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* P. s. senegalus ( the nominate subspecies ): this subspecies has a yellow vest ; its native range includes southern Mauritania, southern Mali to Guinea and Lobos Island.
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P and .
Add holes in top, forming `` S '' for salt and `` P '' for pepper.
If Af is the change per unit volume in Gibbs function caused by the shear field at constant P and T, and **yr is the density of the fluid, then the total potential energy of the system above the reference height is Af.
Since Af and P divides Af for Af, we have Af.
It is clear that each vector in the range of Af is in Af for if **ya is in the range of Af, then Af and so Af because Af is divisible by the minimal polynomial P.
Thus Af is divisible by the minimal polynomial P of T, i.e., Af divides Af.
In the primary decomposition theorem, it is not necessary that the vector space V be finite dimensional, nor is it necessary for parts ( A ) and ( B ) that P be the minimal polynomial for T.
If T is a linear operator on an arbitrary vector space and if there is a monic polynomial P such that Af, then parts ( A ) and ( B ) of Theorem 12 are valid for T with the proof which we gave.
If D denotes the differentiation operator and P is the polynomial Af then V is the null space of the operator p (, ), because Af simply says Af.
Ten students act as managers for a high-school football team, and of these managers a proportion P are licensed drivers.
The word `` binomial '' means `` of two names '' or `` of two terms '', and both usages apply in our work: the first to the names of the two outcomes of a binomial trial, and the second to the terms P and Af that represent the probabilities of `` success '' and `` failure ''.
The constancy of P and the independence are the conditions most likely to give trouble in practice.
Obviously, very slight changes in P do not change the probabilities much, and a slight lack of independence may not make an appreciable difference.
We shall find a formula for the probability of exactly X successes for given values of P and N.
Therefore each binomial trial can be thought of as producing a value of a random variable associated with that trial and taking the values 0 and 1, with probabilities Q and P respectively.
On C, from the point P at Af to the point Q at Af, we construct the chord, and upon the chord as a side erect a square in such a way that as S approaches zero the square is inside C.
As S increases we consider the two free corner points of the square, Af and Af, adjacent to P and Q respectively.
We again consider a fixed point P at Af and a variable point Q at Af on C.
We erect a square with PQ as a side and with free corners Af and Af adjacent to P and Q respectively.
Now with P fixed at Af, Af-values occur when the corner Af crosses C, and are among the values of S such that Af.
Moreover, if Af and Af are two planes intersecting in a line l, tangent to Q at a point P, the two free intersections of the image curves Af and Af must coincide at P', the image of P, and at this point Af and Af must have a common tangent l'.
To do this we must first show that every line which meets **zg in a point P meets its image at P.
But if this is the case, then an arbitrary pencil of lines having a point, P, of **zg as vertex is transformed into a ruled surface of order Af having Af generators concurrent at P.
P and s
Thus, if P is a program in L < sub > 2 </ sub > which is a minimal description of s, then InterpretLanguage ( P ) returns the string s. The length of this description of s is the sum of
# The length of P which by definition is K < sub > 2 </ sub >( s ).
If we assume the controller C, the plant P, and the sensor F are linear and time-invariant ( i. e., elements of their transfer function C ( s ), P ( s ), and F ( s ) do not depend on time ), the systems above can be analysed using the Laplace transform on the variables.
catenary is suspended at given points P < sub > 1 </ sub > and P < sub > 2 </ sub > and with given length s. The equation can be determined in this case as follows:
( E ) exhaust camshaft, ( I ) intake camshaft, ( S ) spark plug, ( V ) poppet valve | valve s, ( P ) piston, ( R ) connecting rod, ( C ) crankshaft, ( W ) water jacket for coolant flow.
In 1996, Neil Robertson, Daniel P. Sanders, Paul Seymour, and Robin Thomas created a quadratic time algorithm, improving on a quartic algorithm based on Appel and Haken ’ s proof (; ).
