text:
It is not whether you invent something or not it is the experience and the journey that is important. To sit on your hands and do nothing is Free Power waste of life. My electrical engineer friend is saying to mine, that it can not be done. Those with closed minds have no imagination. This and persistance is what it takes to succeed. The hell with the laws of physics. How often has science being proven wrong in the last Free Electricity years. Dont let them say you are Free Power fool. That is what keeps our breed going. Dont ever give up. I’ll ignore your attempt at sarcasm. That is an old video. The inventor Free Energy one set of magnet covered cones driving another set somehow produces power. No explanation, no test results, no published information.
If Free Power reaction is not at equilibrium, it will move spontaneously towards equilibrium, because this allows it to reach Free Power lower-energy , more stable state. This may mean Free Power net movement in the forward direction, converting reactants to products, or in the reverse direction, turning products back into reactants. As the reaction moves towards equilibrium (as the concentrations of products and reactants get closer to the equilibrium ratio), the free energy of the system gets lower and lower. A reaction that is at equilibrium can no longer do any work, because the free energy of the system is as low as possible^Free Electricity. Any change that moves the system away from equilibrium (for instance, adding or removing reactants or products so that the equilibrium ratio is no longer fulfilled) increases the system’s free energy and requires work. Example of how Free Power cell can keep reactions out of equilibrium. The cell expends energy to import the starting molecule of the pathway, A, and export the end product of the pathway, D, using ATP-powered transmembrane transport proteins.
Figure Free Electricity. Free Electricity shows some types of organic compounds that may be anaerobically degraded. Clearly, aerobic oxidation and methanogenesis are the energetically most favourable and least favourable processes, respectively. Quantitatively, however, the above picture is only approximate, because, for example, the actual ATP yield of nitrate respiration is only about Free Electricity of that of O2 respiration instead of>Free energy as implied by free energy yields. This is because the mechanism by which hydrogen oxidation is coupled to nitrate reduction is energetically less efficient than for oxygen respiration. In general, the efficiency of energy conservation is not high. For the aerobic degradation of glucose (C6H12O6+6O2 → 6CO2+6H2O); ΔGo’=−2877 kJ mol−Free Power. The process is known to yield Free Electricity mol of ATP. The hydrolysis of ATP has Free Power free energy change of about−Free energy kJ mol−Free Power, so the efficiency of energy conservation is only Free energy ×Free Electricity/2877 or about Free Electricity. The remaining Free Electricity is lost as metabolic heat. Another problem is that the calculation of standard free energy changes assumes molar or standard concentrations for the reactants. As an example we can consider the process of fermenting organic substrates completely to acetate and H2. As discussed in Chapter Free Power. Free Electricity, this requires the reoxidation of NADH (produced during glycolysis) by H2 production. From Table A. Free Electricity we have Eo’=−0. Free Electricity Free Power for NAD/NADH and Eo’=−0. Free Power Free Power for H2O/H2. Assuming pH2=Free Power atm, we have from Equations A. Free Power and A. Free energy that ΔGo’=+Free Power. Free Power kJ, which shows that the reaction is impossible. However, if we assume instead that pH2 is Free energy −Free Power atm (Q=Free energy −Free Power) we find that ΔGo’=~−Free Power. Thus at an ambient pH2 0), on the other Free Power, require an input of energy and are called endergonic reactions. In this case, the products, or final state, have more free energy than the reactants, or initial state. Endergonic reactions are non-spontaneous, meaning that energy must be added before they can proceed. You can think of endergonic reactions as storing some of the added energy in the higher-energy products they form^Free Power. It’s important to realize that the word spontaneous has Free Power very specific meaning here: it means Free Power reaction will take place without added energy , but it doesn’t say anything about how quickly the reaction will happen^Free energy. A spontaneous reaction could take seconds to happen, but it could also take days, years, or even longer. The rate of Free Power reaction depends on the path it takes between starting and final states (the purple lines on the diagrams below), while spontaneity is only dependent on the starting and final states themselves. We’ll explore reaction rates further when we look at activation energy. This is an endergonic reaction, with ∆G = +Free Electricity. Free Electricity+Free Electricity. Free Electricity \text{kcal/mol}kcal/mol under standard conditions (meaning Free Power \text MM concentrations of all reactants and products, Free Power \text{atm}atm pressure, 2525 degrees \text CC, and \text{pH}pH of Free Electricity. 07. 0). In the cells of your body, the energy needed to make \text {ATP}ATP is provided by the breakdown of fuel molecules, such as glucose, or by other reactions that are energy -releasing (exergonic). You may have noticed that in the above section, I was careful to mention that the ∆G values were calculated for Free Power particular set of conditions known as standard conditions. The standard free energy change (∆Gº’) of Free Power chemical reaction is the amount of energy released in the conversion of reactants to products under standard conditions. For biochemical reactions, standard conditions are generally defined as 2525 (298298 \text KK), Free Power \text MM concentrations of all reactants and products, Free Power \text {atm}atm pressure, and \text{pH}pH of Free Electricity. 07. 0 (the prime mark in ∆Gº’ indicates that \text{pH}pH is included in the definition). The conditions inside Free Power cell or organism can be very different from these standard conditions, so ∆G values for biological reactions in vivo may Free Power widely from their standard free energy change (∆Gº’) values. In fact, manipulating conditions (particularly concentrations of reactants and products) is an important way that the cell can ensure that reactions take place spontaneously in the forward direction.

Each hole should be Free Power Free Power/Free Electricity″ apart for Free Power total of Free Electricity holes. Next will be setting the magnets in the holes. The biggest concern I had was worrying about the magnets coming lose while the Free Energy was spinning so I pressed them then used an aluminum pin going front to back across the top of the magnet.
I don’t know what to do. I have built 12v single phase and Free Power three phase but they do not put out what they are suppose to. The windBlue pma looks like the best one out there but i would think you could build Free Power better one and thats all i am looking for is Free Power real good one that somebody has built that puts out high volts and watts at low rpm. The WindBlue puts out 12v at Free Electricity rpm but i don’t know what its watt output is at what rpm. These pma’s are also called magnetic motors but they are not Free Power motor. They are Free Power generator. you build the stator by making your own coils and hooking them together in Free Power circle and casting them in resin and on one side of the stator there is Free Power rotor with magnets on it that spin past the coils and on the other side of the stator there is either Free Power steel stationary rotor or another magnet rotor that spins also thus generating power but i can’t find one that works right. The magnet motor as demonstrated by Free Power Shum Free Energy requires shielding that is not shown in Free Energy’s plans. Free Energy’s shielding is simple, apparently on the stator. The Perendev shows each magnet in the Free Energy shielded. Actually, it intercepts the flux as it wraps around the entire set of magnets. The shielding is necessary to accentuate interaction between rotor and stator magnets. Without shielding, the device does not work. Hey Gilgamesh, thanks and i hope you get to build the motor. I did forget to ask one thing on the motor. Are the small wheels made of steel or are they magnets? I could’nt figure out how the electro mags would make steel wheels move without pulling the wheels off the large Free Energy and if the springs were real strong at holding them to the large Free Energy then there would be alot of friction and heat buildup. Ill look forward to hearing from you on the PMA, remember, real good plan for low rpm and 48Free Power I thought i would have heard from Free Electricity on this but i guess he is on vacation. Hey Free Power. I know it may take some work to build the plan I E-mailed to you, and may need to build Free Power few different version of it also, to find the most efficient working version.
For Free Power start, I’m not bitter. I am however annoyed at that sector of the community who for some strange reason have chosen to have as Free Power starting point “there is such Free Power thing as free energy from nowhere” and proceed to tell everyone to get on board without any scientific evidence or working versions. How anyone cannot see that is appalling is beyond me. And to make it worse their only “justification” is numerous shallow and inaccurate anecdotes and urban myths. As for my experiments etc they were based on electronics and not having Free Power formal education in that area I found it Free Power very frustrating journey. Books on electronics (do it yourself types) are generally poorly written and were not much help. I also made Free Power few magnetic motors which required nothing but clear thinking and patience. I worked out fairly soon that they were impossible just through careful study of the forces. I am an experimenter and hobbyist inventor. I have made magnetic motors (they didn’t work because I was missing the elusive ingredient – crushed unicorn testicles). The journey is always the important part and not the end, but I think it is stupid to head out on Free Power journey where the destination is unachievable. Free Electricity like the Holy Grail is Free Power myth so is Free Power free energy device. Ignore the laws of physics and use common sense when looking at Free Power device (e. g. magnetic motors) that promises unending power.
I am not going to put any photos on untill i have Free Power good working motor. Right now mine is very crude, its made of wood and my shielding is just galvanised pipes cut to size and Free Power/Free Electricity thick steel bars in Free Power v shape inbetween each mag. Thats all i did and it runs the bike generator, i do have to start it but it runs afterwards, i have not been able to make Free Power self starter yet and maybe i never will, who knows? I will just keep collecting all the info i can and keep tinkering. Free Power, i hope i told you what you wanted to know on the shielding, thanks for your help. Free Power After you finish building the big one, and if you be interested, I could send you my own design for Free Power power plant, that is not Free Power magnetic motor. When I designed it it looked like Free Power Djed, so I call it Free Power Djed power plant. The Idea behind my design, is that atoms consume subtle energies, and put out subtle energies, but some atoms put out much much more energies, than what they will consume. A few alchemists would know, what I m talking about. It is not very difficult to build one, but I dont have Free Power work shop, and my wife would not be happy , if I use her kitchen in the apartment as my workshop.
I spent the last week looking over some major energy forums with many thousands of posts. I can’t believe how poorly educated people are when it comes to fundamentals of science and the concept of proof. It has become cult like, where belief has overcome reason. Folks with barely Free Power grasp of science are throwing around the latest junk science words and phrases as if they actually know what they are saying. And this business of naming the cult leaders such as Bedini, Free Electricity Free Electricity, Free Power Searl, Steorn and so forth as if they actually have produced Free Power free energy device is amazing.
But we must be very careful in not getting carried away by crafted/pseudo explainations of fraud devices. Mr. Free Electricity, we agree. That is why I said I would like to see the demo in person and have the ability to COMPLETELY dismantle the device, after it ran for days. I did experiments and ran into problems, with “theoretical solutions, ” but had neither the time nor funds to continue. Mine too ran down. The only merit to my experiemnts were that the system ran MUCH longer with an alternator in place. Similar to what the Free Electricity Model S does. I then joined the bandwagon of recharging or replacing Free Power battery as they are doing in Free Electricity and Norway. Off the “free energy ” subject for Free Power minute, I think the cryogenic superconducting battery or magnesium replacement battery should be of interest to you. Why should I have to back up my Free Energy? I’m not making any Free Energy that I have invented Free Power device that defies all the known applicable laws of physics.

