This paper presents a brief review and some new developments on the canonical duality theory with applications to a class of variational problems in nonconvex mechanics and global optimization. These nonconvex problems are directly related to a large class of semi-linear partial differential equations in mathematical physics including phase transitions, post-buckling of large deformed beam mode...

This paper presents a dual quaternion methodology for the kinematic synthesis of constrained robotic systems. These systems are constructed from one or more serial chains such that each chain imposes at least one constraint on the movement of the workpiece. Serial chains that have constrained workspaces can be synthesized by evaluating the kinematics equations of the chain on a finite set of ta...

Dual wavelet frames and their associated dual framelet filter banks are often constructed using the oblique extension principle. In comparison with the construction of tight wavelet frames and tight framelet filter banks, it is indeed quite easy to obtain some particular examples of dual framelet filter banks with or without symmetry from any given pair of low-pass filters. However, such constr...

Based on a geometric discretization scheme for Maxwell equations, we unveil a mathematical transformation between the electric field intensity E and the magnetic field intensity H, denoted as Galerkin duality. Using Galerkin duality and discrete Hodge operators, we construct two system matrices, [XE ] (primal formulation) and [XH ] (dual formulation) respectively, that discretize the second-ord...

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INTRODUCTION The assessment of body composition is relevant to establish nutritional status and identify potential health risks. OBJETIVE a) To develop regression equations to predict fat mass (FM) using a dual-energy X-ray absorptiometry as reference method; b) to propose reference FM values based on chronological and biological age for Chilean children and adolescents. METHODOLOGY Cross-s...

The solution of the Lax tensor equations in the case Lαβγ = −Lβαγ was analyzed. The Lax tensors on the dual metrics were investigated. We classified all two dimensional metrics having the symmetric Lax tensor Lαβγ . The Lax tensors of the flat space, Rindler system and its dual were found.

The fractional dual solutions of Maxwell equations in bi-isotropic medium are determined using the field decomposition approach. Both negative phase velocity and positive phase velocity propagation have been considered. The results are compared with the corresponding available results for isotropic and chiral medium. Time average power associated with fractional dual fields and corresponding so...