The asymptotic relation between the first crossing point and the last exit time of Gaussian order statistics sequences

In this paper,we study the asymptotic relation between the first crossing point and the last exit time for Gaussian order statistics which are generated by stationary weakly and strongly dependent Gaussian sequences.It is shown that the first crossing point and the last exit time are asymptotically independent and dependent for weakly and strongly dependent cases,respectively.The asymptotic relations between the first crossing point and the last exit time for stationary weakly and strongly dependent Gaussian sequences are also obtained.

Development characteristics of the third-order sequence of Upper Devonian–Lower Carboniferous shore-mixed shelf in Tarim Basin, NW China

Based on the study of stratigraphic sedimentary facies of the prototype sedimentary basin formed in the Late Devonian to Permian Period in the Tarim Basin, the prototype sedimentary basin are divided into five order sequences according to the theory of sequence stratigraphy. It is considered that the Upper Devonian–Lower Carboniferous shore-mixing shelf in the lower part of the prototype sedimentary basin is a typical third-order sequence and a sequence development model is established. The third-order sequence is actually a transgression systems tract and highstand systems tract cycle assemblage, and the type I sequence(no lowstand systems tract) is a typical developmental mode of the third order sequence, and the identification mark is the existence of huge mudstone and limestone wedges from sea to land. The fifth-order parasequence is the basic sequence, which is a single cycle sequence. The thin layer limestone isochronous sediments, which are easy to be identified in the mixed shelf areas, are the isochronous sediments of the largest or secondary marine-flooding surface. The mixed shelf area belongs to the equilibrium sedimentary profile of internal and external sediments, and there is no condensed section. The inclined deposition phenomenon of extraneous source sediments in the sea area weakens or disappears in the mixed shelf area. The paleogeomorphology at the bottom of the third-order sequence is a terrace-slope break zone. This paleogeomorphological feature is not only the main reason for the sedimentary diachronism of Donghe sandstone, but also the main reason for the formation of the transgression-highstand fourth-order cyclic sequences of the Donghe sandstone section and its upper gravel-bearing sandstone section.

A Climatic Sequence Stratigraphic Model in the Terrestrial Lacustrine Basin:A Case Study of Green River Formation,Uinta Basin,USA

在最近的年里，与陆上的顺序地层学的发展，更多的注意全球性集中于陆上的湖的顺序 stratigraphic 模型的学习。不同观点被研究人员比较喜欢。在顺序地层学的理论的指导下面，这篇论文的调查结果显示气候是控制第四顺序的顺序的形成的一个主要因素，在 USA 在 Uinta 盆的格林河形成在顺序地层学的学习之上基于。它也在陆上的湖的盆把第四顺序的顺序划分成二条系统道：湿(升起) 一半周期并且干燥(掉落) 一半周期，为陆上的湖的盆建立一个新式的第四顺序的顺序 stratigraphic 模型，也就是说气候基因的顺序 stratigraphic 模型。作为结果，顺序地层学的理论极大地被充实。

Ordered Generalized Sequence Spaces and their Duals

ＯｒｄｅｒｅｄＧｅｎｅｒａｌｉｚｅｄＳｅｑｕｅｎｃｅＳｐａｃｅｓａｎｄｔｈｅｉｒＤｕａｌｓＭａｎｊｕｌＧｕｐｔａ；ＫａｌｉｋａＫａｕｓｈａｌ（Ｄｅｐｔ．ｏｆＭａｔｈｅｍａｔｉｃｓ，ＩｎｄｉａｎＩｎｓｔｉｔｕｔｅｏｆＴｅｃｈｎｏｌｏｇｙ，Ｋａｎｐｕｒ－...

Sequence stratigraphy and lithofacies paleogeography of the Middle–Upper Cambrian Xixiangchi Group in the Sichuan Basin and its adjacent area, SW China

Based on isotopic, lithologic and electrical data and logging cycle analysis technique, stratigraphic sequences in the Middle-Upper Cambrian Xixiangchi Group in the Sichuan Basin and its adjacent area are divided, and its sedimentary characteristics and evolution are analyzed. The Xixiangchi Group can be divided into 5 third-order sequences(Sql-Sq5), of which sequences Ⅰ to Ⅲ(Sql-Sq3) are relatively complete, sequences Ⅳ and Ⅴ are denuded in the Late Cambrian because of the Dian-Chuan paleo-uplifts.Third-order sequences of the Xixiangchi Group in this area have the characteristics of thin in the west and thick in the east, showing that the Caledonian paleo-uplift is a synsedimentary paleo-uplift and the paleogeomorphology in the platform is a gentle slope. Sequence Ⅰdevelops high stand systems tract and transgressive systems tract. The other third-order sequences are dominated by highstand systems tracts, and the transgressive systems tracts last shortly in time and are limited in area. The basic features of evaporative-restricted platform of gentle slope type developed continuously in the sedimentary period of the Xixiangchi Group, its sedimentary environment of "high in west and low in east" and the change of micro paleogeomorphology in the platform control the continuous development of sedimentary facies. Open platform is developed only in sequence Ⅰ and sequence Ⅱ, and the inner beach of the platform and the edge beach of the platform are mostly developed in sequence Ⅱ and sequence Ⅲ. It indicates that there are two platform margin zones in the study area,a relatively stable, large-scale platform marginal zone in NE Guizhou-Western Hunan and Hubei, and a moving and small-scale platform marginal zone in North Chongqing-Western Hubei.

