In this paper, we introduce a class of totally quasi-φ-asymptotically nonexpansive nonself multi-valued mapping to modify the Halpern-Mann-type iteration algorithm for a totally quasi-φ-asymptotically nonexpansive nonself multi-valued mapping, which has the strong convergence under a limit condition only in the framework of Banach spaces. Our results are applied to study the approximation probl...

In this note we study the differentiability with respect to time-parameter of semigroups consisting Lipschitzian or smooth self-mappings a domain in Banach space.

We refine the construction of quasi-homomorphisms on mapping class groups. It is useful to know that there are unbounded quasihomomorphisms which are bounded when restricted to particular subgroups since then one deduces that the mapping class group is not boundedly generated by these subgroups. In this note we enlarge the class of such subgroups. The generalization is motivated by consideratio...

We describe sufficient conditions which guarantee that a finite set of mapping classes generate a right-angled Artin group quasi-isometrically embedded in the mapping class group. Moreover, under these conditions, the orbit map to Teichmüller space is a quasiisometric embedding for both of the standard metrics. As a consequence, we produce infinitely many genus h surfaces (for any h at least 2)...

Recent results on the theory of the Hamilton{Jacobi equation and the regularity of their solutions, in spite of the non regularity of the data, are reviewed, and discussed with attention to the cancellation mechanisms that make regularity possible. The Hamilton Jacobi equation for an invariant torus in a ` dimensional hamiltonian system close to an integrable system takes one of the forms: (! 0...

Beginning with a tracking code for the LHC, we construct the canonical generator of the full-turn map in polar coordinates. For very fast mapping we adopt a model in which the momentum is modulated sinusoidally with a period of 130 turns (very close to the synchrotron period). We achieve symplectic mapping of 10 turns in 3.6 hours on a workstation. Quasi-invariant tori are constructed on the Po...

The plots in Figure 1 provide a quantitative evaluation of the quality of the smoothed models, measured in terms of the percentage of the model’s area that is flipped when mapped to the sphere, the integrated quasi-conformal factor [Kharevych et al. 2006], and the Dirichlet energy of the mapping. For example, for the Armadillo, the mapping is a bijection after seven iterations and has an averag...

The simulation of light transport often involves specular and transmissive surfaces, which are modeled by functions that are not square integrable. However, in many practical cases unbiased Monte Carlo methods are not able to handle such functions efficiently and consistent Monte Carlo methods are applied. Based on quasi-Monte Carlo integration, a deterministic alternative to the stochastic app...

We propose a program of studying the coarse geometry of combinatorial moduli spaces of surfaces by classifying the quasi-isometric embeddings between them. We provide the first non-trivial examples of quasi-isometric embeddings between curve complexes. These are induced either via orbifold coverings or by puncturing a closed surface. As a corollary, we give new quasiisometric embeddings between...