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  • 1
    Electronic Resource
    Electronic Resource
    Application of the carbon rod atomizer to atomic absorption spectrometry of petroleum products (1971)
    s.l. : American Chemical Society
    Analytical chemistry 43 (1971), S. 1557-1560 
    Details
    ISSN: 1520-6882
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/ac60306a005
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  • 2
    Electronic Resource
    Electronic Resource
    Direct determination of lead airborne particulates by nonflame atomic absorption (1973)
    s.l. : American Chemical Society
    Analytical chemistry 45 (1973), S. 1606-1609 
    Details
    ISSN: 1520-6882
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/ac60331a026
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  • 3
    Electronic Resource
    Electronic Resource
    A Helly-Type Theorem for Unions of Convex Sets (1997)
    Springer
    Discrete & computational geometry 18 (1997), S. 1-12 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. We prove that for any d, k ≥ 1 there are numbers q = q(d,k) and h = h(d,k) such that the following holds: Let ${\cal K}$ be a family of subsets of the d-dimensional Euclidean space, such that the intersection of any subfamily of ${\cal K}$ consisting of at most q sets can be expressed as a union of at most k convex sets. Then the Helly number of ${\cal K}$ is at most h. We also obtain topological generalizations of some cases of this result. The main result was independently obtained by Alon and Kalai, by a different method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00009305
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  • 4
    Electronic Resource
    Electronic Resource
    Almost-Tiling the Plane by Ellipses (1999)
    Springer
    Discrete & computational geometry 22 (1999), S. 367-375 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. For any λ 〉 1 we construct a periodic and locally finite packing of the plane with ellipses whose λ -enlargement covers the whole plane. This answers a question of Imre Bárány. On the other hand, we show that if C is a packing in the plane with circular disks of radius at most 1, then its (1+16 -5 ) -enlargement covers no square with side length 4.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00009466
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  • 5
    Electronic Resource
    Electronic Resource
    On Functional Separately Convex Hulls (1998)
    Springer
    Discrete & computational geometry 19 (1998), S. 105-130 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. Let D be a set of vectors in R d . A function f: R d → R is called D-convex if its restriction to each line parallel to a nonzero vector of D is a convex function. For a set A⊆ R d , the functional D-convex hull of A, denoted by co D (A) , is the intersection of the zero sets of all nonnegative D -convex functions that are 0 on A . We prove some results concerning the structure of functional D -convex hulls, e.g., a Krein—Milman-type theorem and a result on separation of connected components. We give a polynomial-time algorithm for computing co D (A) for a finite point set A (in any fixed dimension) in the case of D being a basis of R d (the case of separate convexity). This research is primarily motivated by questions concerning the so-called rank-one convexity, which is a particular case of D -convexity and is important in the theory of systems of nonlinear partial differential equations and in mathematical modeling of microstructures in solids. As a direct contribution to the study of rank-one convexity, we construct a configuration of 20 symmetric 2 x 2 matrices in a general (stable) position with a nontrivial functionally rank-one convex hull (answering a question of K. Zhang on the existence of higher-dimensional nontrivial configurations of points and matrices).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00009331
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  • 6
    Electronic Resource
    Electronic Resource
    On Constants for Cuttings in the Plane (1998)
    Springer
    Discrete & computational geometry 20 (1998), S. 427-448 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. A theorem of Chazelle and Friedman with numerous applications in combinatorial and computational geometry asserts that for any set L of n lines in the plane and for any parameter r〉1 there exists a subdivision of the plane into at most Cr 2 (possibly unbounded) triangles, C a constant, such that the interior of each triangle is intersected by at most n/r lines of L . (Such a subdivision is called a (1/r) -cutting for L .) We give upper and lower bounds on the constant C . We also consider the canonical triangulation of the arrangement of a random sample of r lines from L . Although this typically is not a (1/r) -cutting, the expectation of the k th degree average of the number of lines intersecting a triangle is O(n/r) for any fixed k . We estimate the constant of proportionality in this result.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00009394
