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We show that the structure of a block outside the critical hyperplanes of category O over a symmetrizable Kac-Moody algebra depends only on the corresponding integral Weyl group and its action on the parameters of the Verma modules.
      
We also prove the uniqueness of Verma embeddings outside the critical hyperplanes.
      
When β is less than some critical value the boundary periodic solution (xs(t), 0, zs(t)) is locally stable, and when β is larger than the critical value there are periodic oscillations in substrate, prey and predator.
      
The critical micelle concentration (cmc) and surface tension of the novel zwitterionic Gemini surfactant in aqueous solution at 15°C are 7.2×10-5 mol/L and 34.5 mN/m, respectively.
      
Then, from the curves, the critical micelle concentration (CMC) and the thermodynamic standard formation functions (ΔH?m, ΔG?m and ΔS?m) were obtained through thermodynamic theories.
      
The results indicate that the infection delay will promote the epidemic outbreaks, increase the prevalence and reduce the critical threshold of epidemic spreading.
      
In terms of continuous decomposition and choosing an appropriate BMO function, the authors obtain a sharp necessary condition for Lp boundedness of the commutators generated by Bochner-Riesz operators below the critical index and BMO functions.
      
In order to describe multiaxial fatigue damage characteristics, a nonlinear multiaxial fatigue cumulative damage model is developed based on the critical plane approach.
      
The application shows that it can solve the diverse problems of collaborative product development effectively, and help enterprises find out the critical factors that affect the collaboration.
      
A method combining the predictor-corrector mechanism and the Netwon-Raphson method is presented to calculate the critical speed at the corresponding Hopf bifurcation point of the system.
      
For this reason, we perform an accurate numerical analysis of the central charge and the critical exponents.
      
The difference between the critical temperature and the pairing temperature is presented, and the Fermi arc, the d-wave symmetry and the poor conductivity, etc., are discussed.
      
Also, there is a critical size for the pore; when the pore size is larger than the critical value, the fatigue strength decreases sharply.
      
The critical aggregation concentration (CAC) was determined in the range of around 10-6 M by fluorescence measurement.
      
However, the heat transfer enhancement decreased near the critical pressure.
      
When pressure is closer to the critical pressure, the temperature difference between the wall and the fluid increased greatly near the pseudo-critical temperature.
      
Besides, the critical crack tip opening displacement of each specimen is calculated, too.
      
At that, it minimizes both the critical (maximum) delay and the chip area required for routing.
      
Conversely, reliably smaller amounts of HSP70 were synthesized in the TT strain as compared to Oregon R under all shock temperatures except the critical one (39.5°C).
      
The critical flow rate was used as an index of fish swimming performance.
      
 

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