We establish some inequalities about the Khovanov-Rozansky cohomologies of braids. These give new upper bounds of the self-linking numbers of transversal links in standard contact S which is sharper than the well known bound given by the HOMFLY polynomial. We also introduce a sequence of transversal link invariants, and discuss some of their properties.

We show that if a line ` is an isolated line transversal to a finite familyF of (possibly intersecting) balls inR and no two balls are externally tangent on ` then there is a subset G ⊆ F of size at most 12 such that ` is an isolated line transversal to G. We generalize this result to families of semi-algebraic ovaloids.

We present a discontinuous Galerkin method for the plate problem. The method employs a discontinuous approximation space allowing, non matching grids and diierent types of approximation spaces. Continuity is enforced weakly through the vari-ational form. Discrete approximations of the normal and twisting moments and the transversal force, which satisfy the equilibrium condition on an element le...

A k-plex in a latin square of order n is a selection of kn entries that includes k representatives from each row and column and k occurrences of each symbol. A 1-plex is also known as a transversal. It is well known that if n is even then Bn, the addition table for the integers modulo n, possesses no transversals. We show that there are a great many latin squares that are similar to Bn and have...

We show that if a line ` is an isolated line transversal to a finite familyF of (possibly intersecting) balls in R and no two balls are externally tangent on ` then there is a subfamily G ⊆ F of size at most 12 such that ` is an isolated line transversal to G. We generalize this result to families of semi-algebraic ovaloids.

We present a necessary and sufficient condition for a family of sets to possess a transversal. Its form follows that of P. Hall's theorem: a family has a transversal if and only if it does not contain one of a set of 'forbidden' substructures.

Melnikov's method for nding necessary conditions for homoclinic chaos is extended to a class of stochastically forced multi-degree of freedom nonlinear systems. The stochastic forcing induces a stochastic Melnikov process, and simple zeros of this process imply transversal intersection of appropriate stable and unstable manifolds. This process can also provide information on probabilities of es...

We carry out extensive computer simulations to study the Lyapunov instability of a two-dimensional hard-disk system in a rectangular box with periodic boundary conditions. The system is large enough to allow the formation of Lyapunov modes parallel to the x-axis of the box. The Oseledec splitting into covariant subspaces of the tangent space is considered by computing the full set of covariant ...

This paper proposes a method for abstracting control systems by timed game automata, and is aimed at obtaining automatic controller synthesis. The proposed abstraction is based on partitioning the state space of a control system using positive and negative invariant sets, generated by Lyapunov functions. This partitioning ensures that the vector field of the control system is transversal to the...

We outline an algorithm for generating nets, a “net” being a geometric graph embedded in a space on which some group acts transitively. We prove that any connected net in such a space can be generated by this process, which can also be regarded as a covering of the net by copies of a connected “transversal” subnet. This paper outlines some of the underlying theory supporting a crystal predictio...