Fixed-Point Study of Generalized Rational Type Multivalued Contractive Mappings on Metric Spaces with a Graph

The main result of this paper is a fixed-point theorem for multivalued contractions obtained through an inequality with rational terms. The contraction is an F-type contraction. The results are obtained in a metric space endowed with a graph. The main theorem is supported by illustrative examples. Several results as special cases are obtained by specific choices of the control functions involved in the inequality. The study is broadly in the domain of setvalued analysis. The methodology of the paper is a blending of both graph theoretic and analytic methods.This paper has been supported by the Basque Government though Grant T1207-19

Magnetism and field-induced effect in a spin-orbit entangled Jeff = 1/2 honeycomb lattice

The interplay between spin-orbit coupling, frustration-induced anisotropic magnetic interaction, and spin correlations can lead to novel states with exotic excitations in rare-earth-based quantum magnets. Herein, we present the crystal structure, magnetization, electron spin resonance (ESR), specific heat, and nuclear magnetic resonance (NMR) experiments on the polycrystalline samples of Ba9Yb2Si6O24 in which Yb3+ ions form a perfect honeycomb lattice without detectable anti-site disorder. Magnetization data reveal antiferromagnetically coupled spin-orbit entangled Jeff = 1/2 degrees of freedom of Yb3+ ions in the Kramers doublet state where the Curie-Weiss temperature is - 2.97 K, as obtained from the low-temperature magnetic susceptibility data. The ESR measurements reveal that the first excited Kramers doublet is 32.3(7) meV above the ground state. The specific heat results suggest the presence of an antiferromagnetic phase transition at 2.26 K. The long-range antiferromagnetic order is completely suppressed upon the application of magnetic field and a field-induced disordered state is observed in an applied magnetic field of 2.5 T, which is also confirmed by NMR measurements. Furthermore, the NMR spin-lattice relaxation rate reveals the presence of a field-induced gap that is attributed to the Zeeman splitting of Kramers doublet state in this quantum material. Our experiments suggest the presence of a phase transition and short-range spin correlations appearing well above the antiferromagnetic phase transition temperature and a field-induced disordered state in this spin-orbit entangled Jeff =1/2 rare-earth magnet on a honeycomb lattice

Fixed points of multivalued mappings in metric spaces

Admissibility of mappings are introduced to create conditions to minimally restrict various contractive conditions on pairs of points from a metric space in order to ensure fixed point property of the respective contractions. In the present work we define new admissibility conditions and control functions to obtain certain multivalued fixed point theorems. The corresponding single valued case is discussed. We define four weak contraction mappings of which two are multivalued and two are single valued. The results are without any assumption of continuity. There is an illustrative example

Diorganotin compounds containing α-aminoacidato schiff base ligands derived from functionalized 2-Hydroxy-5-(aryldiazenyl)benzaldehyde

Three novel bicycloazastannoxides, namely, [nBu2Sn(L1)] (1), [nBu2Sn(L2)] (2) and [Bz2Sn(L3)] (3) were synthesized in one pot procedures by reacting diorganotin(IV) precursors with a mixture composed of an α-amino acid with either (E)-2-hydroxy-5-((4-nitrophenyl)diazenyl)benzaldehyde or (E)-2-hydroxy-5-(phenyldiazenyl)benzaldehyde. Single-crystal X-ray diffraction analysis reveal that compound 1 is monomeric, compound 2 consists of both a monomer and a dimer, while compound 3 is a coordination polymer for which two modifications 3A and 3B were identified. The 119Sn NMR chemical shifts measured in CDCl3 solutions indicate five-coordinate tin atoms for 1–3. Further, compounds 1 and 2 were found to be highly selective for sensing hydrogen sulfide in UV/Vis channel in CH3CN/H2O (9:1) media. The development of orange red color is likely the results of a Brønsted-type acid-base reaction of H2S with compounds 1 and 2, respectively, giving di-n-butyltin sulfide and the corresponding pro-ligands H2L1 and H2L2, respectively. Theoretical calculations accompany the experimental work

First report of Champsodon capensis Regan, 1908 (Champsodontidae) from East coast of India

The gaper Champsodon capensis Regan, 1908 is reported for the first time from the east coast of India on the basis of 3 specimens (55 – 72 mm standard length) collected from Deshpran fishing harbor, West Bengal. Identification of the species is confirmed by ventral scale patterns on chin, breast, and abdomen. Earlier, this species was reported only from Andaman-Nicobar waters of India and the present finding report further range extension of the species to the northern part of the Bay of Bengal. This paper provides a detailed description of the species along with the comparison with other Champsodon species

Experimental signatures of quantum and topological states in frustrated magnetism

Frustration in magnetic materials arising from competing exchange interactions can prevent the system from adopting long-range magnetic order and can instead lead to a diverse range of novel quantum and topological states with exotic quasiparticle excitations. Here, we review prominent examples of such emergent phenomena, including magnetically-disordered and extensively degenerate spin ices, which feature emergent magnetic monopole excitations, highly-entangled quantum spin liquids with fractional spinon excitations, topological order and emergent gauge fields, as well as complex particle-like topological spin textures known as skyrmions. We provide an overview of recent advances in the search for magnetically-disordered candidate materials on the three-dimensional pyrochlore lattice and two-dimensional triangular, kagome and honeycomb lattices, the latter with bond-dependent Kitaev interactions, and on lattices supporting topological magnetism. We highlight experimental signatures of these often elusive phenomena and single out the most suitable experimental techniques that can be used to detect them. Our review also aims at providing a comprehensive guide for designing and investigating novel frustrated magnetic materials, with the potential of addressing some important open questions in contemporary condensed matter physics