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H: Importrange when copied to other cells automatically change range
I am using importrange to pull data from my responses page to my spreadsheet. I have completed the first sheet but I now need to go into the sheet to follow on where sheet one has run out of space. The problem is I have copied the importrange script ... |
H: Automatic merging of duplicate cells under common ID
I have data in column A with IDs and a column B with data for those IDs.
Right now I have multiple (usually 2-3) rows with the same ID but different data. What formula to use to merge those into one row per ID?
AI: =ARRAYFORMULA({UNIQUE(INDIRECT("A2:A"&COUNTA(A1:... |
H: How to generate all combinations of letters in a word?
Using Google Sheets, how would I show all possible ways to type a word, for example:
word
Word
WOrd
WORd
WORD
wOrd
woRd
worD
without any length word?
The given word would go on Row A and the possible combinations would go in Row B.
AI: If you type your word by... |
H: How can I undo deleted comment on YouTube?
I tried to edit a YouTube comment and instead click on delete:
After clicking on delete I get a notification that the comment was deleted but I didn't see any undo option:
How can I undo delete comment on YouTube?
AI: Currently, there is no "undo" functionality on YouTub... |
H: I am looking to fetch a table from a website in Google Sheets
I want the first table on this URL https://www.cashbackmonitor.com/cashback-store/amazon/ in my google sheet.
When I put this function (below), I can retrieve the first column of the first table e.g. Shop at Home, Top Cashback, etc. However, I am not ab... |
H: What does the query parameter "sub_confirmation=1" do on a YouTube link?
I recently came across a link to a YouTube video with
?sub_confirmation=1
appended to the link.
What does this do?
AI: What this does is automatically subscribe the follower of the link to the YouTube channel that posted the video.
It's not t... |
H: What is the correct LinkedIn page cover image size?
I checked the size guide for LinkedIn cover images here
For page, they say:
1192 (w) x 220 (h) pixels (min)
1536 (w) x 768 (h) pixels (recommended)
Doubt 1: Both have different ratios. Why is that?
Doubt 2: When I opened developer tools, I found the dimensions ... |
H: Total of cells formula for numbers as text
I want to total up the numbers of split cells. I have an example as follows:
1234
0000
5678
each number is in its own cell, I want to total it all up underneath to get
6912, so 1234 + 0000 + 5678 = 6912 if this makes sense.
AI: use SUMPRODUCT which is able to sum numbers ... |
H: How to use the SPLIT function in Google Spreadsheets with different delimiters and with some delimiters with multiple characters?
My question is similar to this one:
SPLIT function in Google Spreadsheets with OR statement
but has the following difference:
I want to use the delimiter "apple" and the delimiter "." wi... |
H: Split cells not importing first 0
I am using split formula:
=IFERROR(SPLIT(REGEXREPLACE(" , "&U4, "(\d)", "$1 ,"), ", "))
It works great except if I have 0250, it imports it across as 250, even with the cell it's importing from is set to #000 and it sits in the 1st 3 cells instead of the 2nd 3rd and 4th cells... |
H: What does the "Share it with the same people" option do when making a copy?
When making a copy of a document in Google Docs from File > Make a copy…, there is an option to Share it with the same people. What does that option do? Does it share the doc with the same people as the source folder or the destination fo... |
H: How to aggregate data from multiple Google sheets with a tag
I am importing data (using IMPORTRANGE) from 3 different sheets to 3 different tabs of a google sheet.
Then I am aggregating those three sheets into one and also filter them using a query.
Ex:
=query({BUOne!A1:Y200;BUTwo!A1:Y200;BUThree!A1:Y200},
"Select... |
H: ArrayFormula not showing 0s
I use the following formula to calculate plain text so to show leading zeros.
=ARRAYFORMULA(SUM(S2:S17+0))
but it's only displaying the results without the leading zero.
Example, if It is adding up 0100+0200 it is displaying an answer as 300, but I need it to display 0300.
AI: If this i... |
H: How to refer to elements of a dynamic array in Google Sheets?
I'm trying to create teaching timetables dynamically, by searching through a large table with all of the information about what time a lesson takes place, who the tutor is, what age group is being taught, and what subject it is.
I'm able to generate all ... |
H: How to timestamp on new added cells in LIVE google spreadsheet?