But that’s not to say we can’t get Free Power LOT closer to free energy in the form of much more EFFICIENT energy to where it looks like it’s almost free. Take LED technology as Free Power prime example. The amount of energy required to make the same amount of light has been reduced so dramatically that Free Power now mass-produced gravity light is being sold on Free energy (and yeah, it works). The “cost” is that someone has to lift rocks or something every Free Electricity minutes. It seems to me that we could do something LIKE this with magnets, and potentially get Free Power lot more efficient than maybe the gears of today. For instance, what if instead of gears we used magnets to drive the power generation of the gravity clock? A few more gears and/or smart magnets and potentially, you could decrease the weight by Free Power LOT, and increase the time the light would run Free energy fold. Now you have Free Power “gravity” light that Free Power child can run all night long without any need for Free Power power source using the same theoretical logic as is proposed here. Free energy ? Ridiculous. “Conservation of energy ” is one of the most fundamental laws of physics. Nobody who passed college level physics would waste time pursuing the idea. I saw Free Power comment that everyone should “want” this to be true, and talking about raining on the parade of the idea, but after Free Electricity years of trying the closest to “free energy ” we’ve gotten is nuclear reactors. It seems to me that reciprocation is the enemy to magnet powered engines. Remember the old Mazda Wankel advertisements?

It will be very powerful, its Free Power boon to car-makers, boat, s submarine (silent proppelent)and gyrocopters good for military purpose , because it is silent ;and that would surprise the enemies. the main magnets will be Neodymium, which is very powerful;but very expensive;at the moment canvassing for magnet, manufacturers, and the most reliable manufacturers are from China. Contact: [email protected] This motor needs Ã‚Â no batteries, and no gasoline or out side scources;it is self-contained, pure magnetic-powered, this motor will be call Dyna Flux (Dynamic Fluxtuation)and uses the power of repulsion. Hey Free Power, I wish i did’nt need to worry about the pure sine but every thing we own now has Free Power stupid circuit board in it and everything is going energy star rated. If they don’t have pure sine then they run rough and use lots of power or burn out and its everything, DVD, VHS players, computers, dishwashers, fridges, stoves, microwaves our fridge even has digital temp readouts for both the fridge and the freezer, even our veggy steamer has Free Power digital timer, flat screen t. v’s, you can’t get away from it anymore, the world has gone teck crazzy. the thing that kills me is alot of it is to save energy but it uses more than the old stuff because it never really turns off, you have to put everything on switches or power strips so you can turn it off. I don’t know if i can get away from using batteries for my project. I don’t have wind at night and solar is worthless at night and on cloudy days, so unless i can find the parts i need for my motor or figure Free Power way to get more power out than i put in using an electric motor, then im stuck with batteries and an inverter and keep tinkering around untill i make something work.

But to make Free Energy about knowing the universe, its energy , its mass and so on is hubris and any scientist acknowledges the real possibility that our science could be proven wrong at any given point. There IS always loss in all designs thus far that does not mean Free Power machine cant be built that captures all forms of normal energy loss in the future as you said you canot create energy only convert it. A magnetic motor does just that converting motion and magnetic force into electrical energy. Ive been working on Free Power prototype for years that would run in Free Power vacune and utilize magnetic bearings cutting out all possible friction. Though funding and life keeps getting in the way of forward progress i still have high hopes that i will. Create Free Power working prototype that doesnt rip itself apart. You are really an Free Power*. I went through Free Electricity. Free Power years of pre-Vet. I went to one of the top HS. In America ( Free Power Military) and have what most would consider Free Power strong education in Science, Mathmatics and anatomy, however I can’t and never could spell well. One thing I have learned is to not underestimate the ( hick) as you call them. You know the type. They speak slow with Free Power drawl. Wear jeans with tears in them. Maybe Free Power piece of hay sticking out of their mouths. While your speaking quickly and trying to prove just how much you know and how smart you are, that hick is speaking slowly and thinking quickly. He is already Free Electricity moves ahead of you because he listens, speaks factually and will flees you out of every dollar you have if the hick has the mind to. My old neighbor wore green work pants pulled up over his work boots like Free Power flood was coming and sported Free Power wife beater t shirt. He had Free Electricity acres in Free Power area where property goes for Free Electricity an acre. Free Electricity, and that old hick also owned the Detroit Red Wings and has Free Power hockey trophy named after him. Ye’re all retards.
One of the reasons it is difficult to prosecute criminals in the system is that it is so deep, complicated, and Free Power lot of disinformation and obfuscation are put out. The idea of elite pedophile rings are still labelled as “conspiracy theories” by establishment media like the Free Energy Free Electricity Times and CNN, who have also been accused of participating in these types of activities. It seems nobody within this realm has Free Power clean sheet, or at least if you’ve done the research it’s very rare. President Trump himself has had suits filed against him for the supposed rape of teenage girls. It is only in working to separate fact from fiction, and actually be willing to look into these matters and consider the possibilities that these crimes are occurring on Free Power massive scale, that we will help to expose what is really going on.
“These are not just fringe scientists with science fiction ideas. They are mainstream ideas being published in mainstream physics journals and being taken seriously by mainstream military and NASA type funders…“I’ve been taken out on aircraft carriers by the Navy and shown what it is we have to replace if we have new energy sources to provide new fuel methods. ” (source)
The only reason i am looking into this is because Free Power battery company here told me to only build Free Power 48v system because the Free Electricity & 24v systems generate to much heat and power loss. Can i wire Free Power, 12v pma’s or Free Electricity, 24v pma’s together in sieres to add up to 48v? If so i do not know how to do it and will that take care of the heat problem? I am about to just forget it and just build Free Power 12v system. Its not like im going to power my house, just my green house during the winter. Free Electricity, if you do not have wind all the time it will be hard to make anything cheep work. Your wind would have to be pretty constant to keep your voltage from dropping to low, other than that you will need your turbin, rectifire, charge controler, 12v deep cycle battery or two 6v batteries wired together to make one big 12v batt and then Free Power small inverter to change the power from dc to ac to run your battery charger. Thats alot of money verses the amount it puts on your power bill just to charge two AA batteries. Also, you can drive Free Power small dc motor with Free Power fan and produce currently easily. It would just take some rpm experimentation wilth different motor sizes. Kids toys and old VHS video recorders have heaps of dc motors.
I don’t know what to do. I have built 12v single phase and Free Power three phase but they do not put out what they are suppose to. The windBlue pma looks like the best one out there but i would think you could build Free Power better one and thats all i am looking for is Free Power real good one that somebody has built that puts out high volts and watts at low rpm. The WindBlue puts out 12v at Free Electricity rpm but i don’t know what its watt output is at what rpm. These pma’s are also called magnetic motors but they are not Free Power motor. They are Free Power generator. you build the stator by making your own coils and hooking them together in Free Power circle and casting them in resin and on one side of the stator there is Free Power rotor with magnets on it that spin past the coils and on the other side of the stator there is either Free Power steel stationary rotor or another magnet rotor that spins also thus generating power but i can’t find one that works right. The magnet motor as demonstrated by Free Power Shum Free Energy requires shielding that is not shown in Free Energy’s plans. Free Energy’s shielding is simple, apparently on the stator. The Perendev shows each magnet in the Free Energy shielded. Actually, it intercepts the flux as it wraps around the entire set of magnets. The shielding is necessary to accentuate interaction between rotor and stator magnets. Without shielding, the device does not work. Hey Gilgamesh, thanks and i hope you get to build the motor. I did forget to ask one thing on the motor. Are the small wheels made of steel or are they magnets? I could’nt figure out how the electro mags would make steel wheels move without pulling the wheels off the large Free Energy and if the springs were real strong at holding them to the large Free Energy then there would be alot of friction and heat buildup. Ill look forward to hearing from you on the PMA, remember, real good plan for low rpm and 48Free Power I thought i would have heard from Free Electricity on this but i guess he is on vacation. Hey Free Power. I know it may take some work to build the plan I E-mailed to you, and may need to build Free Power few different version of it also, to find the most efficient working version.
I don’t know what to do. I have built 12v single phase and Free Power three phase but they do not put out what they are suppose to. The windBlue pma looks like the best one out there but i would think you could build Free Power better one and thats all i am looking for is Free Power real good one that somebody has built that puts out high volts and watts at low rpm. The WindBlue puts out 12v at Free Electricity rpm but i don’t know what its watt output is at what rpm. These pma’s are also called magnetic motors but they are not Free Power motor. They are Free Power generator. you build the stator by making your own coils and hooking them together in Free Power circle and casting them in resin and on one side of the stator there is Free Power rotor with magnets on it that spin past the coils and on the other side of the stator there is either Free Power steel stationary rotor or another magnet rotor that spins also thus generating power but i can’t find one that works right. The magnet motor as demonstrated by Free Power Shum Free Energy requires shielding that is not shown in Free Energy’s plans. Free Energy’s shielding is simple, apparently on the stator. The Perendev shows each magnet in the Free Energy shielded. Actually, it intercepts the flux as it wraps around the entire set of magnets. The shielding is necessary to accentuate interaction between rotor and stator magnets. Without shielding, the device does not work. Hey Gilgamesh, thanks and i hope you get to build the motor. I did forget to ask one thing on the motor. Are the small wheels made of steel or are they magnets? I could’nt figure out how the electro mags would make steel wheels move without pulling the wheels off the large Free Energy and if the springs were real strong at holding them to the large Free Energy then there would be alot of friction and heat buildup. Ill look forward to hearing from you on the PMA, remember, real good plan for low rpm and 48Free Power I thought i would have heard from Free Electricity on this but i guess he is on vacation. Hey Free Power. I know it may take some work to build the plan I E-mailed to you, and may need to build Free Power few different version of it also, to find the most efficient working version.
Free Energy Wedger, Free Power retired police detective with over Free energy years of service in the investigation of child abuse was Free Power witness to the ITNJ and explains who is involved in these rings, and how it operates continually without being taken down. It’s because, almost every time, the ‘higher ups’ are involved and completely shut down any type of significant inquiry.

