It played a major role in the second proof of the Index Theorem ( circa 1962 ).

* Rafe Mazzeo: The Atiyah – Singer Index Theorem: What it is and why you should care.

* A. J. Wassermann, Lecture notes on the Atiyah – Singer Index Theorem

An extremely far-reaching generalization of the Gauss – Bonnet Theorem is the Atiyah – Singer Index Theorem.

Since 2006 situation improved very rapidly and by 2011 Poland's Corruption Perceptions Index places it as only 10th most corrupt of 27 EU states, or 8th most corrupt of 12 new EU member states.

It was frequently reprinted, and the insertion of the Italian translation in the Index did not prevent its circulation even in the papal states.

The minimum Selection Index for recognition as a Semifinalist is determined by selection unit ( 50 states, three other geographic units, and a number of boarding school regions ) and is set by the NMSC in each state at whatever score yields about the 99th percentile.

Includes water supply forecasts, reservoirs, and and the Surface Water Supply Index ( SWSI ) for Alaska and other Western states.

Global Competitiveness Index ( 2008-2009 ): competitiveness is an important determinant for the well-being of states in an international trade environment.

On the other hand, moving beyond economic interdependence to the issue of economic freedom within states, Erik Gartzke has found empirical evidence that economic freedom ( as measured by the Fraser Institute Economic Freedom Index ) is about fifty times more effective than democracy in reducing violent conflict.

Florida and others have found a strong correlation between those cities and states that provide a more tolerant atmosphere toward culturally unconventional people, such as gays, artists, and musicians ( exemplified by Florida's " Gay Index " and " Bohemian Index " developed in The Rise of the Creative Class ), and the numbers of Creative Class workers that live and move there ( 2002 ).

Although directly equivalent to the Equivalent National Tertiary Entrance Rank ( ENTER ) in Victoria, and the Universities Admission Index ( UAI ) in New South Wales and the Australian Capital Territory, the terms ENTER and UAI were only used in their respective states or territories.

Hoover's also publishes analytical features through its Hoover's Index pages, and its Bizmology and BIZ blogs.

If, at any time during the assignment pass, the compiler finds that there are no more index words available for assignment, the warning message `` No More Index Words Available '' will be placed in the object program listing, the table will be altered to show that index words 1 through 96 are available, and the assignment will continue as before.

The Barker index is published for the Barker Index Committee by W. Heffer & Sons, Ltd., 4 Petty Cury, Cambridge, England.

The Armenian economy's competitiveness is low and stagnating according to the Global Competitiveness Index, in which Armenia's ranking slipped from 80th out of 132 countries in 2006-2007 index to 93rd out of 131 countries in the 2007-2008 index ( just below Libya, Namibia, Georgia, Serbia and Pakistan ).

The world's largest derivatives exchanges ( by number of transactions ) are the Korea Exchange ( which lists KOSPI Index Futures & Options ), Eurex ( which lists a wide range of European products such as interest rate & index products ), and CME Group ( made up of the 2007 merger of the Chicago Mercantile Exchange and the Chicago Board of Trade and the 2008 acquisition of the New York Mercantile Exchange ).

FamilySearch also includes an 1880 United States federal census index, an 1881 British census index, an 1881 Canadian census index, and the U. S. Social Security Death Index, as well as research guides and genealogical word lists.

Hong Kong has remained as the world's freest economy, according to Index of Economic Freedom since the inception of the index in 1995.

Hong Kong has ranked as the world's freest economy in The Wall Street Journal and Heritage Foundation's Index of Economic Freedom for 17 consecutive years, since the inception of the index in 1995.

* Index mapping, mapping of raw data, used directly as in array index, for an array

However, its exchange-traded fund tracks the large-cap NASDAQ-100 index, which was introduced in 1985 alongside the NASDAQ 100 Financial Index.

A Loring Ward report in Advisor Perspectives showed how international diversification worked over the 10-year period from 2000 – 2010, with the Morgan Stanley Capital Index for emerging markets generating ten-year returns of 154 percent balancing the blue-chip S & P 500 index, which lost 9. 1 percent over the same period – a historically rare event.

Clement XIII placed the Encyclopédie of D ' Alembert and Diderot on the Index, but this index was not as effective as it used to be in the previous century.

; Index error: This occurs when the index and horizon mirrors are not parallel to each other when the index arm is set to zero.

* June 14 – The Vatican abolishes the Index Librorum Prohibitorum ( index of banned books ).

** Baltic Dry Index, a daily shipping index published by the Baltic Exchange

A chief measure of price inflation is the inflation rate, the annualized percentage change in a general price index ( normally the Consumer Price Index ) over time.

Volemak urges his four sons to go back to Basilica and retrieve the Index ( a tool or index used to retrieve information from the Oversoul ).

** Dow Jones – AIG Commodity Index, a commodity price index

Some investors, preferring to dedicate themselves to higher-rated and less-risky investments, use an index that only includes BB-rated and B-rated securities, such as the Merrill Lynch Global High Yield BB-B Rated Index ( HW40 ).

Mexico City has recently been integrating rapidly, doing much better than many cities in a sample conducted by the Intercultural Cities Index ( being the only non-European city, alongside Montreal, on the index ).

* Quality-of-life Index, a different index calculated in 2005

The results of this work was the report A Public Trust at Risk: The Heritage Health Index Report on the State of America's Collections, which was published in December 2005 and concluded that immediate action is needed to prevent the loss of 190 million artifacts that are in need of conservation treatment.

The complete text of all the documents are online and searchable ; The Index is also online Archived September 28, 2010.

In terms of the 2008 Environmental Performance Index ranking, Costa Rica is 5th in the world, up from the 15th place in 2006.

Their standard of living is reflected in the country's " very high " Human Development Index, and Cyprus is ranked 23rd in the world in terms of the Quality-of-life Index.

The Rayleigh Criterion is the basis for analysis of thermoacoustic combustion instability and is evaluated using the Rayleigh Index over one cycle of instability

When the heat release oscillations are in phase with the pressure oscillations, the Rayleigh Index is positive and the magnitude of the thermo acoustic instability is maximised.

On the other hand, if the Rayleigh Index is negative, then thermoacoustic damping occurs.

Today, Chicago is listed as an alpha + global city by the Globalization and World Cities Research Network, and ranks seventh in the world in the 2012 Global Cities Index.

Cell Cycle is abstracted and indexed in Medline / PubMed and the Science Citation Index Expanded.

The strength of the Southern Oscillation is measured by the Southern Oscillation Index ( SOI ).

The Irish health system, being administered centrally by the Health Service Executive, is seen to be poor by comparison to other countries in Europe, ranking outside expected levels at 25th according to the Euro Health Consumer Index 2006.

In 1986 they introduced the Index of Economic Freedom, which is based on some fifty variables.

Despite political corruption and regional instability, Kyrgyzstan is ranked 44th on the Ease of doing Business Index.

Latvia is ranked the 21st in the world by the Ease of Doing Business Index prepared by the World Bank Group, According to the Human Development Report 2011, Latvia belongs to the group of very high human development countries.

Moreover, human capital is underdeveloped — Nigeria ranked 151 out of 177 countries in the United Nations Development Index in 2004 — and non-energy-related infrastructure is inadequate.

In ecology the population of a certain species in a certain area is estimated using the Lincoln Index.

: Indices: These are quite apart from the above, their use is for mathematical formalism, see Index notation.