35,276 results on '"Fourier series"'
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2. Modeling of thermal diffusion process in the presence of volumetric heat release.
- Author
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Kostikov, Yu. A. and Romanenkov, A. M.
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LINEAR differential equations , *BOUNDARY value problems , *INITIAL value problems , *HEAT release rates , *LINEAR systems , *ENTHALPY , *PARABOLIC differential equations , *FOURIER series - Abstract
The paper considers a model problem of the thermal diffusion process in a silicon wafer. The mathematical model of this process is an initial boundary value problem for a system of linear partial differential equations of parabolic type. In this system, one equation describes the process of heat propagation in silicon in the presence of internal heat sources, and the other describes the process of diffusion of impurities in it. Moreover, these equations are related in the same way that the diffusion coefficient of an impurity depends on temperature. A special form of the volumetric heat release function was considered, which made it possible in this particular case to write down an explicit solution in the form of a Fourier series. To find an approximate solution to the boundary value problem, an implicit difference scheme and the classical sweep method are used. A computational experiment is presented. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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3. System gramians computation for the one and two-dimensional heat equations.
- Author
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Perev, Kamen
- Subjects
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HEAT equation , *DISTRIBUTED parameter systems , *DIFFERENTIAL forms , *DIFFERENTIAL equations , *CARLEMAN theorem , *FOURIER series , *SEPARATION of variables - Abstract
The paper considers the problem of observability and controllability gramians computation for one-dimensional and two-dimensional heat equations. The heat equation is a parabolic differential equation representing the process of heat flow. In the one-dimensional case, the heat equation models the physical process of a heat flow in a rod. In the two-dimensional case, this equation shows how the heat flow changes in a plate. The solutions of the heat equations are derived by applying the time-space separation principle and by using the Fourier series approximation. The zero input solution participates in computing the observability gramian of the distributed parameter system. The solution of the nonhomogeneous differential equation under zero initial conditions is used for computing the controllability gramian. Both solutions are based on the state space formulation of the infinite dimensional systems into an abstract differential form. The gramians computation procedure uses the Riesz-spectral framework of trajectory representation. The obtained system gramians are derived in explicit form, which allows their simple form of computation. [ABSTRACT FROM AUTHOR]
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- 2024
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4. Poverty modelling with spline truncated, Fourier series, and mixed estimator geographically weighted nonparametric regression.
- Author
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Laome, Lilis, Budiantara, I. Nyoman, and Ratnasari, Vita
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FOURIER series , *INDEPENDENT variables , *REGRESSION analysis , *POVERTY , *PROBLEM solving , *SPLINE theory , *SPLINES - Abstract
Multiple linear regressions using spatial data are developed as Geographically Weighted Regression (GWR). It is used to solve the problem of regression models that do not meet the assumptions of homogeneity caused by the nature of each location. Consequently, the global model is less appropriate for usage. In addition, the regression function for each predictor variable is considered different, so it is possible to use a mixed estimator. The goal of this study is to model poverty data with Geographically Weighted Nonparametric Regression (GWNR). The study focuses on modelling poverty data with three nonparametric regression models on the spline GWNR, Fourier GWNR and Mixed GWNR. The results showed that the mixed GWNR was better than the others based on Mean Square Error (MSE) and R-Square (R2) values. [ABSTRACT FROM AUTHOR]
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- 2024
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5. Estimation of Fourier series regression curve on the open unemployment rate data in Indonesia in multivariable nonparametric regression.
- Author
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Nufus, Mitha Rabiyatul, Budiantara, I. Nyoman, and Ratnasari, Vita
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FOURIER series , *NONPARAMETRIC estimation , *UNEMPLOYMENT statistics , *INDEPENDENT variables , *REGRESSION analysis , *STATISTICS - Abstract
The statistical analysis method used to determine the effect between two or more variables is called regression analysis. The pattern of relationships between variables in regression analysis does not always have a parametric pattern. There are some cases where one or more predictor variables do not have a pattern that is called nonparametric and even has a combined pattern of parametric and nonparametric, called semiparametric. Nonparametric regression is a statistical method that is used to identify and modelling the pattern of the relationship between predictor variables and response variables whose function is unknown. One method that is widely used to estimate the regression curve using a nonparametric approach is the Fourier series. The advantage of the Fourier series is this method is quite good for describing curves whose data patterns are repeated. This study will examine the estimation of the nonparametric regression curve of the Fourier series and then modelling the Open Unemployment Rate data in Indonesia with the best model criteria based on the maximum R2 value and the minimum Generalized Cross Validation (GCV) and Mean Square Error (MSE). The results of this research shown that with the Fourier series, the minimum GCV is 2.66 with an oscillation number of 3. Then the model goodness value is 91.73% and the MSE model is 2.410. [ABSTRACT FROM AUTHOR]
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- 2024
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6. Complex network based Fourier analysis for signal processing.
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Vijesh, Vijayan, Kumar, Krishan Nair Satheesh, Swapna, Mohanachandran Nair Sindhu, and Sankararaman, Sankaranarayana Iyer
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SIGNAL processing , *ELECTRONIC circuit design , *VIDEO signals , *ELECTRICAL engineering , *SQUARE waves , *FOURIER analysis , *FOURIER series - Abstract
The design and construction of electronic circuits need the creation of innovative methods for analysing signals for increased performance, which led to the birth of the discipline of signal processing. Signal processing is a branch of electronics and electrical engineering that focuses on the creation and analysis of many types of signals, including electrical, electronic, sound, picture, and video signals. Both the characteristics of the signal and the outcome one wants to achieve decide the technique to be used. The present work is a novel attempt of employing complex network for signal analysis. The analysis of the Fourier component of a square wave reveals the untapped potential of complex network and graph properties. Investigation is also done into the changes that occur when the Fourier series' terms are added and how they affect the graph's features. [ABSTRACT FROM AUTHOR]
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- 2024
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7. Detection of defective FinFET logic ICs by using FFTs.
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Widianto, W., Lis, Robert, Sofiani, Inda Rusdia, and Cynthia, La Febry Andira Rose
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SIMULATION Program with Integrated Circuit Emphasis , *COMPLEMENTARY metal oxide semiconductors , *FIELD-effect transistors , *FAST Fourier transforms , *FOURIER series , *METAL foams - Abstract
A FinFET (Fin Field Effect Transistor) is a non-planar transistor. It has a faster-switching speed, lower power consumption, and static leakage current than CMOSs (Complementary Metal Oxide Semiconductors), which are planar transistors. In the FinFET logic ICs (Integrated Circuits) fabrication process, open defects may occur at interconnects between gates inside them. Open metals may cause defects. Since the FinFET ICs may be operated in high-speed time, the defects are more difficult to analyze in time domain signals. There is a method of FFT (Fast Fourier Transform) computing signals converted from the time domain signals into frequency domain signals. Then, the derived frequency signals will be expressed into the function of the Fourier series. In this paper, the FFT analysis is proposed to detect the defects inside the ICs. The logic ICs of Buffer, AND, and OR are designed by a SPICE (Simulation Program with Integrated Circuit Emphasis) netlist library distributed by Nexperia Co. Ltd. Then, the defects are inserted inside the designed ICs and simulated using LTspice created by Analog Devices Inc. Simulation results show that magnitude signals of defective logic ICs in the Fourier series will decrease linearly with increasing sizes of the defects. [ABSTRACT FROM AUTHOR]
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- 2024
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8. Stationary non-axisymmetric deformation of a three-layer viscoelastic cylindrical shell under normal loading.
