Search

Bond line thickness (BLT) is an essential parameter of thermal conductive composite gels as the thermal interface material (TIM). Extensive research has been performed on designing next-generation TIMs with high thermal conductivity; however, it remains elusive how to link laboratory measurements and the theoretically predicted BLT. Here, we propose a new model to estimate BLT based on a rheological property, in which the TIM is assumed to be a simple power law fluid. To avoid the unrealistic situation of the BLT tending to zero, we introduce a decaying exponential function to describe the influence from fillers during the lid attach process and rebuild the force balance equation. Compared with previously reported models, the theoretical prediction BLT based on the proposed model is in good agreement with the experimental data. Our model has a guiding significance in predicting the BLT, which may help to optimize the thermal performance of TIMs. [ABSTRACT FROM AUTHOR]

This study investigates the decomposition of bath correlation functions (BCFs) in terms of complex exponential functions, with an eye on the realistic modeling of open quantum systems based on the hierarchical equations of motion. We introduce the theoretical background of various decomposition schemes in both time and frequency domains and assess their efficiency and accuracy by demonstrating the decomposition of various BCFs. We further develop a new procedure for the decomposition of BCFs originating from highly structured spectral densities with a high accuracy and compare it with existing fitting techniques. Advantages and disadvantages of each methodology are discussed in detail with special attention to their application to the corresponding quantum dynamical problem. This work provides fundamental tools for choosing and using a variety of decomposition techniques of BCFs for the study of open quantum systems in structured environments. [ABSTRACT FROM AUTHOR]

Electronic relaxation dynamics of solution-phase redox-exfoliated molybdenum disulfide (MoS2) monolayer and multilayer ensembles are described. MoS2 was exfoliated using polyoxometalate (POM) reductants. This process yields a colloidal heterostructure consisting of MoS2 2D sheet multilayers with surface-bound POM complexes. Using two-dimensional electronic spectroscopy, transient bleaching and photoinduced absorption signals were detected at excitation/detection energies of 1.82/1.87 and 1.82/1.80 eV, respectively. Approximate 100-fs bandgap renormalization (BGR) and subsequent defect- and phonon-mediated relaxation on the picosecond timescale were resolved for several MoS2 thicknesses spanning from 1 to 2 L to ∼20 L. BGR rates were independent of sample thickness and slightly slower than observations for chemical vapor deposition-grown MoS2 monolayers. However, defect-mediated relaxation accelerated ∼10-fold with increased sample thicknesses. The relaxation rates increased from 0.33 ± 0.05 to 1.2 ± 0.1 and 3.1 ± 0.4 ps−1 for 1–2 L, 3–4 L, and 20 L fractions. The thicknesses-dependent relaxation rates for POM-MoS2 heterostructures were modeled using a saturating exponential function that showed saturation at thirteen MoS2 layers. The results suggest that the increased POM surface coverage leads to larger defect density in the POM-MoS2 heterostructure. These are the first descriptions of the influence of sample thickness on electronic relaxation rates in solution-phase redox-exfoliated POM-MoS2 heterostructures. Outcomes of this work are expected to impact the development of solution-phase exfoliation of 2D metal-chalcogenide heterostructures. [ABSTRACT FROM AUTHOR]

Whether visuomotor plasticity of postural control is a trainable feature in older age remains an open question despite the wealth of visually guided exercise games promising to improve balance skill. We asked how aging affects adaptation and learning of a visual feedback (VF) reversal during visually guided weight shifting and whether this skill is modulated by explicit knowledge. Twenty-four older (71.43 + 2.54 years) and 24 young (24.04 1 0.93 years) participants were exposed to a 180° VF reversal while tracking a horizontally moving target by voluntarily weight shifting between two force platforms. An explicit strategy was available to half of the participants with detailed instruction to counter the VF rotation. Individual error data were fitted to an exponential function to assess adaptation. Fewer older (12/24) than younger (21/24) participants adapted to the VF reversal, displaying error curves that fitted the exponential function. Older adults who adapted to the VF reversal (responders. n= 12) reached an asymptote in performance in the same weight shifting cycle and displayed a similar mean asymptotic error compared with young participants. Young but not older responders exhibited an aftereffect when the VF reversal was removed. Instruction did not influence spatial error modulations regardless of age. The large individual variations within the older adults' group during early adaptation suggest age-specific limitations in using explicit cognitive strategies when older adults are exposed to an abrupt mirror feedback reversal that requires a change in weight shifting direction during whole-body postural tracking. [ABSTRACT FROM AUTHOR]

We deduce equations to calculate coupling coefficients of diamond micro-ring resonators. The equations can be used universally at any wavelength but not limited to the transmission peaks/valleys, and can be adapted with triangular cross-sections and tapered waveguides. Consequently, we build three models in accordance to different diamond processing technologies. These models deal with ring resonators with either rectangular cross sections, or triangular cross sections, or with tapered bus for triangular cross sections. The calculated coupling coefficients can be well fitted by exponential decay functions of gap d. Due to geometrical limitations, triangular-cross-sectional diamond resonators are shown to have much smaller (factor 20) coupling coefficients than those of rectangular-cross-sectional resonators. A tapered bus is shown to be beneficial to increase the coupling coefficient. Besides the calculation of coupling coefficients, the method presented in the paper can also be used to calculate the bending loss of micro-ring resonators, as a complement to the existing methods. [ABSTRACT FROM AUTHOR]

In this work, we study the generalized shallow water wave equation to obtain novel solitary wave solutions. The application of this nonlinear model can be found in tidal waves, weather simulations, tsunami prediction, river and irrigation flows. To obtain the new exact solutions of the considered model, we have applied a novel analytical technique namely ( G ′ G ′ + G + A) -expansion method. Using the aforementioned method and computational software, we have obtained different kinds of periodic and singular solitary wave solutions of the generalized shallow water wave equation. The obtained solutions are exponential function and trigonometric function solutions. Using 2D and 3D plots of the wave solutions, the dynamic behaviors of the developed solutions are displayed. The retrieved solutions validated the effectiveness and robustness of the proposed technique. [ABSTRACT FROM AUTHOR]

