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A constructive method for approximating trigonometric functions and their integrals
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作者 CHEN Xiao-diao WANG Long-quan WANG Yi-gang 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2020年第3期293-307,共15页
This paper presents an interpolation-based method(IBM)for approximating some trigonometric functions or their integrals as well.It provides two-sided bounds for each function,which also achieves much better approximat... This paper presents an interpolation-based method(IBM)for approximating some trigonometric functions or their integrals as well.It provides two-sided bounds for each function,which also achieves much better approximation effects than those of prevailing methods.In principle,the IBM can be applied for bounding more bounded smooth functions and their integrals as well,and its applications include approximating the integral of sin(x)/x function and improving the famous square root inequalities. 展开更多
关键词 Padéapproximant trigonometric function constructive method interpolation-based method two-sided bounds
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A trigonometric series expansion method for the Orr-Sommerfeld equation 被引量:2
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作者 Ying TAN Weidong SU 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2019年第6期877-888,共12页
A trigonometric series expansion method and two similar modified methods for the Orr-Sommerfeld equation are presented. These methods use the trigonometric series expansion with an auxiliary function added to the high... A trigonometric series expansion method and two similar modified methods for the Orr-Sommerfeld equation are presented. These methods use the trigonometric series expansion with an auxiliary function added to the highest order derivative of the unknown function and generate the lower order derivatives through successive integra- tions. The proposed methods are easy to implement because of the simplicity of the chosen basis functions. By solving the plane Poiseuille flow (PPF), plane Couette flow (PCF), and Blasius boundary layer flow with several homogeneous boundary conditions, it is shown that these methods yield results with the same accuracy as that given by the conventional Chebyshev collocation method but with better robustness, and that ob- tained by the finite difference method but with fewer modal number. 展开更多
关键词 Orr-Sommerfeld EQUATION SPECTRAL method trigonometric function PARALLEL SHEAR flow hydrodynamical stability EIGENVALUE problem
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General Solution of Two Generalized Form of Burgers Equation by Using the (<i>G</i><sup>'</sup>/<i>G</i>)-Expansion Method 被引量:1
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作者 Abdollah Borhanifar Reza Abazari 《Applied Mathematics》 2012年第2期158-168,共11页
In this work, the (G'/G)-expansion method is proposed for constructing more general exact solutions of two general form of Burgers type equation arising in fluid mechanics namely, Burgers-Korteweg-de Vries (Burger... In this work, the (G'/G)-expansion method is proposed for constructing more general exact solutions of two general form of Burgers type equation arising in fluid mechanics namely, Burgers-Korteweg-de Vries (Burgers-KdV) and Burger-Fisher equations. Our work is motivated by the fact that the (G'/G)-expansion method provides not only more general forms of solutions but also periodic and solitary waves. If we set the parameters in the obtained wider set of solutions as special values, then some previously known solutions can be recovered. The method appears to be easier and faster by means of a symbolic computation system. 展开更多
关键词 (G'/G)-Expansion method GENERALIZED Burgers-KdV EQUATION GENERALIZED Burgers-Fisher EQUATION Hyperbolic function SOLUTIONS trigonometric function SOLUTIONS
