1. Let ω be a k-form in Rn , Π 〉 k. If k is odd, show that ωΛω 0 4. L et ω be a k-form and let ) be a /-form. Fin d d(da) Λ η_ωΛ đ7) .
1. Let ω be a k-form in Rn , Π 〉 k. If k is odd, show that ωΛω 0 4. L et ω be a k-form and let ) be a /-form. Fin d d(da) Λ η_ωΛ đ7) .
Let ω be a k-form and let η be a 1-form. Find d(don η-ω^ dn)
dc Let an operator K = et + x2 - 5 + log(x), that is, dy K[y] = et y - 5y + log(x) y. This K is a linear operator. + x2 dx O True O False
Consider a very long aluminum fin (k = 237W/m-K) fin, with the temperature at the end of the fin essentially that of the surrounding air. This fin has a diameter of lcm, and is attached to a surface at 80°C. The surface is exposed to ambient air at 22°C with a heat transfer coefficient of 15W/m2-K. Estimate: a) The fin temperature at a distance of 5cm from the base; b) The rate of heat loss from the entire fin; c) The effectiveness of...
proof:
Let be a k-form and η be a 1-form on Rn
Let be a k-form and η be a 1-form on Rn
7. Let A, , An be non-empty subsets of a finite set Ω. If 1 k n and Ek is the set of elements in Ω which belong to at least k of the Ai's show that Pal i-1
7. Let A, , An be non-empty subsets of a finite set Ω. If 1 k n and Ek is the set of elements in Ω which belong to at least k of the Ai's show that Pal i-1
Let {et} denote a white noise process from a normal distribution with E[et] = 0, Var(et) = σe2 and Cov(et, es) = 0 for t ≠ s. Define a new time series {Yt} by Yt = et + 0.6 et -- 1 – 0.4 et – 2 + 0.2 et – 3. 1. Find E(Yt ) and Var(Yt ). 2. Find Cov(Yt , Yt – k) for k = 1, 2, ...
eT. For renstors of 75 Ω, 50 Ω. & 100 Ω are connected as shown to a 9 volt source. a) Make a sketch of this circuit (include correct schematic diagrams for ALL components) b) Determine the curreni through the circuit if the switch S is OFF and if the switch S is ON: c) Determine the power dissipated by the circuit if the switch S is OFF and if the switch S is ON:
For the inverter of Fig. 13.8(a), let the on-resistance of PU be 20 k Ω and that of PD-10 k12. If the capacitance C 10 iF, find (pLH piH. IpHL, and tp
(1) Let w1, be a k-form and w2 be an l- form, both defined in an open subset UC R3. Let d : /\k (U)-ל ЛК +1 (U) be the exterior derivative of differential forms. (a) Show that d is a linear transformation of vector spaces. (b) Show that (c) Show that (d) Show that d(w) -d(d(w)) 0 for every k-form w, i.e. the map is the zero map
(1) Let w1, be a k-form and w2 be an l-...