A note on commutative semifield planes

Letqbe an odd prime power. We prove that a planar functionffrom 𝔽qto itself can be written as an affine Dembowski–Ostrom polynomial if and only if the projective plane derived fromfis a commutative semifield plane.

THERMOACOUSTIC TOMOGRAPHY AND THE CIRCULAR RADON TRANSFORM: EXACT INVERSION FORMULA

Thermoacoustic computed tomography (TACT) is an emerging hybrid imaging method for non-invasive medical diagnosis and fully three-dimensional visualization of biological probes. Within this modality electromagnetic illumination is used to induce acoustic waves inside an object of interest. In this paper, we assume that a cylindrical array of line detectors is used to record the acoustical data. This leads to the mathematical problem of inverting the circular Radon transform.The circular Radon transform arises in several other up-to-date imaging modalities, such as RADAR imaging or ultrasound tomography. In this paper we prove a novel stable formula for recovering a planar function from its circular Radon transform. We apply this formula to obtain an exact three-dimensional imaging algorithm for TACT. Numerical reconstructions from real and synthetic data demonstrate the potential and robustness of our algorithm.

Computer-Aided Design of the RSSR Function Generating Spatial Mechanism Using the Selective Precision Synthesis Method

Planar function generating mechanisms may be synthesized for a limited number of precision points by carrying out a kinematic inversion about the output link. However, this becomes quite difficult for spatial mechanisms. In this paper the general RSSR spatial function generating mechanism is synthesized using the Selective Precision Synthesis technique. In this computer-aided design method, nonlinear constraint equations relating the generated and desired rotations of the output crank are formulated. These constraints which define accuracy neighborhoods around each of the “n” prescribed output crank rotations are then solved using the Generalized Reduced Gradient Method of optimization. The mathematical formulation, the general procedure of synthesis, and numerical examples are presented in this paper.

Computer-Aided Design of the RSSR Function Generating Spatial Mechanism Using the Selective Precision Synthesis Method

Planar function generating mechanisms may be synthesized for a limited number of precision points by carrying out a kinematic inversion about the output link. However, this becomes quite difficult for spatial mechanisms. In this paper the general RSSR spatial function generating mechanism is synthesized using the Selective Precision Synthesis technique. In this computer-aided design method, nonlinear constraint equations relating the generated and desired rotations of the output crank are formulated. These constraints which define accuracy neighborhoods around each of the “n” prescribed output crank rotations, are then solved using the Generalized Reduced Gradient Method of optimization. The mathematical formulation, the general procedure of synthesis and numerical examples are presented in this paper.