Cultivating inquiry about space in a middle school mathematics classroom

During 46 lessons in Euclidean geometry, sixth-grade students (ages 11, 12) were initiated in the mathematical practice of inquiry. Teachers supported inquiry by soliciting student questions and orienting students to related mathematical habits-of-mind such as generalizing, developing relations, and seeking invariants in light of change, to sustain investigations of their questions. When earlier and later phases of instruction were compared, student questions reflected an increasing disposition to seek generalization and to explore mathematical relations, forms of thinking valued by the discipline. Less prevalent were questions directed toward search for invariants in light of change. But when they were posed, questions about change tended to be oriented toward generalizing and establishing relations among mathematical objects and properties. As instruction proceeded, students developed an aesthetic that emphasized the value of questions oriented toward the collective pursuit of knowledge. Post-instructional interviews revealed that students experienced the forms of inquiry and investigation cultivated in the classroom as self-expressive.     

The behaviour of copper on gallium arsenide

Cu has been reported to diffuse rapidly in GaAs at low temperatures (2.3×10^-5 cm² s^-1 at 600°C). The rapid diffusion is attributed to the interstitial movement of Cu atoms. The present investigation was undertaken to examine preferential diffusion of Cu⁺ along dislocations and grain boundaries in GaAs. The experiments consisted of depositing ⁶⁴Cu on a GaAs water surface, annealing in vacuum, and observing the Cu distribution by autoradiography. From these observations no preferential diffusion along dislocations or grain boundaries was detected in SI GaAs annealed between 600 and 1000°C. In the sample annealed above 800°C, the deposited Cu reacted with the GaAs forming a liquid on the sample surface, which solidified into complex Cu-Ga-As compounds. The liquid also produced Cu-rich pipes which extended through the GaAs wafer.     

Die quantitative chemische Bestimmung von Vitamin D

Zusammenfassung Die zur Vitamin D₂-Bestimmung bekannten spezifischen Farbreaktionen nachHalden und H.Brockmann werden durch die Unbeständigkeit des erhaltenen Farbtones und dieser durch Fettbegleitsubstanzen empfindlich gestört. Es gelingt, eine für Vitamin D spezifische, im Farbton beständige Reaktion bei Verwendung einer 20%igen Antimontrichloridund 5%igen Guajakol-Lösung in Chloroform. Die Empfindlichkeit der Reaktion ist 1200000. Es können quantitativ 15 in 2,8 ml Chloroform nachgewiesen werden bei tunlichster Einhaltung der beschriebenen Versuchsbedingungen.Der Einfluß der Sterine auf die Reaktion ist sehr gering, doch werden die Empfindlichkeit und die Spezifität dann vermindert, wenn sehr große Mengen dieser Begleitstoffe vorhanden sind. Mit Hilfe der Adsorption an frisch behandeltes, bei 120 erhitztes Aluminiumoxyd können störende Begleitstoffe abgetrennt werden. Das Vitamin D₂ wird dabei in einer scharf umrissenen Zone festgehalten, die im UV.-Licht weiß aufleuchtet.Die vorliegende Methode ist geeignet zur mengenmäßigen Bestimmung von Vitamin D in tierischen und pflanzlichen Fetten, in Milch und Milcherzeugnissen, in Kindernährmitteln, bestrahlten Hefen und pharmazeutischen Präparaten. Um die hier auftretenden, störenden Begleitstoffe auszuschalten, werden die Präparate nach der Extraktion des Vitamins D verseift, und der unverseifbare Anteil wird an Aluminiumoxyd adsorbiert. Dabei wird das Vitamin D bei Einhaltung der Arbeitsvorschrift immer in einer charakteristischen schmalen Zone festgehalten, die im Tageslicht gelb bis rosafarben erscheint. Durch die Anwesenheit von Vitamin A, Provitamin A und anderen. Carotinoiden kann die Reaktion gestört werden, so daß auch hier eine chromatographische Auftrennung erforderlich ist, die sich aber leicht durchführen läßt.     

Reaction of secondary and tertiary aliphatic halides with aromatic aldehydes mediated by chromium(II): a selective cross-coupling of alkyl and ketyl radicals

Takai-Utimoto reactions with secondary and tertiary aliphatic halides usually failed according to previous reports. Now, significant improvements could be achieved, and especially secondary aliphatic halides can be coupled to aromatic aldehydes in yields of up to >95%. A variety of processes are competing with the desired one, and thus conditions must be adapted to the nature of the aldehyde as well as the aliphatic halide used, as the outcome of these reactions is strongly affected by the putative radical intermediates.     

Isotope dilution for quantitation of steroid estrogens and nonylphenols by gas chromatography with tandem mass spectrometry in septic, soil, and groundwater matrices

A simplified, in-line solid-phase extraction and clean-up process is presented for rapid extraction and analysis of steroid estrogens and nonylphenols by gas chromatography with tandem mass spectrometry. Isotope dilution with multiple deuterated standards has been developed, evaluated, and verified using this method against standard addition for the analysis of estrone, estradiol, estriol, ethinylestradiol, and 4-nonylphenols in septic, soil, and groundwater matrices. The accuracy and precision of isotope dilution was comparable to standard addition yet was able to quantify analytes with the use of fewer samples by including [(2)H(4)]estradiol, [(2)H(4)]ethinylestradiol, [(2)H(4)]nonylphenol, and estradiol-17-acetate as internal standards. Specific details and validation of the method are presented as are data showing the occurrence of estrogens and nonylphenols in an on-site wastewater treatment (septic) system with advanced stages of pretreatment and recirculation to an office building for non-potable reuse.     

A new saponin lactone from Astragalus corniculatus

A new oleanane-type saponin lactone was isolated from the ethanolic extract of the aerial parts of Astragalus corniculatus Bieb. The structure of the saponin was elucidated as 19-hydroxyolean-12-ene-28, 21beta-olide 3beta-D-xylopyranoside (1) by chemical and spectral methods.     

Advantages of using multiple-echo image combination and asymmetric triangular phase masking in magnetic resonance venography at 3 T

The present work explores the possibility of localizing veins with magnetic resonance venography using susceptibility weighted imaging. It also seeks new approaches, directed by the spatial specificity of activated brain regions, that have sufficient precision for practical use in functional MRI studies. A 3D flow compensated multiple gradient echo sequence, featuring optimized T2* weighting within a reasonable time of acquisition (11 min) and a small voxel size (0.5x0.5x1 mm3), was used to acquire MR images at 3 T. Post-processing consisted of homodyne filtering, linear phase scaling and magnitude masking prior to minimum intensity projection (mIP). The multiple echo approach provided a satisfactory (48+/-7%) increase in signal-to-noise ratio with respect to conventional methods. Specific features of the blood oxygenation level-dependent phase effect were simulated and used for designing and exploring different phase masking methods in relation to vessel morphology and MRI voxel geometry. As with simulations, the best results were obtained with an asymmetric triangular phase masking, featuring an improved venographic contrast without any increase in the full-width at half-maximum. The multiple echo approach provided satisfactory vessel localization capacity by using asymmetric triangular phase masking and a 4-mm-thick mIP. The venographic contrast obtained enabled the detection of vessels with diameter down to approximately 500 microm, suggesting the applicability of the proposed method as an additional technique in fMRI studies.