The Zero-Divisor Graph Associated to a Semigroup

The zero-divisor graph of a commutative semigroup with zero is the graph whose vertices are the nonzero zero-divisors of the semigroup, with two distinct vertices adjacent if the product of the corresponding elements is zero. New criteria to identify zero-divisor graphs are derived using both graph-theoretic and algebraic methods. We find the lowest bound on the number of edges necessary to guarantee a graph is a zero-divisor graph. In addition, the removal or addition of vertices to a zero-divisor graph is investigated by using equivalence relations and quotient sets. We also prove necessary and sufficient conditions for determining when regular graphs and complete graphs with more than two triangles attached are zero-divisor graphs. Lastly, we classify several graph structures that satisfy all known necessary conditions but are not zero-divisor graphs.     

Database Survey of Single-and-Half Phosphorus–Oxygen Bonds in Salts with the C2PO2 Segment: Crystal Structure of [NH2C5H4NH][(C6H5)2P(O)(O)]⋅2H2O

Crystallography Reports - For structures with a C2PO2 skeleton, a comparison of “single-and-half” phosphorus–oxygen bonds with single and double phosphorus–oxygen bonds is...     

Noscapine-derived β-amino alcohols as new organocatalysts for enantioselective addition of diethylzinc to aldehydes

In this paper, synthesis of two derivatives of noscapine and their application as organocatalysts in the asymmetric addition of diethylzinc to aromatic aldehydes is reported. The first catalyst (2) was synthesized by the reduction of lactone ring of noscapine to form the corresponding diol, and the second one (3) was prepared by tert-butyl dimethyl silylation of the primary hydroxyl group of 2. Excellent yields and high ees up to 95% were obtained by using 3 as the catalyst. To the best of our knowledge, this is the first report on the application of lactone ring opened noscapinoid compounds as organocatalysts in asymmetric reactions.     

Engineering Biomimetic Microenvironment for Organoid

Organoid is an emerging frontier technology in the field of life science, in which pluripotent stem cells or tissue-derived differentiated/progenitor cells form 3D structures according to their multi-directional differentiation potential and self-assembly ability. Nowadays, although various types of organoids are widely investigated, their construction is still complicated in operation, uncertain in yield, and poor in reproducibility for the structure and function of native organs. Constructing a biomimetic microenvironment for stem cell proliferation and differentiation in vitro is recognized as a key to driving this field. This review reviews the recent development of engineered biomimetic microenvironments for organoids. First, the composition of the matrix for organoid culture is summarized. Then, strategies for engineering the microenvironment from biophysical, biochemical, and cellular perspectives are discussed in detail. Subsequently, the newly developed monitoring technologies are also reviewed. Finally, a brief conclusion and outlook are presented for the inspiration of future research.     

Two single‐enantiomer amidophosphoesters: a database study on the chirality of (O)2P(O)(N)‐based structures

The crystal structures of two single‐enantiomer amidophosphoesters with an (O)₂P(O)(N) skeleton, i.e. diphenyl [(R)‐(+)‐α‐methylbenzylamido]phosphate, (I), and diphenyl [(S)‐(?)‐α‐methylbenzylamido]phosphate, (II), both C₂₀H₂₀NO₃P, are reported. In both structures, chiral one‐dimensional hydrogen‐bonded architectures, along [010], are mediated by N—H…OP interactions. The statistically identical assemblies include the noncentrosymmetric graph‐set motif C(4) and the compounds crystallize in the chiral space group P2₁. As a result of synergistic co‐operation from C—H…O interactions, a two‐dimensional superstructure is built including a noncentrosymmetric R₄⁴(22) hydrogen‐bonded motif. A Cambridge Structural Database survey was performed on (O)₂P(O)(N)‐based structures in order to review the frequency of space groups observed in this family of compounds; the hydrogen‐bond motifs in structures with chiral space groups and the types of groups inducing chirality are discussed. The ^2,3J_X–P (X = H or C) coupling constants from the NMR spectra of (I) and (II) have been studied. In each compound, the two diastereotopic C₆H₅O groups are different, which is reflected in the different chemical shifts and some coupling constants.     

