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.

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.

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.

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.

Linear mixed models are frequently used for analysing heterogeneous data in a broad range of applications. The restricted maximum likelihood method is often preferred to estimate co-variance parameters in such models due to its unbiased estimation of the underlying variance parameters. The restricted log-likelihood function involves log determinants of a complicated co-variance matrix. An efficient statistical estimate of the underlying model parameters and quantifying the accuracy of the estimation requires the first derivatives and the second derivatives of the restricted log-likelihood function, i.e., the observed information. Standard approaches to compute the observed information and its expectation, the Fisher information, is computationally prohibitive for linear mixed models with thousands random and fixed effects. Customized algorithms are of highly demand to keep mixed models analysis scalable for increasing high-throughput heterogeneous data sets. In this paper, we explore how to leverage an averaged information splitting technique and dedicate matrix transform to significantly reduce computations and to accelerate computing. Together with a fill-in reducing multi-frontal sparse direct solver, the averaged information splitting approach improves the performance of the computation process.

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.

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.

The present study focuses on the synthesis, characterization, and investigation of a p-n heterojunction photocatalysis. Titanium dioxide (TiO2) can’t alone induce the photocatalytic water splitting due to its wide bandgap, which decreases its catalytic activity in the visible light. To make redshift of absorptivity for the TiO2, Nickel (Ni)-doped Graphene (rGO) supported TiO2 was synthesized. Several characterization techniques have been employed to validate the composition and the light absorption ability of the prepared photocatalysts including TEM, SEM, EDS, XRD, XPS, and UV-Vis spectroscopy. The characterization revealed successful doping of the Ni and TiO2 on the rGO nanosheet. Moreover, the UV-Vis spectroscopy indicated a significant shift of light absorption toward the visible spectrum. The photon-induced evolution of H2 was remarkably enhanced using the prepared Ni-rGO/TiO2 nanocomposite. Furthermore, the optimum ratio of rGO: TiO2: Ni in the hybrids was 10:1:4, while the higher Ni ratio would decrease the photocatalytic activity. The stability of the photocatalyst was also verified during 8 cycles of photocatalytic reactions. The kinetic study revealed the nature of the integrated reaction and the controlling step governing the reaction sequence. .

For efficient electrode development in an electrolysis system, Fe₂O₃, MnO, and heterojunction Fe₂O₃-MnO materials were synthesized via a simple sol-gel method. These particles were coated on a Ni-foam electrode, and the resulting material was used as an electrode to be used during an oxygen evolution reaction (OER). A 1000-cycle OER test in a KOH alkaline electrolyte indicated that the heterojunction Fe₂O₃-MnO/NF electrode exhibited the most stable and highest OER activity: it exhibited a low overvoltage (n) of 370 mV and a small Tafel slope of 66 mV/dec. X-ray photoelectron spectroscopy indicated that the excellent redox performance contributed to the synergy of Mn and Fe, which enhanced the OER performance of the Fe₂O₃-MnO/NF electrode. Furthermore, the effective redox reaction of Mn and Fe indicated that the structure maintained stability even under 1000 repeated OER cycles.

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.

Clean production of renewable fuels is a great challenge of our scientific community. Iridium complexes have demonstrated a superior catalytic activity in the water oxidation (WO) reaction, which is a crucial step in water splitting process. Herein we have used a defective zirconium MOF with UiO-66 structure as support of a highly active Ir complex based on EDTA with formula [Ir(HEDTA)Cl]Na. The defects are induced by the partial substitution of tereftalic acid with smaller formiate groups. Anchoring of the complex occurs through a post-synthetic exchange of formiate anions, coordinated at the zirconium clusters of the MOF, with the free carboxylate group of the [Ir(HEDTA)Cl]-complex. The modified material was tested as heterogenous catalyst for the WO reaction by using Cerium Ammonium Nitrate as sacrificial agent. Although TOF and TON values are comparable to those of other iridium heterogenized catalysts, the MOF exhibits iridium leaching not limited at the first catalytic run, as usually observed, suggesting a lack of stability of the hybrid system under strong oxidative conditions.

Water electrolysis provides efficient and cost-effective production of hydrogen from renewable energy. Currently, the oxidation half-cell reaction relies on noble-metal catalysts, impeding widespread application. In order to adopt water electrolyzers as the main hydrogen production systems, it is critical to develop inexpensive and earth-abundant catalysts. This review discusses the proton exchange membrane (PEM) water electrolysis (WE) and the progress in replacing the noble-metal catalysts with earth-abundant ones. Researchers within this field are aiming to improve the efficiency and stability of earth-abundant catalysts (EACs), as well as to discover new ones. The latter is particularly important for the oxygen evolution reaction (OER) under acidic media, where the only stable and efficient catalysts are noble-metal oxides, such as IrO_x and RuO_x. On the other hand, there is significant progress on EACs for the hydrogen evolution reaction (HER) in acidic conditions, but how many of these EACs have been used in PEM WEs and tested under realistic conditions? What is the current status on the development of EACs for the OER? These are the two main questions this review addresses.

