# All Questions

50 views

### Why is the covariance a measure of how much two random variables change together?

In descriptive statistics, the empirical covariance of a point cloud $\left\{(x_i,y_i) : 1\le i\le n \right\}$ is defined as ...
127 views

### Functions of 2 variables and applications to economics

Given the production function $Q := \sqrt K + L^2$, determine the optimal level of production and the relative demand of the two inputs capital $K$ and work $L$. The cost of a unit of capital ...
74 views

### How do I count all values that satisfy X mod N=1 in the range [A,B]

I want to count how many values of x in range [A,B] give remainder of 1 when divided by N. Is there any formula I can apply?
34 views

61 views

### Negation of a statement

So I am trying to prove a proposition. It goes like this Let there be $\emptyset\neq X\subset\mathbb{R}$ which is bounded from above. The next two statements are equivalent about $s\in\mathbb{R}$ ...
236 views

### What makes a line “straight”?

In Euclidean space, there can be several definitions that makes a straght line: Line of shortest distance between two points Line that is linear, i.e with the points satisfying a linear equation ...
76 views

### If A represents area of ellipse $3x^2+4xy +3y^2=1$ then the value of $\frac{3\sqrt{3}}{\pi}A = ?$

If A represents area of ellipse $3x^2+4xy +3y^2=1$ then the value of $\frac{3\sqrt{3}}{\pi}A = ?$ My approach : Since area of ellipse is $\pi ab$ where a is semi major axis and b is semi minor ...
66 views

### Any suggestions for a Math book to revive my long lost math skills and knowledge?

Since I got my bachelor degree in computer science in 2005, I have rarely been in touch with or even need to do any significant mathematical calculations. I have consequently lost most of my math ...
154 views

### CR Equations using Polar Form

I have a question to check whether following function is analytic or not using CR Equations. The question is f(z) = 1/(z-z^5) I just don't know how to start and ...
43 views

### Ellipse 1 : E$_1 = \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 ( a > b)$ another ellipse 2 : $E_2$ which passes thru…

Problem : Ellipse 1 : E$_1 = \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 ( a > b)$ another ellipse 2 : $E_2$ which passes thru extremities of major axis of $E_1$ and has its foci at ends of its minor axis. ...
44 views

### effective way to solve isomorphism of groups

Hello I am studying group isomorphisms but I fail to check in a few cases whether two groups are isomorphic or not.for example in $S_3 \times Z_4$ and $S_4$ I have checked with ...
59 views

