Decoupling the electrical conductivity and Seebeck coefficient in the RE2SbO2 compounds through local structural perturbations

Compromise between the electrical conductivity and Seebeck coefficient limits the efficiency of chemical doping in the thermoelectric research. An alternative strategy, involving the control of a local crystal structure, is demonstrated to improve the thermoelectric performance in the RE(2)SbO(2) system. The RE(2)SbO(2) phases, adopting a disordered anti-ThCr(2)Si(2)-type structure (I4/mmm), were prepared for RE = La, Nd, Sm, Gd, Ho, and Er. By traversing the rare earth series, the lattice parameters of the RE(2)SbO(2) phases are gradually reduced, thus increasing chemical pressure on the Sb environment. As the Sb displacements are perturbed, different charge carrier activation mechanisms dominate the transport properties of these compounds. As a result, the electrical conductivity and Seebeck coefficient are improved simultaneously, while the number of charge carriers in the series remains constant.     

Raman spectroscopy of natural cordierite at high water pressure up to 5 GPa

The high‐pressure behaviour of cordierite, a widespread ring aluminosilicate with channels incorporating fluid compounds (H₂O, CO₂), is characterized by the absence of phase transitions up to 2.5 GPa. However, the distortion of the ring tetrahedra observed previously at 2.3 GPa is supposed to introduce a phase transition at higher pressure, which has not been checked so far. This work presents a high‐pressure Raman spectroscopic study of natural cordierite compressed in water medium up to 4.7 GPa in a diamond anvil cell. At P > 4 GPa, a disordering of both the framework and intrachannel H₂O subsystem is apparent from significant broadening of Raman peaks and the evolution of short‐range order parameters. This is followed by abrupt shifts of the framework and O–H stretching modes at about 4.5 GPa, indicating a first‐order phase transition. Its reversibility is seen from the recovery of the initial spectrum at P < 3 GPa. The shift amplitudes of different framework modes indicate the predominance of distortion over contraction of the framework polyhedra upon this transition. The disordering of the H₂O subsystem in the high‐pressure phase is likely a consequence of distortion of the channel‐forming framework elements, which is supposed to be a driving force of this transition. Copyright © 2011 John Wiley & Sons, Ltd.     

On local convexity of nonlinear mappings between Banach spaces

We find conditions for a smooth nonlinear map f: U → V between open subsets of Hilbert or Banach spaces to be locally convex in the sense that for some c and each positive ? < c the image f(B _?(x)) of each ?-ball B _?(x) ? U is convex. We give a lower bound on c via the second order Lipschitz constant Lip₂(f), the Lipschitz-open constant Lip_o(f) of f, and the 2-convexity number conv₂(X) of the Banach space X.     

Metrizability of Clifford topological semigroups

We prove that a countably compact Clifford topological semigroup S is metrizable if and only if the set E={e∈S:ee=e} of idempotents of S is a metrizable G _δ -set in S.     

A topological characterization of LF-spaces

We present a topological characterization of LF-spaces and detect small box-products that are (locally) homeomorphic to LF-spaces.     

A New Quantum Chemical Approach to the Magnetic Properties of Oligonuclear Transition‐Metal Complexes: Application to a Model for the Tetranuclear Manganese Cluster of Photosystem II

Broken‐symmetry DFT calculations on transition‐metal clusters with more than two centers allow the hyperfine coupling constants to be extracted. Application of the proposed theoretical scheme to a tetranuclear manganese complex that models the S₂ state of the oxygen‐evolving complex of photosystem II yields hyperfine parameters that can be directly compared with experimental data. The picture shows the metal–oxo core of the model and the following parameters; exchange coupling constant J_ij, the expectation value of the site‐spin operator , and the isotropic hyperfine coupling parameters.

