Let $X$ be a variety contained in $\mathbb{P}^N$ and let $Y$ be a smooth hyperplane section of $X$. I have read in page 54 of Voisin's book "Hodge theory and complex algebraic geometry II" the following: there exists a Lefschetz pencil of hyperplane sections of $X$ of which $Y$ is one member....

Ok, so I have this world(or maybe it will just be a dimension depending on how things pan out) called 'The Weird' that has air in space, like Earthlike air(for the most part). Also, the 'planets' or worldplanes are pretty much flat(barring mountains and the like), at least at the top. It should b...

Lets consider this scenario in deep void of space where other curvatures of large objects are negligible in this case and we bring 2 objects lets say $A$ and $B$. We give it a force slightly lower Force ($F$) than the gravitational force of attraction ($F_{g}$) of both objects in sense of Newton...

Consider that you are receding at a velocity faster than the cosmic speed limit (say, $2c$ with respect to $A$) due to the expansion of our universe. According to me, $A$ is moving at $2c$ and thus for me, it is invisible. Similarly, according to $A$, I am moving at $2c$ and thus for $A$, I am in...

I was reading wikipage about the simply typed lambda calculus and it says about categorical semantics that: To make the correspondence clear, a type constructor for the Cartesian product is typically added to the above. But I got confused with the "typically". It seems to me that we would need ...

Let $(M,d)$ be a complete metric space and $A$ be a closed subset of $M$. Then the set \begin{equation} B:= \{x\in M: d(x,A) < 1/2\} \quad \text{is open}. \end{equation} ($d(x,A)= \inf_{y\in A} d(x,y)$) Why would that be the case? If $B=\{x\in M:0<d(x,A)<1/2\}$ then one could argue that B is the ...

I want to set C-c j with such a function (called cmd), which can handle subsequent keystrokes. For example, after typing C-c j Emacs will execute cmd, then every subsequent j will invoke cmd again. Any non-j keystroke will interrupt this process. It won't invoke cmd; instead, it acts like a si...

I am currently working on ubuntu 20.04 machine. When i am running the command "journalctl -u sshd.service", i am getting the below response. -- Logs begin at Wed 2022-12-21 13:01:52 UTC, end at Fri 2023-03-31 15:10:32 UTC -- No entries -- . But when i am running "journalctl -u ssh.service", i ma ...

I have this list DeleteDuplicates[Sort[#] & /@ Tuples[Range[4], 3]] which gives me {{1, 1, 1}, {1, 1, 2}, {1, 1, 3}, {1, 1, 4}, {1, 2, 2}, {1, 2, 3}, {1, 2, 4}, {1, 3, 3}, {1, 3, 4}, {1, 4, 4}, {2, 2, 2}, {2, 2, 3}, {2, 2, 4}, {2, 3, 3}, {2, 3, 4}, {2, 4, 4}, {3, 3, 3}, {3, 3, 4}, {3, 4, 4}, {4,...

I need to know the current in a polarized electrolytic capacitor. What is the practical limit for this current and how do I calculate? I want to know what is the maximum current I can get when I put the terminals in contact without considering the rest of the circuit. I know that if only the resi...

Qgis Layer Combinations plugin is now deprecated. These are it's carachteristics: <<Store and restore layer visibilities, foldings and zooms in "combinations". The visibilites can then be dynamically assigned to composer maps.>> They say: "This plugin is deprecated since functionality was added t...

A decimal code is declared legal if it has an even number of zeros$.$ For example $1900200$ is a legal code, but $10002$ is not. Let $a_n$ be the number of legal decimal codes of length $'n'$. Then (A) $a_n=8a_{n-1}+10^{n-1}$ (B)$a_n=\frac{8^n+10^n}{2}$ (C) $a_n=9a_{n-1}+10^n$ (D)$a_n=9^n+10^n$ A...

We loaned our lawn mower to a friend, since at the time we had somebody doing our lawn for us, due to us not being home during the day for the most part. He recently returned it, and noted that he wanted to be helpful, and had replaced the blade. I took a quick look, and the blade looks like it g...

Let ABCD be a parallelogram, the symmetrical point M point B to point D, and N a point located on the right BC like this so that B ∈ (CN) and BN = 2 · BC. Prove that the points M, A, N are collinear. Whether point E is half of BN. At the bottom of the picture, you can see my ideas. Also, I thoug...

