What’s happening Delta Prime?

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What's happening Delta Prime?

Can I compute closest split pair of points where distance is strictly less than delta

I’ve been studying the closest pair algorithm lately and I found this to be an extremely good and intuitive resource: http://serverbob.3x.ro/IA/DDU0221.html. It is also explained in section 33.4, “Finding the closest pair of points” of introduction to algorithms, third edition by CLRS.

I understand why I’d need 7 comparisons for a non pairwise distinct set of points and only 5 otherwise (33.4-2). Both of them follow from the fact that I can fit only 4 points, at least Delta away from each other, on a Delta x Delta box.

What I’ve been wondering though, is if I could trim the number of comparisons down to 3 if I included only points strictly less than Delta away from the middle line, in the middle Delta x 2 Delta strip. The reasoning is that I already have a pair of points Delta away from each other from the recursive calls, I only need points less than Delta and I can only fit 2 points Delta away from each other AND less than Delta from the middle line on each side.

Have I missed something or can I really just compare the 3 following points of every point in a middle strip only containing points strictly less than Delta from the center?

Is 1 hour sufficient time for a Delta connection at LAX from MSP to SYD?

I am making a delta booking MSP/SYD and the connection Delta gives me is one hour. Is that a legal connection and what if my MSP flight is running late? The Delta flight out is the last one for the night to Sydney. What do I do? I am sure that the MSP flight arrives terminal 2 around gate 40 or 50 something and that is where the Delta flight usually departs from.

Magento2 Delta migration, missing products

After I’ve setup a Magento 2 development site. Our initial goal was to use Delta migration using the Magento 1.9.x to Magento 2 CE migration tool to transfer all the missing orders and customer data right before the final migration. This gives us time to test the Magento 2 extensions that the client wants.

But… my client added (and removed) multiple products from his Magento 1 (live) site. The Delta migration does not support tranfer of these missing products as far as I know.

How do I migrate the missing products from Magento 1 to Magento 2 after already done a (succesful) data migration months ago?

How to treat an equation of the form $-\Delta u=G\cdot \nabla I(u)+f(u) ?$

There are plenty of variational techniques (direct methods of calculus of variations, mountain pass type theorems, Lusternik-Schnirelmann theory) to prove the existence of solutions of a semilinear elliptic equation of the form $ $ -\Delta u=f(u)$ $ in $ H^1_0(\Omega)$ , under suitable hypothesis on $ f:\mathbb{R}\to\mathbb{R}$ , thanks to the fact that we can see weak solutions of this problem as the stationary points of the functional: $ $ I:H^1_0(\Omega)\to\mathbb{R}, u\mapsto\frac{1}{2}\|u\|_{H^1_0}^2-\int_\Omega\int_0^{u(x)}f(s)\operatorname{d}s\operatorname{d}x.$ $

If $ G:\Omega\rightarrow\mathbb{R}^n$ , how can we treat the equation: $ $ -\Delta u=G\cdot\nabla I(u)+f(u),$ $ or even, if $ g:\mathbb{R}^n\to\mathbb{R}$ , the equation: $ $ -\Delta u=g\left(\nabla I(u)\right)+f(u)?$ $

If $ n=1$ , I saw in the $ G$ -case that we can transform the equation into another semilinear elliptic equation that hasn’t the dissipative term $ u’$ , with the same trick used in Sturm-Liouville theory, and so we can bring back this problem into the realm of the previous variational problem. However, what about the $ g$ -case if $ n=1$ ? What about the $ G$ -case if $ n\ge2$ ? Can we say anything about the $ g$ -case if $ n\ge 2$ ?

Delta from when a multiple choice option changes values

I am working to create some generic reporting for a list I have created. The list works based on the values in various fields. The field I am currently stuck on, is the field named: “Status”

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Ideally, I need to know how long a specific item remains in that status, or value, from the drop down. I also need to know how many times it changes, and what those changes are, as well as who made them.

My idea is to have a calculated field, that grabs the status, and if it changes, to append that information into the calculated field.

Where would I start in terms of an actual formula for this?

Delta shock solution

I studied that a measure valued solution of a conservation law $ u_t+f(u)_x=0$ is a measurable map $ \eta : y \rightarrow \eta_y \in Prob(\mathbb{R^n})$ which satisfies $ \partial_t(\eta_y, \lambda) +\partial_x (\eta_y, f(\lambda)) =0$ in the sense of distribution on $ \mathbb{R^2_+}$ .

In particular when the conservation law admits $ L^{\infty}$ solution then $ \eta_y=\delta_{u(y)}$

Now I am trying to read “Delta-shock Wave Type Solution of Hyperbolic Systems of Conservation Laws” by V. G. Danilov and V. M. Shelkovich.

In the above article what do they mean by $ \delta-$ shocks?.

In which sense these $ \delta-$ shocks are different from the shocks of the conservation laws ?

According to the definition which I stated in the begining any shock solution $ u \in L^{\infty}$ can be written as a dirac measure $ \eta_y=\delta_{u(y)}$ . So are all shocks delta shocks? Please suggest me the reference

Solutions to $\Delta u\ge u^2$

Let $ (M,g)$ be a complete Riemannian manifold. Suppose that $ u$ is a nonnegative solution to $ \Delta_gu\ge u^2$ . Does it follow that $ u$ must be identically 0?

I know that the answer to above question is yes if one assumes that $ Ric(g)$ has a lower bound, which allows for a maximum principle argument, using the distance function to cut-off.

I wonder if this is true in general, with no additional assumptions?