The code below insert timestamp in google sheet by editing another column.
However, there an issue which I have no idea how to solve. When I add new row manually, it successfully adds timestamp, BUT I have an html form in my website which sends data t... |
H: How can I add details to goals in Google Calendar?
I have been using goals in Google Calendar for quite sometime now. They are very handy and easy to use. Just create a goal you want to accomplish, set preferred time and frequency and you are all set.
However, there are some extra things that i want to do with Goa... |
H: IF AND not working in Google Sheets for Conditional Formatting
I am trying to use the three following functions...
=IF(AND(M3="Funding on Hold",R3>=3,R3<=6),TRUE,FALSE)
=IF(AND(M3="Funding on Hold",R3<=9,R3>=7),TRUE,FALSE)
=IF(AND(M3="Funding on Hold",R3>=10),TRUE,FALSE)
The objective is to conditionally format th... |
H: Count unique values in second column corresponding to unique value in first column
I have a Google sheet with cities corresponding to countries like this. Notice that neither countries nor cities are unique and there can be duplicates.
| A | B |
------------------------
| UK | London |
| UK ... |
H: Assert cell style onto text pasted into that cell
I'm not quite sure how to word this so I couldn't find any answers to my question after some searching.
I am trying to copy and paste values into my Google sheet. These values are copied from another website which has a different font and font size than that which I... |
H: Array Formula with IF function and SUMIFS function
I am trying to convert the below formula into an array formula. I can make it work in an array, but it displays the wrong values, compared to the normal formula which I have to drag down.
Normal formula:
=if(K4>0,
(if(((sumifs($K$4:$K,$A$4:$A,A4)-(sumifs($L$4:$L,$... |
H: How to programmatically drag new rows - running total?
I have the first few rows of my mortgage payments set up, and I want to know how to programmatically print the rest of the rows, as opposed to dragging the little corner box to output the rows.
This is important so that I can adjust the payment period, and auto... |
H: Using a script to only take only take cells with values in google sheets
tl;dr how can I make the script take an entire column (eg A:A) and then ignore the first (header) row, and any blank rows?
Background
I have an array in Google Sheets with date-ordered data (note dates are in UK format), where I will routinely... |
H: How to get correct TimeZone in googlesheet using script?
I have wrote following script in my google sheet hoping to convert a timestamp in GMT to a customized timezone.
function myFunctions(datetimeString,timeZone,format) {
var moment = new Date(datetimeString);
return Utilities.formatDate(moment, timeZone, "yy... |
H: Scroll google calendar month view one week at a time, to span 2 months partially - "vertical scrolling"?
Since years, I'm annoyed when trying to scroll in month view. It always jumps to the beginning of the next month. This feels really bad and sometimes makes it hard to visualize and understand how several events ... |
H: Sorting columns with script instead of macro
I currently use a macro script to filter my sheet upon opening the sheet by column A, and I wondered if there was a more efficient/simple way to do it with scripts?
function Sort() {
var spreadsheet = SpreadsheetApp.getActive();
spreadsheet.getRange('3:138').activa... |
H: App Script to move a row of data from one Google sheet to a different one (different sheet id's) based on a cell entry
I'm currently trying to adjust a script I found that copies the contents of a row from one tab of a google sheet, pastes it into the next descending empty row in a different tab and then deletes th... |
H: Solve errors in a series of FILTER functions within array brackets?
I have been working on a budget project on Google Sheets. My goal is for a range of data to be filtered by date (which is represented as an integer between 1 and 31 for the day of the month). All entries in the first two columns are returned if the... |
H: Submit response but not submit?
I have a form for timesheet, that each row is a different job description, job number, hours booked to job etc.
I have it so when you submit, it fills in the response sheet in order from top to bottom.
Problem I have is I want to run some functions set by a trigger that sends a copy ... |
H: Google Drive link parameter to hint which account (email) to access with
Is it possible to construct a link to a Google Drive file and specify the email account to access the file as? I know that it is possible to use /u/1 or /u/2 in the path, but I am looking at generating a link to send to users who own multiple ... |
H: Outputing Array Formula in one row
I came across the below array formula, which works really well, I'm just struggling to tweak it, and barely understand it's inner workings, but it's very good. Instead of displaying a total of stock left per line, I wondered if someone could help me keep it on one line? Example on... |
H: In ARRAY_LITERAL, an Array Literal was missing values for one or more rows
I've been trying to get this array formula to work, but I get an error. It's just a vlookup array to display multiple columns. It works fine without the {""; bit, but I want it to drop down one row.
