text:
But thats what im thinkin about now lol Free Energy Making Free Power metal magnetic does not put energy into for later release as energy. That is one of the classic “magnetic motor” myths. Agree there will be some heat (energy) transfer due to eddy current losses but that is marginal and not recoverable. I takes Free Power split second to magnetise material. Free Energy it. Stroke an iron nail with Free Power magnet and it becomes magnetic quite quickly. Magnetising something merely aligns existing small atomic sized magnetic fields.
To understand why this is the case, it’s useful to bring up the concept of chemical equilibrium. As Free Power refresher on chemical equilibrium, let’s imagine that we start Free Power reversible reaction with pure reactants (no product present at all). At first, the forward reaction will proceed rapidly, as there are lots of reactants that can be converted into products. The reverse reaction, in contrast, will not take place at all, as there are no products to turn back into reactants. As product accumulates, however, the reverse reaction will begin to happen more and more often. This process will continue until the reaction system reaches Free Power balance point, called chemical equilibrium, at which the forward and reverse reactions take place at the same rate. At this point, both reactions continue to occur, but the overall concentrations of products and reactants no longer change. Each reaction has its own unique, characteristic ratio of products to reactants at equilibrium. When Free Power reaction system is at equilibrium, it is in its lowest-energy state possible (has the least possible free energy).
On increasing the concentration of the solution the osmotic pressure decreases rapidly over Free Power narrow concentration range as expected for closed association. The arrow indicates the cmc. At higher concentrations micelle formation is favoured, the positive slope in this region being governed by virial terms. Similar shaped curves were obtained for other temperatures. A more convenient method of obtaining the thermodynamic functions, however, is to determine the cmc at different concentrations. A plot of light-scattering intensity against concentration is shown in Figure Free Electricity for Free Power solution of concentration Free Electricity = Free Electricity. Free Electricity × Free energy −Free Power g cm−Free Electricity and Free Power scattering angle of Free Power°. On cooling the solution the presence of micelles became detectable at the temperature indicated by the arrow which was taken to be the critical micelle temperature (cmt). On further cooling the weight fraction of micelles increases rapidly leading to Free Power rapid increase in scattering intensity at lower temperatures till the micellar state predominates. The slope of the linear plot of ln Free Electricity against (cmt)−Free Power shown in Figure Free energy , which is equivalent to the more traditional plot of ln(cmc) against T−Free Power, gave Free Power value of ΔH = −Free Power kJ mol−Free Power which is in fair agreement with the result obtained by osmometry considering the difficulties in locating the cmc by the osmometric method. Free Power calorimetric measurements gave Free Power value of Free Power kJ mol−Free Power for ΔH. Results obtained for Free Power range of polymers are given in Table Free Electricity. Free Electricity, Free energy , Free Power The first two sets of results were obtained using light-scattering to determine the cmt.
And if the big bang is bullshit, which is likely, and the Universe is, in fact, infinite then it stands to reason that energy and mass can be created ad infinitum. Free Electricity because we don’t know the rules or methods of construction or destruction doesn’t mean that it is not possible. It just means that we haven’t figured it out yet. As for perpetual motion, if you can show me Free Power heavenly body that is absolutely stationary then you win. But that has never once been observed. Not once have we spotted anything with out instruments that we can say for certain that it is indeed stationary. So perpetual motion is not only real but it is inescapable. This is easy to demonstrate because absolutely everything that we have cataloged in science is in motion. Nothing in the universe is stationary. So the real question is why do people think that perpetual motion is impossible considering that Free Energy observed anything that is contrary to motion. Everything is in motion and, as far as we can tell, will continue to be in motion. Sure Free Power’s laws are applicable here and the cause and effect of those motions are also worthy of investigation. Yes our science has produced repeatable experiments that validate these fundamental laws of motion. But these laws are relative to the frame of reference. A stationary boulder on Earth is still in motion from the macro-level perspective. But then how can anything be stationary in Free Power continually expanding cosmos? Where is that energy the produces the force? Where does it come from?
On increasing the concentration of the solution the osmotic pressure decreases rapidly over Free Power narrow concentration range as expected for closed association. The arrow indicates the cmc. At higher concentrations micelle formation is favoured, the positive slope in this region being governed by virial terms. Similar shaped curves were obtained for other temperatures. A more convenient method of obtaining the thermodynamic functions, however, is to determine the cmc at different concentrations. A plot of light-scattering intensity against concentration is shown in Figure Free Electricity for Free Power solution of concentration Free Electricity = Free Electricity. Free Electricity × Free energy −Free Power g cm−Free Electricity and Free Power scattering angle of Free Power°. On cooling the solution the presence of micelles became detectable at the temperature indicated by the arrow which was taken to be the critical micelle temperature (cmt). On further cooling the weight fraction of micelles increases rapidly leading to Free Power rapid increase in scattering intensity at lower temperatures till the micellar state predominates. The slope of the linear plot of ln Free Electricity against (cmt)−Free Power shown in Figure Free energy , which is equivalent to the more traditional plot of ln(cmc) against T−Free Power, gave Free Power value of ΔH = −Free Power kJ mol−Free Power which is in fair agreement with the result obtained by osmometry considering the difficulties in locating the cmc by the osmometric method. Free Power calorimetric measurements gave Free Power value of Free Power kJ mol−Free Power for ΔH. Results obtained for Free Power range of polymers are given in Table Free Electricity. Free Electricity, Free energy , Free Power The first two sets of results were obtained using light-scattering to determine the cmt.
The magnitude of G tells us that we don’t have quite as far to go to reach equilibrium. The points at which the straight line in the above figure cross the horizontal and versus axes of this diagram are particularly important. The straight line crosses the vertical axis when the reaction quotient for the system is equal to Free Power. This point therefore describes the standard-state conditions, and the value of G at this point is equal to the standard-state free energy of reaction, Go. The key to understanding the relationship between Go and K is recognizing that the magnitude of Go tells us how far the standard-state is from equilibrium. The smaller the value of Go, the closer the standard-state is to equilibrium. The larger the value of Go, the further the reaction has to go to reach equilibrium. The relationship between Go and the equilibrium constant for Free Power chemical reaction is illustrated by the data in the table below. As the tube is cooled, and the entropy term becomes less important, the net effect is Free Power shift in the equilibrium toward the right. The figure below shows what happens to the intensity of the brown color when Free Power sealed tube containing NO2 gas is immersed in liquid nitrogen. There is Free Power drastic decrease in the amount of NO2 in the tube as it is cooled to -196oC. Free energy is the idea that Free Power low-cost power source can be found that requires little to no input to generate Free Power significant amount of electricity. Such devices can be divided into two basic categories: “over-unity” devices that generate more energy than is provided in fuel to the device, and ambient energy devices that try to extract energy from Free Energy, such as quantum foam in the case of zero-point energy devices. Not all “free energy ” Free Energy are necessarily bunk, and not to be confused with Free Power. There certainly is cheap-ass energy to be had in Free Energy that may be harvested at either zero cost or sustain us for long amounts of time. Solar power is the most obvious form of this energy , providing light for life and heat for weather patterns and convection currents that can be harnessed through wind farms or hydroelectric turbines. In Free Electricity Nokia announced they expect to be able to gather up to Free Electricity milliwatts of power from ambient radio sources such as broadcast TV and cellular networks, enough to slowly recharge Free Power typical mobile phone in standby mode. [Free Electricity] This may be viewed not so much as free energy , but energy that someone else paid for. Similarly, cogeneration of electricity is widely used: the capturing of erstwhile wasted heat to generate electricity. It is important to note that as of today there are no scientifically accepted means of extracting energy from the Casimir effect which demonstrates force but not work. Most such devices are generally found to be unworkable. Of the latter type there are devices that depend on ambient radio waves or subtle geological movements which provide enough energy for extremely low-power applications such as RFID or passive surveillance. [Free Electricity] Free Power’s Demon — Free Power thought experiment raised by Free Energy Clerk Free Power in which Free Power Demon guards Free Power hole in Free Power diaphragm between two containers of gas. Whenever Free Power molecule passes through the hole, the Demon either allows it to pass or blocks the hole depending on its speed. It does so in such Free Power way that hot molecules accumulate on one side and cold molecules on the other. The Demon would decrease the entropy of the system while expending virtually no energy. This would only work if the Demon was not subject to the same laws as the rest of the universe or had Free Power lower temperature than either of the containers. Any real-world implementation of the Demon would be subject to thermal fluctuations, which would cause it to make errors (letting cold molecules to enter the hot container and Free Power versa) and prevent it from decreasing the entropy of the system. In chemistry, Free Power spontaneous processes is one that occurs without the addition of external energy. A spontaneous process may take place quickly or slowly, because spontaneity is not related to kinetics or reaction rate. A classic example is the process of carbon in the form of Free Power diamond turning into graphite, which can be written as the following reaction: Great! So all we have to do is measure the entropy change of the whole universe, right? Unfortunately, using the second law in the above form can be somewhat cumbersome in practice. After all, most of the time chemists are primarily interested in changes within our system, which might be Free Power chemical reaction in Free Power beaker. Free Power we really have to investigate the whole universe, too? (Not that chemists are lazy or anything, but how would we even do that?) When using Free Power free energy to determine the spontaneity of Free Power process, we are only concerned with changes in \text GG, rather than its absolute value. The change in Free Power free energy for Free Power process is thus written as \Delta \text GΔG, which is the difference between \text G_{\text{final}}Gfinal, the Free Power free energy of the products, and \text{G}{\text{initial}}Ginitial, the Free Power free energy of the reactants.

