Real analytic expansion of spectral projections and extension of the Hecke-Bochner identity

In this article, we review the Weyl correspondence of bigraded spherical harmonics and use it to extend the Hecke-Bochner identities for the spectral projections f × φ _k ^n?1 for function f ∈ L ^p (? ⁿ ) with 1 ≤ p ≤ ∞. We prove that spheres are sets of injectivity for the twisted spherical means with real analytic weight. Then, we derive a real analytic expansion for the spectral projections f × φ _k ^n?1 for function f ∈ L ²(? ⁿ ). Using this expansion we deduce that a complex cone can be a set of injectivity for the twisted spherical means.     

A Framework for Evaluating Knowledge-Based Interestingness of Association Rules

In Knowledge Discovery in Databases (KDD)/Data Mining literature, interestingness measures are used to rank rules according to the interest a particular rule is expected to evoke. In this paper, we introduce an aspect of subjective interestingness called item-relatedness. Relatedness is a consequence of relationships that exist between items in a domain. Association rules containing unrelated or weakly related items are interesting since the co-occurrence of such items is unexpected. Item-Relatedness helps in ranking association rules on the basis of one kind of subjective unexpectedness. We identify three types of item-relatedness – captured in the structure of a fuzzy taxonomy (an extension of the classical concept hierarchy tree). An item-relatedness measure for describing relatedness between two items is developed by combining these three types. Efficacy of this measure is illustrated with the help of a sample taxonomy. We discuss three mechanisms for extending this measure from a two-item set to an association rule consisting of a set of more than two items. These mechanisms utilize the relatedness of item-pairs and other aspects of an association rule, namely its structure, distribution of items and item-pairs. We compare our approach with another method from recent literature.     

Homogenization of a parabolic equation in perforated domain with Neumann boundary condition

In this article, we study the homogenization of the family of parabolic equations over periodically perforated domains

A novel advanced grey incidence analysis for investigating the level of resilience in supply chains

Annals of Operations Research - Supply chain risk management embroils quite a lot of situations of managerial decision-making under uncertainties. As contemporary supply chains are intricate...     

SHI induced modification in CR-39 polycarbonate by positron annihilation lifetime studies

CR-39 is a polycarbonate widely used as SSNTD for recording nuclear charged particles and in other applications. Latent ion tracks produced in the polymers due to the damage produced by the passage of Swift Heavy Ions contain amorphous material with highest degree of disorder, changing the free volume properties which have strong correlation with the macroscopic properties of the material. Positron annihilation lifetime spectroscopy (PALS) provides direct information about the dimension, content and hole size distribution of free volume in polymers. The effect of irradiation of ⁴⁰Ar (14.9 MeV/n) ions on CR-39 polycarbonate by Positron Annihilation Lifetime Spectroscopy (PALS) is reported here. PALS provides a non-destructive and non-interfering probe, having high detection efficiency for free volume hole properties. From o-Ps lifetime mean free volume hole radius and average free volume of the micro-voids have been calculated. PAL measurement shows an increase in free volume on irradiation.     

Effect of annular apodization and pupil beam parameter in the focal region of high NA lens

Focusing properties of the radially polarized axisymmetric Bessel-modulated Gaussian beam with quadratic radial dependence (QBG beam) and annular aperture are investigated theoretically by vector diffraction theory. Simulation results show that the intensity distribution in the focal region of the radially polarized axisymmetric QBG beam can be adjusted considerably by small beam parameter (μ) and annular aperture (δ). When μ increases, the focal spot may change to focal hole and changes focal pattern remarkably. On introducing annular aperture, focus can split or extends along the optical axis for different μ. In this paper, we have shown the generation of the focal spot, dark focal spot, focal split and increase in focal depth in the axial direction of the incident beam propagating through the aligned optical system.     

Gyroscopic Precession and Inertial Forces in Axially Symmetric Stationary Spacetimes

We study the phenomenon of gyroscopic precession and the analogues of inertial forces within the framework of general relativity. Covariant connections between the two are established for circular orbits in stationary spacetimes with axial symmetry. Specializing to static spacetimes, we prove that gyroscopic precession and centrifugal force both reverse at the photon orbits. Simultaneous non-reversal of these in the case of stationary spacetimes is discussed. Further insight is gained in the case of static spacetime by considering the phenomena in a spacetime conformal to the original one. Gravi-electric and gravi-magnetic fields are studied and their relation to inertial forces is established.     

Particle Sizing Using Frequency Domain Photon Migration

The transport properties of particulate process streams and their final product quality, are directly affected by critical parameters of particle size distribution, f(x), and volume, mass, or number density of particles or dispersed phase droplets. A method is proposed for the potential on-line monitoring of particle size distribution and volume fraction in real time, using frequency-domain photon migration measurements (FDPM). Theory, experimental measurements, and results for the determination of particle size distributions for both a polystyrene latex and a titanium dioxide suspension determined using the photon migration technique are presented. The critical issues associated with the application of photon migration to particulate and dispersed phase processes are discussed, including the effects of interparticle interactions on the transport of light.     

Generation of sub wavelength super long dark channel using azimuthally polarized annular multi-Gaussian beam

We investigate the interesting focal properties of phase modulation azimuthally polarized annular multi Gaussian beam employing a high numerical aperture (NA) lens on the basis of vector diffraction theory. We observe that our proposed system generates a sub wavelength focal hole of \(0.43 \uplambda \) having large uniform focal depth of \(84 \uplambda \) . This kind of nondiffracting focal hole is called dark channel, which may have applications in atom optical experiments, such as with atomic lenses, atom traps, and atom switches.     

Structural and optical properties of ZnSe thin films stacked with PbSe submonolayers

Structural and optical properties of Zinc Selenide (ZnSe) thin films stacked with multiple Lead Selenide (PbSe) submonolayers (ML) were studied. Thermal evaporation was preferred to produce ZnSe–PbSe thin films with the PbSe ML thickness ranges from 2.5 to 10 nm. Polycrystalline nature of the ZnSe was revealed through high resolution X-ray diffractometer measurement. The development of micro strain at the interfaces with increasing PbSe ML thickness was observed. A cross-sectional TEM image shows well-ordered periodicity and reproducibility of the layer thickness. The enhancement of optical absorption of ZnSe was identified upon stacking of PbSe ML. The evidence for quantum confinement in PbSe ML was revealed by the obtained red shift in band gap (2.5–1.8 eV) values as well as photoluminescence emission at 1,071 nm. The presence of tensile strain in the ZnSe layers upon staking of PbSe ML was discussed by the shift in LO phonon modes in Raman spectra.