Let $q \ge 3$ be a positive integer. For any integers $m$ and $n$, the two-term exponential sum $C(m,n,k;q)$ is defined by $C(m,n,k;q) = \sum _{a=1}^q e ({(ma^k +na)}/{q})$, where $e(y)={\rm e}^{2\pi {\rm i} y}$. In this paper, we use the properties of Gauss sums and the estimate for Dirichlet character of polynomials to study the mean value problem involving two-term exponential sums and Dirichlet character of polynomials, and give an interesting asymptotic formula for it.
Photosynthetic and growth characteristics of the control potato plants cv. Zvíkov and those transformed by Agrobacterium were compared during their cultivation in vitro in agar medium with 1 % saccharose, after having been transplanted into pots with soil, or growing from tubers in soil. The average leaf aiea, fresh and dry matter, chlorophyll a and b ratio, and contents calculated per fresh and diy matter of the leaf area were significantly higher in the control plants raised from tubers and in vitro cultivated than in the transplanted ones. The significant increase in oxygen evolution by leaf fragments was found only in the control potato plants raised from tubers. Differences between photochemical activities of chloroplasts isolated from control and transformed plants were statistically significant only when calculated per fresh leaf matter. Chloroplasts from transformed potato plants grown from tubers and from those cultivated in vitro exhibited higher activities of photosystems (PS) 2 and PS 1 independently on the donors and acceptors of electrons ušed. On the contrary, higher activities of both photosystems were found in chloroplasts isolated from the control plants transferred to soil.