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It is said to be defeated by the dark and evil powers of the Black God. On December 23, Hors is resurrected and becomes the new sun, Koleda. Modern scholars tend to associate this holiday with ancestor worship.
Wikipedia - Korochun
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On this day, Western Slavs lit fires at cemeteries to keep their loved ones warm, and organized feasts to honor the dead and keep them fed. They also lit wooden logs at local crossroads. In some Slavic languages, the word came to denote unexpected death of a young person and the evil spirit that shortens life.
Wikipedia - Korochun
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Korteweg (1883) gave a proof "that in any simply connected region, when the velocities along the boundaries are given, there exists, as far as the squares and products of the velocities may be neglected, only one solution of the equations for the steady motion of an incompressible viscous fluid, and that this solution ...
Wikipedia - Extremal principles in non-equilibrium thermodynamics
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Koselleck, R. "Time and History." The Practice of Conceptual History. Timing History, Spacing Concepts.
Wikipedia - Chronology
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Palo Alto: Stanford University Press, 2002. Ronald H. Fritze; et al. (2004). "Chronologies, Calendars, and Lists of Rulers".
Wikipedia - Chronology
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Reference Sources in History: An Introductory Guide (2nd ed.). ABC-CLIO. pp.
Wikipedia - Chronology
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4+. ISBN 978-0-87436-883-3. Olena V. Smyntyna (2009).
Wikipedia - Chronology
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"Chronology". In H. James Birx (ed.). Encyclopedia of Time: Science, Philosophy, Theology, & Culture.
Wikipedia - Chronology
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Sage. ISBN 978-1-4129-4164-8. Daniel Rosenberg; Anthony Grafton (2009).
Wikipedia - Chronology
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Cartographies of Time: A History of the Timeline. New York: Princeton Architectural Press. ISBN 9781568987637.
Wikipedia - Chronology
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Koszul duality, as treated by Alexander Beilinson, Victor Ginzburg, and Wolfgang Soergel can be formulated using the notion of Koszul algebra. An example of such a Koszul algebra A is the symmetric algebra S ( V ) {\displaystyle S(V)} on a finite-dimensional vector space. More generally, any Koszul algebra can be shown...
Wikipedia - Koszul duality
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:= T ( V ∗ ) / R ′ {\displaystyle A^{! }:=T(V^{*})/R'} where V ∗ {\displaystyle V^{*}} is the (k-linear) dual and R ′ ⊂ V ∗ ⊗ V ∗ {\displaystyle R'\subset V^{*}\otimes V^{*}} consists of those elements on which the elements of R (i.e., the relations in A) vanish. The Koszul dual of A = S ( V ) {\displaystyle A=S(V)} is...
Wikipedia - Koszul duality
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= Λ ( V ∗ ) {\displaystyle A^{! }=\Lambda (V^{*})} , the exterior algebra on the dual of V. In general, the dual of a Koszul algebra is again a Koszul algebra. Its opposite ring is given by the graded ring of self-extensions of the underlying field k, thought of as an A-module: ( A ! )
Wikipedia - Koszul duality
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opp = Ext A ∗ ⁡ ( k , k ) . {\displaystyle (A^{! })^{\text{opp}}=\operatorname {Ext} _{A}^{*}(k,k).}
Wikipedia - Koszul duality
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Kotlin's data class construct defines classes whose primary purpose is storing data. This construct is similar to normal classes except that the key functions equals, toString, and hashCode are automatically generated from the class properties. In Java, such classes are expected to provide a standard assortment of func...
Wikipedia - Kotlin (programming language)
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Kozen, Dexter. "CS786 Spring 04, Introduction to Kleene Algebra".
Wikipedia - Kleene algebra
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Kramer, Gregory, ed. (1994). Auditory display: sonification, audification, and auditory interfaces. Addison-Wesley. ISBN 978-0201626049.
Wikipedia - Data sonification
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Kramers–Kronig relations enable exact solutions of nontrivial scattering problems, which find applications in magneto-optics.