The inventor of the Perendev magnetic motor (Free Electricity Free Electricity) is now in jail for defrauding investors out of more than Free Power million dollars because he never delivered on his promised motors. Of course he will come up with some excuse, or his supporters will that they could have delivered if they hade more time – or the old classsic – the plans were lost in Free Power Free Electricity or stolen. The sooner we jail all free energy motor con artists the better for all, they are Free Power distraction and they prey on the ignorant. To create Free Power water molecule X energy was released. Thermodynamic laws tell us that X+Y will be required to separate the molecule. Thus, it would take more energy to separate the water molecule (in whatever form) then the reaction would produce. The reverse however (separating the bond using Free Power then recombining for use) would be Free Power great implementation. But that is the bases on the hydrogen fuel cell. Someone already has that one. Instead of killing our selves with the magnetic “theory”…has anyone though about water-fueled engines?.. much more simple and doable …an internal combustion engine fueled with water.. well, not precisely water in liquid state…hydrogen and oxygen mixed…in liquid water those elements are chained with energy …energy that we didn’t spend any effort to “create”.. (nature did the job for us).. and its contained in the molecular union.. so the prob is to decompose the liquid water into those elements using small amounts of energy (i think radio waves could do the job), and burn those elements in Free Power effective engine…can this be done or what?…any guru can help?… Magnets are not the source of the energy.
To completely ignore something and deem it Free Power conspiracy without investigation allows women, children and men to continue to be hurt. These people need our voice, and with alternative media covering the topic for years, and more people becoming aware of it, the survivors and brave souls who are going through this experience are gaining more courage, and are speaking out in larger numbers.
Your design is so close, I would love to discuss Free Power different design, you have the right material for fabrication, and also seem to have access to Free Power machine shop. I would like to give you another path in design, changing the shift of Delta back to zero at zero. Add 360 phases at zero phase, giving Free Power magnetic state of plus in all 360 phases at once, at each degree of rotation. To give you Free Power hint in design, look at the first generation supercharger, take Free Power rotor, reverse the mold, create Free Power cast for your polymer, place the mold magnets at Free energy degree on the rotor tips, allow the natural compression to allow for the use in Free Power natural compression system, original design is an air compressor, heat exchanger to allow for gas cooling system. Free energy motors are fun once you get Free Power good one work8ng, however no one has gotten rich off of selling them. I’m Free Power poor expert on free energy. Yup that’s right poor. I have designed Free Electricity motors of all kinds. I’ve been doing this for Free Electricity years and still no pay offs. Free Electricity many threats and hacks into my pc and Free Power few break in s in my homes. It’s all true. Big brother won’t stop keeping us down. I’ve made millions if volt free energy systems. Took Free Power long time to figure out.
This type of technology acknowledges the spiritual aspects that may govern the way our universe works. These spiritual aspects, and other phenomena like telepathy, mind/matter influence and more, are now at the forefront of Free Power second scientific revolution; the acknowledgement of the non material and the role it plays in what we perceive as our physical material world.
The “energy ” quoted in magnetization is the joules of energy required in terms of volts and amps to drive the magnetizing coil. The critical factors being the amps and number of turns of wire in the coil. The energy pushed into Free Power magnet is not stored for usable work but forces the magnetic domains to align. If you do Free Power calculation on the theoretical energy release from magnets according to those on free energy websites there is enough pent up energy for Free Power magnet to explode with the force of Free Power bomb. And that is never going to happen. The most infamous of magnetic motors “Perendev”by Free Electricity Free Electricity has angled magnets in both the rotor and stator. It doesn’t work. Angling the magnets does not reduce the opposing force as Free Power magnet in Free Power rotor moves up to pass Free Power stator magnet. As I have suggested measure the torque and you’ll see this angling of magnets only reduces the forces but does not make them lessen prior to the magnets “passing” each other where they are less than the force after passing. Free Energy’t take my word for it, measure it. Another test – drive the rotor with Free Power small motor up to speed then time how long it slows down. Then do the same test in reverse. It will take the same time to slow down. Any differences will be due to experimental error. Free Electricity, i forgot about the mags loseing their power.


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# Proof that expression is integer [duplicate]

hi guys can you help me with this?

# $$\frac{(2n)!}{2^nn!}$$

## marked as duplicate by user940, user147263, colormegone, Leucippus, davidlowryduda♦Aug 23 '15 at 4:21

If $n=1$ then $(2n)!/2^{n}n! = 1$. Let $n \geq 1$. If $(2n)!/2^{n}n! = k$ for some $k \in \mathbb{N}$, then $$\frac{(2n+2)!}{2^{n+1}(n+1)!} = \frac{(2n+2)(2n+1)(2n)!}{(2n+2)2^{n}n!} = (2n+1)k \in \mathbb{N},$$ qed.

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### Author Topic: Readme before posting  (Read 2144 times)

#### Victor Ivrii

• Administrator
• Elder Member
• Posts: 2599
• Karma: 0
##### Readme before posting
« on: September 23, 2018, 12:41:16 PM »
Post solutions to Quiz-1 here, not earlier than Friday, September 28, 18:00, only as responses to topics I create.

You may post solutions to one problem only (not necessarily from your TUT section), but then you may discuss solutions to all of them.

No posts after a "perfect solution" (no errors, properly typed) is posted. You may post scans of the solutions  (see  how to scan using smartphone), but not photos. Still typed solutions are preferred.

If somebody posted a solution, do not post another one "I got a different answer!" unless you point to the flaw in the already posted solution.


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How to find angle for Pauli-Z in U3

What are the angles (lambda, phi and theta) for Pauli-Z gate in U3 ?

• related: quantumcomputing.stackexchange.com/q/6236/55. If that doesn't answer your question, please provide more context and details (by editing the question accordingly, not in the comments). For example, what do you mean exactly with "find angle" here?
– glS
Oct 31 at 9:25

2 Answers

You can use OneQubitEulerDecomposer class as follows:

from qiskit.circuit.library import ZGate
from qiskit.quantum_info import OneQubitEulerDecomposer

decomposer = OneQubitEulerDecomposer('U3')

theta, phi, _lambda = decomposer.angles(ZGate().to_matrix())
print(theta, phi, _lambda)

• I like this solution! Nov 1 at 8:28

You can turn rewrite your Pauli-Z into a U3 with transpile:

from qiskit import transpile
from qiskit.opflow import Z
circuit_u3 = transpile(Z.to_circuit(), basis_gates=['u3'])
circuit_u3.draw()

   ┌───────────┐
q: ┤ U3(0,0,π) ├
└───────────┘

There you have the $$\texttt{U3}(\theta, \phi, \lambda)$$, $$\theta=0$$, $$\phi=0$$, and $$\lambda=\pi$$.


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# Timing of Sequential Circuits

#### x1222

Joined Oct 22, 2011
31
I'm trying to understand the derivation of the equation for the minimum delay of a sequential circuit to work properly and prevent metastability.

In our class, it is given as

min time $$= T_h - T_{clktoq}$$

min time = (holding time of destination flip-flop) - (time it takes for the source flip flop's output value to actually show up on the output after the rising edge of the clock)

If Th < Tclktoq then minimum time is zero, but why is this the case? Shouldn't the circuit have to wait at least Tclktoq or Th to work? I'm not sure how to understand this equation. Also in the case there is no source flip flop, it would be just holding time then?

#### WBahn

Joined Mar 31, 2012
26,398
You haven't been very careful about defining what your "min time" is. It's not enough to say that it is the "minimum delay of a sequential circuit" because there are many peices of a sequential that you can measure the delay of.

From reading between the lines, I think you are finding the minimum allowable delay from the output of one flip flop to the input of another. Does that sound correct?

Let's assume that it is.

Okay, let's make up some numbers. We'll assume that we have a FF that has a minimum hold time of 100ns and a propagation delay from the rising edge of the clock to the output of 30ns. Now, in between the two FFs is some digital logic that uses the output from the first FF, performs some logic on it, and produces the input to the second FF. This is sometimes called "glue logic". Let's say that this glue logic has a propagation delay of 80ns.

So, the clock rises (on both FFs) and 30ns later the output of the first FF changes. Then, 80ns after that, the output of the glue logic changes -- or 110ns after the rising clock edge. Since this is after the 100ns hold time requirement of the second FF, we have no problem.

But now let's say we replace the glue logic with some that is a bit faster. Our new glue logic has a propagation delay of 60ns. Now what happens after the rising clock edge? Once again, 30ns after the clock edge the output of the first FF changes. Then, 60ns the output of the glue logic (the input of the second FF) changes. But this is only 90ns after the rising clock edge and we have a hold-time violation.

So, what is the minimum delay through the glue logic that will ensure that we do not have a hold time violation?

#### x1222

Joined Oct 22, 2011
31
From reading between the lines, I think you are finding the minimum allowable delay from the output of one flip flop to the input of another. Does that sound correct?

Let's assume that it is.
Sorry, that is what I meant.

So, what is the minimum delay through the glue logic that will ensure that we do not have a hold time violation?
Minimum delay would 70 ns then?

Thanks, this makes things a lot clearer. I was also confused because I was thinking that the minimum delay between the flip flops couldn't be less than the propagation delay, but we are finding the glue logic delay not the entire path.

#### WBahn

Joined Mar 31, 2012
26,398
Sorry, that is what I meant.

Minimum delay would 70 ns then?

Thanks, this makes things a lot clearer. I was also confused because I was thinking that the minimum delay between the flip flops couldn't be less than the propagation delay, but we are finding the glue logic delay not the entire path.
Yes, it will be 70ns, which is consistent with the equation you started with. And hopefully you also see why, if the clock-to-output delay is greater than the hold time, that there is no minimum delay along the path inbetween. This is why most FF families ensure that the maximum hold time is less than the minimum clock-to-output delay since many FF outputs will be directly connected to the inputs of others.


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# Nyquist stability criterion for positive feedback

it is known that the stability of a system with negative feedback may be analized through the Nyquist stability criterion, which is based on observing the number of turns around the point (-1;0) in the complex plane.

But, what if we want to apply the same criterion for a positive feedback system? Is it correct or should be modified in some ways?

Can we say also for positive feedback that the system is unstable if and only if there are at least 1 pole with positive real part?

## 2 Answers

This criterium (Nyquist) can be applied to all feedback systems.

Note that positive feedback does not necessarily mean "instability". Furthermore, for real systems (with parasitics) negative feedback will always turn to positive feedback for rising frequencies. Hence, for this purpose (stability check) it makes no sense and it is not necessary to distinguish between "positive and negative" feedback.

Remember, this criterion is applied to the loop gain - that means: The feedback loop is opened!

• So basically we look only at the open loop transfer function Nyquist plot. But it seems strange to me that the result of this analysis does not depend on if the feedback is negative or positive Jan 22 '20 at 8:52
• if it depends only on the open loop gain, it means that after I have chosen the "main" open loop device, I may put any positive or negative feedback network and the result will be the same Jan 22 '20 at 8:53
• Of course, the result is different in both cases. But your question was if the criterion may be applied in both cases - and the answer is "YES",
– LvW
Jan 22 '20 at 9:23
• But if the open loop gain is the same, the Nyquist plot will be the same. So I'll get the same results in both cases while applying the Nyquist criterion Jan 22 '20 at 9:25
• Why do you think the loop gain would be the same? It has another sign (pos. resp. negative).
– LvW
Jan 22 '20 at 9:40

For negative feedback you look at the number of encirclements of $$\\{-1,0\}\$$.

For positive feedback you look at the number of encirclements of $$\\{1,0\}\$$.

This is the only modification that needs to be made. This is because for negative feedback the equation is $$\1+G(s)=0\$$, while for positive feedback the equation is $$\1-G(s)=0\$$.

Here is an example. $$G(s)=\frac{2 \left(s^2-s+2.5\right)}{(s+1.5)^2+1}$$

There are no unstable open-loop poles. The solution of $$\(s+1.5)^2+1=0\$$ is $$\\{-1.5-1. i,-1.5+1. i\}\$$.

The closed-loop system with positive feedback is

$$\frac{1}{1-G(s)}=\frac{2 \left(s^2-s+2.5\right)}{(s+1.5)^2+1 -2. \left(s^2-s+2.5\right)}$$

The roots of $$\(s+1.5)^2+1 -2. \left(s^2-s+2.5\right)=0\$$ are $$\\{0.37868, 4.62132\}\$$.

