Sentence examples for Unique provided from inspiring English sources

Suppose that the conditions in Theorem  2.1 are fulfilled and (b x,t geqslant0), then the bounded solution of Problem (1.1) is unique provided that the following condition holds (mathrm{H}_{3} quad textit{the function }f(s textit{ is decreasing in }sinmathbb{R}.

One can prove that the coupled best proximity point is in fact unique, provided that the product space A × A endowed with the partial order mentioned earlier has the following property: Every pair of elements has either a lower bound or an upper bound.

For every (tauin I_{epsilon,a_{0},a_{1}}), the forcing signal f and the shift α as above are unique, provided that the following constraint is required: (C) f is a piecewise affine forcing signal whose restriction (f|_{ 0,tau)}) has slope (1+epsilon) only on a subinterval whose left boundary is α.  .

\, To justify the definition of logarithms, it is necessary to show that the equation :b^x = y \, has a solution x and that this solution is unique, provided that y is positive and that b is positive and unequal to 1.

Will new forms of engagement with the arts replace the unique experiences provided by museums?

He argued that "there was no substitute for the unique legitimacy provided by the UN".

Nothing is licensed, and all users can upload unique content, provided it's their own.

The evolutionary conservation of this unique pattern provided the most telling evidence supporting function.

Few unique services provided by big data are summarized in Fig. 1.

Then the boundary value problem (1.1) has a unique solution provided (31).

Then problem (45) has a unique solution, provided that h is sufficiently small.