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This paper proposes an efficient simulation method based on importance sampling to estimate the random-coding error probability of coded modulation. The technique is valid for complex-valued modulations over Gaussian channels, channels with memory, and naturally extends to fading channels. The simulation method is built on two nested importance samplers to respectively estimate the pairwise error probability and generate the channel input and output. The effect of the respective number of samples on the overall bias and variance of the estimate of the error probability is characterized. For a memoryless channel, the estimator is shown to be consistent and with a small variance, growing with the square root of the code length, rather than the exponential growth of a standard Monte Carlo estimator. [ABSTRACT FROM AUTHOR]

Purpose: Destinations are focal points for tourist activity and thus for the study of tourism. They are, however, notoriously difficult to manage due to their complex systems of stakeholders. Such complexity implies that destinations are driven by a wide range of forces in their internal and external environments. The purpose of this paper is to highlight the diversity and depth of the challenges at play in destination management and, in doing so, review the primary contributions in the field. Design/methodology/approach: This is a "perspective" paper (i.e. critical literature review). Findings: The study of destinations remains an area of active research interest, with the many challenges that arise from within and external to destinations offering much food for thought with respect to their longevity as viable, sustainable and competitive places for tourists to visit. For the future, the need to view destinations as part of a wider system is paramount with them being inescapable from debates on urban planning, economic inequality, transportation and housing and the omnipresence of all things "smart". Such debates need to incorporate both tourists and resident communities, as the well-being and quality of life of both groups is under threat in many destinations, particularly heritage and culturally rich city destinations around the world, where the term "overtourism" is increasingly heard. Research limitations/implications: This study has implications for the integrated and more holistic management of tourist destinations. Practical implications: This is a "perspective" paper, so it does not offer individual practical implications for destinations. Moreover, it offers a concise and precise summary of core studies in the field and provides a platform for a more future-looking critical debate on the sustainable management of tourist destinations. Social implications: Looking ahead, destinations need to be considered as part of a wider system, one that is inclusive of urban planning, economic inequality, transportation and housing, and "smart" initiatives among others. Most importantly, the views of tourist and resident communities need to be considered and incorporated into future planning at the destination level with wellbeing and quality of life indicators being used to identify the real benefits of tourism to both communities. Originality/value: Integrated and holistic forms of destination management is the way forward, with the exponential growth of technology, as well as the need to manage the exchange of knowledge and data at the destination level, critical to the sustainability of the competitive destination long into the future. [ABSTRACT FROM AUTHOR]

The widespread application of artificial neural networks has prompted researchers to experiment with field-programmable gate array and customized ASIC designs to speed up their computation. These implementation efforts have generally focused on weight multiplication and signal summation operations, and less on activation functions used in these applications. Yet, efficient hardware implementations of nonlinear activation functions like exponential linear units (ELU), scaled ELU (SELU), and hyperbolic tangent (tanh), are central to designing effective neural network accelerators, since these functions require lots of resources. In this paper, we explore efficient hardware implementations of activation functions using purely combinational circuits, with a focus on two widely used nonlinear activation functions, i.e., SELU and tanh. Our experiments demonstrate that neural networks are generally insensitive to the precision of the activation function. The results also prove that the proposed combinational circuit-based approach is very efficient in terms of speed and area, with negligible accuracy loss on the MNIST, CIFAR-10, and IMAGE NET benchmarks. Synopsys design compiler synthesis results show that circuit designs for tanh and SELU can save between ${\times 3.13\sim \times 7.69}$ and ${ {\times 4.45\sim \times 8.45}}$ area compared to the look-up table/memory-based implementations, and can operate at 5.14 GHz and 4.52 GHz using the 28-nm SVT library, respectively. The implementation is available at: https://github.com/ThomasMrY/ActivationFunctionDemo. [ABSTRACT FROM AUTHOR]

Summary: This paper is devoted to investigating the exponential synchronization of coupled Lur'e dynamical networks with multiple time‐varying delays and stochastic disturbance. The problem studied in this paper could be regarded as a kind of leader‐following synchronization issue. As the networks may suffer from certain impulsive disturbance, an effective distributed impulsive control protocol is proposed to synchronize the stochastic Lur'e dynamical networks. According to the comparison principle, the average impulsive interval, and the extended formula for the variation of parameters, sufficient conditions are derived for successful achievement of the network synchronization with consideration to different functions of impulsive effects. Furthermore, the exponential convergence rate is obtained based on the impulsive solution equation. In addition, finally, some numerical simulations are given to illustrate the validity of the control scheme and the theoretical analysis. [ABSTRACT FROM AUTHOR]

The goal of this paper is to establish a more generalized Cameron–Storvick theorem with respect to the conditional generalized integral transform (CGIT) and the generalized first variation. Many results and formulas for Cameron–Storvick theorems established in previous papers are included. We first introduce a CGIT and a generalized first variation of functionals by using the concept of the Gaussian process and bounded linear operators. We then give the existence of them for the exponential functionals on function space. We next establish a generalized Cameron–Storvick theorem. Finally, we describe some applications. [ABSTRACT FROM AUTHOR]

In this paper, the authors illustrate the design of the exponential function based on the conventional and scale free hyperbolic Coordinate Rotation Digital Computer (CORDIC) algorithm which are used in applications of the neural networks Very Large Scale Integrated circuit design. The CORDIC algorithm is introduced to design the function of the neural networks. The design of exponential function based on conventional and scale free hyperbolic CORDIC processor is coded in VHSIC (Very High Speed Integrated Circuit) hardware description language and their simulation and synthesis results are present in this paper. The Xilinx 13.1 software is used for the simulation and synthesis of code design. [ABSTRACT FROM AUTHOR]

