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24,300 | Early CAD was primarily geometry driven (using mathematics and computer science). Then came the engineering use of AI, driven by theories of cognitive science and computational models of cognition (logic and pattern based). More recently, models of collaboration and representation and acquisition of collective knowledg... | Engineering informatics | 0.808306 |
24,301 | It encompasses engineering technology areas in: Neural Network Engineering and Intelligent System Application Decision Support System and Information Modelling System Reverse Software Engineering and Reusable Software Engineering The application of Cryptography in Computer Security System Enterprise Architectural Frame... | Engineering informatics | 0.808306 |
24,302 | Hence, M → C, S → 1/L, D → G where G is electrical conductance, the inverse of resistance. Equivalent circuits produced by this scheme are similar, but are the dual impedance forms whereby series elements become parallel, capacitors become inductors, and so on. Circuit diagrams using the mobility analogy more closely m... | Mechanical filter | 0.808304 |
24,303 | Circuit diagrams produced using this analogy match the electrical impedance of the mechanical system seen by the electrical circuit, making it intuitive from an electrical engineering standpoint. There is also the mobility analogy, in which force corresponds to current and velocity corresponds to voltage. This has equa... | Mechanical filter | 0.808304 |
24,304 | The circuit arrived at is a ladder topology of series resonant circuits coupled by shunt capacitors. This can be viewed as a bandpass filter circuit. | Mechanical filter | 0.808304 |
24,305 | This could be applied to problems that were entirely in the mechanical domain, but for mechanical filters with an electrical application it is necessary to include the transducer in the analogy as well. Poincaré in 1907 was the first to describe a transducer as a pair of linear algebraic equations relating electrical v... | Mechanical filter | 0.808304 |
24,306 | The second moment method typically works in situations in which the corresponding events or random variables are “nearly independent". In this application, the random variables Xn are given as sums In other applications, the corresponding useful random variables are integrals where the functions fn are random. In such ... | Second moment method | 0.808304 |
24,307 | In the other direction, E being "large" does not directly imply that Pr(X = 0) is small. However, we can often use the second moment to derive such a conclusion, using Cauchy–Schwarz inequality. The method can also be used on distributional limits of random variables. Furthermore, the estimate of the previous theorem c... | Second moment method | 0.808304 |
24,308 | In mathematics, the second moment method is a technique used in probability theory and analysis to show that a random variable has positive probability of being positive. More generally, the "moment method" consists of bounding the probability that a random variable fluctuates far from its mean, by using its moments.Th... | Second moment method | 0.808304 |
24,309 | NCBioImpact is a partnership of North Carolina organizations created to enhance the trained workforce for biotechnology and other life science employers by educating students and retraining incumbent workers. The partnership works to promote economic development in North Carolina while offering comprehensive biomanufac... | NCBioImpact | 0.8083 |
24,310 | research and teaching facility provides hands-on training in process and analytical technology, drug discovery and biomanufacturing. Students can pursue undergraduate and graduate degrees in the classroom and gain hands-on experience in laboratories. BRITE also offers short courses for incumbent biotechnology workers a... | NCBioImpact | 0.8083 |
24,311 | Magnetic polarizability defined by spin interactions of nucleons is an important parameter of deuterons and hadrons. In particular, measurement of tensor polarizabilities of nucleons yields important information about spin-dependent nuclear forces.The method of spin amplitudes uses quantum mechanics formalism to more e... | Polarizability tensor | 0.8083 |
24,312 | The program offers continuing education, workforce development, business services and outreach activities for startup companies. The seven BioNetwork centers are located throughout the state in order to provide specialized life science training where it is needed. BioNetwork offers training in the following centers: Ca... | NCBioImpact | 0.8083 |
