text:
2 typo

Well, I've done some reading and (re)discovered an old paper of Peter Johstone which comes pretty close to answering this question using topos theory. It follows the idea I posted as a "possible lead" in my EDIT.

First some background information:

It was shown by Joyal that simplicial sets is the classifying topos for "interval objects" (this is explained for instance in "Sheaves in Geometry and Logic" by Mac Lane and Moerdijk, in which they refer to interval objects as order linear orders). By an interval object in $Set$, one roughly means a linearly ordered set together with a top and bottom element. You can say $I$ in a topos $\mathcal{E}$ is an interval object if and only if $Hom(E,I)$ is an interval object in $Set$ for all $E \in \mathcal{E}$. Since $Set^{\Delta^{op}}$ is the classifying topos for interval objects, for any topos $\mathcal{E}$, there is an equivalence of categories between the category of geometic morphisms $Hom(\mathcal{E},Set^{\Delta^{op}})$ and the category of interval objects in $\mathcal{E}$, $Int(\mathcal{E})$. Notice that the inverse image functor $f^*:Set^{\Delta^{op}} \to \mathcal{E}$ of a geometric morphism $f:\mathcal{E} \to Set^{\Delta^{op}}$ is always left-exact, so, this can be thought of as a "geometric realization functor with values in $\mathcal{E}$".

Now, the classical geometric realization functor $Set^{\Delta^{op}} \to Top$ nearly fits in this framework- it is left-exact and is uniquely determined by the fact that the universal interval object of simplicial sets is mapped to the standard unit interval $[0,1]$. However, $Top$ is not a topos. This is where Peter Johstone's 1977 Paper "On a topological topos" comes in. In this paper he constructs a topos $\mathcal{T}$ which contains sequential topological spaces (and hence e.g. CW-complexes) as a reflective subcategory. (In case you are interested, this topos is the topos of sheaves with respect to the canonical topology on the fullsubcategory of $Top$ consisting of the one-point space and the one-point compactification of $\mathbb{N}$.) Moreover, the inclusion of sequential spaces into $\mathcal{T}$ preserves lots of colimits- e.g. all colimits you'd use to construct CW-complexes. Now, since the standard unit interval $[0,1]$ is an object of $\mathcal{T}$, it corresponds to a unique geometric morphism $r:\mathcal{T} \to Set^{\Delta^{op}}$. Johnstone then proves that if $X$ is a simplicial set, then $r^*(X)$ is exactly $|X|$ (as a sequential space considered as an object of $\mathcal{T}$) AND that if $T \in \mathcal{T}$ is a sequential space, then $r_*(T) \cong Sing(T)$.

This is somewhat satisfying. However, for it to truly be satisfying, we'd have to either make sense out of why $\mathcal{T}$ is a natural choice, or, show that any "suitable choice" of a topos would give the same answer. Moreover, although intuively somehow clear, I would like to make sense out of in what way the "standard unit interval" $[0,1]$ is really a "canonical interval object".

1

Well, I've done some reading and (re)discovered an old paper of Peter Johstone which comes pretty close to answering this question using topos theory. It follows the idea I posted as a "possible lead" in my EDIT.

First some background information:

It was shown by Joyal that simplicial sets is the classifying topos for "interval objects" (this is explained for instance in "Sheaves in Geometry and Logic" by Mac Lane and Moerdijk, in which they refer to interval objects as order linear orders). By an interval object in $Set$, one roughly means a linearly ordered set together with a top and bottom element. You can say $I$ in a topos $\mathcal{E}$ is an interval object if and only if $Hom(E,I)$ is an interval object in $Set$ for all $E \in \mathcal{E}$. Since $Set^{\Delta^{op}}$ is the classifying topos for interval objects, for any topos $\mathcal{E}$, there is an equivalence of categories between the category of geometic morphisms $Hom(\mathcal{E},Set^{\Delta^{op}})$ and the category of interval objects in $\mathcal{E}$, $Int(\mathcal{E})$. Notice that the inverse image functor $f^*:Set^{\Delta^{op}} \to \mathcal{E}$ of a geometric morphism $f:\mathcal{E} \to Set^{\Delta^{op}}$ is always left-exact, so, this can be thought of as a "geometric realization functor with values in $\mathcal{E}$".

Now, the classical geometric realization functor $Set^{\Delta^{op}} \to Top$ nearly fits in this framework- it is left-exact and is uniquely determined by the fact that the universal interval object of simplicial sets is mapped to the standard unit interval $[0,1]$. However, $Top$ is not a topos. This is where Peter Johstone's 1977 Paper "On a topological topos" comes in. In this paper he constructs a topos $\mathcal{T}$ which contains sequential topological spaces (and hence e.g. CW-complexes) as a reflective subcategory. (In case you are interested, this topos is the topos of sheaves with respect to the canonical topology on the fullsubcategory of $Top$ consisting of the one-point space and the one-point compactification of $\mathbb{N}$.) Moreover, the inclusion of sequential spaces into $\mathcal{T}$ preserves lots of colimits- e.g. all colimits you'd use to construct CW-complexes. Now, since the standard unit interval $[0,1]$ is an object of $\mathcal{T}$, it corresponds to a unique geometric morphism $r:\mathcal{T} \to Set^{\Delta^{op}}$. Johnstone then proves that if $X$ is a simplicial set, then $r^*(X)$ is exactly $|X|$ (as a sequential space considered as an object of $\mathcal{T}$) AND that if $T \in \mathcal{T}$ is a sequential space, then $r_*(T) \cong Sing(T)$.

This is somewhat satisfying. However, for it to truly be satisfying, we'd have to either make sense out of why $\mathcal{T}$ is a natural choice, or, show that any "suitable choice" of a topos would give the same answer. Moreover, although intuively somehow clear, I would like to make sense out of in what way the "standard unit interval" $[0,1]$ is really a "canonical interval object".


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### Hidden TFTP of TP-Link routers

I did some more investigation after the positive results with the TL-WR740Nv4 (click the link to get introduced to the way of recovery). Most users report that devices and firmware updates released after a point in time usually have this mode enabled. If a firmware update is available from the vendor for your device, it's a good idea to apply that update before installing OpenWRT or dd-wrt UNLESS you own something for which upgrading will ensure incompatible with OpenWrt, like a TL-WR730N, and possible some other models (please report). Note that some old models have newer updates in different languages, those may also be worth a try (TODO: compatibility?). Also remember that later on, tftp recovery will need a type of firmware image without a boot loader, so strip it with dd if yours has it (grep U-Boot, or check the filename).

Positive reported claims so far (personal results highlighted):
• TL-WDR4300 router 192.168.0.86 server 192.168.0.66 query wdr4300v1_tp_recovery.bin from wdr4300v1_ru_3_13_23_up(130506).bin, TL-WDR4300_V1_130617.zip
• TL-WDR3600 router 192.168.0.86 server 192.168.0.66 query wdr3600v1_tp_recovery.bin from TL-WDR3600_V1_130527_RU.zip
• TL-WR841ND_V8_130620_RU.rar 192.168.0.66 query mr3420v2_tp_recovery.bin
• TL-WR841N v8.3 (unbricked by serial) needs latest to support TFTP by reset: TL-WR841N_V8_140724.zip
• TL-MR3020 router 192.168.0.86 server 192.168.0.66 query mr3020v1_tp_recovery.bin from TL-MR3020_V1_130507_RU, TL-MR3020_V1_140610TL-MR3020_V1_140408
• TL-WR740Nv4 router 192.168.0.86 server 192.168.0.66 query wr740v4_tp_recovery.bin from TL-WR740N_V4_130529.zip (wr740nv4_en_3_16_6_up_boot(130529).bin Rel.62825n) TL-WR740N_V4_140520.zip (wr740nv4_en_3_17_0_up_boot(140520).bin Rel.75075n) (confirmed by majlin), wr740nv4_en_3_17_0_up_boot(150105).bin (confirmed by Christian)
• TL-WR741ND_V4.20_140410
• TL-WR842ND v1.1 router 192.168.1.86 server 192.168.1.66 query wr842ndv1_tp_recovery.bin from TL-WR842ND_V1_130322.ZIP (wr842ndv1_en_3_12_25_up_boot(130322).bin) (some report versions before 2012-08-27?) note that tftp does not accept OpenWRT, only OEM firmware!
• TL-WR1043ND v1.11 3.13.5 Build 140319 Rel41339n wr1043nv1_en_3_13_15_up_boot(140319).bin U-Boot 1.1.4 (Mar 19 2014 - 11:06:29)
• ? TL-MR3220v2 query mr3220v2_tp_recovery.bin from TL-MR3220_V2_130607_RU.zip
• ? TL-MR3420v2
• TL-WR940Nv2 needs latest to support (verified on 3.16.9 Build 150311 Rel.62186n), router 192.168.0.86, server 192.168.0.66, query wr941ndv5_tp_recovery.bin
• ? TL-WR941NDv5 - should work exactly the same as for TL-WR940Nv2 because it has the same board
• ? TL-WR1042NDv1 router 192.168.1.86 server 192.168.1.66 query wr1042nv1_tp_recovery.bin
• ? any TP-Link with firmware (or update) after date XXX TODO (about March of 2013)

Negative reports (personal results highlighted):
• TL-WR740Nv4 3.12.11 Build 120320 Rel.51047n (works after update)
• TL-WR740Nv4 3.16.5 Build 130329 Rel.62825n (confirmed by majlin, works after update))
• TL-MR3420v1 3.11.11 Build 101104 Rel.70817n, TODO try updates
• TL-WR940v2 3.14.5 Build 130709 Rel.36000n (works after update)
• ? TODO: TL-MR3040
• TODO: TL-WR741NDv2
• ? TODO: TL-WR743NDv1
• ? TODO: TL-WR841Nv5
• ? TODO: TL-WR841Nv7
• ? TODO: TL-WR941Nv3
• ? TODO: TL-WR2543ND_V1_121207

Sources:
This post is work in progress and I plan to eventually migrate it to a new page on the OpenWRT wiki. Stay tuned! TODO

1. Hi,

You mention that the latest (tftp enabled) firmware for the WR1043ND is incompatible with OpenWRT. Following the thread in the OpenWRT forum, I can only find references to the WR703N device not accepting non TP-LINK firmware images.