How do I solve this equation: $$2\arcsin\frac{x}{2}+\arcsin(x\sqrt{2})=\frac{\pi}{2}$$ We know that: $$\sin(\alpha+\beta)=\sin\alpha\cos\beta+\cos\alpha\sin\beta$$ So letting $\alpha = ... 0answers 55 views ### Rotation Number of Polynomial I conjectured that Maximum Rotation Number of$n$-th degree polynomial image of unit circle (in the complex plane) is$n$. (for example, if$f(z)=z^n$, then rotation number is$n$) Is it right? 2answers 40 views ### Terms in Fourier Series Can any one explain why? $$\int_0^\pi \sin(nx)\sin(mx)\,dx=\begin{cases}0,&n\not=m,\\ {\pi\over 2},&n=m,\end{cases}$$ and $$\int_0^\pi \cos(nx)\cos(mx)\,dx=\begin{cases} 0, &n\not=m,\\ ... 0answers 13 views ### Stable flag for a self adjoint operator in a symplectic vector space I'm trying to learn some facts concerning symplectic spaces and I have found this affirmation I cannot prove: If x is self adjoint in a symplectic vector space then there's an isotropic flag ... 1answer 36 views ### Surjectivity of a map D^{2n} \to \mathbb{CP}^n I'm solving an exercise about the complex projective space, and during a step of the solution I'm asked to find a surjective map D^{2n} \to \mathbb{CP}^n. I defined the map in this way$$ ... 0answers 51 views ### Primality of Stirling numbers of second kind Apart from the Mersenne primes$M_p=2^p-1=\begin{Bmatrix}p+1\\2\end{Bmatrix}$, and the four primes$\begin{Bmatrix}n\\4\end{Bmatrix}$where$n$is given in http://oeis.org/A100958, are there other ... 0answers 28 views ### Which boundary condition dominates in elliptic boundary value problem? I am working on a solution to a boundary value problem (which is too complicated for me to reproduce here) but have a question about the boundary. In many dimensions, my function is infinite along ... 1answer 1k views ### How mean, median and mode changes with change in one element of set. I have N numbers. Let mean of these numbers be A. Mode of these numbers be B.Median be C. Now if I change one element in these, how will my mean, median and mode change ? Can I calculate it directly? ... 0answers 358 views ### A question about the article 'You can't hear the shape of a drum' I have read the article http://www.math.upenn.edu/~kazdan/425S11/Drum-Gordon-Webb.pdf, , where Gordon and Webb describe in a simple a way the contruction of a pair of isospectral but non isometric ... 0answers 27 views ### LINEAR MAPS and their representation in ordered tuple If$L:F^n\to F^m$is linear map show that it can be written as like.$L(x)=(f_1(x),\cdots,f_m(x))$Where$f_j\in (F^n)' and x\in F^n$I tried to do something involving their basis but ... 0answers 40 views ### quotient by contractible space and homotopy equivalent? [duplicate] Let$X$be a space and$L$be a subspace of$X$that is contractible. Then is$X/L$homotopy-equivalent to$X$itself? it doesn't seem trivial to me at al...If so, how to show it rigorously? Could ... 2answers 72 views ### Use the formal definition of the derivative to find the derivative of$f(x) = \frac1x$Working through some exercises which I have been set in a Stats module. I'm stuck on this problem. I can get to $$\lim_{h\to0}\frac{\frac1{x+h}-\frac1x}h.$$ Then I'm unsure as to where to go from ... 1answer 23 views ### Topic for attribute exploration I'm writing my bachelor theses about the interactive algorithm 'attribute exploration'. For this I want to add an example. In the literature I found many such examples, like exploration of finite ... 0answers 55 views ### Finding volume using triple integral Find the volume of solid bounded by the$x^2+y^2=a^2$,$y^2 + z^2 =a^2$,$x^2 + z^2 = a^2$I can see that shadow in$x$y region is given by$x^2 + y^2 =a^2$. but when I draw ray from shadow to up ... 1answer 140 views ### Smallest$\sigma$-algebra and$\sigma$-algebra generated by a function I'm reading through the following theorem: Let$X=\{X_t,t\in T\}$be a stochastic process. Then$\sigma (X)=\sigma ( \cup_{t\in T} \sigma (X_t))$From my basic knowledge of measure theory, I ... 1answer 79 views ### If$\{X_n\}$is a martingale, then$E[X_n-X_{n-1}]=0$Apparently this should be quite simple, but I have been trying for a while and can't seem to get this. Let$\{X_n\}$be a martingale, then we have: $$E[X_n-X_{n-1}]=0$$ According to some notes I found ... 1answer 56 views ### Bigger and Smaller for numbers - Works in both directions? I wanted to know how to use the right term when explaining the difference between numbers. For example, I have two lenses: Lens 1 = 10x zoom Lens 2 = 5x zoom I know I can say that the 1 has 2x ... 2answers 98 views ### Limit of 2 variables function $$\lim_{(x,y) \to (0,0)} \frac{\sin^2(xy)}{3x^2+2y^2}$$ If I pick$ x = 0$I get: $$\lim_{(x,y) \to (0,0)} \frac{0}{2y^2} = 0$$ So if the limit exists it must be$0$Now for${(x,y) \to (0,0)}$... 3answers 117 views ### Boundary points of a domain bounded by a continuous curve Suppose$F:\mathbb{R^2}\to \mathbb{R}$, which is given by$F(y_1,y_2)=\frac{y_1^2}{4}+\frac{y_2^2}{9}-1$.$S=\{(y_1,y_2) |F(y_1,y_2)=0\}$, and$D=\{(y_1,y_2) |F(y_1,y_2)<0\}$. I want to show ... 0answers 29 views ### Notation for bounds on derivative I am working on a problem where the assumptions are that some derivatives are bounded. I want to refer to the individual bounds in the proof but there are about 7 of them in total. I am wondering if ... 0answers 32 views ### How do I know that min-term can't be combined any further? I'm trying to learn (and implement) Quine-McCluskey algorithm for boolean function minimalisation. I'm learning the algorithm from wikipedia example. From that I understood the following: Take all ... 0answers 60 views ### Unipotent representations of SL(2,R) by quantization I'm a PhD student in mathematical physics and I happen to need some elements of Kirillov's "orbit method" for producing representations of Lie groups. I'm familiar with symplectic geometry, geometric ... 3answers 38 views ### Proving$x^2 < y^2$by means of the Ordering Axioms [closed] How do I prove$x^2 < y^2$, if$0 \le x < y$with the ordering axioms? thanks! 1answer 51 views ### Check the convergence (& absolutely) of parametric integral [closed] $$\int\limits_{-1}^{1} \left(\frac{1+x}{1-x}\right)^{\alpha} \ln(2+x)dx$$ Don't know where to start.. 1answer 73 views ### Finding the oblique asymptote of: Given $$f(x)=\frac{x^2+1}{(x+1)^{\frac{1}{2}}}$$ how would you find the oblique asymptote of that? 2answers 99 views ### Is$\sum i^{1/i}$bounded? I'm trying to find the limit $$\lim_{n\to\infty}\sum_{i=1}^n \frac{i^{1/i}}n\,.$$ I was going to say that$\lim_{n\to\infty} \frac1n=0$and$\sum i^{1/i}$is bounded but I can't prove it. 0answers 37 views ### Huygens formula Let AB - arc of the circle , and the scale degree of the arc, and as the radius of the circle are unknown . For approximate calculation of the length of the arc used as follows. Notes on the arc of ... 1answer 54 views ### Simplifying the quotient$\frac{4x^4+2x^2+x+1}{x^2+1}$I got stuck simplifying the following quotient. How to divide it? $$\frac{4x^4+2x^2+x+1}{x^2+1}$$ Thanks a lot! 1answer 75 views ### Varieties over a field$K$are also varieties over any subfield of$K$. Suppose that$f:X\longrightarrow\text{Spec} K$is a variety over$K$, namely$X$is an integral, separated$K$-scheme of finite type. Now if$L$is a subfield of$K$, it is clear that there exists a ... 2answers 146 views ### Show that there do not exist 3$\times$3 matrices$A$over$\mathbb{Q}$such that$A^8 = I $and$A^4 \neq I.$. Show that there do not exist 3$\times$3 matrices$A$over$\mathbb{Q}$such that$A^8 = I $and$A^4 \neq I.$. I am aware that the minimal polynomial of$A$divides$(x^8−1)=(x^4−1)(x^4+1)$.If the ... 1answer 50 views ### Can we calculate the order of$\hom (G,G')$in terms of$|G| $and$ |G'|$, when$G,G'$are finite abelian groups? Let$G,G'$be abelian groups and let$\hom (G,G')$be the set of all homomorphisms from$G$to$G'$. We define an operation$\ast$on$\hom (G,G')$as: for$f,g \in \hom(G,G') \space , (f\ast ...

15 30 50 per page