- Author
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Safarov, I. I., Teshaev, M. Kh., Boltaev, Z. I., Ruziev, T. R., and Jalolov, F. B.
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CYLINDRICAL shells , *FOURIER integrals , *FOURIER series , *LIVE loads , *MECHANICAL engineering , *STRUCTURAL shells - Abstract
Circular cylindrical shells, as structural elements, have found wide application in various fields of mechanical engineering. The aim of this work is to study the action of a non-axisymmetric moving wave of normal pressure on a cylindrical shell interacting with an ideal compressible fluid. The problem of stationary non-axisymmetric deformation of a three-layer viscoelastic cylindrical shell under normal loading is considered. The relation between the stresses and strains satisfies the hereditary Boltzmann-Volterra relation. The response of an infinitely long three-layer cylindrical shell to the action of a non-axisymmetric normal load moving along the axis with a constant to resonant velocity is investigated in a refined formulation. The solution methods are based on the combined application of the Fourier integral transformation along the grid coordinate and the decomposition of all the given and unknown quantities into a Fourier series along the angular coordinate. An efficient algorithm for joint computation of integrals and Fourier series has been developed and implemented. For dissipative inhomogeneous mechanical systems the nonmonotonicity of the intensity of dissipation of energy of the mechanical system as a whole was found. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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9. Wind speed forecasting with ARIMA fourier time series model.
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Nor, Siti Rohani Mohd, Salleh, Nurul Amiera, Norrulashikin, Siti Mariam, Kamarudin, Adina Najwa, and Khaliludin, Nur Idayu Ah
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WIND speed , *TIME series analysis , *BOX-Jenkins forecasting , *WIND forecasting , *FOURIER series , *RENEWABLE energy sources - Abstract
Wind is one of the most important sustainable energy sources because it uses the kinetic energy provided by moving air to generate electrical renewable energy. To generate the electrical energy, the wind turbine is used to collect the wind's kinetic energy. To generate more wind power, the wind turbine needs to be located at the areas which have strong wind speed and air density. Hence, realizing the significant of wind speed, the study of forecasting wind speed needs to be done to determine the best location for wind turbine and what early risk management plan can be created for the convenience of power grid dispatcher. In this study, the Autoregressive Integrated Moving Average (ARIMA) Fourier time series model was used to forecast the wind speed at Senai station from the year 1985 to 2000. In the analysis, ARIMA Fourier model was compared with ARIMA model in terms of in-sample and out-sample measurement errors. The best fitted model will have the lowest measurement errors of Mean Absolute Percentage Error (MAPE) and Root Mean Square Absolute Error (RMSE). The results showed that ARIMA Fourier model outperformed the ARIMA model. Thus, ARIMA Fourier model is selected as the best forecasting model as compared to ARIMA for the management plan of wind turbine's site. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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10. The approximation of the solution of heat conduction problem in circular plate with concentrated initial heat.
- Author
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Akhmedov, Abdulkasim, Salleh, Mohd Zuki, and Rakhimov, Abdumalik
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NUMERICAL solutions to heat equation , *HEAT conduction , *HEAT equation , *FOURIER series - Abstract
The approximation of the solution of the heat equation by using the spectral decompositions of the distributions on circular region where initially heat source concentrated at a point is studied. A solution of the problem represented as the Fourier Bessel series that will be understood in terms of distributions. Regularized solutions for different values of the order of Riesz means at a singular point are analysed. The numerical approximation of the solution of heat equations on the circular plate with the singular initial heat source is carried out with the help of MATLAB software. The optimization of the regularization of the series solutions at a non-singular point of the plates at initial time and critical index is established, which guaranteed to achieve the good convergence of the Riesz means at the index exceeding a critical point. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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11. Convergence of matrix transform means with respect to the Walsh–Kaczmarz system.
- Author
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Blahota, István and Nagy, Dóra
- Abstract
In this paper the Walsh system will be considered in the Kaczmarz rearrangement. We estimate the difference between matrix transform means of Walsh–Kaczmarz–Fourier series and the corresponding function in norm, and the upper estimation is given by the modulus of continuity of the function. We also prove norm convergence with similar conditions. [ABSTRACT FROM AUTHOR]
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- 2024
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12. Maximal Polarization for Periodic Configurations on the Real Line.
- Author
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Faulhuber, Markus and Steinerberger, Stefan
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FOURIER series , *PROBLEM solving - Abstract
We prove that among all 1-periodic configurations |$\Gamma $| of points on the real line |$\mathbb{R}$| the quantities |$\min _{x \in \mathbb{R}} \sum _{\gamma \in \Gamma } e^{- \pi \alpha (x - \gamma)^{2}}$| and |$\max _{x \in \mathbb{R}} \sum _{\gamma \in \Gamma } e^{- \pi \alpha (x - \gamma)^{2}}$| are maximized and minimized, respectively, if and only if the points are equispaced and whenever the number of points |$n$| per period is sufficiently large (depending on |$\alpha $|). This solves the polarization problem for periodic configurations with a Gaussian weight on |$\mathbb{R}$| for large |$n$|. The first result is shown using Fourier series. The second result follows from the work of Cohn and Kumar on universal optimality and holds for all |$n$| (independent of |$\alpha $|). [ABSTRACT FROM AUTHOR]
- Published
- 2024
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13. Nonlinear stability analysis of embedded restrained nanobeams using the Stokes' transformation.
- Author
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Uzun, Büşra, Civalek, Ömer, and Yaylı, M. Özgür
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STRAINS & stresses (Mechanics) , *EULER-Bernoulli beam theory , *ELASTIC foundations , *FOURIER series - Abstract
The geometrically nonlinear stability analysis of restrained nanobeams under an elastic medium is considered in the presented manuscript. The investigation is based on the nonlocal strain gradient elasticity theory, Euler-Bernoulli beam theory and geometrical nonlinearity which is a significant change in geometry. To the best of the authors' knowledge, the nonlinear stability response of a nanobeam with elastic boundary conditions and on an elastic foundation has not been presented before via the theory of nonlocal strain gradient. The aim of this paper is to fill this gap in the literature by offering a method that can give a solution under general elastic boundary conditions. Using a Fourier sine series, a Fourier coefficient suitable for constructing an eigenvalue problem is computed. The constructed problem has been treated in the transformed region with the help of the Stokes' transform, then the stability analysis is executed for arbitrary boundary conditions (rigid or restrained) based on the nonlocal strain gradient elasticity. The influences of various nonlinear parameters, deformable boundary conditions, small-scale parameters and elastic foundation parameters on the stability of the constrained nanobeam are studied. It is observed that the investigated variables produce significant changes in buckling loads. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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14. Simplified method for evaluating tunnel response induced by a new tunnel excavation underneath.