Given a bipartite graph, find a set of nodes on one side that has greater cardinality than the set of its neighbours on the other side. This is a conceptually simple problem, but I suspect it is actually quite difficult.

What’s the nature of the self awareness of Paul regarding his office of “Apostle of Gentiles”? Can we say that in Paul’s mind he is appointed the office singularly or exclusively as no one else can say the same in the same sense, or he think he is just one among many laborers? (Ephesians 3:1-2)

Reading a recent article which argues on why psychedelic substances are more effective than the naturally occurring neurotransmitters in the brain: *Breakthrough study discovers that psychedelics breach our neurons Now, I am just an undergrad researcher in chemistry so my knowledge is rather limi...

first, I apologize for this very simple question. I'm starting my studies on smart contract can someone explain highest voted function in this contract? // SPDX-License-Identifier: MIT pragma solidity ^0.8.6; pragma experimental ABIEncoderV2; contract Voting{ string[] public members; ma...

I think it was a book from the 70s or thereabouts, possibly older . A boy dies and is reincarnated or somehow put into the body of a cat. He is befriended by another cat who looks after him and teaches him how to behave like an actual cat. That’s not a lot to go on but any help is appreciated.

I was playing a game of Commander, having control of The Beamtown Bullies. With its ability, I gave an opponent a Hellcarver Demon. He then attacked someone with the hellcarver, and attacked with other creatures. This caused my lifetotal to become 0. Now, while my cards get removed from the game,...

I have a full sub-panel and want to add a heat pump water heater next to my electric dryer. Since the water heater doesn't need to be on all the time (they hold temperature pretty well, and usually I'm not using lots of hot water while the dryer is running), I would like to use the same circuit. ...

What could be considered a "foundation/fundamental" text in French? By this I mean a text that would play a role equivalent to Tanakh for Hebrew, works of Homer for Greek, or Aeneid for Latin. That is such a text that one could learn a language by studying it (or build a language course around th...

I am looking to see what the pros/cons and if it is a good idea to swap out old 2 prong receptacles (that are connected to old knob & tube wiring) with dual AFCI/GFCI receptacles or swap them out with just GFCI ones.

Three years ago, I wrote a program to manipulate the CAP_NET_RAW capability of my programs. I used the AMBIENT capability set. But now, I'm not able to compile my program on my actual Debian distro (kernel 5.10) because CAPNG_SELECT_AMBIENT does not exist anymore in cap-ng.h. I notice that a new ...

Would love any insight to this line across each photo from a roll of 35mm film taken with my new (used) Noblex Pro Sport. The line appears at the same height on each and every photo, but is brighter/lighter depending on the photo settings. I have three assumptions thus far, but would love more id...

I have a question about the opening sentence I had intended "The Adventure of the Abbey Grange" to be the last of those exploits of my friend, Mr. Sherlock Holmes, which I should ever communicate to the public. （The Adventure of the Second Stain） I'm not sure what "should" and "ever" mean in th...

Assume that $C_n$ represents axiom of choice for sets that contain $n$ elements. Prove that if $n$ is a factor of $m$, we can conclude $C_n$ from $C_m$. Here, I don't know what axiom of choice for n-elements set is. I know the first and second form of axiom of choice but I don't know how it is re...

I disconnected my hot tub power today as we prepare to dispose of it. The wiring (6 AWG, on a 50 amp breaker) goes through underground conduit underneath a walkway, so while I figure out what to do with the wiring, I wanted to cap it somehow to both prevent water from getting inside the conduit a...

I just read the entry on the Apparatus of Kwalish in the DMG. There is nothing that says what happens to the vehicle when it runs out of hit points. Does it regain hit points? If so, how? Or is it destroyed? What happens to it when it is destroyed?

A few weeks ago, we (2 authors) published a hypothesis paper in the medical sciences. Some days after the manuscript was published online, a researcher wrote me and asked for the full text. I did not know said researcher at that stage. We exchanged some emails back and forth about the content of ...

I want to delete the whole line that contains certain words such as: build, name, disk. I know that there is a search string ^.*?build.*$(\R|\Z) which will find lines containing "build" How do I change this to find "build" or "name" or "disk"?