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.

ON OSCILLATION THEOREMS FOR HIGHER ORDER DIFFERENTIAL EQUATIONS

ＯＮＯＳＣＩＬＬＡＴＩＯＮＴＨＥＯＲＥＭＳＦＯＲＨＩＧＨＥＲＯＲＤＥＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ￥ＣｈｅｎＺｏｎｇｘｕａｎ（ＤｅｐｔｏｆＭａｔｈ，ＪｉａｎｇｘｉＮｏｒｍａｌＵｎｉｖ）ＮａｎｃｈａｎｇＡｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐ...

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.

Infinite Sequence of Conservation Laws and Analytic Solutions for a Generalized Variable-Coefficient Fifth-Order Korteweg-de Vries Equation in Fluids

在这份报纸，为在液体的一个概括可变系数的第五顺序的 Korteweg-de Vries 方程的能量守恒定律的一个无限的序列基于 B 被构造 ? cklund 转变。Hirota 双线性的形式和符号的计算被使用获得三种答案。可变系数能影响典型的线的保存密度，联系流动，和外观。soliton 结构上的波浪数字的效果也被讨论并且 soliton 结构打字，例如，双 periodic soliton，平行 soliton 和 soliton 建筑群，被介绍。

Novel Methods in the Study of the Breast Cancer Genome: Towards a Better Understanding of the Disease of Breast Cancer

Rapidly developing sequencing technologies and bioinformatic approacheshave provided us with an unprecedented instrument allowing for an unbiased and exhaustive characterization of the cancer genome in genetic, epigenetic and transcriptomic dimensions. This review introduces recent excitingfindings and new methodologies in genomic breast cancer research. With this development, cancer genome research will illuminate new delicate interactionsbetween molecular networks and thereby unravelthe underlying biological mechanisms for cancer initiation and progression. It also holds promise for providing a molecular clock for the estimation of the temporal processes of tumorigenesis. These methods in combination with single cell sequencing will make it possible to construct a family tree elucidating the evolutionary lineage relationships between cell populations at single-cell resolution. The anticipatedrapid progress in genomic breast cancer research should lead to anenhanced understanding of breast cancer biology andguide us towardsnovel ways to ultimatelyprevent and cure breast cancer.

There Are Infinitely Many Mersnne Composite Numbers with Prime Exponents

By extending both arithmetical operations into finite sets of natural numbers, from the entire set of natural numbers successively deleting some residue classes modulo a prime, we invented a recursive sieve method or algorithm on natural numbers and their sets. The algorithm mechanically yields a sequence of sets, which converges to the set of all primes p such that 2p + 1 divides the Mersenne number Mp. The cardinal sequence corresponding to the sequence of sets is strictly increasing. So that we have captured enough usable structures, without any estimation, the existing theories of those structures allow us to prove an exact result: there are infinitely many Mersenne composite numbers with prime exponents Mp.

Generating functions for powers of second-order recurrence sequences

For the sequences satisfying the recurrence relation of the second order,the generating functions for the products of the powers of these sequences are established.This study was from Carlita and Riordan who began a study on closed form of generating functions for powers of second-order recurrence sequences.This investigation was completed by Stnica.Inspired by the recent work of Istva'n about the non-closed generating functions of the products of the powers of the second-order sequences,the authors give several extensions of Istva'n's results in this paper.

Type division and controlling factor analysis of 3rd-order sequences in marine carbonate rocks

Type division and controlling factor analysis of 3rd-order sequence are of practical significance to tectonic analysis, sedimentary environment identification, and other geological researches. Based on the comprehensive analysis of carbon and oxygen isotope trends, paleobathymetry and spectral-frequency of representative well logs, 3rd-order sequences can be divided into 3 types:(a) global sea level(GSL)sequence mainly controlled by GSL change;(b) tectonic sequence mainly controlled by regional tectonic activity; and(c) composite sequence jointly controlled by GSL change and regional tectonic activity. This study aims to identify the controlling factors of 3rd-order sequences and to illustrate a new method for classification of 3rd-order sequences of the middle Permian strata in the Sichuan Basin, China. The middle Permian strata in the Sichuan Basin consist of 3 basin-contrastive 3rd-order sequences, i.e., PSQ1,PSQ2 and PSQ3. Of these, PSQ1 is a GSL sequence while PSQ2 and PSQ3 are composite sequences. The results suggest that the depositional environment was stable during the deposition of PSQ1, but was activated by tectonic activity during the deposition of the middle Permian Maokou Formation.

