id int32 0 100k | text stringlengths 20 3.54k | source stringlengths 1 104 | similarity float32 0.8 0.91 |
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200 | "Is evolution compatible with Christianity or other religious systems?" "Are there laws of biology like the laws of physics? "Ideas drawn from philosophical ontology and logic are being used by biologists in the domain of bioinformatics. | Philosophy of biology | 0.858011 |
201 | Since many students who apply to graduate programs in biochemistry do so during the first half of their fourth year, the scope of most questions is largely that of the first three years of a standard American undergraduate biochemistry curriculum. A sampling of test item content is given below: | GRE Biochemistry, Cell and Molecular Biology Test | 0.857973 |
202 | The direct sum of the division ring of quaternions with itself is denoted H ⊕ H {\displaystyle \mathbb {H} \oplus \mathbb {H} } . The product of two elements ( a ⊕ b ) {\displaystyle (a\oplus b)} and ( c ⊕ d ) {\displaystyle (c\oplus d)} is a c ⊕ b d {\displaystyle ac\oplus bd} in this direct sum algebra. Proposition: ... | Split-biquaternion | 0.857918 |
203 | In biology, translation is the process in living cells in which proteins are produced using RNA molecules as templates. The generated protein is a sequence of amino acids. This sequence is determined by the sequence of nucleotides in the RNA. The nucleotides are considered three at a time. | MRNA translation | 0.85783 |
204 | Later, René Descartes (17th century) introduced the modern notation (for example, the use of x—see below) and showed that the problems occurring in geometry can be expressed and solved in terms of algebra (Cartesian geometry).Equally important as the use or lack of symbolism in algebra was the degree of the equations t... | Syncopated algebra | 0.857786 |
205 | He suggests that resolving the first problem will require introducing some material model and employing the theory of elasticity. 1910: Theodor Kaluza points out that there is nothing inherently paradoxical about the static and disk-riding observers obtaining different results for the circumference. This does however i... | Ehrenfest paradox | 0.857695 |
206 | The subset consisting of O and I (highlighted in red in the tables at the right) is also a field, known as the binary field F2 or GF(2). In the context of computer science and Boolean algebra, O and I are often denoted respectively by false and true, and the addition is then denoted XOR (exclusive or). In other words, ... | Field (mathematics) | 0.85766 |
207 | The primary algebra embodies a point noted by Huntington in 1933: Boolean algebra requires, in addition to one unary operation, one, and not two, binary operations. Hence the seldom-noted fact that Boolean algebras are magmas. (Magmas were called groupoids until the latter term was appropriated by category theory.) To ... | Boundary algebra | 0.857601 |
208 | Similarly, a normal subgroup N of G is said to be a maximal normal subgroup (or maximal proper normal subgroup) of G if N < G and there is no normal subgroup K of G such that N < K < G. We have the following theorem: Theorem: A normal subgroup N of a group G is a maximal normal subgroup if and only if the quotient G/N ... | Maximal subgroup | 0.857578 |
209 | Below Level 1 0 – 175 Tasks at this level require the respondents to carry out simple processes such as counting, sorting, performing basic arithmetic operations with whole numbers or money, or recognizing common spatial representations in concrete, familiar contexts where the mathematical content is explicit with litt... | Programme for the International Assessment of Adult Competencies | 0.857471 |
210 | This produces a characteristic 9:7 ratio of pigmented to unpigmented plants. Complementary epistasis in contrast produces an unpigmented plant if and only if the genotype is cc and dd, and the characteristic ratio is 15:1 between pigmented and unpigmented plants.Classical genetics considered epistatic interactions betw... | Autosomal recessive disorder | 0.857466 |
211 | NMT has been widely applied in plant biology in fields such as abiotic/biotic stress, plant nutrition, plant growth and development, plant/microbe interaction, plant defense, photosynthesis, signal transduction research, and more. Roots are commonly measured, in addition to many other plant samples such as leaf tissue,... | Non-invasive micro-test technology | 0.857388 |
212 | The same thing is believed to occur in laboratory measurements. Parallel plate geometry is used in laboratory measurements without corona generation. A stainless steel cup holds the sample. | Electrostatic filter | 0.857387 |
213 | Searching for the real or rational solutions are much more difficult problems that are not considered in this article. The set of solutions is not always finite; for example, the solutions of the system x ( x − 1 ) = 0 x ( y − 1 ) = 0 {\displaystyle {\begin{aligned}x(x-1)&=0\\x(y-1)&=0\end{aligned}}} are a point (x,y) ... | Polynomial system of equations | 0.857347 |
