scholarly journals Locally projective monoidal model structure for complexes of quasi-coherent sheaves on P 1 (k )

2008 ◽  
Vol 77 (1) ◽  
pp. 253-269 ◽  
Author(s):  
E. Enochs ◽  
S. Estrada ◽  
J. R. García-Rozas
Keyword(s):  
Model Structure ◽  
Coherent Sheaves

scholarly journals The projective stable category of a coherent scheme

2018 ◽  
Vol 149 (1) ◽  
pp. 15-43 ◽  
Author(s):  
Sergio Estrada ◽  
James Gillespie
Keyword(s):  
Homotopy Category ◽  
Model Structure ◽  
Stable Category ◽  
Coherent Sheaves ◽  
Chain Complexes

We define the projective stable category of a coherent scheme. It is the homotopy category of an abelian model structure on the category of unbounded chain complexes of quasi-coherent sheaves. We study the cofibrant objects of this model structure, which are certain complexes of flat quasi-coherent sheaves satisfying a special acyclicity condition.

Lattice imaging and pore structure of β ferric oxyhydroxide

1978 ◽  
Vol 36 (1) ◽  
pp. 264-265
Author(s):  
T. Baird ◽  
J.R. Fryer ◽  
S.T. Galbraith
Keyword(s):  
Electron Microscopy ◽  
Room Temperature ◽  
Bulk Material ◽  
Model Structure ◽  
Bulk Crystals ◽  
Lattice Imaging ◽  
Thin Sections ◽  
Ferric Oxyhydroxide ◽  
Resolution Electron ◽  
Hydrolysis Of

Introduction Previously we had suggested (l) that the striations observed in the pod shaped crystals of β FeOOH were an artefact of imaging in the electron microscope. Contrary to this adsorption measurements on bulk material had indicated the presence of some porosity and Gallagher (2) had proposed a model structure - based on the hollandite structure - showing the hollandite rods forming the sides of 30Å pores running the length of the crystal. Low resolution electron microscopy by Watson (3) on sectioned crystals embedded in methylmethacrylate had tended to support the existence of such pores.We have applied modern high resolution techniques to the bulk crystals and thin sections of them without confirming these earlier postulatesExperimental β FeOOH was prepared by room temperature hydrolysis of 0.01M solutions of FeCl3.6H2O, The precipitate was washed, dried in air, and embedded in Scandiplast resin. The sections were out on an LKB III Ultramicrotome to a thickness of about 500Å.

Fiction and reality in the modelling world-balance between simplicity and complexity, calibration and identifiability, verification and falsification

1999 ◽  
Vol 39 (9) ◽  
pp. 1-8 ◽  
Author(s):  
P. Harremoës ◽  
H. Madsen
Keyword(s):  
Model Prediction ◽  
Model Performance ◽  
Data Series ◽  
Urban Drainage ◽  
Model Structure ◽  
And Control

Where is the balance between simplicity and complexity in model prediction of urban drainage structures? The calibration/verification approach to testing of model performance gives an exaggerated sense of certainty. Frequently, the model structure and the parameters are not identifiable by calibration/verification on the basis of the data series available, which generates elements of sheer guessing - unless the universality of the model is be based on induction, i.e. experience from the sum of all previous investigations. There is a need to deal more explicitly with uncertainty and to incorporate that in the design, operation and control of urban drainage structures.

Analysis and design of suitable model structures for activated sludge tanks with circulating flow

1999 ◽  
Vol 39 (4) ◽  
pp. 55-60 ◽  
Author(s):  
J. Alex ◽  
R. Tschepetzki ◽  
U. Jumar ◽  
F. Obenaus ◽  
K.-H. Rosenwinkel
Keyword(s):  
Activated Sludge ◽  
Large Scale ◽  
Wastewater Treatment Plants ◽  
Treatment Plant ◽  
High Sensitivity ◽  
Suitable Model ◽  
Model Structure ◽  
Analysis And Design ◽  
Hydraulic Behaviour ◽  
Model Structures

Activated sludge models are widely used for planning and optimisation of wastewater treatment plants and on line applications are under development to support the operation of complex treatment plants. A proper model is crucial for all of these applications. The task of parameter calibration is focused in several papers and applications. An essential precondition for this task is an appropriately defined model structure, which is often given much less attention. Different model structures for a large scale treatment plant with circulation flow are discussed in this paper. A more systematic method to derive a suitable model structure is applied to this case. Results of a numerical hydraulic model are used for this purpose. The importance of these efforts are proven by a high sensitivity of the simulation results with respect to the selection of the model structure and the hydraulic conditions. Finally it is shown, that model calibration was possible only by adjusting to the hydraulic behaviour and without any changes of biological parameters.

