Nonlinear Exponential Function Research Articles

Adaptive Contrast Enhancement and Effect of Non-linear Exponential Merit Function on Computer Generated Holograms

Adaptive Contrast Enhancement and Effect of Non-linear Exponential Merit Function on Computer Generated Holograms

Quantifying Temperature Effects on Development Rate and Plant Quality of Compact Container-grown Tomato

Mean daily temperature effects on plant development rates and quality were evaluated for compact container-grown tomato (Solanum lycopersicum). Compact tomato varieties ‘Siam’ and ‘Red Velvet’ were grown in greenhouses at 18 to 26 °C (Expt. 1) and 20 to 30 °C (Expt. 2) under supplemental high-pressure sodium lighting and 16-h photoperiod. The number of days to first open flower, first ripe fruit and from flower to ripe fruit were measured and development rates calculated by taking the reciprocal (e.g., 1/d). Temperature effects were predicted by fitting a linear (for first open flower) and a nonlinear exponential function (for first ripe fruit and between first open flower and ripe fruit), which included base temperature (Tmin) and maximum developmental rate (Rmax, 1/d) parameters. Plant quality attributes were measured in Expt. 2. As temperature increased, the time to flower and fruit decreased (i.e., developmental rates increased) for both varieties. Estimated Tmin was 8.7 °C for ‘Siam’ and 11.4 °C for ‘Red Velvet’, whereas Rmax was similar between cultivars (0.030 at fruit and 0.037 from flower to fruit). ‘Siam’ and ‘Red Velvet’ grown at ≈25 °C had a relatively short crop time, compact canopy, adequate fruit size, and a high number of fruits per plant at finish. Compact tomatoes are new crops being grown by greenhouse floriculture operations for ornamental and edible value, and the information from this study can help growers schedule these crops to meet critical market windows and determine the impacts of changing growing temperature on crop timing and quality.

Quantifying Temperature Effects on Plant Development Rates and Quality of Compact Container-grown Pepper

The mean daily temperature effects on plant development rates and quality of compact container-grown pepper were evaluated. Compact pepper cultivars Fresh Bites Yellow and Hot Burrito were grown in greenhouses at 18 to 26 °C (Expt. 1) and 20 to 30 °C (Expt. 2) under supplemental high-pressure sodium lighting and a 16-hour photoperiod. The number of days to first open flower, to first ripe fruit, and from flower to ripe fruit were measured and the development rates calculated by taking the reciprocal (e.g., 1/day). Temperature effects were predicted by fitting a nonlinear exponential function that included the base temperature (Tmin) and maximum developmental rate (Rmax) parameters. Plant quality attributes were measured during Expt. 2. As the temperature increased, the times to flower and fruit decreased (i.e., developmental rates increased) for both cultivars. The estimated Tmin was 13.3 °C for ‘Fresh Bites Yellow’, and that for ‘Hot Burrito’ was 9.3 °C, whereas the Rmax was similar between cultivars (averages of 0.0488 at flower, 0.0190 at fruit, and 0.0252 from flower to fruit). ‘Fresh Bites Yellow’ and ‘Hot Burrito’ grown at ≈25 °C had a relatively short crop time, compact canopy, large fruit size, and high number of fruits per plant at finish. Compact peppers are new crops being grown by greenhouse floriculture operations for their ornamental and edible value, and the information from this study can help growers schedule these crops to meet critical market windows and determine the impacts of changing the growing temperature on crop timing and quality.

On nonlinear Sobolev equation with the Caputo fractional operator and exponential nonlinearity

The initial value problem for the Caputo type time‐fractional Sobolev equation with a nonlinear exponential source function is investigated in this work. We establish the existence and uniqueness of mild solutions corresponding to two different initial data assumptions. We derive global results of a unique mild solution with small initial data using some Sobolev/Sobolev‐Orlicz embeddings, a weighted Banach space, and the fixed point theorem. In the absence of any smallness assumptions, the Cauchy iteration method demonstrates that the mild solution blows up at a finite time or exists globally in time. Finally, we consider some illustrated examples to test the results obtained in theory.

