Sarin gas attack on the Tokyo subway - The injured. The short- and long-term symptoms experienced by those affected included: bleeding from the nose and mouth coma convulsions difficulty breathing disturbed sleep and nightmares extreme sensitivity to light foaming at the mouth high fevers influenza-like symptoms loss of consciousness loss of memory nausea and vomiting paralysis post-tr ...

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Sarin gas attack on the Tokyo subway, Sarin gas attack on the Tokyo subway - Background, Sarin gas attack on the Tokyo subway - The main perpetrators, Sarin gas attack on the Tokyo subway - Hayashi Ikuo, Sarin gas attack on the Tokyo subway - Hirose Ken'ichi, Sarin gas attack on the Tokyo subway - Toyoda Tōru, Sarin gas attack on the Tokyo subway - Yokoyama Masato, Sarin gas attack on the Tokyo subway - Hayashi Yasuo, Sarin gas attack on the Tokyo subway - The attack, Sarin gas attack on the Tokyo subway - Chiyoda line, Sarin gas attack on the Tokyo subway - Marunouchi line Ogikubo-bound, Sarin gas attack on the Tokyo subway - Marunouchi line Ikebukuro-bound, Sarin gas attack on the Tokyo subway - Hibiya line departing Naka-meguro, Sarin gas attack on the Tokyo subway - Hibiya line Naka-meguro-bound, Sarin gas attack on the Tokyo subway - Aftermath, Sarin gas attack on the Tokyo subway - The injured, Sarin gas attack on the Tokyo subway - Emergency services, Sarin gas attack on the Tokyo subway - AUM/Aleph today

Read more here: » Sarin gas attack on the Tokyo subway: Encyclopedia II - Sarin gas attack on the Tokyo subway - Aftermath

The sarin gas attack was the most serious terrorist attack in Japan's modern history. It caused massive disruption and widespread fear in a society that had previously been considered virtually free of crime. AUM attempted four more gas attacks after this one, employing various substances. All were unsuccessful. Shortly after the attack, AUM lost its status as a religious organization, and many of its assets were seized. However, the Diet (Japanese parliament) rejected a request from government officials to outlaw the sect altogether ...

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Sarin gas attack on the Tokyo subway, Sarin gas attack on the Tokyo subway - Background, Sarin gas attack on the Tokyo subway - The main perpetrators, Sarin gas attack on the Tokyo subway - Hayashi Ikuo, Sarin gas attack on the Tokyo subway - Hirose Ken'ichi, Sarin gas attack on the Tokyo subway - Toyoda Tōru, Sarin gas attack on the Tokyo subway - Yokoyama Masato, Sarin gas attack on the Tokyo subway - Hayashi Yasuo, Sarin gas attack on the Tokyo subway - The attack, Sarin gas attack on the Tokyo subway - Chiyoda line, Sarin gas attack on the Tokyo subway - Marunouchi line Ogikubo-bound, Sarin gas attack on the Tokyo subway - Marunouchi line Ikebukuro-bound, Sarin gas attack on the Tokyo subway - Hibiya line departing Naka-meguro, Sarin gas attack on the Tokyo subway - Hibiya line Naka-meguro-bound, Sarin gas attack on the Tokyo subway - Aftermath, Sarin gas attack on the Tokyo subway - The injured, Sarin gas attack on the Tokyo subway - Emergency services, Sarin gas attack on the Tokyo subway - AUM/Aleph today

Read more here: » Sarin gas attack on the Tokyo subway: Encyclopedia II - Sarin gas attack on the Tokyo subway - AUM/Aleph today

While the empty set is a standard and universally accepted concept in mathematics, there are those who still entertain doubts. Jonathan Lowe has argued that while the idea "was undoubtedly an important landmark in the history of mathematics, … we should not assume that its utility in calculation is dependent upon its actually denoting some object." It is not clear that such an idea makes sense. "All that we are ever informed about the empty set is that it (1) is a set, (2) has no members, and (3) is unique amongst sets in having no ...

