S-curve networks and an approximate method for estimating degree distributions of complex networks

In the study of complex networks almost all theoretical models have the property of infinite growth, but the size of actual networks is finite. According to statistics from the China Internet IPv4 （Internet Protocol version 4） addresses, this paper proposes a forecasting model by using S curve （logistic curve）. The growing trend of IPv4 addresses in China is forecasted. There are some reference values for optimizing the distribution of IPv4 address resource and the development of IPv6. Based on the laws of IPv4 growth, that is, the bulk growth and the finitely growing limit, it proposes a finite network model with a bulk growth. The model is said to be an S-curve network. Analysis demonstrates that the analytic method based on uniform distributions （i.e., Barabasi-Albert method） is not suitable for the network. It develops an approximate method to predict the growth dynamics of the individual nodes, and uses this to calculate analytically the degree distribution and the scaling exponents. The analytical result agrees with the simulation well, obeying an approximately power-law form. This method can overcome a shortcoming of Barabasi-Albert method commonly used in current network research.

Programmable robotized‘transfer-and-jet’printing for large,3D curved electronics on complex surfaces

Large,3D curved electronics are a trend of the microelectronic industry due to their unique ability to conformally coexist with complex surfaces while retaining the electronic functions of 2D planar integrated circuit technologies.However,these curved electronics present great challenges to the fabrication processes.Here,we propose a reconfigurable,mask-free,conformal fabrication strategy with a robot-like system,called robotized‘transfer-and-jet’printing,to assemble diverse electronic devices on complex surfaces.This novel method is a ground-breaking advance with the unique capability to integrate rigid chips,flexible electronics,and conformal circuits on complex surfaces.Critically,each process,including transfer printing,inkjet printing,and plasma treating,are mask-free,digitalized,and programmable.The robotization techniques,including measurement,surface reconstruction and localization,and path programming,break through the fundamental constraints of 2D planar microfabrication in the context of geometric shape and size.The transfer printing begins with the laser lift-off of rigid chips or flexible electronics from donor substrates,which are then transferred onto a curved surface via a dexterous robotic palm.Then the robotic electrohydrodynamic printing directly writes submicrometer structures on the curved surface.Their permutation and combination allow versatile conformal microfabrication.Finally,robotized hybrid printing is utilized to successfully fabricate a conformal heater and antenna on a spherical surface and a flexible smart sensing skin on a winged model,where the curved circuit,flexible capacitive and piezoelectric sensor arrays,and rigid digital–analog conversion chips are assembled.Robotized hybrid printing is an innovative printing technology,enabling additive,noncontact and digital microfabrication for 3D curved electronics.

ON HOLOMORPHIC CURVES OF CONSTANT CURVATURE IN THE COMPLEX GRASSMANN MANIFOLD G(2,5)

In this article, it is proved that there doesn’t exist any nonsingular holomorphic sphere in complex Grassmann manifold G（2, 5） with constant curvature k = 4/7, 1/2, 4/9. Thus, from [7] it follows that if φ ： S2 → G（2, 5） is a nonsingular holomorphic curve with constant curvature K, then, K = 4, 2, 4/3, 1 or 4/5.

COMPLEX RATIONAL TYPE INTERPOLATION AT DISTURBED FEJR POINTS ON A CURVE

The results of accurate order of uniform approximation and simultaneous approximation in the early work ＂Jackson Type Theorems on Complex Curves＂ are improved from Fejer points to disturbed Fejer points in this article. Furthermore, the stability of convergence of Tn,∈（f,z） with disturbed sample values f（z^＊） ＋ Sk are also proved in this article.

Riemann-Hilbert problem for first order complex equations of mixed type with degenerate curve

This paper considers the Riemann-Hilbert problem for linear mixed（elliptichyperbolic） complex equations of first order with degenerate curve in a simply connected domain. We first give the representation theorem and uniqueness of solutions for such boundary value problem. Then by using the methods of successive iteration and parameter extension, the existence of solutions for this problem is proved.