Wikipedia - Kramers–Kronig relations
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Kratzer provides a German example: In the above examples, Kratzer notes that although examples (48) and (49) are grammatical, there is an underlying issue with (48). (48) is deemed to be not preferred due to how the bound variable readings in German for any embedded possessives is not allowed. Kratzer mentions that due...
Wikipedia - Bound variable pronoun
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Kraus matrices are not uniquely determined by the quantum operation Φ {\displaystyle \Phi } in general. For example, different Cholesky factorizations of the Choi matrix might give different sets of Kraus operators. The following theorem states that all systems of Kraus matrices representing the same quantum operation ...
Wikipedia - Quantum dynamical map
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Let Φ {\displaystyle \Phi } be a (not necessarily trace-preserving) quantum operation on a finite-dimensional Hilbert space H with two representing sequences of Kraus matrices { B i } i ≤ N {\displaystyle \{B_{i}\}_{i\leq N}} and { C i } i ≤ N {\displaystyle \{C_{i}\}_{i\leq N}} . Then there is a unitary operator matri...
Wikipedia - Quantum dynamical map
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Krill are often referred to as light-shrimp because they emit light through bioluminescent organs. These organs are located on various parts of the individual krill's body: one pair of organs at the eyestalk (cf. the image of the head above), another pair are on the hips of the second and seventh thoracopods, and singu...
Wikipedia - Antarctic krill
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The whole organ can be rotated by muscles, which can direct the light to a specific area. The function of these lights is not yet fully understood; some hypotheses have suggested they serve to compensate the krill's shadow so that they are not visible to predators from below; other speculations maintain that they play ...
Wikipedia - Antarctic krill
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Krill are thought to undergo between one and three vertical migrations from mixed surface waters to depths of 100 m daily. The krill is a very untidy feeder, and it often spits out aggregates of phytoplankton (spit balls) containing thousands of cells sticking together. It also produces fecal strings that still contain...
Wikipedia - Antarctic krill
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This process is called the biological pump. As the waters around Antarctica are very deep (2,000–4,000 metres or 6,600–13,100 feet), they act as a carbon dioxide sink: this process exports large quantities of carbon (fixed carbon dioxide, CO2) from the biosphere and sequesters it for about 1,000 years. If the phytoplan...
Wikipedia - Antarctic krill
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Krill use an escape reaction to evade predators, swimming backwards very quickly by flipping their rear ends. This swimming pattern is also known as lobstering. Krill can reach speeds of over 0.6 metres per second (2.0 ft/s). The trigger time to optical stimulus is, despite the low temperatures, only 55 ms.
Wikipedia - Antarctic krill
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Kripke semantics Sahlqvist formula Interior algebra
Wikipedia - List of mathematical logic topics
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Kripke semantics for intuitionistic logic follows the same principles as the semantics of modal logic, but it uses a different definition of satisfaction. An intuitionistic Kripke model is a triple ⟨ W , ≤ , ⊩ ⟩ {\displaystyle \langle W,\leq ,\Vdash \rangle } , where ⟨ W , ≤ ⟩ {\displaystyle \langle W,\leq \rangle } is...
Wikipedia - Kripke–Joyal semantics
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Kripke semantics has a straightforward generalization to logics with more than one modality. A Kripke frame for a language with { ◻ i ∣ i ∈ I } {\displaystyle \{\Box _{i}\mid \,i\in I\}} as the set of its necessity operators consists of a non-empty set W equipped with binary relations Ri for each i ∈ I. The definition ...
Wikipedia - Relational semantics
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A Carlson model is a structure ⟨ W , R , { D i } i ∈ I , ⊩ ⟩ {\displaystyle \langle W,R,\{D_{i}\}_{i\in I},\Vdash \rangle } with a single accessibility relation R, and subsets Di ⊆ W for each modality. Satisfaction is defined as w ⊩ ◻ i A {\displaystyle w\Vdash \Box _{i}A} if and only if ∀ u ∈ D i ( w R u ⇒ u ⊩ A ) . {...
Wikipedia - Relational semantics
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Krippendorff's alpha brings several known statistics under a common umbrella, each of them has its own limitations but no additional virtues. Scott's pi is an agreement coefficient for nominal data and two coders. When data are nominal, alpha reduces to a form resembling Scott's pi: Scott's observed proportion of agree...
