ια2 1. Consider the operator, o = Σ31-, and the Laplace operator Δ= Σ Under which conditions is the function ф-А П3.1 ekiXi an eigen function ofone or both operators? 10P ια2 1. Consider the...
both pls 1) Which of the following operator(s) is/are Hermitian? a) id/dy? b) d/dy2 c) id/dy You may assume that the functions on which these operators operate are appropriately well behaved at infinity. (Hint #1: .. P dy = f. y pudy where the integral hudu = Uv - Sudv. Hint #2: Use y = e) 2) In each case below show (in the space provided directly) that F(y) is an eigen- function of the operator A and find the...
What is the Laplace transform? Show all steps 0O (e) g(1-Σ e-)κιδ(t-kT) where δ(r) unit-impulse function
Linear System Time-invariant, impulse response function 1. Consider a system R(α, β) which can be represented by operators P,, Qß. R(α, β) Here P is a truncation operator. That is, it performs the following operation for given α 2 0 and u(1), - < t < 00, 11(1) İf12α And a is a shift operator. That is, it performs the following operation for given β 0 and v(1), - < t < ao Assume that R(α, β) is relaxed at...
the Consider reaction A203(s) +2Fe(s) Fe2O3(s) +2AIs) for which ΔH° = 851.5 kJ and Δ So-37.00 J/K at 298.15 K (1) Calculate the entropy change of the UNIVERSE when 2.154 moles of Al203(s) react under standard conditions at 298.15 K JK (2) Is this reaction reactant or product favored under standard conditions? (3) If the reaction is product favored, is it enthalpy favored, entropy favored, or favored by both enthalpy and entropy? If the reaction is reactant favored, choose reactant...
Consider a linear operator, 82 with Po(x) pi(a) 1 p()-0 As a linear space of functions where L is self-adjoint, consider the following "periodic'-like" boundary conditions, where, as usual, po(z) = w(z)po(x). The weighting function w(z) is, so far, unknown. (a) Identify, up to a constant, the weighting function (a) of the inner productu for which L can potentially become a self-adjoint operator; (b) Assume that L acts on a space of functions defined on an interval with b) Show...
1. Consider machine M-(Q, Σ. Γ. δ.ql, qaccept, qreject), where Q-{qi, q2, q3, qaccept, qreject}, -{0.1), Г-{0.1 Ủ}, and the transition function as follows is δ (qi, U)-Greject, U, R) Prove that M is NOT a decider Describe in mathematical terms the language A that M recognises, and verify 1. ii. your answer, ie prove that A-L(M) iii. Is A Turing-decidable? [No need for a formal proof, but give clear reasons for your answer 1. Consider machine M-(Q, Σ. Γ....
Consider the electrophilic addition of one equivalent of HBr to 1-methylcyclopentadiene (1). Under the reaction conditions, all possible allylic carbocations form, but there are no carbocation rearrangements. Which is the kinetically favored product? Br Br" Br Br Select one: a. a O b. b C. C O d. d e. e
Problem 1: Consider the followingtime-invariant channel impulse response c(t)-6(t-td) + (1/2) δ(t-(t0+T)) + (1/2) δ(t(td-T)), td and Tare constants. a Plot this impulse response and show the delay of each path. b- Find the power delay profile for this given channel c Find the rms delay spread by using the power delay profile you find in (b) d- Find the coherence bandwidth°fthis channel (assume 90% correlation). Note that it may be a function oftd and e Find the frequency response...
1. Consider a thin-walled cylinder which is sealed at both ends which contains a gas under a pressure of 1000 MPa. The cylinder is one meter long, 100 mm in diameter and has a wall thickness of 5 mm. • Determine the hoop stress. • Determine the longitudinal stress.
4. (a) Let A [0, oo) and let f.g:AR be functions which are continuous at 0 and are such that f(0) 9(0)-1. Show that there exists some δ > 0 such that ifTE 0,d) then (b) Consider the function 0 l if z e R is rational, if zER is irrational f(z) Show that limfr) does not exists for any ceR. 4. (a) Let A [0, oo) and let f.g:AR be functions which are continuous at 0 and are such...