So, for example, while R < sup > n </ sup > is a Banach space with respect to any norm defined on it, it is only a Hilbert space with respect to the Euclidean norm.

So " Elohim " could refer to any number of " rulers ", such as angels, false gods ( as defined by Torah ), or even human holders of power including rulers or judges within Israel, as described in, without violating the parameters of monotheism.

So the logarithm cannot be defined for the whole complex plane, and even then it is multi-valued – any complex logarithm can be changed into an " equivalent " logarithm by adding any integer multiple of 2πi at will.

So the critical angle is only defined when is less than 1.

So if you had defined a record type in the TPF system of ' FRED ' and gave it 100 records or ordinals, then in a processor shared scheme record type ' FRED ' ordinal ' 5 ' would resolve to exactly the same file address on DASD-clearly necessitating the use of a record locking mechanism.

So if it can be shown that the word means different things across different contexts of use, then cases where its meaning cannot be essentially defined as ' married bachelor ' seem to constitute counterexamples to this method of analysis.

So, for example, in the criminal law case of R v. Rimmington ( 2005 ) UKHL 63 Lord Bingham said " Where Parliament has defined the ingredients of an offence.

So in IE religions there is an introducer god ( as Vedic Vâyu and Roman Janus ) and a god of ending, a nurturer goddess and a genie of fire ( as Vedic Saraswati and Agni, Avestic Armaiti, Anâitâ and Roman Vesta ) who show a sort of mutual solidarity: the concept of ' god of ending ' is defined in connexion to the human referential, i. e. the current situation of man in the universe, and not to endings as transitions, which are under the jurisdiction of the gods of beginning, owing to the ambivalent nature of the concept.

So in mathematical terms a curve is defined by four coordinate functions ( where usually denotes the time coordinate ) depending on one parameter.

So far a world line ( and the concept of tangent vectors ) is defined in spacetime even without a definition of a metric.

So the diameter concept needs to be carefully defined to be meaningful.

So much was she part of it, so much was her star personality defined by it, that the screwball style itself seems almost unimaginable without her.

So a set is not defined by a formula ; rather, there are both and formulas that define the set.

So, the meaning of OWL Full ontologies are defined by extension of the RDFS meaning, and OWL Full is a semantic extension of RDF.

So formidably defined, rumor is but a special case of informal social communications, including myth, legend, and current humor.

So the correct fourth are i and − i, which are the imaginary numbers defined to be.

So the symbol is homogeneous in the variables y, of degree n. The symbol is well defined even though ∂/∂ x < sub > i </ sub > does not commute with x < sub > i </ sub > because we only keep the highest order terms and differential operators commute " up to lower-order terms ".

So, these lines do not intersect at an omega point and such points, although well defined, do not belong to a hyperbolic space itself.

So although it is an ancient and well established locality, it has only recently been officially defined, by the Natural England National Character Area ( NCA ) process, which takes a somewhat wider definition than many previous attempts to define the area.

So the boundary was defined to follow the river until it turned northeast, and then to follow a straight line north to the 35th parallel ( whose role in state borders dates back to the split of North and South Carolina in 1730 ).

So called " priest-penitent " privilege, which precludes forced testimony of confessions made to a priest, minister, or religious adviser are statutorily defined in the United States.

' So what we're doing now is expanding G4 from a network solely defined by videogames to one inspired by them.

So for infinitary logics the notions of strong compactness and strong completeness are defined.

So the Brønsted – Lowry concept can be defined by the reaction:

So, for example, a web browser program might check its local cache on disk to see if it has a local copy of the contents of a web page at a particular URL.

So, given an integral domain R, it is often very useful to know that R has a Euclidean function: in particular, this implies that R is a PID.

So typically, one refers to an individual's genotype with regard to a particular gene of interest and, in polyploid individuals, it refers to what combination of alleles the individual carries ( see homozygous, heterozygous ).

So in particular, every central idempotent a in R gives rise to a decomposition of R as a direct sum of the corner rings aRa and.

So Mill's initial use of the term concerned natural abilities, in contrast to the common contemporary usage, which refers solely to market failure in a particular type of industry, such as rail, post or electricity.

So each radar uses a particular type of signal.

So, the code may not be tuned to any particular CPU, or may be tuned to work best on the most popular CPU and yet still work acceptably well on other CPUs.

So it can be said that an EO's properties persist beyond the life of any particular running application.

Compare Barnette v. State, 481 So. 2d 788, 792 ( Miss. 1985 ) ( cited by the Court ), with McGowen v. State, 859 So. 2d 320, 339-340 ( Miss. 2003 ) ( the Sixth Amendment does not require confrontation with the particular analyst who conducted the test ).

So in this case, the Internet Telephony Service Provider ( ITSP ) knows that a particular user is online, and can relate a specific telephone number to the user.

Fasting — a practice actively promoted in Scripture — and abstinence from certain foods at particular times are good spiritual disciplines, but there is no food from which Catholics must abstain at all times ... So who is Paul condemning regarding abstinence?

So the revenues of the duchies were divided into three equal shares by assigning the revenues of particular areas and landed estates to each of the three brothers, while other general revenues, such as taxes from towns and customs dues, were levied together but then shared among the brothers.

So, by following a particular pattern created by culture we are able to recognise how we use and move information in different ways.

So, perhaps, the dates provided by the narrator may contradict the established dates, for example, claiming that he heard from a particular scholar after the recognized death of that scholar.

So the revenues of the duchies were divided in three equal shares by assigning the revenues of particular areas and landed estates to each of the elder brothers, while other general revenues, such as taxes from towns and customs dues, were levied together but then shared among the brothers.

So, different functions could indeed be ascribed to particular regions of the brain, but that a finer localization was lacking.

So, while Reagan didn't wish for his particular situation to establish a precedent binding future Presidents to turn over their authority every time they underwent surgery, his intent to transfer executive authority in that instance was clear.

So, let x be any one particular friend of Peter, X the set of all Peter's friends, P ( x ) be the predicate ( mathematical logic ) " x likes to dance ", and lastly Q ( x ) the predicate " x likes to go to the beach ".

So the revenues of the duchies, deriving from the rights of overlordship in the various towns and territories of Schleswig and Holstein, were divided in three equal shares by assigning the revenues of particular areas and landed estates, themselves remaining undivided, to each of the elder brothers, while other general revenues, such as taxes from towns and customs dues, were levied together but then shared among the elder brothers.

So far, then, it is meaningless to speak of " Sephardic custom ": all that is meant is Jewish law without the particular customs of the Ashkenazim.

So the usage of this particular picture should not be extended to articles which are only partially related to this photo, such as China or Tiananmen Square protests of 1989 ‎.

So in particular the Gaussian functions with b = 0 and c = 1 are kept fixed by the Fourier transform ( they are eigenfunctions of the Fourier transform with eigenvalue 1 ).

So, for example, concepts like singularities ( the most widely known of which in general relativity is the black hole ) which can not be expressed completely in a real world geometry, can correspond to particular states of a mathematical equation.