Synthesis and biological evaluation of aromatic analogues of conduritol F, L-chiro-inositol, and dihydroconduritol F structurally related to the amaryllidaceae anticancer constituents

Pancratistatin is a potent anticancer natural product, whose clinical evaluation is hampered by the limited natural abundance and the stereochemically complex structure undermining practical chemical preparation. Fifteen aromatic analogues of conduritol F, l-chiro-inositol, and dihydroconduritol F that possess four of the six pancratistatin stereocenters have been synthesized and evaluated for anticancer activity. These compounds serve as truncated pancratistatin analogues lacking the lactam ring B, but retaining the crucial C10a-C10b bond with the correct stereochemistry. The lack of activity of these compounds provides further insight into pancratistatin's minimum structural requirements for cytotoxicity, particularly the criticality of the intact phenanthridone skeleton. Significantly, these series provide rare examples of simple aromatic conduritol and inositol analogues and, therefore, this study expands the chemistry and biology of these important classes of compounds.     

Moving toward shared realities through empathy in mathematical modeling: An ecological systems theory approach

The mathematics education community has routinely called for mathematics tasks to be connected to the real world. However, accomplishing this in ways that are relevant to students’ lived experiences can be challenging. Meanwhile, mathematical modeling has gained traction as a way for students to learn mathematics through real-world connections. In an open problem to the mathematics education community, this paper explores connections between the mathematical modeling and the nature of what is considered relevant to students. The role of empathy is discussed as a proposed component for consideration within mathematical modeling so that students can further relate to real-world contexts as examined through the lens of Ecological Systems Theory. This is contextualized through a classroom-tested example entitled “Tiny Homes as a Solution to Homelessness” followed by implications and conclusions as they relate to mathematics education.     

The New Extensions of the Henstock–Kurzweil and the McShane Integrals of Vector-Valued Functions

In this paper, we define the Hake–Henstock–Kurzweil and the Hake–McShane integrals of Banach space valued functions defined on an open and bounded subset G of m-dimensional Euclidean space \(\mathbb {R}^{m}\). These are ”natural” extensions of the McShane and the Henstock–Kurzweil integrals from m-dimensional closed non-degenerate intervals to bounded and open subsets of \(\mathbb {R}^{m}\). Our goal is not a generalization for the sake of generalization. Indeed, we will show theorems which reduce the study of our integrals to the study of McShane and Henstock–Kurzweil integrals. As applications, we will present Hake-type theorems for the Henstock–Kurzweil and the McShane integrals in terms of our integrals.     

Dynamic spectral response of solid solutions of the bismuth-strontium ferrite Bi1 − x Sr x FeO3 − δ in the frequency range 0.3–200 THz

Ceramic samples of Bi_{1 ? x} Sr _x FeO_{3 ? δ} have been investigated using X-ray diffraction analysis, Raman spectroscopy, and infrared spectroscopy. It has been shown that the spectra of these solid solutions should be considered as a superposition of resonant phonon responses of the cubic perovskite and a relaxation response. No relaxators are observed in the pure compounds BiFeO₃ and SrFeO_{3 ? δ}. It has been found that two concentration phase transitions occurs with the symmetry changes $R3c \leftrightarrow Pm\bar 3m$ in the range 0.1 < x < 0.2 and $Pm\bar 3m \leftrightarrow P4mm$ in the range 0.8 < x < 1.0.     

Growth and morphological study of copper oxide single crystals

Experiments on the growth of CuO single crystals by crystallization from flux in the CuO-Bi₂O₃-PbO-PbF₂, CuO-Bi₂O₃-Li₂O, CuO-Bi₂O₃-B₂O₃, CuO-BaO-Y₂O₃, and CuO-MO_x systems (M = P, V, or Mo) have been performed. The best results were obtained in crystallization in the CuO-Bi₂O₃-PbF₂ system: prismatic single crystals of platelet-and needlelike or isometric habit with dimensions up to 1 × 10 × 10, 1 × 1 × 20, or 6 × 6 × 8 mm, respectively, have been grown. The CuO crystals show polysynthetic twinning in the form of numerous alternating light and dark bands bound by systems of parallel straight lines on the {110} and {111} faces. A possible model of twinning associated with the Cu₂O → CuO transformation is considered.     

Magnetic structure of the quasi-one-dimensional frustrated antiferromagnet LiCu<Subscript>2</Subscript>O<Subscript>2</Subscript> with Spin <Emphasis Type="Italic">S</Emphasis> = 1/2

The magnetic properties of LiCu₂O₂ single-crystal samples without twinning are investigated using electron spin resonance and nuclear magnetic resonance spectroscopy. The experimental results obtained are described in terms of the model of a planar spiral antiferromagnet for the orientation of the magnetic field H ‖ b or H ‖ c and the model of a collinear spin-modulated antiferromagnet for the orientation of the static magnetic field H ‖ a.     

The Radon‐Nikodym property,generalized bounded variation and the average range

A generalized bounded variation characterization of Banach spaces possessing the Radon‐Nikodym property is given in terms of the average range. We prove that a Banach space X has the Radon‐Nikodym property if and only if for each function of generalized bounded variation on [0, 1], the average range is a nonempty set at almost all .     

Low-frequency relaxation processes in Pb<Subscript>5</Subscript>Ge<Subscript>3</Subscript>O<Subscript>11</Subscript> ferroelectric crystals

Measurements and analysis of the temperature and frequency dependences of permittivity and losses and of the electrical resistivity of Pb₅Ge₃O₁₁ ferroelectric crystals at temperatures of 100 to 600 K and frequencies of 0.1 to 100 kHz are reported. The dielectric characteristics of the crystals exhibit, in addition to clearly pronounced anomalies near the Curie point T_C=450 K, less distinct anomalous features of the relaxation character in the range 230–260 K. The data obtained on the effect of various factors (degree of crystal polarization, crystal annealing at different temperatures and in different environments, etc.) on the low-temperature anomalies serve as a basis for discussing the possible mechanisms responsible for these anomalies. It is concluded that the low-temperature dielectric anomalies originate from thermal carrier localization in defect levels in the band gap, which entail the formation of local polarized states.     

Computation of Galois groups associated to the 2-class towers of some quadratic fields

The p-group generation algorithm from computational group theory is used to obtain information about large quotients of the pro-2 group for with d=−445,−1015,−1595,−2379. In each case we are able to narrow the identity of G down to one of a finite number of explicitly given finite groups. From this follow several results regarding the corresponding 2-class tower.