In abstract algebra, a symmetric group defined over a set is the group for which the composition of functions is the group operation, and whose members are all the bijections from the set to itself. Galois theory, invariant theory, lie group representation theory, and combinatorics are just a few of the many branches of mathematics that rely on the symmetric group. The mathematical field of group representation theory studies the effects that groups have on predetermined structures. Particular attention is paid here to group operations on vector spaces. Yet, we also take into account groups that operate upon other groups or sets. The primary goal of this study is to offer an alternate approach of describing group elements of finite simple groups that is both brief and informative. In this research, we show how we found some new symmetric constructions for significant finite groups. As the orders of our photographs are becoming more and bigger, we've started using Magma to help us out with some of the math.
We consider the connectivity of fiber graphs with respect to Grobner basis and Graver basis moves. First, we present a sequence of fiber graphs using moves from a Grobner basis and prove that their edge-connectivity is lowest possible and can have an arbitrarily large distance from the minimal degree. We then show that graph-theoretic properties of fiber graphs do not depend on the size of the right-hand side. This provides a counterexample to a conjecture of Engstrom on the node-connectivity of fiber graphs. Our main result shows that the edge-connectivity in all fiber graphs of this counterexample is best possible if we use moves from Graver basis instead.
Purpose: In recent times, sugarcane production and area under cultivation have been fluctuating from year to year depending on climate and price policy, adversely affecting sugarcane growers' decisions to invest in cultivation and their livelihood. The declining trend of productivity may affect the future competitiveness, and therefore it needs to be investigated. Design/Methodology/Approach: In this study, prediction of sugarcane yielding through regression analysis is performed with the help of Multivariate Adaptive Regression Splines (MARS), Support Vector Regression (SVR), Partial Least Square Regression (PLSR), Elastic-Net Regression, and Multiple Linear Regression (MLR) on the basis of the historical data of sugarcane cultivation from 1971-72 to 2018-19. The prediction is done by training all the regression models with 80% of the data, by taking the overall Indian sugarcane productivity as a dependent variable and other major sugarcane producing states as independent variables. Findings: As a main result, the non-parametric regression model MARS is found to be much better than other well-fitted models. All of these models' performances are cross-validated using the Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), and the Wilcoxon Signed-Rank test. Also, the MARS model is found to be a more flexible and accurate model in predicting the behavior of sugarcane yielding in India. Practical Implications: The practitioners and farmers facilitate the model comparisons to achieve more profits through accurate estimation The research outcome implicates the agricultural industry to improve the sugarcane cultivation and productivity under uncertain environments. Originality/Value: The study suggests best management practices can be developed to increase the large potential of sugarcane production in India towards greater sustainability and food security modelling.
This study was undertaken to explore the determinants which affects the customer's intention to continue digital payment services. The ECM model was extended by using security and responsiveness. The conceptual model of the study was tested on 350 respondents using Partial Least Squares Structured Equation Modelling. The current study looked at how perceived security, responsiveness, and usefulness influenced the quality of digital payment services, digital payment customer satisfaction, and consumers' intentions to use these digital payment services. The findings indicate that perceived security, responsiveness, customer satisfaction and service quality have a significant impact on customers' willingness to continue using digital payments whereas perceived usefulness is not found to have a statistically significant impact on service quality towards digital payment services. Responsiveness found to be the most significant predictor of service quality while security is found to be the most significant predictor of customer satisfaction towards digital payment services. The present research provides a guide to the banking sector and helps them to identify the factors which contribute towards the intention of customers to continue digital payments services. The findings of the study also demonstrate that marketing managers and analysts have enormous potential to capitalize on these opportunities and plan for the long-term success of digital payment systems.
