Fixed order perturbation theory is not able to describe the transversal momentum spectrum of a electro-weak gauge boson. It is needed to resum whole classes of enhanced logarithmic terms. Depending on the phase space region different classes of logarithmic terms can be important. There are different approaches to sum such logarithmic terms including evolution equations of parton density functio...

In this paper, we prove that the composition of a transversal biwave map and a transversally totally geodesic map is a transversal biwave map. We show that there are biwave maps which are not transversal biwave maps, and there are transversal biwave maps which are not biwave maps either. We prove that if f is a transversal biwave map satisfying certain condition, then f is a transversal wave ma...

We present two algorithms for the problem of nding a minimum transversal in a hypergraph of rank 3, also known as the 3-Hitting Set problem. This problem is a natural extension of the vertex cover problem for ordinary graphs. The rst algorithm runs in time O(1:6538 n) for a hypergraph with n vertices, and needs polynomial space. The second algorithm uses exponential space and runs in time O(1:6...

We present new kernelization results for the s-cycle transversal problem for s > 3. In particular, we show a 6k kernel for 4-cycle transversal and a O(k) kernel for s-cycle transversal when s > 4. We prove the NP-completeness of s-cycle transversal on planar graphs and obtain a 74k kernel for 4-cycle transversal on planar graphs. We also give several kernelization results for a related problem ...

In this paper, we provide a geometric construction of a transversal homoclinic orbit for a nonlinear model neuron with time delays. The existence of chaos for time-delay systems in a highdimensional space is theoretically confirmed with several conditions. These units may be used as basic elements for networks with higher-order information processing capabilities.

We introduce random homoclinic points and orbits for random dynamical systems with hyperbolic stationary orbits and investigate their meaning for irregular behaviour in form of a stochastic version of the Birkhoo-Smale Theorem. In particular we show that transversal random homoclinic points cause a conjugacy of the random dynamical system in a part of the phase space to a random shift system.

We prove local “Lp-improving” estimates for a class of multilinear Radon-like transforms satisfying a strong transversality hypothesis. As a consequence, we obtain sharp multilinear convolution estimates for measures supported on fully transversal submanifolds of euclidean space of arbitrary dimension. We also prove global estimates for the same class of Radon-like transforms under a natural ho...