A benzylic carbocation is generated under the conditions of part A. Would the presence of a para CH3O- group on the benzene ring increase or decrease the stability of the benzylic carbocation? Explain.
Use the function V(x,y) = x^2 + y^2 to analyze the stability properties of the zero solution of the nonlinear system
x' = x + 2xy^2
y' = - 2x^2y + y
More specifically, what stability conclution(s) can be drawn? ( Justify your answer)
Please I want a detailed and clear solution. Thanks.
Following is the problem that I solved the first part:
Consider the system x' = f(x), where f: R^2 into R^2, is defined by:
f(x) = [ (x1)^3 + (x1) (x2)^2 ]
[ (x1)^2 (x2) + (x2)^3 ]
a- Find all equilibrium points of the system.
b- Use an appropriate Lyapunov function to determine the stability of the equilibr
Determine the asymptotic stability of the system x' = Ax where
A is 3 x 3 matrix
A = -1 1 1
0 0 1
0 0 -2
( first row is -1 1 1 second is 0 0 1 and third is 0 0 -2)
More specifically, what stability conclusion(s) can be drawn? ( Justify your answer)
1-Chloro-1-phenylethane ionizes easily under E1 conditions to form a benzylic carbocation intermediate. The ion is stabilized due to the delocalization of the positive charge to the aromatic ring. Draw resonance structures that indicate the stability of this ion.
Do you think that stability is more critical to certain aspects of a given organization than others? On the same note, is innovation more important to certain aspects? How do you promote each, simultaneously, as a leader of the organization as a whole?
Please use a step-by-step method to solve the two following exercises:
Consider the linear system x' = Ax, where A is a 2 x 2 matrix with lamda in the diagonal as follows;
A = [lamda, -2]
[1 , lamda],
and lamda is real. Determine if the system has a saddle, node, focus, or center at the ori
I understand how to use Matlab to graph the loci, but I need help to understand how to graph the loci by hand.
Sketch the Loci and find range of K for stability for these two problems
(s-1)(s^2 + 4s + 16)
(s-1)(s^2 + 4s + 7)