A semidefinite relaxation σ(Γ) for the problem of finding the maximum number κ(Γ) of edges in a complete bipartite subgraph of a bipartite graph Γ = (V1 ∪ V2, E) is considered. For a large class of graphs, the relaxation is better than the LP-relaxation described in [9]. It is shown that σ(Γ) is bounded from above by the Lovász theta function θ(LQ(Γ)) of the graph LQ(Γ) related to the line grap...

Given a dictionary of Mn initial estimates of the unknown true regression function, we aim to construct linearly aggregated estimators that target the best performance among all the linear combinations under a sparse q-norm (0 ≤ q ≤ 1) constraint on the linear coefficients. Besides identifying the optimal rates of aggregation for these lq-aggregation problems, our multi-directional (or adaptive...

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S.G.Santhi, Assistant professor, Department of Computer Science and Engineering, Annamalai University [email protected] Dr.K.Venkatachalapathy Professor, Department of Computer Science and Engineering, Annamalai University Abstract In this paper, we propose a method to save energy consumption for the rejoin procedure for Cluster Tree in 802.15.4 Sensor Networks .An improved node rejoin procedure...

An aspect of uncertainty principle in real classical analysis asserts that a function f and its Fourier transform ̂ f cannot decrease simultaneously very rapidly at infinity. As illustrations of this, one has Hardy’s theorem [1], Morgan’s theorem [2], and BeurlingHörmander’s theorem [3–5]. These theorems have been generalized to many other situations; see, for example, [6–10]. In 1983, Cowling a...

The cheap LQ regulator is reinterpreted as an output nulling problem which is a basic problem of the geometric control theory. In fact, solving the LQ regulator problem is equivalent to keep the output of the related Hamiltonian system identically zero. The solution lies on a controlled invariant subspace whose dimension is characterized in terms of the minimal conditioned invariant of the orig...

The paper is concerned with simultaneous linear-quadratic (LQ) optimal control design for a set of LTI systems via piecewise constant output feedback. First, the discrete-time simultaneous LQ optimal control design problem is reduced to solving a set of coupled matrix inequalities and an iterative LMI algorithm is presented to compute the feedback gain. Then, simultaneous stabilization and simu...

An open-loop two-person zero-sum linear quadratic (LQ for short) stochastic differential game is considered. The controls for both players are allowed to appear in both the drift and diffusion of the state equation, the weighting matrices in the payoff/cost functional are not assumed to be definite/nonsingular, and the cross-terms between two controls are allowed to appear. A forward-backward s...

We construct the C∗-algebra C(Lq(p;m1, . . . ,mn)) of continuous functions on the quantum lens space as the fixed point algebra for a suitable action of Zp on the algebra C(S2n−1 q ), corresponding to the quantum odd dimensional sphere. We show that C(Lq(p;m1, . . . ,mn)) is isomorphic to the graph algebra C∗ ( L (p;m1,...,mn) 2n−1 ) . This allows us to determine the ideal structure and, at lea...

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