Which part of my Parallel.For should be fixed and is unsafe?
Parallel.ForEach Slower than ForEach
Using Gimp to batch convert images to another format in Windows As implied by the title, does anybody know how to use the gimp-console-[version].exe program to batch convert images between formats (with default settings) in Windows ? If A is invertible, prove that $\lambda \neq 0$, and $\vec{v}$ is also an eigenvector for $A^{-1}$, what is the corresponding eigenvalue? If A is invertible, prove that $\lambda \neq 0$, and $\vec{v}$ is also an eigenvector for $A^{-1}$, what is the corresponding eigenvalue?  I don't really know where to start with this one. I know that $p(0)=det(0*I_{n}-A)=det(-A)=(-1)^{n}*det(A)$, thus if both $p(0)$ and $det(0) = 0$ then $0$ is an eigenvalue of A and A is not invertible. If neither are $0$, then $0$ is not an eigenvalue of A and thus A is invertible. I'm unsure of how to use this information to prove $\vec{v}$ is also an eigenvector for $A^{-1}$ and how to find a corresponding eigenvalue. Combinatorial expression for all ternary strings that don't have consecutive 1's and 2's Volume form on $(n-1)$-sphere $S^{n-1}$ Let $\omega$ the (n-1) form on $\mathbb{R}^n$ $$\omega=\sum_{j=1}^{n}(-1)^{j-1}x_{j}dx_{1}\wedge\cdots\wedge \hat{dx_{j}}\wedge\cdots dx_{n}$$ Show that the restriction of $\omega$ to $S^{n-1}$ in precisely the volume for this sphere.  What I did was: $\omega$ never vanish on the sphere, because, defining $\sigma\in \Omega^{n-1}(S)$ for $$\sigma_{p}(v_{1},...,v_{n-1})=det(p,v_{1},...,v_{n-1})$$ and $i:S^{n-1}\rightarrow \mathbb{R}^{n}$ the inclusion function, then $\omega=i^{\ast}(\sigma)$ then $\omega\not=0$ and therfore is a volume form.   How proof that $\omega$ is the volume form?   The first thing that comes to mind is show that $\int_{S^{n-1}}\omega=Vol(S^{n-1})$ but I have serious problems with the definition, I think that is to much.   How see that $\omega$ is invariant on $\mathbb{R}^{n}$ under action of $O(n)$ Let $a,b,m,n$ be positive integers such that g.c.d.$(a,b)=1$ and $a^m+b^m|a^n+b^n$ , then is it true that $m$ divides $n$ ? Setting Low Disk Space Alerts on Windows Server 2008 What is the difference between shell, console, and terminal? Is there a word that describes a person who dies on his/her birthdate? My book gives the following definition:     Let $(M,d)$ be a metric space, and let $\mathcal{T}$ be the collection of all subsets of $M$ that are open in the metric space sense...  $\mathcal{T}$ is called the topology generated by d   Then it later says to prove things about two different metrics generating the same topology. However I'm very confused about what all this means.   When I read "all subsets," I think of the theorem that says a set with $n$ elements will have $2^n$ subsets. (ex. all the subsets of $\{1,2,3\}$ are $\{\emptyset, \{1\},\{2\},\{3\},\{1,2\},\{1,3\},\{2,3\},\{1,2,3\} \}$). So I think "all subsets that are open" would be like, If M is the set (1,5), then an open subset would be any set $(a,b)$ where $1&lt;a&lt;b&lt;5$, and then all subsets would be all possible union combinations of these "$(a,b)$" sets.     Its seems to me that metrics have nothing to do with subsets. Clearly there is something i'm not understanding. Please Help me.   It would be very enlightening, if someone could give me some simple examples of 1 set and 2 metrics generating two different typologies. I wanted to tidy up a TeX document and was curious if you can use \lstinputlisting or a similar function to include a certain part of a source-code file.  Example, I have a 500 or so line source file and I want to include just lines 300-400.  Is there a way to do this? Function whose image of every open interval is $(-\infty,\infty)$ How to find a function from reals to reals such that the image of every open interval is the whole of R?  Is there one which maps rationals to rationals? Factoring $x^n + y^n$ over the integers How to construct a pyramid in blender but the edges of the triangles to be equal? How to make a pyramid in blender and all the edges to be equal size? Is there a way to do that in blender? Or if there is no easy way for that, maybe anybody not that lazy can provide me with a math line? Or maybe a link or whatever? Best way to specify whitespace in a String.Split operation Game about placing pennies on table This problem is from The Art and Craft of problem solving book:  Consider the following two player game. Each player takes turns placing a penny on the surface of a rectangular table. No penny can touch a penny which is already on the table. The table starts out with no pennies. The last player who makes a legal move wins. Does the first player have a winning strategy?  Now its not hard to see that the first player will always win if you place the coin in the center. But I have been thinking about what would happen If I also allow Quarter, Loonie and Twoonies. Does the first player have a strategy to always win? Could someone provide an explanation? How do I programmatically create a new content type? Difference between $\sum_{i=1}^{k}{\frac{s_i}{kn_i}}$ and $\frac{\sum_{i=1}^{k}{s_i}}{\sum_{i=1}^{k}{n_i}}$ I am getting confused at how to calculate the average probability.  Suppose we repeat a kind of binary survey $k$ times each of which was done on a completely separate sample group.  For each $i^{th}$ group, $i=1,2,3,...,k$, Let $n_i$ be the number of samples and $s_i$ be the number of positive results. With this we know that the probability $p_i$ of the positive result for the $i^{th}$ group is $s_i/n_i$  With my ignorance, I happened to use two ways to calculate the average probability in my work wrongly assuming that they are the same:  $$\frac{p_1+p_2+p_3+...+p_k}{k}$$ and $$\frac{s_1+s_2+s_3+...+s_k}{n_1+n_2+n_3+...+n_k}$$  I don't know which is the correct way to calculate the average probability. So could you please explain the difference of these two and when to use which? How can the median number of sexual partners be 6.1 and 3.6? Median number of female sexual partners in lifetime, for men 25-44 years of age, 2006-2008: 6.1  Wouldn't it only be able to be x.5 or x.0? What do the numbers in a man page mean? So, for example, when I type man ls I see LS(1). But if I type man apachectl I see APACHECTL(8) and if I type man cd I end up with cd(n).  I'm wondering what the significance of the numbers in the parentheses are, if they have any. A native speaker said: "I have ever went to" I heard a guy from Manchester, UK said &mdash;     It was the best restaurant I have ever went to.   And Google offers 23 million pages for the query "have ever went to", and only 3 millions for "I have ever gone to".  Is this form correct? Has the grammar changed?