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5,000 | In the study of differential equations, a boundary-value problem is a differential equation subjected to constraints called boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions. Boundary value problems arise in several branch... | Boundary-value problem | 0.831474 |
5,001 | – Crest factor – Crossed-field amplifier – Crosstalk – Cruise control – Crystal oscillator – Ćuk converter – Current (electricity) – Current density – Current division – Current source inverter – Current source – Current transformer – Current-to-voltage converter – Cybernetics – Cyber-physical system – Cycloconverter –... | Index of electrical engineering articles | 0.831471 |
5,002 | There are various ways to prove the response theorems: | Response coefficient (biochemistry) | 0.83147 |
5,003 | Metagenomic sequencing could prove especially useful for diagnosis when the patient is immunocompromised. An ever-wider array of infectious agents can cause serious harm to individuals with immunosuppression, so clinical screening must often be broader. Additionally, the expression of symptoms is often atypical, making... | Infectious disease | 0.83147 |
5,004 | Only a week later, the Ciba group in Zurich, Leopold Ruzicka (1887–1976) and A. Wettstein, published their synthesis of testosterone. These independent partial syntheses of testosterone from a cholesterol base earned both Butenandt and Ruzicka the joint 1939 Nobel Prize in Chemistry. | Testosterone | 0.831468 |
5,005 | In physics and engineering, the time constant, usually denoted by the Greek letter τ (tau), is the parameter characterizing the response to a step input of a first-order, linear time-invariant (LTI) system. The time constant is the main characteristic unit of a first-order LTI system. In the time domain, the usual choi... | Thermal time constant | 0.831466 |
5,006 | thesis "Photo-Electric Potentials of Thin Cathode Films" was published in Physical Review(Series I) 34, 459 – June 1, 1912. He was from 1911 to 1914 an assistant in physics at Mount Vernon, Iowa's Cornell College and from 1914 to 1915 an instructor at the University of Missouri. He was a professor of physics from 1915 ... | Paul H. Dike | 0.831464 |
5,007 | Commonsense's reasoning study is divided into knowledge-based approaches and approaches that are based on machine learning over and using a large data corpora with limited interactions between these two types of approaches. There are also crowdsourcing approaches, attempting to construct a knowledge basis by linking th... | Commonsense reasoning | 0.831463 |
5,008 | The set packing problem is not only NP-complete, but its optimization version (general maximum set packing problem) has been proven as difficult to approximate as the maximum clique problem; in particular, it cannot be approximated within any constant factor. The best known algorithm approximates it within a factor of ... | Set packing | 0.831461 |
5,009 | In abstract algebra, the focal subgroup theorem describes the fusion of elements in a Sylow subgroup of a finite group. The focal subgroup theorem was introduced in (Higman 1953) and is the "first major application of the transfer" according to (Gorenstein, Lyons & Solomon 1996, p. 90). The focal subgroup theorem relat... | Focal subgroup theorem | 0.83146 |
5,010 | In a weighted bipartite graph, the optimization problem is to find a maximum-weight matching; a dual problem is to find a minimum-weight matching. This problem is often called maximum weighted bipartite matching, or the assignment problem. The Hungarian algorithm solves the assignment problem and it was one of the begi... | Maximum matching problem | 0.831459 |
5,011 | In order to factor using algebra tiles, one has to start out with a set of tiles that the student combines into a rectangle, this may require the use of adding zero pairs in order to make the rectangular shape. An example would be where one is given one positive x2 tile, three positive x tiles, and two positive unit ti... | Algebra tile | 0.831458 |
5,012 | In non-Euclidean geometry, the assumption that the interior angles of the triangle sum to 180 degrees must be discarded. Centers of tetrahedra or higher-dimensional simplices can also be defined, by analogy with 2-dimensional triangles.Some centers can be extended to polygons with more than three sides. The centroid, f... | Triangle center function | 0.831457 |
5,013 | Thus, thermal radiation contains information about the body that emitted it, while Hawking radiation seems to contain no such information, and depends only on the mass, angular momentum, and charge of the black hole (the no-hair theorem); this leads to the black hole information paradox.However, according to the conjec... | Acoustic Hawking radiation | 0.831456 |
