SOME EULER SPACES OF DIFFERENCE SEQUENCES OF ORDER m

Kizmaz [13] studied the difference sequence spaces ∞（A）, c（A）, and co（A）. Several article dealt with the sets of sequences of m-th order difference of which are bounded, convergent, or convergent to zero. Altay and Basar [5] and Altay, Basar, and Mursaleen [7] introduced the Euler sequence spaces e0^r, ec^r, and e∞^r, respectively. The main purpose of this article is to introduce the spaces e0^r△^（m））, ec^r△^（m））, and e∞^r△^（m））consisting of all sequences whose mth order differences are in the Euler spaces e0^r, ec^r, and e∞^r, respectively. Moreover, the authors give some topological properties and inclusion relations, and determine the α-, β-, and γ-duals of the spaces e0^r△^（m））, ec^r△^（m））, and e∞^r△^（m））, and the Schauder basis of the spaces e0^r△^（m））, ec^r△^（m））. The last section of the article is devoted to the characterization of some matrix mappings on the sequence space ec^r△^（m））.

Sedimentary Facies Architectures of Third-Order Sequences from Early to Middle Triassic in Nanpanjiang Basin

There are complex and regular changes on sedimentary facies from the Early to the Middle Triassic in the Nanpanjiang basin. After the obvious drowned event of carbonate platforms in the transitional period between Permian and Triassic, carbonate platforms have evolved into the ramp type from the rimmed shelf type. The differentiation of sedimentary facies becomes clearer in space, which are marked by the changes from an attached platform to a turbidity basin and several isolated platforms in the basin. The striking characteristics are the development of oolitic banks on isolated platforms in Nanning and Jingxi and the reef and bank limestones in the margin of the attached platform in the Early Triassic. Despite the difference of the time span and the architecture of facies succession of third order sedimentary sequences, the process of the third order relative sea level changes reflected by the sedimentary facies succession of the third order sequences is generally synchronous. Therefore, six third order sequences could be discerned in the strata from the Early to the Middle Triassic in the Nanpanjiang basin. Using two types of facies changing surfaces and two types of diachronisms in stratigraphic records as the key elements, the sedimentary facies architectures of the third order sequences that represent sequence stratigraphic frameworks from the Early to the Middle Triassic in the Nanpanjiang basin could be constructed.

CHARACTERIZATIONS OF COMPACT OPERATORS ON SOME EULER SPACES OF DIFFERENCE SEQUENCES OF ORDER m

In the past, several authors studied spaces of m-th order difference sequences, among them, H.Polat and F.Basar （[17]） defined the Euler spaces of m-th order difference sequences e r 0 （△ （ m ） ）, e r c （△ （ m ） ） and e r ∞ （△ （ m ） ） and characterized some classes of matrix transformations on them. In our paper, we add a new supplementary aspect to their research by characterizing classes of compact operators on those spaces. For that purpose, the spaces are treated as the matrix domains of a triangle in the classical sequence spaces c 0 , c and ∞ . The main tool for our characterizations is the Hausdorff measure of noncompactness.

A new algorithm for computing the convex hull of a planar point set

When the edges of a convex polygon are traversed along one direction,the interior of the convex polygon is always on the same side of the edges. Based on this characteristic of convex polygons,a new algorithm for computing the convex hull of a simple polygon is proposed in this paper,which is then extended to a new algorithm for computing the convex hull of a planar point set. First,the extreme points of the planar point set are found,and the subsets of point candidate for vertex of the convex hull between extreme points are obtained. Then,the ordered convex hull point sequences between extreme points are constructed separately and concatenated by removing redundant extreme points to get the convex hull. The time complexity of the new planar convex hull algorithm is O(nlogh) ,which is equal to the time complexity of the best output-sensitive planar convex hull algorithms. Compared with the algorithm having the same complexity,the new algorithm is much faster.

Research on Outcrop Sequence Stratigraphy of Permian in Middle-Lower Yangtze Region

According to the latest International Chronostratigraphic Scheme (ICS, 2000), the Permian in the Middle Lower Yangtze region of South China can be divided into three series and nine stages relevant to the traditional six stages of South China. From Assellian to Changxingian of Permian, 44 Ma in age range, the strata are composed of 14 third order sequences, each of which is 3.14 Ma in average age range. There is one third order sequence of Zisongian, equivalent to middle and upper Chuanshan Formation or equal to Asselian and two thirds of Sakmarian. There are two third order sequences, corresponding to Liang shan Formation or Zhenjiang Formation and upper Chuanshan Formation, which are assigned to Longlingian, coinciding with Artinskian and one third of Sakmarian. In addition, three third order sequences, equal to Qixia Formation, are attributed to Chihsian, corresponding to Kubergandian and one third of Roadian. Four third order sequences, comprising Gufeng, Maokou, Yanqiao, Yinping and Wuxue formations, are assigned to Maokouan, equivalent to two thirds of Roadian, Wordian and Capitanian. Two third order sequences, equal to Longtan Formation or Wujiaping Formation, are included in Wuchiapingian. Other two third order sequences, corresponding to Changxing Formation or Dalong Formation, are assigned to Changhsingian. In brief, these above third order sequences can be incorporated into 4 sequences sets.

The Formula of General Term of the Sum of Equal Powers of Natural Numbers

The formula of general term of the sum of equal powers of natural numbers.

A Combinatorial Theorem on Ordered Circular Sequences of n_1 u's and n_2 v's with Application to Kernel-perfect Graphs

Abstract An ordered circular permutation S of u's and v' s is called an ordered circular sequence of u' s and v' s. A kernel of a digraph G=(V,A) is an independent subset of V, say K, such that for any vertex vi in V\K there is an arc from vi to a vertex vj in K. G is said to be kernel-perfect (KP) if every induced subgraph of G has a kernel. G is said to be kernel-perfect-critical (KPC) if G has no kernel but every proper induced subgraph of G has a kernel. The digraph G=(V,A)= $\overrightarrow {C_n }$ (j1,j2,...,jk) is defined by: V(G)={0,1,...,nm1}, A(G)={uv | vmuLj, (mod n) for 1 hihk}.In an earlier work, we investigated the digraph G= $\overrightarrow {C_n }$ (1-'d,-2d,-3d,...,-sd), denoted by G(n,d,r,s), where '=1 for d>1 or '=0 for d=1, and n,d,r,s are positive integers with (n,d)=r and n=mr, and gave some necessary and sufficient conditions for G(n,d,r,s) with rS3 and s=1 to be KP or KPC.In this paper, we prove a combinatorial theorem on ordered circular sequences of n1 u's and n2 v's. By using the theorem, we prove that, if (n,d)=rS2 and sS2, then G(n,d,r,s) is a KP graph.