Applications of DFT to the theory of twentieth-century harmony

Music theorists have only recently, following groundbreaking work by Quinn, recognized the potential for the DFT on pcsets, initially proposed by Lewin, to serve as the foundation of a theory of harmony for the twentieth century. This paper investigates pcset “arithmetic” – subset structure, transpositional combination, and interval content – through the lens of the DFT. It discusses relationships between interval classes and DFT magnitudes, considers special properties of dyads, pcset products, and generated collections, and suggest methods of using the DFT in analysis, including interpreting DFT magnitudes, using phase spaces to understand subset structure, and interpreting the DFT of Lewin’s interval function. Webern’s op. 5/4 and Bartok’s String Quartet 4, iv, are discussed.Accepted manuscrip

Decontextualizing contextual inversion

Contextual inversion, introduced as an analytical tool by David Lewin, is a concept of wide reach and value in music theory and analysis, at the root of neo-Riemannian theory as well as serial theory, and useful for a range of analytical applications. A shortcoming of contextual inversion as it is currently understood, however, is, as implied by the name, that the transformation has to be defined anew for each application. This is potentially a virtue, requiring the analyst to invest the transformational system with meaning in order to construct it in the first place. However, there are certainly instances where new transformational systems are continually redefined for essentially the same purposes. This paper explores some of the most common theoretical bases for contextual inversion groups and considers possible definitions of inversion operators that can apply across set class types, effectively decontextualizing contextual inversions.Accepted manuscrip

Fourier phase and pitch-class sum

Music theorists have proposed two very different geometric models of musical objects, one based on voice leading and the other based on the Fourier transform. On the surface these models are completely different, but they converge in special cases, including many geometries that are of particular analytical interest.Accepted manuscrip

Global analysis of data on the spin-orbit coupled A1Σu+A^{1}\Sigma_{u}^{+} and b3Πub^{3}\Pi_{u} states of Cs2

We present experimentally derived potential curves and spin-orbit interaction functions for the strongly perturbed $A^{1}\Sigma_{u}^{+}$ and $b^{3}\Pi_{u}$ states of the cesium dimer. The results are based on data from several sources. Laser-induced fluorescence Fourier transform spectroscopy (LIF FTS) was used some time ago in the Laboratoire Aim\'{e} Cotton primarily to study the $X ^{1}\Sigma_{g}^{+}$ state. More recent work at Tsinghua University provides information from moderate resolution spectroscopy on the lowest levels of the $b^{3}\Pi_{0u}^{\pm}$ states as well as additional high resolution data. From Innsbruck University, we have precision data obtained with cold Cs$_{2}$ molecules. Recent data from Temple University was obtained using the optical-optical double resonance polarization spectroscopy technique, and finally, a group at the University of Latvia has added additional LIF FTS data. In the Hamiltonian matrix, we have used analytic potentials (the Expanded Morse Oscillator form) with both finite-difference (FD) coupled-channels and discrete variable representation (DVR) calculations of the term values. Fitted diagonal and off-diagonal spin-orbit functions are obtained and compared with {\it ab initio} results from Temple and Moscow State universities

Управління виробничими запасами на підприємстві (на матеріалах ПрАТ «Детвілер Ущільнюючі Технології України»)

. The second-order matching problem is the problem of determining, for a finite set {#t i , s i # | i # I} of pairs of a second-order term t i and a first-order closed term s i , called a matching expression, whether or not there exists a substitution # such that t i # = s i for each i # I . It is well-known that the second-order matching problem is NP-complete. In this paper, we introduce the following restrictions of a matching expression: k-ary, k-fv , predicate, ground , and function-free. Then, we show that the second-order matching problem is NP-complete for a unary predicate, a unary ground, a ternary function-free predicate, a binary function-free ground, and an 1-fv predicate matching expressions, while it is solvable in polynomial time for a binary function-free predicate, a unary function-free, a k-fv function-free (k # 0), and a ground predicate matching expressions. 1 Introduction The unification problem is the problem of determining whether or not any two ter..

