To their leaders the Constitution was a compact made by the people of sovereign states, who therefore retained the right to secede from it.

The champions of the Union maintained that the Constitution had formed, fundamentally, the united people of America, that it was a compact among sovereign citizens rather than states, and that therefore the states had no right to secede, though the citizens could.

To hold 'em in a compact mass was `` close herdin' ''.

However, the idea that electrons might revolve around a compact nucleus with definite angular momentum was convincingly argued at least 19 years earlier by Niels Bohr, and the Japanese physicist Hantaro Nagaoka published an orbit-based hypothesis for electronic behavior as early as 1904.

The Athlon XP-M was also offered in a compact microPGA socket 563 version for space constrained applications as an alternative to the larger Socket A.

RAT-A, RAT-B and RAT-C. RAT-A and RAT-B was a program to develop a compact and economical stand-off ASW for smaller warships, but was found to be either unreliable or had too short a range.

This design was further refined and made much more compact as the D84 machine which was completed in 1965.

During this period, a method of manufacturing many interconnected transistors in a compact space was developed.

It could be opened flat at any page, allowing easier reading ; the pages could be written on both front and back ( recto and verso ); and the codex, protected within its durable covers, was more compact and easier to transport.

The term compact was introduced into mathematics by Maurice Fréchet in 1906 as a distillation of this concept.

An example of this phenomenon is Dirichlet's theorem, to which it was originally applied by Heine, that a continuous function on a compact interval is uniformly continuous: here continuity is a local property of the function, and uniform continuity the corresponding global property.

Rather than the original 20 cm size, the diameter of this compact disc was set at 11. 5 cm, the diagonal measurement of a compact cassette.

The Springald's frame was more compact, allowing for use inside tighter confines, such as the inside of a castle or tower.

The Casio Computer Company, in Japan, released the Model 14-A calculator in 1957, which was the world's first all-electric ( relatively ) " compact " calculator.

Although officially classified as a torpedo boat in 1898 by the US Navy, the, a long all steel vessel displacing 165 tons, was described by her commander, LT. John C. Fremont, as "... a compact mass of machinery not meant to keep the sea nor to live in ... as five sevenths of the ship are taken up by machinery and fuel, whilst the remaining two sevenths, fore and aft, are the crew's quarters ; officers forward and the men placed aft.

The matter was resolved with a compact between the states, ratified by U. S. Congress in 1834, which set the boundary line between them as the middle of the Hudson River and New York Harbor.

This was later confirmed by the U. S. Supreme Court in other cases which also expounded on the compact.

The dispute eventually reached the Supreme Court of the United States, which ruled in 1998 that New Jersey had jurisdiction over all portions of the island created after the original compact was approved ( effectively, more than 80 % of the island's present land ).

Forth became very popular in the 1980s because it was well suited to the small microcomputers of that time, as it is compact and portable.

The cover photo was different depending on what format was purchased ( LP, cassette, or compact disc ).

It was possible to predict the number of bases stacked within a single turn of the DNA helix ( 10 per turn ; a full turn of the helix is 27 angströms in the compact A form, 34 angströms in the wetter B form ).

* Corollary If X is a Banach space, then X is reflexive if and only if X ′ is reflexive, which is the case if and only if its unit ball is compact in the weak topology.

* If G is a locally compact Hausdorff topological group and μ its Haar measure, then the Banach space L < sup > 1 </ sup >( G ) of all μ-integrable functions on G becomes a Banach algebra under the convolution xy ( g ) = ∫ x ( h ) y ( h < sup >− 1 </ sup > g ) dμ ( h ) for x, y in L < sup > 1 </ sup >( G ).

The Bolzano – Weierstrass theorem gives an equivalent condition for sequential compactness when considering subsets of Euclidean space: a set then is compact if and only if it is closed and bounded.

* If the metric space X is compact and an open cover of X is given, then there exists a number such that every subset of X of diameter < δ is contained in some member of the cover.

Improvements since then have largely been better phosphors, longer life, and more consistent internal discharge, and easier-to-use shapes ( such as compact fluorescent lamps ).

The Paley – Wiener theorem immediately implies that if f is a nonzero distribution of compact support ( these include functions of compact support ), then its Fourier transform is never compactly supported.

Components could then be integrated and wired into a bidimensional or tridimensional compact grid.

When Volkswagen introduced a sliding side door on their van in 1968, it then had all the features that would later come to define a minivan: compact length, three rows of forward-facing seats, station wagon-style top-hinged tailgate / liftgate, sliding side door, passenger car base.

Bernstein and Robinson show that if is polynomially compact, then there is a hyperfinite index such that the matrix coefficient is infinitesimal.

Sagasta was then Prime Minister and he had made a compact with the Islanders to give them autonomy.

For compact space | compact 2-dimensional surfaces without boundary ( topology ) | boundary, if every loop can be continuously tightened to a point, then the surface is topologically Homeomorphism | homeomorphic to a 2-sphere ( usually just called a sphere ).

In 1958 Bing proved a weak version of the Poincaré conjecture: if every simple closed curve of a compact 3-manifold is contained in a 3-ball, then the manifold is homeomorphic to the 3-sphere .< ref > Bing also described some of the pitfalls in trying to prove the Poincaré conjecture.

For locally compact spaces an integration theory is then recovered.

In order then that the social compact may not be an empty formula, it tacitly includes the undertaking, which alone can give force to the rest, that whoever refuses to obey the general will shall be compelled to do so by the whole body.

An important fact about the weak * topology is the Banach – Alaoglu theorem: if X is normed, then the closed unit ball in X * is weak *- compact ( more generally, the polar in X * of a neighborhood of 0 in X is weak *- compact ).

If the convex hull of X is a closed set ( as happens, for instance, if X is a finite set or more generally a compact set ), then it is the intersection of all closed half-spaces containing X.

It can be shown as a consequence of the above properties that μ ( U ) > 0 for every non-empty open subset U. In particular, if G is compact then μ ( G ) is finite and positive, so we can uniquely specify a left Haar measure on G by adding the normalization condition μ ( G ) = 1.

Since then, the Kamov Design Bureau ( design office prefix Ka ) has specialised in compact helicopters of coaxial rotor design, suitable for naval

The technical statement is as follows: if M is a given m-dimensional Riemannian manifold ( analytic or of class C < sup > k </ sup >, 3 ≤ k ≤ ∞), then there exists a number n ( with n ≤ m ( 3m + 11 )/ 2 if M is a compact manifold, or n ≤ m ( m + 1 )( 3m + 11 )/ 2 if M is a non-compact manifold ) and an injective map ƒ: M → R < sup > n </ sup > ( also analytic or of class C < sup > k </ sup >) such that for every point p of M, the derivative dƒ < sub > p </ sub > is a linear map from the tangent space T < sub > p </ sub > M to R < sup > n </ sup > which is compatible with the given inner product on T < sub > p </ sub > M and the standard dot product of R < sup > n </ sup > in the following sense:

Equivalently, if X is a locally compact metric space, then ƒ is locally Lipschitz if and only if it is Lipschitz continuous on every compact subset of X.