Sentence examples for method of symmetry from inspiring English sources

Once the energies E D 2 + r h 1, r h 2 for the different electron levels as functions of the holes positions are found, then the wave in Equation 4 can be solved approximately by using the method of symmetry structures[16] in which the problem in Equation 3 is reduced to the following one-particle wave equation: − η h Δ h ψ + E D 2 + r h, − r h + V h r h + 1 / r h ψ = E X + / 2 ψ. (5).

It can be said that the method of Lie symmetry groups is the most important approach for constructing analytical solutions of nonlinear partial differential equations.

The case p= 2 corresponds to a family of variational problems on conformally flat metrics which was previously settled by Carlen and Loss with their method of competing symmetries.

The best method for symmetry is by finding the periodic solution of the differential equation.

An effective method of breaking this symmetry is to constrain the assignments of the affected rows and columns to be ordered lexicographically.

By using the properties, one could find a simple and general method for the study of symmetry and monotonicity which has been used in various forms defined in a half-space.

In particular, we present a simple and more general method for the study of symmetry and monotonicity which has been extensively used in various forms on a half-space.

In addition to the common extant applications of hEB, aggregates generated via these methods exhibit consistent levels of symmetry and self-organization not attainable using more traditional methods, laying the foundations for a new paradigm of in vitro tissue-level differentiation.

Approximate principal resonance solutions are first obtained using a two-term harmonic balance and then a consistent second order stability analysis of the associated linearized variational equation is carried out using approximate methods to predict zones of symmetry breaking leading to period-doubling bifurcation and chaos.

Autocorrelation methods are good measures of symmetry or asymmetry in gait patterns [ 18].

It is useful at this point to reconsider this established method from the new perspective of symmetry groups.