scholarly journals Logarithmically regular morphisms

2020 ◽  
Author(s):  
Sam Molcho ◽  
Michael Temkin
Keyword(s):  
Simple Criterion ◽  
Log Schemes ◽  
Log Scheme

AbstractWe consider the stack $${\mathcal {L}}og_{X}$$ L o g X parametrizing log schemes over a log scheme X, and weak and strong properties of log morphisms via $${\mathcal {L}}og_{X}$$ L o g X , as defined by Olsson. We give a concrete combinatorial presentation of $${\mathcal {L}}og_{X}$$ L o g X , and prove a simple criterion of when weak and strong properties of log morphisms coincide. We then apply this result to the study of logarithmic regularity, derive its main properties, and give a chart criterion analogous to Kato’s chart criterion of logarithmic smoothness.

KUMMER COVERINGS AND SPECIALISATION

2021 ◽  
pp. 1-37
Author(s):  
Martin Olsson
Keyword(s):  
Local Ring ◽  
Fundamental Groups ◽  
Technical Result ◽  
Noetherian Local Ring ◽  
Log Schemes ◽  
Log Scheme

Abstract We prove versions of various classical results on specialisation of fundamental groups in the context of log schemes in the sense of Fontaine and Illusie, generalising earlier results of Hoshi, Lepage and Orgogozo. The key technical result relates the category of finite Kummer étale covers of an fs log scheme over a complete Noetherian local ring to the Kummer étale coverings of its reduction.

Paper 7: Control of Variable-Discharge Pumps and Dangers of Pipeline Resonance

1966 ◽  
Vol 181 (1) ◽  
pp. 144-174
Author(s):  
B. J. Cooper ◽  
D. Hartland ◽  
R. Lawson ◽  
A. M. Stone ◽  
R. D. Tyler
Keyword(s):  
Power Input ◽  
Small Region ◽  
Significant Loss ◽  
Pump Efficiency ◽  
Positive Slope ◽  
Simple Criterion ◽  
Wide Range ◽  
Resonant Instability ◽  
Organ Pipe ◽  
Computer Studies

The discharge and power input of Deriaz mixed-flow pumps and pump turbines can be controlled over a wide range without significant loss in efficiency by movement of the blades. The attainment of the highest pump efficiency involves a small region of positive slope in the head discharge graph. This paper examines the limitations of designing pumps which do not exhibit positive slope and the problems of governing if a positive-slope region is accepted. It is shown that operation in the positive-slope region can introduce a serious organ-pipe resonant instability in the pipeline. A simple criterion to determine whether or not such oscillations will occur is given. This stability criterion involves the dynamic characteristics of both the pump and the pipeline. Finally, computer studies of a particular Deriaz pump installation are presented. These underline the severity of the situation should resonance develop and show how it can be avoided by the use of an air bottle of appropriate design.

THE ISOPIESTIC METHOD APPLIED TO SORPTION ISOTHERMS

1949 ◽  
Vol 27b (2) ◽  
pp. 87-100 ◽  
Author(s):  
S. Barnartt ◽  
J. B. Ferguson
Keyword(s):  
Carbon Tetrachloride ◽  
Linear Relation ◽  
Sorption Isotherms ◽  
Sorption Process ◽  
The Other ◽  
Isopiestic Method ◽  
Simple Criterion ◽  
Water Vapors ◽  
Linear Sections ◽  
Wide Pressure

The isopiestic method has been applied to the sorption of carbon tetrachloride and water vapors by activated coconut shell charcoals. The isopiestic charges were found to be linearly related over wide pressure ranges. Isotherms formed by plotting the isopiestic charges of two charcoals one against the other consisted of three linear sections for both carbon tetrachloride and water. If the pressure isotherm of one charcoal be known, those of other charcoals may be computed from it by weighing relatively few isopiestic charges. Errors inherent in the measurement of equilibrium pressures, as well as those caused by the drift of the pressure isotherms towards higher sorption capacities at a given pressure, are eliminated in the isopiestic method of comparing charcoals. The linear relation between the isopiestic charges affords a simple criterion of rejection for equations proposed to fit the pressure isotherms. It also throws into relief the structural regularities in activated charcoals. The existence of discontinuities m the sorption process, reported by previous experimenters, is supported by the isopiestic data.

