Effective approach for conformal subarray design based on maximum entropy of planar mappings

In this paper,an effective algorithm for optimizing the subarray of conformal arrays is proposed.The method first divides theconformal array into several first-level subarrays.It uses the X algorithm to solve the feasible solution of first-level subarray tiling and employs the particle swarm algorithm to optimize the conformal array subarray tiling scheme with the maximum entropy of the planar mapping as the fitness function.Subsequently,convex optimization is applied to optimize the subarray amplitude phase.Data results verify that the method can effectively find the optimal conformal array tiling scheme.

Phase estimation in bispectral domain based on conformal mapping and applications in seismic wavelet estimation

Seismic wavelet estimation is an important part of seismic data processing and interpretation, whose preciseness is directly related to the results of deconvolution and inversion. Wavelet estimation based on higher-order spectra is an important new method. However, the higher-order spectra often have phase wrapping problems, which lead to wavelet phase spectrum deviations and thereby affect mixed-phase wavelet estimation. To solve this problem, we propose a new phase spectral method based on conformal mapping in the bispectral domain. The method avoids the phase wrapping problems by narrowing the scope of the Fourier phase spectrum to eliminate the bispectral phase wrapping influence in the original phase spectral estimation. The method constitutes least-squares wavelet phase spectrum estimation based on conformal mapping which is applied to mixed-phase wavelet estimation with the least-squares wavelet amplitude spectrum estimation. Theoretical model and actual seismic data verify the validity of this method. We also extend the idea of conformal mapping in the bispectral wavelet phase spectrum estimation to trispectral wavelet phase spectrum estimation.

An analytical model for coplanar waveguide on silicon-on-insulator substrate with conformal mapping technique

In this paper, the authors present an analytical model for coplanar waveguide on silicon-on-insulator substrate. The four-element topological network and the conformal mapping technique are used to analyse the capacitance and the conductance of the sandwich substrate. The validity of the model is verified by the full-wave method and the experimental data. It is found that the inductance, the resistance, the capacitance and the conductance from the analytical model show they are in good agreement with the corresponding values extracted from experimental Sparameter until 10 GHz.

NUMERICAL ANALYSIS OF QUASICONFORMAL MAPPINGS BY CIRCLE PACKINGS

Thurston proposed that conformal mappings can be approximated by circle packing isomorphisms and the approach can be implemented efficiently. Based on the circle packing methods the rate of convergence of approximating solutions for quasiconformal mappings in the plane is discussed.

Conformal mapping modeling of metal plastic deformation and die cavity in special-shaped extrusion

With the help of Complex Function Mapping studied results, the analysis function of Conformal Mapping is set up. Since the complicated three dimension’s deformation problems are transferred into two dimension problems, both the stream function and strain ratio field are analyzed in the metal plastic deformation. Using the upper-bound principles, the theory of metal deformation and die cavity optimized modeling is established for random special-shaped product extrusion. As a result, this enables the realization of intelligent technique target in the die cavity of CAD/CAM integration.

CONFORMAL AND GENERALIZED CONCIRCULAR MAPPINGS OF EINSTEIN-WEYL MANIFOLDS

In this article, after giving a necessary and sufficient condition for two Einstein- Weyl manifolds to be in conformal correspondence, we prove that any conformal mapping between such manifolds is generalized concircular if and only if the covector field of the conformal mapping is locally a gradient. Using this fact we deduce that any conformal mapping between two isotropic Weyl manifolds is a generalized concircular mapping. Moreover, it is shown that a generalized concircularly flat Weyl manifold is generalized concircular to an Einstein manifold and that its scalar curvature is prolonged covariant constant.

1-quasiconformal mappings on a (2,2)-type quadric

This paper gets the Beltrami equations satisfied by a 1-quasiconformal mapping, which are exactly CR or anti-CR equations on （2,2）-type quadric Q0. This means a 1-quasiconformal mapping on Q0 is CR or anti-CR. This reduces the determination of 1- quasiconformal mappings to a problem on the theory of several complex analysis. The result about the group of CR automorphisms is used to determine the unit component of group of 1-quasiconformal mappings.