Wikipedia - Krippendorff's Alpha
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It follows that Scott's pi is that special case of alpha in which two coders generate a very large sample of nominal data. For finite sample sizes: nominal α = 1 − n − 1 n ( 1 − π ) ≥ π {\displaystyle {_{\text{nominal}}\alpha }=1-{\tfrac {n-1}{n}}(1-\pi )\geq \pi } . Evidently, lim n → ∞ nominal α = π {\textstyle \lim ...
Wikipedia - Krippendorff's Alpha
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Fleiss’ kappa is an agreement coefficient for nominal data with very large sample sizes where a set of coders have assigned exactly m labels to all of N units without exception (but note, there may be more than m coders, and only some subset label each instance). Fleiss claimed to have extended Cohen's kappa to three o...
Wikipedia - Krippendorff's Alpha
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It is the latter that introduces a bias into the coefficient. However, just as for pi, when sample sizes become very large this bias disappears and the proportion ∑ c n c ( n c − 1 ) n ( n − 1 ) {\textstyle \sum _{c}{\frac {n_{c}(n_{c}-1)}{n(n-1)}}} in nominalα above asymptotically approximates P ¯ e {\displaystyle {\b...
Wikipedia - Krippendorff's Alpha
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In its original form: where ∑ D 2 = ∑ u = 1 N ordinal δ c u k u 2 {\textstyle \sum D^{2}=\sum _{u=1}^{N}{_{\text{ordinal}}\delta }_{c_{u}k_{u}}^{2}} is the sum of N differences between one coder's rank c and the other coder's rank k of the same object u. Whereas alpha accounts for tied ranks in terms of their frequenci...
Wikipedia - Krippendorff's Alpha
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Again, ordinal α ≥ ρ {\displaystyle {_{\text{ordinal}}\alpha }\geq \rho } and lim n → ∞ ordinal α = ρ {\textstyle \lim _{n\to \infty }{_{\text{ordinal}}\alpha }=\rho } . Pearson's intraclass correlation coefficient rii is an agreement coefficient for interval data, two coders, and very large sample sizes. To obtain it,...
Wikipedia - Krippendorff's Alpha
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By entering pairs of values twice, the resulting table becomes a coincidence matrix without reference to the two coders, contains n = 2N values, and is symmetrical around the diagonal, i.e., the joint linear regression line is forced into a 45° line, and references to coders are eliminated. Hence, Pearson's intraclass ...
Wikipedia - Krippendorff's Alpha
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It follows that the reliability the interval alpha assesses is consistent with all variance-based analytical techniques, such as the analysis of variance. Moreover, by incorporating difference functions not just for interval data but also for nominal, ordinal, ratio, polar, and circular data, alpha extends the notion o...
Wikipedia - Krippendorff's Alpha
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Krippendorff's alpha is a versatile statistic that assesses the agreement achieved among observers who categorize, evaluate, or measure a given set of objects in terms of the values of a variable. It generalizes several specialized agreement coefficients by accepting any number of observers, being applicable to nominal...
Wikipedia - Inter-rater agreement
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Krohn–Rhodes theory, sometimes also called algebraic automata theory, gives powerful decomposition results for finite transformation semigroups by cascading simpler components.
Wikipedia - Semigroup action
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Krom (1967) described the following polynomial time decision procedure for solving 2-satisfiability instances.Suppose that a 2-satisfiability instance contains two clauses that both use the same variable x, but that x is negated in one clause and not in the other. Then the two clauses may be combined to produce a third...
Wikipedia - Krom formula
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As he proves, a 2-CNF formula is satisfiable if and only if it is consistent. For, if a formula is not consistent, it is not possible to satisfy both of the two clauses ( x ∨ x ) {\displaystyle (x\lor x)} and ( ¬ x ∨ ¬ x ) {\displaystyle (\lnot x\lor \lnot x)} simultaneously. And, if it is consistent, then the formula ...