The problem of determination of Shape and Size of Plots remains at the foundation of planning and executing controlled field experiments. During sustained research investigations (more than a century) on experimental fields it has been established with confirmation that the premier action-point to be addressed before setting up of evaluation trials is to explore ways and means to minimize the inherent variability existing among the yield observations (role of determination of optimum shape and size of plots offers a milestone-discovery in the precinct of such controlled field experiments with the pioneering work of Smith (1938)). The concept of robust optimum plot size is introduced in the paper [Pal et al. (2015)] and subsequently, it is also considered in another paper in Pal and Basak (2016). An extensive review on the aspect of robust optimum plot size is available in Pal et al. (2016). In this paper, the theoretical model employed in Pal and Basak (2016) is considered under the set-up of a superimposed probability distribution (which mimics the real-life situations arising under the perspective of the class of field experiments) on it. The robust optimum plot sizes (determined basing on the overlaid exponential probability density for the intra-class correlation coefficient) in the form of three layers (in squared meters) are, Layer - I (14 (2x7), 18 (3x6), 21 (3x7), 28 (4x7) and 30 (5x6), robust very near to optimum plot sizes are, Layer - II (10 (2x5), 12 (2x6), and 24 (4x6)), and robust near to optimum plot sizes are, Layer -III (8 (2x4),12 (3x4) and 15 (3x5)), respectively. [ABSTRACT FROM AUTHOR]

Staying current with the literature is of paramount importance to the pharmacist engaged in an evidence-based clinical practice. Given the expanding roles and responsibilities of today’s pharmacists combined with exponential growth in new medical and health sciences literature, staying current has become an extremely daunting task. Traditional journal clubs have focused upon their role as a training vehicle for teaching critical reading skills to residents. However, schools of pharmacy are now required to provide instruction in biostatistics, research design, and interpretation. We present a paradigm shift in the traditional journal club model whereby a collection of periodicals is screened and a short synopsis of the pertinent articles is provided. The associated tasks for screening and presenting of the primary literature are shared among a group of clinicians and trainees with similar practice interests resulting in a more reasonable workload for the individual. This journal club method was effective in identifying a significant majority of articles judged to be pertinent by independent groups of clinicians in the same practice arenas. Details regarding the shared core practice and knowledge base elements, journal club format, identification of journals, and evaluation of the success of the journal club technique are provided. [ABSTRACT FROM AUTHOR]

The exponential growth of esports gives rise to a number of regulatory and governance issues which expose a number of different stakeholders, including vulnerable, young participants, to potential harms. This paper examines critical challenges which currently exist in the esports ecosystem, namely integrity and participant wellbeing, with the aim of addressing the knowledge deficit in relation to best practice governance and policy process aimed at protecting relevant stakeholders in esports. Using a corporate governance framework previously developed by Burger and Goslin, this paper also generates governance reform options in relation to the identified critical issues whilst having regard to the inherently commercial and networked nature of the sector. The paper proposes an integrated policy process model to address the practicality of developing and implementing a robust, dynamic governance system with a focus upon close engagement with stakeholders to influence legitimacy of protectionist policy. This paper builds upon earlier literature on governance and policy process in sport and proposes a research agenda to address the need for governance in this burgeoning landscape. [ABSTRACT FROM AUTHOR]

For a first-order quasilinear equation with a power-law flux function, generalized entropy solutions of the Cauchy problems are constructed with initial conditions coinciding with a power or exponential function at minus infinity. In the case of an exponentially growing initial condition, the one-sided periodicity in the spatial variable of the solution obtained is established. The nonexistence of positive solutions for the Cauchy problems in question is proved. [ABSTRACT FROM AUTHOR]

This paper aims to utilize a novel modification for the generalized exponential rational function method to determine novel analytical solutions to Chen-Lee-Liu equation. In this modified technique a new formulation is employed for the solution rather than the classic method. In the framework of using this method, new solutions for the equation are provided, which have many applications in optical fibers. Moreover, in order to better describe the physical properties of the resulting solutions, various numerical simulations related to the obtained solutions have also been added to the article. The employed method in the paper is straightforward and allows us to discover new solutions to nonlinear models. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of ground state solutions to the following fractional Kirchhoff–Choquard type problem with Trudinger–Moser nonlinearity M ∫ ∫ R 2 N | u (x) - u (y) | N / s | x - y | 2 N d x d y (- ▵) N / s s u = I μ ∗ F (u) f (u) in R N , u = 0 in R N \ Ω , where Ω is a bounded domain with Lipschitz boundary in R N with N ≥ 1 , M : R 0 + → R 0 + is a continuous function, I μ = | x | μ - N with μ ∈ (0 , N) , (- ▵) N / s s is the fractional N/s-Laplacian operator, F(u) is the primitive function of f(u), and f is a continuous function with critical exponential growth in the sense of Trudinger-Moser. The main purpose of this paper is to investigate the existence of nontrival ground state solutions by variational principle. [ABSTRACT FROM AUTHOR]

In the present paper we introduce a new class of analytic functions f in the open unit disk normalized by f(0) = f0 (0) 1 = 0, associated with exponential functions. The aim of the present paper is to investigate the third-order Hankel determinant H3 (1) for this function class and obtain the upper bound of the determinant H3(1). [ABSTRACT FROM AUTHOR]

