数学建模在《图论》教学中的作用

在《图论》课程的教学过程中,根据教学内容适当引入数学建模的思想、方法,激发学生学习《图论》的兴趣,提高学生应用所学知识分析、解决实际问题的能力。

高校理科双语教学模式研究——以《图论基础》课程为例

文章阐述了我国高校理科双语教学模式的内涵、特征和实施目标,概述了国内外双语教学中常见的语言选择模式,最后结合《图论基础》课程的教学实践,在语言选择模式的基础上,论述了构建理科双语教学模式的基本原则:方法原则、主体原则、思维原则、手段原则、目标原则、评价原则,并从内容、方法和流程方面具体研究适合理科教育的双语教学模式。

Oxygen Reduction Reaction Activity of Fe-based Dual-Atom Catalysts with Different Local Configurations via Graph Neural Representation

The performance of proton exchange membrane fuel cells depends heavily on the oxygen reduction reaction(ORR)at the cathode,for which platinum-based catalysts are currently the standard.The high cost and limited availability of platinum have driven the search for alternative catalysts.While FeN4 single-atom catalysts have shown promising potential,their ORR activity needs to be further enhanced.In contrast,dual-atom catalysts(DACs)offer not only higher metal loading but also the ability to break the ORR scaling relations.However,the diverse local structures and tunable coordination environments of DACs create a vast chemical space,making large-scale computational screening challenging.In this study,we developed a graph neural network(GNN)-based framework to predict the ORR activity of Fe-based DACs,effectively addressing the challenges posed by variations in local catalyst structures.Our model,trained on a dataset of 180 catalysts,accurately predicted the Gibbs free energy of ORR intermediates and overpotentials,and identified 32 DACs with superior catalytic activity compared to FeN4 SAC.This approach not only advances the design of high-performance DACs,but also offers a powerful computational tool that can significantly reduce the time and cost of catalyst development,thereby accelerating the commercialization of fuel cell technologies.

TWO IMPROVED GRAPH-THEORETICAL CLUSTERING ALGORITHMS

Graph-theoretical approaches have been widely used for data clustering and image segmentation recently. The goal of data clustering is to discover the underlying distribution and structural information of the given data, while image segmentation is to partition an image into several non-overlapping regions. Therefore, two popular graph-theoretical clustering methods are analyzed, including the directed tree based data clustering and the minimum spanning tree based image segmentation. There are two contributions： （1） To improve the directed tree based data clustering for image segmentation, （2） To improve the minimum spanning tree based image segmentation for data clustering. The extensive experiments using artificial and real-world data indicate that the improved directed tree based image segmentation can partition images well by preserving enough details, and the improved minimum spanning tree based data clustering can well cluster data in manifold structure.

Theoretical prediction of forming limit diagram of AZ31 magnesium alloy sheet at warm temperatures

A theoretical prediction on forming limit diagram（FLD） of AZ31 magnesium alloy sheet was developed at warm temperatures based on the M-K theory. Two different yield criteria of von Mises and Hill＇48 were applied in this model. Mechanical properties of AZ31 magnesium alloy used in the prediction were obtained by uniaxial tensile tests and the Fields-Backofen equation was incorporated in the analysis. In addition, experimental FLDs of AZ31 were acquired by conducting rigid die swell test at different temperatures to verify the prediction. It is demonstrated from a comparison between the predicted and the experimental FLDs at 473 K and 523 K that the predicted results are influenced by the type of yield criterion used in the calculation, especially at lower temperatures. Furthermore, a better agreement between the predicted results and experimental data for AZ31 magnesium alloy sheet at warm temperatures was obtained when Hill＇48 yield criterion was applied.

Overview and Graph Theory of the Immune System of Crustacean

In this paper,different kinds of enzymes,immune factors and regulatory factors of the immune system of crustaceans are summarized and then combed systematically and thoroughly. According to the mutual influence and effects of these factors,different symbolic forms are introduced to express the effects,and ultimately the whole node graph of the system is obtained. The graph theory can be used for further researches on the immune system of crustacean.

Two Results on Uniquely r-Pancyclic Graphs

In this paper,we prove that there does not exist an r-UPC[2]-graph for each r≥5 and there does not exist an r-UPC[C_t^2]-graph for each r≥3,where t is the number of bridges in a graph and C_t^2 is the number of combinations of t bridges taken 2 at a time.