Wikipedia - Krom formula
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At each of these extension steps, one of these two clauses may always be added while preserving consistency, for if not then the other clause could be generated using the inference rule. Once all variables have a clause of this form in the formula, a satisfying assignment of all of the variables may be generated by set...
Wikipedia - Krom formula
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By grouping together all of the clauses that use the same variable, and applying the inference rule to each pair of clauses, it is possible to find all inferences that are possible from a given 2-CNF instance, and to test whether it is consistent, in total time O(n3), where n is the number of variables in the instance....
Wikipedia - Krom formula
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Because finding a satisfying assignment using Krom's method involves a sequence of O(n) consistency checks, it would take time O(n4). Even, Itai & Shamir (1976) quote a faster time bound of O(n2) for this algorithm, based on more careful ordering of its operations. Nevertheless, even this smaller time bound was greatly...
Wikipedia - Krom formula
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In terms of the implication graph of the 2-satisfiability instance, Krom's inference rule can be interpreted as constructing the transitive closure of the graph. As Cook (1971) observes, it can also be seen as an instance of the Davis–Putnam algorithm for solving satisfiability problems using the principle of resolutio...
Wikipedia - Krom formula
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Kronecker's finitism made him a forerunner of intuitionism in foundations of mathematics.
Wikipedia - Leopold Kronecker
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Kruskal's MST algorithm utilises the cycle property of MSTs. A high-level pseudocode representation is provided below. T ← {\displaystyle T\gets } forest with every vertex in its own subtree foreach ( u , v ) ∈ E {\displaystyle (u,v)\in E} in ascending order of weight if u {\displaystyle u} and v {\displaystyle v} in d...
Wikipedia - Parallel algorithms for minimum spanning trees
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Kruskal's algorithm is inherently sequential and hard to parallelize. It is, however, possible to perform the initial sorting of the edges in parallel or, alternatively, to use a parallel implementation of a binary heap to extract the minimum-weight edge in every iteration. As parallel sorting is possible in time O ( n...
Wikipedia - Kruskal’s algorithm
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Krylov subspace methods work by forming a basis of the sequence of successive matrix powers times the initial residual (the Krylov sequence). The approximations to the solution are then formed by minimizing the residual over the subspace formed. The prototypical method in this class is the conjugate gradient method (CG...
Wikipedia - Iterative method
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Kryptolebias marmoratus Serranus fasciatus Serranus baldwini
Wikipedia - Androdioecy
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Krypton difluoride is primarily a powerful oxidising and fluorinating agent: for example, it can oxidise gold to its highest-known oxidation state, +5. It is more powerful even than elemental fluorine due to the even lower bond energy of Kr–F compared to F–F, with a redox potential of +3.5 V for the KrF2/Kr couple, mak...
Wikipedia - KrF2
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Kryten (Rob Grant, Doug Naylor, David Ross, Robert Llewellyn) {Red Dwarf} – Talkie Toaster – (Rob Grant, Doug Naylor, John Lenahan, David Ross) {Red Dwarf} K-9 (Doctor Who) – Robotboy – (Bob Camp, Charlie Bean, Heath Kenny, Prof Moshimo, Laurence Bouvard) {Robotboy} K.T., Eric and Desiree in Robert's Robots
Wikipedia - Outline of robotics
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Kuang identified two types of phonation: pitch-dependent and pitch-independent. Contrast of tones has long been thought of as differences in pitch height. However, several studies pointed out that tone is actually multidimensional. Contour, duration, and phonation may all contribute to the differentiation of tones.
Wikipedia - Tone group
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Recent investigations using perceptual experiments seem to suggest phonation counts as a perceptual cue.Xu, Xiaoying; Liu, Xuefei; Tao, Jianhua; Che, Hao (2012). Pitch and Phonation Type Perception in Wenzhou Dialect Tone. Tonal Aspects of Languages-Third International Symposium.
Wikipedia - Tone group
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Kuftin was invited to Central Asia to carry out explorations in 1949. He first reconnoitered Turkmenistan and selected a very large tepe (hill), the Altyndepe (in Turkmen language meaning: the "Golden Hill" ). This tepe overlooks the Tedzen delta at the foot of Kopetdag. He found a Neolithic settlement extending into B...
