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Trigonometric function solutions of Schwarzian Korteweg–de Vries equations 认领 引用
1
作者 Conghan Wang Xingyu Liu Da-jun Zhang 《Communications in Theoretical Physics》 SCIE CAS CSCD 2025年第9期10-15,共6页
In the paper we derive new solutions for the discrete and continuous Schwarzian Korteweg–de Vries(SKd V)equations.These solutions are characterized by trigonometric functions as backgrounds.For the discrete SKd V equ... In the paper we derive new solutions for the discrete and continuous Schwarzian Korteweg–de Vries(SKd V)equations.These solutions are characterized by trigonometric functions as backgrounds.For the discrete SKd V equation,its solutions are derived by using trigonometric function seeds and B?cklund transformation.Solutions for the continuous SKd V equation are obtained by taking continuum limits. 展开更多
关键词 Schwarzian Korteweg-de Vries equation trigonometric function solution continuum limit
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UNIFORM ANALYTIC CONSTRUCTION OF WAVELET ANALYSIS FILTERS BASED ON SINE AND COSINE TRIGONOMETRIC FUNCTIONS 认领 引用 被引量：1
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作者 李建平 唐远炎 +1 位作者 严中洪 张万萍 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第5期569-585,共17页
Based on sine and cosine functions, the compactly supported orthogonal wavelet filter coefficients with arbitrary length are constructed for the first time. When N = 2(k-1) and N = 2k, the unified analytic constructio... Based on sine and cosine functions, the compactly supported orthogonal wavelet filter coefficients with arbitrary length are constructed for the first time. When N = 2(k-1) and N = 2k, the unified analytic constructions of orthogonal wavelet filters are put forward, respectively. The famous Daubechies filter and some other well-known wavelet filters are tested by the proposed novel method which is very useful for wavelet theory research and many application areas such as pattern recognition. 展开更多
关键词 wavelet analysis filter trigonometric functions analytic construction
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A constructive method for approximating trigonometric functions and their integrals 认领 引用
3
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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Fractional Weierstrass Function by Application of Jumarie Fractional Trigonometric Functions and Its Analysis 认领 引用
4
作者 Uttam Ghosh Susmita Sarkar Shantanu Das 《Advances in Pure Mathematics》 2015年第12期717-732,共16页
The classical example of no-where differentiable but everywhere continuous function is Weierstrass function. In this paper we have defined fractional order Weierstrass function in terms of Jumarie fractional trigonome... The classical example of no-where differentiable but everywhere continuous function is Weierstrass function. In this paper we have defined fractional order Weierstrass function in terms of Jumarie fractional trigonometric functions. The H?lder exponent and Box dimension of this new function have been evaluated here. It has been established that the values of H?lder exponent and Box dimension of this fractional order Weierstrass function are the same as in the original Weierstrass function. This new development in generalizing the classical Weierstrass function by use of fractional trigonometric function analysis and fractional derivative of fractional Weierstrass function by Jumarie fractional derivative, establishes that roughness indices are invariant to this generalization. 展开更多
关键词 Holder Exponent Fractional Weierstrass Function Box Dimension Jumarie Fractional Derivative Jumarie Fractional Trigonometric Function
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Path-tracking control based on a dynamic trigonometric function 认领 引用
5
作者 Yunyi Wang Shuo Zhang +3 位作者 Zhongxiang Zhu Zhen Li Yuefeng Du Lizhi Fang 《Information Processing in Agriculture》 EI 2019年第1期1-10,共10页
With the rapid development of the modern vehicle industry,the automated control of new vehicles is in increasing demand.However,traditional course control has been unable to meet the actual needs of such demand.To sol... With the rapid development of the modern vehicle industry,the automated control of new vehicles is in increasing demand.However,traditional course control has been unable to meet the actual needs of such demand.To solve this problem,more precise pathtracking control technologies have attracted increased attention.This paper presents a new algorithm based on the latitude and longitude information,as well as a dynamic trigonometric function,to improve the accuracy of position deviation.First,the algorithm takes the course deviation and adjustment time as the optimization objectives and the given path and speed as the constraints.The controller continuously adjusts the output through a cyclic“adjustment and