Perturbations of frames

In this paper, we give some sufficient conditions under which perturbations preserve Hilbert frames and near-Riesz bases. Similar results are also extended to frame sequences, Riesz sequences and Schauder frames. It is worth mentioning that some of our perturbation conditions are quite different from those used in the previous literatures on this topic.Comment: to appear in Acta MAth. Sinica, English Serie

The Optimal Mix of Monetary and Climate Policy

Given central banks' recent interest in "greening the financial system", this research theoretically investigates the relationship between monetary and climate policy and tries to find their “optimal mix”. We build an Environmental Dynamic Stochastic General Equilibrium (E-DSGE) model with the consideration of illegal emission which is pervasive in many countries. According to the model, we find: First, the dynamic of monetary policy is influenced by the selection of regimes of climate policy and the effectiveness of enforcement of environmental regulation. Second, the coefficients in the traditional Taylor rule of monetary policy can be better set to enhance welfare when a certain regime of climate policy is given in the economy. This helps find the constrained optimums of a policy mix. Third, if the mitigation of climate change is augmented into the target of monetary policy, the economy’s welfare can be enhanced. However, under certain circumstances, a dilemma in such monetary policy makes it incompatible with the traditional mandate of central bank

(1+)(1+)-complemented, (1+)(1+)-isomorphic copies of L1L_{1} in dual Banach spaces

The present paper contributes to the ongoing programme of quantification of isomorphic Banach space theory focusing on Pe{\l}czy\'nski's classical work on dual Banach spaces containing $L_{1}$ ($=L_{1}[0,1]$) and the Hagler--Stegall characterisation of dual spaces containing complemented copies of $L_{1}$. We prove the following quantitative version of the Hagler--Stegall theorem asserting that for a Banach space $X$ the following statements are equivalent: $\bullet$ $X$ contains almost isometric copies of $(\bigoplus_{n=1}^{\infty} \ell_{\infty}^{n})_{\ell_1}$, $\bullet$ for all $\varepsilon>0$, $X^{*}$ contains a $(1+\varepsilon)$-complemented, $(1+\varepsilon)$-isomorphic copy of $L_{1}$, $\bullet$ for all $\varepsilon>0$, $X^{*}$ contains a $(1+\varepsilon)$-complemented, $(1+\varepsilon)$-isomorphic copy of $C[0,1]^{*}$. Moreover, if $X$ is separable, one may add the following assertion: $\bullet$ for all $\varepsilon>0$, there exists a $(1+\varepsilon)$-quotient map $T\colon X\rightarrow C(\Delta)$ so that $T^{*}[C(\Delta)^{*}]$ is $(1+\varepsilon)$-complemented in $X^{*}$, where $\Delta$ is the Cantor set.Comment: 14 p

Asymptotically isometric copies of c0c_0 and l1l^1 in quotients of Banach spaces

Let $X$ be a real Banach space that does not contain a copy of $\ell^1$. Then $X^\ast$ contains asymptotically sometric copies of $\ell^1$ if and only if $X$ has a quotient which is asymptotically isometric to $c_0$

Experimental characterization of Bowden cable friction and compliance

textThis thesis presents a systematic method for experimental characterization of Bowden cable friction and compliance. A novel tension and elongation measurement method using a motion capture system and a spring is introduced. With the measurement method, the effects of nine variables on friction and cable compliance are investigated through a comprehensive set of experiments under 144 different cases. We have generated specific guidelines for Bowden cable configurations and design parameters to achieve optimal performance which may help robotics researchers in choosing and configuring Bowden cables, and designing control systems for actuation.Mechanical Engineerin

Engaging Central Banks in Climate Change? The Mix of Monetary and Climate Policy

Given the recent debate on central banks’ role under climate change, this research theoretically investigates the mix of monetary and climate policy and provides some insights for central banks who are considering their engagement in the climate change issue. The “climate-augmented” monetary policy is pioneeringly proposed and studied. We build an extended Environmental Dynamic Stochastic General Equilibrium (E-DSGE) model as the method. By this model, we find the following results. First, the making process of monetary policy should consider the existing climate policy and environmental regulation. Second, the coefficients in traditional monetary policy can be better set to enhance welfare when climate policy is given. This provides a way to optimise the policy mix. Third, if a typical form climate target is augmented into the monetary policy rule, a dilemma could be created. This means that it has some risks for central banks to care for the climate proactively by using the narrow monetary policy. At the current stage, central banks could and should use other measures to help the climate and the financial stability