双星S2,6的平面Turán型问题的一个上界

极值图论是图论中的重要内容,主要研究具有某些性质的图的极值问题。平面图的Turán数是指具有n个顶点的平面图G的最大边数,其中图G不包含H作为一个子图。这个问题是由Dowden在2016年提出的。最近Ghosh等人研究了若干双星图的平面Turán数,并得到很多结果。在这里,我们将给出不含双星S2,6且任意相邻两点度数之和不等于12的平面图边数的上界,即设图G是个顶点的平面图,图中不包含S2,6作为子图且任意相邻两点度数之和不等于12,那么有。

三元数函数与解析——从复平面到数空间

本文从复数理论出发,通过推广函数、解析等数学概念,逐步建立了三元数函数与解析的理论.

图的平面Turán数和平面anti-Ramsey数

在所有顶点数为n且不包含图G作为子图的平面图中,具有最多边数的图的边数称为图G的平面Turán数,记为exP(n,G)。给定正整数n以及平面图H,用Tn(H)来表示所有顶点数为n且不包含H作为子图的平面三角剖分图所组成的图集合。设图集合Tn(H)中的任意平面三角剖分图的任意k边染色都不包含彩虹子图H,则称满足上述条件的k的最大值为图H的平面anti-Ramsey数,记作arP(n,H)。两类问题的研究均始于2015年左右,至今已经引起了广泛关注。全面地综述两类问题的主要研究成果,以及一些公开问题。

经阴道超声计数最多卵泡数/平面与诊断多囊卵巢综合征的相关性

目的：探讨经阴道超声计数最多卵泡数／平面与诊断多囊卵巢综合征的相关性。方法：对48例轰囊卵巢综合征患者行阴道二维超声检查，观测其卵巢体积（OV）、包膜厚度和回声强度、髓质回声强度和面积大小。重点计数最多卵泡数／平面，进行分析。结果：卵巢体积≥10cm3者22例；轮廓光滑40例（83．0％）；卵巢内计数最多卵泡数／平面见≥9枚小卵泡（2～9mm）／平面45例（93．8％），卵泡壁回声增强，卵巢中央区和卵泡周围回声增强，面积增大43例（89．6％）。结论：经阴道超声计数最多卵泡数／平面与多囊卵巢综合征的诊断有相关性。

平余式运算规则——从平面数到孙子共数的求解

令形如[a,b]为"平面数"(a,b为整数范围).在平面数[a,b]中,若规定a为除数,b为余数(a,b∈Z且a≠0,0≤b<a),则称平面数[a,b]为"平余算式"简称"平余式".即[a,b]相与y=ax+b的整数值,这就是关于孙子共数的求解思路.

多平面锥形针接触建模与影响因素研究

针对平面锥形针在组织接触变形阶段受力变化难以分析的现状,根据弹性组织与针接触时的变形特点,建立了多平面锥形针的接触模型,并重点探讨了该阶段针的受力与穿刺性能问题。接触模型揭示了在穿刺深度相同的情况下,锥形针的接触受力受组织剪切模量、针形半顶角和针的平面数三个因素共同影响。通过实验对接触模型进行验证,发现实验曲线和理论曲线能够较好地吻合,表明该模型是有效可行的。由研究可得:为减小平面锥形针的接触受力、提高针的穿刺性能,可选择较小剪切模量的组织、减小针形半顶角或减少针的平面数。

外部平面图的平方图的染色(英文)

图G的平方图 ,记作G2 ,是一个以原图的顶点集为顶点集 ,若原图中两点的距离不大于 2则连以边所成的图 .本文确定了圈的平方图的色数 .对于外部平面图 ,得到以下结论 :设G是一个最大度为Δ(G)的简单连通外部平面图 ,G≠C5.则 χ(G2 )≤Δ(G) +2 .

FLOW FIELD ANALYSES OF PLANE JET AT LOW REYNOLDS NUMBERS USING LATTICE BOLTZMANN METHOD

A two-dimensional（2-D） incompressible plane jet is investigated using the lattice Boltzmann method（LBM） for low Reynolds numbers of 42 and 65 based on the jet-exit-width and the maximum jet-exit-velocity. The results show that the mean centerline velocity decays as x-1/3 and the jet spreads as x2/3 in the self-similar region, which are consistent with the theoretical predictions and the experimental data. The time histories and PSD analyses of the instantaneous centerline velocities indicate the periodic behavior and the interaction between periodic components of velocities should not be neglected in the far field region, although it is invisible in the near field region.

