Demeter in his book "Fourier Restriction, Decoupling, and Applications" (P287) used the following estimate:
\begin{equation}
\sup_{0\leq n\leq q}\bigg|\sum_{m=0}^n e^{2\pi i\frac{a}{q}m^2}\bigg|\leq Cq^{\frac{1}{2}},
\end{equation}
where $a,q\in \mathbb{N}_+$ satisfy $(a,q)=1$ and $2\nmid q$.
The...
I've always wondered why the typical plates bolted to rock in order to secure climbers are that thin. I imagine them behaving like a knife under a sudden load in a falling scenario. Wouldn't increasing the surface area in solid to solid contact with the quickdraw carabiner reduce this problem? Ev...
I'm looking for a font for a tattoo. I don't have any preferred font so I thought using the original Unix font could be a great reference to the great history. Can't find any reliable information about that on search engines except that I found out Courier was the original IBM font that was creat...
Cygnus is the second of the most commonly known ISS resupply freighters (the only more commonly used one is progress.) After cygnus launches aboard it's Antares rocket, it rendezvouses with the ISS, and is attached to the station, allowing for vital supplies to be unloaded from the noble ship and...
Last week, I attempted to bake Gougères for the first time. It was my first attempt at baking with Pate a Choux. The recipe I followed called for six large eggs, but I knew adding the last egg would make the dough runnier than the optimal consistency. When I added the mixture into a piping bag, i...
I was reading through the post Is it possible to work full time and complete a PhD and had a few follow up questions:
(1) I read somewhere that one can complete a PhD without funding from a TAship or RAship, getting that funding from one's full-time employment instead. Is this allowed by most (US...
I have came across a YouTube video titled "The 1890's ~ Amazing Rare Footage of Cities Around the World". (2 mins)
Now at 2 mins of this video there is footage of people sitting on a rollercoaster, however the person that owns the YouTube channel does not state which town or city the footage is f...
I'm searching for flights to NZ and back for some time in Feb-Apr next year. I've been using Matrix to find suitable dates and prices, however I ran into something that I thought was odd - the prices for round-trip were about $400NZD higher than for the two one-way flights.
I found suitable one-...
A lot of feats and prestige classes require the dodge feat, and I noticed that the Desert Wind Dodge feat says:
Desert Wind Dodge can be used in place of Dodge to qualify fora feat, prestige class, or other special ability. If you already have Dodge when you select Desert Wind Dodge, you can cho...
In the real world, combat aircraft are generally classified into two main groups; ground attack planes, which deploy weapons against land targets, and fighter planes, which are meant to destroy other aircraft. How would airplane development change when faced with a nearly entirely different threa...
Given two compact orientable connected manifolds $M,N$ of dimension $n$ without boundary, and a continuous (or smooth) map $f:M\to N$, the degree of $f$ is defined as the integer
$$
f_*([M])=(\deg f)[N]\in H_n(N)\cong\mathbb{Z}
$$
where $[M]$ is the fundamental class of $M$.
Suppose $\deg f\neq0$...
What is the probability of a polynomial with integer coefficients has rational roots? For some reason I feel like the probability of having rational roots assuming the coefficients are random integers would get smaller as the degree goes up.
Degree 1: $ax+b=0$ always has 1 rational root
Degree 2:...
I was reading a book by Simon Haykin on neural networks when I came across the following strong statement (on the pdf's page 188):
"However, we still have a computational complexity that is
$\mathcal{O}(W^2)$, where $W$ is the size of weight vector $\mathbf{w}$. Quasi-Newton methods are therefore...
The first time I made this recipe written a few months ago, it worked perfectly. But I've tried making it again two times after that, and it's failed both times.
The first time, the cookie was perfect - great texture, great taste, and amazing gooey pockets of chocolate. It looked exactly like the...
Recently, I've been hearing a good deal about hardware tricks. For instance, the YouTuber Ahoy (see A Brief History of Graphics) mentions that some game programmers resorted to "hardware tricks" to diversify the gamut of colors on the screens of console systems using mode 7 (I'm assuming that's m...
