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These relations are a direct consequence of the basic properties of determinants: evaluation of the ( i, j ) entry of the matrix product on the left gives the expansion by column j of the determinant of the matrix obtained from M by replacing column i by a copy of column j, which is if and zero otherwise ; the matrix product on the right is similar, but for expansions by rows.
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These and relations
These cases, for all their rarity, are so dramatic that friends and relations repeat the story until the general population may get an entirely false notion of how often the hymen is a serious problem to newly-weds.
These dilemmas are often regarded as conflicts between his view on international relations and his other loyalties.
These measures plus the improvement in Israel's relations with Egypt and Jordan, the renunciation of terrorism by the Palestine Liberation Organization, the on-going peace talks between the PLO and Israel, the collapse of the communist states in East Europe, which reduced the scope for sanctuaries for terrorists, and the more cautious attitude of countries such as Libya and Syria after the U. S. declared them State-sponsors of international terrorism, the collapse of ideological terrorist groups such as the Red Army Faction and the tightening of civil aviation security measures by all countries have arrested and reversed the steep upward movement of hijackings.
These directives implied precise emphasis on: the search for political coordination with emerging and developing countries, namely India, South Africa, Russia and China ; creation of the Union of South American Nations and its derivative bodies, such as the South American Security Council ; strengthening of Mercosul ; projection at the Doha Round and WTO ; maintenance of relations with developed countries, including the United States ; undertaking and narrowing of relations with African countries ; campaign for the reform of the United Nations Security Council and for a permanent seat for Brazil ; and defense of social objectives allowing for a greater equilibrium between the States and populations.
( These two identities are often combined, e. g. added or subtracted, to yield various other relations.
These controversies contributed to the deterioration of relations between the Western and the Eastern Churches.
These rights lay outside feudalism, which defined authority in a hierarchy of personal relations, with only a loose relation to territory.
These differences, expressed using inequality relations known as " Bell's inequalities ", are in principle experimentally detectable.
These renounce all outstanding territorial claims and lay the foundation for constructive relations.
These relations were damaged when Jordan proclaimed its neutrality during the Gulf War and maintained relations with Iraq.
These requests were rejected by the Kennedy Administration ( which was involved in the Cuban Missile Crisis during most of the Sino-Indian War ), leading to a cool down in Indo-US relations.
" These allegations were due to Beria's suggestion to his assistants that to improve foreign relations it was reasonable to transfer the Kaliningrad Oblast to Germany, part of Karelia to Finland, the Moldavian Soviet Socialist Republic to Romania and the Kuril Islands to Japan.
These policies make it beneficial for other countries to have relations with Morocco so that they can take advantage of their goods.
These proclamations were known as the Donations of Alexandria and caused a fatal breach in Antony's relations with Rome.
These gifts were intended to cement relations between the two countries, building on the trade agreement signed in 1581 that gave English merchants priority in the Ottoman region.
These and are
These are traversed by another line of vaults, and thus rooms, arched on all four sides, are formed.
These songs ( practically all Persian music, for that matter ) are limited to a range of two octaves.
These my grandmother left in their places ( they are still there, more persistent and longer-lived than the generations of man ) and planted others like them, that flourished without careful tending.
These are like the initial ways in which the world forces itself upon the self and thrusts the self into decision and choice.
These assumptions lead to an organization with one man at the top, six directly under him, six under each of these, and so on until there are six levels of personnel.
These ways are absolutely irreconcilable because they offer two different recipes for man's redemption from chaos.
These are, if the research is done with subtlety and skill, researchable topics, but the research is missing.
These moments are historical events in the lives of individual authors with which the student of comparative literature must be frequently concerned.
These lives are in themselves outside of the moral order and are unburdened with moral responsibility.
These conceptions and the manner in which they were transposed into poetry or engendered by poetic form are intrinsic to western life from the time of Aeschylus to that of Shakespeare.
These biographical analogies are obvious, and far too much time has been spent speculating on their possible implications.
These women whose organization grew out of the old suffrage movement are dedicated to Thomas Jefferson's dictum that one must cherish the people's spirit but `` Keep alive their attention ''.
These are, of course, the same people whose support he has only now rejected to seek the independent vote.
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