Assuming the correctness of the identification of the Pallavas with the pauranic Pahlavas, and of the Pahlavas with the Parthians, there are good historical grounds for supposing that Parthian colonies established themselves in the Deccan at a very early period.

Assuming that the inscription on the James ossuary is genuine, the next question is whether " brother of Jesus " refers to Jesus, the founder of Christianity.

Assuming the crown, he passed Burgundy to his younger brother, Hugh the Black, after only two years as duke.

Assuming the form of a five year old boy, Kabu poses as Sally's younger brother.

Assuming the lower figure for the big blast and one shot estimated by the Japanese at 10 megatons, a conservative computation is that the 24 announced tests produced a total yield of at least 60 megatons.

Assuming the weather is halfway decent that day, hundreds of thousands of persons will mass along this thoroughfare as President John F. Kennedy and retiring President Dwight D. Eisenhower leave Capitol Hill following the oath-taking ceremonies and ride down this historic ceremonial route.

Assuming ZF is consistent, Kurt Gödel showed that the negation of the axiom of choice is not a theorem of ZF by constructing an inner model ( the constructible universe ) which satisfies ZFC and thus showing that ZFC is consistent.

Assuming ZF is consistent, Paul Cohen employed the technique of forcing, developed for this purpose, to show that the axiom of choice itself is not a theorem of ZF by constructing a much more complex model which satisfies ZF ¬ C ( ZF with the negation of AC added as axiom ) and thus showing that ZF ¬ C is consistent.

Assuming that the pixel color is expressed using straight ( non-premultiplied ) RGBA tuples, a pixel value of ( 0. 0, 0. 5, 0. 0, 0. 5 ) implies a pixel which has 50 % of the maximum green intensity and 50 % opacity.

Assuming that the ion is accelerated during a very short interval, the ion can be assumed to be travelling at constant velocity.

Assuming that 10 – 15 % of bread is thrown away as stale, if it could be made to stay fresh another 5 – 7 days then perhaps 2 million tons of flour per year would be saved.

Assuming average population densities of 0. 25 animals per km² in regions where it is known to be common or abundant, and 0. 02 per km² elsewhere, and with a total area of occupancy of 327, 000 km², a total population estimate of approximately 28, 000 is suggested.

Assuming a fixed sample size, the technique gives more accurate results when most of the variation in the population is within the groups, not between them.

:< u > The Copenhagen Interpretation </ u >: Assuming wave functions are not real, wave-function collapse is interpreted subjectively.

Assuming the Axiom of choice, is regular for each α.

Let e be the error in b. Assuming that A is a square matrix, the error in the solution A < sup >− 1 </ sup > b is A < sup >− 1 </ sup > e.

Assuming that the strength of the cable is proportional to its density per unit length, the weight, w, per unit length of the chain can be written T / c, where c is constant, and the analysis for nonuniform chains can be applied.

Assuming that the rule is known, one can derive the function that is used above in the classical heat calculation with respect to pressure.

Assuming that translation is not used transformations can be combined by simply multiplying the associated transformation matrices.

Assuming we can define at least one nonreal complex number, however, a complex number is definable if and only if both its real part and its imaginary part are definable.

Assuming that the visible material makes up only a small part of the cluster is the most straightforward way of accounting for this.

Assuming that the Earth is a uniform sphere ( which is not correct, but is close enough to get an order-of-magnitude estimate ) with M

Assuming the foundational premise is correct, the optimal option for all governments would be an agreement to maintain tax harmonization.

Assuming that the degree of does not exceed, the criterion is correct however, and somewhat stronger than the formulation given above, since if is irreducible modulo, it certainly cannot decompose in into non-constant factors.

Assuming this theory is correct, many scholars consider the possibility that one " chronicler " wrote this book.

Assuming the date of death of Cossa is correct, this one must have been completed prior to the others.

Assuming thermal equilibrium between the anode surface and the transpiring argon, the gas enthalpy rise through the anode was calculated according to the relation Af whereby the specific heat of argon was taken as Af.

Assuming Ignatius ' view was the Apostolic teaching and practice, the line of succession was unbroken and passed through the four ancient Patriarchal sees ( those local churches known to be founded by apostles ), Rome, Jerusalem, Antioch and Alexandria.

Assuming the stones were used for chiefly houses, it can be argued that Chamorro society was becoming more stratified, either from population growth or the arrival of new people.

Assuming that it was not abandoned it would certainly have been closed down in 425 by the Christian emperor Theodosius II when he prohibited the worship of the old Roman and Greek gods.

Statistical hypothesis tests answer the question Assuming that the null hypothesis is true, what is the probability of observing a value for the test statistic that is at least as extreme as the value that was actually observed ?.

Assuming Chavez was approximately 10 years old in 1979, that places the events of Debt of Honor to be in or near 2000, although the overall technology presented in the novel and its successive novels Executive Orders and Rainbow Six ( especially in regards to the sophistication of internet technology ) are more consistent with the mid-1990's.

Assuming Odo commissioned the tapestry, it was probably designed and constructed in England by Anglo-Saxon artists ( Odo's main power base being by then in Kent ); the Latin text contains hints of Anglo-Saxon ; other embroideries originate from England at this time ; and the vegetable dyes can be found in cloth traditionally woven there.

Assuming this was the case, the actual physical work of stitching was most likely undertaken by skilled seamsters.

Assuming Steele was marrying her out of pity, Judith breaks off the engagement and reverts to her former lifestyle.

Assuming that capture of the Chinese capital would be the decisive turning point in the war, there was an eagerness to be among the first to claim the honor of victory.

Assuming the invasion was successful, York had three options: become Protector again ; disinherit the king so that York's son would succeed ; or claim the throne for himself.

Assuming that Sewell is counted as the first Prime Minister, thirty-eight people have held the office since it was established.

Assuming that the bulk of the Austrian army was deployed so as to cover their bridgehead at Landshut and the main highway to Vienna, on 20 April 1809, Napoleon launched most of his army in an attack to the Southwest.

Assuming personae were a Greek and Roman tradition that was abandoned during the Medieval period.

If the tested number n is composite, the strong liars a coprime to n are contained in a proper subgroup of the group, which means that if we test all a from a set which generates, one of them must be a witness for the compositeness of n. Assuming the truth of the generalized Riemann hypothesis ( GRH ), it is known that the group is generated by its elements smaller than O (( log n )< sup > 2 </ sup >), which was already noted by Miller.

Assuming this was the enemy spotter, the tank commander asked for and received permission to fire.

Assuming the fulfillment of certain technical criteria ( such as the sentencing of the accused whose punishment was not yet executed ), wherever it is possible to punish the conspirators with exactly the same punishment through which they had planned to harm their fellow, the court carries out this direct reciprocal justice ( including when the punishment constitutes the death penalty ).

Assuming the soil was contaminated with prions ( PrP < sup > SC </ sup >) from feces

Assuming this meant he would succeed, he attacked — but the kingdom he destroyed was his own.

Assuming that the heading was incorrect, all other evidence points toward an attack on the Bever Dam.

Assuming that George Mallory and Andrew Irvine did not reach higher in 1924, this was the highest than anyone had ever been.