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ан 2. The same as (1) except for the enthalpy H. In class we saw that...
4. The enthalpy H may be written as a function of temperature T and pressure P. If we have a system whose composition remains constant and using Maxwell's equations and the total differential, we...
4. The enthalpy H may be written as a function of temperature T and pressure P. If we have a system whose composition remains constant and using Maxwell's equations and the total differential, we can write dH as avdP where Cp is the heat capacity at constant pressure and the subscript of P on the partial derivative represents the partial of volume with respect to temperature holding pressure connstant. Find the change in enthalpy (A) for an ideal gas undergoing...
1. In class, we saw that immunization reduces a firm or investor's exposure to interest rate...
1. In class, we saw that immunization reduces a firm or investor's exposure to interest rate risk by matching the durations of assets and liabilities. We also know that duration breaks down as a good approximation to interest rate sensitivity for large(r) changes in rates. Could immunization be implemented with a convexity adjustment? Why or why not?
Question 2 Consider the differential equation We saw in class that one solution is the Bessel function (a) Suppose we h...
Question 2 Consider the differential equation We saw in class that one solution is the Bessel function (a) Suppose we have a solution to this ODE in the form y-Σχ0CnXntr where cn 0. By considering the first term of this series show that r must satisfy r2-4-0 (and hence that r = 2 or r =-2) (b) Show that any solution of the form y-ca:0G,2n-2 must satisfy C0 (c) From the theory about singular solutions we know that a linearly...
5. In class we saw that the function r(u, v) = (sin u, (2 + cos...
5. In class we saw that the function r(u, v) = (sin u, (2 + cos u) cos v, (2 + cos u) sin v), 0<u<27, 050521 parametrizes a torus T, which is depicted below. (a) Calculate ||ru x rull. (b) Show that T is smooth. (c) Find the equation of the tangent plane to T at (0,). (d) Find the surface area of T (e) Earlier in the semester, we observed that a torus can be built out of...
1. Using picture or pictures, explain (5) (a) h and under what condition Ax Ap h/2....
1. Using picture or pictures, explain (5) (a) h and under what condition Ax Ap h/2. Ax Ap The meaning of each symbol in the two expressions <mÔjk>, <kIOk> and meanings of the expressions. Using <m |Ö)k>, comment on how O operates and the condition of a Hermitian operator. (8) (b) (5) The scattering and the bound state problems. (c) Why can the solutions a free particle in two-dimension be written as (1/2n) e[i(kx+ kyy)], where ky and ky are...
In the Stackelberg model we saw in class there were two firms 1 and 2. Suppose...
In the Stackelberg model we saw in class there were two firms 1 and 2. Suppose that the market demand is p(Q) = 60−Q, where as in class Q is the aggregate quantity. The const function for firm 1 is c1(q1) = 10q1 and the cost function for firm 2 is c2(q2) = q2. Firm 1 is the leader and Firm 2 is the follower. (a) Solve for the follow’s reaction function, and the leader’s maximization problem. (b) Describe the...
Consider the space V of continuous functions on (0, 1] with the 2-norm 12 J f2 We saw in class that V is an incompl...
Consider the space V of continuous functions on (0, 1] with the 2-norm 12 J f2 We saw in class that V is an incomplete normed linear space. (a) For a continuous function p on [0, 1], define a linear map Mp: V-V by Mpf-pf. Show that Mp is bounded and calculate its norm. (b) Is A = (Mplp E C(0,1)) a Banach algebra? Note that B(V) is necessarily incomplete, so it is not enough to prove that A is...
06) Suppose a paramagnetic system that is under the action of an auxiliary (magnetic) field H....
06) Suppose a paramagnetic system that is under the action of an auxiliary (magnetic) field H. Thus, the work involved, it has to be that the work involved in a reversible process is described as đW = 10Hdm. where m is the total magnetic dipole moment of the system and u0 is the magnetic permeability of the vacuum. a) Determine the expression of the differential du of the internal energy U and indicate the two independent natural variables associated with...
06) Suppose a paramagnetic system that is under the action of an auxiliary (magnetic) field H....