In theory and applications, it is often inevitable to work with projectors onto convex sets, where a linear transform is involved. In this article, a novel projector is presented, which generalizes previous results in that it admits a broader family of linear transforms, but on the other hand it is limited to box-type convex sets in the transformed domain. The new projector has an explicit formula and it can be interpreted within the framework of proximal optimization. The benefit of the new projector is demonstrated on an example from signal processing, where it was possible to speed up the convergence of a signal declipping algorithm by a factor of more than two.

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.

We present an overview over eight brightly luminescent Cu(I) dimers of the type Cu2X2(PN)3 with X = Cl, Br, I and P^N = 2-diphenylphosphino-pyridine (Ph2Ppy), 2-diphenylphosphino-pyrimidine (Ph2Ppym), 1-diphenylphosphino-isoquinoline (Ph2Piqn) including three new crystal structures (Cu2Br2(Ph2Ppy)3, 1-Br, Cu2I2(Ph2Ppym)3, 2-I, and Cu2I2(Ph2Piqn)3, 3-I). However, we mainly focus on their photo-luminescence properties. All compounds exhibit combined thermally activated delayed fluorescence (TADF) and phosphorescence at ambient temperature. Emission color, decay time, and quantum yield varies over large ranges. For deeper characterization, we select Cu2I2(Ph2Ppy)3, 1-I, showing a quantum yield of 81 %. DFT and SOC-TDDFT calculations provide insight into the electronic structures of the singlet S1 and triplet T1 states. Both stem from metal+iodide-to-ligand charge transfer transitions. Evaluation of the emission decay dynamics, measured from 1.2 ≤ T ≤ 300 K, gives ∆E(S1-T1) = 380 cm-1 (47 meV), a transition rate of k(S1→S0) = 2.25×106 s-1 (445 ns), T1 zero-field splittings, transition rates from the triplet substates, and spin-lattice relaxation times. We also discuss the interplay of S1-TADF and T1-phosphorescence. The combined emission paths shorten the overall decay time. For OLED applications, utilization of both singlet and triplet harvesting can be highly favorable for improvement of the device performance.

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.

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 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.

Fracture density, a critical parameter of unconventional reservoirs, can be used to evaluate potential of unconventional reservoirs and location of production wells. Many technologies, such as amplitude variation with offset and azimuth (AVOA) technology, vertical seismic profiling (VSP) technology, and multicomponent seismic technology, are generally used to predict fracture of reservoirs. they can qualitatively predict fracture by analyzing seismic attributes, including seismic wave amplitudes, seismic wave velocities, which are sensitive to fracture. However, it is important to quantitatively describe fracture of reservoirs. In this study, based on a double-layer model, the relationships between fracture density and the double-layer model’s physical parameters, such as velocity of fast shear-wave, velocity of slow shear-wave, and density, were established, and then a powerful quantitative prediction method for fracture density was proposed dramatically. Afterwards, the Hudson model for crack was used to test the applicability of the method. The result shown that the quantitative prediction method for fracture density can be applied suitable to the Hudson model for crack. Finally, the result of validation models indicated that the method can predict fracture density effective, in which absolute relative deviation (ARD) were less than 5% and root-mean-square error (RMSE) was 4.88×10-3.

TiO₂ nanorod as a superior nanostructure has attracted a lot of attention to exert in the photocatalytic and photoelectrocatlytic applications in recent years. Nevertheless, its practical usage is restricted by a number of limitations such as the large band gap energy, the low rate of photo-induced carriers generation and the high rate of charge carriers recombination. Therefore in this study, incorporation of TiO₂ nanorod with WO₃ is proposed as a suitable approach to overcome these defects. In this regard, WO₃-TiO₂ nanorod was constructed by a facile one pot hydrothermal method in two incessant steps and was then employed as a potent photoanode for photoelectrocatalytic hydrogen generation. The morphology, elemental compositions and optical properties were characterized by the FESEM, EDS and DRS analysis, respectively. Furthermore, voltammetry analyses were performed to assay the photoelectrochemical features of WO₃-TiO₂ nanorod. The results confirmed that the incorporation of TiO₂ nanorod with WO₃ not only significantly made the band gap energy narrower (from 3eV to 2eV), but also dramatically intensified the photocurrent density and photoconversion efficiency from 1mA.cm^-2 to 1.8mA.cm^-2 and from 0.3% to 0.45%, respectively. As a consequence of improving optical properties and photoelectrochemical features, WO₃-TiO₂ nanorod could generate 2.43 mmol H₂ during 100 min under UV irradiation, which was 1.71 times more than hydrogen generated over pure TiO₂ nanorod

Degussa P25 is a benchmark form of TiO₂ used worldwide in photocatalysis studies. Currently no such benchmark exists for co-catalysts, which are essential for many photocatalytic reactions. Here, we present the preparation of Pt nanocluster co-catalysts on TiO₂ using an unmodified commercial source and equipment that is commonly available. Transmission electron microscopy reveals that the procedure produces TiO₂ decorated with Pt atom and nanoclusters (1-5 atoms). Optical reflectance and X-ray diffraction measurements show that the procedure does not affect the TiO₂ polymorph or UV-Vis absorbance. Gas phase photocatalytic splitting of heavy water (D₂O) shows that the Pt nanocluster decorated TiO₂ outperforms Pt nanoparticle (produced by photodeposition) decorated TiO₂ in D₂ production. Pt nanoclusters, produced directly from a commercial source, with high co-catalyst activity are prime candidates to be used in benchmark photocatalytic reactions.

