In the present paper we are concerned with convergence in $\mu $-density and $\mu $-statistical convergence of sequences of functions defined on a subset $D$ of real numbers, where $\mu $ is a finitely additive measure. Particularly, we introduce the concepts of $\mu $-statistical uniform convergence and $\mu $-statistical pointwise convergence, and observe that $\mu $-statistical uniform convergence inherits the basic properties of uniform convergence.
Time course of symbiotic N2-fixing and photosynthetic activities during vegetative growth from 30 d after plantation until pod set was measured in the CB5 and 7964 cowpea [Vigna unguiculata (L.) Walp.] genotypes of contrasting senescence traits. At emergence, seedlings were inoculated with a "non-cowpea miscellany" Rhizobium strain generally used to inoculate Cicer arietinum. Maximum N2-fixing activity occurred in inoculated CB5 and 7964 plants about 54 and 68 d after plantation, respectively. A similar temporal shift of maximum was found for net photosynthetic rate
(PN), confirming a good coordination between the two processes. A higher PN was found from the first measurements in inoculated plants of both genotypes as compared with uninoculated plants. Apparently, the maximum activity of both N2-fixation and PN was timed to occur at a particular stage of plant ontogeny correlating the high N supply with the high N demand by the plant. Rhizobium inoculation did not significantly affect partitioning coefficients of biomass to various plant organs but extended leaf longevity by about 10 d in the CB5 genotype, retarding thus the monocarpic senescence. and D. Lippi ... [et al.].
Consider a class of elliptic equation of the form −∆u − λ ⁄ |x| 2 u = u 2 ∗−1 + µu −q in Ω \ {0} with homogeneous Dirichlet boundary conditions, where 0 ∈ Ω ⊂ RN (N ≥ 3), 0 < q < 1, 0 < λ < (N − 2)2 /4 and 2∗ = 2N/(N − 2). We use variational methods to prove that for suitable µ, the problem has at least two positive weak solutions.