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Show Results For
- All HBS Web
(1,958)
- People (5)
- News (539)
- Research (994)
- Events (6)
- Multimedia (15)
- Faculty Publications (527)
- Article
Asymptotic Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions
By: Daniel M. Kane and Scott Duke Kominers
For relatively prime positive integers and r, we consider the least common multiple L_n:=\mathop{\textrm{lcm}}(u_0,u_1,\dots, u_n) of the finite arithmetic progression \{u_k:=u_0+kr\}_{k=0}^n. We derive new lower bounds on L_n that improve upon those obtained... View Details
Keywords: Mathematical Methods
Kane, Daniel M., and Scott Duke Kominers. "Asymptotic Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions." Canadian Mathematical Bulletin 57, no. 3 (September 2014): 551–561.
- 06 Dec 2019
- News
Why Progress Bars Can Make You Feel Better
- 25 May 2018
- News
An Urgent Mission to Speed Progress Against Cancer
- October 2024
- Supplement
Vineyard Wind Starts Spinning (C): Recovery and Progress
By: Rosabeth Moss Kanter and Jacob A. Small
- 25 Mar 2022
- News
How to Make Progress on Your Long-Term Career Goals
- Article
A Note on the Progressivity of Optimal Public Expenditures
By: Jerry R. Green and Eytan Sheshinski
Green, Jerry R., and Eytan Sheshinski. "A Note on the Progressivity of Optimal Public Expenditures." Quarterly Journal of Economics 89, no. 1 (February 1975): 138–144.
- 19 Sep 2010
- News
How stop-and-go science funding puts the brakes on progress
- 29 Aug 2011
- News
The Progress Principle: Using Small Wins as Big Gains
- November 1988 (Revised March 1990)
- Case
Progressive Corp.: Coping with the Problem of Dual Career Parents (A)
By: Shoshana Zuboff
Zuboff, Shoshana. "Progressive Corp.: Coping with the Problem of Dual Career Parents (A)." Harvard Business School Case 489-031, November 1988. (Revised March 1990.)
- October 2024
- Teaching Note
Vineyard Wind Starts Spinning (B): Breakdown and (C): Recovery and Progress
By: Rosabeth Moss Kanter and Jacob A. Small
- 09 Apr 2015
- News
Major economies trail Norway in social progress index - researchers
- March 2010
- Article
Further Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions
By: Shaofang Hong and Scott Duke Kominers
For relatively prime positive integers u_0 and r, we consider the arithmetic progression {u_k := u_0+k*r} (0 <= k <= n). Define L_n := lcm{u_0,u_1,...,u_n} and let a >= 2 be any integer. In this paper, we show that, for integers alpha,r >= a and n >=... View Details
Keywords: Mathematical Methods
Hong, Shaofang, and Scott Duke Kominers. "Further Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions." Proceedings of the American Mathematical Society 138, no. 3 (March 2010): 809–813.
- Forthcoming
- Article
Sixty Years of the Voting Rights Act: Progress and Pitfalls
By: Andrea Bernini, Giovanni Facchini, Marco Tabellini and Cecilia Testa
We review the literature on the effects of the 1965 Voting Rights Act (VRA), which
removed formal restrictions to Black political participation. After a brief description of
racial discrimination suffered by Black Americans since Reconstruction, we introduce
the... View Details
Keywords: Prejudice and Bias; Equality and Inequality; Race; Political Elections; Voting; Policy; Outcome or Result; Government Legislation
Bernini, Andrea, Giovanni Facchini, Marco Tabellini, and Cecilia Testa. "Sixty Years of the Voting Rights Act: Progress and Pitfalls." Oxford Review of Economic Policy (forthcoming).
- January 1992
- Article
Engines of Progress V: New England Electric Systems NEES Energy
By: R. M. Kanter, G. Quinn and J. North
Kanter, R. M., G. Quinn, and J. North. "Engines of Progress V: New England Electric Systems NEES Energy." Journal of Business Venturing 7 (January 1992): 73–89.
- 19 Mar 2012
- News
It Pays to Be Happy: The Progress Principle at Work
- August 1997 (Revised September 1997)
- Case
Hewlett-Packard's Santa Rosa Systems Division (A4): Progress on a Journey
By: Michael Beer and Gregory C. Rogers
Supplements the (A) case. View Details
Keywords: Information Technology Industry
Beer, Michael, and Gregory C. Rogers. "Hewlett-Packard's Santa Rosa Systems Division (A4): Progress on a Journey." Harvard Business School Case 498-015, August 1997. (Revised September 1997.)
- 1996
- Article
Technical Progress and Co-Invention in Computing and in the Use of Computers
By: Timothy Bresnahan and Shane Greenstein
Bresnahan, Timothy, and Shane Greenstein. "Technical Progress and Co-Invention in Computing and in the Use of Computers." Brookings Papers on Economic Activity. Microeconomics (1996): 1–78.