5,014 | Formally, suppose that we have a lower-bound theorem showing that a problem requires Ω(f(n)) time to solve for an instance (input) of size n (see Big O notation § Big Omega notation for the definition of Ω). Then, an algorithm which solves the problem in O(f(n)) time is said to be asymptotically optimal. This can also ... | Asymptotically optimal algorithm | 0.831455 |
5,015 | While expression levels as the gene level can be more or less accurately depicted by second generation sequencing, transcript-level information still remains an important challenge. As a consequence, the role of alternative splicing in molecular biology remains largely elusive. Third generation sequencing technologies ... | Third-generation sequencing | 0.831455 |
5,016 | The expressions manipulated by the CAS typically include polynomials in multiple variables; standard functions of expressions (sine, exponential, etc.); various special functions (Γ, ζ, erf, Bessel functions, etc.); arbitrary functions of expressions; optimization; derivatives, integrals, simplifications, sums, and pro... | Computer algebra systems | 0.831454 |
5,017 | In the knapsack problem, we are given n {\displaystyle n} items with weight w i {\displaystyle w_{i}} and value v i {\displaystyle v_{i}} , along with a maximum weight capacity of a knapsack W {\displaystyle W} . The goal is to solve the following optimization problem; informally, what's the best way to fit the items i... | Pseudo-polynomial time | 0.831454 |
5,018 | I got plenty of practice in doing elementary calculus problems. I don't think there exists a problem—the classical kind of pseudo reality problem which first and second-year students are given—that I haven't seen. One month later he enrolled in a differential equations course ("mostly full of seniors") as well. | Andrew M. Gleason | 0.831453 |
5,019 | To train in the add-on specialty of infection control a physician must first be a specialist in infectious diseases or clinical microbiology. | Residency (medicine) | 0.831453 |
5,020 | Here are some examples of extremely-benevolent problems, that have an FPTAS by the above theorem.1. Multiway number partitioning (equivalently, Identical-machines scheduling) with the goal of minimizing the largest sum is extremely-benevolent. Here, we have a = 1 (the inputs are integers) and b = the number of bins (wh... | Fully polynomial-time approximation scheme | 0.831453 |
5,021 | The main products of Oxford Nanopore are: MinION: this harmonica-sized portable protein nanopore sequencing USB device has been commercially available since May 2015 after having been launched initially through an early access program, the MinION Access Program (MAP). An editorial describes the rapid pace of developmen... | Oxford Nanopore Technologies | 0.831453 |
5,022 | ECDL 2010. Lecture Notes in Computer Science. Vol. 6273. Springer. | Bibliographic coupling | 0.83145 |
5,023 | Ignoring the propagating degrees of freedom, the interaction between nonrelativistic electrons is the coulomb repulsion. In 2+1 dimensions, this is: V ( x , y ) = j 2 | y − x | . {\displaystyle V(x,y)={j^{2} \over |y-x|}.} When coupled to an external potential to model classical positions of nuclei, a Schrödinger field... | Schrödinger field | 0.83145 |
5,024 | In computer science and artificial intelligence, combinatorial search studies search algorithms for solving instances of problems that are believed to be hard in general, by efficiently exploring the usually large solution space of these instances. Combinatorial search algorithms achieve this efficiency by reducing the... | Combinatorial search | 0.83145 |
5,025 | 38. https://ughb.stanford.edu/degree-programs/major-programs/engineering-physics-program | Engineering science | 0.831444 |
5,026 | 1967). With this technology, segments of DNA could be sequenced, amplified, and proteins produced using bacterial transformations. The genetic material along with the proteins could be analyzed and more correct phylogenetic trees could be created. Since E.B. Ford's research, multiple other genetic ecologists have conti... | Genetic ecology | 0.831442 |
5,027 | The basic operations of Boolean algebra are conjunction, disjunction, and negation. These Boolean operations are expressed with the corresponding binary operators (AND and OR ) and the unary operator (NOT ), collectively referred to as Boolean operators.The basic Boolean operations on variables x and y are defined as f... | Switching algebra | 0.83144 |
