Mathematical Sciences
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Mathematical research at MSU is focused primarily on related topics in pure and applied mathematics. Research programs complement each other and are often applied to problems in science and engineering. Research in statistics encompasses a broad range of theoretical and applied topics. Because the statisticians are actively engaged in interdisciplinary work, much of the statistical research is directed toward practical problems. Mathematics education faculty are active in both qualitative and quantitative experimental research areas. These include teacher preparation, coaching and mentoring for in-service teachers, online learning and curriculum development.
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Item Physical and chemical mechanisms that influence the electrical conductivity of lignin-derived biochar(2021-10) Kane, Seth; Ulrich, Rachel; Harrington, Abigail; Stadie, Nicholas P.; Ryan, Cecily A.Lignin-derived biochar is a promising, sustainable alternative to petroleum-based carbon powders (e.g., carbon black) for polymer composite and energy storage applications. Prior studies of these biochars demonstrate that high electrical conductivity and good capacitive behavior are achievable. However, these studies also show high variability in electrical conductivity between biochars (– S/cm). The underlying mechanisms that lead to desirable electrical properties in these lignin-derived biochars are poorly understood. In this work, we examine the causes of the variation in conductivity of lignin-derived biochar to optimize the electrical conductivity of lignin-derived biochars. To this end, we produced biochar from three different lignins, a whole biomass source (wheat stem), and cellulose at two pyrolysis temperatures (900 °C, 1100 °C). These biochars have a similar range of conductivities (0.002 to 18.51 S/cm) to what has been reported in the literature. Results from examining the relationship between chemical and physical biochar properties and electrical conductivity indicate that decreases in oxygen content and changes in particle size are associated with increases in electrical conductivity. Importantly, high variation in electrical conductivity is seen between biochars produced from lignins isolated with similar processes, demonstrating the importance of the lignin’s properties on biochar electrical conductivity. These findings indicate how lignin composition and processing may be further selected and optimized to target specific applications of lignin-derived biochars.Item Interlaboratory study for the evaluation of three microtiter plate-based biofilm quantification methods(2021-07) Allkja, Jontana; van Charante, Frits; Aizawa, Juliana; Reigada, Ines; Guarch-Perez, Clara; Vazquez-Rodriguez, Jesus Augusto; Cos, Paul; Coenye, Tom; Fallarero, Adyary; Zaat, Sebastian A. J.; Felici, Antonio; Ferrari, Livia; Azevado, Nuno F.; Parker, Albert E.; Goeres, Darla M.Microtiter plate methods are commonly used for biofilm assessment. However, results obtained with these methods have often been difficult to reproduce. Hence, it is important to obtain a better understanding of the repeatability and reproducibility of these methods. An interlaboratory study was performed in five different laboratories to evaluate the reproducibility and responsiveness of three methods to quantify Staphylococcus aureus biofilm formation in 96-well microtiter plates: crystal violet, resazurin, and plate counts. An inter-lab protocol was developed for the study. The protocol was separated into three steps: biofilm growth, biofilm challenge, biofilm assessment. For control experiments participants performed the growth and assessment steps only. For treatment experiments, all three steps were performed and the efficacy of sodium hypochlorite (NaOCl) in killing S. aureus biofilms was evaluated. In control experiments, on the log10-scale, the reproducibility SD (SR) was 0.44 for crystal violet, 0.53 for resazurin, and 0.92 for the plate counts. In the treatment experiments, plate counts had the best responsiveness to different levels of efficacy and also the best reproducibility with respect to responsiveness (Slope/SR = 1.02), making it the more reliable method to use in an antimicrobial efficacy test. This study showed that the microtiter plate is a versatile and easy-to-use biofilm reactor, which exhibits good repeatability and reproducibility for different types of assessment methods, as long as a suitable experimental design and statistical analysis is applied.Item Investigation of the role of infusate properties related to midline catheter failure in an ovine model(2020-08) Ryder, Marcia; Gunther, Robert A.; Nishikawa, Reid A.; Stranz, Marc; Meyer, Britt M.; Spangler, Taylor A.; Parker, Albert E.; Sylvia, CharlesPurpose Infusate osmolarity, pH, and cytotoxicity were investigated as risk factors for midline catheter failure. Methods An experimental, randomized, controlled, blinded trial was conducted using an ovine model. Two 10-cm, 18-gauge single-lumen midline catheters were inserted into the cephalic veins of sheep. The animals were divided into 6 study arms and were administered solutions of vancomycin 4 mg/mL (a low-cytotoxicity infusate) or 10 mg/mL (a high-cytotoxicity infusate), doxycycline 1 mg/mL (an acidic infusate), or acyclovir 3.5 mg/mL (an alkaline infusate) and 0.9% sodium chloride injection; or 1 of 2 premixed Clinimix (amino acids in dextrose; Baxter International) products with respective osmolarities of 675 mOsm/L (a low-osmolarity infusate) and 930 mOsm/L (a mid-osmolarity infusate). Contralateral legs were infused with 0.9% sodium chloride injection for control purposes. Catheter failure was evaluated by assessment of adverse clinical symptoms (swelling, pain, leakage, and occlusion). A quantitative vessel injury score (VIS) was calculated by grading 4 histopathological features: inflammation, mural thrombus, necrosis, and perivascular reaction. Results Among 20 sheep included in the study, the overall catheter failure rate was 95% for test catheters (median time to failure, 7.5 days; range, 3–14 days), while 60% of the control catheters failed before or concurrently (median time to failure, 7 days; range, 4.5–14 days). Four of the 6 study arms (all but the Clinimix 675-mOsm/L and acyclovir 3.5-mg/mL arms) demonstrated an increase in mean VIS of ≥77% in test vs control legs (P ≤ 0.034). Both pain and swelling occurred at higher rates in test vs control legs: 65% vs 10% and 70% vs 50%, respectively. The mean difference in rates of occlusive pericatheter mural thrombus between the test and control arms was statistically significant for the vancomycin 10-mg/mL (P = 0.0476), Clinimix 930-mOsm/L (P = 0.0406), and doxycycline 1-mg/mL (P = 0.032) arms. Conclusion Administration of infusates of varied pH, osmolarity, and cytotoxicity via midline catheter resulted in severe vascular injury and premature catheter failure; therefore, the tested infusates should not be infused via midline catheters.