ON MAGNETIC SELF-COLLIMATION OF RELATIVISTIC JETS

2010 ◽  
Vol 19 (06) ◽  
pp. 689-694
Author(s):  
N. GLOBUS ◽  
V. CAYATTE ◽  
C. SAUTY
Keyword(s):  
Black Hole ◽  
Total Energy ◽  
Ideal Fluid ◽  
Polar Axis ◽  
Kerr Metric ◽  
Relativistic Jets ◽  
Simple Criterion ◽  
General Relativistic ◽  
Time Splitting ◽  
Relativistic Magnetohydrodynamics

We present a semi-analytical model using the equations of general relativistic magnetohydrodynamics (GRMHD) for jets emitted by a rotating black hole. We assume steady axisymmetric outflows of a relativistic ideal fluid in Kerr metrics. We express the conservation equations in the frame of the FIDucial Observer (FIDO or ZAMO) using a 3+1 space–time splitting. Calculating the total energy variation between a non-polar field line and the polar axis, we extend to the Kerr metric the simple criterion for the magnetic collimation of jets obtained for a nonrotating black hole by Meliani et al.10 We show that the black role rotation induced a more efficient magnetic collimation of the jet.

The Hilbert series of the irreducible quotient of the polynomial representation of the rational Cherednik algebra of type An−1 in characteristic p for p|n − 1

2021 ◽  
pp. 2250191
Author(s):  
Merrick Cai ◽  
Daniil Kalinov
Keyword(s):  
Hilbert Series ◽  
Positive Characteristic ◽  
Closed Field ◽  
Simple Criterion ◽  
Characteristic P ◽  
Polynomial Representation ◽  
Cherednik Algebra ◽  
Rational Cherednik Algebra ◽  
Polynomial Formula ◽  
Field Of Positive Characteristic

In this paper, we study the irreducible quotient [Formula: see text] of the polynomial representation of the rational Cherednik algebra [Formula: see text] of type [Formula: see text] over an algebraically closed field of positive characteristic [Formula: see text] where [Formula: see text]. In the [Formula: see text] case, for all [Formula: see text] we give a complete description of the polynomials in the maximal proper graded submodule [Formula: see text], the kernel of the contravariant form [Formula: see text], and subsequently find the Hilbert series of the irreducible quotient [Formula: see text]. In the [Formula: see text] case, we give a complete description of the polynomials in [Formula: see text] when the characteristic [Formula: see text] and [Formula: see text] is transcendental over [Formula: see text], and compute the Hilbert series of the irreducible quotient [Formula: see text]. In doing so, we prove a conjecture due to Etingof and Rains completely for [Formula: see text], and also for any [Formula: see text] and [Formula: see text]. Furthermore, for [Formula: see text], we prove a simple criterion to determine whether a given polynomial [Formula: see text] lies in [Formula: see text] for all [Formula: see text] with [Formula: see text] and [Formula: see text] fixed.

scholarly journals Evaluation of the MERIS aerosol product over land with AERONET

2008 ◽  
Vol 8 (1) ◽  
pp. 3721-3759 ◽  
Author(s):  
J. Vidot ◽  
R. Santer ◽  
O. Aznay
Keyword(s):  
Optical Properties ◽  
Surface Reflectance ◽  
Aerosol Optical Properties ◽  
Simple Criterion ◽  
Imaging Spectrometer ◽  
Inherent Optical Properties ◽  
Look Up Table ◽  
Medium Resolution ◽  
Reflectance Model ◽  
Resolution Imaging

Abstract. The Medium Resolution Imaging Spectrometer (MERIS) launched in February 2002 on-board the ENVISAT spacecraft is making global observations of top-of-atmosphere (TOA) radiances. Aerosol optical properties are retrieved over land using Look-Up Table (LUT) based algorithm and surface reflectances in the blue and the red spectral regions. We compared instantaneous aerosol optical thicknesses retrieved by MERIS in the blue and the red at locations containing sites within the Aerosol Robotic Network (AERONET). Between 2002 and 2005, a set of 500 MERIS images were used in this study. The result shows that, over land, MERIS aerosol optical thicknesses are well retrieved in the blue and poorly retrieved in the red, leading to an underestimation of the Angstrom coefficient. Correlations are improved by applying a simple criterion to avoid scenes probably contaminated by thin clouds. To investigate the weakness of the MERIS algorithm, ground-based radiometer measurements have been used in order to retrieve new aerosol models, based on their Inherent Optical Properties (IOP). These new aerosol models slightly improve the correlation, but the main problem of the MERIS aerosol product over land can be attributed to the surface reflectance model in the red.

