Search results for "hyperbolic"
showing 10 items of 156 documents
Painlevé analysis and exact solutions for the coupled Burgers system
2006
We perform the Painleve test to a system of two coupled Burgers-type equations which fails to satisfy the Painleve test. In order to obtain a class of solutions, we use a slightly modified version of the test. These solutions are expressed in terms of the Airy functions. We also give the travelling wave solutions, expressed in terms of the trigonometric and hyperbolic functions.
Generalized John disks
2014
Abstract We establish the basic properties of the class of generalized simply connected John domains.
Blocking sets and partial spreads in finite projective spaces
1980
A t-blocking set in the finite projective space PG(d, q) with d≥t+1 is a set $$\mathfrak{B}$$ of points such that any (d−t)-dimensional subspace is incident with a point of $$\mathfrak{B}$$ and no t-dimensional subspace is contained in $$\mathfrak{B}$$ . It is shown that | $$\mathfrak{B}$$ |≥q t +...+1+q t−1√q and the examples of minimal cardinality are characterized. Using this result it is possible to prove upper and lower bounds for the cardinality of partial t-spreads in PG(d, q). Finally, examples of blocking sets and maximal partial spreads are given.
A Group-theoretical Finiteness Theorem
2008
We start with the universal covering space $${\*M^n}$$ of a closed n-manifold and with a tree of fundamental domains which zips it $${T\longrightarrow\*M^n}$$ . Our result is that, between T and $${\* M^n}$$ , is an intermediary object, $${T\stackrel{p} {\longrightarrow} G \stackrel{F}{\longrightarrow} \*M^n}$$ , obtained by zipping, such that each fiber of p is finite and $${T\stackrel{p}{\longrightarrow}G\stackrel{F}{\longrightarrow} \*M^n}$$ admits a section.
k-Weakly almost convex groups and ? 1 ? $$\tilde M^3 $$
1993
We extend Cannon's notion ofk-almost convex groups which requires that for two pointsx, y on then-sphere in the Cayley graph which can be joined by a pathl1 of length ≤k, there is a second pathl2 in then-ball, joiningx andy, of bounded length ≤N(k). Ourk-weakly almost convexity relaxes this condition by requiring only thatl1 ∝l2 bounds a disk of area ≤C1(k)n1 - e(k) +C2(k). IfM3 is a closed 3-manifold with 3-weakly almost convex fundamental group, then π1∞\(\tilde M^3 = 0\).
The geometry of surfaces in 4-space from a contact viewpoint
1995
We study the geometry of the surfaces embedded in ℝ4 through their generic contacts with hyperplanes. The inflection points on them are shown to be the umbilic points of their families of height functions. As a consequence we prove that any generic convexly embedded 2-sphere in ℝ4 has inflection points.
A Polynomial Approach to the Piecewise Hyperbolic Method
2003
In this paper, a local (third-order accurate) shock capturing method for hyperbolic conservation laws is presented. The method has been made with the same idea as the PHM method, but with a simpler reconstruction. A comparison with the classic high order methods is discussed.
Approximations of Parabolic Equations at the Vicinity of Hyperbolic Equilibrium Point
2014
This article is devoted to the numerical analysis of the abstract semilinear parabolic problem u′(t) = Au(t) + f(u(t)), u(0) = u 0, in a Banach space E. We are developing a general approach to establish a discrete dichotomy in a very general setting and prove shadowing theorems that compare solutions of the continuous problem with those of discrete approximations in space and time. In [3] the discretization in space was constructed under the assumption of compactness of the resolvent. It is a well-known fact (see [10, 11]) that the phase space in the neighborhood of the hyperbolic equilibrium can be split in a such way that the original initial value problem is reduced to initial value prob…
Convexly generic curves in R 3
1988
We study curves immersed in R 3, with special interest in the description of their convex hull frontier structure from a global viewpoint. Genericity conditions are set for these curves by looking at the singularities of height functions on them. We define panel structures for convexly generic curves and work out numerical relations involving the number of tritangent support planes. As a consequence, a generic version of the 4-vertex theorem for convex curves in R 3 is obtained.
Non-accumulation of critical points of the Poincaré time on hyperbolic polycycles
2007
We call Poincare time the time associated to the Poincar6 (or first return) map of a vector field. In this paper we prove the non-accumulation of isolated critical points of the Poincare time T on hyperbolic polycycles of polynomial vector fields. The result is obtained by proving that the Poincare time of a hyperbolic polycycle either has an unbounded principal part or is an almost regular function. The result relies heavily on the proof of Il'yashenko's theorem on non-accumulation of limit cycles on hyperbolic polycycles.