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It is well-known that the ring of invariants associated to a non-modular representation of a finite group is Cohen-Macaulay and hence has depth equal to the dimension of the representation.
      
The essential dimension is a numerical invariant of the group; it is often equal to the minimal number of independent parameters required to describe all algebraic objects of a certain type.
      
Furthermore, it is proved that the minimum of the total number of bends in an at most single-bend embedding of a cubic graph of ordern is less than or equal to 0.5n+1.
      
Generally, The risk-neutral default intensity λQ is not equal to the empirical or actual default intensity λ.
      
Under the condition of irreducibility, it is show that this is equal to the spectral radius of Jacobi matrix of its generating function.
      
The thermal expansion coefficient (2.17 × 10-5 K-1) of the single-phase SmCoO3 is approximately equal to that of doped LaGaO3, but much bigger than that of SDC(Ce0.85Sm0.15O2) above 873 K.
      
We also pseudopolynomially solve a class of QAP whose GLB is equal to the optimal objective function value, which was shown to remain NP-hard.
      
If the helix angle is equal to or slightly smaller than the bigger angle, which makes two meshing boundary lines superpose, a preferable meshing performance is obtained.
      
Research results show that initiation and propagation laws are the same with interior symmetric wedge angles of 30°-120°, while the laws are different with interior symmetric wedge angles equal to or more than ≥150°.
      
For Al and Si atoms arranging along the c axis in an AF-like long-range ordering (-Al-Si-Al-), the calculated electron-phonon coupling constant is equal to 0.8 and the logarithmically averaged frequency is 146.8 K.
      
Renewable energy does not simply equal to using a photovoltaic (PV) board.
      
The results showed that the estimated environmental capacity for 137Cs in sediments was approximately equal to the current input of 137Cs into the sediments.
      
The carbon isotope composition of ethyl alcohol produced during alcohol fermentation depended on the substrate used and was characterized by the value of δ13C equal to -24.7 ± 0.8%.
      
The values of apparentKm, determined for AcLS and AcLDC with pyruvate and AcL, respectively, were equal to 70 mM and 20 mM.
      
A single form of the enzyme was synthesized either in the absence of peptone from the medium or at the initial pH value of the medium, equal to 8.6.
      
At 36-55oС, the temperature dependence of kin(us) was characterized by an activation energy (Eact) of 19.7 kcal/mol, whereas the value of Eact for CAT thermoinactivation was equal to 44.2 kcal/mol.
      
At temperatures below 30°C, the activation energy for β-D-glucose oxidation was 6.42 kcal/mol; at higher temperatures, this parameter was equal to 0.61 kcal/mol.
      
The values of the effective constant of extraction rate (min-1) at pH 6.5, 9.0, and 12.0 were equal to (2.7 ± 0.1) × 10-3, (6.2 ± 0.5) × 10-3, and (15.4 ± 0.7) × 10-3, respectively.
      
Time to half-maximum inactivation of the enzyme at 50°C was equal to 1 h.
      
With colloidal chitosan as the substrate, the value of KМ of the purified chitosanase was equal to 25 mg/ml.
      
 

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