## Pumping lemma: if you can keep pumping, what does this tell you?

Hypothetically, let’s say you are using the pumping lemma for either regular or context free languages. Now using either, you come across a case that remains true despite pumping it. In this situation, do you have to “throw out” the lemma so to speak? I am under the impression that the answer is yes, but I’m just not sure.

## How can I tell an object how many times it has been created?

I have a class that has an attribute called int nth_instance and I want it to count the how many created object it is. ( I’m really sorry for the bad english, I don’t know how to describe this, but I hope you get my point).

Here’s my approach.

class K{     static int nth_instance;     K(){      nth_instance++; // here's the problem, every other instance gets the     }                 //  same value       public static void main(String[] args){      K k1 = new K(); // This object should have nth_instance set to 1      K k2 = new K(); // n_th_instance should be 2, but k1 is now also 2    }  } 

So the problem is that every instance of K gets the nth_instance value of the last created object.

## How can I tell if I am a problem player?

Suppose I suspect that I might be considered a “problem player” but I am not sure. I play using techniques, decisions, or moves that, while not blatantly inappropriate, are atypical or time-consuming, and I am not sure whether others at the table are annoyed.

How can I find out whether I am seen as a problem player? Is the only real answer to say

Ok, my Ranger is going back to town to try to get laid again. Oh by the way, am I a problem player?

or are there techniques or best practices that I can use to self regulate my playing style in order to avoid problems? In other words, I want to avoid being the “problem player” that many DM’s and players speak about on RPG.SE (e.g. How to deal with a disruptive player? and How do I, a novice GM, deal with a PC who is constantly difficult?), without needing to depend on waiting to be told this, or worse, having others debating behind my back on how to “deal with” me.

Alternately, how can I communicate effectively with my GM and/or fellow players to ensure that my behavior in and out of character remains within the expectations of the group, especially when dealing with people who may be conflict-averse and more likely to use subtle passive-aggressive techniques than to directly confront someone.

Note: This is a generic “best practices” question, not a request for specific advice on a specific situation. I almost posted it on Interpersonal Skills.SE, but figured that people here have a better idea on interpersonal aspects of tabletop gaming.

This is not a duplicate of Am I a problem player? as that is a question about a specific situation and a request for an actual adjudication or at least informed opinion on whether or not the OP specifically is or is not a problem player given a specific set of circumstances. This question is about how, in general, one can do this themselves.

## how to tell what cameras a particular lens will fit

I have a 10x High Def. 2 element macro lens, which was purchased for an older Kodak EasyShare Z612 camera. Since it now appears that the camera may be broken beyond repair, I need to know if there is some other camera that this lens will work with. The lens also says: “Digital NC 58 mm Japan Optics” and Bower.

## How do I tell the rank of the electric susceptibility tensor (and others)?

I understand that a tensor is a multilinear map from $$V^*\times\cdots\times V^*\times V\times\cdots\times V$$ to $$V$$‘s underlying field, where $$V$$ is a vector space and $$V^*$$ its dual. This is fine. I also knot that a tensor has rank $$(p,q)$$ if its domain is the cartesian product of $$p$$ instances of $$V^*$$ and $$q$$ instances of $$V$$.

However, I cannot recognize the rank of tensors in examples from examples in textbooks. For instance, the electric susceptibility tensor. I know that, given a vector $$E$$ (from the electric field, which is a vector field), it will give me another vector $$P$$ (the density of electric dipoles moments), which may have direction different from $$E$$:

$$P = \epsilon_0\chi E$$

So $$\chi$$ is a tensor (and $$\epsilon_0$$ is permittivity of vacuum, “included so $$\chi$$ is dimensionless” — says the textbook from where the example was taken).

So, I see that it must have total rank 2, but is it $$(2,0)$$, $$(1,1)$$ or $$(0,2)$$? How would I, just from a formula like that and a description of what the tensor means, tell its rank?

My guess is that it is just a $$(1,1)$$ tensor, hence no more than an ordinary linear map that we study in basic Linear Algebra (because both $$E$$ and $$P$$ are vectors that should represent directions and magnitude in the same space). Is this correct? But from the information given, “it transforms a vector into another vector”, how can one conclude that it is linear, and then write the equation like that?

Also, in this case, how can I tell if $$\epsilon_0$$ is a tensor, and what rank it has if it is really a tensor?

