Continuous Functional Calculus for Quaternionic Bounded Normal Operators

In this article we give an approach to define continuous functional calculus for bounded quaternionic normal operators defined on a right quaternionic Hilbert space.Comment: Submitted to a journal. There was a gap in the previous version. We have corrected it and stated all the results for bounded cas

On the polar decomposition of right linear operators in quaternionic Hilbert spaces

In this article we prove the existence of the polar decomposition for densely defined closed right linear operators in quaternionic Hilbert spaces: If $T$ is a densely defined closed right linear operator in a quaternionic Hilbert space $H$, then there exists a partial isometry $U_{0}$ such that $T = U_{0}|T|$. In fact $U_{0}$ is unique if $N(U_{0}) = N(T)$. In particular, if $H$ is separable and $U$ is a partial isometry with $T = U|T|$, then we prove that $U = U_{0}$ if and only if either $N(T) = \{0\}$ or $R(T)^{\bot} = \{0\}$.Comment: 17 page

Micro Expression Spotting through Appearance Based Descriptor and Distance Analysis

Micro-Expressions (MEs) are a typical kind of expressions which are subtle and short lived in nature and reveal the hidden emotion of human beings. Due to processing an entire video, the MEs recognition constitutes huge computational burden and also consumes more time. Hence, MEs spotting is required which locates the exact frames at which the movement of ME persists. Spotting is regarded as a primary step for MEs recognition. This paper proposes a new method for ME spotting which comprises three stages; pre-processing, feature extraction and discrimination. Pre-processing aligns the facial region in every frame based on three landmark points derived from three landmark regions. To do alignment, an in-plane rotation matrix is used which rotates the non-aligned coordinates into aligned coordinates. For feature extraction, two texture based descriptors are deployed; they are Local Binary Pattern (LBP) and Local Mean Binary Pattern (LMBP). Finally at discrimination stage, Feature Difference Analysis is employed through Chi-Squared Distance (CSD) and the distance of each frame is compared with a threshold to spot there frames namely Onset, Apex and Offset. Simulation done over a Standard CASME dataset and performance is verified through Feature Difference and F1-Score. The obtained results prove that the proposed method is superior than the state-of-the-art methods

Designing a Biosensor Using a Photonic Quasi-Crystal Fiber with Fan-shaped Analyte Channel

Postprin

Discrete distributions with bathtub-shaped hazard rates

Discrete distributions with bathtub shaped hazard rates have recently become of interest in reliability modelling and analysis. In the present work, we address the problem of obtaining distributions having such hazard rates when the lifetime is discrete. The methods considered here include discretising continuous bathtub models, construction using the score function, construction from decreasing hazard rate distributions and some other methods currently available in the continuous case. We discuss properties and applications of the discretised quadratic hazard model which has a bathtub shaped hazard rate

A spectroscopic search for AGN activity in the reionization era

The ubiquity of Lyman alpha (Ly$\alpha$) emission in a sample of four bright [O III]-strong star-forming galaxies with redshifts above 7 has led to the suggestion that such luminous sources represent a distinct population compared to their fainter, more numerous, counterparts. The presence of Ly$\alpha$ emission within the reionization era could indicate that these sources created early ionized bubbles due to their unusually strong radiation, possibly due to the presence of active galactic nuclei. To test this hypothesis we have secured long integration spectra with XSHOOTER on the VLT for three $z\simeq$7 sources selected to have similar luminosities and prominent excess fluxes in the IRAC 3.6 or 4.5$\mu$m band, usually attributed to strong [O III] emission. We secured additional spectroscopy for one of these galaxies at $z$=7.15 using MOSFIRE at the Keck telescope. For this, the most well-studied source in our sample with the strongest IRAC excess, we detect prominent nebular emission from He II and NV indicative of a non-thermal source. For the other two sources at $z$=6.81 and $z$=6.85, for which no previous optical/near infrared spectroscopy was initially available, Ly$\alpha$ is seen in one and CIII] emission in the other. Although a modest sample, our results further support the hypothesis that the phenomenon of intense [O III] emission is associated preferentially with sources lying in early ionized bubbles. However, even though one of our sources at $z$=7.15 clearly indicates the presence of non-thermal radiation, such ionized bubbles may not uniquely arise in this manner. We discuss the unique advantages of extending such challenging diagnostic studies with JWST.Comment: 11 pages, 7 figures, submitted to Ap

Hybrid Thermal-Nonthermal Synchrotron Emission from Hot Accretion Flows

We investigate the effect of a hybrid electron population, consisting of both thermal and non-thermal particles, on the synchrotron spectrum, image size, and image shape of a hot accretion flow onto a supermassive black hole. We find two universal features in the emitted synchrotron spectrum: (i) a prominent shoulder at low (< 10^11 Hz) frequencies that is weakly dependent on the shape of the electron energy distribution, and (ii) an extended tail of emission at high (> 10^13 Hz) frequencies whose spectral slope depends on the slope of the power-law energy distribution of the electrons. In the low-frequency shoulder, the luminosity can be up to two orders of magnitude greater than with a purely thermal plasma even if only a small fraction (< 1%) of the steady-state electron energy is in the non-thermal electrons. We apply the hybrid model to the Galactic center source, Sgr A*. The observed radio and IR spectra imply that at most 1% of the steady-state electron energy is present in a power-law tail in this source. This corresponds to no more than 10% of the electron energy injected into the non-thermal electrons and hence 90% into the thermal electrons. We show that such a hybrid distribution can be sustained in the flow because thermalization via Coulomb collisions and synchrotron self-absorption are both inefficient. The presence of non-thermal electrons enlarges the size of the radio image at low frequencies and alters the frequency dependence of the brightness temperature. A purely thermal electron distributions produces a sharp-edged image while a hybrid distribution causes strong limb brightening. These effects can be seen up to frequencies ~10^11 Hz and are accessible to radio interferometers.Comment: 33 pages with figures, to appear in the Astrophysical Journa