The periodic nonuniform sampling series, involving periodic samples of both the function and its first r derivatives, was initially introduced by Nathan (Inform Control 22: 172–182, 1973). Since then, various authors have extended this sampling series in different contexts over the past decades. However, the application of the periodic nonuniform derivative sampling series in approximation theory has been limited due to its slow convergence. In this article, we introduce a modification to the periodic nonuniform sampling involving derivatives by incorporating a Gaussian multiplier. This modification results in a significantly improved convergence rate, which now follows an exponential order. This is a significant improvement compared to the original series, which had a convergence rate of O (N - 1 / p) where p > 1 . The introduced modification relies on a complex-analytic technique and is applicable to a wide range of functions. Specifically, it is suitable for the class of entire functions of exponential type that satisfy a decay condition, as well as for the class of analytic functions defined on a horizontal strip. To validate the presented theoretical analysis, the paper includes rigorous numerical experiments. [ABSTRACT FROM AUTHOR]

Recently, the demand for nanocomposites in the form of functionally graded materials (FGM) has increased because of their improved weight-to-stiffness ratios, less delamination effects, and ability to have desired qualities at the right location. Additionally, compared to typical composites, static qualities like strength and elasticity are superior. In this research work, a model for an axially graphene-reinforced functionally graded polymer matrix nanocomposite non-uniform beam is prepared, to obtain the dynamic behavior of the beam in form of its Natural Frequencies. Along the length of the beam, the graphene Nano reinforcement is dispersed in an epoxy polymer matrix as "O" pattern using a function. Material modulus at each location of the beam is modelled using Halpin-Tsai micromechanics theory, the mass density and Poisson's Ratio of the beam are determined using rule of mixture. The geometry non-uniformity of the beam is modelled using an exponential function. Using MATLAB software code, simulation and parametric analysis of the beam are performed for various slenderness ratios and varied boundary conditions. The non-uniform beam result is obtained after the result for a uniform beam is used to validate it. In result it is analyzed that for the particular geometric and reinforcement configuration of the beam, as the non-uniformity in the beam geometry is increases, the fundamental frequency decreases, and the slenderness ratio has also the same effect on its fundamental frequency. [ABSTRACT FROM AUTHOR]

The macroscopic physical and mechanical behavior, mesocosmic pore size distribution, and microscopic particle morphology of polyurethane concrete (PUC) during freeze–thaw conditions are thoroughly examined in this research. The results reveal that as the number of freeze–thaw cycles (F-T cycles) increases, the P-wave velocity of PUC drops constantly, the peak shear strength reduces gradually, but the porosity increases. A four-peak exponential function can be used to describe the pore dispersion features of PUC. With the increase in the number of F-T cycles, PUC showed an increasing trend in all characteristic pore radii, but only the volume fraction of macropores increased. The compressive and shear strength of PUC were positively correlated with the volume fraction of nanopores and micropores and negatively correlated with the volume fraction of macropores. It was proved that the macroporous content is the main reason for the decrease in the mechanical properties of PUC. The fractal dimension of PUC decreases with the increase in the number of F-T cycles, indicating that the complexity of the PUC pore structure decreases after F-T cycles. At the micro-meso-macro scale, the damage progression of PUC under freeze–thaw conditions demonstrates a gradual and mutually feeding connection. The damage evolution process can be broadly divided into three stages, beginning with the formation of micropores in the polyurethane agglomeration, progressing to the gradual germination and expansion of cracks in the polyurethane agglomeration, and finally to the connected sum expansion of cracks between the polyurethane agglomeration and the aggregates, resulting in significant deterioration of the macromechanical properties of PUC. [ABSTRACT FROM AUTHOR]

This study proposes a high computationally efficient data-driven predictive entry guidance method for hypersonic vehicles under multiple no-fly zones. The method uses a reduced-order motion-model-based semianalytic guidance framework to obtain a trained neural network that only requires two-dimensional input. First, the sixth-order entry dynamic motion model is simplified to a third-order model by considering height as the independent variable. Second, based on the reduced-order motion model, a novel exponential function is introduced to yield a semianalytic range-to-go expression in longitudinal guidance. Third, to generate sample trajectory data for training the neural network, the semianalytic guidance framework is supported by the reduced-order motion model with the semianalytic range-to-go expression. Then, a new dynamic lateral guidance reversal logic based on a chain mode strategy is employed to avoid no-fly zones with different configurations and numbers. Finally, to obtain real-time trajectory online, a data-driven online predictive guidance method is proposed based on a back propagation neural network trained by sample trajectory data generated by the semianalytic guidance framework. The proposed method overcomes the drawbacks of most predictor–corrector guidance methods; i.e., the corrected guidance parameters are heavily dependent on the initial values of each iteration in each guidance cycle. Advantageously, the proposed method greatly reduces the online command calculation time in one guidance cycle and only requires two input data to train the neural network, i.e., height and range-to-go, thus yielding results that are close to the engineering reality. The effectiveness of the proposed method is verified through simulations. [ABSTRACT FROM AUTHOR]

In this work, we examine the optimal periodic dividend problem with penalty payments for a diffusion model, where dividends are only paid at Poisson arrival times. Moreover, we assume that (observed) ruin or bankruptcy does not occur even if the surplus is negative, but the penalty payments happen. The goal is to seek an optimal periodic dividend strategy to maximize the expectation of the difference between the present value of dividends and penalty payments. We demonstrate that the optimal strategy is a periodic barrier strategy. For the exponential penalty function, the optimal periodic barrier and the explicit expression for the value function are determined. Several numerical instances are also presented. [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]

Considering that large mechanical equipment often has various excitation sources, the signals generated by these excitation sources are often not simply added or multiplied together, but nonlinearly mixed, which exhibit complex non-stationary characteristics, making classical algorithms difficult to extract fault features. Especially when faults just occur, the fault symptom is often weak and submerged by noise, resulting in low diagnosing accuracy. Accordingly, this article develops a new deep attention method, namely deep exponential excitation networks, which improves diagnosing performance by amplifying important information, that is, the discriminative information between normal and weak fault conditions. The developed method introduces an exponential function into the attention mechanism, yielding a stronger focus on important features. Here, our "stronger" means that the attention mechanism has larger weights, and wider weight ranges, which are achieved via three paradigms of exponential excitation blocks. Meanwhile, the weights are automatically learned in deep networks, which can adaptively amplify the information related to early weak faults according to different severities of faults. Finally, extensive experiments on the marine engine datasets containing different noises demonstrate the effectiveness of the developed method. [ABSTRACT FROM AUTHOR]

