Bilateral Symmetry Has No Effect on Stereoscopic Shape Judgments

A single experiment is reported that measured the apparent stereoscopic shapes of symmetric and asymmetric objects at different viewing distances. The symmetric stimuli were specifically designed to satisfy the minimal conditions for computing veridical shape from symmetry. That is to say, they depicted complex, bilaterally symmetric, plane-faced polyhedra whose symmetry planes were oriented at an angle of 45° relative to the line of sight. The asymmetric stimuli were distorted versions of the symmetric ones in which the 3D position of each vertex was randomly displaced. Prior theoretical analyses have shown that it is mathematically possible to compute the 3D shapes of symmetric stimuli under these conditions, but those algorithms are useless for asymmetric objects. The results revealed that the apparent shapes of both types of objects were expanded or compressed in depth as a function of viewing distance, in exactly the same way as has been reported in many other studies, and that the presence or absence of symmetry had no detectable effect on performance.

On 2-metric resolvability in rotationally-symmetric graphs

The 2-metric resolvability is an extension of metric resolvability in graphs having several applications in intelligent systems for example network optimization, robot navigation and sensor networking. Rotationally symmetric graphs are important in intelligent networks due to uniform rate of data transformation to all nodes. In this article, 2-metric dimension of rotationally symmetric plane graphs Rn, Sn and Tn is computed and found to be independent of the number of vertices.

Cyclic Sieving for Plane Partitions and Symmetry

The cyclic sieving phenomenon of Reiner, Stanton, and White says that we can often count the fixed points of elements of a cyclic group acting on a combinatorial set by plugging roots of unity into a polynomial related to this set. One of the most impressive instances of the cyclic sieving phenomenon is a theorem of Rhoades asserting that the set of plane partitions in a rectangular box under the action of promotion exhibits cyclic sieving. In Rhoades's result the sieving polynomial is the size generating function for these plane partitions, which has a well-known product formula due to MacMahon. We extend Rhoades's result by also considering symmetries of plane partitions: specifically, complementation and transposition. The relevant polynomial here is the size generating function for symmetric plane partitions, whose product formula was conjectured by MacMahon and proved by Andrews and Macdonald. Finally, we explain how these symmetry results also apply to the rowmotion operator on plane partitions, which is closely related to promotion.

Dual-/tri-band bandpass filters with fully independent and controllable passband based on multipath-embedded resonators

In this paper, dual-band and tri-band bandpass filters (BPFs) with fully independent and controllable passbands based on multipath-embedded resonators are presented. The dual-band BPF consists of two double open-ended stub-loaded terminal-shorted resonators (DOESL-TSRs) with a common via-hole connected along the symmetric plane of the filter. Based on DOESL-TSRs, a triple open-ended stub-loaded terminal-shorted resonator (TOESL-TSR) is proposed in the design of tri-band BPFs. The resonant characteristics of DOESL-TSR/TOESL-TSR are analyzed by the numerical calculation method. The measured results of the dual-band BPF show that the center frequencies (CFs) are located at 2.595 and 5.75 GHz, respectively, with 3 dB fraction bandwidth (FBWs) of 15 and 12.8%. The measured CFs of the tri-band BPF are located at 2.545, 3.775, and 5.95 GHz, respectively, with 3 dB FBWs of 9.8, 9.3, and 5.5%. Both of the filters exhibit the merits of fully independent and controllable passbands, high selectivity, and compact size.

Metric dimension of heptagonal circular ladder

Let [Formula: see text] be an undirected (i.e., all the edges are bidirectional), simple (i.e., no loops and multiple edges are allowed), and connected (i.e., between every pair of nodes, there exists a path) graph. Let [Formula: see text] denotes the number of edges in the shortest path or geodesic distance between two vertices [Formula: see text]. The metric dimension (or the location number) of some families of plane graphs have been obtained in [M. Imran, S. A. Bokhary and A. Q. Baig, Families of rotationally-symmetric plane graphs with constant metric dimension, Southeast Asian Bull. Math. 36 (2012) 663–675] and an open problem regarding these graphs was raised that: Characterize those families of plane graphs [Formula: see text] which are obtained from the graph [Formula: see text] by adding new edges in [Formula: see text] such that [Formula: see text] and [Formula: see text]. In this paper, by answering this problem, we characterize some families of plane graphs [Formula: see text], which possesses the radial symmetry and has a constant metric dimension. We also prove that some families of plane graphs which are obtained from the plane graphs, [Formula: see text] by the addition of new edges in [Formula: see text] have the same metric dimension and vertices set as [Formula: see text], and only 3 nodes appropriately selected are sufficient to resolve all the nodes of these families of plane graphs.

The influence of leading-edge deflection on the stability of the leading-edge vortices

To examine the effect of leading-edge deflected angle [Formula: see text] on the stability of the leading-edge vortex, the three-dimensional flow field of a flapping wing is simulated by a numerical method. The multi domain mesh generation, dynamic mesh and large eddy simulation technology are employed to capture the finer flowfield structure. The wings perform pure periodic oscillations, and the Reynolds number ( Re) is 4527 based on the chord length c. The folding line formed after the deflection coincides with the pitch axis and is located at the 1/4 c from the leading edge. The results show that the increase of [Formula: see text] maintains the strength of the leading-edge vortex for longer time, and weakens the influence of the motion of the wing on the leading-edge vortex intensity. The flowfield topological analysis shows that the increase of [Formula: see text] also prevents the formation of secondary vortices between the wing surface and the leading-edge vortices, which indirectly contributes to the attachment of the leading-edge vortices to the wing. Moreover, the vortex dynamics equations have been analyzed, and the results indicate that the increase of [Formula: see text] will delay the occurrence of spanwise convection of vorticity and weaken its intensity. In addition, it can also suppress the spanwise flow behind the leading-edge vortices toward the symmetric plane. As a result, increasing [Formula: see text] stabilizes the boundary layer in this region and thereby stabilizes the leading-edge vortices indirectly. Finally, a new parameter is introduced to quantitatively evaluate the proximity of the leading-edge vortex to the surface of the plate. Our method comprehensively considers the influence of the leading-edge vortex scale and the core motion on the approaching of the leading-edge vortex to the wing, and some important conclusions on the developing law of the leading-edge vortex, which are agreement with the experimental measurement, are obtained.