Exponential Function Research Articles

A detailed quartz and feldspar luminescence chronology for the Khonako II loess section (Southern Tajikistan)

Parts of Central Asia have been dominated by high dust flux since the start of the Quaternary. The resulting loess-palaeosol deposits are important archives for landscape and climate changes, but there is a lack of chronological data for the subaerial deposits of Southern Tajikistan. Our study presents a high-resolution luminescence chronology for the Khonako II section in the Khovaling region. Thirty-seven samples were collected from the first ∼8 m of the section, corresponding to the Holocene soil and the upper part of the Loess 1 (L1) unit. We applied quartz OSL dating to the coarse-silt fraction (40–63 μm) and polymineral pIRIR200,290 dating to the very fine sand fraction (63–90 μm). The polymineral pIRIR200,290 signal has satisfactory characteristics. The quartz dose response curve displays a non-single exponential growth above ∼100 Gy, thus, the De values were estimated by fitting a single exponential function plus linear component to the dose response data. To assess the pIRIR200,290 residual dose at deposition, we used the offset between our quartz and polymineral chronologies from Khonako II and equivalent doses measured on modern dust samples from Tajikistan and Uzbekistan. The resulting 9.2 ± 0.4 Gy dose was then subtracted from the pIRIR200,290 doses for final age calculation. The quartz OSL and pIRIR ages are then generally consistent. The obtained high-resolution luminescence chronology shows that the upper part of the L1 unit accumulated during the end of marine isotope stage (MIS) 3 and through MIS 2 (39–20 ka). The average dust accumulation rates (DAR) increased from ∼31 cm ka−1 to 41 cm ka−1 between MIS 3 and MIS 2. The DAR reached a peak of ∼71 cm ka−1 at 21 ka. A hiatus of ∼7–9 ka was then identified between the end of the last glacial maximum (LGM) and the beginning of the Holocene, and the average DAR decreased during the Holocene. Our results indicate a continuous high dust flux in the Khovaling plateau over the last 39 ka, but reworking processes and potential deflation events mark the LGM-Holocene transition. High-resolution luminescence dating studies in Tajikistan are therefore important to detect potential discontinuities in the sequences and provide an independent timescale for interpreting the climate proxies and calculating dust accumulation rates.

Analytical Calculation of Relationship Temperature and Fatigue and Creep Strength Based on Thermal Activation.

The purpose of this study was to formulate a mathematical expression for the temperature dependence of adhesive strength using various parameters. Adhesive structures are typically exposed to a broad temperature range, spanning from low to high temperatures; therefore, understanding how their strength depends on temperature is crucial. The strength was measured through tensile, fatigue, and creep tests at temperatures ranging from -60 °C to 135 °C. The properties of these test types were thoroughly investigated by analyzing the strength of the test results from a thermal activity perspective. The results demonstrate that there is a clear relationship between temperature and strength. The intensity decreased with temperature according to the exponential function and could be accurately represented using the parameters of thermal activity. The temperature at which the strength begins to decrease in the fatigue test was higher than in the static tests. Consequently, we were able to accurately express the relationship between the temperature and intensity using certain parameters. Few studies successfully developed a precise nonlinear relationship between temperature and intensity using approximate expressions.

Investigation of the wave solutions of two space–time fractional equations in physics

In this study, two fractional differential equations describing the characteristics of three-dimensional nonlinear ion-acoustic waves (IAWs) in plasmas are considered with the conformable fractional derivative (CFD). 3+1-dimensional space–time fractional Jimbo–Miwa (JM) equation and 3+1-dimensional space–time fractional modified KdV–Zakharov–Kuznetsov (mKdV-ZK) equation are reduced into ordinary differential equations and an investigation into the exact solutions is carried out through the modified exponential function method (MEFM). These exact wave solutions are beneficial in interpreting the interior structure and characteristics of physical phenomena modeled by the aforementioned nonlinear evolution equations (NLEEs) arising in magnetized plasma. Various analytical methods were applied to such equations. Therefore, it is vital to determine the proper technique for the present problem. The proposed scheme has demonstrated a different spectrum of wave structures. The portrait of the exact solutions permits the exploration of plasmas, plasma models, and optics. The software system Mathematica is employed and the rational, exponential, trigonometric, and hyperbolic function solutions are acquired. The graphical results are presented for the physical nature of the solutions. The results are compared with the integer-order models.