24,313 | In 2002, biomanufacturing executives in the Research Triangle region in North Carolina, working with NCBIO, asked the North Carolina Biotechnology Center to conduct a study of the workforce and training needs of the industry. "Window on the Workplace 2003" was published the following year.As a result of that study, a p... | NCBioImpact | 0.8083 |
24,314 | 24 (1): 1–10. doi:10.1093/bioinformatics/btm546. PMID 18024971.. This review paper provides >100 references to scientific papers and extensive background information. == References == | Computational epigenetics | 0.808298 |
24,315 | The original version of this article was based on a review paper on computational epigenetics that appeared in the January 2008 issue of the Bioinformatics journal: Bock C, Lengauer T (January 2008). "Computational epigenetics". Bioinformatics. | Computational epigenetics | 0.808298 |
24,316 | Evolutionary epigenetics: Learning about epigenome regulation in human (and its medical consequences) by cross-species comparisons. Theoretical modeling: Testing our mechanistic and quantitative understanding of epigenetic mechanisms by in silico simulation. Genome browsers: Developing a new blend of web services that ... | Computational epigenetics | 0.808298 |
24,317 | The first wave of research in the field of computational epigenetics was driven by rapid progress of experimental methods for data generation, which required adequate computational methods for data processing and quality control, prompted epigenome prediction studies as a means of understanding the genomic distribution... | Computational epigenetics | 0.808298 |
24,318 | Computational epigenetics uses statistical methods and mathematical modelling in epigenetic research. Due to the recent explosion of epigenome datasets, computational methods play an increasing role in all areas of epigenetic research. | Computational epigenetics | 0.808298 |
24,319 | Research in computational epigenetics comprises the development and application of bioinformatics methods for solving epigenetic questions, as well as computational data analysis and theoretical modeling in the context of epigenetics. This includes modelling of the effects of histone and DNA CpG island methylation. | Computational epigenetics | 0.808298 |
24,320 | The Histone Database Contains 254 sequences from histone H1, 383 from histone H2, 311 from histone H2B, 1043 from histone H3 and 198 from histone H4, altogether representing at least 857 species. ChromDB Contains 9,341 chromatin-associated proteins, including RNAi-associated proteins, for a broad range of organisms. CR... | Computational epigenetics | 0.808298 |
24,321 | The Cass Shell example relies on the fact that general equilibrium models often possess multiple equilibria. Cass and Shell construct an example with three equilibria in period 2 and they showed that, if a subset of people cannot trade financial securities in period 1, there exist additional equilibria which are constr... | Sunspot equilibrium | 0.808298 |
24,322 | The non-relativistic form is called Lorentz self-force while the relativistic version is called the Lorentz–Dirac force or collectively known as Abraham–Lorentz–Dirac force. The equations are in the domain of classical physics, not quantum physics, and therefore may not be valid at distances of roughly the Compton wave... | Abraham–Lorentz force | 0.808295 |
24,323 | In the physics of electromagnetism, the Abraham–Lorentz force (also known as the Lorentz–Abraham force) is the recoil force (a force of equal magnitude and opposite direction) on an accelerating charged particle caused by the particle emitting electromagnetic radiation by self-interaction. It is also called the radiati... | Abraham–Lorentz force | 0.808295 |
24,324 | In mathematics, the Kleene–Rosser paradox is a paradox that shows that certain systems of formal logic are inconsistent, in particular the version of Haskell Curry's combinatory logic introduced in 1930, and Alonzo Church's original lambda calculus, introduced in 1932–1933, both originally intended as systems of formal... | Kleene–Rosser paradox | 0.808295 |