Precise method to control elastic waves by conformal mapping

The transformation method to control waves has received widespread attention in electromagnetism and acoustics. However, this machinery is not directly applicable to the control of elastic waves, because it has been shown that the Navier＇s equation does not usually retain its form under coordinate transformation. In this letter, we prove the form invariance of the Navier＇s equation under the conformal mapping based on the Helmholtz decomposition method. The needed material parameters are provided to manipulate elastic waves. The validity of this approach is confirmed by an active stealth device which can disguise the signal source by changing its position. Experimental verifications and potential applications may be expected in nondestructive testing, structural seismic design and other fields.

On the Estimates of Hyperbolic Area Distortion of Quasiconformal Mappings

The distortion property of hyperbolic area of planar quasiconformal mappings is studied in this paper. In the case of radial quasiconformal mappings and angular deformed quasiconformal mappings their hyperbolic area distortions are estimated quite sharply. The result can be applied to judge whether the hyperbolic area of a planar subset is explodable.

PARAMETRIC REPRESENTATIONS OF QUASICONFORMAL MAPPINGS

In this article,we first give two simple examples to illustrate that two types of parametric representation of the family ofΣ0 K have some gaps.Then we also find that the area derivative formula(1.6),which is used to estimate the area distortion ofΣ0 K,cannot be derived from[6],but that formula still holds forΣ0 K through our amendatory parametric representation for the one obtained by Eremenko and Hamilton.

Solution of the Third Kind Boundary Value Problem of Laplace’s Equation Based on Conformal Mapping

In order to overcome the difficulty in solving the boundary value problem of electrostatic field with complex boundary and to give a new method for solving the third boundary value problem of Laplace’s equation, in this paper, the third boundary value problem of Laplace’s equation is studied by combining conformal mapping with theoretical analysis, the several analytical solutions of third boundary value problems of Laplace’s equation are gives, the correctness of its solution is verified through computer numerical simulation, and a new idea and method for solving the third boundary value problem of Laplace’s equation is obtained. In this paper, the boundary condition of the solving domain is changed by the appropriate conformal mapping, so that the boundary value problem on the transformed domain is easy to be solved or be known, and then the third kind boundary value of the Laplace’s equation can be solved easily;its electric potential distribution is known. Furthermore, the electric field line and equipotential line are plotted by using the MATLAB software.

AN APPROXIMATE METHOD ON THE CONFORMAL MAPPING FROM A UNIT CIRCLE TO AN ARBITRARY CURVE

In this paper, the conformal mapping problem on the transformation from the interior of a unit circle to the interior of the simply connected region or exterior with an arbitrary curvilinear boundary (including an arbitrary curvilinear cut crack) is discussed. The boundary of the simply connected region is approximated by a polygon. The mapping function from a unit circle to a polygon is founded by using the Schwartz-Christoffel integral. A numerical calculation method to determine the unknown parameters in the Schwartz-Christoffel integral is given.

