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561646a916dcf6eabc9a93f3477f6a75499e66ea	an example of the deployment of applied epistemology	an example of the deployment of applied epistemology in scientific research is the toolbox project. it is an initiative that apply philosophical analysis to enhance collaborative, cross-disciplinary scientific research by improving cross-disciplinary communication. there are also scholars who consider the application o...	wikipedia
baa64d8fd5668ea9cc22f76c7cba4d0281dba1f9	applied epistemology in science has been described as	applied epistemology in science has been described as the specific mental frameworks utilized by scientists in their research and activities that are considered processes of acquiring knowledge. these frameworks also serve as the ground of the sociology of science. there is also the case of the philosophy of science, w...	wikipedia
99ed0abdbcd8256efac09c3ea05d8db36ff5e8d2	according to v.d. singh, since general semantics is	according to v.d. singh, since general semantics is a general theory of evaluation – that it considers the interrelations among events that transpire within ourselves and the world around us as well as how he obtain information or talk about such events and how we behave – makes it an up-to-date and scientifically-base...	wikipedia
ccbf5cbb3efa56b348517329277ccd05d07fef8d	as part of "applied philosophy", applied epistemology has	as part of "applied philosophy", applied epistemology has been applied to different contemporary practices and issues. this include its application to critical thinking or informal logic, information systems, and pressing social concerns. in the area of critical thinking, there is the underlying idea that thinking clea...	wikipedia
8c120904e395b8abe7fc3359f7896653c3d69370	applied epistomology is also considered one of the	applied epistomology is also considered one of the three branches of epistemology along with normative epistemology and metaepistemology. the normative branch is concerned with first-order theorizing about the formation of justified beliefs, knowledge, and truths. metaepistemology, on the other hand, deals with higher ...	wikipedia
c07aa0163ea3a32c84d0d6883cceb87ea48764a0	applied epistemology is informed by skepticism in philosophy,	applied epistemology is informed by skepticism in philosophy, as it maintains that things should not be taken at face value – that, in reflection, what people knew as "truths" could turn out to be false. applied epistemology has been concerned with practical questions about truth, knowledge, and other epistemic values ...	wikipedia
6412adf28bd84b54b8b8216368d2bc3cca9aa569	in its infancy, applied epistemology had been equated	in its infancy, applied epistemology had been equated with social epistemology. later theorizing established that, while there are overlapping aspects, not all social epistemology is applied and not all applied epistemology is social. a proposed analogy to distinguish applied epistemology from epistemology holds that i...	wikipedia
f646dd0f67c3e0f6ca239f186ca4a9b210982e8c	applied epistemology emerged out of epistemologists routine examinations	applied epistemology emerged out of epistemologists routine examinations that determine whether truth-seeking practices like science and mathematics are capable of delivering truths. it draws from epistemological theorizing to address pressing epistemic matters of practical value. an epistemological question assumes a ...	wikipedia
f305c105e20d5c0e4008a6c2c79a28108372e839	applied epistemology forms part of the concept of	applied epistemology forms part of the concept of " applied philosophy " as theorists begin to distinguish it from " applied ethics ". it is argued that "applied philosophy" is a broader field, and that it has parts that are not subdisciplines of applied ethics. the emergence of "applied philosophy" gained traction aft...	wikipedia