A matrixed nonlinear exponential grey Bernoulli model for interval number prediction of crude oil futures prices

PurposeThe effective prediction of crude oil futures prices can provide a reference for relevant enterprises to make production plans and investment decisions. To the nonlinearity, high volatility and uncertainty of the crude oil futures price, a matrixed nonlinear exponential grey Bernoulli model combined with an exponential accumulation generating operator (MNEGBM(1,1)) is proposed in this paper.Design/methodology/approachFirst, the original sequence is processed by the exponential accumulation generating operator to weaken its volatility. The nonlinear grey Bernoulli and exponential function models are combined to fit the preprocessed sequence. Then, the parameters in MNEGBM(1,1) are matrixed, so the ternary interval number sequence can be modeled directly. Marine Predators Algorithm (MPA) is chosen to optimize the nonlinear parameters. Finally, the Cramer rule is used to derive the time recursive formula.FindingsThe predictive effectiveness of the proposed model is verified by comparing it with five comparison models. Crude oil futures prices in Cushing, OK are predicted and analyzed from 2023/07 to 2023/12. The prediction results show it will gradually decrease over the next six months.Originality/valueCrude oil futures prices are highly volatile in the short term. The use of grey model for short-term prediction is valuable for research. For the data characteristics of crude oil futures price, this study first proposes an improved model for interval number prediction of crude oil futures prices.

Experimental studied on suppressing vortex-induced vibration of closed-box girder bridges with various moveable guide vanes

A new moveable guide vane with the combination of the spring and guide vane was proposed to suppress the vortex-induced vibration (VIV) of closed-box girder bridges. This paper studies the influence of two important parameters (i.e., horizonal length and spring stiffness) of a moveable guide vane on controlling the VIV of a super long-span suspension bridge with closed-box girder by using VIV control tests. The VIV test of 1:50 scaled ratio of sectional model of the original closed-box girder under three wind attack angles were firstly conducted. The suppression ratios of vertical and torsional VIV displacements of the closed-box girder as well as the movement characteristics of moveable guide vane were then analyzed, respectively. The results show that the movable guide vane could significantly reduced the Root Mean Square (RMS) values of VIV displacement of the closed-box girder are after installing, especial for the torsional VIV displacement. A moveable guide vane with a relative smaller horizontal lengths or a relative larger spring stiffness could produce a better outcome of VIV control. The double VIV amplitude of the moveable guide vanes results in the energy dissipation of the closed-box girder in the lock-in VIV wind speed region, while the vertical displcement of the moveable guide vane are close to those of the closed-box girder in non-VIV wind speed region. Besides, the nonlinear exponential fitting function could effectively reflect the relationship among the wind speed, the VIV displacement of the MGV and the closed-box girder.

Doubly Type II Censoring of Two Stress-Strength System Reliability Estimation for Generalized Exponential-Poisson Distribution

In this paper, a Bayesian analysis is made to estimate the Reliability of two stress-strength model systems. First: the reliability of a one component strengths X under stress Y. Second, reliability of one component strength under three stresses. Where X and Y are independent generalized exponential-Poison random variables with parameters (α,λ,θ) and (β,λ,θ) . The analysis is concerned with and based on doubly type II censored samples using gamma prior under four different loss functions, namely quadratic loss function, weighted loss functions, linear and non-linear exponential loss function. The estimators are compared by mean squared error criteria due to a simulation study. We also find that the mean square error is the best performance of the estimator from that found in quadratic, weighted, linear and non-linear exponential loss functions.

Development of a One-Parameter New Exponential (ONE) Model for Simulating Rainfall-Runoff and Comparison with Data-Driven LSTM Model

Runoff information can be used for establishing watershed water management plans. However, hydrological models with complex parameters make it difficult to quickly estimate runoff. This study developed a one-parameter new exponential (ONE) model for simulating rainfall-runoff using a single parameter, which was designed based on a nonlinear exponential function and watershed water balance that varies according to the soil water storage. The single parameter was included in the runoff function and implemented to continuously track the state of the soil water storage based on the watershed water balance. Furthermore, to validate the model’s effectiveness, it was applied to two multipurpose dams in Korea and the results showed that the daily results of the ONE model were better than those of a learning-based long short-term memory model in terms of the quantitative evaluation indices, monthly heatmap and annual runoff rate. This study demonstrated that rainfall-runoff can be simulated using only one parameter and that minimizing the number of parameters could enhance the practical utility of a hydrological model. The use of a single parameter is expected to maximize user convenience for simulating runoff, which is essential in the operation of water resource facilities.

An Image Enhancement Method Using Nonlinear Function

Image enhancement plays an important role in image processing. This paper proposed an image enhancement method using a nonlinear(exponential) function. Firstly, we use the exponential function to construct the gray transformation equation. Then, depending on the position of each pixel, the gray scale obtained by gray transformation is further adjusted based on the compression factor. In section 3, the comparative experiment shows that the proposed method could achieve good performance.