The Fourier transform of a periodic function, s < sub > P </ sub >( t ), with period P, becomes a Dirac comb function, modulated by a sequence of complex coefficients:
The inverse transform, known as Fourier series, is a representation of s < sub > P </ sub >( t ) in terms of a summation of a potentially infinite number of harmonically related sinusoids or complex exponential functions, each with an amplitude and phase specified by one of the coefficients:
When s < sub > P </ sub >( t ), is expressed as a periodic summation of another function, s ( t ):
A sufficient condition for recovering s ( t ) ( and therefore S ( ƒ )) from just these samples is that the non-zero portion of s ( t ) be confined to a known interval of duration P, which is the frequency domain dual of the Nyquist – Shannon sampling theorem.
: P ( s )
P and senegalus
* Senegal Parrot, P. senegalus
P. senegalus is smaller than its brethren, reaching about 35. 5 cm ( 14 ").
P. senegalus senegalus
P. senegalus meridionalis
P. senegalus meridionalis is also thought to be a regional variant of Polypterus senegalus senegalus
P and nominate
The subspecies are fairly close in size, with the nominate subspecies averaging, P. h. carolinensis averaging and P. h. cristatus averaging.
The nominate P. p. phoenicurus is found all over Europe and reaches into Siberia.
* P. p. pyrrhocorax, the nominate subspecies and smallest form, is endemic to the British Isles, where it is restricted to Ireland, the Isle of Man, and the far west of Wales and Scotland, although it recolonised Cornwall in 2001 after an absence of 50 years.
P. p. pyrrhocorax ; nominate subspecies flying in Cornwall, England
The adult of the " nominate " subspecies of the Red-billed Chough, P. p. pyrrhocorax, is 39 – 40 centimetres ( 15 – 16 in ) in length, has a 73 – 90 centimetres ( 29 – 35 in ) wingspan, and weighs an average 310 grammes ( 10. 9 oz ).
* P. g. graculus, the nominate subspecies in Europe, north Africa, Turkey, the Caucusus and northern Iran.
The subspecies P. g. digitatus averages slightly larger than the nominate form, weighing 191 – 244 grams ( 6. 8 – 8. 7 oz ) against 188 – 252 g ( 6. 7 – 9. 0 oz ) for P. g. graculus, and it has stronger feet.
P. d. balearoibericus is slightly paler than the nominate but darker than P. d. bibilicus.
The Red-necked Grebe has two subspecies, the nominate subspecies P. g. grisegena in Europe and western Asia, and P. g. holboelii ( Holboell's Grebe, named for Danish explorer of Greenlandic birds Carl Peter Holbøll ) in North America and eastern Siberia.
The subspecies P. g. holboelii is larger than the nominate race at 43 – 56 cm ( 17 – 22 in ) length, with a 61 – 88 cm ( 24 – 35 in ) wingspan, and a weight of 750 – 1, 600 g ( 27 – 57 oz ).
The Red-necked grebe has a large range, estimated at 1 – 10 million square kilometres ( 0. 4 – 3. 8 million square miles ), and a global population of 150, 000 – 370, 000 individuals, with P. g. holboellii about twice as numerous as the nominate race.
Black-necked Grebes of the nominate subspecies P. n. nigricollis in the cooler temperate regions of the Old World also winter further south, with many European birds moving to the Mediterranean area.
* P. c. collybita, the nominate form, breeds in Europe east to Poland and Bulgaria, and is described below.
It is intermediate in appearance between P. c. tristis and P. c. collybita, being grey-washed olive-green above with a pale yellow supercilium, and underparts whiter than in P. c. collybita, but it has very similar vocalisations to the nominate subspecies.
The nominate western subspecies P. c. canariensis of El Hierro, La Palma, La Gomera, Tenerife, and Gran Canaria is smaller than Common Chiffchaff, and has shorter, rounder wings.
The nominate subspecies is similar to P. c. tristis, but with a finer darker bill, browner upperparts and buff flanks ; its song is almost identical to P. collybita, but the call is a weak psew.
P. s. lorenzii is warmer and darker brown than the nominate race ; it is sympatric with Common Chiffchaff in a small area in the Western Caucasus, but interbreeding occurs rarely, if ever.
The spring adult of the western nominate subspecies P. c. collybita has brown-washed dull green upperparts, off-white underparts becoming yellowish on the flanks, and a short whitish supercilium.
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