Thus, the experience of an apple is as close to the Apple concept that one can get.

Thus the concept ' computable ' is in a certain definite sense ' absolute ', while practically all other familiar metamathematical concepts ( e. g. provable, definable, etc.

Thus rta bears a resemblance to the ancient Chinese concept of tao and the Heraclitan, Stoic or Christian conceptions of the logos.

Thus, it is this semi-empirical formula for bond energy that underlies Pauling electronegativity concept.

Within the space of these tendencies there has developed a coherent critique of " orthodox Marxism " that includes not only a rejection of the concept of " the transition " but a reconceptualization of the process of transcending capitalism that has remarkable similarities to ( Peter ) Kropotkin's thinking on this subject ... Thus one of the earliest political tendencies within which this approach appeared after the Russian revolution of 1917 was that of " Council Communism " which saw the " workers councils " in Germany ( see Bavarian Soviet Republic ), or the soviets in Russia, as new organizational forms constructed by the people.

Thus for map projections we must introduce the concept of point scale, which is a function of position, and strive to keep its variation within narrow bounds.

Thus, under head of project Masakatsu, the concept development was turned into a competition between the Mazda design teams in Tokyo and California.

Thus followed the line of Lomonosov and the contributions of the Russian school became more frequent through his disciples, and in the nineteenth century we have great geographers as Vasily Dokuchaev who performed works of great importance as a " principle of comprehensive analysis of the territory " and " Russian Chernozem " latter being the most important where introduces the geographical concept of soil, as distinct from a simple geological strata, and thus founding a new geographic area of study: the Pedology.

Thus the concept of the " Romantic period " may be meaningless outside of Europe and European-influenced cultures.

Thus, Jevons anticipated a key feature of the RSA Algorithm for public key cryptography, although he certainly did not invent the concept of public key cryptography.

Thus, they claim, to conceive of a particular apple and its redness is not to conceive of applehood or redness-in-general, so they question the source of the concept.

Thus the predicate " is not satisfied " attributes something to the concept " is an Albanian philosopher ", and is thus a second-level predicate.

Thus, while there are short-term memory components to working memory models, the concept of short-term memory is distinct from these more hypothetical concepts.

Thus it was Pythagoras who gave the word " theory " the specific meaning which leads to the classical and modern concept of a distinction between theory as uninvolved, neutral thinking, and practice.

Thus, the hierarchies, and the concept involved with lexicographic files, do not apply here the same way they do for nouns and verbs.

Thus rationalizing the criticism that the Qur ' an would direct towards the main corpus of Jews ( and Christians ) for not accepting the concept of Qibla, particularly that of Kaaba.

Thus we might also describe reduction as a process analogous to absorption, by which one theory ( or concept, or property, and so on ) is wholly subsumed under another.

Thus this concept has played a prominent role on the world stage and in world history.

Thus, E-Language is not itself a coherent concept, and Chomsky argues that such notions of language are not useful in the study of innate linguistic knowledge, i. e., competence, even though they may seem sensible and intuitive, and useful in other areas of study.

Thus, it seemed quite logical to promote the group as " Captain Beefheart and His Magic Band ", around the concept that Captain Beefheart had ' magic powers ' and, upon drinking a ' Pepsi ', could summon up " His Magic Band " to appear and perform behind him.

Thus the resulting nuclei become heavier and closer to the sought-after island of stability, a concept wherein some super-heavy atoms can be relatively stable.

Thus, the example of a definition of oak given above ( something that has catkins and grows from acorns ) is not completely useless, even if " acorn " and " catkin " are defined in terms of " oak ", in that it supplies additional concepts ( e. g., the concept of catkin ) in the definition.

Thus, the innermost purpose of the creation of all rational beings is their cognition of the existence of Allah and, hence, their conscious willingness to conform their own existence to whatever they may perceive of His will and plan: and it is this twofold concept of cognition and willingness that gives the deepest meaning to what the Quran describes as " worship ".

Thus the concept of Lebensraum was picked up and expanded by publicists of the day, including Karl Haushofer and General Friedrich von Bernhardi.

Thus we do not score the number of bull's-eyes, and the random variable is not the number of successes.

Thus, they are a type of hardware random number generator.

Thus talk about physical probability makes sense only when dealing with well defined random experiments.

Thus when the record was played multiple times, different recordings would play seemingly at random.

Thus, a random function can be considered to map each input independently at random to any one of the possible outputs.

Thus, the general notion of a statistical ensemble with nearest-neighbor interactions leads to Markov random fields, which again find broad applicability ; for example in Hopfield networks.

Thus according to the central limit theorem, we can model jitter as a gaussian random variable.

Thus, after one of its gyroscopes failed, NASA decided that a controlled crash was preferable to letting the craft come down on its own at random.

Thus, the less random error in the variables, the higher the possible correlation between them.

Thus, contrary to intuition, the number of k-point lines expected from random chance increases much more than linearly with the size of the area considered.

Thus any countably infinite random graph is almost surely the Rado graph, which for this reason is sometimes called simply the random graph.

Thus, the random opening or closing of sodium channels will not affect the membrane potential of the cell ; only the closing of a large number of channels, through absorption of a photon, will affect it and signal that light is in the visual field.

Thus, the second-stage decisions, at time, are actually functions of realization of the random vector, i. e.,.

Thus begins a report about disaffected urban behaviour, which includes " Hell's Grannies " ( antisocial old ladies ), " the Baby Snatchers " ( men dressed as babies, who seize random people off the street ) and vicious gangs of " Keep Left " signs, at which point the sergeant-major stops the sketch, for becoming " too silly ".

Thus, estimates obtained from random samples can be accompanied by measures of the uncertainty associated with the estimate.

Thus creating the perfect location for very many myths and legends about this place, as the destruction of these structures for any reason is said to bring bad luck, today all across the country side of Ireland can be found random mounds of earth.

Thus, orthogonal sampling ensures that the ensemble of random numbers is a very good representative of the real variability, LHS ensures that the ensemble of random numbers is representative of the real variability whereas traditional random sampling ( sometimes called brute force ) is just an ensemble of random numbers without any guarantees.