214 | The second branch in the sub-hierarchy considers the skills associated with advanced substitution. Attribute A7 requires the examinee to substitute numbers into algebraic expressions. The complexity of attribute A7 relative to attribute A4 lies in the concurrent management of multiple pairs of numbers and multiple equa... | Attribute hierarchy method | 0.857326 |
215 | JEE(Advanced) is conducted in two shifts of three hours each - Paper-1 and Paper-2, both the papers consist questions from three major subjects- Physics, Chemistry and Mathematics. Unlike most of the other exams, the type and the number of questions being asked in the paper varies from year to year, with an average of ... | Joint Entrance Examination – Advanced | 0.857305 |
216 | When the bottleneck is localized, optimization usually starts with a rethinking of the algorithm used in the program. More often than not, a particular algorithm can be specifically tailored to a particular problem, yielding better performance than a generic algorithm. For example, the task of sorting a huge list of it... | Software optimization | 0.857269 |
217 | The problems on the competition range from basic algebra to precalculus and are within the grasp of a high schooler's mathematical knowledge. The contest contains concepts from a variety of topics, including geometry and combinatorics. | Michigan Mathematics Prize Competition | 0.857243 |
218 | The P versus NP problem is a major unsolved problem in theoretical computer science. In informal terms, it asks whether every problem whose solution can be quickly verified can also be quickly solved. The informal term quickly, used above, means the existence of an algorithm solving the task that runs in polynomial tim... | P versus NP problem | 0.857202 |
219 | AP Physics 1 is an algebra-based, introductory college-level physics course that includes mechanics topics such as motion, force, momentum, energy, harmonic motion, and rotation; The College Board published a curriculum framework that includes seven big ideas on which the AP Physics 1 and 2 courses are based, along wit... | AP Physics 1 | 0.857159 |
220 | In astronomy, the stellar classification of stars and their place on the Hertzsprung–Russell diagram are based, in part, upon their surface temperature, known as effective temperature. The photosphere of the Sun, for instance, has an effective temperature of 5772 K as adopted by IAU 2015 Resolution B3. Digital cameras... | Kelvin | 0.857158 |
221 | In mathematics, an algebraic structure consists of a nonempty set A (called the underlying set, carrier set or domain), a collection of operations on A (typically binary operations such as addition and multiplication), and a finite set of identities, known as axioms, that these operations must satisfy. An algebraic str... | Structure (algebraic) | 0.857104 |
222 | The second orbit allows eight electrons, and when it is full the atom is neon, again inert. The third orbital contains eight again, except that in the more correct Sommerfeld treatment (reproduced in modern quantum mechanics) there are extra "d" electrons. The third orbit may hold an extra 10 d electrons, but these pos... | Sommerfeld–Wilson quantization | 0.857078 |
223 | Sequencing is used in molecular biology to study genomes and the proteins they encode. Information obtained using sequencing allows researchers to identify changes in genes and noncoding DNA (including regulatory sequences), associations with diseases and phenotypes, and identify potential drug targets. | DNA sequence | 0.857068 |
224 | From Lagrange's theorem we know that any non-trivial subgroup of a group with 6 elements must have order 2 or 3. In fact the two cyclic permutations of all three blocks, with the identity, form a subgroup of order 3, index 2, and the swaps of two blocks, each with the identity, form three subgroups of order 2, index 3.... | Nonabelian group of order 6 | 0.857004 |
225 | The spectral radiance in janskys per steradian can be converted to a brightness temperature, useful in radio and microwave astronomy. Starting with Planck's law, we see B ν = 2 h ν 3 c 2 1 e h ν / k T − 1 . {\displaystyle B_{\nu }={\frac {2h\nu ^{3}}{c^{2}}}{\frac {1}{e^{h\nu /kT}-1}}.} This can be solved for temperatu... | Jansky | 0.856972 |
226 | The dimensionless constants that arise in the results obtained, such as the C in the Poiseuille's Law problem and the κ {\displaystyle \kappa } in the spring problems discussed above, come from a more detailed analysis of the underlying physics and often arise from integrating some differential equation. Dimensional an... | Dimensional units | 0.856971 |