5,028 | Being based on the milliradian, the NATO mil subtends roughly 1 m at a range of 1000 m (at such small angles, the curvature is negligible). Prefixes smaller than milli- are useful in measuring extremely small angles. Microradians (μrad, 10−6 rad) and nanoradians (nrad, 10−9 rad) are used in astronomy, and can also be u... | Rad (angular unit) | 0.831436 |
5,029 | (pp 103,4) Chapter 4 is "Assorted Geometries, Plane and Fancy". Both Non-Euclidean geometry and four-dimensional space are discussed. The authors say (p 112) "Among our most cherished convictions, none is more precious than our beliefs about space and time, yet is more difficult to explain." | Mathematics and the Imagination | 0.831432 |
5,030 | "Learning Quickly When Irrelevant Attributes Abound: A New Linear-threshold Algorithm" (PDF). Machine Learning. 2 (4): 285–318. | Machine Learning (journal) | 0.831431 |
5,031 | The governing equations in classical physics that are lectured at universities are listed below. | Governing equations | 0.831428 |
5,032 | Pell's equation is closely related to the theory of algebraic numbers, as the formula x 2 − n y 2 = ( x + y n ) ( x − y n ) {\displaystyle x^{2}-ny^{2}=(x+y{\sqrt {n}})(x-y{\sqrt {n}})} is the norm for the ring Z {\displaystyle \mathbb {Z} } and for the closely related quadratic field Q ( n ) {\displaystyle \mathbb {Q... | Pell's equation | 0.831426 |
5,033 | All NP-complete problems are also NP-hard (see List of NP-complete problems). For example, the optimization problem of finding the least-cost cyclic route through all nodes of a weighted graph—commonly known as the travelling salesman problem—is NP-hard. The subset sum problem is another example: given a set of integer... | NP-hardness | 0.831425 |
5,034 | Negation normal form Conjunctive normal form Disjunctive normal form Algebraic normal form Prenex normal form Skolem normal form Blake canonical form, also known as the complete sum of prime implicants, the complete sum, or the disjunctive prime form | Normal form (mathematics) | 0.831422 |
5,035 | Recent developments in the field have included the generation of X-ray free electron lasers, allowing analysis of the dynamics and motion of biological molecules, and the use of structural biology in assisting synthetic biology.In the late 1930s and early 1940s, the combination of work done by Isidor Rabi, Felix Bloch,... | Structural Biology | 0.831421 |
5,036 | "On the expressive power of deep neural networks". Icml'17. Proceedings of the 34th International Conference on Machine Learning - Volume 70. | Surya Ganguli | 0.831421 |
5,037 | It is currently being applied in the field of nanotechnology to characterize silver and gold nanorods. A popular alternative for this is the Discrete dipole approximation (DDA) method. | Gans theory | 0.831418 |
5,038 | So in this case one can really use the family of finite subgroups. On the other hand this shows that the isomorphism conjecture for algebraic K-Theory and the family of finite subgroups is not true. One has to extend the conjecture to a larger family of subgroups which contains all the counterexamples. Currently no cou... | Farrell–Jones conjecture | 0.831416 |
5,039 | Evaluation (or "validation") of clustering results is as difficult as the clustering itself. Popular approaches involve "internal" evaluation, where the clustering is summarized to a single quality score, "external" evaluation, where the clustering is compared to an existing "ground truth" classification, "manual" eval... | Clustering algorithm | 0.831415 |
5,040 | Protein structure prediction is the inference of the three-dimensional structure of a protein from its amino acid sequence—that is, the prediction of its folding and its secondary and tertiary structure from its primary structure. Structure prediction is fundamentally different from the inverse problem of protein desig... | Protein chemistry | 0.831412 |
5,041 | There are two main cases where minimal polynomials are considered. In field theory and number theory, an element θ of an extension field L of K is algebraic over K if it is a root of some polynomial with coefficients in K. The minimal polynomial over K of θ is thus the monic polynomial of minimal degree that has θ as a... | Polynomial ring | 0.831409 |
5,042 | Much of computer science and artificial intelligence involves designing automatic systems to solve a specified type of problem: to accept input data and calculate a correct or adequate response, reasonably quickly. Algorithms are recipes or instructions that direct such systems, written into computer programs. Steps fo... | Problem analysis | 0.831406 |
