These two basic malformations have, of course, many variations.

These are equivalent in the sense that, in the presence of other basic axioms of set theory, they imply the axiom of choice and are implied by it.

These include all quadratic surds, all rational numbers, and all numbers that can be formed from these using the basic arithmetic operations and the extraction of square roots.

These two invasions caused English to become " mixed " to some degree ( though it was never a truly mixed language in the strictest sense of the word ; mixed languages arise from the cohabitation of speakers of different languages, who develop a hybrid tongue for basic communication ).

These days it is considered basic among DJs in electronic dance music genres, and it is standard practice in clubs to keep the constant beat through the night, even if DJs change in the middle.

These " extras " to the basic systematic search have been empirically shown to be essential for handling the large SAT instances that arise in electronic design automation ( EDA ).

These are intended to ensure basic political, social and economic standards that a nation state, or intergovernmental body is obliged to provide to its citizens but many do include its governments.

These critics state that Mary Baker Eddy's interpretation of Christian scripture diverges too greatly from basic tenets of Christianity.

These new principles were presented in the Tamworth Manifesto which is considered by historians to be the basic statement of the beliefs of the new Conservative Party.

These groups can be seen as the basic building blocks of all finite groups, in much the same way as the prime numbers are the basic building blocks of the natural numbers.

These first elements of the Calculation Critique of Socialism are the most basic element: economic calculation requires the use of money across all goods.

These " politically neutral " groups tend to avoid global conflicts and view the settlement of inter-human conflict as separate from regard for nature-in direct contradiction to the ecology movement and peace movement which have increasingly close links: While Green Parties and Greenpeace, and groups like the ACTivist Magazine for example, regard ecology, biodiversity and an end to non-human extinction as absolutely basic to peace, the local groups may not, and may see a high degree of global competition and conflict as justifiable if it lets them preserve their own local uniqueness.

These local customs are referred to as differences in typica and are accepted by church leaders since they are not perceived to conflict theologically with basic Orthodox teachings.

These people lead a life of misery and are denied the most basic of human rights: the right to food.

These include: In 1959 he became a fellow of the American Academy of Arts and Sciences ; in 1967 he was elected to the National Academy of Sciences ; the ACM's Turing Award for making " basic contributions to artificial intelligence, the psychology of human cognition, and list processing " ( 1975 ); the Nobel Memorial Prize in Economics " for his pioneering research into the decision-making process within economic organizations " ( 1978 ); the National Medal of Science ( 1986 ); and the APA's Award for Outstanding Lifetime Contributions to Psychology ( 1993 ).

These basic principles are explained in more detail below.

These modifications of the basic 8086 design were one of the first jobs assigned to Intel's then new design office and laboratory in Haifa, Israel.

In addition to the tetrahedra, phyllosilicates have a sheet of octahedra ( elements in six-fold coordination by oxygen ) that balanced out the basic tetrahedra, which have a negative charge ( e. g. < sup > 4 -</ sup >) These tetrahedra ( T ) and octahedra ( O ) sheets are stacked in a variety of combinations to create phyllosilicate groups.

These areas share basic results on logic, particularly first-order logic, and definability.

These life forms possessed the basic traits of self-replication and inheritable traits.

These definitions will usually list the connections that can be made to that kind of device, and some basic properties of that device.

These basic units of poetic form are often combined into larger structures, called poetic forms or poetic modes ( see following section ), as in the sonnet or haiku.

These three institutions: political representation, majority rule and the party system are the basic components of modern political machinery ; they are applicable to both central and local governments and are becoming by their adaptability ends in themselves rather than a machinery to achieve some purpose.

These fundamental ideas -- the indivisibility of sovereignty and its dual ( internal-external ) aspects -- still remain the core of that concept of ultimate political power.

These errors were then collected and written on a blackboard, condensing similar ideas.

These ideas were found in a number of Kabbalistic works from the 13th century, and also among many mystics in the late 16th century.

These " conversations " as he called them, were more or less informal talks on a great range of topics, spiritual, aesthetic and practical, in which he emphasized the ideas of the school of American Transcendentalists led by Emerson, who was always his supporter and discreet admirer.

These openings all exemplify Nimzowitsch's ideas about controlling the center with pieces instead of pawns.

These ideas are part of the basis of concept of a limit in mathematics, and this connection is explained more fully below.

These ideas were initially taken as postulates, but today there are efforts to test each of them.

These ideas were informed by events prior to the Great Depression when — in the opinion of Keynes and others — international lending, primarily by the U. S., exceeded the capacity of sound investment and so got diverted into non-productive and speculative uses, which in turn invited default and a sudden stop to the process of lending.

These ideas were dismissed by his directors.

These may be brought about, for example, by such factors as poor management, lack of consultation with employees, personality conflicts which can result in people delaying or refusing to communicate, the personal attitudes of individual employees which may be due to lack of motivation or dissatisfaction at work, brought about by insufficient training to enable them to carry out particular tasks, or just resistance to change due to entrenched attitudes and ideas.

These ideas were unified by Kenneth Wilson in 1972, under the formalism of the renormalization group in the context of quantum field theory.

These ideas include the proposal that cells contain zones of low and high-density water, which could have widespread effects on the structures and functions of the other parts of the cell.

These ideas were adopted and adapted in western Europe to the high risks and rewards associated with colonial ventures.

These ideas apply to air flight as well.

" These ideas complement MWI and bring the interpretation in line with our perception of reality.

These rituals were designed to reduce that fear ; they helped collect the cultural ideas that we now have in the present.

These rituals also helped preserve the cultural ideas.

These ideas were informed by a moral philosophy derived from epistemological concerns regarding the inherent limits of human knowledge.

These ideas were developed in The Counter-Revolution of Science: Studies in the Abuse of Reason, 1952 and in some of Hayek's later essays in the philosophy of science such as " Degrees of Explanation " and " The Theory of Complex Phenomena ".

These stories originated from the unofficial points-of-view of some Council attendees who discussed their ideas with those not privy to the Council's deliberations.

These numbers are highly speculative ; many sources give vague ideas of the unemployment rating being ( for example, in 2003 ) around 50 %, giving the impression that the actual rate could be several percentage points higher or lower.

These fractures were prompted by issues of government and patronage, but reflected a wider division between the Evangelicals and the Moderate Party over fears of fanaticism by the former and the acceptance of Enlightenment ideas by the latter.

These ideas would become institutionalized in time, for example Ashoka's role in the spread of Buddhism, or the role of platonic philosophy in Christianity at its foundation.

These ideas still retain some power, with faith healing and shrines still used in some places, although the rise of scientific medicine over the past millennium has altered or replaced mysticism in most cases.