In this manuscript, a numerical technique is presented for finding the eigenvalues of the regular Sturm-Liouville problems. The Chebyshev CARDINAL FUNCTIONS are used to approximate the eigenvalues of a regular Sturm-Liouville problem with Dirichlet boundary conditions. These FUNCTIONS defined by the Chebyshev function of the first kind. By using the operational matrix of derivative the problem is reduced to a set of algebraic equation. Finally we use some numerical examples to show that this method include to demonstrate the validity and applicability of technique.

In this paper, an effective direct method to determine the numerical solution of linear and nonlinear Fredholm and Volterra integral and integro-differential equations is proposed. The method is based on expanding the required approximate solution as the elements of Chebyshev CARDINAL FUNCTIONS. The operational matrices for the integration and product of the Chebyshev CARDINAL FUNCTIONS are described in detail. These matrices play the important role of reducing an integral equation to a system of algebraic equations. Illustrative examples are shown, which confirms the validity and applicability of the presented technique.

In this paper, a new numerical method for solving the fractional optimal control problem of the time delay is presented. The fractional integral and the fractional derivative are the Riemann-Liouville type and the Caputo type, respectively. In this method, the CARDINAL Hermite FUNCTIONS are used as a basis to approximate FUNCTIONS. Moreover, we obtain the fractional and delay integral operational matrices and use them to solve this optimal control problem. Using the collocation method, the problem leads to a system of algebraic equations, that is solved by Newton's iterative method. Finally, numerical examples are presented to investigate the efficiency of this method.

A new and effective direct method to determine the numerical solution of linear and nonlinear differential-algebraic equations (DAEs) is proposed. The method consists of expanding the required approximate solution as the elements of Chebyshev CARDINAL FUNCTIONS. The operational matrices for the integration and product of the Chebyshev CARDINAL FUNCTIONS are presented. A general procedure for forming these matrices is given. These matrices play an important role in modelling of problems. By using these operational matrices together, a differentialalgebraic equation can be transformed to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

Improving participation in voluntary activities in Iran is important because increasing productivity among young people, given the country's young population, contributes to community sustainability. Therefore, a better understanding of volunteer motivation in Iranian youth is needed. The Volunteer FUNCTIONS Inventory (VFI) for assessing volunteer motivations has good psychometric properties and is adapted to several languages, but no validated Iranian translation yet exists. The purpose of this study was to investigate the psychometric Characteristics of voluntary FUNCTIONS inventory in members of Iranian Red Crescent Society. Sample size was 595 members of Youth Organization of Iranian Red Crescent Society from 31 provinces and 175 cities of Iran that were selected by multi-stage cluster sampling method and responded to voluntary FUNCTIONS inventory. Data were collected using a demographic sample and voluntary FUNCTIONS inventory (VFI). Confirmatory factor analysis using principal components method was used for data analysis. The results of the present study showed that the voluntary FUNCTIONS inventory had validity and reliability. Also, the factor structure showed that 29 items and 6 factors well assess people's attitudes to volunteering, and the structure of this inventory was well-fitted and confirmed all goodness of fit models. The present study provides the use of the Iranian translation of the Voluntary FUNCTIONS Inventory (6 scales and 29 items) to assess volunteer motivation among young Iranian volunteers.

In this study, an effective numerical method for solving fractional differential equations using Chebyshev CARDINAL FUNCTIONS is presented. The fractional derivative is described in the Caputo sense. An operational matrix of fractional order integration is derived and is utilized to reduce the fractional differential equations to system of algebraic equations. In addition, illustrative examples are presented to demonstrate the efficiency and accuracy of the proposed method.

In this paper, an alternative approach in operational modal analysis is presented, utilizing image processing technique and transmissibility FUNCTIONS. Imaging sensors do not impose additional mass on the structure due to their non-contact nature, while transmissibility FUNCTIONS, independent of excitation type, can directly extract mode shapes. The innovation of this research lies in combining these two techniques to record dynamic responses and identify modal properties. To capture the temporal response history from video signals, the block-matching method with sub-pixel accuracy was employed. Validation was conducted by recording the response of the tip of a cantilevered steel beam subjected to impact excitation, using a high-speed camera and a laser vibrometer, simultaneously. The RMSE plots in the time domain and the PSD in the frequency domain indicate high accuracy of this method. Using this approach, the displacement time histories of various points on the structure were extracted from the video signals, and the modal properties, including natural frequencies, damping ratios, and mode shapes, were identified using the transmissibility matrix method. The results obtained from the proposed method were compared with the stochastic subspace identification (SSI) method and analytical solutions. The findings reveal the accuracy of the modal identification approach introduced in this article. The highest relative error in estimating the natural frequencies of the first and second modes, compared to the values from the laser method, are 0.19% and 0.13%, respectively, and in comparison to the analytical values, they are 0.34% and 1.5%, respectively.

In this paper, the CHEBYCHEV spectral collocation method is applied for the thermal analysis ofconvective-radiative straight fins with the temperature-dependent thermal conductivity. The developed heat transfermodel was used to analyse the thermal performance, establish the optimum thermal design parameters, and also, investigate the effects of thermo-geometric parameters and thermal conductivity (nonlinear) parameters on thethermal performance of the fin. The results of this study reveal that the rate of heat transfer from the fin increases asthe convective, radioactive, and magnetic parameters increase. This study establishes good agreement between theobtained results using CHEBYCHEV spectral collocation method and the results obtained using Runge-Kutta methodalong with shooting, homotopy perturbation, and adomian decomposition methods.