(The example above is from “Tensor Calculus for Physics”, by Dwight Neuenschwander)

## Can the Weyl orbits of fundamental weights tell us the Cartan matrix?

Let $$\mathfrak{g}$$ be a complex semisimple Lie algebra, $$\Delta$$ its root system contained in $$\mathfrak{t}^{\vee}$$ for a Cartan sub-algebra $$\mathfrak{t}$$ of $$\mathfrak{g}$$. Let $$W$$ be its Weyl group. Then we (might) have the following short exact sequence of groups: $$1\rightarrow W \rightarrow Aut(\Delta) \rightarrow E \rightarrow 1$$ where $$Aut(\Delta)\subset GL(\mathfrak{t}^{\vee})$$ is the group of symmetries of $$\Delta$$, and $$E$$ (should) be the group of symmetries of the associated Dynkin diagram.

It is possible to see how the map $$Aut(\Delta) \rightarrow E$$ is defined from the perspective of simple roots (let them be $$\{\alpha_1,\ldots,\alpha_k\}$$): let $$\sigma\in Aut(\Delta)$$, then $$\{\sigma(\alpha_1),\ldots,\sigma(\alpha_k)\}$$ is a set of simple roots with respect to a choice of positive roots which corresponds to its dominant Weyl chamber. By composing $$\sigma$$ with the unique Weyl element mapping this chamber to the original dominant Weyl chamber, we get a permutation of $$\{\alpha_1,\ldots,\alpha_k\}$$. One can see that this permutation preserves the Cartan matrix and thus defines an element of $$E$$.

What I would like to know is whether there is an alternative way to define the above map from the perspective of dominant fundamental weights, namely, let $$\{\lambda_1,\ldots,\lambda_k\}$$ be the corresponding fundamental weights, then I observe that any element $$\sigma\in Aut(\Delta)$$ induces a permutation of the Weyl orbits generated by the $$\lambda_i$$‘s. So we almost get the desired map except we haven’t checked this permutation preserves the Cartan matrix. This raises the following question:

Can these Weyl orbits themselves (as polyhedra in the Euclidean space) tell us the Cartan matrix?

As an example, $$A_3$$, these orbits consist of two congruent tetrahedra and one octahedron. We know that there is no edge joining the two tetrahedra in the Dynkin diagram. Can we see this fact from their configuration?

## How to tell if an inline object tag has loaded its data

I’m using some pre declared <object> tag to load some SVG

<object type="image/svg+xml" data="some.svg"></object> 

I want to manipulate that SVG after it’s loaded. How do I wait for it to load and make sure I get the load event. In other words, do I need to handle a case where the object may have already loaded before I have a chance to attach an load event.

What was doing is calling getSVGDocument and if it returned null then adding the load event. That failed on Firefox and Safari.

My current solution is to try to reload the svg to force a load event 🤮

  class Waiter {     constructor() {       this.promise = new Promise((resolve) => {         this.resolve = resolve;       });     }   }    async function getSVGDocument(elem) {     const data = elem.data;     elem.data = '';     elem.data = data;     const waiter = new Waiter();     elem.addEventListener('load', waiter.resolve);     await waiter.promise;     return elem.getSVGDocument();   } 

It seems to work but also seems like a horrible hack.

Is there some other way to tell if the <object> has loaded. Apparently <img> tag has a completed property but <object> doesn’t appear to have anything similar unless I’m staring right at it.

## What does the determinant of 3×3 matrix mean? how does the determinant tell me the orientation of polygon?

I need help with understanding the problem. The coding isn’t really the problem rather the math part. I don’t understand what a delta test method that tells me determinant of a 3×3 matrix is supposed to help determine if an array of vertices of a simple polygon is convex or not. What does the determinant of 3×3 matrix mean? how does the determinant tell me the orientation of polygon? How can this help me determine if array of vertices of simple polygon is convex or not? I tried to implement using the gift wrapping method but the teacher said that it was too complicated for the class and just said to use the delta test to help. This kind of seems like duplicate of a few question but I still don’t answer the solutions given:

What is the real meaning of the determinant of a matrix?

https://stackoverflow.com/questions/25830932/how-to-find-if-two-line-segments-intersect-or-not-in-java

but as a novice in these fields any help will be appreciated 🙂

## Is there a way to tell if SharePoint was installed using a SQL Alias?

I know that a SQL Alias is listed now but I would like to find out if SharePoint was installed while specifying that alias during the install. On the ‘Servers in Farm’ page, I see both a SQL Alias and the SQL Instance listed, so I am a bit suspicious. How can I determine for certain how SharePoint was initially installed, via the SQL Alias or via the SQL Instance?

## Hi, Can someone please tell me how to get the serial back please ?

All of my old emails got deleted and i’m on my new pc as well, i have nearly every gsa product and i cant use any of them,i will be able to find the paypal info.
Hope someone can help,
Thanks.