24,325 | As a measure of the Euclidean three-dimensional space, volume cannot be physically measured as a negative value, similar to length and area. Like all continuous monotonic (order-preserving) measures, volumes of bodies can be compared against each other and thus can be ordered. Volume can also be added together and be d... | Spatial volume | 0.808287 |
24,326 | He devised Cavalieri's principle, which said that using thinner and thinner slices of the shape would make the resulting volume more and more accurate. This idea would then be later expanded by Pierre de Fermat, John Wallis, Isaac Barrow, James Gregory, Isaac Newton, Gottfried Wilhelm Leibniz and Maria Gaetana Agnesi i... | Spatial volume | 0.808287 |
24,327 | Around this time, volume measurements are becoming more precise and the uncertainty is narrowed to between 1–5 mL (0.03–0.2 US fl oz; 0.04–0.2 imp fl oz). : 8 Around the early 17th century, Bonaventura Cavalieri applied the philosophy of modern integral calculus to calculate the volume of any object. | Spatial volume | 0.808287 |
24,328 | The calculation of volume is a vital part of integral calculus. One of which is calculating the volume of solids of revolution, by rotating a plane curve around a line on the same plane. The washer or disc integration method is used when integrating by an axis parallel to the axis of rotation. The general equation can ... | Spatial volume | 0.808287 |
24,329 | The modern era of testing general relativity was ushered in largely at the impetus of Dicke and Schiff who laid out a framework for testing general relativity. They emphasized the importance not only of the classical tests, but of null experiments, testing for effects which in principle could occur in a theory of gravi... | Classical tests of general relativity | 0.808285 |
24,330 | (A consequence of the no-hair theorems.) Thus, by analyzing the radiation from such systems, it is possible to test Einstein's theory. Most of the radiation from these black hole – accretion disk systems (e.g., black hole binaries and active galactic nuclei) arrives in the form of X-rays. | Classical tests of general relativity | 0.808285 |
24,331 | This effect should be detectable within the next few years via astrometric monitoring of stars at the center of the Milky Way galaxy. By comparing the rate of orbital precession of two stars on different orbits, it is possible in principle to test the no-hair theorems of general relativity.The Gravity Probe B satellite... | Classical tests of general relativity | 0.808285 |
24,332 | Even before the end of the war, various projects directed toward non-military applications of radar and closely related technologies were initiated. The US Army Air Forces and the British RAF had made wartime advances in using radar for handling aircraft landing, and this was rapidly expanded into the civil sector. The... | Range and Direction Finding | 0.808283 |
24,333 | The prototype was operated in Durban before the end of 1939, detecting ships and aircraft at distances up to 80 km, and by the next March a system was fielded by anti-aircraft brigades of the South African Defence Force.Hungary: Zoltán Lajos Bay in Hungary was a Professor of Physics at the Technical University of Budap... | Range and Direction Finding | 0.808283 |
24,334 | In the first half of 1943 additional New Zealand radar units and staff were sent to the Pacific at the request of COMOSPAC, Admiral Halsey.South Africa did not have a representative at the 1939 meetings in England, but in mid-September, as Ernest Marsden was returning by ship to New Zealand, Basil F. J. Schonland came ... | Range and Direction Finding | 0.808283 |
24,335 | In early 1939, the British Government invited representatives from the most technically advanced Commonwealth Nations to visit England for briefings and demonstrations on the highly secret RDF (radar) technology. Based on this, RDF developments were started in Australia, Canada, New Zealand, and South Africa by Septemb... | Range and Direction Finding | 0.808283 |
24,336 | In 1895, Alexander Stepanovich Popov, a physics instructor at the Imperial Russian Navy school in Kronstadt, developed an apparatus using a coherer tube for detecting distant lightning strikes. The next year, he added a spark-gap transmitter and demonstrated the first radio communication set in Russia. During 1897, whi... | Range and Direction Finding | 0.808283 |
24,337 | The Dutch Parliament set up a Committee for the Applications of Physics in Weaponry under G.J. Elias to examine this potential, but the Committee quickly discounted death rays. The Committee did, however, establish the Laboratorium voor Fysieke Ontwikkeling (LFO, Laboratory for Physical Development), dedicated to suppo... | Range and Direction Finding | 0.808283 |
