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Taking into account the fluctuation of the growth rate on the left and right sides of the classic QGLF, a quadratic exponential quality gain-loss function (QGLF) is created based on the asymmetric QGLF. The two scenarios of non-normal distribution (triangular distribution) and truncated normal distribution of quality characteristic values are optimized using the quadratic exponential quality gain-loss process mean. Through the case study approaches, the empirical validity and applicability of the quadratic exponential QGLF model are thoroughly assessed, confirming its effectiveness in improving quality management practices.

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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.

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Magnetorheological elastomers (MREs) are a type of smart material that can change their mechanical properties in response to external magnetic fields. These unique properties make them ideal for various applications, including vibration control, noise reduction, and shock absorption. This paper presents an approach for modeling the impact behavior of MREs. The proposed model uses a combination of exponential functions arranged in a multi-layer Preisach model to capture the nonlinear behavior of MREs under impact loads. The model is trained using particle swarm optimization (PSO) and validated using experimental data from drop impact tests conducted on MRE samples under various magnetic field strengths. The results demonstrate that the proposed model can accurately predict the impact behavior of MREs, making it a useful tool for designing MRE-based devices that require precise control of their impact response. The model's response closely matches the experimental data with a maximum prediction error of 10% or less. Furthermore, the interpolated model's response is in agreement with the experimental data with a maximum percentage error of less than 8.5%.

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This study highlights the use of 89Zr-oxalate in diagnostic applications with the help of WinAct and IDAC2.1 software. It presents the biodistribution of the drug in various organs and tissues, including bone, blood, muscle, liver, lung, spleen, kidneys, inflammations, and tumors, and analyzes the maximum amount of nuclear transformation per Bq intake for each organ. The retention time of the maximum nuclear transformation and the absorbed doses of the drug in various organs and tissues are also examined. Data from clinical and laboratory studies on radiopharmaceuticals are used to estimate the coefficients of transition. The accumulation and excretion of the radiopharmaceutical in the organs is assumed to follow an exponential law. The coefficients of transition from the organs to the blood and vice versa are estimated using a combination of statistical programs and digitized data from the literature. WinAct and IDAC 2.1 software are used to calculate the distribution of the radiopharmaceutical in the human body and to estimate the absorbed doses in organs and tissues. The results of this study can provide valuable information for the biokinetic modeling of wide-spectrum diagnostic radiopharmaceuticals. The results show that 89Zr-oxalate has a high affinity for bones and a relatively low impact on healthy organs, making it helpful in targeting bone metastases. This study provides valuable information for further research on the development of this drug for potential clinical applications.

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The foundation substrate's basal contact stresses are typically thought to have a linear distribution, although the actual form is nonlinear. Basal contact stress in thin plates is experimentally measured using a thin film pressure distribution system. This study examines the nonlinear distribution law of basal contact stresses in thin plates with various aspect ratios under concentrated loading, and it establishes a model for the distribution of contact stresses in thin plates using an exponential function that accounts for aspect ratio coefficients. The outcomes demonstrate that the thin plate's aspect ratio significantly affects how the substrate contact stress is distributed during concentrated loading. The contact stresses in the thin plate's base exhibit significant nonlinearity when the aspect ratio of the test thin plate is greater than 6~8. The aspect ratio coefficient-added exponential function model can better optimize the strength and stiffness calculations of the base substrate and more accurately describe the actual distribution of contact stresses in the base of the thin plate compared to linear and parabolic functions. The correctness of the exponential function model is confirmed by the film pressure distribution measurement system that directly measures the contact stress at the base of the thin plate, providing a more accurate nonlinear load input for the calculation of the internal force of the base thin plate.

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Photodynamic therapy (PDT) has significant advantages in the treatment of malignant tumors, such as high efficiency, minimal invasion and less side effects, and it can preserve the integrity and quality of the organs. The power density, irradiation time and photosensitizer (PS) concentration are three main parameters that play important roles in killing tumor cells. However, until now, the underlying relationships among them for PDT outcomes have been unclear. In this study, human malignant glioblastoma U-118MG and melanoma A375 cells were selected, and the product of the power density, irradiation time and PS concentration was defined as the total photodynamic parameter (TPP), in order to investigate the mechanisms of PS sinoporphyrin sodium (DVDMS)-mediated PDT (DVDMS-PDT). The results showed that the survival rates of the U-118MG and A375 cells were negatively correlated with the TPP value in the curve, and the correlation exactly filed an e-exponential function. Moreover, according to the formula, we realized controllable killing effects of the tumor cells by randomly adjusting the three parameters, and we finally verified the accuracy and repeatability of the formula. In conclusion, the establishment and implementation of a newly functional relationship among the PDT parameters are essential for predicting PDT outcomes and providing personalized precise treatment, and they are contributive to the development of PDT dosimetry.

