The modified $F(R)$ gravity theory with the function $F(R)=-(1/\beta)\ln(1-\beta R)$ is studied. action at small coupling $\beta$ becomes Einstein--Hilbert action. bound on parameter from local tests $\beta\leq 2\times 10^{-6}$ cm$^2$. We find constant curvature solutions and it was shown that de Sitter space unstable but a solution zero Ricci scalar stable. potential mass of field (scalaron) a...

Let $f \in L^{2}(\mathbb{R}^n)$ and suppose we are interested in computing its average at a fixed scale. This is easy: pick the density $u_{}$ of probability distribution with mean 0 some moment desired scale compute convolution $u_{} * f$. Is there particularly natural choice for $u$? question studied space theory Gaussian popular answer. We were whether canonical $u$ can arise from new axiom:...

We present results on the search for double-electron capture ($2\nu\text{ECEC}$) of $^{124}$Xe and neutrinoless double-$\beta$ decay ($0\nu\beta\beta$) $^{136}$Xe in XENON1T. consider captures from K- up to N-shell $2\nu\text{ECEC}$ signal model measure a total half-life $T_{1/2}^{2\nu\text{ECEC}}=(1.1\pm0.2_\text{stat}\pm0.1_\text{sys})\times 10^{22}\;\text{yr}$ with $0.87\;\text{kg}\times\tex...

A simple and rapid method based on 15N labeling and 1H-15N heteronuclear single quantum coherence spectroscopy is presented to directly assess the structural integrity of overexpressed proteins in crude Escherichia coli extracts without the need for any purification. The method is demonstrated using two different expression systems and two different proteins, the B1 immunoglobulin-binding domai...

The following convective Brinkman-Forchheimer (CBF) equations (or damped Navier-Stokes equations) with potential$ \begin{equation*} \frac{\partial \boldsymbol{y}}{\partial t}-\mu \Delta\boldsymbol{y}+(\boldsymbol{y}\cdot\nabla)\boldsymbol{y}+\alpha\boldsymbol{y}+\beta|\boldsymbol{y}|^{r-1}\boldsymbol{y}+\nabla p+\Psi(\boldsymbol{y})\ni\boldsymbol{g},\ \nabla\cdot\boldsymbol{y} = 0, \end{equatio...