new approach for solving multicriteria decision-making problems when the weight information is fixed has been proposed. Finally, the proposed method has been compared with some similar existing computational approaches by virtue of a numerical example to verify its feasibility and rationality.

Covariant integral quantization with rotational symmetry SO(3) is established for the quantum motion on this group manifold, or, alternatively, for Gabor signal analysis on this group. We revisit the action of the related (non-unitary) Weyl-Gabor operator on the Hilbert space of square integrable functions on SO(3) and disclose a set of various properties. By selecting weight functions on the corresponding discrete-continuous phase space, one derives related coherent states and Wigner transform.

In this paper we suggest a first ever construction of fractional integral and differential operators based on signed measures including a vector-valued case. The study focuses on constructing the fractional power of the Riemann-Stieltjes integral with a signed measure, using semigroup theory. The main result is a theorem that provides the exact form of a semigroup for the Riemann-Stieltjes integral with a measure having a countable number of extrema. The article provides examples of semigroups based on integral operators with signed measures and discusses the fractional powers of differential operators with partial derivatives.

As technologies such as eco-friendly ships, electric propulsion vessels, and multi-fuel propulsion systems advance, the scope of IoT applications in maritime field is expanding, resulting in increased complexity in control factors. The gradual progression towards Maritime Autonomous Surface Ships (MASS) is further driving the evolution of ship-based IoT applications. These advancements underscore the necessity for a platform capable of ensuring reliable connectivity between ships and onshore, while also being adaptable for deployment and operation to meet the demands of service availability. The limitations of the existing single cloud architecture become evident in this context. In response to these emerging challenges, this paper presents a cloud-based horizontal data platform structure anchored in the architecture of a Multi-Region Fog Cloud. This approach is tailored to fulfill the crucial requirement of maintaining robust and seamless connectivity for vessels navigating globally. Leveraging the capabilities of the Fog Cloud, the platform enhances service responsiveness by facilitating localized data collection and distribution, complemented by efficient data caching from the Cloud Center, serving users within the same geographical region. We outline a strategic framework for enhancing and executing key ship services within the proposed architecture. These services encompass data sharing between ships to elevate collision avoidance, disseminating weather data for optimized route planning, and constructing an operator training simulator (OTS) environment through the integration of digital twin technology. After, we implement an architecture using the AWS Cloud and gauges latency and Packet Loss Rate (PLR) through connections to Seoul, California, and Frankfurt regions. The test results reveal that latency in different regions is about 2-5 times higher than that in the same region for the payload. Furthermore, packet loss occurred at roughly 2-3 Hz packet generation rate (PGR) in different regions, whereas in the same region, it commenced at approximately 10-20 Hz PGR.