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Marine biology is a branch of biology. It is closely linked to oceanography, especially biological oceanography, and may be regarded as a sub-field of marine science. It also encompasses many ideas from ecology. Fisheries science and marine conservation can be considered partial offshoots of marine biology (as well as ...
Marine creatures
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The Escalation Hypothesis is an evolutionary theory in biology put forward by Geerat J. Vermeij. It states that organisms are in constant conflict with one another and therefore devote many resources to thwarting the adaptations evolution brings to all competing organisms as time advances. This is in contrast to adapta...
Escalation hypothesis
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85,902
In mathematics, a Solinas prime, or generalized Mersenne prime, is a prime number that has the form f ( 2 m ) {\displaystyle f(2^{m})} , where f ( x ) {\displaystyle f(x)} is a low-degree polynomial with small integer coefficients. These primes allow fast modular reduction algorithms and are widely used in cryptography...
Generalized Mersenne prime
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The universal construction is also used to define universal C*-algebras of isometries. Remark. The Gelfand representation or Gelfand isomorphism for a commutative C*-algebra with unit A {\displaystyle A} is an isometric *-isomorphism from A {\displaystyle A} to the algebra of continuous complex-valued functions on the ...
Gelfand–Naimark theorem
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85,904
Taking the completion of A / I relative to this pre-C*-norm produces a C*-algebra B. By the Krein–Milman theorem one can show without too much difficulty that for x an element of the Banach *-algebra A having an approximate identity: sup f ∈ State ⁡ ( A ) f ( x ∗ x ) = sup f ∈ PureState ⁡ ( A ) f ( x ∗ x ) . {\displays...
Gelfand–Naimark theorem
0.782757
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In general (when A is not a C*-algebra) it will not be a faithful representation. The closure of the image of π(A) will be a C*-algebra of operators called the C*-enveloping algebra of A. Equivalently, we can define the C*-enveloping algebra as follows: Define a real valued function on A by ‖ x ‖ C ∗ = sup f f ( x ∗ x ...
Gelfand–Naimark theorem
0.782757
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Let x be a non-zero element of A. By the Krein extension theorem for positive linear functionals, there is a state f on A such that f(z) ≥ 0 for all non-negative z in A and f(−x* x) < 0. Consider the GNS representation πf with cyclic vector ξ. Since ‖ π f ( x ) ξ ‖ 2 = ⟨ π f ( x ) ξ ∣ π f ( x ) ξ ⟩ = ⟨ ξ ∣ π f ( x ∗ ) ...
Gelfand–Naimark theorem
0.782757
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Theorem. The Gelfand–Naimark representation of a C*-algebra is an isometric *-representation. It suffices to show the map π is injective, since for *-morphisms of C*-algebras injective implies isometric.
Gelfand–Naimark theorem
0.782757
85,908
In mathematics, the Gelfand–Naimark theorem states that an arbitrary C*-algebra A is isometrically *-isomorphic to a C*-subalgebra of bounded operators on a Hilbert space. This result was proven by Israel Gelfand and Mark Naimark in 1943 and was a significant point in the development of the theory of C*-algebras since ...
Gelfand–Naimark theorem
0.782757
85,909
The journal was established in March 1986 as the official publication of the Society for Research on Biological Rhythms with Benjamin Rusak as first editor-in-chief; he served from 1986 to 1994. The first issue largely focused on zoology and physiology, but over the years the field of discussion has expanded to include...
Journal of Biological Rhythms
0.782756
85,910
The Journal of Biological Rhythms is a bimonthly peer-reviewed scientific journal that covers chronobiology or any rhythms, especially biological rhythms with a special emphasis on seasonal and circadian rhythms. The journal publishes primary reports, reviews, commentaries, or letters. The Journal of Biological Rhythms...
Journal of Biological Rhythms
0.782756
85,911
Each component in the database is assigned a type (“calculation,” “data,” “logic,” etc.) and a size (from “very small” to “very large”). When a new project must be estimated, it is broken down into tasks that correspond to these types and sizes. A formula based on linear regression is used to calculate the estimate for...
