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The fraction 13/5 = 2.6 and the floor function have that effect; the denominator of 5 sets a period of 5 months. The overall function, mod 7 {\displaystyle \operatorname {mod} \,7} , normalizes the result to reside in the range of 0 to 6, which yields the index of the correct day of the week for the date being analyzed.
Simplification is the process of replacing a mathematical expression by an equivalent one that is simpler (usually shorter), according to a well-founded ordering. Examples include:
By applying the fundamental recurrence formulas we may easily compute the successive convergents of this continued fraction to be 1, 3/2, 7/5, 17/12, 41/29, 99/70, 239/169, ..., where each successive convergent is formed by taking the numerator plus the denominator of the preceding term as the denominator in the next term, then adding in the ...
which we can recognize as eigenvalue problems for the operators for and . If T {\displaystyle T} is a compact, self-adjoint operator on the space L 2 [ 0 , l ] {\displaystyle L^{2}[0,l]} along with the relevant boundary conditions, then by the Spectral theorem there exists a basis for L 2 [ 0 , l ] {\displaystyle L^{2}[0,l]} consisting of ...
A closed formula, also ground formula or sentence, is a formula in which there are no free occurrences of any variable. If A is a formula of a first-order language in which the variables v 1, …, v n have free occurrences, then A preceded by ∀v 1 ⋯ ∀v n is a universal closure of A.
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For the months April through December, the even numbered months are covered by the double dates 4/4, 6/6, 8/8, 10/10, and 12/12, all of which fall on the doomsday. The odd numbered months can be remembered with the mnemonic "I work from 9 to 5 at the 7-11 ", i.e., 9/5, 7/11, and also 5/9 and 11/7, are all doomsdays (this is true for both the ...
In the analysis of the molecular formula of organic molecules, the degree of unsaturation (DU) (also known as the index of hydrogen deficiency (IHD), double bond equivalents (DBE), or unsaturation index [1]) is a calculation that determines the total number of rings and π bonds. A formula is used in organic chemistry to