The cultural dimension of beliefs: an investigation of future primary teachers’ epistemological beliefs concerning the nature of mathematics in 15 countries

Beliefs constitute a central part of a person’s professional competencies and are crucial to the perception of situations as they influence our choice of actions. This paper focuses on epistemological beliefs about the nature of mathematics of future primary teachers from an international perspective. The data reported are part of a larger sample originating from the TEDS-M study which compares primary mathematics teacher education in 15 countries. In this paper we examine the pattern of beliefs of future teachers aiming to teach mathematics at primary level. We explore whether and to what extent beliefs concerning the nature of mathematics are influenced by cultural factors, in our case the extent to which a country’s culture can be characterized by an individualistic versus collectivistic orientation according to Hofstede’s terminology. In the first part of the paper, the literature on epistemological beliefs is reviewed and the role of culture and individualism/collectivism on the formation of beliefs concerning the nature of mathematics will be discussed. In the empirical part, means and distributions of belief ratings will be reported. Finally, multilevel analyses explore how much of the variation of belief preferences between countries can be explained by the individualistic orientation of a country.     

Discrete-to-Continuum Limit of Magnetic Forces: Dependence on the Distance Between Bodies

We investigate force formulae for two rigid magnetic bodies in dependence on their mutual distance. These formulae are derived as continuum limits of atomistic dipole–dipole interactions. For bodies that are far apart in terms of the typical lattice spacing we recover a classical formula for magnetic forces. For bodies whose distance is comparable to the atomistic lattice spacing, however, we discover a new term that explicitly depends on the distance, measured in atomic units, and the underlying crystal lattice structure. This new term links the classical force formula and a limiting force formula obtained earlier in the case of two bodies being in contact on the atomistic scale.     

Stress-Induced Phase Transformations in Shape-Memory Polycrystals

Shape-memory alloys undergo a solid-to-solid phase transformation involving a change of crystal structure. We examine model problems in the scalar setting motivated by the situation when this transformation is induced by the application of stress in a polycrystalline material made of numerous grains of the same crystalline solid with varying orientations. We show that the onset of transformation in a granular polycrystal with homogeneous elasticity is in fact predicted accurately by the so-called Sachs bound based on the ansatz of uniform stress. We also present a simple example where the onset of phase transformation is given by the Sachs bound, and the extent of phase transformation is given by the constant strain Taylor bound. Finally we discuss the stress–strain relations of the general problem using Milton–Serkov bounds.     

On a Sachs bound for stress-induced phase transformations in polycrystalline shape memory alloys

In earlier work [3], a Sachs and a Taylor bound on the transformation yield stress in shape memory polycrystals were derived in the context of a variational model. The aim of this article is to compare the Sachs with the Taylor bound for cubic-toorthorhombic phase transformations under biaxial loading, where the material parameters are chosen explicitly (CuAlNi). It turns out that the gap between the two bounds can be quite large depending on the underlying texture and the loading direction. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comparative Analysis of the Antitumor Activity of Cis- and Trans-Resveratrol in Human Cancer Cells with Different p53 Status

Resveratrol, a natural plant phytoalexin, is produced in response to fungal infection or− UV irradiation. It exists as an isomeric pair with cis- and trans-conformation. Whereas multiple physiological effects of the trans-form, including a pronounced anti-tumoral activity, are nowadays elucidated, much less knowledge exists concerning the cis-isomer. In our work, we analyzed the antiproliferative and cytotoxic properties of cis-resveratrol in four different human tumor entities in direct comparison to trans-resveratrol. We used human cell lines as tumor models for hepatocellular carcinoma (HCC; HepG2, Hep3B), colon carcinoma (HCT-116, HCT-116/p53^(−/−)), pancreatic carcinoma (Capan-2, MiaPaCa-2), and renal cell carcinoma (A498, SN12C). Increased cytotoxicity in all investigated tumor cells was observed for the trans-isomer. To verify possible effects of the tumor suppressor p53 on resveratrol-induced cell death, we used wild type and p53-deleted or -mutated cell lines for every tested tumor entity. Applying viability and cytotoxicity assays, we demonstrated a differential, dose-dependent sensitivity towards cis- or trans-resveratrol among the respective tumor types.     