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This work systematically conducts a data analysis based on the numbers of both cumulative and daily confirmed COVID-19 cases and deaths in a time span through April 2020 to June 2022 for over 200 countries around the world. Such research feature aims to reveal the temporal and spatial evolution of the country-level distribution observed in COVID-19 pandemic, and obtains some interesting results as follows. (1) The distributions of the numbers for cumulative confirmed cases and deaths obey power-law in early stages of COVID-19 and stretched exponential function in subsequent course. (2) The distributions of the numbers for daily confirmed cases and deaths obey power-law in early and late stages of COVID-19 and stretched exponential function in middle stages. The crossover region between power-law and stretched exponential behavior seems to depend on the evolution of "infection" event and "death" event. Such observation implies a kind of important symmetry related to the dynamics process of COVID-19 spreading. (3) The distributions of the normalized numbers for each metric show a temporal scaling behavior in 2-year period, and are well described by stretched exponential function. The observation of power-law and stretched exponential behavior in such country-level distributions suggests underlying intrinsic dynamics of a virus spreading process in human interconnected society. And thus it is important for understanding and mathematically modeling the COVID-19 pandemic.

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A previous acute toxicity study of binary mixtures showed that the combined toxicity can be predicted with the parameter k∙ECx. To systematically investigate the ability of k∙ECx to predict the chronic combined toxicity of binary mixtures, the toxicity of six contaminants and five binary mixtures was determined by long-term microplate toxicity analysis (L-MTA) using Aliivibrio fischeri as the test organism. The independent action model (IA) and the relative model deviation ratio (rMDR) were employed to determine the relationship between the Δ(k∙ECx)% and rMDRx. The results showed that these two factors conformed to the exponential function in long-term toxicity. Owing to the time-dependence of toxicity, the mixture type of chronic toxicity changes to the relative type of acute toxicity. If the acute toxicity of binary mixtures changes their mode of joint action throughout the concentration range, the chronic toxicity will also change their mode of joint action, and vice versa. This study clarified the change rules of the joint action of binary mixtures in acute and chronic toxicity which can promote research on chronic toxicity of binary mixtures.

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This study examined the rate and course of gastric evacuation (GE) in rainbow trout Oncorhynchus mykiss in relation to meal size, body size and temperature. The GE experiments were performed on small (mean ± 95% C.I., 17.7 ± 0.5 cm total length), medium (22. 9 ± 0.2 cm) and large (28.3 ± 0.3 cm) rainbow trout fed meals of different sizes using commercial food pellets at water temperatures T ranging from 7.8°C to 19.2°C. Estimating the shape parameter of a general power function suggested that the square root function adequately described the GE in rainbow trout independently of meal size. The effects of total body length L and weight W on gastric evacuation rate (GER) were described by simple power functions. The square root function was further expanded by a temperature function with temperature optimum to describe the effect of temperature. The expanded square root function revealed a considerable effect of body size and temperature on the GER of rainbow trout. The GER increased exponentially with rising temperature, reached an optimum at c. 18.5°C and then declined abruptly to zero at c. 21°C. The GER of rainbow trout could thus be described by d S t d t = - 0.00152 L 0.75 e 0.08 T 1 - e 1.18 T - 20.9 S t (g h-1 ) or d S t d t = - 0.00440 W 0.26 e 0.08 T 1 - e 0.97 T - 21.1 S t (g h-1 ), where St is the current stomach content mass (g), and at post-prandial time t (h). These functions should prove useful to calculate total GE time as well as stomach fullness at different post-prandial times and therefore provide valuable information to develop optimal feeding strategies for farming of rainbow trout.

