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Physical Sciences and Mathematics Commons™

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Loyola Marymount University and Loyola Law School

2005

Articles 1 - 9 of 9

Full-Text Articles in Physical Sciences and Mathematics

Fractal Dimensions In Perceptual Color Space: A Comparison Study Using Jackson Pollock’S Art, Jonas R. Mureika Dec 2005

Fractal Dimensions In Perceptual Color Space: A Comparison Study Using Jackson Pollock’S Art, Jonas R. Mureika

Physics Faculty Works

The fractal dimensions of color-specific paint patterns in various Jackson Pollock paintings are calculated using a filtering process that models perceptual response to color differences (L*a*b* color space). The advantage of the L*a*b* space filtering method over traditional red-green-blue (RGB) spaces is that the former is a perceptually uniform (metric) space, leading to a more consistent definition of “perceptually different” colors. It is determined that the RGB filtering method underestimates the perceived fractal dimension of lighter-colored patterns but not of darker ones, if the same selection criteria is applied to each. Implications of the findings to Fechner’s “principle of …

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Recounting The Odds Of An Even Derangement, Arthur T. Benjamin, Curtis T. Bennett, Florence Newberger Dec 2005

Recounting The Odds Of An Even Derangement, Arthur T. Benjamin, Curtis T. Bennett, Florence Newberger

Mathematics Faculty Works

No abstract provided.

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Multifractal Structure In Nonrepresentational Art, Jonas R. Mureika, C. C. Dyer, G. C. Cupchik Oct 2005

Multifractal Structure In Nonrepresentational Art, Jonas R. Mureika, C. C. Dyer, G. C. Cupchik

Physics Faculty Works

Multifractal analysis techniques are applied to patterns in several abstract expressionist artworks, painted by various artists. The analysis is carried out on two distinct types of structures: the physical patterns formed by a specific color (“blobs”) and patterns formed by the luminance gradient between adjacent colors (“edges”). It is found that the multifractal analysis method applied to “blobs” cannot distinguish between artists of the same movement, yielding a multifractal spectrum of dimensions between about 1.5 and 1.8. The method can distinguish between different types of images, however, as demonstrated by studying a radically different type of art. The data suggest …

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Toy Blocks And Rotational Physics, Gabriele U. Varieschi, Isabel R. Jully Sep 2005

Toy Blocks And Rotational Physics, Gabriele U. Varieschi, Isabel R. Jully

Physics Faculty Works

Have you ever observed a child playing with toy blocks? A favorite game is to build towers and then make them topple like falling trees. To the eye of a trained physicist this should immediately look like an example of the physics of “falling chimneys,” when tall structures bend and break in mid-air while falling to the ground. The game played with toy blocks can actually reproduce well what is usually seen in photographs of falling towers, such as the one that appeared on the cover of the September 1976 issue of The Physics Teacher.1 In this paper we describe …

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The Effects Of Temperature, Humidity, And Barometric Pressure On Short-Sprint Race Times, Jonas R. Mureika Aug 2005

The Effects Of Temperature, Humidity, And Barometric Pressure On Short-Sprint Race Times, Jonas R. Mureika

Physics Faculty Works

A numerical model of 100 m and 200 m world class sprinting performances is modified using standard hydrodynamic principles to include effects of air temperature, pressure, and humidity levels on aerodynamic drag. The magnitude of the effects are found to be dependent on wind speed. This implies that differing atmospheric conditions can yield slightly different corrections for the same wind gauge reading. In the absence of wind, temperature is found to induce the largest variation in times (0.01 s per 10◦C increment in the 100 m), while relative humidity contributes the least (under 0.01 s for all realistic conditions for …

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Derived Categories And The Analytic Approach To General Reciprocity Laws. Part I, Michael Berg Jan 2005

Derived Categories And The Analytic Approach To General Reciprocity Laws. Part I, Michael Berg

Mathematics Faculty Works

We reformulate Hecke's open problem of 1923, regarding the Fourier-analytic proof of higher reciprocity laws, as a theorem about morphisms involving stratified topological spaces. We achieve this by placing Kubota's formulations of n-Hilbert reciprocity in a new topological context, suited to the introduction of derived categories of sheaf complexes. Subsequently, we begin to investigate conditions on associated sheaves and a derived category of sheaf complexes specifically designed for an attack on Hecke's eighty-year-old challenge.

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A Map On The Space Of Rational Functions, G. Boros, J. Little, V. Moll, Edward Mosteig, R. Stanley Jan 2005

A Map On The Space Of Rational Functions, G. Boros, J. Little, V. Moll, Edward Mosteig, R. Stanley

Mathematics Faculty Works

We describe dynamical properties of a map defined on the space of rational functions. The fixed points of F are classified and the long time behavior of a subclass is described in terms of Eulerian polynomials.

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Commensurability Classes Of Twist Knots, Jim Hoste, Patrick D. Shanahan Jan 2005

Commensurability Classes Of Twist Knots, Jim Hoste, Patrick D. Shanahan

Mathematics Faculty Works

In this paper we prove that if MK is the complement of a non-fibered twist knot K in S3, then MK is not commensurable to a fibered knot complement in a Z/2Z-homology sphere. To prove this result we derive a recursive description of the character variety of twist knots and then prove that a commensurability criterion developed by D. Calegari and N. Dunfield is satisfied for these varieties. In addition, we partially extend our results to a second infinite family of 2-bridge knots.

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From Loop Groups To 2-Groups, John C. Baez, Danny Stevenson, Alissa S. Crans, Urs Schreiber Jan 2005

From Loop Groups To 2-Groups, John C. Baez, Danny Stevenson, Alissa S. Crans, Urs Schreiber

Mathematics Faculty Works

We describe an interesting relation between Lie 2-algebras, the Kac-Moody central extensions of loop groups, and the group String(n). A Lie 2-algebra is a categorified version of a Lie algebra where the Jacobi identity holds up to a natural isomorphism called the "Jacobiator". Similarly, a Lie 2-group is a categorified version of a Lie group. If G is a simply-connected compact simple Lie group, there is a 1-parameter family of Lie 2-algebras g_k each having Lie(G) as its Lie algebra of objects, but with a Jacobiator built from the canonical 3-form on G. There appears to be no Lie 2-group …

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