Gelatin methacrylate (GelMA) is a photocrosslinkable biomaterial that has gained widespread use in tissue engineering due to its favorable biological attributes and customizable physical and mechanical traits. While GelMA is compatible with various cell types, distinct cellular responses are observed within GelMA hydrogels. As such, tailoring hydrogels for specific applications has become imperative. Thus, our objective was to develop GelMA hydrogels tailored to enhance cell viability specifically for TC28a2 chondrocytes in a three-dimensional (3D) cell culture setting. We investigated GelMA synthesis using PBS and 0.25M CB buffer, analyzed the mechanical and physical traits of GelMA hydrogels, and evaluated how varying GelMA crosslinking conditions (GelMA concentration, photoinitiator concentration, and UV exposure time) affected the viability of TC28a2 chondrocytes. The results revealed that GelMA synthesis using 0.25M CB buffer led to a greater degree of methacrylation compared to PBS buffer, and the LAP photoinitiator demonstrated superior efficacy for GelMA gelation compared to Irgacure 2959. Additionally, the stiffness, porosity, and swelling degree of GelMA hydrogels were predominantly affected by GelMA concentration, while cell viability was impacted by all crosslinking conditions, decreasing notably with increasing GelMA concentration, photoinitiator concentration, and UV exposure time. This study facilitated the optimization of crosslinking conditions to enhance cell viability within GelMA hydrogels, a critical aspect for diverse biomedical applications.

Hinge motion is observed in macrocyclic, mortise‐type molecular hinges using variable temperature NMR spectroscopy. The data is consistent with dynamic hinging from a folded‐to‐extended‐to‐folded enantiomeric state. Crystallographic and solution structures of the folded states are reported. Chemical shift predictions derived from crystallographic data corroborate fully revolute hinge motion. The rate of hinging is affected by steric congestion at the hinge axis. A macrocycle containing glycine, 1, hinges faster than one comprising aminoisobutyric acid, 2. The free energies of activation, ΔG^≠, for 1 and 2 were determined to be 13.3±0.3 kcal/mol and 16.3±0.3 kcal/mol, respectively. This barrier is largely independent of solvent across those surveyed (CD₃OD, CD₃CN, DMSO‐d₆, pyridine‐d₅, D₂O). Experiment and computation predict energy barriers that are consistent with disruption of an intramolecular network of hydrogen bonds. DFT calculations reveal a pathway for hinge motion.

While sharing a common, hinge-like motion, steric congestion created by isopropyl groups reduces the barrier to hinging by ∼1.5 kcal mol⁻¹ over macrocycles with less cumbersome substitutions.

The Earth–Moon system has undergone continuous evolution across all timescales since its formation. Earth's rotation is gradually slowing, the Moon's rotation is decelerating, and the Moon is slowly receding from Earth. These progressive changes affect key planetary parameters, including the length of day (LOD), the number of days per year (DOY), and the Earth–Moon distance (DOM). Building on the author's earlier work, this paper presents a set of mathematical equations to model these dynamics and predict LOD, DOY, and DOM over time. The results derived from this model show strong agreement with historical data, offering a robust framework for understanding the long-term evolution of the Earth–Moon system. To address the longstanding Lunar crisis—where conventional tidal friction models predict an unrealistically close Earth–Moon proximity in the distant past and many assumptions and parameters must be introduced to help reconcile the models with observations—this study proposes a novel hypothesis: a significantly lower volume of surface liquid water in Earth's early history may have reduced tidal dissipation. The subsequent increase in oceanic volume could be attributed to the capture of a large icy comet, a scenario supported by precedent such as the 1994 collision of Comet Shoemaker–Levy 9 with Jupiter. This mechanism offers a plausible resolution to the tidal friction discrepancy and deepens our understanding of planetary evolution.

The Density Wave Theory, which aims to explain the formation of spiral arms in disc galaxies, has been subject to discussion. According to this theory, at the co-rotation circle, the rotational velocity of the density waves or spiral arms matches that of the galactic matter. Consequently, this alignment should impede the formation of new stars within this co-rotation circle, leading to the presence of dark or dim gaps within the spiral arms. Additionally, the theory predicts the occurrence of the front side trail effect in the inner region of the co-rotation circle and the rear side trail effect in the outer region. However, despite these expectations, no such spiral patterns have been observed, prompting the need for revision or reconsideration of the Density Wave Theory.

This short paper demonstrates that the galactic spiral equations developed from ROTASE model can be used to morphologically simulate the phyllotactic spiral-ring patterns of plants. It is also noticed during this project that although the numbers in the Fibonacci sequence dominate the phyllotactic numbers, there are still significant phyllotactic numbers are not in the Fibonacci sequence, however, most of those numbers are well fit into a Fibonacci sibling sequence starting with numbers 0 and 2. Many plants show the phyllotactic number pairs of 10-16, 16-26 and 26-42 from the Fibonacci sibling sequence, which is the second dominated sequence in the phyllotaxis.