={"";ARRAYFORMULA(IFERROR(VLOOKUP($AA$4:$A... |
H: Skip arrayformula if the result of that formula is blank
I have an array formula that looks like this:
=ArrayFormula(IF(COUNTIF(B2:B, QUERY('Form Responses'!B2:G, "select G where B != ''"))=0, IFERROR(QUERY('Form Responses'!B2:G, "select B, G where B != ''"), "")))
It retrieves data from a different sheet that's c... |
H: Conversion from LibreOffice to Google Sheets
I use LibreOffice to create xlsx files. There are some formulas to test conditions. Everything is ok under LibreOffice but when I open the file with Google Sheets formulas give the wrong result.
e.g. the following formula
=IF(C32="","",IF(COUNTIF(C6:C28,"SA|PA|MA|PB|MB"... |
H: How can I float text by text in Google Docs
See the attached image below, which shows that a side-note is added so that the normal text of the document "floats around it":
How is that technique called - Is there a name for it?
And how can I accomplish that in Google Docs?
AI: It is called text wrap and you can do ... |
H: Pull image or skip to next cell if empty
I am currently using Google Sheets to make a list of videos and thumbnails.
I have various sheets titled: Frying, Stewing, Baking, etc. Within each sheet, there are only two columns which include a thumbnail image and a text link. I would like to create a page which pulls th... |
H: Dynamically creating column names based on data in another tab
I have a Google sheet that logs all submissions on my website of various contact forms. I need to know how many times each contact form has been submitted, and in which week they were submitted.
The goal is to have a Google sheet to look like this:
(Eac... |
H: Auto forward non alias emails to our G Suite domain
To group emails from projects we send them to a project mail address (for example all mails of project "Vanardenne" are sent to "Vanardenne@reekmansverandabouw.be". To achieve this we make an extra alias. Is there a way to automatically forward these emails withou... |
H: Adding date picker to Google Sheets cells while data validation is customized
I have a column with customized data validation (custom formula) that accepts only dates, provided that a few other conditions are met.
How can I add a date picker to the cells of this column? Changing the Format did not help.
Edit: I wan... |
H: How can I change the font of selected text within a cell in Google Sheets using keyboard shortcuts?
I am attempting to change the font of selected text within a cell in Google Sheets using a keyboard shortcut.
I have attempted the steps meant for google docs here: How can I change the font in Google Docs just wi... |
H: Entire Column green if all cells in it are empty
I would like all columns that only contain empty cells to light up green.
In the below picture these should be: C3:C8, D3:D8, E3:E8, L3:L8
What would be the correct custom formula for this?
Bonus question: I would also like columns that contain only a question mark... |
H: Google Sheets Split row in multiple rows
I'm doing a spreadsheet for an event and I need to split a row into multiple rows. It's getting data from a form.
I need a script that can arrange the data like in the blue rectangle.
AI: ={Sheet1!A1:D1;
ARRAYFORMULA(TRIM(SPLIT(TRANSPOSE(SPLIT(TRIM(QUERY(TRANSPOSE(QUERY(TR... |
H: How to get an array for a range per a column in Google Sheets?
I'm looking for creating a similar formula:
=UNIQUE({A:A;B:B;C:C})
So, I need such kind of a range {A2:A;B2:B;C2:C;...} (each column separated with the semicolon) for several hundred columns.
Seem, it will be a mess if I will try to type it manually.
C... |
H: Force Google Docs/Sheets to ALWAYS paste values only (merge formatting)
I do a LOT of copying from external sources and pasting into Google Docs/Sheets. Is this at all possible? I know the keyboard shortcut but can't seem to get used to it. Would save me so much time!
AI: Google Sheets & Google Docs does not allow ... |
H: How to format clipboard text as data row in Google Sheets?
I've noticed copying text with a link preserves the link when pasted in Google Sheets. I've also tried copying an inline list from an HTML page and noticed it gets copied as two rows.
