The TCR-gamma and -delta chains of six murine hybridomas were compared by one-dimensional SDS-PAGE and two-dimensional NEPHGE/SDS-PAGE analysis. This allowed the identification of three distinct gamma chains (gamma a, gamma b, and gamma c) and three distinct delta chains (delta a, delta b, and delta c). Four gamma/delta chain combinations (gamma a delta a, gamma b delta b, gamma b delta c, and ...

Quantization of the Teichm\"uller space a punctured Riemann surface $S$ is an approach to $3$-dimensional quantum gravity, and prototypical example quantization cluster varieties. Any simple loop $\gamma$ in gives rise natural trace-of-monodromy function $\mathbb{I}(\gamma)$ on space. For any ideal triangulation $\Delta$ $S$, this Laurent polynomial square-roots exponentiated shear coordinates ...

We make the split of integral fractional Laplacian as $(-\Delta)^s u=(-\Delta)(-\Delta)^{s-1}u$, where $s\in(0,\frac{1}{2})\cup(\frac{1}{2},1)$. Based on this splitting, we respectively discretize one- and two-dimensional with inhomogeneous Dirichlet boundary condition give corresponding truncation errors help interpolation estimate. Moreover, suitable corrections are proposed to guarantee conv...

The longitudinal optical conductivity is the most important property for graphene-baseddevices. So investigating this property for spatially separated few-layer graphene systems analytically and numerically is the main purpose of our study. Each layer can be mono- or bi-layer graphene. The density-density correlation function has been screened by the dielectric function using the random p...

For a random set $\mathcal{S} \subset U(d)$ of quantum gates we provide bounds on the probability that $\mathcal{S}$ forms $\delta$-approximate $t$-design. In particular have found for drawn from an exact $t$-design it satisfies inequality $\mathbb{P}\left(\delta \geq x \right)\leq 2D_t \, \frac{e^{-|\mathcal{S}| \mathrm{arctanh}(x)}}{(1-x^2)^{|\mathcal{S}|/2}} = O\left( \left( \frac{e^{-x^2}}{...

Let $$G:\mathbb {R}\rightarrow \mathbb {R}$$ be a continuous function. In the first part of this paper, we investigate sufficient conditions on G such that $$\begin{aligned} \{G(f):f\in {\dot{K}}_{p,q}^{\alpha }F_{\beta }^{s}\}\subset {\dot{K}} _{p,q}^{\alpha }^{s} \end{aligned}$$ holds. Here $${\dot{K}}_{p,q}^{\alpha }^{s}$$ are Herz-type Triebel–Lizorkin spaces. These spaces unify and general...

Following the findings in \cite{wangsawijaya2020}, we re-examine turbulent boundary layers developing over surfaces with spanwise heterogeneous roughness of various wavelengths $0.32 \leq S/\overline{\delta} 3.63$, where $S$ is width strips and $\overline{\delta}$ spanwise-averaged boundary-layer thickness. The cases induce counter-rotating secondary flows, these are compared to large-scale str...

In this paper we study the following class of fractional relativistic Schr\"odinger equations: \begin{equation*} \left\{ \begin{array}{ll} (-\Delta+m^{2})^{s}u + V(\varepsilon x) u= f(u) &\mbox{ in } \mathbb{R}^{N}, \\ u\in H^{s}(\mathbb{R}^{N}), \quad u>0 \end{array} \right. \end{equation*} where $\varepsilon>0$ is a small parameter, $s\in (0, 1)$, $m>0$, $N> 2s$, $(-\Delta+m^{2})^{s}$ operato...