If F ≥ F < sub > Critical </ sub > ( Numerator DF, Denominator DF, α )

Other psychotropic analgesic agents include ketamine ( an NMDA receptor antagonist ), clonidine and other α < sub > 2 </ sub >- adrenoreceptor agonists, and mexiletine and other local anaesthetic analogues.

It exists in four major polymorphs: α, β, γ and T. Whereas α, β and T phases are based on B < sub > 12 </ sub > icosahedra, the γ-phase can be described as a rocksalt-type arrangement of the icosahedra and B < sub > 2 </ sub > atomic pairs.

The ( α, 2n ) reaction induced by the irradiation yielded the < sup > 243 </ sup > Bk isotope and two free neutrons:

At ambient conditions, berkelium assumes its most stable α form which has a hexagonal symmetry, space group P6 < sub > 3 </ sub >/ mmc, lattice parameters of 341 pm and 1107 pm.

Bessel functions of the first kind, denoted as J < sub > α </ sub >( x ), are solutions of Bessel's differential equation that are finite at the origin ( x = 0 ) for integer α, and diverge as x approaches zero for negative non-integer α.

The solution type ( e. g., integer or non-integer ) and normalization of J < sub > α </ sub >( x ) are defined by its properties below.

Plot of Bessel function of the first kind, J < sub > α </ sub >( x ), for integer orders α = 0, 1, 2.

For non-integer α, the functions J < sub > α </ sub >( x ) and J < sub >− α </ sub >( x ) are linearly independent, and are therefore the two solutions of the differential equation.

The Bessel functions of the second kind, denoted by Y < sub > α </ sub >( x ), occasionally denoted instead by N < sub > α </ sub >( x ), are solutions of the Bessel differential equation.

Plot of Bessel function of the second kind, Y < sub > α </ sub >( x ), for integer orders α = 0, 1, 2.

Another important formulation of the two linearly independent solutions to Bessel's equation are the Hankel functions H < sub > α </ sub >< sup >( 1 )</ sup >( x ) and H < sub > α </ sub >< sup >( 2 )</ sup >( x ), defined by:

The functions J < sub > α </ sub >, Y < sub > α </ sub >, H < sub > α </ sub >< sup >( 1 )</ sup >, and H < sub > α </ sub >< sup >( 2 )</ sup > all satisfy the recurrence relations:

In particular, if α = m + 1 / 2 with m a nonnegative integer, the above relations imply directly that

for α > − 1 / 2 and where δ is the Dirac delta function.

Y < sub > α </ sub >, then C < sub > α </ sub > is 2 / π.

The primary ( α < sup > 2 </ sup > Cap ), 109 light-years from Earth, is a yellow-hued giant star of magnitude 3. 6 .; the secondary ( α < sup > 1 </ sup > Cap ), 690 light-years from Earth, is a yellow-hued supergiant star of magnitude 4. 3.

α < sup > 1 </ sup > Capricorni is accompanied by a star of magnitude 9. 2 ; α < sup > 2 </ sup > Capricornus is accompanied by a star of magnitude 11. 0 ; this faint star is itself a binary star with two components of magnitude 11.

Capricornus's brighter stars are found on a triangle whose vertices are α < sup > 2 </ sup > Capricorni ( Giedi ), δ Capricorni ( Deneb Algiedi ), and ω Capricorni.

The goat's tail consists of stars β Cap and α < sup > 2 </ sup > Cap: star β Cap being of the third magnitude.

Alpha ( uppercase Α, lowercase α ; Álpha ) is the first letter of the Greek alphabet.

* α Antliae is the constellation's brightest star at magnitude 4. 25.

* α Apodis is an orange giant 411 light years away, with a magnitude of 3. 8.

Arcturus (; α Boo, α Boötis, Alpha Boötis ) is the brightest star in the constellation Boötes and in fact the northern celestial hemisphere.

This makes Arcturus the third brightest individual star, just ahead of Alpha Centauri A ( α Cen A ), whose visual magnitude is − 0. 01.

Arcturus is notable for its high proper motion, larger than any first magnitude star in the stellar neighborhood other than α Centauri.

Antares ( α Scorpii, α Sco, Alpha Scorpii ) is a red supergiant star in the Milky Way galaxy and the sixteenth brightest star in the nighttime sky.

Altair ( Alpha Aquilae, Alpha Aql, α Aquilae, α Aql, Atair ) is the brightest star in the constellation Aquila and the twelfth brightest star in the night sky.

In Chinese, the asterism consisting of α, β, and γ Aquilae is known as (, ).

Alioth has a relatively weak magnetic field, 15 times weaker than α CVn, but it is still 100 times stronger than that of the Earth.

It contains both α and β ' phase ; the β '- phase is body-centered cubic and is harder and stronger than α. Alpha-beta brasses are usually worked hot.

) For example, Aldebaran is designated α Tauri ( pronounced Alpha Tauri ), which means " Alpha of the Bull ".

Since in a majority of constellations the brightest star is designated Alpha ( α ), many people wrongly assume that Bayer meant to put the stars exclusively in order of their brightness, but in his day there was no way to measure stellar brightness precisely.

Although α and − α produce the same differential equation, it is conventional to define different Bessel functions for these two orders ( e. g., so that the Bessel functions are mostly smooth functions of α ).

On the other hand, for integer order α, the following relationship is valid ( note that the Gamma function becomes infinite for negative integer arguments ):

For non-integer α, Y < sub > α </ sub >( x ) is related to J < sub > α </ sub >( x ) by:

He does not consider β-elements, α-elements, nor α function to actually exist.

Since α < sup > 1 </ sup > Crucis is a spectroscopic binary, this is actually a multiple star.

Although Richard Feynman noted that a simplistic interpretation of the relativistic Dirac equation runs into problems with electron orbitals at Z > 1 / α = 137, suggesting that neutral atoms cannot exist beyond untriseptium, and that a periodic table of elements based on electron orbitals therefore breaks down at this point, a more rigorous analysis calculates the limit to be Z ≈ 173, but also that this limit would not actually spell the end of the periodic table.

If κ is measurable and p ∈ V < sub > κ </ sub > and M ( the ultrapower of V ) satisfies ψ ( κ, p ), then the set of α < κ such that V satisfies ψ ( α, p ) is stationary in κ ( actually a set of measure 1 ).

Despite having the Bayer designation α Ceti, at visual magnitude 2. 54 this star is actually not the brightest star in the constellation Cetus.