Photoelectrocatalytic water splitting by using various TiO₂ nanostructures is a promising approach to generate hydrogen without harmful byproducts. However, their effective performance is restricted by some drawbacks such as high rapid electron-hole pair recombination and backward reaction producing H₂O. Thus in this study, the probability of enhancing hydrogen generation rate by adding methanol as a sacrificial agent to the anodic chamber of a two-compartment photoelectrochemical cell is investigated. Herein, one-dimensional elongated TiO₂ nanorods that were fabricated via a facile one-pot hydrothermal method are utilized as potent photoanode. Voltammetric characterizations confirm that addition of alcoholic sacrificial agent has a significant effect on photoelectrochemical properties of TiO₂ nanorods which by adding 10 wt% of methanol, the photocurrent density and photoconversion efficiency increased from 0.8mA.cm^-2 to 1.5mA.cm^-2 and from 0.28% to 0.45%, respectively. The results of photoelectrocatalytic water splitting indicated that the hydrogen generation rate in the presence of methanol was about 1.2 times higher than that from pure water splitting. These enhancements can be attributed to the key role of methanol. Methanol molecules not only inhibit the electron-hole pair recombination but also accelerate the hydrogen generation rate by sharing their hydrogen atoms.

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.

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.

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.

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.

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.

We describe the direct formation of mixed-phase (1T and 2H) MoS2 layers on Si as a photocathode via atomic layer deposition (ALD) for application in the photoelectrochemical (PEC) reduction of water to hydrogen. Without typical series-metal interfaces between Si and MoS2, our p-Si/SiOx/MoS2 photocathode showed efficient and stable operation in hydrogen evolution reactions (HERs). The resulting performance could be explained by spatially genuine device architectures in three dimensions (that is, laterally homo and vertically heterojunction structures). The ALD-grown MoS2 overlayer with the mixed-phase 1T and 2H homojunction passivates light absorber and surface states and functions as a monolithic structure for effective charge transport within MoS2. It is also beneficial in the operation of p-i-n heterojunctions with inhomogeneous barrier heights due to the presence of mixed-phase cocatalysts. The effective barrier heights reached up to 0.8 eV with optimized MoS2 thicknesses, leading to a 670 mV photovoltage enhancement without employing buried Si p-n junctions. The fast-transient behaviors via light illumination show that the mixed-phase layered chalcogenides can serve as efficient cocatalysts by depinning the Fermi levels at the interfaces. A long-term operation of ~ 70 h was also demonstrated in a 0.5 M H2SO4 solution.

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 .

We study strong optical coupling of metal nanoparticle arrays with dielectric substrates. Based on the Fermi Golden Rule, the particle-substrate coupling is derived in terms of the photon absorption probability assuming a local dipole field. An increase in photocurrent gain is achieved through the optical coupling. In addition, we describe light-induced, mesoscopic electron dynamics via the nonlocal hydrodynamic theory of charges. At small nanoparticle size (<20nm), the impact of this type of spatial dispersion becomes sizable. Both absorption and scattering cross section of the nanoparticle are significantly increased through the contribution of additional nonlocal modes. We observe a splitting of local optical modes spanning several tenths of nanometers. This is a signature of semi-classical, strong optical coupling via the dynamic Stark effect, known as Autler-Townes splitting. The photocurrent generated in this description is increased by up to 2%, which agrees better with recent experiments than compared to identical classical setups with up to 6%. Both, the expressions derived for the particle-substrate coupling and the additional hydrodynamic equation for electrons are integrated into COMSOL for our simulations.

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.

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.

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.

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

Looking at different operating climatic conditions, the electrical behavior predicting photovoltaic modules gets very important. For the estimation of output power from photovoltaic (PV) plants this is a very essential and basic aspect. In this paper, the relationship between the I-V curve and the irradiation spectrum is discussed by combining the single diode model. An explicit elementary analytical model with two defined shape parameters is discussed and improved with three approximations and second order Taylor expansion. Then, the explicit elementary analytical model is investigated under varying conditions leveraging the four parameters I_ph, I₀, R_s and R_sh from the single diode model. The relationship between the physical parameters and the condition parameters are discussed and applied to extract the shape parameters at different scenarios. Considering the aging effect, the process of calculation to predict the I-V curve under different splitting spectra is simplified as follow: (1) two shape parameters are gotten from the I-V data at measurement reference conditions (MRC); (2) the short circuit current, open circuit voltage and shape parameters under any splitting spectrum can be calculated based on the relationship provided in article; (3) the performance of PV panel can be predicted with parameters. The validation of this model was experimentally proven leveraging monocrystalline silicon photovoltaic module with different splitting films. Results showed that the model accurately predicts the I-V characteristics for the examined PV modules at different irradiance spectra and cell temperatures. Moreover, the presented model performs superior compared to other investigated models when looking at accuracy and simplicity.

