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17,300 | Hans Kuhn in 1972 laid out a possible process by which the modern genetic system might have arisen from a nucleotide-based precursor, and this led Harold White in 1976 to observe that many of the cofactors essential for enzymatic function are either nucleotides or could have been derived from nucleotides. He proposed a... | RNA World Hypothesis | 0.813013 |
17,301 | At about the same time (late 1960s) the newly developed technique of C0t analysis was refined to include RNA:DNA hybridization leading to the discovery that considerably less than 10% of the human genome was complementary to mRNA and this DNA was in the unique (non-repetitive) fraction. This confirmed the predictions m... | Junk DNA | 0.813008 |
17,302 | Different methodologies rest on different implicit definitions yield different estimates of the non-functional fraction of the genome.For example, 20% of human genomic DNA shows no detectable biochemical activity, but comparative genomics methods estimate a nonfunctional fraction of 85-92%. Consequently, different exac... | Junk DNA | 0.813008 |
17,303 | Contributing to the debate is that there is no consensus on what constitutes a "functional" element in the genome since geneticists, evolutionary biologists, and molecular biologists employ different approaches and definitions of "function", often with a lack of clarity of what they mean in the literature. Due to the a... | Junk DNA | 0.813008 |
17,304 | One indication of functionality of a genomic region is if that sequence has been maintained by purifying selection (or if mutating away the sequence is deleterious to the organism). Estimates for the functionally constrained fraction of the human genome based on evolutionary conservation using comparative genomics rang... | Junk DNA | 0.813008 |
17,305 | Early proponents of junk DNA did not base their arguments on ignorance; they based their arguments on what was known about genome sizes, gene duplication, mutational load, and population genetics. (See The history of junk DNA.) Some have argued that the term "non-coding DNA" is unfortunate because it sounds like "nonse... | Junk DNA | 0.813008 |
17,306 | The idea that only a fraction of the human genome could be functional dates back to the late 1940s. The estimated mutation rate in humans suggested that if a large fraction of those mutations were deleterious then the human species could not survive such a mutation load (genetic load). This led to predictions in the la... | Junk DNA | 0.813008 |
17,307 | The question of what qualities are needed to teach statistics has been much discussed, and sometimes this discussion is concentrated on the qualifications necessary for those undertaking such teaching. The question arises separately for teaching at both school and university levels, partly because of the need for numer... | Statistics education | 0.813008 |
17,308 | In the United Kingdom, the Smith inquiry Making Mathematics Count suggests teaching basic statistical concepts as part of the science curriculum, rather than as part of mathematics. In the United States, the ASA's guidelines for undergraduate statistics specify that introductory statistics should emphasize the scientif... | Statistics education | 0.813008 |
17,309 | The literature on methods of teaching statistics is closely related to the literature on the teaching of mathematics for two reasons. First, statistics is often taught as part of the mathematics curriculum, by instructors trained in mathematics and working in a mathematics department. Second, statistical theory has oft... | Statistics education | 0.813008 |
17,310 | In addition to the international gatherings of statistics educators at ICOTS every four years, the US hosts a US Conference on Teaching Statistics (USCOTS) every two years and has recently started an Electronic Conference on Teaching Statistics (eCOTS) to alternate with USCOTS. Sessions on statistics education area als... | Statistics education | 0.813008 |
17,311 | In New Zealand, a new curriculum for statistics has been developed by Chris Wild and colleagues at Auckland University. Rejecting the contrived, and now unnecessary due to computer power, approach of reasoning under the null and the restrictions of normal theory, they use comparative box plots and bootstrap to introduc... | Statistics education | 0.813008 |
17,312 | Estonia is piloting a new statistics curriculum developed by the Computer-Based Math foundation based around its principles of using computers as the primary tool of education. in cooperation with the University of Tartu. | Statistics education | 0.813008 |
17,313 | For a doctoral degree in statistics, it has been traditional that students complete a course in measure-theoretic probability as well as courses in mathematical statistics. Such courses require a good course in real analysis, covering the proofs of the theory of calculus and topics like the uniform convergence of funct... | Statistics education | 0.813008 |
