On Rankin triple product $$L$$ L -functions over function fields: central critical values

Wei, Fu‐Tsun

doi:10.1007/s00209-013-1227-9

Cited by 3 publications

(5 citation statements)

References 13 publications

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“…Therefore, metal oxide nanofibers are highly desirable and are a topic of extensive research in decoloration and degradation experiments because of their high surface area, better chemical stability, increased shelf life and higher porosity. 13,14 Among the various metal oxides, nickel oxide, with a wide band gap (3.7-4.0), is widely utilized in photocatalysis, electrochromic materials, electrode materials for lithium-ion batteries, magnetic high storage devices, sensors etc. [15][16][17][18] Here we are going to explore the photocatalytic activity of nickel oxide nanofibers.…”

Section: Nano Impactmentioning

confidence: 99%

Fabrication and characterization of poly(ethylene oxide) templated nickel oxide nanofibers for dye degradation

Malwal

Gopinath

2015

Environ. Sci.: Nano

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In the present study, one dimensional nickel oxide (NiO) nanofibers were successfully fabricated using an inexpensive and simplistic electrospinning technique to evaluate their efficient applicability as a photocatalyst in dye degradation processes. The synthesis part involves the calcination of electrospun poly(ethylene oxide)/ nickel acetate tetrahydrate nanofibers to obtain phase pure cubic NiO nanofibers, which were further characterized using various techniques to determine their physical and chemical properties. Furthermore, the photocatalytic activity of these NiO nanofibers along with their kinetics of degradation was studied with the photodegradation of model dye Congo red (CR) under visible light irradiation. Interestingly, the photocatalytic properties of the NiO nanofibers were found to be better than those of the nanoparticles when compared, and were found to be dependent on the concentrations of the loaded photocatalyst.Besides this, the stability of the nanofibers in aqueous solution was examined along with their reusability.

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Section: Nano Impactmentioning

confidence: 99%

Fabrication and characterization of poly(ethylene oxide) templated nickel oxide nanofibers for dye degradation

Malwal

Gopinath

2015

Environ. Sci.: Nano

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“…The Photonic crystal fibres (PCFs) are optical fibres with air hole microstructures running along with them [1,2]. These materials have attracted attention recently because they have unique optical properties that are not present in conventional optical fibres [2][3][4][5], such as operation in endlessly single-mode [6][7][8], using edge bending loss for short wavelengths [6], the fiber can provide large and small effective mode area in a single-mode region, and the anomalous group-velocity dispersion of these fibers shows two zero dispersion wavelengths in the visible and near-infrared regions [9], control dispersion management [10], low loss, high birefringence [11,12], bio-sensing applications [13] and large mode area operation [14,15].…”

Section: Introductionmentioning

confidence: 99%

“…These materials have attracted attention recently because they have unique optical properties that are not present in conventional optical fibres [2][3][4][5], such as operation in endlessly single-mode [6][7][8], using edge bending loss for short wavelengths [6], the fiber can provide large and small effective mode area in a single-mode region, and the anomalous group-velocity dispersion of these fibers shows two zero dispersion wavelengths in the visible and near-infrared regions [9], control dispersion management [10], low loss, high birefringence [11,12], bio-sensing applications [13] and large mode area operation [14,15]. There are two mechanisms for guiding light in PCFs, depending on the geometry of the fiber core; it is either a solid or hollow core [1][2][3]16]. The first mechanism is known as indexguiding PCFs, which directs light by total internal refraction between the solid core and the cladding area with multiple air holes.…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of strongly coupled multicore photonic crystal fibres for multiplexer and de-multiplexer applications

Mohammed

Ahmad

2022

J. Phys.: Conf. Ser.

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In this study, the coupling properties of multicore photonic crystal fibers (MCPCFs) are analyzed numerically using COMSOL Multiphysics 5.5, based on the finite element method. The dependence of the coupling properties on the structure of the MCPCFs and the wavelength are investigated to realize applications such as multiplexers-demultiplexers for wavelength division multiplexing. The effective mode indexes and transverse electric field distributions of multiple cores are evaluated for different spatial configurations of identical and non-identical cores. A slight change in the central core diameter relative to adjacent cores leads to non-identical cores that lead to wavelength-dependent coupling properties, such as the coupling lengths and strength of the coefficients. The results show that the coupling lengths become longer and the strength coefficients become smaller as the wavelength decreases for non-identical cores than the identical cores. The introduction of anisotropy to all core diameters shows that the coupling lengths become longer and the strength of the coefficients become smaller as the wavelength decreases as well, and both values become lower than the ones for non-identical cores. These results prove that coupling lengths of MCPCF couplers are significantly shorter in μm compared to conventional multicore optical fiber couplers.

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“…This can be applied to the special values of automorphic L-functions via integral representations, for example, Rankin-Selberg method or the Garretttype representation for triple product L-functions (cf. [6,19,25]). Using the Siegel-Weil formula, the central critical derivatives of 'incoherent' Siegel-Eisenstein series can be also understood by theta series.…”

Section: Introductionmentioning

confidence: 99%

“…Rankin-Selberg method or the Garrett-type representation for triple product L-functions (cf. [24], [6], and [19]). Using the Siegel-Weil formula, the central critical derivatives of "incoherent" Siegel-Eisenstein series can be also understood by theta series.…”

Section: Introductionmentioning

confidence: 99%

On derivatives of Siegel–Eisenstein series over global function fields

Wei

2019

J. London Math. Soc.

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The aim of this article is to study the derivative of ‘incoherent’ Siegel–Eisenstein series on symplectic groups over function fields. Comparing the Fourier coefficients of incoherent Siegel–Eisenstein series with ‘coherent’ ones, the Siegel–Weil formula enables us to understand the non‐singular Fourier coefficients of the derivative in question by theta series (together with a local quantity coming from the corresponding Whittaker functions). Restricting to the special case when the incoherent quadratic space has dimension 2, we explicitly compute all the Fourier coefficients, and express the derivative in terms of the degree of the special cycles on the coarse moduli schemes of rank 2 Drinfeld modules with ‘complex multiplication’.

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On Rankin triple product $$L$$ L -functions over function fields: central critical values

Cited by 3 publications

References 13 publications

Fabrication and characterization of poly(ethylene oxide) templated nickel oxide nanofibers for dye degradation

Fabrication and characterization of poly(ethylene oxide) templated nickel oxide nanofibers for dye degradation

Numerical analysis of strongly coupled multicore photonic crystal fibres for multiplexer and de-multiplexer applications

On derivatives of Siegel–Eisenstein series over global function fields

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