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For nondestructive assessment of insulation aging in power transformer, dielectric response technology is usually used to evaluate the oil-paper insulation aging. In this paper, a quantitative evaluation method of insulation aging based on Davidson-Cole model is proposed. The oil-paper insulation equivalent Debye model parameters of transformer are extracted by exponential function fitting. According to the complex permittivity of oil-paper insulation, the parameters of Davidson-Cole model are extracted by fitting algorithm. Under laboratory conditions, accelerated thermal aging test are carried out. The quantitative relationship between Davidson-Cole model parameters and aging of oil-paper insulation is analyzed. The experimental results show that the Davidson-Cole model parameters are directly related to the aging time. It is found that the parameters β and Δε of the Davidson-Cole model gradually decreases and the parameter τ gradually increases with the polymerization degree of oil-impregnated paper. Therefore, according to the quantitative characterization of the model parameters, the aging of transformer oil-paper insulation can be effectively evaluated, which is helpful to realize the nondestructive testing of polymerization degree in oil-impregnated pressboard (paper) power transformer. [ABSTRACT FROM AUTHOR]

This article has two main parts. In the first part we show that some of the basic theory of generalized polynomials on commutative semi-groups can be extended to all semigroups. In the second part we show that if a sub-semigroup S of a group G generates G in the sense that G = S · S−1, then a generalized polynomial on S with values in an Abelian group H can be extended to a generalized polynomial on G into H. Finally there is a short discussion of the extendability of exponential functions and generalized exponential polynomials. [ABSTRACT FROM AUTHOR]

The accuracy of insulation defect diagnosis based on the dielectric spectrum response is severely influenced by temperature for oil-impregnated paper bushing. The dielectric loss (tan δ) mathematical model with a temperature–frequency factor to restrict the application of the frequency domain dielectric spectrum (FDS) for insulation diagnosis is not clear. In this paper, five temperatures are selected to study the frequency temperature characteristic of the FDS and polarization current for oil-impregnated paper bushing. The experimental results show that the temperature has different effects on the lower frequency (0.001 Hz–1 Hz) and higher frequency (1000 Hz–10 kHz) of FDS. With the increasing temperature, the lower frequency tan δ of 1 mHz–1 Hz shows a better pattern of exponential growth, while the higher frequency tan δ at 1 kHz–10 kHz shows the declining law with the rising temperature. With the increasing temperature, the polarization current shows a better pattern of exponential growth, while resistance obviously shows the declining law of the exponential pattern. The FDS curve of oil-impregnated paper bushings can be amended by the mathematical model of tan δ for the dielectric response on site for accuracy diagnosis. [ABSTRACT FROM AUTHOR]

Abstract: The citation distribution of papers of selected individual authors was analyzed using five mathematical functions: power-law, stretched exponential, logarithmic, binomial and Langmuir-type. The former two functions have previously been proposed in the literature whereas the remaining three are novel and are derived following the concepts of growth kinetics of crystals in the presence of additives which act as inhibitors of growth. Analysis of the data of citation distribution of papers of the authors revealed that the value of the goodness-of-the-fit parameter R 2 was the highest for the empirical binomial relation, it was high and comparable for stretched exponential and Langmuir-type functions, relatively low for power law but it was the lowest for the logarithmic function. In the Langmuir-type function a parameter K, defined as Langmuir constant, characterizing the citation behavior of the authors has been identified. Based on the Langmuir-type function an expression for cumulative citations L relating the extrapolated value of citations l 0 corresponding to rank n =0 for an author and his/her constant K and the number N of paper receiving citation l ≥1 is also proposed. [Copyright &y& Elsevier]

Electrowetting display (EWD) is a new type of paper-like reflective display based on colored oil, which has gradually become one of the most potential electronic papers with low power consumption, fast response, and full color. However, oil backflow can occur in EWDs, which makes it difficult to maintain a stable aperture ratio. In order to improve the stability of the aperture ratio of EWDs, a new driving waveform was proposed based on analyzing the phenomenon of oil backflow. The driving waveform was composed of a shrinking stage and a driving stage. Firstly, a threshold voltage of oil splitting was calculated by analyzing the luminance curve of EWDs, which were driven by different direct current (DC) voltages. Then, an exponential function waveform, which increased from the threshold voltage, was applied to suppress oil splitting. Finally, a periodic signal combined with a reset signal with a DC signal was applied during the driving stage to maintain a stable aperture ratio display. Experimental results showed that the charge trapping effect could be effectively prevented by the proposed driving waveform. Compared with an exponential function waveform, the average luminance value was increased by 28.29%, and the grayscale stability was increased by 13.76%. Compared to a linear function waveform, the aperture ratio was increased by 10.44% and the response time was reduced by 20.27%. [ABSTRACT FROM AUTHOR]

The medical field has witnessed an exponential growth of wearable devices mainly due to the advancement in wireless communication and antenna technology. There is a demand for wearable antennas, which are lightweight, flexible, and ease of integration into the fabric which suits on-body applications. Therefore, this work presents the design, fabrication, and analysis of two microstrip antennas using denim cloth and stacked photo paper as substrate material. The novelty of these antennas is the use of silver fabric as ground and radiating patch-conducting layer, which has resulted in significant improvement in overall antenna performance. It is observed that our fabricated antennas have exhibited a gain of 8.71 dB with VSWR of 1.32 for denim and gain of 2.45 dB with VSWR of 1.03 for photo paper substrates respectively. [ABSTRACT FROM AUTHOR]

