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Copyright of Journal of Chongqing University of Technology (Natural Science) is the property of Chongqing University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Abstract. In this paper, we establish some analogues of the Paley-Wiener theorem for the Hankel type transform of half-integer order less than -1 in weighted L²-spaces. These Paley-Wiener-type theorems give a description of the class of even entire functions of exponential type σ ≤ 1 under this transformation in terms of solutions from the corresponding spaces of some differential equations. [ABSTRACT FROM AUTHOR]

This paper focuses on the generalized Calogero–Bogoyavlenskii–Schiff equation to extract new complex solutions by using two analytical methods, namely, Bernoulli sub-equation function method, Modified exponential function method. For better understanding of physical meanings of solutions, simulations are reported by using a computational package program. Moreover, strain conditions for validity of complex solutions are also archived. Finally, a conclusion part completes the paper by mentioning the novelties of paper. [ABSTRACT FROM AUTHOR]

In this paper, we establish two new inequalities of the Masjed Jamei type for inverse trigonometric and inverse hyperbolic functions and apply them to obtain some refinement and extension of Mitrinović–Adamović and Lazarević inequalities. The inequalities obtained in this paper go beyond the conclusions and conjectures in the previous literature. Finally, we apply the main results of this paper to the field of mean value inequality and obtain two new inequalities on Seiffert-like means and classical means. [ABSTRACT FROM AUTHOR]

This paper aims to generate a universal well-fitted mathematical model to aid global representation of the spread of the coronavirus (COVID-19) disease. The model aims to identify the importance of the measures to be taken in order to stop the spread of the virus. It describes the diffusion of the virus in normal life with and without precaution. It is a data-driven parametric dependent function, for which the parameters are extracted from the data and the exponential function derived using multiplicative calculus. The results of the proposed model are compared to real recorded data from different countries and the performance of this model is investigated using error analysis theory. We stress that all statistics, collected data, etc., included in this study were extracted from official website of the World Health Organization (WHO). Therefore, the obtained results demonstrate its applicability and efficiency. [ABSTRACT FROM AUTHOR]

The functional relations between the modified couple stress theory (MCST) and the classical theory (CT) are derived and analyzed in detail for closed-form solutions of Timoshenko micro-beam. The results show that phenomenon of sharp change exists in the internal force fields at two ends of the micro-beam. This phenomenon is related to dimensionless material scale parameter l/h. The phenomenon at fixed end is different from that at free end because the shear force Q at fixed end cannot be degenerated from the MCST to the CT, which is proved from a mathematical point of view. What's more, the exponential functions in the closed-form solutions of the MCST are higher-order terms and can be ignored for the deflection and rotation when Poisson's ratio ν = 0–0.45, h/L = 1/100–1/8 and the l/h = 0–1. After exponential functions are omitted, except rotation of cantilever beam under bending moment M0, the concise solutions are acquired and error is very small. The size effects of the deflection and rotation can be calculated quickly without additional computing tools by the concise solutions. Some results obtained in this paper are compared with the published data in literatures, which prove the correctness of the results in this paper. [ABSTRACT FROM AUTHOR]

Nowadays, the mortality rate due to lung cancer increases rapidly worldwide as it can be classified only at the later stages. Early classification of lung cancer will help patients to take treatment and decrease the death rate. The limited dataset and diversity of data samples are the bottlenecks for early classification. In this paper, robust deep learning generative adversarial network (GAN) models are employed to enhance the dataset and to increase classification accuracy. The activation function plays an important feature‐learning role in neural networks. Since the existing activation functions suffer from various drawbacks such as vanishing gradient, dead neurons, output offset, etc., this paper proposes a novel activation function exponential mean saturation linear unit (EMSLU), which aims to speed up training, reduce network running time, and improve classification accuracy. The experiments were conducted using vanilla GAN, Wasserstein generative adversarial network, Wasserstein generative adversarial network with gradient penalty, conditional generative adversarial network, and deep convolutional generative adversarial network. Each GAN is tested with rectified linear unit, exponential linear unit, and proposed EMSLU activation functions. The results show that all the GAN's with EMSLU yields improved precision, recall, F1‐score, and accuracy. [ABSTRACT FROM AUTHOR]

Free transverse vibration of variable cross-section cantilever FG beams with nonlinear profiles is investigated in this paper. Four thickness functions, namely, linear, parabolic, sinusoidal, and exponential functions are assumed for variation of the cross-section of the beam. Linear and exponential grading rules for axially varying material properties are covered in this paper. The governing differential equation is solved using the weighted residual collocation method with the exact solution shape functions for the uniform beam as the trial functions. This choice for the trial functions showed an increase in the convergence rate. The Gauss–Legendre points are used as the collocation points to reduce the fluctuations in the convergence curve as usually encountered in the point collocation method. The effects of the taper parameter for all kinds of thickness functions on the natural frequencies are studied. The effects of various parameters, including taper parameter, profile, and grading function on the natural frequencies are investigated. Also, a series of finite element simulations are performed for comparison purposes. It is observed that the obtained results are in good agreement with the numerical simulations and available published data with vastly reduced computational cost as a result of using the collocation method. [ABSTRACT FROM AUTHOR]