Inverse kinematic deriving and actuator control of Delta robot using symbolic computation technology

In order to effectively derive the inverse kinematic solution of the Delta robot and realize actuator control a description of the linear graph principle for automatically generating kinematic equations in a mechanical system as well as the symbolic computation implementation of this procedure is reviewed and projected into the Delta robot. Based on the established linear graph representation the explicit symbolic expression of constraint equations and inverse kinematic solutions are obtained successfully using a symbolic computation engine Maple so that actuator control and trajectory tracking can be directly realized.Two practical motions the circular path and Adept motion are simulated for the validation of symbolic solutions respectively.Results indicate that the simulation satisfies the requirement of the quick motion within an acceptable threshold. Thus the precision of kinematic response can be confirmed and the correctness of inverse solution is verified.

Dynamic software allocation algorithm for saving power in pervasive computing

A novel dynamic software allocation algorithm suitable for pervasive computing environments is proposed to minimize power consumption of mobile devices. Considering the power cost incurred by the computation, communication and migration of software components, a power consumption model of component assignments between a mobile device and a server is set up. Also, the mobility of components and the mobility relationships between components are taken into account in software allocation. By using network flow theory, the optimization problem of power conservation is transformed into the optimal bipartition problem of a flow network which can be partitioned by the max-flow rain-cut algorithm. Simulation results show that the proposed algorithm can save si^nificantlv more energy than existing algorithms.

Correlation between the Change in the Number of Apis mellifera Worker Bees and Nectar Secretion of Nectariferous Plants

[Objective] This study aimed to clarify the correlation between changes of Apis mel ifera and the nectar secretion characteristics of nectariferous plants. [Method] Considering the nectar secretion characteristics of major and auxiliary nec-tariferous plants, six Apis mel ifera colonies were selected for measure the number of eggs, larvae, pupae and adult bees from Jan. to Dec. in 2012; based on that, their annual change curves were also plotted. [Result] The results showed that there were three peaks of the total number of A. mel ifera workers throughout the year：the first occurred on May 15th, with bees developed into an ideal population for col-lecting pomegranate nectar, and the second and third peaks occurred on July 15th and Oct. 15th, respectively, with bees developed into an ideal population for col ect-ing E. ciliate （Thuab） Hyland. [Conclusion] Prevention of Varroa jacobsoni should be carried out with two or more types of acaricides at the late nectar flow stages of the two nectariferous plants（pomegranate and E. ciliate （Thuab） Hyland） when there was a nectar deficiency. Prevention of Tropilaelaps clareae should be timely per-formed with sublimed sulfur in conjunction with acaricides. This study provides a theoretical basis for the high-quality and high-yielding production of honey, as wel as for the product safety.

THE APPLICATION OF THE BRANCH AND BOUND METHOD FOR DETERMINING THE MINIMUM FLOW OF A TRANSPORT NETWORK

Blockage is a kind of phenomenon frequently occurred in a transport network, in which the human beings are the moving subjects. The minimum flow of a network defined in this paper means the maximum flow quantity through the network in the seriously blocked situation. It is an important parameter in designing and operating a transport network, especially in an emergency evacuation network. A branch and bound method is presented to solve the minimum flow problem on the basis of the blocking flow theory and the algorithm and its application are illustrated by examples.

On the mode of CRI English assisting college English teaching

The English News of CRI possesses many advantages such as abundance of information and being easily accessible for English learners within the mainland of China. Unfortunately, it has been ignored by most teachers of English and students. Based on the input hypothesis, affective filter hypothesis and schemata theory, this paper probes the mode of CRI English assisting English teaching in college.

The Factorization of Adjoint Polynomials of E^G（i）-class Graphs and Chromatically Equivalence Analysis

Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by Eτp＋（r-1）^G（i） the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r - 1 of S,, while the i-th vertex of each component of （r - 1）G be adjacented to r - 1 vertices of degree 1 of St, respectively. By applying the properties of adjoint polynomials, We prove that factorization theorem of adjoint polynomials of kinds of graphs Eτp＋（r-1）^G（i）∪（r - 1）K1 （1 ≤i≤p）. Furthermore, we obtain structure characteristics of chromatically equivalent graphs of their complements.

