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The journal was established in 1967 as Mathematical Notes of the Academy of Sciences of the USSR and obtained its current title in 1991. The current editor-in-chief is Victor P. Maslov. According to the Journal Citation Reports, the journal has a 2011 impact factor of 0.295. [1] The journal is indexed in Russian Science Citation Index. [2]
In differential geometry, a one-form (or covector field) on a differentiable manifold is a differential form of degree one, that is, a smooth section of the cotangent bundle. [1] Equivalently, a one-form on a manifold is a smooth mapping of the total space of the tangent bundle of to whose restriction to each fibre is a linear functional on the ...
Mathematical notation is widely used in mathematics, science, and engineering for representing complex concepts and properties in a concise, unambiguous, and accurate way. For example, the physicist Albert Einstein's formula = is the quantitative representation in mathematical notation of mass–energy equivalence. [1]
The 1-form dz − y dx. on R 3 maximally violates the assumption of Frobenius' theorem. These planes appear to twist along the y-axis.It is not integrable, as can be verified by drawing an infinitesimal square in the x-y plane, and follow the path along the one-forms.
The apparent plural form in English goes back to the Latin neuter plural mathematica , based on the Greek plural ta mathēmatiká (τὰ μαθηματικά) and means roughly "all things mathematical", although it is plausible that English borrowed only the adjective mathematic(al) and formed the noun mathematics anew, after the pattern of ...
In mathematics, a modular form is a (complex) ... = 0. [note 2] Sometimes a weaker definition of modular functions is used – under the alternative definition, ...
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Thus the form a x dx + a y dy + a z dz corresponds to the "dual form" a z dx ∧ dy + a y dz ∧ dx + a x dy ∧ dz. Thus, identifying 0-forms and 3-forms with scalar fields, and 1-forms and 2-forms with vector fields: grad takes a scalar field (0-form) to a vector field (1-form); curl takes a vector field (1-form) to a pseudovector field (2-form);
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