Instead one needs to define Lie groups modeled on more general locally convex topological vector spaces.

Instead of the standard American system of primary elections to choose each party's candidate, followed by a general election contest between the winners of the primaries, the Louisiana primary allows voters to select any candidate, regardless of party affiliation.

Instead, General Omar Bradley was promoted to lieutenant general.

Instead of killing the general, the attackers wounded an innocent female passerby.

Instead of focusing on what they eat, this system classifies predators by the way in which they eat, and the general nature of the interaction between predator and prey species.

Instead, he challenged Metzenbaum again, whom Gilligan had appointed to the Senate to replace William B. Saxbe, who had resigned to become attorney general.

Instead of gaining Pope Pius VI consent, the cardinal and the queen-mother asked for a general council where Christians of all opinions and from all over Europe would meet to reform the religion.

Instead, George Habash in particular, and various other leaders in general advocated one state with an Arab identity in which Jews were entitled to live with the same rights as any minority. The PFLP declared that its goal was to ‘’ create a people ’ s democratic Palestine, where Arabs and Jews would live without discrimination, a state without classes and national oppression, a state which allows Arabs and Jews to develop their national culture .’’

Instead the climb is given its one general grading, and if any of the other factors is outstanding, this is stated verbally in the short introduction to that climb "

Instead he got Goodyear to form the Southwest Cotton Company in Phoenix, with Litchfield as its president, eventually purchasing some 36, 000 acres in the general Salt River Valley area including 5, 000 acres around the present site of Litchfield Park, then known as Litchfield Ranch.

Instead of holding general elections, General Zia charged Bhutto with conspiring to murder the father of dissident politician Ahmed Raza Kasuri.

Instead, autonomic sensory information is conducted by general visceral afferent fibers.

Instead, a stable algorithm for solving this more general problem can for example be a divide and conquer algorithm where the array is recursively split into two parts for which the sum is calculated respectively, and where these two sums then are summed together to give the final sum.

Instead of both the alphabetic and iconic notational types ' general principle of using one symbol per sound, analphabetic notation uses long sequences of symbols to precisely describe the component features of an articulatory gesture ( MacMahon 1996: 842 – 844 ).

In general, a pricing model function, f, does not have a closed-form solution for its inverse, g. Instead, a root finding technique is used to solve the equation:

Instead, she understood that the health of the environment indicated the general well-being of humanity.

Instead of just taking four classes integrated as part of the general education, Integral majors ' entire curriculum, including subjects not traditionally related to the " classics ," is done in the Seminar style.

Instead, the posts discussed time travel in general, the first one being the " six parts " description of what a time machine would need to have to work ( see below ) and responses to questions about how such a machine would work.

Instead of there being an excess supply ( glut or surplus ) of goods in general, there may be an excess supply of one or more goods but only when balanced by an excess demand ( shortage ) of yet other goods.

Instead Lega Nord, a protest movement with some ideological elements ranging from xenophobia and racism to independence from the rest of Italy and a general loathing of the political system, became the strongest political force in Northern Italy.

Instead of completing the general education requirements at Western, students take interdisciplinary classes at Fairhaven which aim to cover the same breadth and depth of subjects, but within small, interdisciplinary seminars.

Instead, he was appointed a judge of the general court of Virginia and served for two years, resigning in 1827 to return to his seat in the House of Representatives as a Jacksonian.

Instead we resolved to support one another more informally as we pursued our political tradition as individuals, or launched new projects with more general aims that have also engaged people from different traditions, or none.

Instead, it merely proposed general rules for the House to follow when debating bills ( rather than passing a special rule for each bill ), and was dissolved after proposing these general rules.

Instead, several objects may match the query, perhaps with different degrees of relevancy.

Instead, programmers used data structures to store the query information, constructing a query by linking many of these structures together.

Instead, we need to answer a query in the same fashion as the triangulation refinement approach, but the data structure is constructed top-down.

Instead of having the query result stored in a temporary table, where the data cannot be updated directly by the user, the dynaset allows the user to view and update the data contained in the dynaset.

Instead of having the query result stored in a temporary table, where the data cannot be updated directly by the user, the dynaset allows the user to view and update the data contained in the dynaset.