06) Suppose a paramagnetic system that is under the action of an auxiliary (magnetic) field H. Thus, the work involved, it has to be that the work involved in a reversible process is described as đW = 10Hdm. where m is the total magnetic dipole moment of the system and u0 is the magnetic permeability of the vacuum. a) Determine the expression of the differential du of the internal energy U and indicate the two independent natural variables associated with...
plz print ur answer Question2 Consider the differential equation We saw in class that one solution is the Bessel functi...
plz print ur answer
Question2 Consider the differential equation We saw in class that one solution is the Bessel function (-1)" ( 2n+2 2+n)! 2) n=0 (a) Suppose we have a solution to this ODE in the form y = Σ。:0cmFn+r where 0. By considering the first term of this series show that r must satisfy r2-4=0(and hence that r = 2 or r=-2). (b) Show that any solution of the form y-must satisfy co c) From the theory about...
4. The enthalpy H may be written as a function of temperature T and pressure P. If we have a system whose composition remains constant and using Maxwell's equations and the total differential, we can write dH as avdP where Cp is the heat capacity at constant pressure and the subscript of P on the partial derivative represents the partial of volume with respect to temperature holding pressure connstant. Find the change in enthalpy (A) for an ideal gas undergoing...
1. In class, we saw that immunization reduces a firm or investor's exposure to interest rate risk by matching the durations of assets and liabilities. We also know that duration breaks down as a good approximation to interest rate sensitivity for large(r) changes in rates. Could immunization be implemented with a convexity adjustment? Why or why not?
Question 2 Consider the differential equation We saw in class that one solution is the Bessel function (a) Suppose we have a solution to this ODE in the form y-Σχ0CnXntr where cn 0. By considering the first term of this series show that r must satisfy r2-4-0 (and hence that r = 2 or r =-2) (b) Show that any solution of the form y-ca:0G,2n-2 must satisfy C0 (c) From the theory about singular solutions we know that a linearly...
5. In class we saw that the function r(u, v) = (sin u, (2 + cos u) cos v, (2 + cos u) sin v), 0<u<27, 050521 parametrizes a torus T, which is depicted below. (a) Calculate ||ru x rull. (b) Show that T is smooth. (c) Find the equation of the tangent plane to T at (0,). (d) Find the surface area of T (e) Earlier in the semester, we observed that a torus can be built out of...
1. Using picture or pictures, explain (5) (a) h and under what condition Ax Ap h/2. Ax Ap The meaning of each symbol in the two expressions <mÔjk>, <kIOk> and meanings of the expressions. Using <m |Ö)k>, comment on how O operates and the condition of a Hermitian operator. (8) (b) (5) The scattering and the bound state problems. (c) Why can the solutions a free particle in two-dimension be written as (1/2n) e[i(kx+ kyy)], where ky and ky are...
Consider the space V of continuous functions on (0, 1] with the 2-norm 12 J f2 We saw in class that V is an incomplete normed linear space. (a) For a continuous function p on [0, 1], define a linear map Mp: V-V by Mpf-pf. Show that Mp is bounded and calculate its norm. (b) Is A = (Mplp E C(0,1)) a Banach algebra? Note that B(V) is necessarily incomplete, so it is not enough to prove that A is...
06) Suppose a paramagnetic system that is under the action of an auxiliary (magnetic) field H. Thus, the work involved, it has to be that the work involved in a reversible process is described as đW = 10Hdm. where m is the total magnetic dipole moment of the system and u0 is the magnetic permeability of the vacuum. a) Determine the expression of the differential du of the internal energy U and indicate the two independent natural variables associated with...
plz print ur answer
Question2 Consider the differential equation We saw in class that one solution is the Bessel function (-1)" ( 2n+2 2+n)! 2) n=0 (a) Suppose we have a solution to this ODE in the form y = Σ。:0cmFn+r where 0. By considering the first term of this series show that r must satisfy r2-4=0(and hence that r = 2 or r=-2). (b) Show that any solution of the form y-must satisfy co c) From the theory about...
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