SRB Measures for A Class of Partially Hyperbolic Attractors in Hilbert spaces

In this paper, we study the existence of SRB measures and their properties for infinite dimensional dynamical systems in a Hilbert space. We show several results including (i) if the system has a partially hyperbolic attractor with nontrivial finite dimensional unstable directions, then it has at least one SRB measure; (ii) if the attractor is uniformly hyperbolic and the system is topological mixing and the splitting is H\"older continuous, then there exists a unique SRB measure which is mixing; (iii) if the attractor is uniformly hyperbolic and the system is non-wondering and and the splitting is H\"older continuous, then there exists at most finitely many SRB measures; (iv) for a given hyperbolic measure, there exist at most countably many ergodic components whose basin contains an observable set

Existence of SRB Measures for A Class of Partially Hyperbolic Attractors in Banach spaces

In this paper, we study the existence of SRB measures for infinite dimensional dynamical systems in a Banach space. We show that if the system has a partially hyperbolic attractor with nontrivial finite dimensional unstable directions, then it has an SRB measure.Comment: arXiv admin note: text overlap with arXiv:1508.0330

Penelope Fitzgerald's fiction and literary career: form and context

The investigation of Fitzgerald's equivocal success, of the decisive change in Britain's recent cultural perspective, involves raising questions around canon-formation, the consolidation of a national identity, strategies of writing, and the politics of reading. I have found it necessary to examine aspects of theme, form, genre and context in Fitzgerald's writing, focusing successively on convention and subversion in her work. This 'doubleness' has generated the two-part structure of the present thesis, the first book-length study of Fitzgerald's work. Part One examines the canonical literariness of Fitzgerald's novels through studying literary conventions and thematic preoccupations. It aims to elucidate Fitzgerald's fiction through the tradition of liberal humanism. The canon of English literature is more than a settled corpus, it involves a set of prescribed criteria which, I argue, is the cornerstone of Fitzgerald's literary success as a novelist, biographer, and literary critic. Contemporary British fiction has undergone a focal sea-change seen in its preoccupation with linguistic experimentation, typographical innovation, and topical engagement with current issues. Fitzgerald's fiction is out of step with current critical paradigms, and thus tends to get caught between the canonical and the contemporary. Part Two explores the impact of postmodern approaches on Fitzgerald's fiction, and examines the ways in which age, race, gender, identity and the nation have impinged on her writing. The scope of this study, therefore, comprises gender, writing, and the culture industry. In view of the scarcity of criticism on Fitzgerald's work, and apart from the more obvious critical concerns regarding authorship and periodisation, this thesis draws on a variety of critical perspectives in order to achieve a historical and contextual understanding of Fitzgerald's fiction and literary career in relation to contemporary British fiction

On the Cohomology of the Noncritical WW-string

We investigate the cohomology structure of a general noncritical $W_N$-string. We do this by introducing a new basis in the Hilbert space in which the BRST operator splits into a ``nested'' sum of nilpotent BRST operators. We give explicit details for the case $N=3$. In that case the BRST operator $Q$ can be written as the sum of two, mutually anticommuting, nilpotent BRST operators: $Q=Q_0+Q_1$. We argue that if one chooses for the Liouville sector a $(p,q)$ $W_3$ minimal model then the cohomology of the $Q_1$ operator is closely related to a $(p,q)$ Virasoro minimal model. In particular, the special case of a (4,3) unitary $W_3$ minimal model with central charge $c=0$ leads to a $c=1/2$ Ising model in the $Q_1$ cohomology. Despite all this, noncritical $W_3$ strings are not identical to noncritical Virasoro strings.Comment: 38 pages, UG-7/93, ITP-SB-93-7