Inside of the GBCs Cartridge header there is the metadata for the game and the Nintendo logo.
The program that runs on boot (the BIOS or Boot ROM) checks the checksum of the Nintendo logo, and always has, but in the GBC Boot ROM, I noticed an interesting update. Now, the Boot ROM checks the title...
I'm making a "bom" list entry into the "materials" table.
I bring the materials defined for the product group to the grid so that users do not forget the relevant material.
Users define through this template.
But they add extra material (other than the group template) if they want.
If there is a ...
I'm checking new Data Views _AutomationInstance and _AutomationActivityInstance. In the first of them I found a typo in Salesforce documentation. On the page we can see AutomationNotificationRecipient_Compete, but this column name is AutomationNotificationRecipient_Complete.
But I see also an err...
I'm new to C++. How to make a menu without if() {} else {} & switch() case?
I made a menu on an array, but for some reason it doesn't compile. How to correct it?
typedef void (*cbd)(uint8_t, uint8_t);
typedef void (*cbt)(uint8_t, uint8_t);
typedef void (*cba)(uint8_t, uint8_t);
typedef void (*Men...
I have a glmer with a binomial response variable and two binary predictor variables, where there are no observations for one of the four groups. I used emmeans to calculate confidence intervals, and for this group obviously the mean and variance are zero. The model predicts a CI from 0 to 1, and ...
In this scenario a kingdom that has not yet invented black powder has been invaded by an enemy that possess cannons and matchlocks. Since the invaders are few in number the defenders managed to beat them back and steal a large cache of powder. They are extremely concerned that the invaders will ...
I am trying to generate a normal map from voronoi texture + bump but its resulting in blank normal map. I am just a beginner in blender and I am pretty sure am missing out on some of the basic things here but I can't figure it out for 2 days.
Left one is the source for baking normal map. But as y...
When you are sure you want to use a bus in Paris, France, you can buy a ticket in advance, they use the same tickets as the Metro.
As I will only be in Paris for this one cross city connection and not likely to return in quite a while and I prefer to walk the distance, I would like to avoid buyin...
I am trying to evaluate the Hartree--Fock exchange energy density on grids in pyscf with an instance of class "UKS", in order to test some functionals depending on the exchange energy density such as Becke05. I have noticed that there is an example in 31-xc_value_on_grid.py, but it seems that the...
We are currently using a nichrome (80/20) wire based heater to surround a sample chamber that we wish to heat by radiation. Maximum sample temperature is 400degC in an atmosphere of air that may be high humidity. That means the wires get red hot. Our specific problem is that there is corrosion oc...
This question is a bit long, but people often prefer to have all the details instead of being required to ask for them, so I've included as much detail as possible.
I received a frantic call from a friend who had just accidentally deleted their Desktop folder in Windows using shift+delete.
Appare...
Maybe stupid question, but to my understanding, the Einstein equation tells us the differential equation governing the Geometry of spacetime. That's all good and fine , but suppose I had an actual particle with some forces acting on it, how would I find it's trajectory? Would Newton's second law ...
A scheme is equivalent to a functor $\mathcal{F}:\textbf{AffSchemes} \rightarrow \textbf{Set}$ such that it admits a cover of affine schemes and is a sheaf of rings on the Zariski site.
Suppose $\mathcal{C}$ is a subcategory of $\textbf{AffSchemes}$ and $\mathcal{T}:\mathcal{C}\rightarrow \textbf...
In Agents of S.H.I.E.L.D., and again in WandaVision and Doctor Strange in the Multiverse of Madness, the book called "the Darkhold" is used and heavily affects the plot.
However, they both have different appearances, as seen below:
What is actually different about these two books? It seems as if...
I am working on parameterized complexity and started exploring on various structural parameters. The problem I am working on is known to be W[1]-hard parameterized by treewidth of the input graph and I am wondering if there is any known relationship between treewidth and maximum degree of the inp...
I recently moved to another internet provider who provides FTTH (Fibre To The Home).
Now my powerline adapters are incapable of taking full advantage of the increased speeds. I'm currently using Wifi and losing some speed, and don't really want to run CAT5 cable throughout the house.
