Search results for "philosophy of mathematics"
showing 10 items of 246 documents
First-principles phonon calculations of Fe4+impurity in SrTiO3
2012
The results of hybrid density functional theory calculations on phonons in Sr(Fe(x)Ti(1-x))O(3) solid solution within the formalism of a linear combination of atomic orbitals are presented. The phonon density of states (DOS) calculated for 6.25% Fe(4+) impurities is reported and defect-induced phonon modes are identified. Based on our calculations and group-theoretical analysis, we suggest for the first time an interpretation of experimentally observed Raman- and IR-active modes.
Models and Phenomena: Bas van Fraassen’s Empiricist Structuralism
2013
Bas van Fraassen’s recent endorsement of empiricist structuralism is based on a particular approach to representation. He sharply distinguishes between what makes a scientific model M a successful representation of its target T from what makes M a representation of T and not of some other different target T’. van Fraassen maintains that embedment (i.e.: a particular sort of isomorphism which relates structures) gives the answer to the first question while the user’s decision to employ model M to represent T accounts for the representational link. After discussing the rationale for this approach, I defend that indexical constraints like those favoured by van Fraassen cannot be the last word …
Time-Dependent Correlation and Response Functions
2014
The dynamics of liquids is discussed with the help of time-dependent correlation functions. They are related to response functions by the fluctuation-dissipation theorem. This theorem enables to relate experimentally measured inelastic scattering data to the Fourier-transformed correlation and response functions. The Laplace transform of the correlation functions can be represented as a continuous fraction with suitable residual terms (memory functions). The projection formalism of Mori and Zwanzig is introduced.
Coupled cluster calculations of the vertical excitation energies of tetracyanoethylene
2003
The vertical spectrum of tetracyanoethylene was studied using coupled cluster theory. It was found that the lowest singlet-singlet transition, which corresponds to the excitation from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO) excitation, occurs at 5.16 eV in the gas phase and is lowered approximately 0.1 eV due to solvent effects in acetonitrile. A parallel study on the ethene spectrum showed the quality of the basis sets and methods used, by placing the V state 7.92 eV above the ground state and giving an energy for the 0-0 transition of 5.42 eV to be compared with the experimental value of 5.50 eV.
Mössbauer spectroscopic studies of clusters Mn2(CO)8[μ-Sn(hal)Mn(CO)5]2 (hal = Cl, Br) and related Mn and Re compounds
1977
Abstract In order to be acquainted with the nature of bonds at Sn involved in the title compounds, as well as to get information on the configuration of the strictly related derivatives I2Sn2Mn4(CO)18 and Cl2Sn2Re4(CO)18, the Mossbauer spectroscopic investigation reported in this paper has been carried out. The experimental parameters (isomer shifts, δ; nuclear quadrupole splittings, ΔE; for the bromide derivative only, the asymmetry parameter η and the sign of the nuclear quadrupole coupling constant e2qQ) have been discussed in connection with data concerning compounds with tin-transition metal bonds, mainly hal2Sn[Mn(CO)5]2 (hal = Cl, Br) and ClSn[Mn(CO)5]3. Rationalizations of ΔE and η …
Time-dependent Landauer-B\"uttiker formalism for superconducting junctions at arbitrary temperatures
2015
We discuss an extension of our earlier work on the time-dependent Landauer--B\"uttiker formalism for noninteracting electronic transport. The formalism can without complication be extended to superconducting central regions since the Green's functions in the Nambu representation satisfy the same equations of motion which, in turn, leads to the same closed expression for the equal-time lesser Green's function, i.e., for the time-dependent reduced one-particle density matrix. We further write the finite-temperature frequency integrals in terms of known special functions thereby considerably speeding up the computation. Numerical simulations in simple normal metal -- superconductor -- normal m…
Mössbauer studies on tin(IV) and organotin(IV) diacetylbis(benzoylhydrazone) complexes
1974
Abstract The Mossbauer parameters of Ph 2 SnDB, PhClSnDB and Sn(DB) 2 were determined, where DB 2− is the dianion of the multidentate ligand diacetylbis(benzoylhydrazone). According also to data treatment with the point charge model formalism, the configurations of Ph 2 Sn IV and PhSn IV derivatives appear to be essentially octahedral, with linear CSnC and CSnCl skeletons. As to Sn(DB) 2 , it appears that the electrical charge density at the Sn IV nucleus has a cubic symmetry, which is consistent with both tetrahedral and octahedral configurations around Sn IV .
Calculation of size‐intensive transition moments from the coupled cluster singles and doubles linear response function
1994
Coupled cluster singles and doubles linear response (CCLR) calculations have been carried out for excitation energies and dipole transition strengths for the lowest excitations in LiH, CH+, and C4and the results compared with the results from a CI-like approach to equation of motion coupled cluster (EOMCC). The transition strengths are similar in the two approaches for single molecule calculations on small systems. However, the CCLR approach gives size-intensive dipole transition strengths, while title EOMCC formalism does not. Thus, EOMCC calculations can give unphysically dipole transition strengths, e.g., in EOMCC calculations on a sequence of noninteracting LiH systems we obtained a neg…
A natural and rigid model of quantum groups
1992
We introduce a natural (Frechet-Hopf) algebra A containing all generic Jimbo algebras U t (sl(2)) (as dense subalgebras). The Hopf structures on A extend (in a continuous way) the Hopf structures of generic U t (sl(2)). The Universal R-matrices converge in A\(\hat \otimes \)A. Using the (topological) dual of A, we recover the formalism of functions of noncommutative arguments. In addition, we show that all these Hopf structures on A are isomorphic (as bialgebras), and rigid in the category of bialgebras.
Generalized Einstein-Maxwell field equations in the Palatini formalism
2013
We derive a new set of field equations within the framework of the Palatini formalism.These equations are a natural generalization of the Einstein-Maxwell equations which arise by adding a function $\mathcal{F}(\mathcal{Q})$, with $\mathcal{Q}\equiv F^{\alpha\beta}F_{\alpha\beta}$ to the Palatini Lagrangian $f(R,Q)$.The result we obtain can be viewed as the coupling of gravity with a nonlinear extension of the electromagnetic field.In addition,a new method is introduced to solve the algebraic equation associated to the Ricci tensor.