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3. Show that the Christoffel symbol must transform according to eq. (2) not only in flat...
R3. Problem 4. (3+2+3 pts) Consider an arbitrary skew-symmetric tensor 22: R3 (i) Show that I...
R3. Problem 4. (3+2+3 pts) Consider an arbitrary skew-symmetric tensor 22: R3 (i) Show that I be represented by a vector w as follows: VE R3 Ωυ =ωXυ. (ii) Next, show that cofactor of 12 equals wow. (iii) Prove that 1+1 is always invertible.
114 KINEMATICS OF 3.5.3 Infinitesimal Rotation Tensor e displacement gradient tensor can be expre...
Equation 3.5.10 is below
We were unable to transcribe this image114 KINEMATICS OF 3.5.3 Infinitesimal Rotation Tensor e displacement gradient tensor can be expressed as the sum of a tensor and a skew symmetric tensor. We have where the symmetric part is similar to the infinitesimal strain tensor (and a when VuVoul << 1), and the skew symmetric part is known as the infinitesimal rotation tensor 3.i1 We note that there is no restriction placed on the magnitude of Vu...
Can you please answer questions 1-6，thank you a lot！Thumbs up for great answer，Thx！ Remember: to show...
Can
you please answer questions 1-6，thank you a lot！Thumbs up for great
answer，Thx！
Remember: to show that a property is true you must check every possibility (probably using variables and general vectors). To show that a property is false you only need to give one counterexample. 1. Find a set of vectors in R2 which is closed under vector addition but not scalar multiplication. 2. Find a set of vectors in R? which is closed under scalar multiplication but not...
Problem 3. Extensive experimental evidence in the area of image compression has shown that the Discrete...
Problem 3. Extensive experimental evidence in the area of image compression has shown that the Discrete Cosine Transform (DCT) of image patches is a very good approximation to their PCA. It is also well known that all but one of the DCT coefficients (features) have zero mean, and only one has non-zero mean. The latter is the so-called DC coefficient because it results from projecting the image patch into the vector 1 = (1, 1, , 1)T and, therefore, is...
QUESTION 3 Show that the Neumann problem = 9 on a. vu = 0 in 2,...
QUESTION 3 Show that the Neumann problem = 9 on a. vu = 0 in 2, ди an has a unique solution only up to an additive constant, i.e. if u and un are two solutions, then U1 - U2 =C. Hint: Use the identity div (uVu) = Vul? + uvºu, 2 ди where Vul ar vector field u Vu. And then apply the Gauss' Divergence Theorem to the
[132 2 2 3 4 17 marks] Question 4 A plane wave is travelling in a...
[132 2 2 3 4 17 marks] Question 4 A plane wave is travelling in a vacuum in the +z-direction with wavenumber k and angular frequency . It is linearly polarised in the x-direction, and has electric field given by E(t, z) Eo Cos(kz - wt)f This wave is normally incident on a perfectly electrically conducting, semi-infinite slab in the region z > 0 and the resulting field in vacuum (z < 0) is a superposition of the incident and...
3, (10 Points) Show that the vector potential A for the quadrupole arrangement is cos e wtol Hint...
3, (10 Points) Show that the vector potential A for the quadrupole arrangement is cos e wtol Hint: last week we already calculated Griffiths Eq. 11.16 to second order for a dipole. Again, you can use problem 1 to simplify the 1/R terms. Again, you only need teo expand the numerator to first order . (5 Extra Credit Points) You now have A and V. Calculate E and B. 1. (5 Points) In the previous homework, I claimed that the...
fluid mechanics just part 3 and 4 show all steps please These are typical questions to...
fluid mechanics
just part 3 and 4
show all steps please
These are typical questions to answer when examining difficult velocity and acceleration field questions. A three-dimensional velocity field is given by u = x?v=-3xy, and w = 3x + 2 y. Determine the acceleration vector. (a) Are all three components of the velocity field included in this problem? yes (b) In what dimensions can this velocity change? In other words, what independent variables are given in the velocity field?...
SOLVE ANY (2.b) Pts 15 Suppose A' is any matrix whe row reduced echelon form A Show there is a matris D' Mn a wuch thnt A iDMa such that A I Question 3: The matrix condition B2B Ps 30: In this...
SOLVE ANY
(2.b) Pts 15 Suppose A' is any matrix whe row reduced echelon form A Show there is a matris D' Mn a wuch thnt A iDMa such that A I Question 3: The matrix condition B2B Ps 30: In this problen B is n (3.a) Pts 10: If a is an eigenvector for B, what is the attached eigenvalue (3. b) Pts 10: Irge R", why is BU) perpendieular to Bur square, n x n, smmetric matris satisfying...
