Abstract. Let [Formula: see text] be the book graph which consists of [Formula: see text] copies of triangles all sharing a common edge. Let [Formula: see text] be a cycle of length [Formula: see text]. In 1978, Rousseau and Sheehan initiated the study of the book–cycle Ramsey number. A lot of effort has been made to determine the value of [Formula: see text] since then. In [ Ars Combin., 31 (1991), pp. 239–248], Faudree, Rousseau, and Sheehan mentioned the following: “we know practically nothing about [Formula: see text] when [Formula: see text] is even and greater than four. Also, the problem of computing [Formula: see text] when [Formula: see text] is odd and [Formula: see text] and [Formula: see text] are nearly equal provides an unanswered test of strength.” Answering the second part of the question above, the second and fifth authors recently obtained the value of [Formula: see text] for [Formula: see text] and [Formula: see text] being large. However, the value of [Formula: see text] is previously unknown for [Formula: see text] and [Formula: see text] being even as well as [Formula: see text] and [Formula: see text] being odd. In this paper, for even [Formula: see text], we manage to determine the value of [Formula: see text] provided that [Formula: see text] is linear with [Formula: see text] and [Formula: see text] is large enough. Thus this makes progress towards the first part of the question above. In addition, for odd [Formula: see text], we are able to obtain the value of [Formula: see text] for [Formula: see text] and [Formula: see text] being large.

Abstract. Given integers [Formula: see text], we say that a graph [Formula: see text] is [Formula: see text]-free if there exists a red/blue edge coloring of [Formula: see text] such that it contains neither a red [Formula: see text] nor a blue [Formula: see text]. Given a function [Formula: see text], the Ramsey–Turán number [Formula: see text] is the maximum number of edges in an [Formula: see text]-vertex [Formula: see text]-free graph with independence number at most [Formula: see text]. For any [Formula: see text], let [Formula: see text]. We always call [Formula: see text] the Ramsey–Turán density of [Formula: see text] and [Formula: see text]. In 1993, Erdős, Hajnal, Simonovits, Sós, and Szemerédi proposed to determine the value of [Formula: see text] for [Formula: see text], and they conjectured that for [Formula: see text], [Formula: see text]. More recently, in 2019, Kim, Kim, and Liu conjectured that for [Formula: see text], [Formula: see text]. Erdős et al. (1993) determined [Formula: see text] for [Formula: see text] and [Formula: see text]. There has been no progress on the Ramsey–Turán density [Formula: see text] in the past 30 years. In this paper, we obtain [Formula: see text] and [Formula: see text]. Moreover, we show that the corresponding asymptotically extremal structures are weakly stable, which answers a problem of Erdős et al. (1993) for the two cases.

The notion of goodness for Ramsey numbers was introduced by Burr and Erdös in 1983. For graphs $G$ and $H$, let $G+H$ be the graph obtained from disjoint $G$ and $H$ by adding all edges between the vertices of $G$ and $H$. Denote $nH$ by the union of $n$ disjoint copies of $H$. Let $B_n^{(k)}=K_k+nK_1$, which is called a book. We first obtain that if $t\ge1$ and $k\ge2$ are fixed integers and $G$ is a fixed graph, then for all large $n$, $r(K_{1,t}+G, B_n^{(k)})\le (\chi(G)+1)(n+kt-1)+1.$ This is sharp for several classes of graphs. Faudree, Rousseau, and Sheehan in 1978 proved that $q^2+q+2\le r(C_4,B_{q^2-q+1}^{(2)})\le q^2+q+4$ for prime power $q$, which implies that $B_n^{(2)}$ is not $C_4$-good for $q^2-q+1\le n\le q^2+q$. It is very difficult to determine the exact values for $r(C_4,B_{n}^{(2)})$. Moreover, Nikiforov and Rousseau in 2009 already proved that $B_n^{(k)}$ is $(K_2+C_4)$-good for fixed $k\ge 2$ and large $n$. In this paper, we obtain that for fixed $k\ge 2$ and large $n$, \scriptsize$ r(K_1+C_4, B_n^{(k)}) = \left\{ \begin{array}{ll} 2(n+2k-1) {if $n$ is even,}\\ 2(n+2k-1)+1 {if $n$ is odd.} \end{array} \right. $ This implies that $B_n^{(k)}$ is not $(K_1+C_4)$-good for each fixed $k\ge2$.

