## What's the problem with ordinary people being smarter than Trump? Is this a cause for concern or should we just ignore it as white supremacy?

Of course, it will ruin lives or kill a group of people here and there, but why worry about it?

I mean, China will eventually overtake the United States. I think Trump is making the right call, being completely delayed. I'm glad someone has the courage to learn badly (I'm fed up with all those Harvard Democrats who are constantly repairing a recession?!?)

(tagsToTranslate) yahoo (t) answers (t) questions (t) Politics & Government (t) Politics

## ordinary differential equations – Question on the existence of carathéodoral solutions to a discontinuous ODE (scalar) of first order

Consider the scalar i.v.p. in $${ mathbb R}$$
$$x = f (t, x), ; t in (0, T), ; x (0) = x_0$$
or $$T in { mathbb R}$$, $$T> 0$$, $$x_0 in { mathbb R}$$, and $$f: (0, T) times { mathbb R} mapsto { mathbb R}$$ has the properties:

(i) for each measurable (Lebesgue) $$y: (0, T) mapsto { mathbb R}$$, the map $$(0, T) ni t mapsto f (t, y (t)) in { mathbb R}$$ is measurable.

(ii) for almost all $$t in (0, T)$$, $$sup_ {x in { mathbb R}} | f (t, x) | leq l (t)$$, or $$l: (0, T) mapsto { mathbb R}$$ Lebesgue is it integrable?

I am aware of the results in the literature, showing the existence of Carath's solutions to the problem above, in the event that $$f$$ is not continuous. These results were obtained assuming (versions) of (i) and (ii) and that $$f$$ is not decreasing (in some sense), as in, for example, https://projecteuclid.org/euclid.die/1368638179,
https://doi.org/10.1090/S0002-9939-97-03942-7, etc.).

QUESTION: Are there any results proving the existence (and uniqueness) of Carath's solutions to the above problem with discontinuous solutions? $$f$$, in the case where $$f$$ is not growing?

## ordinary differential equations – \$ alpha = 1 \$ can it be a Bifrudition point if \$ alpha geq 1 \$?

Consider the system $$x = alpha x-x ^ 2-y ^ 2, y & # 39; = – y + xy.$$

One of the points of balance for this system is $$(x, y) = (1, sqrt { alpha-1}).$$
Now, for this point of balance to exist, $$alpha geq 1$$ (our bifurcation diagram is of the real plan). My question is: how do we determine if $$alpha = 1$$ is or is not a bifurcation point? Is there a method or an intuition?

## The Holochain project is a new miracle for the cryptography industry or an ordinary project? – The corner of crypto-currencies

Looking at the current scenario of the Holocene market, what do you think of the future of Holocides? What is your price forecast for 2019 and 2020?

You can find out what the journalists of Coinpedia are talking about Holocharine, let me know what you think.

## ordinary differential equations – Search for k in this logarithmic model

Issue 6: The amount of a drug in the blood decreases exponentially
with a half-life of 5 hours. In order to keep a patient safe during a one-hour procedure,
there must be at least 50 mg of drug per kg of body weight. How much medicine
should be given to a 60 kg patient at the beginning of the procedure?

(from MIT 18.03 OCW)

Let $$x (t)$$ the amount of drug in mg present in the blood at the time
$$t$$ in hours.

Then we have the model: $$x (t) = x_0e ^ {- kt}$$

I wonder how in the solution they found $$k = frac { ln2} {5}$$.

How I tried: we know that after $$t = 5$$ hours, the initial amount is halved, so $$x (5) = (1/2) x_0$$.

Then we use this information to solve $$k$$:

$$(1/2) x_0 = x_0e ^ {- k (5)}$$

So what:

$$ln (1/2) = -5k$$

Etc. so that $$k = – frac { ln (1/2)} {5}$$.

However, in the given solution, they omit the minus sign when searching for k (which I can understand) and, more importantly, they find $$k = frac { ln2} {5}$$, where I've $$ln (1/2)$$ in the numerator.

## Is it dangerous to enter administrative Windows credentials when logged in as an ordinary user?

I've recently been informed that when a user is logged in as a standard user and that he needs an administrator to perform (for example, install an application) that Entering administrator credentials while the logged on user is still logged out paves the way for login information. The recommended procedure is to log out as a normal user and log in as an administrator. Is it correct?

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## ordinary differential equations – stability, consistency and convergence of the trapezoidal method

Refer to problem 11 in chapter 5.11 of Numericical Analysis, 9 th ed. R. Burden, J. Faires.

The question asks "Discuss the stability, consistency and convergence of the implicit trapezoidal method." I have the impression that this question is vague and will divide my concerns into three questions.

(1)
For stability, do they ask to calculate a region of stability or to prove stability by satisfying the Lipschitz constant? A-stability was easy to find but Lipschitz's constant I still find it difficult to understand how this proves that the method is unconditionally stable for all $$h> 0$$. Can someone guide me through this?

(2) For the sake of consistency, I know that the method is consistent if $$lim_ {h-> 0} | tau_n | = 0$$
or $$tau_n$$ is the local truncation error and the order of consistency is given by:
$$frac {y (t_ {n + 1}) – y (t_ {n})} {h} – f (t_n, y (t_n))$$
now I have it $$tau_n = frac {h ^ 3} {3!} y & # 39; & # 39; & # 39; (t_n)$$ Which one is $$0$$ for $$h$$ -> $$infty$$ which means that the method is consistent. For the sake of consistency, I get the following:
$$frac {y (t_ {n + 1}) – y (t_ {n})} {h} – f (t_n, y (t_n)) = frac {h ^ 2} {2} y & # 39; & # 39; (t_n) + O (h ^ 3)$$ which suggests that the order of consistency is of order $$O (h ^ 2)$$. My problem is that we can confirm consistency by having
$$phi (t, w, h) = frac {1} {2}[f(t,y) + f(t+h,y+h)]$$
$$phi (t, w, 0) = frac {1} {2}[f(t,y) + f(t+0,y+0)] = f (t, y)$$
and since $$phi (t, w, 0) = f (t, y)$$ the method is considered consistent. This sounds too trivial, can anyone explain this further and perhaps show me how this applies to the trapezoidal rule?

(3) Finally, we say that if the method is stable and consistent, it will converge. Can someone confirm it to me and show me how to calculate the order of convergence?

Any help is greatly appreciated!

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