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'.

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.

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.

We propose and theoretically investigate integrated photonic filters based on coupled Sagnac loop reflectors (SLRs) formed by a self-coupled wire waveguide. By tailoring coherent mode interference in the device, three different filter functions are achieved, including Fano-like resonances, wavelength interleaving, and varied resonance mode splitting. For each function, the impact of device structural parameters is analyzed to facilitate optimized performance. Our results theoretically verify the proposed device as a compact multi-functional integrated photonic filter for flexible spectral shaping.

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].

Results are presented concerning the influence on the water splitting process of enantiopure tartaric acid present in bulk solution. Stainless steel and electrodeposited nickel are used as working electrode (WE) surface. The latter is obtained by electrodeposition on the two poles of a magnet. The influence and role played by the chiral compound in solution has been assessed by comparing the current values, in cyclic voltammetry (CV) experiments, recorded in the potential range at which oxygen evolution reaction (OER) occurs. In the case of tartaric acid and nickel WE a spin polarization of about 4 % is found. The use of the chiral environment (bulk solution) and ferromagnetic chiral Ni electrode allows for observing the OER at a more favourable potential: about 50 mV (i.e. a cathodic, less positive, shift of the potential at which the oxygen evolution is observed).

This paper describes a proposed fractional filter-based multi-scale underwater and hazy image enhancement algorithm. The proposed system combines a modified global contrast operator with fractional order-based multi-scale filters used to generate several images, which are fused based on entropy and standard deviation. The multi-scale-global enhancement technique enables fully adaptive and controlled colour correction and contrast enhancement without over exposure of highlights when processing hazy and underwater images. This in addition to illumination/reflectance estimation coupled with global and local contrast enhancement. The proposed algorithm is also compared with the most recent available state-of-the-art multi-scale fusion de-hazing algorithm. Experimental comparisons indicate that the proposed approach yields better edge and contrast enhancement results without halo effect, colour degradation and is faster and more adaptive than all other algorithms from the literature.

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.

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.

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 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

We present theoretical designs of high performance optical filters in integrated silicon photonic nanowire resonators. We use mode interference in formed by zig-zag waveguide coupled Sagnac loop reflectors (ZWC-SLRs), tailored to achieve diverse filtering functions with good performance. These include compact bandpass filters with improved roll-off, optical analogues of Fano resonances with ultrahigh spectral extinction ratios (ERs) and slope rates, and resonance mode splitting with high ERs and low free spectral ranges. The analysis verifies the feasibility of multi-functional integrated photonic filters based on ZWC-SLR resonators for flexible spectral engineering in diverse applications.

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 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.

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.

In this paper, the author utilizes Saddle Theorem and variational methods to deduce existence of at least six stationary solutions for reaction-diffusion Gilpin-Ayala competition model (RDGACM). To obtain the global stabilization of the positive stationary solution of the RDGACM, the author designs a suitable impulsive event triggered mechanism (IETM) to derive the global exponential stability of the the positive stationary solution. It is worth mentioning that the new mechanism can exclude Zeno behavior and effectively reduce the cost of impulse control through event triggering mechanism. Besides, compared with existing literature, the restrictions on the parameters of the RDGACM are relaxed so that the methods used in existing literature can not be applied to the relaxed case of this paper, and so the author makes comprehensive use of Saddle Theorem, orthogonal decomposition of Sobolev space $H_0^1(\Omega)$ and variational methods to overcome the mathematical difficulty. Numerical examples show the effectiveness of the methods proposed in this paper.

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.

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.

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.

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.

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.

For some decades, the scientific community has been looking for alternatives to the use of fossil fuels that allow the planet's sustainable and environmentally friendly development. To do this, attempts have been made to mimic some processes that occur in nature, among which the photosystem-II stands out, which allows water splitting operating with different steps to generate oxygen and hydrogen. This research presents promising results using synthetic catalysts, which try to simulate some natural processes, and which are based on Au@ZnO-graphene compounds. These catalysts were prepared by incorporating different amounts of gold nanoparticles (1 wt.%, 3 wt.%, 5 wt.%, 10 wt.%) and graphene (1 wt.%) on the surface of synthesized zinc oxide nanowires (ZnO NWs), and zinc oxide nanoparticles (ZnO NPs), along with a commercial form (commercial ZnO) for comparison purposes. The highest amount of hydrogen (1,127 µmol/hg) was reported by ZnO NWs with a gold and graphene loadings of 10 wt.% and 1 wt.%, respectively, under irradiation at 400 nm. Quantities of 759 µmol / hg and 709 µmol / hg were obtained with catalysts based on ZnO NPs and commercial ZnO, respectively. The photocatalytic activity of all composites increased with respect to the bare semiconductors, being 2.5 times higher in ZnO NWs, 8.8 times for ZnO NPs and 7.5 times for commercial ZnO. The high photocatalytic activity of the catalysts is attributed, mainly, to the synergism between the different amount of gold and graphene incorporated, and the surface area of the composites.

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.

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.

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.

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 $\nu$.

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.

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.