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Empty set, Empty set - Notation, Empty set - Properties, Empty set - Common problems, Empty set - Axiomatic set theory, Empty set - Does it exist or is it necessary?, Empty set - Operations on the empty set, Empty set - Bounds, Empty set - The empty set and zero, Empty set - Category theory

Read more here: » Empty set: Encyclopedia II - Empty set - Does it exist or is it necessary?

For any model of computations there exist simple analogs for Busy Beaver. The generalization to Turing machines with n states and m symbols defines the following generalized Busy Beaver functions: Σ(n,m): the largest number of non-zeros printable by an n-state, m-symbol machine before halting, and S(n,m): the largest number of steps taken by an n-state, m-symbol machine before halting. The longest running 3-state 3-symbol machine found so far (found by Gregory Lafitte and Christophe Papazian[1] in ...

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Busy beaver, Busy beaver - Definition and known values, Busy beaver - Generalizations, Busy beaver - Trivial proof for uncomputability of Sn and Σn, Busy beaver - Examples of Busy Beaver Turing machines, Busy beaver - Exact values and lower bounds for some Snm and Σnm

Read more here: » Busy beaver: Encyclopedia II - Busy beaver - Generalizations

If a linear operator is defined on all of a Hilbert space then it is necessarily bounded. However, if we allow ourselves to define a linear map that is defined on a proper subspace of the Hilbert space, then we can obtain unbounded operators. In quantum mechanics, several interesting unbounded operators are defined on a dense subspace of Hilbert space. It is possible to define self-adjoint unbounded operators, and these play the role of the observables ...

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Hilbert space, Hilbert space - Introduction, Hilbert space - Definition, Hilbert space - Examples, Hilbert space - Euclidean spaces, Hilbert space - Sequence spaces, Hilbert space - Lebesgue spaces, Hilbert space - Sobolev spaces, Hilbert space - Operations on Hilbert spaces, Hilbert space - Bases, Hilbert space - Orthogonal complements and projections, Hilbert space - Reflexivity, Hilbert space - Bounded operators, Hilbert space - Unbounded operators

Read more here: » Hilbert space: Encyclopedia II - Hilbert space - Unbounded operators

Let Īs be the s-dimensional unit cube, Īs = [0, 1] × ... × [0, 1]. Let f have bounded variation V(f) on Īs in the sense of Hardy and Krause. Then for any x1, ..., xN in Is = [0, 1) × ... × [0, 1), The Koksma Hlawka inequality is sharp in the following sense: For any point set x1,...,xN in Is< ...

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Low-discrepancy sequence, Low-discrepancy sequence - Definition of discrepancy, Low-discrepancy sequence - The Koksma-Hlawka inequality, Low-discrepancy sequence - The formula of Hlawka-Zaremba, Low-discrepancy sequence - The L2 version of the Koksma-Hlawka inequality, Low-discrepancy sequence - The Erdős-Turan-Koksma inequality, Low-discrepancy sequence - The main conjectures, Low-discrepancy sequence - The best-known sequences, Low-discrepancy sequence - Lower bounds, Low-discrepancy sequence - Applications

Read more here: » Low-discrepancy sequence: Encyclopedia II - Low-discrepancy sequence - The Koksma-Hlawka inequality

The spectrum σ(x) of an element x of B is always compact and non-empty. If the spectrum were empty, then the resolvent function R(λ) = (λe - x)-1 would be defined everywhere on the complex plane and bounded, which would imply by Liouville's theorem that this function is constant, thus everywhere zero as it is zero at infinity, which would be a contradiction. The boundedness of the spectrum follows from the Neumann series expansion in λ, which also help ...

