In 1986 S. Sattolo introduced a simple algorithm for uniform random generation of cyclic permutations on a fixed number of symbols. Recently, H. Prodinger analysed two important random variables associated with the algorithm, and found their mean and variance. H. Mahmoud extended Prodinger’s analysis by finding limit laws for the same two random variables.The present article, starting from the definition of the algorithm, is completely self-contained. After giving a simple new proof of correctness, we generalize the abovementioned probabilistic results by determining the “grand” probability Generating functions of the random variables. The focus throughout is on using standard methods that give a unified approach, and open the door to further study.

We find an explicit expression of the Tutte polynomial of an n-fan. We also find a formula of the Tutte polynomial of an n-wheel in terms of the Tutte polynomial of n-fans. Finally, we give an alternative expression of the Tutte polynomial of an n-wheel and then prove the explicit formula for the Tutte polynomial of an n-wheel.

In this paper, we introduce novel Generating functions of the products of k-Fibonacci numbers, k-Lucas numbers, k-Pell numbers, k-Jacobsthal numbers, k-Mersenne numbers and symmetric functions in multiple variables. Accordingly, the novel Generating functions are assigned to the other orthogonal Chebyshev polynomials with symmetric functions in multiple variables.

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, we derived recurrence relations for joint moment Generating functions of nonadjacent generalized order statistics (GOS) of random samples drawn from doubly truncated class of continuous distributions.Recurrence relations for joint moments of nonadjacent GOS (ordinary order statistics (OOS) and k-upper records (k-RVs) as special cases) are obtained. Single and product moment Generating functions (moments) of nonadjacent GOS are derived. Doubly truncated new modified Weibull (Weibull, Extreme-value, exponential and Rayleigh), three Burr type XII (Lomax) and inverse Weibull distributions, among others, arise as special cases of this doubly truncated class. Two applications are introduced, the first is the characterizations for members of the class based on recurrence relations for moments of GOS, OOS and k-RVs. As the second application we found Tables of single and product moments of OOS from doubly truncated Lomax distribution.

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.

We define [k] ={1, 2, 3,…, k} to be a (totally ordered) alphabet on k letters. A word wof length n on the alphabet [k] is an element of [k] n. A word can be represented by a bargraph which is a family of column-convex polyominoes whose lower edge lies on the x -axis and in which the height of the i -th column in the bargraph equals the size of the i -th part of the word. Thus these bargraphs have heights which are less than or equal to k. We consider the site-perimeter, which is the number of nearest-neighbour cells outside the boundary of the polyomino. The Generating function that counts the site-perimeter of words is obtained explicitly. From a functional equation we find the average site-perimeter of words of length n over the alphabet [k]. We also show how these statistics may be obtained using a direct counting method and obtain the minimum and maximum values of the site-perimeters.

Priority queues have a great importance in the study of computer communication networks in which different types of traffic require different quality of service standards. The discrete-time non-preemptive priority queuing model with priority jumps is proposed in this paper. On the basis of probability Generating functions mean system contents and mean queuing delay characteristics are obtained. The effect of jumping mechanism is analysed which clearly shows that the queuing system provides better results when the fraction of class-1 arrivals in the overall traffic mix is small.