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991.
Tewodros Amdeberhan Olivier Espinosa Victor H. Moll 《Proceedings of the American Mathematical Society》2008,136(9):3211-3221
The definite integral is related to the Laplace transform of the digamma function by when . Certain analytic expressions for in the complementary range, , are also provided.
992.
We study finite rank semicommutators and commutators of Toeplitz operators on the Bergman space with quasihomogeneous symbols.
We show that in this context, the situation is different from the case of harmonic Toeplitz operators.
Submitted: July 23, 2007. Accepted: December 4, 2007. 相似文献
993.
Yang Zheng Dr. Junhua Chen Chunguo Duan Xinyue Zhang Dr. Xuefang Xu Dr. Qian Gou 《Chemphyschem》2023,24(7):e202200804
The pure rotational spectra of 1-phenylethanol and its monohydrate were measured by using a pulsed jet Fourier transform microwave spectrometer. One conformer of the 1-phenylethanol monomer with the trans form was observed in the pulsed jet. The experimental values of rotational constants of ten isotopologues, including eight mono-substituted 13C and one D isotopologues, allow an accurate structure determination of the skeleton of 1-phenylethanol. For its monohydrate, only one isomer has been observed, of which 1-phenylethanol adopts the trans form and binds with water through an O−H⋅⋅⋅Ow and an Ow−H⋅⋅⋅π hydrogen bond. Each rotational transition displays a doublet with a relative intensity ratio of 1 : 3, due to a hindered internal rotation of water around its C2 axis. This study provides the information on accurate geometry of 1-phenylethanol (PE) and large amplitude motion of water in the PE monohydrate. 相似文献
994.
In this paper, we study positive Toeplitz operators on the harmonic Bergman space via their Berezin transforms. We consider the Toeplitz operators with continuous harmonic symbols on the closed disk and show that the Toeplitz operator is positive if and only if its Berezin transform is nonnegative on the disk. On the other hand, we construct a function such that the Toeplitz operator with this function as the symbol is not positive but its Berezin transform is positive on the disk. We also consider the harmonic Bergman space on the upper half plane and prove that in this case the positive Toeplitz operators with continuous integrable harmonic symbols must be the zero operator. 相似文献
995.
Continuous online monitoring of rotating machines is necessary to assess real-time health conditions so as to enable early detection of operation problems and thus reduce the possibility of downtime. Rolling element bearings are crucial parts of many machines and there has been an increasing demand to find effective and reliable health monitoring technique and advanced signal processing to detect and diagnose the size and location of incipient defects. Condition monitoring of rolling element bearings, comprises four main stages which are, statistical analysis, fault diagnostics, defect size calculation, and prognostics. In this paper the effect of defect size, operating speed, and loading conditions on statistical parameters of acoustic emission (AE) signals, using design of experiment method (DOE), have been investigated to select the most sensitive parameters for diagnosing incipient faults and defect growth on rolling element bearings. A modified and effective signal processing algorithm is designed to diagnose localized defects on rolling element bearings components under different operating speeds, loadings, and defect sizes. The algorithm is based on optimizing the ratio of Kurtosis and Shannon entropy to obtain the optimal band pass filter utilizing wavelet packet transform (WPT) and envelope detection. Results show the superiority of the developed algorithm and its effectiveness in extracting bearing characteristic frequencies from the raw acoustic emission signals masked by background noise under different operating conditions. To experimentally measure the defect size on rolling element bearings using acoustic emission technique, the proposed method along with spectrum of squared Hilbert transform are performed under different rotating speeds, loading conditions, and defect sizes to measure the time difference between the double AE impulses. Measurement results show the power of the proposed method for experimentally measuring size of different fault shapes using acoustic emission signals. 相似文献
996.
997.
S. Yakubovich 《Integral Transforms and Special Functions》2016,27(2):137-152
New index transforms, involving the real part of the modified Bessel function of the first kind as the kernel are considered. Mapping properties such as the boundedness and invertibility are investigated for these operators in the Lebesgue spaces. Inversion theorems are proved. As an interesting application, a solution of the initial value problem for the second-order partial differential equation, involving the Laplacian, is obtained. It is noted that the corresponding operators with the imaginary part of the modified Bessel function of the first kind lead to the familiar Kontorovich–Lebedev transform and its inverse. 相似文献
998.
R. S. Pathak 《Integral Transforms and Special Functions》2016,27(6):468-483
Theory of Weierstrass transform is exploited to derive many interesting new properties of the Mexican hat wavelet transform. A real inversion formula in the differential operator form for the Mexican hat wavelet transform is established. Mexican hat wavelet transform of distributions is defined and its properties are studied. An approximation property of the distributional wavelet transform is investigated which is supported by a nice example. 相似文献
999.
Ernst Eberlein M’hamed Eddahbi S. M. Lalaoui Ben Cherif 《Applied Mathematical Finance》2016,23(3):236-260
The aim of this article is to compute Greeks, i.e. price sensitivities in the framework of the Lévy LIBOR model. Two approaches are discussed. The first approach is based on the integration-by-parts formula, which lies at the core of the application of the Malliavin calculus to finance. The second approach consists of using Fourier-based methods for pricing derivatives. We illustrate the result by applying the formula to a caplet price where the jump part of the driving process of the underlying model is given by a time–inhomogeneous Gamma process and alternatively by a Variance Gamma process. 相似文献
1000.
We consider the at-the-money (ATM) strike derivative of implied volatility as the maturity tends to zero. Our main results quantify the behaviour of the slope for infinite activity exponential Lévy models including a Brownian component. As auxiliary results, we obtain asymptotic expansions of short maturity ATM digital call options, using Mellin transform asymptotics. Finally, we discuss when the ATM slope is consistent with the steepness of the smile wings, as given by Lee’s moment formula. 相似文献