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The preparation of C4 olefins from ethanol has become a research hotspot in the field of chemical product production. Based on the test data of given catalyst combination at different temperatures, a neural network prediction model for the effect of different catalyst combination and temperature on C4 olefin yield is proposed in this paper. Firstly, taking the catalyst combination and temperature as independent variables, the C4 olefin yield is analyzed by multiple regression analysis and evaluated by R-square index. Secondly, on the basis of this experiment, the BP neural network model for predicting the yield of coupling reaction is reconstructed, and the adaptive genetic operator is added to the BP neural network to optimize its threshold, weight, and convergence speed, so as to improve the accuracy of yield prediction. Finally, the prediction results of BP and GA-BP models are compared from five aspects: SSE, MAE, MSE, RMSE, and MAPE. The experimental results show that the improved model has good global optimization ability and high yield prediction accuracy in the prediction of coupling reaction yield. Therefore, the multiple control variable model proposed in this paper has a certain positive significance for predicting the effect of catalyst combination on yield in coupling reaction.

Abnormal target detection in hyperspectral remote sensing image is one of the hotspots in image research. The image noise generated in the detection process will lead to the decline of the quality of hyperspectral remote sensing image. In view of this, this paper proposes an abnormal target detection method of hyperspectral remote sensing image based on the convolution neural network. Firstly, the deep residual learning network model has been used to remove the noise in hyperspectral remote sensing image. Secondly, the spatial and spectral features of hyperspectral remote sensing images were used to optimize the clustering dictionary, and then the image segmentation containing target information is completed. Finally, the image was input into the deep convolution neural network with a dual classifier, and the network detects the abnormal target in the image. The test results of this algorithm show that the structural similarity of the denoised image is higher than 0.86, which shows that this method has good noise reduction performance, image details will not damage, segmentation effect is good, and it can obtain high-definition target image information and accurately detect abnormal targets in the image.

Background:: A topological index of a molecular graph is the numeric quantity which can predict certain physical and chemical properties of the corresponding molecule. Xu et al. introduced some graph transformations which increase or decrease the first and second multiplicative Zagreb indices and proposed a unified approach to characterize extremal (n, m)- graphs. Method:: Graph transformations are used to find the extremal graphs, these transformations either increase or decrease the general multiplicative Zagreb indices. By applying the transformations which increase the general multiplicative Zagreb indices we find the graphs with maximal general multiplicative Zagreb indices and for minimal general Zagreb indices we use the transformations which decrease the index. Result:: In this paper, we extend the Xu’s results and show that the same graph transformations increase or decrease the first and second general multiplicative Zagreb indices for . As an application, the extremal acyclic, unicyclic and bicyclic graphs are presented for general multiplicative Zagreb indices. Conclusion:: By applying the transformation we investigated that in the class of acyclic, unicyclic and bicyclic graphs, which graph gives the minimum and the maximum general multiplicative Zagreb indices.

Due to the increasing growth of economy in the last few years, environmental problems have become a prominent difficulty in Chinese economic growth and social development. Therefore, in order to respond to the environmental protection policy of Anhui Province, all prefecture-level cities need to be evaluated for their environmental efficiency. A study of environmental efficiency in Anhui Province is presented in this paper. The time period is from 2015 to 2020. By exploiting MaxDEA software, the input–output system in different years is taken as the decision-making unit, and slacks-based model (SBM-DEA) which is based on an unexpected output is used to construct the index system by selecting two output indexes and four input indexes, so as to calculate the environmental efficiency of Anhui Province, including 16 prefecture-level cities, under the condition of constant non-radial and non-angle scale benefits. In addition, based on the persistence and anti-persistence theory of fractal theory, in this paper, we have analyzed the future trend of environmental efficiency of prefecture-level cities in Anhui Province by rescaled range analysis (R/S). The results show that Anhui province has 16 prefectures that have not achieved an optimal level of environmental performance and fluctuates downward from 2015 to 2020. The average value of comprehensive efficiency is 0.846. As for technical efficiency, the mean value is 0.954, and scale efficiency has an average value of 0.887. The technical progress of environmental efficiency development in Anhui Province is small and the room for improvement is large. Finally, according to the results of the study, some suggestions on environmental technology are put forward.

