Sentence examples for exists a double from inspiring English sources

Then there exists a double sequence (y= y_{mn})in mathcal{M}_{u}) with relation (1.2) that there exists a positive real number (M>0) such that (sup_{m,ninmathbb {N}}|y_{mn}|leq M).

According to the property that the functions from (2.19) are dense in, it follows, for instance, that for any, there exists a double sequence such that in the sense of the canonically induced -norm: (2.20).

Inversely, given two complex numbers g 2 and g 3 such that Δ ( g 2, g 3 ) ≠ 0, then there exists a double period 2 ω 1, 2 ω 2 Weierstrass elliptic function ℘ ( z ) such that the above relations hold.

In order to show that the inclusions are strict, we should show that the sets (B(mathcal{C}_{f})setminusmathcal{C}_{f}) and (B(mathcal {C}_{f_{0}})setminusmathcal{C}_{f_{0}}) are not empty, that is, there exists a double sequence (x=(x_{mn})) which belongs to (B(mathcal {C}_{f})) but not in (mathcal{C}_{f}).

In "Down and Out in Paris and London" he described how French grandeur existed a double-door away from kitchens in which filth ran "like the intestines through a man's body".

for all, then there exists a unique double quadratic centralizer on satisfying (2.5).

Furthermore, since (uinDelta_{2}), we can easily check that there exists a reverse doubling constant (D=D u)>1) independent of Q such that (see Lemma 4.1 in [10]) u(2Q geq Dcdot u(Q),quad mbox{for any cube } Qsubsetmathbb {R}^{n}, which implies that, for any (jinmathbb {Z}^), (u(2^{j+1}Q geq D^{j+1}cdot u(Q)) by iteration.

Let S be a surface of general type with invariants (K_S^2 = 6), (p_g =q = 1) such that there exists an unramified double cover ( hat{S} rightarrow S) with ( q ( hat{S} ) = 3), and such that the Albanese morphism ( hat{alpha } : hat{S} rightarrow A) is birational onto it image Z, a divisor in A with ( Z^3 = 12).

There exists a good linear double-logarithm relation between the Raman signal and the KCN concentration in water in the range from 0.1 ppb to 1 ppm.

I have no idea who would be cold-blooded (or in fact rational) enough to buy this, but it exists: A cabinet that doubles as a coffin [JP] when the owner or anybody else needs one.

Then there exists a relation between the double EC coefficient row vector E ( x, y ) and ( i + j ) th-order partial derivatives of the vector E ( i, j ) ( x, y ) of size 1 × ( m + 1 ) ( n + 1 ) as E ( i, j ) ( x, y ) = E ( x, y ) ( D x ) i ( D y ) j, (2.17).