A New Type of Coincidence and Common Fixed Point Theorem with Applications

Coincidence and common fixed point theorems for a class of 'Ciric-Suzuki hybrid contractions involving a multivalued and two single-valued maps in a metric space are obtained. Some applications including the existence of a common solution for certain class of functional equations arising in a dynamic programming are also discussed..

New generation of two-dimensional spintronic systems realized by coupling of Rashba and Dirac fermions

Intriguing phenomena and novel physics predicted for two-dimensional (2D) systems formed by electrons in Dirac or Rashba states motivate an active search for new materials or combinations of the already revealed ones. Being very promising ingredients in themselves, interplaying Dirac and Rashba systems can provide a base for next generation of spintronics devices, to a considerable extent, by mixing their striking properties or by improving technically significant characteristics of each other. Here, we demonstrate that in BiTeI@PbSb2Te4 composed of a BiTeI trilayer on top of the topological insulator (TI) PbSb2Te4 weakly- and strongly-coupled Dirac-Rashba hybrid systems are realized. The coupling strength depends on both interface hexagonal stacking and trilayer-stacking order. The weakly-coupled system can serve as a prototype to examine, e.g., plasmonic excitations, frictional drag, spin-polarized transport, and charge-spin separation effect in multilayer helical metals. In the strongly-coupled regime, within similar to 100 meV energy interval of the bulk TI projected bandgap a helical state substituting for the TI surface state appears. This new state is characterized by a larger momentum, similar velocity, and strong localization within BiTeI. We anticipate that our findings pave the way for designing a new type of spintronics devices based on Rashba-Dirac coupled systems.

Triglops dorothy, a new species of sculpin (Teleostei: Scorpaeniformes: Cottidae) from the southern Sea of Okhotsk

A new species of the cottid genus Triglops Reinhardt is described on the basis of 21 specimens collected in Aniva Bay, southern Sakhalin Island, Russia, and off Kitami, on the northern coast of Hokkaido, Japan, at depths of 73–117 m. Of the ten species of Triglops now recognized, the new species, Triglops dorothy, is most similar to T. pingeli Reinhardt, well known from the North Atlantic and North Pacific oceans and throughout coastal waters of the Arctic. The new species differs from T. pingeli in a combination of morphometric and meristic characters that includes most importantly the number of dorsolateral scales; the number of oblique, scaled dermal folds below the lateral line; and the number of gill rakers.

Two new species of Zospeum Bourguignat, 1856 from the Basque-Cantabrian Mountains, Northern Spain (Eupulmonata, Ellobioidea, Carychiidae)

Two new species of the genus Zospeum Bourguignat, 1856 are described from caves in the Sierra de Aitzgorri (Gipuzkoa) and the Sierra Salvada (Burgos) in Northern Spain. The taxa Z. vasconicum sp. n. and Z. zaldivarae sp. n. have recently, without a formal name, been included in a molecular study of worldwide members of the Carychiidae. In the present paper, the shell morphology and variation of these species is described and illustrated.