Background and Objectives: In the soil science, echangble sodium percentage and sodium adsorption ratio are two different criteria to evaluate of soil alkality. For measured of ESP, it is essential to have soil Cation Exchange Capacity (CEC). But, CEC determined by using laborious METHOD is expensive and time consuming. Developing a model that predicts ESP indirectly from a easily-measured properties to be more appropriate and economical. Researches showed a relationship between ESP and SAR. So, SAR can be allocated to predict of ESP. For this reason, many attempts have been made to predict ESP from soil. The specific goal of the research develop model to determining ESP based on SAR by (OLS) and BN models for Bonab soils in East Azarbaijan province, Iran. Materials and METHODs: For arrived presented research, 209 soil samples were taken by grid survey (250×250) of Bonab, Iran. The site is located at mean 1300 m above mean sea level, in semiarid climate in the Northwest of Iran. Then, some soil chemical properties such as Sodium, calcium, magnesium, SAR and ESP of the soil samples were measured using laboratory experiments. Then, two model was developed by (OLS) and BN. (OLS) estimators are linear functions of the values of the dependent variable which are linearly combined using weights that are a non-linear function of the values of the explanatory variables. So the (OLS) estimator is respect to how it uses the values of the dependent variable only and irrespective of how it uses the values of the explanatory. So A Bayesian network is a probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). Given symptoms, the network can be used to compute the probabilities of the presence of various diseases. Efficient algorithms can perform inference and learning in Bayesian networks. Generalizations of Bayesian networks that can represent and solve decision problems under uncertainty. Results: The Coefficient of Determination (R2) and Root Mean Square error (RMSE) of the soil ESP-SAR model is reported 0. 99, 0. 71 and 0. 98, 1. 63 by (OLS) and BN respectively. Based on the statistical result, both of soil ESP-SAR model was judged acceptable. T-test were used to compare the soil ESP values predicted using the soil ESP-SAR model with the soil ESP values measured by laboratory tests. The paired samples t-test results indicated that the difference between the soil ESP values predicted by the model and measured by laboratory tests were not statistically significant (P>0. 05). Therefore, the soil ESP-SAR model can provide an easy, economic and brief METHODology to estimate soil ESP. The GMER index also indicated low estimation of two selected land evaluation METHOD. Conclusion: The results of present study illustrated that (OLS) and BN models can predict ESP with acceptable limits. (OLS) and BN are mathematical models between input and output variables and have the ability of modeling between ESP and SAR.

The Mixed LEAST SQUARES Meshfree (MDLSM) METHOD has shown its appropriate efficiency for solving Partial Differential Equations (PDEs) governing the engineering problems. The METHOD is based on the minimizing the residual functional. The residual functional is defined as a summation of the weighted residuals on the governing PDEs and the boundaries. The Moving LEAST SQUARES (MLS) is usually applied in the MDLSM METHOD for constructing the shape functions. Although the required consistency and compatibility for the approximation function is satisfied by the MLS, the METHOD loss its appropriate efficiency when the nodal points cluster too much. In the current study, the mentioned drawback is overcome using the novel approximation function called Mapped Moving LEAST SQUARES (MMLS). In this approach, the cluster of closed nodal points maps to standard nodal distribution. Then the approximation function and its derivatives compute noting the some consideration. The efficiency of suggested MMLS for overcoming the drawback of MLS is evaluated by approximating the mathematical function. The obtained results show the ability of suggested MMLS METHOD to solve the drawback. The suggested approximation function is applied in MDLSM METHOD, and used for solving the Burgers equations. Obtained results approve the efficiency of suggested METHOD.

Predicting stock returns is one of the major issues to be discussed in the financial literature, and investment. Researchers have proposed various METHODs for predicting stock returns, that the most famous of them are the Capital Asset Pricing Model by Sharpe and Lintner, arbitrage pricing model by ross and three factors model by Fama and French. F& F three factor model as the most significant factor models in recent years great attention has been. Despite having many strengths of this model is based on the assumption of constant beta coefficient is founded, However, this assumption does not hold absolute in any circumstances. In this study, we tried to model with constant or variable coefficients fitted separately and then compare the accuracy each of them. For this purpose, the state space model and ORDINARY LEAST SQUARES ((OLS)) models were fit assuming constant and variable coefficients are used. This research will be done on listed companies in Tehran Stock Exchange for a period of 72 months (October 1385 to September1391). The results show that, compared to state-space model of a linear LEAST SQUARES model for predicting stock returns has a better performance, this means that Beta coefficients in three-factor is on the Tehran Stock Exchange are not constant.

