In transition regions, where this pressure dependent dissociation is incomplete, both the differential, constant pressure heat capacity and beta ( the volume / pressure differential ratio ) will greatly increase.

With the corresponding increase in tape length, there was a greater velocity differential between the tape being drawn from the center of the reel and the tape being fed back to the outer edge of the reel as it passed the capstan / pinch-roller assembly ( loop length ).

For example, in charging such a capacitor the differential increase in voltage with charge is governed by:

In transition regions, where this pressure dependent dissociation is incomplete, both beta ( the volume / pressure differential ratio ) and the differential, constant pressure heat capacity will greatly increase.

Differential hardening ( also called differential quenching, selective quenching, selective hardening, or local hardening ) is most commonly used in bladesmithing to increase the toughness of a blade while keeping very high hardness and strength at the edge.

Thus, if 105 g can ( only just ) be distinguished from 100 g, the jnd ( or differential threshold ) is 5 g. If the mass is doubled, the differential threshold also doubles to 10 g, so that 210 g can be distinguished from 200 g. In this example, a weight ( any weight ) seems to have to increase by 5 % for someone to be able to reliably detect the increase, and this minimum required fractional increase ( of 5 / 100 of the original weight ) is referred to as the " Weber fraction " for detecting changes in weight.

where dp is the differential change in perception, dS is the differential increase in the stimulus and S is the stimulus at the instant.

In practice the above definition of marginal cost as the change in total cost as a result of an increase in output of one unit is inconsistent with the differential definition of marginal cost for virtually all non-linear functions.

At differential mode ( the two input voltages change in opposite directions ), the two voltage ( emitter ) followers oppose each other-while one of them tries to increase the voltage of the common emitter point, the other tries to decrease it ( figuratively speaking, one of them " pulls up " the common point while the other " looses " it so that it stays immovable ) and v. v.

However, characters which are neither differential nor diagnostic may be included to increase comprehension ( especially characters that are common to the group, but not unique ).

One disadvantage, at least as compared to the incremental backup method, is that as time from the last full backup ( and, thus, data changes ) increase so does the time to perform the differential backup.

As the differential time rates increase, he again loses control of his body and goes into " pseudo-death ".

" On the other hand, if the characters which lead to differential reproductive success are not heritable, then no meaningful evolution will occur, " survival of the fittest " or not: if improvement in reproductive success is caused by traits that are not heritable, then there is no reason why these traits should increase in frequency over generations.

The Sileighty includes performance-oriented modifications such as a new ECU, a stiffer suspension system, an improved limited slip differential, and an increase in turbocharger boost from to about, resulting in approximately, versus 205 from the standard Silvia's SR20DET or the 180SX's CA18DET.

Due to the constant production of landfill gas, the increase in pressure within the landfill ( together with differential diffusion ) causes the gas's release into the atmosphere.

The increase of the differential resistance around zero bias is called the Coulomb blockade.

The differential entropy of a distribution can be defined in terms of its quantile density, specifically

Other important information theoretic quantities include Rényi entropy ( a generalization of entropy ), differential entropy ( a generalization of quantities of information to continuous distributions ), and the conditional mutual information.

The differential entropy of the multivariate normal distribution is

Since the entropy is an exact differential, using the chain rule, the change in entropy when going from a reference state 0 to some other state with entropy S may be written as where:

Although analytical solutions to this problem are scarce, there are upper and lower bounds to these functions including the famous Shannon lower bound ( SLB ), which in the case of squared error and memoryless sources, states that for arbitrary sources with finite differential entropy,

where h ( D ) is the differential entropy of a Gaussian random variable with variance D. This lower bound is extensible to sources with memory and other distortion measures.

Expand, writing it in terms of the differential entropy:

Evaluating the differential entropy of a Gaussian gives:

From this bound, we infer from a property of the differential entropy that

where is the differential entropy of the Gaussian density with the same mean and variance as and is the differential entropy of:

By extending the discrete information entropy to the continuous information entropy, also called differential entropy, one obtains the expression in Eq.

