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Maximum entropy in the problem of moments
The maximum‐entropy approach to the solution of underdetermined inverse problems is studied in detail in the context of the classical moment problem. In important special cases, such as the HausdorffExpand
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OBSERVATION OF DISCRETE OSCILLATIONS IN A MODEL-INDEPENDENT PLOT OF COSMOLOGICAL SCALE FACTOR VERSUS LOOKBACK TIME AND SCALAR FIELD MODEL
We have observed damped longitudinal cosmological-scale oscillations in a unique model-independent plot of scale factor against lookback time for Type Ia supernovae data. We found severalExpand
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Underdetermined systems of partial differential equations
This paper examines underdetermined systems of partial differential equations in which the independent variables may be classical c-numbers or even quantum operators. One can view an underdeterminedExpand
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Approximate solution of Fredholm integral equations by the maximum‐entropy method
An approximate means of solving Fredholm integral equations by the maximum‐entropy method is developed. The Fredholm integral equation is converted to a generalized moment problem whose approximateExpand
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A new formula describing the scaffold structure of spiral galaxies
We describe a new formula capable of quantitatively characterizing the Hubble sequence of spiral galaxies including grand design and barred spirals. Special shapes such as ring galaxies with inwardExpand
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Continuous Hahn polynomials and the Heisenberg algebra
Continuous Hahn polynomials have surfaced in a number of somewhat obscure physical applications. For example, they have emerged in the description of two‐photon processes in hydrogen, hard‐hexagonExpand
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Model-independent Plotting of the Cosmological Scale Factor as a Function of Lookback Time
In this work we describe a model-independent method of developing a plot of scale factor a(t) versus lookback time t{sub L} from the usual Hubble diagram of modulus data against redshift. This is theExpand
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An analytical example of renormalization in two‐dimensional quantum mechanics
As a concrete example of the idea of renormalization, quantum mechanical scattering of particles by a two‐dimensional delta‐function potential is considered. The renormalization of the scatteringExpand
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Maximum-entropy approach to classical hard-sphere and hard-disk equations of state
The maximum‐entropy procedure for extrapolating series is applied to sum the known virial series for the hard‐disk and hard‐sphere fluids. This procedure is found to produce numerical results moreExpand
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Finite Sum Expressions for Elastic and Reaction Cross Sections
Abstract Nuclear cross section calculations are often performed by using the partial wave method or the Eikonal method through Glauber theory. The expressions for the total cross section, totalExpand
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