A combined measurement of thermal and mechanical relaxation

In order to describe relaxation the thermodynamic coefficient can be generalized into a complex frequency-dependent cross response function. We explore theoretically the possibility of measuring for a supercooled liquid near the glass transition. This is done by placing a thermistor in the middle of the liquid which itself is contained in a spherical piezoelectric shell. The piezoelectric voltage response to a thermal power generated in the thermistor is found to be proportional to but factors pertaining to heat diffusion and adiabatic compressibility κ_S(ω) do also intervene. We estimate a measurable piezoelectric voltage of 1 mV to be generated at 1 Hz for a heating power of 0.3 mW. Together with κ_S(ω) and the longitudinal specific heat c_l(ω) which may also be found in the same setup a complete triple of thermoviscoelastic response functions may be determined when supplemented with shear modulus data.     

The Exponential Nature and Positivity

In the present article, a basis of the coordinate algebra of the multi-parameter quantized matrix is constructed by using an elementary method due to Lusztig. The construction depends heavily on an anti-automorphism, the bar action. The exponential nature of the bar action is derived which provides an inductive way to compute the basis elements. By embedding the basis into the dual basis of Lusztig's canonical basis of , the positivity properties of the basis as well as the positivity properties of the canonical basis of the modified quantum enveloping algebra of type , which has been conjectured by Lusztig, are proved.Presented by A. Verschoren.     

Evaluation of 27Al and 51V electric field gradients and the crystal structure for aluminum orthovanadate (AlVO4) by density functional theory calculations

Three sets of crystal-structure data reported for AlVO(4) from two powder-XRD studies and a density functional theory (DFT) investigation, employing the Vienna ab initio simulation package (VASP), have been examined and refined using the DFT structure-optimization scheme implemented in the WIEN2k software. The crystal structures are evaluated on the basis of (27)Al and (51)V quadrupole coupling parameters recently reported for AlVO(4), employing the corresponding electric-field gradient (EFG) tensor elements obtained from the DFT calculations. The DFT calculations provide a reliable assignment of the (27)Al/(51)V resonances from three distinct Al and three V environments to the specific crystallographic sites in the asymmetric unit for AlVO(4). An improved agreement between experimental quadrupole tensor elements and calculated EFG tensors is achieved after the DFT structure optimizations and consistent results are obtained using the three different structures as starting points. The improvement of the structural data is also supported by an evaluation of the Al-O and V-O bond lengths before and after DFT structure optimization. The (51)V nuclear quadrupole moment, |Q((51)V)| = 4.8 +/- 0.1 fm(2), derived from the present analysis, represents a value of higher accuracy than earlier reported Q((51)V) values. The origin of the (27)Al and (51)V EFGs are investigated by an evaluation of the orientations of the EFG tensors in the crystal frame and by an examination of the individual contributions from the valence electrons and the surrounding lattice. The latter investigation shows that the magnitude and orientation of the tensors are largely determined by the p-p((27)Al) and p-p, d-d((51)V) orbital contributions to the valence electrons, while the lattice part only gives a minor contribution for both nuclei.     

Covering homology

We introduce the notion of covering homology of a commutative S-algebra with respect to certain families of coverings of topological spaces. The construction of covering homology is extracted from Bökstedt, Hsiang and Madsen's topological cyclic homology. In fact covering homology with respect to the family of orientation preserving isogenies of the circle is equal to topological cyclic homology. Our basic tool for the analysis of covering homology is a cofibration sequence involving homotopy orbits and a restriction map similar to the restriction map used in Bökstedt, Hsiang and Madsen's construction of topological cyclic homology.Covering homology with respect to families of isogenies of a torus is constructed from iterated topological Hochschild homology. It receives a trace map from iterated algebraic K-theory and there is a hope that the rich structure, and the calculability of covering homology will make it useful in the exploration of J. Rognes' “red shift conjecture”.     