Because I would like to harden my WR1043NDv1 with an old uboot version against bricks (I already failed hilariously on other devices :D), a tftp enabled uboot without the need for soldering would be perfect.

Searching the OpenWRT forums, searching google and looking at your lists, I cannot find any information regarding the WR1043ND firmwares not accepting OpenWRT images.

Did you test the WR1043ND yourself or where is this information comming from?

Thanks
Christian

2. Dear Christian,

If the linked forum does not contain the reference, I may have assimilated the information from the OpenWRT wiki page about the device:

Which hardware revision are you using, v1 or v2? I have no information on the validity of that claim or the exact u-boot versions causing an issue, as there aren't enough people updating the wiki, and I haven't personally ran into such a device yet. Perhaps you could do some targeted web search about experience with exact firmware revisions and build numbers. All three revisions of the currently linked OEM updates should (might) support tftp updates, but it is very easy to test them. Then just it's a matter of searching for confirmation on which one is supported by OpenWRT. If you can't find anything, you may also consider an OpenWRT side patch. Anyhow, don't take my word on it, but after updating to one that definitely supports tftp, you might just as well try to install OpenWRT yourself and see which one doesn't brick the router. The advantage of tftp recovery...

Feel free to share your experience if you find anything. Or please tell me if there exist other models for which u-boot updates could kill OpenWRT, so we can a place a word of warning here about them too.

I myself am in the process of gathering new devices. My fleet is already in the dozens. I already have specimens of 740, 741, 840, 841, 842, 941, 2543ND, MR3020, 3220, 3420 and perhaps some others I forgot to list. Unfortunately, I have no specimen of 1043ND yet, but I'm working on the issue. For example, the 842ND had tftp u-boot updates, however no update is available to the 2543ND. I'm considering to build its OEM firmware from scratch and patch the u-boot source myself, though I wouldn't like to start by messing up this beauty. I am also considering to risk cross-flashing some models with Chinese firmware, as those are newer in many cases. I will report back when I have results.

Best regards,
bkil

3. Hi,

I guess you are referring to the "WAN port disabled" bug which affected the WR1043ND v1 and seems to be fixed regarding the bug tracker. I did not encounter this bug on my v1.11 model on different uboot versions with 12.09 and 14.07. The Wiki can be confusing...

Anyway, today I tested a WR740N v4.21 and a WR1043ND v1.11. Both had old uboot versions from 2012 without the tftp feature. At least I did not see any traffic with tcpdump.

So I took a leap of faith and updated both devices with the latest stock firmwares and uboot:
WR740N v4.21: wr740nv4_en_3_17_0_up_boot(150105).bin
WR1043ND v1.11: wr1043nv1_en_3_13_15_up_boot(140319).bin

Shown versions after the updates on the stock web interface:
WR740N: 3.17.0 Build 150105 Rel.61576n
WR1043ND: 3.13.5 Build 140319 Rel41339n

WR740N: U-Boot 1.1.4 (Jan 5 2015 - 17:01:20)
WR1043ND: U-Boot 1.1.4 (Mar 19 2014 - 11:06:29)

I had no problems flashing stock firmwares and OpenWRT images back and forth on both devices. So the bug/feature from the WR703N firmware, which does not allow OpenWRT images being flashed over the stock web interface does not affect the WR1043ND.

After the updates, both devices have a tftp enabled uboot now :). I have not tested tftp itself, but I assume the feature is there. I saw bootp, ARP requests and both IP addresses .66 and .86 in tcpdump.
Interestingly bootp and ARP requests on the WR740N, but only ARP requests on the WR1043ND.

No more soldering required, if I mess up an OpenWRT image (again) :)

Greetings
Christian

By the way, it's also good that you pointed out that updated firmware is available. Although, I think I won't be reflashing the dozens of already installed devices just for this new u-boot. I'll have a look whether they have even updated that part since last May.

4. TP-Link TL-WR841ND v8.2 won't work.

1. From the top of my head, I have specimens of TL-WR831N 2*8.2, 8.3, 2*8.4 which work flawlessly. I have installed Barrier Breaker on each one of them using reset+tftp.

Note that on the oldest models, I had firmware from 2012 which I had upgraded to May 2013 before proceeding. If your u-boot is not recent, you will need to proceed with the next method in line: serial, JTAG or SPI soldering, whichever yields first.

If in doubt, it would be great if you could open a thread a thttp://forum.openwrt.org in the hardware section, link your thread here and we will try to help you recover. For example, see: http://forum.openwrt.org/viewtopic.php?id=45567 "TP-Link TL-WR841N v8.4 Bricked" Describe what you have done in detail there so we can see the issue more clearly.

2. Correction: I've consulted my notes and the first firmware which did support tftp on reset on that model may be 3.15.9 Build 140724 Rel.63227n. Or at least that's the one which I install on each new one

3. I was buying today TP-Link MR3220 v2.2, and upgrade to newer official firmware. (TL-MR3220_V2_140929) , and see that 192.168.0.66 on WAN port working (in wireshark i see what want - mr3220v2_tp_recovery.bin)..... But I must upload OpenWRT... so what need I do, to keep bootloader with tftp client? For bricked WR841ND i wait USB <-> TTL...

4. All is OK with OpenWRT on this router (TP-Link MR3220 v2.2) :) TFTP client in boot loader still exists :) ....

5. I'm glad to hear that! Yes, as you have found out: an OpenWrt upgrade keeps the smart boot loader in place.

I hope you're having fun with your new gadgets! :) You can find some cool use cases especially for USB ones.

Over here, the MR3220 v2 and MR3420 v2 cost a lot, so I only have some of the dumb v1 ones. C'est la vie.

6. My bricked TP-Link TL-WR841ND v8.2 is again in life :D With USB <--> TTL adapter, some wires without soldering, SW - Realterm, send command to OpenWRT to remove some package :D But i upgrade now (before stripped official firmware), just in case - wr841nv8_en_3_15_9_up_boot(140724).bin, and TFTP client workin and send request on 192.168.0.66 for wr841nv8_tp_recovery.bin ..

7. Very good! Did you use Barrier Breaker or Chaos Calmer? I'm considering upgrading if you have good experience.

8. Barrier Breaker. Chaos Ch. haven't enought space for web admin - Luci.

9. What do you mean by not enough space? CC final has been released just last week. All release images should include Luci by default. The CC I had installed on a TL-WR741ND v4 definitely has one out of the box.

10. I'm not sure now.. but i tested before one month ... CC was without Luci and image was about 3.4MB .. For my testing purpose and my module in C , BB is good :)

11. I forgot tell - sysupgrade image for WR841ND v8.2, before bricking... But BB is good for my job.. for now :)

5. This comment has been removed by a blog administrator.

6. Looking for contact tp link uk, visit on: contact tp link uk

7. Nice Blog Post thanks for sharing it.

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# Browse Dissertations and Theses - Mathematics by Contributor "Basar, Tamer"

• (1997)
The eighth chapter studies the solvability of HJI equations that arise in nonlinear $H\sp{\infty}$ control problems where the system is affine in the control and the disturbance. In each case the existence of viscosity ...

application/pdf

PDF (11MB)


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# 2009

## On statistical approximation in spaces of continuous functions

Abstract Our goal is to present approximation theorems for sequences of positive linear operators defined on $$C(X)$$, where $$X$$ is…

## Compression-expansion critical point theory in conical shells

AbstractA Krasnoselskii type compression-expansion fixed point theorem is adapted for the treatment of systems of semi-Unear equations. The compression-expansion conditions…

## Mathematical models of the leukemic hematopoiesis

AbstractStarting from a classification of acute myeloid leukemias which takes into account the vital characteristics of the leukemic clones, we…

## Fourth-order p-Laplacian nonlinear systems via the vector version of Krasnoselskii’s fixed point theorem

AbstractIn this paper, existence results for a fourth-order nonlinear system are obtained. Both classical and vector versions of the Krasnosel’skiĭ’s…

## Existence of solutions for second-order differential equations and systems on infinite intervals

Abstract We study the existence of nontrivial solutions to the boundary value problem $$-u^{\prime \prime}+cu\prime+\lambda u$$ $$=f(x,u),\ \ -\infty<x<+\infty$$…

## Data dependence of fixed points for non-self generalized contractions

AbstractData dependence of fixed points for several classes of non-self generalized contractions is studied. A fibre non-self contraction theorem is…

## Existence, localization and multiplicity results for positive radial solutions of semilinear elliptic systems

AbstractExistence, localization and multiplicity results of positive solutions to a system of singular second-order differential equations are established by means…

## The role of matrices that are convergent to zero in the study of semilinear operator systems

AbstractIn this paper we explain the advantage of vector-valued norms and the role of matrices that are convergent to zero…

## Existence results for semilinear elliptic boundary value problems via topological methods

Abstract In this work, existence and localization results for $$C_1$$-solutions to elliptic Dirichlet boundary value problems are established. The approach…

## Programmed motion in the presence of homogeneity

AbstractAuthorsKeywordsReferencesPDFScanned paper. Latex version of the paper. Cite this paper as:Bozis G, Anisiu M-C, Programmed motion in the presence of…


text:
# Quantum mechanical interpretation of resistance and voltage drop

It is generally said that Ohm's law isn't a real law since it is only a fine model found through experiments to explain the nature of circuits. And resistance is defined as the ratio of the voltage difference between two poles and the current flow through the circuit. Often resistance is explained as electrons having collision with the atoms of the conductor and is some kind of drag (?) through which electrons loose energy. This explanation doesn't seem to be exact case.

What is actually going on if we zoom into the quantum level? How are the concepts of resistance and voltage drop interpreted then?

To me, the most interesting characteristics of electrical resistance is the orbital positions, which feeds common quantum calculations. That is the most electrical conductivity, thereby the lowest electrical resistance, comes in the middle of the periodic chart. It is the column, 29-Cu Copper, 47-Ag Silver, and 79-Au Gold.

