Highest scored questions
159,063 questions
-2
votes
1
answer
911
views
Is any prime ideal of $K[X_1,...,X_n]$ the intersection of a finite number of maximal ideals? [closed]
If $K$ is an algebraically closed field,
Is any prime ideal of $K[X_1,...,X_n]$ the intersection of a finite number of maximal ideals ?1
-2
votes
2
answers
2k
views
Taylor series of a complex function that is not holomorphic
I want to create Taylor series of a complex function that has complex conjugate in it. Obviously I cannot do a total derivative but derivations over real and imag parts exist.
Bonus question: Can I ...
-2
votes
1
answer
141
views
Prove the function $g(x,y,t)\ge1$
I have the function
$$
g(x,y,t)=\frac{(8x^2y^2+f_+(x,y,t)-\cos(2t))(8x^2y^2(1+(x+y)^2)+(x+y)^2(f_-(x,y,t)-\cos(t))+4xy(x+y)\sin(2t))}{64x^4y^4(1+(x+y)^2)}
$$
with
$$
f_{\pm}(x,y,t) = 1+2x^2+2y^2\pm4xy\...
- 375
-2
votes
1
answer
192
views
Can we have consistent theories stating opposing provability statements that are non-standardly coded?
I want to coin a notion of "strong provability", to be defined as:
$S$ is strongly provable in $T$ if and only if there is a Gödel code of its proof in $T$ that is strictly smaller than any ...
- 11.3k
-2
votes
1
answer
139
views
Convergence of scrambled product for Dirichlet-$L$ function with modulo 4 character
A Dirichlet-$L$ function is typically defined by its series, and its Euler product is a consequence of the definition. Here my approach is the other way around.
I define the function
$$
L_4^*(s) = \...
- 3,098
-2
votes
3
answers
211
views
A Specific Linear Homogeneous System of Differential Equations with Variable Coefficients
Is there an analytical solution satisfying these 3 equations with non-constant z?
$$\frac{dx}{dt}=-z\cdot\cos(\omega t)$$
$$\frac{dy}{dt}=z\cdot\sin(\omega t)$$
$$\frac{dz}{dt}=x\cdot\cos(\omega t) - ...
- 1,547
-2
votes
1
answer
317
views
Is it natural to hold that Ur-elements, small & big sets and proper classes exists? [closed]
The topic of this post was shifted to
https://philosophy.stackexchange.com/questions/49504/is-it-natural-to-hold-that-big-sets-and-proper-classes-exist
Since it was deemed to be a philosophical ...
- 11.3k
-2
votes
2
answers
298
views
Combinatorial proof of identity [closed]
The following admits of many (easy) proofs, but I am seeing no purely "bijective" argument:
$$
\sum_{j=n}^N \binom{j}{n} = \binom{N+1}{n+1}.
$$
Any ideas?
- 96.4k
-2
votes
1
answer
345
views
Generalizations of the twin primes conjecture [closed]
This is a question about generalizations of the twin primes conjecture.
I would like to know a counterexample, or a proof, for the following couple of related arithmetical sentences. The first is
...
-2
votes
1
answer
796
views
What is the Complete Set of Shortest Axioms of Classical Conditional-Negation Propositional Calculus? [closed]
Suppose that we only have propositional variables and connectives. Suppose our rules of inference are detachment {C$\alpha$$\beta$, $\alpha$} $\vdash$ $\beta$, and uniform substitution. Suppose that ...
- 133
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votes
1
answer
203
views
Holomorphic maps on $\mathbb{R}^{n}$ (for n not necessarily even)
Edit according to the comment of user36931 I remove the "motivation" from the previous version and I add an statement to the first question
We consider the following two classes of smooth maps on $...
- 366
-2
votes
1
answer
331
views
Polygon Problem [closed]
There are $N$ regions which are numbered from $1$ to $N$. Each region is represented by a single simple polygon on the 2D plane. Simple polygon means the boundary of the polygon does not cross itself. ...
