Search results for: Changhong Lu

Authors: Bin Sheng, Changhong Lu

Abstract:

Let G be a simple undirected graph with no isolated vertex. A paired dominating set of G is a dominating set which induces a subgraph that has a perfect matching. The paired domination number of G, denoted by γₚᵣ(G), is the size of its smallest paired dominating set. Goddard and Henning conjectured that γₚᵣ(G) ≤ 4n/7 holds for every graph G with δ(G) ≥ 3, except the Petersen Graph. In this paper, we prove this conjecture for cubic graphs.

Keywords: paired dominating set, upper bound, cubic graphs, weight function

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Authors: Changhong Guo, Shaomei Fang, Yong He

Abstract:

In this paper, fractional Black-Scholes models for the European option pricing were established based on the fractional G-Brownian motion (fGBm), which generalizes the concepts of the classical Brownian motion, fractional Brownian motion and the G-Brownian motion, and that can be used to be a tool for considering the long range dependence and uncertain volatility for the financial markets simultaneously. A generalized fractional Black-Scholes equation (FBSE) was derived by using the Taylor’s series of fractional order and the theory of absence of arbitrage. Finally, some explicit option pricing formulas for the European call option and put option under the FBSE were also solved, which extended the classical option pricing formulas given by F. Black and M. Scholes.

Keywords: European option pricing, fractional Black-Scholes equations, fractional g-Brownian motion, Taylor's series of fractional order, uncertain volatility

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Authors: Shifu Hu, Qiong Yu, Wei Xia, Changhong Zhu

Abstract:

Background: P38α MAPK, which is a member of the canonical MAPK family, is activated in response to various extracellular stresses and plays a role in multiple cellular processes. It is well known that p38α MAPK play vital roles in oocyte maturation, but the localization and functional roles of p38α MAPK during the meiotic maturation of rat oocytes remain unknown. Study Design: In this study, western-blot and immunofluorescent staining were used to investigate the expression and subcellular localization of p38α MAPK during the meiotic maturation of rat oocytes. SB203580, a specific inhibitor of p38α MAPK, was used to study the roles of p38α MAPK in the meiotic cell cycle of rat oocytes. Results: The results found that p38α MAPK phosphorylation (p-p38α MAPK, indicative of p38α MAPK activation) was low at the germinal vesicle (GV) stage, increased 3 h after germinal vesicle breakdown (GVBD), and maintained its maximum at MI (metaphase I) or M II (metaphase II). The p-p38α MAPK mainly accumulated in the germinal vesicle and had no obvious expression in the nucleus. From GVBD to M II, p-p38α MAPK was distributed in the cytoplasm around either the chromosomes or the spindle. We used SB203580, an inhibitor of p38α MAPK, to investigate the possible functional role of p38α MAPK during rat oocyte meiotic maturation. Treatment of GV stage oocytes with 20 μM SB203580 blocked p-p38α MAPK activity, and the spindles appeared abnormal. Additionally, the rate of GVBD after 3h of culture with 20 μM SB203580 (58.8%) was significantly inhibited compared with the control (82.5%, p < 0.05), and the polar body extrusion rate after 12 h of culture with SB203580 was also significantly decreased compared with the control (40.1 vs. 73.3%, p < 0.05). Conclusions: These data indicate that p38α MAPK may play a vital role in rat oocyte meiotic maturation.

Keywords: meiotic maturation, oocyte, p38α MAPK, spindle

Procedia PDF Downloads 159