Analysis of the nonlinear Fitzhugh–Nagumo equation and its derivative based on the Rabotnov fractional exponential function

The Fitzhugh–Nagumo equation is an essential governing equation that explains the process of impulse transmission from the nerves. This work suggests a novel generalized arbitrary-order Fitzhugh–Nagumo equation that is based on the recently developed nonsingular fractional operator. The modified Fitzhugh–Nagumo equation has been generalized using fractional Yang–Abdel–Cattani operator to provide a more accurate representation of the equation with memory effects and non-local behavior. Further, we discussed some interesting and new properties of the proposed fractional operator and the Rabotnov exponential fractional kernel with a modified Sumudu integral transform. In order to solve the proposed nonlinear differential equation, the homotopy perturbation method coupled with the modified Sumudu integral transform technique is implemented to examine the result of a newly proposed Yang–Abdel–Cattani fractional Fitzhugh–Nagumo equation, which converges to the exact solution. The nonlinear terms of this equation are handled in terms of He’s polynomials. The existence and uniqueness of the solution have been demonstrated using the Banach space fixed point theorem. The convergence and error analysis of the suggested technique are also discussed. The findings are expressed in terms of generalized Mittag-Leffler functions. The obtained results are plotted with the help of MATLAB R2016a mathematical software. The results in this work are more accurate, and it is proposed that the new Yang–Abdel–Cattani fractional derivative operator is an effective tool for finding the results of any other nonlinear problems arising in science and engineering. All three problems have been computed for different orders to confirm the significance of the fractionalizing concept in the proposed equation. The increase of the fractional order value ℘ to 1 confirms that our proposed time-fractional Fitzhugh–Nagumo equation in the Yang–Abdel–Cattani sense gets close to the analytic solution.

Pengaruh Penggunaan Abu Cangkang Terhadap Kuat Tekan Beton

The background of this research is that there is still a lot of oyster shell material that has not been utilized, meanwhile the shell has good mechanical properties as well as concrete. Up to this moment, the shell is not used properly so it needs to studied the use as concrete mixture. By the utilization of this waste is expected to reduce the environmental impact. This study was aims to obtain a regression equation of the compressive strength of concrete using shells, the shells used in this study were oyster shells (ostreidae), tested at 28 days of age with 3 variations in the percentage of the use of shell ash material and with 1 variation of normal concrete. The percentage variations used are 0% variation, 5% variation, 10% variation, and 15% variation. In addition, based on the regression equation, the strong relationship between variables will be obtained which is indicated by the value of r square. The implementation of this research was carried out by carrying out a compressive test of concrete cylinder samples with 3 variations of the water cement rasio (W/C), is W/C 0.4, W/C 0.5, and W/C 0.6. The activity was continued by recording and analyzing data by conducting a regression analysis between the relationship between the percentage of shell use and the compressive strength of concrete. The regression equation used is the exponential regression equation, linear regression, polynomial regression order 2. From the test data, it is found that the regression equation is the best for W/C variation 0.4, obtained polynomial regression equation order 2, y = -0.0351x2 + 0, 3279x + 25.075 with r² = 0.9999, for the W/C variation of 0.5, the second order polynomial regression equation is obtained, y = -0.0702x2 + 0.8062x + 23.406 with r² = 0.8983, and for the W/C variation of 0.6 , the second order polynomial regression equation is obtained, y = -0.0404x2 + 0.4008x + 19.074 with a value of r² = 0.9167..

Modulation instability and extraction of fractional optical solitons in the presence of generalized Kudryashov’s law and dual form of non-local nonlinearity

This research delves into the study of optical solitons governed by Kudryashov’s law of nonlinear refractive index, incorporating a conformable fractional derivative, perturbed terms, and a quadrupled-power law in optical fibers. Employing a novel approach known as the generalized exp(− S(ζ) ) expansion method, we identify novel optical soliton solutions characterized by exponential, rational, and hyperbolic functions featuring a conformable fractional derivative. These solutions manifest as unified bright-dark, singular, singular periodic, kink, anti-kink, and novel solitary waves. We employ 3D, contour, and 2D plots to analyze the behavior of these solutions across different temporal and fractional-order derivative parameters, offering an understanding of their physical interpretations. Furthermore, we perform modulation instability (MI) analysis that depends on standard linear stability analysis to derive the MI gain spectrum, demonstrating how well our methodology works for nonlinear problems in the natural sciences and engineering domains. This approach provides an effective way to investigate optical solutions in various integer and fractional Schrödinger equations.

