In order to attain the goal of group solidarity and to relieve tension, the high fertility rate provides more group members for mate selection, and the clustering of members in groups fosters acceptance of group controls.

How altruism is framed, organized, carried out, and what motivates it at the group level is an area of focus that sociologists seek to investigate in order to contribute back to the groups it studies and " build the good society ".

Then, in order to prevent Polk from dissipating his forces by implementing his proposal to allow some men to join a partisan group, Johnston ordered him to send Pillow and 5, 000 men to Fort Donelson.

The systematic position of the order Agnostida within the class Trilobita remains uncertain, and there has been continuing debate whether they are trilobites or a stem group.

One day, Korzybski was giving a lecture to a group of students, and he interrupted the lesson suddenly in order to retrieve a packet of biscuits, wrapped in white paper, from his briefcase.

The order Apiales is placed within the asterid group of eudicots as circumscribed by the APG III system.

One of the earliest group automorphisms ( automorphism of a group, not simply a group of automorphisms of points ) was given by the Irish mathematician William Rowan Hamilton in 1856, in his Icosian Calculus, where he discovered an order two automorphism, writing:

Many scholars see the persistence of Germanic Arianism as a strategy that was followed in order to differentiate the Germanic elite from the local inhabitants and their culture and also to maintain the Germanic elite's separate group identity.

After the termination of this engagement he began to work on his own account, and received from his patron an order for a group, Orpheus and Eurydice.

In the Dymshits – Kuznetsov hijacking affair on 15 June 1970, a group of Soviet refuseniks attempted to hijack a civilian aircraft in order to escape to the West, were caught and spent many years in Soviet prisons.

The group Wee Sing released an alphabet song with the letters in reverse order.

In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on their order ( the axiom of commutativity ).

The Brassicales are an order of flowering plants, belonging to the eurosids II group of dicotyledons under the APG II system.

Continuing violence by British troops escalated, and eventually the order was given to mobilise the troops in an arrest operation, chasing the tail of the main group of marchers to the edge of the field by Free Derry Corner.

In mathematics a combination is a way of selecting several things out of a larger group, where ( unlike permutations ) order does not matter.

The Cucurbitales are an order of flowering plants, included in the rosid group of dicotyledons.

In order to halt the ongoing economic collapse, economic reforms were drafted by a group of technocrats known as the Chicago Boys because many of them had been trained or influenced by University of Chicago professors.

* Lattice AN6017 application note comparing and contrasting filters ( in order of damping coefficient, from lower to higher values ): Gaussian, Bessel, linear phase, Butterworth, Chebyshev, Legendre, elliptic.

In certain circumstances, waves of unchanging shape also can occur in nonlinear media ; for example, the figure shows ocean waves in shallow water that have sharper crests and flatter troughs than those of a sinusoid, typical of a cnoidal wave, a traveling wave so named because it is described by the Jacobi elliptic function of m-th order, usually denoted as.

ECM gets around this obstacle by considering the group of a random elliptic curve over the finite field Z < sub > p </ sub >, rather than considering the multiplicative group of Z < sub > p </ sub > which always has order p − 1.

Remark: You will only find factors if the group order of the elliptic curve over ( denoted by #) is B-smooth, which means that all prime factors of # have to be less or equal to.

Any elliptic curve in Edwards form has a point of order 4.

When the spacecraft has reached its destination orbit, its orbital speed ( and hence its orbital energy ) must be increased again in order to change the elliptic orbit to the larger circular one.

They used additional structures: in the case of the field of rational numbers they use roots of unity in the case of imaginary quadratic extensions of the field of rational numbers they use elliptic curves with complex multiplication and their points of finite order.

To see this consider the case of a supersingular elliptic curve over a finite field of characteristic p. The endomorphism ring of this is an order in a quaternion algebra over the rationals, and should act on the first cohomology group, which should be a 2 dimensional vector space over the coefficient field by analogy with the case of a complex elliptic curve.

For example, a pseudoinverse of an elliptic differential operator of positive order is not a differential operator, but is a pseudodifferential operator.

Pseudodifferential operators have an order, which can be any real number or even −∞, and have symbols ( which are no longer polynomials on the cotangent space ), and elliptic differential operators are those whose symbols are invertible for sufficiently large cotangent vectors.

* If the manifold is allowed to have boundary, then some restrictions must be put on the domain of the elliptic operator in order to ensure a finite index.

