We prove the norm identity ‖Id + T ‖ = 1 + ‖T ‖, which is known as the Daugavet equation, for operators T on C(S) not fixing a copy of C(S), where S is a compact metric space without isolated points.

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...

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...

UNLABELLED Oro-facial and speech motor control disorders represent a variety of speech and language pathologies. Early identification of such problems is important and carries clinical implications. A common and simple tool for gauging the presence and severity of speech motor control impairments is oral-diadochokinesis (oral-DDK). Surprisingly, norms for adult performance are missing from the ...

Using elementary arguments based on the Fourier transform we prove that for 1 ≤ q < p < ∞ and s ≥ 0 with s > n(1/2 − 1/p), if f ∈ L(R) ∩ Ḣ(R) then f ∈ L(R) and there exists a constant cp,q,s such that ‖f‖Lp ≤ cp,q,s‖f‖ θ Lq,∞‖f‖ 1−θ Ḣs , where 1/p = θ/q+(1− θ)(1/2− s/n). In particular, in R we obtain the generalised Ladyzhenskaya inequality ‖f‖L4 ≤ c‖f‖ 1/2 L2,∞ ‖f‖ 1/2 Ḣ1 . We also show that f...

Low-rank matrix recovery (LMR) is a rank minimization problem subject to linear equality constraints, and it arises in many fields such as signal and image processing, statistics, computer vision, system identification and control. This class of optimization problems is generally NP-hard. A popular approach replaces the rank function with the nuclear norm of the matrix variable. In this paper, ...

objective : the major objective of this study was to determine the means and 95% confidence interval of normal 6 years old children&apos;s motor-verbal skills. based on the results of this study we could develop a measure to diagnose abnormal motor skills. in addition, in this follow-up study, we compared the first-graders&apos; motor-verbal skills to their own skills one year earlier. method: ...

We revisit a classical scenario in communication theory: a source is generating a waveform which we sample at regular intervals; we wish to transform the signal in such a way as to minimize distortion in its reconstruction, despite noise. The transformation must be online (also called causal), in order to enable real-time signaling. The noise model we consider is adversarial `1-bounded; this is...

Anderson acceleration (AA) is a technique for accelerating the convergence of fixed-point iterations. In this paper, we apply AA to sequence functions and modify norm in its internal optimization problem H−s norm, some positive integer s, bias it towards low-frequency spectral content residual. We analyze by quantifying improvement over Picard iteration. find that based on H−2 well-suited solve...