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In number theory, Kaprekar's routine is an iterative algorithm named after its inventor, Indian mathematician D. R. Kaprekar. [1] [2] Each iteration starts with a number, sorts the digits into descending and ascending order, and calculates the difference between the two new numbers.
Kalyan Bidhan Sinha (K.B. Sinha) (born 3 June 1944) is an Indian mathematician. He is a professor at the Jawaharlal Nehru Centre for Advanced Scientific Research , [ 1 ] and Professor Emeritus for life of the Indian Statistical Institute .
In thermodynamics, the ebullioscopic constant K b relates molality b to boiling point elevation. [1] It is the ratio of the latter to the former: = i is the van 't Hoff factor, the number of particles the solute splits into or forms when dissolved. b is the molality of the solution.
The Boltzmann constant (k B or k) is the proportionality factor that relates the average relative thermal energy of particles in a gas with the thermodynamic temperature of the gas. [2] It occurs in the definitions of the kelvin (K) and the gas constant , in Planck's law of black-body radiation and Boltzmann's entropy formula , and is used in ...
[c] [2] For example, a hypothetical weak acid having K a = 10 −5, the value of log K a is the exponent (−5), giving pK a = 5. For acetic acid, K a = 1.8 x 10 −5, so pK a is 4.7. A higher K a corresponds to a stronger acid (an acid that is more dissociated at equilibrium).
A formal expression is a kind of string of symbols, created by the same production rules as standard expressions, however, they are used without regard to the meaning of the expression. In this way, two formal expressions are considered equal only if they are syntactically equal, that is, if they are the exact same expression.
The quadratic formula =. is a closed form of the solutions to the general quadratic equation + + =. More generally, in the context of polynomial equations, a closed form of a solution is a solution in radicals; that is, a closed-form expression for which the allowed functions are only n th-roots and field operations (+,,, /).
Given a field K, we can consider the field K(X) of all rational functions in the variable X with coefficients in K; the elements of K(X) are fractions of two polynomials over K, and indeed K(X) is the field of fractions of the polynomial ring K[X]. This field of rational functions is an extension field of K. This extension is infinite.