227 | --gc:arc – Automatic reference counting (ARC) with move semantics optimizations, offers a shared heap. It offers fully deterministic performance for hard realtime systems. Reference cycles may cause memory leaks: these may be dealt with by manually annotating {.acyclic.} | Nim (programming language) | 0.856935 |
228 | One DNA or RNA molecule differs from another primarily in the sequence of nucleotides. Nucleotide sequences are of great importance in biology since they carry the ultimate instructions that encode all biological molecules, molecular assemblies, subcellular and cellular structures, organs, and organisms, and directly e... | Nucleic acids | 0.856883 |
229 | In elementary algebra, the quadratic formula is a formula that provides the two solutions to a quadratic equation. There are other ways of solving a quadratic equation instead of using the quadratic formula, such as completing the square. Given a general quadratic equation of the form whose discriminant b 2 − 4 a c {\d... | Quadratic formula | 0.856707 |
230 | For example, the force between two separated electric charges with spherical symmetry (in the vacuum of classical electromagnetism) is given by Coulomb's law: F C = 1 4 π ε 0 q 1 q 2 r 2 {\displaystyle F_{\text{C}}={\frac {1}{4\pi \varepsilon _{0}}}{\frac {q_{1}q_{2}}{r^{2}}}} Here, q1 and q2 are the charges, r is the ... | Permittivity constant | 0.85669 |
231 | Some non-prime numbers n are such that every group of order n is cyclic. One can show that n = 15 is such a number using the Sylow theorems: Let G be a group of order 15 = 3 · 5 and n3 be the number of Sylow 3-subgroups. Then n3 ∣ {\displaystyle \mid } 5 and n3 ≡ 1 (mod 3). The only value satisfying these constraints i... | Sylow p-subgroup | 0.856656 |
232 | In 2003, Anthony Trewavas led a study to see how the roots interact with one another and study their signal transduction methods. He was able to draw similarities between water stress signals in plants affecting developmental changes and signal transductions in neural networks causing responses in muscle. Particularly,... | Plant intelligence | 0.856618 |
233 | The concept can also be applied to more general systems of equations, such as systems of polynomial equations or partial differential equations. In the case of the systems of polynomial equations, it may happen that an overdetermined system has a solution, but that no one equation is a consequence of the others and tha... | Over-determined system | 0.856614 |
234 | There is a significant runtime overhead in calling a function, including passing the arguments, branching to the subprogram, and branching back to the caller. The overhead often includes saving and restoring certain processor registers, allocating and reclaiming call frame storage, etc.. In some languages, each functio... | Subroutine call | 0.856456 |
235 | Positional Assembly Constructing materials an atom or molecule at a time. Protein Design The design and construction of new proteins; an enabling technology for nanotechnology. Protein folding The process by which proteins acquire their functional, preordained, three-dimensional structure after they emerge, as linear p... | Glossary of nanotechnology | 0.856438 |
236 | 3. The converse of the theorem need not hold. For example, R2 and R3 have isomorphic fundamental groups but are still not homeomorphic. | Induced homomorphism | 0.856358 |
237 | GUIDE-Seq (Genome-wide, Unbiased Identification of DSBs Enabled by Sequencing) is a molecular biology technique that allows for the unbiased in vitro detection of off-target genome editing events in DNA caused by CRISPR/Cas9 as well as other RNA-guided nucleases in living cells. Similar to LAM-PCR, it employs multiple ... | GUIDE-Seq | 0.856345 |
238 | A well-known lower bound for unstructured sorting, in the decision tree model, is based on the factorial number of sorted orders that an unstructured list may have. Because each comparison can at best reduce the number of possible orderings by a factor of two, sorting requires a number of comparisons at least equal to ... | X + Y sorting | 0.856342 |
239 | The laboratory infrastructure and computing resources used to perform this experiment on the MinION nanopore sequencer would be available in most molecular laboratories around the world. Using this system, the concept of portability, and thus sequencing influenza viruses in the clinic or field is now tenable.“ In a pap... | Oxford Nanopore Technologies | 0.856193 |
240 | The number of left cosets of H in G is equal to the number of right cosets of H in G. This common value is called the index of H in G and is usually denoted by . Cosets are a basic tool in the study of groups; for example, they play a central role in Lagrange's theorem that states that for any finite group G, the numbe... | Right coset | 0.856164 |
241 | Very simple algebra skills are often taught to young children. For example, a student might convert an addition equation such as 19 + 15 = ? into a simpler equation, 20 + 14 = ? | NCTM standards | 0.856114 |
