It was possible, however, to decompose the compliance into a sum of a frequency-independent component and two viscoelastic mechanisms, each compatible with the Boltzmann superposition principle and with a consistent set of time-temperature equivalence factors.

If one takes the middle number, 5, and multiplies it by 3 ( the base number of the magic square of three ), the result is 15, which is also the constant sum of all the rows, columns, and two main diagonals.

The sum, difference, product and quotient of two algebraic numbers is again algebraic ( this fact can be demonstrated using the resultant ), and the algebraic numbers therefore form a field, sometimes denoted by A ( which may also denote the adele ring ) or < span style =" text-decoration: overline ;"> Q </ span >.

According to Davis, " It's great triumph was to prove that the sum of two even numbers is even ".

Amicable numbers are two different numbers so related that the sum of the proper divisors of each is equal to the other number.

Each number is the sum of the two directly above it.

The binomial coefficients appear as the entries of Pascal's triangle where each entry is the sum of the two above it.

This role as a sink for CO < sub > 2 </ sub > is driven by two processes, the solubility pump and the biological pump .< ref > The former is primarily a function of differential CO < sub > 2 </ sub > solubility in seawater and the thermohaline circulation, while the latter is the sum of a series of biological processes that transport carbon ( in organic and inorganic forms ) from the surface euphotic zone to the ocean's interior.

* < tt > sum </ tt >, a Unix command ( also ported to Win32 ) that generates order-independent sums ; uses two different algorithms for calculating, the SYSV checksum algorithm and the BSD checksum ( default ) algorithm.

Similarly, if light consisted strictly of classical particles and we illuminated two parallel slits, the expected pattern on the screen would simply be the sum of the two single-slit patterns.

From the above properties an important feature arises: Looking at two triangles ABD and BCD with the common edge BD ( see figures ), if the sum of the angles α and γ is less than or equal to 180 °, the triangles meet the Delaunay condition.

groups ( G, *) and ( H, ●), denoted by G × H. For abelian groups which are written additively, it may also be called the direct sum of two groups, denoted by.

One lemma states that the difference of the cubes of two rational numbers is equal to the sum of the cubes of two other rational numbers, i. e. given any a and b, with a > b, there exist c and d, all positive and rational, such that

The sum of the distances from any point P on the ellipse to those two foci is constant and equal to the major axis ( PF < sub > 1 </ sub > + PF < sub > 2 </ sub > = 2a ).

The characterization of an ellipse as the locus of points so that sum of the distances to the foci is constant leads to a method of drawing one using two drawing pins, a length of string, and a pencil.

In Euclidean geometry, the ellipse is usually defined as the bounded case of a conic section, or as the set of points such that the sum of the distances to two fixed points ( the foci ) is constant.

The parallel postulate: If two lines intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough.

Image: Pythagorean. svg | Pythagoras ' theorem: The sum of the areas of the two squares on the legs ( a and b ) of a right triangle equals the area of the square on the hypotenuse ( c ).

The celebrated Pythagorean theorem ( book I, proposition 47 ) states that in any right triangle, the area of the square whose side is the hypotenuse ( the side opposite the right angle ) is equal to the sum of the areas of the squares whose sides are the two legs ( the two sides that meet at a right angle ).

The Bernoulli numbers appear in the Taylor series expansions of the tangent and hyperbolic tangent functions, in formulas for the sum of powers of the first positive integers, in the Euler – Maclaurin formula, and in expressions for certain values of the Riemann zeta function.

American media critic Herbert Schiller wrote: " The concept of cultural imperialism today best describes the sum of the processes by which a society is brought into the modern world system and how its dominating stratum is attracted, pressured, forced, and sometimes bribed into shaping social institutions to correspond to, or even promote, the values and structures of the dominating centre of the system.

All future cash flows are estimated and discounted to give their present values ( PVs ) — the sum of all future cash flows, both incoming and outgoing, is the net present value ( NPV ), which is taken as the value or price of the cash flows in question.

: The value of a whole must not be assumed to be the same as the sum of the values of its parts ( Principia, § 18 ).

They might have some value, but when we consider the total value of a consciousness experiencing a beautiful object, it seems to exceed the simple sum of these values ( Principia 18: 2 ).

Note that we have to restrict the sum to ordered values of m < sub > 1 </ sub >, ..., m < sub > N </ sub > to ensure that we do not count each multi-particle state more than once.

The sum of the squares of the absolute values of the two components of Jones vectors is proportional to the intensity of light.

Maximize the sum of the values of the items in the knapsack so that the sum of the weights must be less than the knapsack's capacity.

For a data set, the arithmetic mean is equal to the sum of the values divided by the number of values.