Connecting 240v stove top with 5 ft pigtail. Stove end hot leads soldered to circuit board. Ground has screwed connect. Wall end requires electrical connectors to junction box. No plug. Problem is junction box is 6-7 feet making pigtail too short. Options considered… Use longer pigtail. Ei...

What is wrong in this argument? $$ \lim_{x \rightarrow 1^-} \frac{x-1}{|x-1|} = \lim_{x \rightarrow 1^-} \frac{x-1}{\sqrt{(x-1)(x-1)}} = \lim_{x \rightarrow 1^-} \frac{\sqrt{x-1}}{\sqrt{x-1}} = 1$$ I know it is wrong because the book I am working with shows that the limit should be $-1$ and not $...

I am trying to figure out how the electric utility service reads my meter. We have an old electric meter, with a mechanical spinning disc and the analog faces above it. It is similar to the one pictured below. The meter has not been upgraded by the utility in many years (at least 10 for certai...

I hope this question is not too opinion-based, and if there are any problems please tell me about it. I'm currently studying Ives' Concord Sonata for my graduation, but I have many other projects in the meantime. I already have a somewhat clear structure of the piece, and I'm already working on p...

I'm trying to prove it by using invariant subspaces and this theorem, which is a final touch in my proof. I don't understand the theorem though. Why is invariance needed? "$A:V \longrightarrow V$, A-normal operator, $U$ is a subspace of $V$ and is invariant under the operator $A, A^*$. Then $A$ o...

We have this circuit: I make the following assumptions about the current: Such that $$I_1+I_2+I_3=0$$ at the blue junction. I then draw two loops, l_1 and l_2: which yields the equations $$-12 -5I_1 -3 - 10I_2=0\space(l_1)\text{ and} -5I_39-3+10I_2=0\space(l_2)$$ However, solving this equatio...

Context: I recently had this question given to me by my math tutor: Does the following series converge or diverge $$\sum_{n=3}^{\infty} \frac{1}{n \ln n \sqrt{\ln(\ln n)}}$$ My working: As the sum is decreasing and nonnegative we can use the Cauchy condensation test. Applying it once we obtain,...

Vaiṣṇavas usually use Pāñcarātra āgamas. However, there is also another South Indian Vaiṣṇava tradition, that worships according to Vaikhānasa āgamas. What are the principal Vaikhānasa āgamas? If possible, please give an exhaustive list of Vaikhānasa āgamas. Please mention authentic sources.

I am hoping to develop a program capable of predicting when a satellite will fly through the path of a telescope observation. The aim is to make it possible to block or mitigate the light from the satellite while it flies though the observation path. However, while I know that the US DOD tracks s...

The code below produces a graph that is difficult to interpret because the nodes and edges are overlapping. I referred to another Stackexchange post for a solution but it seems not to work in this case. Can anyone explain how to prevent the edges overlapping with either each other or with nodes t...

I have a bill from my doctor for 2 services, one was performed in January and the other was in March. I have had my HSA for several years and these are qualified medical expenses. Since I have a single bill for that is my receipt for services rendered, I plan to submit a reimbursement request f...

I will denote by "X" the area I work in right now. I don't want to explicitly say what X means to keep my privacy. I'm a STEM major and I'm doing my internship in an X setting in a data science department, where the primary task is to develop machine learning models for X. I was genuinely excited...

The Hebrew words תֹהוּ and וָבֹהוּ are translated to empty/formless and void in Genesis 1, but that isn’t what they mean. In my research, I have found that one of the two words is unknown, and the other means chaos or waste. Throughout my research, I have discovered that the reason seems to be th...

This table is buggy somehow, there is this white cell and I want the gradient background to fill the whole 1st line of each main column; any one has an idea to make it cleaner ? \documentclass{article} \usepackage{colortbl} \usepackage{multirow} \usepackage[table]{xcolor} \usepackage{array} \usep...

I'm trying to learn to use USART on an ATmega328P. I'm using this datasheet. I'm using the following code to echo characters I type on my terminal: #include <avr/io.h> #define BAUD 9600 #define F_CPU 16000000UL static void usart_init(void) { unsigned int ubrr = F_CPU / 16 / BAUD - 1; U...

