Let $\epsilon>0$ and let $q$ be a prime going to infinity. We prove that with high probability given $x,y$ in the projective plane over finite field $F_q$ there exists $\gamma$ $SL_3(Z)$, coordinates bounded by $q^{1/3+\epsilon}$, whose projection $SL_{3}(F_q)$ sends $x$ $y$. The exponent $1/3$ is optimal result rank generalization of Sarnak's strong approximation theorem for $SL_2(Z)$.

We study the optical absorption, especially the (far-) infrared absorption by phonons, of semiconducting and metallic nanospheres. In the nanoscopic sphere, phonons as well as states of electronic excitations are quantized by confinement. It is also known that in the nanoscopic geometry, the confined electron-phonon interaction has a different form from the usual one in the bulk. First, we anal...

Let $\mathfrak{j}$ and $\mathfrak{j}^{'}$ be the Cartan subalgebras of complex semi-simple Lie algebras $\mathfrak{g}$ $\mathfrak{g}^{'}$, $\mathfrak{j}^{*}$ $(\mathfrak{j}^{'})^{*}$ their duals, $\mathfrak{j}^{\vee}$ $(\mathfrak{j}^{'})^{\vee}$ biduals respectively. We consider $B(.,.)$, restriction to Killing form $\mathfrak{g}^{'}$. In this work, using kernel $K$ reproducing subalgebra an op...

Measles remains a major cause of child mortality, in part due to an inability to vaccinate young infants with the current live attenuated virus vaccine (LAV). To explore new approaches to infant vaccination, chimeric Venezuelan equine encephalitis/Sindbis virus (VEE/SIN) replicon particles were used to express the hemagglutinin (H) and fusion (F) proteins of measles virus (MV). Juvenile rhesus ...

Experimental studies evaluated the vector competence of Ochlerotatus taeniorhynchus (Wiedemann), Culex cancer Theobald, Culex pseudes (Dyar and Knab), Culex taeniopus Dyar and Knab, and a Culex (Culex) species, probably Culex quinquefasciatus Say, and Culex nigripalpus Theobald from Chiapas, Mexico, and Tocoa, Honduras, for epizootic (IC) and enzootic (IE) strains of Venezuelan equine encephalo...

The ecology of Venezuelan equine encephalitis (VEE) virus transmission was compared at three enzootic foci: two forest sites in the Catatumbo region of western Venezuela that have yielded small numbers of virus isolates since the 1970s, and another focus in the middle Magdalena Valley of Colombia that has consistently yielded many VEE virus isolates. Our results demonstrated dramatic difference...

In this paper, we study the existence and non-existence of normalized solutions to lower critical Choquard equation with a local perturbation $ \begin{equation*} \begin{cases} -\Delta u+\lambda u = \gamma (I_{\alpha}\ast|u|^{\frac{N+\alpha}{N}})|u|^{\frac{N+\alpha}{N}-2}u+\mu |u|^{q-2}u, \quad {\rm{in}}\ \mathbb{R}^N, \\ \int_{\mathbb{R}^N}|u|^2dx c^2, \end{cases} \end{equation*} where \gamma, ...

In this paper, we justify the hydrostatic approximation of primitive equations in maximal $$L^p$$ - $$L^q$$ -settings three-dimensional layer domain $$\varOmega = \mathbb {T} ^2 \times (-1, 1)$$ under no-slip (Dirichlet) boundary condition any time interval (0, T) for $$T>0$$ . We show that solution to $$\epsilon $$ -scaled Navier–Stokes with Besov initial data $$u_0 \in B^{s}_{q,p}(\varOmega )...

Venezuelan equine encephalitis virus (VEE) produces an acute infection in humans and induces a well-characterized cytopathic effect in neurons of the central nervous system (CNS). However, little is known about the role of glial cells in response to VEE infection of the CNS. Our results demonstrate that VEE is capable of a productive infection in primary astrocyte cultures and that this infecti...

Endocytic trafficking is a critical mechanism for cells to decode complex signaling pathways, including those activated by G-protein-coupled receptors (GPCRs). Heterogeneity in the endosomal network enables GPCR activity to be spatially restricted between early endosomes (EEs) and the recently discovered endosomal compartment, the very early endosome (VEE). However, the molecular machinery driv...