A graph’s entropy is a functional one, based on both the graph itself and the distribution of probability on its vertex set. In the theory of information, graph entropy has its origins. Hex-derived networks have a variety of important applications in medication store, hardware, and system administration. In this article, we discuss hex-derived network of type 1 and 2, written as HDN 1 n and HDN 2 n, respectively of order n. We also compute some degree-based entropies such as Randić, (...) ABC, and G A entropy of HDN 1 n and HDN 2 n. (shrink)

The long-periodic/infinite discrete Gabor transform is more effective than the periodic/finite one in many applications. In this paper, a fast and effective approach is presented to efficiently compute the Gabor analysis window for arbitrary given synthesis window in DGT of long-periodic/infinite sequences, in which the new orthogonality constraint between analysis window and synthesis window in DGT for long-periodic/infinite sequences is derived and proved to be equivalent to the completeness condition of the long-periodic/infinite DGT. By using the property of delta function, (...) the original orthogonality can be expressed as a certain number of linear equation sets in both the critical sampling case and the oversampling case, which can be fast and efficiently calculated by fast discrete Fourier transform. The computational complexity of the proposed approach is analyzed and compared with that of the existing canonical algorithms. The numerical results indicate that the proposed approach is efficient and fast for computing Gabor analysis window in both the critical sampling case and the oversampling case in comparison to existing algorithms. (shrink)

Sierpinski networks are networks of fractal nature having several applications in computer science, music, chemistry, and mathematics. These networks are commonly used in chaos, fractals, recursive sequences, and complex systems. In this article, we compute various connectivity polynomials such as M -polynomial, Zagreb polynomials, and forgotten polynomial of generalized Sierpinski networks S k n and recover some well-known degree-based topological indices from these. We also compute the most general Zagreb index known as α, β -Zagreb index and several other general (...) indices of similar nature for this network. Our results are the natural generalizations of already available results for particular classes of such type of networks. (shrink)

A connected graph is called Hamilton-connected if there exists a Hamiltonian path between any pair of its vertices. Determining whether a graph is Hamilton-connected is an NP-complete problem. Hamiltonian and Hamilton-connected graphs have diverse applications in computer science and electrical engineering. The detour index of a graph is defined to be the sum of lengths of detours between all the unordered pairs of vertices. The detour index has diverse applications in chemistry. Computing the detour index for a graph is also (...) an NP-complete problem. In this paper, we study the Hamilton-connectivity of convex polytopes. We construct three infinite families of convex polytopes and show that they are Hamilton-connected. An infinite family of non-Hamilton-connected convex polytopes is also constructed, which, in turn, shows that not all convex polytopes are Hamilton-connected. By using Hamilton connectivity of these families of graphs, we compute exact analytical formulas of their detour index. (shrink)

Based on the Chinese General Social Survey database, this article explores the relationship between income inequality and residents’ subjective well-being from the perspective of inequality of opportunity and inequality of effort. We find that inequality of opportunity has a negative impact on subjective well-being in China, where inequality of effort has a positive impact. Our empirical results are robust for changing the inequality indicators. In the sub-sample studies, consistent conclusions are obtained in rural areas, whereas in urban areas only inequality (...) of effort has a significant impact. The results of mechanism study show that inequality of opportunity decreases residents’ sense of fairness, and inequality of effort increases residents’ sense of fairness, thus affecting their subjective well-being. The results of this study provide a good response to the inconclusive research findings on the impact of income inequality on subjective well-being. (shrink)

A complete classification of simple function germs with respect to Lipschitz equivalence over the field of complex numbers ℂ was given by Nguyen et al. The aim of this article is to implement a classifier in terms of easy computable invariants to compute the type of the Lipschitz simple function germs without computing the normal form in the computer algebra system Singular.

Let H n be the linear heptagonal networks with 2 n heptagons. We study the structure properties and the eigenvalues of the linear heptagonal networks. According to the Laplacian polynomial of H n, we utilize the method of decompositions. Thus, the Laplacian spectrum of H n is created by eigenvalues of a pair of matrices: L A and L S of order numbers 5 n + 1 and 4 n + 1 n! / r! n − r!, respectively. On the (...) basis of the roots and coefficients of their characteristic polynomials of L A and L S, we get not only the explicit forms of Kirchhoff index but also the corresponding total number of spanning trees of H n. (shrink)

In this study, we first introduce polygonal cylinder and torus using Cartesian products and topologically identifications and then find their Wiener and hyper-Wiener indices using a quick, interesting technique of counting. Our suggested mathematical structures could be of potential interests in representation of computer networks and enhancing lattice hardware security.

