The Kirchhoff index of a connected graph is the sum of resistance distances between all unordered pairs of vertices in the graph. Its considerable applications are found in a variety of fields. In this paper, we determine the maximum value of Kirchhoff index among the unicyclic graphs with fixed number of vertices and maximum degree, and characterize the corresponding extremal graph.

A generalized Kowalevski Hamiltonian and new integrable cases on e(3) and so(4). 1 A new integrable case for the Kirchhoff equation. The Kirchhoff equations (see for example [1]) for the motion of a rigid body in an ideal fluid read as follows M t = M × ∂H ∂M + Γ × ∂H ∂Γ , Γ t = Γ × ∂H ∂M ,

banberz, banbor, and sabziabad neighborhoods are three residential districts on the peripheryof ilam city, and are facing a lot of problems namely social, economic, and physical, particularly in housing sectorincluding low quality, poor housing, limited-quantity housing. in order to assess the sustainability of housing, 75indicators and to rank districts, spss software (exploratory factor analy...

We develop a mixed finite-element approximation scheme for Kirchhoff plate theory based on the reformulation of Kirchhoff plate theory of Ortiz and Morris [1]. In this reformulation the moment-equilibrium problem for the rotations is in direct analogy to the problem of incompressible two-dimensional elasticity. This analogy in turn opens the way for the application of diamond approximation sche...

The present work focuses on geometrically exact finite elements for highly slender beams. It aims at the proposal of novel formulations of Kirchhoff-Love type, a detailed review of existing formulations of Kirchhoff-Love and SimoReissner type as well as a careful evaluation and comparison of the proposed and existing formulations. Two different rotation interpolation schemes with strong or weak...

Isochron rays are lines perpendicular to isochrons, which represent surfaces of constant two-way traveltime. The image of a temporal sequence of seismic impulses is a sequence of isochrons in depth. The later the time impulse the deeper the isochron. The term isochron ray arises from an analogy between the isochron “movement” and the wave propagation. While isochrons behave as wavefronts, its p...

Molecular and cell biological processes often use proteins and structures that are significantly longer in one dimension than they are in the other two, for example, DNA, actin, and bacterial flagella. The dynamics of these structures are the consequence of the balance between the elastic forces from the structure itself and viscous forces from the surrounding fluid. Typically, the motion of th...

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h explicitly solvable analog of the Kirchhoff flow for the case of a semipenetrable obstacle is considered. Its application to estimating the efficiency of free flow turbines is discussed. @ 2002 Elsevier Science Ltd. All rights reserved. Keywords-Cavitation flows, Kirchhoff method.

In this note we present a symbolic-numeric method to the problem of tube modeling in CAD systems. Our approach is based on the Kirchhoff kinetic analogy which allows us to find analytic solutions to the static Kirchhoff equations for rods under given boundary conditions.