The challenge for thinking of these using the quantum model is that the electrons are in the toward the max of the current d-shell. These are all d-shell (Xd9) which you get the quantum number from:

What is the right quantum numbers of Copper?

That reference is important because it states that the last electron quantum number for Copper is the same as the last electron quantum number of Zinc, which has very different - low - electrical conductivity -- the opposite of Copper. As such, one would not expect the expression with the same last electron to yield such opposite if the quantum number is the same. One would expect that the last electron is the critical one for electrical conductivity - being the most removed (lowest energy to release).

I believe the answer lies in other research about 'transition metals' which exhibit a number of contradictory. Specifically, at:

https://en.wikipedia.org/wiki/Transition_metal

It states that d-Shell transition provides a) magnetic, b) when in solution color, and c) oxidation, but not electrical resistance.

So, to me the linkage of electrostatic conductivity to current quantum theory remains inadequate. Quantum theory is good at only certain properties.

When I started learning QM in the first lecture we tried a "semi classical" way to imagine these things. Imagine a metallic cube. Let's assume that some current $I$ is flowing through it. The current through an $A$ cross section will be : $$I=qnvA.$$ where $q$ is the unit charge, $v$ is the average speed of the electrons and $n$ is the volumetric concentrations. We can assume that the speed is proportional to the potential energy $E$ $$v=\mu E$$ Where $\mu$ represents the ability of the electrons to move. Then $$I=qn\mu EA.$$ And the current density $j$ is $$j=qn\mu E.$$ Hence the conductivity $\gamma$ is $\gamma=\frac{j}{E}$ then it is $$\gamma=qn\mu$$ And the resistance is $$\rho=\frac{1}{\gamma}=\frac{1}{qn\mu}$$ And where quantum mechanics comes in? It is neccessary when we want knowledge about $\mu$.At first assume that we are working with a metal which has a perfect crystalline structure, then the electrons won't scatter much on the atoms so a perfect crystal would not have any resistance. The resistance is from the defects of the crystal where electrons scatter. So the resistance is due to scattering, not collision, is an electron hits a nucleus it is called electron capture which is another interesting topic. Since $\mu$ is not a number I should better call it $\mu(x,y,z)$ and $n$ is really $n(x,y,z)$ and they are both dependent on the shape of the metal piece and the position too. so it won't be a simple equation to use(And we did not even calculated with the electrons effects on each other!). The voltage drop sould be easy to calculate for you then.I hope my answer was good enough :)

• Thanks for your answer. But what did you mean exactly by electron scattering? And how does electron scattering arise resistance? It will be helpful if you elaborate a little bit. – user102426 Jan 24 '18 at 6:26
• When an electron gets close to an atom it's path can be changed by the electromagnetic force of the nucleus or electromagnetic force of it's electrons. When this happens, the projection of the velocity in the original direction will be smaller and if you substitute a smaller velocity to my first equation you will get a smaller current, which means, voltage drop and resistance are occuring. – L.Gyula Jan 24 '18 at 12:05


text:
When things don’t work like they ought to.

While experimenting with motor speed controls for a planned motor controller for my vintage Adler class 8 sewing machine, I found I needed a better method to detect the rotational speed of the motor. The methods I was using (based on measuring the back EMF of the motor) were not doing well at the low speeds I need.

To get accurate RPM counts at low speeds, I decided to try counting the RPM using a photointerrupter. This will mean adding hardware to the motor (which I wanted to avoid.) The required hardware is the photointerrupter along with a slotted wheel on the motor axle.

I ordered a set of cheap photointerrupters from Amazon because they came with slotted wheels and a small circuit board. They are ideal for experimenting.

Photointerrupter module
The circuit diagram is from the Amazon page for the Youmile modules I ordered.

I attached the slotted wheel to one of the little motors I’ve been using and setup the photointerrupter to have a look at the signals.

Test setup

Once it was all wired, I turned on the juice and looked at the oscilloscope - nada. Nothing. No pulses. The motor was whirring away, but there were no pulses on the digital output of the module.

The wiring is simple enough that it only took a quick glance to see that it was OK.

I connected the scope to the analog output of the module, and got something like this:

Shark fins

The lower trace is the analog output. Given the shape of the slots, I expected that even the analog output would be somewhat square and symmetrical. I sure didn’t expect rounded off “shark fins” whose amplitude varied with the motor speed.

At high speeds, the amplitude of the photointerrupter pulses (on the analog output) are too low to trigger the LM393 comparator. The circuit diagram shows that the comparator triggers when the photointerrupter signal goes above half the operating voltage - that’s a 2.5V trigger level for the 5V power supply from the Arduino.

Besides not triggering at high speed, the pulses also weren’t square and symmetrical. They got narrower as the motor sped up until they disappeared altogether.

The pulses are wider at low(er) speeds, but still not what I’d expect.

Slower shark fins

That’s not what I bought the modules for, so I had a good look at the circuit diagram. I bought the modules I did specifically because the seller included a circuit diagram on the page advertising the modules.

Guilty parties

The circuit diagram also shows why the photointerrupter signal looked like a shark’s fin. There’s a 100 nanofarad capacitor (C1) across the phototransistor. Together with the 10k resistor (R1,) C1 forms a low pass filter with a cutoff of around 160Hz. Given that there are twenty pulses per rotation, that means that the filter starts distorting the signal at around 480 RPM. At about 1500 RPM, the signal is so distorted that the comparator can no longer detect it - the digital output goes flat.

I removed C1, which improved things considerably. The comparator got a good signal up to around 18 thousand RPM - but still with shark fins.

Improved

The phototransistor in the photointerrupter has some capacitance so there’s still a little low pass filtering going on.

I reduced R1 from 10k to 750 ohms, and finally got the clear, sharp square waves I expected.

Clean signal

The analog output is very nearly square, and the digital output from the comparator is sharp and symmetrical.

It works at lower speeds just as well.

Lower speed

That’s at the lower end of the RPM range I’ll need for the sewing machine.

I’m aiming for a low speed of about 1 stitch per second on the sewing maching. The way the Adler 8 works, that means that the hand wheel turns once per second - 60 RPM. There’s a six to one pulley ratio from the motor to the hand wheel, so the motor has to turn at about 360 RPM for the machine to do one stitch per second. That ratio also means that the 1500 RPM limit mentioned above would work out to 250 stitches per minute. That’s a little on the slow side, even for me.

I want the low speed for precision stuff (intricate, decorative stitches,) but at the same time I need to be able to “floor it” and sew straight, simple stuff quickly. The original state of the photointerrupter module would have covered the low end of what I need, but not allowed for the higher speeds.

Here’s how you calculate the RPM.

1. Measure the time between two rising edges - that’s $t_{pulse}$. Make sure to use seconds, not milliseconds.
2. $RPM = \frac{60}{20 \times t_{pulse}}$

If you try to calculate the RPM from the pictures above, watch the units. The cursors mark the time of one pulse. That time period is shown in the measurements section. Sometimes the time is in milliseconds, and sometimes it is in microseconds. You have to convert to seconds to calculate the RPM.


text:
# The nontrivial zeros of the zeta function and the prime counting function

The truncated explicit formula has the shape
$$$$\label{1} \psi(x) =x-\frac{\zeta^{\prime}(0)}{\zeta(0)}-\sum_{|\rho|\leq T}\frac{x^{\rho}}{\rho}+\sum_{n=1}^{\infty}\frac{x^{-2n}}{2n}+O\left(\frac{x\log (Tx)^2}{T} \right) ,$$$$ where $$\rho=\beta+it$$ are the nontrivial zeros of the zeta function, [1, Explicit Formula], and there are other versions of it.

The final paragraph on the proof of Theorem 6.9 in [2, page 181] states the following:

"... On combining these estimates we conclude that $$$$\label{2} \psi(x) =x+O\left(x(\log x^2)\left( \frac{1}{T}+x^{-c/\log T} \right) \right) .$$$$ We choose $$T$$ so that the two terms in the last factor of the error term are equal, $$T = \exp(\sqrt{c\log x})$$. With this choice of $$T$$, the error term above is $$$$\label{3} \ll x(\log x)^2\exp(-\sqrt{c\log x})\ll x\exp(-c\sqrt{\log x})$$$$
since we may suppose that $$0 < c < 1$$. Thus the proof of (6.12) is complete."

Question. Why does the proof of Theorem 6.9, based on the zero free region $$1-c/\log T$$, or any other known zero free region, uses fewer zeros $$\rho=\beta+it$$ in the approximation to $$\psi(x)$$. Specifically, $$t\leq T< \exp(\sqrt{c\log x}).

We should expect that increasing the number of zeta zeros to $$t\leq T=x$$, should have a smaller error term $$E(x)$$ since the approximation to $$\psi(x)=\sum_{n\leq x}\Lambda(n)=x+E(x)$$ is better. But, it does not, in fact, the error term of the truncated explicit formula (2) exceeds the main term. It has the shape $$$$\label{4} \psi(x)=\sum_{n\leq x}\Lambda(n)=x+O(x(\log x)^2).$$$$

Please edit as required to improve the question. Many other paradoxes in the theory of the zeta function are documented in [3].

[1] Harold Davenport, Multiplicative number theory, third ed., Graduate Texts in Mathematics, vol. 74, Springer-Verlag, New York, 2000.

[2] Hugh L. Montgomery and Robert C. Vaughan, Multiplicative number theory. I. Classical theory, Cambridge Studies in Advanced Mathematics, vol. 97, Cambridge University Press, Cambridge, 2007.

[3] David W. Farmer, Currently there are no reasons to doubt the Riemann Hypothesis, arXiv:2211.11671.