Over the past three decades, insights into the role of the cerebellum in emotional processing have substantially increased. Indeed, methodological refinements in cerebellar lesion studies and major technological advancements in the field of neuroscience are in particular responsible to an exponential growth of knowledge on the topic. It is timely to review the available data and to critically evaluate the current status of the role of the cerebellum in emotion and related domains. The main aim of this article is to present an overview of current facts and ongoing debates relating to clinical, neuroimaging, and neurophysiological findings on the role of the cerebellum in key aspects of emotion. Experts in the field of cerebellar research discuss the range of cerebellar contributions to emotion in nine topics. Topics include the role of the cerebellum in perception and recognition, forwarding and encoding of emotional information, and the experience and regulation of emotional states in relation to motor, cognitive, and social behaviors. In addition, perspectives including cerebellar involvement in emotional learning, pain, emotional aspects of speech, and neuropsychiatric aspects of the cerebellum in mood disorders are briefly discussed. Results of this consensus paper illustrate how theory and empirical research have converged to produce a composite picture of brain topography, physiology, and function that establishes the role of the cerebellum in many aspects of emotional processing. [ABSTRACT FROM AUTHOR]

In citation networks, the content relativity of papers is a precondition of engendering citations, which is hard to model by a topological graph. A geometric graph is proposed to predict some features of the citation networks with exponentially growing papers, which addresses the precondition by using coordinates of nodes to model the research contents of papers, and geometric distances between nodes to diversities of research contents between papers. Citations between modeled papers are drawn according to a geometric rule, which addresses the precondition as well as some other factors engendering citations, namely academic influences of papers, aging of those influences, and incomplete copying of references. Instead of cumulative advantage of degree, the model illustrates that the scale-free property of modeled networks arises from the inhomogeneous academic influences of modeled papers. The model can also reproduce some other statistical features of citation networks, e.g. in- and out-assortativities, which show the model provides a suitable tool to understand some aspects of citation networks by geometry. [ABSTRACT FROM AUTHOR]

The subject of the paper is the modelling of multi-bolted connections that are at the pretensioning stage. Taking a systematic approach to the modelling issue, the connection was treated as a composite of four subsystems: a bolt set, a pair of joined elements and a contact layer between them. The first part of the paper describes experimental studies to determine the contact stiffness of a pair of elements separated from an exemplary asymmetric multi-bolted connection. The normal loading and unloading direction of the contact joint was considered. The tests were performed with the use of an INSTRON 8850 servo-hydraulic testing machine equipped with an extensometer. A normal stiffness characteristic in the form of an exponential function was proposed for the tested contact joint. It will be applied in the second part of the paper, in which finite element modelling of the multi-bolted connection will be presented. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we investigated the influences of the age of papers on the preferential attachment on the basis of three actual citation networks. We found that the time dependence of the attachment rate follows a uniform exponentially decreasing function, , in different citation networks. Younger papers are more likely to be cited by new ones than older papers. On the basis of the aging influences, we modified the expression for the preferential attachment, to . Our results show that the modified preferential attachment works well for citation networks. [Copyright &y& Elsevier]

The filled function method is a deterministic algorithm for finding a global minimizer of global optimization problems, and its effectiveness is closely related to the form of the constructed filled function. Currently, the filled functions mainly have three drawbacks in form, namely, parameter adjustment and control (if any), inclusion of exponential or logarithmic functions, and properties that are discontinuous and non-differentiable. In order to overcome these limitations, this paper proposed a parameter-free filled function that does not include exponential or logarithmic functions and is continuous and differentiable. Based on the new filled function, a filled function method for solving unconstrained global optimization problems was designed. The algorithm selected points in the feasible domain that were far from the global minimum point as initial points, and improved the setting of the step size in the stage of minimizing the filled function to enhance the algorithm’s global optimization capability. In addition, tests were conducted on 14 benchmark functions and compared with existing filled function algorithms. The numerical experimental results showed that the new algorithm proposed in this paper was feasible and effective. [ABSTRACT FROM AUTHOR]

In this paper, the Bayesian estimators for the Inverse Weibull Distribution (IWD) scale parameter are derived when the shape parameter of distribution is known. The Bayesian estimators for the parameter are obtained by using the Gamma prior under the different types of loss functions such as square error loss function (Self), Entropy loss function (Elf), Precautionary loss function (Plf), Linear exponential loss function (Linexlf) and nonlinear exponential loss function (Nlinexlf). A classical maximum likelihood estimator (mle) for the parameter is also derived. To compare the efficiency of the parameter estimation methods, a simulation study is carried out. The comparison is based on mean square error. [ABSTRACT FROM AUTHOR]

