The second largest eigenvalue of a tree

AbstractDenote by λ2(T) the second largest eigenvalue of a tree T. An easy algorithm is given to decide whether λ2(T)⩽λ for a given number λ, and a structure theorem for trees withλ2(T)⩽λ is proved. Also, it is shown that a tree T with n vertices has λ2(T)⩽lsqb(n−3)2rsqb12; this bound is best possible for odd n

Derived eigenvalues of symmetric matrices, with applications to distance geometry

AbstractThe concept of derived eigenvalues of a symmetric matrix is introduced and applied to give a new characterization for the embeddability of a finite metric space into Euclidean space. The particular case of two-distance sets is discussed in more detail

A remark on partial linear spaces of girth 55 with an application to strongly regular graphs

We derive a lower bound on the number of points of a partial linear space of girth 5. As an application, certain strongly regular graphs with=2 are ruled out by observing that the first subconstituents are partial linear spaces

Apparent rippling with honeycomb symmetry and tunable periodicity observed by scanning tunneling microscopy on suspended graphene

Suspended graphene is difficult to image by scanning probe microscopy due to the inherent van-der-Waals and dielectric forces exerted by the tip which are not counteracted by a substrate. Here, we report scanning tunneling microscopy data of suspended monolayer graphene in constant-current mode revealing a surprising honeycomb structure with amplitude of 50$-$200 pm and lattice constant of 10-40 nm. The apparent lattice constant is reduced by increasing the tunneling current $I$, but does not depend systematically on tunneling voltage $V$ or scan speed $v_{\rm scan}$. The honeycomb lattice of the rippling is aligned with the atomic structure observed on supported areas, while no atomic corrugation is found on suspended areas down to the resolution of about $3-4$ pm. We rule out that the honeycomb structure is induced by the feedback loop using a changing $v_{\rm scan}$, that it is a simple enlargement effect of the atomic resolution as well as models predicting frozen phonons or standing phonon waves induced by the tunneling current. Albeit we currently do not have a convincing explanation for the observed effect, we expect that our intriguing results will inspire further research related to suspended graphene.Comment: 10 pages, 7 figures, modified, more detailed discussion on errors in vdW parameter

Subsquares Approach - Simple Scheme for Solving Overdetermined Interval Linear Systems

In this work we present a new simple but efficient scheme - Subsquares approach - for development of algorithms for enclosing the solution set of overdetermined interval linear systems. We are going to show two algorithms based on this scheme and discuss their features. We start with a simple algorithm as a motivation, then we continue with a sequential algorithm. Both algorithms can be easily parallelized. The features of both algorithms will be discussed and numerically tested.Comment: submitted to PPAM 201

Gaussian resolutions for equilibrium density matrices

A Gaussian resolution method for the computation of equilibrium density matrices rho(T) for a general multidimensional quantum problem is presented. The variational principle applied to the ``imaginary time'' Schroedinger equation provides the equations of motion for Gaussians in a resolution of rho(T) described by their width matrix, center and scale factor, all treated as dynamical variables. The method is computationally very inexpensive, has favorable scaling with the system size and is surprisingly accurate in a wide temperature range, even for cases involving quantum tunneling. Incorporation of symmetry constraints, such as reflection or particle statistics, is also discussed.Comment: 4 page

Spin blockade in ground state resonance of a quantum dot

We present measurements on spin blockade in a laterally integrated quantum dot. The dot is tuned into the regime of strong Coulomb blockade, confining ~ 50 electrons. At certain electronic states we find an additional mechanism suppressing electron transport. This we identify as spin blockade at zero bias, possibly accompanied by a change in orbital momentum in subsequent dot ground states. We support this by probing the bias, magnetic field and temperature dependence of the transport spectrum. Weak violation of the blockade is modelled by detailed calculations of non-linear transport taking into account forbidden transitions.Comment: 4 pages, 4 figure

Algebraic lattice constellations: bounds on performance

In this work, we give a bound on performance of any full-diversity lattice constellation constructed from algebraic number fields. We show that most of the already available constructions are almost optimal in the sense that any further improvement of the minimum product distance would lead to a negligible coding gain. Furthermore, we discuss constructions, minimum product distance, and bounds for full-diversity complex rotated Z[i]/sup n/-lattices for any dimension n, which avoid the need of component interleaving