Novel heterocyclic inhibitors of matrix metalloproteinases: three 6H‐1,3,4‐thiadiazines

The title compounds, (2S)‐N‐[5‐(4‐chloro­phenyl)‐2,3‐di­hydro‐6H‐1,3,4‐thia­diazin‐2‐yl­idene]‐2‐[(phenyl­sulfonyl)­amino]­pro­pan­amide, C₁₈H₁₇ClN₄O₃S₂, (I), (2R)‐N‐[5‐(4‐fluoro­phenyl)‐6H‐1,3,4‐thia­diazin‐2‐yl]‐2‐[(phenyl­sulfonyl)amino]­propan­amide, C₁₈H₁₇FN₄O₃S₂, (II), and (2S)‐N‐[5‐(5‐chloro‐2‐thienyl)‐6H‐1,3,4‐thia­diazin‐2‐yl]‐2‐[(phenyl­sulfonyl)­amino]­propan­amide, C₁₆H₁₅ClN₄O₃S₃, (III), are potent inhibitors of matrix metalloproteinases. In all three compounds, the thia­diazine ring adopts a screw‐boat conformation. The mol­ecules of compound (I) show a short intramolecular N_Ala—H?N_exo hydrogen bond [N?N 2.661 (3) Å] and are linked into a chain along the c axis by N_endo—H?S_endo and N_endo—H?O_Ala hydrogen bonds [N?S 3.236 (3) and N?O 3.375 (3) Å] between neighbouring mol­ecules. In compound (II), the mol­ecules are connected antiparallel into a chain along the a axis by N_exo—H?O_Ala and N_Ala—H?N_endo hydrogen bonds [N?O 2.907 (6) and N?N 2.911 (6) Å]. The mol­ecules of compound (III) are dimerized antiparallel through N_exo—H?N_endo hydrogen bonds [N?N 2.956 (7) and 2.983 (7) Å]. The different hydrogen‐bonding patterns can be explained by an amido–imino tautomerism (prototropic shift) shown by different bond lengths within the 6H‐1,3,4‐thia­diazine moiety.     

Pharmacomodulation of a ligand targeting the HBV capsid hydrophobic pocket

Hepatitis B virus (HBV) is a small enveloped retrotranscribing DNA virus and an important human pathogen. Its capsid-forming core protein (Cp) features a hydrophobic pocket proposed to be central notably in capsid envelopment. Indeed, mutations in and around this pocket can profoundly modulate, and even abolish, secretion of enveloped virions. We have recently shown that Triton X-100, a detergent used during Cp purification, binds to the hydrophobic pocket with micromolar affinity. We here performed pharmacomodulation of pocket binders through systematic modifications of the three distinct chemical moieties composing the Triton X-100 molecule. Using NMR and ITC, we found that the flat aromatic moiety is essential for binding, while the number of atoms of the aliphatic chain modulates binding affinity. The hydrophilic tail, in contrast, is highly tolerant to changes in both length and type. Our data provide essential information for designing a new class of HBV antivirals targeting capsid–envelope interactions.

Small-molecule binding to the Hepatitis B virus core protein hydrophobic pocket, a possible strategy for targeting viral particle assembly.     

Carbon dioxide reduction by an Al–O–P frustrated Lewis pair

The reaction of tBu₂P(O)H with Bis₂AlH (Bis = CH(SiMe₃)₂) afforded the adduct tBu₂P(H)–O–Al(H)Bis₂ (3). It slowly releases H₂ to form the first oxygen-bridged geminal Al/P frustrated Lewis pair tBu₂P–O–AlBis₂. It is capable of reversibly binding molecular hydrogen to afford 3, shown by NMR and H/D scrambling experiments, and forms a 1,2-adduct with CO₂. Importantly, the H₂ adduct 3 reduces CO₂ in a stoichiometric reaction leading to the formic acid adduct tBu₂P(H)–O–Al(CO₂H)Bis₂. The formation of the different species was explored by density functional theory calculations which provide support for the experimental results. All products were characterized by NMR spectroscopy as well as X-ray diffraction experiments and elemental analyses.

Addition vs. reduction: the geminal FLP Bis₂Al–O–PtBu₂ can reversibly bind molecular hydrogen, it reacts with CO₂ to give an adduct, and its hydrogen adduct reduces CO₂ to an adduct of formic acid.     

Non-Coordinated Phenolate Anions and Their Application in SF6 Activation

The reaction of the strong monophosphazene base with the weakly acidic phenol leads to the formation of a phenol–phenolate anion with a moderately strong hydrogen bond. Application of the more powerful tetraphosphazene base (Schwesinger base) renders the isolation of the corresponding salt with a free phenolate anion possible. This compound represents the first species featuring the free phenolate anion [H₅C₆-O]⁻. The deprotonation of phenol derivatives with tetraphosphazene bases represents a great way for the clean preparation of salts featuring free phenolate anions and in addition allows the selective syntheses of hydrogen bonded phenol-phenolate salts. This work presents a phosphazenium phenolate salt with a redox potential of −0.72 V and its capability for the selective activation of the chemically inert greenhouse gas SF₆. The performed two-electron reduction of SF₆ leads to phosphazenium pentafluorosulfanide ([SF₅]⁻) and fluoride salts.