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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. Hilbert's tenth problem dealt with a more general type of equation, and in that case it was proven that there is no algorithmic way to decide whether a given ...
A simple buffer solution consists of a solution of an acid and a salt of the conjugate base of the acid. For example, the acid may be acetic acid and the salt may be sodium acetate . The Henderson–Hasselbalch equation relates the pH of a solution containing a mixture of the two components to the acid dissociation constant , K a of the acid ...
A buffer solution is a solution where the pH does not change significantly on dilution or if an acid or base is added at constant temperature. [1] Its pH changes very little when a small amount of strong acid or base is added to it. Buffer solutions are used as a means of keeping pH at a nearly constant value in a wide variety of chemical ...
As calculated by the Henderson–Hasselbalch equation, in order to maintain a normal pH of 7.4 in the blood (whereby the pK a of carbonic acid is 6.1 at physiological temperature), a 20:1 ratio of bicarbonate to carbonic acid must constantly be maintained; this homeostasis is mainly mediated by pH sensors in the medulla oblongata of the brain ...
Buffer solutions also play a key role in analytical chemistry. They are used whenever there is a need to fix the pH of a solution at a particular value. Compared with an aqueous solution, the pH of a buffer solution is relatively insensitive to the addition of a small amount of strong acid or strong base.
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.
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In mathematics, to solve an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equals sign. When seeking a solution, one or more variables are designated as unknowns. A solution is an assignment of ...
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