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General Solution of Generalized (2+1)–Dimensional Kadomtsev-Petviashvili (KP) Equation by Using the –Expansion Method
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作者 Abdollah Borhanifar Reza Abazari 《American Journal of Computational Mathematics》 2011年第4期219-225,共7页
In this work, the (G,/G)- --expansion method is proposed for constructing more general exact solutions of the (2 + 1)--dimensional Kadomtsev-Petviashvili (KP) equation and its generalized forms. Our work is motivated ... In this work, the (G,/G)- --expansion method is proposed for constructing more general exact solutions of the (2 + 1)--dimensional Kadomtsev-Petviashvili (KP) equation and its generalized forms. Our work is motivated by the fact that the (G,/G)---expansion method provides not only more general forms of solutions but also periodic and solitary waves. If we set the parameters in the obtained wider set of solutions as special values, then some previously known solutions can be recovered. The method appears to be easier and faster by means of a symbolic computation system. 展开更多
关键词 (G /G)-Expansion method Generalized Kadomtsev-Petviashvili (KP) Equation Hyperbolic function Solutions trigonometric function Solutions
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Thermodynamic Properties for Polybrominated Dibenzothiophenes by Density Functional Theory 被引量:2
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作者 李加友 柳红霞 +2 位作者 于红霞 王遵尧 王连生 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2009年第6期999-1008,共10页
The thermodynamic properties of 135 polybrominated dibenzothiophenes (PBDTs) in the gaseous state at 298.15 K and 1.013×10^5 Pa, are calculated using the density functional theory (the B3LYP/6-311G^**) wit... The thermodynamic properties of 135 polybrominated dibenzothiophenes (PBDTs) in the gaseous state at 298.15 K and 1.013×10^5 Pa, are calculated using the density functional theory (the B3LYP/6-311G^**) with Gaussian 03. Based on these data, the isodesmic reacflons are designed to calculate the standard enthalpy of formation (△fH^θ) and the standard Gibbs energy of formation (△fG^θ) of PBDTs. The relations of these thermodynamic parameters with the number and positionof bromine subsfituents (NPBS) are discussed, and it is found that there exist good correlations between othermody namic parameters (including heat capacity at constant volume, entropy, enthaipy, free energy, △fH^θ, △fG^θ) and NPBS. Thoe relative stability order of PBDT congeners is proposed theoretically based on the relative magnitude of their △fG^θ. In addition, the values of molar heat capacities at constant pressure (Cp,m) for PBDT c ongelaers are calculated. 展开更多
关键词 polybrominated dibenzothiophenes density functional theory method of position of substituted Br atom thermodynamic parameters relative stability
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New Exact Solutions of the Integrable Broer-Kaup Equations in (2+ 1)-DimensionalSpaces 被引量:1
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作者 LIDe-Sheng ZHANGHong-Qing 《Communications in Theoretical Physics》 SCIE CAS CSCD 2004年第4期499-501,共3页
In this paper,by improving some procedure of extended tanh-function method,some new exact solutions to the integrable Broer-Kaup equations in(2 + 1)-dimensional spaces are obtained,which include soliton-like solutions... In this paper,by improving some procedure of extended tanh-function method,some new exact solutions to the integrable Broer-Kaup equations in(2 + 1)-dimensional spaces are obtained,which include soliton-like solutions,solitary wave solutions,trigonometric function solutions,and rational solutions. 展开更多
关键词 extended tanh method soliton-like solutions trigonometric function solutions solitary waves rational solutions
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Exact Solutions of (2+1)-Dimensional Boiti-Leon-Pempinelle Equation with (G'/G)-Expansion Method
