The theory predicts a linear dependence of Af on Af, where J is the experimentally determined Curie-Weiss constant.

For a vector with linear addressing, the element with index i is located at the address B + c · i, where B is a fixed base address and c a fixed constant, sometimes called the address increment or stride.

where r is the position vector of the particle relative to the origin, p is the linear momentum of the particle, and × denotes the cross product.

** for an-sentence conversation where the conversation history must be retransmitted and the person takes linear time to read the query

In linear algebra, a bilinear transformation is a binary function where the sets X, Y, and Z are all vector spaces and the derived functions f < sup > x </ sup > and f < sub > y </ sub > are all linear transformations.

Conversely it may generate too many points in areas where the curve is close to linear.

The internal rendering of all Bézier curves in font or vector graphics renderers will split them recursively up to the point where the curve is flat enough to be drawn as a series of linear or circular segments.

In calculus, this picture also gives a geometric proof of the derivative if one sets and interpreting b as an infinitesimal change in a, then this picture shows the infinitesimal change in the volume of an n-dimensional hypercube, where the coefficient of the linear term ( in ) is the area of the n faces, each of dimension

** An oscillating member where this clutch can then convert the oscillations into intermittent linear or rotational motion of the complimentary member ; others use ratchets with the pawl mounted on a moving member

Matrix methods are significantly limited for MIMO systems where linear independence cannot be assured in the relationship between inputs and outputs.

In principle the database storage can be viewed as a linear address space, where every bit of data has its unique address in this address space.

In principle the database storage can be viewed as a linear address space, where every bit of data has its unique address in this address space.

Multiplying by a linear phase for some integer m corresponds to a circular shift of the output: is replaced by, where the subscript is interpreted modulo N ( i. e., periodically ).

Over time, the limitations have become much less significant, and now most compositing is done in a linear color space, even in cases where the source imagery is in a logarithmic color space.

The term " low ceiling diuretic " is used to indicate that a diuretic has a rapidly flattening dose effect curve ( in contrast to " high ceiling ", where the relationship is close to linear ).

The Earley parser executes in cubic time in the general case, where n is the length of the parsed string, quadratic time for unambiguous grammars, and linear time for almost all LR ( k ) grammars.

In general, a quadratic equation can be expressed in the form, where is not zero ( if it were zero, then the equation would not be quadratic but linear ).

The greatest common divisor g of two nonzero numbers a and b is also their smallest positive integral linear combination, that is, the smallest positive number of the form ua + vb where u and v are integers.

The set of all integral linear combinations of a and b is actually the same as the set of all multiples of g ( mg, where m is an integer ).

This relationship is represented in a linear regression where the change in unemployment rate () is a function of an intercept (), a given value of GNP growth multiplied by a slope coefficient and an error term,:

Ordinary least squares ( OLS ) is often used for estimation since it provides the BLUE or " best linear unbiased estimator " ( where " best " means most efficient, unbiased estimator ) given the Gauss-Markov assumptions.

The in-between region is sometimes considered to be part of the ohmic or linear region, even where drain current is not approximately linear with drain voltage.

However, iterative methods are often useful even for linear problems involving a large number of variables ( sometimes of the order of millions ), where direct methods would be prohibitively expensive ( and in some cases impossible ) even with the best available computing power.

These nodes are areas where the action potential is amplified using a high density of sodium ( Na < big >+</ big >) ions and is subsequently passed along the axon.

where is the acoustic pressure and is the acoustic fluid velocity vector, is the vector of spatial coordinates, is the time, is the static mass density of the medium and is the bulk modulus of the medium.

where is the mass density of the fluid and is the fluid velocity.

The exception is very near absolute zero, where the density of adiabats drops sharply and they become rare ( see Nernst's theorem ).

In cases where the density of the air is significantly different from the calibration value ( as on a high mountain, or with an exceptionally low barometer ) an allowance must be made.

Population density also has a major impact, where dense urbanisation such as in Japan and the far east has led to the adoption of high capacity long multi-axle buses, often double-deckers, while South America and China are implementing large numbers of articulated buses for bus rapid transit schemes.

Furthermore, it describes how the density of states is changed on entering the superconducting state, where there are no electronic states any more at the Fermi energy.

where is the difference in density of particles separated by a height difference of, is Boltzmann's constant ( namely, the ratio of the universal gas constant,, to Avogadro's number, ), and is the absolute temperature.

CNTs are readily aligned in a high density geometry ( i. e., a vertically aligned forest ) but lack high charge density surfaces — the sidewalls of the CNTs are similar to the basal plane of graphene and exhibit low charge density except where edge defects exist.

Population density figures conceal a great disparity between the republic's most crowded island, Nzwani, which had a density of 470 persons per square kilometer in 1991 ; Ngazidja, which had a density of 250 persons per square kilometer in 1991 ; and Mwali, where the 1991 population density figure was 120 persons per square kilometer.

where I is current in the conductor, J is the current density, and A is the cross-sectional area.

The density of the cane toad is significantly lower within its native distribution than in places where it has been introduced.

In the nonrelativistic case, electron degeneracy pressure gives rise to an equation of state of the form, where P is the pressure, is the mass density, and is a constant.

Assuming that the strength of the cable is proportional to its density per unit length, the weight, w, per unit length of the chain can be written T / c, where c is constant, and the analysis for nonuniform chains can be applied.

The total cross-section is related to the absorbance of the light intensity through Beer-Lambert's law, which says absorbance is proportional to concentration:, where C is the concentration as a number density, A < sub > λ </ sub > is the absorbance at a given wavelength λ, and is the path length.

The plasma pressure can be calculated by the state equation of a perfect gas, where is the particle number density, the Boltzmann constant and the plasma temperature.

** Normal dynamics, is a stochastic motion having a Gaussian probability density function in position with variance MSD that follows, MSD ~ t, where MSD is the mean squared displacement of the process, and t is the time the process is seen ( normal dynamics and Brownian dynamics are very similar ; the term used depends on the field )

where ρ is the density, m is the mass, and V is the volume.

In the limit of an infinitesimal volume the density of an inhomogeneous object at a point becomes:, where is an elementary volume at position.

where is the density at a reference temperature, is the thermal expansion coefficient of the material.