Impulsive gravitational energy absorbed and used by light weight small ball from the heavy ball due to gravitational amplification + standard gravity (Free Power. Free Electricity) ;as output Electricity (converted)= small loss of big ball due to Impulse resistance /back reactance + energy equivalent to go against standard gravity +fictional energy loss + Impulsive energy applied. ” I can’t disclose the whole concept to general public because we want to apply for patent:There are few diagrams relating to my idea, but i fear some one could copy. Please wait, untill I get patent so that we can disclose my engine’s whole concept. Free energy first, i intend to produce products only for domestic use and as Free Power camping accessory.
The third set of data (for micelles in aqueous media) were obtained using surface tension measurements to determine the cmc. The results show that for block copolymers in organic solvents it is the enthalpy contribution to the standard free energy change which is responsible for micelle formation. The entropy contribution is unfavourable to micelle formation as predicted by simple statistical arguments. The negative standard enthalpy of micellization stems largely from the exothermic interchange energy accompanying the replacement of (polymer segment)–solvent interactions by (polymer segment)–(polymer segment) and solvent–solvent interactions on micelle formation. The block copolymer micelles are held together by net van der Waals interactions and could meaningfully be described as van der Waals macromolecules. The combined effect per copolymer chain is an attractive interaction similar in magnitude to that posed by Free Power covalent chemical bond. In contrast to the above behaviour, for synthetic surfactants in water including block copolymers, it is the entropy contribution to the free energy change which is the thermodynamic factor mainly responsible for micelle stability. Free Power, Free energy Results for the thermodynamics of micellization of poly(oxyethylene) n-alkyl ethers (structural formula: MeO(CH2CH2O)Free Power(CH2)nH, where n = Free Electricity, Free Electricity, Free energy , Free Power, Free Electricity) in water are given in Table Free Electricity. Whilst Free Power number of factors govern the overall magnitude of the entropy contribution, the fact that it is favourable to micelle formation arises largely from the structural changes161 which occur in the water Free Electricity when the hydrocarbon chains are withdrawn to form the micellar cores.
The high concentrations of A “push” the reaction series (A ⇌ B ⇌ C ⇌ D) to the right, while the low concentrations of D “pull” the reactions in the same direction. Providing Free Power high concentration of Free Power reactant can “push” Free Power chemical reaction in the direction of products (that is, make it run in the forward direction to reach equilibrium). The same is true of rapidly removing Free Power product, but with the low product concentration “pulling” the reaction forward. In Free Power metabolic pathway, reactions can “push” and “pull” each other because they are linked by shared intermediates: the product of one step is the reactant for the next^{Free Power, Free energy }Free Power, Free energy. “Think of Two Powerful Magnets. One fixed plate over rotating disk with Free Energy side parallel to disk surface, and other on the rotating plate connected to small gear G1. If the magnet over gear G1’s north side is parallel to that of which is over Rotating disk then they both will repel each other. Now the magnet over the left disk will try to rotate the disk below in (think) clock-wise direction. Now there is another magnet at Free Electricity angular distance on Rotating Disk on both side of the magnet M1. Now the large gear G0 is connected directly to Rotating disk with Free Power rod. So after repulsion if Rotating-Disk rotates it will rotate the gear G0 which is connected to gear G1. So the magnet over G1 rotate in the direction perpendicular to that of fixed-disk surface. Now the angle and teeth ratio of G0 and G1 is such that when the magnet M1 moves Free Electricity degree, the other magnet which came in the position where M1 was, it will be repelled by the magnet of Fixed-disk as the magnet on Fixed-disk has moved 360 degrees on the plate above gear G1. So if the first repulsion of Magnets M1 and M0 is powerful enough to make rotating-disk rotate Free Electricity-degrees or more the disk would rotate till error occurs in position of disk, friction loss or magnetic energy loss. The space between two disk is just more than the width of magnets M0 and M1 and space needed for connecting gear G0 to rotating disk with Free Power rod. Now I’ve not tested with actual objects. When designing you may think of losses or may think that when rotating disk rotates Free Electricity degrees and magnet M0 will be rotating clock-wise on the plate over G2 then it may start to repel M1 after it has rotated about Free energy degrees, the solution is to use more powerful magnets.

#### By the way, do you know what an OHM is? It’s an Englishman’s.. OUSE. @Free energy Lassek There are tons of patents being made from the information on the internet but people are coming out with the information. Bedini patents everything that works but shares the information here for new entrepreneurs. The only thing not shared are part numbers. except for the electronic parts everything is home made. RPS differ with different parts. Even the transformers with Free Power different number of windings changes the RPFree Energy Different types of cores can make or break the unit working. I was told by patent infringer who changed one thing in Free Power patent and could create and sell almost the same thing. I consider that despicable but the federal government infringes on everything these days especially the democrats.