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  • 7
    Electronic Resource
    Electronic Resource
    On Approximate Geometric k -Clustering (2000)
    Springer
    Discrete & computational geometry 24 (2000), S. 61-84 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. For a partition of an n -point set $X\subset \Rd$ into k subsets (clusters) S 1 ,S 2 ,. . .,S k , we consider the cost function $\sum_{i=1}^k \sum_{x\in S_i} \|x-c(S_i)\|^2$ , where c(S i ) denotes the center of gravity of S i . For k=2 and for any fixed d and ε 〉0 , we present a deterministic algorithm that finds a 2-clustering with cost no worse than (1+ε) -times the minimum cost in time O(n log n); the constant of proportionality depends polynomially on ε . For an arbitrary fixed k , we get an O(n log k n) algorithm for a fixed ε , again with a polynomial dependence on ε .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004540010019
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  • 8
    Electronic Resource
    Electronic Resource
    Dynamic half-space range reporting and its applications (1995)
    Springer
    Algorithmica 13 (1995), S. 325-345 
    Details
    ISSN: 1432-0541
    Keywords: Arrangements ; Cuttings ; Range-searching ; Dynamization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We consider the half-space range-reporting problem: Given a setS ofn points in ℝd, preprocess it into a data structure, so that, given a query half-space γ, allk points ofS ∩ γ can be reported efficiently. We extend previously known static solutions to dynamic ones, supporting insertions and deletions of points ofS. For a given parameterm,n ≤m ≤n ⌊d/2⌋ and an arbitrarily small positive constant ɛ, we achieveO(m 1+ɛ) space and preprocessing time, O((n/m ⌊d/2⌋ logn+k) query time, and O(m1+ɛn) amortized update time (d ≳ 3). We present, among others, the following applications: an O(n1+ɛ)-time algorithm for computing convex layers in ℝ3, and an output sensitive algorithm for computing a level in an arrangements of planes in ℝ3, whose time complexity is O((b+n) nɛ, whereb is the size of the level.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01293483
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  • 9
    Electronic Resource
    Electronic Resource
    A subexponential bound for linear programming (1996)
    Springer
    Algorithmica 16 (1996), S. 498-516 
    Details
    ISSN: 1432-0541
    Keywords: Computational geometry ; Combinatorial optimization ; Linear programming ; Smallest enclosing ball ; Smallest enclosing ellipsoid ; Randomized incremental algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We present a simple randomized algorithm which solves linear programs withn constraints andd variables in expected $$\min \{ O(d^2 2^d n),e^{2\sqrt {dIn({n \mathord{\left/ {\vphantom {n {\sqrt d }}} \right. \kern-\nulldelimiterspace} {\sqrt d }})} + O(\sqrt d + Inn)} \}$$ time in the unit cost model (where we count the number of arithmetic operations on the numbers in the input); to be precise, the algorithm computes the lexicographically smallest nonnegative point satisfyingn given linear inequalities ind variables. The expectation is over the internal randomizations performed by the algorithm, and holds for any input. In conjunction with Clarkson's linear programming algorithm, this gives an expected bound of $$O(d^2 n + e^{O(\sqrt {dInd} )} ).$$ The algorithm is presented in an abstract framework, which facilitates its application to several other related problems like computing the smallest enclosing ball (smallest volume enclosing ellipsoid) ofn points ind-space, computing the distance of twon-vertex (orn-facet) polytopes ind-space, and others. The subexponential running time can also be established for some of these problems (this relies on some recent results due to Gärtner).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01940877
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  • 10
    Electronic Resource
    Electronic Resource
    The effect of bull seminal ribonuclease on spermatogenesis in the rabbit
    Amsterdam : Elsevier
    Animal Reproduction Science 1 (1978), S. 49-59 
    Details
    ISSN: 0378-4320
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1016/0378-4320(78)90009-X
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