磁共振T1rho序列、T2 mapping技术在膝关节早期软骨退变早期诊断中的评估价值

目的探讨磁共振T1rho序列、T2 mapping技术在膝关节早期软骨退变早期诊断中的评估价值。方法选取2020年1月至2022年11月在我院治疗的110例膝关节早期软骨退变患者(观察组),按照疾病严重程度分为轻度退变组及重度退变组,另选取同期在我院进行体检的64例健康者为对照组,受试者均行磁共振T1rho序列、T2 mapping技术扫描,测量受试者T2值及T1ρ值,探讨磁共振T1rho序列、T2 mapping技术在膝关节早期软骨退变早期诊断中的评估价值。结果观察组股骨外侧面、股骨内侧面、胫骨外侧面、胫骨内侧面、髋骨面T2值均明显高于对照组(P<0.05),重度退变亚组患者股骨外侧面、股骨内侧面、胫骨外侧面、胫骨内侧面、髋骨面T2值显著高于轻度退变者(P<0.05);观察组股骨内踝负重区、股骨内踝非负重区、股骨外踝负重区、股骨外踝非负重区、胫骨外侧平台区、胫骨内侧平台区、髌后软骨区磁共振T1ρ值明显高于对照组(P<0.05),重度退变亚组患者股骨内踝负重区、股骨内踝非负重区、股骨外踝负重区、股骨外踝非负重区、胫骨外侧平台区、胫骨内侧平台区、髌后软骨区磁共振T1ρ值明显高于轻度退变亚组患者(P<0.05);磁共振T1rho序列在膝关节早期软骨退变中早期诊断及严重程度评估中的的诊断ROC值及特异度明显高于T2 mapping技术(P<0.05),但后者具有更高的敏感度(P<0.05)。结论磁共振T1rho序列、T2 mapping技术均能有效反映膝关节早期软骨退变中软骨组织学成分变化情况,还可为膝关节软骨退变严重程度评估提供客观依据,二者具有一定互补价值。

Covering Theorems on Two Classes of Quasi-conformal Mappings

In this paper we define two classes of quasiconformal mappings, and study theircovering properties by methods of module. We obtain some new results. In the meantime,we give new methods to prove Koebe 1/2 covering theorem on convex conformal mappings.

On Quasiconformal Mappings Between Hyperbolic Triangles

Quasiconformal mappings between hyperbolic triangles are considered.We give an explicit estimate of the dilation of the quasiconformal mappings,which generalizes Bishop's results.

MR T2^(*)mapping成像技术定量评价腰椎小关节炎软骨损伤

背景:腰椎小关节炎是引起下腰痛的一个主要原因,目前主要依靠MRI进行初步定性诊断,但仍有一定漏诊、误诊的概率发生,因此MR T2^(*)mapping成像技术有望成为定量检查腰椎小关节炎软骨损伤的重要检测手段。目的:探讨MR T2^(*)mapping成像技术在定量分析腰椎小关节炎软骨损伤退变中的应用价值。方法:收集南京医科大学第四附属医院2020年4月至2022年3月门诊或住院合并下腰痛共110例患者,设为病例组;同时招募无症状志愿者80例,设为对照组。对所有纳入对象L1-S1的小关节行3.0 T MR扫描,获取T2^(*)mapping横断位图像和T2WI图像,分别对所有小关节软骨进行Weishaupt分级及T2^(*)值测量,收集数据并行统计学分析。不同小关节Weishaupt分级之间小关节软骨T2^(*)值比较采用单因素方差分析。结果与结论:①经统计分析发现,病例组腰椎小关节软骨T2^(*)值(17.6±1.5)ms明显较对照组(21.4±1.3)ms降低,差异有显著性意义(P<0.05);②在病例组中,随着腰椎小关节Weishaupt分级增加,小关节软骨T2^(*)值也呈逐渐下降趋势,且这种差异有显著性意义(P<0.05);③提示T2^(*)mapping能够较好地显示腰椎小关节软骨损伤的早期病理变化,腰椎小关节软骨的T2^(*)值能够定量评估腰椎小关节的软骨损伤程度;T2^(*)mapping成像技术能为影像学诊断腰椎小关节炎软骨早期损伤提供很好的理论依据,具有重要的临床应用价值。