In this paper, we attempt to use the Dunkl analog to study the convergence properties of q-Phillips operators by using the q-Appell polynomials. By applying the new sequences of continuous functions ν s , q (z) = (z − 1 2 [ s ] q ) ϱ on [ 0 , ∞) , we construct an improved version of the q-Phillips operators. We calculate the qualitative outcomes in weighted Korovkin spaces to better understand the Phillips operators' uniform convergence results. We obtain the approximation properties by use of the modulus of continuity and functions belonging to the Lipschitz class. Moreover, we give some direct theorems for the function belonging to Peetre's K-functional. [ABSTRACT FROM AUTHOR]

Introduction: The presence of water significantly reduces the mechanical strength of rocks and induces various engineering geological hazards. The water weakening coefficient Kp is used to quantify this effect, defined as the ratio of wet uniaxial compressive strength to the dry value. Methods: A comprehensive physico-mechanical test was conducted on fifteen sandstones under dry and saturated conditions to predict the water weakening coefficient using easily obtainable physical parameters. Multiple linear regression was employed to establish the relationship between these parameters and the saturated water weakening coefficient. Results: The saturated water weakening coefficient decreases with increasing porosity and increases with higher Primary wave velocity (P-wave velocity). Rocks with higher porosity but lower P-wave velocity typically absorb more water. The P-wave velocity and clay mineral content were identified as the best predictors of the saturated water weakening coefficient (R2 = 0.82). Unsaturated water weakening coefficients at any water saturation level were well estimated using a previous exponential function. Discussion: The roles of different clay minerals and P-wave velocity in the water weakening process of rocks are comprehensively discussed. This study enhances the understanding of the water weakening mechanism and provides an improved evaluation model for the water weakening coefficient of sandstones using physical parameters. [ABSTRACT FROM AUTHOR]

The marine atmospheric corrosion behavior of 700L high-strength automotive beam steel exposed for 36 months was investigated by scanning electron microscopy, energy dispersive spectroscopy, X-ray diffraction, and electrochemical technology. The corrosion kinetics of 700L steel followed the exponential function: D = 4.85t1.23. The rust layers were mainly composited of γ-FeOOH, α-FeOOH, γ-Fe2O3, and Fe3O4, regardless of the exposure duration. With an extended exposure time, the porosity, cracking, and spalling of the rust layers increased, and the densification and thickness uniformity decreased. Electrochemical measurements displayed that the corrosion resistance of the rusted 700L steel gradually decreased with increasing exposure time. A good correlation was found between rust layer composition, microstructure, and corrosion resistance. [ABSTRACT FROM AUTHOR]

The Three Gorges Reservoir Area (TGRA) has often suffered the most serious soil erosion in recent years. Soil erosion control still remains on the purple soil, the main soil type for the sloping farmland in this area. Among them, enzyme- induced carbonate precipitation (EICP) can rely on the urease enzymes to catalyze urea. Specifically, the urea can be decomposed into ammonium and carbonate anions, and then precipitated the calcium carbonate (CaCO3) with the presence of carbonate anions and external calcium sources. EICP has been proven to efficiently strengthen the soil for less infiltration, in order to restore the rock and heritage. A promising approach can be regarded to effectively control soil erosion. However, the effect of EICP on the soil detachment capacity is still far from clear, especially for the response of soil detachment to the EICP concentration and maintenance time. Therefore, this study aims to clarify the effect of EICP solution concentration and maintenance duration on the soil detachment capacity of purple soil in the Three Gorges Reservoir Area. The purple soil in the TGRA was taken as the research material. The scouring experiments were conducted under five EICP solution concentrations (0 (for control check), 0.5, 1.0, 1.5, and 2.0 mol/L) at six maintenance durations (1, 7, 15, 30, 60, and 120 d), in order to estimate the soil detachment capacity. Also, the apparent cohesion and calcium carbonate content were measured at different experiment conditions. Moreover, the SEM was employed to reveal the micro-mechanism of erosion reduction by EICP. The results indicated that the soil detachment capacity of purple soil significantly decreased with the application of EICP solution. Compared with the CK, the soil detachment capacity decreased by 19.63%-86.92%, 38.79%-89.41%, 48.13%-89.91%, and 31.78%-84.49%, respectively, at the EICP solution concentration of 0.5, 1.0, 1.5 and 2.0 mol/L, with the most pronounced effect at the concentration of 1.5 mol/L. Additionally, the soil detachment capacity decreased rapidly, whereas, the subsequent slowly decreased as maintenance duration increased. Compared with the maintenance for 1 d, the decreases at 7, 15, 30, 60, and 120 d were 19.79%-84.08%, 33.81%-87.80%, 87.27%-94.21%, 91.41%-93.18%, and 91.18%-92.77%, respectively. Moreover, the reduction amplitude in the soil detachment capacity accounted for 85.79%-92.21% of the total reduction amplitude at the maintenance duration of 7 d under the application of the EICP solution. The apparent cohesion and calcium carbonate content of purple soil showed a trend of increase followed by a decrease with the increase of EICP solution concentration. Compared with the CK, the apparent cohesion increased by 43.70%-77.43%, 58.54%-101.21%, 77.06%-135.68%, and 64.08%-87.86%, respectively, at the EICP solution concentration of 0.5, 1.0, 1.5 and 2.0 mol/L, while the calcium carbonate content increased by 10.29-17.35 times, 11.12-23.00 times, 12.00-29.59 times and 10.88-24.35 times, respectively. Additionally, the apparent cohesion increased by 10.46%-36.38%, 21.98%-46.46%, 35.12%-55.41%, 45.15%-65.49%, and 48.61%-72.76%, respectively, at the maintenance for 7, 15, 30, 60 and 120 d, compared with the maintenance for 1 d. The content of calcium carbonate increased by 54.17%-133.48%, 60.94%-134.39%, 61.98%-134.84%, 61.46%-134.84%, and 62.50%-135.29%, respectively, at the maintenance for 7, 15, 30, 60 and 120 d under the application of EICP solution, compared with the stable content in the CK. The increase amplitude in the apparent cohesion and calcium carbonate content accounted for 37.59%-59.56% and 78.26%- 98.66% of the total increase amplitude, respectively, at the maintenance duration of 7 d. Additionally, the microscopic analysis exposed that the soil detachment capacity was reduced to aggregate the calcium carbonate in the soil surface under the application of EICP solution. Furthermore, the soil detachment capacity was better described by the apparent cohesion and calcium carbonate content with an exponential function. The findings can provide theoretical guidance to promote erosion control in the application of EICP on soil detachment of purple soil in the TGRA. [ABSTRACT FROM AUTHOR]