d717b6bdf8c1ae4c041854092c3fdd3cc95b6e79	applied epistemology refers to the study that determines	applied epistemology refers to the study that determines whether the systems of investigation that seek the truth lead to true beliefs about the world. a specific conceptualization cites that it attempts to reveal whether these systems contribute to epistemic aims. it is applied in practices outside of philosophy like ...	wikipedia
407d3f137503e3ddbdcf4bb29575f75bfeafbcd1	in algebraic geometry, the atiyah–bott formula says the	in algebraic geometry, the atiyah–bott formula says the cohomology ring of the moduli stack of principal bundles is a free graded-commutative algebra on certain homogeneous generators. the original work of michael atiyah and raoul bott concerned the integral cohomology ring of bun g ⁡ .	wikipedia
d1def645aa56f66362d12cb5ba731b3eb23ed38e	of the moduli stack of principal bundles is	of the moduli stack of principal bundles is a free graded-commutative algebra on certain homogeneous generators. the original work of michael atiyah and raoul bott concerned the integral cohomology ring of bun g (x) {\displaystyle \operatorname {bun} _{g}(x)}.	wikipedia
4265581779ac9d81c5abbf50ae4d5a8615e5b8be	angelo genocchi was an italian mathematician who specialized	angelo genocchi was an italian mathematician who specialized in number theory. he worked with giuseppe peano. the genocchi numbers are named after him. angelo genocchi was born and grew up and went to school in piacenza, italy. despite his love of mathematics, he studied law at piacenza university. after practicing law...	wikipedia
575f3d2e84ca1fb84b6a8eb924fd4372601108d5	after the revolution genocchi moved to turin, where	after the revolution genocchi moved to turin, where he took up mathematics as the subject of his research and teaching. he became president of the academy of sciences of turin. it was there that he worked with giuseppe peano. his biggest discovery was the genocchi numbers, named after him.	wikipedia
425a974bf6ad7a7e849ea86993ea2c08cea360e3	angelo genocchi was born and grew up and	angelo genocchi was born and grew up and went to school in piacenza, italy. despite his love of mathematics, he studied law at piacenza university. after practicing law in piacenza for a number of years, he was invited by the university to become the chair of law. he was mostly unsuccessful as a teacher however and dis...	wikipedia
bf90aa3997c80a3d182aebfc0d0ac96187b244be	in mathematics, the atiyah algebroid, or atiyah sequence,	in mathematics, the atiyah algebroid, or atiyah sequence, of a principal g -bundle p over a manifold m , where g is a lie group, is the lie algebroid of the gauge groupoid of p . explicitly, it is given by the following short exact sequence of vector bundles over m : it is named after michael atiyah, who introduced the...	wikipedia
e2de8b49a180f469b915ece3ca5c9410303bd9dc	any morphism ϕ: p → p ′ {\displaystyle	any morphism ϕ: p → p ′ {\displaystyle \phi:p\to p'} of principal bundles induces a lie algebroid morphism d ϕ: t p / g → t p / g ′ {\displaystyle d\phi:tp/g\to tp/g'} between the respective atiyah algebroids.	wikipedia
e706cb1f67f7b436ec13354ecd81ad37e261c435	right splittings σ: t m → a {\displaystyle	right splittings σ: t m → a {\displaystyle \sigma:tm\to a} of the atiyah sequence of a principal bundle p → m {\displaystyle p\to m} are in bijective correspondence with principal connections on p → m {\displaystyle p\to m}. similarly, the curvatures of such connections correspond to the two forms Ω σ ∈ Ω 2 (m, p) {\di...	wikipedia
279b693bd7edda2242b1ff6442c140f2015690fb	while any transitive lie groupoid is isomorphic to	while any transitive lie groupoid is isomorphic to some gauge groupoid, not all transitive lie algebroids are atiyah algebroids of some principal bundle. integrability is the crucial property to distinguish the two concepts: a transitive lie algebroid is integrable if and only if it is isomorphic to the atiyah algebroi...	wikipedia
17252c22d168f203d9212cbc77d48a6ed06cb576	the atiyah sequence yields a short exact sequence	the atiyah sequence yields a short exact sequence of c ∞ (m) {\displaystyle {\mathcal {c}}^{\infty }(m)} -modules by taking the space of sections of the vector bundles. more precisely, the sections of the atiyah algebroid of p {\displaystyle p} is the lie algebra of g {\displaystyle g} -invariant vector fields on p {\d...	wikipedia