We present new Mercer variants of Hermite-Hadamard (HH) type inequalities via Atangana-Baleanu (AB) fractional integral operators pertaining non-local and non-singular kernels. We establish trapezoidal type identities for fractional operator involving non-singular kernel and give Jensen-Mercer (JM) variants of Hermite-Hadamard type inequalities for differentiable mapping $ \Upsilon $ possessing convex absolute derivatives. We establish connections of our results with several renowned results in the literature and also give applications to special functions.

The Kirchhoff index and degree-Kirchhoff index have attracted extensive attentions due to their wide applications in physics and chemistry. These indices have been computed for many interesting graphs, such as linear polyomino chain, linear/Mobius/cylinder hexagonal chain, and linear octagonal chain. In the present paper, we consider Mobius octagonal chain ( M n ) and cylinder octagonal chain ( M n ′ ). Explicit closed-form formulae of the Kirchhoff index and the number of spanning trees are obtained for M n and M n ′ .

Let $\Gamma=(V,E)$ be a simple connected graph. A vertex $a$ is said to recognize (resolve) two different elements $b_{1}$ and $b_{2}$ from $V(\Gamma)\cup E(\Gamma)$ if $d(a, b_{1})\neq d(a, b_{2}\}$. A subset of distinct ordered vertices $U_{M}\subseteq V(\Gamma)$ is said to be a mixed metric generator for $\Gamma$ if each pair of distinct elements from $V\cup E$ are recognized by some element of $U_{M}$. The mixed metric generator with a minimum number of elements is called a mixed metric basis of $\Gamma$. Then, the cardinality of this mixed metric basis for $\Gamma$ is called the mixed metric dimension of $\Gamma$, denoted by $mdim(\Gamma)$. The concept of studying chemical structures using graph theory terminologies is both appealing and practical. It enables researchers to more precisely and easily examines various chemical topologies and networks. In this paper, we consider two well known chemical structures; starphene $SP_{a,b,c}$ and six-sided hollow coronoid $HC_{a,b,c}$ and respectively compute their multiset dimension and mixed metric dimension., Comment: 13 pages, 3 figures, 3 tables

After the occurrence of public health emergencies, due to the uncertainty of the evolution of events and the asymmetry of pandemic information, the public’s risk perception will fluctuate dramatically. Excessive risk perception often causes the public to overreact to emergencies, resulting in irrational behaviors, which have a negative impact on economic development and social order. However, low-risk perception will reduce individual awareness of prevention and control, which is not conducive to the implementation of government pandemic prevention and control measures. Therefore, it is of great significance to accurately evaluate public risk perception for improving government risk management. This paper took the evolution of public risk perception based on the COVID-19 region as the research object. First, we analyze the characteristics of infectious diseases in the evolution of public risk perception of public health emergencies. Second, we analyze the characteristics of risk perception transmission in social networks. Third, we establish the dynamic model of public risk perception evolution based on SEIR, and the evolution mechanism of the public risk perception network is revealed through simulation experiments. Finally, we provide policy suggestions for government departments to deal with public health emergencies based on the conclusions of this study.

Chemical graph theory deals with the basic properties of a molecular graph. In graph theory, we correlate molecular descriptors to the properties of molecular structures. Here, we compute some Banhatti molecular descriptors for water-soluble dendritic unimolecular polyether micelle. Our results prove to be very significant to understand the behaviour of water-soluble dendritic unimolecular polyether micelle as a drug-delivery agent.

