Fractional Integrals and Derivatives for Sumudu Transform on Distribution Spaces

We propose, in the present paper, the investigation of the Sumudu transformation for certain distribution spaces with regard to the fractional integral and differential operators of the transform. This paper is organized in two sections, first of which gives an abriged text on fractional operators and the Sumudu transform (which is less discussed and reserached). Basic concept in analysing the investigation is initiated by the fact that the Riemann-Liouville fractional integral can be expressed as one of the appropriate forms of the Abel integral equation, which is the second section of this paper

Mehler-Fock Transformation of Ultradistribution

This paper deals with the testing function space Z and its dual Z\u27, which is known as ultradistrbution. Some theorems and properties are investigated for the Mehler-Fock transformation and its inverse for the ultradistribution

Kinetics & Mechanism of Acid Permanganate Oxidation of Cyclohexanone

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Mesoscopic superposition and sub-Planck-scale structure in molecular wave packets

We demonstrate the possibility of realizing sub-Planck-scale structures in the mesoscopic superposition of molecular wave packets involving vibrational levels. The time evolution of the wave packet, taken here as the SU(2) coherent state of the Morse potential describing hydrogen iodide molecules, produces macroscopicquantum- superposition-like states, responsible for the above phenomenon. We investigate the phase-space dynamics of the coherent state through the Wigner function approach and identify the interference phenomena behind the sub-Planck-scale structures. The optimal parameter ranges are specified for observing these features.Comment: 4 pages, 3 figure

A time frequency analysis of wave packet fractional revivals

We show that the time frequency analysis of the autocorrelation function is, in many ways, a more appropriate tool to resolve fractional revivals of a wave packet than the usual time domain analysis. This advantage is crucial in reconstructing the initial state of the wave packet when its coherent structure is short-lived and decays before it is fully revived. Our calculations are based on the model example of fractional revivals in a Rydberg wave packet of circular states. We end by providing an analytical investigation which fully agrees with our numerical observations on the utility of time-frequency analysis in the study of wave packet fractional revivals.Comment: 9 pages, 4 figure

Development of low cost packaged fibre optic sensors for use in reinforced concrete structures

There is an ongoing need to measure strains in reinforced concrete structures more reliably and under a range of circumstances e.g. long term durability (such as effects of cracking and reinforcement corrosion), response to normal working loads and response under abnormal load conditions. Fibre optic sensors have considerable potential for this purpose and have the additional advantages, including of immunity to electromagnetic interference and light weight (Grattan et al., 2000). This is important in railway scenarios and particularly so when the lines are electrified. Their small size allows for easy installation. However, their use as commercial ‘packaged’ devices (traditionally seen as necessary to achieve adequate robustness) is limited by their high cost relative to other sensor devices such as encapsulated electric resistance strain gauges. This paper describes preliminary work to produce a cost-effective and easy-to-use technique for encapsulating fibre optic sensors in resin using 3D printing techniques to produce a robust, inexpensive ‘packaged’ sensor system suitable for use with concrete structures. The work done to date has shown this to be a convenient and economical way of producing multiple sensors which were suitable for both surface mounting and embedment in reinforced concrete structures. The proof-of-concept testing to which the trial packages were subjected is described in the paper and the results indicate that 3D printed packages have considerable potential for further development and use in a variety of civil engineering applications, competing well with more conventional sensor systems

Wavelet Transform of Fractional Integrals for Integrable Boehmians

The present paper deals with the wavelet transform of fractional integral operator (the Riemann- Liouville operators) on Boehmian spaces. By virtue of the existing relation between the wavelet transform and the Fourier transform, we obtained integrable Boehmians defined on the Boehmian space for the wavelet transform of fractional integrals

Quantitative assessment of the potential fishery resources of the Indian Ocean and adjoining seas

Even -though oceanic fisheries have bccome a major contributing factor in the world production of marine fish, for countries bordering the Indian Ocean which do not have large mechanized fishing fleet capable of operating far away from their ports, the fisheries of shallow-water areas are of primary interes

Multipliers and operators on the tempered ultradistribution spaces of Roumieu type for the distributional Hankel-type transformation spaces

The tempered ultradistribution space of Roumieu type for the space Hμ,ν is defined, which is a subspace of the Hausdörff locally convex topological linear space. Further, results are obtained for the multipliers and operators on the tempered ultradistribution spaces for the distributional Hankel-type transformation spaces