This paper presents data for the physical aging of the density of squalane upon both non-linear and nearly linear temperature jumps from states of thermal equilibrium. Invoking the single-parameter-aging scenario [Hecksher et al., J. Chem. Phys. 142, 241103 (2015); Proc. Natl. Acad. Sci. U. S. A. 116, 16736–16741 (2019)], the linear-response aging relaxation function is extracted from the data. Based on this, it is shown that the relaxation toward equilibrium follows a simple exponential function at long times; a stretched-exponential function provides a poor fit. This demonstrates the existence of a terminal relaxation rate for the physical aging of squalane, corresponding to an effective long-time cutoff in the spectrum of structural relaxation times. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new convexity notion for inter-valued functions, known as Geometrically–Arithmetically Cr-h-convex functions (abbreviated as GA-Cr-h-CFs) and explore its properties. The family of GA-Cr-h-CFs simultaneously covers the family of GA-CFs, GA-h-CFs and GA-Cr-CFs. On the other hand, we demonstrate its equivalence with convex functions (CFs), h-CFs, Cr-CFs and Cr-h-CFs via exponential function. We also investigate necessary and sufficient conditions for GA-Cr-h-CFs via two corresponding real-valued GA-h-CFs. Due to significance and applications of mathematical inequalities, we apply our findings and propose several inequalities such as Jensen–Mercer inequality (JMI), Hermite–Hadamard inequality (HHI) and weighted Hermite–Hadamard-type inequalities (wHHIs) for GA-Cr-h-CFs. Through our results, we re-capture many known results and inequalities for subclasses of GA-Cr-h-CFs studied in the recent literature. [ABSTRACT FROM AUTHOR]

The concept of perfect equilibrium, formulated by Selten (Int J Game Theory 4:25–55, 1975), serves as an effective characterization of rationality in strategy perturbation. In our study, we propose a modified version of perfect equilibrium that incorporates perturbation control parameters. To match the beliefs with the equilibrium choice probabilities, the logistic quantal response equilibrium (logistic QRE) was established by McKelvey and Palfrey (Games Econ Behav 10:6–38, 1995), which is only able to select a Nash equilibrium. By introducing a linear combination between a mixed strategy profile and a given vector with positive elements, this paper develops a variant of the logistic QRE for the selection of the special version of perfect equilibrium. Expanding upon this variant, we construct an equilibrium system that incorporates an exponential function of an extra variable. Through rigorous error-bound analysis, we demonstrate that the solution set of this equilibrium system leads to a perfect equilibrium as the extra variable approaches zero. Consequently, we establish the existence of a smooth path to a perfect equilibrium and employ an exponential transformation of variables to ensure numerical stability. To make a numerical comparison, we capitalize on a variant of the square-root QRE, which yields another smooth path to a perfect equilibrium. Numerical results further verify the effectiveness and efficiency of the proposed differentiable path-following methods. [ABSTRACT FROM AUTHOR]

In this research, we propose a novel technique for visualizing nonstationarity in geostatistics, particularly when confronted with a single realization of data at irregularly spaced locations. Our method hinges on formulating a statistic that tracks a stable microergodic parameter of the exponential covariance function, allowing us to address the intricate challenges of nonstationary processes that lack repeated measurements. We implement the fused lasso technique to elucidate nonstationary patterns at various resolutions. For prediction purposes, we segment the spatial domain into stationary sub-regions via Voronoi tessellations. Additionally, we devise a robust test for stationarity based on contrasting the sample means of our proposed statistics between two selected Voronoi subregions. The effectiveness of our method is demonstrated through simulation studies and its application to a precipitation dataset in Colorado. Supplementary materials accompanying this paper appear online. [ABSTRACT FROM AUTHOR]

This paper introduces a nonlinear PI controller for improved speed regulation in permanent magnet direct current (PMDC) motor drive systems. The nonlinearity comes from the exponential (Exp) block placed in front of the classical PI controller, which uses a tunable exponential function to map the speed error nonlinearly. Such a configuration has not been studied till now, thus meriting further investigation. We consider an exponential PI (EXP-PI) controller and to attain the best performance from this controller, its parameters are optimized offline using salp swarm algorithm (SSA), which borrows its inspiration from the way of forage and navigation of salps living in deep oceans. To indicate the credibility of SSA tuned EXP-PI controller convincingly, numerous experiments on speed regulation in PMDC motor have been implemented using DSP of TMS320F28335. The results obtained are also compared to similar results in the literature. It is shown that the proposed approach performs well in practice by ensuring tight tracking of the speed reference and superb torque disturbance rejection for the closed loop control. Furthermore, superior performance is achieved by the proposed nonlinear PI controller with respect to a fixed-gain PI controller. [ABSTRACT FROM AUTHOR]

In this paper, a numerical formulation was developed to generate the consistent mass matrix for Timoshenko tapered beam-column element for geometrically nonlinear transient analysis. The basis of the suggested solution is the exact shape functions and their derivatives, which describe the non-uniformity of the element properties. To illustrate the variations in section properties along the tapered element length, the section properties were presented as exponential functions with tapering indices. The model can simulate elements with various solid and hollow cross-sections. The suggested formulation is integrated into a Visual Basic program to perform the analysis, along with numerous examples to verify its precision and effectiveness. As a practical application of the proposed formulation, a structural system was proposed for offshore wind turbines with high elevations, and a geometrical nonlinear dynamic analysis was conducted. The results demonstrated the proposed model's ability to perform this type of complex calculation with minimal computational effort. [ABSTRACT FROM AUTHOR]

