The Real Spectrum of Higher Level of a Commutative Ring

1992 ◽  
Vol 44 (3) ◽  
pp. 449-462 ◽  
Author(s):  
Susan Maureen Barton
Keyword(s):  
Commutative Ring ◽  
Real Spectrum ◽  
The Real ◽  
New Type

AbstractThe following paper defines a new type of ordering of higher level on a commutative ring. This definition allows the set of all orderings of level n to be given a topology which we show is consistent with the topology of the real spectrum.

scholarly journals EXPERIMENTAL ONLINE CASE STUDY FOR A BREAKTHROUGH IN STUDENT ENGAGEMENT: FOCUS GROUP RESULTS

2019 ◽  
Vol 8 (3) ◽  
Author(s):  
James Theroux ◽  
Cari Carpenter ◽  
Clare Kilbane
Keyword(s):  
Student Engagement ◽  
Focus Group ◽  
Real Time ◽  
Group Discussion ◽  
Full Time ◽  
The Real ◽  
Building Process ◽  
New Type ◽  
The Subject

A new type of case study, called the real-time case (RTC), was produced in the fall of 2001 and distributed via the Internet to business classes at four universities in the US and Canada. The real-time case presented the story of one company's growth and development throughout a 14-week semester. A case writer stationed full-time at the subject company published case installments weekly on the Web, allowing students to view the company-building process as it happened. The 14-week coverage of RTC enabled students to study the subject company in unprecedented depth and detail. RTC's real-time interactivity allowed students to share their analyses and best thinking with the company leadership during the company’s decision-making process.A major objective in producing the case was to heighten student engagement with the case material. To evaluate whether this objective was achieved, a survey and a focus group discussion were conducted with one of the participating MBA classes. Results from the survey and the focus group showed a high degree of engagement, plus many other benefits from the new type of case study.

scholarly journals Pseudo-hermitian random matrix theory: a review

2021 ◽  
Vol 2038 (1) ◽  
pp. 012009
Author(s):  
Joshua Feinberg ◽  
Roman Riser
Keyword(s):  
Real Axis ◽  
Complex Plane ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Complex Conjugate ◽  
Indefinite Metric ◽  
The Real ◽  
New Type ◽  
Diagrammatic Method

Abstract We review our recent results on pseudo-hermitian random matrix theory which were hitherto presented in various conferences and talks. (Detailed accounts of our work will appear soon in separate publications.) Following an introduction of this new type of random matrices, we focus on two specific models of matrices which are pseudo-hermitian with respect to a given indefinite metric B. Eigenvalues of pseudo-hermitian matrices are either real, or come in complex-conjugate pairs. The diagrammatic method is applied to deriving explicit analytical expressions for the density of eigenvalues in the complex plane and on the real axis, in the large-N, planar limit. In one of the models we discuss, the metric B depends on a certain real parameter t. As t varies, the model exhibits various ‘phase transitions’ associated with eigenvalues flowing from the complex plane onto the real axis, causing disjoint eigenvalue support intervals to merge. Our analytical results agree well with presented numerical simulations.

scholarly journals Real Tropicalization and Analytification of Semialgebraic Sets

2020 ◽  
Author(s):  
Philipp Jell ◽  
Claus Scheiderer ◽  
Josephine Yu
Keyword(s):  
Inverse Limit ◽  
Point Of View ◽  
General Point ◽  
Real Spectrum ◽  
Closed Field ◽  
Topological Properties ◽  
Absolute Value ◽  
The Real ◽  
Semialgebraic Set ◽  
Refined Version

Abstract Let $K$ be a real closed field with a nontrivial non-archimedean absolute value. We study a refined version of the tropicalization map, which we call real tropicalization map, that takes into account the signs on $K$. We study images of semialgebraic subsets of $K^n$ under this map from a general point of view. For a semialgebraic set $S \subseteq K^n$ we define a space $S_r^{{\operatorname{an}}}$ called the real analytification, which we show to be homeomorphic to the inverse limit of all real tropicalizations of $S$. We prove a real analogue of the tropical fundamental theorem and show that the tropicalization of any semialgebraic set is described by tropicalization of finitely many inequalities, which are valid on the semialgebraic set. We also study the topological properties of real analytification and tropicalization. If $X$ is an algebraic variety, we show that $X_r^{{\operatorname{an}}}$ can be canonically embedded into the real spectrum $X_r$ of $X$, and we study its relation with the Berkovich analytification of $X$.

scholarly journals Nonselfadjoint correct restrictions and extensions with the real spectrum

2014 ◽  
Author(s):  
Bazarkhan Nuraldinovich Biyarov ◽  
Madi Raikhan
Keyword(s):  
Real Spectrum ◽  
The Real

Design of Automobile Driving Trainer Simulated Gearbox

2013 ◽  
Vol 312 ◽  
pp. 66-68
Author(s):  
Su Jun Luo ◽  
Xue Ling Zhang ◽  
Shu Feng Chai
Keyword(s):  
Automobile Driving ◽  
Practical Application ◽  
Manual Gearbox ◽  
The Real ◽  
New Type

According to the work principle of the automobile manual gearbox, the author has designed a new type of automobile driving trainer simulated gearbox. The principle of the simulation of various organization compositions of gearbox and the simulation of the feeling to the real organization function and the operation dynamics are introduced, and the practical application effect of the simulated gearbox has been summarized at last.

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