传统武术套路训练对大学生武术运动员膝关节软骨影响的T2-mapping功能磁共振成像研究

目的:本研究旨在通过T2-mapping功能磁共振影像学技术对大学生武术运动员膝关节软骨进行定量评估,探究传统武术套路训练对大学生武术运动员膝关节软骨的影响。方法:选取9名年龄介于18~25岁之间的大学生武术运动员作为实验组,同时选取18名普通健康的大学生作为对照组。在相同条件下,对两组分别进行右膝关节的T2-mapping磁共振检查,并将膝关节软骨分为股骨内侧髁、胫骨内侧髁、髌软骨、股骨外侧髁及胫骨外侧髁5个感兴趣区,比较实验组与对照组之间T2值的差异,分析各组膝关节软骨不同感兴趣区T2值的变化。结果:(1)不论性别,实验组和对照组各个膝关节面软骨感兴趣区的T2值均未见显著性差异(P>0.05);(2)男性对照组、女性对照组以及女性实验组的膝关节各感兴趣区T2值两两之间均无统计学差异(P>0.05);(3)男性实验组膝关节股骨外侧髁与胫骨内侧髁、髌软骨的T2值差异具有统计学意义(P<0.05)。结论:T2-mapping技术可通过无创手段定量评估传统武术套路训练对大学生膝关节软骨的影响。在长期传统武术套路训练后,男性大学生武术运动员的膝关节出现了异质性改变,因此在训练过程中应该注意调整方案,以实现针对性保护。

DWI联合T2 mapping序列鉴别前列腺癌与前列腺增生价值评估

目的探讨扩散加权成像(diffusion-weighted imaging,DWI)联合T2 mapping序列鉴别前列腺癌(prostate cancer,PCa)与前列腺增生(benign prostatic hyperplasia,BPH)的价值。材料与方法回顾性分析本院行3.0 T MRI检查且经病理证实的56例PCa患者及40例BPH患者资料。扫描序列包括T1WI、T2WI、DWI及T2 mapping序列。两名观察者分别测量两组病灶的表观扩散系数(apparent diffusion coefficient,ADC)值及T2值。采用组内相关系数(intra-class correlation coefficient,ICC)评估两名观察者测得参数值的一致性。采用独立样本t检验或Mann-Whitney U检验分析两组病例间ADC值及T2值的差异。Logistic回归用于分析差异具有统计学意义的参数及其与基线资料联合的诊断模型。采用受试者工作特征(receiver operating characteristic,ROC)曲线评估有差异参数及联合模型的诊断效能。采用DeLong检验比较ROC曲线下面积差异。采用Spearman相关系数分析ADC值与T2值相关性。结果两名观察者测量值一致性好(ICC>0.75)。PCa组的ADC值及T2值分别低于BPH组,差异具有统计学意义(P<0.01)。ADC值、T2值、ADC-T2及ADC-T2-年龄-总前列腺特异性抗原(total prostate specific antigen,TPSA)联合鉴别PCa与BPH的AUC值分别为0.843、0.830、0.896及0.927。DeLong检验显示ADC值与ADC-T2联合,ADC值、T2值、ADC-T2模型与ADC-T2-年龄-TPSA联合模型的ROC差异存在统计学意义(P<0.05)。ADC值与T2值呈正相关(r=0.331,P<0.01)。结论DWI及T2 mapping序列在鉴别PCa与BPH方面具有较好的价值,并且两序列联合临床指标时诊断效能提升,可为临床无创诊断PCa及BPH提供很好的指导意义。