detection”process.Second,through an integration of the steering,positioning,and speed control systems,an experimental platform of a path-tracking control system based on the National Instruments(NI)myRIO controller and LabVIEW was developed.In addition,path-tracking experiments were carried out along a linear path,while changing lanes,and on a curved path.When comparing and analyzing the experimental results,it can be seen that the average deviation in lateral displacement along the linear and curved paths was 0.32 and0.8 cm,and the standard deviation of the lateral displacement was 2.65 and 2.39 cm,respectively.When changing lanes,the total adjustment time for the vehicle close to the target line to reach stability was about 1.5 s.Finally,the experimental results indicate that the new algorithm achieves good stability and high control accuracy,and can overcome directional and positional errors caused by road interference while driving,meeting the precision requirements of automated vehicle control. 展开更多
关键词 Path-tracking control Trigonometric function NI myRIO controller LabVIEW
REMARKS ON ASYMPTOTIC EXPANSIONS OF COMPOSITIONS WITH THE ELEMENTARY FUNCTIONS 认领 引用
6
作者 LUO Xiao-Yu SHI Yong-Guo JIANG Zhi-Jie 《数学杂志》 2025年第2期131-139,共9页
In this paper,we study asymptotic power series of the composition f(x)=h(g(x)),where g(x)=∑n=0∞bnx-n,bn∈R,and h is a given elementary function.The asymptotic expansions have been obtained for the com... In this paper,we study asymptotic power series of the composition f(x)=h(g(x)),where g(x)=∑n=0∞bnx-n,bn∈R,and h is a given elementary function.The asymptotic expansions have been obtained for the composition with an exponential or logarithmic function.Using the re-cursive method,we present the asymptotic expansions for the composition with seven trigonometric functions,respectively.As an application,the asymptotic expansions of roots of some equations are given.Computational results show that our recursive formula is more efficient than the method of Lagrange's inverse theorem. 展开更多
关键词 asymptotic expansion asymptotic power series trigonometric function composite function
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Quality-guaranteed Dubins Path Planning for USV Based on Mixed-integer Piecewise linear Programming for Addressing the Extended Minimum-time Intercept Problem 认领 引用 被引量：1
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作者 Xing Zhou Kelin Zhu +3 位作者 Shuang Liu Zhaoqing Li Wenxin Zhang Kang Du 《哈尔滨工程大学学报（英文版）》 CSCD 2026年第1期216-227,共12页
During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive... During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive distance)to a moving target as quickly as possible,resulting in the extended minimum-time intercept problem(EMTIP).Existing research has primarily focused on the zero-distance intercept problem,MTIP,establishing the necessary or sufficient conditions for MTIP optimality,and utilizing analytic algorithms,such as root-finding algorithms,to calculate the optimal solutions.However,these approaches depend heavily on the properties of the analytic algorithm,making them inapplicable when problem settings change,such as in the case of a positive effective range or complicated target motions outside uniform rectilinear motion.In this study,an approach employing a high-accuracy and quality-guaranteed mixed-integer piecewise-linear program(QG-PWL)is proposed for the EMTIP.This program can accommodate different effective interception ranges and complicated target motions(variable velocity or complicated trajectories).The high accuracy and quality guarantees of QG-PWL originate from elegant strategies such as piecewise linearization and other developed operation strategies.The approximate error in the intercept path length is proved to be bounded to h2/(4√2),where h is the piecewise length. 展开更多
关键词 Minimum-time intercept problem Dubins vehicle Mixed-integer piecewise-linear program Linearization Approximate error trigonometric function USV
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Derivatives of Inverse Trigonometric Function 认领 引用
8
作者 梁宇学 《中学生数学（高中版）》 2010年第1期F0004-F0004,共1页
关键词 Derivatives of Inverse Trigonometric Function cot
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Derivatives of Inverse Trigonometric Function 认领 引用
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作者 High School Attached CNU Yuxue Liang 《中学生数学（高中版）》 2010年第2期F0004-F0004,共1页
关键词 Derivatives of Inverse Trigonometric Function
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Jacobian Elliptic Function Method and Solitary Wave Solutions for Hybrid Lattice Equation 认领 引用 被引量：1
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作者 WANG Rui-Min DAI Chao-Qing ZHANG Jie-Fang 《Communications in Theoretical Physics》 SCIE CAS 2006年第6期1057-1062,共6页
