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29-472: (Redirected from Integrating ) [REDACTED] Look up Integration , integrate , integrated , integrating , or integration in Wiktionary, the free dictionary. Integration may refer to: Biology [ edit ] Multisensory integration Path integration Pre-integration complex , viral genetic material used to insert

58-832: A declaration that a contract is the final and complete understanding of the parties A step in the process of money laundering Integrated farming , a farm management system Integration (tax) , a feature of corporate and personal income tax in some countries Territorial integration of independent or dependent territories into a state Engineering [ edit ] Data integration Digital integration Enterprise integration Integrated architecture, in an Enterprise architecture framework approach such as DoDAF Integrated circuit , an electronic circuit whose components are manufactured in one flat piece of semiconductor material Integrated design , an approach to design which brings together specialisms usually considered separately Integrated product team , use of

87-832: A declaration that a contract is the final and complete understanding of the parties A step in the process of money laundering Integrated farming , a farm management system Integration (tax) , a feature of corporate and personal income tax in some countries Territorial integration of independent or dependent territories into a state Engineering [ edit ] Data integration Digital integration Enterprise integration Integrated architecture, in an Enterprise architecture framework approach such as DoDAF Integrated circuit , an electronic circuit whose components are manufactured in one flat piece of semiconductor material Integrated design , an approach to design which brings together specialisms usually considered separately Integrated product team , use of

116-514: A differential equation or a system of differential equations: Integrability conditions for differential systems Integrable system Order of integration , in statistics, a summary statistic for a time series Sociology [ edit ] Social integration , in social science, a movement of newcomers or marginalized minorities into the mainstream of a society Racial integration , including desegregation and other changes in social opportunity and culture Desegregation , ending

145-514: A differential equation or a system of differential equations: Integrability conditions for differential systems Integrable system Order of integration , in statistics, a summary statistic for a time series Sociology [ edit ] Social integration , in social science, a movement of newcomers or marginalized minorities into the mainstream of a society Racial integration , including desegregation and other changes in social opportunity and culture Desegregation , ending

174-408: A numerical method, usually with a computer Integration by parts , a method for computing the integral of a product of functions Integration by substitution , a method for computing integrals, by using a change of variable Symbolic integration , the computation, mostly on computers, of antiderivatives and definite integrals in term of formulas Integration, the computation of a solution of

203-408: A numerical method, usually with a computer Integration by parts , a method for computing the integral of a product of functions Integration by substitution , a method for computing integrals, by using a change of variable Symbolic integration , the computation, mostly on computers, of antiderivatives and definite integrals in term of formulas Integration, the computation of a solution of

232-639: A separation of races, particularly in the context of the American civil rights movement Educational integration of students with disabilities Integration of immigrants Other uses [ edit ] Integration (festival) , an annual technology and cultural festival managed by the Indian Statistical Institute Integration (album) , a 2011 album by Kellee Maize Integration, an album by Kultur Shock See also [ edit ] Desegregation ,

261-484: A separation of races, particularly in the context of the American civil rights movement Educational integration of students with disabilities Integration of immigrants Other uses [ edit ] Integration (festival) , an annual technology and cultural festival managed by the Indian Statistical Institute Integration (album) , a 2011 album by Kellee Maize Integration, an album by Kultur Shock See also [ edit ] Desegregation ,

290-439: A team including multiple disciplines (e.g. customer, engineer, support, testing) Integrated software System integration , engineering practices for assembling large and complicated systems from units, particularly subsystems Mathematics [ edit ] Integration, the computation of an integral Indefinite integration, the computation of antiderivatives Numerical integration , computing an integral with

319-439: A team including multiple disciplines (e.g. customer, engineer, support, testing) Integrated software System integration , engineering practices for assembling large and complicated systems from units, particularly subsystems Mathematics [ edit ] Integration, the computation of an integral Indefinite integration, the computation of antiderivatives Numerical integration , computing an integral with

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348-535: A viral genome into a host genome DNA integration, by means of site-specific recombinase technology , performed by a specific class of recombinase enzymes ("integrases") Economics and law [ edit ] Economic integration , trade unification between different states Horizontal integration and vertical integration , in microeconomics and strategic management, styles of ownership and control Regional integration , in which states cooperate through regional institutions and rules Integration clause ,

377-535: A viral genome into a host genome DNA integration, by means of site-specific recombinase technology , performed by a specific class of recombinase enzymes ("integrases") Economics and law [ edit ] Economic integration , trade unification between different states Horizontal integration and vertical integration , in microeconomics and strategic management, styles of ownership and control Regional integration , in which states cooperate through regional institutions and rules Integration clause ,

406-409: Is ( n − k {\displaystyle n-k} )-dimensional. A Pfaffian system is said to be completely integrable if M {\displaystyle M} admits a foliation by maximal integral manifolds. (Note that the foliation need not be regular ; i.e. the leaves of the foliation might not be embedded submanifolds.) An integrability condition is a condition on

