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Focusing waves inside inhomogeneous media is a fundamental problem for imaging. Spatial variations of wave velocity can strongly distort propagating wavefronts and degrade image quality. Adaptive focusing can compensate for such aberration,…
We develop the diffeomorphism invariant Colombeau-type algebra of nonlinear generalized functions in a modern and compact way. Using a unifying formalism for the local setting and on manifolds, the construction becomes simpler and more…
Let f:\Sigma_1 --> \Sigma_2 be an area preserving diffeomorphism between compact Riemann surfaces of constant curvature. The graph of f can be viewed as a Lagrangian submanifold in \Sigma_1\times \Sigma_2. This article discusses a canonical…
A heat flow method is used to deform convex hypersurfaces in a ring domain to a hypersurface whose harmonic mean curvature is a prescribed function.
By means of the in situ electrokinetic assessment of aqueous particles in conjunction with the addition of anionic adsorbates, we develop and examine a new approach to the scalable characterization of the specific accessible surface area of…
This paper proposes the response surface method for finite element model updating. The response surface method is implemented by approximating the finite element model surface response equation by a multi-layer perceptron. The updated…
We give a local representation for the pseudoholomorphic surfaces in Euclidean spheres in terms of holomorphic data. Similar to the case of the generalized Weierstrass representation of Hoffman and Osserman, we assign such a surface in…
We discuss hypersurface motions in Riemannian manifolds whose normal velocity is a function of the induced hypersurface volume element and derive a second order partial differential equation for the corresponding time function $\tau(x)$ at…
We investigate the nonlinear holomorphic supersymmetry for quantum-mechanical systems on Riemann surfaces subjected to an external magnetic field. The realization is shown to be possible only for Riemann surfaces with constant curvature…
The anisotropic $s$-fractional area measures are introduced as the first variation of the anisotropic fractional $s$-perimeter $P_s(K,L)$, with $L$ an origin symmetric convex body and $s\in(0,1)$. As $s\rightarrow 1^-$, the anisotropic…
This paper aims to describe the behavior of diffeological differential forms under the operation of gluing of diffeological spaces along a smooth map. In the diffeological context, two ways of looking at diffeological forms are available,…
According to the formal holographic principle, a modification to the assumption of holographic principle in Verlinder's investigation of entropy force is obtained. A more precise relation between entropy and area in the holographic system…
The paper studies an Allen-Cahn-type equation defined on a time-dependent surface as a model of phase separation with order-disorder transition in a thin material layer. By a formal inner-outer expansion, it is shown that the limiting…
Because physical phenomena on Earth's surface occur on many different length scales, it makes sense when seeking an efficient approximation to start with a crude global approximation, and then make a sequence of corrections on finer and…
Although methods for estimating the pose of objects in indoor scenes have achieved great success, the pose estimation of underwater objects remains challenging due to difficulties brought by the complex underwater environment, such as…
Our purpose in this article is to study anti-invariant statistical submersions from holomorphic statistical manifolds. Firstly we introduce holomorphic statistical submersions satisfying the certain condition, after we give anti-invariant…
Given a closed orientable surface (\Sigma) of genus at least two, we establish an affine isomorphism between the convex compact set of isotopy-invariant topological measures on (\Sigma) and the convex compact set of additive functions on…
We propose an efficient and accurate parametric finite element method (PFEM) for solving sharp-interface continuum models for solid-state dewetting of thin films with anisotropic surface energies. The governing equations of the…
We construct a smooth nontrivial mixed partially hyperbolic system and explicitly identify its skeleton. This example shares characteristics with the classical examples. Moreover, the support of each physical measure contains three fixed…
We study some conformally invariant integral equations using the method of moving spheres.