IMPORTANCE OF ZAK TRANSFORMS FOR HARMONIC ANALYSIS ...

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REVISTA DE LA UNION MATEMATICA ARGENTINA Vol. 52, No. 2, 2011, 105–113 IMPORTANCE OF ZAK TRANSFORMS FOR HARMONIC ANALYSIS EDWARD N. WILSON Abstract. In engineering and applied mathematics, Zak transforms have been effectively used for over 50 years in various applied settings. As Gelfand observed in a 1950 paper, the variable coefficient Fourier series ideas articulated in Andre Weil's famous book on integration lead to an exceedingly elementary proof of the Plancherel Theorem for LCA groups.

• modulation representatioin φ
• fg
• zak transform z z
• lca groups
• l2 norms
• abelian group representations
• abelian group
• inverse
• fourier transform
• l2

Sujets

• Exposé
• Classics
• Cy'clic
• Wilson
• Analysis
• Saint Louis
• Inverse
• Fourier
• Representations
• Eigenfunction

Informations

• Publié par: vien0
• Nombre de lectures: 8
• Langue: English

Extrait

New Jersey Student and Parent Consumer Information Act Kean University 20102011

http://www.kean.edu/KU/Undergraduate

Link to New Jersey Commission of Higher Education  Student & Parent Consumer Information Act http://www.nj.gov/highereducation/ConsumerInfo.htm

NJ Student and Parent Consumer Information Act Graduation Rates (P.L. 2009 Chapter 197 2. a. (1) thru (3))

Fall 2004 FirstTime FullTime DegreeSeeking Undergraduates

Cohort Number Kean University

(#)

Total 1254

(1)

Men 563

Women 691

White 594

Graduated after 4 Years (2)

Graduated after 4 Years Total Men Women White Kean University (#) 210 72 138 110 (%) 17% 13% 20% 19% * Other includes American Indian or Alaskan Native, nonresident aliens, race unreported or unknown

Graduated after 6 Years Kean University

(#) (%)

(1)

Total 593 47%

Graduated after 6 Years (2)

Men 218 39%

Women 375 54%

White 304 51%

Black 277

Black 35 13%

Black 97 35%

Hispanic 240

Hispanic 37 15%

Hispanic 115 48%

Asian 95

Asian 19 20%

Asian 52 55%

Other* 48

Other* 9 19%

Other* 25 52%

u en Athletes

(3) Student Athletes

(3) Student Athletes

on Athletes

Non Athletes

Non Athletes

Kean University

NJ Student and Parent Consumer Information Act Transfer Rates (P.L. 2009 Chapter 197 2. a. (5), (6))

Fall 2009 FirstTime FullTime DegreeSeeking Undergraduates Transferred Out As of Fall 2010 (12/31/2010)

Firsttime FT Freshmen # 1518

(5)

# 162

Transferred out % 11%

(6) Overview of Transfer Institutions InState OutofState # # 132 30

NJ Student and Parent Consumer Information Act Costs (P.L. 2009 Chapter 197 2. a. (7), (10), (11))

Total Cost

(7) Total Cost for AY 20101011 Commuter Live Resident Live w/Parents Average Kean University Independently Tuition & Fees 9815 9815 9815 9815 Room & Board 12950 2446 16500 9473 Books & Supplies 1800 1800 1800 1800 Transportation 2293 2293 2293 Other Expenses 2082 2082 2082 2082 TOTA 26647 18436 32490 25463 NOTE: All Costs and projected costs are for FullTime New Jersey Resident Students

Projected Cost

Total Projected Cost for Fall 2010 Incoming Freshman (10) Graduates after 4 years (11) Graduates after 6 years Commuter Commuter Live Live Resident Live w/Parents Average Resident Live w/Parents Independentl Independentl Kean University119,71081,398 151,062116,230 194,471130,628 251,467 NOTE: All Costs and projected costs are for FullTime New Jersey Resident Students

Average 191,048

NJ Student and Parent Consumer Information Act Financial Assistance (P.L. 2009 Chapter 197 2. a. (8)

Institutional Financial Assistance Programs

(8) Institutional Financial Assistance Programs (AY 201011)

Senior Public Institution Kean University Kean University Kean University Kean University Kean University Kean University Kean University Kean University

Institutional Financial Aid programs William Livingston (Freshman Merit) Kean (Freshman Merit) Trustee (Freshman Merit) Presidential (Freshman Merit) Academic Merit (Freshman Merit) NJCSTM (Distinguished Freshman) College of Visual & Performing Arts distinguished Freshman) KU Foundation Scholarships (over 300 competitive annual awards)

* Athletes are only those students at NCAA Division 1 institutions who receive athletic aid.

Available To Athletes* NonAthletes es/No es/No Yes Yes Yes Yes Yes Yes Yes Yes

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(9) Students who receive financial assistance Fall 2010 Undergraduate Students Total # Students Kean University Athletes* (NCAA) NonAthletes 13052

Financial Assistance

# Receiving Asst.

9240

% Receiving Asst.

71%

* Athletes are only those students at NCAA Division 1 institutions who receive athletic aid. + NonInstitutional Aid includes private, state, and federal student aid other than athletic aid.

Average Amount Non Institutional Institutional Aid Aid+

2736

12136

Athletic Aid

NA

NJ Student and Parent Consumer Information Act Financial Assistance (P.L. 2009 Chapter 197 2. a. (12) thru (14))

Student Loan Indebtedness 2004 FirstTime FullTime Freshmen Cohort

(12) Average Student Loan Indebtedness Graduating in 4 years Kean University

(13) Average Student Loan Indebtedness Graduating in 6 years Kean University

(14) Average Student Loan Indebtedness Withdrawing after 1 year Kean University

Resident Student when admitted

 21,303

Resident Student when admitted

 29,409

Resident Student when admitted

 3,405

Commuting Student when admitted

 8,464

Commuting Student when admitted

 20,611

Commuting Student when admitted

 1,305

NJ Student and Parent Consumer Information Act Faculty (P.L. 2009 Chapter 197 2. a. (15) thru (16))

(15) Types of Faculty

Kean University

(16) Course Sections Taught by each type of faculty

Kean University

# %

# %

Fall 2010 Faculty

Total Faculty

1367 100%

Total # of Sections

3141 100%

Fulltime Fulltime Non Tenured/ Tenure Track Tenure Track Professors Professors

331 24.2%

12 0.9%

Parttime Faculty

1024 74.9%

# of Course Sections Taught by

Fulltime Fulltime Non Tenured/ Tenure Track Tenure Track Professors Professors

1273 40.5%

50 1.6%

Parttime Faculty

1603 51.0%

Other (TA's, Staff, etc)

Other (TA's, Staff, etc)

215 6.8%