Abstract We report the occurrence of bursting oscillations in a gyroscope oscillator driven by low-frequency external period forcing. The patterns arise when either frequency or amplitude excitation force is varied. They take form pulse-shaped explosions (PSEs) wherein periodic attractors lower periodicity disappear due to loss asymptotic stability equilibrium point between resting and active s...

in this paper, the asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated. furthermore, we obtain the zeros of eigenfunctions.

for a simple digraph $g$ of order $n$ with vertex set${v_1,v_2,ldots, v_n}$, let $d_i^+$ and $d_i^-$ denote theout-degree and in-degree of a vertex $v_i$ in $g$, respectively. let$d^+(g)=diag(d_1^+,d_2^+,ldots,d_n^+)$ and$d^-(g)=diag(d_1^-,d_2^-,ldots,d_n^-)$. in this paper we introduce$widetilde{sl}(g)=widetilde{d}(g)-s(g)$ to be a new kind of skewlaplacian matrix of $g$, where $widetilde{d}(g...

We define solvable quantum mechanical systems on a Hilbert space spanned by bipartite ribbon graphs with fixed number of edges. The is also an associative algebra, where the product derived from permutation group products. existence and structure this algebra has consequences. product, which can be expressed in terms integer graph reconnection coefficients, used to Hamiltonians eigenvalues norm...

We extend to operator mixing—specifically, higher-spin twist-2 operators—the asymptotic theorem on the ultraviolet asymptotics of spectral representation 2-point correlators multiplicatively renormalizable operators in large-N confining QCD-like theories. The extension is based a recent differential geometric approach mixing that involves Poincaré-Dulac and allows us reduce generically case, pr...

Let n 1 be an integer. The hypercube Qn is the graph whose vertex set isf0;1gn, where two n-tuples are adjacent if they differ in precisely one coordinate. This graph has many applications in Computer sciences and other area of sciences. Inthe graph Qn, the layer Lk is the set of vertices with exactly k 1’s, namely, vertices ofweight k, 1 k n. The hyper-star graph B(n;k) is...

‎let $g$ be a graph without an isolated vertex‎, ‎the normalized laplacian matrix $tilde{mathcal{l}}(g)$‎‎is defined as $tilde{mathcal{l}}(g)=mathcal{d}^{-frac{1}{2}}mathcal{l}(g) mathcal{d}^{-frac{1}{2}}$‎, where ‎$‎mathcal{‎d}‎$ ‎is a‎ diagonal matrix whose entries are degree of ‎vertices ‎‎of ‎$‎g‎$‎‎. ‎the eigenvalues of‎‎$tilde{mathcal{l}}(g)$ are ‎called ‎ ‎ as ‎the ‎normalized laplacian ...

In this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. Also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....