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A pairing is called perfect if the above map is an isomorphism of R-modules and the other evaluation map ′: (,) is an isomorphism also. In nice cases, it suffices that just one of these be an isomorphism, e.g. when R is a field, M,N are finite dimensional vector spaces and L=R .
The statement that this is the only quadratic pairing function is known as the Fueter–Pólya theorem. [9] Whether this is the only polynomial pairing function is still an open question. When we apply the pairing function to k 1 and k 2 we often denote the resulting number as k 1, k 2 . [citation needed]
A science fair or engineering fair is an event hosted by a school that offers students the opportunity to experience the practices of science and engineering for themselves. In the United States, the Next Generation Science Standards makes experiencing the practices of science and engineering one of the three pillars of science education.
All India Secondary School Examination, commonly known as the class 10th board exam, is a centralized public examination that students in schools affiliated with the Central Board of Secondary Education, primarily in India but also in other Indian-patterned schools affiliated to the CBSE across the world, taken at the end of class 10. The board ...
Prmkt applies for a job as a janitor at Hubble Middle School, a prestigious public school in southern Maryland that hosts an annual science fair with a cash prize for the winner. Prmkt secretly sends notes to the Manor Estates (ME) kids, children of rich government officials who win the science fair every year by going to a store in the local ...
The Interactive Mathematics Program (IMP) is a four-year, problem-based mathematics curriculum for high schools. It was one of several curricula funded by the National Science Foundation and designed around the 1989 National Council of Teachers of Mathematics (NCTM) standards .
For a scheme X over a commutative ring R, an R-point of X means a section of the morphism X → Spec(R). One writes X(R) for the set of R-points of X. In examples, this definition reconstructs the old notion of the set of solutions of the defining equations of X with values in R. When R is a field k, X(k) is also called the set of k-rational ...
The Regeneron International Science and Engineering Fair (ISEF) is an annual science fair in the United States. [1] It is owned and administered by the Society for Science, [2] a 501(c)(3) non-profit organization based in Washington, D.C. [3] Each May, more than 1800 students from roughly 75 countries and territories compete in the fair for scholarships, tuition grants, internships, scientific ...