WAVELET CONSTRUCTION BASED ON DATA FITTING AND BEARING FAULT DIAGNOSIS by LI HaiYing

“…Constructing the optimal wavelet function is the key to realize lifting Wavelet de-noising.After determining the optimal decomposition level and effective threshold, it tries to introduce data fitting methodin the process of interpolation subdivision. By selecting different basis function, sample points and the dimensions of the basis function, the new wavelet function is constructed with different smoothness, shock and disappear moment, it introducesthe similarity coefficient to analyze the constructed wavelet function and select the optimum wavelet function.It combines with redundant lifting wavelettransform to improve the predict operators and update operators. …”
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On the series solutions of integral equations in scattering by Triki, Faouzi, Karamehmedović, Mirza

“…Furthermore we propose an interpolation method that allows the use of the Neumann series in all cases. …”
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On anisotropic Triebel-Lizorkin type spaces, with applications to the study of pseudo-differential operators by Lasse Borup, Morten Nielsen

“…An explicit atomic decomposition of the Triebel-Lizorkin type spaces is provided, and their interpolation properties are studied. As the main application, we consider Hörmander type classes of pseudo-differential operators adapted to the anisotropy and boundedness of such operators between corresponding Triebel-Lizorkin type spaces is proved.…”
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Modeling and Prediction of Momentum Wheel Speed Data by Jichao Li, Xiaxia Wang, Chaobo Chen, Song Gao

“…To solve the problems of data loss and unequal interval of momentum wheel (MW) speed during a satellite stable operation, this paper presents a multidimensional AR model. A Lagrange interpolation method is used to convert measurements to equal interval data, and the FFT algorithm is adopted to calculate the period of MW speed variation. …”
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Gamma Splines and Wavelets by Hannu Olkkonen, Juuso T. Olkkonen

“…We study the properties of the discrete gamma splines in signal interpolation and approximation. We prove that the gamma splines obey the two-scale equation based on the polyphase decomposition. to introduce the shift invariant gamma spline wavelet transform for tree structured subscale analysis of asymmetric signal waveforms and for systems with asymmetric impulse response. …”
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Dynamic Condensation-Based Reduction Method for Precise Broadband Frequency Analysis by Geomji Choi, Juhwan Lee, Seongmin Chang

“…This method converts the transformation matrix into a frequency-independent form, which allows for a simple interpolation of the reduction model by updating the differences between frequencies. …”
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Three-Dimensional Path Planning of Constant Thrust Unmanned Aerial Vehicle Based on Artificial Fluid Method by Yongqiang Qi, Shuai Li, Yi Ke

“…In particular, this paper addresses a novel algorithm of constant thrust fitting which is proposed through the impulse compensation, and then the constant thrust switching control scheme based on the isochronous interpolation method is given. It is proved that the planned path can avoid all obstacles smoothly and swiftly and reach the destination eventually. …”
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Adaptive weighted progressive iterative approximation based on coordinate decomposition. by Yushi Liu, Yan Wang, Chengzhi Liu

“…During the iterative process of the progressive iterative approximation, it is necessary to calculate the difference between the current interpolation curve and the corresponding data points, known as the adjustment vector. …”
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AMIDE: A Free Software Tool for Multimodality Medical Image Analysis by Andreas Markus Loening, Sanjiv Sam Gambhir

“…Data sets can be freely shifted, rotated, viewed, and analyzed with the program automatically handling interpolation as needed from the original data. Validation has been performed by comparing the output of AMIDE with that of several existing software packages. …”
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Research of the Actual Path for Hybrid Input Five-bar Mechanism by Lin Bin, Yu Haiyan, Zhang Wenjun

“…While the hybrid input five-bar mechanism in the process of actual movement,constant velocity motor will generate speed fluctuation,as a result terminal actuator will come out path error.An actual path synthesis method in consideration of hybrid input mechanism dynamics is proposed in order to generate much more accurate path.By means of five times spline functions interpolation method making the ideal path of servo motor second-order continuous,the dynamics model of hybrid input mechanism which in consideration of motor dynamics is given,the calculation of the dynamics model is described,with the input of the servo motor as design variables to reduce the path error of end executor.Example simulation certifies that the path of the proposed method can generate more accurate path.…”
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Distribution, Risk Assessment, and Quantitative Source Analysis of Soil Heavy Metals in a Typical Agricultural City of East-Central China by Wenyue Du, Peng Zeng, Shi Yu, Fan Liu, Ping’an Sun

