We present an explicit example of a simple viscoelastic mass-spring system whose macroscopic dissipative behavior is plastic, rate independent.
We give an explicit example of a nuclear operator system that is not completely order isomorphic to a unital C⁎-algebra.
The validity of Green's formula and the existence of a finite-displacement solution are justified with an explicit example of finite-displacement solution in the simple case of a half-space elastic solid bounded by a plane.
As another application, we also show that double difference cancellation is possible for linear combinations of four composition operators by constructing an explicit example of a compact double difference formed by two noncompact differences.
For any n⩾2 we provide an explicit example of an n-axially symmetric map u∈H1(B2,S2)∩C0(¯¯¯B2∖¯¯¯B1), where Br="{p∈R3:|p|<r}, with degu|∂B2= 0, "strictly minimizing in B1" the relaxed Dirichlet energy of Bethuel, Brezis and CoronF u,B2):="12∫B2|∇u|2dxdydz+4πΣ(u,B2), and having Σ u,B2)>0, u|B1≢const.
And it's true that if you ask me to give you an explicit example of how you'll use the quadratic formula in your daily life I will struggle.
Now we are ready to see an explicit example of stochastic synchronization, which will be developed in the next section for the complete and the hypercube graphs.
Although neoplastic clonal lineages are often compared to alternative phenotype, oncogenic structures are not typically considered an explicit example of phenotypic form in the macro sense.
In particular, after giving an explicit example of such boundaries, we prove that in a multiply connected domain the boundary is exceptional if, and only if, the external boundary is exceptional.
To obtain an explicit example of this type, take a continuous and bounded map (g_{0}:mathbb{R}tomathbb{R}) and (uin X), and define (g:ell _{infty}(X to X) as (g(mathbf {x})=g_{0}(Vert mathbf {x}Vert_{infty}) u), or (g(mathbf {x})=g_{0}(Vert mathbf {x}(1 Vert_{X}) u).
As an explicit example of how the SFI is calculated at each corresponding visual field point, assume we start with a visual field total deviation of -7 at the point 3°,15°.