242 | 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 | 0.856104 |
243 | The teacher can steer the students either through careful design of the questions (this rules out barometer questions), or through guiding the students to the desired choices. In case of the original barometer question, the examiner may explicitly say that the problem has more than one solution, insist on applying the ... | Barometer question | 0.856095 |
244 | Intuitively, though, it is plausible that if the theorem holds for a single point charge then it would also hold for two opposite point charges connected together. In particular, it would hold in the limit where the distance between the charges is decreased to zero while maintaining the dipole moment – that is, it woul... | Earnshaw's Theorem | 0.85609 |
245 | Each calculation is able to be done with a certain trick or shortcut that makes the calculations easier. The high school exam includes calculus and other difficult topics in the questions also with the same rules applied as to the middle school version. It is well known that the grading for this event is particularly s... | Texas Math and Science Coaches Association | 0.856076 |
246 | The maximum number of electrons that can be placed in a subshell is given by 2(2l + 1). This gives two electrons in an s subshell, six electrons in a p subshell, ten electrons in a d subshell and fourteen electrons in an f subshell. The numbers of electrons that can occupy each shell and each subshell arise from the eq... | Electron shell configuration | 0.856036 |
247 | There are two rounds in the Junior Section: a written round (Round 1) and an invitational round (Round 2). The paper in Round 1 comprises 5 multiple-choice questions, each with five options, and 20 short answer questions. The Junior section is geared towards Lower Secondary students, and topics tested include number th... | Singapore Mathematical Olympiad | 0.85586 |
248 | If Theorem 1 holds, and φ is not satisfiable in any structure, then ¬φ is valid in all structures and therefore provable, thus φ is refutable and Theorem 2 holds. If on the other hand Theorem 2 holds and φ is valid in all structures, then ¬φ is not satisfiable in any structure and therefore refutable; then ¬¬φ is prova... | Original proof of Gödel's completeness theorem | 0.855688 |
249 | Rabin–Karp string-search algorithm radix quicksort radix sort ragged matrix Raita algorithm random-access machine random number generation randomization randomized algorithm randomized binary search tree randomized complexity randomized polynomial time randomized rounding randomized search tree Randomized-Select random... | List of terms relating to algorithms and data structures | 0.855684 |
250 | An ideal constant-force spring is a spring for which the force it exerts over its range of motion is a constant, that is, it does not obey Hooke's law. In reality, "constant-force springs" do not provide a truly constant force and are constructed from materials which do obey Hooke's law. Generally constant-force spring... | Constant-force spring | 0.855635 |
251 | The goal of complexity analysis in this model is to find time bounds that depend only on n and not on the actual size of the input values or the machine words. In modeling integer computation, it is necessary to assume that machine words are limited in size, because models with unlimited precision are unreasonably powe... | Transdichotomous model | 0.855605 |
252 | Therefore, it is a basic tool for the homotopy continuation method described below. Optimization is rarely used for solving polynomial systems, but it succeeded, circa 1970, in showing that a system of 81 quadratic equations in 56 variables is not inconsistent. With the other known methods, this remains beyond the poss... | Polynomial system of equations | 0.855598 |
253 | Calculators are not allowed. The problems chosen are from various areas of secondary school mathematics, broadly classifiable as geometry, number theory, algebra, and combinatorics. They require no knowledge of higher mathematics such as calculus and analysis, and solutions are often elementary. | International Mathematical Olympiad | 0.855541 |
254 | The three letters ABC can be reordered into ABC, ACB, BAC, BCA, CAB, CBA, forming in total 6 (factorial of 3) elements. The group operation is composition of these reorderings, and the identity element is the reordering operation that leaves the order unchanged. This class is fundamental insofar as any finite group can... | Group (mathematics) | 0.855531 |
255 | Computational advances have enabled cheaper and faster sequencing. Research has focused on combinatorial chemistry, genomic mining, omic technologies, and high throughput screening. As the cost per genetic test decreases, the development of personalized drug therapies will increase. | Extensive metabolizer | 0.855511 |
