In cite{p}, Park introduced the quadratic $rho$-functional inequalitiesbegin{eqnarray}label{E01}&& |f(x+y)+f(x-y)-2f(x)-2f(y)| \ && qquad le  left|rholeft(2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}right)- f(x) -  f(y)right)right|,  nonumberend{eqnarray}where $rho$ is a fixed complex number with $|rho|

Genes of the ventrolateral group in Drosophila are dedicated to developmental regulation of Egfr signaling in multiple processes including wing vein development. Among these genes, Egfr encodes the Drosophila EGF-Receptor, spitz (spi) and vein (vn) encode EGF-related ligands, and rhomboid (rho) and Star (S) encode membrane proteins. In this study, we show that rho-mediated hyperactivation of th...

PURPOSE The trabecular meshwork (TM) cell-matrix interactions and factors that influence Rho signaling in TM cells are thought to play a pivotal role in the regulation of aqueous outflow. The current study was designed to evaluate the role of a carbohydrate-binding protein, galectin-8 (Gal8), in TM cell adhesion and Rho signaling. METHODS Normal human TM cells were assayed for Gal8 expression...

Electroacupuncture is beneficial for the recovery of spinal cord injury, but the underlying mechanism is unclear. The Rho/Rho-associated kinase (ROCK) signaling pathway regulates the actin cytoskeleton by controlling the adhesive and migratory behaviors of cells that could inhibit neurite regrowth after neural injury and consequently hinder the recovery from spinal cord injury. Therefore, we hy...

In Escherichia coli, the essential motor protein Rho promotes transcription termination in a tightly controlled manner that is not fully understood. Here, we show that the general post-transcriptional regulatory protein Hfq associates with Rho to regulate Rho function. The Hfq:Rho complex can be further stabilized by RNA bridging both factors in a configuration that inhibits the ATP hydrolysis ...

In this paper, we introduce $rho$-altering $J$-type mappings in modular spaces. We prove some fixed point theorems for $rho$-altering and $rho$-altering $J$-type mappings in modular spaces. We also furnish illustrative examples to express relationship between these mappings. As a consequence, the results are applied to the existence of solution of an integral equation arising from an ODE ...

The property of a rho meson in dense nuclear matter is studied using the +CD sum rule. The spectral function appearing on the hadronic side of the sum rule is evaluated in the vector dominance model that takes into account the interaction between the rho meson and the pion. Including pion modification by the delta-hole polarization in the nuclear medium, we find that as the nuclear density incr...

Abstract Kernelized Gram matrix $W$ constructed from data points $\{x_i\}_{i=1}^N$ as $W_{ij}= k_0( \frac{ \| x_i - x_j \|^2} {\sigma ^2} ) $ is widely used in graph-based geometric analysis and unsupervised learning. An important question how to choose the kernel bandwidth $\sigma $, a common practice called self-tuned adaptively sets _i$ at each point $x_i$ by $k$-nearest neighbor (kNN) dista...

We consider corner scattering for the operator $\nabla \cdot \gamma(x)\nabla +k^2\rho(x)$ in $\mathbb{R}^2$, with $\gamma$ a positive definite symmetric matrix and $\rho$ scalar function. A is referred to one that on boundary of (compact) support $\gamma(x)-I$ or $\rho(x)-1$, where $I$ stands identity matrix. assume function small neighborhood corner. show any admissible incident field will be ...

We consider a conservation law model of traffic flow, where the velocity each car depends on weighted average density $\rho$ ahead. The averaging kernel is exponential type: $w_\varepsilon (s)=\varepsilon^{-1} e^{-s / \varepsilon}$. For any decreasing function $v$, we prove that, as $\varepsilon \to 0$, limit solutions to nonlocal equation coincides with unique entropy-admissible solution scala...