If man is actually the product of his environment and if science can discover the laws of human nature and the ways in which environment determines what people do, then someone -- a someone probably standing outside traditional systems of values -- can turn around and develop completely efficient means for controlling people.

Another recent achievement was the successful development of a method for the complete combustion in a bomb calorimeter of a metal in fluorine when the product is relatively non-volatile.

Average consumer is becoming more sophisticated regarding product and advertising claims, partly because of widespread criticism of such assertions.

Too often it is thought of at the last moment of new product introduction.

On the other hand, the process of obsoleting an old product and introducing the new one is usually mighty expensive.

In the absence of additions to the homogenate, the product formed is an iodinated particulate protein ( Fawcett and Kirkwood, 1953 ; ;

In the notation of the proof of Theorem 12, let us take a look at the special case in which the minimal polynomial for T is a product of first-degree polynomials, i.e., the case in which each Af is of the form Af.

The industry with which this model is concerned is a basic industry, producing a substantial share of gross national product.

In any given time period, the aggregate demand for the industry's product is determined by two things: the price charged by the industry, and the level of Aj.

The form of the industry demand function is one which makes quantity demanded vary inversely with the product price, and vary directly with the level of Aj.

second, that both actual and pending desegregation is, with few exceptions, the product or result of court order.

Though it is not easy to apply the evidence of the Iliad to any specific era, this marvelous product of the epic tradition had certainly taken definitive shape by 750.

The objective of complete sterilization of foods is to produce a wholesome and palatable product capable of being stored without refrigeration for extended periods of time.

The luminous gain of a single stage with Af ( flux gain ) is, to a first approximation, given by the product of the photocathode sensitivity S ( amp / lumen ), the anode potential V ( volts ), and the phosphor conversion efficiency P ( lumen/watt ).

An optimal policy is one which in some sense gets the best out of the process as a whole by maximizing the value of the product.

The objective function, which is to be maximized, is some function, usually piecewise continuous, of the product state.

If T is the total `` length '' of the process, its feed state may be denoted by a vector p(T) and the product state by p(Q).

Lagrange's law says that its velocity is equal to the square root of the product of the depth times the acceleration due to gravity.

The charge that the federal indictment of three Chicago narcotics detail detectives `` is the product of rumor, combined with malice, and individual enmity '' on the part of the federal narcotics unit here was made yesterday in their conspiracy trial before Judge Joseph Sam Perry in federal District court.

Outside the United States, the product is often called bitumen.

In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that " the product of a collection of non-empty sets is non-empty ".

The matrix multiplication | product of a Boolean function and a Walsh matrix is its Walsh spectrum :( 1, 0, 1, 0, 0, 1, 1, 0 ) * H ( 8 ) = ( 4, 2, 0 ,− 2, 0, 2, 0, 2 )

The dual canonical forms of any Boolean function are a " sum of minterms " and a " product of maxterms.

In Boolean logic, an implicant is a " covering " ( sum term or product term ) of one or more minterms in a sum of products ( or maxterms in a product of sums ) of a boolean function.

Formally, a product term P in a sum of products is an implicant of the Boolean function F if P implies F. More precisely:

More precisely, for any cardinal κ, there is a complete Boolean algebra of cardinality 2 < sup > κ </ sup > greater than κ that is generated as a complete Boolean algebra by a countable subset ; for example the Boolean algebra of regular open sets in the product space κ < sup > ω </ sup >, where κ has the discrete topology.

In Boolean logic, a product term is a conjunction of literals, where each literal is

Second, even if the characteristic polynomial factors completely over F into a product of polynomials of degree 1, there may not be enough characteristic vectors for T to span the space V.

Many theorems which are provable using choice are of an elegant general character: every ideal in a ring is contained in a maximal ideal, every vector space has a basis, and every product of compact spaces is compact.

To define angles in an abstract real inner product space, we replace the Euclidean dot product ( · ) by the inner product, i. e.

In a complex inner product space, the expression for the cosine above may give non-real values, so it is replaced with

The tensor product X ⊗ Y from X and Y is a K-vector space Z with a bilinear function T: X × Y → Z which has the following universal property: If T ′: X × Y → Z ′ is any bilinear function into a K-vector space Z ′, then only one linear function f: Z → Z ′ with exists.

Every Hilbert space X is a Banach space because, by definition, a Hilbert space is complete with respect to the norm associated with its inner product, where a norm and an inner product are said to be associated if for all x ∈ X.

A necessary and sufficient condition for a Banach space X to be associated to an inner product ( which will then necessarily make X into a Hilbert space ) is the parallelogram identity:

If the norm of a Banach space satisfies this identity, the associated inner product which makes it into a Hilbert space is given by the polarization identity.

whereas if X is a complex Banach space, then the polarization identity is given by ( assuming that scalar product is linear in first argument ):

Note that if we regard the product as a vector space, then B is not a linear transformation of vector spaces ( unless or ) because, for example.

For a finite-dimensional vector space, using a fixed orthonormal basis, the inner product can be written as a matrix multiplication of a row vector with a column vector:

For a finite-dimensional vector space, the outer product can be understood as simple matrix multiplication:

Two Hilbert spaces V and W may form a third space by a tensor product.

If a system is composed of two subsystems described in V and W respectively, then the Hilbert space of the entire system is the tensor product of the two spaces.

Consider a complete orthonormal system ( basis ),, for a Hilbert space H, with respect to the norm from an inner product.