Sentence examples for minimum with respect from inspiring English sources

This is an example of an extremal principle that a state of stable equilibrium is one in which the potential energy is a minimum with respect to any small changes in configuration.

At the azeotropic composition, the total pressure (at constant temperature) is always either a maximum or a minimum with respect to composition, and the boiling temperature (at constant pressure) is always either a minimum or a maximum temperature.

It is concluded that the natural frequencies are stationary and need not always be minimum, with respect to the arbitrary coefficients; however, they are minimum with respect to the natural modes.

Using the definition of and noting that and taking minimum with respect to in (2.18), then we have (2.19).

Figure 4 shows variations in trough depth, background TEC, and the TEC value at the trough minimum with respect to the daily Kp index during equinox.

As a result it can take several cycles of least-squares refinement to find the global minimum with respect to all of the restraints.

The total porosity of the coatings exhibited a minima with respect to SOD and ranged from 1.8 to 8.2%.

Shown are projections onto the ( h SI, m SO, V ) -coordinates; panels (a) and (b) show two different viewpoints of the surfaces of equilibria, coloured black when stable and red when not; from the same viewpoints, panels (c) and (d) also show maxima and minima with respect to V of the two-parameter families of periodic orbits, coloured blue when stable and magenta when not.

To this effect, the doctors' directives have established minimum standards with respect to the nature, minimum content and length of education and training programmes.

The cone K is called subdual if K ⊆ K ∗ and superdual if K ∗ ⊆ K. Suppose ( H, 〈 ⋅, ⋅ 〉 ) be a Hilbert lattice and K be its positive cone, for any x, y ∈ H, we denote the minimum (supremum) with respect to K as x ∧ y ( x ∨ y ) and the minimum (supremum) with respect to K ∗ as x ∧ ∗ y ( x ∨ ∗ y ).

In other words, if each module is designed to be of minimum weight with respect to the expected mode of response, then their assembly would also be of minimum weight with respect to the same performance requirements.