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Modern Algebra
Ring Theory (XXXIII)
Polynomials over the Rational Field
Euclidean Ring
Irreducible Polynomial
Let D be a Euclidean ring, F its field of quotients. Prove the Gauss lemma for polynomials with coefficients in D factored as product of polynomials with coefficients in F.
How are the vertex and axis of symmetry related on a parabola? Please explain with the help of an example.
Construct an explicit deformation retraction of the torus with one point deleted onto a graph consisting of two circles intersecting in a point, namely, longitude and meridian circles of the torus.
Choose h and k such that the system has (a) no solution, (b) a unique solution and (c) many solutions.
A system consists of four subassemblies connected in series. The individuak subassembly reliabilities are as follows:
Find the test value for two population variances
What is the probability that a randomly selected individual from this population earns less than $60,000 per year? If a randomly selected individual is observed to earn less than $60,000 per year, what is the probability that this person is a man?
Normal subgroups, Second Theorem of Isomorphism, Conjugates and Cyclic Groups
Matrix of transition probabilities. The daily price of a farm commodity is up, down, or unchanged from the day before. Analysts predict that if the last price was down, there is a .5 probability the next will be down,
Carol and David decide to play a game as follows: Carol draws and keeps a card from a shuffled pack number 1 to 6.
Important information about Elliptic boundary value problem (lap) means the Laplacian Vrr means the second derivative of V with respect to r
Setup a network Flow for this Problem using nodes and links but do not solve for optimal solution, A manufacturer must produce a certain product in sufficient quantity to meet contracted sales in the next four months
Based on the parallelogram law, show that the norms ||.||_1 (1-norm) and ||.||_infinity ( infinity or maximum norm) in R^2 are not induced by any inner product.
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