Wikipedia - South Turkmenistan Complex Archaeological Expedition
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This excavated tepe turned out to be a large settlement, 2.5 kilometres (1.6 mi) in length and 0.5 kilometres (0.31 mi) in width, and was identified as a major Bronze Age town. From the highest point of this tepe, a trench was dug to a depth of 30 metres (98 ft) and the section was logged, which revealed layers of the ...
Wikipedia - South Turkmenistan Complex Archaeological Expedition
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One year after he started sequencing the site, he died suddenly and was replaced by Vadim Mikhailovich Masson who published a book on the Bronze Age sequence of this site. The settlement of Ilgynly had also shifted to Altyndepe. Early Bronze period fort walls with decorated towers and a huge entrance had encircled this...
Wikipedia - South Turkmenistan Complex Archaeological Expedition
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Discoveries by Soviet archeologists dated the finds at this place, in a chronological order, to the later half of the third millennium BC. Altyn-Depe also provided a link to the several Bronze Age cultures of Eurasia.The most notable findings in the burial ground of the elite, located in the outskirts of Altyndepe, wer...
Wikipedia - South Turkmenistan Complex Archaeological Expedition
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In the period from late third millennium to early second millennium, the antiquaries revealed an urban habitation with artisans' houses. Also unearthed were 62 double-tiered kilns, beads and seals. Four stepped ziggurats were found.
Wikipedia - South Turkmenistan Complex Archaeological Expedition
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Further were revealed female terracotta figurines with plaited hair, stone vessels, hafted bronze and copper daggers with flat blades, tabbed silver and bronze seals. The further findings were, Paintings of animals such as goats, eagles, and panthers. Three headed composite animal.
Wikipedia - South Turkmenistan Complex Archaeological Expedition
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A priest's tomb with gold heads of a wolf and a bull. Other tombs with silver ornaments, precious stones and seals. One quarter of a ‘nobility’ seal with two signs in Indus script conjectured to be that of Bronze Age settlers in Altyndepe.However, the settlement gradually disappeared (it was deserted around 1600 BC) as...
Wikipedia - South Turkmenistan Complex Archaeological Expedition
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Kugler HK & Keller C (eds) 1985, Gmelin handbook of inorganic and organometallic chemistry, 8th ed., 'At, Astatine', system no. 8a, Springer-Verlag, Berlin, ISBN 3-540-93516-9, pp. 116–117
Wikipedia - Heats of vaporization of the elements (data page)
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Kuhn and Brass wanted to test participant self-knowledge. The first step was that after every decide trial, participants were next asked whether they had actually had time to decide. Specifically, the volunteers were asked to label each decide trial as either failed-to-decide (the action was the result of acting impuls...
Wikipedia - Neuroscience of free will
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Note also that the researchers sorted the participants’ successful decide trials into "decide go" and "decide no-go", but were not concerned with the no-go trials, since they did not yield any RT data (and are not featured anywhere in the diagram on the right). Note that successful stop trials did not yield RT data eit...
Wikipedia - Neuroscience of free will
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In contrast, the "successful decide" trials (where the decision was a "go" and the subject moved) should show a slower RT. Presumably, if deciding whether to veto is a conscious process, volunteers should have no trouble distinguishing impulsivity from instances of true deliberate continuation of a movement. Again, thi...
Wikipedia - Neuroscience of free will
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Kuhn proposed the following coefficient in 1965 I = 2 ( a d − b c ) K ( 2 a + b + c ) = 2 ( a d − b c ) K ( N + a − d ) {\displaystyle I={\frac {2(ad-bc)}{K(2a+b+c)}}={\frac {2(ad-bc)}{K(N+a-d)}}} where a is the number of samples where types A and B are both present, b is where type A is present but not type B and c is...
Wikipedia - Lieberson's isolation index
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Kumar, A., et al. "Sustainability in Environmental Engineering and Science." (2021): 253–262. Kameni Ngounou, M. Bernard, et al. "Corrigendum to “Coagulation and Sedimentation of Concentrated Laterite Suspensions: Comparison of Hydrolyzing Salts in Presence of Grewia spp. Biopolymer”."