Computation of Complex Primes Using Elliptic Curves: Application for Cryptosystem Design

This paper provides several generalizations of Gauss theorem that counts points on special elliptic curves. It is demonstrated how to implement these generalizations for computation of complex primes, which are applicable in several protocols providing security in communication networks. Numerical examples illustrate the ideas discussed in this paper.

Homology Curve Complex

A homological analogue of curve complex of a closed connected orientable surface is developed and studied. The dis-tance in this complex is shown to be quite computable and an algorithm given (Theorem 3.5). As an application of this complex it is shown that for a closed orientable 3-manifold, and any of its Heegaard splittings, one can give an algorithm to decide whether the manifold contains a 2-sided, non-separating, closed incompressible surface (Theorem 1.1).

Discussion on Reverse Design of Components with Complex Curved Surface and Computer Numerical Control Machining

With the continuous development and advancement of science and technology,the work of tool path planning has received extensive attention.Among them,curved surface generation and data processing are the focus of management and design,which necessitate the full application of reverse design of complex curved surface components to complete numerical control processing,effective optimization and upgrading,integration the tasks of point cloud data collection,and point cloud data processing to ensure that the corresponding computer numerical control machining model can exert its actual value.This paper briefly analyzes the basic principles of curved surface reconstruction as well as discusses the reverse design of complex curved components and the experimental processes and results that involved computer numerical control machining,which serves the purpose as reference only.

3D reconstruction of complex curved objects from line drawings

An active research topic in computer vision and graphics is developing algorithms that can reconstruct the 3D surface of curved objects from line drawings. There are a number of algorithms have been dedicated to solve this problem, but they can＇t solve this problem when the geometric structure of a curved object becomes complex. This paper proposes a novel approach to reconstructing a complex curved 3D object from single 2D line drawings. Our approach has three steps： （1） decomposing a complex line drawing into several simpler line drawings and transforming them into polyhedron; （2） reconstructing the 3D wireframe of curved object from these simpler line drawings and generating the curved faces; （3） combining the 3D objects into the complete objects. A number of examples are given to demonstrate the ability of our approach to successfully perform reconstruction of curved objects which are more complex than previous methods.

基于复数小波变换和H-Curve准则对图像的去噪

复数小波变换在某些方面比实数小波变换具有更多的优点,如:平移不变性、更好的方向 性和精确的相空间信息等,可提高图像的去噪能力。采用二树复数小波变换,在基于H Curve准则 确定阈值的基础上进行图像去噪。此准则不需要提前知道噪声标准偏差,在实际应用中适用于不同 类型的噪声,并且和目前多数方法去噪后的图像过于平滑相比,它还能产生较好的视觉效果。典型去 噪试验表明,该方法在去噪能力、取得的视觉效果和确定阈值的广泛性方面都优于目前多数方法.

Higher-Dimensional Integrable Systems Arising from Motions of Curves on S^2(R)and S^3(R)

We show that higher-dimensional integrable systems including the (2+1)-dimensional generalized sine-Gordon equation and the (2+1)-dimensional complex mKdV equation are associated with motions of surfaces inducedby endowing with an extra space variable to the motions of curves on S^2(R) and S^3(R).

Curved and Stepped Breakwater Wall

-This paper introduces the main points of design and operation features of a curved combinative breakwater wall which can not only resist storm surge but also roll wave back and which has the functions of seawall, tide protection, anti-wave, land development, traffic and tourism. The new kind of breakwater optimized by wave model test has been utilized in the seawall in the coast regulation project in Zhanjiang City, and good results have been achieved.

Weakly Disk-busting Curves in the Boundary of a Compression Body

Let V be a nontrivial compression body which is not simple. An essential simple closed curve J in ?;V is called weakly disk-busting if ?;V-J has only one compressing disk up to isotopy. In this paper, we give an upper bound of the diameter of the image of boundaries of essential disks in V under any projection determined by a weakly disk-busting curve. Moreover, we give a sufficient condition for the handle additions to be boundary irreducible.

