Polygamy relations of multipartite systems

We investigate the polygamy relations of multipartite quantum states. General polygamy inequalities are given in the $\alpha$th $(\alpha\geq 2)$ power of concurrence of assistance, $\beta$th $(\beta \geq1)$ power of entanglement of assistance, and the squared convex-roof extended negativity of assistance (SCRENoA)

The Hilbert cube contains a minimal subshift of full mean dimension

We construct a minimal dynamical system of mean dimension equal to $1$, which can be embedded in the shift action on the Hilbert cube $[0,1]^\mathbb{Z}$. Our result clarifies a seemingly plausible impression and finally enables us to have a full understanding of (a pair of) the exact ranges of all possible values of mean dimension, within which there will always be a minimal dynamical system that can be (resp. cannot be) embedded in the shift action on the Hilbert cube. The key ingredient of our idea is to produce a dense subset of the alphabet $[0,1]$ "more gently"

Electric Vehicle charging management algorithm for a UK low-voltage residential distribution network

The integration of Electric Vehicles (EVs) into low-voltage (LV) residential distribution networks inevitably increases the overall demand, especially peak demand, which may cause thermal or voltage issues. In this paper, a 400V practical residential distribution network is modelled and used to quantify these impacts due to the growing penetration of EVs. Residential load profiles in 1-minute resolution and EV charging profiles with recorded State of Charge (SOC) are randomly and statistically created. Then, a simple charging management algorithm with locally made decision is suggested at EV users' charging points. Results prove that this approach can mitigate the negative impacts of EV charging on network assets. Moreover, it can reduce EV users' electricity cost for charging based on existing UK electricity price scheme 'Economy 7,' without compromising EV usage or substantial network infrastructure reinforcement or installation of extensive monitor, control and communication system. The simulation models and analysis are implemented in MATLAB/OpenDSS as an LV distribution network simulation platform

Comparison of centralised and distributed battery energy storage systems in LV distribution networks on operational optimisation and financial benefits

The integration of renewable energy sources and plug-in electric vehicles (PEVs) into the existing low-voltage (LV) distribution network at a high penetration level can cause reverse power flow, increased overall energy demand, network congestion, voltage rise/dip, transformer overloading and other operational issues. In this study, these potentially negative impacts caused by increasing penetration of distributed energy resources and PEVs are stochastically quantified based on a real practical 400 V distribution network as a case study. Battery energy storage (BES) is known to be a promising method for peak shaving and to provide network ancillary services. Two types of BES implementations aiming at distinctive charging and discharging targets without communication infrastructure or control centre are proposed and simulated. Optimisation results and potential financial profit of these two BES systems are compared and discussed in detail

Mean dimension of product spaces: a fundamental formula

Mean dimension is a topological invariant of dynamical systems, which originates with Mikhail Gromov in 1999 and which was studied with deep applications around 2000 by Elon Lindenstrauss and Benjamin Weiss within the framework of amenable group actions. Let a countable discrete amenable group $G$ act continuously on compact metrizable spaces $X$ and $Y$. Consider the product action of $G$ on the product space $X\times Y$. The product inequality for mean dimension is well known: $\mathrm{mdim}(X\times Y,G)\le\mathrm{mdim}(X,G)+\mathrm{mdim}(Y,G)$, while it was unknown for a long time if the product inequality could be an equality. In 2019, Masaki Tsukamoto constructed the first example of two different continuous actions of $G$ on compact metrizable spaces $X$ and $Y$, respectively, such that the product inequality becomes strict. However, there is still one longstanding problem which remains open in this direction, asking if there exists a continuous action of $G$ on some compact metrizable space $X$ such that $\mathrm{mdim}(X\times X,G)<2\cdot\mathrm{mdim}(X,G)$. We solve this problem. Somewhat surprisingly, we prove, in contrast to (topological) dimension theory, a rather satisfactory theorem: If an infinite (countable discrete) amenable group $G$ acts continuously on a compact metrizable space $X$, then we have $\mathrm{mdim}(X^n,G)=n\cdot\mathrm{mdim}(X,G)$, for any positive integer $n$. Our product formula for mean dimension, together with the example and inequality (stated previously), eventually allows mean dimension of product actions to be fully understood