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(ε, δ)-Definition of Limit
In calculus, the (ε, δ)-definition of limit ("epsilon–delta definition of limit") is a formalization of the notion of limit. The concept is due to Augustin-Louis Cauchy, who never gave a formal (ε, δ) definition of limit in his Cours d'Analyse, but occasionally used ε, δ arguments in proofs. It was first given as a formal definition by Bernard Bolzano in 1817, and the definitive modern statement was ultimately provided by Karl Weierstrass. It provides rigor to the following informal notion: the dependent expression f(x) approaches the value L as the variable x approaches the value c if f(x) can be made as close as desired to L by taking x sufficiently close to c.
22 Nov 2022
1994 Scotland RAF Chinook Crash
On 2 June 1994, a Chinook helicopter of the Royal Air Force (RAF), serial number ZD576, crashed on the Mull of Kintyre, Scotland, in foggy conditions. The crash resulted in the deaths of all twenty-five passengers and four crew on board. Among the passengers were almost all the United Kingdom's senior Northern Ireland intelligence experts. The accident is the RAF's worst peacetime disaster. In 1995, an RAF board of inquiry ruled that it was impossible to establish the exact cause of the accident. This ruling was subsequently overturned by two senior reviewing officers, who stated the pilots were guilty of gross negligence for flying too fast and too low in thick fog. This finding proved to be controversial, especially in light of irregularities and technical issues surrounding the then-new Chinook HC.2 variant which were uncovered. A Parliamentary inquiry conducted in 2001 found the previous verdict of gross negligence on the part of the crew to be 'unjustified'. In 2011, an independent review of the crash cleared the crew of negligence.
14 Nov 2022
1D MPC and Thin-Film Analysis
The development of magnetic photonic crystals (MPC) has been a rapidly evolving research area since the late 1990s. Magneto-optic (MO) materials and the techniques for their characterization have also continually undergone functional and property-related improvements. MPC Optimization is a feature-rich Windows software application designed to enable researchers to analyse the optical and magneto-optical spectral properties of multilayers containing gyrotropic constituents. A set of computational approaches, and a custom software package have been described, designed to enable the design and optimization of 1D magnetic photonic crystals in terms of the achievable combinations of Faraday rotation, transmission, and reflection spectra.
25 Aug 2021
2 × 2 Real Matrices
In mathematics, the associative algebra of 2×2 real matrices is denoted by M(2, R). Two matrices p and q in M(2, R) have a sum p + q given by matrix addition. The product matrix p q is formed from the dot product of the rows and columns of its factors through matrix multiplication. For let Then q q* = q* q = (ad − bc) I, where I is the 2×2 identity matrix. The real number ad − bc is called the determinant of q. When ad − bc ≠ 0, q is an invertible matrix, and then The collection of all such invertible matrices constitutes the general linear group GL(2, R). In terms of abstract algebra, M(2, R) with the associated addition and multiplication operations forms a ring, and GL(2, R) is its group of units. M(2, R) is also a four-dimensional vector space, so it is considered an associative algebra. The 2×2 real matrices are in one-one correspondence with the linear mappings of the two-dimensional Cartesian coordinate system into itself by the rule The next section displays M(2,R) is a union of planar cross sections that include a real line. M(2,R) is ring isomorphic to split-quaternions, where there is a similar union but with index sets that are hyperboloids.
01 Nov 2022
2020 Nintendo Data Leak
The 2020 Nintendo data leak, more commonly referred to as the Nintendo Gigaleak is a series of leaks of data from Japanese video game company Nintendo on the anonymous imageboard website 4chan. The releasing of data started in March 2018, but became most prominent in 2020. Nine main sets of data leaked on 4chan, ranging from game and console source code to internal documentation and development tools. The name "Gigaleak" mainly refers to the second leak on July 24, 2020, which was 3 gigabytes in size. The leaks are believed to have come either from companies contracted by Nintendo in the design of these consoles, or from individuals previously convicted of intrusion into Nintendo systems. An earlier, much smaller leak had also occurred in 2018 which had the Nintendo Space World 1997 demos for Pokémon Gold and Silver leaked. The leaks are infamous for the sheer size and the amount of internal material leaked; video game journalists have described the magnitude of the leaks as unprecedented, and suggested that they might have significant effects for emulation and to preservationists, in addition to the legal questions posed by the leak. As of May 2021, Nintendo has not made any official response.
