let (m,g ) be a compact immersed hypersurface of (rn+1,) , λ1 the first nonzeroeigenvalue, α the mean curvature, ρ the support function, a the shape operator, vol (m ) the volume of m,and s the scalar curvature of m. in this paper, we established some eigenvalue inequalities and proved theabove.1) 1 2 2 2 2m ma dv dvn∫ ρ ≥ ∫ α ρ ,2)( )2 2 1 2m 1 mdv s dvn nα ρ ≥ ρ∫ − ∫ ,3) if the scalar curvatu...

Tubular channel angular pressing (TCAP) process was proposed recently as a novel severe plastic deformation technique for producing ultrafine grain and nanostructured tubular components. In this paper, an upper-bound approach was used to analyze the TCAP process. Deformation of the material during TCAP process is analyzed using upper-bound analysis to determine maximum required load. The effect...

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...

A Monte Carlo simulation has been performed to track light rays in cylindrical multimode fibres by ray optics. The trapping efficiencies for skew and meridional rays in active fibres and distributions of characteristic quantities for all trapped light rays have been calculated. The simulation provides new results for curved fibres, where the analytical expressions are too complex to be solved. ...

Soft robot arms possess unique capabilities when it comes to adaptability, flexibility, and dexterity. In addition, soft systems that are pneumatically actuated can claim high power-to-weight ratio. One of the main drawbacks of pneumatically actuated soft arms is that their stiffness cannot be varied independently from their end-effector position in space. The novel robot arm physical design pr...

A. Organization of the Appendix Appendix B presents the proofs for our approximation guarantees and its tightness for the GREEDY algorithm. Appendix C provides details on existing notions of curvature and submodularity ratio, and relates it to the notions in this paper. Appendix D presents detailed proofs for bounding the submodularity ratio and curvature for various applications. Appendix E gi...

Droplets moving in meandering microchannels can serve as a passive and robust strategy to produce chaotic mixing of species in droplet-based microfluidics. In this paper, a simplified theoretical model is proposed for plug-shaped droplets moving in meandering microchannels at Stokes flow. With this model to provide the velocity field, particle tracking, which requires a large computation time, ...