Research on Formal Degree Evaluation and Analysis for Domain Software Based on Evidence

2016 ◽  
Vol 25 (5) ◽  
pp. 793-800
Author(s):  
Tie Bao ◽  
Shufen Liu ◽  
Lu Han
Keyword(s):  
Formal Degree

Generalized Formal Degree

2011 ◽  
Vol 2012 (2) ◽  
pp. 239-298 ◽  
Author(s):  
Yannan Qiu
Keyword(s):  
Formal Degree

scholarly journals ON A CERTAIN LOCAL IDENTITY FOR LAPID–MAO'S CONJECTURE AND FORMAL DEGREE CONJECTURE : EVEN UNITARY GROUP CASE

2021 ◽  
pp. 1-55
Author(s):  
Kazuki Morimoto
Keyword(s):  
Explicit Formula ◽  
Unitary Group ◽  
Fourier Coefficients ◽  
Automorphic Forms ◽  
Unitary Groups ◽  
Reductive Groups ◽  
Local Identity ◽  
Metaplectic Groups ◽  
Group Case ◽  
Formal Degree

Abstract Lapid and Mao formulated a conjecture on an explicit formula of Whittaker–Fourier coefficients of automorphic forms on quasi-split reductive groups and metaplectic groups as an analogue of the Ichino–Ikeda conjecture. They also showed that this conjecture is reduced to a certain local identity in the case of unitary groups. In this article, we study the even unitary-group case. Indeed, we prove this local identity over p-adic fields. Further, we prove an equivalence between this local identity and a refined formal degree conjecture over any local field of characteristic zero. As a consequence, we prove a refined formal degree conjecture over p-adic fields and get an explicit formula of Whittaker–Fourier coefficients under certain assumptions.

A History of Distance Education

2011 ◽  
pp. 1-12
Author(s):  
Wendy Rickman ◽  
Cheryl Wiedmaier
Keyword(s):  
Professional Development ◽  
Distance Education ◽  
Educational Institutions ◽  
Educational Services ◽  
Physical Separation ◽  
For Profit ◽  
Formal Degree ◽  
Postal Services ◽  
History Of ◽  
Secondary Mode

Flash-forward to today’s world of instant-access in a technology driven society, where distance education has grown in viability and become a business. Whether provided via a traditional, land-based university or college to earn a formal degree, to complete professional development, or to seek additional certification, or by a for-profit organization or corporation to train their employees and advance their workers’ skills, people can access a well-developed range of educational services through distance education to better their lives and livelihoods regardless of the physical separation between themselves and the sponsoring institution. The main difference between distance education’s beginnings and today’s educational services is the medium used to conduct learning. The postal services may still be used as a secondary mode of communication and print is still a constant technologic tool, but the expanding success of distance education can be attributed to providing education that 1) spans great distances between citizens and educational institutions, both geographically and socio-economically; 2) quenches the thirst for education; and 3) utilizes the rapid advancement of technology (Casey, 2008).

A Multi-Billion Dollar Growth Industry

1998 ◽  
Vol 7 (1) ◽  
pp. 13-14
Author(s):  
Samantha Johnsen
Keyword(s):  
Hospitality Industry ◽  
Business Sector ◽  
Senior Managers ◽  
Formal Degree ◽  
The Future ◽  
Growth Industry ◽  
Tourism And Hospitality Industry ◽  
Tourism And Hospitality

The tourism and hospitality industry is the world's fastest growing business sector and it has an increasing need for people with formal degree qualifications to be effective senior managers and executives of the future. This case study describes the opportunities in this sector and outlines the facilities and courses of the Australian International Hotel School.

Negative-existentially complete structures and definability in free extensions

1976 ◽  
Vol 41 (1) ◽  
pp. 95-108 ◽  
Author(s):  
Volker Weispfenning
Keyword(s):  
Commutative Ring ◽  
Polynomial Ring ◽  
Wide Class ◽  
First Order ◽  
Formal Degree ◽  
Atomic Relation

Let R be a commutative ring with 1 and R[X1, …, Xn] the polynomial ring in n variables over R. Then for any relation f(X) = 0 in R[X] there exists a conjunction of equations φf such that f(X) = 0 holds in R[X] iff φf holds in R; φf is of course the formula saying that all the coefficients of f(X) vanish. Moreover, φf is independent of R and formed uniformly for all polynomials f up to a given formal degree. In this paper we investigate first order theories T for which a similar phenomenon holds. More precisely, we let TAH be the universal Horn part of a theory T and look at free extensions of models of T in the class of models of TAH. We ask whether an atomic relation t1(X, a) = t2(X, a) or R(t1(X, a), …, tn(X, a)) in can be equivalently expressed by a finite or infinitary formula φ(a) in , such that φ(y) depends only on ti{X, y) and not on or a1, …, am ∈ A.We will show that for a wide class of theories T “defining formulas” φ(y) in this sense exist and can be taken as infinite disjunctions of positive existential formulas.

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