Entropy is a measure of a system's molecular disorder or unpredictability since work is produced by organized molecular motion. Shannon's entropy metric is applied to represent a random graph's variability. Entropy is a thermodynamic function in physics that, based on the variety of possible configurations for molecules to take, describes the randomness and disorder of molecules in a given system or process. Numerous issues in the fields of mathematics, biology, chemical graph theory, organic and inorganic chemistry, and other disciplines are resolved using distance-based entropy. These applications cover quantifying molecules' chemical and electrical structures, signal processing, structural investigations on crystals, and molecular ensembles. In this paper, we look at

Lie symmetry analysis of differential equations proves to be a powerful tool to solve or at least reduce the order and nonlinearity of the equation. Symmetries of differential equations is the most significant concept in the study of DE’s and other branches of science like physics and chemistry. In this present work, we focus on Lie symmetry analysis to find symmetries of some general classes of KS-type equation. We also compute transformed equivalent equations and some invariant solutions of this equation.

Based on the theoretical mechanism analysis of FDI, regional innovation, and green economic efficiency, this article uses China’s provincial panel data to calculate the provincial green economic efficiency level based on the three-stage DEA method and uses the system GMM model, intermediary effect model, and threshold model to empirically test the specific effects and transmission paths of FDI on the efficiency of the green economy. Research shows that FDI is one of the important factors that promote the improvement of green economic efficiency. Subregional tests have found that FDI has a significant regional heterogeneity in promoting the efficiency of the green economy. The mediation effect test found that the mediation effect of regional innovation is significant, and FDI can significantly promote the growth of green economic efficiency through regional innovation. The threshold effect analysis found that there are significant and effective double thresholds for regional economic levels, and the impact of FDI on green economic efficiency is heterogeneous within different threshold intervals. The research conclusions provide new inspiration for China to allocate FDI more rationally and efficiently under the new development pattern.

For the study and valuation of social graphs, which affect an extensive range of applications such as community decision-making support and recommender systems, it is highly recommended to sustain the resistance of a social graph G to active attacks. In this regard, a novel privacy measure, called the k , l -anonymity, is used since the last few years on the base of k -metric antidimension of G in which l is the maximum number of attacker nodes defining the k -metric antidimension of G for the smallest positive integer k . The k -metric antidimension of G is the smallest number of attacker nodes less than or equal to l such that other k nodes in G cannot be uniquely identified by the attacker nodes. In this paper, we consider four families of wheel-related social graphs, namely, Jahangir graphs, helm graphs, flower graphs, and sunflower graphs. By determining their k -metric antidimension, we prove that each social graph of these families is the maximum degree metric antidimensional, where the degree of a vertex is the number of vertices linked with that vertex.

The study of structure-property relations including the transformations of molecules is of utmost importance in correlations with corresponding physicochemical properties. The graph topological indices have been used effectively for such study and, in particular, bond-based indices play a vital role. The bond-additive topological indices of a molecular graph are defined as a sum of edge measures over all edges in which edge measures can be computed based on degrees, closeness, peripherality, and irregularity. In this study, we provide the mathematical characterization of the transformation of a structure that can be accomplished by the novel edge adjacency and incidence relations. We derive the exact expressions of bond type indices such as second Zagreb, sigma indices, and their coindices of total transformation and two types of semitransformations of the molecules which in turn can be used to characterize the topochemical and topostructural properties.

In the chemical industry, topological indices play an important role in defining the properties of chemical compounds. They are numerical parameters and structure invariant. It is a proven fact by scientists that topological properties are influential tools for interconnection networks. In this paper, we will use stellation, medial and bounded dual operations to build transformed networks from zigzag and triangular benzenoid structures. Using M-polynomial, we compute the first and second Zagreb indices, second modified Zagreb indices, symmetric division index, general Randic index, reciprocal general Randic index. We also calculate atomic bond connectivity index, geometric arithmetic index, harmonic index, first and second Gourava indices, first and second hyper Gourava indices.

In this work, we introduce a new topological index called a general power sum-connectivity index and we discuss this graph invariant for some classes of extremal graphs. This index is defined by Y α G = ∑ u v ∈ E G d u d u + d v d v α , where d u and d v represent the degree of vertices u and v , respectively, and α ≥ 1 . A connected graph G is called a k -generalized quasi-tree if there exists a subset V k ⊂ V G of cardinality k such that the graph G − V k is a tree but for any subset V k − 1 ⊂ V G of cardinality k − 1 , the graph G − V k − 1 is not a tree. In this work, we find a sharp lower and some sharp upper bounds for this new sum-connectivity index.