Proxy-based estimating
0.782755
85,912
Proxy-Based Estimating (PROBE) is an estimating process used in the Personal Software Process (PSP) to estimate size and effort. Proxy Based Estimating (PROBE), is the estimation method introduced by Watts Humphrey (of the Software Engineering Institute at Carnegie Mellon University) as part of the Personal Software Pr...
Proxy-based estimating
0.782755
85,913
Its minimum magnitude is 7 and its maximum: 5. Galaxies include NGC 7038, NGC 7049, and NGC 7090. All Sky Automated Survey for SuperNovae (ASAS-SN) in 2015 detected a superluminous supernova, named ASASSN-15lh (also designated SN 2015L). Based on the study conducted by Subo Dong and team from the Kavli Institute for As...
Gamma Indi
0.782754
85,914
In mathematics, Schreier's lemma is a theorem in group theory used in the Schreier–Sims algorithm and also for finding a presentation of a subgroup.
Schreier's lemma
0.782753
85,915
Kapton is a polyimide film used in flexible printed circuits (flexible electronics) and space blankets, which are used on spacecraft, satellites, and various space instruments. Invented by the DuPont Corporation in the 1960s, Kapton remains stable (in isolation) across a wide range of temperatures, from 4 to 673 K (−26...
Kapton
0.782752
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Kapton and ABS adhere to each other very well, which has led to widespread use of Kapton as a build surface for 3D printers. Kapton is laid down on a flat surface and the ABS is extruded onto the Kapton surface. The ABS part being printed will not detach from the build platform as it cools and shrinks, a common cause o...
Kapton
0.782752
85,917
For example, the Daedalus Project study, which proposed a spacecraft powered by the fusion of deuterium and helium-3, would require 36 years to reach the "nearby" Alpha Centauri system. Other proposed interstellar propulsion systems include light sails, ramjets, and beam-powered propulsion. More advanced propulsion sys...
Intergalactic space
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85,918
The absence of air makes outer space an ideal location for astronomy at all wavelengths of the electromagnetic spectrum. This is evidenced by the spectacular pictures sent back by the Hubble Space Telescope, allowing light from more than 13 billion years ago—almost to the time of the Big Bang—to be observed. Not every ...
Intergalactic space
0.782751
85,919
The Earth's atmospheric pressure drops to about 0.032 Pa at 100 kilometres (62 miles) of altitude, compared to 100,000 Pa for the International Union of Pure and Applied Chemistry (IUPAC) definition of standard pressure. Above this altitude, isotropic gas pressure rapidly becomes insignificant when compared to radiatio...
Intergalactic space
0.782751
85,920
The low density of matter in outer space means that electromagnetic radiation can travel great distances without being scattered: the mean free path of a photon in intergalactic space is about 1023 km, or 10 billion light years. In spite of this, extinction, which is the absorption and scattering of photons by dust and...
Intergalactic space
0.782751
85,921
random variables Xn1, ..., Xnn whose sum Sn = Xn1 + … + Xnn has the same distribution F. The concept of infinite divisibility of probability distributions was introduced in 1929 by Bruno de Finetti. This type of decomposition of a distribution is used in probability and statistics to find families of probability distri...
Infinitely divisible probability distribution
0.782751
85,922
In probability theory, a probability distribution is infinitely divisible if it can be expressed as the probability distribution of the sum of an arbitrary number of independent and identically distributed (i.i.d.) random variables. The characteristic function of any infinitely divisible distribution is then called an ...
Infinitely divisible probability distribution
0.782751
85,923
Taxodone was first isolated in 1968 from the seeds of Taxodium distichum (Bald Cypress) by S. Morris Kupchan and coworkers. They reported the structure determination and basic chemistry of taxodone and its oxidized rearrangement product, taxodione. Taxodone occurs naturally in the form of (+)-taxodone.