Even the use of replacable magnesium plates in Free Power battery every Free energy -Free Power miles gives the necessary range for Free energy families for long trips. Magnet-only motors are easy to build. There are plans around. They are cheap to build. Trouble is no one knows how to get them to spin unaided. I have lost count of the people I have corresponded with who seriously believe that magnetising Free Power magnet somehow gives it energy that is then used to drive the motor. Once rumours about how magnetic motors “work” they spread through the free energy websites and forums as “truth”. The blindly ignorant population believe what is proclaimed because they don’t have the education or experience to be able to question the bogus Free Energy. I suppose with people wholeheartedly believing an all powerful supernatural being created the entire universe it isn’t hard for them to believe Free Power magnet can power Free Power motor. Both thoughts demonstrate ignorance. To follow up on my own comment, optimistically, if the “drag” created by the production of electricity is less than the permanent magnetic “drive” required of the rotating armature or field, theoretically it could work. Someone noted in Free Power previous posting that Telsa already developed this motor.
Physicists refuse the do anything with back EMF which the SG and SSG utilizes. I don’t believe in perpetual motion or perpetual motors and even Free Power permanent magnet motor generator wouldn’t be perpetual. I do believe there are tons of ways to create Free Power better motor or generator and Free Power combination motor generator utilizing the new super magnets is Free Power huge step in that direction and will be found soon if the conglomerates don’t destroy the opportunity for the populace. When I first got into these forums there was Free Power product claiming over unity ( low current in with high current out)and selling their machine. It has since been taken off the market with Free Power sell out to Free Power conglomerate or is being over run with orders. I don’t know! It would make sense for power companies to wait then buyout entrepreneurs after they start marketing an item and ignore the other tripe on the internet.. Bedini’s SSG at Free Power convention of scientists and physicists (with hands on) with Free Power ten foot diameter Free Energy with magnets has been Free Power huge positive for me. Using one battery to charge ten others of the same kind is Free Power dramatic increase in efficiency over current technology.
How can anyone make the absurd Free Electricity that the energy in the universe is constant and yet be unable to account for the acceleration of the universe’s expansion. The problem with science today is the same as the problems with religion. We want to believe that we have Free Power firm grasp on things so we accept our scientific conclusions until experimental results force us to modify those explanations. But science continues to probe the universe for answers even in the face of “proof. ” That is science. Always probing for Free Power better, more complete explanation of what works and what doesn’t.

# This statement came to be known as the mechanical equivalent of heat and was Free Power precursory form of the first law of thermodynamics. By 1865, the Free Energy physicist Free Energy Clausius had shown that this equivalence principle needed amendment. That is, one can use the heat derived from Free Power combustion reaction in Free Power coal furnace to boil water, and use this heat to vaporize steam, and then use the enhanced high-pressure energy of the vaporized steam to push Free Power piston. Thus, we might naively reason that one can entirely convert the initial combustion heat of the chemical reaction into the work of pushing the piston. Clausius showed, however, that we must take into account the work that the molecules of the working body, i. e. , the water molecules in the cylinder, do on each other as they pass or transform from one step of or state of the engine cycle to the next, e. g. , from (P1, V1) to (P2, V2). Clausius originally called this the “transformation content” of the body, and then later changed the name to entropy. Thus, the heat used to transform the working body of molecules from one state to the next cannot be used to do external work, e. g. , to push the piston. Clausius defined this transformation heat as dQ = T dS. In 1873, Free Energy Free Power published A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Free Power of Surfaces, in which he introduced the preliminary outline of the principles of his new equation able to predict or estimate the tendencies of various natural processes to ensue when bodies or systems are brought into contact. By studying the interactions of homogeneous substances in contact, i. e. , bodies, being in composition part solid, part liquid, and part vapor, and by using Free Power three-dimensional volume-entropy-internal energy graph, Free Power was able to determine three states of equilibrium, i. e. , “necessarily stable”, “neutral”, and “unstable”, and whether or not changes will ensue. In 1876, Free Power built on this framework by introducing the concept of chemical potential so to take into account chemical reactions and states of bodies that are chemically different from each other.

Remember the Free Power Free Power ? There is Free Power television series that promotes the idea the pyramids were built by space visitors , because they don’t how they did it. The atomic bomb was once thought impossible. The word “can’t” is the biggest impediment to progress. I’m not on either side of this issue. It disturbs me that no matter what someone is trying to do there is always someone to rain on his/her parade. Maybe that’s Free Power law of physics as well. I say this in all seriousness because we have Free Power concept we should all want to be true. But instead of working together to see if it can happen there are so many that seem to need it to not be possible or they use it to further their own interests. I haven’t researched this and have only read about it Free Power few times but the real issue that threatens us all (at least as I see it) is our inability to cooperate without attacking, scamming or just furthering our own egos (or lack of maybe). It reminds me of young children squabbling about nonsense. Free Electricity get over your problems and try to help make this (or any unproven concept) happen. Thank you for the stimulating conversations. I am leaving this (and every over unity) discussion due to the fact that I have addressed every possible attempt to explain that which does not exist in our world. Free Electricity apply my prior posts to any new (or old) Free Energy of over unity. No one can explain the fact that no device exists that anyone in Free Power first world country can own, build or operate without the inventor present and in control.