Nitrogen oxides (NOx = NO + NO2) are air pollutants which are co-emitted with CO2 during high-temperature combustion processes. Monitoring NOx emissions is crucial for assessing air quality and for providing proxy estimates of CO2 emissions. Satellite observations, such as those from the TROPOspheric Monitoring Instrument (TROPOMI) on board the Sentinel-5P satellite, provide global coverage at high temporal resolution. However, satellites measure only NO2 , necessitating a conversion to NOx. Previous studies have applied a constant NO2 -to- NOx conversion factor. In this paper, we develop a more realistic model for NO2 -to- NOx conversion and apply it to TROPOMI data of 2020 and 2021. To achieve this, we analysed plume-resolving simulations from the MicroHH large-eddy simulation model with chemistry for the Bełchatów (PL), Jänschwalde (DE), Matimba (ZA) and Medupi (ZA) power plants, as well as a metallurgical plant in Lipetsk (RU). We used the cross-sectional flux method to calculate NO , NO2 and NOx line densities from simulated NO and NO2 columns and derived NO2 -to- NOx conversion factors as a function of the time since emission. Since the method of converting NO2 to NOx presented in this paper assumes steady-state conditions and that the conversion factors can be modelled by a negative exponential function, we validated the conversion factors using the same MicroHH data. Finally, we applied the derived conversion factors to TROPOMI NO2 observations of the same sources. The validation of the NO2 -to- NOx conversion factors shows that they can account for the NOx chemistry in plumes, in particular for the conversion between NO and NO2 near the source and for the chemical loss of NOx further downstream. When applying these time-since-emission-dependent conversion factors, biases in NOx emissions estimated from TROPOMI NO2 images are greatly reduced from between - 50 % and - 42 % to between only - 9.5 % and - 0.5 % in comparison with reported emissions. Single-overpass estimates can be quantified with an uncertainty of 20 %–27 %, while annual NOx emission estimates have uncertainties in the range of 4 %–21 % but are highly dependent on the number of successful retrievals. Although more simulations covering a wider range of meteorological and trace gas background conditions will be needed to generalise the approach, this study marks an important step towards a consistent, uniform, high-resolution and near-real-time estimation of NOx emissions – especially with regard to upcoming NO2 -monitoring satellites such as Sentinel-4, Sentinel-5 and CO2M. [ABSTRACT FROM AUTHOR]

The rapid development of science and technology has been accompanied by an exponential growth in peer-reviewed scientific publications. At the same time, the review of each paper is a laborious process that must be carried out by subject matter experts. Thus, providing high-quality reviews of this growing number of papers is a significant challenge. In this work, we ask the question "can we automate scientific reviewing?", discussing the possibility of using natural language processing (NLP) models to generate peer reviews for scientific papers. Because it is non-trivial to define what a "good" review is in the first place, we first discuss possible evaluation metrics that could be used to judge success in this task. We then focus on the machine learning domain and collect a dataset of papers in the domain, annotate them with different aspects of content covered in each review, and train targeted summarization models that take in papers as input and generate reviews as output. Comprehensive experimental results on the test set show that while system-generated reviews are comprehensive, touching upon more aspects of the paper than human-written reviews, the generated texts are less constructive and less factual than human-written reviews for all aspects except the explanation of the core ideas of the papers, which are largely factually correct. Given these results, we pose eight challenges in the pursuit of a good review generation system together with potential solutions, which, hopefully, will inspire more future research in this direction. We make relevant resource publicly available for use by future research: https://github. com/neulab/ReviewAdvisor. In addition, while our conclusion is that the technology is not yet ready for use in high-stakes review settings we provide a system demo, ReviewAdvisor (http://review.nlpedia.ai/), showing the current capabilities and failings of state-of-the-art NLP models at this task (see demo screenshot in A.2). A review of this paper written by the system proposed in this paper can be found in A.1. [ABSTRACT FROM AUTHOR]

This paper proposes a novel seismic demand hazard model conditional on the separation distance between two adjacent buildings to fully explore the possibility of seismic pounding occurrence between buildings during their design life. The model uses an exponential function with two model parameters estimated through a two-point approach to yield an explicit expression for deriving a Seismic Demand Hazard Curve (SDHC) for adjacent buildings. The resulting SDHC provides a basis for seismic pounding risk assessment of adjacent buildings with a specific separation distance and a design tool for the risk-targeted separation distance between buildings. To verify the model, this paper compares the SDHCs derived for six pairs of adjacent buildings having different heights and natural period combinations with corresponding numerical simulation results. The results show that the SDHCs derived from the model, within the engineering interest range, closely agree with numerical simulation results. [ABSTRACT FROM AUTHOR]

The analysed the research publications contributions of the LIS researchers in DJLIT (DESIDOC Journal of Library and Information technology) during 2011-2017. The total no. 419bibliographical records were retrieved from DJLIT website during the period of study. The result of the study observed that Maximum of 70 papers was brought out in the year 2012. It followed by 66 papers published in 2013. The study found that DJLIT productivity range of publications between 12.17 and 16.76 over the period of study. RGR and Dt was an increasing and a decreasing trend observed over period of study. It is found that highest RGR was 0.18 in 2012 and lowest RGR was 0.04 known in two years 2014 and 2016 it could be observed RGR and Dt went on exponential growth were does not progress during the period. 36.75% of the publications shared single author. 63.25% of the publications contributed in collaborative nature. It is observed that majority of publications 44.15% representing by the two authors in the analysis BM. Guptha was published 18 papers in DJLIT, who is a ranked 1 author. It followed by Chenupathi K. Ramiah shored second his publications 11.University of Delhi, which is the top ranked institution. It is followed by NISTADS (24), DRDO (22), Pondicherry University (13), Banaras Hindu University (11), Indian Institute of technology (11) and University of Kashmir (10). [ABSTRACT FROM AUTHOR]

Electrowetting displays (EWDs) are one of the most potential electronic papers. However, they have the problem of oil film splitting, which could lead to a low aperture ratio of EWDs. In this paper, a driving waveform was proposed to reduce oil film splitting. The driving waveform was composed of a rising stage and a driving stage. First, the rupture voltage of oil film was analyzed by testing the voltage characteristic curve of EWDs. Then, a quadratic function waveform with an initial voltage was applied at the rising stage to suppress oil film splitting. Finally, a square wave was applied at the driving stage to maintain the aperture ratio of EWDs. The experimental results show that the luminance was increased by 8.78% and the aperture ratio was increased by 4.47% compared with an exponential function driving waveform. [ABSTRACT FROM AUTHOR]

