Let G (V, E) be a simple graph with |V]2 3 and d(u) 2 for all v E V. Prove that G is Hamiltonian. A- =而

Q: Let x(t) be a Brownian motion with x(0). Mathematically prove or disprove that -4x(t)is a Brownian…

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Q: Let G = Z4 x Zp, and S = {(1,0), (3,0), (2,1), (0,1). Prove that Cay(G, S) is not normal Cayley…

A: To prove cay(G , S) is  a normal Cayley graph you need to prove that for any a∈G a-1Sa=S ∀a∈Z4×Z2=G…

Q: Let P denote the path that travels along the graph of y = x2 from (0,0) to (1,1). Let f(x,y) = √1 +…

A: Let P denote the path that travels along with the graph of y=x2 from (0, 0) to (1, 1). Let f(x,…

Q: Consider the two following graphs and answer the following questions. a) Are G and H isomorphic?…

A: Providing the answer for first three parts if you want the answer of other parts please provide us…

Q: Find an upper triangular U (not diagonal) with U2 = I which gives U = u- 1.

A: Given, U2=I

Q: ® Find the_functian that satisfies the following conditions for some constant Eceficients c,and c…

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Q: Use the generalized chain rule Question Let f(x, y, z) = xyz, x = t – 2, y = t² , and z = 2t. Find…

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Q: let H = {n² |n E z*}, determine whether it is closed under

A: Given : H={n2|n∈Z+}   To Check:  H is closed under binary addition or not

Q: B H E RE OF G 3 A E D 2. Determine if each of the graphs above have a Hamiltonian circuit. Explain.

A: Remark: A path begins and ends on the same vertex (i.e., a closed circuit) such that each vertex is…

Q: 25 If A E M, is symmetric, prove that AT is symmetric.

A: Symmetric matrix

Q: 29. Calculate /| (xy +e*)ds, where S is the triangle in Figure 18 with vertices (0,0, 3), (1,0, 2),…

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Q: S :R\{0} → R, S(r)=e4z^+5z=2–1

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Q: 8. Let C be the perimeter of the square with vertices at the points z = z = 1+i, and z = i traversed…

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Q: 8. (a) Show that the system i=y+xf(r)/r, j=-x+yf(r)/r (7=x²+y?) (*) has limit cycles corresponding…

A: Given part (a) x·=y+xfrry·=−x+yfrrr2=x2+y2 By transforming coordinates into polar coordinates Thus…

Q: Show that fc F dr. is not independent of path. [Hint: Compute and , where  c1 and c2  are the upper…

A: To prove that ∫cFdr is not independent of path. Let C1 be the semi circle which lies above x axis…

Q: Let p(x) = kx* + kx + kx + k,x + kg, x E R be a polynomium without a first degree term whose graph…

A: The given polynomial is: p(x)=k4x4+k3x3+k2x2+k1x+k0

Q: Let f(x, y, z) = x³e" Vz² + 5 and let x = rt², y = r2t², and z = sin(t) cos(r). (a) Draw a tree…

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Q: Let p(x) =-2x* + c,x' + c,x + c,x + c, x ER be a polynomium whose graph insersects the points (-2,…

A: Given. We are given a fourth degree polynomial and also four points on the curve of the polynomial…

Q: * Let A E R"Xn, ĩ E R" \ {0} and A = 0. Prove that if the origin is stable if and only if ī is…

A: Given A∈ℝn×n,x¯∈ℝn\0 and Ax¯=0 To prove that the origin is stable if and only if x¯ is stable.  If…

Q: Exercise 2.8. Verify that q eAt-d satisfies the "martingale property" %3D u-d Sug + Sa(1 – q) =…

A: Given,  q= erΔt - du - d Consider ,  su q + sd (1-q) = su erΔt - du-d +sd1-erΔt - du - d= su erΔt -…

Q: Let A = = اه هب را ره and ve lation R, R2R3 and Ry on A, what Would graph be their directed ام مه…

A: R1=a,a,c,c,b,b,d,d The directed graph is:

Q: 비 az and Given that z = e*, x= 2u+ v, y= .y==. Find using the chain rule. au

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Q: if u=f(x,y), x=g(w) and y=h(w), using chain rule, what is ∂u/∂w?