Consideratio...
This determined at once the strength and the
weakness, the achievement and the limitation, of the materialist
theory. What pushed that theory forward was, so Engels writes in
Ludwig Feuerbach, "the powerful and ever more rapidly onrushing
progress of science and industry".
Materialism and the D...
Solve for (x,y) satisfies
$$ \left\{\begin{matrix}
x-y \in \left [ -1,1 \right ]
& \\ 3x-4y \in \left [ 2,3 \right ]
\end{matrix}\right. $$
I have try to solve this by multiplying 4 in the first inequation and subtract the 2 inequation to each other to lead to the solution $ x \in \left [ -7,2...
Trying to ask with as few spoilers as possible.
In episode 9,
walks in the city and passes a building which is burning.
Is this building significant in any way? Was it set on fire on purpose by someone?
I own a baritone ukulele that I tune (lowest pitch to highest) C-G-B-D [plectrum tuning]. The lowest string, the C, is missing. I would like to order the proper string to replace it. I believe it will need to be a wound string, with a nylon core? Where can I look up the proper gauge of string...
I drill holes in cabinets or desks for electrical. I usually drill about a 3/4" hole and I have these little plastic rings I put in to protect the woodwork and just so it looks nicer. Electrical is armored...
So I have seen other examples at builds and I have been a little jealous of their ri...
If the boiling point of water is at 100 Celsius, why does a hydrate need to be heated higher than that to evaporate water from the crystals? Does it have anything to do with their intermolecular forces? Thanks
I am not able to understand why the following reaction cannot occur or rather is not observed in nature:
\begin{equation}
d + d \rightarrow \alpha + \pi^0
\end{equation}
I can see that all the quantum numbers are satisfied, but I am not able to understand why this reaction does not take place?
Why is the arc travelling so far, and what kind of vapor conducts electrons so well?
https://www.youtube.com/watch?v=PXiOQCRiSp0
Why do so many apps log users out after upgrading to a new phone ? (ex: Gmail, Slack, Instagram).
From a technical POV it's easy to keep the user logged in after a phone upgrade.
Is there any upside to logging the user out?
$$\frac12+\frac13=\frac{3+2}{6}=\frac56$$
Ok, I know you divide then multiply. But could you explain WHY?
the meaning behind it? I don’t get the whole picture.
I one time heard that the reason you have בה״ב is because when the seasons change a person could get sick because of the change of seasons so we have בה״ב to daven that we shouldnt get sick has anyone ever heard of that and if yes where is the מקור
I know that if $0$ is an eigenvalue of a matrix $A$, then $A$ is not invertible, but is the opposite also true? If the matrix isn't invertible, is the eigenvalue always $0$?
How many different rectangular rooms, if any, is it possible to cover with all the 55 carpets of different dimensions 1 x 1, 1 x 2, 1 x 3,..., 1 x 9, 2 x 3, 2 x 4, ..., 8 x 9, 8 x 10, 9 x 9, and 10 x 10?
Dr Bees likes bees. Dr Bee is not his real name, but that is how everybody calls him.
I should actually say that he is obsessed with bees. Bees are his whole life. He knows everything about them. Anything anyone published out about bees, he knows.
He never learned the alphabet past the second...
Just wondering how to delete directory/file named "-f", "-r" or other using terminal.
A solar eclipse viewed from Earth reveals the sun's corona and you can only see the brightest stars from Earth.
However a solar eclipse viewed from the moon would show the red ring around Earth.
I have not seen an image / video of what a solar eclipse would look like on one of Jupiter's Galilea...
I came up with a suitable solution to a Hackerrank problem that failed because the execution took longer than 10 seconds on lists that were of very large size.
The problem: Given a list arr and an integer d, find all combinations of length 3 whose sum is divisible by d
My solution:
[
sum(p) %...
I define an ellipse by using an ImplicitRegion:
R = ImplicitRegion[4 z^2 + r^2 == 10, {z, r}]
I would like to get the perimeter of this ellipse. I was hoping to simply use Perimeter:
Perimeter[R]
However this returns "Undefined." Are there any suggestions on how to compute the perimeter of an I...