This paper builds upon the research of Corwin and Knizel (2021) who proved the existence of stationary measures for the KPZ equation on an interval and characterized them through a Laplace transform formula. Bryc et al. (2022) found a probabilistic description of the stationary measures in terms of a Doob transform of some Markov kernels; essentially at the same time, another description connecting the stationary measures to the exponential functionals of the Brownian motion appeared in Barraquand and Le Doussal (2022). Our first main result clarifies and proves the equivalence of the two probabilistic description of these stationary measures. We then use the Markovian description to give rigorous proofs of some of the results claimed in Barraquand and Le Doussal (2022). We analyze how the stationary measures of the KPZ equation on [0,τ] behave at large scale, as τ goes to infinity. We also analyze the behaviour of the stationary measures of the KPZ equation on [0,τ] without rescaling, when τ goes to infinity. Finally, we analyze the measures on [0,∞) at large scale, which according to Barraquand and Le Doussal (2022) should correspond to stationary measures of a hypothetical KPZ fixed point on [0,∞). [ABSTRACT FROM AUTHOR]

As a critical mainstay of any industry, intellectual property rights protection is one of the most challenging issues of entertainment industries as they see their environment strongly reshaped by the proliferation of digital technologies. For the recording industry, the spread of digital music and platforms came with the exponential growth of music piracy - critically jeopardizing artists’ work protection and their ownership towards their projects. This paper examines the various ways to assure the efficient and sustainable protection of intellectual property rights in the music industry through contracts in order to find the best alternative to protect effectively artist's achievements. Our analysis will rely on several methodological tools such as root cause analysis and qualitative and quantitative methods in order to identify and understand better the causes, implications and potential alternatives to such an issue. This research indicates that the need for new and adapted business models within the music industry is required in order to assure a sustainable and efficient protection of artists ownership throughout their projects. [ABSTRACT FROM AUTHOR]

Purpose: Exponential growth in online video content makes viewing choice and video promotion increasingly challenging. While explicit recommendation systems have value, they inherently distract the user from normal behaviour and are open to numerous biases. To enhance user interest evaluation accuracy, the purpose of this paper is to comprehensively examine the relationship between implicit feedback and online video content, and reviews gender differentials in the interest indicated by a comprehensive set of viewer responses. Design/methodology/approach: This paper includes 200 useable observations based on an experiment of user interaction with the Youku platform (one of the largest video-hosting websites in China). Logistic regression was employed for its simple interpretation to test the proposed hypotheses. Findings: The findings demonstrate gender differentials in cursor movement behaviour, explainable via well-studied splits in personality, biological factors, primitive behaviour and emotion management. This work offers a solution to the sparsity of work on implicit feedback, contributing to the literature that combines explicit and implicit feedback. Practical implications: This study offers a launch point for further work on human–computer interaction, and highlights the importance of looking beyond individual metrics to embrace wider human traits in video site design and implementation. Originality/value: This paper links implicit feedback to online video content for the first time, and demonstrates its value as an interest capturing tool. By reviewing gender differentials in the interest indicated by a comprehensive set of viewer responses, this paper indicates how user characteristics remain critical. Consequently, this work signposts highly fruitful directions for both practitioners and researchers. [ABSTRACT FROM AUTHOR]

Prognostics play an increasingly important role in modern engineering systems for smart maintenance decision-making. In parametric regression-based approaches, the parametric models are often too rigid to model degradation signals in many applications. In this paper, we propose a Bayesian multiple-change-point (CP) modeling framework to better capture the degradation path and improve the prognostics. At the offline modeling stage, a novel stochastic process is proposed to model the joint prior of CPs and positions. All hyperparameters are estimated through an empirical two-stage process. At the online monitoring and remaining useful life (RUL) prediction stage, a recursive updating algorithm is developed to exactly calculate the posterior distribution and RUL prediction sequentially. To control the computational cost, a fixed-support-size strategy in the online model updating and a partial Monte Carlo strategy in the RUL prediction are proposed. The effectiveness and advantages of the proposed method are demonstrated through thorough simulation and real case studies. Note to Practitioners—Degradation signals have been widely used in determining the current health condition and estimate the remaining useful life (RUL) of a component or a system. Most of the existing prognostics utilize a parametric regression model to describe the evolution path of degradation signals for RUL prediction. The common functional forms of these models include simple linear, quadratic, and exponential functions. However, in many applications, the degradation signals show multiple-segment characteristics and the existing parametric forms are inadequate to capture the degradation trend. Motivated by such issue, this paper presents a multiple-change-point (CP) modeling approach, where the degradation signal is divided into several consecutive segments by CPs, and each segment is modeled by a unique parametric model. To capture the heterogeneity across different units, all the parameters, including the number and locations of CPs and model parameters of each segment, are assumed to be random variables following certain distributions. Then, we develop a statistical method to estimate these distributions using historical data. At the online monitoring stage, we develop an innovative updating algorithm to exactly calculate the closed forms of the posterior distributions of the latest CP, the current segment, and model parameters of the current segment. We also derive a closed form for the RUL distribution estimation. Later, several efficient approximation strategies are proposed to reduce the computational burden. Simulation studies and real case studies have shown that the proposed methodology has much better performance than those of existing approaches in handling degradation signals of multiple-segment characteristics. [ABSTRACT FROM AUTHOR]

