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Page "Perron–Frobenius theorem" ¶ 98
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| So || Sodium || 11 || Current symbol is Na.
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So and <
So a quasar at an absolute magnitude of − 25. 5 is 100 times brighter than our galaxy ( because ( 10 < sup > 0. 4 </ sup >)< sup >(− 20. 5 -(− 25. 5 ))</ sup >
After Christians in Ephesus first wrote to their counterparts recommending Apollos to them, he went to Achaia where Paul names him as an apostle ( 1 Cor 4: 6, 9-13 ) Given that Paul only saw himself as an apostle ' untimely born ' ( 1 Cor 15: 8 ) it is certain that Apollos became an apostle in the regular way ( as a witness to the risen Lord and commissioned by Jesus-1 Cor 15: 5-9 ; 1 Cor 9: 1 ).< ref > So the Alexandrian recension ; the text in < sup > 38 </ sup > and Codex Bezae indicate that Apollos went to Corinth.
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, substituting the angular momentum and moment of inertia into E < sub > rot </ sub >, the rotational energy levels of a diatomic molecule are given by:
So P < sub > n </ sub > agree with the Bernoulli polynomials on the interval ( 0, 1 ) and are periodic with period 1.
So the parameters are: a — distance from center C to either vertex b — length of a perpendicular segment from each vertex to the asymptotes c — distance from center C to either Focus point, F < sub > 1 </ sub > and F < sub > 2 </ sub >, and θ — angle formed by each asymptote with the transverse axis.
So the logarithm function is in fact a group isomorphism from the group ( R < sup >+</ sup >,< big >×</ big >) to the group ( R ,< big >+</ big >).
) So far, observations show any rotation of the Universe is very slow ( no faster than once every 60 · 10 < sup > 12 </ sup > years ( 10 < sup >− 13 </ sup > rad / yr )), and debate persists over whether there is any rotation.
So in the example above, the has simply been replaced by < code >< nowiki > http :// usemod. com / cgi-bin / mb. pl ?</ nowiki ></ code > in creating the target of the HTML rendered link.
So if there are m factors, there will be 2 < sup > m </ sup > idempotents.
So, in these cases, the lethal concentration may be given simply as LC < sub > 50 </ sub > and qualified by a duration of exposure ( e. g., 10 minutes ).
So < sup > 256 </ sup > Fm was produced by the decays of cyclotron-synthesized mendelevium.
So if L ( r ) is proportional to r < sup >− 2 </ sup >, then for to be finite, N ( r ) must be proportional to r < sup > b </ sup >, where b < 1.
So beginning at the left and moving to the right, find the first ( and in this case, the only ) parenthesis, that is, ( 2 + 2 < sup > 2 </ sup >).
So the correct value for our original expression, 4 × 2 < sup > 2 </ sup > − ( 2 + 2 < sup > 2 </ sup >), is 10.
So, < τέλειος > (< téleios >, meaning " perfect " and " complete ") yields < τέλεια > (< téleia >, " perfectly ") and < τελείως > (< teleíos >, " completely ").
So the output contains sinusoidal terms with frequencies at the sum ω < sub > 1 </ sub > + ω < sub > 2 </ sub > and difference ω < sub > 1 </ sub >-ω < sub > 2 </ sub > of the two original frequencies.

So and >
So, for example, H ( C = O )( CHOH )< sub > 4 </ sub > H is pentose, H ( CHOH )( C = O )( CHOH )< sub > 3 </ sub > H is pentulose, and H ( CHOH )< sub > 2 </ sub >( C = O )( CHOH )< sub > 2 </ sub > H is pent-3-ulose.

