Twisted trilayer graphene is a particularly promising moir\'e superlattice system, due to its tunability, strong superconductivity, and complex electronic symmetry breaking. Motivated by these properties, we study lattice relaxation the long-wavelength phonon modes of this system. We show that mirror-symmetric hosts, aside from conventional acoustic modes, two classes shear which are even odd u...

We discuss mirror symmetry in generalized Calabi–Yau compactifications of type II string theories with background NS fluxes. Starting from type IIB compactified on Calabi– Yau threefolds with NS three-form flux we show that the mirror type IIA theory arises from a purely geometrical compactification on a different class of six-manifolds. These mirror manifolds have SU(3) structure and are terme...

The study examined symmetrical bimanual coordination of children with spastic hemiparetic cerebral palsy (SHCP) and a typically developing (TD) control group under conditions of visual feedback created by placing a glass screen, opaque screen or a mirror ("mirror box") between the arms. The "mirror box" creates a visual illusion, which gives rise to a visual perception of a zero lag, symmetric ...

We propose an eigenvalue contractor for symmetric matrices. Given a symmetric interval matrix A and an interval approximation of its eigenvalue sets λ1, . . . ,λn the contractor reduces the entries of A S such that no matrix with eigenvalues in λ1, . . . ,λn is omitted. Our contractor is based on sequentially reducing the entries of A. We discuss properties of the method and demonstrate its per...

We study how small perturbations of a skew-symmetric matrix pencil may change its canonical form under congruence. This problem is also known as the stratification problem of skewsymmetric matrix pencil orbits and bundles. In other words, we investigate when the closure of the congruence orbit (or bundle) of a skew-symmetric matrix pencil contains the congruence orbit (or bundle) of another ske...

A symmetric matrix A is said to be sign-nonsingular if every symmetric matrix with the same sign pattern as A is nonsingular. Hall, Li and Wang (2001) showed that the inertia of a signnonsingular symmetric matrix is determined uniquely by its sign pattern. The purpose of this paper is to present an efficient algorithm for computing the inertia of such matrices. The algorithm runs in O(nm) time ...

A standard way of treating the polynomial eigenvalue problem P (λ)x = 0 is to convert it into an equivalent matrix pencil—a process known as linearization. Two vector spaces of pencils L1(P ) and L2(P ), and their intersection DL(P ), have recently been defined and studied by Mackey, Mackey, Mehl, and Mehrmann. The aim of our work is to gain new insight into these spaces and the extent to which...

In this paper sufficient conditions are derived for the existence of unique and positive definite solutions of the matrix equations X−A1XA1− . . .−A∗mXAm = Q and X+A1XA1+ . . .+ A∗mXAm = Q. In the case there is a unique solution which is positive definite an explicit expression for this solution is given.

In this paper, we present an iterative algorithm for solving the following coupled Sylvester-transpose matrix equations q ∑ j=1 ( AijXjBij + CijX j Dij ) = Fi, i = 1, 2, . . . , p, over the generalized centro-symmetric matrix group (X1, X2, . . . , Xq). The solvability of the problem can be determined by the proposed algorithm, automatically. If the coupled Sylvester-transpose matrix equations ...

An accelerating boundary (mirror) acts as a horizon and black hole analog, radiating energy with some particle spectrum. We demonstrate that M\"obius transformation on the null coordinate advanced time mirror trajectory uniquely keeps invariant not only flux but clarify how geometric entanglement entropy is also invariant. The transform allows generation of families dynamically distinct traject...