Transseries in the sense of Écalle are constructed using a topological approach. A general contractive mapping principle is formulated and proved, showing the closure of transseries under a wide class of operations. In the second part we give an overview of results and methods reconstruction of actual functions and solutions of equations from transseries by generalized Borel summation with in o...

Let T (S) be the Teichmüller space of an oriented surface S of finite type. We discuss the action of subgroups of the mapping class group of S on the CAT(0)-boundary of the completion of T (S) with respect to the Weil-Petersson metric. We show that the set of invariant Borel probability measures for the Weil-Petersson flow on moduli space which are supported on a closed orbit is dense in the sp...

elastic solutions applicable to single underground openings usually suffer from geometry related simplification. most tunnel shapes possess two axes of symmetry while a wide range of geometries used in tunneling practice involve only one symmetry axis. d-shape or horse-shoe shape tunnels and others with arched roof and floor are examples of the later category (one symmetry axis). in the present...

1. Optimal transportation set up Let D, D∗ be two domains on Sn−1 or bounded domains in a manifold (D might be contained in one manifold and D∗ in another) with |∂D| = 0. LetN be a multi-valued mapping from D onto D∗ such thatN(x) is single-valued a.e. on D. For F ⊂ D∗, we set T (F) = N−1(F) = {x ∈ D : N(x) ∩ F , ∅}. We sayN is measurable if T (F) is Lebesgue measurable for any Borel set F ⊂ D∗...

We discuss the permanence of strong liftings under the formation of projective limits. The results are based on an appropriate consistency condition of the liftings with the projective system called “self-consistency”, which is fulfilled in many situations. In addition, we study the relationship of self-consistency and completion regularity as well as projective limits of lifting topologies. In...

For upper semicontinuous finite-dimensional set-valued mappings with either convex closed or aspheric closed values we prove the existence of special continuous e -approximations that point-wise converge to a Borel measurable selector of the set-valued mapping as e tends to zero. For convex-valued case the convergence holds on the entire domain while for aspheric-valued case — on a certain coun...

Vulvar cancer is a rare gynecological malignancy with mainly lymphatic spread. Sentinel node mapping plays an important role in the management of this gynecological malignancy. In the current study, we reported our experience in sentinel node mapping of vulvar cancer and review the literature accordingly. Since the introduction of sentinel node mapping to the surgical oncology community of our ...