Intra-mathematical connections made by high school students in performing Calculus tasks

In this article, we report the results of research that explores the intra-mathematical connections that high school students make when they solve Calculus tasks, in particular those involving the derivative and the integral. We consider mathematical connections as a cognitive process through which a person relates or associates two or more ideas, concepts, definitions, theorems, procedures, representations and meanings among themselves, with other disciplines or with real life. Task-based interviews were used to collect data and thematic analysis was used to analyze them. Through the analysis of the productions of the 25 participants, we identified 223 intra-mathematical connections. The data allowed us to establish a mathematical connections system which contributes to the understanding of higher concepts, in our case, the Fundamental Theorem of Calculus. We found mathematical connections of the types: different representations, procedural, features, reversibility and meaning as a connection.     

A fluorescence detection scheme for ultra large molecules after gas phase separation

A system was proposed to remove the upper mass limitation of mass spectrometry. In present study, ultra large molecules were separated in the gas phase by mass analyzer after electrospray ionization. Instead of conventional detection with electron multiplier, a laser-induced-fluorescence detection scheme was applied. The instrument sensitivity is independent of molecular weight, but related to the spectroscopic properties of the fluorophores presented by the large biomolecules.     

Practical considerations when using radio frequency-only quadrupole ion guide for atmospheric pressure ionization sources with time-of-flight mass spectrometry

Construction details and performance evaluation of a radio frequency (rf)-only quadrupole ion guide for use with an electrospray ionization time-of-flight mass spectrometer is presented in this paper. Angiotensin III and cytochrome c were used in these experiments to investigate the ion transmission properties of the rf-only quadrupole for different m/z species. In addition, influence of ion kinetic energies along with the characteristic fragmentation due to collision induced dissociation (CID) were studied. These experiments demonstrate that the transmissions of different m/z ions were not only dependent on the frequency and magnitude of the rf waveform, which is similar to a high vacuum rf-only quadrupole ion guide, but also on the pressure inside the quadrupole chamber. For the pressure range tested, low m/z ions are better focused with increasing pressure. As expected, transmission of ions are subject to space charge limitations when significant numbers of ions are focused on the axis of the quadrupole. It is also observed that CID results are related to transverse motion and longitude motion of ions inside the quadrupole region. Consequently, CID is useful for fragmentation of linear peptides and it is not effective (in present configuration) for large bulky proteins. The kinetic energy of ions that enter the repelling region of the TOFMS is ultimately determined by the ensemble effect resulting from the dc bias potential of the quadrupole (the dominant factor), skimmer-2, pressure inside the quadrupole chamber, and jet expansion. While this system is tested with an ESI source, the operational principle and design criteria are directly applicable for improving other atmospheric pressure ionization sources with time-of-flight mass analyzers such as an inductively coupled plasma ion source.     

Click-enabled heterotrifunctional template for sequential bioconjugations

A heterotrifunctional template was developed that utilizes thiol-maleimide and click chemistries (both copper-free and copper-mediated) to effect sequential biomolecule conjugations in a one-pot process. The breadth of compatible substrates was illustrated through highly efficient conjugations of protein, peptide, sugar, lipid, fluoroalkane, biotin and fluorophore molecules. This template should be useful for the creation of chemically-enhanced/enabled biotherapeutics, especially through the expression of discontinuous (and heterogeneous) epitopes.     

The Berge-Martinet Constant and Slopes of Siegel Cusp Forms

We give a theoretical lower bound for the slope of a Siegelmodular cusp form that is as least as good as Eichler's lowerbound. In degrees n = 5, 6 and 7 we show that our new boundis strictly better. In the process we find the forms of smallestdyadic trace on the perfect core for ranks n 8. In degreesn = 5, 6 and 7 we settle the value of the generalized Hermiteconstant introduced by Bergé and Martinet and find all dual-critical pairs. 2000 MathematicsSubject Classification 11H55 (11F46).     

Ascorbic Acid as an Initiator for the Direct CH Arylation of (Hetero)arenes with Anilines Nitrosated In Situ

Ascorbic acid (vitamin C) has been used as a radical initiator in a metal‐free direct C? H arylation of (hetero)arenes. Starting from an aniline, the corresponding arenediazonium ion is generated in situ and immediately reduced by vitamin C to an aryl radical that undergoes a homolytic aromatic substitution with a (hetero)arene. Notably, neither heating nor irradiation is required. This procedure is mild, operationally simple, and constitutes a greener approach to arylation.     

Continuous oxygen monitoring of mammalian cell growth on space shuttle mission STS-93 with a novel radioluminescent oxygen sensor

A compact, flow-through oxygen sensor device based on luminescence quenching was used to monitor dissolved oxygen levels during mammalian cell growth on the STS-93 mission of the Columbia space shuttle. Excitation of an oxygen-sensitive ruthenium complex was provided by a radiolumin escent light source (0.9 mm in diameter, 2.5 mm long), and the intensity of the resulting luminescence was measured by a simple photodiode detector. The use of radiolum inescence for the excitation light source is a unique approach that provides many features important for long-term and remote monitoring applications. For the spaceflight experiment, human lung fibroblast cells (WI-38) were grown in hollow-fiber bioreactors. Oxygen concentration was measured in the flow path both before and after the bioreactor cartridge in order to gain information about the metabolism of the cells. The sensor was found to be nonperturbing to cell growth and withstood the challenging physical conditions of shuttle launch and landing while maintaining a stable calibration function. In addition, the sensor provided physically meaningful oxygen predictions.