Sowing depth and simple blockage can limit the traditional planters in the wheat wheat-wide seedling belt during rotary tillage. In this study, the combination design was adopted with the fertilizer pipe and slide knife-type ditching. The slide knife-type ditching and fertilizer pipe were situated at the front-mounted of the working range gap of the wide seedling belt rotary tillage knife group. The coupling operation was realized for the slide knife-type ditching fertilizer pipe and rotary tillage knife group. Among them, the slide knife-type ditching and fertilizer pipe, rotary tillage knife group, seed distributor, and compaction wheel of the same seedling belt were collinear to create a wide seedling belt fertilization and sowing mode. The fundamental parameters were calculated for the blade line of the slide knife-type ditching fertilizer pipe and the arrangement of the rotary tillage knife group. An exponential function curve was fitted for the blade line, with a working depth of 100 mm. The rotary tillage knife group was featured by a symmetrical spiral arrangement with three rotary blades (L = 3) within the same soil soil-cutting area. In addition, the theoretical analysis was also carried out on the principle of cooperation between the slide knife-type ditching fertilizer pipe and the rotary tillage knife group. The discrete element simulation model was constructed to explore the traction force resistance of different slide knife-type ditching fertilizer pipes in the seedbed over time. A systematic investigation was made to clarify the influence of the relative position of the slide knife-type ditching fertilizer pipe and the rotary tillage knife group on the indexes, such as seedbed and sowing depth. The simulation results showed that there was the smallest resistance of 40° slide knife-type ditching fertilizer pipe. The front-mounted fertilizer pipe and rotary tillage knife group were combined to effectively avoid the influence of the fertilizer ditch on the consistency of sowing depth in the wide seedling belt. The field experiment was carried out with reference to the performance experiment standard of sowing operation. The experiment demonstrated that the new planter was better performed to realize the wide seedling belt sowing, when the forward speed of the machine was 1.11 m/s. The bBetter performance was achieved in the uniform sowing and a highly qualified rate of sowing depth, compared with the traditional planter. The qualified rate of sowing depth was 94.36%, while the coefficient of variation was 3.79%, indicating the excellent sowing. The front-mounted fertilizer pipe and the rotary tillage knife group were combined to form an 'inverted triangle' spatial pattern of three-dimensional distribution in the seed bed. This was also beneficial to the early nutrient absorption of the crop. The blockage was further avoided to cause by the small spacing between the fertilizer pipe and the seed distributor. The high passing was fully met the requirements for the wide seedling belt wheat planting. The findings can provide the support to optimize the wheat sowing device in the wide seedling belt. [ABSTRACT FROM AUTHOR]

ABSTRACT A variable gain amplifier (VGA) is an essential building block used in the automatic gain control (AGC) loop to provide a continuous, adjustable gain for the signal strength. To maintain the stability and consistency of the AGC loop, it is necessary to ensure that the gain of the VGA has an accurate dB‐linear characteristic. This tutorial provides a detailed overview of the development of dB‐linear VGAs based on differential pair structures over recent years. We categorize various VGA cells based on differential pair structures, analyze their operating principles, and explain the key features of each topology. Based on observation and extraction of the dB‐linear implementation schemes used by these VGAs, we summarize three basic methods for achieving dB‐linear gain control. We also discuss specific methods for realizing the exponential function, using a true exponential and a mathematical approximation, and present the different types of approximation functions adopted in the works described here. Considerations in regard to the tuning range, gain error, bandwidth, linearity, process‐temperature robustness, and circuit simplicity are also discussed. Finally, we draw comparisons and give perspectives for future dB‐linear VGAs. [ABSTRACT FROM AUTHOR]

This study introduces a novel family of probability distributions called the "tangent exponential-G family," which is derived using trigonometric transformations of the exponential distribution. The significance of this research lies in developing new statistical models with versatile hazard functions, including j-shaped, S-shaped, increasing, and bathtub shapes. The primary aim is to construct and analyze the properties of this new distribution family. We utilized the exponential distribution function and applied the tangent transformation to develop the tangent exponential-G family. Key statistical properties and characteristics of this family are explored. Parameter estimation is performed using different estimation methods, and its accuracy is confirmed through simulation studies, which show reduced biases and mean square errors with increasing sample sizes. We tested the proposed distribution with real-world data sets to demonstrate practical applicability. Comparative analyses using model selection criteria and goodness-of-fit tests reveal that the tangent exponential-G family and its sub-model outperform compared to existing models, indicating its robustness and utility in statistical modeling. [ABSTRACT FROM AUTHOR]

Studies of macroscopic speed modeling of bidirectional pedestrian cross-flows have relied heavily on scenario experiments, but the data itself may be deficient because large-scale scenario experiments are not easy to organize and subjects may not be walking under normal conditions. In order to explore the possibility of using microscopic pedestrian flow simulations for macroscopic speed modeling of pedestrian flows, a series of two-way pedestrian cross-flow simulation experiments were designed. Bidirectional pedestrian flows are defined as Peds1 and Peds2. The crossing angle and pedestrian flow rate are used as variables, and a bidirectional pedestrian flows simulation is designed as an orthogonal experiment. The crossing angles range from 15 to 165 degrees, and bidirectional pedestrian flow rate range from 1 ped/s to 8 ped/s. A series of simulations are built and performed on the GIS agent-based modeling architecture (GAMA) platform. By analyzing the flow data of bidirectional flows in the crossing area, it is found that when the Peds1 density falls below a threshold, Peds1 speed is determined by pedestrians themselves and mainly remains in a free flow state; otherwise, the Peds1 speed decreases with density. The clear effects such as Peds2 density on the Peds1 speed cannot be determined. A piecewise function combined with a linear function and an exponential function is constructed as the Peds1 speed model considering the influence of the crossing angle. The calibration results show that the piecewise function should be better than the non-piecewise function. Compared to the results of established studies, the results in this paper have some differences. Therefore, the simulation method cannot completely replace the scene experiments. However, this approach can provide suggestions for subsequent refinement of the experimental program, as well as a feasible direction for the construction of a speed relationship for bidirectional pedestrian flows. [ABSTRACT FROM AUTHOR]