17,314 | The ASA recommends that undergraduate students consider obtaining a bachelor's degree in applied mathematics as preparation for entering a master program in statistics.Historically, professional degrees in statistics have been at the Master level, although some students may qualify to work with a bachelor's degree and ... | Statistics education | 0.813008 |
17,315 | As undergraduates, future statisticians should have completed courses in multivariate calculus, linear algebra, computer programming, and a year of calculus-based probability and statistics. Students wanting to obtain a doctorate in statistics from "any of the better graduate programs in statistics" should also take "r... | Statistics education | 0.813008 |
17,316 | The report includes a brief history of the introductory statistics course and recommendations for how it should be taught. In many colleges, a basic course in "statistics for non-statisticians" has required only algebra (and not calculus); for future statisticians, in contrast, the undergraduate exposure to statistics ... | Statistics education | 0.813008 |
17,317 | Enrollments in statistics have increased in community colleges, in four-year colleges and universities in the United States. At community colleges in the United States, mathematics has experienced increased enrollment since 1990. At community colleges, the ratio of the students enrolled in statistics to those enrolled ... | Statistics education | 0.813008 |
17,318 | He developed a list of views of statistics that can lead to this broad view, and describes them as follows: Statistics as number sense: Do I understand what the numbers mean? (seeing data as numbers in context, reading charts, graphs and tables, understanding numerical and graphical summaries of data, etc.) Statistics ... | Statistics education | 0.813008 |
17,319 | Scepticism: Critical thinking is important for receiving new ideas and information and evaluating the appropriateness of study design and analysis. Being logical: The ability to detect when one idea follows from another is important for arriving at valid conclusions. A propensity to seek deeper meaning: This means not ... | Statistics education | 0.813008 |
17,320 | By tradition in the U.K., most professional statisticians are trained at the Master level. A difficulty of recruiting strong undergraduates has been noted: "Very few undergraduates positively choose to study statistics degrees; most choose some statistics options within a mathematics programme, often to avoid the advan... | Statistics education | 0.813008 |
17,321 | Beliefs are defined as one's individually held ideas about statistics, about oneself as a learner of statistics, and about the social context of learning statistics. Beliefs are distinct from attitudes in the sense that attitudes are relatively stable and intense feelings that develop over time in the context of experi... | Statistics education | 0.813008 |
17,322 | Statistician Rob Gould, creator of Data Cycle, The Musical dinner and theatre spectacular, outlines many of these types of data and encourages teachers to find ways to use the data and address issues around big data. According to Gould, curricula focused on big data will address issues of sampling, prediction, visualiz... | Statistics education | 0.813008 |
17,323 | Teachers of statistics have been encouraged to explore new directions in curriculum content, pedagogy and assessment. In an influential talk at USCOTS, researcher George Cobb presented an innovative approach to teaching statistics that put simulation, randomization, and bootstrapping techniques at the core of the colle... | Statistics education | 0.813008 |
17,324 | Statistics educators have cognitive and noncognitive goals for students. For example, former American Statistical Association (ASA) President Katherine Wallman defined statistical literacy as including the cognitive abilities of understanding and critically evaluating statistical results as well as appreciating the con... | Statistics education | 0.813008 |
17,325 | Some studies have shown modest success at improving student attitudes in individual courses, but no generalizable studies showing improvement in student attitudes have been seen. Nevertheless, one of the goals of statistics education is to make the study of statistics a positive experience for students and to bring in ... | Statistics education | 0.813008 |
17,326 | Since students often experience math anxiety and negative opinions about statistics courses, various researchers have addressed attitudes and anxiety towards statistics. Some instruments have been developed to measure college students' attitudes towards statistics, and have been shown to have appropriate psychometric p... | Statistics education | 0.813008 |
17,327 | Quotes on "Who should teach statistics?" | Statistics education | 0.813008 |
17,328 | Only three universities currently offer graduate programs in statistics education: the University of Granada, the University of Minnesota, and the University of Florida. However, graduate students in a variety of disciplines (e.g., mathematics education, psychology, educational psychology) have been finding ways to com... | Statistics education | 0.813008 |
