Local Observation of Field Polarity Dependent Flux Pinning by Magnetic Dipoles

A scanning Hall probe microscope is used to study flux pinning in a thin superconducting Pb film covering a square array of single-domain Co dots with in-plane magnetization. We show that single flux quanta of opposite sign thread the superconducting film below T(c) at the opposite poles of these dipoles. Depending on the polarity of the applied field, flux lines are attracted to a specific pole of the dipoles, due to the direct interaction with the vortexlike structures induced by the local stray field.     

Understanding sulfone behavior in palladium-catalyzed domino reactions with aryl iodides

Unlike traditionally used acyclic 1,2-disubstituted alkenes, the reaction of alpha,beta-unsaturated phenyl sulfones with aryl iodides under Heck reaction conditions takes place mainly by means of a four-component domino process, involving one unit of the alkene and three units of the aryl iodide, affording substituted 9-phenylsulfonyl-9,10-dihydrophenanthrenes. We report here the results of a computational study on the mechanism of this domino arylation reaction. Based on these results we can explain why vinyl sulfones, unlike other electron-deficient alkenes such as enones, preferentially follow this domino pathway instead of the usual Heck pathway. The key step is a C-H activation process in which a five-membered palladacycle is formed. The greater ability of vinyl sulfones, relative to enones, to reach the transition state that leads to the formation of the initial palladacycle makes the difference.     

Growth and some properties of lanthanum sulphate enneahydrate single crystals

A technique for the growth of single crystals of Lanthanum Sulphate Enneahydrate from saturated aqueous solution by slow program-heating under different growing conditions has been developed. Polarized Raman spectrum and vibrational assignments of an oriented single crystal are reported.     

Crossed Products over Weak Hopf Algebras Related to Cleft Extensions and Cohomology

The authors present the general theory of cleft extensions for a cocommutative weak Hopf algebra H.For a right H-comodule algebra,they obtain a bijective correspondence between the isomorphisms classes of H-cleft extensions AH → A,where AH is the subalgebra of coinvariants,and the equivalence classes of crossed systems for H over AH.Finally,they establish a bijection between the set of equivalence classes of crossed systems with a fixed weak H-module algebra structure and the second cohomology group HφZ(AH)2(H,Z(AH)),where Z(AH)is the center of AH.     

Dynamic feedback over principal ideal domains and quotient rings

Let R be a principal ideal domain. In this paper we prove that, for a large class of linear systems, dynamic feedback over R is equivalent to static feedback over a quotient ring of R. In particular, when R is the ring of integers Z one has that the static feedback classification problem over finite rings is equivalent to the dynamic feedback classification problem over Z restricted to a special type of system.     

A collection of examples where Neville elimination outperforms Gaussian elimination

Neville elimination is an elimination procedure alternative to Gaussian elimination. It is very useful when dealing with totally positive matrices, for which nice stability results are known. Here we include examples, most of them test matrices used in MATLAB which are not totally positive matrices, where Neville elimination outperforms Gaussian elimination.     

D-trace estimation of a precision matrix using adaptive Lasso penalties

The accurate estimation of a precision matrix plays a crucial role in the current age of high-dimensional data explosion. To deal with this problem, one of the prominent and commonly used techniques is the \(\ell _1\) norm (Lasso) penalization for a given loss function. This approach guarantees the sparsity of the precision matrix estimate for properly selected penalty parameters. However, the \(\ell _1\) norm penalization often fails to control the bias of obtained estimator because of its overestimation behavior. In this paper, we introduce two adaptive extensions of the recently proposed \(\ell _1\) norm penalized D-trace loss minimization method. They aim at reducing the produced bias in the estimator. Extensive numerical results, using both simulated and real datasets, show the advantage of our proposed estimators.