Various factors should be considered in the modeling of DWC of repairable systems or products, including system structure, component failure processes, discounting methods, and the warranty policy itself. This paper presents discounted warranty cost (DWC) models for repairable series systems subject to Gamma and Mixed Exponential Failure Laws. In particular, a policy on a free repair warranty and a policy on a pro-rata guarantee are being studied. The impact of repair actions on the failure times of the components is assumed to be minimal, hence NHPPs is used to describe the failure processes. This paper considers two types of discounting methods: a continuous discount function and a discrete discount function. Expressions for both the expected value and the variance of DWC are obtained for Gamma and Mixed Exponential Failure Laws. The WRD was calculated for Gamma Failure Laws under application section. Further extension of this research is provided in the conclusion section. [ABSTRACT FROM AUTHOR]

Lutz developed a general theory of resource-bounded measurability and measure on suitable complexity classes C⊆ C (see Proceedings of the 13th IEEE Conference on Computational Complexity, pp. 236–248, ), where Cantor Space C is the class of all decision problems, and classes C include various exponential time and space complexity classes, the class of all decidable languages, and the Cantor space C itself. In this paper, a different general theory of resource-bounded measurability and measure on those complexity classes is developed. Our approach is parallel to the Carathéodory outer measure approach in classical Lebesgue measure theory. We shall show that many nice properties in the classical Lebesgue measure theory hold in the resource-bounded case also. The Carathéodory approach gives short and easy proofs of theorems in the resource-bounded case as well as in the classical case. The class of measurable sets in our paper is strictly larger than that of Lutz, and the two resource-bounded measures assign the same measure for a set if the set is measurable in the sense of Lutz. [ABSTRACT FROM AUTHOR]

To the transformation F(a(s)) = a(s)/ds, this paper brings out two kinds of ways to ascertain parameter d, one way, we let d be arithmetic average of class ration inverse, namely d1 = (Multiple line equation(s) cannot be represented in ASCII text). The other way, we let d be geometric average of class ration inverse, namely d2 = (Multiple line equation(s) cannot be represented in ASCII text). Through the close theory testifying, we find that the model given by this paper has white exponential law coincidence property, that is to say, if we build the model to the normal index, the result has not model error. At the same time, this paper points out, the request d > 1 is not appropriate to monotone decreasing series; even precision of model will decrease. [ABSTRACT FROM AUTHOR]

In order to investigate the characteristics of Trichel pulse in negative corona discharge, a corona discharge measurement system, and a simulation model are proposed. Pulse parameters fit by double exponential function are discussed in this paper. Effects of the magnitude, interval, crest time, and fall time of the pulse on the parameters are discussed for different applied voltages and radii of curvature of the needle electrode. Fitting functions under different conditions are also given in this paper. [ABSTRACT FROM PUBLISHER]

In this paper, we prove maximal exponential inequalities for a class of diffusion processes under certain conditions. The present results extend the well-known maximal inequalities of the power-type proved in the case of a Brownian motion, and in the geometric Brownian motion case. The method of proof is essentially based on explicit forms of optimal stopping problems related to those treated by Shepp and Shiryaev [Ann. Probab. Appl., 3 (1993), pp. 631-640], but considered here with a multiplicative reward functional. The key tool in the proof of one of our main results is a comparison principle for solutions of a system of first-order nonlinear differential equations. This is one of the novel features in this paper. [ABSTRACT FROM AUTHOR]

This paper proposes a novel exponential rational function method, a modification of the well-known exp-function method, to find exact solutions of the time fractional Cahn-Allen equation and the time fractional Phi-4 equation. The solution procedure is reduced to solve a system of algebraic equations, which is then solved by Wu's method. The results show that the present method is effective, and can be applied to other fractional differential equations. [ABSTRACT FROM AUTHOR]

This paper is a contribution to the argument that Engels's work remains topical and may provide us with the analytical tools necessary to approach contemporary manifestations of capitalist contradictions. Based on Engels's work on political economy (with emphasis on his contribution to the labour theory of value and the articulation of the law on the tendency of the rate of profit to fall) it will critically review the concept of "surveillance capitalism" as developed by Shoshana Zuboff, in order to explain central aspects of the process of digital surveillance. In particular, it will criticise the view expressed by Zuboff that surveillance capitalism constitutes a break with capitalism's past and can be tamed through an enhancement of democratic accountability and regulation. Marxist contributions to the critique of digital surveillance have already approached this phenomenon in a many-sided manner. This paper builds upon these contributions and suggests that the exponential growth of digital platforms can be explained as a direct result of the development of capitalist contradictions, especially the contradiction between productive forces and relations of production as expressed in the law of the falling rate of profit. [ABSTRACT FROM AUTHOR]