24,338 | The first observations were of ionized trails in the Geminids meteor shower during December 1945. While the facility soon evolved to become the third largest radio observatory in the world, some radar astronomy continued. The largest (250-ft or 76-m in diameter) of their three fully steerable radio telescopes became op... | Range and Direction Finding | 0.808283 |
24,339 | Radar systems on a number of aircraft and orbiting spacecraft have mapped the entire Earth for various purposes; on the Shuttle Radar Topography Mission, the entire planet was mapped at a 30-m resolution. The Jodrell Bank Observatory, an operation of the University of Manchester in Britain, was originally started by Be... | Range and Direction Finding | 0.808283 |
24,340 | National Science Foundation and contractor operated, it was used primarily for radio astronomy, but equipment was available for radar astronomy. This included transmitters operating at 47 MHz, 439 MHz, and 2.38 GHz, all with very-high pulse power. | Range and Direction Finding | 0.808283 |
24,341 | In fact, essentially all major radar astronomy activities have been conducted as adjuncts to radio astronomy observatories. The radio telescope at the Arecibo Observatory, opened in 1963, was the largest in the world. Owned by the U.S. | Range and Direction Finding | 0.808283 |
24,342 | Zoltán Bay accomplished this on the following February 6. Radio astronomy also had its start following WWII, and many scientists involved in radar development then entered this field. A number of radio observatories were constructed during the following years; however, because of the additional cost and complexity of i... | Range and Direction Finding | 0.808283 |
24,343 | Based on this work, Ioffe recommended that a portion of the LEPI be transferred to the city of Kharkiv, resulting in the Ukrainian Institute of Physics and Technology (LIPT) being formed in 1930. Within the LIPT, the Laboratory of Electromagnetic Oscillations (LEMO), headed by Abram A. Slutskin, continued with magnetro... | Range and Direction Finding | 0.808283 |
24,344 | Mikhail A. Bonch-Bruyevich, a renowned radio physicist previously with TsRL and the University of Leningrad, was named the NII-9 Scientific Director. Research on magnetrons began at Kharkov University in Ukraine during the mid-1920s. Before the end of the decade this had resulted in publications with worldwide distribu... | Range and Direction Finding | 0.808283 |
24,345 | This included all of the then-existing information on radio-location in the USSR, available (in Russian language) to researchers in this field throughout the world.Recognizing the potential value of radio-location to the military, the GAU made a separate agreement with the Leningrad Electro-Physics Institute (LEPI), fo... | Range and Direction Finding | 0.808283 |
24,346 | Kühnhold remained with the NVA, but also consulted with GEMA. He is considered by many in Germany as the Father of Radar. During 1933–6, Hollmann wrote the first comprehensive treatise on microwaves, Physik und Technik der ultrakurzen Wellen (Physics and Technique of Ultrashort Waves), Springer 1938. | Range and Direction Finding | 0.808283 |
24,347 | From a review of his book: ... radar has been the root of a wide range of achievements since the war, producing a veritable family tree of modern technologies. Because of radar, astronomers can map the contours of far-off planets, physicians can see images of internal organs, meteorologists can measure rain falling in ... | Range and Direction Finding | 0.808283 |
24,348 | When the work got underway, Nello Carrara, a civilian physics instructor who had been doing research at the RIEC in microwaves, was added to be responsible for developing the RDT transmitter. Before the end of 1936, Tiberio and Carrara had demonstrated the EC-1, the first Italian RDT system. This had an FM transmitter ... | Range and Direction Finding | 0.808283 |
24,349 | The RIEC had been established in 1916 on the campus of the Italian Naval Academy in Livorno. Lieutenant Ugo Tiberio, a physics and radio-technology instructor at the Academy, was assigned to head the project on a part-time basis.Tiberio prepared a report on developing an experimental apparatus that he called telemetro ... | Range and Direction Finding | 0.808283 |