The aim of this work is the reduction of the throttling noise when the capillary is used as a throttling device. Based on the theory of bubble dynamics, two-phase flow, and aerated supercavitation, four different sizes of aerated devices used in refrigerator refrigeration systems are designed. Throttling noise and the temperature and pressure of inlet and outlet of the capillary are measured under stable operation. To compare the noise suppression effects in different groups of experiments, we introduced the cavitation number (...) to analyze, revealed the principle of aerated supercavitation to suppress noise, and combined the results of Fluent simulations to get the relationship between the noise suppression effect and the aerated quality. The experimental results showed that the aerated device can obviously suppress the throttling noise of the capillary outlet, up to 2.63 dB, which provides a new way for reducing the capillary throttling noise. (shrink)

With the popularization of higher education and the promotion of college enrollment expansion, the number of college graduates increases sharply. At the same time, the continuous transformation and upgrading of the industrial structure put forward higher requirements on the employability of college students, which leads to the imbalance between supply and demand in the labor market. The key to dealing with employment difficulties lie in the improvement of college students’ employability. Therefore, we make a regression analysis of 263 valid samples (...) from universities in Anhui Province and extract the factors that influence the improvement of college students’ employability in the process of talent cultivation in university. The result shows that there is a positive correlation between course setting, course teaching, club activities, and college students’ employability, among which the course teaching and club activities are the most critical factors which may influence college students’ employability. In addition, from the viewpoint of individual college students, the overall grades of college students and the time of participating in the internship are also closely related to their employability, i.e., college students with good overall grades and long internship time should also have stronger employability. (shrink)

In order to fully implement the new development concept, bring into full play the potential of sports development, and maintain the resilience of China’s sports development. This paper studies the resilience evaluation and spatial correlation of Chinese sports development under the new development concept. First, we constructed Resilience Evaluation Indexes System for Sports Development in China based on the analysis of the resilience features of sports development and the DPSIR model, which is from the five aspects of “driving force – (...) pressure – state – influence – response.” Second, used Coefficient of Variation and Technique for Order Preference by Similarity to an Ideal Solution Method to measure the resilience level of sports development in 31 provinces in China from 2013 to 2017. Then, we introduced the obstacle degree model to identify the obstacle factors that hinder the resilience of Chinese sports development in different periods. Finally, we used the global and local Moran indexes to analyze the spatial correlation of China sports regional development. The results showed that: overall, the development level of sports resilience in 31 provinces in China showed an upward trend from 2013 to 2017, while some provinces showed obvious fluctuations. The obstacles to the development of sports resilience in China mainly include sports scientific research equipment, the number of national fitness monitoring stations, the number of national fitness centers, the full-time equivalent of personnel, and the number of sports scientific research projects. The response subsystem is the main obstacle factor that affects the improvement of the resilience level of sports development in China. There is a positive spatial autocorrelation between the resilience level of sports development and regional spatial distribution, and the correlation shows a weakening trend, and the internal difference is significant. Finally, we concluded that we must take the new development philosophy as the guiding principle. First, we should stick to innovation-driven development to fully upgrade the resilience of China’s sports development. Second, we should adhere to the principle of coordinated development to promote the overall and balanced development of sports. Lastly, we should promote shared development so as to deliver benefits for all in an equal way. (shrink)

This study provided a content analysis of studies aiming to disclose how artificial intelligence has been applied to the education sector and explore the potential research trends and challenges of AI in education. A total of 100 papers including 63 empirical papers and 37 analytic papers were selected from the education and educational research category of Social Sciences Citation Index database from 2010 to 2020. The content analysis showed that the research questions could be classified into development layer, application layer, (...) and integration layer. Moreover, four research trends, including Internet of Things, swarm intelligence, deep learning, and neuroscience, as well as an assessment of AI in education, were suggested for further investigation. However, we also proposed the challenges in education may be caused by AI with regard to inappropriate use of AI techniques, changing roles of teachers and students, as well as social and ethical issues. The results provide insights into an overview of the AI used for education domain, which helps to strengthen the theoretical foundation of AI in education and provides a promising channel for educators and AI engineers to carry out further collaborative research. (shrink)