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The discovery of a new FeII oxalate framework of composition K2Fe[(C2O4)2(H2O)2]·0.18H2O is reported. Its crystal structure was solved by means of single crystal and powder X‐ray diffraction. The new organic–inorganic hybrid compound crystallizes in the orthorhombic space group Pca21 with unit‐cell parameters: a = 12.0351 (4) Å, b = 15.1265 (5) Å, c = 10.5562 (4) Å. This crystal structure, containing eight chemical formula, consists of a succession of FeO4(H2O)2 octahedra and K+ cations growing along b direction. Magnetization measurements indicate that the title compound is paramagnetic over the investigated temperature range (2–300 K). Both magnetization and 57Fe Mössbauer data indicate that Fe2+ is in a high‐spin state. [ABSTRACT FROM AUTHOR]

The structure of M2(OH)2(bpdc) (bpdc = biphenyl dicarboxylate, C14H8O4) is distinct from that of the isoreticular compounds M2(OH)2(bdc) (bdc = benzene dicarboxylate, C8H4O4) (M = Mn, Fe), in the sense that no disorder of the bpdc molecules from one layer to the other needs to be considered. The global symmetry is lower in the bpdc compounds (P1) than in the bdc compounds (C2/m). Both Mn2(OH)2(bpdc) and Fe2(OH)2(bpdc) order magnetically at 36.8 and 46.5 K, respectively, and can be considered as uncompensated antiferromagnets, whereas Mn2(OH)2(bdc) (Néel temperature TN = 38.5 K) and Fe2(OH)2(bdc) (TN = 66 K) are compensated antiferromagnets. [ABSTRACT FROM AUTHOR]

We review mathematical models describing how Optical Coherence Tomography works. Hereby, we focus on models based on Maxwell's equations and their simplifications. We highlight especially the effects of different modeling assumptions for the incident illumination, the medium, the light propagation, and the measurement setup and illustrate the qualitatively differing behavior in numerical simulations of the OCT data and compare them with real data from OCT measurements.

Deep space exploration offers the most profound opportunity for the expansion of humanity and our understanding of the universe but remains extremely challenging. Progress will continue to be paced by uncrewed missions followed up by crewed missions to ever further destinations. Major space powers continue to invest in crewed deep space exploration as an important national strategy. An improved model based on previous work is developed, which projects the earliest possible launch dates for human-crewed missions from cis-lunar space to selected destinations in the Solar System and beyond based on NASA’s historic budget trend and overall development trends of deep space exploration research. The purpose of the analysis is to provide a projected timeframe for crewed missions beyond Mars. Our findings suggest the first human missions from a spacefaring nation or international collaboration to the asteroid belt and Jovian system could be scheduled as soon as ~2071 to ~2087 and ~2101 to ~2121, respectively, while a launch to the Saturn system may occur by the year ~2132, with an uncertainty window of ~2129 to ~2153.

Optical coherence tomography (OCT) is a widely used imaging technique in the micrometer regime, which gained accelerating interest in medical imaging in the last twenty years. In up-to-date OCT literature, certain simplifying assumptions are made for the reconstructions, but for many applications, a more realistic description of the OCT imaging process is of interest. In mathematical models, for example, the incident angle of light onto the sample is usually neglected or a plane wave description for the light–sample interaction in OCT is used, which ignores almost completely the occurring effects within an OCT measurement process. In this article, we make a first step to a quantitative model by considering the measured intensity as a combination of back-scattered Gaussian beams affected by the system. In contrast to the standard plane wave simplification, the presented model includes system relevant parameters, such as the position of the focus and the spot size of the incident laser beam, which allow a precise prediction of the OCT data. The accuracy of the proposed model—after calibration of all necessary system parameters—is illustrated by simulations and validated by a comparison with experimental data obtained from a 1300 nm swept-source OCT system.

From the basic geometry of submanifolds will be recalled what are the extrinsic principal tangential directions, (first studied by Camille Jordan in the 18seventies), and what are the principal first normal directions, (first studied by Kostadin Trenčevski in the 19nineties), and what are their corresponding Casorati curvatures. For reasons of simplicity of exposition only, hereafter this will merely be done explicitly in the case of arbitrary submanifolds in Euclidean spaces. Then, for the special case of Lagrangian submanifolds in complex Euclidean spaces, the natural relationships between these distinguished tangential and normal directions and their corresponding curvatures will be established.

In this paper, we prove some inequalities in terms of the normalized δ -Casorati curvatures (extrinsic invariants) and the scalar curvature (intrinsic invariant) of statistical submanifolds in holomorphic statistical manifolds with constant holomorphic sectional curvature. Moreover, we study the equality cases of such inequalities. An example on these submanifolds is presented.

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In this article, we consider statistical submanifolds of Kenmotsu statistical manifolds of constant ϕ-sectional curvature. For such submanifold, we investigate curvature properties. We establish some inequalities involving the normalized δ-Casorati curvatures (extrinsic invariants) and the scalar curvature (intrinsic invariant). Moreover, we prove that the equality cases of the inequalities hold if and only if the imbedding curvature tensors h and h∗ of the submanifold (associated with the dual connections) satisfy h=−h∗, i.e., the submanifold is totally geodesic with respect to the Levi–Civita connection.

The main purpose of the present paper is to well define Minkowskian angles and pseudo-angles between the two null directions and between a null direction and any non-null direction, respectively. Moreover, in a kind of way that will be tried to be made clear at the end of the paper, these new sorts of angles and pseudo-angles can similarly to the previously known angles be seen as (combinations of) Minkowskian lengths of arcs on a Minkowskian unit circle together with Minkowskian pseudo-lengths of parts of the straight null lines.