Analytically, x can also be raised to an irrational power ( for positive values of x ); the analytic properties are analogous to when x is raised to rational powers, but the resulting curve is no longer algebraic, and cannot be analyzed via algebraic geometry.

Analytically, it is helpful to distinguish Russification, as a process of changing one's ethnic self-label or identity from a non-Russian ethnonym to Russian, from Russianization, the spread of the Russian language, culture, and people into non-Russian cultures and regions, distinct also from Sovietization or the imposition of institutional forms established by the Communist Party of the Soviet Union throughout the territory ruled by that party.

Analytically, the culture has been broken down into various stages or horizons.

# Analytically, when the mode ( s ) of the posterior distribution can be given in closed form.

I had come to New Orleans two years earlier after graduating college, partly because I loved the city and partly because there was quite a noted art colony there.

So the verdict was `` death at the hands of a person or persons unknown '', and the elite of the city, accepting Delphine's testimony, welcomed her and the doctor back into the fold.

It was to provide a safe and spacious crossing for these caravans, and also to make a pleasance for the city, that Shah Abbas 2, in about 1657 built, of sun-baked brick, tile, and stone, the present bridge.

Miriam had not yet goaded him into mentioning her directly, but one can feel the generalized anger in Wright's remarks to reporters when he was asked, one morning on arrival in Chicago, what he thought of the city as a whole.

That night a note written in Slocum's hand and dated from inside the captured city came to Sherman stating that the Twentieth Corps was in possession of Atlanta.

Samuel Gorton was born at Gorton, England, near the present city of Manchester, about 1592.

It was not until we had returned to the city to live, while I was still at Brown and Sharpe's, that I felt the full impact of evangelical Christianity.

It is remembered and has been commemorated by a bust in a park and a square in the city which was renamed Piazzo Lauro Di Bosis after the war.

The U.N.-chartered plane which was flying from the conference city of Ndola in Northern Rhodesia had been riddled with machinegun bullets last weekend and was newly repaired.

As we understand, this directive was given to all city and county employes.

The city was a center of manufacture, especially in textiles, and also because of the beauty of some of its surroundings, a residence for many owners of the great industries in north Alabama.

the rather pleasant white city was on the hill where the chief stores were.

For the old preacher who had been there twenty-five years was dead, and the city mourned him.

Port Jervis, basking in the foothills, was the city of God.

The city had recently given him a small salary, but it was not enough to supply even necessities.

The doctor sat down rather wearily, caressing the hen and remarking that the city was not the place for a poultry-loving man, but no sooner was the remark out than a knock at this door obliged him to cover the hen with his greatcoat once more.

But that year was different, for just as the city, in the form of my street clothes, had intruded upon my mountain nights, so an essential part of the summer gave promise of continuing into the fall: Jessica and I, about to be separated not by a mere footbridge or messhall kitchen but by the immense obstacle of residing in cruelly distant boroughs, had agreed to correspond.

From proud pool-owners to perpetual hosts and handymen was a short step -- no more than the change from city clothes to trunks.

It was reported to Welch's office that a thief in the city jail had attempted suicide.

The big factories which are relatively near the centers of our cities -- the rubber factories in Akron, Chrysler's Detroit plants, U.S. Steel's Pittsburgh works -- often began on these sites at a time when that was the edge of the city, yet close to transport ( river ), storage ( piers ) and power ( river ).

There were lights glinting in the city, too, even though it was now dark enough for a few stars to become visible.

Left alone while her husband was miles away in the city, the modern wife assumed more and more duties normally reserved for the male.

It ranks highly in terms of liveability, being listed in the Top 10 of The Economist's World's Most Liveable Cities index in 2010 and being ranked the most liveable city in Australia by the Property Council of Australia in 2011 and again in 2012.

In 2008, Athens was ranked the world's 32nd richest city by purchasing power < ref >

As of 2009 the city was ranked Europe's third and one of the world's most successful as a city brand.

At the same time, the city was ranked Europe's fourth best city for business and fastest improving European city, with growth improved by 17 % per year.

The city has been ranked as high as the second-best place to live in the United States by Money Magazine's annual list, but has not been ranked in the top 100 since 2006.

National Geographic Traveler ranked Columbus 11th on its historic destinations list in late 2008, describing the city as " authentic, unique, and unspoiled.

In 2011, the city was ranked 9th of major world cities on the Copenhagenize Index of Bicycle-Friendly Cities.

The historic centre of Florence attracts millions of tourists each year, and Euromonitor International ranked the city as the world's 72nd most visited in 2009, with 1, 685, 000 visitors.

Due to Florence's artistic and architectural heritage, it has been ranked by Forbes as one of the most beautiful cities in the world, and the city is noted for its history, culture, Renaissance art and architecture and monuments.

Florence is also an important city in Italian fashion, being ranked within the top fifty fashion capitals of the world ; furthermore, it is also a major national economic centre, being a tourist and industrial hub.

" In 2009 and 2011, Geneva was ranked as, respectively, the fourth and fifth most expensive city in the world.

The city is a major tourist destination for both domestic and overseas visitors ; Hamburg ranked 16th in the world for livability in 2011, and, in 2010, the city ranked 10th in the world.

Karachi is ranked as a Beta world city.

These problems continue to earn Karachi low rankings in livability comparisons: The Economist ranked Karachi fourth least livable city amongst the 132 cities surveyed and BusinessWeek ranked it 175 out of 215 in livability in 2007, down from 170 in 2006.

In 2010, Leipzig was ranked 68th in the world as a livable city, by consulting firm Mercer in their quality of life survey.

Luanda was ranked the most expensive city to live in for expatriates by Mercer, in 2011, but was surpassed by Tokyo in 2012.

* In Romania, a municipality ( municipiu ) is a town or a city ranked by law at this level.