Sentence examples similar to multi dimensional scalar from inspiring English sources

In addition, multi-dimensional scalar conservation laws with boundary are more common in practical problems.

Bardos et al. [2] have proved the existence and uniqueness of the weak entropy solution of initial-boundary problems of multi-dimensional scalar conservation laws.

For Cauchy problem of multi-dimensional scalar conservation laws, Conway and Smoller [4] and Kruzkov [1] have proved that weak solution uniquely exists if it also satisfies entropy condition, and it is called weak entropy solutions.

According to the definition of the weak entropy solution and the boundary entropy condition to the general initial-boundary problems of multi-dimensional scalar conservation laws which was proposed by Bardos et al. [2] and Pan and Lin [13], we can obtain the following definition and three lemmas for Riemann initial-boundary value problem (1.1).

We show that the Cauchy Problem for a randomly forced, periodic multi-dimensional scalar first-order conservation law with additive or multiplicative noise is well posed: it admits a unique solution, characterized by a kinetic formulation of the problem, which is the limit of the solution of the stochastic parabolic approximation.

The two dimensional scalar continuity equation is treated implicitly with a preconditioned Jacobian-free Newton Krylov method (JFNK).

Although the algorithm was designed for bathymetric estimation, it could be readily used on other two dimensional scalar fields where variable data density is a driver.

Primer V6 (PRIMER-E, Plymouth) was used to calculate Bray-Curtis similarities, to perform non-metric multi dimensional analysis (nMDS), and Analysis of Similarities (ANOSIM).

Nonmetric multi dimensional scaling (NMDS) analysis of the combined 20 samples showed the strong seasonal structuring of the community at L4 (Fig. 2).

Figure 1 shows an example of an inseparable two-dimensional space that becomes separable after the transformation of the input space from low dimensional to multi dimensional.

It also highlights the importance of inclusion of the role (school) functioning concept in measuring multi dimensional HRQOL.