In this paper, we explore the Padovan numbers and polynomials, and define the Padovan polynomials matrix. We obtain its Binet-like formula and a sum formula. Subsequently, we derive the Padovan polynomials matrix series. Additionally, we establish the generating and exponential generating functions for the Padovan polynomials matrix. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the Fibonacci-sigmoid poly-nomials Sn,F (x) and the Fibonacci-sigmoid matrix Sn,F (x, F). Also, examples of the inverse of the Fibonacci-sigmoid matrix are presented. We factorize the following matrix by the Fibonacci matrix. [ABSTRACT FROM AUTHOR]

We consider the problem of recovering the superposition of |$R$| distinct complex exponential functions from compressed non-uniform time-domain samples. Total variation (TV) minimization or atomic norm minimization was proposed in the literature to recover the |$R$| frequencies or the missing data. However, it is known that in order for TV minimization and atomic norm minimization to recover the missing data or the frequencies, the underlying |$R$| frequencies are required to be well separated, even when the measurements are noiseless. This paper shows that the Hankel matrix recovery approach can super-resolve the |$R$| complex exponentials and their frequencies from compressed non-uniform measurements, regardless of how close their frequencies are to each other. We propose a new concept of orthonormal atomic norm minimization (OANM), and demonstrate that the success of Hankel matrix recovery in separation-free super-resolution comes from the fact that the nuclear norm of a Hankel matrix is an orthonormal atomic norm. More specifically, we show that, in traditional atomic norm minimization, the underlying parameter values must be well separated to achieve successful signal recovery, if the atoms are changing continuously with respect to the continuously valued parameter. In contrast, for the OANM, it is possible the OANM is successful even though the original atoms can be arbitrarily close. As a byproduct of this research, we provide one matrix-theoretic inequality of nuclear norm, and give its proof using the theory of compressed sensing. [ABSTRACT FROM AUTHOR]

In this paper we establish a natural extension of the Wirtinger inequality to the case of complex integral of analytic functions. Applications related to the trapezoid inequalities are also provided. Examples for logarithmic and exponential complex functions are given as well. [ABSTRACT FROM AUTHOR]

The action of a right-angled Artin group on its extension graph is known to be acylindrical because the cardinality of the so-called r-quasi-stabilizer of a pair of distant points is bounded above by a function of r. The known upper bound of the cardinality is an exponential function of r. In this paper we show that the r-quasi-stabilizer is a subset of a cyclic group and its cardinality is bounded above by a linear function of r. This is done by exploring lattice theoretic properties of group elements, studying prefixes of powers and extending the uniqueness of quasi-roots from word length to star length. We also improve the known lower bound for the minimal asymptotic translation length of a right-angled Artin group on its extension graph. [ABSTRACT FROM AUTHOR]

Construction of absorbing boundary conditions (ABCs) for nonlocal models is generally challenging, primarily due to the fact that nonlocal operators are commonly associated with volume constrained boundary conditions. Moreover, application of Fourier and Laplace transforms, which are essential for the majority of available methods for ABCs, to nonlocal models is complicated. In this paper, we propose a simple method to construct accurate ABCs for peridynamic scalar wave‐type problems in viscous media. The proposed ABCs are constructed in the time and space domains and are of Dirichlet type. Consequently, their implementation is relatively simple, since no derivatives of the wave field are required. The proposed ABCs are derived at the continuum level, from a semi‐analytical solution of the exterior domain using harmonic exponential basis functions in space and time (plane‐wave modes). The numerical implementation is done using a meshfree collocation approach employed within a boundary layer adjacent to the interior domain boundary. The modes satisfy the peridynamic numerical dispersion relation, resulting in a compatible solution of the interior region (near‐field) with that of the exterior region (far‐field). The accuracy and stability of the proposed ABCs are demonstrated with several numerical examples in two‐dimensional unbounded domains. [ABSTRACT FROM AUTHOR]