Taxodone
0.78275
85,924
For a morphism of varieties f: X → Y {\displaystyle f:X\to Y} the pushforward maps f ∗ Q _ X H d g {\displaystyle f_{*}{\underline {\mathbb {Q} }}_{X}^{Hdg}} and f ! Q _ X H d g {\displaystyle f_{! }{\underline {\mathbb {Q} }}_{X}^{Hdg}} give degenerating variations of mixed Hodge structures on Y {\displaystyle Y} . In...
Mixed Hodge module
0.782748
85,925
There is a dualizing functor D X {\displaystyle \mathbb {D} _{X}} lifting the Verdier dualizing functor in D c s b ( X ; Q ) {\displaystyle D_{cs}^{b}(X;\mathbb {Q} )} which is an involution on MHM ( X ) {\displaystyle {\textbf {MHM}}(X)} .For a morphism f: X → Y {\displaystyle f:X\to Y} of algebraic varieties, the ass...
Mixed Hodge module
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85,926
One of the defining features of the category of mixed Hodge modules is the fact intersection cohomology can be phrased in its language. This makes it possible to use the decomposition theorem for maps f: X → Y {\displaystyle f:X\to Y} of varieties. To define the intersection complex, let j: U ↪ X {\displaystyle j:U\hoo...
Mixed Hodge module
0.782748
85,927
In mathematics, mixed Hodge modules are the culmination of Hodge theory, mixed Hodge structures, intersection cohomology, and the decomposition theorem yielding a coherent framework for discussing variations of degenerating mixed Hodge structures through the six functor formalism. Essentially, these objects are a pair ...
Mixed Hodge module
0.782748
85,928
Suppose that π is an irreducible unitary representation of G on a Hilbert space H. If f is a compactly supported smooth function on the group G, then the operator on H π ( f ) = ∫ G f ( x ) π ( x ) d x {\displaystyle \pi (f)=\int _{G}f(x)\pi (x)\,dx} is of trace class, and the distribution Θ π: f ↦ Tr ⁡ ( π ( f ) ) {\d...
Distributional character
0.782746
85,929
In mathematics, a compact semigroup is a semigroup in which the sets of solutions to equations can be described by finite sets of equations. The term "compact" here does not refer to any topology on the semigroup. Let S be a semigroup and X a finite set of letters.
Compact semigroup
0.782745
85,930
In mathematics in the branch of differential geometry, the cocurvature of a connection on a manifold is the obstruction to the integrability of the vertical bundle.
Cocurvature
0.782741
85,931
In mathematics, the Manin conjecture describes the conjectural distribution of rational points on an algebraic variety relative to a suitable height function. It was proposed by Yuri I. Manin and his collaborators in 1989 when they initiated a program with the aim of describing the distribution of rational points on su...
Manin conjecture
0.78274
85,932
A 1,3-diaxial interaction happens between the atoms connected to the first and third carbons. The more interactions the more strain on the molecule and the conformations with the most strain are less likely to be seen. An example is cyclopropane which, because of its planar geometry, has six fully eclipsed carbon and a...
Ring flip
0.78274
85,933
In organic chemistry, a ring flip (also known as a ring inversion or ring reversal) is the interconversion of cyclic conformers that have equivalent ring shapes (e.g., from a chair conformer to another chair conformer) that results in the exchange of nonequivalent substituent positions. The overall process generally ta...
Ring flip
0.78274
85,934
Although the field of astrobiology usually investigates possibilities of simple lifeforms that may exist on alien planets, The Zoologist's Guide to the Galaxy considers the possibilities of complex life, and in particular, life that might be considered as animal life. The book begins by laying out the argument that evo...
The Zoologist's Guide to the Galaxy
0.782738
85,935
This chapter explores whether such artificial intelligence would also be subject to the laws of evolution. 11. Humanity, As We Know It Drawing on the principles of the previous chapter, Kershenbaum emphasises that underlying similarities between life on Earth and that on other planets implies that the title of human sh...
