In this paper we analyzed the problem of investigating locally the scalar curvature of the two dimensional kinematic surfaces foliated by the homothetic motion of an eight curve in LorentzMinkowski 5-space . We express the scalar curvature of the corresponding two dimensional kinematic surfaces as the quotient of hyperbolic functions { }. From that point, we derive the necessary and sufficient ...

We construct cubature formulas on spheres supported by homothetic images of shells in some Euclidian lattices. Our analysis of these cubature formulas uses results from the theory of modular forms. Examples are worked out on S for n = 4, 8, 12, 14, 16, 20, 23, and 24, and the sizes of the cubature formulas we obtain are compared with the lower bounds given by Linear Programming.

In this paper we prove that there are no domains E ⊂ R2, other than the ellipses, such that the Lebesgue measure of the intersection of E and its homothetic image εE translated to a boundary point q ∈ ∂E is independent of q, provided that E is ”centered” at a certain interior point O ∈ E (the center of homothety). Similar problems arise in various fields of mathematics, including, for example, ...

We reconsider the CES production functions, focusing on their additive separability properties and the constraints these impose on dual elasticites of gross substitution and complementarity. In particular, we offer some alternative characterizations of the (standard) homogeneous cases that seem to have gone unnoticed, as far as we know. We also start exploring the cases of the (additively separ...

The Equations of motion of vortex sources (examined earlier by Fridman and Polubarinova) are studied, and the problems of their being Hamiltonian and integrable are discussed. A system of two vortex sources and three sources-sinks was examined. Their behavior was found to be regular. Qualitative analysis of this system was made, and the class of Liouville integrable systems is considered. Parti...

A new two-stage approach for nonlinear brain image registration is proposed. In the first stage, an active contour algorithm is used to establish a homothetic one-to-one map between a set of region boundaries in two images to be registered. This mapping is used in the second step: a two-dimensional transformation which is based on an elastic body deformation. This method is tested by registerin...

The main objective of this article is to optimize the walking pattern of a 2D humanoid robot with heel-off and toe-off motions in order to minimize the energy consumption and maximize the stability margin. To this end, at first, a gait planning method is introduced based on the ankle and hip joint position trajectories. Then, using these trajectories and the inverse kinematics, the position tra...

We make an analysis of self-similar solutions for the mean curvature flow (MCF) by surfaces revolution and ruled in R3. prove that MCF non-cylindrical R3 are trivial. Moreover, we characterize revolutions under a homothetic helicoidal motion terms generating curve. Finally, cylindrical Explicit families exact also given.

near-fault ground motions with long-period pulses can place severe demands on structures near an active fault. these pulse-type ground motions can be represented by pulse sequences with simple shapes. half-sinusoidal pulse sequences are used to approximate recorded ground motions and dynamic responses of sdof system under the excitation of these pulse sequences are studied. four cases are consi...