In this paper, we statistically analyzed substorm activity at auroral latitudes for 2007–2020 and its relationship with magnetic disturbances at middle latitudes using the INTERMAGNET, SuperMAG, and IMAGE magnetometer data. The appearance and development of magnetic disturbances at auroral latitudes was monitored by the IL index (similar to the AL index, but calculated according to IMAGE data). For the 2007–2020 period, events that were observed near the meridian of the IMAGE network, in the night sector (2103 MLT), were selected. Two samples of events were used: (1) IL < –200 nT for at least 10 min, with an additional criterion for the presence or absence of positive bays at the Panagyurishte station in Bulgaria, and (2) isolated substorms observed on the IMAGE meridian according to the list of Ohtani and Gjerloev (2020). The distributions of the IL index, as well as the empirical and theoretical cumulative distribution functions, are obtained, and the of the occurrence of extreme events are also estimated. It is shown that, in general, the IL distributions are described well by exponential functions, and out of all events, events accompanied by mid-latitude positive bays were observed in ~65% of cases while their fraction increased with increasing disturbance intensity. Events with positive bays at midlatitudes of MPB and isolated substorms were better described by the Weibull distribution for extreme events. From both distributions, annual and semi-annual variations were identified: annual variations have a summer minimum and a winter maximum, and semi-annual variations have maxima near the equinoxes, which is most likely due to the Russell-McPherron effect. The semi-annual variation is also shown to be more pronounced for events with accompanying mid-latitudinal positive bays. [ABSTRACT FROM AUTHOR]

The variable‐order fractional (VOF) operator has been extensively employed to depict complex physical phenomena of viscoelastic materials, during which the reasonable form of the proper variable‐order (VO) function will significantly affect the applicability and accuracy of proposed fractional model. To this regard, this work aims to provide a technical guidance for VO function selection in VOF viscoelastic modeling. In this paper, we develop a VOF model based on the classical Zener model, the suitable VO function form and the applicability of VOF model are investigated by means of characterizing the stress relaxation and creep recovery behaviors, in which the monotonicity of VO functions (decreasing or increasing) are discussed in detail. The results demonstrate that the stress relaxation and creep recovery responses have a realistic physical meaning only when the VOF rheological model with a monotonically decreasing VO function. Furthermore, three definitions of VOFD are also considered to determine the optimal VO function form and the reasonability of the proposed model is validated by fitting the experimental data of polymer matric materials. The analysis found that the decreasing exponential VO function exhibits good prospects in describing the time‐dependent behaviors, and it was found that the V2 and V3 definition types performed better. The results also show that the proposed model has unique advantage compared to the other existing viscoelastic models. Finally, the proposed VOF model is employed to predict the viscoelastic behavior to test the model's predictive ability. [ABSTRACT FROM AUTHOR]

Interval type-2 trapezoidal fuzzy (IT2TrF) number is a powerful tool to depict fuzzy information. Information measures methods have received more and more attention in recent years as they play an important role in decision-making theory. A new multi-attribute decision-making (MADM) method supported by IT2TrF information measures is investigated in this paper under the IT2TrF information environment. Firstly, three axiomatic definitions of IT2TrF information measures are introduced, which include information entropy, similarity measure and cross-entropy. Secondly, with the help of the exponential function, we formulate some information measure formulas, which are followed by the proofs that the exponential entropy, exponential similarity measure and exponential cross-entropy fit the three axiomatic definitions. Subsequently, a novel IT2TrF MADM method is designed, in which the IT2TrF exponential entropy and cross-entropy are utilized to generate the attribute weights, the IT2TrF exponential similarity measure is employed to obtain the closeness degree of the ideal solution and derive the most satisfying solution. Lastly, we provide a numerical example of corporate investment to demonstrate the applicability and feasibility of the proposed MADM method. The robustness and merits of the developed MADM method are highlighted by the comparative analysis. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the tampered random variable (TRV) modeling in multiple step-stress life testing experiments. Here τ 1 < τ 2 < ... < τ k − 1 be (k − 1) prespecified time points and s 1 , s 2 , ... , s k be k prefixed stress levels with si being the stress level in force during the time interval [ τ i − 1 , τ i) for i = 1 , ... , k with τ 0 = 0 and τ k = ∞. We define the tampered random variable T TRV (k) in multiple step-stress scenario and calculate the PDF, CDF, and Hazard rate for the proposed tampered variable T TRV (k) . We derive a general expression for the expectation of T TRV (k) under different number k of stress levels and also obtain some results on stochastic ordering for different k. All these results are obtained under arbitrary baseline (under normal stress condition with stress level s1) life distribution. In particular, we consider exponential distribution with mean θ and Weibull distribution with scale parameter λ and shape parameter α for specific expressions. We also prove some results on equivalence of the TRV modeling with the two other existing models for step-stress life testing, namely, cumulative exposure and tampered failure rate. Finally, we consider some variations of the modeling approach for T TRV (k) to include incorporation of the stress levels, discrete life time, bivariate or multivariate life times. [ABSTRACT FROM AUTHOR]

Membrane computing is a natural computing branch inspired by the structure of biological cells. The mathematical abstract model of a membrane computing system is called a P System, which is one of the main topics in membrane computing research for the design and verification of a P System. Integer factorization is still a world-class problem and a very important research direction. If a fast method can be found to solve the integer factorization problem, several important cryptographic systems including the RSA public key algorithm will be broken. The aim of this paper is to design a P System capable of implementing integer decomposition, taking advantage of the characteristics of parallelism of P Systems. We construct a process with a main goal to study the modal exponential function f(x) = ax mod N and explore the possible periodic behavior for different values of a. We attempt to compute nontrivial prime factors by the period found and constrain the operation of the P System in polynomial time. [ABSTRACT FROM AUTHOR]

