Can anyone solve this please? 3) Double roots iF (F-r)(F-r) = 0 then F(n) = (A...
Can anyone help with this question please? Consider the problem-Δu = 0 in the annulus 2- E R R where 0<F< R with Dirichlet boundary condition if l u(z) = uテ xuR if |x| = R where ur, uRE R Use the general solution u(A log( problem B with A, B R to solve the Consider the problem-Δu = 0 in the annulus 2- E R R where 0
3) Given the field extensions R c F C C, such that F contains all n'th roots of unity ξ = e2mk/n, k-1, 2,.., n. Let 0メa E F, and let K be the splitting field of /(x) = xn-a E F[a]. T xn-a = 0, and (b) The Galois group G(K, F) is abelian hen show that: (a) K F(u) where u is any root of 3) Given the field extensions R c F C C, such that F...
4. Consider the equation zy" - 2y' y 0 (a) Explain why r 0 is a regular singular point for the given equation (b) Let ri >r2 be two indical roots of the given equation. Using Frobenius' method, find a series solution n(x)-z"Ση_0Cnz". (c) Find the second solution of the form Σ000 bnXntr2 with boメ0, or i (z) Inr +bn+r2 with the first three nonzero terms of the series with coefficient bn 4. Consider the equation zy" - 2y' y...
2. Applying the Routh-Hurwitz criterion can obtain the number of the roots of f (s) 0 with a positive real part. The Routh-Hurwitz criterion can also be applied to find that how many roots have a real part greater than -a. This principle is exercised in this problem Given a characteristic equation: f(s) 3 4s2 3s10 0 Eq(1) By substituting sı = s + α (i.e., s = sı-α) into Eq (1) and apply the Routh-Hurwitz criterion on f(s) 0,...
Can anyone draw the arrow pushing mechanism for this reaction and please explain?? R=Bn 60b 73% yield R=Bn 59b 99% TMEDA DMF
3. For each n E N let fn : (1, 0) -+ R be given by f/(x) = Find the function f : (1, 0) - R to which {fn} converges pointwise. Prove that the convergence is not uniform 3. For each n E N let fn : (1, 0) -+ R be given by f/(x) = Find the function f : (1, 0) - R to which {fn} converges pointwise. Prove that the convergence is not uniform
can anyone please explain how to solve this with steps? Three point charges are located at the corners of a triangle: q1 =-5 μC at (-1,1), q2 = +3pC at ( Q3 = +2 μC at (1,1), with the coordinates given in m. Calculate the electric field E at (0,0) and the force F that would be exerted on a charge of q =-3pC at (0,0). 1-1), and
If f(x) := {n=0 (-1)"x" 3” n2 for x € (-3, 3), find f(100) (0). Hint: use the coefficients in Taylor's Theorem to solve for the required derivative, and invoke the uniqueness of power series with given centers (proved in Thursday's lecture). Or, take the first couple derivatives, evaluate them at r = 0, and find the pattern.
Can anyone help with this question please? Many thanks!!!!! Let Ω Rn be a bounded domain and f : Ω-, R and g : 0Ω-+ R be given functions. Consider the PDE problem -Au = f in Ω, where n is the external unit normal of Q. Show that there is at most one solution u E C2(Q) n Co (O). For this purpose, use an energy argument as before but amend the energy as appropriate. Let Ω Rn be...
Please all thank you Exercise 25: Let f 0,R be defined by f(x)-1/n, m, with m,nENand n is the minimal n such that m/n a) Show that L(f, P)0 for all partitions P of [0, 1] b) Let mE N. Show that the cardinality of the set A bounded by m(m1)/2. e [0, 1]: f(x) > 1/m) is c) Given m E N construct a partition P such that U(f, Pm)2/m. d) Show that f is integrable and compute Jo...