We generalize the ham sandwich theorem to d+1 measures in R as follows. Let μ1, μ2, . . . , μd+1 be absolutely continuous finite Borel measures on R. Let ωi = μi(R ) for i ∈ [d + 1], ω = min{ωi; i ∈ [d + 1]} and assume that ∑d+1 j=1 ωj = 1. Assume that ωi ≤ 1/d for every i ∈ [d + 1]. Then there exists a hyperplane h such that each open halfspace H defined by h satisfies μi(H) ≤ ( ∑d+1 j=1 μj(H)...

We have measured xy coupling of the interaction point(I.P.) at KEKB. When a normal mode is excited by a shaker with tune frequency, the horizontal or vertical betatron oscillations can be measured by a turn-by-turn BPM in the laboratory coordinate system. A harmonic analysis has been performed to extract the xy coupling parameters at I.P. from the detected betatron oscillations. 1 IDEA AND FORM...

The contribution of subleading jet functions to inclusive decay distributions of B mesons are derived from a systematic two-step matching of QCD current correlators onto soft collinear and heavy quark effective theory. Focusing on the tree level matching of QCD onto soft collinear effective theory, the subleading jet functions are defined to all orders in αs(μi) (with μ 2 i ∼ mbΛQCD) and are ca...

In this paper, we derive some properties for Gp,n,l,δ(z) and Fp,n,l,δ(z) considering the classes MT (p, βi, μi) , KD (p, βi, μi) and Np (γ). Two new subclasses KDFp,n,l (β, μ, δ1, δ2, ..., δn) and KDGp,n,l (β, μ, δ1, δ2, ..., δn) are defined. Necessary and sufficient conditions for a family of functions fi and gi, respectively, to be in the KDFp,n,l (β, μ, δ1, δ2, ..., δn) and KDGp,n,l (β, μ, δ...

A. Proof of Theorem 1 Proof. We solve the model here allowing for heteroskedastic dividends σ2 i . Theorem 1 can then be proved as the special case σ 2 = σ 2 i . We assume that assets are ranked in ascending order of β/σ2. We first posit an equilibrium structure. We then check ex-post that it is indeed an equilibrium and that it is a unique equilibrium. Let ī ∈ [2, N ] and let μi be the share h...

Let Sn = X1 + · · · +Xn, n ≥ 1, where (Xi)i≥1 are random variables. Let μ be a constant and I be the identity function on [0, 1]. We study the almost sure convergence to μI of the two polygonal line partial sums processes ζn and ζ ad n with respective vertices (k/n, Sk) and (τk, Sk), 0 ≤ k ≤ n, where τk = Tk/Tn and Tk = |X1|+ · · ·+ |Xk|. These convergences are considered in the space C[0, 1] o...

Abstract. One of the most interesting dynamical systems used in numerical analysis is the QR algorithm. An added maneuver to improve the convergence behavior is the QR iteration with shift which is of fundamental importance in eigenvalue computation. This paper is a theoretical study of the set of all isospectral matrices “reachable” by the dynamics of QR algorithm with shift. A matrix B is sai...

Let X1, . . . , Xn be a collection of iid discrete random variables, and Y1, . . . , Ym a set of noisy observations of such variables. Assume each observation Ya to be a random function of some a random subset of the Xi’s, and consider the conditional distribution of Xi given the observations, namely μi(xi) ≡ P{Xi = xi|Y } (a posteriori probability). We establish a general decoupling principle ...