Boundedness and convergence to zero of solutions of a forced second-order nonlinear differential equation

AbstractSufficient conditions for continuability, boundedness, and convergence to zero of solutions of (a(t)x′)′ + h(t, x, x′) + q(t) f(x) g(x′) = e(t, x, x′) are given

On the positive solutions of a higher order functional differential equation with a discontinuity

The n-th order nonlinear functional differential equation [r(t)x(n−υ)(t)](υ)=f(t,x(g(t)))is considered; necessary and sufficient conditions are given for this equation to have: (i) a positive bounded solution x(t)→B>0 as t→∞; and (ii) all positive bounded solutions converging to 0 as t→∞. Other results on the asymptotic behavior of solutions are also given. The conditions imposed are such that the equation with a discontinuity [r(t)x(n−υ)(t)](υ)=q(t)x−λ,   λ>0is included as a special case

Classification of nonoscillatory solutions of higher order neutral type difference equations

summary:The authors consider the difference equation $$\Delta ^{m} [y_{n} - p_{n} y_{n - k}] + \delta q_{n} y_{\sigma (n + m - 1)} = 0 \qquad \mathrm {(\ast )}$$ where $m \ge 2$, $\delta = \pm 1$, $k \in N_0 = \lbrace 0,1, 2, \dots \rbrace$, $\Delta y_{n} = y_{n + 1} - y_{n}$, $q_{n} > 0$, and $\lbrace \sigma (n)\rbrace$ is a sequence of integers with $\sigma (n) \le n$ and $\lim _{n \rightarrow \infty } \sigma (n) = \infty$. They obtain results on the classification of the set of nonoscillatory solutions of ($\ast$) and use a fixed point method to show the existence of solutions having certain types of asymptotic behavior. Examples illustrating the results are included

Near-surface common-midpoint seismic data recorded with automatically planted geophones

This is the publisher's version, also available electronically from "http://onlinelibrary.wiley.com".[1] We introduce the Autojuggie II as a device to speed the emplacement of geophones for near-surface seismic common-midpoint (CMP) surveys. Hydraulic cylinders force rigidly interconnected geophones into the ground simultaneously and automatically. We demonstrate that accurate CMP data can be recorded with geophones planted by this device, and that a CMP stacked section can be processed, from which reliable geologic information can be extracted. To make this demonstration, we compare the stacked section to a coincident and parallel section, whose data was acquired using conventionally hand-planted geophones. The two sections are very similar in amplitude, phase, and frequency. A slight difference in coherency exists in a ∼35-ms reflection; the stack corresponding to the automatically planted geophones shows better coherency relative to the comparison stack. However, the similarity of the sections indicates that accurate CMP data can be recorded using geophones planted by the Autojuggie II

Oscillation of a higher order neutral difference equation with a forcing term

The authors obtain oscillation results for the even order forced neutral difference equation Δm(yn+pnyn−k)+qnf(yn−ℓ)=hn.                                (*) Examples illustrating the results are included

A Role for the Unfolded Protein Response (UPR) in Virulence and Antifungal Susceptibility in Aspergillus fumigatus

Filamentous fungi rely heavily on the secretory pathway, both for the delivery of cell wall components to the hyphal tip and the production and secretion of extracellular hydrolytic enzymes needed to support growth on polymeric substrates. Increased demand on the secretory system exerts stress on the endoplasmic reticulum (ER), which is countered by the activation of a coordinated stress response pathway termed the unfolded protein response (UPR). To determine the contribution of the UPR to the growth and virulence of the filamentous fungal pathogen Aspergillus fumigatus, we disrupted the hacA gene, encoding the major transcriptional regulator of the UPR. The ΔhacA mutant was unable to activate the UPR in response to ER stress and was hypersensitive to agents that disrupt ER homeostasis or the cell wall. Failure to induce the UPR did not affect radial growth on rich medium at 37°C, but cell wall integrity was disrupted at 45°C, resulting in a dramatic loss in viability. The ΔhacA mutant displayed a reduced capacity for protease secretion and was growth-impaired when challenged to assimilate nutrients from complex substrates. In addition, the ΔhacA mutant exhibited increased susceptibility to current antifungal agents that disrupt the membrane or cell wall and had attenuated virulence in multiple mouse models of invasive aspergillosis. These results demonstrate the importance of ER homeostasis to the growth and virulence of A. fumigatus and suggest that targeting the UPR, either alone or in combination with other antifungal drugs, would be an effective antifungal strategy

On the oscillatory behavior of solutions of second order nonlinear differential equations

AbstractRecently, Kamenev (Differentsialńyl Uravneniya, 13 (1977), 2141–2148), has discussed the oscillatory property of regular solutions of the equation y″ + p(x) f(y) = 0 without the restriction p(x) > 0. The purpose of this paper is to show that Kamenev's results do hold equally well in the case of the more general second order nonlinear equation (r(x)y′)′ + p(x) f(y) = 0