The reciprocal complementary Wiener number of a connected graph G is defined as ( ) { } ( ) ( ) | ∑ u v V G RCW G d d u v G ⊆ = + − , 1 1 , where ( ) V G is the vertex set. ( ) | d u v G , is the distance between vertices u and v, and d is the diameter of G. A tree is known as a caterpillar if the removal of all pendant vertices makes it as a path. Otherwise, it is called a non-caterpillar. Amo...

The mode shapes of piezoelectric metamaterials are tuned by manipulating spatially the electrical boundary conditions piezo-elements, in a desired and controlled manner, order to tailor wave propagation characteristics through these metamaterials. piezo-elements using inductive shunting networks. With appropriate tuning optimization spatial distribution conditions, it would be possible alter sh...

Besides its fundamental importance, non-reciprocity has also found many potential applications in quantum technology. Recently, systems have been proposed to realize non-reciprocity, but stable non-reciprocal process is still experimentally difficult general, due the needed cyclical interactions artificial or operational difficulties solid state materials. Here, we propose a new kind of interac...

In this work, we investigate non-Hermitian elastic waveguides with periodically applied proportional feedback efforts, implemented through piezoelectric sensors and actuators. Using onedimensional spectral models for longitudinal motion, it is shown that dispersion diagrams of family structures exhibit non-reciprocal imaginary frequency components, manifesting as wave attenuation or amplificati...

Non-reciprocal phenomena are widely used in photonic devices. Important applications such as isolators and circulator waveguide structures depend on non-reciprocal effects. The basis of these phenomena is a difference in phase or refractive index for an electromagnetic wave of a given polarization as it travels through a medium in opposite directions. Generally this applies to the real part of ...

Are cooperative decisions typically made more quickly or slowly than non-cooperative decisions? While this question has attracted considerable attention in recent years, most research has focused on one-shot interactions. Yet it is repeated interactions that characterize most important real-world social interactions. In repeated interactions, the cooperativeness of one's interaction partners (t...