- Author
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Feng, Guohui, Xu, Changjie, Ding, Zhi, Liang, Luju, Li, Yujie, and Chi, Minliang
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TUNNELS , *TUNNEL design & construction , *EXCAVATION , *FOURIER series , *QUANTUM tunneling - Abstract
To estimate the tunnel response induced by a new tunnel excavation underneath, theoretical solutions are proposed in this study. The overlying tunnel is idealized as an infinite Timoshenko beam resting on the Kerr foundation model, then the vertical force balance equation is established. The unloading stress can be expressed as Fourier cosine series and a theoretical solution can be derived. The effectiveness of the proposed method is verified by a centrifuge test and an actual field measurement, which are extracted from previous investigations. Calculation results from the proposed method show good accord to centrifuge test results and field‐measured data. Meantime the predictions given by the proposed method are more accurate to estimate tunnel response compared with the previous method. Parametric analysis indicates that the volume loss ratio and the vertical clearance between two tunnels, are both significantly alleviate the tunnel response, but the effect of tunnel shear stiffness is slight. The theoretical solutions can be adopted to predict the overlying tunnel response induced by tunneling underneath in real projects. [ABSTRACT FROM AUTHOR]
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- 2024
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15. Neural network-based hardware-in-the-loop implementation of fourier series parametrized control profiles for re-entry vehicles.
- Author
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Mishra, Deepak and Sushnigdha, Gangireddy
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FOURIER series , *HYPERSONIC planes , *ARTIFICIAL neural networks , *ATMOSPHERIC density , *QUADRATIC programming - Abstract
This paper introduces an innovative approach for generating re-entry trajectories for a reusable winged spacecraft. This approach utilizes Fourier series parametrized control profiles. The Fourier coefficients are derived through a combination of the Improved Search Space Reduction (ISSR) technique and Sequential Quadratic Programming (SQP) optimization methods, which effectively limit the maximum heat rate experienced by the spacecraft. These re-entry trajectories and control profiles are then used to train artificial neural networks, enabling the controller to provide optimal control inputs based on the spacecraft's current altitude and velocity. To validate this methodology, Hardware-in-loop (HIL) simulations are conducted, integrating the designed neural network-based controller with a Texas Instruments TI Delfino TMSF28335 controller and a real-time simulator, the OPAL-RT OP4510. The results of the HIL simulation demonstrate that the generated re-entry trajectory accurately adheres to heat rate and terminal constraints. Additionally, the Fourier series parametrization of control profiles is applied to a high lift-to-drag ratio CAV-H vehicle, showcasing the method's versatility. Furthermore, resilience of proposed method to uncertainties in aerodynamic coefficients and atmospheric density is also demonstrated. The results show that the proposed method is generic and exhibits robustness to uncertainties. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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16. Implementation of Practical Algorithms in the Inverse Problem with Unknown Boundary Conditions.
- Author
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Leu, Jin-Sheng
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LEAST squares , *HEAT conduction , *HEAT flux , *FOURIER series , *NUMERICAL analysis , *INVERSE problems - Abstract
This work attempts to propose a practical methodology for the one-dimensional heat conduction problems with unknown boundary conditions of the first kind at both ends. The methodology can be effectively applied when the remote boundary condition is inaccessible or internal temperature is required, such as a cutting process with cooling lubricant, and ablative thermal protection system. The proposed methodology utilizes the shifting function method in conjunction with the least squares error method to transform the inverse heat conduction problem into an approximate "well-posed" problem. Consequently, the temperature and the heat flux distributions over the entire time and space domains are determined by using half-range Fourier cosine series solutions. Experimental examples of spray cooling problems are provided to illustrate the advantages of the proposed methodology, including fast convergence of the temperature function, fewer discrete measured times in numerical analysis, and regardless of two interior temperature probes positions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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17. The Modeling Method for Vibration Characteristics Analysis of Composite-Laminated Rotationally Stiffened Plate.
- Author
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Zhang, Hong, Ding, Yiqun, He, Lin, Shuai, Changgeng, and Jiang, Chao
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SHEAR (Mechanics) , *RAYLEIGH-Ritz method , *ENERGY function , *STRUCTURAL optimization , *NOISE control , *RAYLEIGH model , *HILBERT-Huang transform , *FOURIER series - Abstract
The composite-laminated rotationally stiffened plate is widely applied in aviation, aerospace, ship, machinery, and other fields. For structural design and optimization, to investigate the vibration characteristics is important. In this paper, a modeling method of composite-laminated rotationally plate is established. The first-order shear deformation theory (FSDT) and the modified Fourier series are applied to construct the admissible displacement function of the stiffened plate-coupled systems. On this basis, the energy function of composite-laminated rotationally stiffened plate is established. Combined with the artificial virtual spring technology, the proposed theory could be used to analyze the vibration characteristics of composite-stiffened plate-coupled systems with various classical boundary conditions or arbitrary elastic boundary conditions. The Rayleigh–Ritz method is used to solve the energy function. Thus, the vibration characteristics of the composite-laminated rotationally stiffened plate are obtained and analyzed. The correctness of the theoretical analysis model was verified through modal experiments. On this basis, the effect of some important parameters on the vibration characteristics of stiffened plate structures is studied, such as the number, thickness, and width of the laminated stiffener, varying structural parameters, and different boundary conditions. This study can provide the theoretical basis for the vibration and noise reduction of such structures. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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18. Estimation of Multiresponse Multipredictor Nonparametric Regression Model Using Mixed Estimator.