Let $B_n^{(k)}$ be the book graph which consists of $n$ copies of $K_{k+1}$ all sharing a common $K_k$, and let $C_m$ be a cycle of length $m$. In this paper, we first determine the exact value of $r(B_n^{(2)}, C_m)$ for $\frac{8}{9}n+112\le m\le \lceil\frac{3n}{2}\rceil+1$ and $n \geq 1000$. This answers a question of Faudree, Rousseau, and Sheehan [ Ars Combin., 31 (1991), pp. 239--248] in a stronger form when $m$ and $n$ are large. Building upon this exact result, we are able to determine the asymptotic value of $r(B_n^{(k)}, C_n)$ for each $k \geq 3$. Namely, we prove that for each $k \geq 3$, $r(B_n^{(k)}, C_n)= (k+1+o_k(1))n$. This extends a result due to Rousseau and Sheehan [ J. London Math. Soc., 18 (1978), pp. 392--396].

In this article, a newsegmentation method based on traditional region growing (RG) is proposed for high resolutionremote sensing imagery. This method takes regional minima from horizontal and vertical gradient maps of the image as seeds for the following region growing processing. The new method consists of several steps as follows: (1)deriving a morphological gradient map from the input multispectral image, (2) morphologically filtering the gradient image to remove local minima with small depthand extracting regional minima of flat areas in the resulting filtered image as seeds, (3) segmenting the multispectral image using the RG approach with reference to the seeds, and (4) merge the resulting initial segments to yield asegmentation map. In a test with a WorldView-2 multispectral image, the proposed method offered segmentation maps with nearly the same accuracy as several current methods.

For graphs $F$ and $G$, let $F\to (G,G)$ signify that any red/blue edge coloring of $F$ contains a monochromatic $G$. Define Folkman number $f(G;p)$ to be the smallest order of a graph $F$ such that $F\to (G,G)$ and $\omega(F) \le p$. It is shown that $f(G;p)\le cn$ for graphs $G$ of order $n$ with $\Delta(G)\le \Delta$, where $\Delta\ge 3$, $c=c(\Delta)$, and $p=p(\Delta)$ are positive constants.

Image segmentation is the basis of object-based information extraction from remote sensing imagery. Image segmentation based on multiple features, multi-resolution, and spatial context is one current research focus. Combining graph theory based optimization with the multi-scale image segmentation framework of the eCognition software, a multi-scale image segmentation method is proposed in this paper. In this method, a coherent enhancement anisotropic diffusion filtering approach and a minimum spanning tree segmentation algorithm are employed to initially segment the image. After that, the resulting segments are merged regarding minimum heterogeneity criteria, which are based on both the spectral characteristics and the shape parameters of segments. Two test images were used for visual and quantitative comparisons of the proposed method with the multi-scale segmentation method FNEA employed in the eCognition software. The results show that the proposed method is effective, and is more sensitive to subtle spectral differences than the FNEA.

This paper presents a new alteration mineral mapping method based on statistical analysis of spectra. First of all, this method processes a cluster of measurement data of spectral of field samples, in order to distinguish different sample area from the overall types. Second, the results of the clustering of different mineral alterations were established their respective discriminant functions. Thus, mapping major alteration type accords with the clustered reference spectra by given remote sensing images. Finally mapping further alteration types based on the discrimant function of second step, which lead to final alteration map. This method takes full account of the different combination of alteration types, as well as the regional differences of alterations, and the establishment of the discriminant function for alteration minerals is more scientific. Moreover, we access the reliability of mapping to a certain extent. The method applied to a study area of Baogutu in Xinjiang Province, which represent a good result.

Finding the target contour information from a remote sensing image is one of the fundamental steps for image analysis. Conventional target contour extraction methods are usually based on the statistics information of the image. In this paper, using the maximum return value of the normalized scattering matrix derived from full-polarized Synthetic Aperture Radar (PolSAR), the relationship between the contour of targets and their corresponding dominate scattering type is preliminary researched. Then a novel target contour information extraction method based on the physical scattering mechanism of terrain targets is proposed, which is more effective and adaptable due to the scattering mechanism of terrain targets do not depend on the radar backscattering intensity, but its proportion among different polarizations. After applying to E-SAR airborne data, the results show that this method has a good capability to extract the target contour information.

