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As the third application, we describe a K-basis for the ring of invariants for the adjoint action of ${\rm SL}_2(K)$ on m copies of $sl_2(K)$ in terms of traces.
      
Existence and uniqueness for third order nonlinear boundary value problems
      
Third, convergence of weak nonnegative splittings and regular splittings is discussed, and we obtain some necessary and sufficient conditions such that the splittings of a Z-matrix converge.
      
For von Mises population M(μ,k), we find that six bootstrap confidence intervals are second-order correct like the approximate normal confidence interval, and STUD-interval is third-order correct.
      
On the existence of periodic solutions for the third-order nonlinear ordinary differential equations
      
In this paper, the existence of periodic solution for the third-order nonlinear ordinary differential equation of the form {} is considered, where f, g, h and p are the continuous functions, and p(t+T)=p(t).
      
It is proved that every 3-connected loopless multigraph has maximum genus at least one-third of its cycle rank plus one if its cycle rank is not less than ten, and if its cycle rank is less than ten, it is upper-embeddable.
      
Periodic solutions of third-order functional differential equations with variable coefficients
      
The sufficient condition for the existence of 2π-periodic solutions of the following third-order functional differential equations with variable coefficients is obtained.
      
A priori bounds for periodic solutions of a kind of third-order delay differential equation
      
By means of continuation theorem of the coincidence degree theory, sufficient conditions are obtained for the existence of periodic solutions of a kind of third-order neutral delay functional differential equation with deviating arguments.
      
The overall yield for the third generation dendrimer 5 from Schlüter dendron is 12%.
      
The IBC on the surface of the medium and the boundary integral equation on the aperture of the cavity are transformed into the third boundary condition, and then the functional of the boundary value problem is obtained.
      
Further research on public-key cryptosystems based on third-order recurrence sequence
      
Properties of third-order recurrence sequences were investigated and a new variant of the GH public-key cryptosystem, which was further improved to be a probabilistic public-key cryptosystem, was proposed.
      
The trusted element, which differs from the traditional trusted hardware such as a smart card or a co-processor, offers a third party service based on an encrypted circuit construction.
      
When transferred onto plum and peach, the spider mite adapted to the new hosts in the second generation; however, on cherry and apricot, it adapted in the third generation.
      
Third, modern ecological means should be taken to protect the original Metasequoia population and its habitat.
      
In the third stage the original MC does not affect the rate of temperature increase, while the effect of the other factors is the same as that at the first stage.
      
The third RAPD group accommodated other isolates including the B morphotype isolate CWS43 from the United States.
      
 

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