5,043 | Viruses are capsid-encoding organisms composed of proteins and nucleic acids that can self-assemble after replication in a host cell using the host's replication machinery. There is a disagreement in science about whether viruses are living due to their lack of ribosomes. Comprehending the viral genome is important not... | Microbial genetics | 0.831402 |
5,044 | For the study of the computational complexity of evaluating conjunctive queries, two problems have to be distinguished. The first is the problem of evaluating a conjunctive query on a relational database where both the query and the database are considered part of the input. The complexity of this problem is usually re... | Conjunctive query | 0.831401 |
5,045 | Hence d(a c) = (d a)c, so that B must be associative. This analysis applies to the inclusion of R in C and C in H. Taking O = H ⊕ H with the product and inner product above gives a noncommutative nonassociative algebra generated by J = (0, 1). This recovers the usual definition of the octonions or Cayley numbers. | Euclidean Hurwitz algebra | 0.831401 |
5,046 | The underlying mechanism is believed to involve the production of antibodies against a person's own tissues. Due to their genetics, some people are more likely to get the disease when exposed to the bacteria than others. Other risk factors include malnutrition and poverty. | Acute rheumatic fever | 0.831399 |
5,047 | Pillay (1994) found that worked examples showing 3 intermediate problem stages were more effective than showing only one but suggested that the distance between stages needs to be small enough to allow students to connect them without having to create their own linkages. Schwonke et al. (2009), in two experiments with ... | Worked-example effect | 0.831399 |
5,048 | Foraminiferal tests are the tests (or shells) of Foraminifera.Foraminifera (forams for short) are single-celled predatory protists, mostly marine, and usually protected with shells. These shells, often called tests, can be single-chambered or have multiple interconnected chambers; the cellular machinery is contained wi... | Foraminifera test | 0.831398 |
5,049 | The original equations used Hamilton's more expressive quaternion notation, a kind of Clifford algebra, which fully subsumes the standard Maxwell vectorial equations largely used today. In the late 1880s there was a debate over the relative merits of vector analysis and quaternions. According to Heaviside the electroma... | Zero point energy | 0.831398 |
5,050 | Depending on the type and variation in training data, machine learning can be roughly categorized into three frameworks: supervised learning, unsupervised learning, and reinforcement learning. Multiple instance learning (MIL) falls under the supervised learning framework, where every training instance has a label, eith... | Multiple instance learning | 0.831397 |
5,051 | A line of research in theoretical computer science is about the number of single-bit arithmetic operations necessary to multiply two n {\displaystyle n} -bit integers. This is known as the computational complexity of multiplication. Usual algorithms done by hand have asymptotic complexity of O ( n 2 ) {\displaystyle O(... | Long multiplication | 0.831397 |
5,052 | Finding matching upper and lower bounds for the complexity of a k {\displaystyle k} -level remains a major open problem in discrete geometry. The best upper bound is O ( n k 1 / 3 ) {\displaystyle O(nk^{1/3})} , while the best lower bound is n 2 Ω ( log k ) {\displaystyle n2^{\Omega ({\sqrt {\log k}})}} . In contrast... | Arrangements of lines | 0.831395 |
5,053 | This field has yielded a wealth of information on the non-spherical part (i.e. the angle dependence) of the intermolecular potential. In addition, several new phenomena were later discovered that had been believed to be non-existing in neutral gases, like transverse transport effects in a magnetic field, comparable to ... | Giacinto Scoles | 0.831394 |
5,054 | But the second LBA problem has an affirmative answer, which is implied by the Immerman–Szelepcsényi theorem proved 20 years after the problem was raised. As of today, the first LBA problem still remains open. Savitch's theorem provides an initial insight, that NSPACE(O(n)) ⊆ DSPACE(O(n2)). | Linear bounded automaton | 0.831393 |
5,055 | : 29 During the winter of his senior year, Pauling taught a chemistry course for home economics majors. It was in one of these classes that Pauling met his future wife, Ava Helen Miller. | Linus Pauling | 0.831393 |
5,056 | It is used in various areas of algebra: | Ground field | 0.831393 |
5,057 | 73) explains how Matiyasevich's solution to Hilbert's 10th problem can be used to obtain a proof to Gödel's first incompleteness theorem. Matiyasevich proved that there is no algorithm that, given a multivariate polynomial p(x1, x2,...,xk) with integer coefficients, determines whether there is an integer solution to th... | Gödel incompleteness theorem | 0.831391 |