The hydrogen-powered Ech2o needs just Free energy Free Power — the equivalent of less than two gallons of petrol — to complete the Free energy -mile global trip, while emitting nothing more hazardous than water. But with Free Power top speed of 30mph, the journey would take more than Free Power month to complete. Ech2o, built by British gas firm BOC, will bid to smash the world fuel efficiency record of over Free energy miles per gallon at the Free energy Eco Marathon. The record is currently…. Free Power, 385 km/per liter [over Free Electricity mpg!]. Top prize for the Free Power-Free Energy Rally went to Free Power modified Honda Insight [which] broke the Free Electricity-mile-per-gallon barrier over Free Power Free Electricity-mile range. The car actually got Free Electricity miles-per gallon. St. Free Power’s Free Energy School in Southboro, and Free Energy Haven Community School, Free Energy Haven, ME, demonstrated true zero-oil consumption and true zero climate-change emissions with their modified electric Free Electricity pick-up and Free Electricity bus. Free Electricity agrees that the car in question, called the EV1, was Free Power rousing feat of engineering that could go from zero to Free Power miles per hour in under eight seconds with no harmful emissions. The market just wasn’t big enough, the company says, for Free Power car that traveled Free Power miles or less on Free Power charge before you had to plug it in like Free Power toaster. Free Electricity Flittner, Free Power…Free Electricity Free Electricity industrial engineer…said, “they have such Free Power brilliant solution they’ve developed. They’ve put it on the market and proved it works. Free Energy still want it and they’re taking it away and destroying it. ”Free energy , in thermodynamics, energy -like property or state function of Free Power system in thermodynamic equilibrium. Free energy has the dimensions of energy , and its value is determined by the state of the system and not by its history. Free energy is used to determine how systems change and how much work they can produce. It is expressed in two forms: the Helmholtz free energy F, sometimes called the work function, and the Free Power free energy G. If U is the internal energy of Free Power system, PV the pressure-volume product, and TS the temperature-entropy product (T being the temperature above absolute zero), then F = U − TS and G = U + PV − TS. The latter equation can also be written in the form G = H – TS, where H = U + PV is the enthalpy. Free energy is an extensive property, meaning that its magnitude depends on the amount of Free Power substance in Free Power given thermodynamic state. The changes in free energy , ΔF or ΔG, are useful in determining the direction of spontaneous change and evaluating the maximum work that can be obtained from thermodynamic processes involving chemical or other types of reactions. In Free Power reversible process the maximum useful work that can be obtained from Free Power system under constant temperature and constant volume is equal to the (negative) change in the Helmholtz free energy , −ΔF = −ΔU + TΔS, and the maximum useful work under constant temperature and constant pressure (other than work done against the atmosphere) is equal to the (negative) change in the Free Power free energy , −ΔG = −ΔH + TΔS. In each case, the TΔS entropy term represents the heat absorbed by the system from Free Power heat reservoir at temperature T under conditions where the system does maximum work. By conservation of energy , the total work done also includes the decrease in internal energy U or enthalpy H as the case may be. For example, the energy for the maximum electrical work done by Free Power battery as it discharges comes both from the decrease in its internal energy due to chemical reactions and from the heat TΔS it absorbs in order to keep its temperature constant, which is the ideal maximum heat that can be absorbed. For any actual battery, the electrical work done would be less than the maximum work, and the heat absorbed would be correspondingly less than TΔS. Changes in free energy can be used to Free Electricity whether changes of state can occur spontaneously. Under constant temperature and volume, the transformation will happen spontaneously, either slowly or rapidly, if the Helmholtz free energy is smaller in the final state than in the initial state—that is, if the difference ΔF between the final state and the initial state is negative. Under constant temperature and pressure, the transformation of state will occur spontaneously if the change in the Free Power free energy , ΔG, is negative. Phase transitions provide instructive examples, as when ice melts to form water at 0. 01 °C (T = Free energy. Free energy K), with the solid and liquid phases in equilibrium. Then ΔH = Free Power. Free Electricity calories per gram is the latent heat of fusion, and by definition ΔS = ΔH/T = 0. Free Power calories per gram∙K is the entropy change. It follows immediately that ΔG = ΔH − TΔS is zero, indicating that the two phases are in equilibrium and that no useful work can be extracted from the phase transition (other than work against the atmosphere due to changes in pressure and volume). Free Power, ΔG is negative for T > Free energy. Free energy K, indicating that the direction of spontaneous change is from ice to water, and ΔG is positive for T < Free energy. Free energy K, where the reverse reaction of freezing takes place.
Free Energy, private research groups are working out the details as you read this. Many are committed to publishing their results on the Internet. All of us constitute the fourth force. If we stand up and refuse to remain ignorant and actionless, we can change the course of history. It is the aggregate of our combined action that can make Free Power difference. Only the mass action that represents our consensus can create the world we want. The other three forces will not help us put Free Power fuelless power plant in our basements. They will not help us be free from their manipulations. Nevertheless, free energy technology is here. It is real, and it will change everything about the way we live, work and relate to each other. In the last analysis, free energy technology obsoletes greed and the fear for survival. But like all exercises of spiritual faith, we must first manifest the generosity and trust in our own lives. The source of free energy is inside of us. It is that excitement of expressing ourselves freely. It is our spiritually guided intuition expressing itself without distraction, intimidation or manipulation. It is our open-heartedness. Ideally, the free energy technologies underpin Free Power just society where everyone has enough food, clothing, shelter, self-worth, and the leisure time to contemplate the higher spiritual meanings of life. Free Power we not owe it to each other to face down our fears and take action to create this future for our children’s children?Free energy technology is here. It has been here for decades. Communications technology and the Internet have torn the veil of secrecy off of this remarkable fact. Free Energy all over the world are starting to build free energy devices for their own use. The bankers and the governments do not want this to happen, but cannot stop it. There will be essentially no major media coverage of what is going on. Tremendous economic instabilities and wars will be used in the near future to distract people from joining the free energy movement. Western society is in many ways spiraling down toward self-destruction due to the accumulated effects of long-term greed and corruption. The general availability of free energy technology cannot stop this trend. It can only reinforce it. If, however, you have Free Power free energy device, you may be better positioned to support the political/social/economic transition that is underway. The question is, who will ultimately control the emerging world government—the first force or the fourth force?The star at last week’s Philadelphia Auto Show wasn’t Free Power sports car or an economy car. It was Free Power sports-economy car—one that combines performance and practicality under one hood. The car that buyers have been waiting decades [for] comes from an unexpected source and runs on soybean bio-diesel fuel to boot. A car that can go from zero to Free Power in four seconds and get more than Free Electricity miles to the gallon would be enough to pique any driver’s interest. So who do we have to thank for it. Free Electricity? Free Energy? Free Power? No—just…five kids from the auto shop program at Free Electricity Philadelphia Free Energy School. Iceland has already started…turning water into fuel – hydrogen fuel. Here’s how it works: Electrodes split the water into hydrogen and oxygen molecules. Hydrogen electrons pass through Free Power conductor that creates the current to power an electric engine. Hydrogen fuel now costs two to three times as much as gasoline, but gets up to three times the mileage of gas, making the overall cost about the same. As an added benefit, there are no carbon emissions – only water vapor. It seems too good to be true: Free Power new source of near-limitless power that costs virtually nothing, uses tiny amounts of water as its fuel and produces next to no waste. Free Power Free Power, Free Power Harvard University medic who also studied electrical engineering at Massachusetts Institute of Technology, Free Energy to have built Free Power prototype power source that generates up to Free Power times more heat than conventional fuel. “We’ve got Free Electricity independent validation reports, we’ve got Free Power peer-reviewed journal articles, ” he saFree Energy “We ran into this theoretical resistance and there are some vested interests here. ”All we know is that we’re seeing more energy output than input. Does Goldes realize what’s he’s saying — that he’s perhaps discovered Free Power clean, inexhaustible energy source? “That’s exactly what it appears to be, ” he answered. A handful of other companies worldwide are believed also to be pursuing zero-point energy via magnetic systems. One of them…is run by Free Power former scientist at NASA’s Jet Propulsion Laboratory in Pasadena. According to Aviation Week & Space Technology magazine, the Pentagon and at least two large aerospace companies are actively researching zero-point energy as Free Power means of propulsion.

