Effects of the killing rate on global bifurcation in an oncolytic-virus system with tumors

Oncologists and virologist are quite concerned about many kinds of issues related to tumor-virus dynamics in different virus models. Since the virus invasive behavior emerges from combined effects of tumor cell proliferation, migration and cell-microenvironment interactions, it has been recognized as a complex process and usually simulated by nonlinear differential systems. In this paper, a nonlinear differential model for tumor-virus dynamics is investigated mathematically. We first give a priori estimates for positive steady-states and analyze the stability of the positive constant solution. And then, based on these, we mainly discuss effects of the rate of killing infected cells on the bifurcation solution emanating from the positive constant solution by taking the killing rate as the bifurcation parameter.     

On an extension of a theorem on conjugacy class sizes

Let G be a finite group. We extend Alan Camina’s theorem on conjugacy classes sizes which asserts that if the conjugacy classes sizes of G are {1, p ^a , q ^b , p ^a q ^b }, where p and q are two distinct primes and a and b are integers, then G is nilpotent. We show that let G be a group and assume that the conjugacy classes sizes of elements of primary and biprimary orders of G are exactly {1, p ^a , n,p ^a n} with (p, n) = 1, where p is a prime and a and n are positive integers. If there is a p-element in G whose index is precisely p ^a , then G is nilpotent and n = q ^b for some prime q ≠ p.     

On Groups with a CC(n)-Subgroup

A subgroup H of G is a CC(n)-subgroup of G if |G: H| >n and |C_G(x): C_H(x)| ≤n for each element x ∈ H ? {1}. In this article, we study the finite p-groups with a nontrivial CC(p)-subgroup, and the locally nilpotent groups with a nontrivial CC(n)-subgroup.     

On theta pairs for a maximal subgroup

For a maximal eubgroup M of a finite group G, a 8-pair is any pair of subgroups (C,D) of G such that (i) D?G, D≤C, (ii) - G, - M and (iii) C/D has no proper normal subgroup of G/D. A partial order may be defined on the family of 8-pairs. Let △(M) - {(C,D)|(C,D) is a maximal 8-pair and CM - G}. The purpose of this note is to prove: (1) A group G is solvable if and only if, for each maximal subgroup M of G, △(M) contains a 8-pair (C,D) such that C/D ie nilpctent. (2) If a group G is S₄-free, then G ia eupersolvable if and only if, for each maximal subgroup M of G, △(M) contains a 8-pair (C,D) auch that C/D is cyclic     

Interaction between trelagliptin and pepsin through spectroscopy methods and molecular dynamics simulation

The interaction between trelagliptin and pepsin was probed through spectroscopy methods and molecular dynamics simulation. Results of fluorescence lifetime and fluorescence spectroscopy analysis showed that trelagliptin can spontaneously interact with pepsin through a static quenching. This interaction was mainly driven by hydrogen bonding and van der Waals, as evident from thermodynamic parameters and molecular dynamics simulation. The microenvironment of tyrosine residues and the secondary structure of pepsin were slightly influenced by trelagliptin based on synchronous fluorescence, three-dimensional fluorescence, and circular dichroism spectra. In addition, the activity of pepsin was hardly affected by the insertion of trelagliptin. Molecular dynamics simulations were used to further analyze the pepsin–trelagliptin complex. This study provides useful information for binding mechanisms of trelagliptin on pepsin.     

Facile preparation of ZrCO composite aerogel with high specific surface area and low thermal conductivity

A novel ZrCO composite aerogel is synthesized using zirconium oxychloride and resorcinol–formaldehyde (RF) as precursors through the sol–gel route and carbothermal reduction process. The effects of different Zr/R molar ratios and calcination temperatures on the physical chemistry properties of ZrCO aerogels are investigated. The ZrCO composite aerogel consists of the C/ZrO₂/ZrC ternary aerogel. The results show that with the increase of R/Zr molar ratios, the specific surface area and bulk density increase with calcination temperature up to 1300?°C, but decrease at even temperature (1500?°C). The specific surface area is as high as 637.4?m²/g for ZrCO composite aerogel (R:Zr?=?2:1), which was higher than ever reported. As the heat-treatment temperature increases to 1500?°C, the ZrC crystalline phase occurs and the t-ZrO₂ phase still appears within the composite. The thermal conductivity of the carbon fiber mat-reinforced composite aerogel is as low as 0.057?W/m/K at room temperature (25?°C).

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Diastereo‐ and Enantioselective Palladium‐Catalyzed Dearomative [3+2] Cycloaddition of 3‐Nitroindoles

Diastereo‐ and enantioselective cycloaddition of 3‐nitroindoles with vinyl aziridine was realized under Pd‐catalysis using commercially available Walphos as the ligand, affording pyrroloindolines in high yields with high diastereo‐ and enantioselectivities. The reaction can be scaled up to a gram scale and the reaction products are easily converted to amino pyrroloindoline and other pyrroloindoline derivatives.