Thus the films seen as they came in ( coordinated for the regular sections ), were often out of context.

Thus ℵ < sub > 0 </ sub > is a regular cardinal.

Thus the category of completely regular spaces CReg is a reflective subcategory of Top, the category of topological spaces.

Thus, John Dryden, among many others, compares the " irregular " Shakespeare with the " regular " Ben Jonson in his Essay of Dramatick Poesie ( 1668 ), and makes use of the unity of time in this passage criticizing Shakespeare's history plays:

Thus, X-ray diffraction results from an electromagnetic wave ( the X-ray ) impinging on a regular array of scatterers ( the repeating arrangement of atoms within the crystal ).

Thus, strict rules apply for entrance, including Church membership and regular attendance.

Thus, the definition of T < sub > 3 </ sub > may cite T < sub > 0 </ sub >, T < sub > 1 </ sub >, or T < sub > 2½ </ sub > instead of T < sub > 2 </ sub > ( Hausdorffness ); all are equivalent in the context of regular spaces.

Thus, regular spaces are usually studied to find properties and theorems, such as the ones below, that are actually applied to completely regular spaces, typically in analysis.

Thus the behavior of the function on the Fatou set is ' regular ', while on the Julia set its behavior is ' chaotic '.

Thus, surfactant as an antiadhesive in the regular collapse and reopening of alveoli may be the primary function of the system in pinnipeds.

Thus chunks with odd lengths will be " padded " to an even byte boundary by adding a so-called " pad byte " after their regular end.

Thus, in the Majors, a " playoff " is actually part of the regular season and thus can be called a " Pennant playoff ".

Thus, as the vehicle goes through the regular bumping and dipping that comes with driving over a terrain, the circuit is completed and the bomb or explosive is allowed to function.

Thus, the transfer of the PC to the regular force of the new military organization was effected under the provisions of Sec.

Thus, although armored riders were used in the Roman army as early as the 2nd century BC ( Polybios, VI, 25, 3 ), the first recorded deployment and use of cataphracts ( equites cataphractarii ) by the Roman Empire comes in the 2nd century AD, during the reign of Emperor Hadrian ( 117-138 AD ), who created the first, regular unit of auxiliary, mailed cavalry called the ala I Gallorum et Pannoniorum catafractata.

Thus trade traffic could easily be controlled and income from tolls was frequent and regular.

Thus, it is not a violation of the PES if one delivers a letter of one's friend even without affixation of postage or if a company has one of its regular employees deliver mail that originates from the company to its customers.

Thus, employers also benefit as experienced interns need little or no training when they begin full-time regular employment.

Thus, regular script has parentage in early semi-cursive as well as neo-clerical scripts.

Thus on 1 May 1961 the TA divisional hedquarters were merged with regular army districts, which were matched with Civil Defence Regions to aid mobilisation for war.

Thus even " regular " mail may make part of its journey on an aircraft.

Thus " regular " 1861-O halves with this crack probably were used by the Confederates for some of the mass striking.

Thus on a regular basis, he quotes secular scientists in his Torah commentary.

Thus the copywriter in the world of the space merchants is the person who in earlier ages might have been a lyric poet, the person `` capable of putting together words that stir and move and sing ''.

Thus the Af are projections which correspond to some direct-sum decomposition of the space V.

Thus, the study of the solutions to the equation Af is reduced to the study of the space of solutions of a differential equation of the form Af.

Thus, the binding energy to contain or trap a particle in a smaller region of space, increases without bound, as the region of space grows smaller.

In mathematics, an associative algebra A is an associative ring that has a compatible structure of a vector space over a certain field K or, more generally, of a module over a commutative ring R. Thus A is endowed with binary operations of addition and multiplication satisfying a number of axioms, including associativity of multiplication and distributivity, as well as compatible multiplication by the elements of the field K or the ring R.

Thus, the vector space B ( X, Y ) can be given the operator norm

By a theorem of Gelfand and Naimark, given a B * algebra A there exists a Hilbert space H and an isometric *- homomorphism from A into the algebra B ( H ) of all bounded linear operators on H. Thus every B * algebra is isometrically *- isomorphic to a C *- algebra.

Thus, the material body will occupy different configurations at different times so that a particle occupies a series of points in space which describe a pathline.

Thus, the most stable configuration of nuclei and electrons is one in which the electrons spend more time between nuclei, than anywhere else in space.

Thus if one chooses an infinite number of points in the closed unit interval, some of those points must get arbitrarily close to some real number in that space.

Thus a representation that compresses a 10MB file to 2MB would yield a space savings of 1-2 / 10 =

Thus, a field due to any particular particle or time-varying electric or magnetic field contributes to the fields present in the same space due to other causes.

Thus, actual address space utilization rates will be small in IPv6, but network management and routing efficiency is improved by the large subnet space and hierarchical route aggregation.

Thus, we might as well treat that eigenspace as the actual Hilbert space of the system.

Thus Euclidean geometry corresponds to the choice of the group E ( 3 ) of distance-preserving transformations of the Euclidean space R < sup > 3 </ sup >, conformal geometry corresponds to enlarging the group to the conformal group, whereas in projective geometry one is interested in the properties invariant under the projective group.

This identifies the tangent space T < sub > e </ sub > at the identity with the space of left invariant vector fields, and therefore makes the tangent space at the identity into a Lie algebra, called the Lie algebra of G, usually denoted by a Fraktur Thus the Lie bracket on is given explicitly by = < sub > e </ sub >.

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, special relativity " mixes " electricity and magnetism into a single, inseparable phenomenon called electromagnetism, analogous to how relativity " mixes " space and time into spacetime.

Thus it made sense to not map the memory between programs for IPC, but instead migrate the program code being used into the local space of the program.

Thus, in place of God's role as guarantor of the coherence of the world, Kant posits a faculty of reason structured by the forms of our intuition ( our sense of time and space ) and the categories of our understanding ( like the notion of cause and effect ).

" Thus, it is She who becomes the time and space, the cosmos, it is She who becomes the five elements, and thus all animate life and inanimate forms.