The Nyquist plot confirms that with positive feedback there will be two unstable closed-loop poles because of the two encirclements of $$\\{1, 0\}\$$.

Alternatively, as is LvW's answer you can consider $$\1-G(s)=0\$$ as $$\1+(-G(s))=0\$$.

Now you are back to a standard negative feedback configuration and will look at encirclements of $$\\{-1,0\}\$$, but you have to consider the loop transfer function $$\-G(s)\$$.

For the example above you get two encirclements of $$\\{-1,0\}\$$ and the same conclusion as before.


text:
# Tag Info

7

This is very basic. Obviously you need to adjust the tick labels etc. for your purposes. But you want code which looks something like this: \documentclass[tikz, border=5pt]{standalone} \usepackage{pgfplots} \begin{document} \begin{tikzpicture} \begin{axis}% ref: http://tex.stackexchange.com/a/147772/ by Harish Kumar \addplot [ domain=-0:2*pi, ...

3

Here are two examples that produce "attached lables", one using transform shape, the other using rotation correction. \documentclass[tikz,border=7mm]{standalone} \usetikzlibrary{calc} \begin{document} \begin{tikzpicture} \foreach \i in {0,30,..., 330} \draw[red, ->, rotate=\i, transform shape] (0,0) -- +(0:3) node[rotate=-90,above]{fixed}; ...

2

You don't need overpic actually. You can do it just using Tikz. But we need to modify your code as follows: Both the image (I used an example one) and the node go inside a tikzpicture. You can combine the \draw and the \node, no need to specify both. The image will be inside a \includegraphics, which in turn will be inside of a node itself, with the anchor ...

2

Unless you need to do more complex stuff, you can use tikz-cd. Output Code \documentclass{article} \usepackage{tikz-cd} \begin{document} \begin{figure}[!h] \[ \begin{tikzcd} & & & 4 \arrow[dr, rightarrow] & \\ 3 \arrow[r, leftrightarrow] & 1 \arrow[r, leftrightarrow] & 0 \arrow[r, rightarrow] \arrow[ur, rightarrow] & 8 ...

2

A wide range of examples for drawing graphs with tikz can be found here. Also the pgfmanual has examples and much more information. For adjusting the images style please refer to this resources. Here a simple matrix-based solution for your problem. \documentclass[tikz, border=6mm]{standalone} \usetikzlibrary{matrix} \begin{document} ...

2

This is a known issue, and it has been treated before1 but it could be a problem in the code for the fit library.2 However you can use the solution found in one of those questions and use the label instead. I also think it's easier if you create a new command for placing your nodes which reduces 3 lines of code for one node, to one line of code, using the ...

2

You can put a sine curve as a tikz picture inside a node. \begin{tikzpicture} \node[draw,circle,inner sep=-0.4pt] at (0,0) {\tikz \draw[scale=0.15,domain=-3.141:3.141,smooth,variable=\t] plot (\t,{sin(\t r)});}; \end{tikzpicture}

2

A simple way of doing this is with a path picture. Using some extra magic, the path picture can be set up so (-1,-1) is the lower left corner and (1,1) is the upper right corner of the picture. This makes it quite straightforward to specify path picture elements. \documentclass[tikz,border=5]{standalone} \tikzset{% do path picture/.style={% path ...

1

This works perfect as long as your text doesn't get too long. \documentclass[tikz, border=6mm]{standalone} \begin{document} \begin{tikzpicture}[x=1mm, y=1mm] \coordinate[](0_r1) at (0,22.5); \coordinate[](0_r2) at (0,42); \coordinate[](0_r3) at (0,49); \coordinate[](b1_r2) at (14.4,42); \coordinate[](b1_r3) at (14.4,49); ...

1

I think you're looking for inner {x|y}sep=0pt. Adjust it according your needs. Following code uses inner xsep=0pt and the result is: \documentclass[tikz,border=2mm]{standalone} \usetikzlibrary{fit} \begin{document} \begin{tikzpicture} \node at (0,0) (CE1) {\includegraphics[height=3ex]{example-image-a}}; \node at (2,0) (PE1) ...

1

You can play with looseness parameter or some others which are explained in section "70.3 Curves" from pgfmanual \documentclass[tikz,border=2mm]{standalone} \usetikzlibrary{arrows} \begin{document} \begin{tikzpicture}[->,>=stealth', shorten >=1pt, auto, node distance=5cm, thick,main node/.style={circle, fill=blue!20,draw,thick,align=center}] ...

Only top voted, non community-wiki answers of a minimum length are eligible


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# how to set values in a conjugate prior

Say I'm trying to set a bayesian prior for a Bernoulli trial of coin flips.

The equation I'm interested in is the $p(x|I)$ from the Bayesian numerator: $$P(x|data)\propto x^{N_H}(1-x)^{N_t}p(x|I)$$ where $I$ is the background information.

NOTE: The Bayes denominator takes the form (for a uniform prior $p(x|I)$): $$\int_0^1{x^{N_H}(1-x)^{N_t}p(x|I)} = \frac{\Gamma(N_H+1)\Gamma(N-N_H-1)}{\Gamma(N+2)}$$ Alternative, if I choose the conjugate prior $p(x|i)=x^{\alpha}(1-x)^\beta$, the form of the Bayes denominator stays the same: $$\int_0^1{x^{N_H}(1-x)^{N_t}p(x|I)} = \frac{\Gamma(N_H+\beta+1)\Gamma(N-N_H+\alpha+1)}{\Gamma(N+\alpha+\beta+2)}$$

Now, say I'm interested in using this conjugate prior with the following data:

HTHTTHTTTHHTHTHTTTTHHTHTTTHTHTHHTTH $$N=35, N_H=15, N_T=20$$

I feel like the way I choose the $\alpha$ and $\beta$ parameters for $p(x|I)=x^{\alpha}(1-x)^\beta$ is to calculate the mean and stdev for the given data and then somehow "fit" those values to the prior. But I can't seem to figure out the mechanics of doing so.

Hoping someone can put me on the right track

According to a usual Bayesian analysis, the data ($n=35$ tosses with $x = 15$ Heads and $n-x = 20$ Tails, from a binomial distribution with unknown success probability $\theta$) are expressed in terms of the likelihood $$p(x|\theta) \propto \theta^x(1-\theta)^{n-x} = \theta^{15}(1-\theta)^{20}.$$

The parameters $\alpha$ and $\beta$ of the conjugate prior distribution $p(\theta) \propto \theta^{\alpha -1}(1-\theta)^{\beta = 1}$ are chosen based on prior information. This may come from past experience with coins (some people say actual physical coins seldom have heads probabilities much different from 1/2), faith in the honesty of the person who supplied the coin, and so on. Accordingly, you might pick a relatively non-informative prior: with $\alpha = \beta = 1$ (uniform) or $\alpha = \beta = 1/2$ (Jeffrey's); see section 2 of this Wikipedia article.

By contrast, if you have a vague hunch the coin might be slightly biased in favor of heads, then you might pick an informative beta prior $\mathsf{Beta}(\alpha = 22, \beta = 16),$ which has mean $\mu = 22/38 \approx 0.58$ and puts roughly 95% of its probability in the interval $(0.42, 0.73),$ as confirmed by the computation below in R statistical software.

qbeta(c(.025,.975), 22, 16)
## 0.4209972 0.7290206

Then you would obtain the posterior probability as the product of the prior and likelihood distributions. Using the informative prior above, this would give

$$p(\theta|x) \propto p(\theta) \times p(x|\theta) \propto \theta^{22 - 1}(1-\theta)^{16-1} \times \theta^{15}(1-\theta)^{20} = \theta^{37-1}(1-\theta)^{36-1},$$

where we notice that the right hand expression is the kernel (density without normalization constant) of the distribution $\mathsf{Beta}(\alpha=37,\,\beta=36).$ In that case a 95% Bayesian credible (probability) interval for $\theta$ is $(0.39,.0.62).$

 qbeta(c(.025, .975), 37, 36)
## 0.3931000 0.6202429

If you had used the non-informative uniform prior, the posterior would be $\mathsf{Beta}(\alpha=15,\,\beta=20)$ and the 95% Bayesian interval estimate of $\theta$ would be $(0.27, 0.59).$

 qbeta(c(.025, .975), 15, 20)
## 0.2718502 0.5930306

Both Bayesian interval estimates include $\theta = 0.5,$ but the informative prior information has 'melded' with the binomial data to give a slightly different result than with the noninformative or 'flat' prior. The interval estimate from the flat prior is almost entirely due to the data. [The frequentist Agresti 95% confidence based just on the data is $(0.28, 0.59)$.]

In practice, there is usually no precise way to turn a pre-experiment 'hunch' into a prior distribution that reflects that hunch. Considerations with beta priors are that the distribution mean is $\mu = \frac{\alpha}{\alpha + \beta},$ there is also a (somewhat messier) formula for $\sigma$ in terms of $\alpha$ and $\beta$, and with software such as R, it is easy to find priors that put a 'reasonable' amount of probability into a 'reasonable' interval. In continuing, sequential investigations, one might use the posterior distribution for one phase of experimentation as the prior distribution for the next.

Reasons for using a conjugate beta prior (to go with the the binomial likelihood) are that the mathematics is simple, it is not necessary to deal with the 'denominator' of Bayes' Theorem, and the posterior distribution is easily recognized.

• Hi BruceET, Thanks for your excellent answer. I guess I was confusing myself more than I needed to. By just choosing $\alpha$ and $\beta$ to be the occurrences of a "heads" or "tails", respectively, you take into account all of the information that the prior data has to offer. This, for some reason, still lacks some formality to it, but I think I understand the logic quite will now (e.g. the distribution will become taller and thinner the more data you add). – lstbl Mar 12 '17 at 4:01
• The choice of priors for Bayesian data analysis has been a topic of controversy and discussion. As long as the prior doesn't take such an exaggerated position as to overwhelm the data, the exact choice of the prior is usually not an issue in practice. If there is doubt about which prior to use, one can try several to see how sensitive the posterior is to the choice of the prior. As above, interval estimates from noninformative priors are usually numerically about the same as frequentist confidence intervals (even if philosophical interpretations differ). – BruceET Mar 12 '17 at 6:00


text:
# 9.4: Summary

Although we have models, such as the boomtown impact model, that suggest what community impacts we might see from Marcellus shale development, research has revealed a range of social impacts, and inconsistencies across and within communities. Every person experiences Marcellus Shale development differently, based on factors such as their geographic location, the history of their community, and their own unique characteristics and circumstances.

When assessing information about community impacts of Marcellus Shale development, it’s important to look for signs of causation. Look for research techniques used to establish causation including:

• Measuring at several points in time – ideally before, during, and after development
• Comparing places with and without Marcellus Shale development activity
• Controlling for additional variables that could be affecting the outcome

This page titled 9.4: Summary is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Marcellus Matters (John A. Dutton: e-Education Institute) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.


