Justpassingby
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Modeling change
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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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59 views
Solving $X x^t+ Y y^t=1$ for a specific case with constraints
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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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Riemannian metric given in polar coordinates
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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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989 views
Point which minimizes the squared sum distances to edges of a triangle
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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{(...

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Connectivity with minimal width
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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 ...

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Addition of two simple periodic waves using Complex Sinusoidal forms. Not making logical sense.
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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.

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2 answers
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103 views
Prove: If $x+y>22$ then $x>11$ and $ y>11$
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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 ...

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1 answers
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64 views
Completely continuous map is not homotopy with antipodal map
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(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 ...

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105 views
Does a zero symmetrized gradient imply a constant function?
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Let $d=2$, $(u^1,u^2)=(x_2,-x_1).$

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3 answers
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218 views
logic- translating quantification in english
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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 ...

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859 views
Why is this function continuous but not differentiable?
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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 $\pm\infty.$

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8 answers
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How to prove $\ln x<x$?
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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 ...

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Trying to find Upperbound!
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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 ...

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669 views
Graph Theory - The 'Delivery Problem'
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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 ...

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48 views
What can we deduce about $k$, given that $i$ is an integer and $k$ is a prime number such that $k|i$ and $k|(i+5)$?
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Yes you are. Write $i $ and $i+5$ explicitly as multiples of $k $ and subtract to conclude that $k $ divides 5.

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subset of a uniform random number.
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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 ...

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44 views
What's the formula- Max A, minimize B, hour restraint.
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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 ...

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2 answers
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30 views
Is $\{a+\frac{h}{\sqrt{n}} \text{ } \forall h \in \mathbb{R}^l\}=\{\sqrt{n}(b-a) \text{ }\forall b \in \mathbb{R}^l\}=\mathbb{R}^l$?
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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 ...

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549 views
Diffeomorphism between an ellipse and unit circle?
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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 ...

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589 views
Probability for Continuous Uniform Distribution
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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 ...

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3 answers
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50 views
Understanding Defiinition of Vector Space
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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 ...

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2 answers
6 votes
187 views
Turn off the ovens! An optimization problem
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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 ...

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1 answers
-2 votes
258 views
Proving the monotonicity of a countably additive set function on a $\sigma$-algebra
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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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4 answers
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232 views
How Many Times The Clock Hands Make an angle Theta?
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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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1 answers
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244 views
A metric between functions on $\mathbb{R}^2$
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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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1 answers
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37 views
Inequality with three unknowns
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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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1 answers
3 votes
277 views
A connectivity-preserving function from a connected set onto an interval
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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 ...

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2 votes
70 views
Seeking more information regarding the "hybriation function."
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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 $\...

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3 answers
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108 views
Areas where closed form solutions are of particular interest
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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 ...

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221 views
Use induction and Pascal's Identity to show that $\sum_{k=0}^{r}C(n+k,k) = C(n+r+1,r)$
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First verify $r=0$, then prove an induction on $r$ using Pascal's identity.

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