We present a new method for the completion of partial globally-symmetric 3D objects, based on the detection of partial and approximate symmetries in the incomplete input dataset. In our approach, symmetry detection is formulated as a constrained sparsity maximization problem, which is solved efficiently using a robust RANSACbased optimizer. The detected partial symmetries are then reused iterat...

Finding design intent embodied as high-level geometric relations between a CAD model’s sub-parts facilitates various tasks such as model editing and analysis. This is especially important for boundary-representation models arising from, e.g., reverse engineering or CAD data transfer. These lack explicit information about design intent, and often the intended geometric relations are only approxi...

Charge independence and charge symmetry are approximate symmetries of nature, violated by the perturbing effects of the mass difference between up and down quarks and by electromagnetic interactions. The observations of the symmetry breaking effects in nuclear and particle physics and the implications of those effects are reviewed.

We show how an operation of inf-convolution can be used to approximate convex functions with C smooth convex functions on Riemannian manifolds with nonpositive curvature (in a manner that not only is explicit but also preserves some other properties of the original functions, such as ordering, symmetries, infima and sets of minimizers), and we give some applications.

We globally classify two-component evolution equations, with homogeneous diagonal linear part, admitting infinitely many approximate symmetries. Important ingredients are the symbolic calculus of Gel’fand and Dikĭı, the Skolem–Mahler–Lech theorem, results on diophantine equations in roots of unity by F. Beukers, and an algorithm of C.J. Smyth.

We consider the nonlinear diffusion equation with a perturbed convection term. The potential symmetries for exact respect to second conservation law are classified. It is found that these exist only in linear case. further shown no nontrivial approximate of order one exists other law.

The main idea in this research is introducing another approximate method to calculate solutions of the fractional Torsion equation, which one applied equations civil engineering. Since order closed an integer, we convert equation a perturbed ordinary differential involving small parameter epsilon. Then can find exact and symmetries for alternative approximation equation. Also, with help definit...