Sentence examples for cups c from inspiring English sources

Suppose that the distinct cups c and c′ are perceptually indistinguishable from each other.

Then (C rightarrow D ) is birational, (f^* (D) = C cup (C + t)).

Cup A = Black Logo1 mug; Cup B = Black Logo2 mug; Cup C = Green Decorative mug; Cup D = Yellow Decorative mug; Cup E = Red Decorative mug; Cup F = Glass Cup.

Note that the algorithm works linearly with attributes within a tuple, producing a set of candidates (t'_j)s that satisfies (Sigma (mathcal{C} cup C) = {phi : X rightarrow A mid (X cup A) subseteq (mathcal{C} cup C) }), where (mathcal{C}) is the attribute that has already been fixed and C is the attribute on which the algorithm has just produced the candidates.

Fig. 2 The original images for fusion, a Infrared image of Cup, b Visible image of Cup, c Infrared image of Yard d Visible image of Yard.

We have added the case of (v'=mathtt{NULL}), so NULL is selected when all values in (texttt {dom}(C)) fail to satisfy (Sigma (mathcal{C} cup C)).

There exist a smooth complex projective surface X and (a,b,c in H^1 XX, {mathbb {Z}}/l)) such that ( a cup b = b cup c = 0,) but (langle {a,b,c}rangle ne 0).

Let X be a topological space, and let (a,b,c in H^i X, R)) be cohomology classes such that begin{aligned} a cup b = b cup c = 0, end{aligned}where R is any ring of coefficients.

(i) There exist a smooth complex projective surface X and (a,b,c in H^1 XX, {mathbb {Z}}/l)) such that ( a cup b = b cup c = 0,) but (langle {a,b,c}rangle ne 0).   (ii) Let (X rightarrow {mathbb {P}}^6) be an embedding and let Y be the blow up of ({mathbb {P}}^6) along X.

To summarize, the overall picture regarding inclusions among the already existing spaces c, S, (S_{alpha}), (S^{f}) and the newly introduced space (S_{alpha}^{f}) is as shown below: textstylebegin{array}c@{quad}c@{quad}c@{quad}c@{quad}c@ & & S^{f} & subset& S & & cup& & cup c & subset& S_{alpha}^{f}& subset& S_{alpha} end{array}.

Keep it simple: "In future, I would appreciate it if you could wash your own coffee cup". C stands for Consequences.