Is it possible to format text such that it gets pasted as a single row an... |
H: How to setup a folder for other people drop photos into?
I want to give people a link and have them click on the link and then be presented with a page where they can drag and drop photos into.
I've tried doing it on OneDrive but that requires everyone to have an MS account.
I've also tried Dropbox, but they wa... |
H: For polynomial prove that $r(x)=0$ or $\deg [r_k(x)]<\deg [b(x)]$
Suppose $a(x),b(x)\in \mathbb R[x]$, $\deg(b(x)) \geq 1$. Show that there exists $m=0,1,\dots$ and $r_0(x),\dots,r_m(x)\in\mathbb R[x]$ such that
$$ a(x)=r_0(x)+r_1(x)b(x) + \cdots + r_m(x)b(x)^m$$
with the property that either $r_k(x)=0$ or $\deg[r_... |
H: On the primality of integers of the form $p^2+k$
I am not able to find an answer to the following question:
For which positive even integers $k$ is the integer
$$p^2+k$$ prime, where $p$ is a prime number $\gt5$?
AI: $p^2 \equiv 1(\mod 3)$
$p^2+ k \not \equiv 0(\mod 3) \implies k $ is of form $3n$ or $3n+1$.
$p... |
H: Find quotient space on $\mathbb{N} $
On $\mathbb{N}$ is given equivalence relation R with $nRm \iff 4|n-m$. Topology on $\mathbb{N}$ is defined with $\tau=\{\emptyset\}\cup\{U\subseteq\mathbb{N}|n\in U \wedge m|n \implies m\in U\}$.
I need to find quotient space $(\mathbb{N}/R,\tau_{R})$.
I have solution: $\tau_{R}... |
H: example of a particular type of graph
I am searching for those classes of graphs where distance between any two vertices of the graph is $d$. Are there such type of graphs, after leaving the $Complete Graphs, K_n$.
Thanks for your help.
AI: I'd say no. If the graph is not complete, there are going to be two nodes $... |
H: How to find the intersection of two given lines
How to find intersection of two lines below:
$$
\left \{ \begin{array}{ccc}
3x − 2y & = & 5\\
7x + 3y & = & 4
\end{array} \right .
$$
I know the answer is $(1,-1)$, but I cannot find it with the methods. I have already tried to solve pairs of linear equations.
AI: try... |
H: Infinitely many solutions vs one solution vs no solution in systems involving an unknown constant
Just need a little clarification in case my assumptions are incorrect. If I were to have the matrix
{{1, 3, 3}, {2, 7, 6}, {1, 4, k^2 - 18}} * {x1, x2, x3} = {1, 3, k+1}
which has a row echelon form of:
{{1, 3, 3... |
H: $\cos(x)+\cos(x\sqrt{2})$ is not periodic
Show that the function $$f(x)=\cos(x)+\cos(x\sqrt{2})$$ is not periodic. I tried $x = a$ and $a\sqrt{2}$. I am guessing that the method of contradiction would be of some help over here. What else should I try?
AI: Assume $ \cos(x) + \cos(\sqrt{2} x) = \cos(x+T) + \cos(\sqrt... |
H: Reordering vector product
If I have vectors $a, b, c \in \mathbb{R}^3$, and if we have e.g. $a = b\times c$, is there any way to express $b$ in terms of the other two?
AI: Write out the vectors as $a=(a_1,a_2,a_3)$, and so on, do the cross product, set the two sides equal, and you'll get a system of three linear eq... |
H: How to solve expectation / first moment of Gaussian Integral?
How can I solve the following integral?
$E[I] = \int_{I=0}^\infty I \frac{1}{\sqrt{2\pi}\sigma}\exp(-\frac{(\mu-f-I)^2}{2\sigma^2}) dI$
The result is supposed to be:
$\sigma[\frac{\mu - f}{\sigma}\Phi(\frac{\mu - f}{\sigma}) + \phi(\frac{\mu - f}{\sigm... |
H: number of solutions to an equation?
Given $x$ and $y$ are multiples of $2$ satisfying
$$x^2 - y^2 = 27234702932$$
Find the number of solutions to $x$ and $y$.