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Spectrum functional analysis, Spectrum functional analysis - Definition, Spectrum functional analysis - Basic properties, Spectrum functional analysis - Spectrum of a bounded operator, Spectrum functional analysis - Classification of points in the spectrum of an operator, Spectrum functional analysis - Point spectrum, Spectrum functional analysis - Approximate point spectrum, Spectrum functional analysis - Compression spectrum, Spectrum functional analysis - Further results, Spectrum functional analysis - Spectrum of unbounded operators

Read more here: » Spectrum functional analysis: Encyclopedia II - Spectrum functional analysis - Basic properties

Finding a worst-case linear algorithm for the general case of selecting the kth largest element is a much more difficult problem, but one does exist, and was published by Blum, Floyd, Pratt, Rivest, and Tarjan in their 1973 paper Time bounds for selection. It uses concepts based on those used in the quicksort sort algorithm, along with an innovation of its own. In quicksort, there is a subprocedure called partition which can, in linear time, group the list into two parts, those less than a certain value, and those greater than or equal to a certain value. Here i ...

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Selection algorithm, Selection algorithm - Selection with sorting algorithm, Selection algorithm - Linear minimum/maximum algorithms, Selection algorithm - Nonlinear general section algorithm, Selection algorithm - Partition based general selection algorithm, Selection algorithm - Linear general selection algorithm, Selection algorithm - Selection as incremental sorting, Selection algorithm - Using data structures to select in sublinear time, Selection algorithm - Selecting k smallest or largest elements, Selection algorithm - Lower bounds, Selection algorithm - Language support

Read more here: » Selection algorithm: Encyclopedia II - Selection algorithm - Partition based general selection algorithm

Monday, 20 March 1995 was for most a normal workday, though the following day was a national holiday. The attack came at the peak of the Monday morning rush hour on one of the world's busiest commuter transport systems: the Tokyo subway system transports millions of passengers daily; during rush hour, trains are frequently so crowded that it is impossible to move. The liquid sarin was contained in plastic bags which each team then wrapped in newspapers. Each perpetrator carried two packets of sarin totalling approximately one litre of sarin, except Hayashi Yasuo, who carried three bags. A si ...

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Sarin gas attack on the Tokyo subway, Sarin gas attack on the Tokyo subway - Background, Sarin gas attack on the Tokyo subway - The main perpetrators, Sarin gas attack on the Tokyo subway - Hayashi Ikuo, Sarin gas attack on the Tokyo subway - Hirose Ken'ichi, Sarin gas attack on the Tokyo subway - Toyoda Tōru, Sarin gas attack on the Tokyo subway - Yokoyama Masato, Sarin gas attack on the Tokyo subway - Hayashi Yasuo, Sarin gas attack on the Tokyo subway - The attack, Sarin gas attack on the Tokyo subway - Chiyoda line, Sarin gas attack on the Tokyo subway - Marunouchi line Ogikubo-bound, Sarin gas attack on the Tokyo subway - Marunouchi line Ikebukuro-bound, Sarin gas attack on the Tokyo subway - Hibiya line departing Naka-meguro, Sarin gas attack on the Tokyo subway - Hibiya line Naka-meguro-bound, Sarin gas attack on the Tokyo subway - Aftermath, Sarin gas attack on the Tokyo subway - The injured, Sarin gas attack on the Tokyo subway - Emergency services, Sarin gas attack on the Tokyo subway - AUM/Aleph today

Read more here: » Sarin gas attack on the Tokyo subway: Encyclopedia II - Sarin gas attack on the Tokyo subway - The attack

Let . For we write and denote by (xu,1) the point obtained from x by replacing the coordinates not in u by 1. Then ...

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Low-discrepancy sequence, Low-discrepancy sequence - Definition of discrepancy, Low-discrepancy sequence - The Koksma-Hlawka inequality, Low-discrepancy sequence - The formula of Hlawka-Zaremba, Low-discrepancy sequence - The L2 version of the Koksma-Hlawka inequality, Low-discrepancy sequence - The Erdős-Turan-Koksma inequality, Low-discrepancy sequence - The main conjectures, Low-discrepancy sequence - The best-known sequences, Low-discrepancy sequence - Lower bounds, Low-discrepancy sequence - Applications

Read more here: » Low-discrepancy sequence: Encyclopedia II - Low-discrepancy sequence - The formula of Hlawka-Zaremba

Any polynomial p(z) of degree d can be written in the form This is important in the theory of difference equations and can be seen as a discrete analog of Taylor's theorem. Newton's binomial series gets the simple form It is not hard to show that the radius of convergence of this series is 1. ...

