Spin-orbit interactions (SOI) of light have emerged as a prominent area of research in nanophotonics, whereas epsilon-near-zero (ENZ) materials are gaining attention for their ability to interact with electromagnetic fields peculiarly. Integrating these two, we show that homogeneous ENZ thin films enable efficient spin-to-vortex conversion even under paraxial illumination. Using a generalized angular-spectrum formalism and experimental verification, we demonstrate that circularly polarized light incident on an indium-tin-oxide slab generates a second-order vortex in the cross-circular channel. Moreover, for elliptically deformed Gaussian excitation, the spin-induced vortex undergoes astigmatic splitting into two generic vortices. In contrast, a Bessel-Gaussian annulus with phase asymmetry from a tilted axicon produces a similar vortex splitting accompanied by a spin-dependent rotation of the double-core vortex pattern. These findings, combined with the intrinsic nonlinearity of ENZ materials, highlight their potential as a versatile platform to explore SOI effects across linear and nonlinear regimes.
In this article, we investigate the focal locus of closed (not necessarily compact) submanifolds in a forward complete Finsler manifold. The main goal is to show that the associated normal exponential map is regular in the sense of F.W. Warner (Am. J. of Math., 87, 1965). As a consequence, we show that the normal exponential is non-injective near any tangent focal point. Extending the ideas of Warner, we study the connected components of the regular focal locus. This allows us to identify an open and dense subset, on which the focal time maps are smooth, provided they are finite. We explicitly compute the derivative at a point of differentiability. As an application of the local form of the normal exponential map, following R.L. Bishop's work (Proc. Amer. Math. Soc., 65, 1977), we express the tangent cut locus as the closure of a certain set of points, called the separating tangent cut points. This strengthens the results from the present authors' previous work (J. Geom. Anal., 34, 2024).
A new octahedral Ni(III) complex, [Ni(L)(L-T)]center dot 2DMSO center dot 2.5H(2)O (1), has been synthesized and thoroughly characterized by spectroscopic methods and single-crystal X-ray analysis, where HL and HLT represent two tautomeric forms of the tridentate ligand, 2-hydroxy-1-naphthaldehydethiosemicarbazone (HL). In complex 1, two deprotonated ligand molecules (L and LT) coordinate to the Ni(III) center: one acts as a mononegative species, while the other functions as a binegative species, facilitated by thione-thiol tautomerism. The +3-oxidation state of nickel was conclusively verified using single-crystal X-ray analysis, Bond Valence Sum (BVS) calculations, Xray photoelectron spectroscopy (XPS), electron paramagnetic resonance (EPR), cyclic voltammetry (CV), and Density Functional Theory (DFT) calculations. Moreover, cytotoxic potential of complex 1 was evaluated towards Dalton's Lymphoma (DL) cells, demonstrating significant anticancer properties. Further, cytotoxicity studies on normal peripheral blood mononuclear cells (PBMCs) indicated a favourable safety profile. Furthermore, molecular docking analyses revealed potential interactions between complex 1 and mouse tumor necrosis factor, suggesting a plausible mechanism of action. This study expands the chemistry of high-valent nickel complexes and provides the first evidence of cytotoxic activity for a Ni(III) species, highlighting its potential in therapeutic applications.
Recent experiments on quantum computers have challenged the limits of classical computation in chemistry, simulating ground states of strongly correlated molecules. Many of these experiments have utilized the unitary cluster Jastrow ansatz, a quantum circuit inspired by the unitary coupled cluster ansatz that can be tailored to current quantum hardware. Notably, the largest experiment in Sci. Adv. 11, 25 (2025) executed a quantum circuit with 77 qubits and 10,570 gates on an IBM quantum computer and performed classical post-processing with up to 6400 nodes on Fugaku to compute ground state energies better than Hartree-Fock. In this work, we present a polynomial time classical algorithm to compute the energy of any single-layer unitary cluster Jastrow circuit, independent of locality constraints for quantum hardware. Our algorithm can reproduce the largest experiment from Sci. Adv. 11, 25 (2025) in less than a minute on a laptop, and through circuit optimization enabled by fast simulation we achieve a lower ground state energy than the experiment.
We relate a well-known identity from order statistics to a curious way of bounding the prime-counting function from below, due to Nair.