In this present study, we reduce the fractional reaction-diffusion equation to a traditional differential equation using the fractional complex transformation and consider the Landau Lifshitz (LLG) equation. Moreover, by using the generalized exponential rational function method and Kudryashov's method respectively we extract new exact and solitary wave solutions for these equations. Some plots of some presented new solutions are represented to exhibit wave characteristics. All results in this paper are essential to understand the physical meaning and behavior of the investigated equation that sheds light on the importance of investigating various nonlinear wave phenomena in mathematical physics. [ABSTRACT FROM AUTHOR]

Traditional object recognition algorithms cannot meet the requirements of object recognition accuracy in the actual warehousing and logistics field. In recent years, the rapid development of the deep learning theory has provided a technical approach for solving the above problems, and a number of object recognition algorithms has been proposed based on deep learning, which have been promoted and applied. However, deep learning has the following problems in the application process of object recognition: First, the nonlinear modeling ability of the activation function in the deep learning model is poor; second, the deep learning model has a large number of repeated pooling operations during which information is lost. In view of these shortcomings, this paper proposes multiple-parameter exponential linear units with uniform and learnable parameter forms and introduces two learned parameters in the exponential linear unit (ELU), enabling it to represent piecewise linear and exponential nonlinear functions. Therefore, the ELU has good nonlinear modeling capabilities. At the same time, to improve the problem of losing information in the large number of repeated pooling operations, this paper proposes a new global convolutional neural network structure. This network structure makes full use of the local and global information of different layer feature maps in the network. It can reduce the problem of losing feature information in the large number of pooling operations. Based on the above ideas, this paper suggests an object recognition algorithm based on the optimized nonlinear activation function-global convolutional neural network. Experiments were carried out on the CIFAR100 dataset and the ImageNet dataset using the object recognition algorithm proposed in this paper. The results show that the object recognition method suggested in this paper not only has a better recognition accuracy than traditional machine learning and other deep learning models but also has a good stability and robustness. [ABSTRACT FROM AUTHOR]

The classical bistable stochastic resonance algorithm has an inherent output saturation defect that restricts the amplitude of the output signal. This paper examines the causes of this phenomenon and its negative impact on the detection of weak signals. Proposing the Unsaturated Bistable Stochastic Resonance (UBSR) detection algorithm involves constructing a segmented potential function using a linear function to eliminate the effect of higher-order terms in the classical stochastic resonance algorithm. A new type of segmented potential function has been created by combining exponential and linear functions. This new function helps to eliminate the impact of higher-order terms in classical algorithms while also improving the noise immunity of the stochastic resonance system. This results in the development of the accelerated stochastic resonance (ASR) detection algorithm. In this paper, the Kramers escape rate and output signal-to-noise ratio of two improved stochastic resonance algorithms are theoretically derived and compared with the classical bistable stochastic resonance algorithms, and the proposed algorithms are able to effectively avoid the output saturation phenomenon and have more excellent detection performance under strong background noise. [ABSTRACT FROM AUTHOR]

In this paper, the development and analysis of a proposed method for solving physical models arising from real-life scenarios are presented. The proposed method is derived via the transcendental function of exponential type, examined and studied for its properties. In addition, the effectiveness of the method is evaluated by applying it to three numerical examples that originated from real-world scenarios. Moreover, this study presents a comparison of the outcomes generated by the proposed method and the existing method, in the context of the exact solution. The study concludes that the proposed method solves real life problems with the expected level of accuracy and, therefore, can be considered among the numerous methods that are appropriate and suitable for solving first-order initial value problems (IVPs). [ABSTRACT FROM AUTHOR]

Harris Hawks Optimization (HHO) is a novel meta-heuristic optimization algorithm. The algorithm is inspired by the behavior of Harris Hawks collaborating with each other to pursue prey in nature. The algorithm has the advantages of simple structure, fewer parameters, easy implementation, and excellent performance on high-dimensional problems. However, the algorithm also suffers from the inability to strike a good balance between exploration and exploitation, low convergence accuracy, and slow convergence speed in the early stage. In response to these defects, this paper will introduce three strategies to the HHO: a non-negative stochastic shrinkage exponential energy function, a Cauchy-Gaussian-based dynamic variance reduction selection strategy, and a greedy-difference-based selection strategy. The improved algorithm TSHHO is analyzed on the well-established 28 benchmark test functions, and four industrial engineering design problems. The experimental results show that the TSHHO algorithm proposed in this paper can achieve a better balance in the exploration and development stages,the strategies significantly improve the search efficiency, convergence accuracy, and robustness of the algorithm. [ABSTRACT FROM AUTHOR]

Growth is an important metric in fisheries and aquaculture. Growth of small fish over relatively short periods of time is commonly modelled with an exponential function using instantaneous growth rate (g). Instantaneous growth rates are logarithmic and inherently difficult to interpret, but specific growth rates (SGR) express growth as the intuitively understandable per cent change in size per unit of time. A simple metric of SGR (G) is easily computed by exponentiating g, subtracting 1 and multiplying by 100. However, several prominent fisheries publications suggest that SGR should be calculated by simply multiplying g by 100 (we call this G*). A search of the fisheries literature found that the number of papers that used SGR for fish increased significantly from 1830 papers in 2009 to 3170 papers in 2018. An extensive review of 300 papers from this search found that 92.6% were related to aquaculture and only 3.3% of all papers correctly used G to calculate SGR. We algebraically show that G* is fundamentally different than G and cannot be interpreted as a per cent change in weight per unit of time. Furthermore we demonstrate, with three examples from the literature, that using G* as if it were the same as G leads to biologically meaningful underestimates of true growth rates and estimated weights. Given these results and the simplicity with which G can be computed from g, we recommend that fisheries scientists abandon the pervasive practice of incorrectly measuring SGR as 100 times the instantaneous growth rate. [ABSTRACT FROM AUTHOR]

