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Consider Z3s. Find all generators for Z3s. List all subgroups of Z36, and find all inclusions...
1. 2. Use the Correspondence Theorem to find all subgroups of S that contain K = {1, (12)(3 4), (13)(2 4), (1 4)(2 3)], Draw its lattice diagram If α : G → C6 is an onto group homomorphism and \ker(...
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Use the Correspondence Theorem to find all subgroups of S that contain K = {1, (12)(3 4), (13)(2 4), (1 4)(2 3)], Draw its lattice diagram If α : G → C6 is an onto group homomorphism and \ker(a)-3, show that \G\ = 18 and G has normal subgroups of orders 3, 6 and 9.
Use the Correspondence Theorem to find all subgroups of S that contain K = {1, (12)(3 4), (13)(2 4), (1 4)(2 3)], Draw...
Consider the additive group ℤ(20). (a) How many subgroups does ℤ(20) have? List all the subgroups....
Consider the additive group ℤ(20). (a) How many subgroups does ℤ(20) have? List all the subgroups. For each of them, give at least one generator. (b) Describe the subgroup < 2 > ∩ < 5 > (give all the elements, order of the group, and a generator). (c) Describe the subgroup <2, 5> (give all the elements, order of the group, and a generator).
10.1.11 (Cubic map) Consider the map x,* -3x,-x a) Find all the fixed points and classify....
10.1.11 (Cubic map) Consider the map x,* -3x,-x a) Find all the fixed points and classify. their stability. b) Draw a cobweb staring at x1.9. c) Draw a cobweb starting at x 2.1. d) Try to explain the dramatic difference between the orbits found in parts (b) and (c). For instance, can you prove that the orbit in (b) will remain bounded for all n ? Or that I → oo in (c)?
(more questions will be posted today in about 6 hrs from now.) December 8, 2018 WORK ALL PROBLEMS. SHOW WORK & INDICATE REASONING \ 1.) Let σ-(13524)(2376)(4162)(3745). Express σ as a product...
(more questions will be posted today in about 6 hrs
from now.)
December 8, 2018 WORK ALL PROBLEMS. SHOW WORK & INDICATE REASONING \ 1.) Let σ-(13524)(2376)(4162)(3745). Express σ as a product of disjoint cycles Express σ as a product of 2 cycles. Determine the inverse of σ. Determine the order of ơ. Determine the orbits of ơ 2) Let ф : G H be a homomorphism from group G to group H. Show that G is. one-to-one if and...
can please explain why F(sigma)= u? We consider the PDE: for given o(t) € H|(12) find...
can please explain why F(sigma)= u?
We consider the PDE: for given o(t) € H|(12) find the (weak) solution u € H}(2) of V. (g(x)Vu(x)) = 1. The corresponding parameter-to-solution map is defined as F: D(F):= H (1) C H²(2) L’(1) F(o)= u uc H (12) c L’(2) solving b(u, w;o) = f(w) for all w e H7(), b(u, w; 0) := ( D2.Vwdi, f(w):=- / w dr. The associated inverse problem is for u E L(12) find o E...
2. Consider tossing a coin twice. Denote H ="head" and T ="tail" (a) List all outcomes...
2. Consider tossing a coin twice. Denote H ="head" and T ="tail" (a) List all outcomes in the sample space S (b) Let X count the number of heads. List all outcomes in the events Ao = {X = 0}, Ai = {X=1 and A2 {X = 2}. Are all the events Ao,A1,A2 mutually exclusive? Explain. (c) Suppose P(H) = 0.6. Find the probability mass function of X: f(x) = P{X =x} (d) Find the cumulative distribution function of X:...
Consider the situation where you have three game chips, each labeled with one of the the...
Consider the situation where you have three game chips, each labeled with one of the the numbers 2, 3, and 8 in a hat: a. If you draw out 2 chips without replacement between each chip draw, list the entire sample space of possible results that can occur in the draw. Use the three events are defined as follows, to answer parts b through n below: Event A: the sum of the 2 drawn numbers is even. Event B: the...
Use phyton TheSieve of Eratosthonesis an algorithm to find all the prime numbers between 1 andsome integerN. It can be implemented with nestedforloops:(a) Make a list of all the integers from 2 throug...
Use phyton TheSieve of Eratosthonesis an algorithm to find all the prime numbers between 1 andsome integerN. It can be implemented with nestedforloops:(a) Make a list of all the integers from 2 throughN.(b) Cross off all the multiples of 2 (except for 2 itself). The smallest number that remains(after 2) is 3.(c) Cross off all the multiples of 3 (except for 3 itself). The smallest number that remainsis 5.(d) Cross off all the multiples of 5 (except for 5 itself)....