This paper concentrates on constructing optical soliton solutions for Kudryashov's law of nonlinear refractive index, stemming from the dual form of nonlocal nonlinearity and the quadrupled-power law. Utilizing the new Kudryashov approach, we derive a range of optical wave patterns for the current model with a conformable fractional derivative. We introduce innovative optical solutions characterized by exponential and hyperbolic functions. These solutions fall into distinct categories, encompassing bell-shaped, bright, singular, and wave optical soliton solutions. To demonstrate the significance of the current optical soliton solutions, we present two-dimensional, three-dimensional, and contour plots for bell-shaped, bright, singular, and wave soliton solutions. Further, we illustrate the behavior of several novel optical solutions through graphical representations for various values of the time parameter and fractional order derivative parameter. It can be asserted that the present method is an efficient technique for investigating optical solutions in various types of Schrödinger equations with fractional and integer orders. [ABSTRACT FROM AUTHOR]

This paper deals with the extraction of exact solutions of nonlinear extended quantum Zakharov–Kuznetsov equation by implementing well founded approaches like generalized exponential rational function method and G ′ G , 1 G expansion method. Singular, periodic, hyperbolic and rational function solutions are achieved for particular values of parameters. The obtained solutions are discussed graphically by plotting 2D line plots and 3D surface plots. This research findings demonstrate that applying these approaches is a feasible means of solving numerous precise PDE solutions. The computations are worked out in this script with the aid of Mathematica software. [ABSTRACT FROM AUTHOR]

The class of geometrically convex functions is a rich class that contains some important functions. In this paper, we further explore this class and present many interesting new properties, including fundamental inequalities, supermultiplicative type inequalities, Jensen-Mercer inequality, integral inequalities, and refined forms. The obtained results extend some celebrated results from the context of convexity to geometric convexity, with interesting applications to numerical inequalities for the hyperbolic and exponential functions. [ABSTRACT FROM AUTHOR]

This article studies robust optimal asset-liability management problems for an ambiguity-averse manager in a possibly non-Markovian environment with stochastic investment opportunities. The manager has access to one risk-free asset and one risky asset in a financial market. The market price of risk relies on a stochastic factor process satisfying an affine-form, square-root, Markovian model, whereas the risky asset’s return rate and volatility are potentially given by general non-Markovian, unbounded stochastic processes. This financial framework includes, but is not limited to, the constant elasticity of variance (CEV) model, the family of 4/2 stochastic volatility models, and some path-dependent non-Markovian models, as exceptional cases. As opposed to most of the papers using the Hamilton-Jacobi-Bellman-Issacs (HJBI) equation to deal with model ambiguity in the Markovian cases, we address the non-Markovian case by proposing a backward stochastic differential equation (BSDE) approach. By solving the associated BSDEs explicitly, we derive, in closed form, the robust optimal controls and robust optimal value functions for power and exponential utility, respectively. In addition, analytical solutions to some particular cases of our model are provided. Finally, the effects of model ambiguity and market parameters on the robust optimal investment strategies are illustrated under the CEV model and 4/2 model with numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we design a competition framework for two insurers with ambiguity aversion under the utility framework and investigate the resulting stochastic reinsurance game problem. Each insurer does not have perfect confidence in the drift terms of the insurance risk and chooses to purchase per-loss reinsurance to reduce her claim risk, and the reinsurance premium is determined via the mean-variance premium principle. The objective of each insurer is to find the optimal reinsurance strategy so as to maximize the ratio of expected utility of her terminal payoff to her competitor's under the worst-case scenario. By the dynamic programming principle and corresponding Hamilton–Jacobi–Bellman–Isaacs equation, we derive the solutions for both the equilibrium reinsurance strategy and value function under the exponential utility function. In particular, we examine the existence and uniqueness of equilibrium strategy. Finally, several numerical examples are presented to illustrate the effects of competitive relationship, ambiguity aversion and some important model parameters on the equilibrium strategy, which provide useful insights for reinsurance in reality. [ABSTRACT FROM AUTHOR]

Modeling of dielectric relaxation function ϕ(t) by a distribution of exponential decay functions is advantageous due to its monotonically decreasing property which ensures that ϕ(t) is integrable over any period of time. Several equivalent circuits based on simple combination of energy storing and dissipating elements are available in literature which are capable of modeling ϕ(t). One of the widely used two-parameter equivalent circuit for dielectric response modeling of various polymeric dielectric as well as oil-paper insulation is the Maxwell ladder structure. In this paper it is shown that for more accurate modeling and better understanding of the dielectric response of complex insulation system like oil-paper insulation of high voltage equipments operating under temperature gradient, modification of Maxwell model is necessary. The proposed model, similar to the classic Maxwell circuit, is also composed of a number of parallel branches, but unlike the former, the proposed model considers each of the parallel branches to be composed of not just one but a number of exponential functions. [ABSTRACT FROM PUBLISHER]

