Hermite Interpolation and Sobolev Orthogonality

In this paper, we study orthogonal polynomials with respect to the bilinear form (f, g) _S = V(f) A V(g) ^T + <u, f ^(N) g ^(N)V(f) =(f(c ₀), f "(c ₀), ..., f ^{(n – 1)} ₀(c ₀), ..., f(c _p ), f "(c _p ), ..., f ^{(n – 1)} _p(c _p )) u is a regular linear functional on the linear space P of real polynomials, c ₀, c ₁, ..., c _p are distinct real numbers, n ₀, n ₁, ..., n _p are positive integer numbers, N=n ₀+n ₁+...+n _p , and A is a N × N real matrix with all its principal submatrices nonsingular. We establish relations with the theory of interpolation and approximation.     

2-Aryl-7,7-dimethyl-5,6,7,8-tetrahydrothieno[3,2-c]azepin-4-ones from 5,5-dimethyl-1,3-cyclohexanedione

A novel synthesis of substituted thieno[3,2-c]azepinones is described. This new approach uses 5,5-dimethyl-1,3-cyclohexanedione (dimedone) as the starting material. Oxime intermediates are obtained in three steps from the aforementioned diketone. Using these intermediates, the title compounds are synthesized in moderate yields.     

On the performance of the ICP algorithm

We present upper and lower bounds for the number of iterations performed by the Iterative Closest Point (ICP) algorithm. This algorithm has been proposed by Besl and McKay as a successful heuristic for matching of point sets in d-space under translation, but so far it seems not to have been rigorously analyzed. We consider two standard measures of resemblance that the algorithm attempts to optimize: The RMS (root mean squared distance) and the (one-sided) Hausdorff distance. We show that in both cases the number of iterations performed by the algorithm is polynomial in the number of input points. In particular, this bound is quadratic in the one-dimensional problem, under the RMS measure, for which we present a lower bound construction of Ω(nlogn) iterations, where n is the overall size of the input. Under the Hausdorff measure, this bound is only O(n) for input point sets whose spread is polynomial in n, and this is tight in the worst case.We also present several structural geometric properties of the algorithm under both measures. For the RMS measure, we show that at each iteration of the algorithm the cost function monotonically and strictly decreases along the vector Δt of the relative translation. As a result, we conclude that the polygonal path π, obtained by concatenating all the relative translations that are computed during the execution of the algorithm, does not intersect itself. In particular, in the one-dimensional problem all the relative translations of the ICP algorithm are in the same (left or right) direction. For the Hausdorff measure, some of these properties continue to hold (such as monotonicity in one dimension), whereas others do not.     

Crystal Structures of Bacterial (6‐4) Photolyase Mutants with Impaired DNA Repair Activity

PhrB from Agrobacterium fabrum is the first prokaryotic photolyase which repairs (6‐4) UV DNA photoproducts. The protein harbors three cofactors: the enzymatically active FAD chromophore, a second chromophore, 6,7‐dimethyl‐8‐ribityllumazine (DMRL) and a cubane‐type Fe‐S cluster. Tyr424 of PhrB is part of the DNA‐binding site and could provide an electron link to the Fe‐S cluster. The PhrB_Y424F mutant showed reduced binding of lesion DNA and loss of DNA repair. The mutant PhrB_I51W is characterized by the loss of the DMRL chromophore, reduced photoreduction and reduced DNA repair capacity. We have determined the crystal structures of both mutants and found that both mutations only affect local protein environments, whereas the overall fold remained unchanged. The crystal structure of PhrB_Y424F revealed a water network extending to His366, which are part of the lesion‐binding site. The crystal structure of PhrB_I51W shows how the bulky Trp leads to structural rearrangements in the DMRL chromophore pocket. Spectral characterizations of PhrB_I51W suggest that DMRL serves as an antenna chromophore for photoreduction and DNA repair in the wild type. The energy transfer from DMRL to FAD could represent a phylogenetically ancient process.     

Chemistry of the oxophosphinidene ligand. 2. Reactivity of the anionic complexes [MCp{P(O)R*}(CO)(2)](-) (M = Mo, W; R* = 2,4,6-C(6)H(2)(t)Bu(3)) toward electrophiles based on elements different from carbon