The Use of a Hidden Mixture Transition Distribution Model in Clustering Few but Long Continuous Sequences: An Illustration with Cognitive Skills Data

In accordance with the theme of this special issue, we present a model that indirectly discovers symmetries and asymmetries between past and present assessments within continuous sequences. More specifically, we present an alternative use of a latent variable version of the Mixture Transition Distribution (MTD) model, which allows for clustering of continuous longitudinal data, called the Hidden MTD (HMTD) model. We compare the HMTD and its clustering performance to the popular Growth Mixture Model (GMM), as well as to the recently introduced GMM based on individual case residuals (ICR-GMM). The GMM and the ICR-GMM contrast with HMTD, because they are based on an explicit change function describing the individual sequences on the dependent variable (here, we implement a non-linear exponential change function). This paper has three objectives. First, it introduces the HMTD. Second, we present the GMM and the ICR-GMM and compare them to the HMTD. Finally, we apply the three models and comment on how the conclusions differ depending on the clustering model, when using a specific dataset in psychology, which is characterized by a small number of sequences (n = 102), but that are relatively long (for the domains of psychology and social sciences: t = 20). We use data from a learning experiment, in which healthy adults (19–80 years old) were asked to perform a perceptual–motor skills over 20 trials.

Developing unconditional moment models of turbulent combustion

Turbulent combustion models are substantially important in CFD simulation of combustion. Some simple models frequently cannot well simulate the finite-rate chemistry. Widely recognized models are good only for certain flame types and flame structures. More general is the PDF equation model, but its computation requirement is very large, in particular when using large-eddy simulation (LES). Alternatively, the statistical moment models, such as unconditional moment models were developed based on the idea of turbulence modeling. However, the difficulty in treating the highly nonlinear exponential function of temperature in the reaction term was encountered. Different investigators adopted various approximations by neglecting different correlation terms, leading to under-predicting the time-averaged reaction rate. The present author entirely abandoned different approximations, proposed a final version of the second-order moment (SOM) model. This final version was used in both RANS modeling and LES of different single-phase and two-phase flames. It was validated by both experimental results and direct numerical simulation (DNS).

A novel image encryption algorithm using chaotic compressive sensing and nonlinear exponential function

This paper presents an optically secure image cryptosystem in the compressed-sensing (CS) domain by using a chaos driven nonlinear function. First, the original image is divided into non-overlapping blocks of uniform size, and then the discrete cosine transform (DCT) is used for obtaining sparse representation of these blocks. A logistic map-based circulant sensing measurement matrix is used to compress the sparse representations of the blocks. This partial cipher is further processed for encryption using a nonlinear function based on a dynamic invertible exponential function. The decorrelation of values is done by applying the Arnold 2-D map on the cipher. The seed values to the logistic equation and the parameters of the Arnold map are based on the original image, which makes the proposed algorithm robust in terms of plain text sensitivity. Not only does the algorithm achieve a considerable amount of security, but it also conceals the original image identity by the compression introduced, thereby reducing the storage and transmission cost. The decryption of the cipher is done using a smooth l0 approximation, giving high-quality reconstruction results. The extensive simulation results and performance analysis illustrates the excellent security and reconstruction results of the proposed scheme in comparison with the existing algorithms.

Bayes Estimation under Conjugate Prior for the Case of Laplace Double Exponential Distribution

The Bayesian estimation approach is a non-classical device in the estimation part of statistical inference which is very useful in real world situation. The main objective of this paper is to study the Bayes estimators of the parameter of Laplace double exponential distribution. In Bayesian estimation loss function, prior distribution and posterior distribution are the most important ingredients. In real life we try to minimize the loss and want to know some prior information about the problem to solve it accurately. The well known conjugate priors are considered for finding the Bayes estimator. In our study we have used different symmetric and asymmetric loss functions such as squared error loss function, quadratic loss function, modified linear exponential (MLINEX) loss function and non-linear exponential (NLINEX) loss function. The performance of the obtained estimators for different types of loss functions are then compared among themselves as well as with the classical maximum likelihood estimator (MLE). Mean Square Error (MSE) of the estimators are also computed and presented in graphs.
 The Chittagong Univ. J. Sci. 40 : 151-168, 2018

Oscillations of Fourier coefficients of $GL(m)$ Hecke-Maass forms and nonlinear exponential functions at primes

Let $F(z)$ be a Hecke-Maass form for $SL(m,\mathbb{Z})$ and $A_F(n,1, \dots, 1)$ be the coefficients of $L$-function attached to $F.$ We study the cancellation of $A_F(n,1, \dots, 1)$ for twisted with a nonlinear exponential function at primes, namely the sum \begin{equation*} \sum_{n \leq N} \Lambda (n)A_F(n,1, \dots, 1)e ( \alpha n^\theta ), \end{equation*} where $0<\theta<2/m$. We also strengthen the corresponding previous results for holomorphic cusp forms for $SL(2,\mathbb{Z}),$ and improve the estimates of Ren-Ye on the resonance of exponential sums involving Fourier coefficients of a Maass form for $SL(m,\mathbb{Z})$.