In last years, chaos-based encryption algorithms have been proposed in the literature to provide information confidentiality in digital images, biometric systems, telemedicine, multiuser networks, among others. In e-health, the confidentiality of biomedical signals is required to avoid illegal activities such as identity theft, wrong medical prescription, fraud or extortion against patients or the healthcare entities. On the other hand, improve the randomness of the chaotic map can increase the randomness of the cryptograms and thus, increase the security of the whole cryptosystem. In this paper, we first propose to improve the randomness of five selected chaotic maps by using trigonometric (sine, cosine and tangent) and the exponential function combined with module one operation. Then, we use the monobit test of NIST 800-22 suite to determine the level of achieved randomness. Finally, we use the selected chaotic map in an encryption algorithm for clinical signals based on improved sequences of two Ushio maps and just one round of confusion-diffusion process. In experimental results, we use electrocardiogram (ECG), electroencephalogram (EEG), and blood pressure signals from PhysioBank ATM data base at different sampling frequency and records of 10 seconds. Based on the simulation results in MATLAB, the main findings are (1) the 2D Ushio map with exponential function and module one achieves the best randomness with 0.9760 in P_value; (2) the encryption scheme presents high robustness against known attacks such extreme sensitivity to plain biosignal and the 128-bit secret key, correlation between plain biosignal and cryptogram close to 0, autocorrelation of cryptogram close to 0, floating frequency of 82.4%, uniform histograms in cryptograms, robustness against noise and occlusion attacks, and high speed of encryption; (3) the cryptosystem can be implemented in (low-cost) limited processing systems such as microcontrollers for wireless body area networks (WBAN) applications in e-health; (4) the propose encryption approach can be used to transmit medical signals securely in e-health for monitoring or diagnosis of diseases. [ABSTRACT FROM AUTHOR]

The key objective of the current manuscript was to investigate the exact solutions of the fractional perturbed Radhakrishnan–Kundu–Lakshmanan model. For this purpose, we applied two reliable and efficient approaches; specifically, the modified simple equation (MSE) and exponential rational function (ERF) techniques. The methods considered in this paper offer solutions for problems in nonlinear theory and mathematical physics practice. We also present solutions obtained graphically with the Maple package program. [ABSTRACT FROM AUTHOR]

In this paper, we try to study the equilibrium structure and stability of a non-uniform self gravitating gaseous slab in vertical direction and in the presence of Cosmic Rays (CRs). Two models have been presented to study the effect of CRs pressure. In the first model, it is assumed that the CRs pressure follows the power law spatial function in vertical direction, and in the second model, it is assumed that the CRs pressure follows an increasing exponential function of z . The results show that the equilibrium structure of the system is different in the presence of CRs and in its absence. Gaseous slab has smaller thickness and lower density in the presence of CRs. Also, the perturbative stability analysis show that a non uniform system without CRs effect is unstable at the regions near to mid-plan and system becomes stable in bigger height. However, in the presence of CRs effect, all regions of system can be unstable. CRs effect increases the growth rate of instability in the inner part of slab and the presence of CRs lead to the instability in outer part of slab. Also, it is found that the critical wave length for instability is dependent to z / H and it is not a constant value in all regions of slab. [ABSTRACT FROM AUTHOR]

The exponential function and its logarithmic counterpart are essential corner stones of nonlinear mathematical modelling. In this paper, we treat their conic extensions, the exponential cone and the relative entropy cone, in primal, dual and polar form, and show that finding the nearest mapping of a point onto these convex sets all reduce to a single univariate root-finding problem. This leads to a fast projection algorithm shown numerically robust over a wide range of inputs. [ABSTRACT FROM AUTHOR]

The vanishing gradient problem under nonconvexity is an important issue when training a deep neural network. The problem becomes prominent in the presence of sigmoid activation. It stops the learning task, which prevents further improvement in the performance of an algorithm. SGD and ADAM are two popular methods frequently used to train deep networks. However, their performance deteriorates in the presence of the vanishing gradient problem. In this paper, we present WSAGrad(AnA daptive Grad ient method with W eighted S ine based step size). It uses a trigonometric function over the exponential moving average of the weight parameters to compute the step size. This is the first work to use a trigonometric function in the calculation of step size. The trigonometric function combined with weight parameters, has the following significance: (1) it will not fade away when the gradient vanishes because the moving average carries information from the past iterations, and (2) as the weight parameters are tuned with each iteration, it approximately shapes the step size based on the geometric properties of the data. Additionally, two new parameters are incorporated to control the stability and convergence of the proposed algorithm. Moreover, we provide a convergence rate under mild assumptions. In the experimental section, we have shown that our proposed step size performs better than the existing baseline on FMNIST, CIFAR − 10, and CIFAR − 100 for the classification task. [ABSTRACT FROM AUTHOR]

The accurate prediction of the stability of open-pit mine slopes is usually one of the difficult problems faced by mining engineers and researchers, which is caused by the indeterminacy and uncertainty contained in the influence factors of stability of open-pit mine slopes. The single-valued neutrosophic number (SVNN) is very suitable for representing the information of truth, falsity, and indeterminacy in inconsistent and indeterminate situations. This paper proposes a method combining SVNN with Gaussian process regression (SVNN-GPR) to evaluate the open-pit mine slopes stability in uncertain environment. At first, the proposed method expresses the uncertain influence factors/indices (dip of potential failure plane, cohesion, friction angle, etc.) and the stability state of open-pit mine slopes as SVNNs. Then, the SVNN-GPR is established to obtain the latent complicated relationship between SVNN influence factors and slope stability. Finally, we use the score values of the SVNN output of the proposed method to predict the stability of each slope. To test the performance of the proposed method, we collected 286 slope cases from Zhejiang Province, China. The practical application results reflect that the SVNN-GPR method based on the exponential covariance function and isotropic distance measure has best training and testing results, and the training accuracy reaches 98.0% and the testing accuracy reaches 96.5%. This shows the proposed SVNN-GPR method provides a new effective way for predicting open-pit mine slopes stability in inconsistent and indeterminate situations. [ABSTRACT FROM AUTHOR]