Study on static in-situ curing characteristics of CFRP based on near infrared laser: The quick curing method of carbon fibre reinforced plastics (CFRP) is one of the hotspots in current research. A static in-situ curing method for CFRP prepreg based on near-infrared laser was put forward in this study. The in-situ curing structural characteristics and the mechanism of CFRP were investigated through real-time surface temperature measurement, COMSOL temperature field simulation, 3D measurement of curing morphology and resin curing degree test. The thermal conductivity of the CFRP along the fiber direction is considerably higher than that along the perpendicular fiber direction. As a result, the temperature profile in the plane takes on an elliptical shape. During the transfer, the temperature field gradually decreases, resulting in an ellipsoidal 3D high-temperature distribution. The different shrinkage phenomena in the different curing regions between the layers lead to an irregular ellipsoidal solidification morphology of the unidirectional CFRP. The temperature in the center of the heat affected zone increases as a power exponential function with time. The area and depth of the heat-affected zone increases with the laser power, and the curing area is positively correlated with the degree of curing. As a result, curing temperature governing equations based on laser power and layer thickness have been proposed, while relationship equations based on laser power, curing depth and curing morphology have been developed. In addition, prediction equations based on curing morphology have been developed for curing degree, in order to achieve precise curing of CFRP. [ABSTRACT FROM AUTHOR]

The main objective of this research is to examine a specific sufficiency criteria for the starlikeness and convexity of order δ , k-uniform starlikeness, k-uniform convexity, lemniscate starlikeness and convexity, exponential starlikeness and convexity, uniform convexity of the Generalized Bessel-Maitland function. Applications of these conclusions to the concept of corollaries are also provided. Additionally, an illustrated representation of these outcomes will be presented. So functional inequalities involving gamma function will be the main research tools of this exploration. The outcomes from this study generalize a number of conclusions from earlier studies. [ABSTRACT FROM AUTHOR]

In this paper, by using q-integers and higher-order generalized Fibonacci numbers, we define the higher-order generalized Fibonacci quaternions with q-integer components. We give some special cases of these newly established quaternions. This article examines q-calculus and quaternions together. We obtain a Binet-like formula, some new identities, a generating function, a recurrence relation, an exponential generating function, and sum properties of quaternions with quantum integer coefficients. In addition, we obtain some new identities for these types of quaternions by using three new special matrices. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the existence of positive periodic solutions of generalized Leslie–Gower-type population models. Using the topological degree, we provide sufficient conditions to demonstrate the existence of positive periodic solutions to the considered models. It is interesting that the positive periodic solutions in this paper are general positive functions, not e exponential functions, which generalizes and improves the existing results. We note that due to the symmetrical property of periodic solutions, the results of this paper provide a deeper understanding of the periodic behavior of biological populations. Two numerical examples show the effectiveness of our main results. [ABSTRACT FROM AUTHOR]

This article investigates a class of multi-agent systems (MASs) with known dynamics external disturbances, where the communication graph is directed, and the followers have undirected connections. To eliminate the impacts of external disturbance, the technologies of disturbance observer-based control are introduced into the containment control problems. Additionally, to save communication costs and energy consumption, a distributed disturbance observer-based event-triggered controller is employed to achieve containment control and reject disturbance. Furthermore, designing the event-triggered function using an exponential function is beneficial for a time-dependent term while ensuring the exclusion of Zeno behavior. Finally, a numerical simulation is provided to validate the effectiveness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

The existence of propane (C3H8) in a CO2-oil mixture has great potential for increasing CO2 solubility and decreasing minimum miscibility pressure (MMP). In this study, the enhanced solubility, reduced viscosity, and lowered MMP of CO2-saturated crude oil in the presence of various amounts of C3H8 have been systematically examined at the reservoir conditions. Experimentally, a piston-equipped pressure/volume/temperature (PVT) cell is first validated by accurately reproducing the bubble-point pressures of the pure component of C3H8 at temperatures of 30, 40, and 50 °C with both continuous and stepwise depressurization methods. The validated cell is well utilized to measure the saturation pressures of the CO2-C3H8-oil systems by identifying the turning point on a P-V diagram at a given temperature. Accordingly, the gas solubilities of a CO2, C3H8, and CO2-C3H8 mixture in crude oil at pressures up to 1600 psi and a temperature range of 25–50 °C are measured. In addition, the viscosity of gas-saturated crude oil in a single liquid phase is measured using an in-line viscometer, where the pressure is maintained to be higher than its saturation pressure. Theoretically, a modified Peng–Robinson equation of state (PR EOS) is utilized as the primary thermodynamic model in this work. The crude oil is characterized as both a single and multiple pseudo-component(s). An exponential distribution function, together with a logarithm-type lumping method, is applied to characterize the crude oil. Two linear binary interaction parameters (BIP) correlations have been developed for CO2-oil binaries and C3H8-oil binaries to accurately reproduce the measured saturation pressures. Moreover, the MMPs of the CO2-oil mixture in the presence and absence of C3H8 have been determined with the assistance of the tie-line method. It has been found that the developed mathematical model can accurately calculate the saturation pressures of C3H8 and/or CO2-oil systems with an absolute average relative deviation (AARD) of 2.39% for 12 feed experiments. Compared to CO2, it is demonstrated that C3H8 is more soluble in the crude oil at the given pressure and temperature. The viscosity of gas-saturated crude oil can decrease from 9.50 cP to 1.89 cP and the averaged MMP from 1490 psi to 1160 psi at 50 °C with the addition of an average 16.02 mol% C3H8 in the CO2-oil mixture. [ABSTRACT FROM AUTHOR]

Relaxation time and frequency spectra are not directly available by measurement. To determine them, an ill-posed inverse problem must be solved based on relaxation stress or oscillatory shear relaxation data. Therefore, the quality of spectra models has only been assessed indirectly by examining the fit of the experiment data to the relaxation modulus or dynamic moduli models. As the measures of data fitting, the mean sum of the moduli square errors were usually used, the minimization of which was an essential step of the identification algorithms. The aim of this paper was to determine a relaxation spectrum model that best approximates the real unknown spectrum in a direct manner. It was assumed that discrete-time noise-corrupted measurements of a relaxation modulus obtained in the stress relaxation experiment are available for identification. A modified relaxation frequency spectrum was defined as a quotient of the real relaxation spectrum and relaxation frequency and expanded into a series of linearly independent exponential functions that are known to constitute a basis of the space of square-integrable functions. The spectrum model, given by a finite series of these basis functions, was assumed. An integral-square error between the real unknown modified spectrum and the spectrum model was taken as a measure of the model quality. This index was proved to be expressed in terms of the measurable relaxation modulus at uniquely defined sampling instants. Next, an empirical identification index was introduced in which the values of the real relaxation modulus are replaced by their noisy measurements. The identification consists of determining the spectrum model that minimizes this empirical index. Tikhonov regularization was applied to guarantee model smoothness and noise robustness. A simple analytical formula was derived to calculate the optimal model parameters and expressed in terms of the singular value decomposition. A complete identification algorithm was developed. The analysis of the model smoothness and model accuracy for noisy measurements was carried out. The equivalence of the direct identification of the relaxation frequency and time spectra has been demonstrated when the time spectrum is modeled by a series of functions given by the product of the relaxation frequency and its exponential function. The direct identification concept can be applied to both viscoelastic fluids and solids; however, some limitations to its applicability have been pointed out. Numerical studies have shown that the proposed identification algorithm can be successfully used to identify Gaussian-like and Kohlrausch–Williams–Watt relaxation spectra. The applicability of this approach to determining other commonly used classes of relaxation spectra was also examined. [ABSTRACT FROM AUTHOR]

