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  • Articles  (15)
  • kriging  (8)
  • 06A10  (7)
  • 2015-2019
  • 1980-1984  (15)
  • 1970-1974
  • 1950-1954
  • 1940-1944
  • 1984  (15)
  • Mathematics  (15)
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  • Articles  (15)
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  • 2015-2019
  • 1980-1984  (15)
  • 1970-1974
  • 1950-1954
  • 1940-1944
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  • 1
    Electronic Resource
    Electronic Resource
    Maximum antichains in the product of chains (1984)
    Springer
    Order 1 (1984), S. 21-28 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; 05A05 ; Partially ordered sets ; Sperner's Theorem ; LYM property ; product of chains
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let P be the poset k 1 × ... × k n , which is a product of chains, where n≥1 and k 1≥ ... ≥k n ≥2. Let $$M = k_1 - \sum\nolimits_{i = 2}^n {(k_i - 1)} $$ . P is known to have the Sperner property, which means that its maximum ranks are maximum antichains. Here we prove that its maximum ranks are its only maximum antichains if and only if either n=1 or M≤1. This is a generalization of a classical result, Sperner's Theorem, which is the case k 1= ... =k n =2. We also determine the number and location of the maximum ranks of P.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00396270
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  • 2
    Electronic Resource
    Electronic Resource
    Finite cutsets and finite antichains (1984)
    Springer
    Order 1 (1984), S. 35-46 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; Ordered set ; chain ; antichains ; width ; cutset
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An ordered set (P,≤) has the m cutset property if for each x there is a set Fx with cardinality less than m, such that each element of Fx is incomparable to x and {x} ∪ Fx meets every maximal chain of (P,≤). Let n be least, such that each element x of any P having the m cutset property belongs to some maximal antichain of cardinality less than n. We specify n for m 〈 w. Indeed, n-1=m= width P for m=1,2,n=5 if m=3 and n⩾ℵ1 if m ≥4. With the added hypothesis that every bounded chain has a supremum and infimum in P, it is shown that for 4⩽m⩽ℵ0, n=ℵ0. That is, if each element x has a finite cutset Fx, each element belongs to a finite maximal antichain.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00396272
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  • 3
    Electronic Resource
    Electronic Resource
    Minimizing the jump number for partially ordered sets: A graph-theoretic approach (1984)
    Springer
    Order 1 (1984), S. 7-19 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; 05C20 ; 68C25 ; Partial order ; linear extension ; jump number ; line digraph ; cyclomatic number ; spanning branching ; Eulerian digraph
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The purpose of this paper is to present a graph-theoretic approach to the jump number problem for N-free posets which is based on the observation that the Hasse diagram of an N-free poset is a line digraph. Therefore, to every N-free poset P we can assign another digraph which is the root digraph of the Hasse diagram of P. Using this representation we show that the jump number of an N-free poset is equal to the cyclomatic number of its root digraph and can be found (without producing any linear extension) by an algorithm which tests if a given poset is N-free. Moreover, we demonstrate that there exists a correspondence between optimal linear extensions of an N-free poset and spanning branchings of its root digraph. We provide also another proof of the fact that optimal linear extensions of N-free posets are exactly greedy linear extensions. In conclusion, we discuss some possible generalizations of these results to arbitrary posets.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00396269
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  • 4
    Electronic Resource
    Electronic Resource
    Powers of ordered sets (1984)
    Springer
    Order 1 (1984), S. 83-92 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; Ordered sets ; exponentiation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Recently there has been significant progress in the study of powers of ordered sets. Much of this work has concerned cancellation laws for powers and uses these two steps. First, logarithmic operators are introduced to transform cancellation problems for powers into questions involving direct product decompositions. Second, refinement theorems for direct product decompositions are brought to bear. Here we present two results with the aim of highlighting these steps.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00396275
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  • 5
    Electronic Resource
    Electronic Resource
    Balancing poset extensions (1984)
    Springer
    Order 1 (1984), S. 113-126 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; 68E05 ; Sorting ; comparison ; information theoretic bound ; linear extension
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We show that any finite partially ordered setP (not a total order) contains a pair of elementsx andy such that the proportion of linear extensions ofP in whichx lies belowy is between 3/11 and 8/11. A consequence is that the information theoretic lower bound for sorting under partial information is tight up to a multiplicative constant. Precisely: ifX is a totally ordered set about which we are given some partial information, and ife(X) is the number of total orderings ofX compatible with this information, then it is possible to sortX using no more thanC log2 e (X) comparisons whereC is approximately 2.17.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00565647
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  • 6
    Electronic Resource
    Electronic Resource
    Ordered sets with no chains of ideals of a given type (1984)
    Springer
    Order 1 (1984), S. 159-172 
    Details
    ISSN: 1572-9273
    Keywords: 06A05 ; 06A10 ; Ordered sets ; ideals ; better quasi-order
