Thus, the Kolmogorov complexity of the raw file encoding this bitmap is much less than 1. 62 million.

Thus far, however, most such cases against file sharers have been settled out of court.

Thus, one can consider data compression as data differencing with empty source data, the compressed file corresponding to a " difference from nothing ".

Thus a representation that compresses a 10MB file to 2MB has a compression ratio of 2 / 10

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

Thus to add a person ( or subject ) to one's kill file is to arrange for that person to be ignored by one's newsreader in the future.

Thus, it is easy to convert from a vector file to a range of bitmap / raster file formats but it is much more difficult to go in the opposite direction, especially if subsequent editing of the vector picture is required.

Thus, rather than describing the outline of the glyph directly, a Metafont file describes the pen paths.

Thus, by changing the value of one of these parameters at one location in the Metafont file, one can produce a consistent change throughout the entire font.

Thus, each square has a unique identification of file letter followed by rank number.

Thus, the minimum memory required for a SAX parser is proportional to the maximum depth of the XML file ( i. e., of the XML tree ) and the maximum data involved in a single XML event ( such as the name and attributes of a single start-tag, or the content of a processing instruction, etc.

Thus, crosscut saws have sawteeth that are usually shaped, often with a metal file, in such a way that they form a series of tiny knifelike edges. The wood cells ( straws ) are contacted by the knife-edge of the tooth and cut.

Thus to get an application to support multiple languages one would design the application to select the relevant language resource file at runtime.

Thus many PostScript printer drivers have an option to save as EPS, or to add EPS DSC information to their output which you can " print to file ".

Thus if all the files in an archive are text files, and have ASCII names, then the archive is essentially an ASCII text file ( containing many NUL characters ).

Thus, an MXF file received & unwrapped may reveal SMPTE D10 compliant essence with eight mono AES audio components ; the recipient has no way of knowing whether these components are multiple stereo pairs, 5. 1 or serve some other purpose.

Thus they were not responsible for controlling any specific file downloads.

Thus, since downloading the Bible through peer-to-peer file sharing software is an addition to the list of well-established legitimate methods for obtaining a free Bible, the benefits of this addition are not substantial and the overall use of P2P software should not be considered a non-infringing use.

Thus it was labeled a combined-primary file or a combined-demand file.

Thus, pre-Sixth Edition Unix versions read an executable file into memory and jumped to the first low memory address of the program, relative address zero.

Thus the IDEF1 language was created to allow a neutral description of data structures that could be applied regardless of the storage method or file access method.

Thus, there is freshness not only in the individual movements of the dance but in the shape of their continuity as well.

Thus jazz is transmuted into something holy, the sacred road to integration of being.

Thus the fictional detective is much more than a simple businessman.

Thus the cocktail party would appear to be the ideal system, but there is one weakness.

Thus in both types attention is focused on the community itself, and its phenomenological life.

Thus, it is no mystical intuition, but an analyzable conception to say that man and his tradition can `` fall out of existence ''.

Thus human perception and human volition is the immanent cause of all social change and this most truly when the change reaches the civilizational level.

Thus, circular motion is itself one of the essential characteristics of completely perfect celestial existence.

Thus, in no ordinary sense of ' simplicity ' is the Ptolemaic theory simpler than the Copernican.

Thus Burns's `` My love is like a red, red rose '' and Hopkins' `` The thunder-purple sea-beach, plumed purple of Thunder '' although clearly intelligible in content, hardly present ideas of the sort with which we are here concerned.

Thus science is the savior of mankind, and in this respect Childhood's End only blueprints in greater detail the vision of the future which, though not always so directly stated, has nevertheless been present in the minds of most science-fiction writers.

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 there is a clearer division of authority, administrative and legislative.

Thus, as a development program is being launched, commitments and obligations must be entered into in a given year which may exceed by twofold or threefold the expenditures to be made in that year.

Thus, the need for the B-70 as a strategic weapon system is doubtful.

Thus technical efficiency is achieved at the expense of actual experience.

Thus, there is an added incentive to stay on the job.

Thus, the Span of its ossification was shortened and the center's ability to `` catch up '' in ossification is demonstrated.

Thus T is not diagonalizable.

Thus Af is divisible by the minimal polynomial P of T, i.e., Af divides Af.

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 in the three-dice example Af, Af, and the independence assumption imply that the probability that the three dice fall ace, not-ace, ace in that order is Af.

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

Thus if E is sufficiently small, there can be only one intersection of C and Af near Q, for if there were more than one intersection for every E then the difference between C and Af near Q would not be a monotone function.

Thus Af is also continuous at Af, and in a neighborhood of Af which does not contain a tangent point.