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LEGENDRIAN RACK INVARIANTS OF LEGENDRIAN KNOTS
Ceniceros, Jose,Elhamdadi, Mohamed,Nelson, Sam Korean Mathematical Society 2021 대한수학회논문집 Vol.36 No.3
We define a new algebraic structure called Legendrian racks or racks with Legendrian structure, motivated by the front-projection Reidemeister moves for Legendrian knots. We provide examples of Legendrian racks and use these algebraic structures to define invariants of Legendrian knots with explicit computational examples. We classify Legendrian structures on racks with 3 and 4 elements. We use Legendrian racks to distinguish certain Legendrian knots which are equivalent as smooth knots.
Jose Ceniceros,Mohamed Elhamdadi,Josef Komissar,Hitakshi Lahrani 대한수학회 2024 대한수학회논문집 Vol.39 No.1
We study RNA foldings and investigate their topology using a combination of knot theory and embedded rigid vertex graphs. Knot theory has been helpful in modeling biomolecules, but classical knots emphasize a biomolecule's entanglement while ignoring their intrachain interactions. We remedy this by using stuck knots and links, which provide a way to emphasize both their entanglement and intrachain interactions. We first give a generating set of the oriented stuck Reidemeister moves for oriented stuck links. We then introduce an algebraic structure to axiomatize the oriented stuck Reidemeister moves. Using this algebraic structure, we define a coloring counting invariant of stuck links and provide explicit computations of the invariant. Lastly, we compute the counting invariant for arc diagrams of RNA foldings through the use of stuck link diagrams.
A New Formulated Stable Papin-pectin Aerosol Spray for Skin Wound Healing
Karla Monzerratt Gregorio Jáuregui,Juan Carlos Cano Cabrera,Elda Patricia Segura Ceniceros,Jose Luis Martínez Hernández,Anna Ilyina 한국생물공학회 2009 Biotechnology and Bioprocess Engineering Vol.14 No.4
A new spray-on topical wound debrider composition consisting of 0.1% w/v papain immobilized in 6% w/v pectin gel was formulated for skin wound healing. The stability of the enzyme activity of this new formulated spray was compared with the 0.1% w/v papain in water solution at the refrigerated temperature of 4 and 75°C. Two aerosol propellants, air and nitrogen, were evaluated for their efficacy. The new formulated spray was then evaluated for its thermal stability under air and N2 at 75°C. All enzyme activity of papain was measured with a spectrophotometer using casein as a substrate at 37°C and in 0.1 M phosphate buffer at pH 6, as well as trichloral acetic acid to separate the product of casein hydrolysis. All the evaluations showed the new aerosol spray formulation to be far better than the liquid formulation in storage stability and thermal stability at 75°C under atmospheric or higher pressures. The new formulation was tested in a rabbit experiment to evaluate the effectiveness of wound healing. As compared to untreated wound, the formulated spray clearly was superior, yielding a 20% more healing progress in the first 4 days alone.