半群理论作业代做 MT5863代写 半群理论代写 数学作业代写
262MT5863 Semigroup theory: Problem sheet 3 半群理论作业代做 Binary relations and equivalences 3-1. Let X = {1, 2, 3, 4, 5, 6}, let ρ be the equivalence relation on X with equivalence classes {1,...
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离散数学与图论代写 Practice Class 4 1. Give recursive definitions of the following sequences. (a) The sequence of powers of 2: 20 = 1, and for n ≥ 1, _
1. Give recursive definitions of the following sequences.
(a) The sequence of powers of 2: 20 = 1, and for n ≥ 1, _______
(b) The Catalan numbers: c0 = 1, and for n ≥ 1, _______
What is the correct order of the lines?
3. Consider the sequence defined by a0 = 0, an = an−1 + 2n for n ≥ 1.
(a) Unravelling gives the non-closed formula _______
(b) Summing the arithmetic progression gives the closed formula _______
(c) Check that the formula in the previous part satisfies the recurrence relation: _______
4. Consider the recurrence relation an = an−1 + 6an−2, for n ≥ 2.
(a) What is the characteristic polynomial?
(b) What are the roots of this polynomial? 离散数学与图论代写
(c) Write down the general solution: _______
(d) Find the solution when a0 = 1, a1 = −1:_______
5. Consider the recurrence relation an = −2an−1 − an−2, for n ≥ 2.
(a) What is the characteristic polynomial?
(b) What are the roots of this polynomial?
(c) Write down the general solution: _______
(d) Find the solution when a0 = 1, a1 = −3: _______
6. Consider the recurrence relation an = −an−2, for n ≥ 2.
(a) What is the characteristic polynomial?
(b) What are the roots of this polynomial?
(c) Write down the general solution: _______
(d) If a0 = 0 and a1 = 1, what is a7?
1. Consider the recurrence relation an = 4an−1 − 4an−2 + 3n + 2, for n ≥ 2.
(a) If pn is a particular solution of this recurrence, the general solution is _______ where bn is a general solution of the homogeneous recurrence relation, i.e.
bn = 4bn−1 − 4bn−2.
(b) The characteristic polynomial of the homogeneous recurrence is x2 − 4x + 4.
Hence _______
(c) A particular solution of the form pn = An + B is _______
(d) Find the solution of the original recurrence when a0 = 15, a1 = 21: _______
2. Write down the general solution of each of the following recurrence relations, by finding a particular solution of the stated form.
(a) an = 3an−1 + 2 for n ≥ 1; pn = A.
(b) an = 2an−1 + n + 1 for n ≥ 1; pn = An + B.
(c) an = 3an−1 − 2n for n ≥ 1; pn = A2n.
4.For each of the sequences (a)–(g), write the number (i)–(vii) of its generating function.
(a) 1, 2, 22 , 23 , · · · _______
(b) 1, 1, 1, 1, · · · _______
(c) 3, 2, 1, 0, 0, 0, · · · _______
(d) 1, 2, 3, 4, 5, · · · _______
(e) 0, 1, 2, 3, 4, · · · _______
(f) 0, 0, 1, 2, 3, 4, · · · _______
(g) 2, 3, 4, 5, 6, · · · _______
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MT5863 Semigroup theory: Problem sheet 3 半群理论作业代做 Binary relations and equivalences 3-1. Let X = {1, 2, 3, 4, 5, 6}, let ρ be the equivalence relation on X with equivalence classes {1,...
View detailsMath 541 HW1 - Linear Algebra Refresher 数学线性代数代写 Remarks: A) Definition is just a definition, there is no need to justify or explain it. B) Answers to questions with proofs should b...
View detailsMATH5806 Applied Regression Analysis Mid-session Test 应用回归分析作业代写 Note: • This assessment is due Thursday 30th June (Week 5), 2:30pm and must be uploaded to Moodle. You have 1.5 ho...
View detailsMath 2415 Final Exam 数学考试代做 To get full credit you must show ALL your work. The problems must be solved without any assistance of others or the usage of unauthorized material To get fu...
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