Frobenius closure and prime characteristic singularities

2020 ◽  
Author(s):  
◽  
Kyle Logan Maddox
Keyword(s):  
Local Ring ◽  
Local Cohomology ◽  
Sufficient Condition ◽  
Zariski Topology ◽  
Prime Characteristic ◽  
Joint Work ◽  
University Of Missouri ◽  
Mild Conditions ◽  
Flat Maps ◽  
The University

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] This dissertation outlines several results about prime characteristic singularities for which the nilpotent part under the induced Frobenius action on local cohomology is either finite colength or the entire module, collectively referred to here as nilpotent singularities. First, we establish a sufficient condition for the finiteness of the Frobenius test exponent for a local ring and apply it to conclude that nilpotent singularities have finite Frobenius test exponent. In joint work with Jennifer Kenkel, Thomas Polstra, and Austyn Simpson, we show that under mild conditions nilpotent singularities descend and ascend along faithfully flat maps. Consequently, we then prove that the loci of primes which are weakly F-nilpotent and F-nilpotent are open in the Zariski topology for rings which are either F-finite or essentially of fiiite type over an excellent local ring.

scholarly journals The lower semicontinuity of the Frobenius splitting numbers

2010 ◽  
Vol 150 (1) ◽  
pp. 35-46 ◽  
Author(s):  
FLORIAN ENESCU ◽  
YONGWEI YAO
Keyword(s):  
Local Ring ◽  
Lower Semicontinuity ◽  
Lower Semicontinuous ◽  
Prime Characteristic ◽  
Frobenius Splitting ◽  
Mild Conditions ◽  
Splitting Numbers

AbstractWe show that, under mild conditions, the (normalized) Frobenius splitting numbers of a local ring of prime characteristic are lower semicontinuous.

scholarly journals Notes on linkage of modules

2019 ◽  
Vol 62 (4) ◽  
pp. 1045-1062
Author(s):  
Arash Sadeghi
Keyword(s):  
Local Ring ◽  
Local Cohomology ◽  
Mild Conditions ◽  
Local Cohomology Modules ◽  
Cohomology Modules

AbstractLet R be a Cohen–Macaulay local ring. It is shown that under some mild conditions, the Cohen–Macaulay property is preserved under linkage. We also study the connection of the (Sn) locus of a horizontally linked module and the attached primes of certain local cohomology modules of its linked module.

scholarly journals On the dimension and multiplicity of local cohomology modules

2002 ◽  
Vol 167 ◽  
pp. 217-233 ◽  
Author(s):  
Markus P. Brodmann ◽  
Rodney Y. Sharp
Keyword(s):  
Local Ring ◽  
Maximal Ideal ◽  
Local Cohomology ◽  
Local Rings ◽  
Zariski Topology ◽  
Finitely Generated Module ◽  
Local Cohomology Modules ◽  
Matlis Duality ◽  
Gorenstein Local Ring ◽  
Cohomology Modules

AbstractThis paper is concerned with a finitely generated module M over a (commutative Noetherian) local ring R. In the case when R is a homomorphic image of a Gorenstein local ring, one can use the well-known associativity formula for multiplicities, together with local duality and Matlis duality, to produce analogous associativity formulae for the local cohomology modules of M with respect to the maximal ideal. The main purpose of this paper is to show that these formulae also hold in the case when R is universally catenary and such that all its formal fibres are Cohen–Macaulay.These formulae involve certain subsets of the spectrum of R called the pseudosupports of M; these pseudo-supports are closed in the Zariski topology when R is universally catenary and has the property that all its formal fibres are Cohen–Macaulay. However, examples are provided to show that, in general, these pseudo-supports need not be closed. We are able to conclude that the above-mentioned associativity formulae for local cohomology modules do not hold over all local rings.

scholarly journals Epsilon multiplicity for graded algebras

2020 ◽  
Author(s):  
◽  
Suprajo Das
Keyword(s):  
Local Ring ◽  
Graded Algebras ◽  
University Of Missouri ◽  
Special Cases ◽  
The University

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] The notion of epsilon multiplicity was originally defined by Ulrich and Validashti as a limsup and they used it to detect integral dependence of modules. It is important to know if it can be realized as a limit. The purpose of our thesis is to show that the relative epsilon multiplicity of reduced standard graded algebras over an excellent local ring exists as a limit. We also obtain some important special cases of Cutkosky's results concerning epsilon multiplicity, as corollaries of our main theorem.

TEM study of boron additions to cobalt aluminide

1988 ◽  
Vol 46 ◽  
pp. 546-547
Author(s):  
Gerald B. Feldewerth
Keyword(s):  
High Temperature ◽  
Turbine Engines ◽  
Major Drawback ◽  
University Of Missouri ◽  
Specific Strength ◽  
Aerospace Applications ◽  
Wide Range ◽  
Ordered Alloys ◽  
The University ◽  
Very High

In recent years an increasing emphasis has been placed on the study of high temperature intermetallic compounds for possible aerospace applications. One group of interest is the B2 aiuminides. This group of intermetaliics has a very high melting temperature, good high temperature, and excellent specific strength. These qualities make it a candidate for applications such as turbine engines. The B2 aiuminides exist over a wide range of compositions and also have a large solubility for third element substitutional additions, which may allow alloying additions to overcome their major drawback, their brittle nature.One B2 aluminide currently being studied is cobalt aluminide. Optical microscopy of CoAl alloys produced at the University of Missouri-Rolla showed a dramatic decrease in the grain size which affects the yield strength and flow stress of long range ordered alloys, and a change in the grain shape with the addition of 0.5 % boron.