5,058 | In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular arc. It can be uniform, with a constant rate of rotation and constant tangential speed, or non-uniform with a changing rate of rotation. The rotation around a fixed axis of a three-dimensional body in... | Circular motion | 0.831386 |
5,059 | The commentary of Liu Hui provided geometrical and algebraic proofs to the problems given within the text.The Nine Chapters on the Mathematical Art was one of the most influential of all Chinese mathematical books and it is composed of 246 problems. It was later incorporated into The Ten Computational Canons, which bec... | Chinese mathematics | 0.831385 |
5,060 | Or, it can form a polycrystal, with various possibilities for the size, arrangement, orientation, and phase of its grains. The final form of the solid is determined by the conditions under which the fluid is being solidified, such as the chemistry of the fluid, the ambient pressure, the temperature, and the speed with ... | Crystallographic form | 0.831384 |
5,061 | Generally, n – 2 polynomials define an algebraic set of dimension two or higher. If the dimension is two, the algebraic set may have several irreducible components. | Surface (mathematics) | 0.831384 |
5,062 | An example is how the soil acts as a part of the biosphere, while also acting as a source of flux exchange. In Aristotelian physics, the term was applied to four spherical natural places, concentrically nested around the center of the Earth, as described in the lectures Physica and Meteorologica. They were believed to ... | Geosphere | 0.831383 |
5,063 | The first is to allow electrical phenomena to be explained in terms of the more familiar mechanical systems. For instance, an electrical inductor-capacitor-resistor circuit has differential equations of the same form as a mechanical mass-spring-damper system. In such cases the electrical domain is converted to the mech... | Elastance | 0.831382 |
5,064 | A complete set of invariants, together with which invariants are realizable, solves the classification problem, and is often a step in solving it. A computable complete set of invariants (together with which invariants are realizable) solves both the classification problem and the equivalence problem. A canonical form ... | Classification theorem | 0.831381 |
5,065 | electric dipole moment A measure of the separation of positive and negative electric charges within an electrical system, i.e. a measure of the system's overall electrical polarity. The SI unit for measuring electric dipole moment is the coulomb-metre (C⋅m), but the debye (D), a non-SI unit, is also widely used in chem... | Glossary of chemistry terms | 0.831378 |
5,066 | For example, most LNO compilers would probably split the kk == 0 iteration off from the rest of the kk iterations, to remove the if statement from the i loop. This is one of the values of such a compiler: while it is straightforward to code the simple cases of this optimization, keeping all the details correct as the c... | Loop nest optimization | 0.831376 |
5,067 | For real-valued functions (e.g., functions to a real interval, ), Pollard's pseudo-dimension can be used. The Rademacher complexity provides similar bounds to the VC, and can sometimes provide more insight than VC dimension calculations into such statistical methods such as those using kernels. The Memory Capacity (som... | Vapnik–Chervonenkis dimension | 0.831374 |
5,068 | Multiple inheritance can solve this, by allowing subclasses to have multiple parents, and thus a few parent classes can be considered rather than every child, without disrupting any existing hierarchy. An example is a taxonomy where different vegetables inherit from their ancestor species. Attempting to compare the tas... | Combinatorial explosion (communication) | 0.831372 |
5,069 | Given an equation, move all of its terms to one side so that it has the form, f (x) = 0, where f is some function of the unknown variable x. A value c that satisfies this equation, that is, f (c) = 0, is called a root or zero of the function f and is a solution of the original equation. If f is a continuous function an... | False position | 0.831371 |
5,070 | It has one vertex per point and one vertex per triple, with an edge connecting two vertices if they correspond to a point and to a triple that contains that point. The configuration may also be described algebraically in terms of the abelian group Z 3 × Z 3 {\displaystyle \mathbb {Z} _{3}\times \mathbb {Z} _{3}} with n... | Möbius–Kantor graph | 0.83137 |
