We characterize convex cocompact subgroups of mapping class groups that arise as subgroups of specially embedded right-angled Artin groups. That is, if the right-angled Artin group G < Mod(S) satisfies certain conditions that imply G is quasi-isometrically embedded in Mod(S), then a purely pseudo-Anosov subgroup H < G is convex cocompact in Mod(S) if and only if it is combinatorially quasiconve...

By Schm udgen's Theorem, polynomials f 2 RX1;::: ; Xn] strictly positive on a bounded basic semialgebraic subset of R n , admit a certain representation involving sums of squares i from RX1 We show the existence of eeective bounds on the degrees of the i by proving rst a suitable version of Schm udgen's Theorem over non-archimedean real closed elds, and then applying the Compactness and Complet...

We give the sharp lower bound of volume product three dimensional convex bodies which are invariant under a discrete subgroup O(3) in several cases. also characterize with minimal each case. In particular, this provides new partial result non-symmetric version Mahler’s conjecture

Let C be a bounded, closed, convex subset of a uniformly convex Banach space X. We investigate the convergence of the generalized Krasnosel’skiiMann and Ishikawa iteration processes to common fixed points of pointwise Lipschitzian semigroups of nonlinear mappings Tt : C → C. Each of Tt is assumed to be pointwise Lipschitzian, that is, there exists a family of functions αt : C → [0,∞) such that ...

and Applied Analysis 3 where J is the normalized duality mapping from E into 2E ∗ . If E = H, a Hilbert space, then (13) reduces to φ(x, y) = ‖x − y‖ 2, for x, y ∈ H. Let E be a reflexive, strictly convex, and smooth Banach space, and letC be a nonempty closed and convex subset ofE. The generalized projectionmapping, introduced byAlber [29], is a mapping Π C : E → C that assigns an arbitrary po...

In this note, we prove that a random extension of either the free group FN of rank N ě 3 or of the fundamental group of a closed, orientable surface Sg of genus g ě 2 is a hyperbolic group. Here, a random extension is one corresponding to a subgroup of either OutpFN q or ModpSgq generated by k independent random walks. Our main theorem is that a k–generated random subgroup of ModpSgq or OutpFN ...

λ1 + . . .+ λm = 1, then we say that y is an affine combination of y1, . . . ,ym ∈Y . If, in addition, λi ≥ 0 for 1 ≤ i ≤ m, then we say that y is a convex combination of y1, . . . ,ym ∈ Y . A convex set is any subset of Rn that is closed under the operation of taking convex combinations. In fact, it can be shown that a subset X is convex if and only if for all x0,x1 ∈ X and 0 ≤ λ ≤ 1, the poin...

By extracting combinatorial structures in well-solved nonlinear combinatorial optimization problems, Murota (1996,1998) introduced the concepts of M-convexity and L-convexity to functions defined over the integer lattice. Recently, Murota–Shioura (2000, 2001) extended these concepts to polyhedral convex functions and quadratic functions defined over the real space. In this paper, we consider a ...

Nakamura [N] introduced the G-Hilbert scheme G-Hilb C3 for a finite subgroup G ⊂ SL(3, C), and conjectured that it is a crepant resolution of the quotient C3/G. He proved this for a diagonal Abelian group A by introducing an explicit algorithm that calculates A-HilbC3. This note calculates A-Hilb C3 much more simply, in terms of fun with continued fractions plus regular tesselations by equilate...

We prove that a Banach space X has normal structure provided it contains a finite codimensional subspace Y such that all spreading models for Y have normal structure. We show that a Banach space X is strictly convex if the set of fixed points of any nonexpansive map defined in any convex subset C C X is convex and give a sufficient condition for uniform convexity of a space in terms of nonexpan...