14 Oct 2022
2020 Twitter Bitcoin Scam
User:RMCD bot/subject notice On July 15, 2020, between 20:00 and 22:00 UTC, around 130 high-profile Twitter accounts were compromised by outside parties to promote a bitcoin scam. Twitter and other media sources confirmed that the perpetrators had gained access to Twitter's administrative tools so that they could alter the accounts themselves and post the tweets directly. They appeared to have used social engineering to gain access to the tools via Twitter employees. The scam tweets asked individuals to send bitcoin currency to a specific cryptocurrency wallet, with the promise of the Twitter user that money sent would be doubled and returned as a charitable gesture. Within minutes from the initial tweets, more than 320 transactions had already taken place on one of the wallet addresses, and more than US$110,000 of equivalent bitcoin had been deposited in one account before the scam messages were removed by Twitter. In addition, full message history data from eight non-verified accounts was also acquired. Dmitri Alperovitch, the co-founder of cybersecurity company CrowdStrike, described the incident as "the worst hack of a major social media platform yet." The FBI and other law enforcement agencies are investigating the scam and the security used by Twitter. Security researchers expressed concerns that the social engineering used to execute the hack can affect the use of social media in important online discussions, including the lead-up into the 2020 United States presidential election.
17 Nov 2022
Two dimensional filters have seen substantial development effort due to their importance and high applicability across several domains. In the 2-D case the situation is quite different from the 1-D case, because the multi-dimensional polynomials cannot in general be factored. This means that an arbitrary transfer function cannot generally be manipulated into a form required by a particular implementation. The input-output relationship of a 2-D IIR filter obeys a constant-coefficient linear partial difference equation from which the value of an output sample can be computed using the input samples and previously computed output samples. Because the values of the output samples are fed back, the 2-D filter, like its 1-D counterpart, can be unstable.
26 Oct 2022
360-Degree Video Bandwidth Reduction Techniques
The usage of 360-degree videos has prevailed in various sectors such as education, real estate, medical, entertainment and more. However, various challenges are faced to provide real-time streaming due to the nature of high-resolution 360-degree videos such as high bandwidth requirement, high computing power and low delay tolerance. To overcome these challenges, streaming methods such as dynamic adaptive streaming over HTTP (DASH), tiling, viewport-adaptive and machine learning (ML) are discussed.
09 Aug 2022
Biometrics have been used to identify humans since the 19th century. Over time, these biometrics became 3D. The main reason for this was the growing need for more features in the images to create more reliable identification models. Three main categories of 3D biometrics were identified. These were face, hand and gait. The corresponding percentages for these categories were 74.07%, 20.37% and 5.56%, respectively. The face is further categorized into facial, ear, iris and skull, while the hand is divided into fingerprint, finger vein and palm. In each category, facial and fingerprint were predominant, and their respective percentages were 80% and 54.55%. The use of the 3D reconstruction algorithms was also determined. These were stereo vision, structure-from-silhouette (SfS), structure-from-motion (SfM), structured light, time-of-flight (ToF), photometric stereo and tomography. Stereo vision and SfS were the most commonly used algorithms with a combined percentage of 51%. The state of the art for each category and the available datasets are also presented. Finally, multimodal biometrics, generalization of 3D reconstruction algorithms and anti-spoofing metrics are the three areas that should attract scientific interest for further research.
02 Sep 2022
In computing, 3D interaction is a form of human-machine interaction where users are able to move and perform interaction in 3D space. Both human and machine process information where the physical position of elements in the 3D space is relevant. The 3D space used for interaction can be the real physical space, a virtual space representation simulated in the computer, or a combination of both. When the real space is used for data input, humans perform actions or give commands to the machine using an input device that detects the 3D position of the human action. When it is used for data output, the simulated 3D virtual scene is projected onto the real environment through one output device or a combination of them.
29 Nov 2022
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Encyclopedia of Social Sciences
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