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作者 熊守全 夏铁成 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第7期35-37,共3页
In this paper,we construct exact solutions for the (2+1)-dimensional Boiti-Leon-Pempinelle equation byusing the (G'/G)-expansion method,and with the help of Maple.As a result,non-travelling wave solutions with thr... In this paper,we construct exact solutions for the (2+1)-dimensional Boiti-Leon-Pempinelle equation byusing the (G'/G)-expansion method,and with the help of Maple.As a result,non-travelling wave solutions with threearbitrary functions are obtained including hyperbolic function solutions,trigonometric function solutions,and rationalsolutions.This method can be applied to other higher-dimensional nonlinear partial differential equations. 展开更多
关键词 (2+1)-dimensional Boiti-Leon-Pempinelle equation (G′/G)-expansion method hyperbolic function solutions trigonometric function solutions
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基于解析法的空间角向孔镗削工艺尺寸转换研究
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作者 杨欢 鞠录岩 +3 位作者 孙若文 张维琨 张耀武 郭龙龙 《制造技术与机床》 北大核心 2024年第9期155-160,共6页
空间角向孔作为行星轮系旋转作动器中的重要结构特征具有很高的加工精度。镗削时必须根据图纸设计尺寸得到准确的镗削工艺尺寸,以便准确定位。文章系统地对双角度、三角度空间角向孔镗削过程、工艺尺寸转换进行了研究,使用图解法、解析... 空间角向孔作为行星轮系旋转作动器中的重要结构特征具有很高的加工精度。镗削时必须根据图纸设计尺寸得到准确的镗削工艺尺寸,以便准确定位。文章系统地对双角度、三角度空间角向孔镗削过程、工艺尺寸转换进行了研究,使用图解法、解析法推导出对应的计算公式,拓展了工艺尺寸转换方法。利用解析法得到的计算公式,实现利用空间角向孔与工艺钢球相对尺寸及空间角向孔角度尺寸,得到所需的镗削工艺尺寸,降低了工艺尺寸转换难度,提高了空间角向孔的镗削效率。同时结合Python编程语言,编写出一套工艺尺寸计算软件,验证了推导公式的有效性和准确性。 展开更多
关键词 空间角向孔 图解法 解析法 立体几何 三角函数
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A Generalized F-expansion Method and Its Application in High-Dimensional Nonlinear Evolution Equation 被引量:1
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作者 CHEN Jiang HE Hong-Sheng YANG Kong-Qing 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第2X期307-310,共4页
A generalized F-expansion method is introduced and applied to (3+ 1)-dimensional Kadomstev-Petviashvili(KP) equation. As a result, some new Jacobi elliptic function solutions of the equation are found, from which the ... A generalized F-expansion method is introduced and applied to (3+ 1)-dimensional Kadomstev-Petviashvili(KP) equation. As a result, some new Jacobi elliptic function solutions of the equation are found, from which the trigonometric function solutions and the solitary wave solutions can be obtained. The method can also be extended to other types of nonlinear evolution equations in mathematical physics. 展开更多
关键词 F-expansion method Jacobi elliptic function KP equation solitary wave solution trigonometric function solution
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New exact solutions of nonlinear differential-difference equations with symbolic computation
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作者 熊守全 夏铁成 《Journal of Shanghai University(English Edition)》 CAS 2010年第6期415-419,共5页
In this paper, the Toda equation and the discrete nonlinear Schrdinger equation with a saturable nonlinearity via the discrete " (G′/G")-expansion method are researched. As a result, with the aid of the symbolic ... In this paper, the Toda equation and the discrete nonlinear Schrdinger equation with a saturable nonlinearity via the discrete " (G′/G")-expansion method are researched. As a result, with the aid of the symbolic computation, new hyperbolic function solution and trigonometric function solution with parameters of the Toda equation are obtained. At the same time, new envelop hyperbolic function solution and envelop trigonometric function solution with parameters of the discrete nonlinear Schro¨dinger equation with a saturable nonlinearity are obtained. This method can be applied to other nonlinear differential-difference equations in mathematical physics. 展开更多
关键词 discrete ("G′/G")-expansion method Toda equation discrete nonlinear Schrdinger equation saturable nonlinearity hyperbolic function solution trigonometric function solution
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Traveling Wave Solutions for Generalized Bretherton Equation