The Zoologist's Guide to the Galaxy
0.782738
85,936
10. Artificial Intelligence – A Universe Full of Bots? Some scientists (e.g. astronomer Seth Shostak) have proposed that alien life is more likely to be technological rather than biological.
The Zoologist's Guide to the Galaxy
0.782738
85,937
Movement – Scuttling and Gliding Across Space How the constrains of physics and mechanics combined with evolutionary laws to produce the movement strategies we see on Earth, and why many of these strategies (e.g. legs) are likely to exist on other planets too. 5. Communication Channels The different ways that animals c...
The Zoologist's Guide to the Galaxy
0.782738
85,938
BBC Science Focus magazine's 15 of the best space and astronomy books 2020 The Times Best science books of the year 2020
The Zoologist's Guide to the Galaxy
0.782738
85,939
As a result, many aspects of animal behavior are likely to be present in the equivalent lifeforms on alien planets. This includes certain features of social behavior, communication, and movement, the evolutionary origin of which on Earth is underpinned by universal processes. The book has been praised by critics for it...
The Zoologist's Guide to the Galaxy
0.782738
85,940
When we finally discover aliens, what might they be like?... Where much writing on astrobiology is joyously speculative, Kershenbaum is doggedly cautious, building his case from first evolutionary principles. "Primatologist Frans de Waal wrote, "If you don't want to be surprised by extraterrestrial life, look no furthe...
The Zoologist's Guide to the Galaxy
0.782738
85,941
Noetherian relation, a binary relation that satisfies the ascending chain condition on its elements. Noetherian topological space, a topological space that satisfies the descending chain condition on closed sets. Noetherian induction, also called well-founded induction, a proof method for binary relations that satisfy ...
Noetherian
0.782738
85,942
The convex hull of any finite set of points on the moment curve is a cyclic polytope. Cyclic polytopes have the largest possible number of faces for a given number of vertices, and in dimensions four or more have the property that their edges form a complete graph. More strongly, they are neighborly polytopes, meaning ...
Moment curve
0.782738
85,943
In geometry, the moment curve is an algebraic curve in d-dimensional Euclidean space given by the set of points with Cartesian coordinates of the form ( x , x 2 , x 3 , … , x d ) . {\displaystyle \left(x,x^{2},x^{3},\dots ,x^{d}\right).} In the Euclidean plane, the moment curve is a parabola, and in three-dimensional s...
Moment curve
0.782738
85,944
The third thread in the development of quantum field theory was the need to handle the statistics of many-particle systems consistently and with ease. In 1927, Pascual Jordan tried to extend the canonical quantization of fields to the many-body wave functions of identical particles using a formalism which is known as s...
History of quantum field theory
0.782737
85,945
It was evident from the beginning that a proper quantum treatment of the electromagnetic field had to somehow incorporate Einstein's relativity theory, which had grown out of the study of classical electromagnetism. This need to put together relativity and quantum mechanics was the second major motivation in the develo...
History of quantum field theory
0.782737
85,946
By the late 1970s, these efforts successfully utilized gauge theory in the strong nuclear force and weak nuclear force, producing the modern Standard Model of particle physics. Efforts to describe gravity using the same techniques have, to date, failed. The study of quantum field theory is still flourishing, as are app...
History of quantum field theory
0.782737
85,947
In particle physics, the history of quantum field theory starts with its creation by Paul Dirac, when he attempted to quantize the electromagnetic field in the late 1920s. Heisenberg was awarded the 1932 Nobel Prize in Physics "for the creation of quantum mechanics". Major advances in the theory were made in the 1940s ...
History of quantum field theory
0.782737
85,948
These directly corresponded (through the Schwinger–Dyson equation) to the measurable physical processes (cross sections, probability amplitudes, decay widths and lifetimes of excited states) one needs to be able to calculate. This revolutionized how quantum field theory calculations are carried-out in practice. Two cla...