Introduction: The quantitative structure-property relationship (QSPR) is a successful strategy for prediction of surfactant properties based on modeling between calculated descriptors from molecular structures of the surfactants and chemical or physical properties of the solution. There are a great number of molecular descriptors that have been used in such QSPR studies, which can be divided into six types, namely constitutional descriptors, topological descriptors, electrostatic descriptors, geometrical descriptors, quantum chemical descriptors and thermodynamic descriptors. There are some reports about the applications of QSPR approaches to predict the CMC of anionic, nonionic and Gemini surfactants.Aim: In the present work, the logCMC of some tetra-alkylammonium and alkylpyridinium salts was mathematically related to the molecular structure properties.Material and METHODs: All critical micelle concentrations data of this investigation were obtained from a set of cationic surfactants. They are measured in water at 25 oC. The data set consists of 44 surfactants were divided into two groups with 29 tetra-alkyl ammonium and 15 alkylpyridinium salts. The 3D molecular structures generated by ChemDraw 2005 and optimized by AM1 rotuine of MOPAC. The molecular descriptors generated ChemSAR and Dragon ver 3.0Results: (OLS) regression analysis provided useful equations that can be used to predict the logCMC of cationic surfactants in this study. Model (I) which was used to estimate the logarithm of CMC tetra-alkyl ammonium surfactants using four structural descriptors could be represented as:logCMC=-1.0097 - 0.1258Lc – 0.0123VH + 0.0960AHG +0.0053RHCIn=20.R2 =0.9860,s2 =0.0210F =135, model (I)The logCMC of alkylpyridinium surfactants with three descriptors can be effectively predicted using following Eq. for model (II).LogCMC=6.0291 – 0.2461Lc – 0.0011VH + 0.0249RHCIModel(II), n = 10,R2 =0.09940,s2 =0.0098,F =159, model (II)simultaneous model, which was used to estimate logCMC all cationic surfactants using four molecular structure descriptors, could be represented as log CMC = -1.4055 - 0.1529Lc - 0.0101VH + 0.1214 AHG + 0.0063RHCI n =30, R2 =0.9820,s2 =F =173,final model where n is the number of compounds used for regression, R2 is the squared correlation coefficient, s2 is the standard error of the regression, and F is the Fisher ratio for the regression.Conclusion: The results indicate that the CMC decreases as the hydrophobic character (L and V) increases and CMC increases as the hydrophilic character (A) of the surfactant increases.

Objective: In this study, the ORDINARY LEAST SQUARES ((OLS)) regression model was applied to estimate the impacts of  land use and land cover (LULC) changes from 1999 to 2023 derived from Landsat satellite imagery on water productivity as a key ecosystem service essential for environmental sustainability. Focusing on the Lavasanat district in Tehran province, which has undergone rapid urbanization and severe land use/cover changes, this study determined the extent to which water production performance (runoff) responded to land use/cover changes, thereby providing significant information on the environmental consequences of land use/cover changes under increasing human pressures.METHOD: This study used Landsat satellite imagery to assess the trends in land use/cover (LULC) changes over time at a spatial resolution of 30 m. Water yield modeling was performed using the annual water yield index of the InVEST software. The model inputs included land use and cover maps from three different time series along with data on precipitation, potential evapotranspiration, soil depth, water availability for plants, and local biophysical tables. The results from the InVEST model were analyzed using an ORDINARY LEAST SQUARES ((OLS)) regression model to estimate the impact of land use/cover changes on water yield. This METHOD allows for a detailed examination of the relationship between land use/cover changes and their impacts on the water yield.Results: The results showed that between 1999 and 2023, the area of green spaces, including agricultural lands, gardens, and pastures, decreased by 161.21 km², or 31 percent. Consequently, the annual water production (runoff) increased from 105 to 130 million cubic meters. In addition, the area of the minimum error zone decreased from 445.3 to 23.5 km², indicating a decrease in the reliability of the model. Such findings indicated the high variability and complexity of hydrological interactions and indicated the severe effects of overdevelopment and increasing land use/cover pressures.Conclusions: The results of this study showed that the water production capacity (runoff) of the ecosystem was vulnerable to changes in land use and land cover. These changes increased runoff, reduced water permeability in the soil, and disrupted the hydrological balance of the region. Therefore, it is necessary to use integrated modeling approaches and simultaneously pay attention to climate change, socio-economic factors, and land use/cover planning. Regional planning should also emphasize preservation and restoration of green spaces and smart management of urban development, which is an inevitable necessity to maintain ecosystem resilience and water resource sustainability.

