The new elements in this equation are the 4 × 4 matrices α < sub > k </ sub > and β, and the four-component wave function ψ.

A negative feedback amplifier is a system of three elements ( see Figure 1 ): an amplifier with gain A < sub > OL </ sub >, an attenuating feedback network with a constant β < 1 and a summing circuit acting as a subtractor ( the circle in the figure ).

If X is a topological space, we say that an α-indexed sequence of elements of X converges to a limit x when it converges as a net, in other words, when given any neighborhood U of x there is an ordinal β < α such that x < sub > ι </ sub > is in U for all ι ≥ β.

Equipped with this product, the exterior algebra is an associative algebra, which means that for any elements α, β, γ.

If E is an elliptic curve over a finite field with q elements, then the number of points of E defined over the field with q < sup > m </ sup > elements is 1 − α < sup > m </ sup >− β < sup > m </ sup > + q < sup > m </ sup >,

The protein structure can be considered as a sequence of secondary structure elements, such as α helices and β sheets, which together constitute the overall three-dimensional configuration of the protein chain.

Many elements will have overlapping peaks ( e. g., Ti K < sub > β </ sub > and V K < sub > α </ sub >, Mn K < sub > β </ sub > and Fe K < sub > α </ sub >).

This reduces to solving a set of N equations with N unknowns ( the elements of β ), which has a unique solution as long as the X are linearly independent.

Let GF ( p < sup > m </ sup >) be a field with p < sup > m </ sup > elements, and β an element of it such that the m elements

When representing elements as a binary string ( e. g. in GF ( 2 < sup > 3 </ sup >) the most significant bit represents β < sup > 4 </ sup >, the least significant bit represents β ), we can square elements by doing a left circular shift with wraparound ( left shifting β < sup > 4 </ sup > would give β < sup > 8 </ sup >, but since we are working in GF ( 2 < sup > 3 </ sup >) this wraps around to β ).

Structurally they can be classified according to the functional groups ' locations as alpha-( α -), beta-( β -), gamma-( γ -) or delta-( δ -) amino acids ; other categories relate to polarity, acid / base / neutral, and side chain group type ( including: aliphatic, acyclic, hydroxyl or sulphur-containing, aromatic ).

Carina has the α, β and ε, Vela has γ and δ, Puppis has ζ, and so on.

This name was applied by the Arabs to the asterism of α, β, and γ Aquilae and probably goes back to the ancient Babylonians and Sumerians, who called α Aquilae the eagle star.

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

* In Chinese, (), meaning Northern Dipper, refers to an asterism consisting of ε Ursae Majoris, α Ursae Majoris, β Ursae Majoris, γ Ursae Majoris, δ Ursae Majoris, ζ Ursae Majoris and η Ursae Majoris.

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.

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.

As to the α and β phases, they might both coexist at ambient conditions with the β phase being more stable.

Bayer assigned a lower-case Greek letter, such as alpha ( α ), beta ( β ), gamma ( γ ), etc., to each star he catalogued, combined with the Latin name of the star ’ s parent constellation in genitive ( possessive ) form.

Polaris ( α UMi ), Kochab ( β UMi ), Pherkad ( γ UMi ), Yildun ( δ UMi ), Urodelus ( ε UMi ), Ahfa al Farkadain ( ζ UMi ) and Anwar al Farkadain ( η UMi ).

* Convex cone, a subset C of a vector space V is a convex cone if αx + βy belongs to C, for any positive scalars α, β, and any x, y in C

In the following chemical equation with arrows pointing both ways to indicate equilibrium, A and B are reactant chemical species, S and T are product species, and α, β, σ, and τ are the stoichiometric coefficients of the respective reactants and products:

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

The α and β anomers of glucose.

Note the position of the hydroxyl group ( red or green ) on the anomeric carbon relative to the CH < sub > 2 </ sub > OH group bound to carbon 5: they are either on the opposite sides ( α ), or the same side ( β ).

where A ∈ N ( i. e., A is a single nonterminal ), α, β ∈ ( N U Σ )* ( i. e., α and β are strings of nonterminals and terminals ) and γ ∈ ( N U Σ )< sup >+</ sup > ( i. e., γ is a nonempty string of nonterminals and terminals ).

Given that estimation is undertaken on the basis of a least squares analysis, estimates of the unknown parameters β < sub > j </ sub > are determined by minimising a sum of squares function

:* the function to be minimised is a quadratic function of the β < sub > j </ sub > for which minimisation is a relatively simple problem ;

:* the derivatives of the function are linear functions of the β < sub > j </ sub > making it easy to find the minimising values ;

where β is the Dirichlet beta function.

function alphabeta ( node, depth, α, β, Player )

As derived above, the ordinary generating function for the sequence of squares is With r = 1, α = 0, β = 3, A ( x ) = 0, and B ( x ) = x ( x + 1 ), we can verify that the squares grow as expected, like the squares:

The open-loop gain A < sub > OL </ sub > in general may be a function of both frequency and voltage ; the feedback parameter β is determined by the feedback network that is connected around the amplifier.

The stability characteristics of the gain feedback product β A < sub > OL </ sub > are often displayed and investigated on a Nyquist plot ( a polar plot of the gain / phase shift as a parametric function of frequency ).

The probability density function of the beta distribution, for 0 ≤ x ≤ 1, and shape parameters α > 0 and β > 0, is a power function of the variable x and of its reflection ( 1-x ) as follows:

In some cases the ( maximum ) value of the density function occurring at the end is finite, for example in the case of α = 2, β = 1 ( or α = 1, β = 2 ), the right-triangle distribution, while in several other cases there is a singularity at the end, and hence the value of the density function approaches infinity at the end, for example in the case α = β = 1 / 2, the arcsine distribution.

The C-terminal parts of the α, β and γ chains contain a domain of about 225 amino-acid residues, which can function as a molecular recognition unit.

# The Right-to-Manage model, developed by the British school during the 1980s ( Nickell ), views the labour union and the firm bargaining over the wage rate according to a typical Nash Bargaining Maximin ( written as Ώ = U < sup > β </ sup > Π < sup > 1-β </ sup >, where U is the utility function of the labour union, Π the profit of the firm and β represents the bargaining power of the labour unions ).

Here, β is a function of the geometry of the space-time in which the string moves.

For non-metals, the physical effects called " field penetration " and " band bending " can make β a function of applied voltage, although – surprisingly – there are few studies of this effect.

For α = β = 0, these are called the Legendre polynomials ( for which the interval of orthogonality is and the weight function is simply 1 ):