Condition number related to the outer inverse of a complex matrix

In this paper we obtain the formula for computing the condition number of a complex matrix, which is related to the outer generalized inverse of a given matrix. We use the Schur decomposition of a matrix. We characterize the spectral norm and the Frobenius norm of the relative condition number of the generalized inverse, and the level-2 condition number of the generalized inverse. The sensitivity for the generalized Drazin-inverse solution of linear systems is presented. We also present the structured perturbation of the generalized inverse.     

Finite-Dimensional Representations of Hyper Loop Algebras over Non-algebraically Closed Fields

We study finite-dimensional representations of hyper loop algebras over non-algebraically closed fields. The main results concern the classification of the irreducible representations, the construction of the Weyl modules, base change, tensor products of irreducible and Weyl modules, and the block decomposition of the underlying abelian category. Several results are interestingly related to the study of irreducible representations of polynomial algebras and Galois theory.     

Low-field EPR studies of levels near the top of the barrier in Mn12-acetate reveal a new magnetization relaxation pathway

We show that X-band electron paramagnetic resonance (EPR) measurements using a dual-mode resonance cavity can directly probe the levels near the top of the magnetization reversal barrier in the single-molecule magnet (SMM) Mn₁₂-acetate. The observed transitions are much sharper than those reported in high-field EPR studies. The observed temperature dependence of the line positions points to the presence of a spin-diffusional mode. The correlation time for such fluctuations is of the order of 6×10⁻⁸ s at 10 K, and follows an Arrhenius activation energy of 35-40 K. These results open a new avenue for understanding the mechanism of tunneling and spin-lattice relaxations in these SMMs.     

Characterizations of $$k$$ k -potent elements in rings

Annali di Matematica Pura ed Applicata (1923 -) - In this paper, we investigate several characterizations of $$k$$ -potent elements in rings in purely algebraic terms and considerably simplify...     

DBU induced formation of 8-bromoguanosine dimer with three hydrogen bonds between the GG− base pairs

Upon hemideprotonation of 8-bromoguanosine (8-BrG) at the N1 position, induced by DBU, the adduct [8-BrG][8-BrG]^?[DBU–H]⁺ was formed. Slow evaporation of the 8-BrG methanol solution, in the presence of 0.5 equiv of DBU, yielded two polymorphic structures (1 and 2), where a neutral [8-BrG] (A) and N1 deprotonated, anionic 8-bromoguanosine [8-BrG]^? (B) were joined together through three intermolecular hydrogen bonds involving O6, N1 and C2–NH₂ sites. Such pairing gave planar GG^? dimers as the basic motif of crystal packing in both polymorphs. Both neutral and deprotonated guanosine molecules in the structure of 1 had the ribose units in a syn conformation. In the structure of polymorph 2, the N1 deprotonated guanosine molecule (B) retained the syn glycosidic conformation, while the non-deprotonated guanosine molecule (A) adopted the natural anti conformation of the ribose unit with respect to the nucleobase. Ribose rings revealed different puckering; only those of deprotonated molecules 1B and 2B possessed the usual C2′-endo envelope conformation. Crystal packing in both structures was guided by the highly complex H-bonded pattern. The CSD was searched for related structures, which are discussed with reference to polymorphs 1 and 2. ¹H and ¹³C NMR spectroscopic evidence is provided showing that the three H-bonded adduct [8-BrG][8-BrG]^?[DBU–H]⁺ was also formed in the highly H-bond competitive DMSO solution.     

Further results on the reverse order law for the Moore-Penrose inverse in rings with involution

We present some equivalent conditions of the reverse order law for the Moore-Penrose inverse in rings with involution, extending some well-known results to more general settings. Then we apply this result to obtain a set of equivalent conditions to the reverse order rule for the weighted Moore-Penrose inverse in C^∗-algebras.