In the case of two-dimensional cyclic quotient singularities, we classify all oneparameter toric deformations in terms of certain Minkowski decompositions introduced by Altmann [1]. In particular, we describe to which components each such deformation maps, show how to induce each deformation from a versal family, give explicit equations for each deformation, describe the singularities in the ge...

We investigate properties of a multivariate function E(m1,m2, . . . ,mr), called orbicyclic, that arises in enumerative combinatorics in counting non-isomorphic maps on orientable surfaces. E(m1,m2, . . . ,mr) proves to be multiplicative, and a simple formula for its calculation is provided. It is shown that the necessary and sufficient conditions for this function to vanish are equivalent to f...

The bracket map was originally considered in [7] for locally compact abelian groups. In this work we extend the study of bracket maps to the noncommutative setting, providing characterizations of bases and frames for cyclic subspaces of the Heisenberg group. We also indicate how to generalize these results to a class of non-abelian nilpotent Lie groups whose irreducible representations are squa...

We give a construction of the moduli space of stable maps to the classifying stack Bμr of a cyclic group by a sequence of r-th root constructions on M0,n. We prove a closed formula for the total Chern class of μreigenspaces of the Hodge bundle, and thus of the obstruction bundle of the genus zero Gromov-Witten theory of stacks of the form [C/μr ]. We deduce linear recursions for all genus-zero ...

This paper studies decentralized output-feedback control of large-scale nonlinear systems in the presence of sensor noise. The measurement errors are dealt with by set-valued maps in the recursive control design of the subsystems. With appropriately designed decentralized controllers, the subsystems are rendered input-to-state stable (ISS) with respect to the outputs of the other subsystems and...

For an arbitrary symmetric monoidal∞-category V, we define the factorization homology of V-enriched∞-categories over (possibly stratified) 1-manifolds and study its basic properties. In the case that V is cartesian symmetric monoidal, by considering the circle and its self-covering maps we obtain a notion of unstable topological cyclic homology, which we endow with an unstable cyclotomic trace ...

Abstract Every non-convex pair $(C, D)$ ( C , D ) may not have proximal normal structure even in a Hilbert space. In this article, we use cyclic relatively nonexpansive maps with respect to orbits show the presence of best proximity points $C...

It is known that there are normal plane maps M5 with minimum degree 5 such that the minimum degree-sum w(S5) of 5-stars at 5-vertices is arbitrarily large. In 1940, Lebesgue showed that if an M5 has no 4-stars of cyclic type (5, 6, 6, 5) centered at 5-vertices, then w(S5) ≤ 68. We improve this bound of 68 to 55 and give a construction of a (5, 6, 6, 5)-free M5 with w(S5) = 48.

We give a construction of the moduli space of stable maps to the classifying stack Bμr of a cyclic group by a sequence of r-th root constructions on M0,n. We prove a closed formula for the total Chern class of μreigenspaces of the Hodge bundle, and thus of the obstruction bundle of the genus zero Gromov-Witten theory of stacks of the form [C/μr ]. We deduce linear recursions for all genus-zero ...