The output byte is selected by looking up the values of S ( i ) and S ( j ), adding them together modulo 256, and then looking up the sum in S ; S ( S ( i ) + S ( j )) is used as a byte of the key stream, K. For as many iterations as are needed, the PRGA modifies the state and outputs a byte of the keystream.

In each iteration, the PRGA increments i, looks up the ith element of S, S, and adds that to j, exchanges the values of S and S, and then uses the sum S + S ( modulo 256 ) as an index to fetch a third element of S, ( the keystream value K below ) which is XORed with the next byte of the message to produce the next byte of either ciphertext or plaintext.

In calculating the arithmetic mean of a sample, for example, the algorithm works by summing all the data values observed in the sample then divides this sum by the number of data items.

In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.

* Summed area table, an algorithm for generating the sum of values in a rectangular subset of a grid

The fitness of the solution is the sum of values of all objects in the knapsack if the representation is valid, or 0 otherwise.

Intuitively, the additivity property says that the probability assigned to the union of two disjoint events by the measure should be the sum of the probabilities of the events, e. g. the value assigned to " 1 or 2 " in a throw of a die should be the sum of the values assigned to " 1 " and " 2 ".

* the sum of all the function values at x is 1, i. e.,.

Sometimes, the requirement is not as strict: the sum of all the function values at a particular point is only required to be positive rather than a fixed number for all points in the space

The sum of all these values will give the standard enthalpy of formation of sodium chloride.

In numerical analysis, a quadrature rule is an approximation of the definite integral of a function, usually stated as a weighted sum of function values at specified points within the domain of integration.

An integer sequence is called a complete sequence if every positive integer can be expressed as a sum of values in the sequence, using each value at most once.

* If it is required to use a single number X as an estimate for the value of numbers, then the arithmetic mean does this best, in the sense of minimizing the sum of squares ( x < sub > i </ sub > − X )< sup > 2 </ sup > of the residuals.

Therefore no complete system, i. e. including the electromagnetic modes, can have negative temperatures, since there is no highest energy state, so that the sum of the probabilities of the states would diverge for negative temperatures.

After describing the manifestation of the Gospel in the Ogdoad and Hebdomad, he adds that the Basilidians have a long account of the innumerable creations and powers in the several ' stages ' of the upper world ( diastemata ), in which they speak of 365 heavens and say that " their great archon " is Abrasax, because his name contains the number 365, the number of the days in the year ; i. e. the sum of the numbers denoted by the Greek letters in ΑΒΡΑΣΑΞ according to the rules of isopsephy is 365:

This shows in particular that is a natural number for any natural numbers n and k. There are many other combinatorial interpretations of binomial coefficients ( counting problems for which the answer is given by a binomial coefficient expression ), for instance the number of words formed of n bits ( digits 0 or 1 ) whose sum is k is given by, while the number of ways to write where every a < sub > i </ sub > is a nonnegative integer is given by.

# for each line, the number of products ( i. e. the sum of the coefficients ) is equal to.

The reflected light being the sum of the incoming light ( L < sub > i </ sub >) from all directions, multiplied by the surface reflection and incoming angle.

Microeconomics theory considers the aggregates ( the sum of ) of quantity demanded by buyers and quantity supplied by sellers, studying each possible price per unit ( i. e. supply and demand ).

For N interacting particles, i. e. particles which interact mutually and constitute a many-body situation, the potential energy function V is not simply a sum of the separate potentials ( and certainly not a product, as this is dimensionally incorrect ).

For non-interacting particles, i. e. particles which do not interact mutually and move independently, the potential of the system is the sum of the separate potential energy for each particle, that is

If R is the direct sum of the rings R < sub > 1 </ sub >,..., R < sub > n </ sub >, then the identity elements of the rings R < sub > i </ sub > are central idempotents in R, pairwise orthogonal, and their sum is 1.

If a decomposition exists with each c < sub > i </ sub > a centrally primitive idempotent, then R is a direct sum of the corner rings c < sub > i </ sub > Rc < sub > i </ sub >, each of which is ring irreducible.

* ( the sum of zero items, i. e., the summation of the empty set )

In particular, solutions can be expressed as the sum of a uniform flow ( i. e. a steady flow equal to the free stream velocity ) plus a free vortex flow, i. e. a circular flow around the airfoil with the speed inversely proportional to the radius.

Every ordered field is a formally real field, i. e., 0 cannot be written as a sum of nonzero squares.

Thus each polynomial is actually equal to the sum of the terms used in its formal expression, if such a term a < sub > i </ sub > X < sup > i </ sup > is interpreted as a polynomial that has zero coefficients at all powers of X other than X < sup > i </ sup >.

Equivalently, a perfect number is a number that is half the sum of all of its positive divisors ( including itself ) i. e. σ < sub > 1 </ sub >( n ) = 2n.

generated R-module, then is a direct sum of cyclic modules, i. e., modules with one generator.