Search results for "Discrete mathematics"
showing 8 items of 1728 documents
On some classes of supersoluble groups
2007
[EN] Finite groups G for which for every subgroup H and for all primes q dividing the index |G:H| there exists a subgroup K of G such that H is contained in K and |K:H|=q are called Y-groups. Groups in which subnormal subgroups permute with all Sylow subgroups are called PST-groups. In this paper a local version of the Y-property leading to a local characterisation of Y-groups, from which the classical characterisation emerges, is introduced. The relationship between PST-groups and Y-groups is also analysed.
Variational parabolic capacity
2015
We establish a variational parabolic capacity in a context of degenerate parabolic equations of $p$-Laplace type, and show that this capacity is equivalent to the nonlinear parabolic capacity. As an application, we estimate the capacities of several explicit sets.
A Complete, Exact and Efficient Implementation for Computing the Edge-Adjacency Graph of an Arrangement of Quadrics
2011
International audience; We present a complete, exact and efficient implementation to compute the edge-adjacency graph of an arrangement of quadrics, i.e. surfaces of algebraic degree 2. This is a major step towards the computation of the full 3D arrangement. We enhanced an implementation for an exact parameterization of the intersection curves of two quadrics, such that we can compute the exact parameter value for intersection points and from that the edge-adjacency graph of the arrangement. Our implementation is complete in the sense that it can handle all kinds of inputs including all degenerate ones, i.e. singularities or tangential intersection points. It is exact in that it always comp…
Modal Consequence Relations Extending S4.3: An Application of Projective Unification
2016
We characterize all finitary consequence relations over $\mathbf{S4.3}$ , both syntactically, by exhibiting so-called (admissible) passive rules that extend the given logic, and semantically, by providing suitable strongly adequate classes of algebras. This is achieved by applying an earlier result stating that a modal logic $L$ extending $\mathbf{S4}$ has projective unification if and only if $L$ contains $\mathbf{S4.3}$ . In particular, we show that these consequence relations enjoy the strong finite model property, and are finitely based. In this way, we extend the known results by Bull and Fine, from logics, to consequence relations. We also show that the lattice of consequence relation…
Computing Subdivision Surface Intersection
2003
Computer surface intersections is fundamental problem in geometric modeling. Any Boolean operation can be seen as an intersection calculation followed by a selection of parts necessary for building the surface of the resulting object. This paper deals with the computing of intersection curveson subdivision surfaces (surfaces generated by the Loop scheme). We present three variants of our algorithm. The first variant calculates this intersection after classification of the object faces into intersecting and non-intersecting pairs of faces. the second variant is based on 1-neighborhood of the intersecting faces. The third variant uses the concept of bipartite graph.
Mappings of Lp-integrable distortion: regularity of the inverse
2016
Let be an open set in ℝn and suppose that is a Sobolev homeomorphism. We study the regularity of f–1 under the Lp-integrability assumption on the distortion function Kf. First, if is the unit ball and p > n – 1, then the optimal local modulus of continuity of f–1 is attained by a radially symmetric mapping. We show that this is not the case when p ⩽ n – 1 and n ⩾ 3, and answer a question raised by S. Hencl and P. Koskela. Second, we obtain the optimal integrability results for ∣Df–1∣ in terms of the Lp-integrability assumptions of Kf.
The Joint Distribution Criterion and the Distance Tests for Selective Probabilistic Causality
2010
A general definition and a criterion (a necessary and sufficient condition) are formulated for an arbitrary set of external factors to selectively influence a corresponding set of random entities (generalized random variables, with values in arbitrary observation spaces), jointly distributed at every treatment (a set of factor values containing precisely one value of each factor). The random entities are selectively influenced by the corresponding factors if and only if the following condition, called the joint distribution criterion, is satisfied : there is a jointly distributed set of random entities, one entity for every value of every factor, such that every subset of this set that corr…
A posteriori error estimates for time-dependent reaction-diffusion problems based on the Payne-Weinberger inequality
2015
We consider evolutionary reaction-diffusion problem with mixed Dirichlet--Robin boundary conditions. For this class of problems, we derive two-sided estimates of the distance between any function in the admissible energy space and exact solution of the problem. The estimates (majorants and minorants) are explicitly computable and do not contain unknown functions or constants. Moreover, it is proved that the estimates are equivalent to the energy norm of the deviation from the exact solution.