17,329 | Journal of Statistics and Data Science Education (formerly the Journal of Statistics Education) published by the American Statistical Association and Taylor & Francis Statistics Education Research Journal published by the International Association for Statistical Education (IASE) Teaching Statistics: An International J... | Statistics education | 0.813008 |
17,330 | Statistical thinking is the type of thinking used by statisticians when they encounter a statistical problem. This involves thinking about the nature and quality of the data and, where the data came from, choosing appropriate analyses and models, and interpreting the results in the context of the problem and given the ... | Statistics education | 0.813008 |
17,331 | In the text rising from the 2008 joint conference of the International Commission on Mathematical Instruction and the International Association of Statistics Educators, editors Carmen Batanero, Gail Burrill, and Chris Reading (Universidad de Granada, Spain, Michigan State University, USA, and University of New England,... | Statistics education | 0.813008 |
17,332 | The College Board has developed an Advanced Placement course in statistics, which has provided a college-level course in statistics to hundreds of thousands of high school students, with the first examination happening in May 1997. In 2007, the ASA endorsed the Guidelines for Assessment and Instruction in Statistics Ed... | Statistics education | 0.813008 |
17,333 | In the United States, schooling has increased the use of probability and statistics, especially since the 1990s. Summary statistics and graphs are taught in elementary school in many states. Topics in probability and statistical reasoning are taught in high school algebra (or mathematical science) courses; statistical ... | Statistics education | 0.813008 |
17,334 | Non-cognitive outcomes include affective constructs such as attitudes, beliefs, emotions, dispositions, and motivation. According to prominent researchers Gal & Ginsburg, statistics educators should make it a priority to be aware of students' ideas, reactions, and feelings towards statistics and how these affect their ... | Statistics education | 0.813008 |
17,335 | Neural coding studies on how the brain encodes simple commands in the form of central pattern generators (CPGs), movement vectors, the cerebellar internal model, and somatotopic maps to understand movement and sensory phenomena. Decoding of these signals in the realm of neuroscience is the process by which neurons unde... | Neural Engineering | 0.813007 |
17,336 | Artificial neural networks can be built from theoretical and computational models and implemented on computers from theoretically devices equations or experimental results of observed behavior of neuronal systems. Models might represent ion concentration dynamics, channel kinetics, synaptic transmission, single neuron ... | Neural Engineering | 0.813007 |
17,337 | Scientists can use experimental observations of neuronal systems and theoretical and computational models of these systems to create Neural networks with the hopes of modeling neural systems in as realistic a manner as possible. Neural networks can be used for analyses to help design further neurotechnological devices.... | Neural Engineering | 0.813007 |
17,338 | The fundamentals behind neuroengineering involve the relationship of neurons, neural networks, and nervous system functions to quantifiable models to aid the development of devices that could interpret and control signals and produce purposeful responses. | Neural Engineering | 0.813007 |
17,339 | The field of neural engineering draws on the fields of computational neuroscience, experimental neuroscience, neurology, electrical engineering and signal processing of living neural tissue, and encompasses elements from robotics, cybernetics, computer engineering, neural tissue engineering, materials science, and nano... | Neural Engineering | 0.813007 |
17,340 | Neurorobotics is the study of how neural systems can be embodied and movements emulated in mechanical machines. Neurorobots are typically used to study motor control and locomotion, learning and memory selection, and value systems and action selection. By studying neurorobots in real-world environments, they are more e... | Neural Engineering | 0.813007 |
17,341 | The study of neuromechanics is aimed at improving treatments for physiological health problems which includes optimization of prostheses design, restoration of movement post injury, and design and control of mobile robots. By studying structures in 3D hydrogels, researchers can identify new models of nerve cell mechano... | Neural Engineering | 0.813007 |
17,342 | Neuromechanics is the coupling of neurobiology, biomechanics, sensation and perception, and robotics (Edwards 2010). Researchers are using advanced techniques and models to study the mechanical properties of neural tissues and their effects on the tissues' ability to withstand and generate force and movements as well a... | Neural Engineering | 0.813007 |
