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  • 1
    Electronic Resource
    Electronic Resource
    Hilbert Bases, Unimodular Triangulations, and Binary Covers of Rational Polyhedral Cones (1999)
    Springer
    Discrete & computational geometry 21 (1999), S. 205-216 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. We present a hierarchy of covering properties of rational convex cones with respect to the unimodular subcones spanned by the Hilbert basis. For two of the concepts from the hierarchy we derive characterizations: a description of partitions that leads to a natural integer programming formulation for the HILBERT PARTITION problem, and a characterization of ``binary covers'' that admits a linear algebra test over GF(2) for the existence of BINARY HILBERT COVERS. Implementation of our test leads to interesting new examples, among them: cones that have a HILBERT PARTITION but no REGULAR one; a four-dimensional cone with unimodular facets that has no HILBERT PARTITION; and two five-dimensional cones that do not have any BINARY HILBERT COVER.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00009416
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  • 2
    Electronic Resource
    Electronic Resource
    Neighborly Cubical Polytopes (2000)
    Springer
    Discrete & computational geometry 24 (2000), S. 325-344 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. Neighborly cubical polytopes exist: for any n≥ d≥ 2r+2 , there is a cubical convex d -polytope C d n whose r -skeleton is combinatorially equivalent to that of the n -dimensional cube. This solves a problem of Babson, Billera, and Chan. Kalai conjectured that the boundary $\partial C_d^n$ of a neighborly cubical polytope C d n maximizes the f -vector among all cubical (d-1) -spheres with 2 n vertices. While we show that this is true for polytopal spheres if n≤ d+1 , we also give a counterexample for d=4 and n=6 . Further, the existence of neighborly cubical polytopes shows that the graph of the n -dimensional cube, where n\ge5 , is ``dimensionally ambiguous'' in the sense of Grünbaum. We also show that the graph of the 5 -cube is ``strongly 4 -ambiguous.'' In the special case d=4 , neighborly cubical polytopes have f 3 =(f 0 /4) log 2 (f 0 /4) vertices, so the facet—vertex ratio f 3 /f 0 is not bounded; this solves a problem of Kalai, Perles, and Stanley studied by Jockusch.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004540010039
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  • 3
    Electronic Resource
    Electronic Resource
    Extremal Properties of 0/1-Polytopes (1997)
    Springer
    Discrete & computational geometry 17 (1997), S. 439-448 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. We provide lower and upper bounds for the maximal number of facets of a d-dimensional 0/1-polytope, and for the maximal number of vertices that can appear in a two-dimensional projection (``shadow'') of such a polytope.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00009303
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  • 4
    Electronic Resource
    Electronic Resource
    Shelling Polyhedral 3-Balls and 4-Polytopes (1998)
    Springer
    Discrete & computational geometry 19 (1998), S. 159-174 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. There is a long history of constructions of nonshellable triangulations of three-dimensional (topological) balls. This paper gives a survey of these constructions, including Furch's 1924 construction using knotted curves, which also appears in Bing's 1962 survey of combinatorial approaches to the Poincaré conjecture, Newman's 1926 explicit example, and M. E. Rudin's 1958 nonshellable triangulation of a tetrahedron with only 14 vertices (all on the boundary) and 41 facets. Here an (extremely simple) new example is presented: a nonshellable simplicial three-dimensional ball with only 10 vertices and 21 facets. It is further shown that shellings of simplicial 3 -balls and 4 -polytopes can ``get stuck'': simplicial 4 -polytopes are not in general ``extendably shellable.'' Our constructions imply that a Delaunay triangulation algorithm of Beichl and Sullivan, which proceeds along a shelling of a Delaunay triangulation, can get stuck in the three-dimensional version: for example, this may happen if the shelling follows a knotted curve.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00009339
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  • 5
    Electronic Resource
    Electronic Resource
    A Direct Hexane Extraction Process for Glanded Cottonseed (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Journal of food science 47 (1982), S. 0 
    Details
    ISSN: 1750-3841
