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The Weil pairing is an important concept in elliptic curve cryptography; e.g., it may be used to attack certain elliptic curves (see MOV attack). It and other pairings have been used to develop identity-based encryption schemes.
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]
The Principles of Mathematics (PoM) is a 1903 book by Bertrand Russell, in which the author presented his famous paradox and argued his thesis that mathematics and logic are identical. [ 1 ] The book presents a view of the foundations of mathematics and Meinongianism and has become a classic reference.
In mathematics, the Poincaré duality theorem, named after Henri Poincaré, is a basic result on the structure of the homology and cohomology groups of manifolds.It states that if M is an n-dimensional oriented closed manifold (compact and without boundary), then the kth cohomology group of M is isomorphic to the (n − k) th homology group of M, for all integers k
Affine schemes are the local building blocks of schemes. The previous result therefore tells that the local theory of schemes is the same as commutative algebra, the study of commutative rings. Noncommutative geometry draws inspiration from Gelfand duality and studies noncommutative C*-algebras as if they were functions on some imagined space.
Anyone who purchased the snacks in the United States with the label from Feb. 2, 2017, through Dec. 6, 2024, could receive money from the settlement. Read on to learn more about the settlement and ...
The 26-year-old charged with murder landed a data engineering job after an Ivy League education. It's unclear what changed for him and when. In Luigi Mangione's Maryland hometown, questions swirl ...
The Principles and Standards for School Mathematics was developed by the NCTM. The NCTM's stated intent was to improve mathematics education. The contents were based on surveys of existing curriculum materials, curricula and policies from many countries, educational research publications, and government agencies such as the U.S. National Science Foundation. [3]