• When you plug in $T=\exp(\sqrt{c\log t})$, then the error term will be significantly smaller than $x(\log x)^2$. Nov 23, 2022 at 20:58
As you can see from the proof, with our current knowledge of the distribution of zeros, your expectation "We should expect that [...] the approximation to $$\psi(x)$$ [...] is better" is false. The problem is that, as far as we know, higher up there can be many zeros with real part very close to $$1$$, which makes the approximation worse, not better. For example, if we did not know that all zeros have real part less than $$1$$, then we could not even prove that $$\psi(x)$$ is asymptotically $$x$$.


text:
This is a set of lecture notes suitable for a Master's course on quantum computation and information from the perspective of theoretical computer science. The first version was written in 2011, with many extensions and improvements in subsequent years. The first 10 chapters cover the circuit model and the main quantum algorithms (Deutsch-Jozsa, Simon, Shor, Hidden Subgroup Problem, Grover, quantum walks, Hamiltonian simulation and HHL). They are followed by 3 chapters about complexity, 4 chapters about distributed ("Alice and Bob") settings, and a final chapter about quantum error correction. Appendices A and B give a brief introduction to the required linear algebra and some other mathematical and computer science background. All chapters come with exercises, with some hints provided in Appendix C.

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iOS 8 提供的应用间和应用跟系统的功能交互特性。
• Today (iOS and OS X): widgets for the Today view of Notification Center
• Share (iOS and OS X): post content to web services or share content with others
• Actions (iOS and OS X): app extensions to view or manipulate inside another app
• Photo Editing (iOS): edit a photo or video in Apple's Photos app with extensions from a third-party apps
• Finder Sync (OS X): remote file storage in the Finder with support for Finder content annotation
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Source: iOS 8 Extensions: Apple’s Plan for a Powerful App Ecosystem

Variational Quantum Eigensolvers (VQEs) have recently attracted considerable attention. Yet, in practice, they still suffer from the efforts for estimating cost function gradients for large parameter sets or resource-demanding reinforcement strategies. Here, we therefore consider recent advances in weight-agnostic learning and propose a strategy that addresses the trade-off between finding appropriate circuit architectures and parameter tuning. We investigate the use of NEAT-inspired algorithms which evaluate circuits via genetic competition and thus circumvent issues due to exceeding numbers of parameters. Our methods are tested both via simulation and on real quantum hardware and are used to solve the transverse Ising Hamiltonian and the Sherrington-Kirkpatrick spin model.

Discrimination between objects, in particular quantum states, is one of the most fundamental tasks in (quantum) information theory. Recent years have seen significant progress towards extending the framework to point-to-point quantum channels. However, with technological progress the focus of the field is shifting to more complex structures: Quantum networks. In contrast to channels, networks allow for intermediate access points where information can be received, processed and reintroduced into the network. In this work we study the discrimination of quantum networks and its fundamental limitations. In particular when multiple uses of the network are at hand, the rooster of available strategies becomes increasingly complex. The simplest quantum network that capturers the structure of the problem is given by a quantum superchannel. We discuss the available classes of strategies when considering $n$ copies of a superchannel and give fundamental bounds on the asymptotically achievable rates in an asymmetric discrimination setting. Furthermore, we discuss achievability, symmetric network discrimination, the strong converse exponent, generalization to arbitrary quantum networks and finally an application to an active version of the quantum illumination problem.

The motivation for this thesis was to recast quantum self-testing [MY98,MY04] in operational terms. The result is a category-theoretic framework for discussing the following general question: How do different implementations of the same input-output process compare to each other? In the proposed framework, an input-output process is modelled by a causally structured channel in some fixed theory, and its implementations are modelled by causally structured dilations formalising hidden side-computations. These dilations compare through a pre-order formalising relative strength of side-computations. Chapter 1 reviews a mathematical model for physical theories as semicartesian symmetric monoidal categories. Many concrete examples are discussed, in particular quantum and classical information theory. The key feature is that the model facilitates the notion of dilations. Chapter 2 is devoted to the study of dilations. It introduces a handful of simple yet potent axioms about dilations, one of which (resembling the Purification Postulate [CDP10]) entails a duality theorem encompassing a large number of classic no-go results for quantum theory. Chapter 3 considers metric structure on physical theories, introducing in particular a new metric for quantum channels, the purified diamond distance, which generalises the purified distance [TCR10,Tom12] and relates to the Bures distance [KSW08a]. Chapter 4 presents a category-theoretic formalism for causality in terms of '(constructible) causal channels' and 'contractions'. It simplifies aspects of the formalisms [CDP09,KU17] and relates to traces in monoidal categories [JSV96]. The formalism allows for the definition of 'causal dilations' and the establishment of a non-trivial theory of such dilations. Chapter 5 realises quantum self-testing from the perspective of chapter 4, thus pointing towards the first known operational foundation for self-testing.

We consider the problem of communicating a general bivariate function of two classical sources observed at the encoders of a classical-quantum multiple access channel. Building on the techniques developed for the case of a classical channel, we propose and analyze a coding scheme based on coset codes. The proposed technique enables the decoder recover the desired function without recovering the sources themselves. We derive a new set of sufficient conditions that are weaker than the current known for identified examples. This work is based on a new ensemble of coset codes that are proven to achieve the capacity of a classical-quantum point-to-point channel.

We introduce a graphical language for coherent control of general quantum channels inspired by practical quantum optical setups involving polarising beam splitters (PBS). As standard completely positive trace preserving maps are known not to be appropriate to represent coherently controlled quantum channels, we propose to instead use purified channels, an extension of Stinespring's dilation. We characterise the observational equivalence of purified channels in various coherent-control contexts, paving the way towards a faithful representation of quantum channels under coherent control.

Intuitionistic belief has been axiomatized by Artemov and Protopopescu as an extension of intuitionistic propositional logic by means of the distributivity scheme K, and of co-reflection $A\rightarrow\Box A$. This way, belief is interpreted as a result of verification, and it fits an extended Brouwer-Heyting-Kolmogorov interpretation for intuitionistic propositional logic with an epistemic modality. In the present paper, structural properties of a natural deduction system $\mathsf{IEL}^{-}$ for intuitionistic belief are investigated also in the light of categorical semantics. The focus is on the analyticity of the calculus, so that the normalization theorem and the subformula property are proven firstly. From these, decidability and consistency of the logic follow as corollaries. Finally, disjunction properties, $\Box$-primality, and admissibility of reflection rule are established by using purely proof-theoretic methods.

Quantum channel estimation and discrimination are fundamentally related information processing tasks of interest in quantum information science. In this paper, we analyze these tasks by employing the right logarithmic derivative Fisher information and the geometric R\'enyi relative entropy, respectively, and we also identify connections between these distinguishability measures. A key result of our paper is that a chain-rule property holds for the right logarithmic derivative Fisher information and the geometric R\'enyi relative entropy for the interval $\alpha\in(0,1)$ of the R\'enyi parameter $\alpha$. In channel estimation, these results imply a condition for the unattainability of Heisenberg scaling, while in channel discrimination, they lead to improved bounds on error rates in the Chernoff and Hoeffding error exponent settings. More generally, we introduce the amortized quantum Fisher information as a conceptual framework for analyzing general sequential protocols that estimate a parameter encoded in a quantum channel, and we use this framework, beyond the aforementioned application, to show that Heisenberg scaling is not possible when a parameter is encoded in a classical-quantum channel. We then identify a number of other conceptual and technical connections between the tasks of estimation and discrimination and the distinguishability measures involved in analyzing each. As part of this work, we present a detailed overview of the geometric R\'enyi relative entropy of quantum states and channels, as well as its properties, which may be of independent interest.

Traditionally, expert epidemiologists devise policies for disease control through a mixture of intuition and brute force. Namely, they use their know-how to narrow down the set of logically conceivable policies to a small family described by a few parameters, following which they conduct a grid search to identify the optimal policy within the set. This scheme is not scalable, in the sense that, when used to optimize over policies which depend on many parameters, it will likely fail to output an optimal disease policy in time for its implementation. In this article, we use techniques from convex optimization theory and machine learning to conduct optimizations over disease policies described by hundreds of parameters. In contrast to past approaches for policy optimization based on control theory, our framework can deal with arbitrary uncertainties on the initial conditions and model parameters controlling the spread of the disease. In addition, our methods allow for optimization over weekly-constant policies, specified by either continuous or discrete government measures (e.g.: lockdown on/off). We illustrate our approach by minimizing the total time required to eradicate COVID-19 within the Susceptible-Exposed-Infected-Recovered (SEIR) model proposed by Kissler \emph{et al.} (March, 2020).

An $n\overset{p}{\mapsto}m$ random access code (RAC) is an encoding of $n$ bits into $m$ bits such that any initial bit can be recovered with probability at least $p$, while in a quantum RAC (QRAC), the $n$ bits are encoded into $m$ qubits. Since its proposal, the idea of RACs was generalized in many different ways, e.g. allowing the use of shared entanglement (called entanglement-assisted random access code, or simply EARAC) or recovering multiple bits instead of one. In this paper we generalize the idea of RACs to recovering the value of a given Boolean function $f$ on any subset of fixed size of the initial bits, which we call $f$-random access codes. We study and give protocols for $f$-random access codes with classical ($f$-RAC) and quantum ($f$-QRAC) encoding, together with many different resources, e.g. private or shared randomness, shared entanglement ($f$-EARAC) and Popescu-Rohrlich boxes ($f$-PRRAC). The success probability of our protocols is characterized by the \emph{noise stability} of the Boolean function $f$. Moreover, we give an \emph{upper bound} on the success probability of any $f$-QRAC with shared randomness that matches its success probability up to a multiplicative constant (and $f$-RACs by extension), meaning that quantum protocols can only achieve a limited advantage over their classical counterparts.

Graphical causal inference as pioneered by Judea Pearl arose from research on artificial intelligence (AI), and for a long time had little connection to the field of machine learning. This article discusses where links have been and should be established, introducing key concepts along the way. It argues that the hard open problems of machine learning and AI are intrinsically related to causality, and explains how the field is beginning to understand them.

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# Compute Trig Function Values, Solve Trig Equation

• Sep 8th 2011, 04:21 PM
qwerty999
Compute Trig Function Values, Solve Trig Equation
I need a little help here !!!