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Water stable isotope analysis using Cavity Ring-Down Spectroscopy (CRDS) has a strong between-sample memory effect. The classic approach to correct this memory effect is to inject the sample at least 6 times and ignore the first two to three injections. The average of the remaining injections is then used as measured value. This is in many cases insufficient to completely compensate the memory effect. We propose a simple approach to correct this memory effect by predicting the asymptote of consecutive repeated injections instead of averaging over them. The asymptote is predicted by fitting a y = a x + b relation to the sample repetitions and keeping b as measured value. This allows to save analysis time by doing less injections while gaining precision. We provide a Python program applying this method and describe the steps necessary to implement this method in any other programming language. We also show validation data comparing this method to the classical method of averaging over the last couple of injections. The validation suggests a gain in time of a factor two while gaining in precision at the same time. The method does not have any specific requirements for the order of analysis and can therefore also be applied to an existing set of analyzes in retrospect.•We fit a simple y = a x + b relation to the sample repetitions of Picarro L2130-i isotopic water analyzer, in order to keep the asymptote (b) as measured value instead of using the average over the last couple of measurements.•This allows a higher precision in the measured value with less repetitions of the injection saving precious time during analysis.•We provide a sample code using Python, but generally this method is easy to implement in any automated data treatment protocol.

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A previous study has revealed that the parameter k∙ECx, characterizing the shape of concentration-response curves (CRCs), could predict the combined toxicity of binary mixtures. This study further explored the predictability of multi-component mixtures. Eleven component mixtures were designed using the uniform design ray, and the acute toxicity of the eleven environmental pollutants and their mixtures to Vibrio fischeri was determined using microplate toxicity analysis. We used independent action (IA) and the effect residual ratio (ERRx) models to evaluate the combined toxicity of multi-component mixtures and ascertain the functional relationship between σ2(k∙ECx), a parameter characterizing the CRC morphological difference of multi-component mixtures, and combined toxicity. The variance σ2(k∙ECx) of each component characteristic parameter of multi-component mixtures gradually increased in the concentration range, and the relationship between σ2(k∙ECx) and ERRx was consistent with the exponential function. The literature verification showed that this rule is generally applicable to the acute toxicity of multi-component mixtures to luminescent bacteria. The exponential function showed the variation rule of the joint action of multi-component mixtures. In the present study, the joint toxicity of multi-component mixtures can be predicted from single toxicity and small amount of multiple toxicity, circumventing complex multi-component toxicity experiments.

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Patch-based medical image registration has been well explored in recent decades. However, the patch fusion process can generate grid-like artifacts along the edge of patches for the following two reasons: firstly, in order to ensure the same size of input and output, zero-padding is used, which causes uncertainty in the edges of the output feature map during the feature extraction process; secondly, the sliding window extraction patch with different strides will result in different degrees of grid-like artifacts. In this paper, we propose an exponential-distance-weighted (EDW) method to remove grid-like artifacts. To consider the uncertainty of predictions near patch edges, we used an exponential function to convert the distance from the point in the overlapping regions to the center point of the patch into a weighting coefficient. This gave lower weights to areas near the patch edges, to decrease the uncertainty predictions. Finally, the dense displacement field was obtained by this EDW weighting method. We used the OASIS-3 dataset to evaluate the performance of our method. The experimental results show that the proposed EDW patch fusion method removed grid-like artifacts and improved the dice similarity coefficient superior to those of several state-of-the-art methods. The proposed fusion method can be used together with any patch-based registration model.

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The purpose of this study was to compare model estimates of linear sprint mechanical characteristics using timing gates with and without time correction. High-level female soccer players (n = 116) were evaluated on a 35-m linear sprint with splits at 5, 10, 20, 30, and 35 m. A mono-exponential function was used to model sprint mechanical metrics in three ways: without a time correction, with a fixed (+0.3 s) time correction, and with an estimated time correction. Separate repeated-measures ANOVAs compared the sprint parameter estimates between models and also the residuals between models. Differences were identified between all modeled sprint mechanical metrics; however, comparable estimates to the literature occurred when either time correction was used. Bias for both time-corrected models was reduced across all sprint distances compared to the uncorrected model. This study confirms that a time correction is warranted when using timing gates at the start line to model sprint mechanical metrics. However, determining whether fixed or estimated time corrections provide greater accuracy requires further investigation.

