A document by Deep Bhattacharjee . Click on the document to view its contents.

Any quantum groups can be filtered via PBW Theorem over a graded algebra where the structure representation for any supercommutator [𝗶,𝗷] when reduced asserts a linear monomial of a canonical origin. Thus, being independent on the swapping order, isomorphism can be seen for any injective takeovers giving the map ψ: ℓ ⟶ U(ℓ) with the Lie ℓ through the U(ℓ) group. This satisfies direct connectivity over 𝙊𝙨𝙥(𝙢,𝙣)⋂𝙊𝙨𝙥(𝙣,𝙢) in Kac-Moody algebras.

The ghost condensation of the early universe in a pre-big bang phase has been presented in this paper through duration of a non-singular bounce. The undergoing universe contracts and passes smoothly in an expanding universe via a post-big bang phase. Initially developing and then taming any ghost like instabilities, the Null Energy Condition (NEC) is explicitly violated through the curvature mechanism of an adiabatic perturbed metric. The vacuum state of the ongoing phase is stabilized via a La-grangian that in essence stabilizes the vacuum state under the higher order derivatives. The violation of the NEC regards a catastrophic vacuum instability, which re-emerges with a correction valid at small energies and momenta, below the UV-cutoff scale that, could potentially be problematic if one tries to construct a UV-completed theory of this Ekpyrotic model. The scale-invariant curvature perturbation, that arises and is sourced out of the scale-invariant entropy perturbations sourced by 2-Ekpyrotic scalar fields, that, in contrast, becomes constant on the super-horizon limits, due to the non-singular nature of the background geometry. Apart, from the ghost condensates, this theory addresses the new Ekpyrotic theory which in order becomes a distinguishable alternative to inflation theory for the birth of the universe. As per the recent WMAP data, the Ekpyrotic model has a spectral red tilt that shows the bounced scalar potential falling through a negative phase shift during the matter-fluid fluctuations in the hot big bang phase.

A detailed analysis of the blazars detected by the Fermi/LAT (3LAC) and (4LAC) along with the 𝛾 −ray Narrow line – Seyfert 1 Galaxies (𝛾-NLSy1s) has been provided here with emphasize to the weak anti-correlation between synchrotron peak frequency and peak luminiosity, jet kinetic power and synchrotron peak frequency along with the properties of FSRQs, BL Lacs (Chen et al, 2020) with the central engine properties that is, the accretion luminosity (𝐿𝑑𝑖𝑠𝑘 ) and black hole mass (𝑀𝐵𝐻 ) where study has been done regarding the broad emission spectral line systems along with the association of more massive black holes with absorption line systems where computations has been made in Eddington units (𝐿𝑑𝑖𝑠𝑐 /𝐿𝐸𝑑𝑑 ) having the broad line objects to have a higher accretion rate (𝐿𝑑𝑖𝑠𝑐 /𝐿𝐸𝑑𝑑 > 0.01) with the sources being identified in recurrence with the HighCompton Dominated (HCD-CD > 1) and Low-Compton Dominated (LCD- CD ≲ 1) objects where according to (Paliya et al, 2021) the physical properties of the Fermi Blazars are to be controlled by the accretion rate in Eddington units. From the known redshifts of the Fermi satellite data, the spectral energy distributions (SEDs) have been computed where the proton dominated jet powers and the luminosity has been computed which is of the same order of (or slightly larger than) the disc luminosity (Ghisellini et al, 2010). In case of Flat Spectrum Radio quasars (FSRQs), the high energy peak of the SED increases with the luminosity where the X-ray spectra becomes harder and harder for larger luminosities, however in case of BL Lacs, they become redder with a softer 𝛾-ray slope and high energy for peak luminosities. For all the blazars (FRSQs + BL Lacs), the higher luminosity bin is vastly populated by FRSQs while the lower luminosity bin is populated by BL Lacs (Ghisellini et al, 2017). In the Fermi LAT – Bright AGN Sample (LBAS) by combining the Fermi 𝛾-ray spectra with Swift, optical, infra-red, radio, hard X-ray, 𝛾-ray data it has been observed with accuracy that in case of 50% of the radio bright high energy peaked BL Lacs (HBL) detected in the LABS Sample, only less than 13% of the known FSRQs and LBL BL Lacs are included. The synchrotron peak frequency (𝑣𝑝𝑒𝑎𝑘 𝑠 ) has been positioned between 1012.5 and 1014.5 Hz in FSRQs and between 1013 and 1017 Hz in featureless BL Lac objects. The LAC detector being more sensitive to flat spectrum 𝛾-ray sources, the exact correlation between 𝑣𝑝𝑒𝑎𝑘 𝑠 and 𝛾-ray spectral index highly favors the detection of the high energy peaked blazars having the Fermi overabundance compared to radio and Energetic Gamma Ray Experiment Telescope (EGRET) samples. This in turn makes a selection effect where in the soft X-ray band, HBL BL Lacs are the most dominant types of blazars (Abdo et al, 2010).

A document by Deep Bhattacharjee . Click on the document to view its contents.

Physics is beautiful & amazing. This paper contains 17 easy-to-read essays on modern physics over various aspects that can easily manifest a curiosity in the young minds. Essays are there without any math which entails for a easier read. They are, Complexity of Physical Law In Unification, Levitation Using Superconductivity, Cryogenics, Nuclear Energies, Speed of The Sound, To Travel In Time Is To Travel In Space, Restricted 3-Body Problem of Mechanics, Sonoluminescence, Acoustic Levitation, Evolution & Physics, 11-Dimensional Super-Gravity, Black Hole Titbits, Frequency & Wavelength (Å), Investigating The Possible shapes Of The Universe, Chaos & Unpredictability, Cat’s Schrodinger, Isoperimetric Inequality.

Comment: Time itself being the temporal dimensions can be manipulated by means of clever physics so as to make a time travelling domain in the backyard of your own garden. The principles of this are introduced along with physics, so as to capture the beauty of time travelling on a grander scale by some arbitrarily modified civilizations in the faraway futures. This starts with the basic notions on the perspectives of time with regards to its implications in the physics of the time travel.