We are announcing our prefix to ISP A and ISP B via BGP, 1.0.0.0/23 to ISP A, and 1.0.0.0/24 and 10.0.1.0/24 to ISP B. What we want is that when we withdraw 1.0.0.0/24 from ISP B, communication for 1.0.0.0/24 switches to ISP A seamlessly. (Because 1.0.0.0/23 includes 1.0.0.0/24) However, when we ...

I have already looked at this question and its answers, but I have a slightly different question. Suppose I buy 100 shares of a stock on July 1, and two weeks later, on July 15, sell 50 of those 100 shares at a price lower than I paid for them. Could the IRS argue that the 50 shares I did not sel...

Can the color cyan (#00FFFF or 0, 255, 255) refer to the color mizuiro? Mizuiro in Japanese literally means "water-colored" so I wanted to know if mizuiro could refer to the cyan color or any of its variations mentioned below. I would also like to know if there are other color words that can be u...

Value Maps can be added to attributes via the loading of a CSV file, as described in the docs: https://docs.qgis.org/3.28/en/docs/user_manual/working_with_vector/vector_properties.html#edit-widgets It is possible to add a CSV (or any format) Value Map to an attribute of a layer using PyQGIS? I h...

During World War Two, Hitler removed the Hohenzollern princes from serving in the German Army after he saw the outpouring of grief and sympathy from the German public upon the death of one of the princes while serving in the army. Was the restoration of the Hohenzollern dynasty ever contemplated ...

Prove without expanding $$ \begin{vmatrix} a^3 & a^2 & 1 \\ b^3 & b^2 & 1 \\ c^3 & c^2 & 1 \end{vmatrix} = (ab + bc + ca)\begin{vmatrix} a^2 & a & 1 \\ b^2 & b & 1 \\ c^2 & c & 1 \end{vmatrix} $$ Well I tried but can't figure out a way to factor out $ (ab + bc + ca) $ directly without expanding....

What's the meaning of the so-called "Accent color" in MacOS and iOS? One sees it in the system-preferences of MacOS ("Appearance"-section), but it isn't clear to me what's there specified.

I have been debugging an issue in our production environment(on-premises) where queries perform slowly even the columns are indexed. The table has roughly 200 million rows, is not partitioned and is in full recovery mode. The DELETEs only affects 1 row and INSERTs are only 1 row too. I can see th...

The point of the twist was to exchange drive select A and B, so that all floppies could be sold with the drive select jumper in the second slot, and thus their position on the cable would cause them to be drive A or B. DS A and B are pins 14 and 12 respectively on the cable, so in theory the job ...

I am a postdoc in Israel (while my passport is Portuguese) and I need to visit the US: while filling out an ESTA (for the first time), I discovered I needed to list any jobs I currently work. I thought of listing my postdoc, but the visa I got for Israel is a student visa, and when I got it the c...

Let $\mathcal{O}_1$ and $\mathcal{O}_2$ be an open subset family of $\mathbb{R}$ as $$\mathcal{O}_1 = \{~(a, \infty)~ | a \in \mathbb{R}\} \cup \{\mathbb{R}, \emptyset\},\\\mathcal{O}_2 ~ \text{is the Euclidean topology.}$$ Moreover, let $\mathcal{O}$ be the product topology of $(\mathbb{R}, \mat...

Let $a,b \in \mathbb{R}$ Given, $$a+b = a^2+b^2 $$ then what is the maximum value of $(a + 7b)$ ? No idea how to deal with this.

Follow up from my previous question, I am not sure if a partition function for a system should be constant or not. If not, what are examples of constrained systems with partition function that varies with the system's state? Here is a particular example that came to mind: Consider a closed rigid ...

Imagine that on each edge of your square stands an enemy, but the diagonals are not occupied (□: unoccupied square, E: enemy, P: player): □ E □ E P E □ E □ Do you need to Tumble Through? Based on its text, tumbling is only necessary if you want to be (temporarily) in a square: [...] During this...

There used to be vertex, face etc. numbers at this lower bar. Why is this not appearing? Is there a way to get it back? PS: I'm not asking about statistics in the Overlay menu.

I'm looking at converting some USD into EUR. I am comparing Revolut's currency exchange rate with Wise' currency exchange rate. As of now: Revolut: 1 USD = 0.9216 EUR (screenshot). Revolut states they use the "interbank rate" (and add some fees in some case, which appear separately). Wise: 1 USD...

