In this paper, we discuss the properties of reversed aging Intensity (RAI) Function for discrete random variable and study its nature for some distributions. Further, using this Function we characterize some discrete related distributions. The closure properties of the aging classes defined in terms of RAI Function are also presented and study its closure properties under different reliability operations, viz., formation of k-out-of-n system. Moreover, we define an ordering, called reversed aging Intensity ordering and study its relationship with some usual stochastic orderings. Also a numerical example is given to explain the theoretical results.

The nonhomogeneous Poisson process is commonly utilized to model the occurrence of events over time‎. ‎The identification of nonhomogeneous Poisson process relies on the Intensity Function‎, ‎which can be difficult to determine‎. ‎A straightforward approach is to set the Intensity Function to a constant value‎, ‎resulting in a homogeneous Poisson process‎. ‎However‎, ‎it is crucial to assess the homogeneity of the Intensity Function through an appropriate test beforehand‎. ‎Failure to confirm homogeneity leads to an infinite-dimensional problem that cannot be comprehensively resolved‎. ‎In this study‎, ‎we analyzed data on the number of passengers using the Tehran metro‎. ‎Our homogeneity test showed a nonhomogeneous arrival rate of passengers‎, ‎prompting us to explore different Functions to estimate the Intensity Function‎. ‎We considered four Functions and used a piecewise Function to determine the best Intensity Function‎. ‎Our findings showed significant differences between the two models‎, ‎highlighting the effectiveness of the piecewise Function model in predicting the number of metro passengers.

Energy Intensity index, at micro level is used commonly to show efficiency of production systems, as well as, at macro level to show country’s energy efficiency. However, this index is affected by several opposite causes that make comparative analysis too hard. This paper besides introducing most energy Intensity causes, based on OLS method estimates a multivariable model to analyze each cause's effect. Results show that the size of service sector (representing structural change) has significant effect on reducing energy Intensity. Square of countries, consistent with theory, has positive significant effect and a size of one forth of service sector effect. Estimating of elasticity effects shows that one percent change (rising) of service sector size, cause one half percent change (declining) of energy Intensity. Square's elasticity coefficient also consists with theory's expectation and has shown significant effect.

In this research, By using data envelopment analysis method and output distance Functions to decomposes energy productivity change into four components; technical efficiency change, technological change, changes in capital to energy ratio and labor in energy ratio In the industrial sector of the country Iran during the period 2014-2004. To this end, the output-axis data envelope analysis method has been used with the assumption of constant returns to scale. The results show that the effect of changing the ratio of capital to energy is a major factor in reducing the of energy Intensity in the industrial sector of the Iran, changes technological progress, changes labor-energy ratio and changes technical efficiency drove up energy Intensity in most industries.

Introduction: Attention and memory are fundamental cognitive processes that play a crucial role in learning. The Intensity of physical exercise can significantly influence cognitive Functions. Aim: The present study aimed to examine the effectiveness of two types of exercise—Low-Intensity persistent exercise and high-Intensity interval training—on selective attention, short-term memory, and executive Functions in sedentary students during the COVID-19 pandemic. Method: This study employed a quasi-experimental design with a pretest-posttest structure and a control group. The statistical population consisted of male students from Shiraz Technical and Vocational University during the 2021–2022 academic year. A total of 51 participants were selected using a convenience sampling method and were randomly assigned to two experimental groups and one control group. The experimental groups participated in an 8-week protocol of either Low-Intensity persistent exercise or high-Intensity interval training. Data were collected using the Stroop Color and Word test and the Wechsler Adult Intelligence Scale. Statistical analyses were conducted using analysis of covariance (ANCOVA) and Tukey's post hoc test in SPSS version 22. Results: The results indicated a significant difference between the post-test mean scores of the experimental and control groups. Specifically, low-Intensity persistent exercise was found to significantly improve selective attention (F = 58.40, p = 0.001, η² = 0.89), short-term memory (F = 36.89, p = 0.003, η² = 0.75), and executive Function (F = 62.66, p = 0.001, η² = 0.94) in sedentary students (p < 0.05). Conclusion: The results showed that the low-Intensity persistence exercise improved  selective attention, memory, short-term, and executive Function in sedentary students. Accordingly, low-Intensity persistence exercise was the most effective exercise in improving cognition Functions as compered with high-Intensity interval training.

A characteristic of Data Envelopment Analysis (DEA) is to allow individual decision making units (DMUs) to select the factor weights which are the most advantageous for them in calculating their efficiency scores. This flexibility in selecting the weights, on the other hand, deters the comparison among DMUs on a common base. For dealing with this difficulty and assessing all the DMUs on the same scale, this paper proposes using a multiple objective linear programming (MOLP) approach based on scalarizing Function for generating common set of weights under the DEA framework. This is an advantageous of the proposed approach against general approaches in the literature which are based on multiple objective nonlinear programming.