Sources and chemical composition of brown carbon are poorly understood, and even less is known about the mechanisms of its atmospheric transformations. This work presents molecular-level investigations of the reactive compound ketolimononaldehyde (KLA, C9H14O3), a second-generation ozonolysis product of limonene (C10H16), as a potent brown carbon precursor in secondary organic aerosol (SOA) thr...

Abstract: Let be a commutative ring and be a unitary module. We define a semiprime submodule of a module and consider various properties of it. Also we define semi-radical of a submodule of a module and give a number of its properties. We define modules which satisfy the semi-radical formula and present the existence of such a module.  

Let $R$ be a commutative ring with identity. A proper submodule $N$ of an $R$-module $M$ is an n-submodule if $rmin N~(rin R, min M)$ with $rnotinsqrt{Ann_R(M)}$, then $min N$. A number of results concerning n-submodules are given. For example, we give other characterizations of n-submodules. Also various properties of n-submodules are considered.

Let $G$ be an abelian group with identity $e$. $R$ a $G$-graded commutative ring and $M$ graded $R$-module. In this paper we will obtain some results concerning the generalized 2-absorbing submodules their homogeneous components. Special attention has been paid, when rings are gr-Noetherian, to find extra properties of these submodules.

Moments of absorbing Markov chain are considered. First moments and non-mixed second moments are determined in classical textbooks such as the book of J. Kemeny and J. Snell “Finite Markov Chains”. The reason is that the first moments and the non-mixed second moments can be easily expressed in a matrix form. Since the representation of mixed moments of higher orders in a matrix form is not stra...

A module MR is called right principally quasi-Baer (or simply right p.q.-Baer) if the right annihilator of a principal submodule of R is generated by an idempotent. Let R be a ring. Let α be an endomorphism of R and MR be a α-compatible module and T = R[[x;α]]. It is shown that M [[x]]T is right p.q.-Baer if and only if MR is right p.q.-Baer and the right annihilator of any countably-generated ...

A new bidirectional isolated Zero-VoltageSwitching (ZVS) DC-DC converter with nonpulsating input and output current is proposed. This converter is ideally suited for battery charging application and is applied as a submodule in a battery storage system based on a modular multilevel converter (MC). The current output of the proposed DC-DC converter enables small current ripple for directly inter...