Please show full working. Please only answer if you know how. Calculate the 2-D flux of a constant vector field F-a across a curve C : r(t) :r(t)s l y/ t 3. (z < t < b. İll(licatiu" il . Wha...
Please show full working.
Please only answer if you know how.
Calculate the 2-D flux of a constant vector field F-a across a curve C : r(t) :r(t)s l y/ t 3. (z < t < b. İll(licatiu" il . What is the ilux when the curve C is closed? Explain e positive direction
Calculate the 2-D flux of a constant vector field F-a across a curve C : r(t) :r(t)s l y/ t 3. (z
R3. Problem 4. (3+2+3 pts) Consider an arbitrary skew-symmetric tensor 22: R3 (i) Show that I be represented by a vector w as follows: VE R3 Ωυ =ωXυ. (ii) Next, show that cofactor of 12 equals wow. (iii) Prove that 1+1 is always invertible.
Equation 3.5.10 is below
We were unable to transcribe this image114 KINEMATICS OF 3.5.3 Infinitesimal Rotation Tensor e displacement gradient tensor can be expressed as the sum of a tensor and a skew symmetric tensor. We have where the symmetric part is similar to the infinitesimal strain tensor (and a when VuVoul << 1), and the skew symmetric part is known as the infinitesimal rotation tensor 3.i1 We note that there is no restriction placed on the magnitude of Vu...
Can
you please answer questions 1-6，thank you a lot！Thumbs up for great
answer，Thx！
Remember: to show that a property is true you must check every possibility (probably using variables and general vectors). To show that a property is false you only need to give one counterexample. 1. Find a set of vectors in R2 which is closed under vector addition but not scalar multiplication. 2. Find a set of vectors in R? which is closed under scalar multiplication but not...
Problem 3. Extensive experimental evidence in the area of image compression has shown that the Discrete Cosine Transform (DCT) of image patches is a very good approximation to their PCA. It is also well known that all but one of the DCT coefficients (features) have zero mean, and only one has non-zero mean. The latter is the so-called DC coefficient because it results from projecting the image patch into the vector 1 = (1, 1, , 1)T and, therefore, is...
QUESTION 3 Show that the Neumann problem = 9 on a. vu = 0 in 2, ди an has a unique solution only up to an additive constant, i.e. if u and un are two solutions, then U1 - U2 =C. Hint: Use the identity div (uVu) = Vul? + uvºu, 2 ди where Vul ar vector field u Vu. And then apply the Gauss' Divergence Theorem to the
[132 2 2 3 4 17 marks] Question 4 A plane wave is travelling in a vacuum in the +z-direction with wavenumber k and angular frequency . It is linearly polarised in the x-direction, and has electric field given by E(t, z) Eo Cos(kz - wt)f This wave is normally incident on a perfectly electrically conducting, semi-infinite slab in the region z > 0 and the resulting field in vacuum (z < 0) is a superposition of the incident and...
3, (10 Points) Show that the vector potential A for the quadrupole arrangement is cos e wtol Hint: last week we already calculated Griffiths Eq. 11.16 to second order for a dipole. Again, you can use problem 1 to simplify the 1/R terms. Again, you only need teo expand the numerator to first order . (5 Extra Credit Points) You now have A and V. Calculate E and B. 1. (5 Points) In the previous homework, I claimed that the...
fluid mechanics
just part 3 and 4
show all steps please
These are typical questions to answer when examining difficult velocity and acceleration field questions. A three-dimensional velocity field is given by u = x?v=-3xy, and w = 3x + 2 y. Determine the acceleration vector. (a) Are all three components of the velocity field included in this problem? yes (b) In what dimensions can this velocity change? In other words, what independent variables are given in the velocity field?...
SOLVE ANY
(2.b) Pts 15 Suppose A' is any matrix whe row reduced echelon form A Show there is a matris D' Mn a wuch thnt A iDMa such that A I Question 3: The matrix condition B2B Ps 30: In this problen B is n (3.a) Pts 10: If a is an eigenvector for B, what is the attached eigenvalue (3. b) Pts 10: Irge R", why is BU) perpendieular to Bur square, n x n, smmetric matris satisfying...
Please show full working.
Please only answer if you know how.
Calculate the 2-D flux of a constant vector field F-a across a curve C : r(t) :r(t)s l y/ t 3. (z < t < b. İll(licatiu" il . What is the ilux when the curve C is closed? Explain e positive direction
Calculate the 2-D flux of a constant vector field F-a across a curve C : r(t) :r(t)s l y/ t 3. (z
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