c7de367d083b495d56b1b9a4a6e86b12edd19ec9	it follows that a = t p /	it follows that a = t p / g {\displaystyle a=tp/g}, while the anchor map a → t m {\displaystyle a\to tm} is given by the differential d π: t p → t m {\displaystyle d\pi:tp\to tm}, which is g {\displaystyle g} -invariant. last, the kernel of the anchor is isomorphic precisely to p × g g {\displaystyle p\times _{g}{\math...	wikipedia
3465f19aef0bbd4b7f4653dac7cedd2d3f273a10	recall that any principal g {\displaystyle g} -bundle	recall that any principal g {\displaystyle g} -bundle p → m {\displaystyle p\to m} has an associated lie groupoid, called its gauge groupoid, whose objects are points of m {\displaystyle m}, and whose morphisms are elements of the quotient of p × p {\displaystyle p\times p} by the diagonal action of g {\displaystyle g}...	wikipedia
bb0b1c4383bb3c7e2e69ed067082de1c7d9c42ec	if p {\displaystyle p} is a principal g	if p {\displaystyle p} is a principal g {\displaystyle g} -bundle, then the group g {\displaystyle g} acts on the vector bundles in this sequence. moreover, since the vertical bundle v p {\displaystyle vp} is isomorphic to the trivial vector bundle p × g → p {\displaystyle p\times {\mathfrak {g}}\to p}, where g {\displ...	wikipedia
548fd3ba74736c9b747869f550d0f1a2962c4be8	for any fiber bundle p {\displaystyle p} over	for any fiber bundle p {\displaystyle p} over a manifold m {\displaystyle m}, the differential d π {\displaystyle d\pi } of the projection π: p → m {\displaystyle \pi:p\to m} defines a short exact sequence:	wikipedia
3c068a571ab4be873b50e4aa5dae76d838a94001	it is named after michael atiyah, who introduced	it is named after michael atiyah, who introduced the construction to study the existence theory of complex analytic connections. it plays a crucial example in the integrability of (transitive) lie algebroids, and it has applications in gauge theory and geometric mechanics.	wikipedia
af58e96a76f7104285f93a40f4b1898e7b16dbc0	in mathematics, the atiyah algebroid, or atiyah sequence,	in mathematics, the atiyah algebroid, or atiyah sequence, of a principal g {\displaystyle g} -bundle p {\displaystyle p} over a manifold m {\displaystyle m}, where g {\displaystyle g} is a lie group, is the lie algebroid of the gauge groupoid of p {\displaystyle p}. explicitly, it is given by the following short exact ...	wikipedia
1b8314554ae04368bd86e1ab64d83834aa289cdb	in algebra, the amitsur–levitzki theorem states that the	in algebra, the amitsur–levitzki theorem states that the algebra of n × n matrices over a commutative ring satisfies a certain identity of degree 2n. it was proved by amitsur and levitsky (1950). in particular matrix rings are polynomial identity rings such that the smallest identity they satisfy has degree exactly 2n.	wikipedia
690085e584ca6366e971a684d9a6a117af74b6da	swan (1963) and swan (1969) gave a simple	swan (1963) and swan (1969) gave a simple combinatorial proof as follows. by linearity it is enough to prove the theorem when each matrix has only one nonzero entry, which is 1. in this case each matrix can be encoded as a directed edge of a graph with n vertices. so all matrices together give a graph on n vertices wit...	wikipedia
11a2a814a19406e6dbf98ebfa2ffd51c561ad82b	in algebra, the amitsur–levitzki theorem states that the	in algebra, the amitsur–levitzki theorem states that the algebra of n × n matrices over a commutative ring satisfies a certain identity of degree 2 n. it was proved by amitsur and levitsky (1950). in particular matrix rings are polynomial identity rings such that the smallest identity they satisfy has degree exactly 2 ...	wikipedia
70e10895da1ff07fa29c1e25158e9d0d3118b7dc	vilsmeier discovered the aldehyde synthesis reaction which bears	vilsmeier discovered the aldehyde synthesis reaction which bears his name in 1926, and it was published in 1927, the year that he began to work for basf in ludwigshafen. he retired in 1959, and died in 1962 in ludwigshafen.	wikipedia