History of quantum field theory
0.782737
85,949
The first approach that bore fruit is known as the "interaction representation" (see the article Interaction picture), a Lorentz-covariant and gauge-invariant generalization of time-dependent perturbation theory used in ordinary quantum mechanics, and developed by Tomonaga and Schwinger, generalizing earlier efforts of...
History of quantum field theory
0.782737
85,950
Algebraic quantum field theory Axiomatic quantum field theory Topological quantum field theory (TQFT)
History of quantum field theory
0.782737
85,951
In the absence of dynamical information, Murray Gell-Mann pioneered the extraction of physical predictions from sheer non-abelian symmetry considerations, and introduced non-abelian Lie groups to current algebra and so the gauge theories that came to supersede it. The 1960s and 1970s saw the formulation of a gauge theo...
History of quantum field theory
0.782737
85,952
Later, there developed the idea that a finite number of generating operators could represent all the correlation functions of the Ising model. The existence of a much stronger symmetry for the scaling limit of two-dimensional critical systems was suggested by Alexander Belavin, Alexander Markovich Polyakov and Alexande...
History of quantum field theory
0.782737
85,953
The remarkable conclusion is that, in general, most observables are "irrelevant", i.e., the macroscopic physics is dominated by only a few observables in most systems. During the same period, Leo Kadanoff (1969) introduced an operator algebra formalism for the two-dimensional Ising model, a widely studied mathematical ...
History of quantum field theory
0.782737
85,954
Parallel breakthroughs in the understanding of phase transitions in condensed matter physics led to novel insights based on the renormalization group. They involved the work of Leo Kadanoff (1966) and Kenneth Geddes Wilson–Michael Fisher (1972)—extending the work of Ernst Stueckelberg–André Petermann (1953) and Murray ...
History of quantum field theory
0.782737
85,955
In the case of the strong interactions, progress concerning their short-distance/high-energy behavior was much slower and more frustrating. For strong interactions with the electro-weak fields, there were difficult issues regarding the strength of coupling, the mass generation of the force carriers as well as their non...
History of quantum field theory
0.782737
85,956
The electron density of the ground state of a molecular system contains cusps at the location of the nuclei, and by identifying these from the total electron density of the system, the positions are thus established. From Kato's theorem, one also obtains the nuclear charge of the nuclei, and thus the external potential...
Kato theorem
0.782736
85,957
The Kato theorem, or Kato's cusp condition (after Japanese mathematician Tosio Kato), is used in computational quantum physics. It states that for generalized Coulomb potentials, the electron density has a cusp at the position of the nuclei, where it satisfies Z k = − a o 2 n ( r ) d n ( r ) d r | r → R k {\displaystyl...
Kato theorem
0.782736
85,958
The rule stated in the Baudhāyana Śulvasūtra is: दीर्घचतुरस्रस्याक्ष्णया रज्जुः पार्श्वमानी तिर्यग् मानी च यत् पृथग् भूते कुरूतस्तदुभयं करोति ॥dīrghachatursrasyākṣaṇayā rajjuḥ pārśvamānī, tiryagmānī,cha yatpṛthagbhūte kurutastadubhayāṅ karoti. The diagonal of an oblong produces by itself both the areas which the two si...
Baudhayana sequences
0.782735
85,959
Baudhāyana i.61-2 (elaborated in Āpastamba Sulbasūtra i.6) gives the length of the diagonal of a square in terms of its sides, which is equivalent to a formula for the square root of 2: samasya dvikaraṇī. pramāṇaṃ tṛtīyena vardhayet tac caturthenātmacatustriṃśonena saviśeṣaḥThe diagonal of a square. The measure is to ...
Baudhayana sequences
0.782735
85,960
The Baudhāyana Śulvasūtra states the rule referred to today in most of the world as the Pythagorean Theorem. The rule was known to a number of ancient civilizations, including also the Greek and the Chinese, and was recorded in Mesopotamia as far back as 1800 BCE. For the most part, the Śulvasūtras do not contain proof...
