The aim of the present paper is to introduce and study a new type of q-Mellin transform [11], that will be called q-finite Mellin transform. In particular, we prove for this new transform an inversion formula and q-co...The aim of the present paper is to introduce and study a new type of q-Mellin transform [11], that will be called q-finite Mellin transform. In particular, we prove for this new transform an inversion formula and q-convolution product. The application of this transform is also earlier proposed in solving procedure for a new equation with a new fractional differential operator of a variational type.展开更多
In this article, we introduce the two dimensional Mellin transform M4（f）（s,t）, give some properties, establish the Paley-Wiener theorem and Plancherel formula, present the Hausdorff-Young inequality, and find seve...In this article, we introduce the two dimensional Mellin transform M4（f）（s,t）, give some properties, establish the Paley-Wiener theorem and Plancherel formula, present the Hausdorff-Young inequality, and find several applications for the two dimensional Mellin transform.展开更多
This paper is a further continuation of the paper [1]. In the present paper Mellin transform and Miints formula of weak functions in complex domain will be treated.
According to the features of the wideband underwater acoustic signals,an algorithm for the wideband ambiguity function is put forward based on Mellin transform.The wideband acoustic signal processing using the fast Me...According to the features of the wideband underwater acoustic signals,an algorithm for the wideband ambiguity function is put forward based on Mellin transform.The wideband acoustic signal processing using the fast Mellin transform is also explored.The theoretical analysis and simulation results show that the algorithm has not only high computation efficiency but also good concentration in wideband ambiguity domain.It suits for the wideband underwater acoustic signal processing.展开更多
The ground roll and body wave usually show significant differences in arrival time, frequency content, and polarization characteristics, and conventional polarization filters that operate in either the time or frequen...The ground roll and body wave usually show significant differences in arrival time, frequency content, and polarization characteristics, and conventional polarization filters that operate in either the time or frequency domain cannot consider all these elements. Therefore, we have developed a time-frequency dependent polarization filter based on the S transform to attenuate the ground roll in seismic records. Our approach adopts the complex coefficients of the S transform of the multi-component seismic data to estimate the local polarization attributes and utilizes the estimated attributes to construct the filter function. In this study, we select the S transform to design this polarization filter because its scalable window length can ensure the same number of cycles of a Fourier sinusoid, thereby rendering more precise estimation of local polarization attributes. The results of applying our approach in synthetic and real data examples demonstrate that the proposed polarization filter can effectively attenuate the ground roll and successfully preserve the body wave.展开更多
Swelling clays are found extensively in various parts of the world, and sodium-montmorillonite(NaMMT) is the main constituent of an expansive clay mineral. In this work, the swelling behavior of NaMMT clay with a wide...Swelling clays are found extensively in various parts of the world, and sodium-montmorillonite(NaMMT) is the main constituent of an expansive clay mineral. In this work, the swelling behavior of NaMMT clay with a wide range of organic fluids, high polar through low polar fluids, is studied using a combination of Fourier transform infrared(FTIR) technique and molecular dynamics(MD) simulations.The construction of the representative clayefluid models is carried out, and the nature of nonbonded interactions between clay and fluids is studied using MD. Our FTIR and MD simulations results suggest the significant nonbonded interactions between Na-MMT clay and polar fluids, such as formamide and water. The nonbonded interactions of Na-MMT with methanol and acetone are significantly less than those in Na-MMT with polar fluids. The interactions of the fluids with various entities of the clay such as Sie O, Fee OH, Mge OH, and Ale OH captured via the spectroscopy experiments and modeling provide a finer understanding of the interactions and their contributions to swelling. The MD simulations are able to capture the band shifts observed in the spectra obtained in the spectroscopy experiments. This work also captures the conformations of interlayer sodium ions with formamide, water, methanol, and acetone during swelling. These nonbonded interactions provide insight into the molecular mechanism that the polarity of fluids plays an important role in the initiation of interlayer swelling, alteration in the orientations, and evolution of microstructure of swelling clays at the molecular scale.展开更多
In order to extract the feature information of ultra wide-band (UWB) radio fuze target and give full play to the warhead's strike ability, a method based on polar Hough transform for scattering centers extraction ...In order to extract the feature information of ultra wide-band (UWB) radio fuze target and give full play to the warhead's strike ability, a method based on polar Hough transform for scattering centers extraction of the target was proposed in this paper. It firstly utilized the fuze scanning to obtain the distance and azimuth information of the target's main scattering centers at different times, i.e. the track information of scattering centers under the polar coordinates, then used the polar Hough transform to transform the track into the parameter space in order to accumulate the dots and drew 3-D parameter space diagram, in which the peak points corresponded to the target's scattering centers. The simulation results indicate that the method can not only extract scattering centers efficiently and accurately, but also has strong anti-noise performance, and the algorithm is simple and easy to be implemented in engineering.展开更多
