In this work we consider the fractional Kirchhoff equations with singular nonlinearity, $$\displaylines{ M\Big( \int_{\mathbb{R}^{2N}}\frac{|u(x)-u(y)|^p}{|x-y|^{N+sp}}dx dy\Big) (-\Delta)^s_p u = \lambda a(x)|u|^{q-2}u +\frac{1-\alpha}{2-\alpha-\beta} c(x)|u|^{-\alpha}|v|^{1-\beta}, \quad \text{in }\Omega,\cr \int_{\mathbb{R}^{2N}}\frac{|v(x)-v(y)|^p}{|x-y|^{N+sp}}dx v \mu b(x)|v|^{q-2}v +\fra...

This paper is concerned with the density-suppressed motility model: $$u_{t}=\Delta \left( \displaystyle \frac{u^m}{v^\alpha }\right) +\beta uf(w), v_{t}=D\Delta v-v+u, w_{t}=\Delta w-uf(w)$$ in a smoothly bounded convex domain $$\Omega \subset {{\mathbb {R}}}^2$$ , where $$m>1$$ $$\alpha>0, \beta >0$$ and $$D>0$$ are parameters, response function f satisfies $$f\in C^1([0,\infty )), f(0)=0, f(w...

The toxigenic corynebacteriophage omega tox+ was isolated from the hypertoxigenic Park-Williams no. 8 (PW8) strain of Corynebacterium diphtheriae and compared with the toxigenic corynebacteriophage beta tox+. The physical size and host range of both phages were found to be identical. An endonuclease restriction map of omega tox+ was constructed, and the locations of the cohesive ends (cos), pha...

We study the elliptic system \begin{equation*} \begin{cases} -\Delta u_1 - \kappa_1u_1 = \mu_1|u_1|^{p-2}u_1 + \lambda\alpha|u_1|^{\alpha-2}|u_2|^\beta u_1, \\ u_2 \kappa_2u_2 \mu_2|u_2|^{p-2}u_2 \lambda\beta|u_1|^\alpha|u_2|^{\beta-2}u_2, u_1,u_2\in D^{1,2}_0(\Omega), \end{cases} \end{equation*} where $\Omega$ is a bounded domain in $\mathbb R^N$, $N\geq 3$, $\kappa_1,\kappa_2\in\mathbb R$, $\...

A simple dual-wavelength (two-color) Z-scan geometry is demonstrated for measuring nonlinearities at frequency omega(p) owing to the presence of light at omega(e). This technique gives the nondegenerate two-photon absorption (2PA) coefficient beta(omega(p); omega(e)) and the nondegenerate nonlinear refractive index n(2)(omega(p); omega(e)), i.e., cross-phase modulation. We demonstrate this tech...

Bacterial DNA-dependent RNA polymerase (RNAP) has subunit composition beta'betaalpha(I)alpha(II)omega. The role of omega has been unclear. We show that omega is homologous in sequence and structure to RPB6, an essential subunit shared in eukaryotic RNAP I, II, and III. In Escherichia coli, overproduction of omega suppresses the assembly defect caused by substitution of residue 1362 of the large...

Amyloid beta protein (A beta), the central constituent of senile plaques in Alzheimer's disease (AD) brain, is known to exert toxic effects on cultured neurons. The role of the voltage-sensitive Ca2+ channel (VSCC) in beta (25-35) neurotoxicity was examined using rat cultured cortical and hippocampal neurons. When L-type VSCCs were blocked by application of nimodipine, beta (25-35) neurotoxicit...

A relativistic quantum harmonic oscillator in 3+1 dimensions is derived from a quaternionic non-relativistic oscillator. This equation also yields the Klein-Gordon wave with covariant (space-time dependent) mass. mass quantized and given by $m_{*n}^2=m_\omega^2\left(n_r^2-1-\beta\,\left(n+1\right)\right)\,,$ where $m_\omega=\frac{\hbar\omega}{c^2}\,,$ $\beta=\frac{2mc^2}{\hbar\,\omega}\, $, $n$...