AI: As $27234702932=2^2\cdot181\cdot37616993$ where the last two factors are primes
If $x=2X,y=2Y$
$$X^2-Y^2=181\cdot37616993$$
If $X^2-Y^2=p\cdot q$ where... |
H: Proof about that operator is self-adjoint
In Linear Algebra:
Suppose I have a matrix $A$ that represents the linear product (the Gramian matrix)
Suppose I have a matrix $B$ that represents a linear transformation from Vector Space $V$ to itself.
I'm trying to prove that $T$ cannot be self adjoint.
I'm reading throu... |
H: Painting chess board
The task is to paint each of the $64$ squares on a chess board either blue or red.
I need to find the number of distinct ways this can be done given that any $2\times 2$ square on the board has two red and two blue squares.
I've tried solving it for a $4\times 4$ board, but I am getting no wher... |
H: Sum of kth roots ($\sum\sqrt[k]{m}$)
I'm trying to find an asymptotic to $$S(n) = \sum_{k=1}^n\sqrt[k]{m}$$ From computational tests, it seems to grow nearly as slowly as $n$. However even $$\sum_{k=1}^\infty\sqrt[k]{m}-1$$ diverges (for $m\neq1$) by the comparison test.
I'm thinking it might be something like $n\l... |
H: On the definition of the structure sheaf attached to $Spec A$
Let $A$ be a ring (commutative with $1$),if $X=Spec A$ we want to attach a sheaf of rings to $X$. If $f\in A$, $D(f)=X\setminus V(f)$ is an element of the base and we define
$$\mathcal O_X(D(f)):=A_f$$
I've problems to show that $\mathcal O_X(\cdot)$ is... |
H: complex holomorphic function which only has finite roots
Suppose that D is a bounded region, f $\in$ H(D)$\bigcap$C($\bar D$).Prove that f has only finite roots if f$\neq$0 on $\partial D$.
AI: Assume $f$ would have an infinite number of distinct roots. Let $(z_i)$ be a sequence of distinct roots. Since $\bar D$ is... |
H: A probability problem involving probability density function
I am going through a probability book where the following has been claimed :
If $$f_{X}(x) = \int_{-\infty}^{\infty}f_{U}(x-y)f_{V}(y)dy$$
then $f_{X}=f_{U}*f_{V}$
where $X, U, V$ are continuous random variables where $U$ and $V$ are independent.
I don'... |
H: Convergence, link with Sierpinski triangle
This image shows the construction of the Sierpinski triangle up to the fourth iteration. My question is simple.
If I construct a sequence of subsets of the triangle in this way :
$\mathcal{E}_{0}=\emptyset$
$\mathcal{E}_{i}$ is the union of the white closed subsets in t... |
H: How prove this equality $\sum\limits_{r=0}^{n_{k}}C_{n}^{r}M^{N-n_{k}+r}x^{n_{k}-r}\le(1+1)^N(M+x)^N$
prove that
$$\sum_{r=0}^{n_{k}}C_{n}^{r}M^{N-n_{k}+r}x^{n_{k}-r}\le(1+1)^N(M+x)^N$$
and $x\in R,x>0, n_{k},N \in N^{+},N-n_{k}+r>0,n_{k}-r>0$
where
$C_{n}^{m}=\dfrac{n!}{m!(n-m)!}$
AI: In fact, you can prove that (... |
H: GgT, (polynomial) division and finite fields...
Exercise: Let $f,g \in \mathbb{Z}_2[x]$ be the polynomials $f = x^6 + x^5 + x^4 + 1$ and $g = x^5 + x^4 + x^3 + 1$. Has the diophantic equation $f u + g u = x^4 + 1$ solutions $u,v \in \mathbb{Z}[x]$? If so, determine them all.
My Solution: First I observed that in $\... |
H: Uniqueness of Seifert graphs
If we make the bands and disks of a Seifert surface really small and really thin the surface collapses to a graph. It is called a Seifert graph.
If it is not a directed and weighted graph, can we say that for every unique Seifert graph there is a Seifert surface and vice versa?
If it ... |
H: Existence of a power series converging non-uniformly to a continuous function
I am wondering whether there exist a function $f(z) = \sum_{n\geq0} a_n z^n$ such that:
$f$ converges and is continuous on the closed unit disk $D$ and
the series $\sum_n a_n z^n$ does not converge uniformly on $D$.