(2) Consider the 'square' of the derivative operator in one dimension, ie., D"--2 ie. Find all...
(2) Consider the 'square' of the derivative operator in one dimension, ie., D"--2 ie. Find all solutions of without any restrictions on , ie.,-oo< (2b) Are there limitations on a? (e.g., any complex number, any real number, only positive real number, integers only, etc.). In mathematis? In physics, when the operator is meant to represent an observable? (2c) Can you find a solution to (4) which is not a solution to DIf(x) Vaf(x)? Hint: try trig functions! Note the 'philosophical'...
(9 points) You are interested in studying recombination frequencies in wasps. You identify a queen that...
(9 points) You are interested in studying recombination frequencies in wasps. You identify a queen that is heterozygous at three different loci on chromosome 5: G, H, and R. As queen wasps can produce haploid male offspring without fertilizing their eggs, you decide to look only at the genotypes of her male offspring in your analysis. Below is a list of the genotypes of her male offspring, and the number of individuals that fall into each genotypic class. 92 168...
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Use the Correspondence Theorem to find all subgroups of S that contain K = {1, (12)(3 4), (13)(2 4), (1 4)(2 3)], Draw its lattice diagram If α : G → C6 is an onto group homomorphism and \ker(a)-3, show that \G\ = 18 and G has normal subgroups of orders 3, 6 and 9.
Use the Correspondence Theorem to find all subgroups of S that contain K = {1, (12)(3 4), (13)(2 4), (1 4)(2 3)], Draw...
10.1.11 (Cubic map) Consider the map x,* -3x,-x a) Find all the fixed points and classify. their stability. b) Draw a cobweb staring at x1.9. c) Draw a cobweb starting at x 2.1. d) Try to explain the dramatic difference between the orbits found in parts (b) and (c). For instance, can you prove that the orbit in (b) will remain bounded for all n ? Or that I → oo in (c)?
(more questions will be posted today in about 6 hrs
from now.)
December 8, 2018 WORK ALL PROBLEMS. SHOW WORK & INDICATE REASONING \ 1.) Let σ-(13524)(2376)(4162)(3745). Express σ as a product of disjoint cycles Express σ as a product of 2 cycles. Determine the inverse of σ. Determine the order of ơ. Determine the orbits of ơ 2) Let ф : G H be a homomorphism from group G to group H. Show that G is. one-to-one if and...
can please explain why F(sigma)= u?
We consider the PDE: for given o(t) € H|(12) find the (weak) solution u € H}(2) of V. (g(x)Vu(x)) = 1. The corresponding parameter-to-solution map is defined as F: D(F):= H (1) C H²(2) L’(1) F(o)= u uc H (12) c L’(2) solving b(u, w;o) = f(w) for all w e H7(), b(u, w; 0) := ( D2.Vwdi, f(w):=- / w dr. The associated inverse problem is for u E L(12) find o E...
2. Consider tossing a coin twice. Denote H ="head" and T ="tail" (a) List all outcomes in the sample space S (b) Let X count the number of heads. List all outcomes in the events Ao = {X = 0}, Ai = {X=1 and A2 {X = 2}. Are all the events Ao,A1,A2 mutually exclusive? Explain. (c) Suppose P(H) = 0.6. Find the probability mass function of X: f(x) = P{X =x} (d) Find the cumulative distribution function of X:...
Consider the situation where you have three game chips, each labeled with one of the the numbers 2, 3, and 8 in a hat: a. If you draw out 2 chips without replacement between each chip draw, list the entire sample space of possible results that can occur in the draw. Use the three events are defined as follows, to answer parts b through n below: Event A: the sum of the 2 drawn numbers is even. Event B: the...
(2) Consider the 'square' of the derivative operator in one dimension, ie., D"--2 ie. Find all solutions of without any restrictions on , ie.,-oo< (2b) Are there limitations on a? (e.g., any complex number, any real number, only positive real number, integers only, etc.). In mathematis? In physics, when the operator is meant to represent an observable? (2c) Can you find a solution to (4) which is not a solution to DIf(x) Vaf(x)? Hint: try trig functions! Note the 'philosophical'...
(9 points) You are interested in studying recombination frequencies in wasps. You identify a queen that is heterozygous at three different loci on chromosome 5: G, H, and R. As queen wasps can produce haploid male offspring without fertilizing their eggs, you decide to look only at the genotypes of her male offspring in your analysis. Below is a list of the genotypes of her male offspring, and the number of individuals that fall into each genotypic class. 92 168...
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