A nuclear pacifier of these dimensions -- roughly some six and a half times bigger than anything the United States has triggered experimentally -- would certainly produce a bigger bang, and, just for kicks, Khrushchev might use it to propel the seminar of the house of delegates from St. Louis to the moon, where there wouldn't even be any beer to drink.

No generalization of these results to spaces of more than three dimensions has so far been found possible.

The dimensions of these waves dwarf all our usual standards of measurement.

Neutrons and protons have comparable dimensions — on the order of — although the ' surface ' of these particles is not sharply defined.

Of these 23, only three, amongst them Brazil, had dimensions politics to justify its creation, as for example, territorial extension and trained and structuralized Armed Forces.

The following may be applied to individual dimensions of multidimensional data, after transformation, although some of these involve their own implicit transformation of the data.

The geometric interpretation of curl as rotation corresponds to identifying bivectors ( 2-vectors ) in 3 dimensions with the special orthogonal Lie algebra so ( 3 ) of infinitesimal rotations ( in coordinates, skew-symmetric 3 × 3 matrices ), while representing rotations by vectors corresponds to identifying 1-vectors ( equivalently, 2-vectors ) and so ( 3 ), these all being 3-dimensional spaces.

" From these principles and some additional constraints —( 1a ) a lower bound on the linear dimensions of any of the parts, ( 1b ) an upper bound on speed of propagation ( the velocity of light ), ( 2 ) discrete progress of the machine, and ( 3 ) deterministic behavior — he produces a theorem that " What can be calculated by a device satisfying principles I – IV is computable.

A drill-across works by grouping ( summarizing ) the data along the keys of the ( shared ) conformed dimensions of each fact participating in the " drill across " followed by a join on the keys of these grouped ( summarized ) facts.

There is no need for higher order derivatives in the equation, nor for time dependence in v ( x ) because these can be eliminated by considering systems of higher dimensions.

In mathematics, Euclidean space is the Euclidean plane and three-dimensional space of Euclidean geometry, as well as the generalizations of these notions to higher dimensions.

One point agreed on is that fractal patterns are characterized by fractal dimensions, but whereas these numbers quantify complexity ( i. e., changing detail with changing scale ), they neither uniquely describe nor specify details of how to construct particular fractal patterns.

It would be impossible to discriminate these events from the background of neutrinos, since the dimensions of the required neutrino shield would ensure collapse into a black hole.

Rushton argues that East Asians and their descendants average a larger brain size, greater intelligence, more sexual restraint, slower rates of maturation, and greater law abidingness and social organization than do Europeans and their descendants, who average higher scores on these dimensions than Africans and their descendants.

Thus, although the joule has the same dimensions as the newton-metre ( 1 J = 1 N · m = 1 kg · m < sup > 2 </ sup >· s < sup >− 2 </ sup >), these units are not interchangeable as the newton-metre ( N · m ) is the unit of torque and joule the unit of energy.

with R < sub > AB </ sub > the five-dimensional Ricci curvature, may be re-expressed so that in four dimensions, these solutions satisfy Einstein's equations

The surface of these grooves can be atomically smooth if the etch is carried out correctly, with dimensions and angles being extremely accurate.

In these contexts, parallel universes are also called " alternative universes ", " quantum universes ", " interpenetrating dimensions ", " parallel dimensions ", " parallel worlds ", " alternative realities ", " alternative timelines ", and " dimensional planes ," among others.

In these uses, the nanometre appears to be supplanting the other common unit for atomic scale dimensions, the angstrom, which is equal to 0. 1 nanometre.

The rotation to do this in three dimensions requires three numbers to uniquely determine ; traditionally these are expressed as three angles.

Many of these people demonstrate a trend in dimensions of their personalities.

The sole surviving protagonist in Operation Counterstrike is the player, who must advance, starting each of the four episodes from a human held but overrun military base, before fighting through into other dimensions, traversing these via slipgate or their otherworld equivalent.

The thinking was that out of these five candidate theories, only one was the actual correct theory of everything, and that theory was the one whose low energy limit, with ten spacetime dimensions compactified down to four, matched the physics observed in our world today.

In physics and all science, dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions.

It is also used to form reasonable hypotheses about complex physical situations that can be tested by experiment or by more developed theories of the phenomena, and to categorize types of physical quantities and units based on their relations to or dependence on other units, or their dimensions if any.

The seven base quantities of the International System of Quantities ( ISQ ) and their corresponding SI units and dimensions are listed in the following table.

The SI base quantities form a set of mutually independent dimensions as required by dimensional analysis commonly employed in science and technology.

Let the quantities u and v be the horizontal and vertical components of the velocity field of a steady incompressible, irrotational flow in two dimensions.

Dimensionless quantities are often defined as products or ratios of quantities that are not dimensionless, but whose dimensions cancel out when their powers are multiplied.

It is defined as change in length over initial length but, since these quantities both have dimensions L ( length ), the result is a dimensionless quantity.

* The ratio of two quantities with the same dimensions is dimensionless, and has the same value regardless of the units used to calculate them.

Another consequence of the Buckingham π theorem of dimensional analysis is that the functional dependence between a certain number ( say, n ) of variables can be reduced by the number ( say, k ) of independent dimensions occurring in those variables to give a set of p = n − k independent, dimensionless quantities.

The matrix can be interpreted as taking in a combination of the dimensional quantities and giving out the dimensions of this product.

There are other relationships between physical quantities which can be expressed by means of fundamental constants, and to some extent it is an arbitrary decision whether to retain the fundamental constant as a quantity with dimensions or simply to define it as unity or a fixed dimensionless number, and reduce the number of fundamental constants by one.

In theory, a system of fundamental quantities ( or sometimes fundamental dimensions ) would be such that every other physical quantity ( or dimension of physical quantity ) can be generated from them.

* 1822 – Joseph Fourier formally introduces the use of dimensions for physical quantities in his Théorie Analytique de la Chaleur

In practice they are used interchangeably ; to prevent duplication of quantities and reduce the number of dimensions of related quantities.

For example, in The Theory of Political Economy, Chapter II, the subsection on " Theory of Dimensions of Economic Quantities ", Jevons makes the statement that " In the first place, pleasure and pain must be regarded as measured upon the same scale, and as having, therefore, the same dimensions, being quantities of the same kind, which can be added and subtraced ...." Speaking of measurement, addition, and subtraction requires cardinality, as does Jevons ' heavy use of integral calculus.

* 1822-Joseph Fourier formally introduces the use of dimensions for physical quantities in his Theorie Analytique de la Chaleur.

Here is a table collecting some important physical quantities according to their dimensions in geometrized units.

Some quantities are such by their inner nature ( as number ), while others are functioning as states ( properties, dimensions, attributes ) of things such as heavy and light, long and short, broad and narrow, small and great, or much and little.

Its progress is chiefly achieved due to rendering the abstract qualities of material entities into physical quantities, by postulating that all material bodies marked by quantitative properties or physical dimensions, which are subject to some measurements and observations.

Simply put, the six quantities D and L correspond to the six conserved angular momenta in four dimensions, associated with the six possible simple rotations in that space ( there are six ways of choosing two axes from four ).

By dimensional analysis these quantities are the ratio of a stock ( with dimensions of Currency ) by a flow ( with dimensions of Currency / Time ), so they have dimensions of Time.