The role of Pb ions doping in the mechanism of chromate adsorption by goethite

Pure and 0.384% Pb²⁺ ions doped goethite samples were prepared in the laboratory by the coprecipitation method. The laboratory-prepared goethite samples were characterized for pH of point of zero charge (pH_pzc), surface area, XRD, TG-DTA, TEM, SEM and FTIR analysis, which suggest that the Pb²⁺ ions are incorporated into the crystals of goethite and are also present on the surface in the hydroxylated form. Chromate adsorption studies were carried out in the concentration range 0.25-2.01 mmol L⁻¹ at pH 3, 5 and 7, which show that maximum chromate is adsorbed at the lowest pH of 3 by both the samples of goethite. Effect of temperature on the adsorption of chromate, in the range 303-323 K, shows that the process of adsorption is endothermic in case of pure goethite and exothermic in case of Pb-doped goethite. The values of isosteric heat of adsorption were positive for pure goethite and negative for Pb-doped goethite, which are consistent with the effect of temperature on the process of adsorption. Langmuir isotherm was found applicable to the experimental data. FTIR analysis and equilibrium pH changes reveal that at pH 3 outersphere while at pH 5 and 7 innersphere complexation is the dominant mechanism for chromate adsorption by both the samples of goethite.     

Full-Field Thermoelastic Stress Analysis of a Finite Structure Containing an Irregularly-Shaped Hole

An assessment of the structural integrity of members containing irregularly-shaped cutouts necessitates knowing the associated stresses. Stress analysis of such structures can be challenging as theoretical solutions are seldom available for finite geometries having non-simple shaped discontinuities and, like numerical methods, they require accurate knowledge of external loads. The latter are often unavailable in practice. This paper describes the ability to process load induced temperature information with an Airy stress function in real polar coordinates to determine the stresses in an isotropic linear elastic finite tensile plate containing an irregularly-shaped hole. Using polar coordinates is significant in that while a relatively simple general solution to the governing biharmonic equation is available in polar coordinates, this is seemingly not so with orthogonal curvilinear coordinates. Compared with displacement-based experimental or finite element techniques, important advantages of the present technique include not having to differentiate recorded data, or know constitutive properties or external loads.     

Hydrangenone, a new isoprenoid with an unprecedented skeleton from Salvia hydrangea

Hydrangenone, a new heptacyclic isoprenoid with a 6/7/6/5/5 membered carbon ring skeleton, was isolated from the aerial parts of Salvia hydrangea. The structure was established by extensive NMR spectroscopic methods. The relative and absolute configuration of 1 was assigned by NOESY and X-ray crystallographic analysis and by comparison of experimental and calculated electronic circular dichroism (ECD) spectra. Compound 1 showed in vitro antiplasmodial activity, with an IC(50) value of 1.4 μM against P. falciparum. A plausible biosynthetic pathway of 1 was also proposed.     

Gelatin methacrylate as a promising hydrogel for 3D microscale organization and proliferation of dielectrophoretically patterned cells

Establishing the 3D microscale organization of cells has numerous practical applications, such as in determining cell fate (e.g., proliferation, migration, differentiation, and apoptosis) and in making functional tissue constructs. One approach to spatially pattern cells is by dielectrophoresis (DEP). DEP has characteristics that are important for cell manipulation, such as high accuracy, speed, scalability, and the ability to handle both adherent and non-adherent cells. However, widespread application of this method is largely restricted because there is a limited number of suitable hydrogels for cell encapsulation. To date, polyethylene glycol-diacrylate (PEG-DA) and agarose have been used extensively for dielectric patterning of cells. In this study, we propose gelatin methacrylate (GelMA) as a promising hydrogel for use in cell dielectropatterning because of its biocompatibility and low viscosity. Compared to PEG hydrogels, GelMA hydrogels showed superior performance when making cell patterns for myoblast (C2C12) and endothelial (HUVEC) cells as well as in maintaining cell viability and growth. We also developed a simple and robust protocol for co-culture of these cells. Combined application of the GelMA hydrogels and the DEP technique is suitable for creating highly complex microscale tissues with important applications in fundamental cell biology and regenerative medicine in a rapid, accurate, and scalable manner.