Existence of solutions for higher order ϕ−\phi-Laplacian BVPs on the half-line using a one-sided Nagumo condition with nonordered upper and lower solutions

In this paper, we consider the following $(n+1)$st order bvp on the half line with a $\phi-$Laplacian operator $$\begin{cases} (\phi(u^{(n)}))'(t)=f(t,u(t),\ldots,u^{(n)}(t)),& a.e., \,t\in [ 0,+\infty ),\\& n\in \mathbb{N}\setminus\{0\}, \\ u^{(i)}(0)=A_{i},\, i=0,\ldots,n-2,\\ u^{(n-1)}(0)+au^{(n)}(0)=B,\\ u^{(n)}(+\infty )=C. \end{cases}$$ The existence of solutions is obtained by applying Schaefer's fixed point theorem under a one-sided Nagumo condition with nonordered lower and upper solutions method where $f$ is a $L^{1}$-Carath\'eodory function

Mobility Edge in Aperiodic Kronig-Penney Potentials with Correlated Disorder: Perturbative Approach

It is shown that a non-periodic Kronig-Penney model exhibits mobility edges if the positions of the scatterers are correlated at long distances. An analytical expression for the energy-dependent localization length is derived for weak disorder in terms of the real-space correlators defining the structural disorder in these systems. We also present an algorithm to construct a non-periodic but correlated sequence exhibiting desired mobility edges. This result could be used to construct window filters in electronic, acoustic, or photonic non-periodic structures.Comment: RevTex, 4 pages including 2 Postscript figure

Chemometrics approach for adsorption multi-response optimization of Cu(II), Zn(II), and Cd(II) ions from phosphoric acid solution using natural clay

This study describes the elimination percentage optimization of Cu(II), Zn(II), and Cd(II) heavy metal ions from a phosphoric acid solution (three-metal ions system) using a natural clay (NC). The response surface methodology (RSM) based on the central composite design (CCD) was used to maximize the elimination percentages of these heavy metals. The natural clay was characterized by FTIR, XRD, TGA-DTG, SEM, and EDX techniques. Several important parameters influencing the adsorption process of these ions in the multi-metallic mixture such as contact time (X1), temperature (X2), and mass of NC (X3) were investigated systematically by batch experiments. The fitted model indicated that the optimal conditions to simultaneously maximize the elimination percentage of these ions were 26.82 min, 16.26 °C, and 3.56 g of NC mass. Under these conditions, the numerical estimation of the elimination percentages was 71.10, 69.06, and 67.83% for Cu(II), Zn(II), and Cd(II), respectively. Freundlich and Langmuir’s models were fitted to evaluate the equilibrium data of the heavy metal adsorption process by natural clay. According to the obtained results, it appeared that Freundlich isotherm gives a good representation of the adsorption phenomenon of Cu(II) ions, and for the adsorption of Cd(II) and Zn(II) on NC, the data shows fit both Freundlich and Langmuir isotherm model.</p

Rootstock resistance to Fusarium wilt and effect on watermelon fruit yield and quality

The potential of grafted watermelon for resistance to Fusarium oxysporum f.sp. niveum on some Curcurbitaceae, Lagenaria, Luffa, Benincasa and commercial rootstocks was evaluated. Effects of grafting on yield and quality of diseased plants were evaluated. All grafted plants and rootstocks were resistant to the three known races (0, 1, and 2) of F oxysporum f.sp. niveum except watermelon cv. 'Crimson Tide', which was susceptible to race 2. Fruit yield was positively (21-112%) affected by Lagenaria rootstocks but negatively affected (200-267%) by Cucurbita rootstocks when compared with the control. While only minor differences in fruit quality were determined in control and grafted plants on Lagenaria rootstocks, the quality parameters for watermelon grafted onto Cucurbita rootstocks were lower than in the control. The reasons for low yield and quality might be due to an incompatibility between Cucurbita rootstocks and watermelon. These results showed that rootstock influence on disease resistance as well as yield and quality of scion fruit is important in determining the potential use of grafting applications in watermelon