- Author
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Chamidah, Nur, Lestari, Budi, Budiantara, I Nyoman, and Aydin, Dursun
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NONPARAMETRIC estimation , *REGRESSION analysis , *FOURIER series , *INDEPENDENT variables , *SPLINES , *HILBERT space , *SYMMETRIC matrices - Abstract
In data analysis using a nonparametric regression approach, we are often faced with the problem of analyzing a set of data that has mixed patterns, namely, some of the data have a certain pattern and the rest of the data have a different pattern. To handle this kind of datum, we propose the use of a mixed estimator. In this study, we theoretically discuss a developed estimation method for a nonparametric regression model with two or more response variables and predictor variables, and there is a correlation between the response variables using a mixed estimator. The model is called the multiresponse multipredictor nonparametric regression (MMNR) model. The mixed estimator used for estimating the MMNR model is a mixed estimator of smoothing spline and Fourier series that is suitable for analyzing data with patterns that partly change at certain subintervals, and some others that follow a recurring pattern in a certain trend. Since in the MMNR model there is a correlation between responses, a symmetric weight matrix is involved in the estimation process of the MMNR model. To estimate the MMNR model, we apply the reproducing kernel Hilbert space (RKHS) method to penalized weighted least square (PWLS) optimization for estimating the regression function of the MMNR model, which consists of a smoothing spline component and a Fourier series component. A simulation study to show the performance of proposed method is also given. The obtained results are estimations of the smoothing spline component, Fourier series component, MMNR model, weight matrix, and consistency of estimated regression function. In conclusion, the estimation of the MMNR model using the mixed estimator is a combination of smoothing spline component and Fourier series component estimators. It depends on smoothing and oscillation parameters, and it has linear in observation and consistent properties. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
19. A hybrid spectral-spatial formulation for the calculation of the transient eddy-current response.
- Author
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Skarlatos, Anastasios and Reboud, Chritophe
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ROTATIONAL symmetry , *FOURIER series , *SYMMETRY - Abstract
A new approach for the solution of transient eddy-current problems involving pieces with one direction of symmetry is presented. The approach is applicable to pieces with translational or rotational symmetry. A Fourier series decomposition of the solution is introduced in the direction of symmetry, which converts the original 3D numerical problem into a series of independent 2D problems. The decomposition has significant benefits in terms of computational time and numerical noise reduction, and is inherently parallelisable. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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20. Notes on the Overconvergence of Fourier Series and Hadamard–Ostrowski Gaps.
- Author
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Stoenchev, Miroslav, Todorov, Venelin, and Georgiev, Slavi
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FOURIER series , *ORTHOGONAL polynomials , *POWER series , *CIRCLE - Abstract
This paper examines the relationship between the overconvergence of Fourier series and the existence of Hadamard–Ostrowski gaps. Ostrowski's result on the overconvergence of power series serves as a motivating factor for obtaining a natural generalization: the overconvergence of Fourier series. The connection between Hadamard–Ostrowski gaps and the overconvergence of Fourier series is clarified by applying the Hadamard three-circle theorem and the theory of orthogonal polynomials. Our main result is obtained by applying the Hadamard three-circle theorem. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
21. Spectral projection and linear regression approaches for stochastic flexural and vibration analysis of laminated composite beams.
- Author
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Bui, Xuan-Bach, Nguyen, Phong T. T., and Nguyen, Trung-Kien
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LAMINATED composite beams , *COMPOSITE construction , *HAMILTON'S principle function , *MONTE Carlo method , *POLYNOMIAL chaos , *FOURIER series , *VIBRATION tests , *CONCRETE fatigue - Abstract
This paper presents a novel approach for assessing the uncertainty in vibration and static responses of laminated composite beams resulting from uncertainty in material properties and distributed loads. The proposed method utilizes surrogate models developed using polynomial chaos expansion (PCE) based on a relatively small sample size. These training samples are computed using a high-order shear beam model in which the governing equations are derived using Hamilton's principle, and solved by Ritz's approach using a trigonometric series approximation. The proposed PCE model's coefficients are estimated using the spectral projection and linear regression techniques. The first four statistical moments and probability distributions of the mid-span displacement and the fundamental frequency of laminated composite beams are predicted. Global sensitivity analysis is also conducted to assess how material property variation and stochastic loads affect the beam's deflection and the fundamental frequency. The accuracy and efficiency of the proposed PCE models are compared with those from Monte Carlo simulation (MCS). A remarkable reduction in the computational cost of PCE models compared to MCS is observed without compromising the predictions' accuracy. As most real-world systems are subjected to multiple sources of uncertainty, this study provides a state-of-the-art method to quantify such uncertain parameters more efficiently and allow for a better reliability assessment in composite beam design. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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22. Inverse coefficient problem for a time‐fractional wave equation with initial‐boundary and integral type overdetermination conditions.
- Author
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Durdiev, D. K. and Turdiev, H. H.
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WAVE equation , *INTEGRAL equations , *VOLTERRA equations , *BOUNDARY value problems , *INITIAL value problems , *SEPARATION of variables , *INVERSE problems - Abstract
This paper considers the inverse problem of determining the time‐dependent coefficient in the time‐fractional diffusion‐wave equation. In this case, an initial boundary value problem was set for the fractional diffusion‐wave equation, and an additional condition was given for the inverse problem of determining the coefficient from this equation. First of all, it was considered the initial boundary value problem. By the Fourier method, this problem is reduced to equivalent integral equations. Then, using the Mittag‐Leffler function and the generalized singular Gronwall inequality, we get a priori estimate for solution via unknown coefficient which we will need to study of the inverse problem. The inverse problem is reduced to the equivalent integral of equation of Volterra type. The principle of contracted mapping is used to solve this equation. Local existence and global uniqueness results are proved. The stability estimate is also obtained. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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23. Approximation by double matrix means of bivariate functions belonging to weighted Lipschitz and Zygmund classes.
- Author
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Devaiya, Sachin and Srivastava, Shailesh Kumar
- Subjects
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FOURIER series , *PARTIAL sums (Series) , *CONTINUOUS functions , *MATRICES (Mathematics) - Abstract
This study focuses on the rate of uniform approximation for continuous functions g(x,y),2π$$ g\left(x,y\right),2\pi $$‐periodic in each variable, using double matrix means of the rectangular partial sums of double Fourier series. The importance of the weighted integral modulus of symmetric smoothness lies in its ability to capture the local behavior of a function. So we obtain the results in terms of the weighted integral modulus of symmetric smoothness. In addition, we introduce the concept of the weighted Lipschitz and Zygmund classes as an extension of the existing Lipschitz classes Lip(α,β)$$ Lip\left(\alpha, \beta \right) $$ and Lip(α,β;p)$$ Lip\left(\alpha, \beta; p\right) $$ and Zygmund classes Z(α,β)$$ Z\left(\alpha, \beta \right) $$ and Z(α,β;p)$$ Z\left(\alpha, \beta; p\right) $$, respectively. These weighted classes allow us a more detailed analysis of the approximation rates of functions by assigning the weights to different regions of the domain of function. Further, we prove two theorems about the degree (error) of approximation of functions belonging to these classes using double matrix means. We also discuss some corollaries from our results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
