The methods of spatial statistics were applied to assess the geographical pattern of risk of Lyme borreliosis in Central Bohemia, the Czech Republic, based on retrospective data on disease contractions. The statistical risk was then compared at 15 selected localities with the infection challenge presented by ticks and insects carrying borreliae. Over 5,000 Ixodes ricinus (L.) ticks and 390 hacmatophagous dipterans were screened by direct immunofluorescence method, and the spatial and seasonal variance of infection rates were studied. Infected ticks were found at each locality throughout the warm season; in nymphs, sample infection rates ranged from 4.9% to 23.1% with a mean of 14.5% in spring, from 7.7% to 28.7% with a mean of 16.1% in summer, and from 7% to 20.6% with a mean of 13.6% in autumn. The statistical risk was found to correlate well with an average nymphal infection challenge, i.e. I. ricinus nymphal abundance x infection rate, at a given locality. Statistically significant cumulation of insect-history recalling patients into several, generally wetland, areas was ascertained; borreliae were revealed in 0.5% of the dipterans examined.
We exploit the properties of Legendre polynomials defined by the contour integral $\bold P_n(z)=(2\pi {\rm i})^{-1} \oint (1-2tz+t^2)^{-1/2}t^{-n-1} {\rm d} t,$ where the contour encloses the origin and is traversed in the counterclockwise direction, to obtain congruences of certain sums of central binomial coefficients. More explicitly, by comparing various expressions of the values of Legendre polynomials, it can be proved that for any positive integer $r$, a prime $p \geqslant 5$ and $n=rp^2-1$, we have $\sum _{k=0}^{\lfloor n/2\rfloor }{2k \choose k}\equiv 0, 1\text { or }-1 \pmod {p^2}$, depending on the value of $r \pmod 6$.
In order to evaluate the effect of leaf age on enzymes of carbon and sulphur metabolism, chlorophyll (Chl) and protein contents and the activities of RuBP- carboxylase (RuBPC), ATP-sulphurylase (ATPS), and 0-acetylserinesulphydrylase (OASS) were determined in leaves of different ages from luceme (Medicago sativa L. cv. Lodi and Sewa) plants grown outdoors. The enzymes of sulphur and carbon metabolism were differently regulated throughout development of luceme leaves, as ATPS reached the highest activity at very early stages of leaf growth, when RuBPC activity was negligible. OASS activity inereased 2-fold during leaf expansion, and deereased with leaf senescence. The two cultivars showed rather similar trends of development in Chl, protein content and enzyme activities. The cultivars differed also in the absolute level of enzyme activities and other biochemical parameters.