24,350 | Similar to point masses, in electromagnetism physicists discuss a point charge, a point particle with a nonzero electric charge. The fundamental equation of electrostatics is Coulomb's law, which describes the electric force between two point charges. Another result, Earnshaw's theorem, states that a collection of poin... | Point-like particle | 0.808283 |
24,351 | The 2− ion adopts an eclipsed conformation as shown at left. The delta bonding orbital is then formed by overlap of the d orbitals on each rhenium atom, which are perpendicular to the Re–Re axis and lie in between the Re–Cl bonds. The d orbitals directed along the Re–Cl bonds are stabilized by interaction with chlorine... | Quadruple bond | 0.808281 |
24,352 | The above definition is useful if the notion of open set is already defined. There is an alternative way to define a topology, by first defining the neighbourhood system, and then open sets as those sets containing a neighbourhood of each of their points. A neighbourhood system on X {\displaystyle X} is the assignment ... | Neighbourhood (mathematics) | 0.808281 |
24,353 | The name "blob" is further borrowed by the deep learning software Caffe to represent multi-dimensional arrays. In the world of free and open-source software, the term is also borrowed to refer to proprietary device drivers, which are distributed without their source code, exclusively through binary code; in such use, t... | Binary large object | 0.808277 |
24,354 | In theoretical physics, composite gravity refers to models that attempted to derive general relativity in a framework where the graviton is constructed as a composite bound state of more elementary particles, usually fermions. A theorem by Steven Weinberg and Edward Witten shows that this is not possible in Lorentz cov... | Composite gravity | 0.808275 |
24,355 | It is also an affiliate member of the World Federation for Culture Collections (WFCC) and is registered with the World Data Centre for Microorganisms (WDCM) under registration number 930. The MCC has a status of International Depositary Authority (IDA), certified on April 2011 by the World Intellectual Property Organiz... | Microbial Culture Collection | 0.808274 |
24,356 | The Microbial Culture Collection (now called the National Centre for Microbial Resource, NCMR) is a microbial culture collection centre in Pune, India. The facility acts as a national depository, supplying authentic microbial cultures and providing related services to research institutions, universities, industries and... | Microbial Culture Collection | 0.808274 |
24,357 | The composition of coordination complexes have been known since the early 1800s, such as Prussian blue and copper vitriol. The key breakthrough occurred when Alfred Werner reconciled formulas and isomers. He showed, among other things, that the formulas of many cobalt(III) and chromium(III) compounds can be understood ... | Ligand | 0.808273 |
24,358 | In probability theory and statistics, the continuous uniform distributions or rectangular distributions are a family of symmetric probability distributions. Such a distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds. The bounds are defined by the parameters, a {\dis... | Uniform probability distribution | 0.80827 |
24,359 | Despite numerous studies conducted, good quality evidence of its efficacy compared to other rehabilitation methods without sophisticated and expensive equipment is lacking for the treatment of Parkinson's disease. A 2018 review on the effectiveness of mirror therapy by virtual reality and robotics for any type of patho... | Simulated environment | 0.808266 |
24,360 | Controllers typically use optical tracking systems (primarily infrared cameras) for location and navigation, so that the user can move freely without wiring. Some input devices provide the user with force feedback to the hands or other parts of the body, so that the human being can orientate himself in the three-dimens... | Simulated environment | 0.808266 |
24,361 | Although the quotient map q is generally not a homeomorphism (since it is not generally injective), it does induce a bijection between the topology on X and the topology on KX. Intuitively, the Kolmogorov quotient does not alter the topology of a space. It just reduces the point set until points become topologically di... | Topological distinguishability | 0.808258 |
