Important results include the Bolzano – Weierstrass and Heine – Borel theorems, the intermediate value theorem and mean value theorem, the fundamental theorem of calculus, and the monotone convergence theorem.

; Important results

Important results include evidence from genomic tiling arrays that most nucleotides are transcribed as coding transcripts, noncoding RNAs, or random transcripts, the discovery of additional transcriptional regulatory sites, further elucidation of chromatin-modifying mechanisms.

Important results in complexity theory allow us to relate this complexity class with other classes, telling us about the relative power of the resources involved.

Important links have been made between world-class, championship individual and team sports performance and business results.

Important results on this type of zero of an L-function were obtained in the 1930s by Carl Ludwig Siegel, from whom they take their name ( he was not the first to consider them, and they are sometimes called Landau-Siegel zeroes to acknowledge also the work of Edmund Landau ).

Important numberings are the Gödel numbering of the terms in first-order predicate calculus and numberings of the set of computable functions which can be used to apply results of computability theory on the set of computable functions itself.

Important artists included Itō Shinsui and Kawase Hasui, who were named Living National Treasures by the Japanese government.

Important irrigated crops include barley, corn, cotton, various fruits, grapes, opium poppies, sugar beets, roses, and tobacco.

Important cities along the coast include Batumi, Burgas, Constanța, Giresun, Hopa, Istanbul, Kerch, Mangalia, Năvodari, Novorossiysk, Odessa, Ordu, Poti, Rize, Samsun, Sevastopol, Sochi, Sukhumi, Trabzon, Varna, Yalta and Zonguldak.

Important sub-disciplines within bioinformatics and computational biology include:

Important constraints to economic development include the CAR's landlocked position, a poor transportation system, a largely unskilled work force, and a legacy of misdirected macroeconomic policies.

Important areas of study include chemical thermodynamics, chemical kinetics, electrochemistry, quantum chemistry, statistical mechanics, and spectroscopy.

Important organocarbonates include dimethyl carbonate, the cyclic compounds ethylene carbonate and propylene carbonate, and the phosgene replacement, triphosgene.

Important areas of study include chemical thermodynamics, chemical kinetics, electrochemistry, statistical mechanics, spectroscopy, and more recently, astrochemistry.

Important manufacturing centres in the region include Pictou County, Truro, the Annapolis Valley and the South Shore, and the Strait of Canso area in Nova Scotia, as well as Summerside in Prince Edward Island, and the Miramichi area, the North Shore and the upper Saint John River valley of New Brunswick.

Important types include:

Important vegetables include tomato, aubergine ( eggplant ), potato, green beans, okra, green peppers, and onions.

Important topics addressed in these letters include ecclesiology, the sacraments, and the role of bishops.

Important Gujarati Muslim communities in the city include the Memon, Chhipa, Ghanchi, Khoja, Bohra and Tai.

Important works from the 100s include the Attic Nights of Aulus Gellius, a collection of anecdotes and reports of literary discussions among his friends ; and the letters of the orator Marcus Cornelius Fronto to Marcus Aurelius.

Important examples include the mica, chlorite, and the kaolinite-serpentine groups.

Important bilateral donors include Canada, Denmark, Germany, Ireland, Iceland, Japan, the Netherlands, Norway, Sweden, Republic of China ( Taiwan ), the United Kingdom, and the United States.

Important philosophers of mind include Plato, Descartes, Leibniz, Kant, Martin Heidegger, John Searle, Daniel Dennett and many others.

Important properties that various operators may exhibit include linearity, continuity, and boundedness.

Important naval victories of the Ottoman Empire in this period include the Battle of Preveza ( 1538 ); Battle of Ponza ( 1552 ); Battle of Djerba ( 1560 ); conquest of Algiers ( in 1516 and 1529 ) and Tunis ( in 1534 and 1574 ) from Spain ; conquest of Rhodes ( 1522 ) and Tripoli ( 1551 ) from the Knights of St. John ; capture of Nice ( 1543 ) from the Holy Roman Empire ; capture of Corsica ( 1553 ) from the Republic of Genoa ; capture of the Balearic Islands ( 1558 ) from Spain ; capture of Aden ( 1548 ), Muscat ( 1552 ) and Aceh ( 1565 – 67 ) from Portugal during the Indian Ocean expeditions ; among others.

Important and commonly encountered probability distributions include the binomial distribution, the hypergeometric distribution, and the normal distribution.

Important widely recognized types of property include real property ( the combination of land and any improvements to or on the land ), personal property ( physical possessions belonging to a person ), private property ( property owned by legal persons or business entities ), public property ( state owned or publicly owned and available possessions ) and intellectual property ( exclusive rights over artistic creations, inventions, etc.

Important punk zines include Maximum RocknRoll, Punk Planet, No Cure, Cometbus, Flipside, and Search & Destroy.