-2
votes
1
answer
614
views
A diffeomorphism between complex manifolds which is not a holomorphic map [closed]
Can someone give an example or a reference on this?
- 1
-2
votes
1
answer
230
views
example of two groups [closed]
Are there two infinite and non- abelian finitely generated groups $G$ and $H$ such that $\frac{G}{ G^{\prime}} \cong \frac{H}{H^{\prime}}$ and $G^{\prime}$ is finite but $H^{\prime}$ is infinite?
- 5
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votes
1
answer
1k
views
holomorphic extension of a function [closed]
hi,
I have the following question: let $U \subset \mathbb{C}^{n}$ be some open set containing zero. let $\tilde{U} = U \cap \mathbb{R}^{n}$. assume we have a real-valued analytic function $f : \tilde{...
- 29
-2
votes
1
answer
708
views
"Strange" prime number" [closed]
Let p = a_1a_2.. a_n be a prime number.
Definition: p is "Strange" if p remains prime after deletion of any a_i.
Example 1: 731. If you delete 7 => 31 (prime), if you delete 3 => 71 (prime)
if ...
-2
votes
1
answer
1k
views
Unpopular "elementary" theorems/identities to impress an audience of mathematicians. [closed]
This question grew out of my recent job interview. Since the interviewers were math professors, I had a hard time searching for interesting elementary theorems in case I got asked for one.
I thought ...
-2
votes
6
answers
3k
views
Is this an if-and-only-if definition of affine? [closed]
x -> A x+ b.
Quoted from Affine transformation:
In general, an affine transformation
is composed of linear transformations
(rotation, scaling or shear) and a
...
- 21
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votes
2
answers
322
views
Bounds for analytic circles
It is known that for certain particular entire functions $f(s)$ of first order, in the circle $|s| = p$, if $\epsilon$ is a positive number as small as desired, the following bound holds:
$$|f(s)| = O(...
- 27
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votes
2
answers
503
views
Can Mereology be bi-interpretable with Set Theory, in absence of the bottom object?
This question is about synonymy between Set theory and Mereology.
David Lewis in Mathematics is Megethology tried to reduce Set Theory to Mereology augmented with a singleton function. The following ...
- 11.3k
-2
votes
2
answers
149
views
Calculate the great common factor between $2^{2n+1}-1$ and $2^{4m+2}+1$ [closed]
How to calculate the great common factor between $2^{2n+1}-1$ and $2^{4m+2}+1$, where $n$ and $m$ are positive numbers.
We guess that: the great common factor is $1$.
- 577
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votes
1
answer
405
views
What is Bernoulli umbra philosophically?
Well, Bernoulli umbra is an umbra whose moments are the Bernoulli numbers.
But what is it philosophically?
For instance, we can consider imaginary unit $i$
an umbra with moments $\{1,0,−1,0,1,\ldots\}$...
- 10.1k
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votes
1
answer
248
views
Are there any non-elementary functions that are computable?
Does a function $\mathit{f}:\mathbb{R}→\mathbb{R}$ being non-elementary (not expressible as a combination of finitely many elementary operations), imply that it is not computable?
The particular case ...
- 11
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votes
1
answer
139
views
Congruence modulo 4 for a generating function leads to perfect squares? [duplicate]
Consider the number of integer partitions $p(n)$ of $n$ whose generating function is
$$\sum_{n\geq0}p(n)\,x^n=\prod_{k\geq1}\frac1{1-x^k}.$$
Also, the number of partitions into distinct parts $Q(n)$ ...
- 43.2k
-2
votes
1
answer
113
views
Does one have $2r_{0}(n)\lesssim k_{0}(n)(\log n)^{1+1/k_{0}(n)}$?
Under Goldbach's conjecture, I'm trying to find an upper bound for $r_{0}(n):=\inf\{r>0,(n-r,n+r)\in\mathbb{P}^{2}\}$ that would generalize Cramer's conjecture.
Denoting by $k_{0}(n)$ the quantity ...
