Introduction/purpose: Molodtsov introduced the concept of soft sets as a new mathematical tool for dealing with problems containing uncertainties. In the literature, different kinds of operations of soft sets are defined and used in theory and applications. Methods: This study is based on the paper "A New Operation on Soft Sets: Extended Difference of Soft Sets" by Sezgin, Ahmad and Mehmood [Journal of New Theory 27 (2019) 33-42]. Results: In this paper, we define a new operation on soft sets, called extended symmetric difference and investigate its relationship between extended symmetric difference and restricted symmetric difference and some other operations of soft sets. Conclusion: The author believes that the obtained results represent a significant improvement of many known results in the existing literature.

In this paper, tiling a plane with equilateral semi-regular convex polygons is considered, and, that is, tiling with equilateral polygons of the same type. Tiling a plane with semi-regular polygons depends not only on the type of a semi-regular polygon, but also on its interior angles that join at a node. In relation to the interior angles, semi-regular equilateral polygons with the same or different interior angles can be joined in the nodes. Here, we shall first consider tiling a plane with semi-regular equilateral polygons with 2m-sides. The analysis is performed by determining the set of all integer solutions of the corresponding Diophantine equation in the form of , whereare the non-negative integers which are not equal to zero at the same time, and are the interior angles of a semi-regular equilateral polygon from the characteristic angle. It is shown that of all semi-regular equilateral polygons with 2m-sides, a plane can be tiled only with the semi-regular equilateral quadrilaterals and semi-regular equilateral hexagons. Then, the problem of tiling a plane with semi-regular equilateral quadrilaterals is analyzed in detail, and then the one with semi-regular equilateral hexagons. For these semi-regular polygons, all possible solutions of the corresponding Diophantine equations were analyzed and all nodes were determined, and then the problem for different values of characteristic elements was observed. For some of the observed cases of tiling a plane with these semi-regular polygons, some graphical presentations of tiling constructions are also given.

This paper presents the first comprehensive tutorial on a promising research field located at the frontier of two well-established domains, neurosciences and wireless communications, motivated by the ongoing efforts to define the Sixth Generation of Mobile Networks (6G). In particular, this tutorial first provides a novel integrative approach that bridges the gap between these two seemingly disparate fields. Then, we present the state-of-the-art and key challenges of these two topics. In particular, we propose a novel systematization that divides the contributions into two groups, one focused on what neurosciences will offer to future wireless technologies in terms of new applications and systems architecture (Neurosciences for Wireless Networks), and the other on how wireless communication theory and next-generation wireless systems can provide new ways to study the brain (Wireless Networks for Neurosciences). For the first group, we explain concretely how current scientific understanding of the brain would enable new applications within the context of a new type of service that we dub brain-type communications and that has more stringent requirements than human- and machine-type communication. In this regard, we expose the key requirements of brain-type communication services and discuss how future wireless networks can be equipped to deal with such services. Meanwhile, for the second group, we thoroughly explore modern communication systems paradigms, including Internet of Bio-Nano Things and wireless-integrated brain–machine interfaces, in addition to highlighting how complex systems tools can help bridging the upcoming advances of wireless technologies and applications of neurosciences. Brain-controlled vehicles are then presented as our case study to demonstrate for both groups the potential created by the convergence of neurosciences and wireless communications, probably in 6G. In summary, this tutorial is expected to provide a largely missing articulation between neurosciences and wireless communications while delineating concrete ways to move forward in such an interdisciplinary endeavor.

An optical sensor IC in 0.35-<inline-formula> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula> CMOS is presented containing a single-photon avalanche diode (SPAD) and a fast quadruple-voltage quenching circuit (QVQC). The QVQC features a fast active quenching time of 0.93 ns, a total quenching time of 1.9 ns, and an adjustable total dead time (8.6–200 ns) to reduce the afterpulsing probability (APP). To verify the quenching performance, the circuit was integrated with a 40-<inline-formula> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula> diameter SPAD. Experiments show the reduction of afterpulsing by a low detection threshold and by fast quenching with a slew rate of 13.8 GV/s. Thus, an APP of 3.2% at 27-ns dead time, a peak photon detection probability (PDP) of 67.6% at 652 nm, and a PDP of 34.7% at 854 nm were measured at 13.2-V excess bias.