We apply complex Morlet wavelet transform to three polar motion data series,and derive quasi-instantaneous periods of the Chandler and annual wobble by differencing the wavelettransform results versus the scale factor...We apply complex Morlet wavelet transform to three polar motion data series,and derive quasi-instantaneous periods of the Chandler and annual wobble by differencing the wavelettransform results versus the scale factor, and then find their zero points. The results show thatthe mean periods of the Chandler (annual) wobble are 430.71+-1.07 (365.24+-0.11) and 432.71+-0.42(365.23+-0.18) mean solar days for the data sets of 1900-2001 and 1940-2001, respectively. Themaximum relative variation of the quasi-instantaneous period to the mean of the Chandler wobble isless than 1.5% during 1900-2001 (3%-5% during 1920-1940), and that of the annual wobble is less than1.6% during 1900-2001. Quasi-instantaneous and mean values of Q are also derived by using theenergy density―period profile of the Chandler wobble. An asymptotic value of Q = 36.7 is obtainedby fitting polynomial of exponential of σ^(-2) to the relationship between Q and σ during1940-2001.展开更多
In the present paper, we obtain asymptotic expansion of the wavelet transform for large value of dilation parameter a by using López technique. Asymptotic expansion of Shannon wavelet, Morlet wavelet and Mexican ...In the present paper, we obtain asymptotic expansion of the wavelet transform for large value of dilation parameter a by using López technique. Asymptotic expansion of Shannon wavelet, Morlet wavelet and Mexican Hat wavelet transform are obtained as special cases.展开更多
The transition from a known Taylor series ?of a known function f(x) to a new function ?primarily defined by the infinite power series ?with coefficients f(n)(0)?from the Taylor series of the function f(x)?can be made ...The transition from a known Taylor series ?of a known function f(x) to a new function ?primarily defined by the infinite power series ?with coefficients f(n)(0)?from the Taylor series of the function f(x)?can be made by an integral transformation which is a modified Laplace transformation and is called Sumudu transformation. It makes the transition from the Exponential series to the Geometric series and may help to evaluate new infinite power series from known Taylor series. The Sumudu transformation is demonstrated to be a limiting case of Fractional integration. Apart from the basic Sumudu integral transformation we discuss a modification where the coefficients ?from the Taylor series are not changed to f(n)(0)?but only to . Beside simple examples our applications are mainly concerned to calculate new Generating functions for Hermite polynomials from the basic ones.展开更多
文摘The aim of the present paper is to introduce and study a new type of q-Mellin transform [11], that will be called q-finite Mellin transform. In particular, we prove for this new transform an inversion formula and q-convolution product. The application of this transform is also earlier proposed in solving procedure for a new equation with a new fractional differential operator of a variational type.
文摘In this article, we introduce the two dimensional Mellin transform M4（f）（s,t）, give some properties, establish the Paley-Wiener theorem and Plancherel formula, present the Hausdorff-Young inequality, and find several applications for the two dimensional Mellin transform.
文摘This paper is a further continuation of the paper [1]. In the present paper Mellin transform and Miints formula of weak functions in complex domain will be treated.
基金Sponsored by National Nature Science Foundation of China(10474079)
文摘According to the features of the wideband underwater acoustic signals,an algorithm for the wideband ambiguity function is put forward based on Mellin transform.The wideband acoustic signal processing using the fast Mellin transform is also explored.The theoretical analysis and simulation results show that the algorithm has not only high computation efficiency but also good concentration in wideband ambiguity domain.It suits for the wideband underwater acoustic signal processing.
基金supported by the National Science and Technology Major Project of China(Grant No.2011ZX05014 and 2011ZX05008-005)
文摘The ground roll and body wave usually show significant differences in arrival time, frequency content, and polarization characteristics, and conventional polarization filters that operate in either the time or frequency domain cannot consider all these elements. Therefore, we have developed a time-frequency dependent polarization filter based on the S transform to attenuate the ground roll in seismic records. Our approach adopts the complex coefficients of the S transform of the multi-component seismic data to estimate the local polarization attributes and utilizes the estimated attributes to construct the filter function. In this study, we select the S transform to design this polarization filter because its scalable window length can ensure the same number of cycles of a Fourier sinusoid, thereby rendering more precise estimation of local polarization attributes. The results of applying our approach in synthetic and real data examples demonstrate that the proposed polarization filter can effectively attenuate the ground roll and successfully preserve the body wave.
