Recently, Mingo has analyzed the properties of I imp, an importance index, and demonstrated that its range is not symmetrical. While agreeing with this comment, we believe that more light needs to be shed on the issue of symmetry in relation to such indices. Importance indices are calculated using three values: performance of the organism in the absence and in the presence of neighbors and maxi...

Spine deformations and faulty posture may be evaluated by assessing trunk surface deformation. POTSI index (Posterior Trunk Symmetry Index) was introduced in 2003 to assess asymmetry of the trunk seen from the back. However, deformations may also affect the anterior surface of the trunk and this can be noticed more easily by the patient owing to the visual accessibility of the anterior surface....

We consider discrete invertible dynamical systems L with the property that the kth iterate L k possesses (reversing) symmetries that are not possessed by L. A map U is called a (reversing) k-symmetry of L if k is the smallest positive integer for which U is a (reversing) symmetry of L k. In this paper we discuss the particular case that L possesses a cyclic reversing k-symmetry group. We derive...

We show that the space of algebraic covariant derivative curvature tensors R is generated by Young symmetrized product tensors T ⊗ T̂ or T̂ ⊗ T , where T and T̂ are covariant tensors of order 2 and 3 whose symmetry classes are irreducible and characterized by the following pairs of partitions: {(2), (3)}, {(2), (2 1)} or {(1), (2 1)}. Each of the partitions (2), (3) and (1) describes exactly one s...

the aim of this study was to evaluate mesiodistal diameter of permanent teeth and evaluating it's distribution in iran. in current study, 850 plastery impressions or 16590 teeth were precisely measured by a digital coulis with 0.01 mm accuracy.the obtained measures of the permanent teeth are shown in table 1. table (4) demonstrates the symmetry of left and right maxillary and mandibular te...