THE BERNSTEIN TYPE INEQUALITY AND SIMULTANEOUS APPROXIMATION BY INTERPOLATION POLYNOMIALS IN COMPLEX DOMAIN

In this paper we investigate simultaneous approximation for arbitrary system of nodes on smooth domain in complex plane. Some results which are better than those of known theorems are obtained.

Uniform Convergence of Higher Order Fejér Interpolation Polynomials in a Complex Domain

For a Jordan domain D in the complex plane satisfying certain boundary conditions a function f B(D), we prove that the corresponding higher order Fejer interpolation polynomials based on Fejer points converge to f(z) uniformly on D. These extend some known results.

Group tracking algorithm for split maneuvering based on complex domain topological descriptions

A group tracking algorithm for split maneuvering based on complex domain topological descriptions is proposed for the tracking of members in a maneuvering group. According to the split characteristics of a group target, split models of group targets are established based on a sliding window feedback mechanism to determine the occurrence and classification of split maneuvering, which makes the tracked objects focus by group members effectively. The track of an outlier single target is reconstructed by the sequential least square method. At the same time, the relationship between the group members is expressed by the complex domain topological description method, which solves the problem of point-track association between the members. The Singer method is then used to update the tracks. Compared with classical multi-target tracking algorithms based on Multiple Hypothesis Tracking （MHT） and the Different Structure Joint Probabilistic Data Association （DS-JPDA） algorithm, the proposed algorithm has better tracking accuracy and stability, is robust against environmental clutter and has stable time-consumption under both classical radar conditions and partly resolvable conditions.

THEORY OF SINGULAR POINTS OF ORDINARY DIFFERENTIAL EQUATIONS IN COMPLEX DOMAIN

In this paper, the topological of integral surfaces near certain of Lyapunov type singularpoints and certain type of nodes of ordinary differential equations in complex domain are studied.We introduce Briot-Bouquet transformation, in order to study the topological structure of integralsurfaces near higher order singular points. At last we give an estimate of the makimum numberof isolated limit integral surfaces passing through certain type of higher order singular points.

Bayesian seismic multi-scale inversion in complex Laplace mixed domains

Seismic inversion performed in the time or frequency domain cannot always recover the long-wavelength background of subsurface parameters due to the lack of low-frequency seismic records. Since the low-frequency response becomes much richer in the Laplace mixed domains, one novel Bayesian impedance inversion approach in the complex Laplace mixed domains is established in this study to solve the model dependency problem. The derivation of a Laplace mixed-domain formula of the Robinson convolution is the first step in our work. With this formula, the Laplace seismic spectrum, the wavelet spectrum and time-domain reflectivity are joined together. Next, to improve inversion stability, the object inversion function accompanied by the initial constraint of the linear increment model is launched under a Bayesian framework. The likelihood function and prior probability distribution can be combined together by Bayesian formula to calculate the posterior probability distribution of subsurface parameters. By achieving the optimal solution corresponding to maximum posterior probability distribution, the low-frequency background of subsurface parameters can be obtained successfully. Then, with the regularization constraint of estimated low frequency in the Laplace mixed domains, multi-scale Bayesian inversion inthe pure frequency domain is exploited to obtain the absolute model parameters. The effectiveness, anti-noise capability and lateral continuity of Laplace mixed-domain inversion are illustrated by synthetic tests. Furthermore,one field case in the east of China is discussed carefully with different input frequency components and different inversion algorithms. This provides adequate proof to illustrate the reliability improvement in low-frequency estimation and resolution enhancement of subsurface parameters, in comparison with conventional Bayesian inversion in the frequency domain.

Low complexity domains, condensates, and stem cell pluripotency

Biological reactions require self-assembly of factors in the complex cellular milieu.Recent evidence indicates that intrinsically disordered,low-complexity sequence domains(LCDs)found in regulatory factors mediate diverse cellular processes from gene expression to DNA repair to signal transduction,by enriching specific biomolecules in membraneless compartments or hubs that may undergo liquidliquid phase separation(LLPS).In this review,we discuss how embryonic stem cells take advantage of LCD-driven interactions to promote cell-specific transcription,DNA damage response,and DNA repair.We propose that LCDmediated interactions play key roles in stem cell maintenance and safeguarding genome integrity.

THE POINCAR-BERTRAND FORMULA ON THE BUILDING DOMAIN OF COMPLEX BIBALLS

The Poincare-Bertrand formula takes an important position in the study of complex singular integral. The Poincare-Bertrand formula on the complex sphere in the multidimensional complex Euclidian spaces was given by Sheng Gong. Using the method of solid angular coefficient, the authors extend the Poincare-Bertrand formula on the complex sphere to the building domain of the complex biballs, and obtain a more general Poincare- Bertrand formula with the solid angular coefficients.

Direct Solutions of Some Singular Integral Equations on the Building Domain of Complex Biballs

By means of the method of solid angle coefficients and the permutation formula on the building domain of complex biballs,direct solutions of some singular integral equations with variable coefficients are discussed and the explicit formulas for these solutions are obtained.