24,362 | ISBN 9780192506474 Helmreich, Stefan (2009) Alien Ocean: Anthropological Voyages in Microbial Seas University of California Press. ISBN 9780520942608 Munn, Colin B. (2019) Marine Microbiology: Ecology & Applications CRC Press. | Marine microplankton | 0.808256 |
24,363 | (1998) Introduction to Marine Micropaleontology Elsevier. ISBN 9780080534961 Kirchman, David L. (2018) Processes in Microbial Ecology Oxford University Press. | Marine microplankton | 0.808256 |
24,364 | If I {\displaystyle I} is infinite and ∏ X ∙ = ∏ j ∈ I X j {\displaystyle {\textstyle \prod }X_{\bullet }={\textstyle \prod \limits _{j\in I}}X_{j}} is not empty, then the axiom of choice would (in general) still be needed to conclude that the projections π i: ∏ X ∙ → X i {\displaystyle \pi _{i}:{\textstyle \prod }X_{\... | Net (mathematics) | 0.808255 |
24,365 | A net in the product space has a limit if and only if each projection has a limit. Explicitly, let ( X i ) i ∈ I {\displaystyle \left(X_{i}\right)_{i\in I}} be topological spaces, endow their Cartesian product with the product topology, and that for every index l ∈ I , {\displaystyle l\in I,} denote the canonical proje... | Net (mathematics) | 0.808255 |
24,366 | Phytogeography is part of a more general science known as biogeography. Phytogeographers are concerned with patterns and process in plant distribution. Most of the major questions and kinds of approaches taken to answer such questions are held in common between phyto- and zoogeographers. Phytogeography in wider sense (... | Plant geography | 0.80825 |
24,367 | Membership was open to all those interested in chemistry, but fellowship was for long restricted to men. In 1904, Edith Humphrey, thought to be the first British woman to gain a doctorate in chemistry (at the University of Zurich), was one of nineteen women chemists to petition the Chemical Society for admission of wom... | Chemical Society | 0.808249 |
24,368 | On 23 February 1841, a meeting was convened to take into consideration the formation of a Chemical Society. The Provisional Committee appointed for carrying that object into effect invited a number of gentlemen engaged in the practice and pursuit of chemistry to become original members. The following 77 communicated th... | Chemical Society | 0.808249 |
24,369 | PPRHs could be used as gene silencing tools acting by different mechanisms than triplex forming oligonucleotides (TFOs), antisense oligonucleotides or siRNAs. Upon binding to their targets, PPRHs can decrease the mRNA and protein levels of the selected genes. Their action has been demonstrated in vitro for a number of ... | Polypurine Reverse-Hoogsteen hairpins | 0.808244 |
24,370 | KEGG (Kyoto Encyclopedia of Genes and Genomes) is a collection of databases dealing with genomes, biological pathways, diseases, drugs, and chemical substances. KEGG is utilized for bioinformatics research and education, including data analysis in genomics, metagenomics, metabolomics and other omics studies, modeling a... | KEGG PATHWAY Database | 0.808244 |
24,371 | The microorganisms in such endeavors consequently should be recognized as organisms rather than simply as molecular or evolutionary reductionist model systems. Thus, the study of RNA in vitro evolution is not microbial population biology and nor is the in silico generation of phylogenies of otherwise non-microbial sequ... | Microbial population biology | 0.808237 |
24,372 | On the other hand, typically microbial population biologists (unlike microbial ecologists) are less concerned with questions of the role of microorganisms in ecosystem ecology, which is the study of nutrient cycling and energy movement between biotic as well as abiotic components of ecosystems. Microbial population bio... | Microbial population biology | 0.808237 |
24,373 | Microbial population biology, in practice, is the application of population ecology and population genetics toward understanding the ecology and evolution of bacteria, archaebacteria, microscopic fungi (such as yeasts), additional microscopic eukaryotes (e.g., "protozoa" and algae), and viruses. Microbial population bi... | Microbial population biology | 0.808237 |
24,374 | Microbial population biology is the application of the principles of population biology to microorganisms. | Microbial population biology | 0.808237 |