The anionic oxophosphinidene complexes (H-DBU)[MCp{P(O)R*}(CO)(2)] (M = Mo, W; R* = 2,4,6-C(6)H(2)(t)Bu(3); Cp = η(5)-C(5)H(5), DBU = 1,8-diazabicyclo [5.4.0] undec-7-ene) displayed multisite reactivity when faced with different electrophilic reagents. The reactions with the group 14 organochloride compounds ER(4-x)Cl(x) (E = Si, Ge, Sn, Pb) led to either phosphide-like, oxophosphinidene-bridged derivatives [MCp{P(OE')R*}(CO)(2)] (E' = SiMe(3), SiPh(3), GePh(3), GeMe(2)Cl) or to terminal oxophosphinidene complexes [MCp{P(O)R*}(CO)(2)(E')] (E' = SnPh(3), SnPh(2)Cl, PbPh(3); Mo-Pb = 2.8845(4) ? for the MoPb compound). A particular situation was found in the reaction with SnMe(3)Cl, this giving a product existing in both tautomeric forms, with the phosphide-like complex [MCp{P(OSnMe(3))R*}(CO)(2)] prevailing at room temperature and the tautomer [MCp{P(O)R*}(CO)(2)(SnMe(3))] being the unique species present below 203 K in dichloromethane solution. The title anions also showed a multisite behavior when reacting with transition-metal based electrophiles. Thus, the reactions with the complexes [M'Cp(2)Cl(2)] (M' = Ti, Zr) gave phosphide-like derivatives [MCp{P(OM')R*}(CO)(2)] (M = Mo, M' = TiCp(2)Cl, ZrCp(2)Cl; M = W, M' = ZrCp(2)Cl), displaying a bridging κ(1),κ(1)-P,O- oxophosphinidene ligand connecting MCp(CO)(2) and M'Cp(2)Cl metal fragments (W-P = 2.233(1) ?, O-Zr = 2.016(4) ? for the WZr compound]. In contrast, the reactions with the complex [AuCl{P(p-tol)(3)}] gave the metal-metal bonded derivatives trans-[MCp{P(O)R*}(CO)(2){AuP(p-tol)(3)}] (M = Mo, W; Mo-Au = 2.7071(7) ?). From all the above results it was concluded that the terminal oxophosphinidene complexes are preferentially formed under conditions of orbital control, while charge-controlled reactions tend to give derivatives with the electrophilic fragment bound to the oxygen atom of the oxophosphinidene ligand (phosphide-like, oxophosphinidene-bridged derivatives).     

Crosslink effect and albumin adsorption onto chitosan/alginate multilayered systems: an in situ QCM-D study

The adsorption of HSA onto CHI/ALG multilayer assemblies was assessed in situ using QCM-D. It was found that the behavior of HSA on biomaterials surface can be tuned by adjusting parameters of the polyelectrolyte system such as pH, layer number, crosslinker and polymer terminal layer. Our results confirmed the key role of electrostatic interactions during HSA adsorption, since oppositely charged surfaces were more effective in promoting protein adhesion. QCM-D data revealed that crosslinking (CHI/ALG)(5) CHI films allows HSA to become adsorbed in physiological conditions. Our results suggested that the biological potential of biopolymers and the mild conditions of the LbL technique turn these natural nanoassemblies into a suitable choice to be used as pH-sensitive coatings.     

Optimization and validation of an LC-fLD method for biotin in infant formula, infant cereals, cocoa-malt beverages, and clinical nutrition products

A fast and simple chromatographic method to determine biotin in foods is presented. Biotin is extracted using papain (60 degrees C, 1 h). After pH adjustment and filtration, biotin is determined by LC with fluorescence detection using postcolumn reagent avidin-FITC (avidin labeled with fluorescein isothiocyanate). The method has been validated in a large range of products: milk- and soy-based infant formulas, cereals, cocoa-malt beverages, and clinical nutrition products. The method showed recovery rates of 98.1 +/- 5.7% (average +/- SD) in a large range of concentrations. Biotin concentrations determined in infant formula standard reference materials 1846 and 1849 were in agreement with reference values. RSD of repeatability (RSDr) varied from 2.0 to 4.5%, and intermediate reproducibility (RSD(iR)) from 5.8 to 9.4%. LOD and LOQ were 3.0 and 5.0 microg/100 g, respectively. The proposed method is suitable for routine analysis of biotin in fortified foods (infant formulas, infant cereals, cocoa-malt beverages, and clinical nutrition products). It can be used as a faster, more selective, and precise alternative to the classical microbiological determination, and is easily transferable among laboratories.     

Graphical Representations of Speed: Obstacles Preservice K‐8 Teachers Experience

This study examines the difficulties college students experience when creating and interpreting graphs in which speed is one of the variables. Nineteen students, all preservice elementary or middle school teachers, completed an upper‐level course exploring algebraic concepts. Although all of these preservice teachers had previously completed several mathematics courses, including calculus, they demonstrated widespread misconceptions about the variable speed. This study identifies four cognitive obstacles held by the students, provides excerpts of their graphical constructions and verbal interpretations, and discusses potential causes for the confusion. In particular, misconceptions arose when students interpreted the behavior and nature of speed within a graphical context, as well as in situations where they were required to construct a graph involving speed as a variable. The study concludes by offering implications for the teaching and learning of speed and its interpretation within a graphical setting.     

A networking method to compare theories: metacognition in problem solving reformulated within the Anthropological Theory of the Didactic

An important role of theory in research is to provide new ways of conceptualizing practical questions, essentially by transforming them into scientific problems that can be more easily delimited, typified and approached. In mathematics education, theoretical developments around ‘metacognition’ initially appeared in the research domain of Problem Solving closely related to the practical question of how to learn (and teach) to solve non-routine problems. This paper presents a networking method to approach a notion as ‘metacognition’ within a different theoretical perspective, as the one provided by the Anthropological Theory of the Didactic. Instead of trying to directly ‘translate’ this notion from one perspective to another, the strategy used consists in going back to the practical question that is at the origin of ‘metacognition’ and show how the new perspective relates this initial question to a very different kind of phenomena. The analysis is supported by an empirical study focused on a teaching proposal in grade 10 concerning the problem of comparing mobile phone tariffs.