Find the following values exactly:

a) sin (7pi/6) I got -1/2 but i don't know how i got it please someone explain
b) sin (-11pi/4)

2) Find the general soln of the trig eqn

3cosx = 2sin^2x
My answer is : (2 cos x - 1) (cos x + 2) is that right ?
• Sep 8th 2011, 07:00 PM
steinmath
Re: Compute Trig Function Values, Solve Trig Equation
Firstly, $\frac{7\pi}{6}$ is equivalent to 210 degrees (multiply by 180/pi). 210 degrees has a "reference angle" of 30, meaning that it has the same sin/cos/tan as 30 degrees except that it is in a different quadrant and thus may be negative. In this case, the sine of 210 degrees is negative, because sine is negative in the third quadrant.

This means that $\sin \frac{7\pi}{6}=\sin 210^\circ = -\sin 30^\circ = -\frac{1}{2}$

See if you can do part b) yourself by using the same strategy--convert to degrees if it makes things easier for you, find a reference angle, and determine whether sine should be positive or negative in the appropriate quadrant.

----

For part 2), I think you misunderstand what the problem is asking. The problem is asking for the numbers (angles) such that the equation is true. So trig functions should not appear in the answer. Hint: rewrite $\sin^2 x$ as $1-\cos^2 x$, bring all the terms to one side, factor, and solve.


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# To write a function f describing the average cost of sealable books. Given information: The printing and binding cost for a college algebra book is $10. The editorial cost is$200,000. The first 2500 books are free.

To write a function f describing the average cost of sealable books.
Given information:
The printing and binding cost for a college algebra book is $10. The editorial cost is$200,000. The first 2500 books are free.
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

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tabuordy
Calculation:
Let the number of books be x. Since the printing and blinding cost for a college algebra cost is $10. The printing and blinding cost for 10 algebra books is 10x. The editorial cost is$200,000. The first 2500 books are free.
Thus, the average cost of sealable books is

$f\left(x\right)=\frac{10x+200,00}{x-2500}$
Hence, the required function is $f\left(x\right)=\frac{10x+200,00}{x-2500}$.


text:
# nLab n-localic 2-topos

### Context

#### 2-Category theory

2-category theory

## Definitions

• 2-category

• strict 2-category

• bicategory

• enriched bicategory

• ## Transfors between 2-categories

• 2-functor

• 2-natural transformation

• modification

• Yoneda lemma for bicategories

• ## Morphisms in 2-categories

• fully faithful morphism

• faithful morphism

• conservative morphism

• pseudomonic morphism

• discrete morphism

• eso morphism

• ## Structures in 2-categories

• mate

• cartesian object

• fibration in a 2-category

• codiscrete cofibration

• ## Limits in 2-categories

• 2-limit

• 2-pullback

• comma object

• inserter

• inverter

• equifier

• ## Structures on 2-categories

• monoidal 2-category

• Gray tensor product

• proarrow equipment

• # Contents

## Definition

Let $K$ be a Grothendieck 2-topos. We say that $K$ is $n$-truncated if it has a small eso-generator? consisting of $(n-1)$-truncated objects. It is easy to see that if a coproduct of $(n-1)$-truncated objects is $(n-1)$-truncated (as is the case for all $n\ge 1$), then this is equivalent to saying that $K$ has enough $(n-1)$-truncated objects (i.e. every object admits an eso from an $(n-1)$-truncated one). In particular:

• $K$ is always 2-truncated.
• $K$ is (2,1)-truncated if it has enough groupoids.
• $K$ is 1-truncated if it has enough discretes.
• $K$ is (0,1)-truncated if the subterminal objects are eso-generating.
• $K$ is (-1)-truncated if the terminal object is an eso-generator.

## $n$-sites and $n$-sheaves

By the 2-Giraud theorem, small eso-generating sets of objects correspond to small 2-sites of definition for $K$. Thus, if we define an $n$-site to be a 2-site which is an $n$-category (where $n\le 2$ as usual), we have:

###### Theorem

A Grothendieck 2-topos is $n$-truncated iff it is equivalent to the 2-category of 2-sheaves on some $n$-site.

Note that a 1-site is the same as the usual notion of site, and a (0,1)-site is sometimes called a posite. In particular, any frame is a (0,1)-site with its canonical coverage (the covering families are given by unions).

Particular cases include:

• $K$ is 1-truncated iff it is equivalent to the 2-category of 2-sheaves (stacks) on an ordinary small (1-)site, and therefore to the 2-category of stacks for the canonical coverage on some Grothendieck 1-topos.

• $K$ is (0,1)-truncated iff it is equivalent to the 2-category of stacks on a posite, and therefore also to the 2-category of stacks on some locale. We call such a $K$ localic.

• If $K$ is (-1)-truncated, then it is in particular localic, and its terminal object is a (strong) generator. It is not hard to see that this is equivalent to saying that the corresponding locale $X$ is a sublocale of the terminal locale $1$. Thus, just as (-1)-categories are subsets of $1$, (-1)-toposes are sublocales of $1$. If $Cat$ has classical logic, this implies that either $X\cong 0$ or $X\cong 1$; and hence that either $K\simeq 1$ or $K\simeq Cat$. However, constructively there may be many other sublocales of $1$.

• It would be nice if the only (-2)-truncated Grothendieck 2-topos were $Cat$. However, I don’t see a way to make this happen except by fiat.

## Grothendieck $n$-toposes

Now, if $C$ is an $n$-site, it is also reasonable to consider $n$-sheaves on $C$, by which we mean 2-sheaves taking values in $(n-1)$-categories. Thus, a 1-sheaf on a 1-site is precisely the usual notion of sheaf on a site. And a (0,1)-sheaf on a (0,1)-site is easily seen to be a lower set that is an “ideal” for the coverage.

We define a Grothendieck $n$-topos to be an $n$-category equivalent to the $n$-category of $n$-sheaves on an $n$-site. The case $n=1$ gives classical Grothendieck toposes; the case $n=(0,1)$ gives locales. Note the distinction between a Grothendieck $n$-topos and an $n$-truncated Grothendieck 2-topos. The relationship is that

1. The 2-category of 2-sheaves for the canonical coverage on a Grothendieck $n$-topos is an $n$-truncated Grothendieck 2-topos, and
2. Any $n$-truncated Grothendieck 2-topos arises in this way from the Grothendieck $n$-topos which is its full subcategory of $(n-1)$-truncated objects.

This relationship is completely analogous to the classical relationship between locales and localic toposes. In fact, if $Gr n Top$ denotes the $(n+1)$-category of Grothendieck $n$-toposes (that is, $n$-categories of $n$-sheaves on an $n$-site), we have inclusions

$\array{ &&&&&& Gr(1,2)Top\\ &&&&& \nearrow && \searrow\\ Gr (-1) Top &\to& Gr(0,1)Top &\to & Gr1Top &&&& Gr2Top\\ &&&&& \searrow && \nearrow\\ &&&&&& Gr(2,1)Top }$

where the inclusion from $Gr n Top$ to $Gr (n+1) Top$ is given by taking the $(n+1)$-category of $(n+1)$-sheaves for the canonical coverage. (See 2-geometric morphism? for the morphisms in these categories.)

## References

The material on this page is taken from

Created on November 27, 2012 at 17:09:06. See the history of this page for a list of all contributions to it.


text:
Making given metric space bounded

I just encountered a claim, that for any given metric space (X,d), there exists another topologically equivalent metric d' so that (X,d') is bounded. Anyone knowing anything about the proof for this?


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FangQuant › Daily Morning

### Daily Market Review on Specified Futures Products 2020.10.09

submitted 2020-10-09 15:19:18

Crude oil

Yesterday, oil prices rebounded to the highest point in the month. There are currently three main factors supporting the rise of oil prices: 1. Hurricane Delta hit the U.S. Gulf offshore oil production. As of yesterday, nearly 92% of the production capacity of approximately 1.7 million barrels per day has been closed; Norwegian oil workers' strike continues to ferment, and the strike time may be further extended (previously it was expected to mainly affect the output of about 100,000 barrels per day in the Oseberg and Ekofisk oil fields, and probably one less cargo per week); 3. The US fiscal stimulus bill has once again turned around. After Pelosi's phone call with Treasury Secretary Mnuchin, negotiations continued, and Trump still hopes to reach a comprehensive package agreement. However, in the future, we believe that the basis for rising oil prices is still not strong enough. The current core support point is still supply and macro sentiment. However, referring to history, whether it is a hurricane or a strike, the market usually has an impulsive impact. The current demand recovery is still weak, the price of refined oil has risen less than that of crude oil, and the development of the epidemic is still the sword of Damox for the rising oil market. Vaccines are unlikely to be available within the year. We believe the oil distribution will fluctuate at 40 to 45 dollar/barrel, and the continued rebound of oil prices requires cooperation from the demand side.

Strategy: Neutral and bearish relatively, reverse cash and carry arbitrage strategy on Brent, long the sixth lines and short the first line

Risk: Norway strikes longer than expected. Supply disruption caused by sudden geopolitical events. The dollar continues to depreciate sharply.

Iron Ore

Before the holiday, the position on I2101 contract closed at ¥809 per ton, the position on I2105 contract closed at ¥749.5 per ton.

Important Information

1. In China, Handan City issued an urgent notice of recent air quality strengthening control measures. To ensure the continuous improvement of air quality in our city, on the basis of implementing the "Handan City's October to December 2020 Key Industry Production Regulation Plan", the citywide implementation of strengthen management measures for particulate matter pollution, control period from the evening of October 7th to the morning of October 12th, 2020. Iron and steel companies have tightened production control with peak restriction. The sintering machines of Wu'an City, Yongnian District, Fengfeng Mining District, and Shexian Iron and Steel Enterprises implemented production control with peak restriction from 8 pm to 8 am the next day. On the basis of the existing production control measures in Handan Iron and Steel's West District, the sintering machine stopped production of another simple fan, and the chain grate rotary kiln was shut down for maintenance.

