Beliefs and engagement structures: behind the affective dimension of mathematical learning

Beliefs influencing students’ mathematical learning and problem solving are structured and intertwined with larger affective and cognitive structures. This theoretical article explores a psychological concept we term an engagement structure, with which beliefs are intertwined. Engagement structures are idealized, hypothetical constructs, analogous in many ways to cognitive structures. They describe complex “in the moment” affective and social interactions as students work on conceptually challenging mathematics. We present engagement structures in a self-contained way, paying special attention to their theoretical justification and relation to other constructs. We suggest how beliefs are characteristically woven into their fabric and influence their activation. The research is based on continuing studies of middle school students in inner-city classrooms in the USA.     

Genuine quantum and classical correlations in multipartite systems

Generalizing the quantifiers used to classify correlations in bipartite systems, we define genuine total, quantum, and classical correlations in multipartite systems. The measure we give is based on the use of relative entropy to quantify the distance between two density matrices. Moreover, we show that, for pure states of three qubits, both quantum and classical bipartite correlations obey a ladder ordering law fixed by two-body mutual informations, or, equivalently, by one-qubit entropies.     

Solvability of the Dirichlet Problem in W~（2,p ）for a Class of Elliptic Equations with Singular Data

We prove an existence and uniqueness result for the Dirichlet problem for a class of elliptic equations with singular data in weighted Sobolev spaces.     

Exclusively Heteronuclear NMR Experiments to Obtain Structural and Dynamic Information on Proteins

Provided that ¹³C‐detected NMR experiments are either preferable or complementary to ¹H detection, we report here tools to determine C^α? C′, C′? N, and C^α? H^α residual dipolar couplings on the basis of the CON experiment. The coupling constants determined on ubiquitin are consistent with the subset measured with the ¹H‐detected HNCO sequences. Since the utilization of residual dipolar couplings may depend on the mobility of the involved nuclei, we also provide tools to measure longitudinal and transverse relaxation rates of N and C′. This new set of experiments is a further development of a whole strategy based on ¹³C direct‐detection NMR spectroscopy for the study of biological macromolecules.     

THE EFFECT OF ALCOHOLS WITH DIFFERENT STRUCTURES ON THE FORMATION OF WARM O/W MICROEMULSIONS

The influence of twenty five different alcohols on the formation of warm oil-in-water (O/W) microemulsions was investigated. Selected concentrations of each alcohol were added to fixed amounts of stearic acid, Tween 20 and water at 65 ° C. Fifteen alcohols formed microemulsions, at least at one of the concentrations. A pattern recognition study was performed to elucidate the activities of the alcohols by Principal Component Analysis (PCA). Linear Discriminant Analysis (LDA) was used to classify them. Two classification functions, obtained for alcohols forming / not forming microemulsions, suggest that the formation of warm O/W microemulsion is linked to the nature and the dimension/lipophilicity of the alcohol.     

Existence and Non-Existence Results for Quasilinear Elliptic Exterior Problems with Nonlinear Boundary Conditions

Existence and non-existence results are established for quasilinear elliptic problems with nonlinear boundary conditions and lack of compactness. The proofs combine variational methods with the geometrical feature, due to the competition between the different growths of the nonlinearities.     

1H, 13C and 15N NMR assignments for N6‐isopentenyladenosine/inosine analogues

The complete ¹H, ¹³C and ¹⁵N NMR signals assignments of some new isopentenyladenosine analogues were achieved using one‐ and two‐dimensional experiments (gs‐NOESY, gs‐HMQC and gs‐HMBC). Copyright © 2010 John Wiley & Sons, Ltd.     

1H, 13C and 15N NMR assignments for N‐ and O‐acylethanolamines,important family of naturally occurring bioactive lipid mediators

The complete ¹H, ¹³C and ¹⁵N NMR signal assignments of some N‐ and O‐acylethanolamines, important family of naturally occurring bioactive lipid mediators, were achieved using one‐dimensional and two‐dimensional experiments (gs‐HMQC and gs‐HMBC). Copyright © 2012 John Wiley & Sons, Ltd.