Accurate prediction of extreme flood peak discharge is essential in developing the best management practices to avoid and reduce flood disaster. In recent years, many techniques have been pronounced as a branch of computer science to... more
Accurate prediction of extreme flood peak discharge is essential in developing the best management practices to avoid and reduce flood disaster. In recent years, many techniques have been pronounced as a branch of computer science to model wide range of hydrological process. Nevertheless, exploration of more efficient technique is necessary in terms of accuracy and applicability. In this study, a novel hermite-PPR model with SSO and LS algorithm is proposed for designing annual maximum flood peak discharge forecasting model at Yichang station on Yangtze River in China. The statistical properties of the data series are utilized for identifying an appropriate input vector to the model and then the performance of the proposed models were compared with adaptive neuro-fuzzy inference system (ANFIS), artificial neural network (ANN) and multiple linear regression (MLR) methods in terms of root mean squared error (RMSE), mean absolute relative error (MARE), coefficient of correlation (CC), Nash-Sutcliffe efficiency coefficient (NSEC) and qualified rate (QR). The results indicate that the presented methodology in this research can obtain significant improvement in forecasting accuracy in terms of different evaluation criteria during training and validation phases.
A description of Orthogonal Tensor Hermite Polynomials in 3-D is presented. These polynomials, as introduced by Grad in 1949 [1], can be used to obtain a series solution to the Boltzmann Transport Equation. The properties that are... more
A description of Orthogonal Tensor Hermite Polynomials in 3-D is presented. These polynomials, as introduced by Grad in 1949 [1], can be used to obtain a series solution to the Boltzmann Transport Equation. The properties that are explored are scaling, translation and rotation. Order 6 Hermite Tensors are studied while obtaining the rotation relations. From the scaling of the independent variables of particle velocities, a criterion on temperature is obtained which implies that the equation can be applied to binary gas mixtures only if the temperature of the hotter constituent is less than four times that of the cooler one. This criterion and other properties of the tensor hermite polynomials obtained in this paper can be used to study gas dynamics in the thermosphere.
In recent years there has been a renewed interest in finding fast algorithms to compute accurately the linear canonical transform (LCT) of a given function. This is driven by the large number of applications of the LCT in optics and... more
In recent years there has been a renewed interest in finding fast algorithms to compute accurately the linear canonical transform (LCT) of a given function. This is driven by the large number of applications of the LCT in optics and signal processing. The well-known integral transforms: Fourier, fractional Fourier, bilateral Laplace and Fresnel transforms are special cases of the LCT. In this paper we obtain an O(N*Log N) algorithm to compute the LCT by using a chirp-FFT-chirp transformation yielded by a convergent quadrature formula for the fractional Fourier transform. This formula gives a unitary discrete LCT in closed form. In the case of the fractional Fourier transform the algorithm computes this transform for arbitrary complex values inside the unitary circle and not only at the boundary. In the case of the ordinary Fourier transform the algorithm improves the output of the FFT.
The paper presents the neuro-fuzzy approach to the recognition and classification of heart rhythms on the basis of ECG waveforms. The important part in recognition fulfills the Hermite characterization of the QRS complexes. The Hermite... more
The paper presents the neuro-fuzzy approach to the recognition and classification of heart rhythms on the basis of ECG waveforms. The important part in recognition fulfills the Hermite characterization of the QRS complexes. The Hermite coefficients serve as the features of the process. These features are applied to the fuzzy neural network for the recognition. The results of numerical experiments have confirmed the very good performance of such a solution.
It is known that the anti-Wick (or standard coherent state) quantization of the complex plane produces both canonical commutation rule and quantum spectrum of the harmonic oscillator (up to the addition of a constant). In the present... more
It is known that the anti-Wick (or standard coherent state) quantization of the complex plane produces both canonical commutation rule and quantum spectrum of the harmonic oscillator (up to the addition of a constant). In the present work, we show that these two issues are not necessarily coupled: there exists a family of separable Hilbert spaces, including the usual Fock-Bargmann space, and in each element in this family there exists an overcomplete set of unit-norm states resolving the unity. With the exception of the Fock-Bargmann case, they all produce non-canonical commutation relation whereas the quantum spectrum of the harmonic oscillator remains the same up to the addition of a constant. The statistical aspects of these non-equivalent coherent states quantizations are investigated. We also explore the localization aspects in the real line yielded by similar quantizations based on real Hermite polynomials.
