Let G be a graph of order n, and let a and b be integers, such that 1 ≤ a b. Let H be a subgraph of G with m(≤b) edges, and δ(G) be the minimum degree. We prove that G has a [a,b]-factor containing all edges of H i...Let G be a graph of order n, and let a and b be integers, such that 1 ≤ a b. Let H be a subgraph of G with m(≤b) edges, and δ(G) be the minimum degree. We prove that G has a [a,b]-factor containing all edges of H if , , and when a ≤ 2, .展开更多
Let a, b, r be nonnegative integers with 1 ≤ a ≤ b and r ≥ 2. Let G be a graph of order n with n 〉（a＋2 b）（r（a＋b）-2）/b.In this paper, we prove that G is fractional ID-[a, b]-factor-critical if δ（G）≥bn/a...Let a, b, r be nonnegative integers with 1 ≤ a ≤ b and r ≥ 2. Let G be a graph of order n with n 〉（a＋2 b）（r（a＋b）-2）/b.In this paper, we prove that G is fractional ID-[a, b]-factor-critical if δ（G）≥bn/a＋2 b＋a（r-1）and ｜NG（x1） ∪ NG（x2） ∪…∪ NG（xr）｜ ≥（a＋b）n/（a＋2 b） for any independent subset {x1,x2,…,xr} in G. It is a generalization of Zhou et al.＇s previous result [Discussiones Mathematicae Graph Theory, 36： 409-418（2016）]in which r = 2 is discussed. Furthermore, we show that this result is best possible in some sense.展开更多
Background: Tenofovir (TFV) is widely used to treat patients with hepatitis B virus (HBV) infection. But kidney abnormalities are the main concern using this drug. Few studies have described the renal impairment due t...Background: Tenofovir (TFV) is widely used to treat patients with hepatitis B virus (HBV) infection. But kidney abnormalities are the main concern using this drug. Few studies have described the renal impairment due to the TFV in chronic hepatitis B (CHB) in Sub-Saharan Africa. The objective was to evaluate factors associated with renal impairment observed in patients on TFV for CHB. Method: It was a hospital based cross sectional prospective study carried out from June 2023 to July 2023 in Yaoundé (Cameroon) and included any patient treated with TFV for CHB during at least a period of 6 months. For each participant, we collected in the medical report socio-demographic data, clinical data, baseline creatinine, treatment information (type of TFV which was Disoproxil Fumarate (TDF) or Alafenamide (TAF), duration). Then, we collected blood samples to measure serum creatinine and phosphate levels and urine dipstick analysis. Factors associated with renal impairment were assessed with the Odds Ratio. A p value of Results: A total of 60 participants were included. The median age was 44 years [36-55] and median duration of TFV therapy was 17.5 months [11.7-25.7]. The prevalence of reduced eGFR (Conclusion: Kidney function was impaired in some patients receiving TFV for CHB. It should be monitored, particularly after 36 months and for those receiving TDF prodrug.展开更多
文摘Let G be a graph of order n, and let a and b be integers, such that 1 ≤ a b. Let H be a subgraph of G with m(≤b) edges, and δ(G) be the minimum degree. We prove that G has a [a,b]-factor containing all edges of H if , , and when a ≤ 2, .
基金supported by the National Natural Science Foundation of China(Nos.11371052,11731002)the Fundamental Research Funds for the Central Universities(Nos.2016JBM071,2016JBZ012)the 111 Project of China(B16002)
文摘Let a, b, r be nonnegative integers with 1 ≤ a ≤ b and r ≥ 2. Let G be a graph of order n with n 〉（a＋2 b）（r（a＋b）-2）/b.In this paper, we prove that G is fractional ID-[a, b]-factor-critical if δ（G）≥bn/a＋2 b＋a（r-1）and ｜NG（x1） ∪ NG（x2） ∪…∪ NG（xr）｜ ≥（a＋b）n/（a＋2 b） for any independent subset {x1,x2,…,xr} in G. It is a generalization of Zhou et al.＇s previous result [Discussiones Mathematicae Graph Theory, 36： 409-418（2016）]in which r = 2 is discussed. Furthermore, we show that this result is best possible in some sense.
文摘Background: Tenofovir (TFV) is widely used to treat patients with hepatitis B virus (HBV) infection. But kidney abnormalities are the main concern using this drug. Few studies have described the renal impairment due to the TFV in chronic hepatitis B (CHB) in Sub-Saharan Africa. The objective was to evaluate factors associated with renal impairment observed in patients on TFV for CHB. Method: It was a hospital based cross sectional prospective study carried out from June 2023 to July 2023 in Yaoundé (Cameroon) and included any patient treated with TFV for CHB during at least a period of 6 months. For each participant, we collected in the medical report socio-demographic data, clinical data, baseline creatinine, treatment information (type of TFV which was Disoproxil Fumarate (TDF) or Alafenamide (TAF), duration). Then, we collected blood samples to measure serum creatinine and phosphate levels and urine dipstick analysis. Factors associated with renal impairment were assessed with the Odds Ratio. A p value of Results: A total of 60 participants were included. The median age was 44 years [36-55] and median duration of TFV therapy was 17.5 months [11.7-25.7]. The prevalence of reduced eGFR (Conclusion: Kidney function was impaired in some patients receiving TFV for CHB. It should be monitored, particularly after 36 months and for those receiving TDF prodrug.
