l h e problem of approximating a high order controller by a low order one is tackled with the aid of a frequency-weighted Hankel norm approximation procedure. Bounds are obtained which weight those arising in the unweighted Hankel norm approximation procedure by a factor depending solely on the weighting function. Keywards. Controllers; approximation theory; controller reduction; system order r...

Citation: Uchida S, Yamamoto H, Okada I and Sasaki T (2018) A Theoretical Approach to Norm Ecosystems: Two Adaptive Architectures of Indirect Reciprocity Show Different Paths to the Evolution of Cooperation. Front. Phys. 6:14. doi: 10.3389/fphy.2018.00014 A Theoretical Approach to Norm Ecosystems: Two Adaptive Architectures of Indirect Reciprocity Show Different Paths to the Evolution of Cooper...

Given a 3–manifold the second author defined functions δn : H (M ;Z) → N, generalizing McMullen’s Alexander norm, which give lower bounds on the Thurston norm. We reformulate these invariants in terms of Reidemeister torsion over a non– commutative multivariable Laurent polynomial ring. This allows us to show that these functions are semi-norms.

This paper studies certain inverse problems in the optimal frequency-domain synthesis of robust controllers, in both the 2-norm and the infinity-norm. These inverse problems identify the class of controllers which are optimal for some choice of weights. Their implications for loopshaping are discussed. Keywords—Inverse optimality, loopshaping, H2 control, H∞ control. c.t/ g− + K.s/ u.t/ G0.s/ g...

We estimate the essential norm of a weighted composition operator relatively to the class of Dunford-Pettis operators or the class of weakly compact operators, on the space H∞ of Dirichlet series. As particular cases, we obtain the precise value of the generalized essential norm of a composition operator and of a multiplication operator.

This paper studies L2 norm error estimate for the div-curl leastsquares finite element method for Stokes equations with homogenous velocity boundary condition. The analysis using a different way from that in [11] shows that, without the divergence of the vorticity, the L2 norm error bound of the velocity is O(h 3 2 ) in the standard linear element method. AMS Subject Classification: 65N30

We prove that a composition operator is bounded on the Hardy space H of the right half-plane if and only if the inducing map fixes the point at infinity non-tangentially, and has a finite angular derivative λ there. In this case the norm, essential norm, and spectral radius of the operator are all equal to √ λ.

My current main project concerns the study of the interaction between the theory of operads and genuine equivariant homotopy theory. Briefly, an operad (introduced by May in [13]) consists of a sequence Oˆn of sets/spaces of “n-ary operations” together with Σn-actions and suitable compositions. The main point of operad theory is then the study of the algebras over a fixed operad O, which are o...