17,343 | Neuroimaging techniques are used to investigate the activity of neural networks, as well as the structure and function of the brain. Neuroimaging technologies include functional magnetic resonance imaging (fMRI), magnetic resonance imaging (MRI), positron emission tomography (PET) and computed axial tomography (CAT) sc... | Neural Engineering | 0.813007 |
17,344 | Microelectrode arrays are recent advances that can be used to study neural networks (Cullen & Pfister 2011). Optical neural interfaces involve optical recordings and optogenetics, making certain brain cells sensitive to light in order to modulate their activity. Fiber optics can be implanted in the brain to stimulate o... | Neural Engineering | 0.813007 |
17,345 | Neural engineering and rehabilitation applies neuroscience and engineering to investigating peripheral and central nervous system function and to finding clinical solutions to problems created by brain damage or malfunction. Engineering applied to neuroregeneration focuses on engineering devices and materials that faci... | Neural Engineering | 0.813007 |
17,346 | Neural engineering (also known as neuroengineering) is a discipline within biomedical engineering that uses engineering techniques to understand, repair, replace, or enhance neural systems. Neural engineers are uniquely qualified to solve design problems at the interface of living neural tissue and non-living construct... | Neural Engineering | 0.813007 |
17,347 | All triatomic molecules may be classified as possessing either a linear, bent, or cyclic geometry. | Triatomic molecule | 0.813 |
17,348 | Linear triatomic molecules owe their geometry to their sp or sp3d hybridised central atoms. Well-known linear triatomic molecules include carbon dioxide (CO2) and hydrogen cyanide (HCN). Xenon difluoride (XeF2) is one of the rare examples of a linear triatomic molecule possessing non-bonded pairs of electrons on the ce... | Triatomic molecule | 0.813 |
17,349 | If the lattice of pixels is not fine enough for the scene, aliasing occurs as evidenced by the appearance of the Moiré pattern in the image obtained. The image in Figure 6 is obtained when a smoothened version of the scene is sampled with the same lattice. In this case the conditions of the theorem are satisfied and no... | Multidimensional sampling | 0.812999 |
17,350 | A gray-scale image can be interpreted as a function in two-dimensional space. An example of aliasing is shown in the images of brick patterns in Figure 5. The image shows the effects of aliasing when the sampling theorem's condition is not satisfied. | Multidimensional sampling | 0.812999 |
17,351 | The theorem gives conditions on sampling lattices for perfect reconstruction of the sampled. If the lattices are not fine enough to satisfy the Petersen-Middleton condition, then the field cannot be reconstructed exactly from the samples in general. In this case we say that the samples may be aliased. Again, consider t... | Multidimensional sampling | 0.812999 |
17,352 | As an example suppose that Ω {\displaystyle \Omega } is a circular disc. Figure 3 illustrates the support of f ^ s ( ⋅ ) {\displaystyle {\hat {f}}_{s}(\cdot )} when the conditions of the Petersen-Middleton theorem are met. We see that the spectral repetitions do not overlap and hence the original spectrum can be exactl... | Multidimensional sampling | 0.812999 |
17,353 | If the conditions of the Petersen-Middleton theorem are met, then the function f ^ s ( ξ ) {\displaystyle {\hat {f}}_{s}(\xi )} is equal to f ^ ( ξ ) {\displaystyle {\hat {f}}(\xi )} for all ξ ∈ Ω {\displaystyle \xi \in \Omega } , and hence the original field can be exactly reconstructed from the samples. In this case ... | Multidimensional sampling | 0.812999 |
17,354 | The theorem provides conditions on the lattice under which perfect reconstruction is possible. As with the Nyquist–Shannon sampling theorem, this theorem also assumes an idealization of any real-world situation, as it only applies to functions that are sampled over an infinitude of points. Perfect reconstruction is mat... | Multidimensional sampling | 0.812999 |
17,355 | In digital signal processing, multidimensional sampling is the process of converting a function of a multidimensional variable into a discrete collection of values of the function measured on a discrete set of points. This article presents the basic result due to Petersen and Middleton on conditions for perfectly recon... | Multidimensional sampling | 0.812999 |
17,356 | The Petersen–Middleton theorem is useful in designing efficient sensor placement strategies in applications involving measurement of spatial phenomena such as seismic surveys, environment monitoring and spatial audio-field measurements. == References == | Multidimensional sampling | 0.812999 |
17,357 | The theorem of Petersen and Middleton can be used to identify the optimal lattice for sampling fields that are wavenumber-limited to a given set Ω ⊂ ℜ d {\displaystyle \Omega \subset \Re ^{d}} . For example, it can be shown that the lattice in ℜ 2 {\displaystyle \Re ^{2}} with minimum spatial density of points that adm... | Multidimensional sampling | 0.812999 |
