On the following pages, each of the major commercial foamed plastics is described in detail, as to properties, applications, and methods of processing.

In this sense, the electrons have the following properties:

Area can be defined as a function from a collection M of special kind of plane figures ( termed measurable sets ) to the set of real numbers which satisfies the following properties:

With regard to historic properties ( those properties that are listed or that are eligible for listing in the National Register of Historic Places, or properties designated as historic under State or local law ), those facilities must still comply with the provisions of Title III of the ADA to the " maximum extent feasible " but if following the usual standards would " threaten to destroy the historic significance of a feature of the building " then alternative standards may be used.

Certain natural substances are reputed to have anxiolytic properties, including the following:

* James ` s Theorem For a Banach space the following two properties are equivalent:

A Banach *- algebra A is a Banach algebra over the field of complex numbers, together with a map *: A → A called involution which has the following properties:

Morphisms can have any of the following properties.

such that the following two properties hold:

Each Chaitin constant Ω has the following properties:

The collection of convex subsets of a vector space has the following properties:

A clerihew has the following properties:

The map * has the following properties:

The commutator has the following properties:

The following properties can all be derived from the ordinary differentiation rules of calculus.

While there is no single definition of a distributed system, the following defining properties are commonly used:

Other typical properties of distributed systems include the following:

This example video has the following properties:

Hence the three defining properties of equivalence relations can be proved mutually independent by the following three examples:

We then assume that the following three conditions hold for all positive properties ( which can be summarized by saying " the positive properties form a principal ultrafilter "):

and < sup >− 1 </ sup > have the following axiomatic properties.

A function f: X → Y between two topological spaces ( X, T < sub > X </ sub >) and ( Y, T < sub > Y </ sub >) is called a homeomorphism if it has the following properties:

In the following example, a program has defined two data items which are adjacent in memory: an 8-byte-long string buffer, A, and a two-byte integer, B.

On the other hand, for integer order α, the following relationship is valid ( note that the Gamma function becomes infinite for negative integer arguments ):

When α is an integer, moreover, as was similarly the case for the functions of the first kind, the following relationship is valid:

The following relationships are valid, whether α is an integer or not:

A real number a is said to be computable if it can be approximated by some computable function in the following manner: given any integer, the function produces an integer k such that:

Then, for any given sequence of integers a < sub > 1 </ sub >, a < sub > 2 </ sub >, …, a < sub > k </ sub >, there exists an integer x solving the following system of simultaneous congruences.

Using the following observation, one can create a recursive algorithm that computes x < sup > n </ sup > for an integer n using squaring and multiplication:

In mathematics, the Fibonacci numbers or Fibonacci series or Fibonacci sequence are the numbers in the following integer sequence:

For the convenience of the reader, the formula given above is based on Chapront's latest parameters and expressed with a single integer variable, and the following additional terms have been added:

In the following table, n is the value of the header byte as a signed integer.

Consider the following operation on an arbitrary positive integer:

The Julian day number can be calculated using the following formulas ( integer division is used exclusively, that is, the remainder of all divisions are dropped ):

The routine in the following example written in Eiffel takes as an argument an integer which must be a valid value for an hour of the day, i. e., 0 through 23, inclusively.

Informally it solves the following problem: Given an integer N, find its prime factors.

The necessary conditions can be stated as following: if a Gaussian integer is a Gaussian prime, then either its norm is a prime number, or its norm is a square of a prime number.

In mathematics and computer science, the floor and ceiling functions map a real number to the largest previous or the smallest following integer, respectively.

: 3 ) For every compact set K ⊂ D there exists a constant C such that for every x ∈ K and every non-negative integer k the following bound holds:

This is followed by a 32-bit unsigned integer ( all integers in IFF files ' structure are big-endian ) specifying the size of the following data ( the chunk content ) in bytes.

The following are equivalent definitions of an algebraic integer.

In Haskell, the following line defines an algebraic data type that has a single data constructor that wraps an integer and a string.

Concerning the observables, and states | v ), we get a representation U ( a, L ) of Poincaré group, on integer spin subspaces, and U ( a, A ) of the inhomogeneous SL ( 2, C ) on half-odd-integer subspaces, which acts according to the following interpretation:

* Frobenius also has proved the following fundamental theorem: If a positive integer n divides the order | G | of a finite group G, then the number of solutions of the equation x < sup > n </ sup > = 1 in G is equal to kn for some positive integer k. He also posed the following problem: If, in the above theorem, k = 1, then the solutions of the equation x < sup > n </ sup > = 1 in G form a subgroup.