A double-layer lens consists of a first gradient-index/geodesic profile in an upper waveguide, partially surrounded by a mirror that reflects the wave into a lower guide where there is a second profile. Here, we
In addition to providing insights into the modeling processes, this notation enables us to compute useful quantities that are unavailable without strain gradient notation. For example, the strain gradient form of the polynomials enables us to determine the displacements associated with a particular strain...
2.1.167 Section 7.1.3, Alphabetical Index Mark 2.1.168 Section 7.1.4, Bibliography Index Mark 2.1.169 Section 7.2, Index Structure 2.1.170 Section 7.2.1, Index Source 2.1.171 Section 7.2.2, Index Body Section 2.1.172 Section 7.2.3, Index Title Section 2.1.173 Section 7.3, Table Of C...
Prove in direct notation that λ./λ=D·(n⊗n). Solution To begin, we take the material derivative of (3.33), which leads to 2λλ.=C.·(N⊗N),where we have used result (3.22)6; note that N⊗N¯·=0. Now, working with the right-hand side, we have C.·(N⊗N)=...
K. Gęba, Degree for gradient equivariant maps and equivariant Conley index, in: Topological nonlinear analysis, II (Frascati, 1995), 247-272, Progr. Nonlinear Differ- ential Equations Appl., 27, Birkha¨user, Boston, MA, 1997.K. Ge¸eba, "Degree for gradient equivariant maps and ...
Each entry in iT specifies a time index. Example: iT = 1:5:21 specifies every fifth time-step up to 21. Data Types: double Output Arguments collapse all gradx— x-component of the gradient array x-component of the gradient, returned as an array. For query points that are outside the...
1.1Aim and scope This paper aims to explore the fine pointwise first-order properties as well as the gradient regularity of solutions to parabolic nonlinear nonlocal equations of the type $$\begin{aligned} \partial _t u+{\mathcal {L}}u=\mu \quad \text {in }\Omega _T \subset \Omega...
To compute the cumulative reward, the agent first computes a next action by passing the next observationS'ifrom the sampled experience to the target actor. Then, the agent adds noiseεto the computed action using theTargetPolicySmoothModel, and clips the action based on the upper and lower noi...
The boldface notation is therefore meant to emphasize the random nature of the iterates in Eq. (1.12). We refer to recursion (1.12) as a synchronous implementation because updates occur continuously over the iteration index i. This terminology is meant to distinguish the above recursion from its...
where the notation is consistent with that used in Section 1.8. H. Lamb, in Hydrodynamics (1945, 6th Edition, p. 456) writes, “Since the condition of stable equilibrium is that the free energy be a minimum, the surface tends to contract as much as is consistent with the other condition...