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 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.

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.

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.

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.

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.

A sustainable, scalable source of energy‐dense chemical fuel is urgently needed to ensure the security of our energy supply for future generations. Solar energy is the only renewable energy source of sufficient scale to replace fossil fuels and meet rising environmental demand. Hydrogen is expected to play a key role as an energy carrier in future energy systems of the world. As fossil fuel supplies become scarcer and environmental concerns increase, hydrogen is likely to become an increasingly important chemical energy carrier and eventually may become the principal chemical energy carrier. When most of the world’s energy sources become non-fossil based, hydrogen and electricity are expected to be the two dominant energy carriers for the provision of end-use services. Photocatalytic hydrogen evolution from water by solar energy over semiconductors offers a promising way for clean and renewable production of hydrogen. The TiO2-based materials have received considerable attention in recent years due to their extensive application in photocatalysis for hydrogen evolution. Though TiO2 is the most widely investigated photocatalyst for hydrogen evolution, it still provides low photocatalytic activity due to the wide bandgap that results in photocatalytic activity only under ultraviolet (UV) irradiation. Modification of TiO2 photocatalysts with several transition metals has been extensively studied to extend the absorbance capacity of TiO2 into the visible range. The effect of different photocatalytic deposition and reaction parameters also play major roles in enhancing the photostability of photoanode and increasing the hydrogen gas output, respectively.

In the present study. At first, some properties of r-fuzzy soft β-closed sets are introduced on fuzzy soft topological spaces based on the paper Aygunoglu et al. (Hacet. J. Math. Stat. 2014, 43, 193-208). Also, we define the closure and interior operators with respect to the classes of r-fuzzy soft β-closed and r-fuzzy soft β-open sets, and investigate some of their properties. In addition, the concept of r-fuzzy soft β-connected sets is introduced and characterized with help of fuzzy soft β-closure operators. Thereafter, some properties of a fuzzy soft β-continuity are studied. Furthermore, we introduce and study the concepts of fuzzy soft almost (weakly) β-continuous functions, which are weaker forms of a fuzzy soft β-continuity. Also, the relationships between these classes of functions are specified with the help of some illustrative examples. Finally, we explore new types of fuzzy soft functions called, fuzzy soft β-irresolute (strongly β-irresolute, β-irresolute open, β-irresolute closed and β-irresolute homeomorphism) functions, and discuss some properties of them. Also, we show that fuzzy soft strongly β-irresolute → fuzzy soft β-irresolute → fuzzy soft β-continuity, but the converse may not be true.

We theoretically investigate advanced multi-functional integrated photonic filters formed by three waveguide coupled Sagnac loop reflectors (3WC-SLRs). By tailoring the coherent mode interference, the spectral response of the 3WC-SLR resonators is engineered to achieve diverse filtering functions with high performance. These include optical analogues of Fano resonances that yield ultrahigh spectral extinction ratios (ERs) and slope rates, resonance mode splitting with high ERs and low free spectral ranges, and classical Butterworth, Bessel, Chebyshev, and elliptic filters. A detailed analysis of the impact of the structural parameters and fabrication tolerances is provided to facilitate device design and optimization. The requirements for practical applications are also considered. These results theoretically verify the effectiveness of using 3WC-SLR resonators as multi-functional integrated photonic filters for flexible spectral engineering in diverse applications.

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.

Long unpunctuated texts containing complex linguistic sentences are a stumbling block to processing any low-resource languages. Thus, approaches that attempt to segment lengthy texts with no proper punctuation into simple candidate sentences are a vitally important preprocessing task in many hard-to-solve NLP applications. In this paper, we propose (PDTS) a punctuation detection approach for segmenting Arabic text, built on top of a multilingual BERT-based model and some generic linguistic rules. Furthermore, we showcase how PDTS can be effectively employed as a text tokenizer for unpunctuated documents (i.e., mimicking the transcribed audio-to-text documents). Experimental findings across two evaluation protocols (involving an ablation study and a human-based judgment) demonstrate that PDTS is practically effective in both performance quality and computational cost.

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.

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.

Symbolic pole/zero analysis is an important step when designing an analog operational amplifier. Generally, a simplified symbolic analysis of analog circuits suffers from NP-hardness, i.e., an exponential growth of the number of symbolic terms of the transfer function with the circuit size. In this study, we present a mathematical model combined with a heuristic-metaheuristic solution method for the symbolic pole/zero simplification in operational transconductance amplifiers (OTA). At first, the circuit is symbolically solved and an improved root splitting method is applied to extract symbolic poles/zeroes from the exact expanded transfer function. Then, a hybrid algorithm based on heuristic information and a metaheuristic technique using simulated annealing is performed for the simplification of the derived symbolic pole/zero expressions. The developed method has been tested on three analog OTAs. The obtained results show the effectiveness of the proposed method to achieve accurate simplified symbolic pole/zero expressions with the least complexity.

