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The conjecture is that there is a simple way to tell whether such equations have a finite or infinite number of rational solutions. More specifically, the Millennium Prize version of the conjecture is that, if the elliptic curve E has rank r, then the L-function L(E, s) associated with it vanishes to order r at s = 1.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
In nature, methoxy groups are found on nucleosides that have been subjected to 2′-O-methylation, for example in variations of the 5′-cap structure known as cap-1 and cap-2. They are also common substituents in O -methylated flavonoids , whose formation is catalyzed by O-methyltransferases that act on phenols , such as catechol- O -methyl ...
The Riemann Hypothesis. Today’s mathematicians would probably agree that the Riemann Hypothesis is the most significant open problem in all of math. It’s one of the seven Millennium Prize ...
Smale's problems is a list of eighteen unsolved problems in mathematics proposed by Steve Smale in 1998 [1] and republished in 1999. [2] Smale composed this list in reply to a request from Vladimir Arnold, then vice-president of the International Mathematical Union, who asked several mathematicians to propose a list of problems for the 21st century.
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
Larry Mullen Jr. is opening up about a recent diagnosis. The drummer for U2, 63, revealed in an interview with Times Radio that he's been diagnosed with dyscalculia, which makes it challenging for ...
Indicator function: maps x to either 1 or 0, depending on whether or not x belongs to some subset. Step function: A finite linear combination of indicator functions of half-open intervals. Heaviside step function: 0 for negative arguments and 1 for positive arguments. The integral of the Dirac delta function. Sawtooth wave; Square wave ...