The light-use efficiency-based gross primary productivity (LUE-GPP) model is widely utilized for simulating terrestrial ecosystem carbon exchanges owing to its perceived simplicity and reliability. Variations in cloud cover and aerosol concentrations can affect ecosystem LUE, thereby influencing the performance of the LUE-GPP model, particularly in humid regions. In this study, the performance of six big-leaf LUE-GPP models and one two-leaf LUE-GPP model were evaluated in a humid agroforestry ecosystem from 2018–2020. All big-leaf LUE-GPP models yielded GPP values consistent with that derived from the eddy covariance system (GPPEC), with R2 ranging from 0.66–0.73 and RMSE ranging from 1.81–3.04 g C m−2 d−1. Differences in model performance were attributed to the differences in the quantification of temperature (Ts) and moisture constraints (Ws) and their combination forms in the models. The Ts and Ws algorithms in the eddy covariance-light-use efficiency (EF-LUE) model well characterized the environmental constraints on LUE. Simulation accuracy under the common limitation of Ts and Ws (Ts × Ws) was higher than the maximum limitation of Ts or Ws (Min (Ts, Ws)), and the combination of the Ts algorithm in the Carnegie–Ames–Stanford Approach (CASA) and the Ws algorithm in the EF-LUE model was optimized in combination forms, thereby constraining LUE for GPP estimates (GPPBLO, R2 = 0.76). Various big-leaf LUE-GPP models overestimated or underestimated GPP on sunny or cloudy days, respectively, while the two-leaf LUE-GPP model, which considered the transmission of diffuse radiation and the difference in photosynthetic capacity of canopy leaves, performed well (R2 = 0.72, p < 0.01). Nevertheless, the underestimation/overestimation for shaded/sunlit leaves remained under different weather conditions. Then, the clearness index (Kt) was introduced to calculate the dynamic LUE in the big-leaf and two-leaf LUE-GPP models in the form of exponential or power functions, resulting in consistent performance even in different weather conditions and an overall higher simulation accuracy. This study confirmed the potential applicability of different LUE-GPP models and emphasized the importance of dynamic LUE on model performance. [ABSTRACT FROM AUTHOR]

Hypothesis testing for the exponential distribution family consistently gains significant attentions from the statistical community, especially in situations characterized by small sample sizes. In this paper, we propose a novel approach for constructing a Kolmogorov-Smirnov type test based on representative points. This testing statistic is derived through a comparison between two empirical functions: one from the observed data and another from chosen representative points. A distribution-free quantile estimator is used for sample standardization. We also discuss how to select an optimal number of representative points based on the loss function, which is recommended for constructing the empirical function from the exponential distribution family. To evaluate the efficiency of this new test, a comprehensive Monte Carlo simulation is conducted to compare this new test with tailor-made tests. Simulation results show that our test statistic will be more powerful especially for small sample sizes, and it is competitive in the comparison with tailor-made tests. Some datasets are analyzed to further illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

In this work, we are interested in studying the existence of a ground state solution for the problem Δ (w β (x) Δ u) ± div (w β (x) | ∇ u | p − 2 ∇ u) = f (x , u) in B , and u = ∂ u ∂ ν = 0 on ∂ B , where B is the unit ball in R 4 , w β (x) = (log e | x |) β or w β (x) = (log (1 | x |) β for β ∈ (0 , 1) , 2 < p < 4 and f : R → R is a superlinear continuous class function with supercritical exponential growth. We utilize the Nehari manifold method to establish the existence result. [ABSTRACT FROM AUTHOR]

The researchers have developed numerous analytical and numerical techniques for solving fractional partial differential equations most of which provide approximate solutions. Exact solutions, however, are vitally important in a convenient conception of the qualitative properties of the concerned phenomena and processes. In this paper, the pseudo-parabolic-type equations with conformable fractional derivatives are reduced to conformable fractional nonlinear ordinary differential equations by implementing a simple wave transformation. An important benefit of the proposed transformation is that it yields analytical solutions of the conformable pseudo-parabolic type equations by applying the exponential rational function strategy. The sensitivity behaviour of the model has been mentioned thoroughly. [ABSTRACT FROM AUTHOR]

this article's goal is to present the indefinite refined neutrosophic integrals by parts. All situations where integration by parts can be used are covered, including the use of rotating integrals to solve recurring and non-terminating functions like the product of trigonometric and exponential functions. Furthermore, the Tabular method has been implemented in the computation of the indefinite refined neutrosophic integrals. [ABSTRACT FROM AUTHOR]

Load frequency regulation (LFR) is an indispensable scheme in planning electrical power production to provide consumers with stable, reliable and uninterrupted power. In the face of complicated power system (PS) structures with increasing and intricate power demand, new controllers that offer not only good performance, but also easy commissioning in practice are required. To this end, this research introduces an exponential PID (EXP-PID) controller as a new control scheme to ameliorate the LFR performance of PSs. This controller is simple to design and has a nonlinear feature inherited from two tunable exponential functions, which are placed in front of the PID controller and act on the error signal and its time derivative individually. To achieve the utmost performance, the EXP-PID controller's parameters are procured by a corrected variant of the snake optimizer (co-SO). To validate the proposed control scheme, various single-/multi-area single-/multi-source PSs favored in the area are considered as test benches. A thorough comparison with the state-of-the-art approaches is performed to disclose the true efficacy of our proposal. Among the rivals, co-SO tuned EXP-PID controller, despite its simplicity, is found to render credible and promising performance in mitigating frequency and tie-line power deviations effectively. • An EXP-PID controller is introduced for LFR of power systems. • The new controller enjoys advantages of nonlinear feature and adaptive gains. • Corrected variant of snake optimizer is presented for controller optimization. • Several power systems are studied for performance validation. • The dominance of our proposal is vividly affirmed over the state-of-the-art. [ABSTRACT FROM AUTHOR]