Numerical Simulation of the Influence of Mean Sea Level Rise on Typhoon Storm Surge in the East China Sea

In this paper, ECOMSED （Estuarine Coastal Ocean Model with sediment transport） model is employed to simulate storm surge process caused by typhoon passing across East China Sea in nearly years. Capability of ECOMSED to simulate storm surge is validated by comparing model result with observed data. Sensitivity experiments are designed to study the influence of sea level rise on typhoon storm surge. Numerical experiment shows that influence of mean sea level rise on typhoon storm surge is non-uniform spatially and changes as typhoon process differs. Maybe fixed boundary method would weaken the influence of mean sea level rise on storm surge, and free boundary method is suggested for the succeeding study.

Construction of a database of average cross-sections in Chinese proximal femurs

The process of constructing a database of average cross-sections in Chinese proximal femurs is described. The main goal of creating the database is for designing hip stems for Chinese patients. Methods for constructing the database are introduced. According to some existing software and programs developed by the authors, a database of average cross-sections in Chinese proximal femurs was built based on CT images of eighty femur-specimens. 3-D shape of a patient's proximal femurs can be reconstructed according to the database and X-ray radiographs. Theoretical analyses and results of clinical application indicate that the database can be used to design hip stems for Chinese patients.

NOTE ON FUNCTIONS WITH DIFFERENCE UNIFORMITY

Functions with difference uniformity have important applications in cryptography. Some planar functions and almost perfect nonlinear（APN） functions are presented in the note. In addition, an upper bound of the uniformity of some power mappings is provided by using an interesting identity on Dickson polynomials. When the character of the finite field is less than 11, the upper bound is proved to be the best possibility.

Random α-Bloch Function

In this note, we consider power series f w(z)=∑∞n=0a ne iw n z nwhere moduli a n of the coefficients are given but the argument α n are random. We discuss the conditions of f w is in α_ Bloch space and little α_ Bloch space. Our results generalize Anderson, Clunie and Pommerenke's.

Effect of sea surface wind on the seasonal variation of sea level in the east of China seas

Sea level seasonal variations in the east of China seas from 2004 to 2006 are simulated by the advanced ROMS model. The results show similar sea level spatial features with TOPEX/Poseidon observations, with annual ranges decreasing gradually from the sea coast to the Kuroshio region. By getting rid of wind stress in ROMS model, the simulated sea level results still show obvious seasonal variations. However, the phenomenon of sea level anomaly disappears in Min Zhe Current Coastwise （MZCF） and Su Bei current coastwise （SBCF）, and the change of it from coastal area to ocean recedes. The seal level difference between Bohai, Yellow Sea （BYS） and East China Sea （ECS） becomes weaker in spring and autumn. The annual differences decrease obviously, and the gradual change of annual ranges from seacoast to the Kuroshio almost disappears. The annual ranges in BYS are nearly identical. The annual range ratio without the wind stress to with the wind stress increases gradually from the sea coast to Kuroshio region.

LEARNING ALGORITHM OF FEEDFORWARD NEURAL NETWORK WITH HARD LIMITER USED FOR CLASSIFICATION

A learning algorithm based on a hard limiter for feedforward neural networks (NN) is presented,and is applied in solving classification problems on separable convex sets and disjoint sets.It has been proved that the algorithm has stronger classification ability than that of the back propagation (BP) algorithm for the feedforward NN using sigmoid function by simulation.What is more,the models can be implemented with lower cost hardware than that of the BP NN.LEARNIN

Relationship between Rice Planthopper Occurrence Area in China and Atmospheric Circulation Indices