The degenerate versions of special polynomials and numbers, initiated by Carlitz, have regained the attention of some mathematicians by replacing the usual exponential function in the generating function of special polynomials with the degenerate exponential function. To study the relations between degenerate special polynomials, λ -umbral calculus, an analogue of umbral calculus, is intensively applied to obtain related formulas for expressing one λ -Sheffer polynomial in terms of other λ -Sheffer polynomials. In this paper, we study the connection between degenerate higher-order Daehee polynomials and other degenerate type of special polynomials. We present explicit formulas for representations of the polynomials using λ -umbral calculus and confirm the presented formulas between the degenerate higher-order Daehee polynomials and the degenerate Bernoulli polynomials, for example. Additionally, we investigate the pattern of the root distribution of these polynomials. [ABSTRACT FROM AUTHOR]

Boosting has proven its superiority by increasing the diversity of base classifiers, mainly in various classification problems. In reality, target variables in classification often are formed by numerical variables, in possession of ordinal information. However, existing boosting algorithms for classification are unable to reflect such ordinal target variables, resulting in non‐optimal solutions. In this paper, we propose a novel algorithm of ordinal encoding adaptive boosting (AdaBoost) using a multi‐dimensional encoding scheme for ordinal target variables. Extending an original binary‐class AdaBoost, the proposed algorithm is equipped with a multi‐class exponential loss function. We show that it achieves the Bayes classifier and establishes forward stagewise additive modeling. We demonstrate the performance of the proposed algorithm with a base learner as a neural network. Our experiments show that it outperforms existing boosting algorithms in various ordinal datasets. [ABSTRACT FROM AUTHOR]

Under the Pythagorean fuzzy environment, this paper presents a multi-attribute decision-making (MADM) model based on exponential entropy measure and exponential similarity measure to evaluate new energy battery supplier's performance. In this method, the notion of Pythagorean fuzzy linguistic sets (PFLSs) is first introduced by combining the linguistic fuzzy sets (LFSs) and the Pythagorean fuzzy sets (PFSs). Then, the axiomatic definitions of Pythagorean fuzzy entropy and Pythagorean fuzzy similarity measure are developed to measure the degree of uncertainty and similarity between two Pythagorean fuzzy linguistic values (PFLVs). The PFLVs can be expressed by the linguistic membership degree (LMD) and linguistic non-membership degree (LNMD). In addition, we construct two new information measure formulas based on exponential function. Through a series of proofs, we verify that they satisfy the axiomatic conditions of entropy and similarity measure of Pythagorean fuzzy language respectively. On this basis, we research the relationship between the two information measures. Finally, we present a novel Pythagorean fuzzy linguistic MADM model. An example for evaluating performance of new energy battery supplier is given to explain the effectiveness of the newly-developed approach. The stability and validity of the newly-developed approach is performed by sensitivity analysis and comparative analysis. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the necessary conditions to optimize a given functional, involving a generalization of the tempered fractional derivative. The exponential function is replaced by the Mittag–Leffler function, and the kernel depends on an arbitrary increasing function. The Lagrangian depends on time, the state function, its fractional derivative, and we add a terminal cost function to the formulation of the problem. Since this new fractional derivative is presented in a general form, some previous works are our own particular cases. In addition, for different choices of the kernel, new results can be deduced. Using variational techniques, the fractional Euler–Lagrange equation is proved, as are its associated transversality conditions. The variational problem with additional constraints is also considered. Then, the question of minimizing functionals with an infinite interval of integration is addressed. To end, we study the case of the Herglotz variational problem, which generalizes the previous one. With this work, several optimization conditions are proven that can be useful for different optimization problems dealing with various fractional derivatives. [ABSTRACT FROM AUTHOR]

This paper deals with the numerical implementation of the exponential Drucker-Parger plasticity model in the commercial finite element software, ABAQUS, via user subroutine UMAT for adhesive joint simulations. The influence of hydrostatic pressure on adhesive strength was investigated by a modified Arcan fixture designed particularly to induce a different state of hydrostatic pressure within an adhesive layer. The developed user subroutine UMAT, which utilizes an associated plastic flow during a plastic deformation, can provide a good agreement between the simulations and the experimental data. Better numerical stability at highly positive hydrostatic pressure loads for a very high order of exponential function can also be achieved compared to when a non-associated flow is used. [ABSTRACT FROM AUTHOR]

This paper derives distributions from the U-quadratic and the T-X family of distributions labeled as the T-extended Standard U-quadratic-G family of distributions or simply, TeSU-G family. In particular, the TeSU-Weibull distribution (TeSU-W) is explored with respect to some statistical properties such as its limiting distribution, moment, mean and variance and moment generating function. Also, the statistical properties of the TeSU-Exponential distribution (TeSU-E) which is a special case of the TeSU-W are also derived. The Weibull and Exponential distributions are mostly used in life data analysis because of its ability to adapt to different situations. Moreover, the formula for the median is derived via a proposed algorithm. Simulation study is conducted to verify the performance of the ML estimates of the TeSU-W distribution for varied sample sizes. Further, real life data analysis reveals that derived extended distribution can provide a better fit than several well-known distributions. [ABSTRACT FROM AUTHOR]

