Abstract Purpose of Review Society is concerned about the long-term condition forests. Although a clear definition forest health still missing, to evaluate health, monitoring efforts in past 40 years have concentrated on assessment tree vitality, trying estimate photosynthesis rates and productivity. Used decline Central Europe since 1980s, crown foliage transparency has been commonly believed ...

A common study to investigate gene-environment interaction is designed to be longitudinal and population-based. Data arising from longitudinal association studies often contain missing responses. Naive analysis without taking missingness into account may produce invalid inference, especially when the missing data mechanism depends on the response process. To address this issue in the ana...

we introduce the class of “right almost v-rings” which is properly between the classes of right v-rings and right good rings. a ring r is called a right almost v-ring if every simple r-module is almost injective. it is proved that r is a right almost v-ring if and only if for every r-module m, any complement of every simple submodule of m is a direct summand. moreover, r is a right almost v-rin...

in this paper, we show that every element of a discrete module is a sum of two units if and only if its endomorphism ring has no factor ring isomorphic to $z_{2}$. we also characterize unit sum number equal to two for the endomorphism ring of quasi-discrete modules with finite exchange property.

let $r$ be an associative ring with identity and $z^*(r)$ be its set of non-zero zero divisors.  the zero-divisor graph of $r$, denoted by $gamma(r)$, is the graph whose vertices are the non-zero  zero-divisors of  $r$, and two distinct vertices $r$ and $s$ are adjacent if and only if $rs=0$ or $sr=0$.  in this paper, we bring some results about undirected zero-divisor graph of a monoid ring ov...

Quantum chemical (MNDo)caleulations have beenused toelucidate the molecular properties and structure - activity relationships of dihydropyridine (DHP) type calcium antagonists. There is a good corielation between the net atomic charges on various atoms of the 4 - phenyl ring of dihydropyridines and pharmacological activity. .Also, activity decreases with increasing free rotation of the phen...

let r be a ring,  be an endomorphism of r and mr be a -rigid module. amodule mr is called quasi-baer if the right annihilator of a principal submodule of r isgenerated by an idempotent. it is shown that an r-module mr is a quasi-baer module if andonly if m[[x]] is a quasi-baer module over the skew power series ring r[[x; ]].

in this paper, we introduce a class of rings which is a generalization of reversible rings. let r be a ring with identity. a ring r is called central reversible if for any a,b ∈ r, ab=0 implies ba belongs to the center of r. since every reversible ring is central reversible, we study sufficient conditions for central reversible rings to be reversible. we prove that some results of reversible ri...