5,071 | Chatbot competitions focus on the Turing test or more specific goals. Two such annual contests are the Loebner Prize and The Chatterbox Challenge (the latter has been offline since 2015, however, materials can still be found from web archives).Chatbots may use neural networks as a language model. For example, generativ... | IM bot | 0.831369 |
5,072 | In this way, genes are clues to organismal metabolism and identity. Genetics enables us to ask 'who is there?' and 'what are they doing?' This approach is called metagenomics. | Geobiology | 0.831367 |
5,073 | McGraw-Hill's 500 College Calculus Questions to Know by Test Day (paperback). McGraw-Hill's 500 College Questions to Know by Test Day. New York: McGraw-Hill. | Elliott Mendelson | 0.831367 |
5,074 | These operations are well-defined, meaning that the end result does not depend on the choices of representatives that were made to obtain the result. The m congruence classes with these two defined operations form a ring, called the ring of integers modulo m. There are several notations used for these algebraic objects... | Modular inverse | 0.831367 |
5,075 | MMP can be defined as a pair of molecules that differ in only a minor single point change (See Fig 1). Matched molecular pairs (MMPs) are widely used in medicinal chemistry to study changes in compound properties which includes biological activity, toxicity, environmental hazards and much more, which are associated wit... | Matched molecular pair analysis | 0.831364 |
5,076 | Skin is opaque to light. In physics light reception, heat or other type of radiant energy on the part of molecules is called absorption. When tissues are illuminated during translumination, some light is absorbed and some reflected. It is known that an object which absorbs all radiation is seen as black; the pigments t... | Venous translucence | 0.831364 |
5,077 | Randomization is used in statistics and in gambling. | Randomization | 0.831363 |
5,078 | The National Biomedical Research Foundation (NBRF) was on the cutting edge of utilizing computers for medicine and biology at this time. Dayhoff and her team made use of their facilities for determining amino acid sequences of protein molecules in mainframe computers. The number of discovered sequences continued to gro... | Sequence database | 0.83136 |
5,079 | A 2013 report concluded that Carnegie Learning Curricula and Cognitive Tutor® was found to have mixed effects on mathematics achievement for high school students. The report identified 27 studies that investigate the effectiveness of Cognitive Tutor ®, and the conclusion is based on 6 studies that meet What Works Clear... | Cognitive Tutor | 0.83136 |
5,080 | These feature vectors are then used to directly predict the final potentials. In 2017, the first-ever MPNN model, a deep tensor neural network, was used to calculate the properties of small organic molecules. Advancements in this technology led to the development of Matlantis in 2022, which commercially applies machine... | Interatomic potential | 0.831356 |
5,081 | Structure can be complex systems that undergo different loads during their lifetime, e.g. Lithium-ion batteries. Some complex structures, such as the turbo machinery in a liquid-fuel rocket, can also cost millions of dollars. Engineers will commonly model these structures as coupled second-order systems, approximating ... | Flaw detection | 0.831354 |
5,082 | The revolution in molecular genetics has provided more effective tools for describing the genome, and many researchers are pursuing molecular genetics in order to directly assess the influence of alleles and environments on traits. An initial limitation of the twin design is that it does not afford an opportunity to co... | Equal environments assumption | 0.83135 |
5,083 | neXtProt is an on-line knowledge platform on human proteins. It strives to be a comprehensive resource that provides a variety of types of information on human proteins, such as their function, subcellular location, expression, interactions and role in diseases. The major part of the information in neXtProt is obtained... | NeXtProt | 0.831345 |
5,084 | Although primarily aimed at researchers, this book (and especially its earlier chapters) could also be used as the textbook for a graduate course in its material. Reviewer Peter Hajnal calls it "very important to any specialist in computational geometry" and "highly recommended to anybody who is interested in this new ... | Davenport–Schinzel Sequences and Their Geometric Applications | 0.831345 |
5,085 | Games of chance are also good examples of combinations, permutations, and arrangements, which are met at every step: combinations of cards in a player's hand, on the table, or expected in any card game; combinations of numbers when rolling several dice once; combinations of numbers in lottery and Bingo; combinations of... | Gaming mathematics | 0.831342 |
