Take the smallest cellular structure forthe circle X = S1 consisting
of a single 0-cell and a single 1-cell. Let Y be the same circle with two 0-cells and two
1-cells with the ends attached to the two different 0-cells. Count (in particular, describe)
all possible (up to homotopy) cellular maps X → Y and Y → X

question related to Topological data analysis 2

Take the smallest cellular structure forthe circle X = S1 consisting
of a single 0-cell and a single 1-cell. Let Y be the same circle with two 0-cells and two
1-cells with the ends attached to the two different 0-cells. Count (in particular, describe)
all possible (up to homotopy) cellular maps X → Y and Y → X

1.Evaluate the integral C where C is x=t^3 and y=t, 0 ≤ t ≤ 1
2.Find the area of the surface with vectorial equation r(u,v)=<u,u sinv, cu >, 0 ≤ u ≤ h, 0≤ v ≤ 2pi

3) The Gross method of apportionment works as follows: Assign each state its lower quota. If k states remain to be assigned, then assign them to the k largest states.

a) Does the Gross method satisfy Quota rule?

b) Does the Gross method satisfy Population monotonicity?

Suppose C_t is the concentration of a drug in the bloodstream t hours after the initial dose is administered. Suppose the initial dose C₂was 217.6 ug/mL and suppose that every hour is administered 174 g/mL. If the body metabolizes and eliminates 54% of the concentration of the drug C_t over a period of one hour; determine C₂, the concentration of the drug in the bloodstream two hours after the initial dose is administered.

Response at two decimal valors.

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You buy a sofa for $1499, 2 chairs (each at $299),$249 coffee table,$199 end table, $153 for tax, $75 for delivery. What is the minimum monthly payment using the promotion to the nearest cent?

prove that the product of 2 dilation is either a translation or a dilation

Let G be a group acting on a set S, and let H be a group acting on a set T. The product group G × H acts on the disjoint union S ∪ T as follows. For all g ∈ G, h ∈ H,

s ∈ S and t ∈ T,

(g, h) · s = g · s, (g, h) · t = h · t.

(a) Consider the groups G = C₄, H = C₅, each acting as usual. Calculate the cyclic polynomial Z_C4×C5 .

(b) Explain why in general Z_G×H = Z_GZ_H.

how does word fire equal 166538? clues decoded. each letter to its number begins the code. times the days in the longest month is next owed. raised to the letters position less one. the sum of the letters combined must be won. do all work on one letter first

Solve the Boundary Value Problem, PDE: U_tt-a²u_xx=0, 0≤x≤1, 0≤t<∞

BCs: u(0,t)=0

u(1,t)=cos(t)

u(x,0)=0

u_t(x,0)=0

Please solve questions 1 and 2. Please show all work and all steps.

1.) Find the solution x_a of the Bessel equation t²x'' + tx' + t²x = 0 such that x_a(0) = a

2.) Find the solution x_a of the Bessel equation t²x'' + tx' + (t²-1)x = 0 such that x'_a(0) = a

This is a Matlab Question

Create MATLAB PROGRAM that can solve First Order Linear Differential Equation ( 1 example contains condition and the other does not have condition).

1. ty′ + 2y = t^2 − t + 1, y(1)=12

The correct answer is y(t) = 1/4 t^2 − 1/3 t + 1/2 + 1/12t^2

2. (x-1) dy/dx + 2y = (x+1)^2

The correct answer is y = (x(x+1) / x-1 ) + C(x+1) / x-1

The correct answer is

Let R be a ring (not necessarily commutative), and let X denote the set of two-sided ideals

of R.

(i) Show that X is a poset with respect to to set-theoretic inclusion, ⊂.

(ii) Show that with respect to the operations I ∩ J and I + J (candidates for meet and join;

remember that I+J consists of the set of sums, {i + j} where i ∈ I and j ∈ J) respectively,

X is a lattice.

(iii) Give an example of a commutative ring for which the corresponding X is not a Boolean

algebra, and one for which it is.