353 research outputs found
Counting faces of cubical spheres modulo two
AbstractSeveral recent papers have addressed the problem of characterizing the f-vectors of cubical polytopes. This is largely motivated by the complete characterization of the f-vectors of simplicial polytopes given by Stanley (Discrete Geometry and Convexity, Annals of the New York Academy of Sciences, Vol. 440, 1985, pp. 212–223) and Billera and Lee (Bull. Amer. Math. Soc. 2 (1980) 181–185) in 1980. Along these lines Blind and Blind (Discrete Comput. Geom. 11(3) (1994) 351–356) have shown that unlike in the simplicial case, there are parity restrictions on the f-vectors of cubical polytopes. In particular, except for polygons, all even dimensional cubical polytopes must have an even number of vertices. Here this result is extended to a class of zonotopal complexes which includes simply connected odd dimensional manifolds. This paper then shows that the only modular equations which hold for the f-vectors of all d-dimensional cubical polytopes (and hence spheres) are modulo two. Finally, the question of which mod two equations hold for the f-vectors of PL cubical spheres is reduced to a question about the Euler characteristics of multiple point loci from codimension one PL immersions into the d-sphere. Some results about this topological question are known (Eccles, Lecture Notes in Mathematics, Vol. 788, Springer, Berlin, 1980, pp. 23–38; Herbert, Mem. Amer. Math. Soc. 34 (250) (1981); Lannes, Lecture Notes in Mathematics, Vol. 1051, Springer, Berlin, 1984, pp. 263–270) and Herbert's result we translate into the cubical setting, thereby removing the PL requirement. A central definition in this paper is that of the derivative complex, which captures the correspondence between cubical spheres and codimension one immersions
Five-Torsion in the Homology of the Matching Complex on 14 Vertices
J. L. Andersen proved that there is 5-torsion in the bottom nonvanishing
homology group of the simplicial complex of graphs of degree at most two on
seven vertices. We use this result to demonstrate that there is 5-torsion also
in the bottom nonvanishing homology group of the matching complex on
14 vertices. Combining our observation with results due to Bouc and to
Shareshian and Wachs, we conclude that the case is exceptional; for all
other , the torsion subgroup of the bottom nonvanishing homology group has
exponent three or is zero. The possibility remains that there is other torsion
than 3-torsion in higher-degree homology groups of when and .Comment: 11 page
The pre-WDVV ring of physics and its topology
We show how a simplicial complex arising from the WDVV
(Witten-Dijkgraaf-Verlinde-Verlinde) equations of string theory is the
Whitehouse complex. Using discrete Morse theory, we give an elementary proof
that the Whitehouse complex is homotopy equivalent to a wedge of
spheres of dimension . We also verify the Cohen-Macaulay
property. Additionally, recurrences are given for the face enumeration of the
complex and the Hilbert series of the associated pre-WDVV ring.Comment: 13 pages, 4 figures, 2 table
Restricted Colored Permutations and Chebyshev Polynomials
Several authors have examined connections between restricted permutations and Chebyshev polynomials of the second kind. In this paper we prove analogues of these results for colored permutations. First we define a distinguished set of length two and length three patterns, which contains only 312 when just one color is used. Then we give a recursive procedure for computing the generating function for the colored permutations which avoid this distinguished set and any set of additional patterns, which we use to find a new set of signed permutations counted by the Catalan numbers and a new set of signed permutations counted by the large Schr¨oder numbers. We go on to use this result to compute the generating functions for colored permutations which avoid our distinguished set and any layered permutation with three or fewer layers. We express these generating functions in terms of Chebyshev polynomials of the second kind and we show that they are special cases of generating functions for involutions which avoid 3412 and a layered permutation
Phase Transitions on Nonamenable Graphs
We survey known results about phase transitions in various models of
statistical physics when the underlying space is a nonamenable graph. Most
attention is devoted to transitive graphs and trees
Atmospheric Muon Flux at Sea Level, Underground, and Underwater
The vertical sea-level muon spectrum at energies above 1 GeV and the
underground/underwater muon intensities at depths up to 18 km w.e. are
calculated. The results are particularly collated with a great body of the
ground-level, underground, and underwater muon data. In the hadron-cascade
calculations, the growth with energy of inelastic cross sections and pion,
kaon, and nucleon generation in pion-nucleus collisions are taken into account.
For evaluating the prompt muon contribution to the muon flux, we apply two
phenomenological approaches to the charm production problem: the recombination
quark-parton model and the quark-gluon string model. To solve the muon
transport equation at large depths of homogeneous medium, a semi-analytical
method is used. The simple fitting formulas describing our numerical results
are given. Our analysis shows that, at depths up to 6-7 km w. e., essentially
all underground data on the muon intensity correlate with each other and with
predicted depth-intensity relation for conventional muons to within 10%.
However, the high-energy sea-level data as well as the data at large depths are
contradictory and cannot be quantitatively decribed by a single nuclear-cascade
model.Comment: 47 pages, REVTeX, 15 EPS figures included; recent experimental data
and references added, typos correcte
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High Involvement Management, High Performance Work Systems and Well-being
Studies on the impact of high-performance work systems on employees' well-being are emerging but the underlying theory remains weak. This paper attempts to develop theory of the effects on well-being of four dimensions of high-performance work systems: enriched jobs, high involvement management, employee voice, and motivational supports. Hypothesized associations are tested using multilevel models and data from Britain's Workplace Employment Relations Survey of 2004 (WERS2004). Results show that enriched jobs are positively associated with both measures of well-being: job satisfaction and anxiety–contentment. Voice is positively associated with job satisfaction, and motivational supports with neither measure. The results for high involvement management are not as predicted because it increases anxiety and is independent of job satisfaction
Center of mass, spin supplementary conditions, and the momentum of spinning particles
We discuss the problem of defining the center of mass in general relativity
and the so-called spin supplementary condition. The different spin conditions
in the literature, their physical significance, and the momentum-velocity
relation for each of them are analyzed in depth. The reason for the
non-parallelism between the velocity and the momentum, and the concept of
"hidden momentum", are dissected. It is argued that the different solutions
allowed by the different spin conditions are equally valid descriptions for the
motion of a given test body, and their equivalence is shown to dipole order in
curved spacetime. These different descriptions are compared in simple examples.Comment: 45 pages, 7 figures. Some minor improvements, typos fixed, signs in
some expressions corrected. Matches the published version. Published as part
of the book "Equations of Motion in Relativistic Gravity", D. Puetzfeld et
al. (eds.), Fundamental Theories of Physics 179, Springer, 201
Detroit's East Side Village Health Worker Partnership: Community-Based Lay Health Advisor Intervention in an Urban Area
In recent years, there have been few reports in the literature of interventions using a lay health advisor approach in an urban area. Consequently, little is known about how implementation of this type of community health worker model, which has been used extensively in rural areas, may differ in an urban area. This article describes the implementation of the East Side Village Health Worker Partnership, a lay health advisor intervention, in Detroit, Michigan, and notes how participatory action research methods and principles for community-based partnership research are being used to guide the intervention. Findings are presented on how the urban context is affecting the design and implementation of this intervention. Implications of the findings for health educators are also presented and include the utility of a participatory action research approach, the importance of considering the context and history of a community in designing a health education intervention, and the importance of recognizing and considering the differences between rural and urban settings when designing a health education intervention.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67390/2/10.1177_109019819802500104.pd
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