The Effect of Rekattidiri Ovitrap Towards Aedes Aegypti Larval Density

Dengue Hemorrhagic Fever (DHF) is a health problem in Indonesia. The entire region of Indonesia at risk of contracting dengue disease. The study aims to prove the effect of modifications ovitrap rekattidiri on the density of larvae (HI: House Index, CI: Container Index and BI: Breteu Index) as well as comparing the differences between the mean larvae trapped between ovitrap Rekattidiri with standard ovitrap. Using a quasi experimental design, time series experimental design with Control group. Population subjects were Aedes aegypti at the endemic sites in Pontianak, West Borneo. The results showed larval density index in the intervention area decreased each ie HI from 26% to 3%, CI of 6.95% to 2.19 %, and BI from 29% to 13%. The number of larvae trapped in ovitrap rekattidiri ie 70% (12,770 larvae) more than the standard ovitrap in the control and intervention, namely: 17% (3,057 larvae) and 13% (2,334 larvae). It is concluded that there are significant modifications Rekattidiri ovitrap against larval density index (HI p-value: 0.025, CI p-value: 0.052, BI value of p: 0.04) and there are differences between the mean larvae trapped in ovitrap Rekattidiri and standard ovitrap with p value: 0.001

A bound for the eigenvalue counting function for Krein--von Neumann and Friedrichs extensions

For an arbitrary open, nonempty, bounded set $\Omega \subset \mathbb{R}^n$, $n \in \mathbb{N}$, and sufficiently smooth coefficients $a,b,q$, we consider the closed, strictly positive, higher-order differential operator $A_{\Omega, 2m} (a,b,q)$ in $L^2(\Omega)$ defined on $W_0^{2m,2}(\Omega)$, associated with the higher-order differential expression $$\tau_{2m} (a,b,q) := \bigg(\sum_{j,k=1}^{n} (-i \partial_j - b_j) a_{j,k} (-i \partial_k - b_k)+q\bigg)^m, \quad m \in \mathbb{N},$$ and its Krein--von Neumann extension $A_{K, \Omega, 2m} (a,b,q)$ in $L^2(\Omega)$. Denoting by $N(\lambda; A_{K, \Omega, 2m} (a,b,q))$, $\lambda > 0$, the eigenvalue counting function corresponding to the strictly positive eigenvalues of $A_{K, \Omega, 2m} (a,b,q)$, we derive the bound $$N(\lambda; A_{K, \Omega, 2m} (a,b,q)) \leq C v_n (2\pi)^{-n} \bigg(1+\frac{2m}{2m+n}\bigg)^{n/(2m)} \lambda^{n/(2m)} , \quad \lambda > 0,$$ where $C = C(a,b,q,\Omega)>0$ (with $C(I_n,0,0,\Omega) = |\Omega|$) is connected to the eigenfunction expansion of the self-adjoint operator $\widetilde A_{2m} (a,b,q)$ in $L^2(\mathbb{R}^n)$ defined on $W^{2m,2}(\mathbb{R}^n)$, corresponding to $\tau_{2m} (a,b,q)$. Here $v_n := \pi^{n/2}/\Gamma((n+2)/2)$ denotes the (Euclidean) volume of the unit ball in $\mathbb{R}^n$. Our method of proof relies on variational considerations exploiting the fundamental link between the Krein--von Neumann extension and an underlying abstract buckling problem, and on the distorted Fourier transform defined in terms of the eigenfunction transform of $\widetilde A_{2} (a,b,q)$ in $L^2(\mathbb{R}^n)$. We also consider the analogous bound for the eigenvalue counting function for the Friedrichs extension $A_{F,\Omega, 2m} (a,b,q)$ in $L^2(\Omega)$ of $A_{\Omega, 2m} (a,b,q)$. No assumptions on the boundary $\partial \Omega$ of $\Omega$ are made.Comment: 39 pages. arXiv admin note: substantial text overlap with arXiv:1403.373