Thus, a low intensity of hypothalamic-cortical discharges prevails in sleep and a high one during wakefulness, resulting in synchronous EEG potentials in the former and asynchrony in the latter condition.

This latter construal is sometimes expressed by saying " there is no fact of the matter as to whether or not P ." Thus, we may speak of anti-realism with respect to other minds, the past, the future, universals, mathematical entities ( such as natural numbers ), moral categories, the material world, or even thought.

Thus for example two extant plays, The Phoenicean Women and Iphigenia at Aulis, are significantly corrupted by interpolations ( the latter possibly being completed post mortem by the poet's son ) and the very authorship of Rhesus is a matter of dispute.

Thus, for example, two objects may be group isomorphic without being ring isomorphic, since the latter isomorphism selects the additional structure of the multiplicative operator.

Thus, he saw private property as both essential to liberty and a road to tyranny, the former when it resulted from labour and was required for labour and the latter when it resulted in exploitation ( profit, interest, rent, tax ).

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

#* Proof: Then so Thus However, is prime, so or In the former case, hence ( which is a contradiction, as neither 1 nor 0 is prime ) or In the latter case, or If however, which is not prime.

Thus the court accepted that a modified doctrine of tenure operated in Australia, and that the law of tenure ( as a product of the common law ) could co-exist with the law of native title ( as a product of customary laws and traditions ), though where there had been a valid grant of fee simple by the Crown the latter title would be extinguished.

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, sometimes the president and prime minister can be allies, sometimes rivals ; the latter situation is known in France as cohabitation.

Thus, the former is clipped, with a break between " quick " and " send ," while the latter " well " is held pensively.

Thus the Council Fathers meant to say that the being of the Church as such is a broader entity than the Roman Catholic Church, but within the latter it acquires, in an incomparable way, the character of a true and proper subject.

Thus former choose to focus on fiscal policy i. e., the relationship between expenditures and allocated revenues ( vertical imbalance ) while latter pay attention to regulatory or financial mechanisms i. e. the nature of intergovernmental transfers ".

Thus, modelling programs which understand the RenderMan Interface protocol can send data to rendering software which implements the RenderMan Interface, without caring what rendering algorithms are utilized by the latter.

Thus, there are several pairs of villages such as Marion – Skala Maries, where the former is inland and the latter on the coast.

Thus the term " Paregoric " should be used instead of " Camphorated Opium Tincture ," since the latter may be confused with Laudanum.

Thus, if we consider the correlation coefficient between the heights of fathers and their sons over all adult males, and compare it to the same correlation coefficient calculated when the fathers are selected to be between 165 cm and 170 cm in height, the correlation will be weaker in the latter case.

Thus in Ethiopia he was once called upon to decide between the swarthy king and the king's wife ; the latter having been accused of infidelity because she had borne her lord a white child.

Thus Salar de Uyuni can be loosely translated as a salt flat with enclosures, the latter possibly referring to the " islands " of the Salar ; or as " salt flat at town named ' pen for animals '".

Thus the latter test is usually the more powerful of the two.

Thus, he wrote: " if 0 is interpreted as falsehood, 1 as truth, and other numbers in the interval 0-1 as the degrees of probability corresponding to various possibilities, a many-valued logic is obtained which is expansion of three-valued logic and differs from the latter in certain details.

Thus the Governor-General hit upon the notion to name the outpost Nueva ( meaning new Ecija ). Both the New and Old Ecija were washed by navigable rivers-the former, by Rio Grande de Pampanga and the latter, by the river Genil.

Thus, after two successful wars, Greece had doubled its territory by gaining most of Macedonia, Epirus, Crete and the rest of the Aegean islands, although the status of the latter remained as yet undetermined and a cause of tension with the Ottomans.

Thus, Xiahou Ba discussed the issue with Xiahou Xuan, and persuaded the latter to flee with him to Shu-Han.

Thus organized, museum displays would illustrate the evolution of civilization from its crudest to its most refined forms.

Thus, a museum is seen as just another business competing for entertainment dollars from the public, rather than as an institution that serves the public welfare through education or historical preservation.

Thus, after 13 years of great acquisitions, the museum increased its collection only by spontaneous donations of artists, companies and private collectors.

Thus places such as the Gazi Husrev-beg's Mosque, Cathedral of Jesus ' Heart, and the Jewish cemetery were damaged, while places like the old City Hall and the Olympic museum were completely destroyed.

Thus, in 1989, the European Archeological Center of Mont Beuvray was created, which will reassemble the site, the museum, and the research center of Glux-en-Glenne.

Thus Billy Singer must seek the telepathic creature only known as " Cat ", whom he had caught and trapped for a museum.

Thus, he became the youngest artist ever shown in this museum.

For every group G there is a natural group homomorphism G → Aut ( G ) whose image is the group Inn ( G ) of inner automorphisms and whose kernel is the center of G. Thus, if G has trivial center it can be embedded into its own automorphism group.

