Sentence examples for for a test function from inspiring English sources

Then, for a test function one obtains (1.27).

For a test function (omegain L^{infty}({mathbb{R}}^{3})) which has compact support and is nonnegative on (V_{varepsilon }^{c}), define rho_{tau}:= rho_{0}+ tauomega- taufrac{intomega,dy}{operatorname{meas}(V_{varepsilon })} chi_{V_{varepsilon }}, where (taugeq0) is small, such that rho_{tau}geq0, quad intrho_{tau}=intrho_{0} =M.

For a test function (omegain L^{infty}({mathbb{R}}^{4})) that has compact support and is nonnegative on (V_{epsilon}^{c}), define rho_{tau}:= rho_{0}+ tauomega- taufrac{intomega,dy}{operatorname{meas}(V_{epsilon})} chi_{V_{epsilon}}, where (taugeq0) is small such that rho_{tau}geq0,qquad intrho_{tau}= intrho_{0} =M.

For any constant (k>1), we take (u^{k-1}) as a test function for the first equation in (1.1) and integrate by parts.

In these estimates, we use the fractional maximal function as a test function for the capacity.

We compute a trace formula for a test function on PGL 3,A)— twisted by the outer automorphism σ(g)=Jtg−1J, J=01110 The resulting formula is then compared with trace formulae for H = H00 = SL(2) and H1 = PGL(2), and matching functions f0 and f1 thereof.

The metrics ({d_{L^p}}) and ({breve{e}_{L^p}}) are constructed in a very similar way, namely in terms of a supremum for all test functions in a unit ball.

Finally, bold entries designate the best values achieved for a given test function.

for all test functions, for all.

Since is an admissible test function for (3.5), using also (3.3) we get (3.11).

Next, for being an arbitrary nonnegative test function, we put (3.9).