In this paper, we have successfully extended the Jacobian elliptic function expansion approach to nonlinear differential-difference equations. The Hybrid lattice equation is chosen to illustrate this approach. As a co... In this paper, we have successfully extended the Jacobian elliptic function expansion approach to nonlinear differential-difference equations. The Hybrid lattice equation is chosen to illustrate this approach. As a consequence, twelve families of Jacobian elliptic function solutions with different parameters of the Hybrid lattice equation are obtained. When the modulus m → 1 or O, doubly-periodic solutions degenerate to solitonic solutions and trigonometric function solutions, respectively. 展开更多
关键词 extended Jacobian elliptic function expansion approach hybrid lattice equation Jacobian elliptic function solutions solitonic solutions trigonometric function solutions
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The Maximum Trigonometric Degrees of Quadrature Formulae with Prescribed Nodes 认领 引用
11
作者 Luo Zhong-xuan Yu Ran Meng Zhao-liang 《Communications in Mathematical Research》 CSCD 2014年第4期334-344,共11页
The purpose of this paper is to study the maximum trigonometric degree of the quadrature formula associated with m prescribed nodes and n unknown additional nodes in the interval（-π, π]. We show that for a fixed n,... The purpose of this paper is to study the maximum trigonometric degree of the quadrature formula associated with m prescribed nodes and n unknown additional nodes in the interval（-π, π]. We show that for a fixed n, the quadrature formulae with m and m ＋ 1 prescribed nodes share the same maximum degree if m is odd. We also give necessary and sufficient conditions for all the additional nodes to be real, pairwise distinct and in the interval（-π, π] for even m, which can be obtained constructively. Some numerical examples are given by choosing the prescribed nodes to be the zeros of Chebyshev polynomials of the second kind or randomly for m ≥ 3. 展开更多
关键词 quadrature formula trigonometric function bi-orthogonality truncated complex moment problem
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A New Method for Calculating Inverse Involute Functions with High Precision 认领 引用
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作者 Zhou Ruzhong School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, China 《Journal of Modern Transportation》 1997年第1期70-72,共3页
Two equations are presented for calculating inverse involute functions. Precise values can be obtained easily with an ordinary calculator.
关键词 inverse involute precision trigonometric function
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例析tanA+tanB+tanC=tanAtanBtanC的应用 认领 引用
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作者 杜海洋 《中学生数理化（高一数学）》 2025年第7期22-22,共1页
重要结论:在△ABC中,tanA+tanB+tanC=tanAtanBtanC。
关键词 identity trigonometric functions triangle
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Best m-term One-sided Trigonometric Approximation of Some Function Classes Defined by a Kind of Multipliers 认领 引用 被引量：1
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作者 Ren Suo LI Yong Ping LIU 《Acta Mathematica Sinica,English Series》 SCIE 2010年第5期975-984,共10页
In this paper, we continue studying the so-called non-linear best m-term one-sided approximation problems and obtain the asymptotic estimations of non-linear best m-term one-sided trigonometric approximation under the... In this paper, we continue studying the so-called non-linear best m-term one-sided approximation problems and obtain the asymptotic estimations of non-linear best m-term one-sided trigonometric approximation under the norm Lp （1 ≤ p ≤ ∞） of multiplier function classes and the corresponding m-term Greedy-liked one-sided trigonometric approximation results. 展开更多
关键词 non-linear best m-term approximation one-sided approximation Lp spaces trigonometric function system and Greedy approximation algorithm
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New Exact Solutions of the Integrable Broer-Kaup Equations in (2+ 1)-DimensionalSpaces 认领 引用 被引量：1
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作者 LIDe-Sheng ZHANGHong-Qing 《Communications in Theoretical Physics》 SCIE CAS 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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Non-polynomial Zig-Zag and ESL shear deformation theory to study advanced composites 认领 引用
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作者 J.L.MANTARI I.A.RAMOS J.C.MONGE 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2019年第4期906-920,共15页
