## differential geometry – Is inversion globally well defined on complete anaytic manifods

Let $$M$$ be a complete analytic Riemannian manifold. Let $$p$$ be a point in $$M$$ and let $$u,v$$ be tangents at $$p$$ such that $$exp(u)=exp(v)$$, must we have $$exp(-u)=exp(-v)$$ ?

This property seems to good to be true, so I would not be surprised if there is a counterexample ,on the other hand I dont know any counterexamples.

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File size: 8.5 MB

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## magento2 – Magento 2: Set order status to complete programmatically results in “Please provide payment for the order”

i would like to set order to complete programmatically after they have been processed in another software. This is the typical code i found all over the internet:

``````\$orderId = 1000120319;
\$orderState = MagentoSalesModelOrder::STATE_COMPLETE;
\$order->setState(\$orderState)->setStatus(\$orderState);
\$order->save();
``````

All i get is this result:

Uncaught MagentoFrameworkExceptionLocalizedException: Please provide payment for the order.

What i have to do, to set the payment completed as well?

Best regards

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## Proof that n-dependent Set in Graph theory is NP Complete

Consider an undirected graph $$G$$. A subset $$S subseteq V(G)$$ is n-dependent if for every $$x in S, d_{}(x) leq n-1$$. The n-dependence number of $$G$$, denoted $$beta_n(G)$$, is maximum cardinality of an n-dependent set of $$G$$. That is, the n-dependence number of $$G$$ is the maximum cardinality of a subset of vertices $$S$$ such that $$Delta() < n$$.

Consider the following question:

Instance: Given a graph $$G$$ and positive integers $$n$$ and $$k$$

Question: Does there exist $$S subseteq V(G)$$ such that $$S$$ is an n-dependent set and $$|S| geq k$$?
Prove that the n-dependent set problem in undirected graphs is NP-complete

For the sake of argument let’s assume that there exists an algorithm $$mathcal{A}(G, n, k)$$ that can solve the given problem in polynomial-time. Now let’s say we are given an undirected graph $$G$$ with a number $$k$$ and are asked to check if the graph contains an independent set of size $$k$$. To solve this problem in polynomial-time, we are going to call $$mathcal{A}(G, 1, k)$$. But since the independent set decision is NP-complete, we can’t solve it in polynomial-time, hence $$mathcal{A}$$ does not exist.

I can’t understand why this answer is wrong (I got 0). Please explain.

## How do we define the complete lattice for a data flow problem

I have narrowed down the data flow items that would constitute the elements of a lattice. But I’m not sure what is the partial ordering operation to be used for the further data flow analysis. Take for example, a sign analysis. Once I know that D={n, p, ?} and the lattice L= D{variable in my program}. What is the partial ordering operator to be used here?

## Is there a super-linear lower bound on the time complexity of all solutions of NP complete problems?

$$P ne NP$$ would imply that any polynomial is a lower bound on the time complexity of any NP complete problem.

Is some non-trivial lower bound known at all?

## magento2 – Magento 2.3.4 does not complete index broken by Catalog Search indexing

Running bin/magento indexer:reindex
results in the following error
Can do with help here Thanks

Catalog Product Rule index has been rebuilt successfully in 00:00:00
PHP Fatal error: Uncaught Error: Cannot instantiate interface MagentoInventorySalesApiApiStockResolverInterface in /var/www/vhosts/blueridge.co.uk/htdocs/vendor/magento/framework/ObjectManager/Factory/AbstractFactory.php:121
Stack trace:
#0 /var/www/vhosts/blueridge.co.uk/htdocs/vendor/magento/framework/ObjectManager/Factory/Compiled.php(108): MagentoFrameworkObjectManagerFactoryAbstractFactory->createObject(‘MagentoInvento…’, Array)
#1 /var/www/vhosts/blueridge.co.uk/htdocs/vendor/magento/framework/ObjectManager/Factory/Compiled.php(150): MagentoFrameworkObjectManagerFactoryCompiled->create(‘MagentoInvento…’)
#2 /var/www/vhosts/blueridge.co.uk/htdocs/vendor/magento/framework/ObjectManager/Factory/Compiled.php(79): MagentoFrameworkObjectManagerFactoryCompiled->get(‘MagentoInvento…’)
#3 /var/www/vhosts/blueridge.co.uk/htdocs/vendor/magento/framework/ObjectManager/Factory/Compiled.php(150): MagentoFrameworkObjectManagerFactoryCompiled->create(‘AmastyShopbyM…’)
#4 /var/www/vhosts/blueridge.co in /var/www/vhosts/blueridge.co.uk/htdocs/vendor/magento/framework/ObjectManager/Factory/AbstractFactory.php on line 121

## C# design for handling a high rate of async network operations that complete with a callback (hundreds per second)

I am working with a message broker technology, to which events will be published (following an “event carried state transfer” architecture) for consumption by other applications.

The vendor library uses a pattern where a message is handed to a `Session` object defined by the vendor’s client library code, which sends it over the network to the broker, and the vendor’s client code will call an `OnSessionEvent` method which includes data in the event args indicating whether the message was successfully published to the broker. A message may be initially accepted by the `Session` object but fail to be published to the broker if, for example, the broker’s buffer is full (typically a temporary state of affairs).

It could easily be the case that the original source of events is raising them at the rate of up-to-thousands of messages a second.

To further complicate matters, it may be the case that multiple different event sources may be publishing to the same `Session`, and so the `OnSessionEvent` response needs to be routed back to the appropriate publisher.

In any case, my struggle right now is trying to figure out an appropriate pattern to efficiently send messages and handle the callbacks. It would of course be less than ideal to send a single message and then wait for the callback result before sending the next message, since the network response may take several milliseconds.

I could create a `Task` for each message send attempt, collect up a bunch of these tasks, and wait on them as a batch of, say, 100. This is clearly faster than one-message-at-a-time. However it would mean generating hundreds or possibly up to thousands of `Tasks` every second. Note that the vendor code does not natively expose the network operation as an `async` operation using a `Task`. In order to use this pattern, I would add a `TaskCompletionSource` object to the (local) message object, and `SetResult` on that `TaskCompletionSource` when the (local) message object is made available via the callback argument. I am concerned about the rate of object construction that this could cause.

I am hoping for advice or articles which talk about situations like this. I am also curious as to the threading implications of asynchronous callbacks, so a comment or article that covers both would be idea.