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...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.展开更多
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 problem...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.展开更多
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 capacitan...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.展开更多
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 t...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.展开更多
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 arb...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.展开更多
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 s...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.展开更多
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 approximatin...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 quasiconformai mappings in the plane is discussed.展开更多
This paper gets the Beltrami equations satisfied by a 1-quasiconformal map- ping, 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 ...This paper gets the Beltrami equations satisfied by a 1-quasiconformal map- ping, 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.展开更多
The scientific community recognizes the seriousness of rockbursts and the need for effective mitigation measures.The literature reports various successful applications of machine learning(ML)models for rockburst asses...The scientific community recognizes the seriousness of rockbursts and the need for effective mitigation measures.The literature reports various successful applications of machine learning(ML)models for rockburst assessment;however,a significant question remains unanswered:How reliable are these models,and at what confidence level are classifications made?Typically,ML models output single rockburst grade even in the face of intricate and out-of-distribution samples,without any associated confidence value.Given the susceptibility of ML models to errors,it becomes imperative to quantify their uncertainty to prevent consequential failures.To address this issue,we propose a conformal prediction(CP)framework built on traditional ML models(extreme gradient boosting and random forest)to generate valid classifications of rockburst while producing a measure of confidence for its output.The proposed framework guarantees marginal coverage and,in most cases,conditional coverage on the test dataset.The CP was evaluated on a rockburst case in the Sanshandao Gold Mine in China,where it achieved high coverage and efficiency at applicable confidence levels.Significantly,the CP identified several“confident”classifications from the traditional ML model as unreliable,necessitating expert verification for informed decision-making.The proposed framework improves the reliability and accuracy of rockburst assessments,with the potential to bolster user confidence.展开更多
基金National Natural Science Foundation of China(11971182)the Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University(ZQN-PY402)+1 种基金Research projects of Young and Middle-aged Teacher's Education of Fujian Province(JAT190508)Scientific research project of Quanzhou Normal University(H19009).
文摘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.
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant No.10775166)the Zhejiang Provincial Science Technology Foundation,China(Grant No.2008C31002)
文摘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.
文摘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.
文摘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.
基金supported by the National Natural Science Foundation of China (90916007 and 91116008)
文摘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.
基金This project is supported in part by NSF of China(60575004, 10231040)NSF of GuangDong, Grants from the Ministry of Education of China(NCET-04-0791)Grants from Sun Yat-Sen University
文摘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 quasiconformai mappings in the plane is discussed.
基金Supported by the National Natural Science Foundation of China (10571155)
文摘This paper gets the Beltrami equations satisfied by a 1-quasiconformal map- ping, 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.
基金Supported by the Natural Science Foundation of Huaqiao University(02HZR12)Supported by the Natural Science Foundation of Overseas Chinese Affairs Office under the State Council(01QZR01)
文摘背景: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。
文摘The scientific community recognizes the seriousness of rockbursts and the need for effective mitigation measures.The literature reports various successful applications of machine learning(ML)models for rockburst assessment;however,a significant question remains unanswered:How reliable are these models,and at what confidence level are classifications made?Typically,ML models output single rockburst grade even in the face of intricate and out-of-distribution samples,without any associated confidence value.Given the susceptibility of ML models to errors,it becomes imperative to quantify their uncertainty to prevent consequential failures.To address this issue,we propose a conformal prediction(CP)framework built on traditional ML models(extreme gradient boosting and random forest)to generate valid classifications of rockburst while producing a measure of confidence for its output.The proposed framework guarantees marginal coverage and,in most cases,conditional coverage on the test dataset.The CP was evaluated on a rockburst case in the Sanshandao Gold Mine in China,where it achieved high coverage and efficiency at applicable confidence levels.Significantly,the CP identified several“confident”classifications from the traditional ML model as unreliable,necessitating expert verification for informed decision-making.The proposed framework improves the reliability and accuracy of rockburst assessments,with the potential to bolster user confidence.