T_(1)-mapping鉴别腮腺常见肿瘤的初探

目的:探讨T_(1)-mapping和分段读出DWI(RESOLVE-DWI)在腮腺常见肿瘤鉴别诊断中的价值。方法:回顾性分析2018年6月-2022年8月经病理证实的169例腮腺常见肿瘤患者的T_(1)-mapping及分段读出DWI资料。其中,多形性腺瘤85例,Warthin瘤32例,恶性肿瘤52例。测量并比较三组肿瘤的T_(1)及ADC值,运用受试者工作特征(ROC)曲线评价T_(1)、ADC及二者联合(T_(1)+ADC)对腮腺肿瘤的鉴别诊断价值。采用Delong检验比较各参数的AUC的差异。结果:三组肿瘤的T_(1)值和ADC值的差异均有统计学意义(P<0.001);组间两两比较,差异均有统计学意义(P<0.001);多形性腺瘤的T_(1)值及ADC值最高;恶性肿瘤次之,Warthin瘤最低。T_(1)和ADC鉴别多形性腺瘤与Warthin瘤、多形性腺瘤与恶性肿瘤、Warthin瘤与恶性肿瘤的AUC分别为0.914和0.997、0.664和0.869、0.835和0.695,Delong检验显示2个参数AUC的差异均无统计学意义(P>0.05)。T_(1)+ADC鉴别多形性腺瘤与Warthin瘤、多形性腺瘤与恶性肿瘤的AUC均显著高于T_(1)(1.000 vs.0.914、0.873 vs.0.664,P均<0.001);T_(1)+ADC鉴别Warthin瘤与恶性肿瘤的AUC显著高于T_(1)(0.895 vs.0.835,P<0.001)和ADC(0.895 vs.0.695,P<0.001)。结论:T_(1)-mapping和RESOLVE-DWI有助于鉴别诊断腮腺常见肿瘤,二者联合诊断可提高鉴别诊断效能。

2型糖尿病老年病人心肌纤维化T1-Mapping与左心室应变参数的相关性分析

目的探究2型糖尿病(T2DM)老年病人心肌纤维化T1-Mapping参数与左心室应变参数之间的相关性。方法以2019年8月至2022年8月在孝感市中心医院就诊的T2DM病人82例为研究对象,根据病人的病程分为短期T2DM组40例(病程<5年)和长期T2DM组42例(病程≥5年),以同期招募的健康志愿者40例为对照组。比较各组间左心室应变参数及T1-Mapping参数。采用多元线性逐步回归法分析T1-Mapping参数的影响因素。采用相关性分析T1-Mapping参数与左心室应变参数的相关性。结果短期T2DM组病人左室周向峰值舒张应变率(PDSR)[1.25(0.95,1.50)1/s比1.40(1.20,1.70)1/s]较对照组降低(P<0.05),细胞外体积(ECV)[31.00(29.00,33.50)%比29.00(27.00,32.00)%]较对照组升高(P<0.05)。与对照组比较,长期T2DM组病人左室纵向峰值应变(PS)[−14.50(−12.38,−16.50)%比−16.15(−14.60,−18.30)%]、径向PDSR[(−2.58±0.83)1/s比(−3.32±0.88)1/s]、周向PDSR[0.90(0.70,1.20)1/s比1.40(1.20,1.70)1/s]、纵向PDSR[0.70(0.58,0.90)1/s比1.10(0.80,1.38)1/s]降低(P<0.05),ECV[34.00(32.00,35.00)%比29.00(27.00,32.00)%]升高(P<0.05)。与短期T2DM组比较,长期T2DM组病人左室纵向PS[−14.50(−12.38,−16.50)%比−16.15(−14.45,−18.38)%]、径向PDSR[(−2.58±0.83)1/s比(−3.61±0.76)1/s]、周向PDSR[0.90(0.70,1.20)1/s比1.25(0.95,1.50)1/s]、纵向PDSR[0.70(0.58,0.90)1/s比1.10(0.80,1.30)1/s]降低(P<0.05),ECV[34.00(32.00,35.00)%比31.00(29.00,33.50)%]升高(P<0.05)。多元线性回归分析结果示,糖尿病病程是T2DM病人ECV的独立影响因素(β=0.29,P<0.05)。Spearman相关性分析结果示,T2DM病人ECV与左室纵向PS(r_(s)=0.35,P<0.05)、纵向峰值收缩应变率(PSSR)(r_(s)=0.31,P<0.05)呈显著正相关,与左室周向PDSR(r_(s)=−0.29,P<0.05)、纵向PDSR(r_(s)=−0.43,P<0.05)呈显著负相关。结论心脏磁共振T1-Mapping可能发现T2DM病人早期心肌纤维化,T1-Mapping参数与左心室应变参数显著相关。