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Non-point source pollution has become an important factor affecting the aquatic ecological environment and human health, and the analysis of spatial-temporal variations in non-point source pollution risks is an important prerequisite for pollution control. Based on land-use and land-cover data from 1980 to 2020, the potential non-point source pollution index (PNPI) model was applied in the upper Beiyun River Basin using different weighting methods. The results showed that:① The potential risk of non-point source pollution is high in the southeast and low in the northwest of the basin. Between 1980 and 2020, the total area of extremely high-risk and high-risk non-point source pollution regions showed a decreasing trend, and the main types of land use for extremely high-risk and high-risk regions gradually evolved from paddy fields, drylands, and orchards to urban and rural residential land; ② The weighting of the land use index determined by the mean-square deviation decision, entropy, coefficient of variation, and expert scoring methods was largest among the three PNPI indices, with average weightings of 0.46, 0.53, 0.45, and 0.48, respectively. However, the weightings for runoff and distance indices determined by different weighting methods were notably different, and the proportions of regions with different levels of non-point source pollution risk also varied; ③ The exponential function method, which describes the relationship between source factors and transport factors by constructing the exponential functions of land use, runoff, and distance indices, provided results that are more consistent with the spatial distribution characteristics of non-point source pollution risk in the basin. The proportions of extremely low-risk and extremely high-risk regions are 54.22% and 6.23%, respectively. These results provide scientific reference for risk analysis and the control of non-point source pollution in this basin.

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The evaluation of joint toxicity of mixtures is an important topic in toxicology. Previous studies have found that the parameter k∙ECx of concentration response curves (CRCs) can be used to assess the applicability of concentration addition model (CA). This study further assesses the predictability of k∙ECx on the joint toxicity evaluation. The toxicities of the twelve environmental pollutants, as well as those of binary mixtures with an equivalent-effect concentration ratio, to Vibrio fischeri were determined by using the microplate toxicity analysis. The toxicity evaluation of mixtures was conducted by CA and independent action model (IA). The relationship between the joint toxicity (measured by the relative model deviation ratio (rMDR)) and the k∙ECx was studied. The results shows that the k∙ECx could reflect the shape of CRCs in the whole concentration range. According to the IA and CA, 65% of the mixtures produce strong antagonistic or synergistic effect due to the significant difference of k∙ECx. The percentage of the relative difference of k∙ECx of components and the rMDRx can be fitted by an exponential function. Different types of interactions could be described using this function. It is suggested that the joint toxicity of binary mixtures can be assessed with the parameter k∙ECx, which can quickly get very important data when planning experiments, but also reduce the number of experiments.

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Non-extensive statistical mechanics (NESM), introduced by Tsallis based on the principle of non-additive entropy, is a generalisation of the Boltzmann-Gibbs statistics. NESM has been shown to provide the necessary theoretical and analytical implementation for studying complex systems such as the fracture mechanisms and crack evolution processes that occur in mechanically loaded specimens of brittle materials. In the current work, acoustic emission (AE) data recorded when marble and cement mortar specimens were subjected to three distinct loading protocols until fracture, are discussed in the context of NESM. The NESM analysis showed that the cumulative distribution functions of the AE interevent times (i.e., the time interval between successive AE hits) follow a q-exponential function. For each examined specimen, the corresponding Tsallis entropic q-indices and the parameters ßq and τq were calculated. The entropic index q shows a systematic behaviour strongly related to the various stages of the implemented loading protocols for all the examined specimens. Results seem to support the idea of using the entropic index q as a potential pre-failure indicator for the impending catastrophic fracture of the mechanically loaded specimens.

