In the paper a linear-quadratic optimization problem (LCTOR) with unseparated two-point boundary conditions is considered. To solve this problem is proposed a new sweep algorithm which increases doubles the dimension of the original system. In contrast to the well-known methods, here it refuses to solve linear matrix and nonlinear Riccati equations, since the solution of such multi-point optimi...

We study a class of topological materials which in their momentum-space band structure exhibit three-fold degeneracies known as triple points. Focusing specifically on $\mathcal{P}\mathcal{T}$-symmetric crystalline solids with negligible spin-orbit coupling, we find that such points can be stabilized by little groups containing three-, four- or six-fold rotation axis, and develop classification...

We study the ray optics of generalized lenses (glenses), which are ideal thin lenses generalized to have different object- and image-sided focal lengths, and the most general light-ray-direction-changing surfaces that stigmatically image any point in object space to a corresponding point in image space. Gabor superlenses [UK patent541,753 (1940); J. Opt. A1, 94 (1999)JOAOF81464-425810.1088/1464...

In this paper, the inverse problem of recovering the potential function, on a general finite interval, of a singular Sturm–Liouville problem with a new spectral parameter, called the nodal point, is studied. In addition, we give an asymptotic formula for nodal points and the density of the nodal set. c © 2006 Elsevier Ltd. All rights reserved.

Examples 1.1. • Y ∼= P, D a nodal cubic. • Y a complete nonsingular toric surface, D the toric boundary (i.e, the complement of the big torus orbit Gm). • Blowups: Given a Looijenga pair (Y ,D), we can take “toric blowups,” where Y is the blowup of Y at a nodal point of D and D is the inverse image of D). Note that toric blowups do not change U . “non-toric blowups,” where Ỹ is the blowup of Y ...

Nodal-point and Nodal-line structures in the dispersion of electron energy bands are characterized by their high degeneracy certain corners or lines Brillouin zone (BZ). These nodal can also exist itinerant electrons magnetically ordered materials whose symmetry groups anti-unitary called magnetic space groups. In present work, we provide a complete list which host symmetry-protected nodal-poin...

In this paper, we will show that, for elliptic problems in heterogeneous media , there exists a local (generalized) finite element basis (AL basis) consisting of O log 1 h d+1 basis functions per nodal point such that the convergence rates of the classical finite element method for Poisson-type problems are preserved. We provide several numerical examples beyond our theory, where even O(1) basi...