When applied to vector spaces of functions ( which typically are infinite-dimensional ), dual spaces are employed for defining and studying concepts like measures, distributions, and Hilbert spaces.

When planning a visit from Bonn, where he was immersed in studying physics, his fellow mathematician and friend Hermann Minkowski joked he had to spend 10 days in quarantine before being able to visit Hilbert.

When studying inorganic compounds, one often encounters parts of the different classes of inorganic chemistry ( an organometallic compound is characterized by its coordination chemistry, and may show interesting solid state properties ).

When Beethoven was finished studying with Albrechtsberger he decided to get a few more tips and pointers, so to speak, from Haydn.

When working on a major specimen like an eagle, he would spend up to four 15-hour days, preparing, studying, and drawing it.

When she was not studying, she took independent courses from Ohio University and spent her free time casting bronzes in the school foundry.

When studying the mathematics of games, the mathematical analysis of the game is more important than actually playing the game.

When asked how he developed his mathematical abilities so rapidly, he replied " by studying the masters, not their pupils.

When studying axiomatic probability theory, many deep consequences follow from merely these three axioms.

When night came, they would deny her warm clothes and a fire for her bedroom to try to keep her from studying, but after they left she would take out candles, wrap herself in quilts and do mathematics.

When he was eleven, his parents sent him to the Protestant Academy at Sedan, where he spent four years studying Greek under Jacques du Rondel.

When the word " seashells " is used to refer only to the shells of marine mollusks then studying seashells is part of conchology.

When this topic turned out not to be feasible, he switched to studying the question of Italian unification over a two-year period.

When the school's high school was founded in the late 1940s, he instituted a number of innovations in the curriculum, including teaching Talmud to boys and girls studying in classes together.

When studying the etiology of a disease, it is better to analyze incidence rather than prevalence since prevalence considers the duration of a condition rather than providing a measure of risk alone.

When Steinberg and Kincheloe wrote the first edition of Kinderculture: The Corporate Construction of Childhood in 1997 ( second edition, 2004 ) many people who made their living studying, teaching, or caring for children were not yet aware of the nature of the changes in childhood that they encountered daily.

When studying the anatomy of the human body, he did not believe that the living organisms could be explained mechanistically.

When Thalberg returned to school, he lacked the stamina to enroll in college which he felt would have required constant late-night studying and cramming for exams.

When he was 17, he moved to the United States with the intention of studying towards eventually entering medical school, but Wang changed his mind and ended up in the arts, studying film and television at California College of Arts and Crafts in Oakland.

When Shunryu had first come to Zoun-in, 8 other boys were studying there.

When about a year old he lost his sight through smallpox ; but this did not prevent him from acquiring a knowledge of Latin and Greek, and studying mathematics.

When Wüthrich joined the Bell Labs, he was put in charge of one of the first superconducting NMR spectrometers, and started studying the structure and dynamics of proteins.

When I hold my son he stiffens his whole body in my arms until he is as straight and stiff as a board.

When the whole bottom has hardened, use a disk sander to feather the edges of the cloth at the keel line and near the spray rail.

When paper electrophoresis was to be used for preparation, eight strips of a whole serum sample or a chromatographic fraction concentrated by negative pressure dialysis were run/chamber under the conditions described above.

When Af has been found it may be transferred into the storage location of Af and the whole calculation repeated.

`` When the roles of husband and wife are reversed, so that the wife becomes leader and the husband follower '', Dr. Linden says, `` the effects on their whole relationship, sexual and otherwise, can be disastrous ''.

When Felix first opened the door on it, all these shades were tightly drawn and the whole studio was as dark as night.

When Charlie came up from the beach for his four-o'clock pill, the whole establishment ( gaudy enough when seen through mist and fog ) looked like a floodlit modern painting -- great blocks of dizzy color, punctuated at regular intervals by the glaring white of five community refrigerators.

When that student observed an infraction, he or she reported it to the rest of the class and, as a whole, they deliberated on punishment.

When she persuades him to blurt out the whole story, a twist is revealed — Charlotte's little sister is a school friend of Anne's.

When the audience applauded — testimonies differ over whether at the end of the scherzo or the whole symphony — Beethoven was several measures off and still conducting.

When Havana surrendered, the admiral of the British fleet, George Keppel, the 3rd Earl of Albemarle, entered the city as a conquering new governor and took control of the whole western part of the island.

When brain tissue from a CJD patient is examined under a microscope, many tiny holes can be seen where whole areas of nerve cells have died.

When they came to possess the whole of southern Mesopotamia, the name " Chaldean " became synonymous with " Babylonian ", particularly to the Greeks and Jews.

When working together as a group, these player characters ( PCs ) are often described as a ' party ' of adventurers, with each member often having his or her own areas of specialty that contributes to the success of the whole.

When natural resource management is applied to whole ecosystems, rather than single species, it is termed ecosystem management.

When Francis took the title in 1804, the Habsburg lands as a whole were dubbed the Kaisertum Österreich.

# When the newly elected Reichstag first convened on March 23, 1933, ( not including the Communist delegates, since their party had already been banned by that time ) it passed the Enabling Act ( Ermächtigungsgesetz ), transferring all legislative powers to the Nazi government and, in effect, abolishing the remainder of the Weimar constitution as a whole.

When he identified himself as " Carver's George ," as he had done his whole life, she replied that from now on his name was " George Carver ".

When the measured pressure is rapidly pulsing, such as when the gauge is near a reciprocating pump, an orifice restriction in the connecting pipe is frequently used to avoid unnecessary wear on the gears and provide an average reading ; when the whole gauge is subject to mechanical vibration, the entire case including the pointer and indicator card can be filled with an oil or glycerin.

He recommended, " When you wish to see whether your whole picture accords with what you have portrayed from nature take a mirror and reflect the actual object in it.

When Franz Halder, the Chief of the Army General Staff, heard of the state of the Kriegsmarine, and its plan for the invasion, he noted in his diary, on 28 July 1940, " If that plan is true, all previous statements by the navy were so much rubbish and we can throw away the whole plan of invasion ".

La Russa said, " I think it's fair to say he misunderstood how he compared to Royce in spring training ... When I and the coaches evaluated the play in spring training — the whole game — Royce started very slowly offensively and you could see him start to get better.

When Attalus III ( 138-133 BC ) died without an heir in 133 BC, he bequeathed the whole of Pergamon to Rome, in order to prevent a civil war.

When Alexander the Great reached Egypt, he put his whole vast enterprise on hold, while he made his way with a small band deep into the Libyan desert, to consult the oracle of Ammun.

When a flock of this huge a size established itself in an area, the number of local animal predators ( such as wolves, foxes, weasels, and hawks ) was so small compared to the total number of birds that little damage would be inflicted on the flock as a whole.