Investigating the cores of fossil systems with Chandra

We investigate the cores of fossil galaxy groups and clusters (`fossil systems') using archival Chandra data for a sample of 17 fossil systems. We determined the cool-core fraction for fossils via three observable diagnostics, the central cooling time, cuspiness, and concentration parameter. We quantified the dynamical state of the fossils by the X-ray peak/brightest cluster galaxy (BCG), and the X-ray peak/emission weighted centre separations. We studied the X-ray emission coincident with the BCG to detect the presence of potential thermal coronae. A deprojection analysis was performed for z < 0.05 fossils to obtain cooling time and entropy profiles, and to resolve subtle temperature structures. We investigated the Lx-T relation for fossils from the 400d catalogue to see if the scaling relation deviates from that of other groups. Most fossils are identified as cool-core objects via at least two cool-core diagnostics. All fossils have their dominant elliptical galaxy within 50 kpc of the X-ray peak, and most also have the emission weighted centre within that distance. We do not see clear indications of a X-ray corona associated with the BCG unlike that has been observed for some other objects. Fossils do not have universal temperature profiles, with some low-temperature objects lacking features that are expected for ostensibly relaxed objects with a cool-core. The entropy profiles of the z < 0.05 fossil systems can be well-described by a power law model, albeit with indices smaller than 1. The 400d fossils Lx-T relation shows indications of an elevated normalisation with respect to other groups, which seems to persist even after factoring in selection effects.Comment: Accepted for publication in Astronomy and Astrophysic

On a new parameter involving Ramanujan's theta-functions

We define a new parameter $A'_{k,n}$ involving Ramanujan's theta-functions for any positive real numbers $k$ and $n$ which is analogous to the parameter $A_{k,n}$ defined by Nipen Saikia \cite{NS1}. We establish some modular relation involving $A'_{k,n}$ and $A_{k,n}$ to find some explicit values of $A'_{k,n}$. We use these parameters to establish few general theorems for explicit evaluations of ratios of theta functions involving $\varphi(q)$

Locating Legal Certainty in Patent Licensing

This open access book presents global perspectives and developments within the information and communication technology (ICT) sector, and discusses the bearing they have on policy initiatives that are relevant to the larger digital technology and communications industry. Drawing on key developments in India, the USA, UK, EU, and China, it explores whether key jurisdictions need to adopt a different legal and policy approach to address the unique concerns that have emerged within the technology-intensive industries. The book also examines the latest law and policy debates surrounding patents and competition in these regions. Initiating a multi-faceted discussion, the book enables readers to gain a comprehensive understanding of complex legal and policy issues that are beginning to emerge around the globe

Complications and Quandaries in the ICT Sector: Standard Essential Patents and Competition Issues

With technology standards becoming increasingly common, particularly in the information and communications technology (ICT) sector, the complexities and contradictions at the interface of intellectual property law and competition law have emerged strongly. This book talks about how the regulatory agencies and courts in the United States, European Union and India are dealing with the rising allegations of anti-competitive behaviour by standard essential patent (SEP) holders. It also discusses the role of standards setting organizations / standards developing organizations (SSO/SDO) and the various players involved in implementing the standards that influence practices and internal dynamics in the ICT sector. This book includes discussions on fair, reasonable and non-discriminatory (FRAND) licensing terms and the complexities that arise when both licensors and licensees of SEPs differ on what they mean by “fair”, “reasonable” and “non-discriminatory” terms. It also addresses topics such as the appropriate royalty base, calculation of FRAND rates and concerns related to FRAND commitments and the role of Federal Trade Commission (FTC) in collaborative standard setting process. This book provides a wide range of valuable information and is a useful tool for graduate students, academics and researchers

Free-energy functional for freezing transitions: Hard sphere systems freezing into crystalline and amorphous structures

A free-energy functional that contains both the symmetry conserved and symmetry broken parts of the direct pair correlation function has been used to investigate the freezing of a system of hard spheres into crystalline and amorphous structures. The freezing parameters for fluid-crystal transition have been found to be in very good agreement with the results found from simulations. We considered amorphous structures found from the molecular dynamics simulations at packing fractions $\eta$ lower than the glass close packing fraction $\eta_{J}$ and investigated their stability compared to that of a homogeneous fluid. The existence of free-energy minimum corresponding to a density distribution of overlapping Gaussians centered around an amorphous lattice depicts the deeply supercooled state with a heterogeneous density profile

Extending the LX−TL_{\mathrm{X}}-T relation from clusters to groups-Impact of cool core nature, AGN feedback, and selection effects

We aim to investigate the bolometric $L_{\mathrm{X}}-T$ relation for galaxy groups, and study the impact of gas cooling, feedback from supermassive black holes, and selection effects on it. With a sample of 26 galaxy groups we obtained the best fit $L_{\mathrm{X}}-T$ relation for five different cases depending on the ICM core properties and central AGN radio emission, and determined the slopes, normalisations, intrinsic and statistical scatters for both temperature and luminosity. Simulations were undertaken to correct for selection effects (e.g. Malmquist bias) and the bias corrected relations for groups and clusters were compared. The slope of the bias corrected $L_{\mathrm{X}}-T$ relation is marginally steeper but consistent with clusters ($\sim 3$). Groups with a central cooling time less than 1 Gyr (SCC groups) show indications of having the steepest slope and the highest normalisation. For the groups, the bias corrected intrinsic scatter in $L_{\mathrm{X}}$ is larger than the observed scatter for most cases, which is reported here for the first time. Lastly, we see indications that the groups with an extended central radio source have a much steeper slope than those groups which have a CRS with only core emission. Additionally, we also see indications that the more powerful radio AGN are preferentially located in NSCC groups rather than SCC groups.Comment: Accepted for publication in Astronomy and Astrophysic

LINE RATE HARDWARE FLOW TELEMETRY ARCHITECTURE ON FIBRE CHANNEL APPLICATION-SPECIFIC INTEGRATED CIRCUIT

Techniques are provided herein for offering line rate flow telemetry on all ports of a Fibre Channel (FC) switch by implementing a bidirectional flow correlation engine inside an FC switching Application-Specific Integrated Circuit (ASIC). This enables a specialized set of flow analytics solutions to be implemented using machine learning models. These models may be trained with full flow visibility, including every outlier, and may have very high prediction accuracy. This may enable building of a switch integrated solution for this use case without involving external appliances