- 6,982
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votes
2
answers
360
views
Basic research problems references [closed]
I have been looking for research problems in pure mathematics that I can try to solve for publishing papers. I am quite aware that it takes a lot of time and effort to get to a level where I can do ...
-2
votes
2
answers
223
views
Early examples of proof appraisals [closed]
What are the earliest known examples for attributing proofs as 'deep', 'elegant' or 'beautiful' (or their equivalents in other languages)?
Gauß for example called one of his results 'remarkable' ...
- 13.2k
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votes
2
answers
120
views
Does $\omega(G)\leq k$ imply $\chi(G)\leq k$ for $n\geq 3$? [closed]
Let $G$ be a simple graph with $n$ vertices. Let $\omega(G)$ and $\chi(G)$ denotes the clique number and chromatic number of $G$ respectively. Then
Does $\omega(G)\leq k$ imply $\chi(G)\leq k$ for $...
- 4,195
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votes
1
answer
159
views
Chromatic number of transposition graph of permutations
For any $n\in\mathbb{N}$ let $[n] = \{1,\ldots,n\}$ and let $S_n$ be the set of all bijections (permutations) $\pi:[n]\to [n]$. For any set $X$ let $[X]^2 = \big\{\{x,y\}: x\neq y\in X\big\}$. We let ...
- 48.9k
-2
votes
1
answer
516
views
no classification of nilpotent lie groups
there is no classification of (simply connected) nilpotent lie groups, but I am tempted to try to generalize the construction of the Heisenberg group. For an upper triangular matrix:
$$ \left(
\...
- 22.8k
-2
votes
1
answer
141
views
English Translation of French Verseurs [closed]
Trying to read Lamaitres 1948 paper on Quaternions, in reply to Klein's Verlangen program, but can not find a translation of term Verseurs, which is even a section heading:
"Un quaternion dont la ...
- 13
-2
votes
3
answers
447
views
Determinant of matrix from set {-1, 1} [closed]
Let $A \in \mathbb{R}^{11 \times 11}$ and it's elements are form set $\{ -1,1 \}$. $\mathbb{P}(-1) = \mathbb{P}(1) = 0.5$. What is a probability to get such a matrix, that $\det A > 4000$?
I have ...
- 45
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votes
3
answers
279
views
algebra group theory [closed]
If A, B, C be abelian grops and if A isomorph with direct sum of B and C and A be isomorph with B what we can say about C?
- 1
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votes
2
answers
298
views
examples of totally geodesic subset
Could you give examples of totally geodesic subset of codim>1 in positively curved Alexandrov space?
- 689
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votes
1
answer
1k
views
Why should I believe in the Siegel's and Hasse's rationale ?
Hello everyone,
I was deeply attracted by the Hasse and Siegel's theorems while studying $p$-adic analysis. While reading a paper B.J. Birch and H.P.F. Swinnerton-Dyer - Notes on elliptic curves. I, ...
-2
votes
3
answers
697
views
Is this isomorphism canonical?
Suppose $A\leq A',B$ and $C' \leq C$ are (finite dimensional) vector spaces.
Suppose that
$$ 0 \to A \to B \to C \to 0 $$
$$ 0 \to A' \to B \to C' \to 0 $$
are exact. Then using a dimension argument ...
- 2,810
-2
votes
1
answer
142
views
Solution to Erdos-Ulam problem [closed]
I have solved the Erdos-Ulam problem (see link) and can construct a set that satisfies the conditions (dense in R2 with all interpoint distances rational). I have expanded the solution from two ...
-2
votes
1
answer
298
views
Is polynomial not bijective, on this finited field?
Let $(a,b,c) \in \mathbb F_p,p=2^{127}-1$ and $P(x)=x^{16}+ax^{11}+bx^{5}+c$.
Is it true that $P(x)$ not bijective on $\mathbb F_p$?
I have asked this question here (*), but no answer.
(*) : https://...