In this paper, we used the generalized exponential rational function approach to extract a collection of different optical wave solutions to the highly nonlinear Schrödinger equation in (3+1) dimensions, which illustrates the formation of ultra-short optical pulses in highly nonlinear media. The applied approach is straightforward and robust, and it can extract various types of optical soliton solutions into a single framework. Dark and bright solitons, singular-form solitons, periodic waves, mixed-form solitons, and rational, exponential, and complex solutions are among the outcomes that are significant to diverse applied scientific applications in nonlinear optics, and nonlinear sciences. Finally, several soliton solutions in 3D, 2D and contour graphics, as well as the interactions of evolutionary waves, are presented to better understand the changing dynamics of soliton wave solutions in the model under consideration. The findings of this study are more beneficial, useful, and favorable in the real-world applications of nonlinear optics, optical communications, and optical fibers. [ABSTRACT FROM AUTHOR]

The paper is intended to investigate of the extended time fractional (2+1) dimensional Zakharov–Kuznetsov (tf-ZK) equation with the sense of Riemann–Liouville (R–L) fractional derivative operator. Utilizing the planar dynamical system theory, determined the equilibrium points for different cases and properties revealed. We also show phase portraits of propagating wave solutions for taking the some parameters with special values. At the same time, we employ the fractional complex transformation for the generalized exponential rational function method (GERFM) and sub equation method, we construct abundant exact solitary wave, kink wave, refracted wave and periodic wave solutions. Taking the special values for some parameters interesting figures of traveling wave solutions were depicted. [ABSTRACT FROM AUTHOR]

This paper focuses on simulating the collision breakage process between the agglomerate and hammer in a hammer crusher by the discrete element method (DEM) as the interaction between particles. This enables us to consider the energy change in the collision breakage process of the hammer. The agglomerate model is built by using the EDEM 2.7 software according to the principle of closest packing in crystallography, while the hammer model is modeled into an assembly of different sizes of spherical particles to make the collision breakage process between the agglomerate and hammer as the one of interrelation of particles. With these models, we mainly investigated collision force, collision impulse, energy breaking agglomerate, and the relationship between the specific breakage energy and agglomerate damage ratio. The collision force is represented as Gaussian function, the collision impulse is represented by the function of the mass ratio of agglomerate to hammer and the product of agglomerate mass and collision velocity, and the relationship between the specific breakage energy and agglomerate damage ratio is represented by exponential function. Finally, it can be seen from this study that, when crushing the agglomerate by hammer impact, it is necessary to increase the specific breakage energy by 1.75 times in order to increase the agglomerate damage ratio from 85% to 90% but 2.13 times in order to increase 95%. The proposed method can be used for the further development and design of the various types of crusher. [ABSTRACT FROM AUTHOR]

It is known that discrete analogs of differential operators play an important role in constructing optimal quadrature, cubature, and difference formulas. Using discrete analogs of differential operators, optimal interpolation, quadrature, and difference formulas exact for algebraic polynomials, trigonometric and exponential functions can be constructed. In this paper, we construct a discrete analogue D m (h β) of the differential operator d 2 m d x 2 m + 2 d m d x m + 1 in the Hilbert space W 2 (m , 0) . We develop an algorithm for constructing optimal quadrature formulas exact on exponential-trigonometric functions using a discrete operator. Based on this algorithm, in m = 2 , we give an optimal quadrature formula exact for trigonometric functions. Finally, we present the rate of convergence of the optimal quadrature formula in the Hilbert space W 2 (2 , 0) for the case m = 2 . [ABSTRACT FROM AUTHOR]

Copyright of Hydrogeology & Engineering Geology / Shuiwendizhi Gongchengdizhi is the property of Hydrogeology & Engineering Geology Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The objective of the current paper is to study and extend the exponential-polynomial-closure (EPC) method in analyzing the non-stationary response probabilistic solutions of nonlinear stochastic oscillators excited by combined deterministic harmonic and Gaussian white noise excitations. The probabilistic solution of the non-stationary responses of nonlinear stochastic oscillator is expressed as an exponential function of polynomial with time-variant coefficients and then the Fokker–Planck–Kolmogorov equation is solved approximately. Two validation examples are presented. The results obtained by Monte Carlo simulation (MCS) and EPC method are presented to show their good agreement, which confirms the effectiveness of the EPC method for the probabilistic solutions to nonlinear stochastic oscillators. The advantage of the EPC method for analyzing the oscillators with strong nonlinearities is investigated by comparison with Equivalent Linearization method. Furthermore, compared with MCS, the computational efficiency by using the EPC method is increased by about 56 times in the first example and 44 times in the second example. [ABSTRACT FROM AUTHOR]