256 | From the viewpoint of the experimental physics, the requirement that the marks be made simultaneously is redundant for a stationary object with constant shape and size, and can in this case be dropped from such definition. Since the rod is stationary in K0, the distance between the marks is the proper length of the rod... | Proper length | 0.855466 |
257 | During the lessons Four Team Selection Tests are held which are considered the four parts of the Selection Competition above 15.5 and are called Euclides. All the student have the same test. In each of the competition five students are eliminated. So after the fourth competition the six member of national team for IMO ... | Cyprus Mathematical Society | 0.855455 |
258 | DNA sequencing is the process of determining the nucleic acid sequence – the order of nucleotides in DNA. It includes any method or technology that is used to determine the order of the four bases: adenine, guanine, cytosine, and thymine. The advent of rapid DNA sequencing methods has greatly accelerated biological and... | DNA sequence | 0.855444 |
259 | This variable represents the difference between the two sides of the inequality and is assumed to be non-negative. For example, the inequalities x 2 + 2 x 3 ≤ 3 − x 4 + 3 x 5 ≥ 2 {\displaystyle {\begin{aligned}x_{2}+2x_{3}&\leq 3\\-x_{4}+3x_{5}&\geq 2\end{aligned}}} are replaced with x 2 + 2 x 3 + s 1 = 3 − x 4 + 3 x 5... | Pivot operations | 0.855429 |
260 | An associative quasigroup is either empty or is a group, since if there is at least one element, the invertibility of the quasigroup binary operation combined with associativity implies the existence of an identity element, which then implies the existence of inverse elements, thus satisfying all three requirements of ... | Quasigroup | 0.855376 |
261 | Referring back to the pictorial representation of Ratio and Algebra hierarchy, an item can be constructed to measure the skills described in each of the attributes. For example, attribute A1 includes the most basic arithmetic operation skills, such as addition, subtraction, multiplication, and division of numbers. An i... | Attribute hierarchy method | 0.855326 |
262 | The slope of a line is a number that describes both the direction and the steepness of the line. Slope is often denoted by the letter m.Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged during the 3rd century BC from applications of geometry ... | Elementary mathematics | 0.855319 |
263 | Other applications include medical image classification, genomic sequence analysis, as well as protein structure classification and prediction. Deep learning has been applied to regulatory genomics, variant calling and pathogenicity scores. Natural language processing and text mining have helped to understand phenomena... | Machine learning in bioinformatics | 0.855227 |
264 | Saha had previously reached the following conclusion on the subject: It will be admitted from what has gone before that the temperature plays the leading role in determining the nature of the stellar spectrum. Too much importance must not be attached to the figures given, for the theory is only a first attempt for quan... | Meghnad Saha | 0.855222 |
265 | However, in some cases a compiler optimization is possible, namely performing escape analysis and proving that escape is not possible, and thus the object can be allocated on the stack; this is significant in Java. In this case object destruction will occur promptly – possibly even during the variable's lifetime (befor... | Object creation | 0.855214 |
266 | Equations involving linear or simple rational functions of a single real-valued unknown, say x, such as 8 x + 7 = 4 x + 35 or 4 x + 9 3 x + 4 = 2 , {\displaystyle 8x+7=4x+35\quad {\text{or}}\quad {\frac {4x+9}{3x+4}}=2\,,} can be solved using the methods of elementary algebra. | Equation solving | 0.855124 |
267 | Automated DNA sequencing techniques have revolutionized the field of molecular biology – generating vast amounts of DNA sequence data. However, the sequence data is produced at a significantly higher rate than can be manually processed (i.e. interpreting the trace data to produce the sequence data), thereby creating a ... | Phred base calling | 0.855113 |
268 | There are several theorems and conjectures regarding the worst-case runtime for performing a sequence S of m accesses in a splay tree containing n elements. | Splay tree | 0.855104 |
269 | The multiple choice section is scored by computer, with a correct answer receiving 1 point, with omitted and incorrect answers not affecting the raw score. This total is multiplied by 1.2 to calculate the adjusted multiple-choice score.The free response section is hand-graded by hundreds of educators each June. The raw... | AP Calculus | 0.855103 |