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A modified filter funnel apparatus was used to determine mass flow velocities for extraction of uncooked glanded cottonseed flakes, and the results were compared with a continuous pilot-plant-scale extractor. A mass velocity of 2,000 lb/hr/ft2 or higher (considered adequate for oilseed extraction) was obtained in all cases. Both the initial meat moisture before flaking and the flake moisture during extraction were found to affect the mass velocity. A meat moisture before flaking of less than 9% decreased the mass velocity, probably as a result of increased fines and thus smaller flake size. A high flake moisture (about 9%) during heated-hexane extraction caused a decrease in mass velocity compared to that of lower-moisture flakes. The correlation of filter-funnel mass velocity data to a continuous pilot-plant extractor confirmed that uncooked flakes can be satisfactorily extracted to yield low residual lipids by using a low solvent-to-flake ratio and ambient-temperature hexane solvent.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-2621.1982.tb11087.x
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  • 6
    Electronic Resource
    Electronic Resource
    AIR CLASSIFICATION OF DEFATTED, GLANDED COTTONSEED FLOURS TO PRODUCE EDIBLE PROTEIN PRODUCT (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Journal of food science 44 (1979), S. 0 
    Details
    ISSN: 1750-3841
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A modified air-classification technique for producing a low-gossypol, edible cottonseed product from defatted glanded cottonseed flour was investigated. Several milling methods, including fixed hammer disintegating, pin milling, and air-gun pulverizing, were used to prepare flour from defatted flakes. The milled flours were evaluated for particle size distribution prior to air classification. The yields and the proximate composition of the final fractions indicated that both are affected by the method of milling. With a fixed-hammer disintegrator, a low gossypol edible product was produced. The other milling methods ruptured excessive amounts of pigment glands or did not sufficiently comminute the defatted material. The edible fraction yield can be increased if heat is used to lower the free gossypol content of the final product. Heat converted free gossypol into bound gossypol, therefore total gossypol was unchanged.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-2621.1979.tb06478.x
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  • 7
    Electronic Resource
    Electronic Resource
    PROTEIN DISPLACEMENT DURING CLASSIFICATION OF GLANDED COTTONSEED (1980)
    Oxford, UK : Blackwell Publishing Ltd
    Journal of food science 45 (1980), S. 0 
    Details
    ISSN: 1750-3841
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The effects of classification of glanded cottonseed flour on protein displacement were studied. Media were liquid (nonpolar solvent) and air. The fines and coarse fractions had different ratios of water-soluble functional and storage proteins than the starting material. The difference in protein distribution was reflected in the contents of essential amino acids of each fraction. Fines or “overs” fractions had lower amounts of some limiting essential amino acids such as lysine, threonine and leucine as compared with the coarse fraction. Degossypolised cottonseed flour therefore had lower protein quality than the starting material. Although the fines fractions have lower amounts of essential amino acids as compared with the coarse fractions, they did not differ in the type of proteins as shown by gel electrophoresis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-2621.1980.tb07564.x
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  • 8
    Electronic Resource
    Electronic Resource
    Branchings in rooted graphs and the diameter of greedoids (1988)
    Springer
    Combinatorica 8 (1988), S. 217-234 
    Details
    ISSN: 1439-6912
    Keywords: 05 B 35 ; 05 c 20 ; 68 Q 20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetG be a 2-connected rooted graph of rankr andA, B two (rooted) spanning trees ofG We show that the maximum number of exchanges of leaves that can be required to transformA intoB isr 2−r+1 (r〉0). This answers a question by L. Lovász. There is a natural reformulation of this problem in the theory ofgreedoids, which asks for the maximum diameter of the basis graph of a 2-connected branching greedcid of rankr. Greedoids are finite accessible set systems satisfying the matroid exchange axiom. Their theory provides both language and conceptual framework for the proof. However, it is shown that for general 2-connected greedoids (not necessarily constructed from branchings in rooted graphs) the maximum diameter is 2r−1.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02122803
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