Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 161

Arrows in a presheaf category covariantly induce maps between subfunctors

I am currently reading Sheaves in Geometry and Logic and have hit a little bit of a snag that I can't figure out. In the book it is claimed that...

Asked on 01/02/2021 by subobject_classifier

1 answer

Showing that a family is not normal

Suppose $f : mathbb{D}setminus {0} rightarrow mathbb{C} $ is analytic and $z=0$ is an essential singularity of $f$. Show that the family ${f_n} $ defined by...

Asked on 01/01/2021 by Kabouter9

1 answer

1991 IMO shortlist problem $#11$

PROBLEM : Prove that $sum_{k=0}^{995} frac{(-1)^k}{1991-k} {1991-kchoose k} = frac{1}{1991}$ As usual there isn't anything special about the number $1991$.Problem appears to hold for any odd numbers I...

Asked on 01/01/2021 by Mathematical Curiosity

2 answer

Fubini's Theorem on periodic function.

I'm preparing for my qualifying exam and i want some imput in my solution of this problem.Let $f:Bbb{R} to Bbb{R}$ measurable and $1-$periodic(i.e $f(x+1)=f(x),forall x in Bbb{R}$)...

Asked on 01/01/2021 by Marios Gretsas

0 answer

For an non-constant and non-vanishing entire function $f$ , the set $ U = { z in C : | f(z) | <1 } $ has unbounded connected component.

Suppose $f$ is an non constant entire function with $ f(z) neq 0 $ for all $ z in C $. Then the set $ U...

Asked on 01/01/2021 by Learner_Shas

1 answer

Examples of countable and uncountable Bernstein sets

I'm looking for concrete examples of a countable Bernstein set and an uncountable Bernstein set. I haven't been able to find or construct any specific examples so far....

Asked on 01/01/2021 by Newman

1 answer

How can I prove the dimension axiom here?

Here is the problem:I want to prove the dimension axiom in (a). My professor gave me the dimension axiom for reduced...

Asked on 01/01/2021

1 answer

swap integral to polar

Trying to swap to polar and solve the following double integral, but I am not getting the same answer. $displaystyleint_{-3/4}^{3/4} int_{-sqrt{3/4-x^2}}^{sqrt{3/4-x^2}} 1/2left(3-4sqrt{x^2+y^2}right) dy dx$ Here is the...

Asked on 01/01/2021 by kapios

1 answer

Evaluating $sin 10^circ + sin 20^circ + sin 30^circ + cdots +sin 90^circ$

The question is finding$$S = sin 10^circ + sin 20^circ + sin 30^circ + cdots +sin 90^circ$$I tried to do it, but I can't eliminate the $cos...

Asked on 12/31/2020 by Crevious

1 answer

Plotting multiple planes with three variables in 3D using MATLAB

I couldn't figure out, how I could plot three different equations with three variables, namely x,y and z in MATLAB or any other Mathematical Softwares. I know that there's a...

Asked on 12/31/2020

1 answer

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