for a simple connected graph $g$ with $n$-vertices having laplacian eigenvalues‎ ‎$mu_1$‎, ‎$mu_2$‎, ‎$dots$‎, ‎$mu_{n-1}$‎, ‎$mu_n=0$‎, ‎and signless laplacian eigenvalues $q_1‎, ‎q_2,dots‎, ‎q_n$‎, ‎the laplacian-energy-like invariant($lel$) and the incidence energy ($ie$) of a graph $g$ are respectively defined as $lel(g)=sum_{i=1}^{n-1}sqrt{mu_i}$ and $ie(g)=sum_{i=1}^{n}sqrt{q_i}$‎. ‎in th...

A characteristic feature of wave propagation in cold plasma is the possibility that a hybrid resonance surface, along which the linearized equation for the scalar potential changes from elliptic to hyperbolic type, may be tangent to a flux surface. This property can be represented in two dimensions by setting the hybrid resonance curve tangent to the line x = 0 at the origin of coordinates. The...

The Oseledec splitting of the tangent space into covariant subspaces for a hyperbolic dynamical system is numerically accessible by computing the full set of covariant Lyapunov vectors. In this paper, the covariant Lyapunov vectors, the orthogonal Gram-Schmidt vectors, and the corresponding local (time-dependent) Lyapunov exponents, are analyzed for a planar system of rough hard disks (RHDS). T...

The gradient fields v of nonsingular functions f on compact 3folds X with boundary are used to generate their spines K(f, v). We study the transformations of K(f, v) that are induced by deformations of the data (f, v). We link the Matveev complexity of c(X) with counting the trajectories of the v-flow that are tangent to the boundary ∂X at a pair of distinct points (call them double-tangent tra...

To model advanced 3-D forming strategies for paper materials, the effects of environmental conditions on the mechanical behavior must be quantitatively and qualitatively understood. A tensile test method has been created, verified, and implemented to test paper at various moisture content and temperature levels. Testing results for one type of paper for moisture contents from 6.9 to 13.8 percen...

We show that for a closed hyperbolic 3-manifold, the size of first eigenvalue Hodge Laplacian acting on coexact 1-forms is comparable to an isoperimetric ratio relating geodesic length and stable commutator with comparison constants depend polynomially volume lower bound injectivity radius, refining estimates Lipnowski Stern. use this estimate there exist sequences 3-manifolds radius bounded be...