A map is at the same time a group. To represent a map (that is, a graph drawn on the sphere or on another surface) we usually use a pair of permutations on the set of the \ends" of edges. These permutations generate a group which we call a cartographic group. The main motivation for the study of the cartographic group is the so-called theory of \dessins d'enfants" of Grothendieck, which relates...

In this paper we find all solvable groups that act effectively on the circle as realanalytic diffeomorphisms, and we find all of their actions. Our starting point is the procedure of ramified lifting of group actions with a global fixed point, which we develop in Section 1. To summarize the discussion there, we say that a real analytic map π : S → S is a ramified covering map over p ∈ S if the ...

1 D e f i n i t i o n s Given a graph G, let V(G) be the set of vertices of G, E(G) the set of edges of G. For A, B subsets of V(G), let E(A) be the set of edges of G with both ends in A, and let E(A, B) be the set of edges of G with one end in A, the other in B. A map M on a surface S is a connected graph G toge~..her with a 2-cell embedding of G in S. Two maps are equivalent if there is a hom...

Let A be a Banach algebra, and let E be a Banach A-bimodule. A linear map S :AMNE is intertwining if the bilinear map (a, b)PN (δ"S ) (a, b)B a[Sb®S(ab)­Sa[b, A¬AMNE, is continuous, and a linear map D :AMNE is a deriŠation if δ"D ̄ 0, so that a derivation is an intertwining map. Derivations from A to E are not necessarily continuous. The purpose of the present paper is to prove that the continui...

(1.1) Some of the main results described in [Report] are the following (in rough terms; notations and precise references will be given below): (1) A map (f>:{M,g)-+(N,h) between Riemannian manifolds which is continuous and of class L\ is harmonic if and only if it is a critical point of the energy functional. (2) Let (M, g) and (N, h) be compact, and <̂ 0: (M, g) -> (N, h) a map. Then ^0 can be ...

BACKGROUND AND AIMS Primula sieboldii is a perennial clonal herb that is distributed around the Sea of Japan and is endangered in Japan. Its breeding system is characterized by heteromorphic self-incompatibility, and the morph ratio within a population is very important for reproductive success. The aims of this study were to construct a linkage map, map the S locus as a qualitative trait and q...

Let S, T be complete lattices. One can check that there exists a connection between S and T which is Galois. Next we state the proposition (1) Let S, T , S, T ′ be non empty relational structures. Suppose that (i) the relational structure of S = the relational structure of S, and (ii) the relational structure of T = the relational structure of T . Let c be a connection between S and T and c be ...

A set of precomputed functional maps are used for SpecTN pretraining. We mentioned in the main paper that the functional map C from S to the average shape S̄ could be induced from the spatial correspondences between S and S̄, by the primal-dual relationship. Once we have the bases of S and S̄, as well as the rough spatial correspondences between them from the volumetric occupancy, the functional m...

In this paper, it was constructed quantum codes from cyclic codes over finite ring S = F2 + uF2 + vF2, u2 = u, v2 = v, uv = vu = 0 for arbitrary length n. It was given a new Gray map Ψ which is both an isometry and weight preserving map. It was shown that C is self orthogonal codes over S, so is Ψ(C). It was given a necessary and sufficient condition for cyclic codes over S that contains its du...