Here, for the case of squares inscribed in plane curves, we remove the restriction to convexity and give certain other results.

Generalizations of Bézier curves to higher dimensions are called Bézier surfaces, of which the Bézier triangle is a special case.

Ellipses are closed curves and are the bounded case of the conic sections, the curves that result from the intersection of a circular cone and a plane that does not pass through its apex ; the other two ( open and unbounded ) cases are parabolas and hyperbolas.

In this case, with perfect competition in the output market the long-run equilibrium will involve all firms operating at the minimum point of their long-run average cost curves ( i. e., at the borderline between economies and diseconomies of scale ).

In algebraic geometry, the parabola is generalized by the rational normal curves, which have coordinates the standard parabola is the case and the case is known as the twisted cubic.

These new PowerBooks took design cues from the 500 series PowerBook, sporting dramatic curves and a jet-black plastic case.

As in the case of curves in two dimensions, the curvature of a regular space curve C in three dimensions ( and higher ) is the magnitude of the acceleration of a particle moving with unit speed along a curve.

Light curves can be periodic, as in the case of eclipsing binaries, Cepheid variables, other periodic variables, and transiting extrasolar planets, or aperiodic, like the light curve of a nova, a cataclysmic variable star, a supernova or a microlensing event.

Monge's paper gives the ordinary differential equation of the curves of curvature, and establishes the general theory in a very satisfactory manner ; the application to the interesting particular case of the ellipsoid was first made by him in a later paper in 1795.

Solutions to variational problems, such as the brachistochrone and tautochrone questions, introduced properties of curves in new ways ( in this case, the cycloid ).

However, in the case of algebraic curves it is very common not to restrict the curve to having points only defined over the real numbers.

k gives us the above case of nonsingular affine curves.

* The special case where one of the curves is a line can be derived from the fundamental theorem of algebra.

Global L-functions can be associated to elliptic curves, number fields ( in which case they are called Dedekind zeta-functions ), Maass forms, and Dirichlet characters ( in which case they are called Dirichlet L-functions ).

The normal vector space or normal space of a manifold at a point P is the set of the vectors which are orthogonal to the tangent space at P. In the case of differential curves, the curvature vector is a normal vector of special interest.

The case of elliptic curves with complex multiplication was proved by Shimura in 1964.

In case circular arc primitives are not supported in a particular environment, they may be approximated by Bézier curves.

Here he supervised the PhD of Andrew Wiles, and together they proved a partial case of the Birch and Swinnerton-Dyer conjecture for elliptic curves with complex multiplication.

They used additional structures: in the case of the field of rational numbers they use roots of unity in the case of imaginary quadratic extensions of the field of rational numbers they use elliptic curves with complex multiplication and their points of finite order.

The Weil conjectures in the special case of algebraic curves were conjectured by.

New Orleans had a notorious red-light district extending over twenty-eight city blocks, and the business-minded mayor of the city journeyed to Washington to present the case for `` the God-given right of men to be men ''.

Besides the lack of an adequate ethical dimension to the Governor's case, one can ask seriously whether our lead over the Russians in quality and quantity of nuclear weapons is so slight as to make the tests absolutely necessary.

Skopas expressed no curiosity over the case, offered no expression of sympathy, made no move to escort McFeely to the door.

By making inroads in the name of law enforcement into the protection which Congress has afforded to the marriage relationship, the Court today continues in the path charted by the recent decision in Wyatt v. United States, 362 U.S. 525, where the Court held that, under the circumstances of that case, a wife could be compelled to testify against her husband over her objection.

But if true, it was the case of which he had dreamed, the case which would throw him into headlines all over America as the hero of a great murder trial.

In any case, he refused to accept the implications of the analysis, that he needed to be made over.

Under the 1939 Code this item was permitted to survive a tax-free reorganization in the Stanton Brewery case, but only over the dissent of Judge Learned Hand, who wrote the majority opinion in the Sansome case, a leading case requiring carryover of earnings and profits in a non-taxable reorganization.

In any case, anyone who fails to make significant distinction between primary and secondary applications of economic pressure would in principle already have justified that use of economic boycott as a means which broke out a few years ago or was skillfully organized by White Citizens' Councils in the entire state of Mississippi against every local Philco dealer in that state, in protest against a Philco-sponsored program over a national TV network on which was presented a drama showing, it seemed, a `` high yellow gal '' smooching with a white man.

does not carry over to the unbalanced case.

The highest state court, generally known as the Supreme Court, exercises discretion over whether it will review the case.

The first assumption is that in the case where the background is opaque ( i. e. ), the over operator represents the convex combination of and:

In 2002, O ' Donohue launched a court action that argued the Act of Settlement violates the Canadian Charter of Rights and Freedoms, but the case was dismissed by the court, which found that, as the Act of Settlement is part of the Canadian constitution, the Charter of Rights and Freedoms does not have supremacy over it.

The Tokyo Convention states in Article 11, defining the so-called unlawful takeover of an aircraft, that the parties signing the agreement are obliged, in case of hijacking or a threat of it, to take all the necessary measures in order to regain or keep control over an aircraft.

If a is algebraic over K, then K, the set of all polynomials in a with coefficients in K, is not only a ring but a field: an algebraic extension of K which has finite degree over K. In the special case where K = Q is the field of rational numbers, Q is an example of an algebraic number field.

Again a classic of Renaissance literature was the basis of the libretto by Boccherini, in this case a comic mock-epic by Tassoni, in which a war between Modena and Bologna ensues over a stolen bucket.

The primary benefits over rifled barrels is reduced barrel wear, longer ranges that can be achieved ( due to the reduced loss of energy to friction and gas escaping around the projectile via the rifling ) and larger explosive cores for a given caliber artillery due to less metal needing to be used to form the case of the projectile because of less force applied to the shell from the non-rifled sides of the barrel of smooth bore guns.

In this case, a separate source ( a deuterium lamp ) with broad emission is used to measure the background absorption over the entire width of the exit slit of the spectrometer.

Extreme cases like Mira undergo large swings over hundreds of days ; Arcturus is not very red and is a borderline case between variability and stability with its short period and tiny range.

ASCII included the distinction of upper and lower case alphabets and a set of control characters to facilitate the transmission of written language as well as printing device functions, such as page advance and line feed, and the physical or logical control of data flow over the transmission media.

Often, this is the case with a large bridge that serves as an entrance to a city, or crosses over a main harbor entrance.

Chiefs and other leaders preside over customary, traditional courts, though all persons have the right to request that their case be considered under the formal British-based legal system.