Characterization of a probability distribution gives a unique property enjoyed by that distribution. Various approaches are available in the literature to characterize distributions through record values. Many researchers have characterized Exponential, Pareto, and Power function distributions using moments, conditional expectation, and some other characteristics of record values. In this paper, we have characterized these three distributions through conditional variance of adjacent record values. The results have been verified using numerical computation. [ABSTRACT FROM AUTHOR]

In this paper, we study Horn formulas from the perspective of read-once resolution refutations (RORs). A Horn formula is a Boolean formula in conjunctive normal form (CNF), in which each clause contains at most one positive literal. Horn formulas are used in a number of domains, including program verification, logic programming, and econometrics. In particular, deduction in ProLog is based on unification. Unification is based on resolution and instantiation. Resolution is a system used to prove the infeasibility of Boolean formulas. It is important to note that resolution is both sound and complete. However, resolution is inefficient in the following sense: There exist CNF formulas with resolution refutations whose lengths are bounded below by an exponential function of the input size. At the same time, these formulas admit shorter (polynomially bounded) proofs of infeasibility in other proof systems, such as Frege Systems. Despite this inefficiency, resolution is simple and easy to implement and hence used in a wide variety of theorem provers. In this paper, we study two variants of resolution. These are read-once resolution (ROR) and read-once unit resolution (UROR). Both ROR and UROR are sound. However, they are incomplete since there exist infeasible Boolean formulas which do not have either an ROR or a UROR. In this paper, we look at the problems of determining if a Horn formula has an ROR or a UROR. We also examine the problem of finding the optimal length ROR of a Horn formula from both the computational complexity and the approximation perspectives. Finally, we analyze the copy complexity of Horn formulas with respect to URORs. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new family of the generalized k-Leonardo numbers and study their properties. We investigate the Gaussian Leonardo numbers and associated new families of these Gaussian forms. We obtain combinatorial identities like Binet formula, Cassini’s identity, partial sum, etc. in the closed form. Moreover, we give various generating and exponential generating functions. [ABSTRACT FROM AUTHOR]

This paper investigates the application of the enhanced modified tanh expansion method and the Kudryashov method in deriving optical solutions for a conformable nonlinear Schrödinger equation. This equation includes Kudryashov's arbitrary refractive index and incorporates two distinct nonlocal nonlinearities. The resulting optical solutions are expressed using a combination of exponential and hyperbolic functions, encompassing kink-type, mixed dark-bright, bright, bell-shaped, multi-bright, and wave solitons. Visualization of these solutions is provided through two-dimensional, three-dimensional, and contour plots to elucidate their characteristics. Furthermore, the behavior of these optical solutions is analyzed via illustrative graphs, considering different values of the time parameter and conformable order derivative. The proposed methods are posited as precise approaches for investigating optical solutions across various formulations of Schrödinger equations. The methods proposed in the paper offer precise approaches for studying and understanding the behavior of light in complex optical systems described by Schrödinger equations. This research contributes to advancing our knowledge of nonlinear optics and may have practical applications in fields such as telecommunications, laser technology, and optical signal processing. [ABSTRACT FROM AUTHOR]

The symmetry features of fractional differential equations allow effective explanation of physical and biological phenomena in nature. The generalized form of the fractional differential equations is the variable-order fractional differential equations that describe the physical and biological applications. This paper discusses the closed-form traveling wave solutions for the nonlinear space-time variable-order fractional modified Kawahara and (2 + 1)-dimensional Burger hierarchy equations. The variable-order fractional differential equation has a derivative operator in the Caputo sense that is converted into the integer-order ordinary differential equation (ODE) by fractional transformation. The obtained ODE is solved by the exponential rational function method, and as a result, new exact solutions are constructed. Two problems are proposed to confirm the solutions of the space-time variable-order fractional differential equations. [ABSTRACT FROM AUTHOR]

High-modulus asphalt mixtures (HMAMs) are potential materials for achieving long-life pavement performance, and understanding their long-term performance degradation mechanism is crucial for analyzing pavement performance degradation under long-term exposure to traffic and environmental coupling conditions. This paper aims to examine the long-term evolution of high- and low-temperature performance and water stability in HMAMs derived from modified nature asphalt, prepared using microparticle suspension technology, under heavy load and humid heat conditions. Four asphalt mixtures (AC-13, BBME-13, SMA-13, SBSAC-13) were prepared, and then their dynamic moduli were tested. A test plan for the long-term performance of the mixtures was designed, and the performances of HMAMs with different gradations and time were analyzed. Furthermore, corresponding long-term performance degradation models of HMAMs were established. The results show that the HMAMs of modified natural asphalt have better high-temperature performance than HMAMs of high-modulus agent/SBS-modified asphalt. However, following prolonged thermal aging and freeze-thaw cycles, the low-temperature performance shows the opposite trend. In addition, thermal aging had the same effect on the long-term low-temperature performance of both types of HMAM, with the HMAMs of modified natural asphalt being less affected by long-term freeze-thaw cycling. The long-term bending tensile strain attenuation of HMAMs can be simulated using an exponential function. Both types of HMAMs display similar water stability under dry-wet cycles and dynamic water erosion condition. The variations in residual stability during dry-wet cycles can be accurately represented using a power function. [ABSTRACT FROM AUTHOR]

