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Page "Integer factorization" ¶ 11
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For and quantum
For example, an electron in the state is in a quantum superposition of the states and.
For example, in the 19th century, the Sun appeared to be no more than 20 million years old, but the Earth appeared to be no less than 300 million years ( resolved by the discovery of nuclear fusion and radioactivity, and the theory of quantum mechanics ); or current attempts to resolve theoretical differences between quantum mechanics and general relativity.
For example, quantum mechanics and solid state physics might be relevant to an engineer working on VLSI ( the design of integrated circuits ), but are largely irrelevant to engineers working with macroscopic electrical systems.
For example, in quantum field theory " locality " means that quantum fields at different points of space do not interact with one another.
For instance, when measuring the position of an electron, one imagines shining a light on it, thus disturbing the electron and producing the quantum mechanical uncertainties in its position.
For example, as the only neutral atom with an analytic solution to the Schrödinger equation, the study of the energetics and bonding of the hydrogen atom played a key role in the development of quantum mechanics.
For example, at very high temperature and high pressure, unless there are sufficiently many flavors of quarks, the theory of quantum chromodynamics ( QCD ) predicts that quarks and gluons will no longer be confined within hadrons < i > because the strength of the strong interaction diminishes with energy .</ i > This property, which is known as asymptotic freedom, has been experimentally confirmed in the energy range between 1 GeV ( gigaelectronvolt ) and 1 TeV ( teraelectronvolt ).
For all pictures the magnetic quantum number m has been set to 0, and the cross-sectional plane is the xz-plane ( z is the vertical axis ).
For example, every electron is the same and in quantum mechanics, one can not keep track of an individual electron precisely.
For example, the founder of quantum field theory, Paul Dirac, stated in 1951 in an article in Nature, titled " Is there an Aether?
For atomic and subatomic particles, Newton ’ s laws were superseded by quantum theory.
For instance, the motion of a spacecraft, regarding its orbit and attitude ( rotation ), is described by the relativistic theory of classical mechanics, while the analogous movements of an atomic nucleus are described by quantum mechanics.
For example, one can talk about motion of a wave or a quantum particle ( or any other field ) where the configuration consists of probabilities of occupying specific positions.
For quantum mechanics, this translates into the need to study the so-called classical limit of quantum mechanics.
For example, we cannot create backup copies of a state in the middle of a quantum computation, and use them to correct subsequent errors.
For example, in classical mechanics, the derivative is used ubiquitously, and in quantum mechanics, observables are represented by linear operators.
For example, Albert Einstein's revolutionary " Annus Mirabilis " papers in the 1905 issue of Annalen der Physik were not peer-reviewed by anyone other than the journal's editor-in-chief, Max Planck ( the father of quantum theory ), and its co-editor, Wilhelm Wien.
For example, no two electrons in a single atom can have the same four quantum numbers ; if n, l, and m < sub > l </ sub > are the same, m < sub > s </ sub > must be different such that the electrons have opposite spins, and so on.
For this purpose he introduced a new two-valued quantum number, identified by Samuel Goudsmit and George Uhlenbeck as electron spin.
For details, see the article on measurement in quantum mechanics.
For example, a single electron in an unexcited atom is pictured classically as a particle moving in a circular trajectory around the atomic nucleus, whereas in quantum mechanics it is described by a static, spherically symmetric wavefunction surrounding the nucleus ( Fig.

For and computer
For this step the computer memory is separated into three regions: cells in the W-region are used for storage of the forms in the text-form list ; ;
For general computer use access technology such as screen readers, screen magnifiers and refreshable Braille displays has been widely taken up along with standalone reading aids that integrate a scanner, optical character recognition ( OCR ) software, and speech software in a single machine.
* Antwerp ( Quest For Glory ), a monster in the Quest for Glory computer role-playing game series
For example, compositing is used extensively when combining computer rendered image elements with live footage.
For example, when a user logs into a computer that is part of a Windows domain, Active Directory checks the submitted password and determines whether the user is a system administrator or normal user.
For distinction between units of computer storage and bases kbp, Mbp, Gbp, etc.
For example a B205 console was often shown in the television series Batman as the Bat Computer ; also as the computer in Lost in Space.
For example, programming language theory studies approaches to description of computations, while the study of computer programming itself investigates various aspects of the use of programming languages and complex systems, and human-computer interaction focuses on the challenges in making computers and computations useful, usable, and universally accessible to humans.
For example, programming language theory considers various approaches to the description of computation, whilst the study of computer programming itself investigates various aspects of the use of programming language and complex systems.
For instance, it seemed to be unrealistic to comprehensively list human knowledge in a form usable by a symbolic computer program.
For a narrative explaining the overall developments, see the related history of computing hardware and history of computer science.
For 3D animations, objects ( models ) are built on the computer monitor ( modeled ) and 3D figures are rigged with a virtual skeleton.
For example, a payroll file might contain information concerning all the employees in a company and their payroll details ; each record in the payroll file concerns just one employee, and all the records have the common trait of being related to payroll — this is very similar to placing all payroll information into a specific filing cabinet in an office that does not have a computer.
For example, CP / M used a command syntax similar to RT-11's, and even retained the awkward PIP program used to copy data from one computer device to another.
For example, there is P2P ( peer-to-peer ) Internet television software that can be used to watch TV on a computer.
For example, if the authoritative name server for < tt > example. org </ tt > is < tt > ns1. example. org </ tt >, a computer trying to resolve < tt > www. example. org </ tt > first resolves < tt > ns1. example. org </ tt >.
For example, it may be more cost-efficient to obtain the desired level of performance by using a cluster of several low-end computers, in comparison with a single high-end computer.
: For computer network models, see network topology, packet generation model and channel model.
For example, the Kothmale Community Radio Internet uses both radio broadcasts and computer and Internet technologies to facilitate the sharing of information and provide educational opportunities in a rural community in Sri Lanka.
For example, the computer baseball games Earl Weaver Baseball and Tony La Russa Baseball each had highly detailed simulations of the game strategies of those two baseball managers.
For example, a popular software program, Adobe Acrobat, can be used to create content for most computer platforms, under various operating systems.
For example, one version said that if an infected computer contained a hard drive, it could be destroyed.
For example, take the following comparison of execution time of computer programs:
For computer savvy do-it-yourself hobbyists CNC ( Computer Numerical Control ) machining is also popular.
For a computing machine to be a practical general-purpose computer, there must be some convenient read-write mechanism, punched tape, for example.

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