Intercalation of noble metals can produce giant Rashba-type spin-orbit splittings in graphene. The spin-orbit splitting more than 100 meV has not yet been achieved in graphene on a metallic or a semiconductor substrate. Here, we report the p-type graphene obtained by Pt intercalation of zero-layer graphene on SiC substrate. The spin splitting of ∼200 meV was observed at a wide range of binding energies. Comparing the results of theoretical studies of different models with the experimantal ones measured by spin-ARPES, XPS and STM methods, we came to the conclusion that inducing giant spin-orbit splitting requires not only a fairly close arrangement of graphene to Pt layer, but also the presence of graphene corrugation caused by non-flat Pt layer. This makes it possible to find a compromise between strong hybridization and increased spin-orbit interaction. In our case, this is achieved by forming Pt submonolayer ordered on a nanometer scale under graphene.

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.

In this paper, we first define the concepts of r-fuzzy soft α-open (semi-open and δ-open) sets on fuzzy soft topological spaces based on the article Aygunoglu et al. (Hacet. J. Math. Stat., 43 (2014), 193-208), and the relations of these sets with each other are established. In addition, we introduce the concepts of fuzzy soft δ-closure (δ-interior) operators, and study some properties of them. Also, the concept of r-fuzzy soft δ-connected sets is introduced and studied with help of fuzzy soft δ-closure operators. Thereafter, we define the concepts of fuzzy soft α-continuous (β-continuous, semi-continuous, pre-continuous and δ-continuous) functions, which are weaker forms of fuzzy soft continuity, and some properties of these functions along with their mutual relationships are discussed. Moreover, a decomposition of fuzzy soft α-continuity and a decomposition of fuzzy soft semi-continuity is obtained. Finally, as a weaker form of a fuzzy soft continuity, the concepts of fuzzy soft almost (weakly) continuous functions are defined, and some properties are specified. Additionally, we explore the notion of continuity in a very general setting called, fuzzy soft (L, M, N, O)-continuous functions and a historical justification is introduced.

In this study, the pristine MgO, MgO/CNT and Ni-MgO/CNT nanocomposites were processed by the impregnation and chemical vapour deposition methods and analyzed for hydrogen evolution (HER) via electrochemical water splitting process. Furthermore, effect of nickel on the deposited carbon was systematically elaborated in this study. The highly conductive carbon nanotubes (CNTs) deposited on the metal surface of the Ni-MgO nanocomposite heterostructure provides the robust stability and superior electrocatalytic activity. The optimized Ni-MgO/CNT nanocomposite exhibited hierarchical helical-shaped carbon nanotubes adorned on the surface of the Ni-MgO flakes, forming a hybrid metal-carbon network structure. The HER catalytic reaction was carried out in 1M alkaline KOH electrolyte, and the optimized Ni-MgO/CNT nanocomposite achieves the low 117 mV overpotential value (ɳ) at the 10 mA cm-2 and needs low 116 mV/dec Tafel value denoted Volmer-Heyrovsky pathway. Also, high electrochemical active surface area (ECSA) value of Ni-MgO/CNT nanocomposite acquires 515 cm2, which is favorable for the generation of abundant electro-active species and the prepared electrocatalyst durability was also performed by chronoamperometry test for prolonged duration of 20 h at 10 mA cm-2 and exhibits the good stability with 72% retention. Hence, obtained results demonstrated that the optimized Ni-MgO/CNT nanocomposite is highly active and cost-effective electrocatalyst towards hydrogen energy production.

Due to increasing concerns about global warming and energy crisis, intensive efforts have been made to explore renewable and clean energy sources. Single-atom metals and two-dimensional (2D) nanomaterials have attracted extensive attention in the fields of energy and environment because of their unique electronic structures and excellent properties. In this review, we sum-marize the state-of-art progress on the single-atom metal supported at 2D MoS2 (single-atom metal/2D MoS2) for electrochemical CO2 reduction and water splitting. First, we introduce the advantages of single-atom metal/2D MoS2 catalysts in the fields of electrocatalytic CO2 reduction and water splitting, followed by the strategies for improving electrocatalytic performances of single-atom metal/2D MoS2 hybrid nanomaterials and the typical preparation methods. Further, we discuss the important applications of the nanocomposites in electrocatalytic CO2 reduction and water splitting via some typical examples, particularly focusing on their synthesis routes, modification approaches, and physiochemical mechanisms for improving their electrocatalytic performances. Finally, our perspectives on the key challenges and future directions of exploring high-performance metal single-atom catalysts are presented based on recent achievements in the development of single-atom metal/2D MoS2 hybrid nanomaterials.

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.

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.

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.

In this manuscript, we first introduce some properties of r-fuzzy soft α-open sets in fuzzy soft topological spaces based on the manuscript Aygunoglu et al. (Hacet. J. Math. Stat. 2014, 43, 193-208). In addition, we define the concepts of fuzzy soft α-closure (α-interior) operators, and investigate some properties of them. Furthermore, the concept of r-fuzzy soft α-connected sets is defined and characterized with help of fuzzy soft α-closure operators. Thereafter, we introduce and study the concepts of fuzzy soft almost (weakly) α-continuous mappings, which are weaker forms of fuzzy soft α-continuous mappings, and we discuss some properties of fuzzy soft α-continuity. Moreover, we establish that fuzzy soft α-continuity → fuzzy soft almost α-continuity → fuzzy soft weakly α-continuity, but the converse may not be true. It is also we show that the composition is fuzzy soft almost α-continuous mapping if, is fuzzy soft α-continuous mapping and is fuzzy soft almost continuous mapping. Finally, some new types of compactness via r-fuzzy soft α-open sets are defined, and the relationships between them are examined.

