the aim of the present study was to examine the effect of grafting of watermelon hybrids ‘obla f1’ and ‘vanessa f1’ on to cucurbita maxima × cucurbita moschata rootstock tz 148 and lagenaria sp. rootstock ‘dias f1’, on the volatiles and yield of fruit and the plant growth. fruit volatiles analysis showed the presence of two aldehydes, namely (e)-2-nonenal and (e,z)-2,6-nonadien-1-al, with (e)-2...

(1) Let F , F1, F2 be finite sequences of elements of R and given r1, r2. If F1 = 〈r1〉 F or F1 = F a 〈r1〉 and if F2 = 〈r2〉 F or F2 = F a 〈r2〉, then ∑(F1−F2) = r1− r2. (2) Let F1, F2 be finite sequences of elements of R. If lenF1 = lenF2, then len(F1 +F2) = lenF1 and len(F1−F2) = lenF1 and ∑(F1 +F2) = ∑F1 +∑F2 and ∑(F1−F2) = ∑F1−∑F2. (3) Let F1, F2 be finite sequences of elements of R. If lenF1 ...

In this paper F1 denotes a non empty finite topology space and A, B, C denote subsets of F1. Let us consider F1. One can check that ∅(F1) is connected. We now state two propositions: (1) For all subsets A, B of F1 holds (A ∪ B) b = A ∪ B. (2) (∅(F1)) b = ∅. Let us consider F1. Observe that (∅(F1)) b is empty. Next we state the proposition (3) Let A be a subset of F1. Suppose that for all subset...

(3) (δh[f ])(x) = (∇h 2 [f ])(x)− (∇−h2 [f ])(x). (4) (~ ∆h[r f1 + f2])(n+ 1)(x) = r · (~ ∆h[f1])(n+ 1)(x) + (~ ∆h[f2])(n+ 1)(x). (5) (~ ∆h[f1 + r f2])(n+ 1)(x) = (~ ∆h[f1])(n+ 1)(x) + r · (~ ∆h[f2])(n+ 1)(x). (6) (~ ∆h[r1 f1 − r2 f2])(n+ 1)(x) = r1 · (~ ∆h[f1])(n+ 1)(x)− r2 · (~ ∆h[f2])(n+ 1)(x). (7) (~ ∆h[f ])(1) = ∆h[f ]. (8) (~ ∇h[r f1 + f2])(n+ 1)(x) = r · (~ ∇h[f1])(n+ 1)(x) + (~ ∇h[f2])(...