scholarly journals A simple criterion to design optimal non-pharmaceutical interventions for mitigating epidemic outbreaks

2021 ◽  
Vol 18 (178) ◽  
Author(s):  
Marco Tulio Angulo ◽  
Fernando Castaños ◽  
Rodrigo Moreno-Morton ◽  
Jorge X. Velasco-Hernández ◽  
Jaime A. Moreno
Keyword(s):  
Disease Transmission ◽  
Reproduction Number ◽  
Contact Rate ◽  
Simple Criterion ◽  
Societal Costs ◽  
Public Events ◽  
Maximum Decrease ◽  
Minimal Reduction ◽  
Theoretical Results ◽  
Pharmaceutical Interventions

For mitigating the COVID-19 pandemic, much emphasis is made on implementing non-pharmaceutical interventions to keep the reproduction number below one. However, using that objective ignores that some of these interventions, like bans of public events or lockdowns, must be transitory and as short as possible because of their significant economic and societal costs. Here, we derive a simple and mathematically rigorous criterion for designing optimal transitory non-pharmaceutical interventions for mitigating epidemic outbreaks. We find that reducing the reproduction number below one is sufficient but not necessary. Instead, our criterion prescribes the required reduction in the reproduction number according to the desired maximum of disease prevalence and the maximum decrease of disease transmission that the interventions can achieve. We study the implications of our theoretical results for designing non-pharmaceutical interventions in 16 cities and regions during the COVID-19 pandemic. In particular, we estimate the minimal reduction of each region’s contact rate necessary to control the epidemic optimally. Our results contribute to establishing a rigorous methodology to design optimal non-pharmaceutical intervention policies for mitigating epidemic outbreaks.

scholarly journals Learning With Heterogeneous Misspecified Models: Characterization and Robustness

Econometrica ◽  
2021 ◽  
Vol 89 (6) ◽  
pp. 3025-3077 ◽  
Author(s):  
J. Aislinn Bohren ◽  
Daniel N. Hauser
Keyword(s):  
Learning Environments ◽  
Unified Framework ◽  
Simple Criterion ◽  
Partisan Bias ◽  
Misspecified Models ◽  
Long Run ◽  
The Face ◽  
Parametric Specification ◽  
The Impact ◽  
Source Of Information

This paper develops a general framework to study how misinterpreting information impacts learning. Our main result is a simple criterion to characterize long‐run beliefs based on the underlying form of misspecification. We present this characterization in the context of social learning, then highlight how it applies to other learning environments, including individual learning. A key contribution is that our characterization applies to settings with model heterogeneity and provides conditions for entrenched disagreement. Our characterization can be used to determine whether a representative agent approach is valid in the face of heterogeneity, study how differing levels of bias or unawareness of others' biases impact learning, and explore whether the impact of a bias is sensitive to parametric specification or the source of information. This unified framework synthesizes insights gleaned from previously studied forms of misspecification and provides novel insights in specific applications, as we demonstrate in settings with partisan bias, overreaction, naive learning, and level‐k reasoning.

On the braid index of links with nested diagrams

1992 ◽  
Vol 111 (2) ◽  
pp. 273-281 ◽  
Author(s):  
D. A. Chalcraft
Keyword(s):  
Lower Bound ◽  
Large Class ◽  
Upper Bound ◽  
Simple Criterion ◽  
Braid Index

AbstractThe number of Seifert circuits in a diagram of a link is well known 9 to be an upper bound for the braid index of the link. The -breadth of the so-called P-polynomial 3 of the link is known 5, 2 to give a lower bound. In this paper we consider a large class of links diagrams, including all diagrams where the interior of every Seifert circuit is empty. We show that either these bounds coincide, or else the upper bound is not sharp, and we obtain a very simple criterion for distinguishing these cases.

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