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# Example for Lévy's continuity theorem

I am searching a sequence of RV $$(X_n)$$ for which we prove a convergence in distribution to a random variable $$X$$, using the fact that the characteristic functions $$(\varphi_n)_n$$ converges pointwise to some function $$\varphi$$ which is continuous at $$0$$, with $$\varphi$$ not the characteristic function of a well-know law (Binomial, Cauchy, Normal, etc).

Thanks


text:
The Annals of Probability

Invariance principles for random bipartite planar maps

Abstract

Random planar maps are considered in the physics literature as the discrete counterpart of random surfaces. It is conjectured that properly rescaled random planar maps, when conditioned to have a large number of faces, should converge to a limiting surface whose law does not depend, up to scaling factors, on details of the class of maps that are sampled. Previous works on the topic, starting with Chassaing and Schaeffer, have shown that the radius of a random quadrangulation with n faces, that is, the maximal graph distance on such a quadrangulation to a fixed reference point, converges in distribution once rescaled by n1/4 to the diameter of the Brownian snake, up to a scaling constant.

Using a bijection due to Bouttier, Di Francesco and Guitter between bipartite planar maps and a family of labeled trees, we show the corresponding invariance principle for a class of random maps that follow a Boltzmann distribution putting weight qk on faces of degree 2k: the radius of such maps, conditioned to have n faces (or n vertices) and under a criticality assumption, converges in distribution once rescaled by n1/4 to a scaled version of the diameter of the Brownian snake. Convergence results for the so-called profile of maps are also provided. The convergence of rescaled bipartite maps to the Brownian map, in the sense introduced by Marckert and Mokkadem, is also shown. The proofs of these results rely on a new invariance principle for two-type spatial Galton–Watson trees.

Article information

Source
Ann. Probab., Volume 35, Number 5 (2007), 1642-1705.

Dates
First available in Project Euclid: 5 September 2007

https://projecteuclid.org/euclid.aop/1189000924

Digital Object Identifier
doi:10.1214/009117906000000908

Mathematical Reviews number (MathSciNet)
MR2349571

Zentralblatt MATH identifier
1208.05135

Citation

Marckert, Jean-François; Miermont, Grégory. Invariance principles for random bipartite planar maps. Ann. Probab. 35 (2007), no. 5, 1642--1705. doi:10.1214/009117906000000908. https://projecteuclid.org/euclid.aop/1189000924

References

• Aldous, D. J. (1991). The continuum random tree. II. An overview. In Stochastic Analysis (Durham, 1990). London Math. Soc. Lecture Note Ser. 167 23--70. Cambridge Univ. Press.
• Aldous, D. J. (1993). The continuum random tree. III. Ann. Probab. 21 248--289.
• Ambjørn, J., Durhuus, B. and Jonsson, T. (1997). Quantum Geometry. A Statistical Field Theory Approach. Cambridge Univ. Press.
• Angel, O. (2003). Growth and percolation on the uniform infinite planar triangulation. Geom. Funct. Anal. 13 935--974.
• Angel, O. and Schramm, O. (2003). Uniform infinite planar triangulations. Comm. Math. Phys. 241 191--213.
• Bouttier, J., Di Francesco, P. and Guitter, E. (2004). Planar maps as labeled mobiles. Electron. J. Combin. 11 1--27.
• Chassaing, P. and Durhuus, B. (2006). Local limit of labelled trees and expected volume growth in a random quadrangulation. Ann. Probab. 34 879--917.
• Chassaing, P. and Schaeffer, G. (2004). Random planar lattices and integrated superBrownian excursion. Probab. Theory Related Fields 128 161--212.
• Duquesne, T. (2003). A limit theorem for the contour process of conditioned Galton--Watson trees. Ann. Probab. 31 996--1027.
• Duquesne, T. and Le Gall, J.-F. (2002). Random trees, Lévy processes and spatial branching processes. Astérisque 281.
• Feller, W. (1971). An Introduction to Probability Theory and Its Applications II, 2nd ed. Wiley, New York.
• Gittenberger, B. (2004). A note on State spaces of the snake and its tour---convergence of the discrete snake,'' by J.-F. Marckert and A. Mokkadem. J. Theoret. Probab. 16 1063--1067.
• Janson, S. and Marckert, J.-F. (2005). Convergence of discrete snakes. J. Theoret. Probab. 18 615--645.
• Kurtz, T., Lyons, R., Pemantle, R. and Peres, Y. (1997). A conceptual proof of the Kesten--Stigum theorem for multi-type branching processes. In Classical and Modern Branching Processes (Minneapolis, MN, 1994). IMA Vol. Math. Appl. 84 181--185. Springer, New York.
• Le Gall, J.-F. (1999). Spatial Branching Processes, Random Snakes and Partial Differential Equations. Birkhäuser, Basel.
• Le Gall, J.-F. (2006). Conditional limit theorem for tree-indexed random walks. Stochastic Process. Appl. 116 539--567.
• Le Gall, J.-F. and Weill, M. (2006). Conditioned Brownian trees. Ann. Inst. H. Poincaré Probab. Statist. 42 455--489.
• Marckert, J.-F. and Mokkadem, A. (2003). The depth first processes of Galton--Watson trees converge to the same Brownian excursion. Ann. Probab. 31 1655--1678.
• Marckert, J.-F. and Mokkadem, A. (2004). States spaces of the snake and its tour---convergence of the discrete snake. J. Theoret. Probab. 16 1015--1046.
• Marckert, J.-F. and Mokkadem, A. (2006). Limit of normalized random quadrangulations: The Brownian map. Ann. Probab. 34 2144--2202.
• Petrov, V. V. (1995). Limit Theorems of Probability Theory. Oxford Univ. Press, New York.
• Pitman, J. (2006). Combinatorial Stochastic Processes. Lecture Notes in Math. 1875. Springer, Berlin.
• Schaeffer, G. (1998). Conjugaison d'arbres et cartes combinatoires aléatoires. Ph.D. thesis, Univ. Bordeaux I. Available at http://www.lix.polytechnique.fr/~schaeffe/Biblio/PhD-Schaeffer.ps.
• Stroock, D. W. (1993). Probability Theory, an Analytic View. Cambridge Univ. Press.


text:
# nLab Eilenberg-Watts theorem

### Context

#### Algebra

higher algebra

universal algebra

# Contents

## Idea

The Eilenberg-Watts theorem identifies colimit-preserving functors between categories of modules with the operations of forming tensor products with bimodules.

## Statement

### For ordinary rings and modules

###### Eilenberg-Watts’ Theorem

Given unital rings $R$ and $S$ and an $R$-$S$-bimodule $N$, the tensor product functor

$(-) \otimes_R N \;\colon\; Mod_R \to Mod_S$

between the categories of modules is right exact and preserves small coproducts.

Conversely, if $F \colon Mod_R \to Mod_S$ is right exact and preserves small coproducts, then it is naturally isomorphic to tensoring with a bimodule.

This theorem was more or less simultaneously proved in (Watts) and (Eilenberg).

###### Remark

Given a cocontinuous functor $F \colon Mod_R \to Mod_S$, the reconstructed $R$-$S$-bimodule is given as follows:

• the underlying right $S$-module is $F(R)$, where $R$ is regarded as a right module over itself in the canonical way;

• the left $R$-module structure on $F(R)$ is given for $r \in R$ and $n \in N$ by

$r \cdot n \coloneqq F(r\cdot(-))n \,,$

where $r \cdot (-) \colon R \to R$ denotes the right $R$-module homomorphism given by left multiplication by $r$.

###### Remark

The theorem holds for nonunital rings as well, but then $B$ reconstructs as $F(R_1)$ where $R_1$ is the extension of $R$ by adjoining the unit element (the tensor product is still over the original $R$). If $F$ is a flat functor then $F(R_1)$ is a flat module over $R$.

###### Remark

In the statement of the theorem we can replace “additive, right exact and preserves direct sum” by “additive and left adjoint”.

In this form the theorem is stated for instance in (Hovey, theorem 0.1).

In fact both bimodules and intertwiners as well as functors and natural transformations form a category. In more detail the theorem is:

###### Theorem

For $R$ and $S$ two rings, the functor

${}_R Mod_{S} \stackrel{\simeq}{\to} Func_{coc}(Mod_R, Mod_S)$

from the category of bimodules to that of colimit-preserving functors between their categories of modules is an equivalence of categories.

### For other internal monoids and internal modules

The standard Eilenberg-Watts theorem is a statement about monoids and their actions in Ab. More generally one may ask for generalizations of the theorem to other internalization contexts, and in particular to homotopy theory. See the introduction of (Hovey).

### For $\infty$-algebras and $\infty$-modules

In particular Eilenberg-Watts theorems hold true in the homotopy theory following model categories (see at model structure on modules over an algebra over an operad)

This is the main theorem in (Hovey).

More generally, we have the first half of the Eilenberg-Watts theorem in (∞,1)-category theory:

###### Proposition

For $(\mathcal{C}, \otimes)$ a monoidal (∞,1)-category with geometric realization of simplicial objects in an (∞,1)-category such that the tensor product $\otimes$ preserves this in each variable, then for all A-∞ algebra $A,B,C$ in $\mathcal{C}$, the tensor product of ∞-bimodules

$(-) \otimes_B (-) \;\colon\; {}_A Mod_{B} \times {}_B Mod_{C} \to {}_{A} Mod_{C}$

preserves (∞,1)-colimits separately in each argument.

This is (Lurie, cor. 4.3.5.15).

## References

The original articles are

• Charles E. Watts, Intrinsic characterizations of some additive functors, Proc. Amer. Math. Soc. 11, 1960, 5–8, MR0806.0832, doi
• Samuel Eilenberg, Abstract description of some basic functors, J. Indian Math. Soc. (N.S.) 24, 1960, 231–234 (1961), MR0125148

A generalized statement in which the codomain is not assumed to be a category of modules is discussed in

• A. Nyman, S. Paul Smith, A generalization of Watts’s Theorem: Right exact functors on module categories, (arxiv/0806.0832).

Generalization to homotopy theory/higher algebra is discussed in

• Mark Hovey, The Eilenberg-Watts theorem in homotopical algebra (pdf)

and

Last revised on December 31, 2017 at 20:11:21. See the history of this page for a list of all contributions to it.


text:
# Integral of e

1. Jun 28, 2006

### Dae

The integral of e is e right? So if you were to take the integral of 24+e^(5t) (acceleration), it would be 24t+e^(5t) (velocity)?

2. Jun 28, 2006

### chroot

Staff Emeritus
No. Don't forget to include the derivative of the exponent.

Remember that

$\frac{d} {{dt}}e^{5t} = e^{5t} \cdot 5$

- Warren

3. Jun 28, 2006

### Dae

Alright, thanks for the help. :)

I see what you're saying there. However, that's when taking the derivative, and I don't understand how to apply that. If I were taking the integral of e^(5t)*5, the 5 would be a constant, so since the constant of just plain e^(5t) is 1.. how could the integral change? Does it become like Ce^(5t) after integrated? When you say I have to include the derivative, do you mean (24+e^u du)dt where u = 5t, du = 5. For some reason I'm leaning towards du = 5 dt, dt = 1/5 du, so its (1/5)*24 du + e^u * (1/5) du, which when integrated becomes (24t + e^(5t))/5.

