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Question on relations [duplicate]

-1 down vote favorite Define the relation on Q by [m,n]<[j,k] if and only if jn−mk belongs to N, j and m belong to Z, n and k belong to N. (a) Show that < is well defined, that is if ...
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3answers
117 views

Nonnegative function satisfying integral constraints [closed]

Find a real function $w(t)\in L_2[0,1]$ such that: $w(t)\geq 0 \quad \forall t\in [0,1];$ $\displaystyle\int_0^{s}w(t)dt\leq s \quad \forall s\in [0,1];$ $\displaystyle \int_0^1 w(t)dt\leq 2;$ ...
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2answers
75 views

Is there a sequence of $v_{n}$ such that $G=\prod_{n=1}^{\infty} \frac{2\tan^{-1}(v_{n})}{\pi}> 1$?

Let $G=\prod_{n=1}^{\infty} \frac{2\tan^{-1}(v_{n})}{\pi}$, where $v_{n}$ is an increasing, monotonic sequence of natural numbers: is it true that there is no sequence of $v_{n}\in\mathbb{N}$ such ...
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861 views

elliptic functions on the 17 wallpaper groups

In doubly periodic functions as tessellations (other than parallelograms), we learned about the Dixonian elliptic functions. There are 17 wallpaper groups -- are there elliptic function analogues for ...