Baudhayana sequences
0.782735
85,961
This joint action plan was constructed in order for the U.S. and Canada to protect and improve safety and environmental impacts of NMs without hindering growth and investment in NMs for both countries. The RCC oversees both countries and has maintained regulations, worked to create new regulations with the goal of alig...
Nanomaterials pollution
0.782733
85,962
This R&D initiative involves 20 departments and independent agencies that focus on nanotechnology innovation and regulation in the United States. Projects and activities of NNI span from R&D to policy on environment and safety regulations of NMs.
Nanomaterials pollution
0.782733
85,963
Knowledge of the effects of industrial nanoparticles (NPs) released into the environment remains limited. Effects vary widely over aquatic and terrestrial environments as well as types of organisms. The characteristics of the nanoparticle itself plays a wide variety of roles including size, charge, composition, surface...
Nanomaterials pollution
0.782733
85,964
Dejean's theorem (formerly Dejean's conjecture) is a statement about repetitions in infinite strings of symbols. It belongs to the field of combinatorics on words; it was conjectured in 1972 by Françoise Dejean and proven in 2009 by Currie and Rampersad and, independently, by Rao.
Dejean's theorem
0.782733
85,965
More strongly, the Thue–Morse sequence contains no substring that is a power strictly greater than two.In 1972, Dejean investigated the problem of determining, for each possible alphabet size, the threshold between exponents e {\displaystyle e} for which there exists an infinite e {\displaystyle e} -power-free word, an...
Dejean's theorem
0.782732
85,966
Instead, it resembles the complex, organic cycles of biology, where basic intervals endure but precise timing is difficult to predict. Strauss and Howe compare the saecular rhythm to the four seasons, which they say similarly occur in the same order, but with slightly varying timing. Just as winter may come sooner or l...
Strauss–Howe generational theory
0.782732
85,967
According to Strauss and Howe, however, this is not the case. As long as the transition to adulthood occurs around age 20, the transition to midlife around age 40, and the transition to old age around age 60, they say the basic length of both generations and turnings will remain the same.In their book, The Fourth Turni...
Strauss–Howe generational theory
0.782732
85,968
Further, Brooks wrote that the generations aren't treated equally: "Basically, it sounds as if America has two greatest generations at either end of the age scale and two crummiest in the middle".In 2001, reviewer Dina Gomez wrote in NEA Today that they make their case "convincingly," with "intriguing analysis of popul...
Strauss–Howe generational theory
0.782732
85,969
Set-valued functions arise in optimal control theory, especially differential inclusions and related subjects as game theory, where the Kakutani fixed-point theorem for set-valued functions has been applied to prove existence of Nash equilibria. This among many other properties loosely associated with approximability o...
Set-valued function
0.78273
85,970
Since the publication of Men at Arms, others have also made reference to the theory. In 2013, an article by the US ConsumerAffairs made reference to the theory in regard to purchasing items on credit, specifically regarding children's boots from the retailer Fingerhut; a $25 pair of boots, at the interest rates being o...
Boots theory
0.78273
85,971
In mechanical engineering and materials science, a notch refers to a V-shaped, U-shaped, or semi-circular defect deliberately introduced into a planar material. In structural components, a notch causes a stress concentration which can result in the initiation and growth of fatigue cracks. Notches are used in materials ...
Notch (engineering)
0.782729
85,972
Cell survival fractions are exponential functions with a dose-dependent term in the exponent due to the Poisson statistics underlying the stochastic process. Whereas single lethal events lead to an exponent that is linearly related to dose, the survival fraction function for a two-stage mechanism carries an exponent pr...
Cell survival curve
0.782729
85,973
A cell survival curve is a curve used in radiobiology. It depicts the relationship between the fraction of cells retaining their reproductive integrity and the absorbed dose of radiation. Conventionally, the surviving fraction is depicted on a logarithmic scale, and is plotted on the y-axis against dose on the x-axis. ...