Purpose: To investigate the dose rate dependence of MapCHECK3 and its influence on measurement accuracy, as well as the effect of dose rate correction. Materials and methods: The average and instantaneous dose rate dependence of MapCHECK2 and MapCHECK3 were studied. The accuracy of measurements was investigated where the dose rate differed significantly between dose calibration of the MapCHECK and the measurement. Measurements investigated include: the central axis dose for different fields at different depths, off‐axis doses outside the field, and off‐axis doses along the wedge direction. Measurements using an ion chamber were taken as the reference. Exponential functions were fit to account for average and instantaneous dose rate dependence for MapCHECK3 and used for dose rate correction. The effect of the dose rate correction was studied by comparing the differences between the measurements for MapCHECK (with and without the correction) and the reference. Results: The maximum dose rate dependence of MapCHECK3 is greater than 2.5%. If the dose calibration factor derived from a 10 × 10 cm2 open field at 10 cm depth was used for measurements, the average differences in central diode dose were 0.8% ± 1.0% and 1.0% ± 0.8% for the studied field sizes and measurement depths, respectively. The introduction of wedge would not only induce −1.8% ± 1.3% difference in central diode dose, but also overestimate the effective wedge angle. After the instantaneous dose rate correction, above differences can be changed to 1.9% ± 8.1%, 0.2% ± 0.1%, and 0.0% ± 0.9%. The pass rate can be improved from 98.4% to 98.8%, 98.3%–100.0%, and 96.3%–100.0%, respectively. Conclusion: Compared with MapCHECK2 (SunPoint1 diodes), the more pronounced dose rate dependence of MapCHECK3 (SunPoint2 diodes) should be carefully considered. To ensure highly accurate measurement, it is suggested to perform the dose calibration at the same condition where measurement will be performed. Otherwise, the dose rate correction should be applied. [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]

Formulas to calculate multivector exponentials in a basis‐free representation and orthonormal basis are presented for an arbitrary Clifford geometric algebra Clp,q$$ C{l}_{p,q} $$. The formulas are based on the analysis of roots of characteristic polynomial of a multivector. Elaborate examples how to use the formulas in practice are presented. The results are generalized to arbitrary functions of multivector and may be useful in the quantum circuits or in the problems ofanalysis of evolution of the entangled quantum states. [ABSTRACT FROM AUTHOR]

In this paper, we examine a novel generalized (2 + 1) -dimensional Bogoyavlensky–Konopelchenko (gBK) model analytically via application of five mathematical methods, namely called Extended Simple Equation (ESE) method, Modified Extended Auxiliary equation mapping (MEAEM) method, (G ′ / G) -expansion method, Exp (− Ψ (ϕ)) -expansion method and modified F-expansion method, respectively, to obtain different types solitary wave solutions in the form of trigonometric, hyperbolic, rational and exponential functions as compared to solutions exist in [S. T. Chen and W. X. Ma, Math. China 13 (2018) 525; A. Sonia, A. Jamshad, S.-U. Rehman and A. Ali, Int. J. Appl. Comput. Math. 9 (2023)]. The research focuses on physical systems, physiology, mathematical applications, engineering fields, and the chemical processes of species in the porous nanoparticles, examining the impact of various parameters on the nonlinear model. The graphs of some solutions are plotted in the form of two-dimensional and three-dimensional by assigning the particular values to the paraments with the assistance of mathematica software which illustrated the physical behavior of the concern model. The derived solution has numerous applications in fluid dynamics and the interaction of Riemann waves and long waves. [ABSTRACT FROM AUTHOR]

Context. The extreme teraelectronvolt (TeV) blazar 1ES 0229+200 is a high-frequency-peaked BL Lacertae object. It has not shown intraday variability in extensive optical and X-ray observations, nor has it shown any significant variability on any measurable timescale in the 1–100 GeV energy range over a 14-year span; however, variations in the source flux around its average are present in the energy range above 200 GeV. Aims. We aim to search for intraday optical variability in 1ES 0229+200 as part of an ongoing project to search for variability and quasi-periodic oscillations in the high-cadence (2 min), nearly uniformly sampled optical light curves of blazars provided by the Transiting Exoplanet Survey Satellite (TESS). Methods. 1ES 0229+200 was monitored by TESS in its Sectors 42, 43, and 44. We analysed the data of all these three sectors both with the TESS-provided lightkurve software and the eleanor reduction pipeline. We detected a strong, essentially symmetric flare that lasted about 6 h in Sector 42. We fitted the flare's rising and declining phases to exponential functions. We also analysed the light curve of Sector 42 using the Lomb-Scargle periodogram (LSP) and continuous auto-regressive moving average (CARMA) methods. Results. The optical light curve of Sector 42 of the TESS observations displayed in the present work provides the first evidence of a strong, rapid, short-lived optical flare on the intraday timescale in the TeV blazar 1ES 0229+200. The variability timescale of the flare provides the upper limit for the size of the emission region to be within (3.3 ± 0.2–8.3 ± 0.5)×1015 cm. Away from the flare, the slope of the periodogram's power spectrum is fairly typical of many blazars (α < 2), but the nominal slopes for the flaring regions are very steep (α ∼ 4.3), which may indicate that the electron distribution undergoes a sudden change. We discuss possible emission mechanisms that could explain this substantial and rapid flare. [ABSTRACT FROM AUTHOR]

A vast literature highlights the prevalence of impulsive decision making in maladaptive outcomes. Most research has focused on one form—delay discounting. Less research has focused on effort discounting, possibly because of a lack of a standardized task for assessment. In published effort‐discounting tasks, effort is conceptualized in many ways, making it difficult to compare findings across studies. Additionally, most effort‐discounting tasks do not control for the time inherent in completing the effortful task, which makes it difficult to disentangle effort discounting from delay discounting. The current study evaluated the validity of a novel hypothetical effort‐discounting task. The novel task was used to evaluate the influence of the effort‐delay confound on rates of effort discounting in humans. Participants were randomly assigned to complete a confounded or a controlled version of the novel effort‐discounting task. The effort‐discounting data were well described by hyperbolic and exponential functions. When effort and delay were confounded, effort‐discounting rates were significantly higher than when effort alone influenced discounting. The results suggest that data that are produced by effort‐discounting tasks that do not control the effort‐delay confound should be interpreted cautiously because they are also influenced by delay discounting. Task limitations and future directions are discussed. [ABSTRACT FROM AUTHOR]

