Since the last function is negative on \((1,\infty )\) if \(p>2\) and positive for \(p\in (1,2)\), the claim is proved. Consequently, the function \(s\mapsto h(s)^{2}\) is decreasing on \((1,\infty )\), so we get...
{{\mathcal {a}}}_k\,, \end{array}\right. } \end{aligned}$$ with \(\chi : {\mathbb {r}}\rightarrow {\mathbb {r}}\) a \(c^\infty\) -function, built in such a way that $$\begin{aligned} \chi ({s} )= {\left\{ \begin{array}{ll} 1\,, \textit{ if } s \in ...
{.} \end{array} &{} \begin{array}{ccc} \text {.} &{} &{} \\ &{} \text {.} &{} \\ &{} &{} \text {.} \end{array} &{} \\ &{} &{} y_{N-2} &{} x_{N-1} &{} y_{N-1} \\ &{} &{} &{} y_{N-1} &{} x_{N} \end{array} \right) \end{...
The functions fj represent the cost or penalty for taking items; they are non-decreasing non-negative functions that depend on total accumulated weight of the taken items i, 1 ≤ i ≤ j. On the other hand, the functions gj represent the cost or penalty for leaving items; they ...
As the dimensionless parameter g is growing, the effective temperature (16) of the final excitation distribution is decreasing. Characteristic annealing times The currently studied QA systems use a slowly changing transverse magnetic field with
These findings can also be seen as a sign of strong consumer demand for imported goods, which would raise imports while decreasing exports into the economy and eventually lead to a trade deficit. Since there is a significant demand for trading currencies, this action will put upward pressure on...
Undeniably, the highest global anemia burden lies within South and Southeast Asian countries, but progress in decreasing anemia has almost ground to a halt. This study's goal was to delve into the individual and community variables correlated with childhood anemia within the six chosen Southeast ...
Let us consider a decreasing sequence r_i\downarrow 0, such that \begin{aligned} \liminf _{r\rightarrow 0}\inf _{x\in X}\frac{\mathscr {H}^N(B_r(x))}{v(N,K/(N-1),r)}=\lim _{i\rightarrow +\infty } \inf _{x\in X}\frac{\mathscr {H}^N(B_{r_i}(x))}{v(N...
The dual value shows a decreasing trend (maximization objective function). The best primal solution is depicted as a green line in Fig. 5 to illustrate the improvement of the duality gap from 24.3 to 4.2% during refinement of the inner approximation. Fig. 5 Improvement of the dual bound ...
(tES), have been widely used to investigate healthy and pathological systems2. However, these approaches show a steep depth–focality tradeoff3, with focality decreasing as depth increases. As a result, deep brain structures, such as the basal ganglia and hippocampus, cannot be reached directly...