Recently, we have used the symmetric bracket of vector fields, and developed the notion of the symmetric derivation. Using this machinery, we have defined the concept of symmetric curvature. This concept is natural and is related to the notions divergence and Laplacian of vector fields. This concept is also related to the derivations on the algebra of symmetric forms which has been discu...

The n-tuple of Laplacian characteristic values of a graph is majorized by the conjugate sequence of its degrees. Using that result we find a collection of general inequalities for a number of Laplacian indices expressed in terms of the conjugate degrees, and then with a maximality argument, we find tight general bounds expressed in terms of the size of the vertex set n and the average degree dG...

The impregnation method was used to synthesize Pt and Pt3Co supported on MWCNTs applying NaBH4 as the reducing agent. The structure, morphology, and chemical composition of the electrocatalysts were characterized through SEM, XRD, and EDX. X-ray diffraction showed a good crystallinity of the supported Pt nanoparticles on the composites and showed the formation of Pt3<...

The binding energy and Thermodynamic Parameters of cis- Platinum Di Ammino Chlorine (cis-[Pt(NH3)2Cl]+) and trans- Platinum Di Ammino Chlorine (trans- [Pt(NH3)2Cl]+) complexes withGuanine has been studied by density functional theory (DFT) calculations in water. The bindingenergies (Ebin) of cis- and trans-[Pt(NH3)2ClG]+ are calculated to be 79.38 kcal/mol and 74.98kcal/mol, respectively. The b...

We consider overdetermined boundary value problems for the ∞-Laplacian in a domain Ω of Rn and discuss what kind of implications on the geometry of Ω the existence of a solution may have. The classical ∞-Laplacian, the normalized or game-theoretic ∞-Laplacian and the limit of the p-Laplacian as p→∞ are considered and provide different answers. Mathematics Subject Classification (2000). 35R35, 4...

Suppose μ1, μ2, ... , μn are Laplacian eigenvalues of a graph G. The Laplacian energy of G is defined as LE(G) = ∑n i=1 |μi − 2m/n|. In this paper, some new bounds for the Laplacian eigenvalues and Laplacian energy of some special types of the subgraphs of Kn are presented. AMS subject classifications: 05C50

For a graph, the least signless Laplacian eigenvalue is the least eigenvalue of its signless Laplacian matrix. This paper investigates how the least signless Laplacian eigenvalue of a graph changes under some perturbations, and minimizes the least signless Laplacian eigenvalue among all the nonbipartite graphs with given matching number and edge cover number, respectively.

For a graph, the least signless Laplacian eigenvalue is the least eigenvalue of its signless Laplacian matrix. This paper investigates how the least signless Laplacian eigenvalue of a graph changes under some perturbations, and minimizes the least signless Laplacian eigenvalue among all the nonbipartite graphs with given matching number and edge cover number, respectively.