A graph $G$ is called irregular if the degrees of all its vertices are not the same. A graph is said to be \textit{Stepwise Irregular} (SI) if the difference of the degrees of any two adjacent vertices is always 1 (one). This paper deals with \textit{2-Stepwise Irregular} (2-SI) graphs in which the degrees of every pair of adjacent vertices differ by 2. Here we discuss some properties of 2-SI graphs and generalize them for $k$-SI graphs for which the imbalance of every edge is $k$. Besides, we also compute bounds of irregularity for the Albertson index in any 2-SI graph.

Rock structures are subjected to cyclic tension-compression loading due to a blasting, earthquake, traffic, and injection-production in an underground storage case. Therefore, studying the fatigue behavior of rock samples under this type of loading is required. In this study, the accumulated fatigue damage for a Green Onyx rock sample consisting only one mineral composition with two-step high-low sequences of loading levels was investigated under a completely reversed loading condition. New apparatus based on the R. R. Moore fatigue test machine was designed to assess this type of loading. A comparison was conducted between the predicted behavior of the Linear Damage Rule and the experimental data and a new damage Model was proposed based on the experimental observation. The results showed a good agreement between the proposed damage Model and the experimental data.

In recent decades, necessity to protect environment has been a serious concern for all people and international communities. In appropriate development of human economic activities, subsistence dependence of the growing world population on nature decreases the natural diversity of ecosystems and habitats day by day and provides additional constraints for life and survival of wildlife. As a result, implementation of programs to protect species and ecosystems is of great importance. The current study was carried out to implement a comprehensive strategic environmental management plan in the Mond protected area in southern Iran. Accordingly, the protected area was zoned using multi criteria decision method. According to the numerical Models, fifteen data layer were obtained on a scale of 1: 50,000. The results revealed that 28.35% out of the entire study area belongs to nature conservation zone. In the following step, in order to offer the strategic planning using strength, weaknesses, opportunities and threats method, a total number of 154 questionnaires were prepared and filled by the relevant experts. For this purpose, after identifying the internal and external factors, they were weighted in the form of matrices as; internal factor evaluation and external factor evaluation. Analytical hierarchy process and expert choice software were applied to weight the factors. At the end, by considering the socioeconomic and environmental issues, the strategy of using protective strategies in line with international standards as well as a strong support of governmental national execution with a score of 6.05 was chosen as the final approach.

This research addresses the essential need for assessing and managing water quality in reservoirs, which play a pivotal role in various socioeconomic aspects. To achieve this, a Stepwise automatic calibration approach is proposed, specifically targeting the CE-QUAL-W2 Model. This two-dimensional hydrodynamic and water quality Model is widely employed in studies worldwide. Calibration, a fundamental aspect of Model development, is complex and traditionally relies on manual, trial-and-error methods, which can be time-consuming and require substantial expertise. In this study, an alternative approach is introduced, incorporating the JAYA optimization algorithm, which reduces the complexity associated with fine-tuning optimization parameters. Furthermore, a clustering framework is adopted, grouping related variables for independent calibration. The research is conducted on the Dez reservoir in southwest Iran, using a two-step calibration process. The first step focuses on hydrodynamics, while the second step addresses water quality variables, including phosphate, ammonium, nitrate, and dissolved oxygen. The proposed methodology applied to Dez reservoir and tested against the observed data, where it demonstrates promising results.

In this study, 115 samples taken from the stream sediments were analyzed to determine the concentrations of As, Co, Cr, Cu, Ni, Pb, W, Zn, Au, Ba, Fe, Mn, Sr, Ti, U, V and Zr. In order to outline mineralization-derived stream sediments, various mapping techniques including fuzzy factor score, geochemical halos and fractal Model were used. Based on these Models, concentrations of Co, Cr, Ni, Zn, Ba, Fe, Mn, Ti, U, V and Zr showed anomalies which are distributed over the andesitic volcanic rocks. In addition, an anomaly map for each element also ascertained the most ideal results for the exploration of deposits. Anomaly element associations can be successfully used in future geochemical exploration projects. According to the stream sediment study, it characterized a high Ti anomaly in central and northern parts of the area which was confirmed by heavy mineral study in sediments and litho-geochemical study in the andesitic unites.

Introduction: The world prevalence of type 2 diabetes and its related increment mortality rate which needs high controls cost has attracted high scientific attention. Early detection of individuals who face this disease more than the others can prevent getting sick or at least reduce the disease consequences on public health. Regarding the costs and limitations of diagnostic tests, a statistical Model is presented that helps predict the time of diabetes incidence and determines its risk factors. Furthermore, this Model determines the significant predictor variables on response and considers them as Model equation parameters. Materials and Methods: In this study, 803 pre-diabetic women in the age range of more than 20 years were selected from Tehran lipid and glucose study (TLGS) to examine the predictor variables on time of diabetes incidence. They were entered into the study in the phases 1 and 2 and were followed up to the phase 4. The predictor variables selection was performed using the Stepwise Model (SM) and the Bayesian Model Averaging (BMA). Then, the predictive discrimination was used to compare the results of both Models. The Log-rank test was performed and the Kaplan-Meier Curve was plotted. The statistical analyses were performed using R software (version 3. 1. 3). Results: The Backward Stepwise Model (BSM), the Forward Stepwise Model (FSM) and the BMA have used 9, 10 and 6 variables, respectively. Although the BMA selected predictor variables number is much lower than the SM, the prediction ability remains nearly constant. Conclusions: The BMA has averaged on the supported Models using dataset. This Model has shown nearly constant accuracy despite the selection of lower predictor variables number in comparison to the SM.

Background: Citrus is among the cold temperature (freezing) susceptible plants. The performance of storage and breeding of horticultural crops is mainly dependent on the correlation among the traits. Objectives: The present study was conducted to identify the physiological and biochemical traits of some citrus cultivars with the greatest influence on stress tolerance and determine the direct and indirect effects of these traits on the median Lethal Time (LT50) using integrated pathway analysis (i. e., Stepwise regression and causality coefficient). Methods: Pathway analysis (i. e., Stepwise regression and causality coefficient) based on additive Models, which is among the robust statistical methods to describe the relationship among the traits, was used to investigate the physiological and biochemical charac, teristics of four citrus cultivars (i. e., Japanese mandarin, Thomson orange, Ruby Star grapefruit, and Lisbon lemon) at temperature levels (-8,-4, and +4°, C) in a completely randomized design with three replications in 2021. Results: The results showed that Japanese mandarin and Thomson orange cultivars had the highest stress tolerance (LT50). The results of the correlation coefficient demonstrated that the highest positive and significant correlations belonged to the LT50 with total flavonoid (0. 443**), chlorophyll a with chlorophyll b (0. 613**), carotenoid with chlorophyll a (0. 929**), chlorophyll b (0. 573**), and total chlorophyll (0. 849**), relative moisture content with malondialdehyde (0. 559**), glycine-betaine with catalase (0. 919**), hydrogen peroxide with total flavonoid (0. 405**), and catalase (0. 611**). Conclusions: The results of Stepwise regression for all traits indicated the importance and critical role of total flavonoid, proline, and LT50 characteristics.