The number of independent basis points with infinite order is called the rank of the curve, and is an important invariant property of an elliptic curve.

# showed that if a modular elliptic curve has a first-order zero at s = 1 then it has a rational point of infinite order ; see Gross – Zagier theorem.

# showed that for elliptic curves defined over an imaginary quadratic field K with complex multiplication by K, if the L-series of the elliptic curve was not zero at s = 1, then the p-part of the Tate – Shafarevich group had the order predicted by the Birch and Swinnerton-Dyer conjecture, for all primes p > 7.

If P = ( x, y ) is a rational point of finite order on C, for the elliptic curve group law, then:

For example, the p-torsion of an elliptic curve in characteristic zero is locally isomorphic to the constant elementary abelian group scheme of order p < sup > 2 </ sup >, but over F < sub > p </ sub >, it is a finite flat group scheme of order p < sup > 2 </ sup > that has either p connected components ( if the curve is ordinary ) or one connected component ( if the curve is supersingular ).

The ring of endomorphisms of an elliptic curves can be of one of three forms: the integers Z ; an order in an imaginary quadratic number field ; or an order in a definite quaternion algebra over Q.

Indeed, let K be an imaginary quadratic field with class field H. Let E be an elliptic curve with complex multiplication by the integers of K, defined over H. Then the maximal abelian extension of K is generated by the x-coordinates of the points of finite order on some Weierstrass model for E over H.

Let L be an elliptic operator of order 2k with coefficients having 2k continuous derivatives.

Let Q be a nonsingular quadric surface bearing reguli Af and Af, and let **zg be a Af curve of order K on Q.

The order of this congruence is Af, since Af secants of a curve of symbol ( B ) on a quadric surface pass through an arbitrary point.

By ( 1 ), the image of this pencil is a ruled surface of order Af which is met by the plane of the pencil in a curve, C, of order Af.

To avoid this contradiction it is necessary that C be composite, with the secant of **zg and a curve of order Af as components.

A Bézier curve is defined by a set of control points P < sub > 0 </ sub > through P < sub > n </ sub >, where n is called its order ( n

For a population of size n, with a sequence of values y < sub > i </ sub >, i = 1 to n, that are indexed in non-decreasing order ( y < sub > i </ sub > ≤ y < sub > i + 1 </ sub >), the Lorenz curve is the continuous piecewise linear function connecting the points ( F < sub > i </ sub >, L < sub > i </ sub > ), i

With the fierce price competitiveness created by this sticky-upward demand curve, firms use non-price competition in order to accrue greater revenue and market share.

Each had clearly been worked with the final visual effect in mind ; the orthostats widen slightly towards the top in order that their perspective remains constant when viewed from the ground, while the lintel stones curve slightly to continue the circular appearance of the earlier monument.

A Van de Graaff generator terminal doesn't need to be sphere shaped in order to work, and in fact the optimum shape is a sphere with an inward curve around the hole where the belt enters.

In the illustration, the results for the diluted test samples can be compared to the results of the standard curve ( the blue line in the illustration ) in order to determine an estimate of the amount of protein in the unknown sample.

In three-dimensions, the third order behavior of a curve is described by a related notion of torsion, which measures the extent to which a curve tends to perform a corkscrew in space.

The ESD determines the external parameters such as acceleration curve, temperature and pressure and only activates the weapon when these external effects occur in the correct order and must fall within specific parameters.

Until 1964, trains were forced to follow a sharp curve along a contour in order to avoid steep gradients.

Every Edwards curve with a point of order 3 can be written in the ways shown above.

Firms face a kinked demand curve if, when one firm decreases its price, other firms will follow suit in order to maintain sales, and when one firm increases its price, its rivals are unlikely to follow, as they would lose the sales ' gains that they would otherwise get by holding prices at the previous level.

In order to be an isochrone, the Lagrangian must be that of a simple harmonic oscillator: the height of the curve must be proportional to the arclength squared.

In particular, the steepness and complexity of the response curve is a deciding factor for the filter order and feasibility.

In the late 1980s, and in line with Japanese, French and German thinking of the time, British Rail put forward a track realignment scheme to raise speeds on the WCML ; a proposed project called InterCity 250, which entailed realigning parts of the line in order to increase curve radii and smooth gradients in order to facilitate higher speed running.