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study the possible order types of chains of ideals in an ordered set. Our main result is this. Given an indecomposable countable order type α, there is a finite listA 1 α , ...,A n α of ordered sets such that for every ordered setP the setJ(P) of ideals ofP, ordered by inclusion, contains a chain of type α if and only ifP contains a subset isomorphic to one of theA 1 #x03B1; , ...,A n α . The finiteness of the list relies on the notion of better quasi-ordering introduced by Nash-Williams and the properties of scattered chains obtained by Laver.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00565651
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  • 7
    Electronic Resource
    Electronic Resource
    Compactness and subsets of ordered sets that meet all maximal chains (1984)
    Springer
    Order 1 (1984), S. 147-157 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; 54D30 ; Maximal chain ; cutset ; chain complete ; antichain ; cofinal subset
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetP be a chain complete ordered set. By considering subsets which meet all maximal chains, we describe conditions which imply that the space of maximal chains ofP is compact. The symbolsP 1 andP 2 refer to two particular ordered sets considered below. It is shown that the space of maximal chains ℳ (P) is compact ifP satisfies any of the following conditions: (i)P contains no copy ofP 1 or its dual and all antichains inP are finite. (ii)P contains no properN and every element ofP belongs to a finite maximal antichain ofP. (iii)P contains no copy ofP 1 orP 2 and for everyx inP there is a finite subset ofP which is coinitial abovex. We also describe an example of an ordered set which is complete and densely ordered and in which no antichain meets every maximal chain.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00565650
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  • 8
    Electronic Resource
    Electronic Resource
    Robust kriging—A proposal (1984)
    Springer
    Mathematical geology 16 (1984), S. 3-18 
    Details
    ISSN: 1573-8868
    Keywords: Geostatistics ; kriging ; robust estimation ; time series
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Geological data frequently have a heavy-tailed normal-in-the-middle distribution, which gives rise to grade distributions that appear to be normal except for the occurrence of a few outliers. This same situation also applies to log-transformed data to which lognormal kriging is to be applied. For such data, linear kriging is nonrobust in that (1)kriged estimates tend to infinity as the outliers do, and (2)it is also not minimum mean squared error. The more general nonlinear method of disjunctive kriging is even more nonrobust, computationally more laborious, and in the end need not produce better practical answers. We propose a robust kriging method for such nearly normal data based on linear kriging of an editing of the data. It is little more laborious than conventional linear kriging and, used in conjunction with a robust estimator of the variogram, provides good protection against the effects of data outliers. The method is also applicable to time series analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01036237
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  • 9
    Electronic Resource
    Electronic Resource
    Smoothing and interpolation by kriging and with splines (1984)
    Springer
    Mathematical geology 16 (1984), S. 601-615 
    Details
    ISSN: 1573-8868
    Keywords: kriging ; splines ; interpolation ; smoothing ; prediction ; Green's function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Let scalar measurements at distinct points x1, ⋯, xn be y1, ⋯, yn.We may look for a smooth function f(x)that goes through or near the points (xi, yi).Kriging assumes f(x)is a random function with known (possibly estimable) covariance function (in the simplest case). Splines assume a definition of the smoothness of a nonrandom function f(x).An elementary explanation is given of the fact that spline approximations are special cases of the solution of a kriging problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01029320
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  • 10
    Electronic Resource
    Electronic Resource
    Cokriging of aquifer transmissivities from field measurements of transmissivity and specific capacity (1984)
    Springer
    Mathematical geology 16 (1984), S. 19-35 
    Details
    ISSN: 1573-8868
    Keywords: groundwater ; geostatistics ; cokriging ; kriging ; transmissivity ; specific capacity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract This paper presents a new application of the cokriging technique for constructing maps of aquifer transmissivity from field measurements of transmissivity and specific capacity. The technique is illustrated using data from Yolo Basin, California. Cokriging is well-suited for estimating undersampled variables. To improve the accuracy of the estimation, cokriging considers the spatial auto-correlation of the variable to be estimated and the spatial cross-correlation between the variable to be estimated and other, better-sampled variables. Consequently, in regions that lack data of the variable to be estimated, accurate estimation can still be made on the basis of auto- and cross-correlation. In addition, estimation variances can be obtained with a little additional computation effort.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01036238
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  • 11
    Electronic Resource
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    A geostatistically based approach to the identification of aquifer transmissivities in Yolo Basin, California (1984)
    Springer
    Mathematical geology 16 (1984), S. 125-137 
    Details
    ISSN: 1573-8868
    Keywords: kriging ; cokriging ; hydrology ; groundwater