Bayesian Estimation under Different Loss Functions Using Gamma Prior for the Case of Exponential Distribution

The Bayesian estimation approach is a non-classical estimation technique in statistical inference and is very useful in real world situation. The aim of this paper is to study the Bayes estimators of the parameter of exponential distribution under different loss functions and compared among them as well as with the classical estimator named maximum likelihood estimator (MLE). Since exponential distribution is the life time distribution, we have studied exponential distribution using gamma prior. Here the gamma prior is used as the prior distribution of exponential distribution for finding the Bayes estimator. In our study we also used different symmetric and asymmetric loss functions such as squared error loss function, quadratic loss function, modified linear exponential (MLINEX) loss function and non-linear exponential (NLINEX) loss function. We have used simulated data using R-coding to find out the mean squared error (MSE) of different loss functions and hence found that non-classical estimator is better than classical estimator. Finally, mean square error (MSE) of the estimators of different loss functions are presented graphically.

Estimation of inventory for deteriorating items with non-linear demand considering discount and without discount policy

This paper develops an inventory model for deteriorating items consisting the ordering cost, unit cost, opportunity cost, deterioration cost and shortage cost. In this inventory model instead of linear demand function nonlinear exponential function of time for deteriorating items with deterioration rate has been considered. The effects of inflation and cash flow are also taken into account under a trade-credit policy of discount and without discount with time. In order to validate the model, numerical examples have been solved by bisection method deploying Matlab. Further, in order to estimate the cash flow the sensitivity of different parameters is considered.

Study of Inventory Model for Deteriorating Items With Exponential Demand Function

This paper develops an inventory model for deteriorating items consisting the ordering cost, unit cost, opportunity cost, deterioration cost and shortage cost. In this inventory model instead of linear demand function nonlinear exponential function of time for deteriorating items with deterioration rate has been considered. The formulated model has numerically solved by bisection method. The effects of inflation and cash flow are also taken into account under a trade-credit policy of discount with time. In order to validate the model, numerical examples have been solved by bisection method using Matlab. Further, the sensitivity of different parameters is considered in order to estimate the cash flow.GANIT J. Bangladesh Math. Soc.Vol. 34 (2014) 89-100

Numerical Evaluation of CO Emissions for Catalytic Combustion over Noble Metal Disc Burners of Turbulent Gaseous Fuel Jet Diffusion Flames

Performance of a combustion system is often constrained by limits of pollutant emissions such as CO. Catalytic combustion over noble metals promotes efficient combustion with minimum pollutant formation. In this study, the volumetric percentage of carbon-monoxide distribution along the catalytic flames operating over noble metal disc burners Pt, Pd, and (Pt + Pd) supported on γ-Al2O3 discs are analyzed through non-linear exponential model function. The numerical prediction correlates the response variable (CO %) with two explanatory (independent) variables: the axial mean temperature and axial distances over each catalytic burner simultaneously. The fitting process indicates high adequacy matching with the experimental data. The response surface construction, with corresponding contour maps, has been established to visually analyze the proposed model equations and to fully identify the extent of the estimated relationship in the combustion domain. These constructions reveal clearly that the response variable (CO %) is mainly dependant on the axial mean temperature distribution and slightly on the axial distances along the catalytic flames and also indicate the effectiveness of the three noble disc burners in reducing CO emissions along the catalytic flames minimizing the environmental pollution.

Brightness and Color Transfer for Infrared Images in Vehicle Night Vision System

The automotive night vision system can significantly improve the safety of driving at night by fusion of visible and infrared images. Due to the aim at helping driving at night, it’s important to develop the visibility and the consistency of the image and the real condition on the road. In this paper, visible light image is enhanced its light and shadow information based on nonlinear exponential function and the infrared image is increased its contrast by S-Retriex method. Then the enhancement images are fused and the color space of fusion image is adjusted by the reference statistical characteristics. Simulations have shown that the result image has good visual scene which retains the details of the infrared image and has original light, shadow and color information.

A novel classification model for cotton yarn quality based on trained neural network using genetic algorithm

This paper introduces a novel classification model for cotton yarn quality. The proposed model is composed of two major techniques namely: Artificial Neural Network (ANN) and genetic algorithm (GA). First, training the ANN on encoding database to extract the weights between input and hidden layer, and hidden and output layer. Consequently, the output function for each output node of ANN can be constructed as a function of input attributes values and the specific obtained weights. This function is nonlinear exponential function depending only on the values of input attributes. Second, the genetic algorithm is used to find the optimal values of the input chromosomes (attributes) which maximize the nonlinear exponential function of the output node of ANN. Finally, the results of the optimum chromosomes are decoded and used to get a rule belonging to a specific class.