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Hodge conjecture for Kähler varieties, vector bundle version. Let X be a complex Kähler manifold. Then every Hodge class on X is a linear combination with rational coefficients of Chern classes of vector bundles on X. Hodge conjecture for Kähler varieties, coherent sheaf version. Let X be a complex Kähler manifold.
The full set of solutions to Apollonius' problem can be found by considering all possible combinations of internal and external tangency of the solution circle to the three given circles. Isaac Newton (1687) refined van Roomen's solution, so that the solution-circle centers were located at the intersections of a line with a circle. [ 15 ]
Each curve in this example is a locus defined as the conchoid of the point P and the line l.In this example, P is 8 cm from l. In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.
Apollonius' problem is to construct circles that are simultaneously tangent to three specified circles. The solutions to this problem are sometimes called the circles of Apollonius. The Apollonian gasket—one of the first fractals ever described—is a set of mutually tangent circles, formed by solving Apollonius' problem iteratively.
A new study of decades worth of seismogram data shows that the surface of Earth’s iron and nickel core is more malleable than scientists thought ...
The method of loci is a strategy for memory enhancement, which uses visualizations of familiar spatial environments in order to enhance the recall of information. The method of loci is also known as the memory journey , memory palace , journey method , memory spaces , or mind palace technique .
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Each eigenvector corresponds to a set of loci, which are not necessarily linearly contiguous, that share structural features. [65] A significant confounding factor in 3C technologies is the frequent non-specific interactions between genomic loci that occur due to random polymer behavior. An interaction between two loci must be confirmed as ...