for n71. Using Cauchy Criterim, Let χ.--and en ti -nnt ri u nI)l for n71. Using Cauchy Criterim, Let χ.--and en ti -nnt ri u nI)l
3. Using the Cauchy Schwartz inequality show that if u, veR" then ||u-<H4+ -
NiSO4· 6H2O + en --> A. Using the moles of each species in your Ni-en complex, show the calculations to determine the empirical formula for your Ni-en complex. Each complex’s moles / Ni 2+ moles: Ni2+ = 0.000824 mol / 0.000824 mol = 1 SO42-= 0.000824 mol / 0.000824 mol = 1 H2O = 0.006061 mol / 0.000824 mol = 7 en = 0.001001 mol / 0.000824 mol = 1 Empirical Formula: ??? B. Knowing your Ni-en complex’s empirical formula,...
9. Let X be a set, A a sigma algebra and u a measure. Let L = {E € AM(E) = 0 ). a. Show that if EE L and F E A then ENFEL. b. Show that if En E Lin 2 1, then Un=1 En € L.
l. Assume that j : R-→ R-s C and satisfies what are known as the Cauchy-Riemann equations: (c) Let r-(r1, 2) and (s1, s2) be vectors in IR2 and suppose that (ri, 2)f(s1, 82) and Df(81,82)メ0. Show that f-1 satisfies the Cauchy-Riemann equations when evaluated at r. (Hint: Might I make a notational suggestion: Leta(s) = sim) = % (n, s) and b(s) 쓺(81, 82) =-警( )) 81,82 (d) For this last bit, drop the assumption that f satisfies the...
6. Consider the Ti-Ni system in the figure below. Atomic Percent Nickel 20 I800 1600 L 1450C 1400 200 TIN (Ni) 1000 Un) re s00 Hati) s00 Ti Weight Percent Nickel N a. What are the melting temperatures of pure Ni and pure Ti? b. Label the liquidus and solidus lines in the figure. c. Label al field containing two phases in the figure. d. What is the maximum solubility of Ni in a-Ti and Ti in Ni? e. Write...
Let U be an open set of R3 and f:U Ri is a smooth function. Prove that the graph of f.e.i. the set M={(u,f(u)) E R4: ueU} is a 3-dimensional submanifold of R*.
Let H be a complex Hilbert space. 6. (a) Let φ, ψ E H \ {0} . Define the linear operator T on H by Using the Cauchy-Schwarz inequality, show that llll = Hell ll [4 marks] (b) A bounded linear operator A is said to have rank one if there exists v e H [0 such that for any u E H we have Au cu, where cu E C is a constant depending on u. (i) Show that...
Name the following metal complexes or complex ions: formula name [Au (CN), (co)]" [Feci.] [Ni(en),] L O X 6 ?
Let u(t)= ti+ln(t)j + et k and v(t) = ti+2tj+1k. Compute the derivative of the dot product [u(t)- v(t)] in two ways and confirm they agree: • Compute the dot product u(t). v(t) first and then differentiate the result. • Alternatively, use the following “Dot Product Rule" v(t)] = u'(t) . v(t) + u(t) . v'(t). (1)
Let us look again at the time-optimal positioning problem (Section 1.4 of the textbook): with initial state ri (0) = X, X < 0, and x2(0) = 0, to be steered to the final state x1 (t) = 0, 2 (t1)0, and with cost given by J (t, r1, 2, u) t. Assume now that we want to use an nsymmetric bang bang control; thai i, ea only asse valu u=-a or u=b where a, b > 0. Show that...