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...

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 ...

The purpose of this paper is to derive some subordination and superordination results for functions of the form f(z) = zp + ∞ ∑ k=p+1 akz k which are p−valent in the open unit disk U = {z ∈ C : |z| < 1} by using certain differential operator Aλ,p(α, β, μ)f(z) and integral operator F m p (ρ, θ)f(z). Some special cases are also considered.

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...

and Applied Analysis 3 Let T be a positive number. In the following we take ΩT 0, T × 0, 1 . Let vl and vr be in C0 0, T , R and m0 ∈ L∞ 0, 1 , ρ0 ∈ W1,∞ 0, 1 . We set Γl {t ∈ 0, T | vl t > 0}, Γr {t ∈ 0, T | vr t < 0}. 1.3 In the following, we will always suppose that the sets Pl {t ∈ 0, T | vl t 0}, Pr {t ∈ 0, T | vr t 0} 1.4 have a finite number of connected components. Finally, let ml, ρl ∈...

This supplement contains the proofs of Theorem 2, Propositions 2 and 3, Lemma 1 and Eq.(14). 7 Proof of Theorem 2 Rather than prove Theorem 2 directly it is convenient to first prove an analogue of the Theorem in the context of multivariate Normal random vectors. This is done in section 7.1. The proof of Theorem 2 is then given in section 7.2 7.1 Confidence Bound For Multivariate Normal Vectors...

We build a variational theory of geodesics of the Tanaka-Webster connection ∇ on a strictly pseudoconvex CR manifold M . Given a contact form θ on M such that (M, θ) has nonpositive pseudohermitian sectional curvature (kθ(σ) ≤ 0) we show that (M, θ) has no horizontally conjugate points. Moreover, if (M, θ) is a Sasakian manifold such that kθ(σ) ≥ k0 > 0 then we show that the distance between an...