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It is well known that the duration of apnea is longer in static than in dynamic conditions, but the impact of exercise intensity on the apnea duration needs to be investigated. The aim of this study was to determine the relationship between apnea duration and exercise intensity, and the associated metabolic parameters. Ten healthy active young non-apnea trained (NAT) men participated in this study. During the first visit, they carried out a maximum static apnea (SA) and a maximal progressive cycle exercise to evaluate the power output achieved at peak oxygen uptake (PVO2peak). During the second visit, they performed four randomized dynamic apneas (DAs) at 20, 30, 40, and 50% of PVO2peak (P20, P30, P40, and P50) preceded by 4 min of exercise without apnea. Duration of apnea, heart rate (HR), arterial oxygen saturation (SpO2), blood lactate concentration [La], rating of perceived exertion (RPE), and subjective feeling were recorded. Apnea duration was significantly higher during SA (68.1 ± 23.6 s) compared with DA. Apnea duration at P20 (35.6 ± 11.7 s) was higher compared with P30 (25.6 ± 6.3 s), P40 (19.2 ± 6.7 s), and P50 (16.9 ± 2.5 s). The relationship between apnea duration and exercise intensity followed an exponential function (y = 56.388e-0.025 x ). SA as DA performed at P20 and P30 induces a bradycardia. Apnea induces an SpO2 decrease which is higher during DA (-10%) compared with SA (-4.4%). The decreases of SPO2 recorded during DA do not differ despite the increase in exercise intensity. An increase of [La] was observed in P30 and P40 conditions. RPE and subjective feeling remained unchanged whatever the apnea conditions might be. These results suggest that the DA performed at 30% of VO2peak could be the best compromise between apnea duration and exercise intensity. Then, DA training at low intensity could be added to aerobic training since, despite the moderate hypoxia, it is sufficient to induce and increase [La] generally observed during high-intensity training.

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In this paper, the authors review origins, motivations, and generalizations of a series of inequalities involving finitely many exponential functions and sums. They establish three new inequalities involving finitely many exponential functions and sums by finding convexity of a function related to the generating function of the Bernoulli numbers. They also survey the history, backgrounds, generalizations, logarithmically complete monotonicity, and applications of a series of ratios of finitely many gamma functions, present complete monotonicity of a linear combination of finitely many trigamma functions, construct a new ratio of finitely many gamma functions, derive monotonicity, logarithmic convexity, concavity, complete monotonicity, and the Bernstein function property of the newly constructed ratio of finitely many gamma functions. Finally, they suggest two linear combinations of finitely many trigamma functions and two ratios of finitely many gamma functions to be investigated.

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The traditional driving waveform of the electrowetting display (EWD) has many disadvantages, such as the large oscillation of the target grayscale aperture ratio and a long time for achieving grayscale. Therefore, a driving waveform based on the exponential function was proposed in this study. First, the maximum driving voltage value of 30 V was obtained by testing the hysteresis curve of the EWD pixel unit. Secondly, the influence of the time constant on the driving waveform was analyzed, and the optimal time constant of the exponential function was designed by testing the performance of the aperture ratio. Lastly, an EWD panel was used to test the driving effect of the exponential-function-driving waveform. The experimental results showed that a stable grayscale and a short driving time could be realized when the appropriate time constant value was designed for driving EWDs. The aperture ratio oscillation range of the gray scale could be reduced within 0.95%, and the driving time of a stable grayscale was reduced by 30% compared with the traditional driving waveform.

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There has been a growing interest in the assessment of container closure systems (CCS) for cold storage and shipment. Prior publications have lacked systematic considerations for the impact of dynamic time temperature transition on sealing performance associated with the viscoelastic characteristics of rubber stoppers used in container closure systems (CCSs). This paper demonstrates that sealing performance changes inherently and is fundamentally both time- and temperature-dependent. Our research results display this critical time temperature transition impact on CCS sealing performance by applying compression stress relaxation (CSR) on a rubber stopper for experimental data collection and modeling evaluation. The experimental results agree with modeling evaluation following Maxwell-Wiechert theory and the time temperature superposition based on the Arrhenius and Williams-Landel-Ferry methods. Both testing and modeling data show good consistency, demonstrating that the sealing force inevitably changes over time together with temperature transition because of the viscoelastic nature of the rubber stoppers. Our results show that compression seal force decreases quickly as temperature decreases. The significant loss of rubber stopper sealing force at lower temperature transitions could contribute significant risk to CCI at low storage and transport temperatures. Modeling evaluation, with a powerful capability to handle actual testing data, can be employed as a predictive tool to evaluate the time- and temperature-dependent sealing force throughout the entire sealed drug product life span. The present study is only applicable before reaching the rubber glass transition temperature Tg - a critical transition phase that can not be skipped/separated from real time temperature transition, and it will further determine the CCS sealing performance while approaching cryogenic temperature. The present work provides a new, integrated methodology framework and some fresh insights to the parenteral packaging industry for practically and proactively considering, designing, setting up, controlling, and managing stopper sealing performance throughout the entire sealed drug product life span.

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