The interactions between H1 and H2, the two polypeptides comprising the human asialoglycoprotein receptor (ASGP-R), were investigated by immunofluorescence and lateral mobility measurements combined with antibody-mediated cross-linking and immobilization. Immunofluorescence microscopy revealed two ASGP-R populations on the cell surface, one homogeneously distributed and the other in micropatche...

Fundamentals of Wireless Communications Homework 1 Solutions Handout date: April 1, 2014 Problem 1 Identification of LTV Systems 1. Suppose x stably identifiesQ. ForH1, H2 ∈ QwithH1x = H2xwe have 0 = H1x−H2x = (H1 −H2)x sinceH1, H2 are linear operators. Moreover,H1 −H2 ∈ Q. Since x stably identifiesQ, α‖H1 −H2‖H ≤ ‖(H1 −H2)x‖ = 0 with α > 0, which implies thatH1 −H2 = 0, i.e.,H1 = H2. 2. We sta...

Let h1, · · · , hn be positive integers. We study new sums m(h1, · · · , hn) = h1−1 ∑ r1=0 · · · hn−1 ∑ rn=0 min { r1 h1 , · · · , rn hn } and M(h1, · · · , hn) = h1−1 ∑ r1=0 · · · hn−1 ∑ rn=0 max { r1 h1 , · · · , rn hn } , the first of which times h1 · · ·hn is the number of lattice points in a pyramid of dimension n + 1. We show that m(h1, · · · , hn) (h1 − 1) · · · (hn − 1) = 1 + ∑ ∅6 =I⊆{1...

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Given graphs H1, . . . ,Hk, let f(H1, . . . ,Hk) be the minimum order of a graph G such that for each i, the induced copies of Hi in G cover V (G). We prove constructively that f(H1,H2) ≤ 2(n(H1) + n(H2) − 2); equality holds when H1 = H2 = Kn. We prove that f(H1,Kn) = n + 2 √ δ(H1)n + O(1) as n → ∞. We also determine f(K1,m−1,Kn) exactly.

We study the intersection of finitely generated subgroups of free groups by utilizing the method of linear programming. We prove that if H1 is a finitely generated subgroup of a free group F , then the Walter Neumann coefficient σ(H1) of H1 is rational and can be computed in deterministic exponential time of size of H1. This coefficient σ(H1) is a minimal nonnegative real number such that, for ...

The approximation-solvability of a generalized system of nonlinear variational inequalities (SNVI) involving relaxed pseudococoercive mappings, based on the convergence of a system of projection methods, is presented. The class of relaxed pseudococoercive mappings is more general than classes of strongly monotone and relaxed cocoercive mappings. Let K1 and K2 be nonempty closed convex subsets o...

The general form of non-entangling unitary maps for measurement schemes is determined. It is shown that any POVM admits a non-entangling measurement. We prove the following. Proposition 1 Let H1,H2 be complex separable Hilbert spaces, φ0 a unit vector in H2. Assume U : H1 ⊗ H2 → H1 ⊗ H2 is a unitary map such that for all φ ∈ H1, U(φ ⊗ φ0) = φ′ ⊗ φ′ for some unit vectors φ′ ∈ H1, φ′ ∈ H2. Then U...