Important themes include:

Important Alien civilisations include the Puppeteers, paranoid pacifist herbivore centaurs, and the Kzinti, carnivorous warlike felines, who fought multiple wars over hundreds of years against the Humans, being defeated each time.

Important potential properties of statistics include completeness, consistency, sufficiency, unbiasedness, minimum mean square error, low variance, robustness, and computational convenience.

Important news topics at that time included the Northern Ireland Peace Process, the Death of Diana, Princess of Wales ( 1997 ), and increasing European integration ( Maastricht Treaty ) and discussion over switching the currency to the Euro.

Important as these differences are, they should not obscure the basic fact that by shifting the hypothalamic balance sufficiently to the parasympathetic side, we produce depressions, whereas a shift in the opposite direction causes excitatory effects and, eventually, maniclike changes.

Important examples of low-molecular aliphatic compounds can be found in the list below ( sorted by the number of carbon-atoms ):

Important military and political figures in modern Chinese history continued to be influenced by Confucianism, like the Muslim warlord Ma Fuxiang.

Important features of natural language syntax such as agreement and reference are not part of the context-free grammar, but the basic recursive structure of sentences, the way in which clauses nest inside other clauses, and the way in which lists of adjectives and adverbs are swallowed by nouns and verbs, is described exactly.

The island has been identified as an Important Bird Area ( IBA ) by BirdLife International because it supports a large and diverse population of breeding seabirds and other waterbirds.

Important museums in Ghent are the Museum voor Schone Kunsten ( Museum of Fine Arts ), with paintings by Hieronymus Bosch, Peter Paul Rubens, and many Flemish masters ; the SMAK or Stedelijk Museum voor Actuele Kunst ( City Museum for Contemporary Art ), with works of the 20th century, including Joseph Beuys and Andy Warhol ; and the Design Museum with masterpieces of Victor Horta and Le Corbusier.

Important leaders of the GIA in France fell afterward: Khaled Kelkal was killed in Lyon by the EPIGN and Rachid Ramda was arrested in London although it took ten years for the French justice to have him extradited.

An early influence in this vein was Henry David Thoreau and his famous book Walden Important promoters of this were Henri Zisly and Emile Gravelle who collaborated in La Nouvelle Humanité followed by Le Naturien, Le Sauvage, L ' Ordre Naturel, & La Vie Naturelle.

Users with an Australian IP address were greeted with the message " Important Notice: The download of the Kazaa Media Desktop by users in Australia is not permitted " when visiting the Kazaa website.

Important for Kashubian literature was Xążeczka dlo Kaszebov by Doctor Florian Ceynowa ( 1817 – 1881 ).

Important government decisions are vetted by the Council of Ministers.

The headland has been designated as an Important Plant Area, by the organisation Plantlife, for rare species of flora.

Important lysosomal enzymes, such as acid sphingomyelinase, may be inhibited by lysososomally accumulated drugs.

The lake has been identified by BirdLife International as an Important Bird Area ( IBA ) because, when flooded, it supports major breeding events of the Banded Stilt and Australian Pelican, as well as over 1 % of the world populations of Red-necked Avocets, Sharp-tailed Sandpipers, Red-necked Stints, Silver Gulls and Caspian Terns.

Brando was named the fourth greatest male star in the history of American cinema by the American Film Institute, and part of Time magazine's Time 100: The Most Important People of the Century.

Important one-day matches, international and domestic, often have two days set aside, the second day being a " reserve " day to allow more chance of the game being completed if a result is not possible on the first day ( for instance if play is prevented or interrupted by rain ).

Important subgroups are the kinases of the ERK subfamily, typically activated by mitogenic signals, and the stress-activated protein kinases JNK and p38.

* The Rolling Stone Illustrated History of Rock and Roll: The Definitive History of the Most Important Artists and Their Music by editors James Henke, Holly George-Warren, Anthony Decurtis, Jim Miller ( 1992 ), Random House ( ISBN 0-679-73728-6 )

The Strait has been identified as an Important Bird Area by BirdLife International because hundreds of thousands of seabirds use it every year to pass between the Mediterranean and the Atlantic, including large numbers of Cory's and Balearic Shearwaters, Audouin's, Yellow-legged and Lesser Black-backed Gulls, Razorbills and Atlantic Puffins.

The island has been identified as an Important Bird Area ( IBA ) by BirdLife International because of its significance as a seabird breeding site.

Important tallages were made by Edward I in the second, third and fourth years, (£ 1, 000 ) and in the fifth year ( 25, 000 marks ), of his reign.

* Important role of music ( composed by Ennio Morricone ).

Important work in the scholastic tradition has been carried on, however, well past Aquinas ' time, for instance by Francisco Suárez and Molina, and also among Lutheran and Reformed thinkers.