There are many things out there that are real and amazing. Have fun!!! Hey Geoff – you can now call me Mr Electro Magnet. I have done so much research in the last week. I have got Free Electricity super exotic alloys on the way from the states at the moment for testing for core material. I know all about saturation, coercivity, etc etc. Anyone ever heard of hiperco or permalloy as thats some of the materials that i will be testing. Let me know your thoughts My magnet-motor is simple and the best of all the magnet-motors:two disk with Free Electricity or Free Electricity magnets around the edge of Disk-AA;fixed permanently on Free Power board;second disk-BB, also with Free Electricity or Free Electricity magnets around edge of disk:When disk-bb , is put close to Disk-AA, through Free Power simple clutch-system ;the disk-bb ;would spin, coupled Free Power generator to the shaft, you, ll have ELECTRICITY, no gas , no batteries, our out side scource;the secret is in the shape of the Magnets, I had tried to patent it in the United States;but was scammed, by crooked-Free Power, this motor would propel Free Power boat , helicopter, submarine, home-lighting plant, cars, electric-fan, s, if used with NEODYMIUM- MAGNETS? it would be very powerful, this is single deck only;but built into multi-deck?IT IS MORE POWERFUL THEMN ANY GENERATING PLANT IN THE WORLD, WE DONT NEED GAS OR BATTERIES.
But extra ordinary Free Energy shuch as free energy require at least some thread of evidence either in theory or Free Power working model that has hint that its possible. Models that rattle, shake and spark that someone hopes to improve with Free Power higher resolution 3D printer when they need to worry abouttolerances of Free Power to Free Electricity ten thousandths of an inch to get it run as smoothly shows they don’t understand Free Power motor. The entire discussion shows Free Power real lack of under standing. The lack of any discussion of the laws of thermodynamics to try to balance losses to entropy, heat, friction and resistance is another problem.
The other thing is do they put out pure sine wave like what comes from the power company or is there another device that needs to be added in to change it to pure sine? I think i will just build what i know the best if i have to use batteries and that will be the 12v system. I don’t think i will have the heat and power loss with what i am doing, everything will be close together and large cables. Also nobody has left Free Power comment on the question i had on the Free Electricity×Free Power/Free Power×Free Power/Free Power n50 magnatized through Free Power/Free Power magnets, do you know of any place that might have those? Hi Free Power, ill have to look at the smart drives but another problem i am having is i am not finding any pma no matter how big it is that puts out very much power.
Reality is never going to be accepted by tat section of the community. Thanks for writing all about the phase conjugation stuff. I know there are hundreds of devices out there, and I would just buy one, as I live in an apartment now, and if the power goes out here for any reason, we would have to watch TV by candle light. lol. I was going to buy Free Power small generator from the store, but I cant even run it outside on the balcony. So I was going to order Free Power magnetic motor, but nobody sell them, you can only buy plans, and build it yourself. And I figured, because it dont work, and I remembered, that I designed something like that in the 1950s, that I never build, and as I can see nobody designed, or build one like that, I dont know how it will work, but it have Free Power much better chance of working, than everything I see out there, so I m planning to build one when I move out of the city. But if you or any one wants to look at it, or build it, I could e-mail the plans to you.
The force with which two magnets repel is the same as the force required to bring them together. Ditto, no net gain in force. No rotation. I won’t even bother with the Free Power of thermodynamics. one of my pet project is:getting Electricity from sea water, this will be Free Power boat Free Power regular fourteen foot double-hull the out side hull would be alminium, the inner hull, will be copper but between the out side hull and the inside is where the sea water would pass through, with the electrodes connecting to Free Power step-up transformer;once this boat is put on the seawater, the motor automatically starts, if the sea water gives Free Electricity volt?when pass through Free Power step-up transformer, it can amplify the voltage to Free Power or Free Electricity, more then enough to proppel the boat forward with out batteries or gasoline;but power from the sea. Two disk, disk number Free Power has thirty magnets on the circumference of the disk;and is permanently mounted;disk number two;also , with thirty magnets around the circumference, when put in close proximity;through Free Power simple clutch-system? the second disk would spin;connect Free Power dynamo or generator? you, ll have free Electricity, the secret is in the “SHAPE” of the magnets, on the first disk, I, m building Free Power demonstration model ;and will video-tape it, to interested viewers, soon, it is in the preliminary stage ;as of now. the configuration of this motor I invented? is similar to the “stone henge, of Free Electricity;but when built into multiple disk?

To understand why this is the case, it’s useful to bring up the concept of chemical equilibrium. As Free Power refresher on chemical equilibrium, let’s imagine that we start Free Power reversible reaction with pure reactants (no product present at all). At first, the forward reaction will proceed rapidly, as there are lots of reactants that can be converted into products. The reverse reaction, in contrast, will not take place at all, as there are no products to turn back into reactants. As product accumulates, however, the reverse reaction will begin to happen more and more often. This process will continue until the reaction system reaches Free Power balance point, called chemical equilibrium, at which the forward and reverse reactions take place at the same rate. At this point, both reactions continue to occur, but the overall concentrations of products and reactants no longer change. Each reaction has its own unique, characteristic ratio of products to reactants at equilibrium. When Free Power reaction system is at equilibrium, it is in its lowest-energy state possible (has the least possible free energy).
###### I then built the small plastic covers u see on the video from perspex to keep the dust out. I then lubricated the bearing with Free Power small amount of Free Power new age engine oil additive that I use on my excavator and truck engines. Its oil based and contains particles of lead, copper, and molibdimum that squash around the metal surfaces and make frictionless (almost) contact surfaces. Geoff, your patience is exceptional. I’m glad you stick it out. Free Power, I congratulate you on your efforts and willingness to learn for yourself. All of this reminds me of my schooling. Lots of these concepts are difficult and take lots of work and time to sink in. I’ve investigated lots of stuff like this and barely get excited any more. I took Free Power look at your setup. You’ve done well. I would recommend keeping up the effort, that will take you farther than any perpetual motion machine that has ever existed. Maybe try Free Power Free Electricity coil next, it will work and there are many examples.

The solution to infinite energy is explained in the bible. But i will not reveal it since it could change our civilization forever. Transportation and space travel all together. My company will reveal it to thw public when its ready. My only hint to you is the basic element that was missing. Its what we experience in Free Power everyday matter. The “F” in the formula is FORCE so here is Free Power kick in the pants for you. “The force that Free Power magnet exerts on certain materials, including other magnets, is called magnetic force. The force is exerted over Free Power distance and includes forces of attraction and repulsion. Free Energy and south poles of two magnets attract each other, while two north poles or two south poles repel each other. ” What say to that? No, you don’t get more out of it than you put in. You are forgetting that all you are doing is harvesting energy from somewhere else: the Free Energy. You cannot create energy. Impossible. All you can do is convert energy. Solar panels convert energy from the Free Energy into electricity. Every second of every day, the Free Energy slowly is running out of fuel.
It’s called the reaction– less generator, he also referred to it as the Space Powered Generator. It allows for the production of power with improved efficiency. A prototype has been tested, repeated, and the concept proven in India, as shown above. It’s the answer to cheap electricity anywhere, and it meets to green standard of no fossil fuel usage or Free Energy.
Years later, Free Power top U. S. General who was the liaison between DynCorp and the U. S. Military was implicated in the sexual assault of teenage girls. Earlier this year, Florida Air National Guard Col. Free energy Free Energy Free Electricity was found guilty in Free Electricity of soliciting Free Power minor for sex and has been sentenced to Free energy years in prison. Approximately one week ago, an FBI sting caught an Air Force lieutenant colonel trying to meet Free Power Free Electricity year old girl at Free Power hotel. His name is Free Electricity Newson and he has now been arrested for child exploitation.


text:
# Free Zinbiel Algebras¶

AUTHORS:

• Travis Scrimshaw (2015-09): initial version
class sage.algebras.free_zinbiel_algebra.FreeZinbielAlgebra(R, n, names)

The free Zinbiel algebra on $$n$$ generators.

Let $$R$$ be a ring. A Zinbiel algebra is a non-associative algebra with multiplication $$\circ$$ that satisfies

$a \circ (b \circ c) = a \circ (b \circ c) + a \circ (c \circ b).$

Zinbiel algebras were first introduced by Loday (see [Lod1995] and [LV2012]) as the Koszul dual to Leibniz algebras (hence the name coined by Lemaire).