A DISCRETE ALGORITHM FOR COMPLEX FREQUENCY-DOMAIN CONVOLUTIONS

A discrete algorithm suitable for the computation of complex frequency-domain convolution on computers was derived. The Durbin's numerical inversion of Laplace transforms can be used to figure out the time-domain digital solution of the result of complex frequency-domain convolutions. Compared with the digital solutions and corresponding analytical solutions, it is shown that the digital solutions have high precision.

The Complex Analysis Method of Numerical Identification of Parameters of Quasiideals Processes in Doubly-Connected Nonlinear-Layered Curvilinear Domains

The method of numerical solving of nonlinear model problems of theory of a complex quasi-potential in doubly-connected nonlinear-layered curvilinear domains considering inverse influence function of flow on a conductivity coefficient of medium was developed on the basis of synthesis of numerical methods of the quasi-conformal mappings and summary representations in conjunction with domain decomposition by method Schwartz. The proposed algorithm allows finding the potential of the quasiideals field, construction a motion grid （fluid-flow grid） simultaneously defining the flow lines that separate of sub-domains constancy of coefficient conductivity and identification the piecewise-constant values of coefficient conductivity, the local flows for the known measurements on boundary of domain.

Approximate Method of Riemann-Hilbert Problem for Elliptic Complex Equations of First Order in Multiply Connected Unbounded Domains

In this article, we discuss the approximate method of solving the Riemann-Hilbert boundary value problem for nonlinear uniformly elliptic complex equation of first order (0.1) with the boundary conditions (0.2) in a multiply connected unbounded domain D, the above boundary value problem will be called Problem A. If the complex Equation (0.1) satisfies the conditions similar to Condition C of (1.1), and the boundary condition (0.2) satisfies the conditions similar to (1.5), then we can obtain approximate solutions of the boundary value problems (0.1) and (0.2). Moreover the error estimates of approximate solutions for the boundary value problem is also given. The boundary value problem possesses many applications in mechanics and physics etc., for instance from (5.114) and (5.115), Chapter VI, [1], we see that Problem A of (0.1) possesses the important application to the shell and elasticity.

Systematic review of macular ganglion cell complex analysis using spectral domain optical coherence tomography for glaucoma assessment

AIM: To review the use of spectral domain optical coherence tomography(SD-OCT) for macular retinal ganglion cells(RGC) and ganglion cell complex(GCC) measurement in glaucoma assessment, specifically for early detection and detection of disease progression. METHODS: A systematic review was performed by searching Pub Med, Medline, and Web of Science for articles published in English through July 2014 describing the various macular SD-OCT scanning strategies developed for glaucoma assessment. The review focused on papers evaluating the use of macular RGC/GCC SDOCT to detect early glaucoma and its progression. The search included keywords corresponding to the index test(macular ganglion cell/RGC/GCC/Spectral domain OCT), the target condition(glaucoma), and diagnostic performance. The RGC/GCC SD-OCT scanning strategies used to assess glaucoma of most commonly used SD-OCT instruments were described and compared. These included the Cirrus high definition-OCT(Carl Zeiss Meditec, Inc., Dublin, CA, United States), RTVue(Optovue, Inc., Fremont, CA, United States), Spectralis(Heidelberg Engineering, Heidelberg, Germany) and the 3D OCT 2000(Topcon Corporation, Tokyo, Japan). Studies focusing on the ability of RGC/GCC SD-OCT to detect early glaucomatous damage and on the correlation between glaucomatous progression and RGC/GCC measurement by SD-OCT were reviewed.RESULTS: According to the literature, macular RGC/GCC SD-OCT has high diagnostic power of preperimetric glaucoma, reliable discrimination ability to differentiate between healthy eyes and glaucomatous eyes, with good correlation with visual filed damage. The current data suggests that it may serve as a sensitive detection tool for glaucomatous structural progression even with mild functional progression as the rate of change of RGC/GCC thickness was found to be significantly higher in progressing than in stable eyes. Glaucoma assessment with RGC/GCC SD-OCT was comparable with and sometimes better than circumpapillary retinal nerve fiber layer thickness measurement.CONCLUSION: An increasing body of evidence supports using macular RGC/GCC thickness as an indicator for early glaucoma. This might be a useful tool for monitoring disease progression.

Equivalence of three kinds of well-posed-ness of discontinuous Riemann-Hilbert problem for elliptic complex equation in multiply connected domains

In this article, we first introduce the general linear elliptic complex equation of first order with certain conditions, and then propose discontinuous Riemann-Hilbert problem and some kinds of modified well-posed-ness for the complex equation. Then we verify the equivalence of three kinds of well-posed-ness. The discontinuous boundary value problem possesses many applications in mechanics and physics etc.