Cell survival curve
0.782729
85,974
Research areas include the theoretical and practical aspects of condensed matter and atomically resolved dynamics, fundamental light-matter interaction, accelerator-based light sources, coherent imaging, coherent controlled molecular and solid state dynamics, molecule imaging, extreme timescale spectroscopy, ultrafast ...
International Max Planck Research School for Ultrafast Imaging and Structural Dynamics
0.782728
85,975
One rule to rewrite a term could be applied in many different ways to that term, or more than one rule could be applicable. Rewriting systems then do not provide an algorithm for changing one term to another, but a set of possible rule applications. When combined with an appropriate algorithm, however, rewrite systems ...
Rewrite system
0.782727
85,976
In mathematics, computer science, and logic, rewriting covers a wide range of methods of replacing subterms of a formula with other terms. Such methods may be achieved by rewriting systems (also known as rewrite systems, rewrite engines, or reduction systems). In their most basic form, they consist of a set of objects,...
Rewrite system
0.782727
85,977
This results in a general life expectancy of 10 to 15 years. These materials are also available in colors, but are subject to limited manufacturing runs. Tio2 (Titanium Dioxide) Top coating "Titan W": TITAN W is a surface finish whose formulation was prepared by Naizil S.p.A. in collaboration with the Chemical Engineer...
Fabric structure
0.782727
85,978
In computer science, a zombie computer is a computer connected to the Internet that has been compromised by a hacker, computer virus or trojan horse and can be used to perform malicious tasks under remote direction. Botnets of zombie computers are often used to spread e-mail spam and launch denial-of-service attacks (D...
Command and control server
0.782726
85,979
Since most botnets using IRC networks and domains can be taken down with time, hackers have moved to P2P botnets with C&C to make the botnet more resilient and resistant to termination. Some have also used encryption as a way to secure or lock down the botnet from others, most of the time when they use encryption it is...
Command and control server
0.782726
85,980
Like many commonly used statistics, the sample statistic r is not robust, so its value can be misleading if outliers are present. Specifically, the PMCC is neither distributionally robust, nor outlier resistant (see Robust statistics § Definition). Inspection of the scatterplot between X and Y will typically reveal a s...
Pearson correlation coefficient
0.782723
85,981
A few types of vehicle use only rear-wheel steering, notably fork lift trucks, camera dollies, early pay loaders, Buckminster Fuller's Dymaxion car, and the ThrustSSC.In cars, rear-wheel steering tends to be unstable because, in turns, the steering geometry changes, hence decreasing the turn radius (oversteer), rather ...
Four wheel steering
0.782723
85,982
Each wheel is steered with a pivot point ahead of the wheel, which tends to make the steering self-centering towards the direction of travel. The steering linkages connecting the steering box and the wheels usually conform to a variation of Ackermann steering geometry, to account for the fact that in a turn, the inner ...
Four wheel steering
0.782723
85,983
The principal ideal theorem was conjectured by David Hilbert (1902), and was the last remaining aspect of his program on class fields to be completed, in 1929. Emil Artin (1927, 1929) reduced the principal ideal theorem to a question about finite abelian groups: he showed that it would follow if the transfer from a fin...
Principalisation property
0.782722
85,984
In mathematics, the principal ideal theorem of class field theory, a branch of algebraic number theory, says that extending ideals gives a mapping on the class group of an algebraic number field to the class group of its Hilbert class field, which sends all ideal classes to the class of a principal ideal. The phenomeno...
Principalisation property
0.782722
85,985
By gluing the local trivializations together using these transition functions, one may reconstruct the original principal bundle. This is an example of the fiber bundle construction theorem. For any x ∈ Ui ∩ Uj we have s j ( x ) = s i ( x ) ⋅ t i j ( x ) . {\displaystyle s_{j}(x)=s_{i}(x)\cdot t_{ij}(x).}
Principle bundle
0.782721
85,986
In terms of the associated local section s the map φ is given by φ ( s ( x ) ⋅ g ) = g . {\displaystyle \varphi (s(x)\cdot g)=g.} The local version of the cross section theorem then states that the equivariant local trivializations of a principal bundle are in one-to-one correspondence with local sections.
