Prove or give a counter-example:
(c) If G1∼= H 1and G2∼=H2, then G1×G2 ∼= H1 × H2.
(d) If N1 is normal in G1 and N2 is normal in G2 with N1∼=N2 and G1/N1 ∼= G2/N2, then G1 ∼= G2.
Prove or give a counter-example: (c) If G1∼= H 1and G2∼=H2, then G1×G2 ∼= H1 ×...
s G1 = G2 = S-8 G2 s2+1 G3= G4 = R(s) C(s) S G1 G3 G4 H1 H2 si 28+3 H1 H2 a) Find the characteristic equation by subtracting the transfer function (C (s) / R (s)) of the system, whose block diagram is given above. b) Determine the stability of the given system with Routh-Hurwitz stability analysis method.
Abstract Algebra (Direct Products of Groups)
Let G1, G2 and H be finitely generated abelian groups. Prove that if G1 XHG2 x H, then G G2
G1 = (A’+C’+D) (B’+A) (A+C’+D’) G2 = (ABC’) + (A’BC) + (ABD) G3 = (A+C) (A+D) (A’+B+0) G4 = (G1) (A+C) G5 = (G1) (G2) G6 = (G1) (G2) Determine the simplest product-of-sums (POS) expressions for G1 and G2. Determine the simplest sum-of-products (SOP) expressions for G3 and G4. Find the maxterm list forms of G1 and G2 using the product-of-sums expressions. Find the minterm list forms of G3 and G4 using the sum-of-products expression. Find the minterm list forms...
Try this example with water first: H1 H1 H2 H2 H H Water, H20 Partial charges: His +0.38, O is -0.75 Formal charges: His O, O is o Oxidation State: His +1, O is-2 Electrostatic potential description: The blue (positive) and red (negative) potentials are separated. That makes the molecule polar. The molecule is dark blue (quite positive) over the hydrogen atoms and dark red (quite negative) over the oxygen atom, making water very polar. And now do these two...
D Let fi, f2 A - B and g B -C and h1, h2 C (a) Prove that if g o fi = go f2 and g is injective, then fi = f2 = h2. (b) Prove that if h1 0 g h20g and g is surjective, then h
Q15
(14 / Suppose that Gl ะ G2 and Hi ex H2. Prove that GI E HIN G-DH2. State the general case. If G H is cyclic, prove that G and H are cyclic. State the (1 eneral case. h Zso D Zso. find two subgroups of order 12. If r is a divisor of m and s is a divisor of n, find a subgroup of Zm Z, isomorphic to Z, ®Z,
Problem 3. Prove or give a counter example 1. If an converges to a real limit then limn700 (m)" = 0. 2. If an is a positive sequence satisfying limn+ ()" = 0 then it con- verges.
Prove (using the definition of O) or disprove (via counter-example): If f(n) = O(n)), and g(n) = O(n2), then f(n) + g(n) = O(n5). Prove (using the definition of O) or disprove (via counter-example): If f(n) = O(n), and g(n) = O(n2), then fin)/g(n) = O(n).
using following parameters as defined
G1(s)=1/(s+50)
G2(s)=K/s
G3(s)=1/(s+10)
H(s)=1
R(s) is the unit step function
a) find the closed loop transfer function as a function of K
b) what is the maximum value of the K the system can
tolerate?
c) is there an effect on the system if the pole in G1(s) is
changed to :
1) G1(s)= 1/(s+500)
2) G1(s)=1/(s+11)
G1(s) G2(s) G3(s) C(s) H(s)
Prove, or give a counter example to disprove the following
statements.
a)
b)
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