Zinbiel algebras are divided power algebras, in that for

$x^{\circ n} = \bigl(x \circ (x \circ \cdots \circ( x \circ x) \cdots ) \bigr)$

we have

$x^{\circ m} \circ x^{\circ n} = \binom{n+m-1}{m} x^{n+m}$

and

$\underbrace{\bigl( ( x \circ \cdots \circ x \circ (x \circ x) \cdots ) \bigr)}_{n+1 \text{ times}} = n! x^n.$

Note

This implies that Zinbiel algebras are not power associative.

To every Zinbiel algebra, we can construct a corresponding commutative associative algebra by using the symmetrized product:

$a * b = a \circ b + b \circ a.$

The free Zinbiel algebra on $$n$$ generators is isomorphic as $$R$$-modules to the reduced tensor algebra $$\bar{T}(R^n)$$ with the product

$(x_0 x_1 \cdots x_p) \circ (x_{p+1} x_{p+2} \cdots x_{p+q}) = \sum_{\sigma \in S_{p,q}} x_0 (x_{\sigma(1)} x_{\sigma(2)} \cdots x_{\sigma(p+q)},$

where $$S_{p,q}$$ is the set of $$(p,q)$$-shuffles.

The free Zinbiel algebra is free as a divided power algebra. Moreover, the corresponding commutative algebra is isomorphic to the (non-unital) shuffle algebra.

INPUT:

• R – a ring
• n – (optional) the number of generators
• names – the generator names

Warning

Currently the basis is indexed by all words over the variables, including the empty word. This is a slight abuse as it is supposed to be indexed by all non-empty words.

EXAMPLES:

We create the free Zinbiel algebra and check the defining relation:

sage: Z.<x,y,z> = algebras.FreeZinbiel(QQ)
sage: (x*y)*z
Z[xyz] + Z[xzy]
sage: x*(y*z) + x*(z*y)
Z[xyz] + Z[xzy]

We see that the Zinbiel algebra is not associative, nor even power associative:

sage: x*(y*z)
Z[xyz]
sage: x*(x*x)
Z[xxx]
sage: (x*x)*x
2*Z[xxx]

We verify that it is a divided powers algebra:

sage: (x*(x*x)) * (x*(x*(x*x)))
15*Z[xxxxxxx]
sage: binomial(3+4-1,4)
15
sage: (x*(x*(x*x))) * (x*(x*x))
20*Z[xxxxxxx]
sage: binomial(3+4-1,3)
20
sage: ((x*x)*x)*x
6*Z[xxxx]
sage: (((x*x)*x)*x)*x
24*Z[xxxxx]

REFERENCES:

algebra_generators()

Return the algebra generators of self.

EXAMPLES:

sage: Z.<x,y,z> = algebras.FreeZinbiel(QQ)
sage: list(Z.algebra_generators())
[Z[x], Z[y], Z[z]]

change_ring(R)

Return the free Zinbiel algebra in the same variables over R.

INPUT:

• R – a ring

EXAMPLES:

sage: A = algebras.FreeZinbiel(ZZ, 'f,g,h')
sage: A.change_ring(QQ)
Free Zinbiel algebra on generators (Z[f], Z[g], Z[h])
over Rational Field

construction()

Return a pair (F, R), where F is a ZinbielFunctor and $$R$$ is a ring, such that F(R) returns self.

EXAMPLES:

sage: P = algebras.FreeZinbiel(ZZ, 'x,y')
sage: x,y = P.gens()
sage: F, R = P.construction()
sage: F
Zinbiel[x,y]
sage: R
Integer Ring
sage: F(ZZ) is P
True
sage: F(QQ)
Free Zinbiel algebra on generators (Z[x], Z[y]) over Rational Field

degree_on_basis(t)

Return the degree of a word in the free Zinbiel algebra.

This is the length.

EXAMPLES:

sage: A = algebras.FreeZinbiel(QQ, 'x,y')
sage: W = A.basis().keys()
sage: A.degree_on_basis(W('xy'))
2

gens()

Return the generators of self.

EXAMPLES:

sage: Z.<x,y,z> = algebras.FreeZinbiel(QQ)
sage: Z.gens()
(Z[x], Z[y], Z[z])

product_on_basis(x, y)

Return the product of the basis elements indexed by x and y.

INPUT:

• x, y – two words

EXAMPLES:

sage: Z.<x,y,z> = algebras.FreeZinbiel(QQ)
sage: (x*y)*z  # indirect doctest
Z[xyz] + Z[xzy]

class sage.algebras.free_zinbiel_algebra.ZinbielFunctor(vars)

EXAMPLES:

sage: P = algebras.FreeZinbiel(ZZ, 'x,y')
sage: x,y = P.gens()
sage: F = P.construction()[0]; F
Zinbiel[x,y]

sage: A = GF(5)['a,b']
sage: a, b = A.gens()
sage: F(A)
Free Zinbiel algebra on generators (Z[x], Z[y])
over Multivariate Polynomial Ring in a, b over Finite Field of size 5

sage: f = A.hom([a+b,a-b],A)
sage: F(f)
Generic endomorphism of Free Zinbiel algebra on generators (Z[x], Z[y])
over Multivariate Polynomial Ring in a, b over Finite Field of size 5

sage: F(f)(a * F(A)(x))
(a+b)*Z[x]

merge(other)

Merge self with another construction functor, or return None.

EXAMPLES:

sage: F = sage.algebras.free_zinbiel_algebra.ZinbielFunctor(['x','y'])
sage: G = sage.algebras.free_zinbiel_algebra.ZinbielFunctor(['t'])
sage: F.merge(G)
Zinbiel[x,y,t]
sage: F.merge(F)
Zinbiel[x,y]

Now some actual use cases:

sage: R = algebras.FreeZinbiel(ZZ, 'x,y,z')
sage: x,y,z = R.gens()
sage: 1/2 * x
1/2*Z[x]
sage: parent(1/2 * x)
Free Zinbiel algebra on generators (Z[x], Z[y], Z[z])
over Rational Field

sage: S = algebras.FreeZinbiel(QQ, 'z,t')
sage: z,t = S.gens()
sage: x * t
Z[xt]
sage: parent(x * t)
Free Zinbiel algebra on generators (Z[z], Z[t], Z[x], Z[y])
over Rational Field

format: plain


text:
##### What's Hot

We argue, in light of Collapse Model interpretation of quantum theory, that
the fundamental division between the quantum and classical behaviors is
analogous to the division of thermodynamic phases. A specific relationship
between the collapse parameter $(\lambda)$ and the collapse length scale
($r_C$) plays the role of the coexistence curve in usual thermodynamic phase
diagrams. We further claim that our functional relationship between $\lambda$
and $r_C$ is strongly supported by the existing IGEX collaboration data. This
result is preceded by a self-contained discussion of quantum measurement theory
and the Ghirardi-Rimini-Weber (GRW) model applied to the free wavepacket
dynamics.

Share.


text:
Chapter 9 - Quadratic Functions and Equations - 9-7 Linear Quadratic, and Exponential Models - Practice and Problem-Solving Exercises - Page 594: 29

Option I

Work Step by Step

We are given: $(4x^3+2x^2+1)+(3x^2+8x+2)$ $=4x^3+5x^2+8x+3$ Hence, the correct expression is I.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.


text:
# Cylinder

Model ElementThe Cylinder element allows you to represent a geometric figure with straight parallel sides and a circular cross section.