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作者 Amin Esfahani 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第3期381-386,共6页
This paper studies the Generalized Bretherton equation using trigonometric function method including the sech-function method, the sine-cosine function method, and the tanh-function method, and He's semi-inverse meth... This paper studies the Generalized Bretherton equation using trigonometric function method including the sech-function method, the sine-cosine function method, and the tanh-function method, and He's semi-inverse method (He's variational method). Various traveling wave solutions are obtained, revealing an intrinsic relationship among the amplitude, frequency, and wave speed. 展开更多
关键词 Bretherton equation traveling wave trigonometric function method variational method
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Variable-Coefficient Mapping Method Based on Elliptical Equation and Exact Solutions to Nonlinear SchrSdinger Equations with Variable Coefficient
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作者 GE Jian-Ya WANG Rui-Min +1 位作者 DAI Chao-Qing ZHANG Jie-Fang 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第4X期656-662,共7页
In this paper, by means of the variable-coefficient mapping method based on elliptical equation, we obtain explicit solutions of nonlinear Schrodinger equation with variable-coefficient. These solutions include Jacobi... In this paper, by means of the variable-coefficient mapping method based on elliptical equation, we obtain explicit solutions of nonlinear Schrodinger equation with variable-coefficient. These solutions include Jacobian elliptic function solutions, solitary wave solutions, soliton-like solutions, and trigonometric function solutions, among which some are found for the first time. Six figures are given to illustrate some features of these solutions. The method can be applied to other nonlinear evolution equations in mathematical physics. 展开更多
关键词 variable-coefficient mapping method based on elliptical equation nonlinear Schrodinger equation Jacobian elliptic function solutions solitonic solutions trigonometric function solutions
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A Comparative Numerical Study of Parabolic Partial Integro-Differential Equation Arising from Convection-Diffusion
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作者 Kamil Khan Arshed Ali +2 位作者 Fazal-i-Haq Iltaf Hussain Nudrat Amir 《Computer Modeling in Engineering & Sciences》 SCIE EI 2021年第2期673-692,共20页
This article studies the development of two numerical techniques for solving convection-diffusion type partial integro-differential equation(PIDE)with a weakly singular kernel.Cubic trigonometric B-spline(CTBS)functio... This article studies the development of two numerical techniques for solving convection-diffusion type partial integro-differential equation(PIDE)with a weakly singular kernel.Cubic trigonometric B-spline(CTBS)functions are used for interpolation in both methods.The first method is CTBS based collocation method which reduces the PIDE to an algebraic tridiagonal system of linear equations.The other method is CTBS based differential quadrature method which converts the PIDE to a system of ODEs by computing spatial derivatives as weighted sum of function values.An efficient tridiagonal solver is used for the solution of the linear system obtained in the first method as well as for determination of weighting coefficients in the second method.An explicit scheme is employed as time integrator to solve the system of ODEs obtained in the second method.The methods are tested with three nonhomogeneous problems for their validation.Stability,computational efficiency and numerical convergence of the methods are analyzed.Comparison of errors in approximations produced by the present methods versus different values of discretization parameters and convection-diffusion coefficients are made.Convection and diffusion dominant cases are discussed in terms of Peclet number.The results are also compared with cubic B-spline collocation method. 展开更多