Wikipedia - National Environmental Engineering Research Institute
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Journal of Chemistry 2021 (2021): 1-1. Dhodapkar, Rita S., and Kavita N. Gandhi. "1CSIR-National Environmental Engineering Research Institute, Nagpur, India, 2Environmental Impact and Sustainability Division, CSIR-National Environmental Engineering Research Institute, Nagpur, India."
Wikipedia - National Environmental Engineering Research Institute
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Pharmaceuticals and Personal Care Products: Waste Management and Treatment Technology (2019): 63. Arfin, Tanvir. "Environmental Materials Division, CSIR-National Environmental Engineering Research Institute (CSIR-NEERI), Nagpur, India."
Wikipedia - National Environmental Engineering Research Institute
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Advanced Functional Textiles and Polymers: Fabrication, Processing and Applications (2019): 291. Singh Kachhawaha, A., and A. B. A. Boxall. "A small scale monitoring study for a range of pharmaceuticals in the River Foss catchment and comparison to concentrations in the River Nag, India: report of researcher exchange M...
Wikipedia - National Environmental Engineering Research Institute
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(2019). Kumar, Sunil, et al. "Challenges and opportunities associated with waste management in India." Royal Society open science 4.3 (2017): 160764.
Wikipedia - National Environmental Engineering Research Institute
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Thakur, N. S. "Scientometric analysis of research productivity: A case study of National Environmental Engineering Research Institute, Nagpur." International Journal of Library Information Network and Knowledge 3.1 (2018): 43–53.
Wikipedia - National Environmental Engineering Research Institute
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Chandra, Ram, ed. Environmental waste management. CRC Press, 2016.
Wikipedia - National Environmental Engineering Research Institute
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Lohiya, Rajesh Kumar, K. P. S. Sengar, and Jiji Cyriac. "Research Performance of CSIR-NEERI, Nagpur during 1989-2013: A Scientometric Study." Journal of Information and Knowledge (2016): 297–305.
Wikipedia - National Environmental Engineering Research Institute
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Kumar, Sunil. "Sunil Kumar." Int.
Wikipedia - National Environmental Engineering Research Institute
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J. Environmental Technology and Management 17.2/3 (2014): 4. Mumtaz, Neha, Govind Pandey, and Pawan Kumar Labhasetwar. "Assessment of electrolytic process for water defluoridation."
Wikipedia - National Environmental Engineering Research Institute
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Journal Issues ISSN 2360 (2014): 8803., Aruna, and Ashok Gadgil. "Aluminum electrocoagulation: defluoridation technology for Andhra Pradesh, India." (2014).
Wikipedia - National Environmental Engineering Research Institute
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Andey, Subhash, et al. "Performance evaluation of solar power based electrolytic defluoridation plants in India." International Journal of Water Resources and Arid Environments 2.3 (2013): 139–145. Kanherkar, S. V., et al. "Study of the Efficiency of Immobilized Algal Technology for Wastewater Treatment."
Wikipedia - National Environmental Engineering Research Institute
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Journal of Environmental Science & Engineering 54.1 (2012): 121–127. Saini, Samir, Prakash Rao, and Yogesh Patil. "City based analysis of MSW to energy generation in India, calculation of state-wise potential and tariff comparison with EU."
Wikipedia - National Environmental Engineering Research Institute
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Procedia-Social and Behavioral Sciences 37 (2012): 407–416. Sharma, Abhinav. "Effect of ozone pretreatment on biodegradability enhancement and biogas production of biomethanated distillery effluent.
Wikipedia - National Environmental Engineering Research Institute
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"Sharma, Asheesh, et al. "NutriL-GIS: A Tool for Assessment of Agricultural Runoff and Nutrient Pollution in a Watershed." National Environmental Engineering Research Institute (NEERI). India (2010).
Wikipedia - National Environmental Engineering Research Institute
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Sinnarkar, S. N., and Rajesh Kumar Lohiya. "External user in an environmental research library." Annals of library and information studies 55.4 (2008): 275–280.
