Learning beginning algebra in a computer-intensive environment

We present a design research on learning beginning algebra in an environment where spreadsheets were available at all times but the decision about using them or not, and how, in any particular situation was left to the students. Students’ activity is analyzed in Kieran’s framework of generational, transformational and global/meta-level activity, and compared to the designers’ intentions. We do this by focusing on the activity of one student in four sessions spread over several months and discussing the activity of 51 additional students in view of the analysis of the focus student. We show that the environment enables a number of different entries into algebra and as such supports students in becoming autonomous learners of algebra, and in making the shift from arithmetic to algebra via generational and global/meta-level activity before dealing with the more technical transformational activities.     

Which finite simple groups are unit groups?

We prove that if G$G$ is a finite simple group which is the unit group of a ring, then G$G$ is isomorphic to: (a) a cyclic group of order 2; or (b) a cyclic group of prime order 2^k−1$2^k-1$ for some k$k$; or (c) a projective special linear group _PSLn(_F2)${PSL}_n\left({\mathbb{F}}_2\right)$ for some n≥3$n\ge 3$. Moreover, these groups do all occur as unit groups. We deduce this classification from a more general result, which holds for groups G$G$ with no non-trivial normal 2-subgroup.     

Lp-estimates for the nonlinear spatially homogeneous Boltzmann equation

This paper studies L^p-estimates for solutions of the nonlinear, spatially homogeneous Boltzmann equation. The molecular forces considered include inverse k^th-power forces with k > 5 and angular cut-off.The main conclusions are the following. Let f be the unique solution of the Boltzmann equation with f(v,t)(1 + ¦v²¦)^(s ₁ ^{+ /p)/2} L¹, when the initial value f ₀ satisfies f ₀(v) 0, f ₀(v) (1 + ¦v¦²)^(s ₁ ^{+ /p)/2} L¹, for some s₁ 2 + /p, and f ₀(v) (1 + ¦v¦²)^s/2 L^p. If s 2/p and 1 < p < , then f(v, t)(1 + ¦v¦²)^{(s s} ₁)^/2 L^p, t > 0. If s >2 and 3/(1+ ) < p < , thenf(v,t) (1 + ¦v¦²)^(s(s ₁ ^{+ 3/p))/2} L^p, t > 0. If s >2 + 2C₀/C₁ and 3/(l + ) < p < , then f(v,t)(1 + ¦v¦²)^s/2 L^p, t > 0. Here 1/p + 1/p = 1, x y = min (x, y), and C₀, C₁, 0 < 1, are positive constants related to the molecular forces under consideration; = (k – 5)/ (k – 1) for k^th-power forces.Some weaker conclusions follow when 1 < p 3/ (1 + ).In the proofs some previously known L-estimates are extended. The results for L^p, 1 < p < , are based on these L-estimates coupled with nonlinear interpolation.     

Cerebral abnormalities in Wilson''s disease as evaluated by ultra-low-field magnetic resonance imaging and computerized image processing

The cerebral involvement of a 13-yr-old boy with Wilson's disease was serially evaluated during the first 18 mo of D-penicillamine treatment. An ultra-low-field magnetic resonance imaging (ULF MRI) system, operating at 0.02 T, with computerized image processing was used. The half-yr period prior to the clinical diagnosis was set, the patient had showed poor school performance, emotional lability, deteriorating handwriting, progressively slow, gross, and fine motor functions, and a fixed rigid smile. No overt signs of liver disease were found. With D-penicillamine treatment (1–1.5 g/d) a continuous improvement was seen. The pretreatment MRI investigation showed pronounced pathological transformation in the basal ganglia. However, changes were seen also in most other parts of the brain indicating diffuse involvement. During treatment the computerized MR images became gradually more normal. The current magnetic resonance imaging system with computerized image processing is a sensitive and simple method for evaluation of subtle parenchymal changes of the brain.     

Threshold effects on renormalization group running of neutrino parameters in the low-scale seesaw model

We show that, in the low-scale type-I seesaw model, renormalization group running of neutrino parameters may lead to significant modifications of the leptonic mixing angles in view of so-called seesaw threshold effects. Especially, we derive analytical formulas for radiative corrections to neutrino parameters in crossing the different seesaw thresholds, and show that there may exist enhancement factors efficiently boosting the renormalization group running of the leptonic mixing angles. We find that, as a result of the seesaw threshold corrections to the leptonic mixing angles, various flavor symmetric mixing patterns (e.g., bi-maximal and tri-bimaximal mixing patterns) can be easily accommodated at relatively low energy scales, which is well within the reach of running and forthcoming experiments (e.g., the LHC).     