A Novel Method of Newton Iteration in Complex Field and Lattice Search for Locating Partial Discharges in Transformers

在变压器局部放电特高频定位的多传感器时间差测量中不可避免地存在误差,这往往导致时间差方程组在实数域内无解。为了得到时间差方程组的最优近似解,提出了复数域牛顿迭代网格搜索方法。该方法在复数域内进行迭代;当迭代结果为实数时就将其作为定位结果;当迭代结果为复数时,以其实部为中心点坐标,在该点周围局部区域内采用网格搜索法计算最优近似解。通过在变压器上开展试验检验了该方法的可行性和准确性。研究表明,在一定时间误差下,在实数域采用牛顿迭代法计算时不收敛,而在复数域可以收敛,平均定位误差为0.20 m。复数域牛顿迭代网格搜索方法能够在一定时间误差下求解时间差方程组,给出最优近似解,实现局部放电定位。

基于区块链和压缩前缀树的去中心化域名系统

现存的基于区块链的去中心化域名方案多存在去中心化不彻底、时间复杂度高、区块链存储膨胀等问题,为此提出了一个兼顾时空复杂度和去中心化程度的域名方案。首先,借助区块链实现去中心化,使用对等节点充当域名服务器,不另设特殊节点,实现彻底的去中心化;其次,设计了一种基于压缩前缀树的数据结构(DNT)以改善区块链的存储膨胀问题和降低系统的时间复杂度,并针对DNT提出了一种高效检索算法;最后,提出了一种基于非对称密钥的零集中管理机制用于系统在去中心环境下运营。实验结果表明:DNT在改善存储膨胀问题上有着良好的效果,总体空间占用约为每千万条0.87 GB,仅为同类方案的10%;DNT对节点总数和深度都有出色的抑制效果,节点总数比前缀树(Trie)少了2个数量级;吞吐率几乎不会随着区块高度的增加而衰减。

Catalytic domain of PDC-E2 contains epitopes recognized by antimitochondrial antibodies in primary biliary cirrhosis

AIM:To search for further immunodominant peptides of the pyruvate dehydrogenase complex E2-component (PDC-E2) recognized by antimitochondrial antibodies (AMA) in primary biliary cirrhosis (PBC). METHODS:Sera from 95 patients with PBC were tested by enzyme-linked immunosorbent assay against 33 synthetic overlapping peptides (25 amino acids; aa) covering the entire length of the E2-subunit of PDC-E2. Furthermore,the inner lipoyl peptide 167-184 was used in an unlip oylated and a lipoylated form as well as coupled to ovalbumin. Sera from 11 AMA negative/ANA posit ive PBC patients,63 patients with other liver disorders and 22 healthy blood donors served as controls.RESULTS:Of the 95 PBC-sera,74% reacted with the peptide 475-499 and 58% with the pept ide 407-431 located within the catalytic domain of PDC-E2. Patients with other disorders or healthy controls were positive in only up to 18%. Antibodies to the unlipoylatedand lip oylated pept ide 167-184 within the inner lipoyl domain were found in only 5% and 11% of the PBC sera,respectively; using ovalbumin-coupled peptides,the incidence increased up to 57% (unlipoylated form). CONCLUSION:Peptides within the catalytic site of PDC-E2 rather than the previously reported lipoyl binding peptide 167-184 may represent major immunodomin ant epitopes recognized by AMA in PBC.

Evolution of a protein domain interaction network

In this paper, we attempt to understand complex network evolution from the underlying evolutionary relationship between biological organisms. Firstly, we construct a Pfam domain interaction network for each of the 470 completely sequenced organisms, and therefore each organism is correlated with a specific Pfam domain interaction network; secondly, we infer the evolutionary relationship of these organisms with the nearest neighbour joining method; thirdly, we use the evolutionary relationship between organisms constructed in the second step as the evolutionary course of the Pfam domain interaction network constructed in the first step. This analysis of the evolutionary course shows： （i） there is a conserved sub-network structure in network evolution; in this sub-network, nodes with lower degree prefer to maintain their connectivity invariant, and hubs tend to maintain their role as a hub is attached preferentially to new added nodes; （ii） few nodes are conserved as hubs; most of the other nodes are conserved as one with very low degree; （iii） in the course of network evolution, new nodes are added to the network either individually in most cases or as clusters with relative high clustering coefficients in a very few cases.

_b-EQUATION ON COMPLEX MANIFOLDS

By using Koppelman-Leray kernel and under suitable condition the integral representation formula of equation on complex manifolds is obtained.

基于电导率加权平均法的频率域航空电磁三维谱元正演模拟研究

三维电磁正演算法的精确性和有效性对于实测电磁数据的反演和解释至关重要。近年来,谱元法逐渐被应用于三维电磁正演中,其中基于规则/形变六面体网格的谱元法在航空电磁正演模拟中的效果已得到了验证。然而,常规谱元法在处理每个离散单元时,通常赋予其单一的物理属性,导致在模拟复杂模型时仍需采用精细网格以满足模型离散需求,对复杂模型的适用性存在不足。鉴于谱元法基函数的高阶性,提出了一种基于电导率体积加权平均的谱元法。该方法将物理模型离散化与数值网格离散化相分离,实现了对单元内物理属性变化的精细描述,同时避免了正演方程未知数数量的增加。以频率域航空电磁三维正演为例,对改进的谱元法的精度与效率进行了分析。数值算例结果表明,改进的谱元正演算法能够在保证不低于常规正演算法精度的前提下,减少所需的自由度,从而提高计算效率。