270 | Curves on the graph can be traced by a cursor, where local maximum, local minimum, and intersections of the curves can be solved by a graph solver tool. Conics having their axes parallel to x-axis or y-axis can be plotted through a separate application. This means that the calculators cannot plot other conic/quadratic ... | Casio Algebra FX Series | 0.855085 |
271 | 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 | 0.854971 |
272 | The third problem is the clinical utility of personal genome kits and associated risks, and the benefits of introducing them into clinical practices.People need to be educated on interpreting their results and what they should be rationally taking from the experience. Concerns about customers misinterpreting health inf... | Genome analysis | 0.854935 |
273 | Many computer science problems are contained in NP, like decision versions of many search and optimization problems. | NP class | 0.854919 |
274 | That gives rise to 3 equivalent classes, from the code review itself. To solve the input problem, we take refuge in the inequation z m i n ≤ x + y ≤ z m a x {\displaystyle z_{min}\leq x+y\leq z_{max}} we note that there is a fixed size of Integer (computer science) hence, the z can be replaced with:- INT_MIN ≤ x + y ≤ ... | Equivalence partitioning | 0.854872 |
275 | As long as they are not twisted beyond their elastic limit, torsion springs obey an angular form of Hooke's law: τ = − κ θ {\displaystyle \tau =-\kappa \theta \,} where τ {\displaystyle \tau \,} is the torque exerted by the spring in newton-meters, and θ {\displaystyle \theta \,} is the angle of twist from its equilibr... | Torsion spring | 0.854829 |
276 | An almost perfect blackbody spectrum is exhibited by the cosmic microwave background radiation. Hawking radiation is the hypothetical blackbody radiation emitted by black holes, at a temperature that depends on the mass, charge, and spin of the hole. If this prediction is correct, black holes will very gradually shrink... | Thermal cavity | 0.854784 |
277 | In computer science, heapsort is a comparison-based sorting algorithm. Heapsort can be thought of as an improved selection sort: like selection sort, heapsort divides its input into a sorted and an unsorted region, and it iteratively shrinks the unsorted region by extracting the largest element from it and inserting it... | Heap Sort | 0.854777 |
278 | Applications of group theory abound. Almost all structures in abstract algebra are special cases of groups. Rings, for example, can be viewed as abelian groups (corresponding to addition) together with a second operation (corresponding to multiplication). Therefore, group theoretic arguments underlie large parts of the... | Group Theory | 0.854764 |
279 | Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%). These concepts have been give... | Probability | 0.85476 |
280 | : 21 Rather, each mathematical theory describes its objects by some of their properties, precisely those that are put as axioms at the foundations of the theory. : 20 Distances and angles cannot appear in theorems of projective geometry, since these notions are neither mentioned in the axioms of projective geometry nor... | List of mathematical spaces | 0.854753 |
281 | In genetics, a three-point cross is used to determine the loci of three genes in an organism's genome. An individual heterozygous for three mutations is crossed with a homozygous recessive individual, and the phenotypes of the progeny are scored. The two most common phenotypes that result are the parental gametes; the ... | Three-point cross | 0.854752 |
282 | In algebraic form we have two equations: a + b + c + d = 1a + b + c + d + e + f + g = 1Here a, b, c, and d correspond to the top four grayed cells in Figure 6. The cell with Δ is represented by the variable f, and the other two grayed cells are marked as e and g. If we set f = 1, then a = 0, b = 0, c = 0, d = 0, e = 0,... | Board puzzles with algebra of binary variables | 0.854741 |
283 | Other examples are readily found in different areas of mathematics, such as vector addition, matrix multiplication, and conjugation in groups. An operation of arity two that involves several sets is sometimes also called a binary operation. For example, scalar multiplication of vector spaces takes a scalar and a vector... | Binary operation | 0.854728 |
284 | Robbins Equation: n(n(x + y) + n(x + n(y))) = x,do (1), (2), and (4) form a basis for Boolean algebra? Calling (1), (2), and (4) a Robbins algebra, the question then becomes: Is every Robbins algebra a Boolean algebra? This question (which came to be known as the Robbins conjecture) remained open for decades, and becam... | Boolean lattice | 0.854726 |
285 | However, this alternative definition includes one exceptional structure of order 2 which fails to satisfy various basic theorems (such as x ⋅ 0 = 0 {\displaystyle x\cdot 0=0} for all x {\displaystyle x} ). Thus it is much more convenient, and more usual, to use the axioms in the form given above. The difference is that... | Near-field (mathematics) | 0.854713 |