     

High resolution Fourier transform infrared spectra and analysis of the ν14, ν15 and ν16 bands of azetidine

Rotationally resolved vibrational spectra of the three lowest frequency bands of the four-membered heterocycle azetidine (c-C₃H₆NH) have been collected with a resolution of 0.00096 cm⁻¹ using the far infrared beamline at the Canadian Light Source synchrotron. The modes observed correspond principally to motions best described as: β-CH₂ rock (ν₁₄) at 736.701310(7) cm⁻¹, ring deformation (ν₁₅) at 648.116041(8) cm⁻¹, and the ring puckering mode (ν₁₆) at 207.727053(9) cm⁻¹. A global fit of 14 276 rovibrational transitions from the three bands provided an accurate set of ground state spectroscopic constants as well as excited state parameters for each of the three vibrational modes. The ground state structure was determined to be that of the puckered conformer having the NH bond in an equatorial arrangement.     

On index of total boundedness of (strictly) o-bounded groups

Let G be a metrizable topological group. Denote by itb(G) the smallest cardinality of a cover of G by totally bounded subsets of G. A group G is defined to be σ-bounded if itb(G)₀. The group G is called o-bounded if for every sequence (U_n)_nω of neighborhoods of the identity in G there exists a sequence (F_n)_nω of finite subsets in G such that G=_nωF_n·U_n; G is called strictly o-bounded (respectively OF-determined) if the second player (respectively one of the players) has a winning strategy in the following game OF: two players, I and II, choose at every step n an open neighborhood U_n of the identity in G and a finite subset F_n of G, respectively. The player II wins if G=_nωF_n·U_n.

For a second countable group G the following results are proven. . If G is strictly o-bounded, then itb(G)₁ and G is σ-bounded or meager. If the space G is analytic, then the group is OF-determined and satisfies . G is σ-bounded if it is strictly o-bounded and one of the following conditions holds: (i) G is analytic; (ii) ; (iii) (MA+¬CH) holds; (iv) analytic games are determined; (v) there exists a measurable cardinal. Also we show that under (MA) every non-locally compact Polish Abelian divisible group contains a Baire o-bounded OF-undetermined subgroup.     

Free energies of adsorption of amino acids, short linear peptides and 2,5-piperazinediones on silica from water as estimated from high-performance liquid-chromatographic retention data

Equilibrium constants (K) and free energies (— G) of adsorption of amino acids, short linear peptides and cyclic dipeptides (2,5-piperazinediones) on silica from neutral aqueous solutions were calculated from the retention values measured by means of high-performance liquid chromatography on a silica gel column. For most amino acids and linear peptides — G values were negative and K < 1, thus showing very weak adsorption. 2,5-Piperazinediones exhibited higher adsorbability (for most of them, — G > 0 and K > 1) as compared to related dipeptides. Influence of the structure of a-substituent on the adsorbability is analyzed. A linear dependence of — G on the number of aliphatic carbon atoms in a sorbate molecule was found for the series of aliphatic bifunctional amino acids, related dipeptides and 2,5-piperazinediones, as well as for the group from glycine to triglycyl glycine.     

A Non-Standard Analysis of a Cultural Icon: The Case of Paul Halmos

We examine Paul Halmos’ comments on category theory, Dedekind cuts, devil worship, logic, and Robinson’s infinitesimals. Halmos’ scepticism about category theory derives from his philosophical position of naive set-theoretic realism. In the words of an MAA biography, Halmos thought that mathematics is “certainty” and “architecture” yet 20th century logic teaches us is that mathematics is full of uncertainty or more precisely incompleteness. If the term architecture meant to imply that mathematics is one great solid castle, then modern logic tends to teach us the opposite lesson, namely that the castle is floating in midair. Halmos’ realism tends to color his judgment of purely scientific aspects of logic and the way it is practiced and applied. He often expressed distaste for nonstandard models, and made a sustained effort to eliminate first-order logic, the logicians’ concept of interpretation, and the syntactic vs semantic distinction. He felt that these were vague, and sought to replace them all by his polyadic algebra. Halmos claimed that Robinson’s framework is “unnecessary” but Henson and Keisler argue that Robinson’s framework allows one to dig deeper into set-theoretic resources than is common in Archimedean mathematics. This can potentially prove theorems not accessible by standard methods, undermining Halmos’ criticisms.