Structure-preserving Runge-Kutta methods for stochastic Hamiltonian equations with additive noise

There has been considerable recent work on the development of energy conserving one-step methods that are not symplectic. Here we extend these ideas to stochastic Hamiltonian problems with additive noise and show that there are classes of Runge-Kutta methods that are very effective in preserving the expectation of the Hamiltonian, but care has to be taken in how the Wiener increments are sampled at each timestep. Some numerical simulations illustrate the performance of these methods.

Family representatives in family firms

Research Question/Issue: Family control in family firms can extend beyond the direct involvement of family members, but identifying these mechanisms is difficult in most markets. We utilize unique disclosures made by Taiwanese firms to examine the role played by family representatives in listed family firms. Family representatives are non-family members that represent the controlling family’s indirect shareholdings in the firm. We examine whether family representatives are used in the same manner as family members and whether they provide net benefits or costs to shareholders. Research Findings/Insights: In our sample of listed family firms, we find that omitting family representatives understates the influence of controlling families by 46 percent. We show that family representatives are associated with net costs to shareholders, but to a lesser extent than family members. We also find that controlling families use family members and family representatives differently. Family members are more involved in older family firms and in firms founded by the family. Family representatives are more involved in acquired and second generation family firms and in larger firms with more fixed assets. Theoretical/Academic Implications: We apply agency theory to the use of family representatives and show that family representatives are being used by controlling families to extend their influence within their firms, increasing agency costs to minority shareholders. Practitioner/Policy Implications: For policymakers, our analysis shows that disclosure of family member and representative relationships within firms is important and value-relevant to investors. Furthermore, our results suggest that firm performance could be improved by limiting the involvement of family members and family representatives in family firms.

Reconceptualizing Early Mathematics Learning : The Fundamental Role of Pattern and Structure

The Pattern and Structure Mathematics Awareness Program (PASMAP) was developed concurrently with the studies of AMPS and the development of the Pattern and Structure Assessment (PASA) interview. We summarize some early classroom-based teaching studies and describe the PASMAP that resulted. A large-scale two-year longitudinal study, Reconceptualizing Early Mathematics Learning (REML) resulted. We provide an overview of the REML study and discuss the consequences for our view of early mathematics learning. A purposive sample of four large primary schools, two in Sydney and two in Brisbane, representing 316 students from diverse socio-economic and cultural contexts, participated in an evaluation of the PASMAP intervention throughout the 2009 school year and a follow-up assessment in 2010. Two different mathematics programs were implemented: in each school, two Kindergarten teachers implemented the PASMAP and another two implemented their regular program. The study shows that both groups of students made substantial gains on the ‘I Can Do Maths’ standardized assessment and the PASA interview, but highly significant differences were found on the latter with PASMAP students outperforming the regular group on PASA scores. Qualitative analysis of students’ responses for structural development showed increased levels for the PASMAP students. Implications for pedagogy and curriculum are discussed.

Structure, magnetism and colour in simple bis­(phosphine)nickel(II) dihalide complexes : an experimental and theoretical investigation

The complex [1,2-bis­(di-tert-butyl­phosphan­yl)ethane-[kappa]2P,P']di­iodido­nickel(II), [NiI2(C18H40P2] or (dtbpe-[kappa]2P)NiI2, [dtbpe is 1,2-bis­(di-tert-butyl­phosphan­yl)ethane], is bright blue-green in the solid state and in solution, but, contrary to the structure predicted for a blue or green nickel(II) bis­(phos­phine) complex, it is found to be close to square planar in the solid state. The solution structure is deduced to be similar, because the optical spectra measured in solution and in the solid state contain similar absorptions. In solution at room temperature, no 31P{1H} NMR resonance is observed, but the very small solid-state magnetic moment at temperatures down to 4 K indicates that the weak paramagnetism of this nickel(II) complex can be ascribed to temperature independent paramagnetism, and that the complex has no unpaired electrons. The red [1,2-bis­(di-tert-butyl­phosphan­yl)ethane-[kappa]2P,P']di­chlorido­nickel(II), [NiCl2(C18H40P2] or (dtbpe-[kappa]2P)NiCl2, is very close to square planar and very weakly paramagnetic in the solid state and in solution, while the maroon [1,2-bis­(di-tert-butyl­phosphan­yl)ethane-[kappa]2P,P']di­bromido­nickel(II), [NiBr2(C18H40P2] or (dtbpe-[kappa]2P)NiBr2, is isostructural with the diiodide in the solid state, and displays paramagnetism inter­mediate between that of the dichloride and the diiodide in the solid state and in solution. Density functional calculations demonstrate that distortion from an ideal square plane for these complexes occurs on a flat potential energy surface. The calculations reproduce the observed structures and colours, and explain the trends observed for these and similar complexes. Although theoretical investigation identified magnetic-dipole-allowed excitations that are characteristic for temperature-independent paramagnetism (TIP), theory predicts the mol­ecules to be diamagnetic.