The Relevance of the New Exponential Equation of State for Semiconductors

The Relevance of the New Exponential Equation of State for Semiconductors

Spectrality of infinite convolutions and random convolutions

In this paper, we explore spectral measures whose square integrable spaces admit a family of exponential functions as an orthonormal basis. Our approach involves utilizing the integral periodic zeros set of Fourier transform to characterize spectrality of infinite convolutions generated by a sequence of admissible pairs. Then we delve into the analysis of the integral periodic zeros set. Finally, we show that given finitely many admissible pairs, almost all random convolutions are spectral measures. Moreover, we give a complete characterization of spectrality of random convolutions in some special cases.

Identifying and estimating solar cell parameters using an enhanced slime mould algorithm

This study proposed an enhanced slime mould algorithm (ESMA) for identifying the solar cells’ parameters for five photovoltaic (PV) models, making two modifications to the original slime mould algorithm (SMA). The first modification was an arbitrary average position among the new individual position of slime and the best individual position of the slime mound currently found to resolve the issue of local optimum. Second, the tangent hyperbolical function of the formula p in the original SMA was replaced with an exponential function to create more variations for selecting the updated equation. The proposed ESMA was used to resolve the problem of estimating PV parameters based on the empirical current-voltage (I-V) data. Specifically, ESMA was evaluated on the parameter estimation in several photovoltaic models, i.e., the one-diode model (ODM), dual-diode model (DDM), and PV-module model (PMM). In general, ESMA outperformed the original SMA and other recent algorithms. Also, in order to provide a close approximation of the empirical I-V data of the real PV modules and cells, ESMA was able to determine the optimal parameter values for photovoltaic models.

Cell size induced bias of current density in hypertrophic cardiomyocytes

ABSTRACT Alterations in ion channel expression and function known as “electrical remodeling” contribute to the development of hypertrophy and to the emergence of arrhythmias and sudden cardiac death. However, comparing current density values – an electrophysiological parameter commonly utilized to assess ion channel function – between normal and hypertrophied cells may be flawed when current amplitude does not scale with cell size. Even more, common routines to study equally sized cells or to discard measurements when large currents do not allow proper voltage-clamp control may introduce a selection bias and thereby confound direct comparison. To test a possible dependence of current density on cell size and shape, we employed whole-cell patch-clamp recording of voltage-gated sodium and calcium currents in Langendorff-isolated ventricular cardiomyocytes and Purkinje myocytes, as well as in cardiomyocytes derived from trans-aortic constriction operated mice. Here, we describe a distinct inverse relationship between voltage-gated sodium and calcium current densities and cell capacitance both in normal and hypertrophied cells. This inverse relationship was well fit by an exponential function and may be due to physiological adaptations that do not scale proportionally with cell size or may be explained by a selection bias. Our study emphasizes the need to consider cell size bias when comparing current densities in cardiomyocytes of different sizes, particularly in hypertrophic cells. Conventional comparisons based solely on mean current density may be inadequate for groups with unequal cell size or non-proportional current amplitude and cell size scaling.

Predictive Pattern of Undrained Shear Strength in Stabilized Sulfur Rich Silty Soil Based on Binder and Initial Mixing Water Content

AbstractA laboratory investigation was conducted to identify principal variables-initial mixing water content, porosity, and binder content- impacting undrained shear strength (qu) of stabilized sulfur-rich silty soil. An equation for predicting qu of stabilized soil was established based on the experimental data. Initially, samples were prepared with soils sample with different initial water and binder contents. Multicem, a binder consisting of a mix of cement and cement kiln dust, was added to the samples. Three different percentages of Multicem were mixed at five different soil water contents to measure qu of stabilized mixtures to understand how water content and porosity levels in the samples affect the performance of the binder and their combined impact on the strength of the samples. The soil-binder mixtures were compacted and subsequently cured in laboratory-controlled environment. The prepared samples were tested in uniaxial compression test apparatus. The results evidenced that binder content and corresponding porosity affect the strength of specimens at an equal water content. The results showed that at equal initial mixing water content, the qu of a sample increased by increasing binder content. Furthermore, it was observed that increase of binder content has a reverse effect on porosity. It was appeared lowering the soil water content, initially increased the strength until an optimum water content. Further lowering water content increased the porosity and consequently decreased qu of samples. Moreover, a ratio of porosity/volumetric binder content was chosen to evaluate the impact of these two variables on strength of samples. This study showed that qu is an exponential function of porosity/binder volumetric content ratio which depends on initial mixing water content of mixtures. It was shown at water content lower than the optimum, results of stabilization are more effective than in soil at higher water contents. Therefore, reducing the water content and thereby porosity has more significant effect on improving qu than increasing the binder content.