So and k
So that the propagation velocity v is v = x / t = ω / k.
So, when a reaction has a rate constant that obeys the Arrhenius equation, a plot of ln ( k ) versus T < sup > − 1 </ sup > gives a straight line, whose gradient and intercept can be used to determine E < sub > a </ sub > and A.
This proves that B is the direct sum of im q and ker t. So, for all b in B, b can be uniquely identified by some a in A, k in ker t, such that b
So, λ < sub > k </ sub > is the rate of change of the quantity being optimized as a function of the constraint variable.
So whether the sound is written with the letters " c " or " k " in I. T. A.
So a nonzero number is a residue mod 8, 16, etc., if and only if it is of the form 4 < sup > k </ sup >( 8n + 1 ).
However, it is often desirable to study hypergraphs where all hyperedges have the same cardinality ; a k-uniform hypergraph is a hypergraph such that all its hyperedges have size k. ( In other words, it is a collection of sets of size k .) So a 2-uniform hypergraph is a graph, a 3-uniform hypergraph is a collection of unordered triples, and so on.
* Spec k, the spectrum of the polynomial ring over a field k, which is also denoted, the affine line: the polynomial ring is known to be a principal ideal domain and the irreducible polynomials are the prime elements of k. If k is algebraically closed, for example the field of complex numbers, a non-constant polynomial is irreducible if and only if it is linear, of the form t − a, for some element a of k. So, the spectrum consists of one closed point for every element a of k and a generic point, corresponding to the zero ideal.
So for k even the polynomials Z ( E, T ) have no zeros in this region, or in other words the eigenvalues of Frobenius on the stalks of E < sup > k </ sup > have absolute value at most q < sup > k ( d − 1 )/ 2 + 1 </ sup >.
So construct the midpoint H between O and P, and draw a circle centered at H through O and P. By Thales ' theorem, the sought point T is the intersection of this circle with the given circle k, because that is the point on k that completes a right triangle OTP.
always keeping in mind that n is the position of the node among the ones of level k or higher for integer k. So the search time is constant in the best case ( if the found node is the highest possible level ) and 2 times the worst case for the search time for the totally derandomized skip-list ( because we have to keep moving left twice rather than keep moving left once ).
So, q is collated just after k, x ( pronounced like a German ch ) is collated just after h and ə ( pronounced roughly like an English short a ) is collated just after e.
So RLL's are generally specified as ( d, k ) RLL.
So, at every iteration, the vector b < sub > k </ sub > is multiplied by the inverse of the matrix and normalized.
So the choice of the constant C < sub > k </ sub > is especially important-taking too small value will lead to fast growth of the norm of b < sub > k </ sub > and to the overflow ; for too big C < sub > k </ sub > vector b < sub > k </ sub > will tend to zero.

So and is
So great a man could not but understand, too, that the thing that moves men to sacrifice their lives is not the error of their thought, which their opponents see and attack, but the truth which the latter do not see -- any more than they see the error which mars the truth they themselves defend.
So we see that a specialist is a man who knows more and more about less and less as he develops, as contrasted to the generalist, who knows less and less about more and more.
So in these pages the term `` technology '' is used to include any and all means which could amplify, project, or augment man's control over himself and over other men.
So it is that we relive his opening statement in the first television address with the dramatic immediacy of the present.
So far as the existing body of formal principle and procedure is concerned, categorical novelties are not to be anticipated in Jewish-Gentile relationships ; ;
Again omitting recent developments, E.T. Leeds' dictum of 1913 has stood unchallenged: `` So far as archaeology is concerned, there is not the least warrant for the second ( shore occupied by ) of these theories ''.
So far as I am concerned, the child is unmistakably father to the man, despite the obvious fact that child and father differ greatly -- sometimes for the better and sometimes for the worse.
So far as the record is concerned, the Western powers have not acquiesced and should not do so.
So, while we properly inveigh against the new poisoning, history is not likely to justify the pose of righteousness which some in the West were so quick to assume when Mr. Khrushchev made his cynical and irresponsible threat.
So don't see yourself as a heroine or fancy this little adventure is an event of major importance ''.
( Note: So far as State Police cars are concerned, only their replacement is under this division ).
So many times I have wondered why veterinarians do not wipe the table clean before each new canine patient is placed on it for examination.
So far as I can see, there is only one way out for the positivist.
So far these remarks, like most criticisms of Hardy, have tacitly assumed that his poetry is all of a piece, one solid mass of verse expressing a sensibility at a single stage of development.
So it is with Great Expectations, whether the hands be Orlick's as he strikes down Mrs. Gargery or Pip's as he steals a pie from her pantry.
So Dartmouth is moving closer to the others in the Ivy group.
So, too, is the mathematical competence of a college graduate who has majored in mathematics.
So is the time of the novel.
`` So there it is '', he said.
So what I am trying to tell you is the ' why ' -- that is my point -- and that concerns the spirit of the matter.
So you can see that Gerald G. Ramsey, director of SMU's food services, is not the ordinary type of craven, women-trodden chef.
So it is too with many other spirits which we all know: the spirit of Nazism or Communism, school spirit, the spirit of a street corner gang or a football team, the spirit of Rotary or the Ku Klux Klan.
The biblical symbol for this affirmation is expressed in the words: `` So God created man in his own image ; ;

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