Theoretical model for ultracold molecule formation via adaptive feedback control

We investigate pump-dump photoassociation of ultracold molecules with amplitude- and phase-modulated femtosecond laser pulses. For this purpose a perturbative model for the light-matter interaction is developed and combined with a genetic algorithm for adaptive feedback control of the laser pulse shapes. The model is applied to the formation of 85Rb2 molecules in a magneto-optical trap. We find for optimized pulse shapes an improvement for the formation of ground state molecules by more than a factor of 10 compared to unshaped pulses at the same pump-dump delay time, and by 40% compared to unshaped pulses at the respective optimal pump-dump delay time. Since our model yields directly the spectral amplitudes and phases of the optimized pulses, the results are directly applicable in pulse shaping experiments

High-precision calculations of van der Waals coefficients for heteronuclear alkali-metal dimers

Van der Waals coefficients for the heteronuclear alkali-metal dimers of Li, Na, K, Rb, Cs, and Fr are calculated using relativistic ab initio methods augmented by high-precision experimental data. We argue that the uncertainties in the coefficients are unlikely to exceed about 1%.Comment: 11 pages, 2 figs, graphicx.st

Photoassociation inside an optical dipole trap: absolute rate coefficients and Franck-Condon factors

We present quantitative measurements of the photoassociation of cesium molecules inside a far-detuned optical dipole trap. A model of the trap depletion dynamics is derived which allows to extract absolute photoassociation rate coefficients for the initial single-photon photoassociation step from measured trap-loss spectra. The sensitivity of this approach is demonstrated by measuring the Franck-Condon modulation of the weak photoassociation transitions into the low vibrational levels of the outer well of the 0g- state that correlates to the 6s+6p3/2 asymptote. The measurements are compared to theoretical predictions. In a magneto-optical trap these transitions have previously only been observed indirectly through ionization of ground state molecules

Identity integration, psychological coherence and identity threat: linking identity process theory and notions of integration

The goal of the current chapter is threefold, namely: (i) to explain how individuals, in times of change, come to integrate new identities intra-individually in their sense of self and maintain a feeling of psychological coherence in this process; (ii) to highlight how the identity principles proposed by identity process theory (IPT) come into play throughout this change process and how the satisfaction of these principles may actually facilitate the integration of new and multiple social identities in the self; and (iii) to identify some factors that may actively block the integration of these identities, namely feelings of identity threat and the social devaluation of certain identities relative to others. We base ourselves on different strands of research to make these points, and more specifically, the cognitive-developmental model of social identity integration (CDMSII; Amiot, de la Sablonnière, Terry, & Smith, 2007), IPT (Breakwell, 1986), and the concept of psychological coherence (Jaspal & Cinnirella, 2010). Throughout the chapter, an implicit goal is to build bridges between these different social psychological theories as they are each relevant to addressing these issues, and also provide a broad and integrative framework to understand how diversity can be reconciled subjectively and intra-individually – within each individual

Dark resonances for ground state transfer of molecular quantum gases

One possible way to produce ultracold, high-phase-space-density quantum gases of molecules in the rovibronic ground state is given by molecule association from quantum-degenerate atomic gases on a Feshbach resonance and subsequent coherent optical multi-photon transfer into the rovibronic ground state. In ultracold samples of Cs_2 molecules, we observe two-photon dark resonances that connect the intermediate rovibrational level |v=73,J=2> with the rovibrational ground state |v=0,J=0> of the singlet $X^1\Sigma_g^+$ ground state potential. For precise dark resonance spectroscopy we exploit the fact that it is possible to efficiently populate the level |v=73,J=2> by two-photon transfer from the dissociation threshold with the stimulated Raman adiabatic passage (STIRAP) technique. We find that at least one of the two-photon resonances is sufficiently strong to allow future implementation of coherent STIRAP transfer of a molecular quantum gas to the rovibrational ground state |v=0,J=0>.Comment: 7 pages, 4 figure