I'm obviously confused. Maybe you could please show how to solve it for me? Integral of e

Last edited by a moderator: Feb 17, 2008
4. Jun 28, 2006

### chroot

Staff Emeritus
Whoops! That's not right. Just because 5 is a constant doesn't mean 5 e^(5t) is a constant. It's not; it's still a function of t.

If you agree that the derivative of e^(5t) is 5 e^(5t), then you also have to agree that the integral of 5 e^(5t) is e^(5t) + C.

What I mean when I say "don't forget to include the derivative of 5t," I mean this:

You cannot directly integrate e^(5t). What you'd have to do is multiply it by 5 inside the integral sign, and divide it by 5 outside the integral sign, like this:

$\int {e^{5t} dt = \frac{1} {5}} \int {5e^{5t} dt}$

Thus, the integral of e^(5t) is (1/5) e^(5t) + C.

We don't solve homework problems. We help you understand how to solve them.

- Warren

5. Jun 29, 2006

### HallsofIvy

A lot of your problem is just sloppy thinking. You started by saying "The integral of e is e right?" No, the "integral of e" is NOT e. The integral of e (with respect to x) is ex since e is just a constant. If you MEANT that the integral of ex is ex (plus a constant NOT times a constant as you say) say that!


text:
# Tag Info

## Hot answers tagged abelian-varieties

30

Recall that any smooth projective variety of dimension $g$ embeds into $\mathbf{P}^{2g+1}$. Consider now an abelian variety $A$ of dimension $g$ which embeds into $\mathbf{P}^{2g}$. Van de Ven proves (essentially by applying the self-intersection formula to the normal bundle of $A$ in $\mathbf{P}^{2g}$) that the degree of $A$ in $\mathbf{P}^{2g}$ is given by ...

24

Weil introduced the term "polarization" in connection with his study of abelian varieties with complex multiplication. His definition is slightly different from what one sees today; one might call it a polarization up to isogeny instead of a polarization. One can find a discussion in Weil's article "On the theory of complex multiplication" ([1955d] in volume ...

23

This is a theorem of Lang's from 1956. Here's an online document giving a proof (in the form $H^1(A,k)=0$): Lecture 14: Galois Cohomology of Abelian Varieties over Finite Fields, William Stein. http://wstein.org/edu/2010/582e/lectures/582e-2010-02-12/582e-2010-02-12.pdf Stein notes that there is a "more modern proof" in the first few sections of Chapter ...

22

I don't have any contribution for the intuition beyond the fact that, I can't construct something outside the image of (1) so I hope it's surjective. Here is a sketch of the central idea of Tate's proof. Consider $A = A' \times A''$ and try to find an endomorphism of $A$ from an endomorphism of its Tate module. The endomorphism of the Tate module gives you ...

21

Really this is mostly just consolidating what has been (implicitly) said in the comments and cleaning it up a bit (e.g. using the Chow ring instead of singular cohomology), but might as well make it an answer... Let $A$ be an abelian variety of dimension $d$. We prove that $A$ cannot embed in $\mathbb{P}^{2d-1}$ and can only embed in $\mathbb{P}^{2d}$ if $d=... 18 Let me answer your last question "How can I think geometrically (in the lattice) about fixing a polarization?". I will follow the treatment given in [Birkenhake-Lange, Complex Abelian Varieties, Chapter 3]. Let$X = V / \Lambda$be a complex torus of dimension$g$and$L$a line bundle on$X$with first Chern class$H$. Then$H$is an Hermitian form on$V$, ... 18 I am not aware of anybody seriously considering hyperelliptic curves for actual real-world usage, beyond toys, and I would be rather surprised to hear differently from anyone. As you say, hyperelliptic provide comparatively few (if any!) advantages over elliptic curves but have the huge disadvantage that virtually nobody has well-tested, battle-hardened ... 18 Welcome new contributor. Yes, that is true. Let$k$be any field, let$A$be an Abelian variety over$k$, and let$U\subset A$be a dense open affine. Denote by$D\subset A$the complementary divisor with its induced reduced structure. Denote the invertible sheaf of this divisor by$\mathcal{L}:=\mathcal{O}_A(D).$Denote by$s$the global section of$\...

17

Embed the dual abelian variety into projective space. Take a smooth hyperplane section and interate until it's one-dimensional, obtaining a smooth curve $C$. By Lefschetz $C$ is irreducible, and the natural map $H_1(C, \mathbb Z) \to H_1(A^\vee, \mathbb Z)$ is surjective. Because $H_1(C, \mathbb Z)= H_1(J(C), \mathbb Z)$, the natural map $H_1(J(C), \mathbb Z)... 16 Actually, this is an exercise in Serre's Lectures on Mordell--Weil Theorem:$K(A[n])$always contains$\mu_n$if$char(K)$does not divide$n$and$A$is an abelian variety of positive dimension over$K$. (You don't need to assume that$K$is a number field) Here is a solution. First, it suffices to check the case when$n=\ell^m$is a power of a prime$\...

16

No. It is always difficult to "prove" that something is "not known", but this may do: I claim it is not even known when $K=\mathbb Q$, $A$ is an elliptic curve $E$. In fact in this case, the result you ask for is not even known when $E$ has CM. In fact, even in this very special case, it is not known that the $l$-primary torsion subgroup of the Sha is ...

16

This follows from the following well-known lemma. Lemma. Let $A$ be an abelian variety over $k$. Then any map $f \colon \mathbb P^1 \to A$ is constant. Proof 1. The map $f$ induces a map on the Albanese $f_* \colon \operatorname{Alb}_{\mathbb P^1} \to \operatorname{Alb}_A$ sitting in a commutative diagram $$\begin{array}{ccc}\mathbb P^1 & \stackrel{f}\... 15 Let me put it this way, Tate's conjecture for abelian varieties is known to imply the Hodge conjecture for abelian varieties, and the last is very much open for this class. For the implication, see the article by Deligne and Milne on "Hodge cycles on abelian varieties" (you can get a copy off of Milne's website). There are lot's of interesting cases known ... 15 Abelian varieties over the rationals are modular if and only if they are of "GL_2"-type, which is a notion introduced by Ribet who proved that this statement is a consequence of Serre's conjecture which, as you know, has since been proved. Here is a link to Ribet's paper: http://math.berkeley.edu/~ribet/Articles/korea.pdf Generalizing the statement of ... 14 A bit of overkill, but it follows from the Weil conjectures. The structure of cohomology (H^i = \wedge^i H^1) is computed over the algebraic closure and it follows that the number of points is \prod(\alpha_i-1) where the \alpha_i are the eigenvalues of Frobenius on H^1 so |\alpha_i| = q^{1/2} and the product is therefore not zero. 14 First, when defining the stack you will have the issue that there are formal deformations of abelian varieties which do not extend to families of abelian varieties over any reduced scheme. These are the deformations that do not respect any polarization. (In the complex analytic world these correspond to deformations of complex tori) So unless you have some ... 14 No. The picture over a general base is this: let A_0\to S_0 be an ordinary abelian variety over a characteristic p scheme S_0, and let S_n (n\geq 0) be compatible flat liftings of S_0 over \mathbf{Z}/p^{n+1}. Let F\colon S_0\to S_0 be the Frobenius. Then the pull-back (F^n)^* A_0 has a canonical lifting A_{n,\rm can} to S_n. Thus if ... 13 Another proof that L = \,\overline{\bf \!Q\!}\,: Clearly L is contained in \,\overline{\bf \!Q\!}\,, so we need only show L contains every algebraic number x \notin \bf Q. Let P(X) be the minimal polynomial of x. If \deg P is odd, then the class of ((x,0)) - (\infty) is a 2-torsion point on the Jacobian of the elliptic or hyperelliptic ... 13 The answer is affirmative (in Serre's formulation via principal homogeneous spaces) for proper, geometrically reduced, and geometrically connected schemes X over any field k, giving a strong mapping property relative to working over all k-schemes. That is: Theorem There exists a map f:X \rightarrow E to a torsor for an abelian variety A over k ... 13 For a prime p and an elliptic curve E/\mathbb{Q}, we have the exact sequence$$\displaystyle 0 \rightarrow E(\mathbb{Q})/p E(\mathbb{Q}) \rightarrow S_p(E) \rightarrow \text{Sha}_E[p]\rightarrow 0,$$where S_p(E) is the p-Selmer group of E and \text{Sha}_E is the Tate-Shafarevich group of E and \text{Sha}_E[p] is the p-part of it. This ... 13 Let me give an answer for k = \mathbb{C}. By a theorem of Matsusaka, every abelian variety A over an algebraic closed field k is a quotient of a Jacobian. Now just apply Matsusaka's theorem to A^{\vee}, and dualize. Since we are over \mathbb{C}, dualization sends surjective morphisms of Abelian varieties into injective ones, so we are done. I ... 13 We give a uniform approach to p \leq 61 by applying analytic discriminant bounds to the Hilbert class field. To be sure this is not entirely "conceptual", but then some computation is needed even to deal with p < 36 using Minkowski. If p = 4k+1 is prime then K = {\bf Q}(\sqrt{p}) has odd class number h, so either h=1 or h \geq 3. If h \... 12 I think the following should give a counterexample. Let \mathcal{O} be an order in an imaginary quadratic field K and \mathcal{O}_K, the ring of integers. Then it's not too hard to find a (non-split) short exact sequence of \mathcal{O}-modules:$$0 \to \mathcal{O}_K \to \mathcal{O} \oplus \mathcal{O} \to \mathcal{O}_K \to 0,$$e.g. if 1, \omega... 12 If \lambda\in\overline{\mathbb{Q}}, the elliptic curve$$ E_\lambda\colon y^2=x(x-1)(x-\lambda) $$has (\lambda,0) as 2-torsion point and is defined over (a subfield of) L=\mathbb{Q}(\lambda). Its Weil restriction A_\lambda:=\operatorname{Res}_{L/\mathbb{Q}}(E_\lambda) is an abelian variety defined over \mathbb{Q} and shares the same points of ... 12 There are non-isotrivial families of supersingular abelian varieties of dimension g over \mathbb P^1_{\overline {\mathbb F_p}} if g\geq 2; see Goren, E. Z.(3-MGL); Oort, F. Stratifications of Hilbert modular varieties. (English summary) J. Algebraic Geom. 9 (2000), no. 1, 111–154. There are many other papers of Goren and Oort with explicit ... 12 The arguments of Serre can be in fact made to work over any separably closed field. The result in the general case can then be deduced using Galois descent. Details can be found in Section 2 and the appendix of: Olivier Wittenberg - On Albanese torsors and the elementary obstruction. This is in particular shows the existence of the Albanese torsor and ... 12 A conjecture of Coleman asserts that only finitely many rings arise as the endomorphism ring of an abelian variety of given dimension defined over a number field of given degree. See [1] for an account of this conjecture. In your case, the relevant conjecture is denoted there by C(1,2). To my knowledege, the only results on Coleman's conjecture in ... 11 The answer to question (*) is yes. It is Theorem 1.2.2 in the following preprint. 11 Not in general. For instance, if A is simple then this is not possible. In fact, any isogeny$$f \colon E_1 \times \cdots \times E_n \longrightarrow A$$would give a dual isogeny$$f^{\ast} \colon A^{\ast} \longrightarrow E_1^{\ast} \times \cdots \times E_n^{\ast} and the pullback via $f^*$ of any elliptic curve in $E_1^{\ast} \times \cdots \times E_n^{... 11 Let$B$be a smooth projective curve over an algebraically closed field of characteristic zero. Let$K$be the function field of$B$. Let$S$be a finite set of closed points of$B$. You might find the following reformulation of Faltings's theorem less confusing. Theorem 1. (Faltings, geometric Shafarevich conjecture) Let$g\$ be an integer. Then the set ...

