We study some properties of the Rovelli-Smolin-DePietri volume operator in loop quantum gravity, which significantly simplify diagonalization problem and shed light on pattern degeneracy eigenstates. The is defined by its action spaces tensor products $\mathcal{H}_{j_1}\otimes \ldots \otimes \mathcal{H}_{j_N}$ irreducible SU(2) representation $\mathcal{H}_{j_i}, i=1,\ldots,N$, labelled with spi...

Abstract Mirfentanil, a fentanyl derivative that is μ ‐opioid partial agonist, hyperpolarised via Signal Amplification By Reversible Exchange (SABRE), para ‐hydrogen‐based technique. [Ir(IMes)(COD)Cl] (IMes=1,3‐ bis (2,4,6‐trimethylphenyl)imidazole‐2‐ylidene, COD=cyclooctadiene) was employed as the polarisation transfer catalyst. Following at 6.5 mT, pyrazine‐protons were enhanced by 78‐fold (p...

A commutative ring A is said to be clean if every element of A can be written as a sum of a unit and an idempotent. This definition dates back to 1977 where it was introduced by W. K. Nicholson [7]. In 2002, V. P. Camillo and D. D. Anderson [1] investigated commutative clean rings and obtained several important results. In [4] Han and Nicholson show that if A is a semiperfect ring, then A[Z2] i...

Let $a, b, k,in K$ and $u, v in U(K)$. We show for any idempotent $ein K$, $(a 0|b 0)$ is e-clean iff $(a 0|u(vb + ka) 0)$ is e-clean and if $(a 0|b 0)$ is 0-clean, $(ua 0|u(vb + ka) 0)$ is too.

Let $R$ be a commutative ring and let $I$ be an ideal of $R$. In this paper, we will introduce the notions of 2-absorbing $I$-prime and 2-absorbing $I$-second submodules of an $R$-module $M$ as a generalization of 2-absorbing and strongly 2-absorbing second submodules of $M$ and explore some basic properties of these classes of modules.

The Ru-hydride precursors (Im(OMe)2)(PPh3)2RuHCl () and (Me2Im(OMe)2)(PPh3)2RuHCl () reacted with ethyl-vinyl-sulfide to give ((MeOCH2CH2)C3H2N2(CH2CH(OMe))RuCl(PPh3)2 () and ((MeOCH2CH2)C3Me2N2(CH2CH(OMe))RuCl(PPh3)2 (), respectively. Dissolution of () in C6D6 prompts formation of ((MeOCH2CH2)C5H6N2(CHCH)RuCl(PPh3)2 (). The analogous reactions of the bis-carbene Ru-hydride precursors (Im(OMe)2...

Suppose $j_N(\tau)$ and $j_N^{*}(\tau)$ are the Hauptmoduln of congruence subgroup $\Gamma_0(N)$ Fricke group $\Gamma^{*}_0(N)$, respectively. In [7], authors predicted that, like Klein's $j$-function, Fourier coefficients $j_{N}^{*}(\tau)$ in some arithmetic progression both even odd with density $\frac{1}{2}$. this article, we can find $n$ where $j_6(\tau)$ (resp. $j_6^{*}(\tau)$ $j_{10}(\tau...

Reaction of 1,3-dimesitylimidazolium chloride [IMesH]Cl with InMe3 results in (IMes)InMe2Cl, which on treatment with one equivalent of TMS-OTf affords (IMes)InMe2(OTf), which can be converted to the bistriflate complex (IMes)In(Me)(OTf)2 on addition of HOTf.

The reactions of Me(2)NH·BH(3) with cationic Rh(III) and Ir(III) complexes have been shown to generate the 18-electron aminoborane adduct [Ir(IMes)(2)(H)(2){κ(2)-H(2)BNMe(2))](+) and the remarkable 14-electron aminoboryl complex [Rh(IMes)(2)(H)-{B(H)NMe(2))](+). Neutron diffraction studies have been used for the first time to define H-atom locations in metal complexes of this type formed under ...