The $SU(2)$ unitary matrix $U$ employed in chiral descriptions of hadronic low-energy processes has both exponential and analytic representations, related by $U=\mathrm{exp}[i\mathbit{\ensuremath{\tau}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{^}{\mathbit{\ensuremath{\pi}}}\ensuremath{\theta}]=\mathrm{cos}\ensuremath{\theta}I+i\mathbit{\ensuremath{\tau}}\ifmmode\cdot\else\textperiodce...

let $r$ be a commutative ring with identity and $mathbb{a}(r)$ be the set   of ideals of $r$ with non-zero annihilators. in this paper, we first introduce and investigate the principal ideal subgraph of the annihilating-ideal graph of $r$, denoted by $mathbb{ag}_p(r)$. it is a (undirected) graph with vertices $mathbb{a}_p(r)=mathbb{a}(r)cap mathbb{p}(r)setminus {(0)}$, where   $mathbb{p}(r)$ is...

The frequency stability of lasers is limited by thermal noise in state-of-the-art references. Further improvement requires operation at cryogenic temperature. In this context, we investigate a fiber-based ring resonator. Our system exhibits first-order temperature-insensitive point around $3.55$ K, much lower than that crystalline silicon. observed low sensitivity with respect to vibrations ($<...

In this work, we studied the curvature tensors of (k,$\mu$) satisfying conditions $\widetilde{Z}(\xi ,\alpha _{3})\cdot P=0$, S=0$, $R(\xi S=0$ and $P\cdot C=0$. Besides this, classify $(k,\mu)$-paracontact manifolds. Also researched conformally flat $\phi $-conformally a $(k,\mu )-$paracontact metric

Two-dimensional (2D) ferrovalley materials that exhibit spontaneous valley polarization are both fundamentally intriguing and practically appealing to be used in valleytronic devices. Usually, the research on 2D is mainly focused inorganic systems, severely suffering from in-plane magnetization. Here, we alternatively show by k\ifmmode\cdot\else\textperiodcentered\fi{}p model analysis high-thro...

Photocatalytic nitrogen fixation from air directly under sunlight can contribute significantly to carbon neutralization. It is an ideal pathway replace the industrial Haber Bosch process in future. A Fe-doped layered WO$_3$ photocatalyst containing oxygen vacancies was developed which fix at atmospheric pressure. The iron doping enhances transport efficiency of photogenerated electrons. photoca...

in this paper we define the notions of ultra and involution ideals in bck-algebras. then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. specially, we show that in a bounded implicative bck-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower bck-semilattice, the notions of...

Abstract In this paper, we mainly consider the real interpolation spaces for variable Lebesgue defined by decreasing rearrangement function and corresponding martingale Hardy spaces. Let $$0&lt;q\le \infty $$ 0 &lt; q ≤ ∞ </mml:mat...

Aims. We aim to explain line formation of He I D3 and 10830 {\AA} in small-scale reconnection events. Methods. make use a simulated Ellerman bomb (EB), present Bifrost-generated radiative Magnetohydrodynamics (rMHD) snapshot. The resulting \AA\ intensities are synthesized 3D using the non-LTE Multi3D code. compare synthetic helium spectra with observed SST/TRIPPEL raster scans EBs D3. Results. ...