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Since the topology on R < nowiki ></ nowiki > X < nowiki ></ nowiki > is the ( X )- adic topology and R < nowiki ></ nowiki > X < nowiki ></ nowiki > is complete, we can in particular apply power series to other power series, provided that the arguments don't have constant coefficients ( so that they belong to the ideal ( X )): f ( 0 ), f ( X < sup > 2 </ sup >− X ) and f ( ( 1 − X )< sup >− 1 </ sup > − 1 ) are all well defined for any formal power series f ∈ R < nowiki ></ nowiki > X < nowiki ></ nowiki >.
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Since and topology
Since Euclidean space is a metric space it is also a topological space with the natural topology induced by the metric.
Since radio circuits inherently possess a broadcast network topology ( i. e., many or all nodes are connected to the network simultaneously ), one of the first technical challenges faced in the implementation of packet radio networks was a means to control access to a shared communications channel.
Since the bus topology consists of only one wire, it is rather inexpensive to implement when compared to other topologies.
* Since it is a variation of bus topology, if the backbone fails, the entire network is crippled.
Since the latter matrices can be uniquely expressed as the exponential of symmetric traceless matrices, then this latter topology is that of ( n + 2 )( n-1 )/ 2 dimensional Euclidean space.
Since QuickRing was built in a ring topology there was no need for a dedicated switch or router, potentially making the system lower cost to deploy.
Since Y is reflexive, the continuous dual of is equal to the image J ( X ) of X under the canonical embedding J, but the topology on X is not the strong topology, that is equal to the norm topology of Y.
Since the overall chemical composition and connectivity of the DNA does not change, the tangled and untangled DNAs are chemical isomers, differing only in their global topology, thus their name.
Since T is compact, the topology on the dual group is that of uniform convergence, which turns out to be the discrete topology.
Since polynomials over a field K are zero on finite sets, or the whole of K, the Zariski topology on K ( considered as affine line ) is the cofinite topology.
The use of a rat sequence also confirmed this topology and estimated date of divergence from the swine / human strains was 7. 44 × 10 < sup > 4 </ sup > years ago ( range 2. 1 × 10 < sup > 4 </ sup > to 1. 4 × 10 < sup > 5 </ sup > years ago ) Since this date is approximately coincident with the advent of agriculture it may be that this virus originally infected rats and subsequently spread to pigs and then to humans.
Since the weak operator topology is weaker than the strong operator topology, it is also immediate that ii ) ⇒ iii ).
Since the only Hausdorff topology on a finite set is the discrete one, a finite Hausdorff topological group must necessarily be discrete.
Since G is compact in this topology, there is a unique Haar measure μ on G. For every prime v of K not in S there is an associated Frobenius conjugacy class F < sub > v </ sub >.
Since railways are entirely linear in topology, the " mileage " is sufficient to identify a place uniquely on any given route.
Since addition and multiplication are continuous operations with respect to the usual topology of the plane, the split-complex numbers form a topological ring.
Since link-state routing requires the topology database to be synchronized across the network, OSPF and IS-IS perform topology flooding using a reliable algorithm.
Since and on
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 his Christ was to be life size, how was Mary to hold him on her lap without the relationship seeming ungainly??
Since that time the demands of the citizens for new and expanded services have placed financial burdens on the state which could not have been foreseen in earlier years.
Since the validity of all subsequent planning depends on the accuracy of the basic inventory information, great care is being taken that the inventory is as complete as possible.
Since April 15, 1962, is on Sunday your return for the calendar year 1961 will be timely filed if it is filed on or before Monday, April 16, 1962.
Since you contributed more than half of his support, you may also claim an exemption for him on your return.
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 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 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 her bereavement this individual has reported to the writer on numerous occasions about how helpful the class discussions were to her in this adjustment crisis.
Since the details of the elections were settled the change of government had no direct effect on the technical aspects of the elections, and may have been more important as an indication of royal displeasure with the U.N.F.P.
Since on the one hand school desegregation has come in Virginia hand-in-glove with pupil assignment, shall we support the plan??
Since I have already discussed his moral position, that discussion is incorporated by reference into the following pages, which will focus on the empirical and analytic side of Fromm's treatment.
Since the earth is rotating and the unleveled gyro-stabilized platform is fixed with respect to a reference in space, an observer on the earth will see the platform rotating ( with respect to the earth ).
Since the psychiatric interview, like any other interview, depends on communication, it is significant to note that the therapist in this interview was a man of marked skill and long experience.
Since the change to better nutrition, he feels he can report on improvements in health, though he considers the following statements observations and not scientific proof.
Since 1949, the St. Louis club has been below on May 1 just four times.
Since the railroad cannot reduce the salary of individual union members under contract, it must accomplish its payroll reduction by placing some of the men on furlough, a B. & O. spokesman said.
( page 33 ) On the other hand, a little later on he says: `` Since 1692 a great but superficial change has wiped out God's beard and the Devil's horns, but the world is still gripped between two diametrically opposed absolutes.
Since the hero, a sterling and upright fellow, is a rich Brown senior, while two Yalies are cast as virtual rapists, I suppose I should disqualify myself from sitting in judgment on `` Where The Boys Are '', but I shall do nothing of the sort.
Since then and during the first decade, the results were given to newspapers for publication at 11 pm on the night of the awards.
Since then, it has focused on improving relationships with Western countries, cultivating links with other Portuguese-speaking countries, and asserting its own national interests in Central Africa through military and diplomatic intervention.
Since 1998, Angola has successfully worked with the United Nations Security Council to impose and carry out sanctions on UNITA.
Since membership is based on a province's communion with Canterbury, expulsion would require the Archbishop of Canterbury's refusal to be in communion with the affected jurisdiction ( s ).
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