2. Ferrexpo released a quarterly report on October 6. The quarterly report showed that the company's iron ore pellet output in the third quarter was 2.537 million tons, a decrease of 11.7% from the previous quarter. In terms of varieties, 65% pellets was 2.537 million tons, a decrease of 10.9% month-on-month.

3. In terms of spot, the PB powder in Rizhao Port was ¥880 per ton before the holiday, golden bubba powder price was equivalent to ¥953 per ton, and the platts price was stable during the holiday.

1. Arbitrage: The accumulation of iron ore port stocks before the holiday is relatively large. During the holiday, there is limited production policy in some areas of Hebei, but the actual impact is small. The steel mills mainly consume their own iron ore inventory. There will be a certain replenishment demand after the holiday. The spot is expected to be supported in the short term. In the long run, it is unlikely that molten iron production will continue to increase. The delivery level in Australia and Brazil is currently high. In the later stage, iron ore will continue to accumulate pressure. After the short-term replenishment demand is over, the spot price is expected to face pressure, and the market will rebound sharply before the holiday.

The basis is significantly narrowed, it is recommended to consider buying 01 coking coal and selling 01 iron ore.

2. Option strategy: It is advised to hold the short position on i2101-C-870.

PTA

Polyester production and sales increased during the second half of National Day, upstream PX rebounded with crude oil

Iin October, if all the overhauls are fulfilled, the inventory will continue to decrease, and it is advised to focus on the overhauls development. There is an expectation of rigid accumulation in November and December. In terms of the unilateral strategy, it is advised to be neutral; for the strategy across varieties, the high inventory problem has not been resolved yet, and it is not advised to maintain the strategy across varieties, but the willingness of the upstream factory to maintain and control should still be judged based on the change in processing fees; for strategy across period, it is advised to focus on the reverse cash and carry strategy opportunity after the next round of TA overhauls fullfilling and rebound of 1-5 spread. It is advised to focus on PTA factory inspection and fulfillment wishes, and the downstream restocking space and improvement of demand.

Natural Rubber

RU: Before the holiday, the main force contract of RU01 fell by 275 or 2.18% and closed at 12,350. The main force contract of JRU03 rose by 8.1 or 4.40% and closed at 192.0. Yunnan WF closed at 11,800 to 12,050 yuan per ton, Hainan SCRWF closed at 12,000 and 12,200 yuan per ton, the secondary standard rubber closed at 10,700 to 10,800 per ton, and Thailand’s RSS3 closed at 15,900 to 16,200 yuan per ton.

NR: The main force contract of NR12 fell by 200 or 2.09% and closed at 9,360. The main force contract of TF12 rose by 5.7 or 4.21% closed at 141.2. The market for Qingdao rubber in USD was scarce. The spot or CIF of STR20 was $1,480 to$1,490 per ton. The CIF of SIR20 in October was $1,410 to$1,415 per ton. The CIF of mixed rubber from Thailand in January was \$1,430 per ton.

QinRex news: On September 23, the Rubber Authority of Thailand participated in online business negotiation and matching activities for rubber products and latex products, looking for new foreign importers, and increasing exports of domestic rubber products and latex products to the world market. The Rubber Authority of Thailand pointed out that a total of 17 countries and regions have participated in the negotiation of imported RSS3, rubber cup and latex. The amount of natural latex required is about 853,100 tons per year, and latex pillows and housekeeping latex gloves are the most popular.

As of September, the latest NINO 3.4 index closed at -0.6°C, a La Nina report. During the holidat, Thailand had a lot of rain. The average daily rainfall in early October was 11.12mm, but the 90-day cumulative rainfall year-on-year increase dropped from +45.3% last month to the current +33.8%. The climate data lacked speculation factors. Pre-holiday RU inventory futures closed at 212.6 thousand tons, and the de-stocking trend has stopped, and the week-on-week ratio was slightly accumulated by 400 tons.

Futures Operation Advice: The main RU01 contract is expected to rise and go strong following the rise of overseas market during the holiday. (For reference only).


text:
# difference between Lipschitz on any bounded set and Locally Lipschitz?

Please, what is the difference between the following expressions "Lipschitz on any bounded set" and "Locally Lipschitz"?

The function $\sqrt x$ is locally Lipschitz on $(0,1)$ but is not Lipschitz on the bounded see $(0,1)$. This example is possible because $(0,1)$ is not compact.


text:
Math Help - Completing the square.

1. Completing the square.

In a triangle, ABC, AB=(2-x)cm, BC=(x+1)cm and angle ABC=120;

a) show that $AC^2 = x^2 - x + 7$ - i did this using the cosine rule.

b) Find the value of x for which AC has a minimum value: (I need to complete the square to find x)

I get this far;

$(x - \frac{1}{2})^2 - (-\frac{1}{2})^2 + 7$

$(x - \frac{1}{2})^2 = - \frac{27}{4}^2$

Can you show me in stages how to resolve to find a minimum value for x?

Thanks,

F.

2. Originally Posted by Flexible

In a triangle, ABC, AB=(2-x)cm, BC=(x+1)cm and angle ABC=120;

a) show that $AC^2 = x^2 - x + 7$ - i did this using the cosine rule.

b) Find the value of x for which AC has a minimum value: (I need to complete the square to find x)

I get this far;

$(x - \frac{1}{2})^2 - (-\frac{1}{2})^2 + 7{\color{red}=0}$

$(x - \frac{1}{2})^2 = - \frac{27}{4}$ I took the exponent off your right hand side to make it correct.

Can you show me in stages how to resolve to find a minimum value for x?

Thanks,

F.
You don't have to complete the square to find the min value.

Just use $x=-\frac{b}{2a}$ in $ax^2+bx+c=0$

This will give you the x-coordinate of the vertex of your parabola.

$x^2-x+7=0$

$\frac{-(-1)}{2(1)}=\frac{1}{2}$

Now, find $f\left(\frac{1}{2}\right)$ and that will be your min value.

3. i found this video helpful on completing the square


text:
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If x² - y² = 55, and x - y = 11, then y = [#permalink]

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12 May 2016, 01:58
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If x^2 - y^2 = 55, and x - y = 11, then y =

A. 8
B. 5
C. 3
D. -8
E. -3
[Reveal] Spoiler: OA

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If x² - y² = 55, and x - y = 11, then y = [#permalink]

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12 May 2016, 07:10
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Bunuel wrote:
If x^2 - y^2 = 55, and x - y = 11, then y =

A. 8
B. 5
C. 3
D. -8
E. -3

Hi
we have x - y = 11
=> x = 11+y
replace x into the first equation
=>$$(11+y)^2 - y^2 = 55$$
EXPANDING:
=>$$(11)^2 + 2*(11)*y + y^2 - y^2 = 55$$
=>$$121 + 22y = 55$$
=>$$22y = 55 - 121$$
=>$$22y = -66$$
=>$$y = -66/22 = -3$$
=> answer is E (-3)

Last edited by HungNguyen on 12 May 2016, 08:18, edited 1 time in total.
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Re: If x² - y² = 55, and x - y = 11, then y = [#permalink]

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12 May 2016, 07:56
Bunuel wrote:
If x^2 - y^2 = 55, and x - y = 11, then y =

A. 8
B. 5
C. 3
D. -8
E. -3

$$x^2 - y^2$$ = $$( x - y )( x + y )$$

$$55$$ = $$( 11 )( x + y )$$

$$5$$ = $$x + y$$-------> (1)

$$11$$ = $$x - y$$-------> (2)

$$2x$$ = $$16$$

Or, $$x$$ = $$8$$

SO,$$y$$ = $$-3$$

Hence answer will be (E)

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Re: If x² - y² = 55, and x - y = 11, then y = [#permalink]

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12 May 2016, 11:29
(x+y)(x-y)= 55

x+y= 5 (its given that (x-y)= 11)

Solving two equations:-

x+y=5
x-y=11

y= -3
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Re: If x² - y² = 55, and x - y = 11, then y = [#permalink]

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Re: If x² - y² = 55, and x - y = 11, then y =   [#permalink] 15 Oct 2017, 09:49
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text:
## Introductory Chemistry (5th Edition)

$Cu$ is the metal that has the least tendency to be oxidized.
From the list of metals $(Sn, Mg, Cu, and Fe)$ the metal which has the least tendency to be oxidized or lose it electrons is $Cu$ since Cu wants to gain electrons (i.e. be reduced and not oxidized) and this is because it is lower on the activity series.


text:
This work is supported by Continuum Analytics and the XDATA Program as part of the Blaze Project

tl;dr: We analyze JSON data on a cluster using pure Python projects.

Dask, a Python library for parallel computing, now works on clusters. During the past few months I and others have extended dask with a new distributed memory scheduler. This enables dask’s existing parallel algorithms to scale across 10s to 100s of nodes, and extends a subset of PyData to distributed computing. Over the next few weeks I and others will write about this system. Please note that dask+distributed is developing quickly and so the API is likely to shift around a bit.

Today we start simple with the typical cluster computing problem, parsing JSON records, filtering, and counting events using dask.bag and the new distributed scheduler. We’ll dive into more advanced problems in future posts.

A video version of this blogpost is available here.

## GitHub Archive Data on S3

GitHub releases data dumps of their public event stream as gzipped compressed, line-delimited, JSON. This data is too large to fit comfortably into memory, even on a sizable workstation. We could stream it from disk but, due to the compression and JSON encoding this takes a while and so slogs down interactive use. For an interactive experience with data like this we need a distributed cluster.

### Setup and Data

We provision nine m3.2xlarge nodes on EC2. These have eight cores and 30GB of RAM each. On this cluster we provision one scheduler and nine workers (see setup docs). (More on launching in later posts.) We have five months of data, from 2015-01-01 to 2015-05-31 on the githubarchive-data bucket in S3. This data is publicly avaialble if you want to play with it on EC2. You can download the full dataset at https://www.githubarchive.org/ .

