Quantum mechanical modeling of Zn-based spinel oxides: Assessing the structural,vibrational, and electronic properties

The structural, electronic, and vibrational properties of two leading representatives of the Zn-based spinel oxides class, normal ZnX₂O₄ (X = Al, Ga, In) and inverse Zn₂MO₄ (M = Si, Ge, Sn) crystals, were investigated. In particular, density functional theory (DFT) was combined with different exchange-correlation functionals: B3LYP, HSE06, PBE0, and PBESol. Our calculations showed good agreement with the available experimental data, showing a mean percentage error close to 3% for structural parameters. For the electronic structure, the obtained HSE06 band-gap values overcome previous theoretical results, exhibiting a mean percentage error smaller than 10.0%. In particular, the vibrational properties identify the significant differences between normal and inverse spinel configurations, offering compelling evidence of a structure-property relationship for the investigated materials. Therefore, the combined results confirm that the range-separated HSE06 hybrid functional performs the best in spinel oxides. Despite some points that cannot be directly compared to experimental results, we expect that future experimental work can confirm our predictions, thus opening a new avenue for understanding the structural, electronic, and vibrational properties in spinel oxides.     

Cleft extensions of a family of braided Hopf algebras

We introduce a family of braided Hopf algebras that (in characteristic zero) generalizes the rank 1 Hopf algebras introduced by Krop and Radford and we study its cleft extensions.     

Beijing Lectures on the Grade Restriction Rule

The authors describe the relationships between categories of B-branes in different phases of the non-Abelian gauged linear sigma model.The relationship is described explicitly for the model proposed by Hori and Tong with non-Abelian gauge group that connects two non-birational Calabi-Yau varieties studied by Rφdland.A grade restriction rule for this model is derived using the hemisphere partition function and it is used to map B-type D-branes between the two Calabi-Yau varieties.     

Cluster Partition Function and Invariants of 3-Manifolds

The author reviews some recent developments in Chern-Simons theory on a hyperbolic 3-manifold M with complex gauge group G.The author focuses on the case of G =SL(N,C) and M being a knot complement:M =S3 \ k.The main result presented in this note is the cluster partition function,a computational tool that uses cluster algebra techniques to evaluate the Chern-Simons path integral for G =SL(N,C).He also reviews various applications and open questions regarding the cluster partition function and some of its relation with string theory.     

A Lower Bound for the Determinantal Complexity of a Hypersurface

We prove that the determinantal complexity of a hypersurface of degree \(d > 2\) is bounded below by one more than the codimension of the singular locus, provided that this codimension is at least 5. As a result, we obtain that the determinantal complexity of the \(3 \times 3\) permanent is 7. We also prove that for \(n> 3\), there is no nonsingular hypersurface in \({\mathbb {P}}^n\) of degree d that has an expression as a determinant of a \(d \times d\) matrix of linear forms, while on the other hand for \(n \le 3\), a general determinantal expression is nonsingular. Finally, we answer a question of Ressayre by showing that the determinantal complexity of the unique (singular) cubic surface containing a single line is 5.     

Lipid-Based Nanostructures for the Delivery of Natural Antimicrobials

Encapsulation can be a suitable strategy to protect natural antimicrobial substances against some harsh conditions of processing and storage and to provide efficient formulations for antimicrobial delivery. Lipid-based nanostructures, including liposomes, solid lipid nanoparticles (SLNs), and nanostructured lipid nanocarriers (NLCs), are valuable systems for the delivery and controlled release of natural antimicrobial substances. These nanostructures have been used as carriers for bacteriocins and other antimicrobial peptides, antimicrobial enzymes, essential oils, and antimicrobial phytochemicals. Most studies are conducted with liposomes, although the potential of SLNs and NLCs as antimicrobial nanocarriers is not yet fully established. Some studies reveal that lipid-based formulations can be used for co-encapsulation of natural antimicrobials, improving their potential to control microbial pathogens.     

Synthesis of New Brassinosteroid 24-Norcholane Type Analogs Conjugated in C-3 with Benzoate Groups

The metabolism of brassinosteroid leads to structural modifications in the ring skeleton or the side alkyl chain. The esterification and glycosylation at C-3 are the most common metabolic pathways, and it has been suggested that conjugate brassinosteroids are less active or inactive. In this way, plants regulate the content of active brassinosteroids. In this work, the synthesis of brassinosteroid 24-norcholane type analogs conjugated at C-3 with benzoate groups, carrying electron donor and electron attractant substituents on the aromatic ring, is described. Additionally, their growth-promoting activities were evaluated using the Rice Lamina Inclination Test (RLIT) and compared with that exhibited by brassinolide (used as positive control) and non-conjugated analogs. The results indicate that at the lowest tested concentrations (10⁻⁸–10⁻⁷ M), all analogs conjugated at C-3 exhibit similar or higher activities than brassinolide, and the diasteroisomers with S configuration at C-22 are the more active ones. Increasing concentration (10⁻⁶ M) reduces the biological activities of analogs as compared to brassinolide.     

Growth and Atomic-Scale Characterization of Ultrathin Silica and Germania Films: The Crucial Role of the Metal Support

The present review reports on the preparation and atomic-scale characterization of the thinnest possible films of the glass-forming materials silica and germania. To this end state-of-the-art surface science techniques, in particular scanning probe microscopy, and density functional theory calculations have been employed. The investigated films range from monolayer to bilayer coverage where both, the crystalline and the amorphous films, contain characteristic XO₄ (X=Si,Ge) building blocks. A side-by-side comparison of silica and germania monolayer, zigzag phase and bilayer films supported on Mo(112), Ru(0001), Pt(111), and Au(111) leads to a more general comprehension of the network structure of glass former materials. This allows us to understand the crucial role of the metal support for the pathway from crystalline to amorphous ultrathin film growth.