Let E be the ellipse with major and minor radii a and b respectively, and Pbe its perimeter, then P = lim 4 tan(p/n)(a + b + 2) Σ a2 cos2 (2k-2)Pi/n+ sin2 (2k-2)Pi/n; where n = 2m. So without considering the limit, it gives a reasonable approxi-mation for P, it means that we can choose n large enough such that the amountof error be less than any given small number. On the other hand, the form...

 Let $R$ be a ring‎, ‎and let $n‎, ‎d$ be non-negative integers‎. ‎A right $R$-module $M$ is called $(n‎, ‎d)$-projective if $Ext^{d+1}_R(M‎, ‎A)=0$ for every $n$-copresented right $R$-module $A$‎. ‎$R$ is called right $n$-cocoherent if every $n$-copresented right $R$-module is $(n+1)$-coprese-nted‎, ‎it is called a right co-$(n,d)$-ring if every right $R$-module is $(n‎, ‎d)$-projective‎. ‎$R$...

Unraveling the assembly mechanism is a core research topic of microbial ecology. Abundant and rare communities are crucial for diversity, function host health in given ecosystem, but few studies focused on their strategies. Here, we explored diversity abundant water, shrimp intestine sediment habitats cultural ponds. Our results found that numbers operational taxonomic units (OTUs) (6,003, 4,56...

the effects of different levels of nitrogen (100, 200, 300 and 400 mg/l) and potassium (125, 250 and 375 mg/l) on yield and leaf n and k concentrations of tomato were investigated in perlit culture using a factorial randomized design with three replications. the highest fruit yield was obtained with 200 mg/l n. higher levels of nitrogen decreased tomato yield. with increasing nitrogen concentra...

MNDO semi-empirical SCF MO calculations are used to study the pyramidal nitrogen atom inversion and configurational equilibria in the title compounds.

the effects of grape pomace extract (0, 2 and 4%) on quality and shelf life of silver carp ( hypophthalmicthys molitrix ) fillets during chill storage (4°c) were investigated. the control and the treated fillets were analyzed periodically for microbiological (tvc and ptc), chemical (tvb-n), and sensory characteristics. the results showed that grape pomace-treated samples have lower tvb-n (24.2 ...