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Binomial coefficient, Binomial coefficient - Example, Binomial coefficient - Derivation from binomial expansion, Binomial coefficient - Pascal's triangle, Binomial coefficient - Combinatorics and statistics, Binomial coefficient - Formulas involving binomial coefficients, Binomial coefficient - Divisors of binomial coefficients, Binomial coefficient - Bounds for binomial coefficients, Binomial coefficient - Generalization to multinomials, Binomial coefficient - Generalization to real and complex argument, Binomial coefficient - Newton's binomial series, Binomial coefficient - Generalization to q-series

Read more here: » Binomial coefficient: Encyclopedia II - Binomial coefficient - Newton's binomial series

Using the Taylor series expansion (some might say the definition) of the exponential function the above expression can be approximated as Therefore, An even coarser approximation is given by which, as the graph illustrates, is still fairly accurate. ...

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Birthday paradox, Birthday paradox - Understanding the paradox, Birthday paradox - Calculating the probability, Birthday paradox - Approximations, Birthday paradox - Same birthday as you, Birthday paradox - Reverse problem, Birthday paradox - Sample calculations, Birthday paradox - Generalization, Birthday paradox - Applications, Birthday paradox - An upper bound and a different perspective, Birthday paradox - Empirical test, Birthday paradox - Near matches, Birthday paradox - Collision counting, Birthday paradox - Notes

Read more here: » Birthday paradox: Encyclopedia II - Birthday paradox - Approximations

For a fixed probability p: Find the greatest n for which the probability p(n) is smaller than the given p, or Find the smallest n for which the probability p(n) is greater than the given p. An approximation to this can be derived by inverting the approximation above: Birthday paradox - Sample calculations. Note: some values are coloured showin ...

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Birthday paradox, Birthday paradox - Understanding the paradox, Birthday paradox - Calculating the probability, Birthday paradox - Approximations, Birthday paradox - Same birthday as you, Birthday paradox - Reverse problem, Birthday paradox - Sample calculations, Birthday paradox - Generalization, Birthday paradox - Applications, Birthday paradox - An upper bound and a different perspective, Birthday paradox - Empirical test, Birthday paradox - Near matches, Birthday paradox - Collision counting, Birthday paradox - Notes

Read more here: » Birthday paradox: Encyclopedia II - Birthday paradox - Reverse problem

The birthday problem can be generalised as follows: given n random integers drawn from a discrete uniform distribution with range [1,d], what is the probability p(n;d) that at least two numbers are the same? The generic results can be derived using the same arguments given above. ...

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Birthday paradox, Birthday paradox - Understanding the paradox, Birthday paradox - Calculating the probability, Birthday paradox - Approximations, Birthday paradox - Same birthday as you, Birthday paradox - Reverse problem, Birthday paradox - Sample calculations, Birthday paradox - Generalization, Birthday paradox - Applications, Birthday paradox - An upper bound and a different perspective, Birthday paradox - Empirical test, Birthday paradox - Near matches, Birthday paradox - Collision counting, Birthday paradox - Notes

Read more here: » Birthday paradox: Encyclopedia II - Birthday paradox - Generalization

BEATING THE BOUNDS: This act is performed by a group of local folk perambulating their farms, manors, kirkyards or specific geographical boundaries stopping at particular markers such as trees, walls, hedges, wells and standing stones that mark the extent of the boundary in order to ritually *beat'* specific landmarks with sticks (of Ash and Birch) to chase off such things as the spirit of the old year and negative energies for protective measures. 

(See also: BEATING THE BOUNDS, Witch, Witchcraft, Paganism, Pagan Dictionary)