AbstractAsymptotic goodness-of-fit methods in contingency table analysis can struggle with sparse data, especially in multi-way tables where it can be infeasible to meet sample size requirements for a robust application of distributional assumptions. However, algebraic statistics provides exact alternatives to these classical asymptotic methods that remain viable even with sparse data. We apply these methods to a context in psychometrics and education research that leads naturally to multi-way contingency tables: the analysis of differential item functioning (DIF). We explain concretely how to apply the exact methods of algebraic statistics to DIF analysis using the R package algstat, and we compare their performance to that of classical asymptotic methods. [ABSTRACT FROM AUTHOR]

In this work, the author reviews the origination of normalized tails of the Maclaurin power series expansions of infinitely differentiable functions, presents that the ratio between two normalized tails of the Maclaurin power series expansion of the exponential function is decreasing on the positive axis, and proves that the normalized tail of the Maclaurin power series expansion of the exponential function is absolutely monotonic on the whole real axis. [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]

We obtain the exact order estimates for approximation of the functions of many variables from the generalized Nikol'skii–Besov classes B p , θ Ω R d by de la Vallée Poussin sums in the metrics of the spaces L ∞ R d and L 1 R d . These classes of functions for some given Ω coincide with the well-known classical isotropic Nikol'skii–Besov classes. [ABSTRACT FROM AUTHOR]

This paper investigates the variational approach using nabla (denoted as ∇) within the framework of time scales. By employing two different methods, we derive the Euler-Lagrange equations for first-order variational approach to optimization problems involving exponential functions, as well as for those with both exponential functions and their ∇-derivatives. To establish the high-order variational approach to optimization problem, we present the Leibniz Formula for ∇-derivatives along with its proof. Additionally, we determine the high-order variational approach to optimization problem incorporating ∇-derivatives of exponential functions. Through these analyses, we aim to contribute to the understanding and application of the variational calculus on time scales, offering insights into the behavior of dynamic systems governed by exponential functions and their derivatives. [ABSTRACT FROM AUTHOR]

In this paper, we prove the null controllability of a one-dimensional degenerate parabolic equation with a weighted Robin boundary condition at the left endpoint, where the potential has a singularity. We use some results from the singular Sturm–Liouville theory to show the well-posedness of our system. We obtain a spectral decomposition of a degenerate parabolic operator with Robin conditions at the endpoints, we use Fourier–Dini expansions and the moment method introduced by Fattorini and Russell to prove the null controllability and to obtain an upper estimate of the cost of controllability. We also get a lower estimate of the cost of controllability by using a representation theorem for analytic functions of exponential type. [ABSTRACT FROM AUTHOR]

This paper aims to introduce a new fractional extension of the interval Hermite–Hadamard ( H H ), H H –Fejér, and Pachpatte-type inequalities for left- and right-interval-valued harmonically convex mappings ( L R I V H convex mappings) with an exponential function in the kernel. We use fractional operators to develop several generalizations, capturing unique outcomes that are currently under investigation, while also introducing a new operator. Generally, we propose two methods that, in conjunction with more generalized fractional integral operators with an exponential function in the kernel, can address certain novel generalizations of increasing mappings under the assumption of L R I V convexity, yielding some noteworthy results. The results produced by applying the suggested scheme show that the computational effects are extremely accurate, flexible, efficient, and simple to implement in order to explore the path of upcoming intricate waveform and circuit theory research. [ABSTRACT FROM AUTHOR]

In this paper, the spectral problem of the mKdV equation satisfying the compatibility condition on time scales is directly constructed. By using the zero-curvature equation on time scales, the mKdV equation on time scales is obtained. When  x ∈ R  and  t ∈ R , the equation degenerates to the classical mKdV equation. Then, the single-soliton, two-soliton, and N-soliton solutions of the mKdV equation under the zero boundary condition on time scales are presented via employing the Darboux transformation (DT). Particularly, we obtain the corresponding single-soliton solutions expressed using the Cayley exponential function on four different time scales (R ,  Z , q-discrete,  C). [ABSTRACT FROM AUTHOR]

Early detection of cable trench fires by locating the fire source in a timely manner can reduce the risk of fire. However, existing fire warning methods have low accuracy, long calculation times and difficulty coping with sudden fire situations. We established experimental platforms for cable trenches with different structures and combined these with simulation analysis to investigate the relationship between the ignition point position and the temperature distribution at the ceiling. An exponential function for predicting the ignition point position and the maximum temperature rise of tunnels is proposed based on the extreme values of ceiling temperature. The results indicate that the vertical temperature of the ceiling exhibits an exponential function variation pattern. The maximum deviation for identifying the ignition point is 0.098 m, with an average deviation of 0.044 m and an average accuracy of 98.77%. The maximum temperature prediction error for the ceiling is 14 °C, with an average deviation of 12.33 °C and an average accuracy of 98.30%. Compared to traditional fire prediction methods, the method proposed here has higher accuracy and provides a theoretical basis for early prevention and control of cable trench fires. [ABSTRACT FROM AUTHOR]

In real-life data, count data are considered more significant in different fields. In this article, a new form of the one-parameter discrete linear-exponential distribution is derived based on the survival function as a discretization technique. An extensive study of this distribution is conducted under its new form, including characteristic functions and statistical properties. It is shown that this distribution is appropriate for modeling over-dispersed count data. Moreover, its probability mass function is right-skewed with different shapes. The unknown model parameter is estimated using the maximum likelihood method, with more attention given to Bayesian estimation methods. The Bayesian estimator is computed based on three different loss functions: a square error loss function, a linear exponential loss function, and a generalized entropy loss function. The simulation study is implemented to examine the distribution's behavior and compare the classical and Bayesian estimation methods, which indicated that the Bayesian method under the generalized entropy loss function with positive weight is the best for all sample sizes with the minimum mean squared errors. Finally, the discrete linear-exponential distribution proves its efficiency in fitting discrete physical and medical lifetime count data in real-life against other related distributions. [ABSTRACT FROM AUTHOR]