This paper considers the fractional order dual-mode nonlinear Schrödinger equation (FDMNLSE) with cubic law nonlinearity. The FDMNLSE interprets the concurrent propagation of two-mode waves instead of a single wave. Throughout this work, the fractional derivative is given in terms of time and space conformable sense. The FDMNLSE introduces three physical parameters: dispersive factor, phase speed, and nonlinearity. This new model has many applications in nonlinear physics and fiber optics. We will use two methods to get new optical solutions: the generalized exponential rational function method (GERFM) and the functional variable method (FVM). Using the GERFM, we get unique wave solutions in the forms of shock wave solutions, singular soliton solutions, singular periodic waves, and exponential function solutions. Thanks to FVM, we reach bright optical soliton solutions, singular optical soliton solutions, and periodic singular wave solutions, and the restraint conditions for solutions are reported. The analytical outcomes are supplemented with numerical simulations of the got solutions to understand the dynamic behavior of obtained solutions. The results of this study may have a high-importance application while handling the other nonlinear partial differential equations (NLPDEs). [ABSTRACT FROM AUTHOR]

This paper studies the (1 + 1) -dimensional nonlinear Schrödinger equation via polynomial law of nonlinearity which arises in nonlinear optical fibers and Bragg gratings. The envelope solitons as a entire are separated into two types: dark and bright solitons, which exist in the anomalous and normal dispersion regions, respectively. Grey and black optical solitons of the stated model are reported through appropriate complex envelope ansatz solution. With the usage of Chupin Liu's theorem to the grey and black solitons, we evaluate new categories of combined optical soliton solutions. In addition, propagation behaviours for homoclinic breathers, multiwaves and M-shaped rational solitons are analytically examined via logarithmic transformation with ansatz functions approach. Multiwave solitons are reported by using three-waves technique. Furthermore two kinds of interactions for M-shape soliton through exponential functions are examined. [ABSTRACT FROM AUTHOR]

This paper studies the consensus tracking problem based on optimised backstepping technique for multiagent systems with power exponential functions and the privacy protection. Under the optimised backstepping technique, the controllers with power functions are designed by utilising the reinforcement learning strategy. Moreover, the synchronisation error converges to a predetermined region within a user-defined settling time by utilising a speed function. To ensure the safety of communication, the privacy protection is applied to multiagent systems, which effectively prevent information exposure. Based on Lyapunov stability theory, the tracking errors of the system with power exponential functions converge to a predetermined region, and a simulation example proves the feasibility of the proposed strategy. [ABSTRACT FROM AUTHOR]

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Let A be an expansive dilation on Rn, and p(·): Rn →(0, ∞) be a variable exponent function satisfying the globally log-Hölder continuous condition. Let HAP(·) A (Rn) be the variable anisotropic Hardy space introduced by Liu [15]. In this paper, the authors obtain that the Fourier transform of f ∈ HAP(·)(Rn) coincides with a continuous function F on Rn in the sense of tempered distributions. As applications, the authors further conclude a higher order convergence of the continuous function F at the origin and then give a variant of the Hardy-Littlewood inequality in the setting of anisotropic Hardy spaces with variable exponents. [ABSTRACT FROM AUTHOR]

In this paper, we generalize a sequence of positive linear operators introduced by Ismail and May and we study some of their approximation properties for different classes of continuous functions. First, we estimate the error of approximation in terms of the usual modulus of continuity and the second-order modulus of Ditzian and Totik. Then, we characterize the bounded functions that can be approximated uniformly by these new operators. In the last section, we obtain the most important results of the paper. We give the complete asymptotic expansion for the operators and we deduce a Voronovskaya-type theorem, results that hold true for smooth functions with exponential growth. [ABSTRACT FROM AUTHOR]

In order to improve the quality of edge details of remote sensing image and solve the problem of large-scale holes and edge loss in remote sensing image, a new hole filling and optimization algorithm of remote sensing image based on bilateral filtering is proposed in this paper. The compensation function of similarity discrimination and Thiele continued fraction approximate exponential function are used to improve the traditional bilateral filtering algorithm. After the threshold is determined by histogram, the image is binarized to generate hole mask. The constraint term is added to the improved bilateral filtering algorithm for further optimization. According to the characteristics that pixels with the same color have the same gray value in a certain range, the hole area of remote sensing image is filled. The experimental results show that the algorithm can accurately fill the holes in the remote sensing image, not only restore the edge of the image, but also maintain the smoothness of the image. It has good filling performance, high image quality after optimization, image signal-to-noise ratio remains above 32 dB, and time complexity is low. [ABSTRACT FROM AUTHOR]

