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203
A decidable spatial logic with coneshaped cardinal directions
 In Proc. of the 18th EACSL Annual Conference on Computer Science Logic (CSL), volume 5771 of LNCS
, 2009
"... Abstract. We introduce a spatial modal logic based on coneshaped cardinal directions over the rational plane and we prove that, unlike projectionbased ones, such as, for instance, Compass Logic, its satisfiability problem is decidable (PSPACEcomplete). We also show that it is expressive enough t ..."
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Cited by 5 (3 self)
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Abstract. We introduce a spatial modal logic based on coneshaped cardinal directions over the rational plane and we prove that, unlike projectionbased ones, such as, for instance, Compass Logic, its satisfiability problem is decidable (PSPACEcomplete). We also show that it is expressive enough
Reasoning about cardinal directions between extended objects
 Artif. Intell
"... Direction relations between extended spatial objects are important commonsense knowledge. Recently, Goyal and Egenhofer proposed a formal model, known as Cardinal Direction Calculus (CDC), for representing direction relations between connected plane regions. CDC is perhaps the most expressive qualit ..."
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Cited by 5 (2 self)
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Direction relations between extended spatial objects are important commonsense knowledge. Recently, Goyal and Egenhofer proposed a formal model, known as Cardinal Direction Calculus (CDC), for representing direction relations between connected plane regions. CDC is perhaps the most expressive
Construction of modular curves and computation of their cardinality over Fp
"... Abstract. Following [3], and in using several results, we describe an algorithm which compute with a level N given the cardinality over Fp of the Jacobian of elliptic curves and hyperelliptic curves of genus 2 which come from X0(N). We will also sketch how to get a plane affine model for these curve ..."
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Abstract. Following [3], and in using several results, we describe an algorithm which compute with a level N given the cardinality over Fp of the Jacobian of elliptic curves and hyperelliptic curves of genus 2 which come from X0(N). We will also sketch how to get a plane affine model
On the number of halving planes
 Combinatorica
, 1990
"... Let S ⊂ IR 3 be an nset in general position. A plane containing three of the points is called a halving plane if it dissects S into two parts of equal cardinality. It is proved that the number of halving planes is at most O(n 2.998). As a main tool, for every set Y of n points in the plane a set N ..."
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Cited by 26 (3 self)
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Let S ⊂ IR 3 be an nset in general position. A plane containing three of the points is called a halving plane if it dissects S into two parts of equal cardinality. It is proved that the number of halving planes is at most O(n 2.998). As a main tool, for every set Y of n points in the plane a set N
Algebraic Integrability of Foliations of the Plane
, 2005
"... We give an algorithm to decide whether an algebraic plane foliation F has a rational first integral and to compute it in the affirmative case. The algorithm runs whenever we assume the polyhedrality of the cone of curves of the surface obtained after blowingup the set BF of infinitely near points n ..."
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Cited by 5 (5 self)
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We give an algorithm to decide whether an algebraic plane foliation F has a rational first integral and to compute it in the affirmative case. The algorithm runs whenever we assume the polyhedrality of the cone of curves of the surface obtained after blowingup the set BF of infinitely near points
Reduced Words and Plane Partitions
 J. ALGEBR. COMB
, 1997
"... Let w 0 be the element of maximal length in the symmetric group S n , and let Red(w 0 ) be the set of all reduced words for w 0 . We prove the identity (a1 ;a2 ;:::)2Red(w0 ) (x + a 1 )(x + a 2 ) \Delta \Delta \Delta = ; () which generalizes R. P. Stanley's [S2] formula for the c ..."
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Cited by 5 (1 self)
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for the cardinality of Red(w 0 ), and I. G. Macdonald 's [M1] formula a 1 a 2 \Delta \Delta \Delta = ! .
On odd cuts and plane multicommodity flows
 PROC. LONDON MATH. SOC. SER
, 1981
"... Let T be an even subset of the vertices of a graph G. A Tcut is an edgecutset of the graph which divides T into two odd sets. We prove that if G is bipartite, then the maximum number of disjoint!Tcuts is equal to the minimum cardinality of a set of edges which meets every Tcut. (A weaker form of ..."
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Cited by 21 (0 self)
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Let T be an even subset of the vertices of a graph G. A Tcut is an edgecutset of the graph which divides T into two odd sets. We prove that if G is bipartite, then the maximum number of disjoint!Tcuts is equal to the minimum cardinality of a set of edges which meets every Tcut. (A weaker form
Shifted plane partitions of trapezoidal shape
 Proc. Amer. Math. Soc
, 1983
"... Abstract. The number of shifted plane partitions contained in the shifted shape [p + q — l,p + q — 3,..., p — 9 + 1] with part size bounded by mis shown to be equal to the number of ordinary plane partitions contained in the shape (p, p,..., p) (q rows) with part size bounded by m. The proof uses kn ..."
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Cited by 14 (0 self)
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known combinatorial descriptions of finitedimensional representations of semisimple Lie algebras. A separate simpler argument shows that the number of chains of cardinality k in the poset underlying the shifted plane partitions is equal to the number of chains of cardinality fc in the poset underlying
Inertial Sensor Measurement of HeadCervical Range of Motion in Transverse Plane
"... Abstract: This paper describes a method for measuring range of motion (RoM) of head in transverse plane. The measurement is performed using single inertial measurement unit MTx XSens sensor (XSens Motion Technologies, Netherlands). Specialized software for sensor data acquisition, with high visuali ..."
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visualization abilities has been developed in LaBACAS. MTx XSens sensor can provide useful, noninvasive measurement of head motion in three cardinal planes for fast evaluation of disturbances related to head/neck problems and cervical dysfunctions. The aim of this work is to investigate the feasibility
A DECIDABLE WEAKENING OF COMPASS LOGIC BASED ON CONESHAPED CARDINAL DIRECTIONS
"... Abstract. We introduce a modal logic, called Cone Logic, whose formulas describe properties of points in the plane and spatial relationships between them. Points are labelled by proposition letters and spatial relations are induced by the four coneshaped cardinal directions. Cone Logic can be seen ..."
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Abstract. We introduce a modal logic, called Cone Logic, whose formulas describe properties of points in the plane and spatial relationships between them. Points are labelled by proposition letters and spatial relations are induced by the four coneshaped cardinal directions. Cone Logic can
Results 11  20
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203