Instead of calculating the distance between the query and every single database entry, Musipedia just calculates the distance between the query and each of a few vantage objects.

Instead, in their research and writing, many postmodern scholars have adopted “ alternatives that encourage reflection about the ‘ politics and poetics ’ of their work.

Instead, the aim is to create room for critical thinking and more inclusive understanding of the past and conceptions of “ the other .”

Instead, he advocated that the “ little horn ” was the Antichrist:

Instead of “ absolute ” and “ definitive ”, Dupuis speaks in terms of “ constitutive ” and “ universal ”.

Instead he proposed that a revolutionary society should “ transform itself immediately into a communist society ,” that is, should go immediately into what Marx had regarded as the “ more advanced ,” completed, phase of communism.

Instead, Bujold builds prejudice into the “ locale ,” i. e. planetary, economics and history.

Mill notes that, contrary to what its critics might say, there is “ no known Epicurean theory of life which does not assign to the pleasures of the intellect … a much higher value as pleasures than to those of mere sensation .” However, he accepts that this is usually because the intellectual pleasures are thought to have circumstantial advantages, i. e. “ greater permanency, safety, uncostliness, & c .” Instead, Mill will argue that some pleasures are intrinsically better than others.

Adams concludes that “ right action, by act-utilitarian standards, and right motivation, by motive-utilitarian standards, are incompatible in some cases .” The necessity of this conclusion is rejected by Fred Feldman who argues that “ the conflict in question results from an inadequate formulation of the utilitarian doctrines ; motives play no essential role in it …( and that )… Precisely the same sort of conflict arises even when MU is left out of consideration and AU is applied by itself .” Instead, Feldman proposes a variant of act utilitarianism that results in there being no conflict between it and motive utilitarianism.

Instead, the proceedings became notorious for the large number of demonstrators and the use of force by the Chicago police during what was supposed to be, in the words of the Yippie activist organizers, “ A Festival of Life .” Rioting took place between demonstrators and the Chicago Police Department, who were assisted by the Illinois National Guard.

Instead of dialing directly “ into ” the host computer – which would require the host to have its own pool of modems and phone lines, and require non-local callers to make long-distance calls – the host could have an X. 25 connection to a network service provider.

Instead of paying for sexual favors and “ love ” on the streets with the risk of being arrested, publicly humiliated, or catching sexually transmitted diseases, internet dating websites offer matchmaking services for people to find love or whatever else they may be looking for.

Under the 1966 Social Security Act, newly unemployed individuals were no longer denied assistance during their first month of unemployment, while men who had had their unemployment benefit disallowed for six weeks ( on the grounds that they had been at fault for losing their job ) were no longer subjected to a harsh rule applied by the National Assistance confining their payments to below “ benefit rate .” Instead, a policy was adopted of paying these individuals their full entitlement less 15 shillings. T he Act also introduced a long term addition of 9 shillings for all pensioners receiving supplementary benefit and for others ( with the exception of those required register for employment ) receiving supplementary benefits for two years.

Instead, a phrase along the lines of “ first to reach ” would be needed as this conforms to rules of grammar.

Instead of the word Verdrängung ( repression ), which laid stress on unconscious repression of the past, Rank preferred to use the word Verleugnung ( denial ), which focused instead on the emotional will to remain ill in the present: “ The neurotic lives too much in the past to that extent he actually does not live.

Instead they applied the term “ deep “ for the deepest parts of the ocean, such as Challenger Deep.

Instead, it was convened by Arthur Griffith as “ Chairman of the Irish Delegation of Plenipotentiaries ” ( who had signed the Anglo-Irish Treaty ) under the terms of the Treaty.

Instead Frankfurter focused on his belief that there were no provisions within the constitution that occupied a “ preferred position ” over others.

Instead of financial stability inducing deregulation and financial instability after 1980, as later suggested by David Moss and Elizabeth Warren, Thomas Huertas and other critics of traditional bank regulation argued Regulation Q limits on interest rates ( mandated by the 1933 Banking Act ) created the “ disintermediation ” that began in the 1960s, led to the phase-out of Regulation Q through the Depository Institutions Deregulation and Monetary Control Act of 1980, and opened banking to greater competition.