Lectotypification of Kengyilia mutica (Keng ex Keng & S. L. Chen) J. L. Yang, Yen & Baum (Poaceae), and Change of Circumscription

Endophyte species influence the biomass production of the native grass Achnatherum sibiricum (L.) Keng under high nitrogen availability

Research on the interaction of endophytes and native grasses normally takes infection status into account, but less often considers the species of endophyte involved in the interaction. Here, we examined the effect of endophyte infection, endophyte species, nitrogen availability, and plant maternal genotype on the performance of a wild grass, Achnatherum sibiricum. Six different Epichloë-infect...

Effective Packing Dimension and Traceability Rod Downey and Keng

The concern of this paper is with effective packing dimension. This concept can be traced back to the work of Borel and Lebesgue who studied measure as a way of specifying the size of sets. Carathéodory later generalized Lebesgue measure to the n-dimensional Euclidean space, and this was taken further by Hausdorff [Hau19] who generalized the notion of s-dimensional measure to include non-intege...

Lowness for Bounded Randomness Rod Downey and Keng

In [3], Brodhead, Downey and Ng introduced some new variations of the notions of being Martin-Löf random where the tests are all clopen sets. We explore the lowness notions associated with these randomness notions. While these bounded notions seem far from classical notions with infinite tests like Martin-Löf and Demuth randomness, the lowness notions associated with bounded randomness turn out...

existence and approximate $l^{p}$ and continuous solution of nonlinear integral equations of the hammerstein and volterra types

بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی ‎‏بیان شد‎‎‏ه اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...

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