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This study addresses the standardization of Singular Distributed Parameter Systems (SDPSs). It focuses on classifying and simplifying first- and second-order linear SDPSs using characteristic matrix theory. First, the study classifies first-order linear SDPSs into three canonical forms based on characteristic curve theory, with an example illustrating the standardization process for parabolic SDPSs. Second, under regular conditions, first-order SDPSs can be decomposed into fast and slow subsystems, where the fast subsystem reduces to an Ordinary Differential Equation (ODE) system, while the slow subsystem retains the spatiotemporal characteristics of the original system. Third, the standardization and classification of second-order SDPSs is proposed using three reversible transformations that achieve structural equivalence. Finally, an illustrative example of a building temperature control is built with SDPSs. The simulation results show the importance of system standardization in real-world applications. This research provides a theoretical foundation for SDPS standardization and offers insights into the practical implementation of distributed temperature systems.

Ginsenoside Rg1 is an important active substance isolated from the root of ginseng. In previous studies, Rg1 has shown excellent therapeutic effects in antioxidant, anti-inflammatory, and metabolic modulation. However, the therapeutic targets of Rg1 are still unknown. In this study, we investigated the therapeutic effects of Rg1 on oxidative stress-related liver damage. The oxidative stress damage model was achieved by intraperitoneal injection of D-galactose (D-gal) for 42 consecutive days in C57BL/6J mice. Rg1 treatment started on Day 16. Body weight, liver weight, degree of hepatic oxidative stress damage, serum lipid levels, and hepatic lipid and glucose metabolism were measured. Proteomics analysis was used to measure liver protein expression. The differential expression proteins were analyzed with bioinformatics. The results showed that Rg1 treatment attenuated liver damage from oxidative stress, reduced hepatic fat accumulation, promoted hepatic glycogen synthesis, and attenuated peripheral blood low-density lipoprotein (LDL), cholesterol (CHO), and triglycerides (TG) levels. Proteomic analysis suggested that Rg1 may regulate hepatocyte metabolism through ECM–Receptor, the PI3K-AKT pathway. The epidermal growth factor receptor (EGFR) and activator of transcription 1 (STAT1) may be the key protein. In conclusion, this study provides an experimental basis for further clarifying the specific mechanism of Rg1 in the treatment of oxidative stress damage-related liver disease.

Background. An important feature of aging cells is the gradual loss of physiological integrity. As aging progresses, MSCs change preferring to differentiate toward adipocytes rather than osteoblasts. Oxidative stress accumulation is an important factor in age-related bone loss. Many experiments have demonstrated the good therapeutic effect of Ginsenoside (Rg1) on oxidative stress injury. In this study, we investigated the effect of Rg1 on the osteogenic-adipogenic differentiation balance of bone marrow mesenchymal stem cells (BMMSC). Objective. To analyze the potential application value of Rg1 in the treatment of senile osteoporosis. Methods. BMMSCs were isolated from healthy donors of different ages and identified based on isotype and by multi-differentiation induction. Rg1 was used to treat BMMSCs, The differentiation propensity was analyzed by induction of differentiation assay. Antioxidant capacity of BMMSCs as measured by oxidative stress product assay Related mechanism studies were confirmed by quantitative real-time reverse transcription-polymerase chain reaction (qRT‐PCR), immunofluorescence, western blotting, and inhibitor treatment. Moreover, Observation of the effects of Rg1 on aging BMMSCs under in vivo conditions by treatment of aged mice with Rg1 injections. Results. Rg1 treatment rescued age‐induced switch of BMMSCs differentiation fate in vitro. In elderly people, Rg1 markedly increased osteogenic differentiation of BMMSCs by decreasing oxidative stress, while inhibiting adipogenic differentiation. However, this effect was abolished in BMMSCs by an Nrf2-inhibitor. Notably, aging mice showed a reduction in adipocyte distribution in the bone marrow and a decrease in oxidative stress products after a 3-month period of Rg1 treatment. Conclusion. We have uncovered a novel function for Rg1 that involves attenuating bone loss via Nrf2 antioxidant signaling, which in turn may potentially be utilized as a therapeutic agent for improving osteogenic differentiation in aging BMMSCs.