24,375 | Metamaterials Handbook is a two-volume handbook on metamaterials edited by Filippo Capolino (University of California).The series is designed to cover all theory and application topics related to electromagnetic metamaterials. Disciplines have combined to study, and develop electromagnetic metamaterials. Some of these ... | Metamaterials Handbook | 0.808234 |
24,376 | The change in kinetic energy is proportional to the change in frequency. Because it takes work to speed up or slow down rotating mass, this inertia dampens the effects of active power imbalances and therefore stabilizes the frequency. Because inverter-based generation inherently lacks inertia, increasing penetration of... | Synchronous converter | 0.808232 |
24,377 | There are still simply-stated unsolved problems remaining in Diophantine approximation, for example the Littlewood conjecture and the lonely runner conjecture. It is also unknown if there are algebraic numbers with unbounded coefficients in their continued fraction expansion. | Diophantine approximations | 0.808231 |
24,378 | Over more than a century, there were many efforts to improve Liouville's theorem: every improvement of the bound enables us to prove that more numbers are transcendental. The main improvements are due to Axel Thue (1909), Siegel (1921), Freeman Dyson (1947), and Klaus Roth (1955), leading finally to the Thue–Siegel–Rot... | Diophantine approximations | 0.808231 |
24,379 | }=0.110001000000000000000001000\ldots \,,} which does not satisfy Liouville's theorem, whichever degree n is chosen. This link between Diophantine approximations and transcendental number theory continues to the present day. Many of the proof techniques are shared between the two areas. | Diophantine approximations | 0.808231 |
24,380 | In the 1840s, Joseph Liouville obtained the first lower bound for the approximation of algebraic numbers: If x is an irrational algebraic number of degree n over the rational numbers, then there exists a constant c(x) > 0 such that | x − p q | > c ( x ) q n {\displaystyle \left|x-{\frac {p}{q}}\right|>{\frac {c(x)}{q^{... | Diophantine approximations | 0.808231 |
24,381 | Diophantine approximations and transcendental number theory are very close areas that share many theorems and methods. Diophantine approximations also have important applications in the study of Diophantine equations. The 2022 Fields Medal was awarded to James Maynard for his work on Diophantine approximation. | Diophantine approximations | 0.808231 |
24,382 | Thus a real number that may be better approximated than the bound for algebraic numbers is certainly a transcendental number. This knowledge enabled Liouville, in 1844, to produce the first explicit transcendental number. Later, the proofs that π and e are transcendental were obtained by a similar method. | Diophantine approximations | 0.808231 |
24,383 | This problem was solved during the 18th century by means of continued fractions. Knowing the "best" approximations of a given number, the main problem of the field is to find sharp upper and lower bounds of the above difference, expressed as a function of the denominator. It appears that these bounds depend on the natu... | Diophantine approximations | 0.808231 |
24,384 | In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus of Alexandria. The first problem was to know how well a real number can be approximated by rational numbers. For this problem, a rational number a/b is a "good" approxi... | Diophantine approximations | 0.808231 |
24,385 | And indeed, V. Jarník proved that the Hausdorff dimension of this set is equal to one. This result was improved by W. M. Schmidt, who showed that the set of badly approximable numbers is incompressible, meaning that if f 1 , f 2 , … {\displaystyle f_{1},f_{2},\ldots } is a sequence of bi-Lipschitz maps, then the set of... | Diophantine approximations | 0.808231 |
24,386 | For this function, the relevant series diverges and so Khinchin's theorem tells us that almost every number is ψ ε {\displaystyle \psi _{\varepsilon }} -approximable. This is the same as saying that every such number is well approximable, where a number is called well approximable if it is not badly approximable. So an... | Diophantine approximations | 0.808231 |
24,387 | The Jarník-Besicovitch theorem, due to V. Jarník and A. S. Besicovitch, states that the Hausdorff dimension of this set is equal to 1 / c {\displaystyle 1/c} . In particular, the set of numbers which are ψ c {\displaystyle \psi _{c}} -approximable for some c > 1 {\displaystyle c>1} (known as the set of very well approx... | Diophantine approximations | 0.808231 |