关键词 Partial integro-differential equation CONVECTION-DIFFUSION collocation method differential quadrature cubic trigonometric B-spline functions weakly singular kernel
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隧道开挖对建筑物条形基础效应的理论研究
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作者 田晓艳 熊家全 +2 位作者 代建波 刘静 李源 《科学技术与工程》 北大核心 2023年第27期11786-11794,共9页
基于隧道开挖引发的深部土层沉降槽曲线特点,首先利用反分析法研究其开挖对条形基础效应的影响,利用微元体力的平衡条件建立隧道开挖与条形基础与地基协同工作的微分方程,然后采取概念明确的初参数法求解相应的齐次方程,之后根据平截面... 基于隧道开挖引发的深部土层沉降槽曲线特点,首先利用反分析法研究其开挖对条形基础效应的影响,利用微元体力的平衡条件建立隧道开挖与条形基础与地基协同工作的微分方程,然后采取概念明确的初参数法求解相应的齐次方程,之后根据平截面假定,结合材料力学基本理论,考虑双曲线三角函数的微分特点,并借助MATLAB、mathmatica软件得出隧道穿越条形基础效应的理论计算表达式,最后结合工程算例分析研究隧道与基础相对位置变化以及主要参数变化对基础效应的影响。结果表明:隧道对基础的影响范围为[-0.5~1.5]倍的基础长度,且当隧道中心位于基础端部时沉降最大;隧道参数中土体损失率、隧道开挖断面及埋深对基础效应的影响很大,而基础自身参数变化对其变形影响较小,但基础高度的参数变化对其内力影响较大,基础的高度主要是由基础抗冲切与剪切来确定。 展开更多
关键词 沉降槽曲线 反分析法 条形基础效应 初参数法 双曲线三角函数 理论计算表达式
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基于优序图法和隶属函数的燃气管道腐蚀评价模型
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作者 李云云 李美莹 +3 位作者 王欢 申思 李康 李超 《粘接》 CAS 2023年第6期119-122,共4页
城镇燃气管道作为市政管网的一部分,因其所处环境多样,腐蚀因素复杂,腐蚀评价指标与等级分区存在随机性和模糊性,目前基本采用半定量与定性的方法评价。研究通过大量文献调研统计分析,选取对燃气管道腐蚀影响较大的8个因素作为评价指标... 城镇燃气管道作为市政管网的一部分,因其所处环境多样,腐蚀因素复杂,腐蚀评价指标与等级分区存在随机性和模糊性,目前基本采用半定量与定性的方法评价。研究通过大量文献调研统计分析,选取对燃气管道腐蚀影响较大的8个因素作为评价指标,并按照8级事故体系将事故后果分为由弱到强八个等级。在指标权重计算中通过专家打分,选用优序图法进行权重计算,并用模糊综合评价法建立腐蚀风险评价模型。运用此模型对国内6~8月燃气事故和文献地区埋地燃气管道进行腐蚀风险评价,结果与案例结果吻合,表明此模型在燃气管道风险评价的适用性。 展开更多
关键词 优序图法 三角隶属函数 八级事故等级 风险评价 燃气管道腐蚀
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基于血流向量测量颈动脉血流量的稳定性研究
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作者 刘微丽 吴徐峰 +5 位作者 郑庆斌 孟丽君 冯亚平 姜雪川 李玉呈 袁文杰 《实用临床医药杂志》 CAS 2023年第3期29-34,共6页
目的 探讨基于血流向量测量颈动脉血流量的不同方法及其稳定性。方法 选取健康志愿者15例和40例患者为研究对象,5名重症医学科医师采用三角函数双切面测量法、三角函数单切面测量法、横切固定角度测量法、纵切测量法、最大血流速度近似... 目的 探讨基于血流向量测量颈动脉血流量的不同方法及其稳定性。方法 选取健康志愿者15例和40例患者为研究对象,5名重症医学科医师采用三角函数双切面测量法、三角函数单切面测量法、横切固定角度测量法、纵切测量法、最大血流速度近似法、流速均值近似法和改良环形近似法通过超声检查对颈总动脉血流量进行测量,并对测量结果进行稳定性分析以寻找稳定性较好的血流量的测量方法。结果 三角函数单切面测量法稳定性高于三角函数双切面测量法、横切固定角度测量法、纵切测量法,差异有统计学意义(P<0.05)。最大血流速度近似法与流速均值近似法的稳定性比较,差异无统计学意义(P>0.05)。改良环形近似法与最大血流速度近似法的稳定性比较,差异无统计学意义(P>0.05),但分析结果显示,前者的稳定性优于后者,差异有统计学意义(P<0.05)。结论 三角函数单切面测量法可测得较为稳定的血流速度。颈动脉斑块患者采用改良环形近似法可获得较稳定的血流量,但评估稳定性仍然有待进一步提高。 展开更多
关键词 向量速度 血流量 稳定性 改良环形近似法 颈动脉 三角函数
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三角函数有理式不定积分的探讨
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作者 徐慧 冯军庆 +1 位作者 王亚男 郑芳 《高等数学研究》 2023年第6期12-15,19,共5页
本文把常见三角函数有理式不定积分归纳为三种类型,对于不同类型的积分借助例题给出了详细的计算过程,主要利用的是凑微分法,变量代换和三角函数恒等变形.
关键词 三角函数 不定积分 有理式 凑微分法
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对称正则长波方程的精确行波解 被引量:1
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作者 黄雪 刘小华 +1 位作者 朱引 曾职云 《新乡学院学报》 2023年第6期8-14,19,共8页
利用(G'/G,1/G)展开法导出了对称正则长波方程的双曲函数解、有理函数解和三角函数解,给出了解在具体参数值下的2D和3D效果图以及解的性态,验证了所求的解均满足方程。
关键词 对称正则长波方程 双曲函数解 三角函数解 有理函数解 (G'/G 1/G)展开法
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一道定积分数学竞赛题的解法研究 被引量:1
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作者 徐伟孺 《遵义师范学院学报》 2023年第1期120-121,共2页
第五届全国大学生数学竞赛初赛(非数学类)试题中有一道关于求定积分的计算题,基于定积分的性质,并使用一个反正切函数的恒等式,将该题进行推广和延伸,并归纳了两个结论,给出了所构造新题的简洁解法。
关键词 定积分 反正切函数 换元法 拉格朗日中值定理
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无机紫外非线性光学晶体材料的研究进展
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作者 邹国红 《四川师范大学学报(自然科学版)》 CAS 2023年第2期165-174,F0002,共11页
紫外(UV)非线性光学(NLO)晶体材料作为全固态紫外激光器的核心部件,在当前的科学和技术应用中发挥着至关重要的作用.目前,传统NLO材料的倍频基因类型相对单一,使得UV NLO材料的实际应用从根本上受到限制.因此,为了突破性能壁垒,亟需发... 紫外(UV)非线性光学(NLO)晶体材料作为全固态紫外激光器的核心部件,在当前的科学和技术应用中发挥着至关重要的作用.目前,传统NLO材料的倍频基因类型相对单一,使得UV NLO材料的实际应用从根本上受到限制.因此,为了突破性能壁垒,亟需发展新的合成方法、开发新的功能基团、拓展新的UV NLO材料体系来进一步筛选新型高性能晶体.对目前UV NLO材料的研究进展进行总结,且结合近年来的相关工作详细描述化学取代定向设计合成策略在开发具有新型结构的高性能UV NLO材料中的应用,并对该领域的未来发展进行展望,强调化学取代定向设计合成策略的优势以及大尺寸晶体生长在光电器件实际应用中的重要性. 展开更多
关键词 紫外非线性光学材料 功能基团 硼酸盐 四面体结构 化学取代法
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