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You need to decide between a discrete-time (one data point per hour) or a continuous-time model. In the discrete model, at each step first update the number of virus copies according to the growth ...

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If we ignore the title then there is no actual constraint on $\alpha$ and $\beta.$ For arbitrary $\alpha$ and $\beta$ you can set $a=\alpha,$ $b=0$ and $c=\beta$ and the quadratic equation is ...

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The exponential mapping creates a metric of the form \begin{align*} ds^2=dr^2+\psi(r,\theta)^2d\theta^2, \end{align*} locally in a sufficiently small neighbourhood of any point $p$ on a two-...

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Let $(x_i,y_i)$ denote the coordinates of the $i$-th vertex and $d_i(x,y)$ the function given by the signed distance to the side (as an infinite line) opposite the $i$-th vertex: $$d_1(x,y)=\frac{(... View answer 1 answers 0 votes 19 views Accepted answer 2 votes To avoid complications from describing how the car should behave in curves, let us suppose it to have the shape of an open disk of diameter w. Then your condition (in addition to pathwise ... View answer 1 answers 0 votes 46 views Accepted answer 0 votes I think there is a factor 2 missing in the product term when you are working out the square of (\cos\phi+\cos\psi), and again with the sines. View answer 2 answers -2 votes 103 views Accepted answer 5 votes You cannot add two equations joined by a logical or. The original statement is false so there is nothing to prove. If you replace the and in the original statement with or, then the or in your proof ... View answer 1 answers 1 votes 64 views Accepted answer 1 votes (Updated after modification of question) If A is completely continuous then the closure of its range does not include all of \Omega, since the unit sphere is closed but not compact. This ... View answer 1 answers 0 votes 105 views Accepted answer 1 votes Let d=2, (u^1,u^2)=(x_2,-x_1). View answer 3 answers 0 votes 218 views 0 votes It sounds nicer if you eliminate the variable: "All ICS students spend more than 4 hrs surfing" Idem + ambiguous subclause + get rid of the technical word false: "There is an ICS student who hasn't ... View answer 3 answers 0 votes 859 views 2 votes In the calculation of the limit you have substituted r=1/x. The limit is not \frac{r\sin r}r as r goes to 0 but (the same expression) as r goes to \pm\infty. View answer 8 answers 4 votes 10k views 1 votes The inequality is true at x=1 and it holds between the derivatives for x>1 (and the inverse inequality holds between the derivatives for 0<x<1, so that gives another proof for that ... View answer 1 answers 2 votes 28 views Accepted answer 0 votes I am going to assume that you want to find a c_2 for any given K and c_1 such that the inequality holds for arbitrary a and b. Such c_2 cannot be found for all K and c_1. For example ... View answer 1 answers 3 votes 669 views Accepted answer 2 votes It is unlikely that this is possible in a time complexity that you consider reasonable, because some problems that resemble the travelling salesman problem very closely can be modeled as special cases ... View answer 4 answers 2 votes 48 views 1 votes Yes you are. Write i  and i+5 explicitly as multiples of k  and subtract to conclude that k  divides 5. View answer 1 answers 0 votes 72 views Accepted answer 2 votes The uniform measure on the convex region is by definition the (normalized) restriction of Lebesgue measure on the unit square. Therefore your approach is correct on the condition that the convex ... View answer 1 answers 0 votes 44 views Accepted answer 0 votes Hint: for any given choice of hours for A, find the number of hours for B such that 100 hours are filled. This gives an expression of the hours of B in terms of the hours of A. Substitute ... View answer 2 answers -1 votes 30 views 1 votes Hint: in both cases the LHS is obviously a subset of the RHS so the question is really: can every x\in\mathbb R^l be written this way? In order to answer that, solve a (relatively easy) system of ... View answer 2 answers 2 votes 549 views 1 votes You need to use a specific ellipse, and presumably the person asking the question would not accept the unit circle as an example of an ellipse (in which case the identity mapping would deliver). I ... View answer 2 answers 0 votes 589 views 0 votes Hint: the condition (X-5)(X-2)>0 can be restated as a logical combination of the separate conditions X>5 and X>2. That should tell you how to partition the interval [0,10] into a ... View answer 3 answers 1 votes 50 views 1 votes That would be a different kind of structure. The idea of a vector space is to have a "parallelogram" type construct that permits the addition of two vectors to obtain a third vector (as well as the ... View answer 2 answers 6 votes 187 views 1 votes The inefficiency is a quadratic function of your variables, and the constraint is a hyperplane. By an appropriate (fairly easy) linear transformation the inefficiency is the Euclidean distance of your ... View answer 1 answers -2 votes 258 views Accepted answer 1 votes Write B as the union of the disjoint sets A and B-A. The latter is also an element of \mathcal A and m(B-A)\geq0. Then$$m(A)+m(B-A)=m(A\cup(B-A))=m(B)$$and therefore$$m(A)=m(B)-m(B-A)\...

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Your equation $|\theta_m - \theta_h|= \frac{\pi}{2}$ does not measure the time interval between successive events, but the time between midnight and the first event after midnight. That is why the '...

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You need to put the absolute value sign within the double integral. It is well possible for the integral of $f-g$ to be zero without $f$ being equal to $g,$ even for the nicest imaginable continuous ...

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The inequality for large $x$ implies that $\lambda_2\geq1.$ The function $f(x)=\lambda_1+\lambda_3x^2$ determines a parabola centered around the $Y$ axis (where in order to cover the case $\lambda_3=0$...

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(Incomplete answer, I may get back when I understand these sets better) Connectedness is a necessary condition because we can take $I'=I.$ I will enumerate a few sufficient conditions but I have not ...
Let $\mathcal K$ be a fixed closed collection. For all $x\in X$ define $R(x)\subset Y$ as $\{f(x)|f\in\mathcal K\}$ and set $$\mathcal L=\{g:X\to Y|\forall x\in X,g(x)\in R(x)\}.$$ Obviously $\... View answer 3 answers 2 votes 108 views 3 votes The definition of a closed form solution, in particular what people agree to call an 'elementary' function, is culturally determined. A certain solution to a problem might be expressed as a series, or ... View answer 1 answers 0 votes 221 views 0 votes First verify$r=0$, then prove an induction on$r\$ using Pascal's identity.