24. Propagation characteristics of lamb waves in a functionally graded material plate with periodic gratings.
- Author
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Gu, Chunlong, Ma, Liansheng, Ou, Zhiying, and Lei, Fangming
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LAMB waves , *BAND gaps , *FUNCTIONALLY gradient materials , *ELASTIC waves , *FOURIER series , *OPTICAL gratings , *DIFFERENTIAL equations - Abstract
The propagation characteristics of Lamb waves in a functionally graded material (FGM) plate with periodic gratings have been studied. The power series technique is employed to solve the governing differential equations with variable coefficients. In the propagation direction, the displacements of Lamb waves are expanded in the Fourier series due to the periodicity of the structure. The convergences of the power series and Fourier series are proved and the method presented in the article is verified by the finite element method (FEM). The band gaps are obtained by the couplings between the different modes of Lamb waves induced by FGM. The effects of the structural parameters (such as the periodicity, mass, and length of the gratings) and gradient coefficient on band gaps are investigated. Numerical results show that the band gaps shift up as the gradient coefficient increases and the second band gap (SBG) is closed when the gradient coefficient is large enough. The conclusions are of practical significance for designing elastic wave filters with high-performance. [ABSTRACT FROM AUTHOR]
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- 2024
- Full Text
- View/download PDF
25. On the soliton structures to the space-time fractional generalized reaction Duffing model and its applications.
- Author
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Tariq, Kalim U., Inc, Mustafa, and Hashemi, Mir Sajjad
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NONLINEAR evolution equations , *SPACETIME , *TRIGONOMETRIC functions , *FOURIER series , *OPTICAL solitons , *ION acoustic waves , *FREE convection - Abstract
In this study, the space-time fractional generalised reaction duffing model is investigated analytically, which is a generalization for a collection of prominent fractional models describing various key phenomenon in science and engineering. The governing equation is converted to a nonlinear ODE by the compatible travelling wave transform. The investigation established that for analysing nonlinear evolution equations of fractional order, the recommended approach is more effective and realistic. The findings are given extensively in rational forms of trigonometric function series or clearly in powers of specific trigonometric functions. A collection of bright, dark, periodic, and optical solitons is discovered. Mathematica is used to flourish the presence of some obtained solutions in 3D graphs with different fractional orders. The results show that the recommended methods are more practical and effective ways to illustrate the dynamics of several complex wave structures in modern science and technology. [ABSTRACT FROM AUTHOR]
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- 2024
- Full Text
- View/download PDF
26. Valuation of variable annuities with guaranteed minimum maturity benefits and periodic fees.
- Author
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Ai, Meiqiao, Wang, Yunyun, Zhang, Zhimin, and Zhu, Dan
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VARIABLE annuities , *VALUATION , *ADMINISTRATIVE fees , *CHARACTERISTIC functions , *FOURIER series - Abstract
This paper focuses on the valuation of variable annuities with a guaranteed minimum maturity benefit under a regime-switching Lévy model. The model allows policyholders to surrender their annuities and receive a surrender benefit at predetermined tenor times before maturity. Additionally, we consider a state-dependent periodic fee structure where fees are deducted from the policyholder's account if it exceeds a certain level at discrete time points. Incorporating this fee structure, the Fourier cosine series expansion method based on characteristic functions is employed to determine the values and optimal surrender strategies for variable annuity contracts. Finally, we provide a comprehensive set of numerical examples to demonstrate and assess the effectiveness of our approach thoroughly. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
27. A Synthesis Method of Open-Chain Coupled Serial Linkage Mechanism Fusing Trajectory and Posture.
- Author
-
Zeng, Gongjun, Wang, Lei, Yu, Gaohong, Zheng, Mingfeng, Wu, Guohuan, and Ye, Bingliang
- Subjects
- *
PLANETARY gearing , *POSTURE , *FOURIER series , *BIVECTORS , *EQUATIONS of motion , *INDEPENDENT variables - Abstract
In order to meet the motion characteristics requirements of multi-objective fusion of execution components, a synthesis method of open-chain coupled serial linkage mechanism fusing trajectory and posture is proposed. According to periodic change characteristics of the execution component trajectory and posture of the linkage mechanism, the motion characteristics equation including trajectory and posture information is established by using Fourier series. The harmonic parameters of the link trajectory and posture are calculated according to the principle of discrete Fourier transform. The complex vector theory is applied to determine the functional relationship between the harmonic parameters of the trajectory and posture and the independent variable of the linkage mechanism, and furthermore the motion synthesis equation of the open-chain linkage mechanism fusing trajectory and posture information is established. The linkage mechanism parameters are calculated using Mathcad Prime software. The single-degree-of-freedom open-chain coupled serial linkage mechanism fusing trajectory and posture information is obtained by using a noncircular gear planetary gear train to couple the connection points of the linkage mechanism. The correctness of the method is verified through an example. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
28. Fast spectral solver for the inversion of boundary data problem of Poisson equation in a doubly connected domain.
- Author
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Wen, Jin, Wang, Shan‐Shan, and Liu, Zhuan‐Xia
- Subjects
- *
REGULARIZATION parameter , *DIFFERENTIAL equations , *TIKHONOV regularization , *FOURIER series , *LINEAR systems - Abstract
In this paper, we study the inversion of the inner boundary data for Poisson equation in a doubly connected domain by fast Fourier ultraspherical spectral solver. The solver depends on the truncated Fourier series expansion, where the differential equations of the Fourier coefficients are solved by an ultraspherical spectral method. Because this problem is seriously ill‐posed, the Cauchy data with noise will lead to ill‐conditioned linear system. Hence, we apply Tikhonov regularization to solve the obtained linear system and use generalized cross‐validation (GCV) criterion to select regularization parameters. The accuracy and efficiency of the proposed method are illustrated by several numerical results of different regions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
29. Multiphysics modeling and analysis of laminated composites with interfacial imperfections in thermal environments.
- Author
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Vattré, Aurélien
- Subjects
- *
LAMINATED materials , *IMPERFECTION , *FOURIER series , *TEMPERATURE distribution - Abstract
This work presents novel three-dimensional solutions for the multiphysics response of magneto-electro-elastic multilayered plates with interfacial imperfections in a thermal environment. The Stroh formalism is employed, incorporating thermal coupling with the Eringen nonlocal theory to capture small-scale effects. The laminated structures are simply supported and subjected to time-harmonic temperature distributions and extended tractions represented using Fourier series expansions. The dual variable and position technique is used to address the challenges posed by non-ideal thermal and mechanical bonded contacts between constituents, ensuring the consistency and stability of the recursive field relations. A wide range of application examples are analyzed, including the influence of material arrangements, aspect ratio and nonlocal length characteristics, elastically compliant and thermally/dielectrically weakly conducting interfaces, as well as forced vibrations in combined thermo-mechanical environments. The comprehensive results shed light on the intricate multiphysics response of multilayered structures and provide valuable insights into practical engineering implications for advanced materials and structures. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
30. Phase transition of traffic congestion in lattice hydrodynamic model: Modeling, calibration and validation.
- Author
-
Huang, Li, Zhang, Sai-Nan, Li, Shu-Bin, Cui, Feng-Ying, Zhang, Jing, and Wang, Tao
- Subjects
- *
PHASE transitions , *TRAFFIC congestion , *CALIBRATION , *STABILITY criterion , *FOURIER series , *NONLINEAR functions - Abstract
In actual transportation systems, the response time of drivers to the stimulus from the preceding vehicle varies at different speeds. The traditional car-following model cannot capture the heterogeneity of drivers for the response time is regarded as a constant. This paper designed a sigmoid function to describe the relation between the response time of drivers and the current speed. Then, a new hydrodynamic lattice model is developed by introducing the proposed nonlinear function. The model is analyzed by using Fourier series, and the linear stability criterion is derived. Numerical experiments are conducted in a ring road. Simulation results show that the evolution of density waves occurring in actual traffic is reproduced well. Finally, the model is calibrated and verified with the real data, and the simulation results are quantitatively consistent with the detector data. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
31. An analysis of the convergence problem of a function of hexagonal Fourier series in generalized Hölder norm using Hausdorff operator.
