## Online traffic policy problem solution

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## java – Pattern / solution for Boolean decision making chains

I need a solution for decision making chain. There are number of criteria that may return true, false or be inconclusive. A non-functional code (Java) would look like this:

``````Boolean res = nullValuesCheck(fieldValue, node);
if (res != null) {
return res;
}
res = typeCheck(node);
if (res != null) {
return res;
}
res = dictCheck(dict, fieldValue);
if (res != null) {
return res;
}
return finalCheck(fieldName, fieldValue); //also returns a Boolean
``````

I’m considering creating an extended predicate that would return a nullable `Boolean` instead of `boolean`, so that an inconclusive result could be returned.

I tried googling, but found no apparent solution (got lot of mishits on some simple java problems instead). I am wondering whether there exists a pattern, a library maybe, that would handle this problem properly. The problem seems generic and simple to solve and someone must’ve solved it already. I don’t want to reinvent the wheel.

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## Solution to \$ax_1 frac{partial F}{partial x_1} + bar{a} x_2 frac{partial F}{partial x_2} = F\$

I’m encountering a PDE taking form of $$ax_1 frac{partial F}{partial x_1} + bar{a} x_2 frac{partial F}{partial x_2} = F,$$ where $$ain mathbb{C}$$ and $$F: mathbb{R}^2 to mathbb{C}$$. Can anyone give me a hint on how to solve $$F(x_1, x_2)$$?

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## differential equations – NDsolve Initial Condition is a Function of the Solution

So this may be a terribly no good bad thing to ask of NDSolve, but it is physically relevant. I am trying to solve something like Fick’s Law:
$$frac{partial varphi}{partial t}=frac{partial^2 varphi}{partial r^2}+F(r,t)$$
Subject to a boundary condition which looks something like:
$$varphi (R,t)=varphi_0-int_0^R varphi(r,t)dr$$
Which is an attempt to simulate the case where whatever is diffusing into the medium of interest is limited in quantity. I assume simply plugging a recursive boundary condition is going to go poorly, is there any option here other than writing my own solver?

## linear algebra – A matrix Riccati differential equation with constant coefficients? Is there a solution for this in closed form?

The following is a matrix Riccati differential equation with constant coefficient matrices.

$$Dfrac{partial{C(t)}}{partial{t}}S + frac{1}{n}C(t)QDC(t)S – EC(t)Q = 0$$ or
$$Ddot{C}(t)S + frac{1}{n}C(t)QDC(t)S – EC(t)Q = 0$$
given initial condition $$C(0) = C_0$$.

I stumbled upon this from some other problem and I don’t have any background in matrix differential equations and I’d like to know if there is any way to solve this equation. I read it can be reduced to an algebraic Riccati equation. Is there any closed form expression for solution of this equation? Or anything that is closest to solving this equation?

Matrix dimensions

$$C(t)$$———-> $$(m+1)times n$$

$$S$$————–>$$ntimes 1$$

$$Q$$————–>$$ntimes(m+1)$$

$$D$$————–>$$(m+1)times(m+1)$$ diagonal matrix. (it is also singular, as there is a diagonal entry that is 0).

$$E$$————–>$$1times (m+1)$$

If its useful to know, $$n>>m$$ and $$mge 3$$

## usability – How can I phrase questions to user tests to not give away the solution?

Say if it’s a travel site, tell them to book a flight and a hotel.

Just give them the final objectives.

And then tell them to “think aloud” ( not what they think about xyz, but “I am pressing the red button”)

If you want to ask questions as you go along you end up asking mangled English “why did you press the ‘thing,’ you just pressed”

You can’t call the thing by what it does because that gives the game away.

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## Numerical solution for an integro-differential equation

I would like to solve numerically the following integro-differential equation
$$partial_t rho(t,x) ,=, partial_xbig(f'(x),rho(t,x)) int_0^infty f(xi),rho(t,xi),dxi ;+\ +; partial_xbig(g'(x),rho(t,x)) int_0^infty g(xi),rho(t,xi),dxi$$
where:

• $$rho$$ is a probability distribution on $$(0,infty)$$ which actually can degenerate to a convex combination of a Dirac delta and a density function;
• the initial condition $$rho(0,x)$$ can be suitably chosen, such that $$int_0^inftyrho(0,x)=1$$;
• let’s say the functions $$f,g$$ are given.

I’ve tried with DSolve, but an exact solution is not found. Then I’ve tried with NDSolve and I get the following error:

NDSolve::delpde: Delay partial differential equations are not currently supported by NDSolve.

Is it possible to solve this equation using Mathematica? I am using Mathematica 11.