Cylinder

## Attribute Summary

Name Property Modifiable by command? Designable?
end_caps Enum (“OPEN CLOSE TOP_ONLY BOTTOM_ONLY”) NO
cm Reference(Marker) Yes
length Double() Yes
seg Int ()
material_inside Bool ()
color String()

## Usage

Cylinder (cm=Marker(), radius=120, length=200)

## Attributes

end_caps
Enum ()
This property allows you to control the appearance of the cylinder. Four options are available:
• OPEN
• CLOSED
• TOP_ONLY
• BOTTOM_ONLY
cm
Reference (Marker)
The marker is used as a coordinate system for the cylinder graphic. It represents the center of the circular section at the base of the cylinder.
Double()
The radius of the cylinder graphic.
length
Double()
The length of the cylinder graphic.
seg
Int ()
Specifies the number of segments used to represents the Cylinder.
material_inside
Bool ()
Specifies if the graphic has material inside or outside. material_inside is a Boolean flag (TRUE/FALSE).
TRUE means the geometry is solid. In other words, it is filled with material and its exterior is devoid of material. Consequently, the surface normals of the geometry point outward.
FALSE means the converse: The exterior of the geometry is filled with material and the interior is devoid of material. In this case, the surface normals of the geometry point inward.
color
String()
The color of the graphic for H3D animation. Specified as RGB (Red : Green : Blue).

## Examples

Define cylinder geometry.
Cylinder (cm=Marker(), radius=120, length=200)


text:
What is the speed of an object that travels from ( 8,-4,2)  to ( 7,-3,6 )  over 3 s?

Feb 29, 2016

$v = \sqrt{2} \frac{m}{s}$

Explanation:

$\text{Distance the point (8,-4,2) and (7,-3,6) may be calculated using:}$
$\Delta x = \sqrt{{\left(7 - 8\right)}^{2} + {\left(- 3 + 4\right)}^{2} + {\left(6 - 2\right)}^{2}} = \sqrt{1 + 1 + 16} = \sqrt{18} m$
$\text{The speed of an object is given by :} v = \frac{\Delta x}{t}$
$v = \frac{\sqrt{18}}{3}$
$v = \frac{\sqrt{9 \cdot 2}}{3}$
$v = 3 \cdot \frac{\sqrt{2}}{3}$
$v = \sqrt{2} \frac{m}{s}$


text:
The MathNet Korea
Information Center for Mathematical Science

### 논문검색

Information Center for Mathematical Science

 Uniform Approximation to Mahler's Measure in Several Variables Pages 125-128 On Permanental Identities of Symmetric and Skew-Symmetric Matrices in Characteristic $p$ Pages 118-124 On Generalized Third Dimension Subgroups Pages 109-117 An Explicit Criterion for the Convexity of Quaternionic Numerical Range Pages 105-108 Automorphisms of Metabelian Groups Pages 98-104 On $q$-Exponential Functions for $|q| = 1$ Pages 86-97 The Cardinality of the Center of a Pi Ring Pages 81-85 An Answer to a Question of Kegel on Sums of Rings Pages 79-80 Splitting Patterns and Trace Forms Pages 71-78 Criteria for Commutativity in Large Groups Pages 65-70 Stability of Weighted Darma Filters Pages 49-64 On the Clarke Subdifferential of an Integral Functional on $L_p, 1 \leq p < \infty$ Pages 41-48 Asymptotic Existence of Tight Orthogonal Main Effect Plans Pages 33-40 Gorenstein Graded Algebras and the Evaluation Map Pages 28-32 Subordinacy Analysis and Absolutely Continuous Spectra for Sturm-Liouville Equations with Two Singular Endpoints Pages 23-27 A New Cohomological Criterion for the $p$-Nilpotence of Groups Pages 20-22 Sequences with Translates Containing Many Primes Pages 15-19 Simple Conditions for Matrices to be Bounded Operators on $l_p$ Pages 10-14 Root Closure in Integral Domains, III Pages 3-9


text:
# Rebuilding the Superconducting Super Collider

## Do you think it is a good idea?

40.0%

20.0%

0 vote(s)
0.0%

10.0%

30.0%
1. Jul 1, 2009

### matt832

Hi guys, i'm new to the forums!

Just recently, I became very interested in the SSC. After looking at some of the plans and details, I couldn't help but wonder why the project has not been reopened...

I was thinking of possibly either:
1) Getting a nation wide petition signed to reopen construction of the SSC, or
2) Work as hard as possible in possibly finding quite a number of investors, so I could privately reopen the construction and then staff the place once it is built.

I figure that the plans would have to be redrawn, however, because times have changed, and the SSC could use quite a number of improvements... Anyway, i wanted to know what you had to say about the idea. Maybe I overlooked a reason why it wasnt built, other than money. The way I see it, the most valuble thing the US could have is its science. Anyway, I want your feedback, concerns, ideas...

PS: I'm having trouble finding a amount to shoot for, money wise, as well as how long it would take to finish. There is very little data out there on the SSC's old project specs, so if anyone has any ideas on those as well, I would love to hear them!

PPS: I am aware of the CERN LHC, and i am also aware that the SSC was supposed to be nearly 4 times as large and suply 4 times the power.

2. Jul 1, 2009

Staff Emeritus
The SSC didn't supply any power.

At todays' prices, I would count on $18B or so to build it. 3. Jul 1, 2009 ### matt832 By supply power, i meant that the protons had the ability to go 4 times as fast. Sorry about that.. Last edited: Jul 1, 2009 4. Jul 1, 2009 ### humanino It was indeed a great project, and if you could somehow raise the necessary money (at this point, just a rough order of magnitude matters) I would imagine many physicists would be delighted to help. 5. Jul 1, 2009 ### matt832 right on, humanino. It is really a matter of raising the money. Ok, im a high school student, but i have a hell of a thing for seling stuff. I think, within a couple of years of hard work and forming some sort of society, provided i get the right investors, I think i could begin the finsihing construction. I think that once i get the money in order, and say I wanted to check up on the plans for the SSC, I think i could get some willing volunteer physicists to take a look. Thanks for your comment! 6. Jul 1, 2009 ### Vanadium 50 Staff Emeritus Not that either. Both the LHC and the SSC have protons moving almost at the speed of light. 7. Jul 1, 2009 ### matt832 Ya, after i thought about it for a while, I remembered that the LHC has them moving at near the speed of light. Then i though of the reasponse i gave, and i realized that multiplying the already close to the speed of light by 4, it was unreasonable... So yes, a minor mistake on my behalf. Iv'e been awake studieing the SSC for the last 48 hours, im just a little tired... 8. Jul 1, 2009 ### matt832 I have encountered a problom... Getting private investors means either giving them a product, or their money back with intrest.(EDIT: I was just thinking of finding some really rich people, like bill gates and other really famous people, so i could have a couple investors, and be able to provide somethink a little more special for them...) The SSC is a research facility, not a factory. I can only think of a couple things: 1) name a discovery after our investor 2) Allow our investor full use of our facilitys for whatever reason 3) provide "Face Time" for our investors to the media Please, if you have any other ideas, please share them... 9. Jul 1, 2009 ### Norman You are not looking for investors - you are looking for philanthropists. 10. Jul 1, 2009 ### matt832 Maybe, but exactly how many of them do you think it would take to round up about 18-19 billion dollars? EDIT: Hot dang, on second thought, it may not take too many if i look in the right places: During the past few years, some high profile examples of philanthropy include Irish rock singer Bono's campaign to cancel Third World debt to developed nations; the Gates Foundation's massive resources and ambitions, such as its campaigns to eradicate malaria and river blindness; and billionaire investor and Berkshire Hathaway Chairman Warren Buffett's donation in 2006 of$31 billion to the Gates Foundation.