In many research studies, multiple objectives need to be considered simultaneously to ensure an effective and efficient investigation. A compound optimal design provides a viable solution to this problem, allowing for the maximization of overall benefits through the integration of several factors. The paper addresses the application of compound optimal designs in the context of progressive first‐failure censoring, with a particular focus on the Generalized Exponential distribution with two parameters. The paper provides an illustrative example of compound designs by considering the cost function along with trace, variance, and determinant of inverse Fisher information. The best design is determined using a graphical solution technique that is both comprehensible and precise. Using a simple example, we demonstrate the advantage of compound optimal designs over constraint optimal designs. Furthermore, the paper examines real‐world data collection to demonstrate the practical utility of compound optimal designs. [ABSTRACT FROM AUTHOR]

Considering the load uncertainty and unmodeled dynamics in multicylinder hydraulic systems, this paper proposes a balance control algorithm based on safe reinforcement learning to release the restrictions of classical model-based control methods that depend on fixed gain. In this paper, the hydraulic press is controlled by a trained agent that directly maps the system states to control commands in an end-to-end manner. By introducing an action modifier into the algorithm, the system states are kept within security constraints from the beginning of training, making safe exploration possible. Furthermore, a normalized exponential reward function has been proposed. Compared with a quadratic reward function, the precision is greatly improved under the same training steps. The experiment shows that our algorithm can achieve high precision and fast balance for multicylinder hydraulic presses while being highly robust. To the best of our knowledge, this research is the first to attempt the application of a reinforcement learning algorithm to multi-execution units of hydraulic systems. [ABSTRACT FROM AUTHOR]

In this paper, we study analogues of the van der Corput lemmas involving Mittag-Leffler functions. The generalisation is that we replace the exponential function with the Mittag-Lefflertype function to study oscillatory-type integrals appearing in the analysis of time-fractional partial differential equations. Several generalisations of the first and second van der Corput lemmas are proved. Optimal estimates on decay orders for particular cases of the Mittag-Leffler functions are also obtained. As an application of the above results, the generalised Riemann–Lebesgue lemma and the Cauchy problem for the time-fractional evolution equation are considered. [ABSTRACT FROM AUTHOR]

In recent years, the vigorous development of the Internet has led to the exponential growth of network information. The recommendation system can analyze the potential preferences of users according to their historical behavior data and provide personalized recommendations for users. In this study, the social network model was used for modeling, and the recommendation model was improved based on variational modal decomposition and the whale optimization algorithm. The generalized regression neural network structure and joint probability density function were used for sequencing and optimization, and then the genetic bat population optimization algorithm was used to solve the proposed algorithm. An intelligent recommendation algorithm for social networks based on improved generalized regression neural networks (RA-GNN) was proposed. In this study, three kinds of social network data sets obtained by real crawlers were used to solve the proposed RA-GNN algorithm in the real social network data environment. The experimental results showed that the RA-GNN algorithm proposed in this paper could implement efficient and accurate recommendations for social network information. [ABSTRACT FROM AUTHOR]

This paper introduces iterated monodromy groups for transcendental functions and discusses them in the simplest setting, for post-singularly finite exponential functions. These groups are self-similar groups in a natural way, based on an explicit construction in terms of kneading sequences. We investigate the group theoretic properties of these groups, and show in particular that they are amenable, but they are not elementary subexponentially amenable. [ABSTRACT FROM AUTHOR]

The adverse effects of the frequent reservoir earthquakes (REs) and the severe degradation of the hydrofluctuation belt (HFB) on the long-term stability of bedding bank slope since the Three Gorges Reservoir Area (TGRA) impoundment were considered fully in this paper. Under such complex conditions, the dynamic response pattern and instability mechanism of typical bank slopes were investigated systematically by using a method of combining field survey, laboratory shaking table (ST) model test, and Universal Distinct Element Code (UDEC) numerical exploration. The research shows that the degradation forms of the HFB of typical bank slopes in the key field survey of the TGRA can be arranged into four types: erosion (denudation), corrosion (suffosion), avalanche (collapse), and slip (flow). The dynamic response of slope shows obvious characteristics of "surface effect" and "elevation effect," and the cumulative displacement (CD), damping ratio (DR) and natural frequency (NF) of slopes show a trend of gradually increasing, and increasing and decreasing, respectively. Meanwhile, the "S–type" cubic function and "Steep rise type" exponential function can be used to characterize the cumulative damage degree (CDG) of slope at the excitation stages of microseisms—small seisms and strong seisms, respectively. Subsequently, the dynamic evolvement process for cumulative damage and unstable failure of slope considering the impact of degradation of rock mass in the HFB was obtained, and there are good agreement between the model test and numerical exploration results. Furthermore, fully considering the influence of slope height (SH), slope angle (SA), thickness of bedding plane (TBP), dip angle of bedding plane (DABP), dynamic load amplitude (DLA), dynamic load frequency (DLF), height of water level of the HFB (HWHB), degradation range of the HFB (DRHB), and degradation shape of the HFB (DSHB), the CD of slope subjected to continuous excitation of multiple seismic loads increases in the form of exponential function, the dynamic stability coefficient (DSC) of slope decreases slowly first and then drops sharply, and the response degree of slope deformation and sliding velocity is obviously different. Especially, the sensitivity level of every preceding factor to the dynamic stability of slope based on the orthogonal analysis method (OAM) is in the order of DLA > DRHB > SA > SH > DLF > HWHB > DSHB > DABP > TBP. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present the class of atomic basis functions (ABFs) which are of exponential type and are denoted by EFupn(x, ω). While ABFs of the algebraic type are already represented in the numerical modeling of various problems in mathematical physics and computational mechanics, ABFs of the exponential type have not yet been sufficiently researched. These functions, unlike the ABFs of the algebraic type Fupn(x), contain the tension parameter ω, which gives them additional approximation properties. Exponential monomials up to the nth degree can be described exactly by the linear combination of the functions EFupn(x, ω). The function EFupn for n = 0 is called the “mother” ABF of the exponential type, i.e., EFup0(x, ω) ≡ Eup(x, ω). In other words, the functions EFupn(x, ω) are elements of the linear vector space EUPn and retain all the properties of their “mother” function Eup(x, ω). Thus, this paper, in terms of its content and purpose, can be understood as a sequel of the article by Brajčić Kurbaša et al., which shows the basic properties and application of the basis function Eup (x, ω). This paper presents, in an analogous way, the development and application of the exponential basis functions EFupn(x, ω). Here, for the first time, expressions for calculating the values of the functions EFupn(x, ω) and their derivatives are given in a form suitable for application in numerical analyses, which is shown in the verification examples of the approximations of known functions. [ABSTRACT FROM AUTHOR]