Optical power splitters play a crucial role as the fundamental building blocks for many integrated optical devices. They should have low losses, broad bandwidth, and a high tolerance to fabrication errors. Adiabatic optical power splitters inherently possess these qualities while being compatible with foundry processes well-suited for mass-production. The long device lengths of adiabatic power splitters, however, are a limiting factor to achieve compact device sizes, which must be reduced. Here, we use a polynomial taper profile optimization algorithm to design 1×2 and 2×2 adiabatic power splitters with significantly shorter lengths than their adiabatic counterparts. The best performing 1×2 and 2×2 power splitters have 20 μm and 16 μm coupling lengths, respectively. Our designs have minimum feature sizes ranging from 140 nm to 200 nm, and our measurements averaged across 9 different chips show excellent consistency in performance for devices with 180 nm and 200 nm minimum features. Both the 1×2 and 2×2 adiabatic optical power splitters have excess losses less than 0.7 dB over a 100 nm bandwidth, with a standard deviation lower than 0.3 dB. Furthermore, our measurements show greater than 20 dB extinction ratios over 130 nm bandwidth. We also demonstrate the design of 1×2 power splitters with arbitrary splitting ratios, where splitting ratios ranging from 50:50 to 94:6 were achieved with standard deviations between 2% and 6%.

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.

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.

Posttraumatic stress disorder (PTSD) and/or specific PTSD symptoms may evoke disordered eating and unhealthy lifestyles, resulting in adverse cardiometabolic events (e.g., hypertension and obesity) in certain groups, which may implicate the treatment of this complex condition. The diagnostic criteria of PTSD have lately expanded beyond the three common symptoms (intrusion, avoidance, and hyperarousal). Simultaneously, four-, five-, and six-dimensional structures of the Impact of Event Scale-Revised (IES-R), a popular PTSD measure, seem to be more robust than the original three-dimension structure. Within the context of COVID-19, this instrumental study used a convenience sample of 58 dental healthcare workers (HCWs) from Russia (mean age = 44.1±12.2 years, 82.8% females) to examine the criterion and predictive validity of two IES-R structures: the IES-R3 and the IES-R6 (with the added symptoms of numbing, sleep disturbance, and irritability). The subscales of the two IES-R structures expressed good internal consistency, strong correlations with the PTSD Symptom Scale (PSS), hypertension diagnosis, and high body mass index (BMI). In receiver-operating characteristic (ROC) curve analysis, all IES-R models perfectly predicted the PSS (all area under the curve (AUC) >0.9, p values <0.001). The IES-R, both hyperarousal subscales, and the IES-R3 intrusion subscale significantly predicted high BMI. Both avoidance subscales and the IES-R3 intrusion subscale, not the IES-R, significantly predicted hypertension. In conclusion, both IES-R structures can reliably measure PTSD symptoms. The IES-R, hyperarousal, and intrusion may be credible criterion variables for predicting high BMI within PTSD while the intrusion and avoidance subscales may reflect the cardiovascular consequences associated with PTSD more reliably than the IES-R itself. The IES-R subscales may predict cardiometabolic adversities in PTSD, signifying a need for proper assessment of lifestyle and the application of dietary and exercise interventions in order to lower physical morbidity in PTSD. Replicating the study in larger samples, which comprise different physical and mental conditions from heterogenous cultural contexts is pivotal to validate the results (e.g., in specific groups such as those with confirmed traumatic exposure and comorbid mood dysfunction).

Paving blocks are concrete pieces placed in exposed places to the weather, which are sub-jected to loads and wear. Hence, quality control in the manufacture of paving blocks is es-sential to guarantee the properties and durability of the product in construction projects. In Ecuador, the requirements are described in the Ecuadorian technical standard "NTE INEN 3040", and tensile splitting strength is a fundamental requirement to guarantee product quality. It is analyzed using quality control measurements such as dimensions, the weight of the fresh paving block in the vibro-compacted process, and the percentage of water absorption in order to know how the variables influence and manage to predict the tensile splitting strength to avoid product non-conformity in advance, having a timely and better control of the manufacturing process. The data was obtained from a company that can produce 30 000 units per day of rectangular paving blocks with 6 cm thickness. Mul-tivariate models such as multiple linear regression, regression trees, random forests and neural networks are performed to predict the tensile splitting strength variable through two groups of predictors; the first group is the thickness mm, width mm, length mm, mass of fresh paving block g and percentage of water absorption %. The second group of pre-dictor variables is the density of the fresh paving block kg/m3 and the percentage of water absorption %. It is concluded that the multiple linear regression method performs better in predicting the first group of predictor variables with a mean square error (MSE) of 0.110086, followed by the neural network without hidden layers resulting in an MSE of 0.112198. The best method for the second set of predictors was the neural network with-out hidden layers with a mean square error ( MSE ) of 0.112402, closely followed by the multiple linear regression model with an MSE of 0.115044.