I have tried to cons... |
H: How to show that $|f(x)-g(x)|<\epsilon~\forall~x\in[a,b]?$
Let $[a,b]$ be a closed and bounded interval in $\mathbb R$ and $f$ is continuous on $[a,b].$ How to show that for $\epsilon>0~\exists$ a piecewise linear continuous function $g$ on $[a,b]$ such that $|f(x)-g(x)|<\epsilon~\forall~x\in[a,b]?$
Help me! I'm c... |
H: Coinflip statistics
There is a betting strategy for coinflips, called Martingale, in which the player should pick heads or tails and keep betting on it (doubling their bet on every loss) to eventually make a win when it appears. In theory this is watertight, but with one caveat: there can be very long strings of lo... |
H: Possible ways to do stability analysis of non-linear, three-dimensional Differential Equations
For example Lorenz system,
$$
\frac{d}{dt}\begin{pmatrix}
x\\
y\\
z
\end{pmatrix}=\begin{pmatrix}
-\sigma & \sigma & 0\\
\rho & -1 & -x\\
y & 0 & -\beta
\end{pmatrix}\begin{pmatrix}
x\\
y\\
z
\end{pmatrix}
$$
The ar... |
H: Limit as n approaches infinity involving roots
$$\lim_{n\to\infty}\frac{n}{1+2\sqrt{n}}$$
Given my understanding of how to solve these problems, I need to take the highest power of $n$ in the denominator and then divide both the numerator and denominator by that power. But the highest power in the denominator is lo... |
H: If $f^2(b) - f^2(a) = b^2 - a^2$, then the equation $f'(x)f(x) = x$ has at least one root in (a, b).
Suppose $f$ is continuous on [a, b] and differentiable on the open
interval (a, b). How to that if $f^2(b) - f^2(a) = b^2 - a^2$,
then the equation
$f'(x)f(x) = x$
has at least one root in (a, b).
AI: Consider
... |
H: Is it ever proper to say that the limit of a function equals infinity?
If I calculate a limit and get the value $\infty$, what is the proper way to communicate this? Can I say that the $\lim_{n\to\infty}a_n=\infty$ and therefore the sequence $\{a_n\}$ diverges, or do I say that the limit does not exist?
AI: I would... |
H: Solving the simultaneous equations
I need to solve the following simultaneous equations for the constants $A$ and $B$:
$$zA + (1-z)B = 1$$
$$\hspace{1.8cm} z^2A + (1-z)B = z^2 - z + 1$$
where$z$ is just a variable. What I did was this:
$$zA = 1 - (1-z)B \implies z^2A = z - (z - z^2)B$$
and so subbing this into the ... |
H: Linear bijection between a normed vector space and its proper subspace
Let $X,Y$ be normed vector spaces such that $X$ is a proper subspace of $Y$ (i.e., $X$ is a subspace of $Y$ and $X\neq Y$), and $X$ is dense in $Y$. Is there a linear bijection $T$ from $X$ to $Y$? If it does exist, can $T$ and $T^{-1}$ both be ... |
H: GCD of elementary symmetric functions
It is easy to show that p/ $\sigma_j$ ( where $\sigma_j$ is the sum of all products of j distinct members of the set {1,2,...,p-1}) for all $1 \leq j \leq p-2$, but how would you go about showing that the greatest common divisor of $\sigma_1,\sigma_2,...,\sigma_{p-2}$ is in fac... |
H: Contour Integral
I have this question:
I'm aware that $e^{iz^2}$ is analytic, and hence $I_R = 0$ by Cauchy's Integral theorem. I'm not really sure what to do from there. Thanks!
AI: The closed contour is split into 3 pieces:
The original integral:
$$\int_0^R dx \, e^{i x^2}$$
The integral over the angled line of ... |
H: Find the limit of $2+\left(-\frac{2}{e}\right)^n$, as $n\to\infty$, if it exists
I'm absolutely unsure about how to approach this. I've considered changing it to $-2=\left(-\frac{2}{e}\right)^n$ and then using the properties of lograrithms, but $\ln(-2)$ is undefined, as is $\ln(-\frac{2}{e})$.
