Numerical crack modeling is an important and basic problem for researchers. Also, Finite element has good availability in crack modeling, but there are a few problems in using standard shape functions. Meshless methods shape functions, so Discrete least square, which is used in this research, makes them more efficient with Finite element, especially in high-gradient problems. In this study, the cohesive crack theory leaving the usual numerical methods for crack behavior is investigated. In this way, doing the model conditions that do not occur crack with force out on the edges crack, and gradually become more open crack, and decrease the cohesive tension, that done zero, it means the whole crack is opening. Therefore, meshless methods use some techniques, such as visibility criterion and diffraction method, to encounter this problem. This technique is the simplest method for discontinuity modeling in meshless methods and has more compatibility with general domain discretization in meshless methods. Through engineering problems, the domain of the problem may contain nonconvex boundaries, particularly the fractured ones having discontinuous displacement fields. In such conditions, the shape functions associated with particles, whose supports intersect with the discontinuity, should be modified. One of these criteria is the visibility. In this approach, if the assumed light beam meets the discontinuity line, the shape function after the barrier will be cut. Therefore, discontinuity is applied to the geometry. In other words, the shape function of the particles, which prevents the crack or discontinuity from reaching the light beam, will be modified to amount to a zero. In this study, Cohesive Crack Theory is investigated for modeling and simulating crack behavior in DLS meshless method. This method gradually decreases the resistance of the cracked area to simulate splitting of the material. Finally, the high efficiency and accuracy of DLSM is given by comparing the DLSM results with experimental or FEM ones.

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.

Estimation methods of parameters of fuzzy least-squares regression have very sensitivity to unusual data (e.g. outliers). In the presence of outliers, most of the existing estimation methods of parameters of this kind of models using least-squares approach provide unexpected and unreliable estimators with amounts of errors. Therefore, in this paper a robust least trimmed squares fuzzy regression model is described for modeling for crisp input-fuzzy output variables. In this approach, the constructed target function in model parameter estimation problem in such a way which minimizes the sum of the h smallest squared residuals. This method has an algorithm that estimates the optimal values of the parameters based on different selected combinations of h good observations of the data set of size n. Therefore, this method has the ability of reducing the effects of such a data in estimation of the parameters of the model. Finally, the investigated fuzzy regression model is applied and studied to modeling real-world data set in hydrology which sometimes contains outlier points. In this regard, a comparison study between the proposed method and ordinary least squares fuzzy regression method is considered. The comparison results of the applied study reveal that for this particular data set the proposed method performs better fitting than the well-known ordinary fuzzy least-squares regression model. Also the proposed method identified the points that have bad effect on estimation problem of the parameters.

Iron is an essential element used as supplement in different dosage-forms. Different time and expenditure-consuming methods introduced for detection and determination of elemental ions such as Atomic Absorption Spectroscopy. In this research, two different and routine methods containing ATR-IR and atomic absorption were applied to define the amount of iron in 198 samples containing different concentrations of commercial iron drops and syrups and the output data of the methods was transferred to chemometric model to compare the accuracy and robustness of the methods. By applying this mathematical model, in addition to the confirmation of ATR-IR (a time and energy-saving method) as a replacement of Atomic Absorption Spectroscopy to produce the same results, chemometrical model was used to evaluate the output data in a faster and easier method. At first, ATR-IR spectra data converted to normal matrix by SNV preprocessing approach. Then, a relationship between iron concentrations achieved by AAS and ATR-IR data was established using PLS-LS-SVM. Consequently, model was able to predict ~99% of the samples with low error-values (root mean square-error of cross-validation equal to 0. 98). Y-permutation test performed to confirm that the model was not assessed accidentally. Although, chemometric methods for detection of some heavy metals have been reported in the literature, combination of PLS-LS-SVM with ATR-IR was not cited. In this study a fast and robust method for iron assay was suggested. As a result, ATR-IR can be a suitable method in detection and qualification of iron-content in pharmaceutical dosage forms with less energy-consumption but similar accuracy.

Entrepreneurship development is a set of public and private policies and practices that can accelerate entrepreneurship. Tourism as an important economic sector requires the presence of entrepreneurs, so it is necessary to identify the factors that have an impact on entrepreneurship development in this area. Cultural tourism is one of the important types of tourism that has a major share among the types of tourism. This article is designed to design a model for this development. The study was conducted in Yazd city and partial least squares structural equation modeling was used for modeling. The statistical population consisted of academic experts, business owners and practitioners of public and private sectors related to tourism. The conceptual model has been designed using 3M model and has been used by experts and theoretical literature and states that three variables of behavioral, structural and environmental factors and conditions are effective on entrepreneurship development. Calculations have been made for the measurement, structural and overall fit of the model, indicating that the model is suitable. According to the path coefficients, 34. 6% behavioral factors and 46. 5% structural factors directly explain the changes related to the cultural tourism entrepreneurship development variable. Also the environmental condition variable indirectly affects this variable and accounts for 65. 1% of the variations in this variable. Meanwhile, among structural factors, introduction of tourism destination and among behavioral factors, empowerment of active tourism elements have the most impact on entrepreneurship development of a cultural tourism destination.

The aim of the research was to estimate the effects of acquiring, storing, sharing and applying knowledge on religion-based knowledge management in the first step and to design a model for the religionbased knowledge management process using structural equation modeling method, at least partial squares in the second step. The research method was survey and the type of correlation schemes was path analysis and structural equation modeling. The research was performed using Delphi technique. The statistical population of the study consisted of religious experts and experts. Sampling was in purposeful method. 10 religious experts were selected as the main sample. The data collection tool was a questionnaire. Structural equation modeling (SEM), partial least squares (Smart PLS 3. 3) was used to create the measurement model and draw the structural relationship model. In this section were used the extracted mean variance, Cronbach’ s alpha, combined reliability, divergent validity, convergent validity, differential validity, R2, Q2 and GOF indices. The results of the partial least squares test indicated that the research hypotheses were confirmed and based on this, the measurement model and the structural model were statistically appropriate. The results showed that the process of knowledge management of religion foundation includes acquiring, storing, sharing and applying knowledge and this process had a positive and significant effect on knowledge management.

Pedomodels have become a popular topic in soil science and environmental research. They are predictive functions of certain soil properties based on other easily or cheaply measured properties. The common method for fitting pedomodels is to use classical regression analysis, based on the assumptions of data crispness and deterministic relations among variables. In modeling natural systems such as soil system, in which the above assumptions are not held true, prediction is influential and we must therefore attempt to analyze the behavior and structure of such systems more realistically. In this paper we consider fuzzy least squares regression as a means of fitting pedomodels. The theoretical and practical considerations are illustrated by developing some examples of real pedomodels.