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The resulting algebraic object satisfies the axioms for a group. Specifically: Associativity The binary operation on G × H is associative. Identity The direct product has an identity element, namely (1 G, 1 H), where 1 G is the identity element of G and 1 H is the identity element of H.
The sum of proper divisors of a number is called its aliquot sum, so a perfect number is one that is equal to its aliquot sum. Equivalently, a perfect number is a number that is half the sum of all of its positive divisors; in symbols, σ 1 ( n ) = 2 n {\displaystyle \sigma _{1}(n)=2n} where σ 1 {\displaystyle \sigma _{1}} is the sum-of ...
Specific choices of give different types of Riemann sums: . If = for all i, the method is the left rule [2] [3] and gives a left Riemann sum.; If = for all i, the method is the right rule [2] [3] and gives a right Riemann sum.
In quantum mechanics, a sum rule is a formula for transitions between energy levels, in which the sum of the transition strengths is expressed in a simple form. Sum rules are used to describe the properties of many physical systems, including solids, atoms, atomic nuclei, and nuclear constituents such as protons and neutrons.
In linear algebra, an element of a vector space, a sum of finitely many elements from a given basis set multiplied by real, complex, or other numerical coefficients. In the study of series (mathematics) , a sum of an infinite sequence of numbers or other quantities, considered as an abstract mathematical object regardless of whether the sum ...
Lydia Shum Din-ha or Lydia Tin Ha Sum (Chinese: 沈殿霞; 21 July 1945 – 19 February 2008) was a Hong Kong-Canadian comedian, MC, actress and singer. Known for her portly figure, signature dark-rimmed glasses and bouffant hairstyle, she was affectionately known to peers and fans as Fei-fei ( Chinese : 肥肥 , lit.