MARS — Its Tenth Anniversary of Operation and its Future

1980 ◽  
Vol 19 (03) ◽  
pp. 125-132
Author(s):  
G. S. Lodwick ◽  
C. R. Wickizer ◽  
E. Dickhaus
Keyword(s):  
Conceptual Development ◽  
Administrative Support ◽  
Final Section ◽  
Economic Benefits ◽  
Hospital Environment ◽  
Computer Scientist ◽  
University Of Missouri ◽  
Complete Bibliography ◽  
The University ◽  
Economic Considerations

The Missouri Automated Radiology System recently passed its tenth year of clinical operation at the University of Missouri. This article presents the views of a radiologist who has been instrumental in the conceptual development and administrative support of MARS for most of this period, an economist who evaluated MARS from 1972 to 1974 as part of her doctoral dissertation, and a computer scientist who has worked for two years in the development of a Standard MUMPS version of MARS. The first section provides a historical perspective. The second deals with economic considerations of the present MARS system, and suggests those improvements which offer the greatest economic benefits. The final section discusses the new approaches employed in the latest version of MARS, as well as areas for further application in the overall radiology and hospital environment. A complete bibliography on MARS is provided for further reading.

An Interactive Morphological Matrix Computational Design Tool: A Hybrid of Two Methods

2007 ◽  
Author(s):  
Cari R. Bryant ◽  
Matt Bohm ◽  
Robert B. Stone ◽  
Daniel A. McAdams
Keyword(s):  
Computational Design ◽  
Design Tool ◽  
Design Tools ◽  
Concept Generation ◽  
University Of Missouri ◽  
Generation Algorithm ◽  
Design Theories ◽  
The University ◽  
Matrix Generator

This paper builds on previous concept generation techniques explored at the University of Missouri - Rolla and presents an interactive concept generation tool aimed specifically at the early concept generation phase of the design process. Research into automated concept generation design theories led to the creation of two distinct design tools: an automated morphological search that presents a designer with a static matrix of solutions that solve the desired input functionality and a computational concept generation algorithm that presents a designer with a static list of compatible component chains that solve the desired input functionality. The merger of both the automated morphological matrix and concept generation algorithm yields an interactive concept generator that allows the user to select specific solution components while receiving instantaneous feedback on component compatibility. The research presented evaluates the conceptual results from the hybrid morphological matrix approach and compares interactively constructed solutions to those returned by the non-interactive automated morphological matrix generator using a dog food sample packet counter as a case study.

Beyond the border war : student civil rights activism at the University of Kansas and the University of Missouri, 1946-1954

2020 ◽  
Author(s):  
◽  
Mary Beth Brown
Keyword(s):  
World War Ii ◽  
Civil Rights ◽  
Race Relations ◽  
Student Activism ◽  
University Of Kansas ◽  
University Of Missouri ◽  
Effect Change ◽  
Student Activists ◽  
The University ◽  
The 19Th Century

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI-COLUMBIA AT REQUEST OF AUTHOR.] This dissertation examines post-World War II student civil rights activism at two Midwestern college campuses, the University of Missouri (MU) and the University of Kansas (KU). Missouri and Kansas have conflicting histories concerning race dating back to Bleeding Kansas and the history of race relations on the campuses of KU and MU. This history is especially complicated during the period between 1946 and 1954 because of heightened student activism that challenged racial injustices. Race relations on campus largely mirrored that of the state's political environment, with KU having integrated in the 19th century, whereas MU did not desegregate until 1950. However, the same did not apply to the success of student activists at each school where MU students found success fighting against discriminatory practices in Columbia, whereas local business leaders and the university administration stymied KU students. The dissertation examines the exchange of ideas and strategy among students, which occurred through athletics, debates, guest speakers, and various regional and national groups. In particular, the study argues that campus spaces, such as residential co-ops and student organizations, were deeply significant because they served as incubators of activism by offering students a place to talk about racial and social injustice and plan ways to challenge these inequalities and effect change on campus and in the broader community.

Sharp things, or the silver lines are not scars

2019 ◽  
Author(s):  
◽  
Teresa Milbrodt
Keyword(s):  
Financial Stability ◽  
Romantic Relationship ◽  
Insurance Coverage ◽  
Health Insurance Coverage ◽  
Stained Glass ◽  
University Of Missouri ◽  
Adjunct Instructor ◽  
Constant Change ◽  
Part Time ◽  
The University

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] This novel is the story of Tianne, a twenty-eight-year-old stained glass artist. She works two part-time jobs as a clerk at a stained glass supply store, and as an adjunct instructor at a community college. Her boyfriend Jeremiah is an academic adviser at the same college, but wants a career performing in comedy clubs. He uses a wheelchair due to spina bifida, and is cheerfully blunt that he could die from an undetected kidney infection. Tianne wrangles her own invisible disability, since endometriosis causes her to have awful cramps during her period that can keep her home from work. Tianne loves her jobs but worries about bills after her car breaks down. She envies Jeremiah's financial stability until he's fired for speaking his mind too many times to administration. Tianne fears for his health insurance coverage, while Jeremiah debates careers as a high school guidance counselor or touring comedy clubs. Throughout the book Tianne tries to chart a path though the instabilities of her body, Jeremiah's body, their career paths, and their romantic relationship, knowing that nothing is permanent. Hers is a story not of looking for stability, but coming to terms with instability, and finding spaces of adaptation to constant change.

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