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Operators in the Cowen-Douglas Class and Related Topics
Published in Kehe Zhu, Handbook of Analytic Operator Theory, 2019
There are many closely related notions like the locally free module and the quasi-free module (cf. [13, 26]). No matter which notion one adopts, the goal is to ensure the existence of a holomorphic Hermitian vector bundle such that the equivalence class of the module and that of the vector bundle are in one to one correspondence. The generalized Bergman kernel and the sharp kernel appearing in [21] and [2] achieve a similar objective. The polynomial density in an analytic Hilbert module ensures that the joint kernel ∩i=1mker(Mi−wi)∗,w∈Ω∗,
Slicing Floorplans
Published in Charles J. Alpert, Dinesh P. Mehta, Sachin S. Sapatnekar, Handbook of Algorithms for Physical Design Automation, 2008
Ting-Chi Wang, Martin D.F. Wong
Boundary constraints can be specified as follows. The set of all modules is divided into five disjoint module sets MF,ML,MR,MT,MB. Each module in MF is a free module that can be placed anywhere in a floorplan. On the other hand, each module in ML (MR,MT, MB, respectively) is a boundary-constrained module with the left (right, top, bottom, respectively) boundary constraint and has to be placed along the left (right, top, bottom, respectively) boundary of the floorplan. Note that ML (MR, MT, MB, respectively) may be an empty set if no module must be placed along the left (right, top, bottom, respectively) boundary. For example, for the two slicing floorplans shown in Figure 9.7a and b, if module 2 is constrained to be placed along the left boundary, then the one in Figure 9.7a is infeasible while the one in Figure 9.7b is feasible.
Electrical systems
Published in Tom Denton, Automobile Mechanical and Electrical Systems, 2018
In the Ford diagram shown in Figure 3.69, the powertrain control module (PCM) allows the engine to start only when the passive anti-theft system (PATS) reads a key that transmits a valid code. In a key-free vehicle, the passive key is recognized by the key-free module and if the key is valid the permission to start is issued directly. In vehicles with a manual transmission it is necessary to depress the clutch pedal; on those with automatic transmission the brake pedal must be pressed. In a key-free system the key-free module switches on the control voltage for the starter relay.
L 0-convex compactness and its applications to random convex optimization and random variational inequalities
Published in Optimization, 2021
Tiexin Guo, Erxin Zhang, Yachao Wang, Mingzhi Wu
For any positive integer d, let be the -module of equivalence classes of -valued random vectors on , where is the Cartesian product of K by d times, it is a free -module of rank d. As is well known, any finitely generated subspace of a linear space over K must be of finite dimension, for example, simple like some . However, a finitely generated submodule of an -module is rather different from a free -module of finite rank, whose structure was already characterized in [34, Theorem 1.1]. Since we are often forced to work with finitely generated -modules rather than free -modules of finite rank, (see Section 4), we restate it for the sake of convenience.
Modelling and economic evaluation of pressure-retarded osmosis power plant case study: Iran
Published in International Journal of Ambient Energy, 2019
Abolfazl Ansari, Majid Abbaspour
The obtained energy from the existing RO/FO membranes was far below the expectation due to unsuitable membrane structure. As a result the development of PRO was stopped for a long time mainly because of a serious lack of effective membrane. Chung et al.’s studies provide useful insights to design and operate PRO modules. They have tried to clarify the fundamental relationship among various membrane properties and operation parameters and investigated the instant and accumulative effects of salt permeability on the sustainability of high power density in PRO (Zhang and Chung 2013; Wan and Chung 2016a; Xiong et al. 2016). The optimal operating pressure to harvest energy can be greater than one half of the osmotic pressure gradient across the membrane, if one can carefully design a PRO membrane with a large water permeability (Zhang and Chung 2013; Straub, Lin, and Elimelech 2014). Because of high packing density and spacer free module fabrication, hollow fibre membranes, especially TFC PRO hollow fibre membranes, have great potential for osmotic power harvesting (Han, Wang, and Chung 2013; Chung et al. 2015). Moreover, the operating profit of SWRO-PRO is also studied by Wan et al. (Wan and Chung 2016a, 2016b).
Block conjugacy of irreducible toral automorphisms
Published in Dynamical Systems, 2019
Lennard F. Bakker, Pedro Martins Rodrigues
We fix an irreducible polynomial of degree n. This determines an algebraic number field . The class of t, which we denote from now on by β, is a simple root of f in K and we identify K with the isomorphic field . The notation denotes the ring of all algebraic integers of K. An automorphism with characteristic polynomial acts on and so there exists a right eigenvector associated to β, namely, , where the entries of u determine a (fractional) ideal of . The action of A, on the right, on , is thus identified with multiplication by β in I, namely, if for some , then . That the entries of u are a basis of the free -module I has the obvious but important consequence that if then m=0, and so, if (an integer matrix) and Mu=0 then M=0.