Curtis-Ingerman-Morrow studied the space of circular planar electrical networks, and classified all possible response matrices for such networks. Lam and Pylyavskyy found a Lie group EL2n whose positive part (EL2n)≥0 naturally acts on the circular planar electrical network via some combinatorial description, where the action is inspired by the star-triangle transformation of the electrical netw...

To a simple graph $G=(V,E)$, we correspond a simple graph $G_{triangle,square}$ whose vertex set is ${{x,y}: x,yin V}$ and two vertices ${x,y},{z,w}in G_{triangle,square}$ are adjacent if and only if ${x,z},{x,w},{y,z},{y,w}in Vcup E$. The graph $G_{triangle,square}$ is called the $(triangle,square)$-edge graph of the graph $G$. In this paper, our ultimate goal is to provide a link between the ...

The Umehara algebra is studied with motivation on the problem of non-existence common complex submanifolds. In this paper, we prove some new results in and obtain applications. particular, if a manifolds admits holomorphic polynomial isometric immersion to one indefinite space form, then it cannot another form different type. Other consequences include submanifolds for projective or hyperbolic ...

purpose: to compare the results of two different methods of frontalis suspension using fascia lata in congenital ptosis. methods: in a randomized clinical trial, double triangle sling was compared with single triangle sling using fascia lata. eight patients with unilateral and 11 patients with bilateral congenital ptosis were randomly assigned for each procedure. results: there was no statistic...

Utilizing the linking algebra of a Hilbert $C^*$-module $\big(\mathscr{V}, {\|\!\cdot\!\|}_{_{\mathscr{V}}}\big)$, we introduce $\Omega(x)$ as definition numerical radius for an element $x\in\mathscr{V}$ and then show that $\Omega(\cdot)$ is norm on $\mathscr{V}$ such $\frac{1}{2}{\|x\|}_{_{\mathscr{V}}} \leq \Omega(x) {\|x\|}_{_{\mathscr{V}}}$. In addition, obtain equivalent condition $\Omega(...

To each symmetric n × n matrix W with non-zero complex entries, we associate a vector space N , consisting of certain symmetric n × n matrices. If W satisfies n ∑ x=1 Wa,x Wb,x = nδa,b (a, b = 1, . . . , n), then N becomes a commutative algebra under both ordinary matrix product and Hadamard product (entry-wise product), so that N is the Bose-Mesner algebra of some association scheme. If W sati...

Originally a model for wave propagation on the line, the Toda lattice is a wonderful case study in mechanics and symplectic geometry. In Flaschka’s variables, it becomes an evolution given by a Lax pair on the vector space of Jacobi matrices, with a very special asymptotic behavior. It is a completely integrable system on the coadjoint orbit of the upper triangular group, for which the Liouvill...

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Three point-like massive particles/atoms are connected with three springs forming an equilateral triangle replicating a prototype triatomic molecule. The is inscribed within stationary frame via additional confining the vibrations of molecule to 2D space. It objective this research flavored investigation seek normal vibrational modes for three-body six-spring structure. entire analysis includin...