Vibrational spectroscopy of the silicate mineral plumbotsumite Pb5(OH)10Si4O8 : an assessment of the molecular structure

We have used scanning electron microscopy with energy dispersive X-ray analysis to determine the precise formula of plumbotsumite, a rare lead silicate mineral of formula Pb5(OH)10Si4O8. This study forms the first systematic study of plumbotsumite from the Bigadic deposits, Turkey. Vibrational spectroscopy was used to assess the molecular structure of plumbotsumite as the structure is not known. The mineral is characterized by sharp Raman bands at 1047, 1055 and 1060 cm−1 assigned to SiO stretching vibrational modes and sharp Raman bands at 673, 683 and 697 cm−1 assigned to OSiO bending modes. The observation of multiple bands offers support for a layered structure with variable SiO3 structural units. Little information may be obtained from the infrared spectra because of broad spectral profiles. Intense Raman bands at 3510, 3546 and 3620 cm−1 are ascribed to OH stretching modes. Evidence for the presence of water in the plumbotsumite structure was inferred from the infrared spectra.

Vibrational spectroscopy of the borate mineral chambersite MnB7O13Cl – Implications for the molecular structure

Chambersite is a manganese borate mineral with formula: MnB7O13Cl and occurs as colorless crystals in the monoclinic pyramidal crystal system. Raman bands at 902, 920, 942 and 963 cm-1 are assigned to the BO stretching vibration of the B7O13 units. Raman bands at 1027, 1045, 1056, 1075 and 1091 cm-1 are attributed to the BCl in-plane bending modes. The intense infrared band at 866 cm-1 is assigned to the trigonal borate stretching modes. The Raman band at 660 cm-1 together with bands at 597, 642 679, 705 and 721 cm-1 are assigned to the trigonal and tetrahedral borate bending modes. The molecular structure of a natural chambersite has been assessed using vibrational spectroscopy.

Vibrational spectroscopic characterization of the phosphate mineral althausite Mg2(PO4)(OH,F,O) – implications for the molecular structure

Natural single-crystal specimens of althausite from Brazil, with general formula Mg2(PO4)(OH,F,O) were investigated by Raman and infrared spectroscopy. The mineral occurs as a secondary product in granitic pegmatites. The Raman spectrum of althausite is characterized by bands at 1020, 1033 and 1044 cm-1, assigned to ν1 symmetric stretching modes of the HOPO33- and PO43- units. Raman bands at around 1067, 1083 and 1138 cm-1 are attributed to both the HOP and PO antisymmetric stretching vibrations. The set of Raman bands observed at 575, 589 and 606 cm-1 are assigned to the ν4 out of plane bending modes of the PO4 and H2PO4 units. Raman bands at 439, 461, 475 and 503 cm-1 are attributed to the ν2 PO4 and H2PO4 bending modes. Strong Raman bands observed at 312, 346 cm-1 with shoulder bands at 361, 381 and 398 cm-1 are assigned to MgO stretching vibrations. No bands which are attributable to water were found. Vibrational spectroscopy enables aspects of the molecular structure of althausite to be assessed.