Hydroxylated Fatty Acids: The Role of the Sphingomyelin Synthase and the Origin of Selectivity

Sphingolipids are a class of lipids acting as key modulators of many physiological and pathophysiological processes. Hydroxylation patterns have a major influence on the biophysical properties of sphingolipids. In this work, we have studied the mechanism of action of hydroxylated lipids in sphingomyelin synthase (SMS). The structures of the two human isoforms, SMS1 and SMS2, have been generated through neural network supported homology. Furthermore, we have elucidated the reaction mechanism that allows SMS to recover the choline head from a phosphocholine (PC) and transfer it to ceramide, and we have clarified the role of the hydroxyl group in the interaction with the enzyme. Finally, the effect of partial inhibition of SMS on the levels of PC and sphingomyelin was calculated for different rate constants solving ordinary differential equation systems.

Existence of Solitary Waves in a Perturbed KdV-mKdV Equation

In this paper, we establish the existence of a solitary wave in a KdV-mKdV equation with dissipative perturbation by applying the geometric singular perturbation technique and Melnikov function. The distance of the stable manifold and unstable manifold is computed to show the existence of the homoclinic loop for the related ordinary differential equation systems on the slow manifold, which implies the existence of a solitary wave for the KdV-mKdV equation with dissipative perturbation.

Pemodelan Matematika SEIR Penyebaran Penyakit Pneumonia pada Balita dengan Pengaruh Vaksinasi di Kota Makassar

Abstrak. Penelitian ini bertujuan untuk membangun model penyebaran penyakit pneumonia pada balita tipe SEIR (Susceptible- Exposed- Infected- Recovered-), menganalisis model, dan menentukan proporsi minimum vaksinasi. Data yang digunakan adalah data jumlah penderita pneumonia pada balita di Kota Makassar tahun 2019. Hasil penelitian diperoleh model matematika SEIR penyakit pneumonia dalam bentuk sistem persamaan diferensial biasa; titik keseimbangan bebas kecanduan dan titik keseimbangan kecanduan yang keduanya bersifat stabil; bilangan reproduksi dasar untuk simulasi tanpa vaksinasi lebih besar dari 1 yang artinya penyakit masih tetap ada dalam populasi, sedangkan bilangan reproduksi dasar untuk simulasi dengan vasksinasi kurang dari 1 yang artinya penyakit akan menghilang dan tidak meluas dari populasi.Kata Kunci: Titik Ekuilibrium, Bilangan Reproduksi Dasar, Pneumonia, Model SEIR.Abstract.This study aims to build a model of the spread of pneumonia in SEIR (Susceptible-Exposed-Infected-Recovered) toddlers, analyze the model, and determine the minimum proportion of vaccinations. The data used are data on the number of pneumonia sufferers in toddlers in Makassar City in 2019.The results obtained by the SEIR mathematical model of pneumonia in the form of ordinary differential equation systems; addiction free balance points and addiction balance points which are both stable; basic reproduction numbers for simulations without vaccination greater than 1, which means that the disease still exists in the population, while basic reproduction numbers for simulations with vasksination less than 1, which means the disease will disappear and not spread from the population.Keywords: Equilibrium Points, Basic Reproductive Numbers, Pneumonia, SEIR Model.

Global, Non-Parametric, Non-Iterative Optimization of Time-Averaged Quantities under Small, Time-Varying Forcing: An Application to a Thermal Convection Field

This study demonstrates a global, non-parametric, non-iterative optimization of time-mean value of a kind of index vibrated by time-varying forcing. It is based on the fact that the (steady) forced vibration of non-autonomous ordinary differential equation systems is well approximated by an analytical solution when the amplitude of forcing is sufficiently small and its base state without forcing is linearly stable and steady. It is applied to optimize a time-averaged heat-transfer rate on a two-dimensional thermal convection field in a square cavity with horizontal temperature difference, and the globally optimal way of vibrational forcing, i.e. the globally optimal, spatial distribution of vibrational heat and vorticity sources, is first obtained. The maximized vibrational thermal convection corresponds well to the state of internal gravity wave resonance. In contrast, the minimized thermal convection is weak, keeping the boundary layers on both sidewalls thick.

Global, Non-Parametric, Non-Iterative Optimization of Time-Averaged Quantities under Small, Time-Varying Forcing: An Application to a Thermal Convection Field

This study demonstrates a global, non-parametric, non-iterative optimization of time-mean value of a kind of index vibrated by time-varying forcing. It is based on the fact that the (steady) forced vibration of non-autonomous ordinary differential equation systems is well approximated by an analytical solution when the amplitude of forcing is sufficiently small and its base state without forcing is stable and steady. It is applied to optimize a time-averaged heat-transfer rate on a two-dimensional thermal convection field in a square cavity with horizontal temperature difference, and the globally optimal way of vibrational forcing, i.e. the globally optimal, spatial distribution of vibrational heat and vorticity sources, is first obtained. The maximized vibrational thermal convection corresponds well to the state of internal gravity wave resonance. In contrast, the minimized thermal convection is weak, keeping the boundary layers on both sidewalls thick.