Sentence examples for inhomogeneous space from inspiring English sources

The application of our results might be particularly interesting in the investigations in homogeneous and inhomogeneous space and laboratory plasma [32, 33, 34, 35, 36].

Kolac et al. [22] explain this large energy spread from multi-mode lasers with high temporal intensity fluctuations which lead to an inhomogeneous space charge distribution in the emission current.

In particular, we should stress here that dividing space into N compartments is equivalent to replacing a single species existing in (inhomogeneous) space with N species living in a well-stirred mixture (each species being the population of a bin).

We demonstrate that the model is able to realistically hindcast the expansion speed and the inhomogeneous space-time evolution of the transition to agropastoralism in western Eurasia.

We can also define the inhomogeneous space-time Triebel-Lizorkin space (tilde{L}^{r}(I; F_{p,q}^{s}(mathbb{R}^{N}))).

Figure 13: Cartan's generalization Figure 14: Cartan's generalized space Cartan's generalized space \(\Sigma\)(M) is the space of all "Tangent Spaces" (i.e., all Klein spaces \(\Sigma(M_{p}))\) and contains a mixture of homogeneous and inhomogeneous spaces (see figure 14).

We prove that (T_{n, beta, gamma}) is bounded on the α-modulation spaces, including the inhomogeneous Besov spaces and the classical modulation spaces.

Such a treatment converts the original contact problem concerning an inhomogeneous half space into a homogeneous half-space contact problem, for which governing equations with unknown contact load distribution can be conveniently formulated.

For a tempered distribution f, we define the (inhomogeneous) Besov space (B_{p,q}^{s}) as B_{p,q}^{s}bigl(mathbb{R}^{n}bigr):= Biggl{ f inmathcal{S}': Vert f Vert _{B_{p,q}^{s}(mathbb{R}^{n})} = Biggl(sum _{j=0}^{infty}2^{sjq} Vert Delta_{j}f Vert _{L^{p}}^{q} Biggr)^{frac {1}{q}}< infty Biggr}.

Consequently, the usual function spaces used in the study of the Navier-Stokes equations such as the homogeneous and inhomogeneous Besov spaces (dot{B}^{s}_{p,r}(mathbb{R}^{3})) and (B^{s}_{p,r}(mathbb {R}^{3})) with (pneq2) and the space (operatorname {BMO}^{-1}(marebb{R}^{3})) are not suitable for the primitive equations.

The method developed here can be used to calculate the force-distance response of adhesive contacts on various inhomogeneous half-spaces that can be modeled as multi-layer coated half-spaces.