17,358 | Let Λ {\displaystyle \Lambda } denote a lattice in ℜ n {\displaystyle \Re ^{n}} and Γ {\displaystyle \Gamma } the corresponding reciprocal lattice. The theorem of Petersen and Middleton states that a function f ( ⋅ ) {\displaystyle f(\cdot )} that is wavenumber-limited to a set Ω ⊂ ℜ n {\displaystyle \Omega \subset \Re... | Multidimensional sampling | 0.812999 |
17,359 | In biology, parts of the DNA double helix that need to separate easily, such as the TATAAT Pribnow box in some promoters, tend to have a high AT content, making the strands easier to pull apart.In the laboratory, the strength of this interaction can be measured by finding the melting temperature Tm necessary to break h... | DNA strand | 0.812996 |
17,360 | Nucleases are enzymes that cut DNA strands by catalyzing the hydrolysis of the phosphodiester bonds. Nucleases that hydrolyse nucleotides from the ends of DNA strands are called exonucleases, while endonucleases cut within strands. The most frequently used nucleases in molecular biology are the restriction endonuclease... | DNA strand | 0.812996 |
17,361 | Power off brakes stop or hold a load when electrical power is either accidentally lost or intentionally disconnected. In the past, some companies have referred to these as "fail safe" brakes. These brakes are typically used on or near an electric motor. Typical applications include robotics, holding brakes for Z axis b... | Electromagnetic brake | 0.812992 |
17,362 | Let Z {\displaystyle Z} be the set of integers and ' − {\displaystyle -} ' be the binary operation 'subtraction'. Then the algebraic structure ( Z , − ) {\displaystyle (Z,-)} obeys the following properties: x − x = 0 {\displaystyle x-x=0} x − 0 = x {\displaystyle x-0=x} 0 − ( x − y ) = y − x {\displaystyle 0-(x-y)=y-x} | BF-algebra | 0.812988 |
17,363 | A BF-algebra is a non-empty subset X {\displaystyle X} with a constant 0 {\displaystyle 0} and a binary operation ∗ {\displaystyle *} satisfying the following: x ∗ x = 0 {\displaystyle x*x=0} x ∗ 0 = x {\displaystyle x*0=x} 0 ∗ ( x ∗ y ) = y ∗ x {\displaystyle 0*(x*y)=y*x} | BF-algebra | 0.812988 |
17,364 | In mathematics, BF algebras are a class of algebraic structures arising out of a symmetric "Yin Yang" concept for Bipolar Fuzzy logic, the name was introduced by Andrzej Walendziak in 2007. The name covers discrete versions, but a canonical example arises in the BF space x of pairs of (false-ness, truth-ness). | BF-algebra | 0.812988 |
17,365 | The references in this page were collected from the following Stack Exchange threads: "Are there problems without efficient algorithms, where existence theorems have proved such algorithms must exist?". CS Theory Stack Exchange. Retrieved 21 November 2014. "Are there non-constructive algorithm existence proofs?". | Non-constructive algorithm existence proofs | 0.812983 |
17,366 | CS Theory Stack Exchange. Retrieved 21 November 2014. "Is there an algorithm that provably exists although we don't know what it is?". Computer Science Stack Exchange. Retrieved 21 November 2014. | Non-constructive algorithm existence proofs | 0.812983 |
17,367 | Every query can be represented as a 1-by-n vector whose elements are all in the set {0,1}. The response to the query is just the dot product of the query vector by v. Every set of k queries can be represented by an k-by-n matrix over {0,1}; the set of responses is the product of the matrix by v. A matrix M is "good" if... | Non-constructive algorithm existence proofs | 0.812983 |
17,368 | In particular, the set of "yes" instances has a finite number of minor-minimal elements.Given an input graph G, the following "algorithm" solves the above problem: For every minor-minimal element H: If H is a minor of G then return "yes". return "no".The non-constructive part here is the Robertson–Seymour theorem. Alth... | Non-constructive algorithm existence proofs | 0.812983 |
17,369 | The proof relies on the following facts: The set of graphs for which the answer is "yes" is closed under taking minors. I. e., if a graph G can be embedded linklessly in 3-d space, then every minor of G can also be embedded linklessly. For every two graphs G and H, it is possible to find in polynomial time whether H is... | Non-constructive algorithm existence proofs | 0.812983 |
17,370 | Non-constructive algorithm proofs for problems in graph theory were studied beginning in 1988 by Michael Fellows and Michael Langston.A common question in graph theory is whether a certain input graph has a certain property. For example: Input: a graph G. Question: Can G be embedded in a 3-dimensional space, such that ... | Non-constructive algorithm existence proofs | 0.812983 |
17,371 | The main tasks of the centre, according to VECTOR, are: Basic research of causative agents of especially dangerous and socially important viral infections, and their genetic variability and diversity, pathogenesis of viral infections. Ensuring constant readiness for implementing diagnostics of especially dangerous infe... | State Research Center of Virology and Biotechnology VECTOR | 0.812982 |
