Let G be a connected reductive linear algebraic group over C with an involution θ. Denote by K the subgroup of fixed points. In certain cases, the K-orbits in the flag variety G/B are indexed by the twisted identities ι(θ) = {θ(w−1)w | w ∈ W} in the Weyl group W . Under this assumption, we establish a criterion for rational smoothness of orbit closures which generalises classical results of Car...

We show that two open books in a given closed, oriented three-manifold admit isotopic stabilizations, where the stabilization is made by successive plumbings with Hopf bands, if and only if their associated plane fields are homologous. Since this condition is automatically fulfilled in an integral homology sphere, the theorem implies a conjecture of J. Harer, namely, that any fibered link in th...

M-estimators and their consistency This handout is adapted from Section 3.3 of 18.466 lecture notes on mathematical statistics, available on OCW. A sequence of estimators T n , one for each sample size n, possibly only defined for n large enough, is called consistent if for X 1 , X converges in probability as n → ∞ to a function g(θ) being estimated. We will consider consistency of estimators m...

some considerable damage to steel structures during the hyogo-ken nanbu earthquake occurred. among them, many exposed-type column bases failed in several consistent patterns, such as brittle base plate fracture, excessive bolt elongation, unexpected early bolt failure, and inferior construction work, etc. the lessons from these phenomena led to the need for improved understanding of column base...

We present improved upper bounds on the spanning ratio of a large family of θ-graphs. A θ-graph partitions the plane around each vertex into m disjoint cones, each having aperture θ = 2π/m. We show that for any integer k ≥ 1, θ-graphs with 4k + 4 cones have spanning ratio at most 1 + 2 sin(θ/2)/(cos(θ/2) − sin(θ/2)). We also show that θ-graphs with 4k + 3 and 4k + 5 cones have spanning ratio at...

Two neutrinos of Majorana masses m1,2 with mixing angle θ are unstable against radiative corrections in the limit m1 = m2, but are stable for m1 = −m2 (i.e. opposite CP eigenstates) with θ = 45◦ which corresponds to an additional symmetry. Pick two neutrinos, say νe and νμ. Assume their mass eigenstates to be ν1 = νe cos θ − νμ sin θ, ν2 = νe sin θ + νμ cos θ, (1) with eigenvalues m1 and m2 res...

In this paper, the concepts of derived sets and derived operators are generalized to $(L, M)$-fuzzy topological spaces and their characterizations are given.What is more, it is shown that the category of stratified $(L, M)$-fuzzy topological spaces,the category of stratified $(L, M)$-fuzzy closure spaces and the category of stratified $(L, M)$-fuzzy quasi-neighborhood spaces are all isomorphic ...

The vector-valued function m(θ) of a p-vector θ has components m1(θ),m2(θ), . . . ,mp(θ). For each i, exp(mi(−θ)) is the (multivariate) Laplace transform of a discrete measure concentrated on [0,∞)p with only a finite number of atoms. The main objective is to give conditions for the functional iterates m(n) of m to grow like ρn for a suitable ρ > 1. The initial stimulus was provided by results ...

through the origin containing vθ and projθ : R 2 → Lθ the orthogonal projection. From now on, we’ll restrict θ to the interval [−π/2, π/2], because Lθ = Lθ+π. In 1954, J. M. Marstrand [10] proved the following result on the fractal dimension of plane sets. Theorem 1.1. If K ⊂ R is a Borel set such that HD(K) > 1, then m(projθ(K)) > 0 for m-almost every θ ∈ R. The proof is based on a qualitative...

Let μ be a rational distribution over a finite alphabet, and ( t χ ) be a n-periodic sequences which first n elements are drawn i.i.d. according to μ. We consider automata of bounded size that input 1 t χ − and output t y at stage t. We prove the existence of a constant C such that, whenever ln m m Cn ≥ , with probability close to 1 there exists an automaton of size m such that the empirical fr...