A lot of phenomena have fractal characteristics (Chen and Chen, 1998), including the city we human being build. In the research of fractal cities, fractal dimension is very important (Chen, 2005). It can describe the fractal characteristic of the city. And, through the process of calculating the fractal dimension, we also can determine whether a city is a fractal object. Scholars often calculate the fractal dimension of the city when they do the city research. And they will introduce the method of calculating the fractal dimension. For example, Chinese scholar Fengjian in his paper of Spatial-temporal Evolution of Urban Morphology and land use structure in Hang Zhou (Feng, 2003), Israelite scholar Benguigui in his paper of when and where is a city fractal?(Benguigui, 2000). But few scholars will introduce the steps of the realization of calculating the fractal dimension in details. In fact, since the amount of data of calculating the fractal dimension is very large, it is very meaningful to work out a kind of quick and easy way to calculate the fractal dimension. There are three methods to calculate the fractal dimension of urban form: using geometry measure relationship; using turning radius method; using the box-counting method. We will use the box-counting method to calculate the fractal dimension and introduce two ways to realize it. According to the file formats used in operation, we name them as vector method and grid method. In our paper we will introduce the steps and the key techniques in details and compare these two ways in a certain degree.

In most cases especially rock types detection, the pixels in remote sensing image are mixed, and so common methods based on pure pixels to detect target are not appropriate here. Orthogonal Subspace Projection has two important properties: one is to eliminate or suppress the undesired signals by projecting each pixel onto the space orthogonal to interfering signals, another is to detect the presence of desired signal by projecting the residuals onto the space of interesting signal and maximizing the signal-to-noise ratio (SNR). It can be used simultaneously on mixed pixels and the pure ones. Using Thematic Mapper (TM) data to classify different rock types shows OSP to perform well.

Remote sensing plays an important role in the mineral exploration. One of the common applications is to locate alteration zones related to gold deposits. Many studies based on landsat thematic mapper (TM) imagery have been carried out and several methods have been developed. However, the advanced spaceborne thermal emission and reflection radiometer (ASTER) imagery, which has better spectral resolution (14 bands) and spatial resolution (15 m in VNIR bands), was not widely used in this application field. This article indicates the ASTER imagery application in locating alteration zones in Laizhou area of Shandong Province. First, we studied the geological information and main alteration minerals' spectral features of the study area. Based on the above work, we calculated some band ratios (b4/bl, b4/b6, b3/b2) to enhance spectral response of some mineral materials and vegetations. Then, a principal component analysis was applied to these band ratios. After applying PCA, the eigenvector matrix was analyzed to identify which PC (principal component) contained more useful information of alteration minerals. We chose the PC that enhanced the response of alteration minerals and reduced the response of vegetations, from which we could discriminate the alteration rocks. The satisfactory result shows that ASTER imagery works well in the exploration of alteration zones

Lakes are valuable watersystems, used for production of drinking water, for fisheries and recreation, and can be important indirect or proxy indicator of climatic change. An important aspect to consider is the coverage of lakes, both temporal and spatial, which remote sensing satellites can provide. Modis data is suitable for regional to global operational observations, costing little and having high temporal coverage. But the mixed pixel is a common problem. The Tibetan Plateau is the most sensitive about climatic change and has hundreds of medium and small lakes whose cover is sensitive to the mixed pixels in image. The objective in our study is to develop high accuracy sub-pixel mapping algorithm for lakes cover monitoring in Tibetan Plateau. Firstly, we use the linear spectral unmixing technique to estimate the lake fraction in the mixed pixels. Secondly, we developed an algorithm, based on the concept of spatial dependence, to locate spatially the water within mixed pixel corresponding to the water proportion in the pixel. Finally, we used Aster data as "ground truth" to validate our algorithm. The algorithm produces a finer sub-pixel lake map comparative to the source Modis image.

The spectral signature of a pixel in remotely sensed image in most cases is the result of the reflected spectral properties of mixed land cover types constituting the area of a pixel. This paper introduced an improved method of spectral unmixing of a remote sensing image and its application in water pollution monitoring and assessing. In this paper, a TM image of the Dianchi Lake received on October 4, 2001 was processed and analyzed. The method can not only give the abundance images of surface cover types constituting the area of a pixel, but also get the classification image. By the classification image, we can know the distribution of each type of water pollution in Dianchi Lake. Moreover, the factors affecting the classification product were discussed and some research aspects for the future were put forward.