2b24159eb168646dc27168f0bc2a25debbdda8ff	anton vilsmeier was born to the mill owner,	anton vilsmeier was born to the mill owner, wolfgang vilsmeier, and his wife, philomena, in burgweinting, oberpfalz. he attended the volksschule and the altes gymnasium in regensburg. during world war i, he served in the 11th bavarian infantry regiment, and became a british prisoner following the battle of the somme, r...	wikipedia
2a37a5ce97988efeaa8a7c1d4ccfb3669e2658e6	armand salvador b. mijares is a filipino archaeologist	armand salvador b. mijares is a filipino archaeologist from manila, philippines. he works as professor of archaeology at the archaeological studies program of the university of the philippines-diliman. he specializes in lithic analysis, ceramic petrology, soil micromorphology, paleolithic archaeology and early human mi...	wikipedia
83e08854c6def1b530daace0bedbeef37c7c4958	the hominin fossils and teeth are from three	the hominin fossils and teeth are from three individuals and were collectively nicknamed 'ubag', after a mythical cave man that were excavated in 2007, 2011 and 2015. the internationally pooled team of specialists and archaeologists consist of paleoanthropologist florent détroit of the muséum national d’histoire nature...	wikipedia
7bec49dae4b4d050620764925591d20a4253180c	mijares' research primarily focuses on understanding early human	mijares' research primarily focuses on understanding early human migration in maritime southeast asia. he is also interested in reconstructing hunter-gatherer subsistence strategy during the late pleistocene and early holocene period through thorough excavations in northern luzon, especially in callao cave complex, whe...	wikipedia
7a0775e59fe6e2821bb3e83f4824b47b0d23588f	after he received his master's degree, he taught	after he received his master's degree, he taught at the university of the philippines manila. afterwards he pursued archaeological research work at the national museum of the philippines in 1994, and worked as an archaeologist in the museum until 2006. after earning his ph.d., mijares returned to university of the phil...	wikipedia
a458e2d10cf6b6933d6e44786571cde186bfde6c	mijares earned his bachelor of arts in development	mijares earned his bachelor of arts in development studies from the university of the philippines manila and his master of arts in anthropology at the university of the philippines diliman. in 1996, he did his diploma in archaeology at up-diliman 's newly established archaeological studies program and went on with a fu...	wikipedia
5d718d74615f82e6348992ecf87525a393262dcb	armand salvador b. mijares is a filipino archaeologist	armand salvador b. mijares is a filipino archaeologist from manila, philippines. he works as professor of archaeology at the archaeological studies program of the university of the philippines-diliman. he specializes in lithic analysis, ceramic petrology, soil micromorphology, paleolithic archaeology and early human mi...	wikipedia
ea4639c8eb61bb8414c7cabf01117dfdd55b43a5	albert george demarco, sr. was a canadian professional	albert george demarco, sr. was a canadian professional ice hockey player. demarco started his national hockey league career with the chicago black hawks. he would also play with the new york rangers, boston bruins and toronto maple leafs. he played in the nhl from 1938 to 1947. he played several years in minor professi...	wikipedia
0cddccdf695b49ce482ee1d2f45abeb9d38a4e0c	albert was born in north bay, ontario. he	albert was born in north bay, ontario. he played junior and minor hockey from 1933 until 1937, when he became a professional with the baltimore orioles of the eastern american hockey league. demarco signed with the chicago black hawks in 1938, splitting time with the providence reds of the international-american hockey...	wikipedia
37f0c37c79bae9deeed705381bcae360bddde05a	albert george demarco, sr. (may 10, 1916 –	albert george demarco, sr. (may 10, 1916 – may 25, 1989) was a canadian professional ice hockey player. demarco started his national hockey league career with the chicago black hawks. he would also play with the new york rangers, boston bruins and toronto maple leafs. he played in the nhl from 1938 to 1947. he played s...	wikipedia