MicroRNAs (miRNAs) are a class of small regulatory RNAs that are found in almost all of the eukaryotes. Arabidopsis (Arabidopsis thaliana) miRNAs are processed from primary miRNAs (pri-miRNAs), mainly by the ribonuclease III-like enzyme DICER-LIKE1 (DCL1) and its specific partner, HYPONASTIC LEAVES1 (HYL1), a double-strand RNA-binding protein, both of which contain two double-strand RNA-binding...

Consider a tensor product H = H1⊗H2⊗· · ·⊗Hk of finite dimensional Hilbert spaces with dimension of Hi = di, 1 ≤ i ≤ k. Then the maximum dimension possible for a subspace of H with no non-zero product vector is known to be d1d2 . . . dk− (d1 +d2 + · · ·+dk)+k−1. We obtain an explicit example of a subspace of this kind. We determine the set of product vectors in its orthogonal complement and sho...

n(n + d) . . . (n + (k − 1)d) = by (1.1) in positive integers n, k ≥ 2, d > 1, b, y, l ≥ 3 with l prime, gcd(n, d) = 1 and P (b) ≤ k. We write d = D1D2 (1.2) where D1 is the maximal divisor of d such that all prime divisors of D1 are congruent to 1 ( mod l). Thus D1 and D2 are relatively prime positive integers such that D2 has no prime divisor which is congruent to 1 (mod l). Shorey [Sh88] pro...

and has propagating number 3. The graph representing d is not unique. The composition d1 ◦ d2 of partition diagrams d1, d2 ∈ Ak is the set partition obtained by placing d1 above d2 and identifying the bottom dots of d1 with the top dots of d2, removing any connected components that live entirely in the middle row. For k ∈ 1 2Z>0 and n ∈ C, the partition algebra CAk(n) is the associative algebra...

von Willebrand factor (VWF) is a multimeric plasma protein that mediates platelet adhesion to sites of vascular injury. The hemostatic function of VWF depends upon the formation of disulfide-linked multimers, which requires the VWF propeptide (D1D2 domains) and adjacent D'D3 domains. VWF multimer assembly occurs in the trans-Golgi at pH ~ 6.2 but not at pH 7.4, which suggests that protonation o...

The assembly of von Willebrand factor multimers in the Golgi apparatus requires D1D2 domains of the von Willebrand factor propeptide, which may act as an oxidoreductase to promote disulfide bond formation or rearrangement between two D3 domains in the mature subunit. This mechanism predicts that the propeptide should form a transient intrachain disulfide bond with the D3 domain before multimeri...