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.

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.

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.

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 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.

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.

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.

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.

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.

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.

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.

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

In 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.

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 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 ).

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.

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.

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.

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.

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].

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.

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.

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.

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'.

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

This 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.