I can't use L'Hopita... |
H: $\int_0^1\frac{(f(x)-1)^2 -4x^2}{x^{3.5}}\,dx$ exists. Calculate $f(0)$ and $f'(0)$
I've tried somehow using Taylor to try and figure this one out.
Unfortunately, I couldn't seem to get a solid answer.
Thank you very much for your help!
Let f be a continuos function,
$$f:R\rightarrow R$$
$$f(x), \ f'(x) \ , \ f'... |
H: Use of epsilon in proofs about diameters
I have been working on the following question:
Assume that $K$ is a compact metric space. Prove that there are two points $x,y \in K$ such that $d(x,y)=$diam $K$. (Recall that diam $K = sup${$d(x,y) | x,y \in K$}.
Here is an attempted proof (imitating Baby Rudin proof 3.10... |
H: Who was V. Viskovatov?
I'd be interested to learn some biographical detail about Vasilii Viskovatov, whose name is associated with a method for converting (a ratio of) power series to a "corresponding" continued fraction, c.f. Handbook of Continued Fractions for Special Functions, p. 20 (Springer, 2008).
A few Inte... |
H: Reciprocal of Laurent series
I understand how to use long division to find the reciprocal of a power series.
Are there any theorems that allow you to divide Laurent series that have a finite number of terms with negative exponents? That is, if I have a Laurent series around $0$, such as
$f(z) = \frac{1}{z^2} + 3z ... |
H: Gaussian Elimination, Question Check.
I'm going through my practice problems, and just want to know if I am doing this right:
$$ 2x_1 - 3x_2 = -2$$
$$ 2x_1 + x_2 = 1$$
$$ 3x_1 + 2x_2 = 1$$
And this is my solution:
$$
\begin{align}
\begin{bmatrix}
2 & 3 & -2\\
2 & 1 & 1\\
3 & 2 & 1
\end{bmatrix}
\end{align}
$$
$$
\b... |
H: A completely regular topological space which is $T_0$ but not $T_1$?
The question pretty much says it all. I need a completely regular (the definition not requiring $T_1$) topological space which is $T_0$ but not $T_1$. I've sifted through Counterexamples in Topology but I just can't find one. I've also tried go... |
H: Poisson process of alternating sources, pairing products of the two of them
I have a problem I've been thinking for a while, but it's confusing me quite a lot.
There are two independen machines, A and B. A produces a product at a rate of 2/minute, and B does it at a rate of 3/minute, both of them following a Poisso... |
H: Integrate: $\int_0^\infty \frac{\sin^2(x)}{x^2}dx$
I am trying to integrate $\displaystyle \int_0^\infty \frac{\sin^2(x)}{x^2} dx$ by method of contour. I am considering the following contour but I am not being able to. Also I am not sure if it's right approach.
$$\int_\Gamma f(z) dz + 2 \int_0^\infty f(z) dz + \... |
H: A question regarding moment generating function
The moment generating function of a real-valued random variable $X$ on a probability space $(\Omega,\mathscr A,P)$ is defined as $G_{X}(t)=E[e^{tx}]$ $(t \in \mathbb{R})$. Prove that $G_{\alpha X+\beta}(t)=e^{\beta t}G_{X}(\alpha t)$ for $\alpha, \beta \in \mathbb{R}$... |
H: Evaluating a Gaussian Integral
How to prove that
$$\int_{\mathbb{R}^N}e^{-\langle Ax,x\rangle}\operatorname{dm}(x)=\left(\frac{\pi^N}{\det A}\right)^{\frac{1}{2}}$$
Where $A:\mathbb{R}^{N}\to\mathbb{R}^{N}$ is a symmetric positive-definite linear transformation.
My approach: Given a $x\in\mathbb{R}$, one have
$$\... |
H: An open cover that is not locally finite
I could not understand why example $13.4$ is not locally finite.
Can you give me an explanation please.
AI: An open cover $\mathscr{U}$ of a space $X$ is point-finite if $\{U\in\mathscr{U}:x\in U\}$ is finite for each $x\in X$: each point of $X$ belongs to only finitely man... |
H: What is an overlap?
I want to ask what an overlap is.
My teacher said that for example $1$: Everything is an overlap hence it is not locally finite.
For example $2$, it doesnt overlap.