- Author
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Nigam, H. K. and Kumar Sah, Manoj
- Subjects
- *
GENERALIZED spaces , *HAUSDORFF spaces , *CONTINUOUS functions , *FOURIER series - Abstract
In the present paper, we obtain the results on the degree of convergence of an H$$ H $$‐periodic continuous function in generalized Hölder spaces using Hausdorff operator with monotonically non‐decreasing and monotonically non‐increasing rows of its hexagonal Fourier series. Some important corollaries are also deduced from our main theorems. Applications of main theorems are also obtained in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
32. Improving Realism of Facial Interpolation and Blendshapes with Analytical Partial Differential Equation-Represented Physics.
- Author
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Day, Sydney, Xiao, Zhidong, Chaudhry, Ehtzaz, Hooker, Matthew, Zhu, Xiaoqiang, Chang, Jian, Iglesias, Andrés, You, Lihua, and Zhang, Jianjun
- Subjects
- *
INTERPOLATION , *PARTIAL differential equations , *MATHEMATICAL models , *FOURIER series , *EQUATIONS of motion - Abstract
How to create realistic shapes by interpolating two known shapes for facial blendshapes has not been investigated in the existing literature. In this paper, we propose a physics-based mathematical model and its analytical solutions to obtain more realistic facial shape changes. To this end, we first introduce the internal force of elastic beam bending into the equation of motion and integrate it with the constraints of two known shapes to develop the physics-based mathematical model represented with dynamic partial differential equations (PDEs). Second, we propose a unified mathematical expression of the external force represented with linear and various nonlinear time-dependent Fourier series, introduce it into the mathematical model to create linear and various nonlinear dynamic deformations of the curves defining a human face model, and derive analytical solutions of the mathematical model. Third, we evaluate the realism of the obtained analytical solutions in interpolating two known shapes to create new shape changes by comparing the shape changes calculated with the obtained analytical solutions and geometric linear interpolation to the ground-truth shape changes and conclude that among linear and various nonlinear PDE-based analytical solutions named as linear, quadratic, and cubic PDE-based interpolation, quadratic PDE-based interpolation creates the most realistic shape changes, which are more realistic than those obtained with the geometric linear interpolation. Finally, we use the quadratic PDE-based interpolation to develop a facial blendshape method and demonstrate that the proposed approach is more efficient than numerical physics-based facial blendshapes. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
33. Adaptive saturated two-bit-triggered bipartite consensus control for networked MASs with periodic disturbances: a low-computation method.
- Author
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Wu, Wenjing, Zhang, Liang, Wu, Yuhang, and Zhao, Heng
- Subjects
- *
RADIAL basis functions , *BIPARTITE graphs , *MULTIAGENT systems , *ADAPTIVE control systems , *TRANSMISSION of sound , *FOURIER series , *PERIODIC functions - Abstract
This paper investigates the bipartite tracking control problem for a family of networked multi-agent systems with periodic disturbances as well as input saturation. A low-computation two-bit-triggered adaptive control strategy is proposed to achieve precise trajectory tracking and maintain the boundedness of the closed-loop signals. Compared with the existing results, first, this paper considers the problems for the coexistence of cooperation and competition in multi-agent systems, which represents a more common situation; secondly, the explosion of complexity issue is avoided without introducing any auxiliary filters, making our result more applicable and less complex; thirdly, a function approximator incorporating Fourier series expansion and a radial basis function neural network is utilized to model time-varying periodic disturbance functions and lastly, unlike traditional event-triggered control, the issue of controlling signal transmission bits is further explored to conserve system transmission resources. The result from a comparative simulation illustrates the advantages of the proposed method. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
34. A study of the 3-phase lag model to a two-dimensional isotropic micro-polar thermoelastic medium with memory-dependent properties.
- Author
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Jojare, Kirti K. and Gaikwad, Kishor R.
- Subjects
- *
DIFFERENTIAL forms , *TWO-dimensional models , *LAPLACE transformation , *DIFFERENTIAL equations , *FOURIER transforms , *FOURIER series - Abstract
This article enlightens the two-dimensional (2D) isotropic micro-polar thermoelastic problem of the three-phase-lag (3PHL) model and heat conduction equation is formulated in the context of memory-dependent derivative (MDD). The equations are converted into the domain of the Laplace transform vector matrix differential equation form and solved by using the eigenvalue technique. To obtain an analytical solution of displacement, temperature, and stress components Silicon material properties are used. Inversion of the Laplace transform with Fourier series expansion technique is used to obtain the numerical solution. For obtaining graphical results Mathematica software is used. For the purpose of exhibiting the beauty of MDD in the present model comparisons are made between the time delay parameters and kernel functions (constant, linear, and non-linear kernels), respectively, over the micro-polar panel. The results obtained have a valuable impact on structural analysis, especially in the design of rotating machinery structures using accurate material properties. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
35. Low complexity beamspace super‐resolution for direction‐of‐arrival estimation via prior information encoding.
- Author
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Jie, Pan
- Subjects
- *
DIRECTION of arrival estimation , *SEMIDEFINITE programming , *COMPUTATIONAL complexity , *FOURIER series , *VIDEO coding , *ENCODING , *MULTIPLIERS (Mathematical analysis) - Abstract
Beamspace processing is widely applied in Direction‐of‐Arrival (DOA) estimation thanks to dimensional reduction and super‐resolution characterisations. However, the conventional atomic norm minimisation (ANM) based methods for beamspace DOA estimation are of high computational complexity for large arrays. To deal with this issue, the proposed method focuses on locating the sources in the mainlobe of the beamspace and encodes such prior information into the ANM problem without frequency‐selective constraints. The proposed method approximates the beamspace array manifold in the mainlobe sector with the truncated sector Fourier series. The theoretical analysis shows that such approximation with the properly designed fitting error relaxation on the boundary yields the low dimensional semidefinite programming (SDP) approximate implementation of the proposed ANM method and guarantees the support recovery inside the mainlobe. Furthermore, the low complexity Burer‐Monteiro factorisation based alternating direction method of multipliers method is proposed to solve the SDP problem. The complexity analysis and simulations show that the proposed method results in significant computational complexity reduction and slightly better performance compared with state‐of‐art benchmarks. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