The main goal of this paper is to study exchange rate impact on the export of dates as one of the most important exported horticultural products in Iran. For this purpose, ORDINARY LEAST SQUARES ((OLS)) METHOD was used to estimate the relationship between volume of exported dates and other selected variables. The required data were collected from various official resources. Results showed that exchange rate is a critical factor and exporters reacted to its changes. In addition, other factors such as foreign currency written promise, exchange rate unification and stabilization policy, had impacts on volume of date’s exports. Outsourcing foreign policy that was always considered a short-term policy had negative effect on export. Unification of the exchange rate did not have significant impact on dates export. Also, exchange rate stabilization policy led to reduce the potential exporter’s income due to prevailing inflation in the country and increased production costs.

Determination of the diffusion coefficient on the base of solution of a linear inverse problem of the parameter estimation using the LEAST-square METHOD is presented in this research. For this propose a set of temperature measurements at a single sensor location inside the heat conducting body was considered. The corresponding direct problem was then solved by the application of the heat fundamental solution.

The main purpose of this article is to increase the efficiency of the LEAST SQUARES METHOD in numerical solution of ill-posed functional and physical equations. Determining the LEAST SQUARES of a given function in an arbitrary set is often an ill-posed problem. In this article, by defining artificial constraint and using Lagrange multipliers METHOD, the attempt is to turn n-dimensional LEAST SQUARES problems into (n-1) ones, in a way that the condition number of the corresponding system with(n-1) -dimensional problem will be low. At first, the new METHOD is introduced for2 and 3-term basis, then the presented METHOD is generalized for n-term basis. Finally, the numerical solution of some ill-posed problems like Fredholm integral equations of the first kind and singularly perturbed linear Fredholm integral equations of the second kind are approximated by chain LEAST SQUARES METHOD. Numerical comparisons indicate that the chain LEAST SQUARES METHOD yields accurate and stable approximations in many cases.

One of the most efficient statistical to(OLS) for modeling the relationship between a dependent variable and several independent variables is regression‎. ‎In practice‎, ‎observations relating to one or more variables‎, ‎or the relationship between variables‎, ‎may be vague or non-specific‎. ‎In such cases‎, ‎classic regression METHODs will not have enough capability to model data‎, ‎and one of the alternative METHODs is regression in a fuzzy environment‎. ‎The fuzzy logistic regression model provides a framework in the fuzzy environment to investigate the relationship between a binary response variable and a set of covariates‎. ‎The purpose of this paper is to attempt to develop a fuzzy model that is based on the idea of the possibility of success‎. ‎These possibilities are characterized {by several} linguistic phrases‎, ‎including low‎, ‎medium‎, ‎and high‎, ‎among others‎. ‎Next‎, ‎we {use a set of precise explanatory variable observations to model the logarithm transformation of‎ "‎possibilistic odds.‎" ‎We assume that the model's parameters are triangular fuzzy numbers.} We use the LEAST SQUARES METHOD in fuzzy linear regression to estimate the parameters of the provided model‎. ‎We compute three types of goodness-of-fit criteria to evaluate the model‎. ‎Ultimately‎, ‎we model suspected cases of Systemic Lupus Erythematosus (SLE) disease based on significant risk factors to identify the model's application‎. ‎We do this due to the widespread use of logistic regression in clinical studies and the prevalence of ambiguous observations in clinical diagnosis‎. ‎Furthermore‎, ‎to assess the prevalence of diabetes in the community‎, ‎we will collect a sample of plasma glucose levels‎, ‎measured two hours after a meal‎, ‎from each participant in a clinical survey‎. ‎The proposed model has the potential to rationally replace an ORDINARY model in modeling the clinically ambiguous condition‎, ‎according to the findings‎.