Water resources management is dependent on wet and dry spells occurrences in an alternative manner. Therefore, information about their probabilistic occurrence frequencies and statistical parameters are the most required quantities for optimum and well-balanced operations for water demand. Among the most important dry spells are the meteorological (precipitation) and hydrological (runoff, stream flow, reservoir level, ground water level, etc.) drought occurrences and their future expectations under a certain level of risk (exceedance probability) or return period, which is the inverse of the risk. Firstly, this paper presents detection of wet and dry spell parameters among which are the duration, maximum surplus or deficit, magnitude, and intensity. Secondly, a set of beneficial charts is presented in the new graphical form for each dry (wet) spell characteristic versus different risk levels (0.50, 0.20, 0.10, 0.04 0.02, 0.01, 0.004 and 0.002) corresponding to return periods (2-year, 5-year, 10-year, 25-year, 50-year, 100-year, 250-year and 500-year). These applications of the methodology are presented for New Jersey Statewide annual precipitation and Danube River annual discharge records each with more than 100 years records. Finally, it is found that the mathematical relationship between each wet and dry spell parameter and the return periods abide with exponential function, which appears on semi-logarithmic papers as straight lines. Consequently, it can be generalized for the study area that any drought (wet) parameters variation with the return period appears as exponential function for hydro-meteorological records. [ABSTRACT FROM AUTHOR]

The classical theory of collision induced emission (CIE) from pairs of dissimilar rare gas atoms was developed in Paper I [D. Reguera and G. Birnbaum, J. Chem. Phys. 125, 184304 (2006)] from a knowledge of the straight line collision trajectory and the assumption that the magnitude of the dipole could be represented by an exponential function of the inter-nuclear distance. This theory is extended here to deal with other functional forms of the induced dipole as revealed by ab initio calculations. Accurate analytical expression for the CIE can be obtained by least square fitting of the ab initio values of the dipole as a function of inter-atomic separation using a sum of exponentials and then proceeding as in Paper I. However, we also show how the multi-exponential fit can be replaced by a simpler fit using only two analytic functions. Our analysis is applied to the polar molecules HF and HBr. Unlike the rare gas atoms considered previously, these atomic pairs form stable bound diatomic molecules. We show that, interestingly, the spectra of these reactive molecules are characterized by the presence of multiple peaks. We also discuss the CIE arising from half collisions in excited electronic states, which in principle could be probed in photo-dissociation experiments. [ABSTRACT FROM AUTHOR]

This paper is a response to the comment by Lynn et al. (2020, https://doi.org/10.1029/2019JA027575) on the paper by Jiang, Yang, et al. (2019, https://doi.org/10.1029/2018JA026040). Although we disagree with Lynn et al. (2020), nevertheless, we do thank them for their comments, since they have given us the opportunity to revisit and clarify some points. In Jiang, Yang, et al. (2019, https://doi.org/10.1029/2018JA026040) and this reply, we found that the F2 layer stratification induced by gravity waves/TIDs can last for about 40 min. The shape of the F2 layer stratification is similar to the F3 layer referred to by Lynn et al. (2020). However, the evolution of the F2 layer stratification by Jiang, Yang, et al. (2019, https://doi.org/10.1029/2018JA026040) is different from the F3 layer referred to in the comment by Lynn et al. (2020). Key Points: The F2 layer stratification induced by gravity waves/TIDs can last for about 40 minThe shape of the F2 layer stratification by gravity waves/TIDs is similar to the traditional F3 layer, but their evolutions are differentIt might be still suitable to call the type‐1 Puer observations the F2 layer stratification according to its shape [ABSTRACT FROM AUTHOR]

Background: Scientific activity for 3D bioprinting has increased over the past years focusing mainly on fully functional biological constructs to overcome issues related to organ transplants. This research performs a scientometric analysis on bioprinting based on a competitive technology intelligence (CTI) cycle, which assesses scientific documents to establish the publication rate of science and technology in terms of institutions, patents or journals. Although analyses of publications can be observed in the literature, the identification of the most influential authors and affiliations has not been addressed. This study involves the analysis of authors and affiliations, and their interactions in a global framework. We use network collaboration maps and Betweenness Centrality (BC) to identify of the most prominent actors in bioprinting, enhancing the CTI analysis. Results: 2088 documents were retrieved from Scopus database from 2007 to 2017, disclosing an exponential growth with an average publication increase of 17.5% per year. A threshold of five articles with ten or more cites was established for authors, while the same number of articles but cited five or more times was set for affiliations. The author with more publications was Atala A. (36 papers and a BC = 370.9), followed by Khademhosseini A. (30 documents and a BC = 2104.7), and Mironov (30 documents and BC = 2754.9). In addition, a small correlation was observed between the number of collaborations and the number of publications. Furthermore, 1760 institutions with a median of 10 publications were found, but only 20 within the established threshold. 30% of the 20 institutions had an external collaboration, and institutions located in and close to the life science cluster in Massachusetts showed a strong cooperation. The institution with more publications was the Harvard Medical School, 61 publications, followed by the Brigham and Women's hospital, 46 papers, and the Massachusetts Institute of Technology with 37 documents. Conclusions: Network map analysis and BC allowed the identification of the most influential authors working on bioprinting and the collaboration between institutions was found limited. This analysis of authors and affiliations and their collaborations offer valuable information for the identification of potential associations for bioprinting researches and stakeholders. [ABSTRACT FROM AUTHOR]