Let $D$ be a positive integer, and let $p$ be an odd prime with $p\nmid D$. In this paper we use a result on the rational approximation of quadratic irrationals due to M. Bauer, M. A. Bennett: Applications of the hypergeometric method to the generalized Ramanujan-Nagell equation. Ramanujan J. 6 (2002), 209–270, give a better upper bound for $N(D, p)$, and also prove that if the equation $U^2-DV^2=-1$ has integer solutions $(U, V)$, the least solution $(u_1, v_1)$ of the equation $u^2-pv^2=1$ satisfies $p\nmid v_1$, and $D>C(p)$, where $C(p)$ is an effectively computable constant only depending on $p$, then the equation $x^2-D=p^n$ has at most two positive integer solutions $(x, n)$. In particular, we have $C(3)=10^7$.
The rare and endangered plant, Begonia fimbristipula, shows red and green phenotypes, differentiated by a coloration of the abaxial leaf surface. In this study, we compared morphological and physiological traits of both phenotypes. The results showed that the red phenotype contained a significantly higher chlorophyll content, closer arrangement of chloroplasts, and a more developed grana. In addition, the red phenotype transferred significantly more light energy into the electron transport during the photoreaction. Similarly, the maximum photosynthetic rate, instantaneous water-use and light-use efficiencies of the red B. fimbristipula were all significantly higher than those of the green individuals. The differentiation between these two phenotypes could be caused by their different survival strategies under the same conditions; epigenetic variations may be in some correlation with this kind of phenotype plasticity. Red B. fimbristipula has an advantage in resource acquisition and utilization and possesses a better self-protection mechanism against changes in environmental conditions, therefore, it might adapt better to global climate change compared to the green phenotype. Further studies on the possible epigenetic regulation of those phenotypic differentiations are needed., Y. Wang, L. Shao, J. Wang, H. Ren, H. Liu, Q. M. Zhang, Q. F. Guo, X. W. Chen., and Seznam literatury
Studie zasazuje Vodseďálkovu prozaickou tvorbu z let padesátých do kontextu literární historie. Autor dále odkrývá křesťanské motivy v próze Kalvárie, pojmenovává jednotlivé náboženské momenty v textu, zjišťuje, že vlastně celý text je možno ve své gradaci připodobnit k „zastavením na křížové cestě“, současně však též upozorňuje na celkově neodekadentní náladu textu, stylizaci hlavní postavy do podoby karikatury hrdiny textů dekadentní literatury přelomu 19. a 20. století, a z toho vyplývající ironii a tragikomičnost. Studie též poukazuje na souvislost takto koncipované prózy s Vodseďálkovou koncepcí tzv. trapnosti v poesii.
A one-dimensional version of a gradient system, known as ''Kobayashi-Warren-Carter system'', is considered. In view of the difficulty of the uniqueness, we here set our goal to ensure a ''stability'' which comes out in the approximation approaches to the solutions. Based on this, the Main Theorem concludes that there is an admissible range of approximation differences, and in the scope of this range, any approximation method leads to a uniform type of solutions having a certain common features. Further, this is specified by using the notion of ''energy-dissipative solution'', proposed in a relevant previous work.