36. A Family of New Generating Functions for the Chebyshev Polynomials, Based on Works by Laplace, Lagrange and Euler.
- Author
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Brezinski, Claude and Redivo-Zaglia, Michela
- Subjects
- *
CHEBYSHEV polynomials , *GENERATING functions , *GEGENBAUER polynomials , *ORTHOGONAL polynomials , *LAGRANGE multiplier , *FOURIER series - Abstract
Analyzing, developing and exploiting results obtained by Laplace in 1785 on the Fourier-series expansion of the function (1 − 2 α cos θ + α 2) − s , we obtain a family of new expansions and generating functions for the Chebyshev polynomials. A relation between the generating functions of the Chebyshev polynomials T n and the Gegenbauer polynomials C n (2) is given. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
37. The Existence of Almost Periodic Response Solutions for Superlinear Duffing's Equations.
- Author
-
Yu, Yan, Dong, Yingdu, and Li, Xiong
- Subjects
- *
DUFFING equations , *FOURIER series - Abstract
In this paper, we are concerned with the existence of almost periodic response solutions for the superlinear Duffing's equation with an almost periodic external force. Assume that the system is reversible, and if the almost periodic forcing term admits a rapidly converging Fourier series, moreover the Diophantine condition for the frequencies is satisfied, the existence of response solutions will be proved. The proof is based on a modified KAM (Kolmogorov–Arnold–Moser) theorem for reversible systems. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
38. Effect of porosity on the thermal buckling of functionally graded material (FGM) sandwich plates under different boundary conditions.
- Author
-
Chedad, Abdelbasset, Elmeiche, Noureddine, Hamzi, Souad, and Abbad, Hichem
- Subjects
- *
FUNCTIONALLY gradient materials , *LAMINATED composite beams , *FOURIER series , *POROSITY , *VIRTUAL work , *HYPERBOLIC functions , *CERAMIC materials - Abstract
This document deals with the effect of porosity on the buckling of functionally graded sandwich plates under a nonlinear thermal loading using the four-variable refined plate theory. Different types of functionally graded material (FGM) sandwich plates, as well as various boundary conditions were used to highlight the influence of transverse shear, which is composed of two displacement fields, one is related to transverse displacement, and the second is due to the shearing effect. The transverse shear field follows a new warping hyperbolic function. The governing equations were derived from the virtual work principle based on von-Karman nonlinear geometric strains. This study aims to examine a sandwich-type plate, composed of three layers, the core of the plate is entirely made of ceramic material, and the upper and lower faces of the plate are made of functionally graded material. To solve the governing equations, double trigonometric series were used to simplify computations instead of a highly complicated numerical method. While various parameters are considered such as the volume faction index, porosity, and geometrical configurations, the study shows a perfect agreement between the proposed model and those of different works reported in the literature. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
39. Photonic generation of rectified cosinusoidal and sinusoidal shaped microwave waveforms with tunable duty cycle.
- Author
-
You, Haidong, Xu, Jian, Xu, Jun, Ning, Tigang, Gao, Yuanyuan, and Li, Lin
- Subjects
- *
PHASE shifters , *PHASE modulation , *FOURIER series , *BREWSTER'S angle , *MICROWAVE generation - Abstract
We propose a photonics scheme to generate rectified cosinusoidal shaped (RCS) and rectified sinusoidal shaped (RSS) microwave waveforms and the duty cycle of the generated waveforms can be freely tunable. In this proposed method, two cascaded Mach-Zehnder modulators (MZMs) with polarization sensitive characteristics are employed. By setting the rotation angle of polarization controller, phase shift of the phase shifters and modulation index of the front MZM's (modulation index of the rear MZM is unfixed) properly, the obtained RCS and RSS microwave waveforms with arbitrary duty cycle by the superposition of beating signals, can be seen as an approximation of the first three terms of the Fourier series expansion of the ideal waveforms. The detailed theoretical analysis and simulations are given. In the simulations, the duty cycle of 100%, 80% and 50% of the RCS and RSS microwave waveforms are successfully obtained. Also, fitting errors are introduced to measure the similarity between the generated waveforms and the ideal waveforms. Different from previous works, the RCS and RSS microwave waveforms can be both generated by our scheme and the duty cycle is freely tunable. Moreover, the modulation index of the rear MZM is unfixed, thus increasing the flexibility of the scheme. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
40. Analytical Prediction of the Jet Force in Pelton Turbine
- Author
-
Bhatta, Nishant, Dura, Hari Bahadur, Tharu, Janak Kumar, Luintel, Mahesh Chandra, Ceccarelli, Marco, Series Editor, Agrawal, Sunil K., Advisory Editor, Corves, Burkhard, Advisory Editor, Glazunov, Victor, Advisory Editor, Hernández, Alfonso, Advisory Editor, Huang, Tian, Advisory Editor, Jauregui Correa, Juan Carlos, Advisory Editor, Takeda, Yukio, Advisory Editor, Tiwari, Rajiv, editor, Ram Mohan, Y. S., editor, Darpe, Ashish K., editor, Kumar, V. Arun, editor, and Tiwari, Mayank, editor
- Published
- 2024
- Full Text
- View/download PDF
41. Research on the Influence and Weakening of Pole-Arc Coefficient on Cogging Torque in Consequent-Pole Permanent Magnet Synchronous Motors
- Author
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Wu, Fan, Wang, Xiaolin, Wang, Ziyu, Li, Ruixuan, Angrisani, Leopoldo, Series Editor, Arteaga, Marco, Series Editor, Chakraborty, Samarjit, Series Editor, Chen, Jiming, Series Editor, Chen, Shanben, Series Editor, Chen, Tan Kay, Series Editor, Dillmann, Rüdiger, Series Editor, Duan, Haibin, Series Editor, Ferrari, Gianluigi, Series Editor, Ferre, Manuel, Series Editor, Jabbari, Faryar, Series Editor, Jia, Limin, Series Editor, Kacprzyk, Janusz, Series Editor, Khamis, Alaa, Series Editor, Kroeger, Torsten, Series Editor, Li, Yong, Series Editor, Liang, Qilian, Series Editor, Martín, Ferran, Series Editor, Ming, Tan Cher, Series Editor, Minker, Wolfgang, Series Editor, Misra, Pradeep, Series Editor, Mukhopadhyay, Subhas, Series Editor, Ning, Cun-Zheng, Series Editor, Nishida, Toyoaki, Series Editor, Oneto, Luca, Series Editor, Panigrahi, Bijaya Ketan, Series Editor, Pascucci, Federica, Series Editor, Qin, Yong, Series Editor, Seng, Gan Woon, Series Editor, Speidel, Joachim, Series Editor, Veiga, Germano, Series Editor, Wu, Haitao, Series Editor, Zamboni, Walter, Series Editor, Tan, Kay Chen, Series Editor, Yang, Qingxin, editor, Li, Zewen, editor, and Luo, An, editor
- Published
- 2024
- Full Text
- View/download PDF
42. A Machine-Learning Approach to Queue Length Estimation Using Tagged Customers Emission
- Author