This paper presents a series of structure-preserving model order reduction algorithms for K-power bilinear systems via Laguerre functions. The method first aims to rewritten the K-power bilinear system as a general bilinear system and calculate the approximate low-rank factors of the cross Gramian of the bilinear system by combining the idea of Laguerre functions expansion of the matrix exponential function. After that, the approximate balanced system of the K-power bilinear system is constructed by the corresponding projection transformation of each subsystem. In order to achieve the purpose of model order reduction, the states with smaller singular values are then truncated, so as to further obtain the reduced order model. For this approach, there is a disadvantage that unstable systems may be generated although the original one is stable. To alleviate the inadequacies of this approach, we have improved the model reduction procedure, which is based upon the dominant subspace projection method. In addition, we also carried out a correlation analysis on the stability of improved algorithms. Finally, numerical experiments are employed to substantiate the effectiveness of the presented algorithms. [ABSTRACT FROM AUTHOR]

Rock-filled concrete (RFC) technology is a new type of mass concrete construction technology, which consists of two basic components: the force transfer frame formed by large-size rock accumulation and the matrix formed by self-compacting concrete (SCC) filling. Its unique construction method also distinguishes RFC from ordinary concrete in terms of its force characteristics. In this paper, RFC is considered as a composite material consisting of aggregate and SCC; based on the realistic failure process analysis (RFPA) method, the effects of specimen size and aggregate size on the compressive strength of RFC were studied. Firstly, RFC cube specimens were prepared and uniaxial compression tests were conducted. During the preparation process, in order to eliminate the influence of factors such as shape, spatial distribution state, and volume share of aggregates on the compressive strength, aggregates of different sizes were set as spheres and arranged in simple cubic stacking; then a numerical model of RFC with different specimen sizes and different aggregate sizes was established for uniaxial compression numerical simulation experiments to analyze the variation law and failure pattern of the RFC compressive strength. The results indicate that the compressive strength of RFC exhibits a significant size effect and follows a negative exponential function distribution law; with the same volume fraction of aggregate, the smaller the aggregate size, the higher the compressive strength of the RFC will be, and this increasing trend gradually levels off. Based on the findings of this study, it is recommended that the size effect and the reduction of aggregate size on dam strength be taken into account in the design of RFC dams. [ABSTRACT FROM AUTHOR]

In this paper, the numerical micromodulus is derived for the plane stress problem to develop a new insight into the application of bond-based peridynamics. Considering the nonlocal property of peridynamics, the numerical micromodulus coupled with influence function provides a reasonable description of the long-range force effect. Through several numerical applications, the effectiveness of the numerical modulus coupled with various influence functions to simulate deformation and failure is analyzed. In addition, a load increment algorithm based on fictitious density is developed specifically for quasi-static problems. It is indicated that the introduction of the influence function can enhance the accuracy in deformation and failure simulation, which is valuable for the advancement and application of numerical micromoduli. Through a comprehensive trade-off between simulation accuracy and stability, the numerical micromodulus coupled with the exponential influence function proves to be the more effective option for brittle material. [ABSTRACT FROM AUTHOR]

This paper proposed a closed-form solution for the 2D transient heat conduction in a rectangular cross-section of an infinite bar with the general Dirichlet boundary conditions. The boundary conditions at the four edges of the rectangular region are specified as the general case of space–time dependence. First, the physical system is decomposed into two one-dimensional subsystems, each of which can be solved by combining the proposed shifting function method with the eigenfunction expansion theorem. Therefore, through the superposition of the solutions of the two subsystems, the complete solution in the form of series can be obtained. Two numerical examples are used to investigate the analytic solution of the 2D heat conduction problems with space–time-dependent boundary conditions. The considered space–time-dependent functions are separable in the space–time domain for convenience. The space-dependent function is specified as a sine function and/or a parabolic function, and the time-dependent function is specified as an exponential function and/or a cosine function. In order to verify the correctness of the proposed method, the case of the space-dependent sinusoidal function and time-dependent exponential function is studied, and the consistency between the derived solution and the literature solution is verified. The parameter influence of the time-dependent function of the boundary conditions on the temperature variation is also investigated, and the time-dependent function includes harmonic type and exponential type. [ABSTRACT FROM AUTHOR]

The Pantograph equation is a fundamental mathematical model in the field of delay differential equations. A special case of the Pantograph equation is well known as the Ambartsumian delay equation which has a particular application in Astrophysics. In this paper, the Laplace transform is successfully applied to solve the Pantograph delay equation. The solution is obtained in a closed series form in terms of exponential functions. This closed form reduces to the corresponding solution in the relevant literature for the Ambartsumian delay equation as a special case. In addition, the convergence of the obtained series is proved theoretically and validated graphically. Furthermore, the accuracy of the numerical results are estimated through several computations of the residual errors. It is shown that such residuals tend to zero, even in a huge domain. The obtained results reveal that the Laplace transform is a powerful approach to solve linear delay differential equations, including the Pantograph model. [ABSTRACT FROM AUTHOR]