- 4,074
-2
votes
1
answer
210
views
Reference request on dynamics and hyperbolic dynamics (hyperbolicity in absence of periodic orbits)
I would appreciate if you introduce me a reference (paper or book) who address the concept of hyperbolic dynamics but with emphasis on absence of periodic orbits. a possible ...
- 366
-2
votes
1
answer
241
views
Does a group representation being transitive on a basis imply irreducibility?
Let $G$ be an infinite discrete group and $\pi$ a representation of $G$ on the Hilbert space $H$.
Suppose that the group representation is transitive on an orthonormal basis $B = \{e_j\}_{j=1}^{\infty}...
-2
votes
1
answer
141
views
Interpretation and validity of modified Heisenberg uncertainty principle in a metric context? [closed]
Considering the Heisenberg uncertainty principle, which states $\Delta x \cdot \Delta p \geq h$, I've explored a modified version by computing $(\Delta x + 1)(\Delta p + 1) \geq \Delta x \cdot \Delta ...
- 3,074
-2
votes
1
answer
175
views
Simple closed form for $\int \lfloor x \rfloor dx$? [closed]
Wolfram Alpha claims there is no closed form in terms of standard funcions
for $\int \lfloor x \rfloor dx$ but we believe we found
simple closed form agreeing with experimental data.
Define $i_1(x)=x -...
- 25.4k
-2
votes
1
answer
176
views
Which extension of ZFC proves that ZFC can only prove CH satisfied by the first two sets?
Which extension of $\sf ZFC$ prove that
$$ {\sf ZFC} \not \vdash \exists x \, ( \operatorname {CH}(x) \land x \neq \emptyset \land x \neq 1)$$
Where $\operatorname {CH}(x) \iff \neg \exists \kappa \, (...
- 11.3k
-2
votes
1
answer
134
views
A generalized norm function in $\mathbb{R}^n$ [closed]
We defined a new norm. The norm of $x \in \mathbb{R}^n$ is defined as
$$ N_P(x) = \min \{t \geq 0 : x \in t\cdot P\} \enspace,$$
where $P$ is a centrally symmetric and convex body centered at the ...
- 31
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votes
2
answers
487
views
Does function $f(x)=f(2x)$, $f(x)$ - non const, exist? ($f(x)$ - continuous function on real numbers) [closed]
When I tried solve it I had found just answer "No". I spoke with some people but I cannot understand why the answer is exactly it...
Frankly speaking, this function haunts me:
$f(x) = abs((...
-2
votes
1
answer
277
views
Is equational logic in universal algebra a proof system not a logic system?
As far as I know a logic system defines its own semantics (e.g. $\models$), but not a proof calculus/system on its language. See p261 in Ebbinghaus et al's Mathematical Logic:
In universal algebra, ...
- 357
-2
votes
1
answer
587
views
Is the conjecture true for n-sphere $(n>2)$? [closed]
This is higher dimension conjecture of Problem 3845 in Crux Mathematicorum and Theorem 2 in here:
PS: This figure is very nice, this is also generalization of Brianchon’s theorem, The Pascal theorem, ...
- 1,776
-2
votes
1
answer
131
views
Graph Coloring Proof χ (G) ≤ δ + 1 for k-criticals [closed]
I need this proof:
Let $G$ be a graph such that $\chi (H) <\chi (G)$ for every subgraph $H$ of $G$. A graph is called $k$-critical, if in addition $\chi (G) = k$. Prove that $\chi (G) ≤ \delta + 1$...
- 7
-2
votes
1
answer
169
views
Ricci flow and evolution of the shape of drops in spray
Several years ago, I was a trainee in a physics lab where I was supposed to study atomisation in sprays (ensemble of liquid drops). As we did observe that the drops tended to adopt a spherical shape ...
- 6,982
-2
votes
1
answer
514
views
Arranging blue and red balls in a circle [closed]
Suppose we have $b$ identical blue balls and $r$ identical red balls. How many ways are there to arrange them in a circle?
Clearly, if we wanted to arrange the balls in a row, the answer would have ...
- 419