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  • Author: Xiang-Gao x
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A necessary and sufficient condition for some steady Ricci solitons to have positive asymptotic volume ratio

Abstract

In this paper, we firstly establish a useful ODE relationship between R1(c) and V1(c) on the steady Ricci soliton. Based on this, we obtain a necessary and sufficient condition for some complete noncompact steady gradient Ricci solitons to have positive asymptotic volume ratio.

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Genetic Diversity in the mtDNA control region and population structure of Chrysichthys nigrodigitatus from selected Nigerian rivers: Implications for conservation and aquaculture

Abstract

The genetic diversity and population structure of Chrysichthys nigrodigitatus were evaluated using a 443 base pair fragment of the mitochondrial control region. Among the eight populations collected comprising 129 individuals, a total of 89 polymorphic sites defined 57 distinct haplotypes. The mean haplotype diversity and nucleotide diversity of the eight populations were 0.966±0.006 and 0.0359±0.004, respectively. Analysis of molecular variance showed significant genetic differentiation among the eight populations (FST =0.34; P < 0.01). The present results revealed that C. nigrodigitatus populations had a high level of genetic diversity and distinct population structures. We report the existence of two monophyletic matrilineal lineages with mean genetic distance of 10.5% between them. Non-significant negative Tajima’s D and Fu’s Fs for more than half the populations suggests that the wild populations of C. nigrodigitatus underwent a recent population expansion, although a weak one since the late Pleistocene.

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Estimates on the non-compact expanding gradient Ricci solitons

Abstract

In this paper, we deal with the complete non-compact expanding gradient Ricci soliton (Mn,g) with positive Ricci curvature. On the condition that the Ricci curvature is positive and the scalar curvature approaches 0 towards infinity, we derive a useful estimate on the growth of potential functions. Based on this and under the same assumptions, we prove that ∫t 0 Rc (γ'(s) , γ' (s))ds and ∫t 0 Rc (γ' (,s). v)ds at least have linear growth, where 7(5) is a minimal normal geodesic emanating from the point where R obtains its maximum. Furthermore, some other results on the Ricci curvature are also obtained.

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A new proof of the bound for the first Dirichlet eigenvalue of the Laplacian operator

Abstract

In this paper, we present a new proof of the upper and lower bound estimates for the first Dirichlet eigenvalue λ1D(B(p,r)) of Laplacian operator for the manifold with Ricci curvature Rc−K, by using Li-Yau’s gradient estimate for the heat equation.

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Vertex-Distinguishing IE-Total Colorings of Complete Bipartite Graphs Km,N(m < n)

Abstract

Let G be a simple graph. An IE-total coloring f of G is a coloring of the vertices and edges of G so that no two adjacent vertices receive the same color. Let C(u) be the set of colors of vertex u and edges incident to u under f. For an IE-total coloring f of G using k colors, if C(u) 6= C(v) for any two different vertices u and v of G, then f is called a k-vertex-distinguishing IE-total-coloring of G, or a k-VDIET coloring of G for short. The minimum number of colors required for a VDIET coloring of G is denoted by χie vt(G), and is called vertex-distinguishing IE-total chromatic number or the VDIET chromatic number of G for short. VDIET colorings of complete bipartite graphs Km,n(m < n) are discussed in this paper. Particularly, the VDIET chromatic numbers of Km,n(1 ≤ m ≤ 7,m < n) as well as complete graphs Kn are obtained.

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Pathogenicity of FtsK mutant of avian pathogenic Escherichia coli

Abstract

Introduction: Avian pathogenic Escherichia coli (APEC) is a leading cause of extraintestinal infection and heavy economic losses. Imparting immunity after vaccination with live attenuated strain vaccination is an ideal strategy for infection control. This study considers an FtsK knockout mutant strain as a candidate. Material and Methods: An FtsK knockout mutant of APEC strain E058 was constructed and the pathogenicity of the mutant and wild-type strains was further evaluated in chickens. Results: The 50% lethal doses of each strain for one-day-old specific-pathogen-free (SPF) chickens challenged experimentally via trachea were 105.5 and 107.0 colony-forming units (CFU) respectively. Chickens challenged with the wild-type strain exhibited typical signs and lesions of avian colibacillosis, while those inoculated with the mutant strain showed mild pericarditis and pulmonary congestion. The growth rate of the FtsK mutant strain was much slower than the wild-type strain in the heart, spleen, liver, and lung of infected chickens. Conclusion: These results indicated that the APEC FtsK mutant can be attenuated for chickens, and that this mutant has the potential for the development of an APEC vaccine.

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Lower left lung abscess from combined stomach and left diaphragm perforation by an intragastric foreign body

Abstract

Background: Usually children mistakenly swallow foreign bodies, and most objects are spontaneously discharged through the digestive tract without consequence. However, sometimes the objects can cause gastrointestinal perforation, with serious complications.

Objective: To report the case of a 26-year-old male patient, who mistakenly swallowed a bamboo chopstick 14 years ago. The chopstick eventually perforated the gastric fundus and left diaphragm, pierced the lower left lobe of the lung, and caused a lower left lung abscess.

Method: A thoracotomy was conducted to remove the foreign body and the lower left lobe of the lung, followed by a patch fundoplication.

Result: The object was removed and the patient’s lesions healed after surgery.

Conclusion: The ingestion of foreign bodies rarely causes serious problems, but we should be vigilant to the occurrence of complications, and close follow-up should be conducted. This follow-up should include confirmation that the foreign body has passed through the alimentary tract.

Open access
Inhibitory effects on the HMG-CoA Reductase in the chemical constituents of the Cassia mimosoides Linn

Abstract

Cassia mimosoides Linn has been used from ancient times and used for treating hepatitis for its supposedly medically beneficial properties. In this study, different constituents of the Cassia mimosoides Linn (β-Sitosterol, Oleanolic Acid, Emodin, Carotene, Resorcinol, Luteolin, and α-L-Rhamnose) were evaluated for potential anti-HMG-CoA reductase effect. The inhibitory effects of HMG-CoA reductase of Cassia mimosoides Linn extracts and Pravastatin inhibitor at different concentrations (at doses of 1, 5, 25 or 125 μg/mL, respectively) in reaction system (70 mmol/L phosphate buffer, 200mmol/L NADPH, 5 μg HMG-CoA reductase, 2 mmol/L EDTA, 2 mmol/L cysteamine, 0.06% BSA) into 37°C preheat HMG-CoA for initiating this reaction, and then determined the change of HMG-CoA reductase activity (ΔAΔt) at 340 nm, the inhibition ratio of HMG-CoA reductase activity and its dynamic change of inhibitory effect within 15 min and the descent rate of NADPH. Emodin, Luteolin, β-Sitosterol, Oleanolic Acid, α-L-Rhamnose and Carotene showed good inhibition of HMG-CoA reductase activity. Among them, only the Emodin (1 and 5 μg/mL) groups showed a significant decrease of HMG-CoA reductase activity compared to the Pravastatin (1 and 5 μg/mL) groups respectively. In addition, the HMG-CoA reductase activity in the Emodin and Luteolin (25 and 125 μg/mL) groups was clearly lower than the Pravastatin (25 and 125 μg/mL) groups respectively. And the Emodin and Luteolin (1, 5, 25 or 125 μg/mL) groups exhibited a stable effect on inhibiting the HMG-CoA reductase within 15 min. These findings further support the exploration of Cassia mimosoides Linn as a potential agent for the treatment of hepatitis in future studies.

Open access