Beef and pork longissimus dorsi and semimembranosus muscles and chicken breast and thigh muscles were excised 24 hr postmortem from carcasses of marketweight grain-finished feedlot beef cattle, marketweight hogs on a typical finishing diet, and broilers on a commercial grain diet. Muscle samples were immediately ground and formed into patties and stored raw or after cooking, at 4ЊC (cooked) or Ϫ20ЊC (raw and cooked). TBA values (on sample weight basis) of frozen raw samples were higher for beef and pork than for chicken, as was heme iron content. However, TBA values of cooked samples were highest for chicken thigh muscles, which contained the most polyunsaturated fatty acids, at all storage temperatures.
We explore a combinatorial theory of linear dependency in complex space, complex matroids, with foundations analogous to those for oriented matroids. We give multiple equivalent axiomatizations of complex matroids, showing that this theory captures properties of linear dependency, orthogonality, and determinants over C in much the same way that oriented matroids capture the same properties over R. In addition, our complex matroids come with a canonical S 1 action analogous to the action of C * on a complex vector space.Our phirotopes (analogues of determinants) are the same as those studied previously by Below, Krummeck, and Delucchi [7].We further show that complex matroids cannot have vector axioms analogous to those for oriented matroids.
Matroid bundles, introduced by MacPherson, are combinatorial analogues of real vector bundles. This paper sets up the foundations of matroid bundles. It defines a natural transformation from isomorphism classes of real vector bundles to isomorphism classes of matroid bundles. It then gives a transformation from matroid bundles to spherical quasifibrations, by showing that the geometric realization of a matroid bundle is a spherical quasifibration. The poset of oriented matroids of a fixed rank classifies matroid bundles, and the above transformations give a splitting from topology to combinatorics back to topology. A consequence is that the mod 2 cohomology of the poset of rank k oriented matroids (this poset classifies matroid bundles) contains the free polynomial ring on the first k Stiefel-Whitney classes. (2000). Primary 55R25; Secondary 52C40, 57R22.
Mathematics Subject ClassificationOriented matroids have long been of use in various areas of combinatorics [BLS + 93]. Gelfand and MacPherson [GM92] initiated the use of oriented matroids in manifold and bundle theory, using them to formulate a combinatorial formula for the rational Pontrjagin classes of a differentiable manifold. MacPherson [Mac93] abstracted this into a manifold theory (combinatorial differential (CD) manifolds) and a bundle theory (which we call combinatorial vector bundles or matroid bundles). In this paper we explore the relationship between combinatorial vector bundles and real vector bundles. As a consequence of our results we get theorems relating the topology of the combinatorial Grassmannians to that of their real analogs.The theory of oriented matroids gives a combinatorial abstraction of linear algebra; a k-dimensional subspace of R n determines a rank k oriented matroid with elements {1, 2, . . . , n}. Such oriented matroids can be given a partial order by using the notion of weak maps, which geometrically corresponds to moving * Partially supported by grants from the National Science Foundation.
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