let $m_r$ be a non-zero‎ ‎module and ${mathcal f}‎: ‎sigma[m_r]times sigma[m_r]‎ ‎rightarrow$ mod-$bbb{z}$ a bifunctor‎. ‎the‎ ‎$mathcal{f}$-reversibility of $m$ is defined by ${mathcal‎ ‎f}(x,y)=0 rightarrow {mathcal f}(y,x)=0$ for all non-zero $x,y$‎ ‎in $sigma[m_r]$‎. ‎hom (resp‎. ‎rej)-reversibility of $m$ is‎ ‎characterized in different ways‎. ‎among other things‎, ‎it is shown‎ ‎th...

The mechanism of the chiral VANOL-BOROX Brønsted acid catalyzed aziridination reaction of imines and ethyldiazoacetate has been studied using a combination of experimental kinetic isotope effects and theoretical calculations. A stepwise mechanism where reversible formation of a diazonium ion intermediate precedes rate-limiting ring closure to form the cis-aziridine is implicated. A revised mode...

We study dynamical fluctuations in the macroscopic paths around most probable path of Kac ring model, which is a simple deterministic and reversible system exhibiting irreversible relaxation. derive form generating function for show that small deviations are described by discrete-time Ornstein–Uhlenbeck process. also argue microscopic reversibility leads to fluctuation relation rate function, p...

Let $M_R$ be a non-zero‎ ‎module and ${mathcal F}‎: ‎sigma[M_R]times sigma[M_R]‎ ‎rightarrow$ Mod-$Bbb{Z}$ a bifunctor‎. ‎The‎ ‎$mathcal{F}$-reversibility of $M$ is defined by ${mathcal‎ ‎F}(X,Y)=0 Rightarrow {mathcal F}(Y,X)=0$ for all non-zero $X,Y$‎ ‎in $sigma[M_R]$‎. ‎Hom (resp‎. ‎Rej)-reversibility of $M$ is‎ ‎characterized in different ways‎. ‎Among other things‎, ‎it is shown‎ ‎th...

We propose to generate steady-state microbunching in a storage ring with a reversible seeding scheme. High gain harmonic generation (HGHG) and echo-enabled harmonic generation (EEHG) are two promising methods for microbunching linac electron beams. Because both schemes increase the energy spread of the seeded beam, they cannot drive a coherent radiator turn-by-turn in a storage ring. However, r...

Jacobson introduced the concept of K-rings, continuing the investigation of Kaplansky and Herstein into the commutativity of rings. In this note we focus on the ring-theoretic properties of K-rings. We first construct basic examples of K-rings to be handled easily. It is shown that a semiprime K-ring of bounded index of nilpotency is a commutative domain. It is proved that if R is a prime K-rin...

To develop a π-conjugation circuit switched by redox reaction between 3-pyridone and 3-hydroxypyridine, ring-contracted analogue of oxypyriporphyrin, 2-oxypyritriphyrin(1.2.1) was prepared. When 2-oxypyritriphyrin treated with NaBH4, not only the 3-oxypyridine unit, but also meso-carbon reduced. The reduced analog could be oxidized again to afford in reversible manner.

The effects of local anesthetics were examined on a family of transiently expressed neuronal calcium channels. Fomocaine, a local anesthetic containing a morpholine ring, preferentially blocked (Y,~ channels (Ki = 100 PM), and had a lower affinity (3to 15fold) for (Y,~, (Y,~, and cz,c channels. Block was incompletely reversible, followed I:1 kinetics, and did not affect steady-state inactivatio...

Let $R$ be a reversible ring which is $alpha$-compatible for an endomorphism $alpha$ of $R$ and $f(X)=a_0+a_1X+cdots+a_nX^n$ be a nonzero skew polynomial in $R[X;alpha]$. It is proved that if there exists a nonzero skew polynomial $g(X)=b_0+b_1X+cdots+b_mX^m$ in $R[X;alpha]$ such that $g(X)f(X)=c$ is a constant in $R$, then $b_0a_0=c$ and there exist nonzero elements $a$ and $r$ in $R$ such tha...

Photochromic nucleosides were designed that combine the structural features and molecular recognition properties of nucleic acids with the light-sensitivity of diarylethenes. Target compounds 1a-c consist of a 7-deazaadenosine unit that is linked to a thiophene as the second aryl functionality via a 1,2-cyclopentenyl linker. These nucleoside analogues undergo a reversible electrocyclic rearrang...