5,086 | This simple approach is reasonably insensitive to the effects of spin diffusion or non-uniform correlation times and can usually lead to definition of the global fold of the protein, provided a sufficiently large number of NOEs have been identified. NOESY cross peaks can be classified as strong, medium or weak and can ... | Nuclear Overhauser effect spectroscopy | 0.831338 |
5,087 | Table data obtained from CRC Handbook of Chemistry and Physics 47th ed. Note that "(s)" annotation indicates equilibrium temperature of vapor over solid. Otherwise the temperature is equilibrium of vapor over liquid. | Carbon tetrachloride (data page) | 0.831338 |
5,088 | One might object that A and B are related by the algebraic equation A − B − 2√3 = 0, which does not remain true when A and B are exchanged. However, this relation is not considered here, because it has the coefficient −2√3 which is not rational. We conclude that the Galois group of the polynomial x2 − 4x + 1 consists o... | Solvability by radicals | 0.831334 |
5,089 | -A simple example of the Evelyn effect is the sophomore level chemistry lab experiment involving two popular examples that are listed below. a) Dehydration of 4-methylcyclohexanol b) Dehydration of 2-Methylcyclohexanol c) Mechanism for the dehydration of 2-methylcyclohexanol | Evelyn effect | 0.831333 |
5,090 | We first present the isomorphism theorems of the groups. | Isomorphism theorem | 0.831331 |
5,091 | The 1913 discovery by English physicist Henry Moseley that the nuclear charge is the physical basis for an atom's atomic number, further refined when the nature of protons and neutrons became appreciated, eventually led to the current definition of an element based on atomic number (number of protons per atomic nucleus... | Light element | 0.831329 |
5,092 | Studies using MeDIP-seq or MeDIP-chip are both genome-wide approaches that have the common aim of obtaining the functional mapping of the methylome. Once regions of DNA methylation are identified, a number of bioinformatics analyses can be applied to answer certain biological questions. One obvious step is to investiga... | Methylated DNA immunoprecipitation | 0.831327 |
5,093 | Benchmarks often measure performance for small numerically intensive programs. In some rare real-life programs, Java out-performs C. One example is the benchmark of Jake2 (a clone of Quake II written in Java by translating the original GPL C code). The Java 5.0 version performs better in some hardware configurations th... | Java performance | 0.831325 |
5,094 | Physics Letters. Elsevier BV. 1 (7): 251–253. | History of superconductivity | 0.831324 |
5,095 | In biochemical reactions involving phosphate groups (e.g. adenosine triphosphate), a "phosphoryl" group is usually transferred between the substrates by the "phosphoryl transfer reactions" (see phosphorylation). Examples of molecules containing those groups in biology, biochemistry and biomedicine are adenosine monopho... | Phosphoryl group | 0.831321 |
5,096 | The famous theorem of Feit and Thompson states that every group of odd order is solvable. Therefore, every finite simple group has even order unless it is cyclic of prime order. The Schreier conjecture asserts that the group of outer automorphisms of every finite simple group is solvable. This can be proved using the c... | Simple groups | 0.83132 |
5,097 | Or, the problem with 5 cookies and 2 people can be solved by cutting one cookie in half, which introduces the idea of fractions (5/2 = 2+1/2) . The problem with 5 cookies and 0 people, on the other hand, cannot be solved in any way that preserves the meaning of "divides". In elementary algebra, another way of looking a... | Division by zero | 0.831314 |
5,098 | Photosynthetic dinoflagellates contain membrane-bound light-harvesting complexes similar to those found in green plants. They additionally contain water-soluble protein-pigment complexes that exploit carotenoids such as peridinin to extend their photosynthetic capacity. Peridinin absorbs light in the blue-green wavelen... | Peridinin-chlorophyll-protein complex | 0.831313 |
5,099 | In higher-dimensional geometry, the faces of a polytope are features of all dimensions. A face of dimension k is called a k-face. For example, the polygonal faces of an ordinary polyhedron are 2-faces. In set theory, the set of faces of a polytope includes the polytope itself and the empty set, where the empty set is f... | Ridge (geometry) | 0.831312 |
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