The role of chlorine promoters in mediating particle size effects in silver-catalyzed ethylene epoxidation

Measured chlorine coverages over Ag/α-Al2O3 catalysts with varying Ag weight loadings (1.3–35 wt%) and different Ag particle size distributions when parsed in terms of Cl coverages over particles of varying size constituted in the distribution reveal that Ag particles of size below ∼30 nm are covered in more than 1 monolayer (ML) of chlorine in presence of 3.5 ppm C2H5Cl. These assessments of Cl coverages were made possible by correlating the cumulative Cl coverage to the lognormal surface area distribution of 22 Ag/α-Al2O3 samples using a single exponential decay function. Fully chlorided small Ag particles exhibit low rates of epoxidation and only large Ag particles which exhibit sub-monolayer Cl coverages catalyze ethylene epoxidation with high ethylene oxide (EO) rates and selectivity. The Ag particle size dependence of Cl coverages plausibly explains why ≥ 100 nm Ag particles are typical in promoted Ag/α-Al2O3 ethylene epoxidation catalysts.

ADAPTIVE CONTROL OF A SUBMARINE FOR VARIOUS DIVING DEPTHS USING AN EXPONENTIAL

Due to the progress of deep submergence capabilities, a submarine is extensively employed on many sides of marine science. For that reason, it has become necessary to design an effective submarine position controller while achieving a fast and stable mission. An adaptive analytical scheme for the underwater submarine was developed. The main purpose of the adaptive analytical scheme is to provide a powerful analytical controller that can successfully steer the submarine from the current state under the water to the surface of water in a short time. To achieve that, a seventh-term exponential function was proposed to reshape the reference diving depth while maintaining the control variable limitation and satisfying initial and final boundary conditions. The direct search method with two cascade loops was employed to achieve a minimum cost function by determining an appropriate constant of the function and minimum final time. However, using the direct search method can be time-consuming since a number of algebraic operations are executed inside these two loops. Therefore, the curve fitting method was used to fit the set of direct search method data using power functions. Then, at a certain diving depth, the function coefficients were computed based on the final settling time and function constant using the Gaussian elimination method. A nominal numerical simulation of the submarine’s model was implemented using both adaptive analytical and linear controllers.

Improved weighted nuclear norm with total variation for removing multiplicative noise

This paper introduces an improved weighted nuclear norm with a total variation model tailored for removing multiplicative noise. The model incorporates a weight matrix to regularize the residual matrix, effectively leveraging image redundancy to differentiate various statistical properties of the noise. Since there is no guarantee of a unique solution, the model is reformulated as a linear equality constraint problem and decomposed into two subproblems. These are addressed by using the alternating direction method of multipliers and the split Bregman method, respectively. In addition, each alternative update step has a closed-form and convergent solution. After obtaining the denoised image in the log-domain, the recovered image is given by using the exponential function and bias correction. Experimental evaluations demonstrate the efficacy of our algorithms in enhancing image restoration quality.

Novel exact traveling wave solutions of the space-time fractional Sharma Tasso-Olver equation via three reliable methods

The dominant intention of this article is to extract the new exact traveling waves solutions of the nonlinear space-time fractional Sharma-Tasso-Olver equation in the sense of beta-derivative by using three integration schemes namely, Riccati-Bernoulli (RB) sub-ODE method, Generalized Bernoulli (GB) sub-ODE method and Generalized tanh (GT) method. By the virtue of employed techniques, different types of solutions are obtained in the form of trigonometric, hyperbolic, and exponential functions respectively. The obtained solutions are also verified for the aforesaid equation through symbolic soft computations. To promote the vital propagated features; some investigated solutions are exhibited in the form of 2D and 3D graphics by passing on the specific values to the parameters under the confined conditions. Further, based on the bifurcation theory, we examine the phase portrait of the proposed nonlinear equation. Furthermore, we ensure that all the solutions are innovative and have remarkable impacts on the prevailing solitary wave theory literature.