Let M = ρ − 1 I ∈ M n (R) be an expanding matrix with 0 < ∣ ρ ∣ < 1 and D ⊂ Z n be a finite digit set with 0 ∈ D and Z (m D) − Z (m D) ⊂ Z (m D) ∪ { 0 } ⊂ m − 1 Z n for a prime m, where Z (m D) := { x : ∑ d ∈ D e 2 π i ⟨ λ , x ⟩ = 0 } . Let μM,D be the associated self-similar measure defined by μ M , D (⋅) = 1 | D | ∑ d ∈ D μ M , D (M (⋅) − d) . In this paper, the necessary and sufficient conditions for L2(μM,D) to admit infinite orthogonal exponential functions are given. Moreover, by using the order theory of polynomial, we estimate the number of orthogonal exponential functions for all cases that L2(μM,D) does not admit infinite orthogonal exponential functions. [ABSTRACT FROM AUTHOR]

In the paper, the authors find a sufficient and necessary condition for the power-exponential function 1 + 1 x α x to be a Bernstein function, derive closed-form formulas for the nth derivatives of the power-exponential functions 1 + 1 x α x and (1 + x) α / x , and present a closed-form formula of the partial Bell polynomials B n , k (H 0 (x) , H 1 (x) , ⋯ , H n − k (x)) for n ≥ k ≥ 0 , where H k (x) = ∫ 0 ∞ e u − 1 − u e u u k − 1 e − x u d u for k ≥ 0 are completely monotonic on (0 , ∞) . [ABSTRACT FROM AUTHOR]

Let f (z) be an entire function of exponential type τ, D ζ [ f (z) ] = τ f (z) + i (1 − ζ) f ′ (z) , and h f (θ) = lim sup r → ∞ log ⁡ | f (r e i θ) | / r . Gardner and Govil [Proc Am Math Soc. 1995;123:2757–2761] proved that if h f (π / 2) = 0 , and f (z) ≠ 0 in y = ℑ z > 0 , then sup − ∞ ≤ x ≤ ∞ | D ζ f (x) | ≤ τ 2 (| ζ | e τ | y | + 1) sup − ∞ ≤ x ≤ ∞ | f (x) | , for ℑ z ≤ 0 and | ζ | ≥ 1. In this paper, we present an extension of this result for entire functions of exponential type belonging to L p (R) , p>0. It also contains several known results as special cases. [ABSTRACT FROM AUTHOR]

This paper presents a simplified analytical model for predicting nonlinear mechanical responses of flexible composite sheet (FCS) subjected to out-of-plane loading. New geometric model based on three-parameter exponential function is proposed to depict 3D funnel-like geometric shape of out-of-plane loaded FCS, and nonlinear constitutive model is then derived to describe the load-displacement curves of out-of-plane loaded FCS. Finally, model parameters are determined through the principle of minimum potential energy. In order to verify new models, out-of-plane loading tests are performed on PWF (plain woven fabric) polyester reinforced HNR (hydrogenated nitrile rubber) composite sheets with three length-width ratios of 1, 2 and 3, and the predictions agree well with the experiments, demonstrating the practical and effective use of the proposed model. [ABSTRACT FROM AUTHOR]

This paper is the sequel to " B n − 1 -bundles on the flag variety, I". We continue our study of the orbits of a Borel subgroup B n − 1 of G n − 1 = G L (n − 1) (resp. S O (n − 1)) acting on the flag variety B n of G = G L (n) (resp. S O (n)). We begin by using the results of the first paper to obtain a complete combinatorial model of the B n − 1 -orbits on B n in terms of partitions into lists. The model allows us to obtain explicit formulas for the number of orbits as well as the exponential generating functions for the sequences { | B n − 1 ﹨ B n | } n ≥ 1. We then use the combinatorial description of the orbits to construct a canonical set of representatives of the orbits in terms of flags. These representatives allow us to understand an extended monoid action on B n − 1 ﹨ B n using simple roots of both g n − 1 and g and show that the closure ordering on B n − 1 ﹨ B n is the standard ordering of Richardson and Springer. [ABSTRACT FROM AUTHOR]

The parameter values of complex media can be uncertain in reality and uncertainty quantification (UQ) in the simulation of wave propagation is essential. In this paper, an efficient surrogate model based on the artificial neural network (ANN) is developed to imitate the concerned ground penetrating radar (GPR) calculation. A two-dimensional GPR system is simulated with the auxiliary differential equation (ADE) finite-difference time-domain (FDTD), and the soil is considered as a nonmagnetic medium with the frequency-dependent dielectric permittivity represented by a two-term Debye model. A solid metallic object and a piece of dry granite are buried in the dispersive soil whose parameter values are considered uncertain. The framework of the surrogate model is presented for GPR system modeling. Different popular activation functions are applied to the proposed surrogate model and their results are analyzed. Compared with other activation functions, the activation function of exponential linear unit has a better performance in the training process. Moreover, the dropout method is used to reduce overfitting to a large extent. At last, the well trained surrogate model is applied for UQ to GPR calculation instead of running one thousand full-wave GPR simulations, and the results show its accuracy and efficiency. [ABSTRACT FROM AUTHOR]

In this paper, we study the nonuniform fast Fourier transform with nonequispaced spatial and frequency data (NNFFT) and the fast sinc transform as its application. The computation of NNFFT is mainly based on the nonuniform fast Fourier transform with nonequispaced spatial nodes and equispaced frequencies (NFFT). The NNFFT employs two compactly supported, continuous window functions. For fixed nonharmonic bandwidth, we show that the error of the NNFFT with two sinh -type window functions has an exponential decay with respect to the truncation parameters of the used window functions. As an important application of the NNFFT, we present the fast sinc transform. The error of the fast sinc transform is estimated as well. [ABSTRACT FROM AUTHOR]