435-451: Is an immersed (not necessarily embedded) submanifold whose tangent space at every point p ∈ N {\displaystyle \textstyle p\in N} is annihilated by (the pullback of) each α i {\displaystyle \textstyle \alpha _{i}} . A maximal integral manifold is an immersed (not necessarily embedded) submanifold such that

464-500: Is different from Wikidata All article disambiguation pages All disambiguation pages Integration [REDACTED] Look up Integration , integrate , integrated , integrating , or integration in Wiktionary, the free dictionary. Integration may refer to: Biology [ edit ] Multisensory integration Path integration Pre-integration complex , viral genetic material used to insert

493-524: Is different from Wikidata All article disambiguation pages All disambiguation pages Integrability conditions for differential systems Given a collection of differential 1-forms α i , i = 1 , 2 , … , k {\displaystyle \textstyle \alpha _{i},i=1,2,\dots ,k} on an n {\displaystyle \textstyle n} -dimensional manifold M {\displaystyle M} , an integral manifold

522-553: Is just the curvature of M: Ω = d ω + ω ∧ ω = 0. {\displaystyle \Omega =d\omega +\omega \wedge \omega =0.} After an application of the Frobenius theorem, one concludes that a manifold M is locally flat if and only if its curvature vanishes. Many generalizations exist to integrability conditions on differential systems which are not necessarily generated by one-forms. The most famous of these are

551-484: The α i {\displaystyle \alpha _{i}} to guarantee that there will be integral submanifolds of sufficiently high dimension. The necessary and sufficient conditions for complete integrability of a Pfaffian system are given by the Frobenius theorem . One version states that if the ideal I {\displaystyle {\mathcal {I}}} algebraically generated by

580-600: The Poincaré lemma , the θ locally will have the form d x for some functions x on the manifold, and thus provide an isometry of an open subset of M with an open subset of R . Such a manifold is called locally flat. This problem reduces to a question on the coframe bundle of M . Suppose we had such a closed coframe If we had another coframe Φ = ( ϕ 1 , … , ϕ n ) {\displaystyle \Phi =(\phi ^{1},\dots ,\phi ^{n})} , then

609-415: The collection of α i inside the ring Ω( M ) is differentially closed, in other words then the system admits a foliation by maximal integral manifolds. (The converse is obvious from the definitions.) Not every Pfaffian system is completely integrable in the Frobenius sense. For example, consider the following one-form on R − (0,0,0) : If dθ were in the ideal generated by θ we would have, by

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638-446: The kernel of the restriction map on forms is spanned by the α i {\displaystyle \textstyle \alpha _{i}} at every point p {\displaystyle p} of N {\displaystyle N} . If in addition the α i {\displaystyle \textstyle \alpha _{i}} are linearly independent, then N {\displaystyle N}

667-432: The problem of finding an orthogonal coframe θ , i.e., a collection of 1-forms forming a basis of the cotangent space at every point with ⟨ θ i , θ j ⟩ = δ i j {\displaystyle \langle \theta ^{i},\theta ^{j}\rangle =\delta ^{ij}} which are closed (dθ = 0, i  = 1, 2, ...,  n ). By

696-458: The process of ending the separation of two groups, usually races Interdisciplinarity , involves the combining of two or more academic disciplines into one activity (e.g. a research project) Integrity , a concept of consistency of actions, values, methods, measures, principles, expectations, and outcomes Disintegration (disambiguation) Integral (disambiguation) All pages with titles containing integration Topics referred to by

725-458: The process of ending the separation of two groups, usually races Interdisciplinarity , involves the combining of two or more academic disciplines into one activity (e.g. a research project) Integrity , a concept of consistency of actions, values, methods, measures, principles, expectations, and outcomes Disintegration (disambiguation) Integral (disambiguation) All pages with titles containing integration Topics referred to by

754-419: The same term [REDACTED] This disambiguation page lists articles associated with the title Integration . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Integration&oldid=1258218471 " Category : Disambiguation pages Hidden categories: Short description

783-419: The same term [REDACTED] This disambiguation page lists articles associated with the title Integration . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Integration&oldid=1258218471 " Category : Disambiguation pages Hidden categories: Short description

812-492: The skewness of the wedge product But a direct calculation gives which is a nonzero multiple of the standard volume form on R . Therefore, there are no two-dimensional leaves, and the system is not completely integrable. On the other hand, for the curve defined by then θ defined as above is 0, and hence the curve is easily verified to be a solution (i.e. an integral curve ) for the above Pfaffian system for any nonzero constant c . In Riemannian geometry , we may consider

841-581: The two coframes would be related by an orthogonal transformation If the connection 1-form is ω , then we have On the other hand, But ω = ( d M ) M − 1 {\displaystyle \omega =(dM)M^{-1}} is the Maurer–Cartan form for the orthogonal group . Therefore, it obeys the structural equation d ω + ω ∧ ω = 0 , {\displaystyle d\omega +\omega \wedge \omega =0,} and this

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