The mechanical behavior of advanced composites can be modeled mathematically through unknown variables and Shear Strain Thickness Functions(SSTFs). Such SSTFs can be of polynomial or non-polynomial nature and some par... The mechanical behavior of advanced composites can be modeled mathematically through unknown variables and Shear Strain Thickness Functions(SSTFs). Such SSTFs can be of polynomial or non-polynomial nature and some parameters of non-polynomial SSTFs can be optimized to get optimal results. In this paper, these parameters are called ‘‘r" and ‘‘s" and they are the argument of the trigonometric SSTFs introduced within the Carrera Unified Formulation(CUF). The Equivalent Single Layer(ESL) governing equations are obtained by employing the Principle of Virtual Displacement(PVD) and are solved using Navier method solution. Furthermore, trigonometric expansion with Murakami theory was implemented in order to reproduce the Zig-Zag effects which are important for multilayer structures. Several combinations of optimization parameters are evaluated and selected by different criteria of average error. Results of the present unified trigonometrical theory with CUF bases confirm that it is possible to improve the stress and displacement results through the thickness distribution of models with reduced unknown variables. Since the idea is to find a theory with reduced numbers of unknowns, the present method appears to be an appropriate technique to select a simple model. However these optimization parameters depend on the plate geometry and the order of expansion or unknown variables. So, the topic deserves further research. 展开更多
关键词 Analytical solution Composite materials CUF ESL Plate Trigonometric functions Zig-Zag effects
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Exact Solutions of (2+1)-Dimensional Boiti-Leon-Pempinelle Equation with (G'/G)-Expansion Method 认领 引用 被引量：1
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作者 熊守全 夏铁成 《Communications in Theoretical Physics》 SCIE CAS 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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Traveling Wave Solutions for Generalized Bretherton Equation 认领 引用 被引量：1
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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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A Differential Quadrature Based Approach for Volterra Partial Integro-Differential Equation with a Weakly Singular Kernel 认领 引用 被引量：1
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作者 Siraj-ul-Islam Arshed Ali +1 位作者 Aqib Zafar Iltaf Hussain 《Computer Modeling in Engineering & Sciences》 SCIE EI 2020年第9期915-935,共21页
Differential quadrature method is employed by numerous researchers due to its numerical accuracy and computational efficiency,and is mentioned as potential alternative of conventional numerical methods.In this paper,a... Differential quadrature method is employed by numerous researchers due to its numerical accuracy and computational efficiency,and is mentioned as potential alternative of conventional numerical methods.In this paper,a differential quadrature based numerical scheme is developed for solving volterra partial integro-differential equation of second order having a weakly singular kernel.The scheme uses cubic trigonometric B-spline functions to determine the weighting coefficients in the differential quadrature approximation of the second order spatial derivative.The advantage of this approximation is that it reduces the problem to a first order time dependent integro-differential equation(IDE).The proposed scheme is obtained in the form of an algebraic system by reducing the time dependent IDE through unconditionally stable Euler backward method as time integrator.The scheme is validated using a homogeneous and two nonhomogeneous test problems.Conditioning of the system matrix and numerical convergence of the method are analyzed for spatial and temporal domain discretization parameters.Comparison of results of the present approach with Sinc collocation method and quasi-wavelet method are also made. 展开更多
关键词 Partial integro-differential equation differential quadrature cubic trigonometric B-spline functions weakly singular kernel
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ON GENERALIZED COMPLETE(p,q)-ELLIPTIC INTEGRALS 认领 引用
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作者 Li YIN Barkat Ali BHAYO Nihat Gokhan GOGUS 《Acta Mathematica Scientia》 SCIE CSCD 2021年第2期475-486,共12页
In this paper,we study the generalized complete(p,q)-elliptic integrals of the first and second kind as an application of generalized trigonometric functions with two parameters,and establish the monotonicity,generali... In this paper,we study the generalized complete(p,q)-elliptic integrals of the first and second kind as an application of generalized trigonometric functions with two parameters,and establish the monotonicity,generalized convexity and concavity of these functions.In particular,some Turán type inequalities are given.Finally,we also show some new series representations of these functions by applying Alzer and Richard's methods. 展开更多
关键词 Generalized elliptic integrals generalized trigonometric functions Turán type inequalities
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