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"...

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

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

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

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

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 −...

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

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

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...

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

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

the gradient image is: Compare the edge strength of the current pixel with the edge strength of the pixel in the positive and negative gradient directions...

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

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

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

{\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...

In numerical optimization, the nonlinear conjugate gradient method generalizes the conjugate gradient method to nonlinear optimization. For a quadratic...

E} is the total energy, and m 0 {\displaystyle m_{0}} is rest mass. Four-gradient: ∂ ν = ∂ ∂ x ν = ( 1 c ∂ ∂ t , − ∇ ) , {\displaystyle \partial ^{\nu...

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

c} is the speed of light. Setting the four-momentum P α {\displaystyle P_{\alpha }} equal to the four-gradient of the action S {\displaystyle S} , P α...

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

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:...

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

The wave functions are denoted ψ, and ∂μ are the components of the four-gradient operator. In matrix equations, the Pauli matrices are denoted by σμ...

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...

the membrane, and Complex I translocates four protons (H+) across the membrane, thus producing a proton gradient. Complex I is one of the main sites at...

proportional to the particle's concentration gradient. Fick's second law: Prediction of change in concentration gradient with time due to diffusion. A diffusion...