Assuming the fluctuations are small, the probability distribution function can be expressed through the second differential of the entropy

Alternatively, one can apply the thermodynamic identity for differential entropy:

( See the differential entropy article for a derivation.

This is especially useful in thermodynamics where temperature becomes the integrating factor that makes entropy an exact differential.

Flux F through a surface, dS is the Differential ( infinitesimal ) | differential vector area element, n is the unit normal to the surface.

A process S is said to follow a geometric Brownian motion with volatility σ and drift μ if it satisfies the stochastic differential equation dS

Suppose a stock price follows a Geometric Brownian motion given by the stochastic differential equation dS = S ( σdB + μ dt ).

Illustration of how flux j passes through open curved surfaces S ( dS is differential vector area ).

These results can be generalized further to curved surfaces by reducing the vector surfaces into infinitely many differential surface elements ( that is S → dS ), then integrating over the surface:

where is the view factor between differential areas d < sub > Σ </ sub > and dS.

* Basis ( options ), the value differential between a call option and a put option

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 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.

The k-th exterior power of the cotangent space, denoted Λ < sup > k </ sup >( T < sub > x </ sub >< sup >*</ sup > M ), is another important object in differential geometry.

Thus differential geometry may study differentiable manifolds equipped with a connection, a metric ( which may be Riemannian, pseudo-Riemannian, or Finsler ), a special sort of distribution ( such as a CR structure ), and so on.

The analysis of linear systems is possible because they satisfy a superposition principle: if u ( t ) and w ( t ) satisfy the differential equation for the vector field ( but not necessarily the initial condition ), then so will u ( t ) + w ( t ).

* Xuejia Lai and James L. Massey and S. Murphy, Markov ciphers and differential cryptanalysis, Advances in Cryptology — Eurocrypt ' 91, Springer-Verlag ( 1992 ), pp17 – 38.

They provide a natural framework for analysing the continuous symmetries of differential equations ( differential Galois theory ), in much the same way as permutation groups are used in Galois theory for analysing the discrete symmetries of algebraic equations.

The rule is named after the 17th-century French mathematician Guillaume de l ' Hôpital, who published the rule in his book Analyse des Infiniment Petits pour l ' Intelligence des Lignes Courbes ( literal translation: Analysis of the Infinitely Small for the Understanding of Curved Lines ) ( 1696 ), the first textbook on differential calculus.

An online resource focusing on algebraic, ordinary differential, partial differential ( mathematical physics ), integral, and other mathematical equations.

If the fluid being measured is significantly dense, hydrostatic corrections may have to be made for the height between the moving surface of the manometer working fluid and the location where the pressure measurement is desired except when measuring differential pressure of a fluid ( for example across an orifice plate or venturi ), in which case the density ρ should be corrected by subtracting the density of the fluid being measured.

The main difference is that notation symbols are differential rather than absolute, i. e. they indicate pitch change ( rise or fall ), and the musician has to deduce correctly, from the score and the note they are singing presently, which note comes next.

* Node ( autonomous system ), behaviour for an ordinary differential equation near a critical point

Conventional radiography is useful, both by itself and in conjunction with CT or MRI, for detecting complications of osteopenia ( reduced bone mass ; pre-osteoporosis ), such as fractures ; for differential diagnosis of osteopenia ; or for follow-up examinations in specific clinical settings, such as soft tissue calcifications, secondary hyperparathyroidism, or osteomalacia in renal osteodystrophy.

Other types of differential amplifier include the fully differential amplifier ( similar to the op-amp, but with two outputs ), the instrumentation amplifier ( usually built from three op-amps ), the isolation amplifier ( similar to the instrumentation amplifier, but with tolerance to common-mode voltages that would destroy an ordinary op-amp ), and negative feedback amplifier ( usually built from one or more op-amps and a resistive feedback network ).