The first record looks like the following:

 {'actor': {'avatar_url': 'https://avatars.githubusercontent.com/u/9152315?',
'gravatar_id': '',
'id': 9152315,
'url': 'https://api.github.com/users/davidjhulse'},
'created_at': '2015-01-01T00:00:00Z',
'id': '2489368070',
'commits': [{'author': {'email': [email protected]/* <![CDATA[ */!function(t,e,r,n,c,a,p){try{t=document.currentScript||function(){for(t=document.getElementsByTagName('script'),e=t.length;e--;)if(t[e].getAttribute('data-cfhash'))return t[e]}();if(t&&(c=t.previousSibling)){p=t.parentNode;if(a=c.getAttribute('data-cfemail')){for(e='',r='0x'+a.substr(0,2)|0,n=2;a.length-n;n+=2)e+='%'+('0'+('0x'+a.substr(n,2)^r).toString(16)).slice(-2);p.replaceChild(document.createTextNode(decodeURIComponent(e)),c)}p.removeChild(t)}}catch(u){}}()/* ]]> */',
'name': 'davidjhulse'},
'distinct': True,
'message': 'Altered BingBot.jar\n\nFixed issue with multiple account support',
'sha': 'a9b22a6d80c1e0bb49c1cf75a3c075b642c28f81',
'url': 'https://api.github.com/repos/davidjhulse/davesbingrewardsbot/commits/a9b22a6d80c1e0bb49c1cf75a3c075b642c28f81'}],
'distinct_size': 1,
'push_id': 536740396,
'size': 1},
'public': True,
'repo': {'id': 28635890,
'name': 'davidjhulse/davesbingrewardsbot',
'url': 'https://api.github.com/repos/davidjhulse/davesbingrewardsbot'},
'type': 'PushEvent'}

So we have a large dataset on S3 and a moderate sized play cluster on EC2, which has access to S3 data at about 100MB/s per node. We’re ready to play.

## Play

We start an ipython interpreter on our local laptop and connect to the dask scheduler running on the cluster. For the purposes of timing, the cluster is on the East Coast while the local machine is in California on commercial broadband internet.

>>> from distributed import Executor, s3
>>> e = Executor('54.173.84.107:8786')
>>> e

Our seventy-two worker processes come from nine workers with eight processes each. We chose processes rather than threads for this task because computations will be bound by the GIL. We will change this to threads in later examples.

We start by loading a single month of data into distributed memory.

import json
records = e.persist(records)

The data lives in S3 in hourly files as gzipped encoded, line delimited JSON. The s3.read_text and text.map functions produce dask.bag objects which track our operations in a lazily built task graph. When we ask the executor to persist this collection we ship those tasks off to the scheduler to run on all of the workers in parallel. The persist function gives us back another dask.bag pointing to these remotely running results. This persist function returns immediately, and the computation happens on the cluster in the background asynchronously. We gain control of our interpreter immediately while the cluster hums along.

The cluster takes around 40 seconds to download, decompress, and parse this data. If you watch the video embedded above you’ll see fancy progress-bars.

We ask for a single record. This returns in around 200ms, which is fast enough that it feels instantaneous to a human.

>>> records.take(1)
({'actor': {'avatar_url': 'https://avatars.githubusercontent.com/u/9152315?',
'gravatar_id': '',
'id': 9152315,
'url': 'https://api.github.com/users/davidjhulse'},
'created_at': '2015-01-01T00:00:00Z',
'id': '2489368070',
'commits': [{'author': {'email': [email protected]/* <![CDATA[ */!function(t,e,r,n,c,a,p){try{t=document.currentScript||function(){for(t=document.getElementsByTagName('script'),e=t.length;e--;)if(t[e].getAttribute('data-cfhash'))return t[e]}();if(t&&(c=t.previousSibling)){p=t.parentNode;if(a=c.getAttribute('data-cfemail')){for(e='',r='0x'+a.substr(0,2)|0,n=2;a.length-n;n+=2)e+='%'+('0'+('0x'+a.substr(n,2)^r).toString(16)).slice(-2);p.replaceChild(document.createTextNode(decodeURIComponent(e)),c)}p.removeChild(t)}}catch(u){}}()/* ]]> */',
'name': 'davidjhulse'},
'distinct': True,
'message': 'Altered BingBot.jar\n\nFixed issue with multiple account support',
'sha': 'a9b22a6d80c1e0bb49c1cf75a3c075b642c28f81',
'url': 'https://api.github.com/repos/davidjhulse/davesbingrewardsbot/commits/a9b22a6d80c1e0bb49c1cf75a3c075b642c28f81'}],
'distinct_size': 1,
'push_id': 536740396,
'size': 1},
'public': True,
'repo': {'id': 28635890,
'name': 'davidjhulse/davesbingrewardsbot',
'url': 'https://api.github.com/repos/davidjhulse/davesbingrewardsbot'},
'type': 'PushEvent'},)

This particular event is a 'PushEvent'. Let’s quickly see all the kinds of events. For fun, we’ll also time the interaction:

>>> %time records.pluck('type').frequencies().compute()
CPU times: user 112 ms, sys: 0 ns, total: 112 ms
Wall time: 2.41 s

[('ReleaseEvent', 44312),
('MemberEvent', 69757),
('IssuesEvent', 693363),
('PublicEvent', 14614),
('CreateEvent', 1651300),
('PullRequestReviewCommentEvent', 214288),
('PullRequestEvent', 680879),
('ForkEvent', 491256),
('DeleteEvent', 256987),
('PushEvent', 7028566),
('IssueCommentEvent', 1322509),
('GollumEvent', 150861),
('CommitCommentEvent', 96468),
('WatchEvent', 1321546)]

And we compute the total count of all commits for this month.

>>> %time records.count().compute()
CPU times: user 134 ms, sys: 133 µs, total: 134 ms
Wall time: 1.49 s

14036706

We see that it takes a few seconds to walk through the data (and perform all scheduling overhead.) The scheduler adds about a millisecond overhead per task, and there are about 1000 partitions/files here (the GitHub data is split by hour and there are 730 hours in a month) so most of the cost here is overhead.

## Investigate Jupyter

We investigate the activities of Project Jupyter. We chose this project because it’s sizable and because we understand the players involved and so can check our accuracy. This will require us to filter our data to a much smaller subset, then find popular repositories and members.

>>> jupyter = (records.filter(lambda d: d['repo']['name'].startswith('jupyter/'))
.repartition(10))
>>> jupyter = e.persist(jupyter)

All records, regardless of event type, have a repository which has a name like 'organization/repository' in typical GitHub fashion. We filter all records that start with 'jupyter/'. Additionally, because this dataset is likely much smaller, we push all of these records into just ten partitions. This dramatically reduces scheduling overhead. The persist call hands this computation off to the scheduler and then gives us back our collection that points to that computing result. Filtering this month for Jupyter events takes about 7.5 seconds. Afterwards computations on this subset feel snappy.

>>> %time jupyter.count().compute()
CPU times: user 5.19 ms, sys: 97 µs, total: 5.28 ms
Wall time: 199 ms

747

>>> %time jupyter.take(1)
CPU times: user 7.01 ms, sys: 259 µs, total: 7.27 ms
Wall time: 182 ms

({'actor': {'avatar_url': 'https://avatars.githubusercontent.com/u/26679?',
'gravatar_id': '',
'id': 26679,
'url': 'https://api.github.com/users/marksteve'},
'created_at': '2015-01-01T13:25:44Z',
'id': '2489612400',
'org': {'avatar_url': 'https://avatars.githubusercontent.com/u/7388996?',
'gravatar_id': '',
'id': 7388996,
'url': 'https://api.github.com/orgs/jupyter'},
'public': True,
'repo': {'id': 5303123,
'name': 'jupyter/nbviewer',
'url': 'https://api.github.com/repos/jupyter/nbviewer'},
'type': 'WatchEvent'},)

So the first event of the year was by 'marksteve' who decided to watch the 'nbviewer' repository on new year’s day.

Notice that these computations take around 200ms. I can’t get below this from my local machine, so we’re likely bound by communicating to such a remote location. A 200ms latency is not great if you’re playing a video game, but it’s decent for interactive computing.

Here are all of the Jupyter repositories touched in the month of January,

>>> %time jupyter.pluck('repo').pluck('name').distinct().compute()
CPU times: user 2.84 ms, sys: 4.03 ms, total: 6.86 ms
Wall time: 204 ms

['jupyter/dockerspawner',
'jupyter/design',
'jupyter/docker-demo-images',
'jupyter/jupyterhub',
'jupyter/configurable-http-proxy',
'jupyter/nbshot',
'jupyter/sudospawner',
'jupyter/colaboratory',
'jupyter/strata-sv-2015-tutorial',
'jupyter/tmpnb-deploy',
'jupyter/nature-demo',
'jupyter/nbcache',
'jupyter/jupyter.github.io',
'jupyter/try.jupyter.org',
'jupyter/jupyter-drive',
'jupyter/tmpnb',
'jupyter/tmpnb-redirector',
'jupyter/nbindex',
'jupyter/nbviewer',
'jupyter/oauthenticator']

And the top ten most active people on GitHub.

>>> %time (jupyter.pluck('actor')
.frequencies()
.topk(10, lambda kv: kv[1])
.compute())
CPU times: user 8.03 ms, sys: 90 µs, total: 8.12 ms
Wall time: 226 ms

[('rgbkrk', 156),
('minrk', 87),
('Carreau', 87),
('KesterTong', 74),
('jhamrick', 70),
('bollwyvl', 25),
('pkt', 18),
('ssanderson', 13),
('smashwilson', 13),
('ellisonbg', 13)]

Nothing too surprising here if you know these folks.

## Full Dataset

The full five months of data is too large to fit in memory, even for this cluster. When we represent semi-structured data like this with dynamic data structures like lists and dictionaries there is quite a bit of memory bloat. Some careful attention to efficient semi-structured storage here could save us from having to switch to such a large cluster, but that will have to be the topic of another post.

Instead, we operate efficiently on this dataset by flowing it through memory, persisting only the records we care about. The distributed dask scheduler descends from the single-machine dask scheduler, which was quite good at flowing through a computation and intelligently removing intermediate results.

From a user API perspective, we call persist only on the jupyter dataset, and not the full records dataset.

