and General Motors and Du Pont were to be ordered to terminate any agreement that provided for the purchase by General Motors of any specified percentage of its requirements of any Du Pont manufactured product, or for the grant of exclusive patent rights, or for a grant by General Motors to Du Pont of a preferential right to make or sell any chemical discovery of General Motors, or for the maintenance of any joint commercial enterprise by the two companies.

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 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 >.

In the Euclidean plane, the angle θ between two vectors u and v is related to their dot product and their lengths by the formula

Ada Lovelace reported in her notes on the Analytical Engine: " Mr. Babbage believes he can, by his engine, form the product of two numbers, each containing twenty figures, in three minutes ".

The following year the Amiga product line was expanded with the introduction of two new models: the Amiga 2000 for high-end graphics and business use, and the Amiga 500 for home use.

These two product lines were the very first acrylic emulsion artists paints.

It is not known whether a pair of coprime amicable numbers exists, though if any does, the product of the two must be greater than 10 < sup > 67 </ sup >.

It is so called because the inner product ( or dot product ) of two states is denoted by a bra | c | ket ;

The inner product of two vectors is a complex number.

Bra-ket notation splits this inner product ( also called a " bracket ") into two pieces, the " bra " and the " ket ":

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.

If is a ket in V and is a ket in W, the direct product of the two kets is a ket in.

In quantum mechanics it often occurs that little or no information about the inner product of two arbitrary ( state ) kets is present, while it is possible to say something about the expansion coefficients and of those vectors with respect to a chosen ( orthonormalized ) basis.

are just different notations for expressing an inner product between two elements in a Hilbert space ( or for the first three, in any inner product space ).

* Measure algebra: A Banach algebra consisting of all Radon measures on some locally compact group, where the product of two measures is given by convolution.

These categories surely have some objects that are " special " in a certain way, such as the empty set or the product of two topologies, yet in the definition of a category, objects are considered to be atomic, i. e., we do not know whether an object A is a set, a topology, or any other abstract concept – hence, the challenge is to define special objects without referring to the internal structure of those objects.

Within chemical engineering, two broad subgroups include 1 ) design, manufacture, and operation of plants and machinery in industrial chemical and related processes (" chemical process engineers "); and 2 ) development of new or adapted substances for products ranging from foods and beverages to cosmetics to cleaners to pharmaceutical ingredients, among many other products (" chemical product engineers ").

Then the previous expression is equal to the product of two factors:

When this happens, the limit of the product of these two factors will equal the product of the limits of the factors.

The dot product of the two vector quantities ( A and J ) is a scalar that represents the electric current.

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.

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 ".