differential geometry, the four-gradient (or 4-gradient) ∂ {\displaystyle {\boldsymbol {\partial }}} is the four-vector analogue of the gradient ∇ → {\displaystyle...

In vector calculus, the gradient of a scalar-valued differentiable function f {\displaystyle f} of several variables is the vector field (or vector-valued...

unit vectors, capital bold for four dimensional vectors (except for the four-gradient), and tensor index notation. A four-vector A is a vector with a "timelike"...

denote the d'Alembertian; see below.) Quad, the 4-vector gradient operator or four-gradient, ( ∂ ∂ t , ∂ ∂ x , ∂ ∂ y , ∂ ∂ z ) {\displaystyle \textstyle...

Christoffel symbols are no longer all zero. Four-vector Four-velocity Four-momentum Four-force Four-gradient Proper acceleration Tsamparlis M. (2010). Special...

convention (+ − − −), are written in terms of the electromagnetic four-potential and the four-gradient as: F μ ν = ∂ μ A ν − ∂ ν A μ = [ 0 − E x / c − E y / c −...

where ∂ / ∂ x α {\displaystyle \partial /\partial x^{\alpha }} is the four-gradient. This is the continuity equation. In general relativity, the continuity...

is the four-velocity, and q {\displaystyle q} is the electric charge. four-vector four-velocity four-acceleration four-momentum four-gradient Grot, Richard...

}+\partial ^{\mu }f,} where ∂ μ {\displaystyle \partial ^{\mu }} is the four-gradient and f {\displaystyle f} is any harmonic scalar function: that is, a...

particle of matter with number n {\displaystyle n} . Physics portal Four-force Four-gradient Pauli–Lubanski pseudovector Taylor, Edwin; Wheeler, John (1992)...

definition of the Lorentz factor. Physics portal Four-acceleration Four-momentum Four-force Four-gradient Algebra of physical space Congruence (general relativity)...

the time-averaged four-velocity, ∂ x μ {\displaystyle \partial ^{x^{\mu }}} are the contravariant components of the four-gradient and   ∗ {\displaystyle...

{r}{c}}\right)} where Θ {\displaystyle \Theta } is the Heaviside step function. Four-gradient d'Alembert's formula Klein–Gordon equation Relativistic heat conduction...

Perlin noise is a type of gradient noise developed by Ken Perlin in 1983. It has many uses, including but not limited to: procedurally generating terrain...

relatively steep gradient, causing an increase in water velocity and turbulence. Flow, gradient, constriction, and obstacles are four factors that are...

faster-than-light biquaternion conjugate diameters four-vector four-acceleration four-force four-gradient four-momentum four-velocity hyperbolic orthogonality hyperboloid...

A^{\mu }} is the four potential ( ϕ / c , A ) {\displaystyle (\phi /c,\mathbf {A} )} ∂ ν {\displaystyle \partial _{\nu }} is the four gradient ( ∂ ∂ ( c t...

The histogram of oriented gradients (HOG) is a feature descriptor used in computer vision and image processing for the purpose of object detection. The...

A pulsed field gradient is a short, timed pulse with spatial-dependent field intensity. Any gradient is identified by four characteristics: axis, strength...

coordinates are shown below in the expression for the square of the four-gradient operator: We may rewrite the Kerr metric (1) in the following form:...

{\displaystyle {\mathcal {L}}(\varphi ,\partial _{\mu }\varphi ,x_{\mu })} see four-gradient. The μ is an index which takes values 0 (for the time coordinate), and...

}A_{\mu }.} where ∂ {\displaystyle \partial } is the four-gradient and A {\displaystyle A} is the four-potential. SI units for Maxwell's equations and the...

fields in manifest covariance; the partial derivatives that form the four-gradient ∂μ alone are not enough. The components which act on the color triplet...

stress–energy tensor, and ∂ are partial derivatives that make up the four-gradient (in non-Cartesian coordinates this must be replaced by the covariant...

{\displaystyle \partial _{\gamma }T^{\beta \gamma }=0} where ∂γ is the four-gradient. (In non-Cartesian coordinates and general relativity this would be...

electrochemical gradient is a gradient of electrochemical potential, usually for an ion that can move across a membrane. The gradient consists of two...

The grade (US) or gradient (UK) (also called stepth, slope, incline, mainfall, pitch or rise) of a physical feature, landform or constructed line is either...

Image Gradient Operator" at a talk at SAIL in 1968. Technically, it is a discrete differentiation operator, computing an approximation of the gradient of...

Saint-Hilaire in Rouen, an 800-metre (2,600 ft) climb with an average gradient of 10.6%, which topped with 5 kilometres (3.1 mi) to go. On that climb...

parries, including Gradient Attacks, Gradient Counters, and Gradient Skills, all of which deal devastating damage. The use of gradient attacks is monitored...