>>> full = (s3.read_text('githubarchive-data', '2015', compression='gzip')

>>> jupyter = (full.filter(lambda d: d['repo']['name'].startswith('jupyter/'))
.repartition(10))

>>> jupyter = e.persist(jupyter)

It takes 2m36s to download, decompress, and parse the five months of publicly available GitHub events for all Jupyter events on nine m3.2xlarges.

There were seven thousand such events.

>>> jupyter.count().compute()
7065

We find which repositories saw the most activity during that time:

>>> %time (jupyter.pluck('repo')
.pluck('name')
.frequencies()
.topk(20, lambda kv: kv[1])
.compute())
CPU times: user 6.98 ms, sys: 474 µs, total: 7.46 ms
Wall time: 219 ms

[('jupyter/jupyterhub', 1262),
('jupyter/nbviewer', 846),
('jupyter/jupyter_notebook', 507),
('jupyter/jupyter-drive', 505),
('jupyter/notebook', 451),
('jupyter/docker-demo-images', 363),
('jupyter/tmpnb', 284),
('jupyter/jupyter_client', 162),
('jupyter/dockerspawner', 149),
('jupyter/colaboratory', 134),
('jupyter/jupyter_core', 127),
('jupyter/strata-sv-2015-tutorial', 108),
('jupyter/jupyter_nbconvert', 103),
('jupyter/configurable-http-proxy', 89),
('jupyter/hubpress.io', 85),
('jupyter/jupyter.github.io', 84),
('jupyter/tmpnb-deploy', 76),
('jupyter/nbconvert', 66),
('jupyter/jupyter_qtconsole', 59)]

We see that projects like jupyterhub were quite active during that time while, surprisingly, nbconvert saw relatively little action.

## Local Data

The Jupyter data is quite small and easily fits in a single machine. Let’s bring the data to our local machine so that we can compare times:

>>> %time L = jupyter.compute()
CPU times: user 4.74 s, sys: 10.9 s, total: 15.7 s
Wall time: 30.2 s

It takes surprisingly long to download the data, but once its here, we can iterate far more quickly with basic Python.

>>> from toolz.curried import pluck, frequencies, topk, pipe
>>> %time pipe(L, pluck('repo'), pluck('name'), frequencies,
dict.items, topk(20, key=lambda kv: kv[1]), list)
CPU times: user 11.8 ms, sys: 0 ns, total: 11.8 ms
Wall time: 11.5 ms

[('jupyter/jupyterhub', 1262),
('jupyter/nbviewer', 846),
('jupyter/jupyter_notebook', 507),
('jupyter/jupyter-drive', 505),
('jupyter/notebook', 451),
('jupyter/docker-demo-images', 363),
('jupyter/tmpnb', 284),
('jupyter/jupyter_client', 162),
('jupyter/dockerspawner', 149),
('jupyter/colaboratory', 134),
('jupyter/jupyter_core', 127),
('jupyter/strata-sv-2015-tutorial', 108),
('jupyter/jupyter_nbconvert', 103),
('jupyter/configurable-http-proxy', 89),
('jupyter/hubpress.io', 85),
('jupyter/jupyter.github.io', 84),
('jupyter/tmpnb-deploy', 76),
('jupyter/nbconvert', 66),
('jupyter/jupyter_qtconsole', 59)]

The difference here is 20x, which is a good reminder that, once you no longer have a large problem you should probably eschew distributed systems and act locally.

## Conclusion

Downloading, decompressing, parsing, filtering, and counting JSON records is the new wordcount. It’s the first problem anyone sees. Fortunately it’s both easy to solve and the common case. Woo hoo!

Here we saw that dask+distributed handle the common case decently well and with a Pure Python stack. Typically Python users rely on a JVM technology like Hadoop/Spark/Storm to distribute their computations. Here we have Python distributing Python; there are some usability gains to be had here like nice stack traces, a bit less serialization overhead, and attention to other Pythonic style choices.

Over the next few posts I intend to deviate from this common case. Most “Big Data” technologies were designed to solve typical data munging problems found in web companies or with simple database operations in mind. Python users care about these things too, but they also reach out to a wide variety of fields. In dask+distributed development we care about the common case, but also support less traditional workflows that are commonly found in the life, physical, and algorithmic sciences.

By designing to support these more extreme cases we’ve nailed some common pain points in current distributed systems. Today we’ve seen low latency and remote control; in the future we’ll see others.

## What doesn’t work

I’ll have an honest section like this at the end of each upcoming post describing what doesn’t work, what still feels broken, or what I would have done differently with more time.

• The imports for dask and distributed are still strange. They’re two separate codebases that play very nicely together. Unfortunately the functionality you need is sometimes in one or in the other and it’s not immediately clear to the novice user where to go. For example dask.bag, the collection we’re using for records, jupyter, etc. is in dask but the s3 module is within the distributed library. We’ll have to merge things at some point in the near-to-moderate future. Ditto for the API: there are compute methods both on the dask collections (records.compute()) and on the distributed executor (e.compute(records)) that behave slightly differently.

• We lack an efficient distributed shuffle algorithm. This is very important if you want to use operations like .groupby (which you should avoid anyway). The user API here doesn’t even cleanly warn users that this is missing in the distributed case which is kind of a mess. (It works fine on a single machine.) Efficient alternatives like foldby are available.

• I would have liked to run this experiment directly on the cluster to see how low we could have gone below the 200ms barrier we ran into here.


text:
To perform the Raise Dead ritual, you must have a part of the corpse of a creature that died no more than 30 days ago.

It says a couple of other things, and then says this:

The subject is freed of any temporary conditions suffered at death, but permanent conditions remain

So, my question is: can you use raise dead on ANY part of a person's corpse and bring the whole person (ie their entire body) back to life? If a person had their legs ripped off either before or after they died, would their legs return?

• I think it means permanent conditions, like Blinded or something like that. I don't think 4e has a "Legs ripped off" condition defined anywhere. Though I'd be sure to use that in my next session if you can find it :) – dpatchery Aug 25 '11 at 19:47

This is purely, totally, entirely up to the GM.

I say that very emphatically because, as far as I know, there is no such thing as bodily dismemberment in the rules. So you, or your GM, will have to figure out if it is permanent or temporary, and act accordingly.

My best guess: being bodily dismembered is a permanent condition. As such, I'd think Raise Dead wouldn't actually fix it. If I were the GM, I'd probably allow the players to combine Raise Dead with Remove Affliction (which removes permanent conditions) into one casting with the combined ritual component cost, and that the result is that the target's body is whole afterwards regardless of any previous damage that went beyond mere HP.

But if Remove Affliction didn't exist, I'd probably just say that Raise Dead fully restored the body anyway, because it's just not fun for a player to wander around with no legs.

EDIT: To answer your first question, you should be able to use Raise Dead on anything that was part of the corpse, and by RAW rules, get the whole body back, even if you started with some random hairs that you tore off your PC's head after he died. It's up to your group and your GM to figure out whether you want to create and use more detailed rules.

• @Chad: That is a very 3.5e view of the world, but 4e does not work that way. There isn't a Regeneration spell or ritual any more (Remove Affliction seems like a similar equivalent), and the Resurrection spell is recast as a level 8 Essentials Cleric power which works almost exactly like the Raise Dead ritual but only for creatures who died in the last 24 hours. All of the old spells to which you refer require a very simulationist game, which 4e is decidedly not. Even something like the Rogue's Leg-Breaker power doesn't include any affliction beyond HP damage. – jprete Aug 26 '11 at 14:39
• what happens with the vorpal swords then? – user2015 Aug 26 '11 at 14:48
• @Chad: The Vorpal property now means that, any time you are rolling damage dice in connection with an attack, if it comes up as its maximum value, add in that maximum value and then roll it again (repeating as many times as you keep getting maximum value). It does not automatically kill by severing a creature's head, so it is not applicable here. – jprete Aug 26 '11 at 14:52
• OK well i removed my original comment since it no longer applies. – user2015 Aug 26 '11 at 14:53

We've always interpreted this to mean that permanent conditions occurring before death remain, while those occurring after are reverted. Legs lost before death are still lost, while those lost to wolves afterwards, are regenerated.

So, as long as a sufficiently large, identifiable part of the creature is still around (even as much as a lock of hair), the spel will work.

Technically, this is up to your discretion. If you want to make things simple, then just assume things work with the least bit of body part available. Otherwise, make your players jump through hoops. Maybe the missing body parts have to be reconstructed from magical materials before the spell will complete. Or the spell rebuilds the body, but it remains frail until additional magic is performed to heal it. Etc... etc...


text:
Free Version
Difficult

# Groups of Order 99: Properties

ABSALG-5YXZ6M

Let $G$ be a group of order $99$.

Which of the following are true?

Select ALL that apply.

A

$G$ is cyclic

B

$G$ is abelian

C

$G$ has an element of order $9$

D

$G$ has an element of order $11$


text:
# Effective Laguerre asymptotics

Borwein, David and Borwein, Jonathan M. and Crandall, Richard E. (2008) Effective Laguerre asymptotics. SIAM J. Numerical Anal., 6 . pp. 3285-3312.

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It is known that the generalized Laguerre polynomials can enjoy sub-exponential growth for large primary index. Specifically, for certain fixed parameter pairs $(a,z)$ one has the large-$n$ asymptotic $$L_n^{(-a)}(-z) \sim C(a,z) n^{-a/2-1/4} e^{2\sqrt {nz}}.$$ We introduce a computationally motivated contour integral that allows highly efficient numerical evaluation of $L_n$, yet also leads to general asymptotic series over the full domain for sub-exponential behavior. We eventually lay out a fast algorithm for generation of the rather formidable expansion coefficients. Along the way we address the difficult problem of establishing effective (i.e. rigorous and explicit) error bounds on the general expansion. To this end, we avoid classical stationary-phase and steepest-descent techniques in favor of an exp-arc" method that amounts to a natural bridge between converging series and effective asymptotics. Finally, we exhibit an absolutely convergent exp-arc series for Bessel-function evaluation as an alternative to conventional ascending-asymptotic switching.