Please teach me these two examples.
Thanks.
AI: There are two families of sets mentioned on that page.
One is $\left\{\left(-\fr... |
H: How to find the inverse Laplace Transforms?
How do you find the inverse Laplace Transform of the following,
$$\frac{2 (s^2+4 s+5)^2+40}{(s^2+4 s+5)^2}$$
Separating them into complex coefficients is to long.
AI: Let $F(s)$ denote the fraction in the post, hence $F(s)=2+40\frac1{(s^2+4s+5)^2}$. The $2$ part of $F(s)$... |
H: Prove that $c^3f(c)+c f(c)\ge1$
Let $f:[0,1] \rightarrow \mathbb{R}$ a continuous function that satisfies $\int_0^1 2 x f(x) dx >\pi/2$. I need to prove there is
$c\in(0,1)$ such that $c^3f(c)+c f(c)\ge1$.
My guess is the mean value theorem. Am I on the right track?
AI: Since
$$\int_0^1\big(xf(x)-\frac{1}{1+x^2}\bi... |
H: Inclusion Exclusion Principle Problem
There are 28 people in your family consisting of 18 adults, 13 females, and 11 who have purple hair. There are 11 adult females, 6 of whom sport purple hair. There are 10 adults with purple hair. No female children have purple hair. How many male children without purple ha... |
H: Finding two numbers when having their sum and product
I have two numbers, their sum is 41 and their product is 238. What are the numbers?
I got during this far in my calculations:
$a+b=41,\quad ab=238,\quad 238=41-b.$
I appreciate answers or tips to help me complete this. Thanks in advance
AI: Your first two equa... |
H: Is it true $\operatorname{st}(^\ast A) = \overline{A}$, when $A$ is a bounded subset of $\mathbb{R}$?
Given a bounded subset of $\mathbb{R}$, let $\operatorname{st}(^\ast A)$ be the set of the standard parts of all elements in $^\ast$-transform of $A$, $\overline{A}$ is the closure of $A$.Is it true $\operatorname{... |
H: Addition in polar form
$$u_{1}(t) = 120\sqrt{2}e^{j5000t}$$
$$u_{2}(t) = -j160\sqrt{2}e^{j5000t}$$
I need to add these two values, so:
$u(t) = u_{1}(t) + u_{2}(t) = (120 - j160)\sqrt{2}e^{j5000t} = ...$
What next? How can I do this without changing the form of the numbers?
AI: Write $120-j160$ in polar form; that i... |
H: Question on a French math text by P. Masani
I'm trying to translate a paper on matrix-valued functions by P. Masani, published in C. R. Acad. Sci. Paris, 249, 1959, p. 873. (see http://temp-share.com/show/FHKd40yi6 for scanned pdf). My specific question is now as follows:
On the first page, in the first section aft... |
H: Whether the limit on representable functors be non-representable?
I'm looking for examples of the following situation:
Let $A$ be a complete and cocomplete category, $B$ is a small category and $T\colon B\to\mathbf{Set}^{A^{op}}$ be a functor, such that for any $b\in B$ functor $T(b)$ is representable. Could it be ... |
H: Does this proof contain a contradiction?
I have made the following proof and I am asking if there is anything wrong in my steps:
Let $f:\mathbb{R}\to\mathbb{R}$ be a real analytic function with infinitely many zeros. Let $a\neq 0$ be a real number. We know that the set $f^{-1}(a)$ is discrete. I want to make a bije... |
H: Why do we need to find the intersection between these lines?
We have the functions
$$ x = -1 + 2 \cos(t)$$
$$ y = 3 + 2 \sin(t)$$
They give P's orbit
with $t$ on $\left[0, \dfrac{3}{2} \pi\right]$
Find (to 2 decimal places accurate) for which values of t the Point t is left of the line $x=-2.$
So we're allowed to u... |
H: Convergence of $\int_0^1 \sqrt[3]{\ln(1/x)} \mathrm{d}x $
Does $$\int_0^1 \sqrt[3]{\ln\left(\frac{1}{x}\right)} \mathrm{d}x$$ converge? WA says it is equal to $\Gamma(4/3)$, however calculating the antiderivative seems approachless to me and can't compare to other functions. I would appreciate any help. Thanks.
AI... |
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