Intensification of grape marc (Vitis vinifera) exploitation by subcritical water-ethanol extraction: Effect on polyphenol bioactivities and kinetic modelling

Subcritical solvent extraction (SSE) is an efficient and versatile technology for the recovery of bioactive compounds from food by-products. The present work aims to study the SSE efficiency and kinetics for the extraction of grape marc polyphenols. Water, ethanol, and a 50% water-ethanol mixture (EtOH 50%) were used as green solvents. The higher polyphenol content (4.05 ± 0.23 gGAE/100 gd. m.) and antioxidant activity (42.30 ± 0.68 mg α-toc/mL) were obtained with subcritical EtOH 50% at 120 °C and 10.3 MPa, respectively, 1.5- and 3-fold higher than the conventional extraction. According to kinetic modeling, SSE was four-fold faster and a degradation phenomenon of polyphenols was highlighted for times longer than 10 min. The two-site kinetic model and a second order exponential decay function suitably described the extraction kinetics and degradation phase, respectively (R2 > 0.97). A remarkable effect was highlighted on the polymerization degree and galloylation percentage of proanthocyanidins by SSE, and an increase in their antioxidant activity was observed.

Investigation on optimization-oriented EPC method in analyzing the non-linear oscillations under multiple excitations

The optimization-oriented exponential-polynomial-closure (OEPC) method is extended and investigated to analyze stochastic nonlinear oscillators under multiple excitations, with the purpose of obtaining probabilistic solutions for the corresponding system. The presented method extends the original EPC projection procedure for solving the FPK equation by minimizing an objective function, which is defined as the spatial integration of the weighted square residual error. Using the exponential polynomial function, the parameters within it can be located by seeking the minimum of the objective function. In this paper, the novel method has been tested with four examples of strong nonlinearities raised by polynomial nonlinear terms and parametric excitations. The results provide adequate evidence that the OEPC approach delivers notably improved accuracy compared to the Gaussian closure method and demonstrates superior efficiency compared to Monte Carlo simulation. The OEPC method presents a viable alternative for investigating stochastic nonlinear oscillators.

Nonlinear two-component system of time-fractional PDEs in [formula omitted]-dimensions: Invariant subspace method combined with variable transformation

In this article, we develop a systematic approach of the invariant subspace method combined with variable transformation to find the generalized separable exact solutions of the nonlinear two-component system of time-fractional PDEs (TFPDEs) in (2+1)-dimensions for the first time. Also, we explicitly explain how to construct various kinds of finite-dimensional invariant linear product spaces for the given system using the invariant subspace method combined with variable transformation. Additionally, we present how to use the obtained invariant linear product spaces to derive the generalized separable exact solutions of the discussed system. We also note that the discussed method will help to reduce the nonlinear two-component system of TFPDEs in (2+1)-dimensions into the nonlinear two-component system of TFPDEs in (1+1)-dimensions, which again reduces to a system of time-fractional ODEs through the obtained invariant linear product spaces. More specifically, the significance and efficacy of the systematic investigation of the discussed method have been investigated through the initial and boundary value problems of the generalized nonlinear two-component system of time-fractional reaction–diffusion equations (TFRDEs) in (2+1)-dimensions for finding the generalized separable exact solutions, which can be expressed in terms of the exponential, trigonometric, polynomial, Euler-Gamma and Mittag-Leffler functions. Also, 2D and 3D graphical representations of some of the obtained solutions are presented for different values of fractional orders.

Thermodynamic characteristics and mechanism of low-rank coal oxidation in oxygen-poor environment

Aiming at the restricted oxygen environment of coal mine, this paper focus on the whole process from physical adsorption to chemical reaction between coal and oxygen, and quantum chemical calculations investigate the potentiating or inhibiting effects of different active groups on the amount of oxygen adsorbed and thermally released from the main coal structure, and experimentally investigate the effect of OC on the transformation relationship between active functional groups and active sites. The results showed the coal side-chain structure has an effect on the heat release characteristics of the aromatic ring in the process of oxygen adsorption, and the heat of adsorption of the aromatic ring with alkyl and aldehyde side-chains reaches 422.706 kJ/mol. The relationship between carbon oxide release and temperature at different OC all conformed to the exponential function model, and the apparent activation energy was positively correlated with the OC. The increase of OC narrows the gap between the production and consumption rates of active sites, which is helpful for the further understanding of the coal spontaneous combustion(CSC).

Study and Analysis of Some Impact on GDP of Nepal by Increase the Exports and Decreasing Import, on Economic Growth of Nepal with the Help of Exponential Function

Study and Analysis of Some Impact on GDP of Nepal by Increase the Exports and Decreasing Import, on Economic Growth of Nepal with the Help of Exponential Function