基金the support of USDoT,Mountain Plains Consortium,UGPTI under grant No.#69A3551747108
文摘Swelling clays are found extensively in various parts of the world, and sodium-montmorillonite(NaMMT) is the main constituent of an expansive clay mineral. In this work, the swelling behavior of NaMMT clay with a wide range of organic fluids, high polar through low polar fluids, is studied using a combination of Fourier transform infrared(FTIR) technique and molecular dynamics(MD) simulations.The construction of the representative clayefluid models is carried out, and the nature of nonbonded interactions between clay and fluids is studied using MD. Our FTIR and MD simulations results suggest the significant nonbonded interactions between Na-MMT clay and polar fluids, such as formamide and water. The nonbonded interactions of Na-MMT with methanol and acetone are significantly less than those in Na-MMT with polar fluids. The interactions of the fluids with various entities of the clay such as Sie O, Fee OH, Mge OH, and Ale OH captured via the spectroscopy experiments and modeling provide a finer understanding of the interactions and their contributions to swelling. The MD simulations are able to capture the band shifts observed in the spectra obtained in the spectroscopy experiments. This work also captures the conformations of interlayer sodium ions with formamide, water, methanol, and acetone during swelling. These nonbonded interactions provide insight into the molecular mechanism that the polarity of fluids plays an important role in the initiation of interlayer swelling, alteration in the orientations, and evolution of microstructure of swelling clays at the molecular scale.
文摘In order to extract the feature information of ultra wide-band (UWB) radio fuze target and give full play to the warhead's strike ability, a method based on polar Hough transform for scattering centers extraction of the target was proposed in this paper. It firstly utilized the fuze scanning to obtain the distance and azimuth information of the target's main scattering centers at different times, i.e. the track information of scattering centers under the polar coordinates, then used the polar Hough transform to transform the track into the parameter space in order to accumulate the dots and drew 3-D parameter space diagram, in which the peak points corresponded to the target's scattering centers. The simulation results indicate that the method can not only extract scattering centers efficiently and accurately, but also has strong anti-noise performance, and the algorithm is simple and easy to be implemented in engineering.
基金Supported by the National Natural Science Foundation of China
文摘We apply complex Morlet wavelet transform to three polar motion data series,and derive quasi-instantaneous periods of the Chandler and annual wobble by differencing the wavelettransform results versus the scale factor, and then find their zero points. The results show thatthe mean periods of the Chandler (annual) wobble are 430.71+-1.07 (365.24+-0.11) and 432.71+-0.42(365.23+-0.18) mean solar days for the data sets of 1900-2001 and 1940-2001, respectively. Themaximum relative variation of the quasi-instantaneous period to the mean of the Chandler wobble isless than 1.5% during 1900-2001 (3%-5% during 1920-1940), and that of the annual wobble is less than1.6% during 1900-2001. Quasi-instantaneous and mean values of Q are also derived by using theenergy density―period profile of the Chandler wobble. An asymptotic value of Q = 36.7 is obtainedby fitting polynomial of exponential of σ^(-2) to the relationship between Q and σ during1940-2001.
文摘In the present paper, we obtain asymptotic expansion of the wavelet transform for large value of dilation parameter a by using López technique. Asymptotic expansion of Shannon wavelet, Morlet wavelet and Mexican Hat wavelet transform are obtained as special cases.
文摘The transition from a known Taylor series ?of a known function f(x) to a new function ?primarily defined by the infinite power series ?with coefficients f(n)(0)?from the Taylor series of the function f(x)?can be made by an integral transformation which is a modified Laplace transformation and is called Sumudu transformation. It makes the transition from the Exponential series to the Geometric series and may help to evaluate new infinite power series from known Taylor series. The Sumudu transformation is demonstrated to be a limiting case of Fractional integration. Apart from the basic Sumudu integral transformation we discuss a modification where the coefficients ?from the Taylor series are not changed to f(n)(0)?but only to . Beside simple examples our applications are mainly concerned to calculate new Generating functions for Hermite polynomials from the basic ones.