MULTIPLE RECIPROCITY METHOD WITH TWO SERIES OF SEQUENCES OF HIGH-ORDER FUNDAMENTAL SOLUTION FOR THIN PLATE BENDING

The boundary value problem of plate bending problem on two_parameter foundation was discussed.Using two series of the high_order fundamental solution sequences, namely, the fundamental solution sequences for the multi_harmonic operator and Laplace operator, applying the multiple reciprocity method(MRM), the MRM boundary integral equation for plate bending problem was constructed. It proves that the boundary integral equation derived from MRM is essentially identical to the conventional boundary integral equation. Hence the convergence analysis of MRM for plate bending problem can be obtained by the error estimation for the conventional boundary integral equation. In addition, this method can extend to the case of more series of the high_order fundamental solution sequences.

RELIABILITY ANALYSIS OF FRP LAMINATED PLATES WITH CONSIDERATION OF BOTH INITIAL IMPERFECTION AND FAILURE SEQUENCE

A probabilistie progressive failure analyzing method is applied to estimating the reliability of asimply supported laminated eomposite plate with an initial imperfection under bi-axial eompression load.Theinitial imperfection and the strength parameters are considered as random variables.Ply-level failure proba-bility is evaluated by the first order reliability method(FORM)together with the Tsai-Wu strength eriterionand Tan criterion.Current stresses in the laminated structure are calculated by the classical lamination theorywith the stiffness modified based on the last step ply failure.Probabilistieally dominant ply-level failure se-quences leading to overall system failure are identified,based on which the system failure probability is esti-mated.A numerieal example is presented to demonstrate the methodology proposed.Through parameter stud-ies it is shown that the deviation of the initial imperfeetion and some of the strength parameters largely influ-ence the system reliability.

SOME EULER SPACES OF DIFFERENCE SEQUENCES OF ORDER m

Kizmaz [13 ] 学习了差别顺序空格 ? ∞(Δ) ， c (Δ) ，和 c0 (Δ) 。几篇文章处理了哪个被围住的 m-th 顺序差别的序列的集合，对零会聚，或会聚。Altay 和 Ba ? ar [5 ] 并且 Altay， Ba ? ar，和 Mursaleen [7 ] 介绍了 Euler 顺序空格 e (r) 0， e (r) c，和 e (r) ∞分别地。这篇文章的主要目的是介绍空格 e (r) 0 (Δ( m ))， e (r) c (Δ( m ))，并且 e (r)∞(Δ( m ))由其 m ( th )命令差别在 Euler 空格的所有序列组成 e (r) 0 ， e (r) c ，和 e (r)∞分别地。而且，作者给一些拓扑的性质和包括关系，并且决定空格 e (r)的α-，β-，和γ- duals 0 (Δ( m ))， e (r) c (Δ( m ))，并且 e (r)∞(Δ( m ))，并且空格 e (r)的 Schauder 基础 0 (Δ( m ))， e (r) c (Δ( m ))。文章的最后节在顺序空间 e (r) c (Δ(m ) 上被奉献给一些矩阵地图砰的描述) 。给词调音：顺序 m 的差别顺序空格；Schauder 基础；α - ，β - ，和γ - duals；

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.

Existence of Ordered Solutions to Quasilinear Schrodinger Equations with General Nonlinear Term

In this paper, the existence of a pair of ordered solutions for the following class of equations in ?(1)?was studied. A bounded (PS) (Palais-Smale) sequence was constructed and the related variational principle was used to prove the existence of the positive solution. The existence of the ordered solutions is finally found.

Two Sequences of Operator Monotone Functions and Strictly Chaotic Order

In this paper we introduce two sequences of operator functions and their dual functions:f_k(t)=((tlog t)~k-(t-1)~k)/(log^k+1t)(k=1,2,...),gk(t)=((t-1)~k-log^k t)/(log^k+1t)(k=1,2,...)and f_k~*=(t^klog^(k+1)t)/((tlog t)~k-(t-1)~k)(k=1,2,...),g_k~*(t)=(t^klog^(k+1)t)/((t-1)~k-log^k t)(k=1,2,...)definedon(0,+∞). We find that they are all operator monotone functions with respect to the strictly chaotic order and some ordinary orders among positive invertible operators.Indeed,we extend the results of the operator monotone function(tlog t -t+1)/(log^2t)which is widely used in the theory of heat transfer of the heat engineering and fluid mechanics[1].

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.