286 | (from the Turing–Wittgenstein debate) Do Gödel's incompleteness theorems imply that physical theories will always be incomplete? (from Stephen Hawking) Is mathematics invented or discovered? (millennia-old question, raised among others by Mario Livio) | Relationship between mathematics and physics | 0.854688 |
287 | Now, through bioinformatics, there are computer programs that can in some cases predict and model the structure of proteins. These programs use the chemical properties of amino acids and structural properties of known proteins to predict the 3D model of sample proteins. This also allows scientists to model protein inte... | Protein analysis | 0.854652 |
288 | These rules are summarized as follows: Example: The quantum numbers used to refer to the outermost valence electrons of a carbon (C) atom, which are located in the 2p atomic orbital, are; n = 2 (2nd electron shell), ℓ = 1 (p orbital subshell), mℓ = 1, 0, −1, ms = 1/2 (parallel spins). Results from spectroscopy indicate... | Quantum numbers | 0.854591 |
289 | The analog of Lagrange's theorem for double cosets is false. This means that the size of a double coset need not divide the order of G. For example, let G = S3 be the symmetric group on three letters, and let H and K be the cyclic subgroups generated by the transpositions (1 2) and (1 3), respectively. If e denotes the... | Double coset | 0.854561 |
290 | Targeted analysis sequencing (sometimes called target amplicon sequencing) (TAS) is a next-generation DNA sequencing technique focusing on amplicons and specific genes. It is useful in population genetics since it can target a large diversity of organisms. The TAS approach incorporates bioinformatics techniques to prod... | Targeted analysis sequencing | 0.854549 |
291 | For example: a) Things would be different if Microsoft were located in Georgia.In sentence (a), a shallow information extraction system might infer wrongly that Microsoft's headquarters was located in Georgia. While as humans, we understand from the sentence that Microsoft office was never in Georgia. b) The National I... | Deep linguistic processing | 0.854487 |
292 | It has in the past been combined with array technology (ChIP-chip) with some success. Next gen sequencing can also be applied in this area. Methylation immunoprecipitation (MeDIP) can also be performed and also on arrays. The ability to learn more about methylation and TF binding sites on a genome wide scale is a valua... | ABI Solid Sequencing | 0.85446 |
293 | In computer science, splaysort is an adaptive comparison sorting algorithm based on the splay tree data structure. | Splaysort | 0.854435 |
294 | Such an overdetermined system has no solution in general (that is if the coefficients are not specific). If it has a finite number of solutions, this number is at most 53 = 125, by Bézout's theorem. However, it has been shown that, for the case of the singular points of a surface of degree 6, the maximum number of solu... | Polynomial system of equations | 0.854415 |
295 | This is the defining arithmetical identity of group theory, in boundary notation. The primary algebra differs from an abelian group in two ways: From A2, it follows that ≠ . If the primary algebra were a group, = would hold, and one of a = or a = a would have to be a primary algebra consequence. Note that and are mutua... | Boundary algebra | 0.854396 |
296 | In computer science, smoothsort is a comparison-based sorting algorithm. A variant of heapsort, it was invented and published by Edsger Dijkstra in 1981. Like heapsort, smoothsort is an in-place algorithm with an upper bound of O(n log n), but it is not a stable sort. The advantage of smoothsort is that it comes closer... | Smoothsort | 0.854355 |
297 | In Euclidean geometry, it is possible to associate a set of coordinates to each point in space, for example by an orthogonal grid. This method allows one to characterize geometric figures by equations. A plane in three-dimensional space can be expressed as the solution set of an equation of the form a x + b y + c z + d... | Equation | 0.854324 |
298 | If mathematicians sometimes talk about a field with one element, this abstract and somewhat mysterious mathematical object is not a field. In categories where the multiplicative identity must be preserved by morphisms, but can equal to zero, the {0} object can exist. But not as initial object because identity-preservin... | Zero vector space | 0.854312 |
299 | For example, a multiple-choice exam designed to assess knowledge of key concepts in natural selection does not meet a number of standards of quality control. One problem with the exam is that the two members of each of several pairs of parallel items, with each pair designed to measure exactly one key concept in natura... | Concept inventory | 0.854277 |
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