In this paper wavelet functions are introduced in the context of q-theory. We precisely extend the case of Bessel and q-Bessel wavelets to the generalized q-Bessel wavelets. Starting from the （q,v）-extension （v = ...In this paper wavelet functions are introduced in the context of q-theory. We precisely extend the case of Bessel and q-Bessel wavelets to the generalized q-Bessel wavelets. Starting from the （q,v）-extension （v = （α,β）） of the q-case, associated generalized q-wavelets and generalized q-wavelet transforms are developed for the new context. Reconstruction and Placherel type formulas are proved.展开更多
The purpose of this paper is to study some famous inequalities in Euclidean space.We are able to reveal an elegant relation between the famous Selberg inequality and Bessel inequality in Euclidean space.
We propose a superposed Bessel optical lattice formed by multiple Bessel optical lattices.The static and rotational structures are formed in the presence of a spin-orbit coupling(SOC)interaction in the atomic in Bose...We propose a superposed Bessel optical lattice formed by multiple Bessel optical lattices.The static and rotational structures are formed in the presence of a spin-orbit coupling(SOC)interaction in the atomic in Bose–Einstein condensates are investigated,it is shown that the two structures can be manipulated by adjusting the parameters of the superposed Bessel optical lattices.The results show that the SOC interaction has an important effect on the two structures in the superposed Bessel optical lattices,and the SOC interaction can enhance the robustness of the structures.The Gaussian,toroidal and vortex superposition structures in the superposition lattice are presented,the interference processes in the steady state structures are analyzed,and the effects of SOC interactions on the Gaussian vortex and toroidal vortex structures are investigated,and the angular momentum of the vortex states can be increased by SOC interactions.展开更多
Femtosecond laser processing is an important machining method for micro-optical components such as Fresnel zone plate(FZP).However,the low processing efficiency of the femtosecond laser restricts its application.Here,...Femtosecond laser processing is an important machining method for micro-optical components such as Fresnel zone plate(FZP).However,the low processing efficiency of the femtosecond laser restricts its application.Here,a femtosecond laser Bessel beam is proposed to process micro-FZP,which is modulated from a Gaussian beam to a Bessel annular beam.The processing time for FZP with an outer diameter of 60μm is reduced from 30 min to 1.5 min on an important semiconductor material gallium arsenide(GaAs),which significantly improves the processing efficiency.In the modulation process,a central ablation hole that has an adverse effect on the diffraction performance is produced,and the adverse effect is eliminated by superimposing the blazed grating hologram.Meanwhile,the FZP machined by spatial light modulator(SLM)has good morphology and higher diffraction efficiency,which provides a strong guarantee for the application of micro-FZP in computed tomography and solar photovoltaic cells.展开更多
The aim of this paper is to prove another variation on the Heisenberg uncertainty principle,we generalize the quantitative uncertainty relations in n different(time-frequency)domains and we will give an algorithm for ...The aim of this paper is to prove another variation on the Heisenberg uncertainty principle,we generalize the quantitative uncertainty relations in n different(time-frequency)domains and we will give an algorithm for the signal recovery related to the canonical Fourier-Bessel transform.展开更多
The spherically layered media theory has wide applications for electromagnetic wave scattering analysis.Due to the involved Bessel functions,the conventional formulations of spherically layered media theory suffer fro...The spherically layered media theory has wide applications for electromagnetic wave scattering analysis.Due to the involved Bessel functions,the conventional formulations of spherically layered media theory suffer from numerical overflow or underflow when the Bessel function’s order is large,the argument is small or the argument has a large imaginary part.The first two issues have been solved recently by employing small-argument asymptotic formulas of Bessel functions,while the third issue remains unsolved.In this paper,the Bessel functions in the conventional formulation of the theory are replaced by scaled Bessel functions which have good numerical properties for high loss media,and stable formulas are derived.Numerical tests show that this approach can work properly with very high lossy media.Also,this approach can be seamlessly combined with the stable computation method for cases of small argument and large order of Bessel functions.展开更多
文摘In this paper wavelet functions are introduced in the context of q-theory. We precisely extend the case of Bessel and q-Bessel wavelets to the generalized q-Bessel wavelets. Starting from the （q,v）-extension （v = （α,β）） of the q-case, associated generalized q-wavelets and generalized q-wavelet transforms are developed for the new context. Reconstruction and Placherel type formulas are proved.
基金Supported by Shandong Provincial Natural Science Foundation(ZR2024MA053).
文摘The purpose of this paper is to study some famous inequalities in Euclidean space.We are able to reveal an elegant relation between the famous Selberg inequality and Bessel inequality in Euclidean space.
基金supported by the Longdong University Doctoral Fund Program Projects(Grant Nos.XYBYZK2227,XYBYZK2219).
文摘We propose a superposed Bessel optical lattice formed by multiple Bessel optical lattices.The static and rotational structures are formed in the presence of a spin-orbit coupling(SOC)interaction in the atomic in Bose–Einstein condensates are investigated,it is shown that the two structures can be manipulated by adjusting the parameters of the superposed Bessel optical lattices.The results show that the SOC interaction has an important effect on the two structures in the superposed Bessel optical lattices,and the SOC interaction can enhance the robustness of the structures.The Gaussian,toroidal and vortex superposition structures in the superposition lattice are presented,the interference processes in the steady state structures are analyzed,and the effects of SOC interactions on the Gaussian vortex and toroidal vortex structures are investigated,and the angular momentum of the vortex states can be increased by SOC interactions.
基金Projects(51875584,51875585,51975590)supported by the National Natural Science Foundation of China。
文摘Femtosecond laser processing is an important machining method for micro-optical components such as Fresnel zone plate(FZP).However,the low processing efficiency of the femtosecond laser restricts its application.Here,a femtosecond laser Bessel beam is proposed to process micro-FZP,which is modulated from a Gaussian beam to a Bessel annular beam.The processing time for FZP with an outer diameter of 60μm is reduced from 30 min to 1.5 min on an important semiconductor material gallium arsenide(GaAs),which significantly improves the processing efficiency.In the modulation process,a central ablation hole that has an adverse effect on the diffraction performance is produced,and the adverse effect is eliminated by superimposing the blazed grating hologram.Meanwhile,the FZP machined by spatial light modulator(SLM)has good morphology and higher diffraction efficiency,which provides a strong guarantee for the application of micro-FZP in computed tomography and solar photovoltaic cells.
文摘The aim of this paper is to prove another variation on the Heisenberg uncertainty principle,we generalize the quantitative uncertainty relations in n different(time-frequency)domains and we will give an algorithm for the signal recovery related to the canonical Fourier-Bessel transform.
文摘The spherically layered media theory has wide applications for electromagnetic wave scattering analysis.Due to the involved Bessel functions,the conventional formulations of spherically layered media theory suffer from numerical overflow or underflow when the Bessel function’s order is large,the argument is small or the argument has a large imaginary part.The first two issues have been solved recently by employing small-argument asymptotic formulas of Bessel functions,while the third issue remains unsolved.In this paper,the Bessel functions in the conventional formulation of the theory are replaced by scaled Bessel functions which have good numerical properties for high loss media,and stable formulas are derived.Numerical tests show that this approach can work properly with very high lossy media.Also,this approach can be seamlessly combined with the stable computation method for cases of small argument and large order of Bessel functions.