In this paper, dual bicomplex Balancing and Lucas-Balancing numbers are defined, and some identities analogous to the classic properties of the Fibonacci and Lucas sequences are produced. We give the relationship between these numbers and Pell and Pell-Lucas numbers. From these, the basic bicomplex properties for the norm and its conjugate of these numbers are also developed. These in turn lead to the Binet formula, the generating functions and exponential generating functions, which are important concepts for number sequences. The Cassini identity, which is important for number sequences, actuallyemerged to solve the famous Curry paradox. We calculated the Cassini, Catalan, Vajda and d'Ocagne identities for these numbers. [ABSTRACT FROM AUTHOR]

In this paper, we study the entire solutions of two quadratic functional equations in the complex plane. One consists of three basic terms, f(z), f'(z) and f(z+c), and the other one consists of f(z),f'(z) and f (qz). These two equations can be transformed into functional equations of Fermattype. We prove that if these two equations admit finite order transcendental entire solutions, then the solutions of these two equations are both exponential functions, and their exponents are one degree polynomials, whose coefficients of the first degree term are closely related to the coefficients of the functional equation. Moreover, examples are given to show that the theorems are true. The feature of this paper is that the Fermat-type equations contain three quadratic terms, while the equations that have been studied in the previous articles in this field contain only two quadratic terms. The addition of f (qz) will make the proof methods in this paper very different from those in the existing literature. The proof becomes more difficult, and the number of cases that need to be discussed becomes much larger. In addition, when dealing with the analytical property of f, we also use a different method from the previous literature. [ABSTRACT FROM AUTHOR]

In this paper, the exponential convergence of delayed inertial Cohen-Grossberg neural networks (CGNNs) is studied. Two methods are adopted to discuss the inertial CGNNs, one is expressed as two first-order differential equations by selecting a variable substitution, and the other does not change the order of the system based on the nonreduced-order method. By establishing appropriate Lyapunov function and using inequality techniques, sufficient conditions are obtained to ensure that the discussed model converges exponentially to a ball with the prespecified convergence rate. Finally, two simulation examples are proposed to illustrate the validity of the theorem results. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to design an event-triggered adaptive prescribed performance controller for flexible manipulators, with the primary objectives of achieving output performance constraints and addressing communication resource limitations. Design/methodology/approach: The authors propose a novel prescribed performance barrier Lyapunov function (PP-BLF) that considers both output and tracking performance constraints. The PP-BLF ensures that the system's output, transient behavior and steady-state performance, adhere to prescribed constraints. The boundary of the PP-BLF is established by an exponential function that decays over time. Notably, the PP-BLF can be applied seamlessly in unconstrained cases without necessitating controller redesign. Moreover, the controller design incorporates an event-triggered mechanism, effectively reducing the frequency of controller updates and optimizing the utilization of communication resources. Additionally, the authors employ adaptive techniques to estimate the system's unknown parameters and approximate unknown nonlinear functions using radial basis function neural networks (RBFNN). To address the challenge of "complexity explosion", dynamic surface technology is employed. Findings: Numerical simulations are conducted under five different cases to verify the effectiveness of the proposed controller. The results demonstrate that the controller successfully constrains the output tracking error within the prescribed performance boundary. Moreover, compared with the traditional time-triggered mechanism, the event-triggered mechanism significantly reduces the controller's update frequency, resolving the problem of limited communication resources. Originality/value: The paper reduces the update frequency of control signals and improves resource utilization through an event-triggered mechanism in the form of relative thresholds. The authors recognize that the event-triggered mechanism may impact the output performance of the system. To address this challenge, the authors propose a prescribed performance Barrier Lyapunov Function (PP-BLF). The PP-BLF is designed to effectively constrain the output performance of the system, ensuring satisfactory control even when the control signal updates are reduced. [ABSTRACT FROM AUTHOR]