Many of the behaviors observed in actual systems are comparable to scale-free and small world structures in network research. In contrast to conventional hierarchical networks, the unusual fractal hierarchical network we created in this research has a pyramidal structure. The findings we get from this network are expanded to be applicable to arbitrary hierarchical networks. The average path length of unweighted and weighted hierarchical networks are the main topics of this paper. We demonstrate that, in the unweighted case, when the number of iterations z tends to infinity, the average path length is only related to the number of blocks of the hierarchical network. Additionally, in the weighted network, the average path length is related to the number of blocks r and the weighting factor w of the hierarchical network.

Nowadays, with the development of the times, network structure analysis has become a hot issue in some fields. The eigenvalues of normalized Laplacian are very important for some network structure properties. Let Qn be octagonal-quadrilateral networks composed of n octagons and n squares and let Q2n be the strong prism of Qn. The strong product of a complete graph of order 2 and a complete graph of order G forms a strong prism of the graph G. In this paper, the decomposition theorem of the associated matrix is used to completely investigate the normalized Laplacian spectrum of Qn2. In addition, we establish exact formulas for the degree-Kirchhoff index and the number of spanning trees of Qn2.

In recent years, spectrum analysis and computation have developed rapidly in order to explore and characterize the properties of network sciences. Let Ln be obtained from the transformation of the graph L6,4,4 n , which obtained by attaching crossed two four-membered rings to the terminal of crossed phenylenes. Firstly, we study the (nomalized) Laplacian spectrum of Ln based on the decomposition theorem for the corresponding matrices. Secondly, we obtain the closed-term fomulas for the (multiplicative degree) Kirchhoff index and the number of spanning trees from the relationship between roots and coefficients in linear chain networks. Finally, we are surprised to find that the (multiplicative degree) Kirchhoff index of Ln is nearly to one quarter of its (Gutman) Wiener index when n tends to infinity.

Metal-Organic Networks (MON’s) is the central bone for the chemical compounds of the latest study for the energy department. The study of MON’s structure provides us numerous benefits in different fields related to chemical sciences, electrical and civil sectors. The MON’s structure is also used to restore different chemical compounds, especially those elements which can be used for the energy purpose such as hydrogen and carbon. Topological indices of the MON’s structure provide relationships between physical and chemical characteristics of the this compound such as melting points, boiling points, chemically stability, pressure, chemical reaction factors and many other basic properties. In this paper we calculate different topological indices based on first, second and third distances for two different metal-organic networks with expanding number of layers consisting on both organic ligands and metal vertices. A comparison between the calculated different kinds of the Topological Indices with the help of the numerical values and their graphical representation is also included.

The Sombor indices, a new category of degree-based topological molecular descriptors, havebeen widely investigated due to their excellent chemical applicability. This paper aims to establishSombor indices distributions in random polygonal chain networks and to achieve expressions of theexpected values and variances. The expected values and variances of the Sombor indices for polyonino,pentachain, polyphenyl, and cyclooctane chains are obtained. Since the end connection of a randomchain network follows a binomial distribution, the Sombor indices of any chain network follow the normaldistribution when the number of polygons connected by the chain, indicated by n, approaches infinity.

Let G = G 1 × G 2 × ⋯ × G m be the strong product of simple, finite connected graphs, and let ϕ : ℕ ⟶ 0 , ∞ be an increasing function. We consider the action of generalized maximal operator M G ϕ on ℓ p spaces. We determine the exact value of ℓ p -quasi-norm of M G ϕ for the case when G is strong product of complete graphs, where 0 < p ≤ 1 . However, lower and upper bounds of ℓ p -norm have been determined when 1 < p < ∞ . Finally, we computed the lower and upper bounds of M G ϕ p when G is strong product of arbitrary graphs, where 0 < p ≤ 1 .