Thus, ocular albinism occurs more frequently in males as they have a single X and Y chromosome, unlike females, whose genetics are characterized by two X chromosomes.

Thus the discovery report by the Berkeley group reads: " It is suggested that element 97 be given the name berkelium ( symbol Bk ) after the city of Berkeley in a manner similar to that used in naming its chemical homologue terbium ( atomic number 65 ) whose name was derived from the town of Ytterby, Sweden, where the rare earth minerals were first found.

Thus the castrati came to supplant both boys ( whose voices broke after only a few years ) and falsettists ( whose voices were weaker and less reliable ) from the top line in such choirs.

Thus the harmonisation was replaced in the 5th century by the canonical four gospels individually, in the Peshitta version, whose Syriac text nevertheless contains many Diatessaronic readings.

Thus an equivalence relation over X, a partition of X, and a projection whose domain is X, are three equivalent ways of specifying the same thing.

Thus, for example, the funerary god Anubis was portrayed as a jackal, a creature whose scavenging habits threatened the preservation of the body, in an effort to counter this threat and employ it for protection.

Thus, any periodic summation in the frequency domain can be represented by a Fourier series, whose coefficients are samples of a related continuous time function:

Thus, there was a short-lived eleventh century attempt to re-establish an independent Galatia by native Galatians whose aristocracy and people appealed to Anglo-Saxon and Russo-Norman mercenaries of the Byzantine Varangian Guard and Frankish Crusaders alike in establishing a new kingdom.

Thus, most knowledge of Roman Britain has derived from archaeological investigations, and the epigraphic evidence lauding the Britannic achievements of an Emperor of Rome, such as Hadrian ( r. 117 – 38 ) and Antoninus Pius ( r. 138 – 61 ), whose walls demarcated the northern borders of Roman Britain.

Thus, in giving a speech in defense of a poet whose Roman citizenship had been questioned, the orator should examine not only the specifics of that poet's civic status, he should also examine the role and value of poetry and of literature more generally in Roman culture and political life.

Thus the kings of Epirus claimed their lineage from Achilles, and so did Alexander the Great, whose mother was of that royal house.

Thus, a nonlinear system is one whose behavior can't be expressed as a sum of the behaviors of its parts ( or of their multiples ).

The French word was derived from the Spanish embarazar, whose first recorded usage was in 1460 in Cancionero de Stúñiga ( Songbook of Stúñiga ) by Álvaro de Luna .< sup > 7 </ sup > The Spanish word likely comes from the Portuguese embaraçar, which probably is a combination of the prefix em-( from Latin in-for " in -") with baraça " a noose ", or " rope ", which makes sense with the synonym encinta (" on noose, on rope " because of the old usage of women to wear a strap of cloth on their dresses when pregnant ).< sup > 8 </ sup > Baraça originated before the Romans began their conquest of the Iberian Peninsula in 218 BCE .< sup > 9 </ sup > Thus, baraça could be related to the Celtic word barr, " tuft ".

Thus, the Low Countries consisted of fiefs whose sovereignty resided with either the Kingdom of France or the Holy Roman Empire.

Thus, what the axiom schema is really saying is that, given a set A and a predicate P, we can find a subset B of A whose members are precisely the members of A that satisfy P. By the axiom of extensionality this set is unique.

Thus " double star " remains a useful term for pairs whose status is not fully known.

Thus one writer alleges that Johnson's campaign manager, future Texas governor John B. Connally, was connected with 202 ballots in Precinct 13 in Jim Wells County that had curiously been cast in alphabetical order and just at the close of polling, with all of the people whose names appeared on the ballots being dead on election day.

Thus, an LFSR is most often a shift register whose input bit is driven by the exclusive-or ( XOR ) of some bits of the overall shift register value.

Thus, for example, the Conservative movement typically does not accept Reform converts to Judaism whose conversions did not meet the requirements of Jewish law as being Jews.

Thus, what came out in the media: from newspapers, magazines, TV, and the movies, was a product of the stereotypes of the 30s and 40s — though garbled — of a cross between a 1920s Greenwich Village bohemian artist and a Bop musician, whose visual image was completed by mixing in Daliesque paintings, a beret, a Vandyck beard, a turtleneck sweater, a pair of sandals, and set of bongo drums.

In his book Greek Religion, Walter Burkert notes the connection with the motif of far-off Dilmun: " Thus Achilles is transported to the White Isle, which may refer to Mount Teide on Tenerife, whose volcano is often snowcapped and as the island was sometimes called the white isle by explorers, and becomes the Ruler of the Black Sea, and Diomedes becomes the divine lord of an Adriatic island ".

“ Thus says the Lord of hosts: Here is a man whose name is Branch ( Hebrew: Zemah ): for he shall branch out in his place, and he shall build the temple of the Lord … he shall bear royal honor, and shall sit upon his throne and rule.