How do I go about plotting the equation: $$y^2 + 4x - 2y + 3 = 0$$ I am in my first year in the university. I am taking a course on Analytical Geometry and formulas are all over the place. I could just cram the formulas for questions, but there are so many, plus I prefer to understand what I am s...

I've noticed that many retailers still sell 74HC logic gate chips, which I also used in my digital design class. I'm curious to know whether these older components are still profitable for chip makers and whether they are still widely used in industry.

Both Jewish sources and Muslim sources seem to take for granted that at least some Arabs and/or Muslims are somehow descended from Abraham's son Ishmael (whether biologically or spiritually). See, for example, Mishneh Torah end of Hilchot Melakhim 11; Sefer HaIkkarim 4:42; Mefarshim to Genesis 37...

While reading a thread about coroutines, I stumbled upon a random user's comment that coroutines may not fire at all: Just so you are aware, there is a coroutine limit and if you hit this some coroutines will not fire or fail, leading to very weird and hard to track down behaviour if you have ne...

The law of large numbers states for $X_1,...,X_n$ random variables with finite expectation, \begin{equation} \mathbb{P}\bigg(\lim_{n\to\infty}\frac{S_n}{n}=\mu\bigg) = 1 \end{equation} where $S_n = \frac{X_1,...,X_n}{n}$. I'm struggling to understand the difference between this definition and \be...

If $$x^2+y^2=2015$$ find the maximum value of $$x^2+2xy-y^2$$ I have actually solved this question but as you see this question is apparently of number theory and I have solved this using trigonometry. I want to know about other methods of solving this question. If they include just number theo...

Cohen's d and Hedges'g effect sizes are used when two distributions have equal variances, which is a requirement and assumption to use these statistical tests. When two distributions have unequal variances, Glass'delta should be used instead, putting in the equation only the standard deviation of...

I would like to have the content in the first and second columns are centered aligned within its respected cells in a table with two column paper template as follows. The current table is as follows. Here is the code: \documentclass[journal]{IEEEtran} \usepackage{caption} \usepackage{tabularx} ...

For $2N$ qubits $\{i_1,j_1\ldots i_N,j_N\}$ I would like to have a circuit changing the value of an ancillary register from $0$ to $1$ if $i_1=j_1$ AND $i_2=j_2$ AND ... AND $i_N=j_N$. One way to construct such a circuit is to use a separate ancillary qubit to store the value of comparison of $i_...

In an economy, the agriculture, industrial and services sectors have initial shares of 50, 20 and 30 percent respectively in the total GDP. They also subsequently grow at the following constant annual rates for the next 60 years: Agriculture-2 percent; Industry-5 percent, and Services-6 percent p...

I have a setence: text= {Concerning the main ecological question on the complexity-stability relationship, our findings reveal that high species diversities and dynamical stability of growing ecological networks are very constrained under a widespread biochemical warfare between the interacting s...

What is the real probability that a person will be murdered tomorrow somewhere in the world? It seems like there should be a right answer to this. In fact, most of us would bet tens of millions of dollars that atleast one person will be murdered tomorrow. But what is the correct probability then?...

I'm reinstalling a threadless stem after cleaning and degreasing. There are two sets of bolts: the faceplate bolts that attach the handlebars to the stem and the pinch bolts that clamp the stem to the fork's steerer tube. To be clear, since some discussion I've read online just uses a catch-all t...

If I'm not wrong, 'ceci' is used for singular substantives naming things, but what pronoun would you use in plural? ... ne sont pas des pipes? What if we are talking about persons, singular/plural and masculine/feminine? How would you complete these sentences? ... n'est pas un professeur? ... n'e...

The paragraph we say on burning the chametz is in Aramaic. What is the reason for that part being in Aramaic, but not most of the Haggada? (The search is part of the prescribed Pesach ritual, as is the Haggada.) Was that part added to the Pesach ritual after the Hagadda was written?

Least Squares channel estimation (or equalization) can be accomplished using the "Wiener Hopf Equations", or the Discrete Fourier Transform. Both appear to be least squares solutions. How do the two compare and contrast? Under what conditions would one approach be preferred over the other, and if...

This implementation of thread pool that includes support for suspend functionality, which is necessary for refreshing reference data periodically. I would appreciate your review to ensure that there are no bugs and that the implementation is well-structured. Although everything seems to be workin...

