In this paper we propose a method to approximate a parametric 3D -function by BICUBIC B-spline FUNCTIONS.

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 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,  rstly, we review approximation of fuzzy FUNCTIONS by fuzzy BICUBIC splines interpo-lation and present a new approach based on the two-dimensional fuzzy splines interpolation and iterative method to approximate the solution of two-dimensional linear fuzzy Fredholm integral equa-tion (2DLFFIE). Also, we prove convergence analysis and numerical stability analysis for the proposed numerical algorithm. Finally, by an example, we show the e ciency of the proposed method.

Let G = (VG, EG) be a graph and let I be a finite set of size m ≥ 1. A mapping T: VG → I is called a perfect m-coloring with a parameter matrix A = (aij )i, j∈I of G if it is surjective and for all i, j, every vertex of color i has aij neighbors of color j. In this paper, we classify all the realizable parameter matrices of perfect 3-colorings of the line graphs of the connected BICUBIC graphs of order at most 12.

Probability density FUNCTIONS of the involved random variables are essential for the reliability-based design of offshore structures. The objective of present research was the derivation of probability density function (PDF) for the local joint flexibility (LJF) factor, fLJF, in two-planar tubular DK-joints commonly found in jacket-type offshore structures. A total of 162 finite element (FE) analyses were carried out on 81 FE models of DK-joints subjected to two types of axial loading. Generated FE models were validated using available experimental data, FE results, and design formulas. Based on the results of parametric FE study, a sample database was prepared for the fLJF values and density histograms were generated for respective samples based on the Freedman-Diaconis rule. Nine theoretical PDFs were fitted to the developed histograms and the maximum likelihood (ML) method was applied to evaluate the parameters of fitted PDFs. In each case, the Kolmogorov-Smirnov and chi-squared tests were used to evaluate the goodness of fit. Finally, the Inverse Gaussian model was proposed as the governing probability distribution function for the fLJF. After substituting the values of estimated parameters, two fully defined PDFs were presented for the fLJF in tubular DK-joints subjected to two types of axial loading.

Restricted equivalence function, as an effective tool for the theoretical research and practical applications of fuzzy sets and systems along with fuzzy logic, has been continuously considered by scholars since it was proposed. In particular, recently, Bustince, Campi'{o}n, De Miguel et al. (H. Bustince, M.J. Campi'{o}n, L. De Miguel, E. Indur'{a}in, Strong negations and restricted equivalence FUNCTIONS revisited: An analytical and topological approach, Fuzzy Sets and Systems (2021), https://doi.org/10.1016/j.fss.2021.10.013.) investigated it using analytical and topological approach and proposed an open problem to ask whether the binary function $F(x,y)=T(I(x,y),I(y,x))$ obtained from a t-norm $T$ and a fuzzy implication function $I$ is a restricted equivalence function or not. In this paper, we pay attention to this problem and give positive answer of it. Specifically, first, we consider the binary FUNCTIONS obtained from overlap FUNCTIONS and fuzzy implication FUNCTIONS by following the construction way of $F$ and get the necessary and sufficient condition that makes such obtained $F$ to be a restricted equivalence function. Second, we introduce the so-called $\heartsuit$-FUNCTIONS, which are binary FUNCTIONS on unit closed interval with few additional axioms and obtain the necessary and sufficient condition that ensures the binary function constructed via any non-decreasing $\heartsuit$-function and fuzzy implication function as the way of $F$ to be a restricted equivalence function. Finally, we give the necessary and sufficient condition that makes $F$ to be a restricted equivalence function.