Principle bundle
0.782721
85,987
In the second half of 2010, the testing forum applied STEP-NC to set up compensation with on-machine measurement of part and fixture datums using a FaroArm portable measurement device.In 2012, the testing focused on machine tool accuracy calculations, culminating in a demonstration in June at the KTH production enginee...
STEP-NC
0.78272
85,988
Bordeaux, Boeing, Eurostep, KTH Royal Institute of Technology, NIST, Sandvik Coromant, Scania, STEP Tools, and Univ. of Vigo.On October 1–2, 2008, the STEP Manufacturing team met at the Connecticut Center for Advanced Technology, in Hartford, Connecticut to demonstrate closed-loop machining, feed optimization, and meas...
STEP-NC
0.78272
85,989
In addition, Boeing cut parts on a variety of machines at their Tulsa facility and a machine at NIST in Gaithersburg.In June 2006, a live 5-axis STEP-NC machining demonstration was hosted by Airbus at the Université Paul Sabatier Laboratoire de Génie mécanique in Toulouse. Further machining and measurement demonstratio...
STEP-NC
0.78272
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Visual process, to show toolpaths in context of the machine and workpiece, and eliminate drawings. On-Machine Simulation, to check for gouges, machine interference and other undesired behavior. Simplified Inspection, with linked tolerances, on-machine probes and inspection workplans tied to part tolerances. Feed and Sp...
STEP-NC
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Input to a CNC in the ISO 6983/RS274D G-code control language is often machine-specific and limited to axis motion commands. The machine tool is given little or no information about the desired result of the machining. STEP-NC allows more information about the machining process to be sent to the machine control and add...
STEP-NC
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Schrödinger's Kittens and the Search for Reality is a 1995 book by John Gribbin, in which the author attempts to explain the mysteries of modern quantum mechanics in a popular-scientific way. It is a sequel to his earlier book, In Search of Schrödinger's Cat (1984). In his epilogue, Gribbin touches on what were then th...
Schrödinger's Kittens and the Search for Reality
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STEP-NC is not the first attempt at providing better quality information to a CNC. The EIA 494 Basic Control Language (BCL) defined a control language that was portable and had toolpaths independent of machine geometry, but did not contain any of the other product model information found in STEP-NC.The core of STEP-NC ...
STEP-NC
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A STEP-NC program can use the full range of geometric constructs from the STEP standard to communicate device-independent toolpaths to the CNC. It can provide CAM operational descriptions and STEP CAD geometry to the CNC so workpieces, stock, fixtures and cutting tool shapes can be visualized and analyzed in the contex...
STEP-NC
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STEP-NC can communicate a complete machining process description to a machine tool control or between manufacturing software applications. The information handled by STEP-NC can be divided into the following general categories. The standard handles technology-specific parameters for milling and turning, and extensions ...
STEP-NC
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A catenated sulfophosphate has the sulfur and phosphorus joined by an oxygen atom. In biochemistry, metabolism of sulfate may use such a group, for example with adenosine-5'-phosphosulfate. == References ==
Phosphate sulfate
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More generally, Laver proved the same result for order embeddings of countable unions of scattered orders.In reverse mathematics, the version of the theorem for countable orders is denoted FRA (for Fraïssé) and the version for countable unions of scattered orders is denoted LAV (for Laver). In terms of the "big five" s...
Laver's theorem
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Laver's theorem, in order theory, states that order embeddability of countable total orders is a well-quasi-ordering. That is, for every infinite sequence of totally-ordered countable sets, there exists an order embedding from an earlier member of the sequence to a later member. This result was previously known as Fraï...
Laver's theorem
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Su-7BM variable geometry wing demonstrator.
Su-22 Fitter
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