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A geostatistically based approach is developed for the identification of aquifer transmissivities in Yolo Basin, California. The approach combines weighted least-squares with universal kriging and cokriging techniques in an overall scheme that (1)considers a prioriknown information on aquifer transmissivity and specific capacities of wells, (2)considers uncertainties in water level and transmissivity data, and (3)estimates the reliability of the generated transmissivity values. Minimization of a global least-squares function that incorporates calibration and plausibility criteria leads to a transmissivity map that shows a good agreement with pumping-test results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01032212
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  • 12
    Electronic Resource
    Electronic Resource
    Analysis of nonintrinsic spatial variability by residual kriging with application to regional groundwater levels (1984)
    Springer
    Mathematical geology 16 (1984), S. 499-521 
    Details
    ISSN: 1573-8868
    Keywords: Spatial variability ; nonintrinsic ; nonstationary ; drift ; kriging ; residuals ; groundwater levels
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A method for obtaining pointwise or spatially averaged estimates of a nonintrinsic function is introduced based on residual kriging. The method relies on a stepwise iterative regression process for simultaneously estimating the global drift and residual semivariogram. Estimates of the function are then obtained by solving a modified set of simple kriging equations written for the residuals. The modification consists of replacing the true variogram in the kriging equations by the variogram of the residual estimates as obtained from the iterative regression process. The method is illustrated by considering groundwater levels in an Arizona aquifer. The results are compared with those obtained for the aquifer by the generalized covariance package BLUEPACK-3D.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01886329
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  • 13
    Electronic Resource
    Electronic Resource
    Kriging in a global neighborhood (1984)
    Springer
    Mathematical geology 16 (1984), S. 249-265 
    Details
    ISSN: 1573-8868
    Keywords: kriging ; moving neighborhood ; global neighborhood ; geostatistics ; automatic contouring
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The kriging estimator is usually computed in a moving neighborhood; only the data near the point to be estimated are used. This moving neighborhood approach creates discontinuities in mapping applications. An alternative approach is presented here, whereby all points are estimated using all the available data. To solve the resulting large linear system the kriging estimator is expressed in terms of the inverse of the covariance matrix. The covariance matrix has the advantage of being positive definite and the size of system which can be solved without encountering numerical instability is substantially increased. Because the kriging matrix does not change, the estimator can be written in terms of scalar products, thus avoiding the more time-consuming matrix multiplications of the standard approach. In the particular case of a covariance which is zero for distances greater than a fixed value (the range), the resulting banded structure of the covariance matrix is shown to lead to substantial computational savings in both run time and storage space. In this case the calculation time for the kriging variance is also substantially reduced. The present method is extended to the nonstationary case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01032690
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  • 14
    Electronic Resource
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    Application of fuzzy clustering and fuzzy classification to evaluate the provenance of glacial till (1984)
    Springer
    Mathematical geology 16 (1984), S. 283-301 
    Details
    ISSN: 1573-8868
    Keywords: Bayesian classifiers ; classification ; cluster analysis ; cluster validity ; fuzzyc means ; fuzzyc varieties ; fuzzy covariances ; geochemical prospecting ; glacial till ; kriging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract To evaluate the provenance of glacial till, the trace element content of magnetite was used. Magnetite was present in all known rock types and all till samples in the area investigated. By using fuzzy-set theory it was possible to group samples of magnetite taken from bedrock into relatively homogeneous and geologically meaningful groups and also, by fuzzy classification, to relate the till samples to the rocks in such a way that the relative contribution of each rock type to the till is estimated. Each rock and till sample is assigned a membership value between 0 and 1 for each rock type. The membership values, for a certain rock type in the till, are then interpolated by kriging onto maps. Magnetites from skarns associated with sulfide ores especially are rather distinct, and so a map of such membership values for till unveils all known ore deposits some 1–5 km “downstream”in the general direction of the ice flow. Other anomalies show up which cannot be related to hitherto known ores or mineralizations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01032692
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  • 15
    Electronic Resource
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    Robustness of variograms and conditioning of kriging matrices (1984)
    Springer
    Mathematical geology 16 (1984), S. 809-822 
    Details
    ISSN: 1573-8868
    Keywords: variogram ; robustness ; kriging ; conditioning number
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Current ideas of robustness in geostatistics concentrate upon estimation of the experimental variogram. However, predictive algorithms can be very sensitive to small perturbations in data or in the variogram model as well. To quantify this notion of robustness, nearness of variogram models is defined. Closeness of two variogram models is reflected in the sensitivity of their corresponding kriging estimators. The condition number of kriging matrices is shown to play a central role. Various examples are given. The ideas are used to analyze more complex universal kriging systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01036706
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