[Objective] This study aimed to establish models based on atmospheric cir- culation indices for forecasting the area attacked by rice planthopper every year, and to provide guide for preventing and controlling planthopper damage. [Method] The data related to rice planthopper occurrence and atmospheric circulation were collected and analyzed with the method of stepwise regression to establish the prediction models. [Result] The factors significantly related to the area attacked by rice plan-thopper were selected. Two types of prediction models were established. One was for Sogatella furcifera （Horvath）, based on Atlantic-Europe circulation pattern W in October in that year, Pacific polar vortex area index in October in that year, North America subtropical high index in August in that year, Atlantic-Europe circulation pattern W in June in that year, northern boundary of North America subtropical high in February in that year, Atlantic-Europe polar vortex intensity index in October in that year and Asia polar vortex intensity index in November in the last year; the other type of prediction models were for Nilaparvata lugens （Stal）, based on the Eastern Pacific subtropical high intensity index in July in that year, northern hemi- sphere polar vortex area index in October in the last year, Asia polar vortex strength index in November in the last year, north boundary of North America-At- lantic subtropical high in September in that year, north boundary of North Africa-At- lantic-North America subtropical high in January in that year, sunspot in September of the last year and eastern Pacific subtropical high area index in September in that year. [Conclusion] With the stepwise regression, the forecasting equations of the rice planthopper occurrence established based on the atmospheric circulation indices could be used for actual forecast.

Computer Simulation of Compensation Method for Infrared Focal Plane Array

A major motivation for this work is to investigate a method of computer simulation for compensating fixed pattern noise of the infrared focal plane arrays. A mathematical model of the output signal of focal plane array was established; a compensating algorithm utilizing reference source was derived and simulating programs were designed. The images of compensating process verify the influence of nonuniformity of responsibility and offset on fixed pattern noise. The result show that simulating method of investigating compensation technology for focal plane arrays is feasible, the generated images and methods can be used to the study of image recognition.

On Reliability-optimized Controller Placement for Software-Defined Networks

By decoupling control plane and data plane,Software-Defined Networking(SDN) approach simplifies network management and speeds up network innovations.These benefits have led not only to prototypes,but also real SDN deployments.For wide-area SDN deployments,multiple controllers are often required,and the placement of these controllers becomes a particularly important task in the SDN context.This paper studies the problem of placing controllers in SDNs,so as to maximize the reliability of SDN control networks.We present a novel metric,called expected percentage of control path loss,to characterize the reliability of SDN control networks.We formulate the reliability-aware control placement problem,prove its NP-hardness,and examine several placement algorithms that can solve this problem.Through extensive simulations using real topologies,we show how the number of controllers and their placement influence the reliability of SDN control networks.Besides,we also found that,through strategic controller placement,the reliability of SDN control networks can be significantly improved without introducing unacceptable switch-to-controller latencies.

On Generality of the Data Plane and Scalability of the Control Plane in Software-Defined Networking

The control and data planes are decoupled in software-defined networking(SDN),which enables both planes to evolve independently,and brings about many advantages such as high flexibility,programmability,and rapid implementation of new network protocols.However,in order to improve the scalability of the control plane at present,some control functionalities are added to the data plane,which is probably to impact on the generality of the data plane.The key challenge of adding control functionalities to the data plane is to strike a careful balance between the generality of the data plane and the scalability of the control plane.We propose some basic principles that both control and data planes should comply with,based on the evolutionary trend of SDN.Moreover,we take two approaches for reference according to the principles,viewed from the control messages in OpenFlow-based SDN.Our evaluations demonstrate that the approaches can maintain the generality of the data plane and improve the scalability of the control plane.

Calibration of anisotropic yield function by introducing plane strain test instead of equi-biaxial tensile test

The equi-biaxial tensile test is often required for parameter identification of anisotropic yield function and it demands thespecial testing technique or device. Instead of the equi-biaxial tensile test, the plane strain test carried out with the traditional uniaxialtesting machine is suggested to provide the experimental data for calibration of anisotropic yield function. This simplified method byusing plane strain test was adopted to identify the parameters of Yld2000-2d yield function for 5xxx aluminum alloy and AlMgSialloy sheets. The predicted results of yield stresses, anisotropic coefficients and yield loci by the proposed method were very similarwith the experimental data and those by the equi-biaxial tensile test. It is validated that the plane strain test is effective to provideexperimental data instead of equi-biaxial tensile test for calibration of Yld2000-2d yield function.

Multi-Symplectic Splitting Method for Two-Dimensional Nonlinear Schrodinger Equation

Using the idea of splitting numerical methods and the multi-symplectic methods, we propose a multisymplectic splitting （MSS） method to solve the two-dimensional nonlinear Schrodinger equation （2D-NLSE） in this paper. It is further shown that the method constructed in this way preserve the global symplectieity exactly. Numerical experiments for the plane wave solution and singular solution of the 2D-NLSE show the accuracy and effectiveness of the proposed method.