Hyperbolic Programming (HP) –minimizing a linear functional over an affine subspace of a finite-dimensional real vector space intersected with the so-called hyperbolicity cone– is a class of convex optimization problems that contains well-known Linear Programming (LP). In particular, for any LP one can readily provide a sequence of HP relaxations. Based on these hyperbolic relaxations, a new Sh...

Novel decision-feedback (DF) linear prediction (LP) receivers, which process multiple samples per symbol interval in conjunction with optimal sample combining, are proposed for differential space–time modulation (DSTM) over Rayleigh fast-fading channels. Performance analysis demonstrates that multisampling DF-LP receivers outperform their symbol-rate sampling counterpart in fast fading substant...

We consider statistical procedures for feature selection defined by a family of regularization problems with convex piecewise linear loss functions and penalties of l1 nature. Many known statistical procedures (e.g. quantile regression and support vector machines with l1 norm penalty) are subsumed under this category. Computationally, the regularization problems are linear programming (LP) prob...

3. Since Lp and Lr are subspaces of CX , their intersection is a vector space. It is clear that ‖ · ‖ is a norm (this follows directly from the fact that ‖ · ‖p and ‖ · ‖r are norms). Let 〈fn〉n=1 be a Cauchy sequence in Lp ∩ Lr. Since ‖fm − fn‖p ≤ ‖fm − fn‖ and ‖fm − fn‖r ≤ ‖fm − fn‖ for all m,n ∈ N, it is clear that 〈fn〉n=1 is a Cauchy sequence in both Lp and Lr. Let gp ∈ Lp and gr ∈ Lr be the...

The affine synthesis operator Sc = ∑j>0 ∑k∈Zd cj,kψj,k is shown to map the coefficient space (Z+ × Zd ) surjectively onto Lp(Rd ), for p ∈ (0, 1]. Here ψj,k(x) = | det aj |ψ(aj x − k) for dilation matrices aj that expand, and the synthesizer ψ ∈ Lp(Rd ) need satisfy only mild restrictions, for example, ψ ∈ L1(Rd ) with nonzero integral or else with periodization that is real-valued, nontrivial ...

By w, we denote the space of all real or complex valued sequences. If x ∈ w, then we simply write x xk instead of x xk ∞ k 1. Also, we will use the conventions that e 1, 1, . . . . Any vector subspace of w is called a sequence space. We will write l∞, c, and c0 for the sequence spaces of all bounded, convergent, and null sequences, respectively. Further, by lp 1 ≤ p < ∞ , we denote the sequence...

Abstract. Let L be an elliptic differential operator with bounded measurable coefficients, acting in Bochner spaces Lp(Rn;X) of X-valued functions on Rn. We characterize Kato’s square root estimates ‖ √ Lu‖p h ‖∇u‖p and the H-functional calculus of L in terms of R-boundedness properties of the resolvent of L, when X is a Banach function lattice with the UMD property, or a noncommutative Lp spac...

Spacetime is composed of a fluctuating arrangement of bubbles or loops called spacetime foam, or quantum foam. We use the holographic principle to deduce its structure, and show that the result is consistent with gedanken experiments involving spacetime measurements. We propose to use laserbased atom interferometry techniques to look for spacetime fluctuations. Our analysis makes it clear that ...

The paper deals with the problem of nonparametric estimating Lp–norm, p∈(1,∞), a probability density on Rd, d≥1 from independent observations. unknown is assumed to belong ball in anisotropic Nikolskii’s space. We adopt minimax approach, and derive lower bounds risk. In particular, we demonstrate that accuracy estimation procedures essentially depends whether p integer or not. Moreover, develop...