Multi-resolution graph-based clustering analysis for lithofacies identifi cation from well log data: Case study of intraplatform bank gas fi elds, Amu Darya Basin

In this study, we used the multi-resolution graph-based clustering （MRGC） method for determining the electrofacies （EF） and lithofacies （LF） from well log data obtained from the intraplatform bank gas fields located in the Amu Darya Basin. The MRGC could automatically determine the optimal number of clusters without prior knowledge about the structure or cluster numbers of the analyzed data set and allowed the users to control the level of detail actually needed to define the EF. Based on the LF identification and successful EF calibration using core data, an MRGC EF partition model including five clusters and a quantitative LF interpretation chart were constructed. The EF clusters 1 to 5 were interpreted as lagoon, anhydrite flat, interbank, low-energy bank, and high-energy bank, and the coincidence rate in the cored interval could reach 85%. We concluded that the MRGC could be accurately applied to predict the LF in non-cored but logged wells. Therefore, continuous EF clusters were partitioned and corresponding LF were characteristics ＆different LF were analyzed interpreted, and the distribution and petrophysical in the framework of sequence stratigraphy.

On the Spectral Radius of Trees with the Given Diameter d

Let T denote a tree with the diameter d(d≥2) and order n. Let Pd,r,n-d-1 denote the tree obtained by identifying the rth vertex of path Pd+1 and the center of star K1,n-d-1, where r = r(d) is the integer part about d+2/2. Then p(T) ≤p(Pd,r,n-d-1),and equality holds if and only if T≌ Pd,r,n-d-1

A Class of Star Extremal Circulant Graphs

The circular chromatic number and the fractional chromatic number are two generalizations of the ordinary chromatic number of a graph. A graph is called star extremal if its fractional chromatic number equals to its circular chromatic number (also known as the star chromatic number). This paper studies the star extremality of the circulant graphs whose generating sets are of the form {±1,±k} .

On the Total Domination Number of Graphs with Minimum Degree at Least Three

Let G be a simple graph with no isolated vertices. A set S of vertices of G is a total dominating set if every vertex of G is adjacent to some vertex in S . The total domination number of G , denoted by γ t (G) , is the minimum cardinality of a total dominating set of G . It is shown that if G is a graph of order n with minimum degree at least 3, then γ t (G)≤n/2 . Thus a conjecture of Favaron, Henning, Mynhart and Puech is settled in the affirmative.

Restricted Edge Connectivity of Binary Undirected Kautz Graphs

A restricted edge cut is an edge cut of a connected graph whose removal resultsin a disconnected graph without isolated vertices. The size of a minimum restricted edge cutof a graph G is called its restricted edge connectivity, and is denoted by λ′(G). Let ξ(G) bethe minimum edge degree of graph G. It is known that λ′(G) ≤ξ(G) if G contains restrictededge cuts. Graph G is called maximal restricted edge connected if the equality holds in thethe preceding inequality. In this paper, undirected Kautz graph UK(2, n) is proved to bemaximal restricted edge connected if n ≥ 2.

Qualitative Algebra and Graph Theory Methods for Dynamic Trend Analysis of Continuous System

Qualitative algebraic equations are the basis of qualitative simulation,which are used to express the dynamic behavior of steady-state continuous processes.When the values and operation of qualitative variables are redefined,qualitative algebraic equations can be transformed into signed direct graphs,which are frequently used to predict the trend of dynamic changes.However,it is difficult to use traditional qualitative algebra methods based on artificial trial and error to solve a complex problem for dynamic trends.An important aspect of modern qualitative algebra is to model and characterize complex systems with the corresponding computer-aided automatic reasoning.In this study,a qualitative affection equation based on multiple conditions is proposed,which enables the signed di-rect graphs to describe complex systems better and improves the fault diagnosis resolution.The application to an industrial case shows that the method performs well.

The Roots of Adjoint Polynomial of the Graphs Contain Triangles

We denote h(G,x) as the adjoint polynomial of graph G. In [5], Ma obtained the interpolation properties of the roots of adjoint polynomial of graphs containing triangles. By the properties, we prove the non-zero root of adjoint polynomial of Dn and Fn are single multiple.