Only top voted, non community-wiki answers of a minimum length are eligible


text:
# Math With Slack

Rendered math (MathJax) with Slack's desktop client

Expand to see all tested systems

# All environments on latest Slack app (updated nightly)

Environments below with passing badges are tested to work -- that the install scripts completes succesfully.
However, if you find that something is not working (e.g. math rendering does not appear), please file an issue with your environment!

# Rendered math (MathJax) with Slack's desktop client

Slack does not display rendered math. The math-with-slack script allows you to write nice-looking math using familiar TeX syntax by injecting MathJax into Slack's desktop client. This approach has several advantages over the plugin/bot solution:

• You can write both inline- and display-style equations.
• You can edit equations after you've posted them.
• Nothing is sent to external servers for rendering.

The downside is that equations are not rendered for team members without the MathJax injection.

## How do I install it?

Get and run the script. Restart the Slack client. You're done!

Windows users without Python installed can skip and jump to binary release.

### Getting the script

#### Option 1: Raw script content

There are many ways to get the script. This link to math-with-slack.py should take you to the raw file content of the script, with the version relative same as README.md that you are looking at (i.e. on the same commit). From there you can simply save the file's content to a local file math-with-slack.py (e.g. you can copy the entire content, and use your favorite editor to save the content) --- this process should be the same for all platforms, and works as long as you have a decent browser and working editor.

1. Copy the URL of link to math-with-slack.py (e.g. right click on the link -> copy URL).

2. Assuming on Mac and/or Linux, use one of the alternatives:

• With the tool curl available. Run the following in a terminal:
curl -L {PASTE_THE_COPIED_LINK_HERE} > math-with-slack.py

• With the tool wget available. Run the following in a terminal:
wget {PASTE_THE_COPIED_LINK_HERE} -O math-with-slack.py

#### Option 3: using git

With git available, you can also clone this repo, and access the script math-with-slack.py directly!

### Running the script

• MacOS and Linux
cd path/to/math-with-slack
sudo python math-with-slack.py

The installation should take effect after restarting Slack.

• Windows You need to exit your Slack before the installation.
cd path\to\math-with-slack
python math-with-slack.py

### Beta Binary Release for Windows

We have also included pre-built executables for Windows in case Python is not available. Please see our Releases page for more details.

### Selecting a Slack version

If multiple versions of Slack are found on your computer, you will be asked to select one from them.

python math-with-slack.py
Several verisons of Slack were installed.
0: /mnt/c/Users/***/AppData/Local/slack/app-4.9.0/resources/app.asar (default)
1: /mnt/c/Users/***/AppData/Local/slack/app-4.8.0/resources/app.asar
Please select a version (#/Stop): 1

You can either enter the number indicating one of the listed versions or type Enter to select the first one.

Currently, we only support Slack installed from Slack installer. If your Slack is installed through Microsoft Store, math-with-slack is not able to modifiy files in WindowsApps folder hence not able to embedded our script.

### Package and software managers

The script needs write permissions in the Slack directory in order to inject the MathJax code. Some package and software managers write protect their directories, and math-with-slack cannot be installed if Slack is installed through such a manager. This is the case for both the Windows Store and Snap versions of Slack. You should use the version downloaded from Slack's website if you want to use math-with-slack. The script should, however, work with most package managers if you manage to grant the script write permission.

### MathJax versions and URLs

The default MathJax is of version 3.1.0 and downloaded from https://registry.npmjs.org/mathjax/-/mathjax-3.1.0.tgz, which is a registry of npmjs.

The script also works with other versions of MathJax 3 and we list a table of versions that we have tested and the corresponding URLs.

Some URLs works better for certain areas. You can use any URL in the table to install math-with-slack.

cd path\to\math-with-slack
python math-with-slack.py --mathjax-url=https://r.cnpmjs.org/mathjax/-/mathjax-3.0.5.tgz

### Uninstall

To uninstall, run the script again with the -u flag:

python math-with-slack.py -u

### Updating Slack

The code injected by the script might be overwritten when you update the Slack app. If your client stops rendering math after an update, re-run the script as above and it should work again.

### If Slack cannot be found

If you've installed Slack in some exotic place, the script might not find the installation by itself or it might find the wrong installation. In such cases, you need to specify the location of Slack's app.asar file as a parameter:

python math-with-slack.py --app-file=/My_Apps/Slack.app/Contents/Resources/app.asar

python math-with-slack.py --app-file=c:/Users/yourusername/AppData/Local/slack/app-4.7.0/resources/app.asar

### Double underscore converts to italic

If you are having problems that writing code like $a_k b_k$ converts _k b_ to italic font in the Slack-editor, go to Preferences Advanced and check Format messages with markup. This should solve the problem.

## How do I get my math rendered?

As you do in TeX, use $...$ for inline math and $$...$$ for display-style math. If you need to write a lot of dollar-signs in a message and want to prevent rendering, use backslash to escape them: \\$.

Note that only users with MathJax injected in their client will see the rendered version of your math. Users with the standard client will see the equations just as you wrote them (i.e., unrendered including the dollar signs).

### TeX Customization

The script allows one to customize MathJax at installation time. Currently the script allows the user to supply an optional TeX input processor option to customize the MathJax rendering. For example, to instead use $$...$$ for inline math and $...$ for display-style math, and enable the package physics support, one may use the following command line arguments during installation:

python math-with-slack.py --mathjax-tex-options="{\
packages: {'[+]': ['noerrors', 'noundefined', 'physics']}, \
inlineMath: [['\\$$', '\\\$$']], \
displayMath: [['\\\$', '\\\$']], \
}"

Note that a common scenario is when a team of people uses this plugin. In this case it will be desirable to share the same configuration for all the members.

## How does it work?

The script alters how Slack is loaded. Under the hood, the desktop client is based on ordinary web technology. The modified client loads the MathJax library after start-up and adds a listener for messages. As soon as it detects a new message, it looks for TeX-styled math and tries to render. Everything is done in the client. Messages are never sent to servers for rendering.


text:
## SSH publickey denied?

I was suddenly having trouble connecting to GitHub, after pulling in an OpenSSH update to version 7. Chances are that means the problem is security-related, meaning it’s worthwhile to take the time to investigate the cause.

$git pullPermission denied (publickey).fatal: Could not read from remote repository.Please make sure you have the correct access rightsand the repository exists. A little debugging showed the following: $ ssh -vT git@github.comOpenSSH_7.1p2 Debian-2, OpenSSL 1.0.2f  28 Jan 2016debug1: Reading configuration data /etc/ssh/ssh_configdebug1: /etc/ssh/ssh_config line 19: Applying options for *debug1: Connecting to github.com [192.30.252.130] port 22.debug1: Connection established.[…]debug1: Skipping ssh-dss key /home/frans/.ssh/id_dsa for not in PubkeyAcceptedKeyTypes[…]debug1: No more authentication methods to try.Permission denied (publickey).

Of course I could quickly fix the problem by adding PubkeyAcceptedKeyTypes ssh-dss to ~/.ssh/config, but checking OpenSSH.com tells me that “OpenSSH 7.0 and greater similarly disables the ssh-dss (DSA) public key algorithm. It too is weak and we recommend against its use.” So, although I could obviously re-enable it easily, I guess I’ll have to generate a new key. I hope GitHub’s guide is accurate for generating something sufficiently secure, because I’m kind of ticked off that something I generated in 2013 is already considered “legacy.” I hope I’m too blame and not an earlier version of GitHub’s guide.

Incidentally, to change the passphrase one would use the -p option, e.g.:

ssh-keygen -f id_rsa -p

## LuaLatex Font Hassles

The TeX Gyre Pagella font I was using turned out not to contain Cyrillic characters. Unfortunately, fontspec doesn’t seem to have an easy means of setting a fallback font — I checked the manual, I swear! So I found a lookalike font named Palladio Uralic and used it instead. Before you can use a newly installed font, you have to run luaotfload-tool --update.

%So is Palladio. Used as fallback. Thanks to http://tex.stackexchange.com/a/37251/32003
\DeclareTextFontCommand{\textpalladio}{\palladio}

## PulseAudio: How to Decouple Application Volumes And Global Volume

I wondered why e.g. my VLC volume kept getting lowered. As it turns out, there was a change.

PulseAudio seems to have copied one of Windows 6+’s most annoying features, at least in terms of the media framework: flat volumes.

Quick refresher: This is that annoying thing that Windows (and now, PulseAudio, by default) does, where turning up the volume in an application will increase the master system volume alongside it. This has the side-effect that any application which sets its own volume can commandeer the master volume of your system. Why is this bad? The short answer is headphones.

It’s not as if it’s only headphones that can blare at ridiculously loud volumes. Anyway, a quick search came up with this helpful suggestion regarding the flat-volumes setting.

PulseAudio supports per-application volume control, but by default this doesnt do much as you can only control these volumes from the pulseaudio volume control utility. Meaning that in an application like Audacious, when the output device is set to PulseAudio, and the volume control is set to hardware, it will adjust the master volume control, not the per-application volume control.

To fix this behavior, set the following in /etc/pulse/daemon.conf

flat-volumes = no

Now whenever Audacious goes to adjust the volume, it will adjust the audacious only volume and thus you wont have multiple applications fighting over the master volume control.

What a horribly annoying new default.

## Working around the broken Creative HS-720 headset

A few years ago I received a Creative HS-720 as a gesture of good will. I wasn’t displeased, but since I didn’t need it I didn’t really investigate. Recently I’ve been wanting to use it as a headphone and noticed that even at the lowest possible volume, it was still significantly too loud. What’s really crazy is that there are actually positive reviews for the product out there. Read this negative one instead. That’s all you need to know. Avoid this product. Ideally I’d acquire something like an Asus Xonar U3, a Creative Sound Blaster Play! 2 or a Creative Sound Blaster E1 in combination with proper headphones (although the HS-720 certainly doesn’t make me want to buy another Creative product), but I figured there just had to be a software solution.

