A code is called isodual if it is equivalent to its dual code, and a lattice is called isodual if it is isometric to its dual lattice. In this note, we investigate isodual codes over Z(2k). These codes give rise to is...
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A code is called isodual if it is equivalent to its dual code, and a lattice is called isodual if it is isometric to its dual lattice. In this note, we investigate isodual codes over Z(2k). These codes give rise to isodual lattices;in particular, we construct a 22-dimensional isodual lattice with minimum norm 3 and kissing number 2464.
The first step of the construction of Nezondet's models of finite arithmetics which are counter-models to Erdos-Woods conjecture is to add to the natural numbers the non-standard numbers generated by one of them, ...
The first step of the construction of Nezondet's models of finite arithmetics which are counter-models to Erdos-Woods conjecture is to add to the natural numbers the non-standard numbers generated by one of them, using addition, multiplication and divisions by a natural factor allowed in an ultrapower construction. After a review of some properties of such a structure, we show that the choice of the ultrafilter can be managed, using just the Chinese remainder's theorem, so that a model as desired is obtained as early as at the first time.
In this paper we present some results concerning the median points of a discrete set according to a distance defined by means of two directions p and q. We describe a local characterization of the median points and sh...
In this paper we present some results concerning the median points of a discrete set according to a distance defined by means of two directions p and q. We describe a local characterization of the median points and show how these points can be determined from the projections of the discrete set along directions p and q. We prove that the discrete sets having some connectivity properties have at most four median points according to a linear distance, and if there are four median points they form a parallelogram. Finally, we show that the 4-connected sets which are convex along the diagonal directions contain their median points along these directions.
A generalization of a classical discrete tomography problem is considered: Reconstruct binary matrices from their absorbed row and columns sums, i.e., when some known absorption is supposed. It is mathematically inter...
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ISBN:
(纸本)3540413960
A generalization of a classical discrete tomography problem is considered: Reconstruct binary matrices from their absorbed row and columns sums, i.e., when some known absorption is supposed. It is mathematically interesting when the absorbed projection of a matrix element is the same as the absorbed projection of the next two consecutive elements together. We show that, in this special case, the non-uniquely determined matrices contain a certain configuration of 0s and 1s, called alternatively corner-connected components. Furthermore, such matrices can be transformed into each other by switchings the 0s and 1s of these components.
We discuss some linear acceleration methods for alternating series which are in theory and in practice much better than that of Euler-Van Wijngaarden. One of the algorithms, for instance, allows one to calculate Sigma...
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We discuss some linear acceleration methods for alternating series which are in theory and in practice much better than that of Euler-Van Wijngaarden. One of the algorithms, for instance, allows one to calculate Sigma(-1)(k)a(k) with an error of about 17.93(-n) from the first n terms for a wide class of sequences {a(k)}. Such methods are useful for high precision calculations frequently appearing in number theory.
Equiangularity (also called max-min angle criterion) is a well-known property of some planar triangulations that refine the Delaunay diagram. In this paper we generalize the notion of equiangularity to decompositions ...
Equiangularity (also called max-min angle criterion) is a well-known property of some planar triangulations that refine the Delaunay diagram. In this paper we generalize the notion of equiangularity to decompositions in inscribable polygons and we show that it characterizes the planar Delaunay diagram, even if more than three sites are cocircular. This result does not extend to higher dimensions. However, we characterize the Delaunay diagram in any dimension by a kind of dual property that we prove both with line angles and with solid angles. We also establish a local equiangularity of Delaunay diagrams in any dimension, and an angular characterization of self-centered diagrams. Finally, we show that these angular properties can, when appropriately defined, be generalized to the farthest point Delaunay diagram.
In Computer Science, n-tuples and lists are usual tools;we investigate both notions in the framework of first-order logic within the set of nonnegative integers. Godel had firstly shown that the objects which can be d...
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In Computer Science, n-tuples and lists are usual tools;we investigate both notions in the framework of first-order logic within the set of nonnegative integers. Godel had firstly shown that the objects which can be defined by primitive recursion schema, can also be defined at first-order, using natural order and some coding devices for lists. Second he had proved that this encoding can be defined from addition and multiplication. We show this can be also done with addition and a weaker predicate, namely the coprimeness predicate. The theory of integers equipped with a pairing function can be decidable or not. The theory of decoding of lists (under some natural condition) is always undecidable. We distinguish the notions encoding of n-tuples and encoding of lists via some properties of decidability-undecidability. At last, we prove it is possible in some structure to encode lists although neither addition nor multiplication are definable in this structure. (C) 1999 Elsevier Science B.V. All rights reserved.
We show that the independence relation defining a trace monoid M admits a transitive orientation if and only if the characteristic series xi of a lexicographic cross section of ill is the inverse of the determinant of...
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We show that the independence relation defining a trace monoid M admits a transitive orientation if and only if the characteristic series xi of a lexicographic cross section of ill is the inverse of the determinant of (Id-X), where X is a matrix representing the minimum finite automaton recognizing xi and Id is the identity matrix. This implies that, if the independence relation of a trace monoid M admits a transitive orientation, then any unambiguous lifting of the Mobius function of M is the determinant of a matrix defined by the smallest acceptor of the corresponding cross section. (C) 1999 Elsevier Science B.V. All rights reserved.
A partial word is a word that is a partial mapping into an alphabet. We prove a variant of Fine and Wilf's theorem for partial words, and give extensions of some general combinatorial properties of words. (C) 1999...
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A partial word is a word that is a partial mapping into an alphabet. We prove a variant of Fine and Wilf's theorem for partial words, and give extensions of some general combinatorial properties of words. (C) 1999 Elsevier Science B.V. All rights reserved.
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