Modelling Agricultural Controls for Flooding and Soil Erosion

2018 ◽  
pp. 776-796
Author(s):  
Roger Moussa ◽  
Bruno Cheviron
Keyword(s):  
Spatial Distribution ◽  
Model Structure ◽  
Land Uses ◽  
Research Challenges ◽  
Water And Sediment ◽  
Flow Processes ◽  
Cultivation Practices ◽  
Modelling Strategies ◽  
The Impact ◽  
Significant Factors

Floods are the highest-impact natural disasters. In agricultural basins, anthropogenic features are significant factors in controlling flood and erosion. A hydrological-hydraulic-erosion diagnosis is necessary in order to choose the most relevant action zones and to make recommendations for alternative land uses and cultivation practices in order to control and reduce floods and erosion. This chapter first aims to provide an overview of the flow processes represented in the various possible choices of model structure and refinement. It then focuses on the impact of the spatial distribution and temporal variation of hydrological soil properties in farmed basins, representing their effects on the modelled water and sediment flows. Research challenges and leads are then tackled, trying to identify the conditions in which sufficient adequacy exists between site data and modelling strategies.

scholarly journals Curved Rickard complexes and link homologies

2020 ◽  
Vol 2020 (769) ◽  
pp. 87-119
Author(s):  
Sabin Cautis ◽  
Aaron D. Lauda ◽  
Joshua Sussan
Keyword(s):  
Spectral Sequence ◽  
Quantum Groups ◽  
Braid Group ◽  
Derived Categories ◽  
Duke Math ◽  
Khovanov Homology ◽  
Hilbert Schemes ◽  
Coherent Sheaves ◽  
Knot Homology ◽  
Original Motivation

AbstractRickard complexes in the context of categorified quantum groups can be used to construct braid group actions. We define and study certain natural deformations of these complexes which we call curved Rickard complexes. One application is to obtain deformations of link homologies which generalize those of Batson–Seed [3] [J. Batson and C. Seed, A link-splitting spectral sequence in Khovanov homology, Duke Math. J. 164 2015, 5, 801–841] and Gorsky–Hogancamp [E. Gorsky and M. Hogancamp, Hilbert schemes and y-ification of Khovanov–Rozansky homology, preprint 2017] to arbitrary representations/partitions. Another is to relate the deformed homology defined algebro-geometrically in [S. Cautis and J. Kamnitzer, Knot homology via derived categories of coherent sheaves IV, colored links, Quantum Topol. 8 2017, 2, 381–411] to categorified quantum groups (this was the original motivation for this paper).

scholarly journals EULER CLASSES: SIX-FUNCTORS FORMALISM, DUALITIES, INTEGRALITY AND LINEAR SUBSPACES OF COMPLETE INTERSECTIONS

2021 ◽  
pp. 1-66
Author(s):  
Tom Bachmann ◽  
Kirsten Wickelgren
Keyword(s):  
Commutative Algebra ◽  
Vector Bundles ◽  
Euler Class ◽  
Complete Intersections ◽  
Bilinear Forms ◽  
Euler Numbers ◽  
Coherent Sheaves ◽  
Linear Subspaces ◽  
Algebraic Vector

Abstract We equate various Euler classes of algebraic vector bundles, including those of [12] and one suggested by M. J. Hopkins, A. Raksit, and J.-P. Serre. We establish integrality results for this Euler class and give formulas for local indices at isolated zeros, both in terms of the six-functors formalism of coherent sheaves and as an explicit recipe in the commutative algebra of Scheja and Storch. As an application, we compute the Euler classes enriched in bilinear forms associated to arithmetic counts of d-planes on complete intersections in $\mathbb P^n$ in terms of topological Euler numbers over $\mathbb {R}$ and $\mathbb {C}$ .

A novel LSSVM-L Hammerstein model structure for system identification and nonlinear model predictive control of CSTR servo and regulatory control

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Akshaykumar Naregalkar ◽  
Subbulekshmi Durairaj
Keyword(s):  
Linear System ◽  
Regulatory Control ◽  
Hammerstein Model ◽  
Support Vector ◽  
Model Structure ◽  
Linear Dynamics ◽  
Vector Machines ◽  
Non Linear ◽  
Laguerre Filters ◽  
Non Linear System

Abstract A continuous stirred tank reactor (CSTR) servo and the regulatory control problem are challenging because of their highly non-linear nature, frequent changes in operating points, and frequent disturbances. System identification is one of the important steps in the CSTR model-based control design. In earlier work, a non-linear system model comprises a linear subsystem followed by static nonlinearities and represented with Laguerre filters followed by the LSSVM (least squares support vector machines). This model structure solves linear dynamics first and then associated nonlinearities. Unlike earlier works, the proposed LSSVM-L (least squares support vector machines and Laguerre filters) Hammerstein model structure solves the nonlinearities associated with the non-linear system first and then linear dynamics. Thus, the proposed Hammerstein’s model structure deals with the nonlinearities before affecting the entire system, decreasing the model complexity and providing a simple model structure. This new Hammerstein model is stable, precise, and simple to implement and provides the CSTR model with a good model fit%. Simulation studies illustrate the benefit and effectiveness of the proposed LSSVM-L Hammerstein model and its efficacy as a non-linear model predictive controller for the servo and regulatory control problem.

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