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Efrosinin, Dmitry, Vishnevsky, Vladimir, Stepanova, Natalia, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Vishnevskiy, Vladimir M., editor, Samouylov, Konstantin E., editor, and Kozyrev, Dmitry V., editor
- Published
- 2024
- Full Text
- View/download PDF
43. On the Convergence Fourier Series and Greedy Algorithm by Multiplicative System
- Author
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Grigoryan, M. G., Grigoryan, T. M., Simonyan, L. S., Cardona, Duván, editor, Restrepo, Joel, editor, and Ruzhansky, Michael, editor
- Published
- 2024
- Full Text
- View/download PDF
44. Game Physics Engine Using Optimised Geometric Algebra RISC-V Vector Extensions Code Using Fourier Series Data
- Author
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Saribatir, Ed, Zurstraßen, Niko, Hildenbrand, Dietmar, Stock, Florian, Piña, Atilio Morillo, Wegner, Frederic von, Yan, Zheng, Wen, Shiping, Arnold, Matthew, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Sheng, Bin, editor, Bi, Lei, editor, Kim, Jinman, editor, Magnenat-Thalmann, Nadia, editor, and Thalmann, Daniel, editor
- Published
- 2024
- Full Text
- View/download PDF
45. Discrete-Time Fourier Transform
- Author
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Sobot, Robert and Sobot, Robert
- Published
- 2024
- Full Text
- View/download PDF
46. Continuous Time Fourier Transform
- Author
-
Sobot, Robert and Sobot, Robert
- Published
- 2024
- Full Text
- View/download PDF
47. Computation of Human-Sperm Local Flagellar Instantaneous Velocity
- Author
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Díaz-Guerrero, Dan Sidney, Montoya, Fernando, Hernández, Haydee Olínca, Hernández-Herrera, Paul, Darszon, Alberto, Corkidi, Gabriel, Magjarević, Ratko, Series Editor, Ładyżyński, Piotr, Associate Editor, Ibrahim, Fatimah, Associate Editor, Lackovic, Igor, Associate Editor, Rock, Emilio Sacristan, Associate Editor, Flores Cuautle, José de Jesús Agustín, editor, Benítez-Mata, Balam, editor, Salido-Ruiz, Ricardo Antonio, editor, Alonso-Silverio, Gustavo Adolfo, editor, Dorantes-Méndez, Guadalupe, editor, Zúñiga-Aguilar, Esmeralda, editor, Vélez-Pérez, Hugo A., editor, Hierro-Gutiérrez, Edgar Del, editor, and Mejía-Rodríguez, Aldo Rodrigo, editor
- Published
- 2024
- Full Text
- View/download PDF
48. An improved Mickens' solution for nonlinear vibrations.
- Author
-
Hossain, M.M. Ayub and Haque, B.M. Ikramul
- Subjects
NONLINEAR equations ,DUFFING equations ,ELECTRICAL engineering ,MECHANICAL engineering ,NONLINEAR oscillations - Abstract
The Duffing equation and other nonlinear equations of motion of nonlinear vibrations are widely applied in the fields of engineering and science, especially mechanical and electrical engineering. The modified Mickens extended iteration method has been utilized in this article to investigate for further accurate solutions to the Duffing equation and an equation of motion of nonlinear vibrations. The third approximate frequency shows good agreement with the exact result for both oscillators. For simplicity in algebraic calculations, the increasing harmonic terms have been taken to the fifth order. In order to establish the reliability and effectiveness of the proposed approach, the results obtained through this method are compared with those available in the literature. The comparison of the obtained solutions with numerical solutions shows a remarkable accuracy. Also, it becomes evident that the modified Mickens extended iteration method is significantly simpler, more accurate, efficient, and straightforward than other existing methods. The highest percentage error in the third approximate frequency of an equation of motion of nonlinear vibrations is less than 0.0488 , and the maximal percentage error in the third approximate frequency of the Duffing oscillator is less than 0.0065. The proposed technique is principally exhibited in nonlinear models where the nonlinear terms are strong, but it can also be broadly applicable to other problems arising in engineering. 34A34, 34C25, 37N15 (AMS Mathematics Subject Classification 2010) [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
49. A novel algorithm for open switch fault detection and fault tolerant control of interleaved DC‐DC boost converters.
- Author
-
Zandi, Omid and Poshtan, Javad
- Subjects
DC-to-DC converters ,FAULT-tolerant computing ,FOURIER series ,BOOSTING algorithms ,ARTIFICIAL intelligence ,MICROCONTROLLERS ,KALMAN filtering - Abstract
This paper presents a novel algorithm for fault diagnosis and fault tolerant control of interleaved boost converters (IBCs) in the presence of single or double simultaneous open‐circuit faults (OCFs) in power switches. An innovative diagnosis signal (recorded by a cheap current sensor) will be introduced whose waveform mainly depends on the healthy or faulty condition of the converter. Since the diagnosis signal is periodic in the steady‐state operation of the converters, its Fourier Series coefficients, together with the duty cycle of the converter are used as distinguishing features for fault diagnosis of the OCFs in the converter. The well‐known Kalman filter is utilized for robust estimation of the Fourier‐based features. Finally, the modulation of the remaining healthy phases is rearranged in a way that the pre‐fault performance recovers. The proposed algorithm is verified in a laboratory four‐phase IBC setup in which the experimental results show its satisfactory performance. Also, the structure of the proposed method is straightforward and can be implemented in the same microcontroller which is used for voltage and current regulation of the converter. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
50. Using Fourier series to obtain cross periodic wall response factors.
- Author
-
Varela, Fernando, Theirs, Eduardo, González-Gaya, Cristina, and Sánchez-Orgaz, Susana
- Subjects
FOURIER series ,HEAT flux ,COOLING loads (Mechanical engineering) ,HEAT transfer ,BUILDING envelopes ,TRIANGLES - Abstract
Wall periodic response factors are a very usual calculation method of transient heat transfer through building envelope elements (walls, roofs ...) in steady periodic conditions, used in popular heat load calculation procedures as ASHRAE's RTS method [Spitler, Jeffrey D., Daniel E. Fisher, and Curtis O. Pedersen. 1997. "The Radiant Time Series Cooling Load Calculation Procedure." ASHRAE Transactions 103 (2): 503–515]. This response factors, time sampled heat flux responses of a multi-layer wall to a 24h-periodic unit triangle function, can be obtained by means of multiple methods: Laplace's method, state space method, frequency domain methods, etc. These methods are numerical since there is no analytical way of obtaining these response factors. The aim of this work is, taking advantage of the periodic nature of excitations, use Fourier series to represent boundary conditions, and this way find an easier and less computationally demanding procedure to calculate these response factors. Additionally, the convergence of these Fourier series will be analysed to determine the minimum set of frequencies needed to ensure a fixed admissible error for wall periodic response factors. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
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