I'm stuck on what this could mean. the context is:
おい、庭園や屋敷を傷つけるような真似するんじゃねえぞ？
Is the speaker implying that damage has been done by the other person before? Is this some sort of saying? I'll leave more context below if needed.
I have to check if $f(s)=s,~g(s)=e^{ks},~k\in\mathbb{C}$ are linearly independent over $\mathbb{R}$.
The wronskian is $W[s,e^{ks}]=e^{ks}(ks-1)$. Then, if we take $s=1,~k=1+0i$, it becomes $0$ and hence, it is not linearly independent.
Is my reasoning correct?
People have been stealing catalytic converter’s from cars in New Jersey recently. Why are people stealing this specific part all of a sudden. It happened to my 4 people on my parents street. Wondering why this is the new thing and why they are specifically targeting Toyotas and Hondas?
The other day I was reading a paper on IEEE. To access the paper I needed to sign in through my institution. On the bottom of the paper, it read:
Accessed through [my institution name] at Oct 24, 9:30 PM
Will my institution be able to see all the papers I'm reading?
Ideally, in all analysis, one would like to be completely objective and unbiased. Is this possible? What are the indicators that my view is not objective or unbiased?
I have a file with lines similar to the following (unfortunately, this is the only format in which another software outputs results):
1 2 3 5/2 7 17/5 9 10/3 15
I need to replace it with the following line:
1 2 3 2.5 7 3.4 9 3.33 15
In other words, I want GAWK to do the division a...
In this answer a quote from Horace's, "Satire of Persius" (Satires 4, line 47):
"...si facis in penem quidquid tibi venit...",
was translated by Tyler Durden to:
"...and come to do whatever your prick suggests...".
(The only translation I could find, on the net:
"...if you follow your prick..."
I noticed that when using AES-256-CBC with a 128-bit IV, the ciphertext is always at least 16 bytes long (size of IV).
I also noticed that when using AES-256-GCM with a 96-bit IV, the ciphertext size can be smaller than the IV.
Normal? Why?
There is some kind of plastic coating over my drain that is peeling and needs replacing. I can't work out what kind of product I would need to use to recover it to protect the plug and would appreciate any advice!
I had a lecture on BigO notation, and I received a problem set to solve, but unfortunately we always get harder examples to solve that those presented(those which are presented are always some basic cases) during the lecture.
Here is the actual question: check if: $2^n = O(n^2) $
For sure it's ...
I have two very simple polygons.
a = Polygon[{{2, 0}, {2, 100}, {502, 100}, {502, 0}, {2, 0}}]
b = Polygon[{{202, -200}, {202, 296}, {300, 296}, {300, -200}, {202, -200}}]
I wish to produce a new polygon which (for example) describes their union as pictured above, but is expressed as a single...
I am doing some proofreading and have a question. In the following line of a poem, should it be who or whom? It's talking about monsters and the fact that they have a lot of options as to who they choose to eat so they can grow larger.
The line:
So many decisions of who to choose so they can grow,
Would you tell me which one is more correct and naturar: drive in a car or drive with a car? For example:
Because my car broke down, I had to drive home in a rental car.
Because my car broke down, I had to drive home with a rental car.
I haven't been able to find an answer on the internet, but ...
I got 20 kg of LEGO bricks from family friend.
I found a lot of original sets, but these are still unknown.
In the following diagram, I want the node containing the label "P" to be placed at the other endpoint of the gray line segment. Why is the "P" being typeset at the origin?
\documentclass[10pt]{amsart}
\usepackage{mathtools,array}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
...
I was wondering out of the functions (MD5, SHA-1, SHA-256, and SHA-512), do all provide 128-bit pre-image resistance and 128-bit second-image resistance?
Also, out of these hash functions, do only SHA-256 and SHA-512 provide 128-bit collision resistance? (Due to $l/2$ bits of security)
I know a longer name is "The Order of the Seekers for Truth and Penitence," but I remember there being an even more formal name mentioned at one point. Something that is like the "The Fraternal and Beneficent...." Or am I misremembering?