24,388 | An important example of a function ψ {\displaystyle \psi } to which Khinchin's theorem can be applied is the function ψ c ( q ) = q − c {\displaystyle \psi _{c}(q)=q^{-c}} , where c > 1 is a real number. For this function, the relevant series converges and so Khinchin's theorem tells us that almost every point is not ψ... | Diophantine approximations | 0.808231 |
24,389 | Molecular models of meiotic recombination have evolved over the years as relevant evidence accumulated. A major incentive for developing a fundamental understanding of the mechanism of meiotic recombination is that such understanding is crucial for solving the problem of the adaptive function of sex, a major unresolved... | Meiotic recombination | 0.80823 |
24,390 | It is a complex microflora that is directly related to human health. Therefore, regulation of intestinal microecology will help in the treatment of many diseases. It was reported that intestinal flora is involved in anti-tumor immunotherapy and affects the curative effect of an anti-malignant tumor therapy to varying d... | Microecology | 0.808228 |
24,391 | Microecology has many applications in the fields of medicine, agriculture, and biotechnology. It is also important for understanding the cycling of nutrients in the environment, and the behavior of microorganisms in various environments. Moving onwards Intestinal microecology is a new area of microecology study. | Microecology | 0.808228 |
24,392 | Additionally, it is a multidisciplinary area of study, combining elements of biology, chemistry, physics, and mathematics. It focuses on the study of the interactions between microorganisms and the environment they inhabit, their effects on the environment, and their effects on other organisms. Microecology also studie... | Microecology | 0.808228 |
24,393 | Studying the microbiome can help us better understand these diseases and develop treatments. Microecology is a large field that includes many topics such as; evolution, biodiversity, exobiology, ecology, bioremediation, recycling, and food microbiology. It is the study of the interactions between living organisms and t... | Microecology | 0.808228 |
24,394 | Microecology means microbial ecology or ecology of a microhabitat. In humans, gut microecology is the study of the microbial ecology of the human gut which includes gut microbiota composition, its metabolic activity, and the interactions between the microbiota, the host, and the environment. Research in human gut micro... | Microecology | 0.808228 |
24,395 | The Helmholtz free energy is defined as where F is the Helmholtz free energy (sometimes also called A, particularly in the field of chemistry) (SI: joules, CGS: ergs), U is the internal energy of the system (SI: joules, CGS: ergs), T is the absolute temperature (kelvins) of the surroundings, modelled as a heat bath, S ... | Helmholtz free energy | 0.808227 |
24,396 | The causes of the current crisis in taxonomy have been ascribed to a loss of perspective in ecology and evolutionary biology as the modern evolutionary synthesis developed during the 1930s and 40s: a conflation of "pattern with process", "confusing the methods and goals of the emerging science of population genetics wi... | Taxonomic impediment | 0.808226 |
24,397 | PMC technology was developed by Michael Kozicki, professor of electrical engineering at Arizona State University in the 1990s. Early experimental PMC systems were based on silver-doped germanium selenide glasses. Work turned to silver-doped germanium sulfide electrolytes and then to the copper-doped germanium sulfide e... | Programmable metallization cell | 0.808226 |
24,398 | A new complex S ′ {\displaystyle {\mathcal {S'}}} , can be obtained by replacing S ∗ ∂ K {\displaystyle S*\partial K} by ∂ S ∗ K {\displaystyle \partial S*K} . This replacement is called a Pachner move. The theorem of Pachner states that whenever two triangulated manifolds are PL- equivalent, there is a series of Pachn... | Triangulation (topology) | 0.808226 |
24,399 | Furthermore it was shown that singular and simplicial homology groups coincide. This workaround has shown the invariance of the data to homeomorphism. Hauptvermutung lost in importance but it was initial for a new branch in topology: The piecewise linear (short PL- topology) topology examines topological properties of ... | Triangulation (topology) | 0.808226 |
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