General solutions of plane problem for power function curved cracks

A new exact and universal conformal mapping is proposed. Using Muskhelishvili＇s complex potential method, the plane elasticity problem of power function curved cracks is investigated with an arbitrary power of a natural number, and the general solutions of the stress intensity factors （SIFs） for mode I and mode II at the crack tip are obtained under the remotely uniform tensile loads. The present results can be reduced to the well-known solutions when the power of the function takes different natural numbers. Numerical examples are conducted to reveal the effects of the coefficient, the power, and the projected length along the x-axis of the power function curved crack on the SIFs for mode I and mode II.

NORMAL CRITERIA FOR A FAMILY OF HOLOMORPHIC CURVES

In this paper,we extend the concept of holomorphic curves sharing hyperplanes and introduce definitions of restricted hyperplanes and partial shared hypersurfaces.Then,we prove several normal criteria of the family of holomorphic curves and holomorphic mappings that concern restricted hyperplanes and partial shared hypersurfaces.These results generalize the Montel-type normal criterion of holomorphic curves.

Effects of Dissipative Terms on Dissipative Soliton Resonance Curve

Dissipative soliton resonance (DSR) is a phenomenon where the energy of a soliton in a dissipative system increases without limit at certain values of the system parameters. Using the method of collective variable approach, we have found an approximate relation between the parameters of the normalized complex cubic-quintic Ginzburg-Landau equation where the resonance manifests itself. Comparisons between the results obtained by collective variable approach, and those obtained by the method of moments show good qualitative agreement. This choice also helps to see the influence of the active terms on the resonance curve, so can be very useful in constructing passively mode-locked laser that generate solitons with the highest possible energies.

Construction of Endpoint Constrained Cubic Rational Curve with Chord-Length Parameterization

This paper discusses the problem that constructing a curve to satisfy the given endpoint constraints and chord-length parameters. Based on the research of Lu, the curve construction method for the entire tangent angles region （α0, α1）∈（-r, r）×（-r, r） is given. Firstly, to ensure the weights are always positive, the three characteristics of cubic rational Bezier curve is proved, then the segment construction idea for the other tangent angles are presented in view of the three characteristics. The curve constructed with the new method satisfies the endpoint constraint and chord-length parameters, it＇s G1 continuous in every segment curve, and the shapes of the curve are well.

复杂曲面零件的五轴数控加工技术研究

随着科技水平的不断提升,精密复杂曲面零件的应用越来越广泛。曲面驱动是复杂曲面零件加工的重要方法,驱动刀轨的规划直接关系到曲面物理特性的调控,应用五轴数控加工技术能够提升复杂曲面零件的加工质量。文章主要研究复杂曲面零件的五轴数控加工技术,以佛像这个复杂曲面零件为例,分析了曲面驱动刀轨规划、工装方案设计、加工策略以及试制加工过程。在实际加工过程中,技术人员应充分理解驱动刀轨规划思路与原理,在粗加工、精加工中完善刀轨设计,并进行试制加工。

基于计算机辅助的船舶复杂曲面结构设计

本文研究计算机辅助技术在船舶复杂曲面结构设计中的应用,分析复杂曲面结构设计的特点,阐述复杂曲面结构设计的流程,重点研究基于计算机辅助的曲面展开技术,对比B样条方法和NURBS法在复杂曲线和曲面表达中的应用效果,提出一种自适应网格优化算法的实现方法,并和传统网格划分进行对比。结果表明,自适应网格划分加强了复杂曲面结构的细节表达,有效降低了结构的设计误差。

基于图形复杂度的空间矢量数据划分和索引技术

矢量空间数据的划分存在计算性能及跨区域的问题。基于空间位置的划分虽可满足空间索引和快速查询的需求,但难以实现并行空间分析的计算负载均衡。本文提出了一种基于图形复杂度的空间矢量数据划分和索引技术,该技术基于图形复杂度,结合Hilbert空间填充曲线进行矢量数据划分,并采用R树建立分布式索引,不仅提升了数据访问速度,还解决了数据倾斜导致的计算失衡问题,为矢量空间计算任务的负载均衡提供了更优支持。