हाइपर्स इसके अंग्रेजी अर्थ का उदाहरण

Cefotaxime is contraindicated in patients with a known hypersensitivity to cefotaxime or other cephalosporins.

upper] hemicontinuous if and only if the mapping \Gamma : A \to Pis continuous where the hyperspace Phas been endowed with the lower [resp.

(For the notion of hyperspace compare also power set and function space).

J(n,k) forms the graph of vertices and edges of an (n"nbsp;−"nbsp;1)-dimensional polytope, called a hypersimplex.

In the plant Arabidopsis thaliana, mutant strains defective in genes necessary for recombination during meiosis and mitosis are hypersensitive to killing by mitomycin C.

In supersonic and hypersonic flows rarefaction is characterized by Tsien's parameter, which is equivalent to the product of Knudsen number and Mach number (KnM) or M^2/Re, where Re is the Reynolds number.

For example, the Bombieri–Lang conjecture predicts that a smooth hypersurface of degree d in projective space Pn over a number field does not have Zariski dense rational points if d ≥ n + 2.

In the case of a hypersurface X of degree d in Pn over a number field, there are good results when d is much smaller than n, often based on the Hardy–Littlewood circle method.

For example, the Hasse–Minkowski theorem says that the Hasse principle holds for quadric hypersurfaces over a number field (the case d 2).

Christopher Hooley proved the Hasse principle for smooth cubic hypersurfaces in Pn over Q when n ≥ 8.

More generally, Birch's theorem says that for any odd positive integer d, there is an integer N such that for all n ≥ N, every hypersurface of degree d in Pn over Q has a rational point.

For hypersurfaces of smaller dimension (in terms of their degree), things can be more complicated.

For example, extending work of Beniamino Segre and Yuri Manin, János Kollár showed: for a cubic hypersurface X of dimension at least 2 over a perfect field k with X not a cone, X is unirational over k if it has a k-rational point.