“…Among different land use types, the carcinogenic and non-carcinogenic risks of soil heavy metals in orchards are the highest. (3) Combining the kriging interpolation method and the PCA and PMF models, it can be determined that there are two main sources of heavy metals in the study area: one is natural and the other is anthropogenic. …”
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On the implementation of a global optimization method for mixed-variable problems by Nannicini, Giacomo

“…We propose several modifications aimed at generalizing and improving these two algorithms: (i) the use of an extended space to represent categorical variables in unary encoding; (ii) a refinement phase to locally improve a candidate solution; (iii) interpolation models without the unisolvence condition, to both help deal with categorical variables, and initiate the optimization before a uniquely determined model is possible; (iv) a master-worker framework to allow asynchronous objective function evaluations in parallel. …”
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Adaptive Hierarchical Collocation Method for Solving Fractional Population Diffusion Model by Linqiang Yang, Yafei Liu, Hongmei Ma, Xue Liu, Shuli Mei

“…This function, an improvement over previous constructs, mitigates the need for iterative computation of parameters and boasts advantages like interpolation, symmetry, and compact support. The method’s extension to other time-fractional partial differential equations (PDEs) is also possible. …”
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A Comparative Study on Solving Optimization Problems With Exponentially Fewer Qubits by David Winderl, Nicola Franco, Jeanette Miriam Lorenz

“…In addition, we propose a method to embed the linear interpolation of the MaxCut problem on a quantum device. …”
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Near-Field/Far-Field Transformation with Helicoidal Scanning from Irregularly Spaced Data by Francesco D'Agostino, Flaminio Ferrara, Claudio Gennarelli, Rocco Guerriero, Massimo Migliozzi

“…Once these helicoidal data have been recovered, those required by a classical cylindrical near-field/far-field transformation are efficiently determined by using an optimal sampling interpolation algorithm. Some numerical tests assessing the effectiveness of the proposed approach and its stability with respect to random errors affecting the near-field data are shown.…”
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Optimal Trajectory Planning for Glass-Handing Robot Based on Execution Time Acceleration and Jerk by Honggang Duan, Rongmin Zhang, Fei Yu, Jun Gao, Yuan Chen

“…A three-dimensional kinematics model of the glass-handing robot is then established and nonuniform fifth-order B-splines are used to interpolate its path points. The acceleration and jerk are expressed as functions of time through mathematical simulation. …”
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Universality of the close packing properties and markers of isotropic-to-tetratic crossover in quasi-one-dimensional superdisk fluid by Sakineh Mizani, Martin Oettel, Péter Gurin, Szabolcs Varga

“…We study equilibrium states and ordering regimes of a quasi-one-dimensional system of hard superdisks (anisotropic particles interpolating between disks and squares) where the centers of the particles are constrained to move on a line. …”
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Numerical Algorithms for Finding Zeros of Nonlinear Equations and Their Dynamical Aspects by Amir Naseem, M. A. Rehman, Thabet Abdeljawad

“…In this paper, we developed two new numerical algorithms for finding zeros of nonlinear equations in one dimension and one of them is second derivative free which has been removed using the interpolation technique. We derive these algorithms with the help of Taylor’s series expansion and Golbabai and Javidi’s method. …”
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Antenna Array Design in MIMO Radar Using NSK Polynomial Factorization Algorithm by Shuainan Gu, Ke Li, Xiukun Ren, Na-e Zheng

“…Then, undermined high-order factors are confirmed with Newton interpolation and certain high-order factors should be searched for within the undermined ones. …”
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RESEARCH ON YIELD STRENGTH PROBLEM OF HERTZ CONTACT STRESS by YANG XianQi, LIU ShengRong, CAO JianHua

“…Then,a elliptical rate is calculated directly by contacting curvature function,no longer need to process the look-up table and interpolation calculation that would be a kind of trouble and not accurate. …”
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