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In an open, bounded subset Omega of R-N such that 0 is an element of Omega we consider the nonlinear eigenvalue problem -Sigma(N)(i,j,=1) partial derivative(i){A(ij)(x)partial derivative(j)u} + V(x)u + n(x,del u)+ g(x, u) = lambda u in Omega integral(Omega ...
The concept of quasi-symmetry-a perturbatively small deviation from exact symmetry-is introduced and leads to topological materials with strong resilience to perturbations. The crystal symmetry of a material dictates the type of topological band structure ...
We investigate cloaking property of negative-index metamaterials in the time-harmonic electromagnetic setting for the so-called doubly complementary media. These are media consisting of negative-index metamaterials in a shell (plasmonic structure) and posi ...
This paper consists of three parts. In part I, we microscopically derive Ginzburg–Landau (GL) theory from BCS theory for translation-invariant systems in which multiple types of superconductivity may coexist. Our motivation are unconventional superconducto ...
This monograph contains a study of the global Cauchy problem for the Yang-Mills equations on (6+1) and higher dimensional Minkowski space, when the initial data sets are small in the critical gauge covariant Sobolev space. (H) over dot(A)((n-4)/2). Regular ...
We investigate the regularity of the free boundary for the Signorini problem in Rn+1. It is known that regular points are (n−1)-dimensional and C∞. However, even for C∞ obstacles φ, the set of non-regular (or degenerate) points could be very large—e.g. wit ...
Diffractive zone plates have a wide range of applications from focusing x-ray to extreme UV radiation. The Gabor zone plate, which suppresses the higher-order foci to a pair of conjugate foci, is an attractive alternative to the conventional Fresnel zone p ...
This thesis consists of two parts. The first part is about a variant of Banach's fixed point theorem and its applications to several partial differential equations (PDE's), abstractly of the form [ \mathcal Lu + \mathcal Q(u) = f.] The main result of thi ...
In the present thesis, we delve into different extremal and algebraic problems arising from combinatorial geometry. Specifically, we consider the following problems. For any integer n≥3, we define e(n) to be the minimum positive integer such that an ...
We consider the distance from a (square or rectangular) matrix pencil to the nearest matrix pencil in 2-norm that has a set of specified eigenvalues. We derive a singular value optimization characterization for this problem and illustrate its usefulness fo ...
