abstract. let r be a 2-torsion free ring with identity. in this paper, first we prove that any jordan left derivation (hence, any left derivation) on the full matrix ringmn(r) (n  2) is identically zero, and any generalized left derivation on this ring is a right centralizer. next, we show that if r is also a prime ring and n  1, then any jordan left derivation on the ring tn(r) of all n×n up...

Let R be a differentiably simple Noetherian commutative ring of characteristic p > 0 (then (R,m) is local with n := emdim(R) < ∞). A short proof is given of the Theorem of Harper [1] on classification of differentiably simple Noetherian commutative rings in prime characteristic. The main result of the paper is that there exists a nilpotent simple derivation of the ring R such that if δ i 6= 0 t...

Optical closure is essential for the determination of biogeochemical properties from ocean color remote sensing information. Mie scattering theory, a radiative transfer model, and a semi-analytical inversion algorithm were used to investigate the influence of particles and their properties on optical closure. Closure results were generally poor. Absorption coefficient (a(t)) inversions were mor...

ing away from the effect of the phonological rules mentioned, the template of Nicobarese reduplication is a syllable PuC. A standard copyand-association analysis involving a prespecified CVC template will have to somehow insure that the coda segment in a form like cim ends up in coda position. Since prelinked segments, if used at all, must be interpreted conditionally, we are faced with the cho...

The sets Sj are the sets of points to which μj is the closest center. In each step of the algorithm the potential function is reduced. Let’s examine that. First, if the set of centers μj are fixed, the best assignment is clearly the one which assigns each data point to its closest center. Also, assume that μ is the center of a set of points S. Then, if we move μ to 1 |S| ∑ i∈S xi then we only r...

let a be a unital r-algebra and m be a unital a-bimodule. it is shown that every jordan derivation of the trivial extension of a by m, under some conditions, is the sum of a derivation and an antiderivation.

There is an error in “Stability and Hypothesis Transfer Learning” (Kuzborskij & Orabona, 2013) which appeared in proceedings of ICML 2013. The Leave-One-Out generalization bound for Hypothesis Transfer Learning algorithm through Regularized Least Squares with biased regularization does not have the right convergence rate with respect to the regularization parameter λ and the source risk on the ...