For each mass flow rate the arc voltage was measured.

For the low-temperature measurements the sample was cooled by a cold nitrogen gas flow method similar to that of Andrew and Eades.

For most acoustics problems we assume that the flow is irrotational, that is, the vorticity is zero.

For example, while the behavior of hypersonic flow is understood, building a scramjet aircraft to fly at hypersonic speeds has seen very limited success.

For flow through a tube with one inlet ( state 1 ) and exit ( state 2 ) as shown in the figure in this section, the continuity equation may be written and solved as:

For instance, F could be expanded into an expression for the frictional force acting on an internal flow.

For higher speeds, the flow will compress more significantly as it comes into contact with surfaces and slows.

For a steady flow of charge through a surface, the current I ( in amperes ) can be calculated with the following equation:

For a net current to flow, more states for one direction than for the other direction must be occupied.

For example, Darwinism may be used to refer to Darwin's proposed mechanism of natural selection, in comparison to more recent mechanisms such as genetic drift and gene flow.

For a flow, it will occur when there are eigenvalues on the imaginary axis.

For systems where the volume is preserved by the flow, Poincaré discovered the recurrence theorem: Assume the phase space has a finite Liouville volume and let F be a phase space volume-preserving map and A a subset of the phase space.

For electrical systems which use alternating current the electrodes are the connections from the circuitry to the object to be acted upon by the electric current but are not designated anode or cathode since the direction of flow of the electrons changes periodically, usually many times per second.

For fluids which are sufficiently dense to be a continuum, do not contain ionized species, and have velocities small in relation to the speed of light, the momentum equations for Newtonian fluids are the Navier-Stokes equations, which is a non-linear set of differential equations that describes the flow of a fluid whose stress depends linearly on velocity gradients and pressure.

For flow of gases, to determine whether to use compressible or incompressible fluid dynamics, the Mach number of the flow is to be evaluated.

For liquids, whether the incompressible assumption is valid depends on the fluid properties ( specifically the critical pressure and temperature of the fluid ) and the flow conditions ( how close to the critical pressure the actual flow pressure becomes ).

Direction of causal flow is upward. For a multivariate function, functional decomposition generally refers to a process of identifying a set of functions such that

" For a related issue regarding trade execution, see payment for order flow.

For stationary and shaft engines including propeller engines, fuel consumption is measured by calculating the brake specific fuel consumption, which measures the mass flow rate of fuel consumption divided by the power produced.

For example, if a liquid or gas contains ions, then the ions can be made to flow as an electric current, and the material is a conductor.

For example, most network cards implement transmit and receive ring buffers, interrupt rate limiting, and hardware flow control.

For instance, an LC may flow like a liquid, but its molecules may be oriented in a crystal-like way.

For vector spaces over non-algebraically closed fields, we still need to find some substitute for characteristic values and vectors.

For each picture frame, the 6502 writes graphics commands for the DVG into a defined area of RAM ( the vector RAM ), and then asks the DVG to draw the corresponding vector image on the screen.

For example an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces.

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.

For an object with a fixed mass that is rotating about a fixed symmetry axis, the angular momentum is expressed as the product of the moment of inertia of the object and its angular velocity vector:

For any system, the following restrictions on measurement results apply, where is the reduced Planck constant and is any direction vector such as x, y, or z:

For a finite-dimensional vector space, using a fixed orthonormal basis, the inner product can be written as a matrix multiplication of a row vector with a column vector:

For a finite-dimensional vector space, the outer product can be understood as simple matrix multiplication:

For 2D vector animations, the rendering process is the key frame illustration process, while tweened frames are rendered as needed.

For example, binary string 1011 is represented by the vector ( 1, 0, 1, 1 ).

For the purposes of this article, we call this constructed vector the transmitted vector.

For a vector expressed in cylindrical coordinates as

For twisting rotation to exist, it is necessary to tilt the body sideways after takeoff, so that there is now a small component of this horizontal angular momentum vector along the body's long axis.

Malaria Foundation International states, " The outcome of the treaty is arguably better than the status quo going into the negotiations ... For the first time, there is now an insecticide which is restricted to vector control only, meaning that the selection of resistant mosquitoes will be slower than before.

For the special case, this implies that the length of a vector is preserved as well — this is just Parseval's theorem:

For a more useful solution, we utilize vector identities, which work for any vector, as follows:

For example, an endomorphism of a vector space V is a linear map ƒ: V → V, and an endomorphism of a group G is a group homomorphism ƒ: G → G. In general, we can talk about endomorphisms in any category.

For any positive integer n, the set of all n-tuples of real numbers forms an n-dimensional vector space over R, which is denoted R < sup > n </ sup > and sometimes called real coordinate space.

For example, a bijective linear map is an isomorphism between vector spaces, and a bijective continuous function whose inverse is also continuous is an isomorphism between topological spaces, called a homeomorphism.