It is calculated the number of symmetric r-colorings of vertices of a regular n-gon and the number of equivalence classes of symmetric r-colorings [1, 2]. A coloring is symmetric if it is invariant in respect to some mirror symmetry with an axis crossing center of polygon and one of its vertices. Colorings are equivalent if we can get one from another by rotating about the polygon center.

since the time man observed his picture in the water, mirror has en-tered both man’s spiritual and material life. the role of mirror has un-dergone a lot of changes, ranging from foretelling to its use by barbers in different situations, to its use as warfare, mystic allegories, literal metaphors and historical narrations such as alexander mirror located in alexandria. the present study aims to...

A new numerical procedure is proposed to solve the symmetric matrix polynomial equation A T (?s)X(s) + X T (?s)A(s) = 2B(s) that is frequently encountered in control and signal processing. It is based on interpolation and takes fully advantage of symmetry of the equation by reducing the original problem dimension. The algorithm is more eecient and more general than older methods and, namely, it...

Repetitive mirror symmetric bilateral upper limb may be a suitable priming technique for upper limb rehabilitation after stroke. Here we demonstrate neurophysiological and behavioural after-effects in healthy participants after priming with 20 minutes of repetitive active-passive bimanual wrist flexion and extension in a mirror symmetric pattern with respect to the body midline (MIR) compared t...

For problems of linear control system synthesis, an apparatus of polynomial equations (for single-variable case) and of matrix polynomial equations (for multivariable case) was successfully developed in recent times, cf. [1]. In connection with quadratic criteria, we are led to equations of special type, containing an operation of conjugation ah-* a* representing a(s) i-> a( — s) for continuous...

Mirror-symmetrical bimanual movement is more stable than parallel bimanual movement. This is well established at the kinematic level. We used functional MRI (fMRI) to evaluate the neural substrates of the stability of mirror-symmetrical bimanual movement. Right-handed participants (n=17) rotated disks with their index fingers bimanually, both in mirror-symmetrical and asymmetrical parallel mode...

In this note we consider completions of n×n symmetric (0,−1)-matrices to symmetric alternating sign matrices by replacing certain 0s with +1s. In particular, we prove that any n×n symmetric (0,−1)-matrix that can be completed to an alternating sign matrix by replacing some 0s with +1s can be completed to a symmetric alternating sign matrix. Similarly, any n × n symmetric (0,+1)-matrix that can ...

With no object to hide behind in 3D space, the open ocean represents a challenging environment for camouflage. Conventional strategies for reflective crypsis (e.g., standard mirror) are effective against axially symmetric radiance fields associated with high solar altitudes, yet ineffective against asymmetric polarized radiance fields associated with low solar inclinations. Here we identify a b...