What complex number x do I multiply by a given complex number c to equal another given complex number d? [on hold]

I have a known complex number c and a known complex number d.

I need to find the complex number x that gives d when multiplied by c.

I want to find this number x using c and d. What is the equation for finding x using the known values c and d?

The reason I need this is because I am writing a graphics program that needs to scale and rotate an arbitrary set of complex numbers (using multiplication) so that the set conforms to a desired space in the complex plane.


Applying functions to leaves of nested list structure, when these leaves are more complex expression trees

Is there a way to apply a function h to the following nested list

{{a, b}, {c, d}, {{d, e }, {f, g}}}

where this should should become

{h[a], h[c], {h[d], h[f]}}

h is applied to the first element of each (deepest nested) sublist, replacing this sublist. The nesting is never deeper than the example displayed above. I.e. the expression tree for the list has at most depth 3.

The rest of the list structure pattern is preserved.

Here, a, c, d and f are not atoms. They are again expressions with heads. The heads are however not list-heads.

As an example, consider

{{u[a], u[b]}, {u[v[c]], d}, {{d, e}, {f, g}}}

applying h to this should yield:

{h[u[a]], h[u[v[c]]], {h[d], h[f]}}

In other words, h is applied to the leaves" of the list expression given above, where theseleaves” are more complicated expressions.

In ASP.NET, is the concept of a Complex Type analogous to a View Model? [on hold]

Is a Complex Type to the Entity Framework, what a View Model is to a View? If I understand, the Complex Type is a type that represents columns and/or fields from real EF entities. A View Model is similar in that is has a class that has types from various sources. Neither of them can exist independently of the underlying real entities, models, and classes.

Granted the Complex Type is Model and one is View, are they analogous for understanding purposes?

Azure Search Indexer for Complex Data Type

We have been using Azure Search for a number of years and it has been working well. I just became aware of the new complex data types, and am very interested in implementing them. I can find good examples of how to create the index, but my challenge is with how to implement the indexer.

We use indexers to our SQL Server database, with the integrated change detection enabled to update our indexes automatically when we run the indexer. For this to work, the datasource must point to a table.

For our current implementation, we have flattened our data to place several multi-value fields into lists so that they can be brought into the index. It would be awesome if we could avoid having to do this flattening.

Any pointers on how I could accomplish this? My only thought is to have multiple indexers. One for the base information, and others for each complex data type. But that does not seem very elegant.


Picard group of the moduli space of semistable rank 2 parabolic vector bundles over smooth complex projective curves with trivial determinant

I am looking for the Picard group of the moduli space of semistable rank 2 parabolic vector bundles over smooth complex projective curves with trivial determinant.

Having determinant trivial, I believe we can consider the bundles as parabolic $ SL(n,\mathbb{C})$ -bundles as well. The closest result have found in this regard is a paper by Laszlo and Sorger, ‘The Picard group of the moduli of G-bundles on a curve’, but they only talk about quasi-parabolic bundles rather than parabolic bundles.

My question is: Is the picard group known already? Does anyone know of any reference? I need it urgently if possible. Any help would be appreciable.

bare hand integration of euler class of blow up of a complex surface at a point

let X be a product of two Riemann surface of genus $ \geq1$ and p be a point of X. If X’ is the blow up of X at p. Let E denote the exceptional divisor I am aware that the the second Chern number of X’ since it’s the euler characteristic. I would to verify this by integration of the second chern class. Up to now I try as follows:

Let W be a tubular neighborhood of the exceptional divisor E. Let N be the normal bundle of E $ c_2(X’) = p^*(c_2(X))+c_2(TN)=p^*(c_2(X))+ c_1(TE)c_1(N)$ Now I am not sure how to proceed. $ \int_{X’}p^*(c_2(X))+ c_1(TE)c_1(N)$ This reduces to $ \int_{X’}c_1(TE)c_1(N)$ which I tend to understand as the intersection number. But usually one performs this computation in $ \mathbb{C}P^n$ , which is not the case here. Could anybody give me some help? Thanks.

Parse complex XML with arrays in Java

I have a complex xml structure which I receive from 3rd party.I want to parse above xml document & create a Map with the respective values. Which library can be used to parse complex xml’s

I tried XPath however i was unable to get desired result

AA BB CC DD EE FF 10 20 30 40 50 60

I want to parse above xml document & create a Map with the respective values i.e. AA –>10, BB–>20 and so on. How do i achieve this in JAVA.

Rigging Sizes & Complex Orders

I have a player that oftenly asked his Drones to protect someone in autopilot or follow someone then he lost link (because of Noise) to come back to safehouse.

Is this possible ? Is an autosoft is required ?

Also in the Core, they don’t really define the size of some drones. For the Ares Duelist or Shiawase Kanmushi it’s ok but I don’t really know the size of a steel lynx.