Wikipedia - National Environmental Engineering Research Institute
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Mishra, C. S. K. Environmental biotechnology. APH Publishing, 2007. Schools, Greywater Reuse In Rural.
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"Guidance Manual." National Environmental Engineering Research Institute (2007). Thawale, P. R., Asha A. Juwarkar, and S. K. Singh.
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"Resource conservation through land treatment of municipal wastewater." Current Science (2006): 704–711. Rao, Padma S., et al. "Performance evaluation of a green belt in a petroleum refinery: a case study."
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Ecological engineering 23.2 (2004): 77–84. Sinnarkar, S. N. "Development of an institutional database of citations using CDS-ISIS software."
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(2003). Chaudhuri, Nilay, et al. "BOD test for tropical countries." Journal of Environmental Engineering 118.2 (1992): 298–303.
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Murty, K. S. "Groundwater in India." Studies in Environmental Science.
Wikipedia - National Environmental Engineering Research Institute
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Vol. 17. Elsevier, 1981. 733–736. == References ==
Wikipedia - National Environmental Engineering Research Institute
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Kummer made several contributions to mathematics in different areas; he codified some of the relations between different hypergeometric series, known as contiguity relations. The Kummer surface results from taking the quotient of a two-dimensional abelian variety by the cyclic group {1, −1} (an early orbifold: it has 1...
Wikipedia - Ernst Kummer
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He studied what were later called Kummer extensions of fields: that is, extensions generated by adjoining an nth root to a field already containing a primitive nth root of unity. This is a significant extension of the theory of quadratic extensions, and the genus theory of quadratic forms (linked to the 2-torsion of th...
Wikipedia - Ernst Kummer
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Kummer's theorem states that the number of carries involved in adding two numbers in base p {\displaystyle p} is equal to the exponent of the highest power of p {\displaystyle p} dividing a certain binomial coefficient. When several random numbers of many digits are added, the statistics of the carry digits bears an un...
Wikipedia - Carry (arithmetic)
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Kundra launched the Data.gov platform on May 21, 2009 with the goal of providing public access to raw datasets generated by the Executive Branch of the Federal Government to enable public participation and private sector innovation. Data.gov draws conceptual parallels from the DC Data Catalog launched by Kundra when he...
Wikipedia - Vivek Kundra
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Internationally, over 46 countries have launched open data sites patterned after Data.Gov, some using the U.S. Data.gov software which was made open source and made available on GitHub. Additionally, states, cities and counties have launched sites, notablysome cities in Canada, and the UK are following suit.
Wikipedia - Vivek Kundra
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Kurt Fischer, director of Harvard University's Mind, Brain and Education graduate program states "One of the reasons there is so much junk out there is that there are so few people who know enough about education and neuroscience to put the thing together". Educators have been reliant upon others’ expertise for the int...
Wikipedia - Educational neuroscience
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In order to negate the need for middlemen, some researchers have suggested the need to developed a group of neuro-educators, a specially trained class of professionals whose role would be to guide the introduction of cognitive neuroscience into educational practice in a sensible and ethical manner. Neuro-educators woul...
Wikipedia - Educational neuroscience
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Bennett & Rolheiser-Bennett (2001) point out that "teachers must be aware of and act on the science within the art of teaching". They suggest that educators must become aware of other methods and incorporate them into their practice. Furthermore, Bennett and Rolheiser-Bennett suggest that specific bodies of knowledge w...
Wikipedia - Educational neuroscience
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The bodies of knowledge discussed include multiple intelligences, emotional intelligences, learning styles, the human brain, children at risk and gender. As the authors explain these and other areas are just "lenses designed to extend teachers’ understanding of how students learn, and from that understanding, to make d...
Wikipedia - Educational neuroscience
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Kurt Gödel indicated one of the weak points of formalism by addressing the question of consistency in axiomatic systems. Bertrand Russell has argued that formalism fails to explain what is meant by the linguistic application of numbers in statements such as "there are three men in the room".
Wikipedia - Formalism (philosophy of mathematics)
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