A: Silution : Given that u = f(x,y)

Q: Compute the Jacobian of the map G(r, s) = (er cosh(s), er sinh(s))

A: The given function is G(r, s) = (er cosh(s), er sinh(s)). Compute the Jacobian as follows.

Q: Let G = (V, E) be bipartite graph, with vertex partition V = XuY. Assume further that • every z in X…

A: Let GV,E be a bipartite graph, with vertex partition V=X∪Y.And every x in X has the same degree dx≥1…

Q: 5. (a) Make a tree diagram for the chain rule for f(x, y, z) = x²y² + y²z² + x²z², x = rt, y = r²t³,…

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Q: give an example or prove it doesn't exist j. an orientation on K44 which contains no sources or…

A: The given statement is,  An orientation on k4,4 which contains no sources or sinks but is not…

Q: Construct a table that displays the number of directed paths of length 1 or 2 between each pair of…

A: Fill table by the number of directed path between two vertices . If the number of directed path…

Q: Show that if, in using the Laplace development, you accidentally multiply the elements of one row by…

A: A 3×3 matrix a11a12a13a21a22a23a31a32a33.

Q: Let F(x, y, z)=z²i+ 2xj+y°k and let S be the graph of z = 4-x² -y², z 20 oriented counterclockwise.…

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Q: If T: H→→H is a bounded self-adjoint linear operator and T‡0, then T"#0. Prove this (a) for n = 2,…

A: Given T:H→H is a bounded self-adjoint linear operator and T≠0. We know that if T is a self adjoint…

Q: Let A ∈ M nxn(F). Show that A is diagonalizable if and only if At isdiagonalizable

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Q: Prove that a complete bipartile graph Ks,s has (s−1)!s!/2 Hamiltonian walks for s >1

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Q: Given the states lp) = 3|0) – 2i|1) and |ø) = |0) + 5|1) , (a) Show that these states obey the…

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Q: Show that the following system undergo a saddle-node bifurcation. Find the vale H= Ho where such a…

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Q: Determine whether the work done along the path C is positive, negative, or zero. c/

A: we know that Work W=∫C F→·dr→

Q: 3) Show that the following graphs Hamiltonian are hot a a) d d 137 c) d) ol

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Q: The linearization at a = 0 to √8+7e is A + Ba. Compute A and B. A B= || ||

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Q: If the Wronskian of f and g is t cos t - sin t, and if u = f+ 2g, v = f - g, find the Wronskian of u…

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Q: Find the Runet'ion FCA] such that =t+ cost and such that

A: Let y"(t)=d2ydt2=t+cos t and y(0) = 1 and y'(0) = 2 Integrating on both sides, ∫y"(t)dt=∫t+cos t dt…

Q: 1. Consider the system ' = 3x + 6xy?, W =x² + 1. Are there any closed orbits? Explain your answer.

A: Given - Consider the system  x' = 3x + 6xy2, y' = x2 + 1. To find - Are there any closed orbits ?…

Q: Evaluate I = Se(sin æ + 7y) dæ + (3x + y) dy for the nonclosed path ABCD in the figure. А 3 (0,0),…

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Q: Compute the Jacobian of the mapping. G(r, t) = (2re", 3 + 8e")

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Q: 19: Find two linear operator T, and T,on V(R) such that T,T, = 0 but T,7, - 0.

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Q: if A=x²ya, - ya, find the circulation of A around the closed path shown in the Figure

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Q: Given w = f(x, y, z), x = g1(r, s), y = g2(r, s), and z = 93(r, s), write the chain rule for ow and…

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Q: The work af the veeken fieled aleng the edge y the set Path one Hime in an onti -elockwise wes Ast 2…

A: Given : vector field F→x, y=x-y2, x+y2 and set D=x, y∈ℝ2 : 1≤x-32+y2≤4 , y≥0 To find : the work of…

Q: 4. Show that the distance between the two points z1 and z2 in an Argand diagram is |z1 – z2). In…

A: (6) z-1=2 Given that:The points z=x+iy satisfies the condition z-1=2 The complex number z=x+iy…

Q: Find the domain corresponding to the inner loop of r=1+2cos(theta)

A: The domain  inner loop of r=1+2cos(θ)  is 0,1