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Search Results: 1 - 10 of 1695 matches for " Laurence Boxer "
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Continuous Maps on Digital Simple Closed Curves  [PDF]
Laurence Boxer
Applied Mathematics (AM) , 2010, DOI: 10.4236/am.2010.15050
Abstract: We give digital analogues of classical theorems of topology for continuous functions defined on spheres, for digital simple closed curves. In particular, we show the following. ? A digital simple closed curve of more than 4 points is not contractible, i.e., its identity map is not nullhomotopic in . ? Let and be digital simple closed curves, each symmetric with respect to the origin, such that (where is the number of points in ). Let be a digitally continuous antipodal map. Then is not nullho- motopic in . ? Let be a digital simple closed curve that is symmetric with respect to the origin. Let be a digitally continuous map. Then there is a pair of antipodes such that .
Homotopy relations for digital images
Laurence Boxer,P. Christopher Staecker
Mathematics , 2015,
Abstract: We introduce three generalizations of homotopy equivalence in digital images, to allow us to express whether a finite and an infinite digital image are similar with respect to homotopy. We show that these three generalizations are not equivalent to ordinary homotopy equivalence, and give several examples. We show that, like homotopy equivalence, our three generalizations imply isomorphism of fundamental groups, and are
Remarks on pointed digital homotopy
Laurence Boxer,P. Christopher Staecker
Mathematics , 2015,
Abstract: We present and explore in detail a pair of digital images with $c_u$-adjacencies that are homotopic but not pointed homotopic. For two digital loops $f,g: [0,m]_Z \rightarrow X$ with the same basepoint, we introduce the notion of {\em tight at the basepoint (TAB)} pointed homotopy, which is more restrictive than ordinary pointed homotopy and yields some different results. We present a variant form of the digital fundamental group. Based on what we call {\em eventually constant} loops, this version of the fundamental group is equivalent to that of Boxer (1999), but offers the advantage that eventually constant maps are often easier to work with than the trivial extensions that are key to the development of the fundamental group in Boxer (1999) and many subsequent papers. We show that homotopy equivalent digital images have isomorphic fundamental groups, even when the homotopy equivalence does not preserve the basepoint. This assertion appeared in Boxer (2005), but there was an error in the proof; here, we correct the error.
Alternate version of continuity for digital multivalued functions
Laurence Boxer,P. Christopher Staecker
Mathematics , 2015,
Abstract: We introduce weakly continuous multivalued functions between digital images. This notion generalizes that of continuous multivalued functions studied mostly in the setting of the digital plane $Z^2$. We show that weakly continuous multivalued functions, like continuous multivalued functions, are appropriate models for digital morpholological operations. Weak continuity, unlike continuity, is preserved by compositions, and generalizes easily to higher dimensions and arbitrary adjacency relations.
Digital Fixed Points, Approximate Fixed Points, and Universal Functions
Laurence Boxer,Ozgur Ege,Ismet Karaca,Jonathan Lopez,Joel Louwsma
Computer Science , 2015,
Abstract: A. Rosenfeld introduced the notion of a digitally continuous function between digital images, and showed that although digital images need not have fixed point properties analogous to those of the Euclidean spaces modeled by the images, there often are approximate fixed point properties of such images. In the current paper, we obtain additional results concerning fixed points and approximate fixed points of digitally continuous functions. Among these are several results concerning the relationship between universal functions and the approximate fixed point property (AFPP).
Torsion in the Coherent Cohomology of Shimura Varieties and Galois Representations
George Boxer
Mathematics , 2015,
Abstract: We introduce a method for producing congruences between Hecke eigenclasses, possibly torsion, in the coherent cohomology of automorphic vector bundles on certain good reduction Shimura varieties. The congruences are produced using some "generalized Hasse invariants" adapted to the Ekedahl-Oort stratification of the special fiber.
C.Ch. Goslinga, The Dutch in the Caribbean and on the Wild Coast, 1580-1680
C.R. Boxer
BMGN : Low Countries Historical Review , 1972,
Abstract:
G. Asaert, Maritieme geschiedenis der Nederlanden, I, Prehistorie, romeinse tijd, middeleeuwen, vijftiende en zestiende eeuw
G. Asaert, Maritieme geschiedenis der Nederlanden, II, Zeventiende eeuw, van 1585 tot ca 1680

C.R. Boxer
BMGN : Low Countries Historical Review , 1978,
Abstract:
J.Th. de Smidt, T. van der Lee, Plakkaten, ordonnanti n en andere wetten, uitgevaardigd in Suriname, 1667-1816
C.R. Boxer
BMGN : Low Countries Historical Review , 1975,
Abstract:
G. Asaert, Maritieme geschiedenis der Nederlanden, III, achttiende eeuw en eerste helft negentiende eeuw, van circa 1680 tot 1850-1870
C.R. Boxer
BMGN : Low Countries Historical Review , 1979,
Abstract:
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