Water splitting technology is an efficient approach to generate hydrogen (H2) energy, which can well address the problems of environmental deterioration and energy shortage, as well as establishment of a clean and sustainable hydrogen economy powered by renewable energy sources due to the green reaction of H2 with O2. While the efficiency of H2 production by water splitting technology is intimately related with the reactions on electrode. Nowadays, the efficient electrocatalysts in water splitting reactions are the precious metal-based materials, i.e., Pt/C, RuO2 and IrO2. Ni (Co, Fe)-based layered double hydroxides (LDH) 2D materials are the typical non-precious metal-based materials in water splitting with advantages of low cost, excellent electrocatalytic performance and simple preparation methods, which exhibits a great potential for the substitution for precious metal-based materials. This review summarizes the recent progress of Ni (Co, Fe)-based LDH 2D materials for water splitting, which mainly focuses on discussing and analyzing the different strategies to modify LDH materials towards high electrocatalytic performance. We also discuss the recent achievements including their electronic structure, electrocatalytic performance, catalytic center, preparation process and catalytic mechanism. Furthermore, the characterization progress in revealing electronic structure and catalytic mechanism of LDH is highlighted in this review. Finally, we put forward some future perspectives related to design and explore advanced LDH catalysts in water splitting.

The photocatalytic hydrogen evolution reaction (HER) by water splitting has been studied, using catalysts based on TiO2 nanowires (TiO2NWs), which were synthesized by a hydrothermal procedure. This nanomaterial was subsequently modified by incorporating different loadings of gold nanoparticles (AuNPs) on the surface, previously exfoliated MoS2 nanosheets, and CeO2 nanoparticles (CeO2NPs). These nanomaterials, as well as the different synthesized catalysts, were characterized by electron microscopy (HR-SEM and HR-TEM), XPS, XRD, Raman, Reflectance and BET surface area. HER studies were performed in aqueous solution, under irradiation at different wavelengths, which were selected through the appropriate use of optical filters. The results obtained show that there is a synergistic effect between the different nanomaterials of the catalysts. The specific area of the catalyst, and especially the increased loading of MoS2 and CeO2NPs in the catalyst substantially improved the H2 production. Recyclability studies showed only a decrease in activity of approx. 7% after 15 cycles of use, which opens many possibilities regarding the potential use and scaling of these heterostructures in photocatalytic production of H2 from water.

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.

Photocatalytic technology based on specific band structure of semiconductors offers a promising way to solve the urgent energy and environmental issues in modern society. In particular, hydrogen production from water splitting over semiconductor photocatalysts attracts great attention owing to the clean source and application of energy, which highly depends on the performance of photocatalysts. Among the various photocatalysts, TiO2 has been intensively investigated and used extensively due to its outstanding photocatalytic activity, high chemical stability, non-toxicity and low cost. However, pure TiO2 has a wide band gap of approximately 3.2 eV, which limits its photocatalytic activity for water splitting to generate hydrogen only under ultraviolet light, excluding most of the inexhaustible sunlight for human beings. Fortunately, the band gap of semiconductors can be manipulated, in which introducing oxygen defects is one of the most effective measures to narrow the band gap of titanium oxides. This review starts out by the fundamentals of photocatalytic water splitting for hydrogen production over TiO2, discusses the latest progress in this field, and summarizes the various methods and strategies to induce oxygen defects in TiO2 crystals. Then, the next section outlines the modification approaches of oxygen-deficient titanium oxide (TiO2-δ) to further improve its photocatalytic performance. Finally, a brief summary and outlook of the researches on TiO2-δ photocatalysts for water splitting to produce hydrogen were presented.

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.

A model is proposed that describes the transfer of ions and the process of water dissociation in a system with a bipolar membrane and adjacent diffusion layers. The model considers the transfer of four types of ions: the cation and anion of salt and the products of water dissociation – hydrogen and hydroxyl ions. To describe the process of water dissociation, a model for accelerating the dissociation reaction with the participation of ionogenic groups of the membrane is adopted. The boundary value problem is solved numerically using COMSOL® Multiphysics 5.5 software. An analysis of the results of a numerical experiment shows that, at least in a symmetric electromembrane system, there is a kinetic limitation of the water dissociation process, apparently associated with the occurrence of water recombination reaction at the of the bipolar region. An interpretation of the entropy factor (β) is given as a characteristic length which shows the possibility of an ion that appeared as a result of the water dissociation reaction to be removed from the reaction zone without participating in recombination reactions.

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.

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.

This paper studies a multihop amplify-and-forward (AF) simultaneous wireless information and power transfer (SWIPT) relaying system. Each relaying node harvests energy using power splitting (PS) scheme from a part of its received signal to amplify and forward the rest the received signal to the next relay. Based on this system model and signal flow, we derived and solved the convex energy minimization problem with optimal PS ratio. The influence of processing cost was then investigated for the AF-SWIPT system with the decode-and-forward SWIPT as benchmark, where AF-SWIPT was found to be superior.