The problem of construction of the harmonic space based on choquet simplex

1988 ◽  
pp. 214-215
Author(s):  
D. G. Keselman
Keyword(s):  
Harmonic Space ◽  
Choquet Simplex

scholarly journals Dark Energy Survey Year 1 Results: Wide-field mass maps via forward fitting in harmonic space

2020 ◽  
Vol 493 (4) ◽  
pp. 5662-5679 ◽  
Author(s):  
B Mawdsley ◽  
D Bacon ◽  
C Chang ◽  
P Melchior ◽  
E Rozo ◽  
...  
Keyword(s):  
Dark Energy ◽  
Mapping Technique ◽  
Harmonic Space ◽  
Wide Field ◽  
Direct Inversion ◽  
Dark Energy Survey ◽  
Central Regions ◽  
Fitting In ◽  
Energy Survey ◽  
Good Agreement

ABSTRACT We present new wide-field weak lensing mass maps for the Year 1 Dark Energy Survey (DES) data, generated via a forward fitting approach. This method of producing maps does not impose any prior constraints on the mass distribution to be reconstructed. The technique is found to improve the map reconstruction on the edges of the field compared to the conventional Kaiser–Squires method, which applies a direct inversion on the data; our approach is in good agreement with the previous direct approach in the central regions of the footprint. The mapping technique is assessed and verified with tests on simulations; together with the Kaiser–Squires method, the technique is then applied to data from the DES Year 1 data and the differences between the two methods are compared. We also produce the first DES measurements of the convergence Minkowski functionals and compare them to those measured in simulations.

Perturbation theory of the pair correlation function in molecular fluids

1978 ◽  
Vol 56 (5) ◽  
pp. 571-580 ◽  
Author(s):  
R. L. Henderson ◽  
C. G. Gray
Keyword(s):  
Perturbation Theory ◽  
Correlation Function ◽  
Pair Correlation Function ◽  
Pair Correlation ◽  
Mean Field ◽  
Pair Potential ◽  
Harmonic Series ◽  
Harmonic Space ◽  
Potential Symmetries ◽  
Harmonic Components

We study the perturbation theory of the angular pair correlation function g(rω1ω2)in a molecular fluid. We consider an anisotropic pair potential of the form u = u0 + ua, where u0 is an isotropic 'reference' potential, and for simplicity in this paper we assume the perturbation potential ua to be 'multipole-like', i.e., to contain no l = 0 spherical harmonics. We expand g in powers of ua about g0, the radial distribution function appropriate to u0. This series is examined by expanding ha = h−h0 (where h = g−1) and its corresponding direct correlation function ca in spherical harmonic components. We consider approximate summations of the series in ua that automatically truncate the corresponding harmonic series, so that the Ornstein–Zernike (OZ) equation relating ha and ca can be solved in closed form. We first expand ca = c1 + c2 + … where cn includes all terms in ca of order (ua)n. Taking ua to be a quadrupole–quadrupole interaction, we find that a 'mean field' (MF) approximation ca = c1 gives rise to only three nonvanishing harmonic components in ha, so that OZ is solved explicitly in Fourier space. The MF solution for multipoles of general order is given in an appendix. Graphical methods are then used to identify the class of all terms in the ua series that are restricted to the harmonic space defined by MF. A portion of this class can be summed by solving OZ with the closure ca = −βg0ua + h0(ha−ca), where β = (kT)−1, h0 = g0−1 This system is designated as generalized MF (GMF), and solved by numerical iteration. Numerical results from MF and GMF are presented for quadrupolar ua, taking u0 to be a Lennard-Jones potential. Symmetries imposed by the restricted harmonic space are foreign to the full g, yet harmonics within this space are sufficient for evaluation of many macroscopic properties. The results are therefore evaluated in harmonic form by comparison with the corresponding harmonic components of the 'correct' g as evaluated by Monte Carlo simulation.

scholarly journals A note on bi-contractive projections on spaces of vector valued continuous functions

2018 ◽  
Vol 5 (1) ◽  
pp. 42-49
Author(s):  
Fernanda Botelho ◽  
T.S.S.R.K. Rao
Keyword(s):  
Hilbert Space ◽  
Continuous Functions ◽  
Choquet Simplex ◽  
Contractive Projections ◽  
Vector Valued

Abstract This paper concerns the analysis of the structure of bi-contractive projections on spaces of vector valued continuous functions and presents results that extend the characterization of bi-contractive projections given by the first author. It also includes a partial generalization of these results to affine and vector valued continuous functions from a Choquet simplex into a Hilbert space.

scholarly journals A Choquet-Deny theorem for affine functions on a Choquet simplex

1969 ◽  
Vol 16 (4) ◽  
pp. 325-327 ◽  
Author(s):  
H. A. Priestley
Keyword(s):  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Present Note ◽  
Continuous Functions ◽  
Choquet Simplex ◽  
Affine Functions ◽  
Stone Theorem

The closed wedges in C(X) (the space of real continuous functions on a compact Hausdorff space X) which are also inf-lattices have been characterized by Choquet and Deny (2); see also (5). The present note extends their result to certain wedges of affine continuous functions on a Choquet simplex, the generalization being in the same spirit as the generalization of the Kakutani- Stone theorem obtained by Edwards in (4).I should like to thank my supervisor, Dr D. A. Edwards, for suggesting this problem and for his subsequent help. I am also grateful to the referee for correcting several slips.

John Cage and the Theory of Harmony

2017 ◽  
Author(s):  
James Tenney
Keyword(s):  
General Theory ◽  
Careful Analysis ◽  
Pitch Perception ◽  
Multidimensional Space ◽  
Harmonic Space ◽  
John Cage ◽  
Musical Perception ◽  
True Theory ◽  
Extended Range ◽  
Compositional Practice

James Tenney examines some of John Cage's theoretical ideas and their possible implications for a new theory of harmony that he argues requires new definitions of “harmony,” “harmonic relations,” etc.; such definitions, he contends, will emerge from a more careful analysis of the “total soundspace” of musical perception. Tenney begins with a discussion of the current disparity between harmonic theory and compositional practice before explaining what a true theory of harmony should be: a theory of harmonic perception (one component in a more general theory of musical perception) consistent with the most recent data available from the fields of acoustics and psychoacoustics but also taking into account the extended range of musical experiences available to us today. Tenney outlines the conditions that such a theory ought to satisfy and goes on to consider a multidimensional space of pitch perception called harmonic space.

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