extremal orders of an arithmetic function are best possible bounds of the given arithmetic function. Specifically, if f(n) is an arithmetic function and...

(f)=q^{2n}(1-q^{-1}).} Divisor summatory function Normal order of an arithmetic function Extremal orders of an arithmetic function Divisor sum identities Hardy,...

order of log(d(n)), where d(n) is the number of divisors of n, is log(2) log(log(n)). Average order of an arithmetic function Divisor function Extremal orders...

median; if two values, the median is the arithmetic mean of these two. This method takes the list 1, 7, 3, 13 and orders it to read 1, 3, 7, 13. Then the 1...

floating-point arithmetic (FP) is arithmetic on subsets of real numbers formed by a significand (a signed sequence of a fixed number of digits in some...

even to find the extremal answer f(n) exactly and one can only give an asymptotic estimate. Ramsey theory is another part of extremal combinatorics. It...

growing processes balanced by production and dissipation, the use of an extremal principle of Shannon entropy shows that σ = 1 6 {\displaystyle \sigma ={\frac...

membership in function domains fails to be decidable, the extremal function granted by that principle is not provably always a choice function on the whole...

the graph of the successor function on D or the order relation <, possibly with other arithmetic predicates). Conversely, the Cayley tables of any finite...

integration of fractional orders using methods of fractional calculus. Fredholm theory part of spectral theory studying integral equations. Function theory an ambiguous...

reals, including the usual arithmetic operations (addition, subtraction, multiplication, and division); as such, they form an ordered field. If formulated...

procedure seems to presuppose arithmetic in some form or other (p. 134). He deduces that "one obtains integers of different orders" (p. 134-135); the proof...

external quicksort external radix sort external sort extrapolation search extremal extreme point facility location factor (see substring) factorial fast Fourier...

of Stirling's approximation; easier to apply than Lanczos AGM method — computes arithmetic–geometric mean; related methods compute special functions FEE...

equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. Differential...

three-dimensional shapes can have their volume easily calculated using arithmetic formulas. Volumes of more complicated shapes can be calculated with integral calculus...

where the CPU consists of two main parts: The control unit and the arithmetic logic unit (ALU). The former controls the flow of data between the CPU and...

number of ordered multiplicative partitions that (as a function of the number of prime factors) is between these two extreme cases. A parking function, in...

definition of: "an interesting basis for recursive function theory involving programs of only the simplest arithmetic operations" (Minsky (1961) p. 437). His "Theorem...

long-standing problem that is stated in terms of elementary arithmetic. In physics and cosmology, it is an open question whether the universe is spatially...

the social function of arithmetic prodigies may be weaker because of larger activation in certain brain areas enhancing their arithmetic performance...

determinant among matrices with entries of absolute value less than or equal to 1 and so is an extremal solution of Hadamard's maximal determinant problem...

opponent's warriors. These fights are resolved using dice and simple arithmetic. Warhammer 40,000 is set in the distant future, where a stagnant human...

mechanical device used to perform the basic operations of arithmetic automatically, or a simulation like an analog computer or a slide rule. Most mechanical...

operator, there are also discrete analogs of these multiplicative derivatives. Arithmetic derivative – Function defined on integers in number theory Automatic...

on arithmetic and advanced algebra for astronomical uses, they were also the first to develop negative numbers, algebraic geometry, and the usage of decimals...

memory addresses or allow memory addresses to be manipulated with pointer arithmetic. In C++ one can construct pointers to pointers, pointers to ints and doubles...

be proved that such an area function actually exists. Every unit of length has a corresponding unit of area, namely the area of a square with the given...

our understanding of buoyancy, and practical solutions such as Archimedes' screw. Brahmagupta, an Indian mathematician, used arithmetic in the 7th century...

certain arithmetical functions", Ramanujan defined the so-called delta-function, whose coefficients are called τ(n) (the Ramanujan tau function). He proved...