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来源:Abstract and Applied Analysis , 2017

作者:Ryuichi Ashino, Mawardi Bahri

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The continuous quaternion wavelet transform (CQWT) is a generalization of the classical continuous wavelet transform within the context of quaternion algebra. First of all, we show that the directional quaternion Fourier transform (QFT) uncertainty principle can be obtained using the component-wise QFT uncertainty principle. Based on this method, the directional QFT uncertainty principle using representation of polar coordinate form is easily derived. We derive a variation on uncertainty principle related to the QFT. We state that the CQWT of a quaternion function can be written in terms of the QFT and obtain a variation on uncertainty principle related to the CQWT. Finally, we apply the extended uncertainty principles and properties of the CQWT to establish logarithmic uncertainty principles related to generalized transform.

    来源:Abstract and Applied Analysis , 2017

    作者:Benoît F. Sehba, Justice S. Bansah

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    We consider two families of multilinear Hilbert-type operators for which we give exact relations between the parameters so that they are bounded. We also find the exact norm of these operators.

      来源:Abstract and Applied Analysis , 2017

      作者:Gabriel Deugoué

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      We consider a nonautonomous 2D Leray-α model of fluid turbulence. We prove the existence of the uniform attractor Aα. We also study the convergence of Aα as α goes to zero. More precisely, we prove that the uniform attractor Aα converges to the uniform attractor of the 2D Navier-Stokes system as α tends to zero.

        来源:Abstract and Applied Analysis , 2017

        作者:Ryuichi Ashino, Mawardi Bahri

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        The continuous quaternion wavelet transform (CQWT) is a generalization of the classical continuous wavelet transform within the context of quaternion algebra. First of all, we show that the directional quaternion Fourier transform (QFT) uncertainty principle can be obtained using the component-wise QFT uncertainty principle. Based on this method, the directional QFT uncertainty principle using representation of polar coordinate form is easily derived. We derive a variation on uncertainty principle related to the QFT. We state that the CQWT of a quaternion function can be written in terms of the QFT and obtain a variation on uncertainty principle related to the CQWT. Finally, we apply the extended uncertainty principles and properties of the CQWT to establish logarithmic uncertainty principles related to generalized transform.

          来源:Abstract and Applied Analysis , 2017

          作者:Wenqing Hu

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          We provide an Itô formula for stochastic dynamical equation on general time scales. Based on this Itô’s formula we give a closed-form expression for stochastic exponential on general time scales. We then demonstrate Girsanov’s change of measure formula in the case of general time scales. Our result is being applied to a Brownian motion on the quantum time scale (q-time scale).

            来源:Abstract and Applied Analysis , 2017

            作者:Suguna Selvaraj, Chikkanna R. Selvaraj

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            This paper deals with matrix transformations that preserve the (p,q)-convexity of sequences. The main result gives the necessary and sufficient conditions for a nonnegative infinite matrix A to preserve the (p,q)-convexity of sequences. Further, we give examples of such matrices for different values of p and q.