Thus the set of strings of length k in the domain is exactly the set of such strings already enumerated.

Thus an 8-course Renaissance lute will usually have 15 strings, and a 13-course Baroque lute will have 24.

Thus, the vocal lines for Papageno — sung by Schikaneder himself — and Monostatos ( Johann Joseph Nouseul ) are often stated first in the strings so the singer can find his pitch, and are frequently doubled by instruments.

Thus one prevents long strings without change via such devices as run length limited codes.

Thus the full dictionary does not need be sent with the encoded data ; just the initial dictionary containing the single-character strings is sufficient ( and is typically defined beforehand within the encoder and decoder rather than being explicitly sent with the encoded data.

Thus, the performer plays on two strings most of the time, creating a typical bourdon style.

Thus, the tuning hammer is used on the top side of the wrest plank, but the strings are wrapped around the pins on the bottom side.

Thus, it needs to be capoed individually since it is not covered by a capo on the other four strings.

Thus the strings are about 25 cm above the floor.

Thus, when used to aid in fuzzy string searching in applications such as record linkage, the compared strings are usually short to help improve speed of comparisons.

Thus, if two strings have the same digest, one can be very confident that they are identical.

Thus, he refused to play any music for the villagers, instead hitting his lyre's strings with a rock over and over.

Thus finding more repeated strings narrows down the possible lengths of the keyword, since we can take the greatest common divisor of all the distances.

Thus, a process calculus is to a history monoid what a formal language is to a free monoid ( a formal language is a subset of the set of all possible finite-length strings of an alphabet generated by the Kleene star ).

*" Thus strings of unconnected words, and constant repetitions of words and phrases, are very properly condemned in written speeches: but not in spoken speeches — speakers use them freely, for they have a dramatic effect.

Thus, two strings in C are added by adding the bits in the strings modulo 2 ( that is, addition without carry, or exclusive disjunction ).

Thus, given actions and attributes, the grammar can be used for translating strings from its language by applying the actions and carrying information through each symbol's attribute.

Thus the masterworks of William Byrd and his contemporaries were often played on full-size, Italian or Flemish harpsichords and not only on the virginals as we call it today.

Thus, a bore with a wide " bell " at the bottom of the instrument ( as with Renaissance recorders ) responds best to holding the throat wide open, to direct the airflow in a wide current so as to resonate the entire length and width of the bore.

Thus, what started as an effort to translate between languages evolved into an entire discipline devoted to understanding how to represent and process natural languages using computers.

Thus, he used " rare " rather than " strange " to represent the Spanish " raro ", and " syndicate " rather than " trade union " for the Spanish " sindicato ".

Thus we must write either to represent the former, or to represent the latter.

Thus, according to Murray, reports of Satan actually represented pagan gatherings with their priest wearing a horned helmet to represent their Horned God.

Thus making a conscious entity impossible to exist without cause, and a conscious entity impossible to represent first cause, or solve infinite regress.

Thus, one would expect to find a factor that roughly corresponds to " left " and " right ", as this is the dominant framing for politics in our society, but the basis of Eysenck's " tough / tender-minded " thesis ( the second, " T "- factor ) may well represent nothing beyond an abstract mathematical construct.

Thus, Benbili comes to represent south-east Asia, an allusion to the Vietnam War.

Thus two arrows and in space represent the same free vector if they have the same magnitude and direction: that is, they are equivalent if the quadrilateral ABB ′ A ′ is a parallelogram.

Thus, ( 1 – x ) would represent the operation of selecting all things in the world except horned things, that is, all not horned things, and ( 1 – x ) ( 1 – y ) would give all things neither horned nor sheep.

Thus Rome began with a fratricide, a story that was later taken to represent the city's history of internecine political strife and bloodshed.

Thus, they had to represent themselves, though they received significant pro bono assistance.

Thus the diagram below does not represent an evolutionary tree.

Thus, for an application like routing, might represent the straight-line distance to the goal, since that is physically the smallest possible distance between any two points or nodes.

Thus, for example, a government budget that is balanced over the course of the business cycle is considered to represent a neutral fiscal policy stance.

Thus, values of 1500 ( 0x05DC ) and below for this field indicate that the field is used as the size of the payload of the Ethernet Frame while values of 1536 and above indicate that the field is used to represent EtherType.

Thus, the Russbach did represent a formidable obstacle for cavalry and it needed to be bridged in order for artillery to cross.

Thus, the representative parties would be unaware of the talents and abilities, ethnicity and gender, religion or belief system of the citizens they represent.

Thus, South Korea argues that the current name reflects active promotion by Japan during a time when Korea could not represent its interests internationally.

Thus, each side of the chemical equation must represent the same quantity of any particular element.

Thus, the most important aspect of the Stufe concept is the negative one: not all chords represent Stufen.

Thus the price of the finished product bears no resemblance to the costs of production, since the two represent market conditions at very different points in time.

Thus, it became widely accepted that ophiolites represent oceanic crust that had been emplaced on land.

Thus while the two terms may sound similar, they represent products that are quite different.

Thus, operational satellites represent a small minority of the population of man-made objects in space.