17,372 | The State Research Center of Virology and Biotechnology VECTOR, also known as the Vector Institute (Russian: Государственный научный центр вирусологии и биотехнологии „Вектор“, romanized: Gosudarstvennyy nauchnyy tsentr virusologii i biotekhnologii "Vektor"), is a biological research center in Koltsovo, Novosibirsk Obl... | State Research Center of Virology and Biotechnology VECTOR | 0.812982 |
17,373 | Primary energy is used in energy statistics in the compilation of energy balances, as well as in the field of energetics. In energetics, a primary energy source (PES) refers to the energy forms required by the energy sector to generate the supply of energy carriers used by human society.Total primary energy supply (TPE... | Secondary energy | 0.812979 |
17,374 | From approximately 1960 through 2005, robotics education at post-secondary institutions took place through elective courses, thesis experiences and design projects offered as part of degree programs in traditional academic disciplines, such as mechanical engineering, electrical engineering, industrial engineering or co... | Educational robotics | 0.812979 |
17,375 | Educational robotics teaches the design, analysis, application and operation of robots. Robots include articulated robots, mobile robots or autonomous vehicles. Educational robotics can be taught from elementary school to graduate programs. Robotics may also be used to motivate and facilitate the instruction other, oft... | Educational robotics | 0.812979 |
17,376 | This can lead to an increased ability in "problem solving, reasoning and planning in typically developing preschool children." Through eight weeks of weekly forty-five-minute group sessions using the Bee-Bot, an increase in interest, attention, and interaction between both peers and adults was found in the school and p... | Educational robotics | 0.812979 |
17,377 | Using Lego Mindstorms NXT, schoolteachers were able to work with middle school aged children in order to develop programs and improve the children's social and personal skills. Additionally, problem solving skills and creativity were utilized through the creation of artwork and scenery to house the robots. Other studie... | Educational robotics | 0.812979 |
17,378 | Educational robotics can be a useful tool in early and special education. According to a journal on new perspectives in science education, educational robotics can help to develop abilities that promote autonomy and assist their integration into society. Social and personal skills can also be developed through educatio... | Educational robotics | 0.812979 |
17,379 | The Robotics Certification Standards Alliance (RCSA) is an international robotics certification authority that confers various industry- and educational-related robotics certifications. | Educational robotics | 0.812979 |
17,380 | Several summer camp programs include robotics as part of their core curriculum. In addition, youth summer robotics programs are frequently offered by celebrated museums such as the American Museum of Natural History and The Tech Museum of Innovation in Silicon Valley, CA, just to name a few. There are of benefits that ... | Educational robotics | 0.812979 |
17,381 | Robotics engineers design robots, maintain them, develop new applications for them, and conduct research to expand the potential of robotics. Robots have become a popular educational tool in some middle and high schools, as well as in numerous youth summer camps, raising interest in programming, artificial intelligence... | Educational robotics | 0.812979 |
17,382 | Leachim, was a robot teacher programmed with the class curricular, as well as certain biographical information on the 40 students whom it was programmed to teach. Leachim could synthesize human speech using Diphone synthesis. It was invented by Michael J. Freeman in 1974 and was tested in a fourth grade classroom in th... | Educational robotics | 0.812979 |
17,383 | In 1947, synchrotron radiation was discovered with a 70 MeV electron synchrotron at General Electric. This radiation was caused by the acceleration of electrons through a magnetic field as they moved near the speed of light.With a beam energy of 1.5 GeV, the first high-energy particle collider was ADONE, which began op... | Mass of electron | 0.812979 |
17,384 | Electrons are involved in many applications, such as tribology or frictional charging, electrolysis, electrochemistry, battery technologies, electronics, welding, cathode-ray tubes, photoelectricity, photovoltaic solar panels, electron microscopes, radiation therapy, lasers, gaseous ionization detectors, and particle a... | Mass of electron | 0.812979 |
17,385 | Virtual particles cause a comparable shielding effect for the mass of the electron.The interaction with virtual particles also explains the small (about 0.1%) deviation of the intrinsic magnetic moment of the electron from the Bohr magneton (the anomalous magnetic moment). The extraordinarily precise agreement of this ... | Mass of electron | 0.812979 |