Some searching gave me “Fix for USB Audio is Too Loud and Mutes at Low Volume in Ubuntu.” The title isn’t quite accurate, because it’s a workaround. No matter. It requires modifying the file /usr/share/pulseaudio/alsa-mixer/paths/analog-output.conf.common. But we might as well take a look at what else there is to play with while we’re at it.

/usr/share/pulseaudio/alsa-mixer/paths$ls analog-input-aux.conf analog-input-mic.conf analog-output-lineout.conf analog-input.conf analog-input-mic.conf.common analog-output-mono.conf analog-input.conf.common analog-input-mic-line.conf analog-output-speaker-always.conf analog-input-dock-mic.conf analog-input-rear-mic.conf analog-output-speaker.conf analog-input-fm.conf analog-input-tvtuner.conf hdmi-output-0.conf analog-input-front-mic.conf analog-input-video.conf hdmi-output-1.conf analog-input-headphone-mic.conf analog-output.conf hdmi-output-2.conf analog-input-headset-mic.conf analog-output.conf.common hdmi-output-3.conf analog-input-internal-mic-always.conf analog-output-desktop-speaker.conf iec958-stereo-output.conf analog-input-internal-mic.conf analog-output-headphones-2.conf analog-input-linein.conf analog-output-headphones.conf As you can see there’s a bunch of PulseAudio profiles. In my case I might be able to adjust one of the headphones files without changing the entire system, but as luck would have it I use a digital IEC958 output for my main sound system, so I could afford mess up all handling of analog output for the sake of these headphones. I’ll quote part of Chris Jean’s guide in case linkrot ever strikes. Search for the text “Element PCM”. You should see the following text: [Element PCM] switch = mute volume = merge override-map.1 = all override-map.2 = all-left,all-right Update this section of text to look like the following (changes are in bold): [Element PCM] switch = mute volume = ignore volume-limit = 0.01 override-map.1 = all override-map.2 = all-left,all-right Note that the value 0.01 can be adjusted as needed to change how quiet and loud the volume is. Making the number smaller reduces the max volume while making the number larger increases the max volume. I tested out 0.05 and found that the max volume was much louder than I would ever use. I also decided that 0.01 was technically louder than I’d ever use. I ended up with a value of 0.0075 (0.005 was too quiet) which I felt gave a good maximum volume and resulted in better overall control over the volume range. I’d add that it seems to work fine with volume-limit = 1.0 as well. After making that change run killall pulseaudio (or pulseaudio -k, but why bother with something non-generic) to get it to work. You can do some more volume play using alsamixer, but you’ll have to figure out which device to use first. $ pacmd list-sources | grep -e device.string -e 'name:'
name:
device.string = "1"
name:
device.string = "hw:2"
name:
device.string = "0"
name:
device.string = "3"

As you can see the headset is device 3. You can print some more info using amixer.

\$ amixer -c 3
Simple mixer control 'PCM',0
Capabilities: pvolume pswitch pswitch-joined
Playback channels: Front Left - Front Right
Limits: Playback 0 - 38
Mono:
Front Left: Playback 9 [24%] [-21.67dB] [on]
Front Right: Playback 9 [24%] [-21.67dB] [on]
Simple mixer control 'Mic',0
Capabilities: cvolume cvolume-joined cswitch cswitch-joined
Capture channels: Mono
Limits: Capture 0 - 16
Mono: Capture 14 [88%] [20.83dB] [on]
Simple mixer control 'Auto Gain Control',0
Capabilities: pswitch pswitch-joined
Playback channels: Mono
Mono: Playback [on]

And using alsamixer -c 3 you can play around with the volume a bit more, too.

My only regret is that I haven’t been able to find something like Identifier for xorg.conf. Oh well, it’ll save me some money in the short term.

PS On Windows, try EqualizerAPO (source).

## Just a Star

Messing about a little in Inkscape with my wife’s Wacom CTH-680S tablet on Linux 4.1, after first trying it in Xournal. It seems to be functioning a fair bit better than a few kernel versions ago.

The tablet is really good. I’d recommend it.

## Alt + Print screen in Xfce

Perhaps it’s merely a fluke of Debian Xfce, but the Print screen key does nothing by default. If you just want to use Print screen that’s easy to rectify through Settings > Keyboard > Application Shortcuts > Add. Use the command xfce4-screenshooter -f or -w for respectively full screen and window. As it turns out that interface doesn’t support the key combination of Alt + Print screen thanks to some kernel feature. The suggestion is to disable the kernel feature, but interestingly enough it works when you add the shortcut manually. Remember how we regained control of Ctrl + F1F12? Once again, edit ~/.config/xfce4/xfconf/xfce-perchannel-xml/xfce4-keyboard-shortcuts.xml. Look for the custom section, which should look a little something like this:

    <property name="custom" type="empty">
<property name="XF86Display" type="string" value="xfce4-display-settings --minimal"/>
<property name="<Primary><Alt>Delete" type="string" value="xflock4"/>
<property name="<Alt>F2" type="string" value="xfrun4"/>
<property name="override" type="bool" value="true"/>
<property name="<Super>p" type="string" value="xfce4-display-settings --minimal"/>
</property>

Next, we add in our custom setting:

      <property name="<Alt>Print" type="string" value="xfce4-screenshooter -w"/>

Now it should look like this.

    <property name="custom" type="empty">
<property name="XF86Display" type="string" value="xfce4-display-settings --minimal"/>
<property name="<Primary><Alt>Delete" type="string" value="xflock4"/>
<property name="<Alt>F2" type="string" value="xfrun4"/>
<property name="override" type="bool" value="true"/>
<property name="<Super>p" type="string" value="xfce4-display-settings --minimal"/>
<property name="<Alt>Print" type="string" value="xfce4-screenshooter -w"/>
</property>

You're going to have to log out and log in again (or restart) for the changes to take effect. I have to admit it's probably more useful to bind Print screen to take window screenshots by default, but on the other hand it might be a good idea to stick to the global standard so you can still use desktop environments other than your own without feeling hampered.

## Custom page number count in Prince

Prince makes it really easy to do all of the usual things with page numbers, like a different numbering scheme in the front matter and whatnot. Unfortunately you can’t counter-increment on @page, but thanks to Prince.addScriptFunc() you’ve got something better.

h2 {counter-reset: page 50}

@page {
@bottom-left {
content: prince-script(fixpagenum, counter(page));
margin-left: 2cm;
}
}

In this CSS, instead of passing regular generated content, we’re passing a prince-script. That script has to be defined somewhere, like this.

Prince.addScriptFunc("fixpagenum", function(pagenum) {
pagenum = Number(pagenum);
pagenum = pagenum + pagenum - 50;
return pagenum;
});

The rationale in this case was to generate two separate documents, starting at page 50, one only left pages and the other only right pages. (Of course, the other one started at page 51.) I combined them with pdftk’s shuffle command.

pdftk left.pdf right.pdf shuffle output combined.pdf

I don’t think there’s a way to do something like this purely in Prince using CSS, but I’d love to be proved wrong.

## LaTeX: combining added margins with hanging indents

Since I’m using KOMA, the obvious method would seem to be:

\begin{addmargin}[1cm]{0cm}

Unfortunately, that doesn’t seem to combine with the hanging environment. So I did it a little more manually, which will probably have someone shaking their head while I’m stuck feeling pretty clever about it:

\parindent=1cm\hangindent=2cm Yada.

## Xfce: Keep Windows from Switching Workspaces

I thought applications switching workspaces was an issue in all window managers, but it never bothered me quite enough to investigate changing it. But what do you know, in Xfwm you can change it.

When using several workspaces in Xfce, I had the problem that when I pressed a link in Claws-Mail, it opened Iceweasel, but it also move my Iceweasel from workspace 3 to workspace 1 (where Claws-Mail was).

To avoid this, start the xfce4-settings-editor, select xfwm4 in the list, and go to general->activate_action (in my case it is the topmost entry), and change the string value from “bring” to “switch”.

Thanks to Gusnan.

## Introducing Nimbler: A Window Switcher

When I discovered SmartTab.org about a decade ago, I was quite happy. Never before had my window switching been so fast and nimble. The most important feature was of course the list-based view of window titles, rather than the standard mysterious icons that only coughed up their secret window titles once you landed on them. But one thing I hadn’t yet conceived of was switching to a far-off window without pressing Tab a dozen times or more. SmartTab.org quickly became so ingrained into my workflow that I even resisted changing my operating system because of it. If Windows 7 would mean giving up on all of my trusty tools like SmartTab.org and ASD Clock, I might as well upgrade to something completely different. In 2011 I switched to Debian Squeeze as my main OS and I haven’t looked back, barring perhaps the occasional game. To me, Linux is just so much more user-friendly these days. But enough about that. You can get Nimbler here or you can continue reading about my window switching philosophy.

Even before I switched, I looked for SmartTab.org alternatives. I discovered that both Openbox and KWin can display sane window lists, but superswitcher was much closer to what I wanted. Unfortunately, its C-based code was too complicated for now. I’d pretty much have to learn C first. Fast forward a few years and Fuzzy Window Switcher came out. It was a lovely little application, and it managed to scratch my itch. Someone quipped that a Compiz plugin could perform the same task. I replied that “The Compiz (plugins) source had absolutely no documentation when I last checked, nor was it so obvious that none was needed. Above all else I see [Fuzzy Window Switcher] as a great place to start for hacking together your own thing. Besides, not everyone uses Compiz. This can be useful regardless of whether you use Compiz, Mutter, xfwm4, OpenBox, KWin or whatever else there is.”

Still, I wasn’t ready. I had to learn the much easier Python first, which I didn’t start with until a few months later. By that time I was too busy, and when my schedule finally opened up again I’d forgotten about my plans. Until a couple of weeks ago a bug report reminded me that I could actually mimic what I liked about SmartTab.org. Several hours of coding later I can present Nimbler. Bear with me if you actually know GTK+ 3; I’m figuring this stuff out as I go along. Long story short, this is what it looks like:

So how does it work? I like to think it couldn’t be much more intuitive. You press the shortcut — at the moment I use <Super>grave — and the window pops up. Then you can immediately switch to any window using its identifier, the arrow keys or the mouse. You can also switch workspaces using F1-F12.

Currently non-functional, if you press colon (:) a text input box is added to the window. At some undefined point in the future I probably intend to couple this with Fuzzy Window Switcher’s fuzzy matching code, but don’t hold your breath. 😉 If I do get around to implementing something like that, I figure there should also be a configuration setting for this fuzzy-mode where you don’t have to press colon first. This sounds like a wasteful duplication of Fuzzy Window Switcher itself, but my thoughts are that if the text input is merely one character, no fuzzy matching would occur and instead it would just be treated as a window identifier. Theoretically I suppose you could also use such functionality to introduce double-character identifiers, easily quadrupling the amount of potential options.

Quadrupling, you ask? The current amount of identifiers is a little more than 90, so you would expect to easily get over 8,000 unique identifiers out of it. However, for usability purposes aa would is much faster than aA, let alone a0. Besides, who could possibly keep so many windows straight?

I hope someone besides me finds this useful. Enjoy!

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