App-based scaffolds for writing two-column proofs

This paper presents apps designed to assist students in understanding and developing proofs in geometric theorems. These technologies focus on triangle congruence, triangle similarity and properties of parallelograms. Focus group discussions and initial testing of the apps revealed that the apps offered a more engaging medium for learning proving and were capable of facilitating proof-writing skills in geometry.     

How does imposing a step-by-step solution method impact students’ approach to mathematical word problem solving?

This paper presents the second phase of a larger research program with the purpose of exploring the possible consequences of a gap between what is done in the classroom regarding mathematical word problem solving and what research shows to be effective in this particular field of study. Data from the first phase of our study on teachers’ self-proclaimed practices showed that one-third of elementary teachers from the region of Quebec require their students to follow a specific sequential problem-solving method, known as the ‘what I know, what I look for’ method. These results led us to hypothesize that the observed gap may have an impact on students’ comprehension of mathematical word problems. The use of this particular method was the foundation for us to study, in the second phase, the effect of the imposition of this sequential method on students’ literal and inferential understanding of word problems. A total of 278 fourth graders (9–10 years old) solved mathematical word problems followed by a test to assess their understanding of the word problems they had just solved. The results suggest that the use of this problem solving method does not seem to improve or impair students’ understanding. From a more fundamental point of view, our study led us to the conclusion that the way word problem solving is addressed in the mathematics classroom, through sequential and inflexible methods, does not help students develop their word problem solving competence.     

Compressing strongly connected subgroups in social networks: An entropy-based approach

To detect and study cohesive subgroups of actors is a main objective in social network analysis. What are the respective relations inside such groups and what separates them from the outside. Entropy-based analysis of network structures is an up-and-coming approach. It turns out to be a powerful instrument to detect certain forms of cohesive subgroups and to compress them to superactors without loss of information about their embeddedness in the net: Compressing strongly connected subgroups leaves the whole net’s and the (super-)actors’ information theoretical indices unchanged; i.e., such compression is information-invariant. The actual article relates on the reduction of networks with hundreds of actors. All entropy-based calculations are realized in an expert system shell.     

Are women better mindreaders? Sex differences in neural correlates of mentalizing detected with functional MRI

Background

Oxidative stress plays a key role in the neuropathogenesis of Human Immunodeficiency Virus-1 (HIV-1) infection causing apoptosis of astroglia cells and neurons. Recent data have shown that oxidative stress is also responsible for the acceleration of human fibroblast telomere shortening in vitro. In the present study we analyzed the potential relations occurring between free radicals formation and telomere length during HIV-1 mediated astroglial death.

Results

To this end, U373 human astrocytoma cells have been directly exposed to X4-using HIV-1IIIB strain, for 1, 3 or 5 days and treated (where requested) with N-acetylcysteine (NAC), a cysteine donor involved in the synthesis of glutathione (GSH, a cellular antioxidant) and apoptosis has been evaluated by FACS analysis. Quantitative-FISH (Q-FISH) has been employed for studying the telomere length while intracellular reduced/oxidized glutathione (GSH/GSSG) ratio has been determined by High-Performance Liquid Chromatography (HPLC). Incubation of U373 with HIV-1IIIB led to significant induction of cellular apoptosis that was reduced in the presence of 1 mM NAC. Moreover, NAC improved the GSH/GSSG, a sensitive indicator of oxidative stress, that significantly decreased after HIV-1IIIB exposure in U373. Analysis of telomere length in HIV-1 exposed U373 showed a statistically significant telomere shortening, that was completely reverted in NAC-treated U373.

Conclusion

Our results support the role of HIV-1-mediated oxidative stress in astrocytic death and the importance of antioxidant compounds in preventing these cellular damages. Moreover, these data indicate that the telomere structure, target for oxidative damage, could be the key sensor of cell apoptosis induced by oxidative stress after HIV infection.     

Special Lagrangian Submanifolds with Isolated Conical Singularities. II. Moduli spaces

This is the second in a series of five papers studying special Lagrangiansubmanifolds (SLV m-folds) X in (almost) Calabi–Yau m-folds M with singularities x ₁ , ..., x _n locally modelled on specialLagrangian cones C ₁, ..., C _n in ^m with isolated singularities at 0.Readers are advised to begin with Paper V.This paper studies the deformation theory of compact SL m-folds X in Mwith conical singularities. We define the moduli space _X of deformations of X in M, and construct a natural topology on it. Then we show that _X is locally homeomorphic to the zeroes of a smooth map : _{X X} between finite-dimensional vector spaces.Here the infinitesimal deformation space _X depends only on the topology of X, and the obstruction space _X only on the cones C ₁, ..., C _n at x ₁, ..., x _n . If the cones C _i are stable then _X is zero, and _X is a smooth manifold. We also extend our results to families of almost Calabi–Yau structures on M.     