17,386 | These particles emit synchrotron radiation as they pass through magnetic fields. The dependency of the intensity of this radiation upon spin polarizes the electron beam—a process known as the Sokolov–Ternov effect. Polarized electron beams can be useful for various experiments. Synchrotron radiation can also cool the e... | Mass of electron | 0.812979 |
17,387 | At the end of its lifetime, a star with more than about 20 solar masses can undergo gravitational collapse to form a black hole. According to classical physics, these massive stellar objects exert a gravitational attraction that is strong enough to prevent anything, even electromagnetic radiation, from escaping past th... | Mass of electron | 0.812979 |
17,388 | There is also a physical constant called the "classical electron radius", with the much larger value of 2.8179×10−15 m, greater than the radius of the proton. However, the terminology comes from a simplistic calculation that ignores the effects of quantum mechanics; in reality, the so-called classical electron radius h... | Mass of electron | 0.812978 |
17,389 | In such cases, electrons 'split' into three independent particles, the spinon, the orbiton and the holon (or chargon). The electron can always be theoretically considered as a bound state of the three, with the spinon carrying the spin of the electron, the orbiton carrying the orbital degree of freedom and the chargon ... | Mass of electron | 0.812978 |
17,390 | It is approximately equal to one Bohr magneton, which is a physical constant equal to 9.27400915(23)×10−24 joules per tesla. The orientation of the spin with respect to the momentum of the electron defines the property of elementary particles known as helicity.The electron has no known substructure. Nevertheless, in co... | Mass of electron | 0.812978 |
17,391 | Like all elementary particles, electrons exhibit properties of both particles and waves: They can collide with other particles and can be diffracted like light. The wave properties of electrons are easier to observe with experiments than those of other particles like neutrons and protons because electrons have a lower ... | Mass of electron | 0.812978 |
17,392 | Once spin and the interaction between multiple electrons were describable, quantum mechanics made it possible to predict the configuration of electrons in atoms with atomic numbers greater than hydrogen.In 1928, building on Wolfgang Pauli's work, Paul Dirac produced a model of the electron – the Dirac equation, consist... | Mass of electron | 0.812978 |
17,393 | In 1926, this equation, the Schrödinger equation, successfully described how electron waves propagated. Rather than yielding a solution that determined the location of an electron over time, this wave equation also could be used to predict the probability of finding an electron near a position, especially a position ne... | Mass of electron | 0.812978 |
17,394 | The Stackelberg concept has been extended to dynamic Stackelberg games. With the addition of time as a dimension, phenomena not found in static games were discovered, such as violation of the principle of optimality by the leader.In recent years, Stackelberg games have been applied in the security domain. In this conte... | Stackelberg game | 0.812978 |
17,395 | Boolean functions play a basic role in questions of complexity theory as well as the design of processors for digital computers, where they are implemented in electronic circuits using logic gates. The properties of Boolean functions are critical in cryptography, particularly in the design of symmetric key algorithms (... | Boolean functions | 0.812976 |
17,396 | A Boolean function may be specified in a variety of ways: Truth table: explicitly listing its value for all possible values of the arguments Marquand diagram: truth table values arranged in a two-dimensional grid (used in a Karnaugh map) Binary decision diagram, listing the truth table values at the bottom of a binary ... | Boolean functions | 0.812976 |
17,397 | This is the sense in which universal lightspeed can be deduced rather than postulated. For some historical information, see History of special relativity § Spacetime physics and the section "Lorentz transformation without second postulate" for the approaches of Ignatowski and Frank/Rothe. According to Pauli (1921), Res... | Formulations of special relativity | 0.81297 |
17,398 | Spacetime algebra is a type of geometric algebra, closely related to Minkowski space, and is equivalent to other formalisms of special relativity. It uses mathematical objects such as bivectors to replace tensors in traditional formalisms of Minkowski spacetime, leading to much simpler equations than in matrix mechanic... | Formulations of special relativity | 0.81297 |
17,399 | Here one sets the Riemann-Christoffel tensor to zero instead of using the Einstein field equations. This is the sense in which "special relativity" can handle accelerated frames. A description of physics including gravity governed by the Einstein field equations, i.e. full general relativity.Special relativity cannot b... | Formulations of special relativity | 0.81297 |
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