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"Function wins," he said.
If they have the same number, the one with a smaller achievement function wins.
Low light detail and HDR performance gave the iPhone an edge, and its much more natural background blur function wins handily (especially in the Plus).
In fitting the model to data, the best basis function wins!
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Telomeres are tiny caps on the end of DNA strands -- the discovery of their function won several scientists the 2009 Nobel Prize in medicine.
Let the function (win C( mathbb{R}_, mathbb{R}_)) be nondecreasing, (w(r)>0 ) for (r>0), (phiin C^{1}( mathbb{R}_, mathbb{R}_)) with (phi') being nonnegative and nondecreasing.
The Hadamard fractional derivative of order q applied to the function (win operatorname {AC}_{delta}^{n}) is defined as bigl(^{H}D_{1}^{q}wbigr) (x)= delta^{n} bigl(^{H}I_{1}^{n-q}wbigr) (x).
The left-sided mixed Riemann-Liouville integral of order (r>0) of a function (win L^{1}(J)) is defined by bigl( I_{1}^{r}w bigr) (t) =frac{1}{Gamma(r)} int_{1}^{t}( t-s) ^{r-1}w(s),ds quad text{for a.e.
The Hadamard fractional derivative of order (q>0) applied to the function (win operatorname {AC}_{delta}^{n}) is defined as bigl(^{H}D_{1}^{q}w bigr) (x)= delta^{n} bigl(^{H}I_{1}^{n-q}w bigr) (x).
The Caputo-Hadamard fractional derivative of order (q>0) applied to the function (win operatorname {AC}_{delta}^{n}) is defined as bigl(^{Hc}D_{1}^{q}w bigr) (x)= bigl(^{H}I_{1}^{n-q}delta^{n}w bigr) (x).
For each point (p_0=(x_0,t_0)in partial Omega times (0,T)) one can construct a positive function (win C^2(Q)) such that begin{aligned} Q(w)le & 0 text { in }Vcap Q text { with }Vtext { a parabolic neighborhood of } p_0,nonumber w(p_0)= & 0 text { and }wge v_epsilon text { in }partial _pVcap Q. end{aligned} (8.11).
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