A thermally stable Pt/Y-based metal-organic framework: Exploring the accessibility of the metal centers with spectroscopic methods using H2O, CH3OH, and CH3CN as probes

A metal-organic framework (MOF) based on Pt, Y, and 2,2'-bipyridine-5,5'-dicarboxylate (BPDC), stable up to 400 degrees C, has been synthesized and characterized. In this MOF, the Pt centers are coordinated to Cl and the N atoms of the BPDC unit, giving a local environment similar to that found in a series of Pt-organic complexes with catalytic activity toward C-H bond cleavage of alkanes. This new material is a heterogeneous counterpart to the corresponding metal-organic complex. The structure, determined by single-crystal XRD data, is the repetition of three covalently bonded layers. These layers form a block, which is stacking as an (a)(b)(c) sequence along the crystallographic b-axis. Each layer contains the Pt-organic unit, while Y atoms represent the connection between adjacent layers. No covalent connection is present between layer (a) of a block and layer (c) of an adjacent block. EXAFS (BM29 at the ESRF) analysis supports the XRD data. As this MOF crystallizes under hydrothermal conditions, water acts both as solvent and as a direct ligand of Y. Accessibility to the metal centers is demonstrated by reversible water desorption/readsorption, as determined by TPA/TPD, FTIR, UV-vis, EXAFS, and XANES. Importantly, the results show that the as-synthesized material will not suffer a permanent loss in porosity upon solvent removal. In addition to water, methanol, ethanol, and acetonitrile can also access the internal void of the dehydrated phase.     

Conceptualizing inquiry-based education in mathematics

The terms inquiry-based learning and inquiry-based education have appeared with increasing frequency in educational policy and curriculum documents related to mathematics and science education over the past decade, indicating a major educational trend. We go back to the origin of inquiry as a pedagogical concept in the work of Dewey (e.g. 1916, 1938) to analyse and discuss its migration to science and mathematics education. For conceptualizing inquiry-based mathematics education (IBME) it is important to analyse how this concept resonates with already well-established theoretical frameworks in mathematics education. Six such frameworks are analysed from the perspective of inquiry: the problem-solving tradition, the theory of didactical situations, the realistic mathematics education programme, the mathematical modelling perspective, the anthropological theory of didactics, and the dialogical and critical approach to mathematics education. In an appendix these frameworks are illustrated with paradigmatic examples of teaching activities with inquiry elements. The paper is rounded off with a list of ten concerns for the development and implementation of IBME.     

The Translation Invariant Massive Nelson Model: II. The Continuous Spectrum below the Two-Boson Threshold

In this paper we continue the study of the energy-momentum spectrum of a class of translation invariant, linearly coupled, and massive Hamiltonians from non-relativistic quantum field theory. The class contains the Hamiltonians of E. Nelson (J Math Phys 5:1190–1197, 1964) and H. Fröhlich (Adv Phys 3:325–362, 1954). In Møller (Ann Henri Poincaré 6:1091–1135, 2005; Rev Math Phys 18:485–517, 2006) one of us previously investigated the structure of the ground state mass shell and the bottom of the continuous energy-momentum spectrum. Here we study the continuous energy-momentum spectrum itself up to the two-boson threshold, the threshold for energetic support of two-boson scattering states. We prove that non-threshold embedded mass shells have finite multiplicity and can accumulate only at thresholds. We furthermore establish the non-existence of singular continuous energy-momentum spectrum. Our results hold true for all values of the particle-field coupling strength but only below the two-boson threshold. The proof revolves around the construction of a certain relative velocity vector field used to construct a conjugate operator in the sense of Mourre.     

No Arbitrage and the Growth Optimal Portfolio

Abstract

Recently, several papers have expressed an interest in applying the Growth Optimal Portfolio (GOP) for pricing derivatives. We show that the existence of a GOP is equivalent to the existence of a strictly positive martingale density. Our approach circumvents two assumptions usually set forth in the literature: 1) infinite expected growth rates are permitted and 2) the market does not need to admit an equivalent martingale measure. In particular, our approach shows that models featuring credit constrained arbitrage may still allow a GOP to exist because this type of arbitrage can be removed by a change of numéraire. However, if the GOP exists the market admits an equivalent martingale measure under some numéraire and hence derivatives can be priced. The structure of martingale densities is used to provide a new characterization of the GOP which emphasizes the relation to other methods of pricing in incomplete markets. The case where GOP denominated asset prices are strict supermartingales is analyzed in the case of pure jump driven uncertainty.