Investigating secondary students beliefs about mathematical problem-solving

Many studies over the past 30 years have highlighted the important role of students’ beliefs for successful problem-solving in mathematics. Given the recent emphasis afforded to problem-solving on the reformed Irish secondary school mathematics curriculum, the main aim of this study was to identify Irish students’ (n = 975) beliefs about the field. A quantitative measure of these beliefs was attained through the use of the Indiana Mathematical Belief Scale, an existing 30-item (five-scale) self-report questionnaire. A statistical analysis of the data revealed that students who were further through their secondary education had a stronger belief that not all problems could be solved by applying routine procedures. In contrast, the same students held less positive beliefs than their younger counterparts that they could solve time-consuming problems and that conceptual understanding was important. The analysis also indicated that gender had a significant impact on three of the five belief scales.     

Stability and fragmentation of organic silicon functionalizations studied by laser desorption mass spectrometry

A method is introduced to investigate organic functionalizations on silicon by laser-induced thermal desorption (LITD), where well-ordered Si(1 1 1)-(1 × 1):H(D) surfaces are used to determine the desorption temperature as a function of laser fluence. To demonstrate the potential of this technique silicon surfaces with ultrathin oxide layers were functionalized with organic end groups. The species desorbed with focused XeCl laser pulses were monitored at an oblique angle and their time-of-flight (TOF) distributions were measured with a quadrupole mass analyzer after electron impact ionization. By assuming a negligible contribution of the oxide and organic layers to the heating effect, the TOF temperatures measured for Si(1 1 1)-(1 × 1):H(D) could be used to determine the mass of the desorbed species. Detailed results are presented for dimethylsilyl (DMS), bromomethyldimethylsilyl (BMDMS), and chloromethyldimethylsilyl (CMDMS) terminated surfaces which were prepared by silanization with suitable chloro and disilazane compounds. While for the DMS termination dimethylsilanol (76 u) is desorbed as a single species, clearly identifying the terminating group, in the case of BMDMS and CMDMS further fragmentation of the end group occurs at the surface.     

Initial incorporation of sulfur into the Pd(1 1 1) surface: A theoretical study

Density functional theory is used to investigate the initial inclusion of sulfur into the subsurface interstitial sites of Pd(1 1 1) surface. Pure subsurface adsorption is found to be less energetically favorable than on-surface adsorption. The incorporation of sulfur into the metal becomes more favorable than continuous adsorption on the surface after a critical on-surface sulfur coverage. We find subsurface sulfur occupation to be energetically favorable after adsorption of more than half a monolayer on the surface. Occupation of subsurface sites induces a pronounced structural distortion of the Pd(1 1 1) surface. We find significant expansion of interplanar spacing between the uppermost surface metal layers and rearrangement of the S overlayer. The interplay between the energy cost due to structural distortion of Pd(1 1 1) and the energy gain due to bond formation for different structures is discussed.     

Ideals and solutions of nonlinear field equations

Families of horizontal ideals of contact manifolds of finite order are studied. Each horizontal ideal is shown to admit ann-dimensional module of Cauchy characteristic vectors that is also a module of annihilators (in the sense of Cartan) of the contact ideal. Since horizontal ideals are generated by 1-forms, any completely integrable horizontal ideal in the family leads to a foliation of the contact manifold by submanifolds of dimensionn on which the horizontal ideal vanishes. Explicit conditions are obtained under which an open subset of a leaf of this foliation is the graph of a solution map of the fundamental ideal that characterizes a given system of partial differential equations of finite order withn independent variables. The solution maps are obtained by sequential integration of systems of autonomous ordinary differential equations that are determined by the Cauchy characteristic vector fields for the problem. We show that every smooth solution map can be obtained in this manner. Let {_Vi¦1in} be a basis for the module of Cauchy characteristic vector fields that are in Jacobi normal form. If a subsidiary balance ideal admits each of then vector fieldsV _i as a smooth isovector field, then certain leaves of the foliation generated by the corresponding closed horizontal ideal are shown to be graphs of solution maps of the fundamental ideal. A subclass of these constructions agree with those of the Cartan-Kähler theorem. Conditions are also obtained under which every leaf of the foliation is the graph of a solution map. Solving a given system ofr partial differential equations withn independent variables on a first-order contact manifold is shown to be equivalent to the problem of constructing a complete system of independent first integrals. Properties of systems of first integrals are analyzed by studying the collection ISO[A _ij ] of all isovectors of the horizontal ideal. We show that ISO[A _ij ] admits the direct sum decomposition ^*[A _ij ]W[A _ij ] as a vector space, where ^*[A _ij ] is the module of Cauchy characteristics of the horizontal ideal. ISO[A _ij ] also forms a Lie algebra under the standard Lie product,^*[A _ij ] andW[A _ij ] are Lie subalgebras of ISO[A _ij ], and [A _ij ] is an ideal. A change of coordinates that resolves (straightens out) the canonical basis for ^*[A _ij ] is constructed. This change of coordinates is used to reduce the problem of solving the given system of PDE to the problem of root extraction of a system ofr functions ofn variables, and to establish the existence of solutions to a second-order system of overdetermined PDE that generate the subspaceW[A _ij ]. Similar results are obtained for second-order contact manifolds. Extended canonical transformations are studied. They are shown to provide algorithms for calculating large classes of closed horizontal ideals and a partial analog of classical Hamilton-Jacobi theory.