In Burrage and Burrage (1996) it was shown that by introducing a very general formulation for stochastic Runge-Kutta methods, the previous strong order barrier of order one could be broken without having to use higher derivative terms. In particular, methods of strong order 1.5 were developed in which a Stratonovich integral of order one and one of order two were present in the formulation. In ...

Self-incompatibility in Brassica species is regulated by a set of S-locus genes: SLG, SRK, and SP11/SCR. In the vicinity of the S-locus genes, several expressed genes, SLL2 and SP2/ClpP, etc., were identified in B. campestris. Arabidopsis thaliana is a self-compatible Brassica relative, and its complete genome has been sequenced. From comparison of the genomic sequences between B. campestris an...

Introduction. Previous cataract surgery studies assumed that first-eye predicted and observed postoperative refractions are equally important for predicting second-eye postoperative refraction. Methods. In a retrospective analysis of 173 patients having bilateral sequential phacoemulsification, multivariable linear regression was used to predict the second-eye postoperative refraction based on ...

ARC1 is a novel U-box protein required in the Brassica pistil for the rejection of self-incompatible pollen; it functions downstream of the S receptor kinase (SRK). Here, we show that ARC1 has E3 ubiquitin ligase activity and contains several motifs that influence its subcellular localization. ARC1 can shuttle between the nucleus, cytosol, and proteasome/COP9 signalosome (CSN) when expressed in...

Let $kgeq 1$ be an integer, and $G=(V,E)$ be a finite and simplegraph. The closed neighborhood $N_G[e]$ of an edge $e$ in a graph$G$ is the set consisting of $e$ and all edges having a commonend-vertex with $e$. A signed Roman edge $k$-dominating function(SREkDF) on a graph $G$ is a function $f:E rightarrow{-1,1,2}$ satisfying the conditions that (i) for every edge $e$of $G$, $sum _{xin N[e]} f...

Following the identification of the male (S-locus Cysteine Rich/S-locus Protein 11) and female (S Receptor kinase [SRK]) factors controlling self-incompatibility in the Brassicaceae, research in this field has focused on understanding the nature of the cellular responses activated by these regulators. We previously identified the ARM Repeat Containing1 (ARC1) E3 ligase as a component of the SRK...

We study the construction of symplectic Runge-Kutta methods for stochastic Hamiltonian systems (SHS). Three types of systems, SHS with multiplicative noise, special separable Hamiltonians and multiple additive noise, respectively, are considered in this paper. Stochastic Runge-Kutta (SRK) methods for these systems are investigated, and the corresponding conditions for SRK methods to preserve th...

In Brassica , the thioredoxin h proteins, THL1 and THL2, were previously found to be potential inhibitors of the S receptor kinase (SRK) in the Brassica self-incompatibility response. To investigate the biological roles of THL1 and THL2 in pollen-pistil interactions, the stigma-specific SLR1 promoter was used to drive antisense THL1/2 expression in Brassica napus cv. Westar. This cultivar is no...