I need to create a multidimensional array with bash and I read that there is no such thing as multidimensional arrays in bash . Here are my possible data, what they look like and what I need. This is not a bash array: DATACOL = [ "1"=>("Santiago","Barcelona","AWG","6792992","Male"), "2"=>("...

I understand -i but I don't know how it is different from -I and why the manual says that -i is deprecated. For example what is the difference between using the two lines below: ls -t | tail -n 4 | xargs -I{} mv {} test2/ ls -t | tail -n 4 | xargs -i mv {} test2/ For the first line can anything e...

I setup a ZFS pool on my "home server" (Raspberry Pi 4b) that consists of various HDD and SSD drives connected over USB to the Pi. I have noticed that whenever a reboot occurs, the ZFS pool fails to be imported by the zfs-import-cache.service.

The answer to the puzzle is a seven letter word. May it be yours!

I have recently read about the quantization of the energy levels that the electron in a neutral hydrogen atom can be in, and I noticed that all available treatments seem to treat the nucleus as a point charge $+e$ which determines the shape of the electronic wavefunction. However, are there any t...

Given a set of n points, and a number k decide whether there exist k straight lines such that all of the points are covered. Here a point is covered by a line if that point lies on that line. I can formulate an ILP for the same. The problem seems to be hard. I want to formally prove its NP-Comple...

I know the answer seems trivial but believe me, it is not! In Unicode There are different characters for Roman numerals. For example, one is not i but ⅰ which is a different character; or a better example, two is not ii (that is a string of two characters juxtaposed) but ⅱ (that is a single chara...

I was reading Mathematical Aspects of Quantum Field Theory by. E. de Faria and W. de Melo, and the following caught my attention. In (Hamiltonian) mechanics, the states of a system are described by points in a phase space $\Gamma$. The observables - physical quantitites that are measurable in ex...

The setting is Jesus in the wilderness, being tempted by the devil (vs. 1) and the second temptation is for Jesus to hurl himself down from a pinnacle in the temple “in the holy city” (vss. 5 & 6). The devil is, again, trying to get Jesus disbelieving the very words of God in heaven to him at his...

I ran the transient analysis for the this circuit with NMOS and NPN respectively. Once with the NPN BJT, the results look reasonable. The current through R1 is about 20mA. When I change to NMOS, the results are about 0.2mA. What did I miss for using a NMOS in an op-amp analysis?

For a perfect transformer, 1:1 turns ratio, V1=V2, I1=I2. Z1=V1/I1. Z2=V2/I2. => Z1=Z2. When I keep the 2nd coil open circuit, Z2 is infinite. Since Z1=Z2=infinite, if I apply perfect AC voltage zource at 1st coil, the impedance seen by the AC voltage is infinite? No current flow through 1st coil...

I would like to use the F9 key to toggle between the modus-themes-select and ef-themes-select functions. When I call the ef-themes-select, a minibuffer pops up to select an Ef theme: Now when I press the F9 one more time I want to switch to the modus-themes-select instead, and when I press the F...

I'm trying to display three components in one horizontal line. The components are: A picklist - ComboBox. An input text field. A button. I have an issue where the ComboBox label is on the same line as the other components, but the selection dropdown is not. I tried putting them inside a grid an...

"I had never thought I would be surprised again in my life until I did it ." Does it work ? I think so because doing this thing makes the man realised he had not thought about it before.But it seems that "had never thought with would" is very rarely used . I have never found it so it may be wron...

The recently discovered monotyle known as the hat is a polykite that tiles the plane aperiodically. A tiling looks like this:                                                              I wonder whether it is possible to tile this 13-edge hat-shaped figure with smaller copies of itself. These co...

I have been awarded a Graduate Research Fellowship from the grad school I intend to attend. It will start in Fall 2023. Should I add it to my CV in advance? If yes, how should I mention it there? If no, why do you think that? Thanks in advance.

Electric cars use a DC-DC converter to charge the 12 V service battery and power the various 12 V devices from the ~400 V traction battery. What happen if you pull too much amps from it? Does it break somehow or does it just provide the maximum power it can? I can't find any spec about the conver...

Recently, I saw a question in my exam regarding surface tension. It was mentioned in the answer key that the surface tension of copper and cadmium in the molten state increases with an increase in temperature. In contrast, the surface tension of other liquids continuously decreases with an increa...