Since Af is ferromagnetic, we felt that any results obtained from the magnetically contaminated Af would be suspect.

Since Af and P divides Af for Af, we have Af.

Since D' and N' commute with one another and Af, we see that D' and N' commute with T.

Since D and D' are both diagonalizable and they commute, they are simultaneously diagonalizable, and Af is diagonalizable.

Since N and N' are both nilpotent and they commute, the operator Af is nilpotent ; ;

Since Af are linearly independent functions and the exponential function has no zeros, these R functions Af, form a basis for the space of solutions.

Since the complex of singular lines is of order K and since there is no complex of invariant lines, it follows from the formula Af that the order of the involution is Af.

A final class of exceptional lines is identifiable from the following considerations: Since no two generators of Af can intersect, it follows that their image curves can have no free intersections.

Since two curves of symbol Af on Q intersect in Af points, it follows that there are Af lines of Af which are tangent to Aj.

Since the load L, under actual cutting conditions is caused by Af, it can be seen that Af

Since by the principle of optimality the remaining stages use an optimal Af-stage policy with respect to Af, we may enter section Af of the table at this state Af and read off the optimal policy for stage Af and the resulting state Af.

Since the hazards of poor communication are so great, p can be justified as a habitable site only on the basis of unusual productivity such as is made available by a waterfall for milling purposes, a mine, or a sugar maple camp.

Since the slogans have little application to reality and are sanctimonious to boot, the applause is faint even in areas of the world where we should expect to find the greatest affection for free government.

Since we can neither undo nor redo the past, we are limited to the events of today and tomorrow.

Since the recognition of Israel as a nation state, claims are made in many cases which identify the claimant as a member of the new body politic.

Since accurate base maps are necessary for any planning program, the first step taken by the planning division to implement the long-range state plan has been to prepare two series of base maps -- one at a scale of 1 inch to a mile, and the second a series of 26 sheets at a scale of 1 inch to 2000 feet, covering the entire state.

Since conventional methods are insensitive at the low frequencies of these molecular transitions, the paramagnetic resonance method is being used instead.

Since broadcast frequencies are very limited in number, these objectives are to some extent inconsistent in that not all of them can be fully realized, and to the extent that each is realized, there is a corresponding reduction of the possibilities for fullest achievement of the others.

Since the provision of skywave service requires adequate freedom from interference, only class 1, stations are capable of rendering skywave service.

Since the sides are also covered up to the spray rails, they are also rough-sanded in that area.

Since fly cutters are one sided and not balanced, they should be used at the slowest speed available, and fed very slowly to avoid binding.

Since there are almost no schools in the country offering graduate work in interior design this rule cannot at present be observed.

Since charges are relatively the same, reserving a car before you leave for Europe will assure you of having one on tap when you want it.

Since practical washing procedures are both lengthy and expensive, a number of laboratory tests have been developed for the numerical evaluation of detergents.

Since the circulating thyroid hormones are the amino acids thyroxine and tri-iodothyronine ( cf. Section C ), it is clear that some mechanism must exist in the thyroid gland for their release from proteins before secretion.

Since emotional reactions in the higher vertebrates depend on individual experience and are aroused in man, in addition, by complex symbols, one would expect that the hypothalamus could be excited from the cortex.

Since the choice is by lot each week, the outcomes of different trials are independent.

Since Chinese traditional thought focuses more on ethics rather than metaphysics, it has developed several schools distinct from the originating Indian schools.

Since there are only four distinct eigenvalues for this matrix, they have some multiplicity.

Since every equivalence relation over X corresponds to a partition of X, and vice versa, the number of possible equivalence relations on X equals the number of distinct partitions of X, which is the nth Bell number B < sub > n </ sub >:

Since history and memory ( representations of or belief about the past ) are distinct in all philosophy and ontology from plan, vision or intent ( representations of or will to change the future ), statements that confuse these are category errors: No statement about history or memory can imply a similar statement about a plan or vision or intent, nor vice versa-a distinction sometimes credited to Hume who distinguished also the morality of a statement from its truth.

Since many distinct tissue types express the IGF-1 receptor, IGF-1's effects are diverse.

Since terms of linear equations cannot contain products of distinct or equal variables, nor any power ( other than 1 ) or other function of a variable, equations involving terms such as xy, x < sup > 2 </ sup >, y < sup > 1 / 3 </ sup >, and sin ( x ) are nonlinear.

Since the early 1970s, however, the dominant scholarship has noted dissimilarities between Persian Mithra-worship and the Roman Mithraic mysteries, and the mysteries of Mithras are now generally seen as a distinct product of the Roman Imperial religious world.

Since some applications ( notably, but not exclusively, the parts of Microsoft Office ) allow macro programs to be embedded in documents, so that the programs may be run automatically when the document is opened, this provides a distinct mechanism by which viruses can be spread.

Since the Oneness position claims that the Name of " Jesus " and the concept of " Person " are common to all three manifestations of Father, Son and Holy Ghost, and yet the manifestations of Father, Son and Holy Ghost are distinct from each other, Oneness theology proposes that Jesus suffered on the cross as Son, but not as Father.

Since that time, the straits have come to foster the development of two very distinct and varied cultures on either side of the straits.

Since the mid-1990s, in particular due to insights from dualities shown to relate the five theories, an eleven-dimensional theory called M-theory is believed to encompass all of the previously distinct superstring theories.

Since the first player to move in Hex has a distinct advantage, the pie rule is generally implemented for fairness.

Since taxonomists can legitimately disagree as to whether two genera or two species are distinct or not, more than one name can be in use.

Since 1 and 2 are not equal, these roots are distinct.

Since 1 and 1 are ( of course ) equal, the roots are not distinct ; they coincide.

Since then, the pan-national Crown has had both a shared and separate character and the sovereign's role as monarch of Canada has been distinct to his or her position as monarch of any other realm, including the United Kingdom.

Since at least the 1970s, Anglo-Catholicism has been dividing into two distinct camps, along a fault-line which can perhaps be traced back to Bishop Charles Gore's work in the 19th century.

Since around 1970, the significant national Belgian political parties have split into distinct representations for each communities ' interests besides defenders of their ideologies.

Since, contrary to what some would imprudently lead us to believe, there were no distinct religions but only successive states of the same religious system ... – such an approach would be excessive, even pointless.

Since its recognition as a different species from the similar-appearing chestnut oak ( Quercus prinus ), Q. muehlenbergii has generally been regarded as a distinct species ; no subspecies or varieties are currently recognized within it, although a few infraspecific variants had been accepted in the past.

Since all these values are distinct, this is usually done using a bit vector.

Since the former city of Hull represents a large area distinct from what was formerly known as Gatineau, to be officially correct and specific many people say " vieux secteur Hull " ( the former Hull part of town ) when speaking of it.

Since the former city of Hull represents a large area distinct from what was formerly known as Gatineau, to be officially correct and specific many people say " vieux secteur Hull " ( the former Hull part of town ) when speaking of it.

Since the 1950s, historians, linguists, and archeologists have found evidence of a distinct people, the St. Lawrence Iroquoians, who inhabited the areas along the St. Lawrence River from before 1300 until the late 16th century.