In this paper, we consider the inverse scattering problem and, in particular, of reconstructing spectral density associated with Yukawian potentials from sequence partial-waves fℓ Fourier–Legendre expansion amplitude. We prove that if satisfy a suitable Hausdorff-type condition, then they can be uniquely interpolated by function f˜(λ)∈C, analytic half-plane. Assuming also Martin condition to ho...

dr ≤ K2. C3 φn,θ(u,β) is differentiable with respect to θ and β, and for |φn,θ(u,β)|, |dφn,θ(u,β)/dβ| and |dφn,θ(u,β)/dθ|, the supremum over u ∈ R ,β ∈ b(β,K3), θ ∈ b(θ ,K3) is bounded for some K3 > 0, where b(x, r) denotes the ball centred at x with radius r > 0. C4 |Wn| (θ̃n − θ ) is bounded in probability. C5 l = lim infn ln > 0, where for each n, ln denotes the minimal eigenvalue of S̄n,θ∗(β ...

In this paper we consider the following model. We consider n nonnegative random variables T1, T2, . . . , Tn such that they are conditionally independent given some random vector Θ, where Θ takes values on some set χ ⊆ R. If Fi(·|θ) denotes the marginal distribution of Ti(θ) ≡ (Ti|Θ = θ), and G(θ) denotes the joint distribution function of Θ, then the joint distribution of (T1, T2, . . . , Tn) ...

The number of vertices missed by a maximum matching in a graph G is the multiplicity of zero as a root of the matchings polynomial μ(G,x) of G, and hence many results in matching theory can be expressed in terms of this multiplicity. Thus, if mult(θ,G) denotes the multiplicity of θ as a zero of μ(G,x), then Gallai’s lemma is equivalent to the assertion that if mult(θ,G\u) < mult(θ,G) for each v...

1. Hopefully, every group accomplished at least some work this week on project 2. 2. (a) You can do this problem in two ways. The first way is attaching frames to each link and determining the Denavit–Hartenberg parameters, as illustrated in Figure 1. Referring to the figure, the link parameters are: i α i−1 a i−1 d i θ i 1 0 0 0 θ 1 2 0 l 1 0 θ 2 3 0 l 2 0 θ 3 Using equation 3.6 or your Mathem...

Let f and g be two continuous functions on the unit sphere Sn−1 in Rn , n ≥ 3, and let their restrictions to any one-dimensional great circle E coincide after some rotation φE of this circle: f (φE (θ)) = g(θ)∀θ ∈ E . We prove that in this case f (θ) = g(θ) or f (θ) = g(−θ) for all θ ∈ Sn−1. This answers the question posed by Richard Gardner and Vladimir Golubyatnikov. Published by Elsevier Inc.

This paper investigates the notions of θ-bordered words and θ-unbordered words for various pseudo-identity functions θ. A θ-bordered word is a non-empty word u such that there exists a word v which is a prefix of u while θ(v) is a suffix of u. The case where θ is the identity function corresponds to the classical notions of bordered and unbordered words. Here we explore cases where θ is a pseud...

The utility function u is then extended to a utility function G(u) on G(A)×Θ by assigning each pair (λ, θ) the expectation of the random variable uθ under the measure λ, i.e. Eλ [ uθ ] . Every pure action a ∈ A then can uniquely be identified with the Dirac-measure δa ∈ G(A) and we have u(a, θ) = G(u)(δa, θ) for all (a, θ) ∈ A × Θ. Further, also (1) can easily be extended to randomized actions ...

Firstly, a new state feedback model reference adaptive control approach is developed for uncertain systems with gain scheduled reference models in a multi-input multi-output (MIMO) setting. Specifically, adaptive state feedback for output tracking control problem of MIMO nonlinear systems is studied and gain scheduled reference model system is used for generating desired state trajectories. Usi...

1. INTRODUCTION We consider the assessment of a vector valued parameter for a regular statistical model with data. The approach involves the Taylor expansion of the log-model, the separation of terms by asymptotic accuracy O(1), O(n −1/2), and O(n −1), and the subsequent recombination of terms in a coordinate-free form. Our particular interest centers on vector valued parameters in the presence...