# Tagged Questions

15 views

### Implementing Equation on current data

I am trying to implement Personality, Gender, and Age in the Language of Social Media equation. I have 5 patterns and one list of 100 text = 900 words. The result of find a Match in the 900 to the ...
Suppose $f,g$ are real valued on $\mathbb{R}$ (and no further restrictions apart from the obvious requirement that the integrals exist), then when does $\displaystyle\int f(x)g(x)\,dx = \int f(x) \, ... 0answers 62 views ### Fourier transform of a function involving$\sec(\omega)$The summary of my question is: What should I make of$\mathcal{F}^{-1}\left[\frac{\csc(\omega)}{\omega^2-\beta^2}\right]$where$\mathcal{F}^{-1}$is the inverse fourier transform (taking$F(\omega)... 0answers 45 views ### What is the analytical solution to a Volterra integral equation? I need to solve a following equation: $$r_{k+1} = -\sum\limits_{l=0}^{k-1} r_l \cdot (k-l) \cdot \left(\frac{\omega}{t_c - l}\right)^{2 \beta} + \delta_{k,0}$$ subject to ... 0answers 40 views ### regarding a set of integro-PDE Let say I have a minimal example that contains most of the mathematics I am looking for. The example is as follows: \begin{align} &\frac{\partial u^0}{\partial t}(x,t)+\frac{\partial^2 ... 1answer 34 views ### A question on functional equations. Question: If it is given that $$e^xf(x) = 2 + \int_0^x\sqrt{1+x^4}\,dx$$ then what is the value of \dfrac {d} {dx} \Big(f^{-1}(x)\Big)\Bigg|_{x=2} $Where I am stuck: Now, since we are to ... 1answer 66 views ### Solving the equation$\displaystyle \frac{e^x}{x}=\int_n^{n+1}f(t)\,dt$Suppose the equation$\displaystyle \frac{e^x}{x}=\int_n^{n+1}f(t)\,dt$as$f(t)=\frac{e^t}{t}$and$n\in \mathbb{N} \setminus{0}$. How to prove that: The equation above has a unique solution$U_n$... 0answers 24 views ### Multiple integrals satisfying functional equations If$f:\mathbb{R}_+\to\mathbb{R}_+$is a positive function which is locally$L^1$with$\int_0^t{f(s)ds}=at^n$for all$t\geq0$then, by differentiating, it follows that$f(t)=a$if$n=1$and$f=0=a$... 1answer 177 views ### Integral Inequality$|f''(x)/f(x)|$Let$f$be a$C^2$function in$[0,1]$such that$f(0)=f(1)=0$and$f(x)\neq 0\,\forall x\in(0,1).\$ Prove that $$\int_0^1 \left|\frac{f{''}(x)}{f(x)}\right|dx\ge4$$
I have an equation like this: $$te^{t} = \int_0^t e^\tau u(\tau)d\tau$$ I don't really know how to solve it.. Would it be possible to differentiate both sides of the equation? If so, how can I do it ...