On generalized square-full numbers in an arithmetic progression

Czechoslovak Mathematical Journal - Let a and $$b \in \mathbb{N}$$ . Denote by Ra,b the set of all integers n > 1 whose canonical prime representation $$n = p_1^{{\alpha _1}}p_2^{{\alpha...     

Unique Continuation for Fractional Schrödinger Equations with Rough Potentials

This article deals with the weak and strong unique continuation principle for fractional Schrödinger equations with scaling-critical and rough potentials via Carleman estimates. Our methods extend to “variable coefficient” versions of fractional Schrödinger equations and operators on non-flat domains.     

Influence of Degree of Polymerization of Low-Molecular-Weight Chitosan Oligosaccharides on the α-Glucosidase Inhibition

Chitosan oligosaccharide (COS) is a bioactive compound derived from marine by-products. COS consumption has been demonstrated to lower the risk of diabetes. However, there are limited data on the inhibitory effect of low-molecular-weight COSs with different degrees of polymerization (DP) on α-glucosidase. This study investigates the α-glucosidase inhibitory activity of two low-molecular-weight COSs, i.e., S-TU-COS with DP2–4 and L-TU-COS with DP2–5, both of which have different molecular weight distributions. The inhibition constants of the inhibitors binding to free enzymes (K_i) and an enzyme–substrate complex (K_ii) were investigated to elucidate the inhibitory mechanism of COSs with different chain lengths. The kinetic inhibition model of S-TU-COS showed non-completive inhibition results which are close to the uncompetitive inhibition results with K_i and K_ii values of 3.34 mM and 2.94 mM, respectively. In contrast, L-TU-COS showed uncompetitive inhibition with a K_ii value of 5.84 mM. With this behavior, the IC₅₀ values of S-TU-COS and L-TU-COS decreased from 12.54 to 11.84 mM and 20.42 to 17.75 mM, respectively, with an increasing substrate concentration from 0.075 to 0.3 mM. This suggests that S-TU-COS is a more potent inhibitor, and the different DP of COS may cause significantly different inhibition (p < 0.05) on the α-glucosidase activity. This research may provide new insights into the production of a COS with a suitable profile for antidiabetic activity.     

A Shear-Thinning,Self-Healing,Dual-Cross Linked Hydrogel Based on Gelatin/Vanillin/Fe3+/AGP-AgNPs: Synthesis,Antibacterial, and Wound-Healing Assessment

A shear-thinning and self-healing hydrogel based on a gelatin biopolymer is synthesized using vanillin and Fe³⁺ as dual crosslinking agents. Rheological studies indicate the formation of a strong gel found to be injectable and exhibit rapid self-healing (within 10 min). The hydrogels also exhibited a high degree of swelling, suggesting potential as wound dressings since the absorption of large amounts of wound exudate, and optimum moisture levels, lead to accelerated wound healing. Andrographolide, an anti-inflammatory natural product is used to fabricate silver nanoparticles, which are characterized and composited with the fabricated hydrogels to imbue them with anti-microbial activity. The nanoparticle/hydrogel composites exhibit activity against Escherichia coli, Staphylococcus aureus, and Burkholderia pseudomallei, the pathogen that causes melioidosis, a serious but neglected disease affecting southeast Asia and northern Australia. Finally, the nanoparticle/hydrogel composites are shown to enhance wound closure in animal models compared to the hydrogel alone, confirming that these hydrogel composites hold great potential in the biomedical field.     

A Rigidity Result for a Reduced Model of a Cubic-to-Orthorhombic Phase Transition in the Geometrically Linear Theory of Elasticity

In this article we study a simplified two-dimensional model for a cubic-to-orthorhombic phase transition occurring in certain shape-memory-alloys. In the low temperature regime the linear theory of elasticity predicts various possible patterns of martensite arrangements: Apart from the well known laminates this phase transition displays additional structures involving four martensitic variants—so called crossing twins.Introducing a variational model including surface energy, we show that these structures are rigid under small energy perturbations. Combined with an upper bound construction this gives the optimal scaling behavior of incompatible microstructures. These results are related to papers by Capella and Otto (Commun. Pure Appl. Math. 62(12):1632–1669, 2009; Proc. R. Soc. Edinb., Sect. A, Math. 142:273–327, 2012) as well as to a paper by Dolzmann and Müller (Meccanica 30:527–539, 1995).     

The Cubic-to-Orthorhombic Phase Transition: Rigidity and Non-Rigidity Properties in the Linear Theory of Elasticity

In this paper we investigate the cubic-to-orthorhombic phase transition in the framework of linear elasticity. Using convex integration techniques, we prove that this phase transition represents one of the simplest three-dimensional examples in which already the linearised theory of elasticity displays non-rigidity properties. As a complementary result, we demonstrate that surface energy constraints rule out such highly oscillatory behaviour. We give a full characterization of all possibly emerging patterns for generic material parameters.     

Eight Indole Alkaloids from the Roots of Maerua siamensis and Their Nitric Oxide Inhibitory Effects

Maerua siamensis (Capparaceae) roots are used for treating pain and inflammation in traditional Thai medicine. Eight new indole alkaloids, named maeruanitriles A and B, maeroximes A–C, and maeruabisindoles A–C, were isolated from them. Spectroscopic methods and computational analysis were applied to determine the structure of the isolated compounds. Maeroximes A–C possesses an unusual O-methyloxime moiety. The bisindole alkaloid maeruabisindoles A and B possess a rare azete ring, whereas maeruabisindole C is the first indolo[3,2-b]carbazole derivative found in this plant family. Five compounds [maeruanitriles A and B, maeroxime C, maeruabisindoles B, and C] displayed anti-inflammatory activity by inhibiting nitric oxide (NO) production in the lipopolysaccharide-induced RAW 264.7 cells. Maeruabisindole B was the most active inhibitor of NO production, with an IC₅₀ of 31.1 ± 1.8 μM compared to indomethacin (IC₅₀ = 150.0 ± 16.0 μM) as the positive control.     

Convex Integration Arising in the Modelling of Shape-Memory Alloys: Some Remarks on Rigidity,Flexibility and Some Numerical Implementations

Journal of Nonlinear Science - We study convex integration solutions in the context of the modelling of shape-memory alloys. The purpose of the article is twofold, treating both rigidity and...