Structural properties of 1-planar graphs and an application to acyclic edge coloring

A graph is called 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, we establish a local property of 1-planar graphs which describes the structure in the neighborhood of small vertices (i.e. vertices of degree no more than seven). Meanwhile, some new classes of light graphs in 1-planar graphs with the bounded degree are found. Therefore, two open problems presented by Fabrici and Madaras [The structure of 1-planar graphs, Discrete Mathematics, 307, (2007), 854-865] are solved. Furthermore, we prove that each 1-planar graph $G$ with maximum degree $\Delta(G)$ is acyclically edge $L$-choosable where $L=\max\{2\Delta(G)-2,\Delta(G)+83\}$.Comment: Please cite this published article as: X. Zhang, G. Liu, J.-L. Wu. Structural properties of 1-planar graphs and an application to acyclic edge coloring. Scientia Sinica Mathematica, 2010, 40, 1025--103

Edge covering pseudo-outerplanar graphs with forests

A graph is called pseudo-outerplanar if each block has an embedding on the plane in such a way that the vertices lie on a fixed circle and the edges lie inside the disk of this circle with each of them crossing at most one another. In this paper, we prove that each pseudo-outerplanar graph admits edge decompositions into a linear forest and an outerplanar graph, or a star forest and an outerplanar graph, or two forests and a matching, or $\max\{\Delta(G),4\}$ matchings, or $\max\{\lceil\Delta(G)/2\rceil,3\}$ linear forests. These results generalize some ones on outerplanar graphs and $K_{2,3}$-minor-free graphs, since the class of pseudo-outerplanar graphs is a larger class than the one of $K_{2,3}$-minor-free graphs.Comment: This paper was done in the winter of 2009 and has already been submitted to Discrete Mathematics for 3rd round of peer revie

Graphic Style Transfer Technology in Multimedia Communication: An Application of Deep Residual Adaptive Networks in Graphic Design

With the rapid development of wireless network technology and the rapid popularity of portable smart terminals, multimedia communication based on images and videos has become the favorite way of communication in the new era. Image style transfer technology is one of the research directions that has attracted much attention in the field of multimedia communication. To achieve the diversification of images and ease of use in the multimedia communication process, this paper researches the multimedia network communication technology and image style transfer technology. By combining visual style transfer technology and depth residual adaptive network technology in multimedia communication technology, the redesign and creation of graphics can be carried out effectively. The resulting graphics can meet the needs of the art creators and the technique provides higher creative efficiency, excellent peak model signal-to-noise ratio and structural similarity performance, and output levels that meet the basic needs compared to traditional manual design. The method can be effectively used in urban building appearance design and art creation and has good theoretical and practical research value

Threshold dynamics of a nonlocal diffusion West Nile virus model with spatial heterogeneity

In this study, we investigated the threshold dynamics of a spatially heterogeneous nonlocal diffusion West Nile virus model. By employing semigroup theory and continuous Fréchet-differentiable, we established the well-posedness of the solution. The expression for the basic reproduction number derived using the next-generation matrix method. The authors demonstrated the threshold dynamics of the system by constructing a Lyapunov function and applying the comparison principle. Finally, numerical simulations were used to validate the theorem results. It can be suggested that to control disease development rapidly, measures should be taken to reduce the spread of mosquitoes and birds

Highly efficient and stable p-type ZnO nanowires with piezotronic effect for photoelectrochemical water splitting

Unremitting efforts have been made to develop high-performance photoelectrochemical (PEC) water-splitting system to produce clean hydrogen fuel using sunlight. In this work, a novel way, combining highly-ordered nanowires (NWs) structure and piezotronic effect of p-type ZnO has been demonstrated to dramatically enhance PEC hydrogen evolution performance. Systematic characterizations indicate that the Sb atoms uniformly dope into ZnO NWs and substitute Zn sites with the introduction of two zinc vacancies to form the shallow acceptor SbZn–2VZn complex. Detailed synchrotron-based X-ray absorption near-edge structure (XANES) experiments in O K-edge and Zn L-edge further confirm the formation of the complex, and theoretical calculation verifies the Sb5+ state dominating the complex. The optimal photocurrent density of the 0.2Sb/ZnO-anneal NWs can reach −0.85 mA/cm2 (0 VRHE) which is 17.2 times larger than that of the n-ZnO NWs under sunlight illumination (100 mW/cm2). Furthermore, the piezotronic effect can be introduced to regulate the charge separation and transfer in the ZnO NWs through modulating the band structure near the interface. The photocurrent density can further increase to −1.08 mA/cm2 (0 VRHE) under a 0.6% tensile strain, which is 27.4% enhancement with respect to the ZnO sample without strain. These results provide an efficient way to design and develop high-performance photoelectrodes toward PEC hydrogen evolution

Dynamics analysis of a nonlocal diffusion dengue model

Abstract Due to the unrestricted movement of humans over a wide area, it is important to understand how individuals move between non-adjacent locations in space. In this research, we introduce a nonlocal diffusion introduce for dengue, which is driven by integral operators. First, we use the semigroup theory and continuously Fréchet differentiable to demonstrate the existence, uniqueness, positivity and boundedness of the solution. Next, the global stability and uniform persistence of the system are proved by analyzing the eigenvalue problem of the nonlocal diffusion term. To achieve this, the Lyapunov function is derived and the comparison principle is applied. Finally, numerical simulations are carried out to validate the results of the theorem, and it is revealed that controlling the disease’s spread can be achieved by implementing measures to reduce the transmission of the virus through infected humans and mosquitoes

New Upper Bounds for the Heights of Some Light Subgraphs in 1-Planar Graphs with High Minimum Degree

Combinatoric

New Upper Bounds for the Heights of Some Light Subgraphs in 1-Planar Graphs with High Minimum Degree

CombinatoricsA graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is shown that each 1-planar graph of minimum degree 6 contains a copy of 4-cycle with all vertices of degree at most 19. In addition, we also show that the complete graph K 4 is light in the family of 1-planar graphs of minimum degree 7, with its height at most 11

The Study of Large-Scale Fading Using a Wavelet Transform Method

A wavelet method is proposed to evaluate the modeling of the first- and second-order statistics of large-scale fading from the signal strength measurement. The selection of wavelet is very important in using a wavelet method, and the steps of the wavelet method are given for the study of wave propagation loss. The path loss of measurement is analysed with different levels of wavelet decomposition and compared with an optimized Hata model. The correlation of slow fading on different scales shows that the correlation distance is related to the spatial scale