Buffer capacity appears in a variety of fields, and its approximate calculation is of practical importance for the design of new buffer solutions, being also a quantity related to titrations. The aims of this paper are (i) to devise simple expressions for the buffer capacity and its first derivative for a polyprotic acid, which may be easily extended to a mixture of acids, e.g., universal buffer solutions; (ii) to evaluate overlapping acidity constants (pKa' s) for diprotic acids, from the knowledge of the singular points in the buffer capacity curve; and (iii) at the same time to provide a critical overview of the topic, with some twist of novelty. Hyperbolic functions in analytical chemistry have been surveyed. Conditions for the appearance of singular points in the buffer capacity curve for monoprotic acids and diprotic acids with overlapping pKa values have been established. Methods to evaluate strong and moderate overlapping pKa' s are suggested and applied to literature data. To check the computed values, the acidity constants were also determined by the graphical method of Irving and Rossotti, taken as reference. Results obtained agree well for moderate overlapping pKa' s values, whereas in the case of strong overlapping pKa' s values the agreement is excellent. Limiting Ka1/Ka2 ratio as well as the relation between the acidity constants ratio and the half-values of the formation function, and the problem of distinguishing polyprotic acids from monofunctional ones have been envisaged. An attempt has also been made to derive compact expressions suitable for computer usage for the V = f (pH) derivative curves and buffer capacity curves, taken into account the dilution effects. [ABSTRACT FROM AUTHOR]

Shallow mixing layers developed in partially-distributed canopy flows (PCFs) are important for water conveyance, sediment transport and solute dispersion. In this paper, we address the response of shallow mixing layers in PCFs to several influential factors associated with bed friction, water shallowness and canopy denseness using depth-averaged Large Eddy Simulation (DA-LES). The results show that under certain canopy denseness, shallow mixing layers in PCFs display asymptotic behaviour for the variation of bed friction and water shallowness, consistent with classic shallow mixing layers. The canopy drag encourages the asymmetric growth of the inner and outer parts of the mixing layer, and this effect decreases when bed friction and water shallowness become pronounced. Characteristic velocity and length scales show similarity well delineated by exponential decay function regarding a stabilization efficiency parameter. The exception happens for the inner length scale of the mixing layer when only changing canopy density. We conclude that changing the canopy denseness can encourage the overall shift of mixing layer scaling regarding a broad range of bed friction and water shallowness. Furthermore, the bed friction parameter thresholding triggering flow instability of mixing layers in PCFs is found about 0.03, lower than 0.09 for splitter-plate induced mixing layers. [ABSTRACT FROM AUTHOR]

• Performance of different loading models is compared in reproducing the observed results of typical real-world footbridges. • SMD model with (inconsistent) parameters may result in significant differences in response predictions. • This paper modifies the SMD model and proposes a pedestrian synchronization ratio formula. • Modified SMD can reliably and conveniently reproduce lateral responses as the real-world data. The pedestrian-induced lateral vibration of footbridges has attracted much attention since the London Millennium Bridge incident. Significant investigations were mainly performed by external-excited force models and self-excited force models. The first type models consider pedestrians as harmonic forces and/or spring-mass-damping (SMD) systems. The second type consider the self-excited forces of pedestrians that initialize the instability of footbridges by e.g. applying the inverted pendulum (IP) model. This study compares performance of different models in reproducing the observed results of typical living footbridges: the London Millennium Bridge (UK), T-bridge (Japan) and Pedro e Inês footbridge (Portugal). With varying step frequencies and pedestrian numbers, both the acceleration time history and the discrepancy between the input work and consumed work exhibit a consistent trend for the harmonic force (HF) model and SMD model, yet a notable difference for the IP model. The HF model and SMD model are better suited for assuming synchronization, making them convenient for estimating the serviceability of pedestrian-induced lateral vibration. On the other hand, the IP model is more appropriate for incorporating random step frequencies and can better capture observed instability phenomena realistically. Because the SMD model with (inconsistent) parameters from literature may result in significant differences in predicting the acceleration amplitudes, this paper modifies the SMD model and proposes a pedestrian synchronization ratio formula as an exponential function of the maximum lateral acceleration. It is validated by comparing the analytical and numerical results for the three footbridges. Furthermore, by the modified SMD model, the lateral lock-in phenomenon of footbridges is simulated reliably and conveniently. This work contributes to analyze pedestrian-induced lateral vibration of footbridges. [ABSTRACT FROM AUTHOR]

This paper mainly studies the synchronization problem of memristor-based bidirectional associative memory neural networks (MBAMNNs) via finite-time technology. Different from the existing neural network dynamic models, the given model in this paper is focused on the impact of parameter perturbation and strong mismatch, where strong mismatch includes parameter mismatch and time-varying delay mismatch. These characteristics can make the model be closer to the actual situation. A delay-independent feedback control scheme, which can stabilize the error system within finite-time regardless of whether the past state is known or not, is designed. It is worth noting that the constant is replaced by a function with the exponential term in the delay-independent controller, which can save the control cost to a certain extent. Based on the integral inequality technique, some sufficient conditions for MBAMNNs to converge to the equilibrium point within finite-time are provided. The validity and correctness of the theoretical results are finally confirmed by numerical simulation. [ABSTRACT FROM AUTHOR]

This paper investigates the estimation of the unknown parameter in the XLindley distribution using record values and inter-record times, both in classical and Bayesian frameworks. It also delves into Bayesian prediction of a future record value. We also study the problem of estimation and prediction for the XLindley distribution based on lower records alone. A simulation study, as well as an analysis of a real data example, are conducted for comparison and illustration. The numerical findings underline that including the inter-record times in the study may enhance the performance of the estimators and predictors. [ABSTRACT FROM AUTHOR]