A BRST Analysis of WW-symmetries

We perform a classical BRST analysis of the symmetries corresponding to a generic $w_N$-algebra. An essential feature of our method is that we write the $w_N$-algebra in a special basis such that the algebra manifestly has a ``nested'' set of subalgebras $v_N^N \subset v_N^{N-1} \subset \dots \subset v_N^2 \equiv w_N$ where the subalgebra $v_N^i\ (i=2, \dots ,N)$ consists of generators of spin $s=\{i,i+1,\dots ,N\}$, respectively. In the new basis the BRST charge can be written as a ``nested'' sum of $N-1$ nilpotent BRST charges. In view of potential applications to (critical and/or non-critical) $W$-string theories we discuss the quantum extension of our results. In particular, we present the quantum BRST-operator for the $W_4$-algebra in the new basis. For both critical and non-critical $W$-strings we apply our results to discuss the relation with minimal models.Comment: 32 pages, UG-4/9

Online Energy Generation Scheduling for Microgrids with Intermittent Energy Sources and Co-Generation

Microgrids represent an emerging paradigm of future electric power systems that can utilize both distributed and centralized generations. Two recent trends in microgrids are the integration of local renewable energy sources (such as wind farms) and the use of co-generation (i.e., to supply both electricity and heat). However, these trends also bring unprecedented challenges to the design of intelligent control strategies for microgrids. Traditional generation scheduling paradigms rely on perfect prediction of future electricity supply and demand. They are no longer applicable to microgrids with unpredictable renewable energy supply and with co-generation (that needs to consider both electricity and heat demand). In this paper, we study online algorithms for the microgrid generation scheduling problem with intermittent renewable energy sources and co-generation, with the goal of maximizing the cost-savings with local generation. Based on the insights from the structure of the offline optimal solution, we propose a class of competitive online algorithms, called CHASE (Competitive Heuristic Algorithm for Scheduling Energy-generation), that track the offline optimal in an online fashion. Under typical settings, we show that CHASE achieves the best competitive ratio among all deterministic online algorithms, and the ratio is no larger than a small constant 3.Comment: 26 pages, 13 figures. It will appear in Proc. of ACM SIGMETRICS, 201

Decentralized Complete Dictionary Learning via ℓ4\ell^{4}-Norm Maximization

With the rapid development of information technologies, centralized data processing is subject to many limitations, such as computational overheads, communication delays, and data privacy leakage. Decentralized data processing over networked terminal nodes becomes an important technology in the era of big data. Dictionary learning is a powerful representation learning method to exploit the low-dimensional structure from the high-dimensional data. By exploiting the low-dimensional structure, the storage and the processing overhead of data can be effectively reduced. In this paper, we propose a novel decentralized complete dictionary learning algorithm, which is based on $\ell^{4}$-norm maximization. Compared with existing decentralized dictionary learning algorithms, comprehensive numerical experiments show that the novel algorithm has significant advantages in terms of per-iteration computational complexity, communication cost, and convergence rate in many scenarios. Moreover, a rigorous theoretical analysis shows that the dictionaries learned by the proposed algorithm can converge to the one learned by a centralized dictionary learning algorithm at a linear rate with high probability under certain conditions

In situ crystal growth of zeolitic imidazolate frameworks (ZIF) on electrospun polyurethane nanofibers

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.This paper reports for the first time in situcrystal growth of ZIF-8 on electrospun polyurethane (PU) nanofibers. In SEM images, continuous and compact ZIF-8 nanocrystals grow along electrospun PU nanofibers. The highest loading capacity of ZIF-8 on PU reaches 63%. By N2adsorption–desorption, ZIF-8-PU shows a high surface area of 566 cm2g−1. Combining the good flexibility of PU with the high adsorption properties of ZIF-8, ZIF-8-PU can be easily tailored into clothes or other forms as adsorption material. Furthermore, the gas adsorption ability of ZIF-8-PU was measured for H2, N2, O2and CO2at room temperature (20 °C) under different pressure gradients. The results show that the adsorption capacity of ZIF-8-PU for CO2is nearly 11 times that for H2, 50 times that for O2and 75 times that for N2at 800 mmHg