Magnetic response of microbially synthesized transition metal- and lanthanide-substituted nano-sized magnetites

The magnetic susceptibility (κ_RT) and saturation magnetization (M_S) of microbially synthesized magnetites were systematically examined. Transition metal (Cr, Mn, Co, Ni and Zn)- and lanthanide (Nd, Gd, Tb, Ho and Er)-substituted magnetites were microbially synthesized by the incubation of transition metal (TM)- and lanthanide (L)-mixed magnetite precursors with either thermophilic (TOR-39) or psychrotolerant (PV-4) metal-reducing bacteria (MRB). Zinc incorporated congruently into both the precursor and substituted magnetite, while Ni and Er predominantly did not. Microbially synthesized Mn- and Zn-substituted magnetites had higher κ_RT than pure biomagnetite depending on bacterial species and they exhibited a maximum κ_RT at 0.2 cationic mole fraction (CMF). Other TMs’ substitution linearly decreased the κ_RT with increasing substitution amount. Based on the M_S values of TM- and L-substituted magnetite at 0.1 and 0.02 CMF, respectively, Zn (90.7 emu/g for TOR-39 and 93.2 emu/g for PV-4)- and Mn (88.3 emu/g by PV-4)-substituted magnetite exhibited higher M_S than standard chemical magnetite (84.7 emu/g) or pure biomagnetite without metal substitution (76.6 emu/g for TOR-39 and 80.3 emu/g for PV-4). Lanthanides tended to decrease M_S, with Gd- and Ho-substituted magnetites having the highest magnetization. The higher magnetization of microbially synthesized TM-substituted magnetites by the psychrotroph, PV-4 may be explained by the magnetite formation taking place at low temperatures slowing mechanics, which may alter the magnetic properties compared to the thermophile, through suppression of the random distribution of substituted cations.     

Automatic analysis of multiplex ligation-dependent probe amplification products (exemplified by a commercial kit for prenatal aneuploidy detection)

For use in routine prenatal diagnostics, we developed software and methods for automatic aneuploidy detection based on a commercial multiplex ligation-dependent probe amplification (MLPA) kit. Software and methods ensure a reliable, objective, and fast workflow, and may be applied to other types of MLPA kits. Following CE of MLPA amplification products, the software automatically identified the peak area for each probe, normalized it in relation to the neighboring peak areas of the test sample, computed the ratio relative to a reference created from normal samples, and compensated the ratio for a side effect of the normalization procedure that scaled all chromosomally normal DNA peak areas slightly up or down depending on the kind of aneuploidy present. For the chromosomes 13, 18, 21, X, and Y, probe reliability weighted mean ratio values and corresponding SDs were calculated, and the significance for being outside a reference interval around ratio 1.0 was tested. p < or = 1% suggested aneuploidy and 1 < p < or = 5% suggested potential aneuploidy. Individual peaks, where the normalized area was situated more than 4 SD from the corresponding reference, suggested possible partial deletion or gain. Sample quality was automatically assessed. Control probes were not required. Having used the software and methods for two years, we conclude that a reliable, objective, and fast workflow is obtained.     

A Validated LC Method for the Quantitation of Cefotaxime in pH-Sensitive Nanoparticles

A sensitive and rapid routine LC method was validated for measuring cefotaxime incorporated in three different pH-sensitive nanoparticles. The drug was chromatographed on a C18 reversed-phase column; the mobile phase used was 0.05 M aqueous ammonium acetate, acetonitrile and tetrahydrofuran (87:11:2, v/v) adjusted to pH 5.5 with acetic acid. The flow rate was 1 mL min^?1 and cefotaxime was quantified at 254 nm, with a sensitivity range of 0.005 AUFS. The validated method was specific, linear (R ² ≥ 0.999), precise and accurate in a concentration range of 0.2–50.0 μg mL^?1. The method was rapid, selective and suitable for evaluation of cefotaxime in pH-sensitive Eudragit nanoparticles.