Sentence examples for be an arbitrary mapping from inspiring English sources

Proof Let α : X → ( 0, 1 ] be an arbitrary mapping. Consider two fuzzy mappings S, T : X → F ( X ) defined by ( S x ) ( t ) = { α ( x ), if  t ∈ F x, 0, if  t ∉ F x. and ( T x ) ( t ) = { α ( x ), if  t ∈ G x, 0, if  t ∉ G x.

Let (alpha: X rightarrow 0, 1]) be an arbitrary mapping.

Let (j: Ito I) be an arbitrary mapping of the index set I into itself.

Let φ L : X → L ∖ { 0 L } be an arbitrary mapping.

Then there exists (x^{ast}) in (overline{B_{d_{lb}}(x_{0},r)}) such that (x^{ast}) is a common fixed point of R and G. Let (alpha: X rightarrow 0, 1]) be an arbitrary mapping.

Let w be a metric modular on X and X w be a modular metric space induced by w and T : X w → X w be an arbitrary mapping.

Let (T:Wsubseteq Xto X) is an arbitrary mapping.

The first mapping is an arbitrary mapping which does not respect the first rule devised in our solution, whereas the second mapping referred to as optimum mapping does.

A circling gesture can be more readily apprehended than a word, which is an arbitrary mapping of meaning to sound requiring knowledge of the language.

Assume (mathbf {u} in H^{s}(Omega_{1})^{3}) for some integer (1 leq s leq k) and u transforms such that it preserves the divergence, i.e. if (F : hat{T} to T), (hat{mathbf {u}} mapsto mathbf {u}) is an arbitrary mapping then u transforms as begin{aligned} mathbf {u} circ F = frac{1}{ lvertdet(mathrm {D}F) rvert} mathrm {D}F hat{mathbf {u}}.

If ( S, Γ, ≤ ) is an ordered Γ-semigroup and A is a subset of S, we denote by ( A ] the subset of S defined as follows: ( A ] = { t ∈ S | t ≤ a  for some  a ∈ A }. Given an ordered Γ-semigroup S, a fuzzy subset of S (or a fuzzy set in S) is an arbitrary mapping f : S → [ 0, 1 ], where [ 0, 1 ] is the usual closed interval of real numbers.