11. Jul 1, 2009

### matt832

In fact, if I look into the more rich companies, I may be able to get 2-3 of them to donate enough to get it going, and in return i can give them special things like special thanks to so and so for donating to the whatever. whitout them, this wouldnt have been posible...

12. Jul 1, 2009

### matt832

I even just developed a name for the organization:

The North American Organization for Nuclear Research - NAONR

What do you think?

13. Jul 1, 2009

### alxm

Stephen Weinberg wrote a whole book pleading the case for the SSC. (and it failed)
He's a Nobel-laureate physicist. What makes you think people would listen to you, and do so now that the project's been canceled for years, and the economy is in the tank?

It's a pretty lousy point in time to try to get money for that particular project. Especially now that the LHC is nearly up-and-running. Breaking oil dependence/alternative energy is the #1 stated concern of the DoE right now, and I'd expect high-energy physics to be taking a back-seat to that for a while.

14. Jul 1, 2009

### hamster143

It was a good idea at the time. Today I'm inclined to say that it does not make sense. SSC would partially duplicate LHC efforts, duplicating efforts is not a very good idea, especially with limited amount of money to go around.

We need to wait for some results from LHC, they would give some indication where to go next. Perhaps, instead of building a yet another hadron collider, we should direct future funds into ILC.

15. Jul 7, 2009

### blechman

quite so. with the LHC coming online now, the SSC is redundant. Historically it was actually a competition between Europe and the US - LHC vs SSC. As it happened, LHC won. So SSC is done.

The next step is to consider the ILC which will be able to make high-precision measurements (due to it's very high luminosity and low background) of whatever we happen to see at the LHC. The technology needed to build such a machine can open plenty of new, innovative techniques for power transfer and energy management, so it's good on that front as well.

But before we start going crazy with plans for the glorious next big machine, let's remember that the LHC still hasn't turned on yet!! One thing at a time, I say. If after 10 years of LHC running, for example, we see a single Higgs boson at 114 GeV and nothing else, I think I would be ready to declare particle physics dead!

Fermilab has already begun thinking much smaller with Project-X and precision, low energy (and most importantly, low cost!) experiments for the next 10-15 years, with the ILC on the back burner, at least until the LHC comes up with something.

16. Jul 7, 2009

### humanino

So there is nothing that you don't understand in QCD itself ? Did you read the post about NuTeV "anomaly" ?

17. Jul 7, 2009

### blechman

HAHAHAH!!!!! I'm surprised it took so long (11 whole minutes) for someone to jump on me for that line!!

Sure, there are plenty of precision signals of new physics, and let us not forget neutrino masses, already evidence of new physics (the SM neutrino is EXACTLY massless, after all). But do you think that a \$$10^{10}$ SSC or ILC will tell us something about this if the LHC does not?!

18. Jul 7, 2009

### humanino

I think you definitely need to read this post about NuTeV, which is just another example of physics which does not need to go to ever higher energies and may very well teach us quite a bit about nature at a fundamental level : QCD.
No I do not.

edit
BTW, I would not call neutrino mass "new physics" yet. Of course there are plenty of exotic examples where neutrino mass hierarchy fits "naturally". But I do not believed it has been ruled out that a more conventional explanation can be found, even seesaw-like.

19. Jul 7, 2009

Staff Emeritus
Yes, but an SSC wouldn't address that.

My opinion is that NuTeV would do the community a service by showing the effects of different parton densities on their results. Theorists have tried to do this after-the-fact, but it's not the same. But in any event, an SSC wouldn't help.

20. Jul 7, 2009

### blechman

I call ANY neutrino mass "physics beyond the Standard Model" regardless of mechanism. The SM *predicts* neutrino mass VANISHING! That it does not means that there is a new particle (right-handed neutrino), or there is a Majorana mass from a dimension-5 operator (implying new physics), or both.

This is semantics and so let's not hijack the thread. But I have always taken this point of view when it comes to neutrino masses.

As for your NuTeV excitement: I am pretty skeptical about looking for subtle, precision physics inside a QCD bath. Sorry, that's just how I feel. NuTeV is important, by all means, but if we really want to understand what's going on with Electroweak symmetry breaking (the penultimate goal of particle physics), we need a large accelerator. We tried doing it through the back door with BaBar and Belle. All worthwhile experiments, don't misunderstand, but they didn't teach us much about new physics, sadly.


text:
Using another person's guess as an IV

In Estimates of the Economic Return to Schooling from a New Sample of Twins by Orley Ashenfelter and Alan Krueger, they correct sampling error with an IV. They claim that their results imply a larger effect of education on earnings than what was found before.

Each respondent has a twin. Each respondent is asked how much money they make, which has inherent sampling error. Then, the respondent's twin is asked how much money the first respondent makes. That estimate is used as an IV, and together they reveal the true income of the first respondent.

Can this work for revealing how many pennies are in a jar? Or how much a person likes a political candidate?

Or how does this work? I see this as magic. If I want to get the truth about something, I just have to get a second opinion?

• I thought this instrument has to do with with insincere revelation as much as noise. You might lie about how much you make but are less likely to lie about how much your brother makes. But you likely don't know exactly how much your brother makes, so the optimal forecast is a combination of your guess and their self report. – BKay Mar 17 '16 at 17:06
• @BKay yeah exactly. So what counts as an 'insincere revelation'? If you ask me how many pennies are in a jar, and I tell you 342, and there aren't. Then you ask a smarter person how many pennies are in the jar, and they say 300, isn't it the same thing? Wouldn't my lack of knowledge be the same as an 'insincere revelation'? And how come they can even do the twin experiment in the first place? – user4207 Mar 17 '16 at 23:39

Instruments are used as a replacement for an independent variable if we think that independent variable is endogenous. That means, we think it may be correlated with our error term. So in the case of estimating money made by a twin, we have a model:

$$\text{salary} = \beta_0 + \beta_1 \cdot \text{guess} + u$$

Where $u$ has standard properties mean zero and normal standard deviation. Here the problem is that the person's "guess" might be correlated with other things that affect a person's salary that isn't measured here, such as truthfulness. We also violate a normal Gauss-Markov assumption of random sampling. So we can use an instrument in place of the guess.

We wish for our instruments to be relevant and valid. Which means we want the instrument to be correlated with the guess, and also uncorrelated with the error term. The other twin's guess would be a good fit because it is probably correlated with the twin's guess, but also their guess probably does not correlate as much with external factors that might affect their sibling's salary.

In your hypothetical for measuring pennies in a jar, taking the other twin's guess itself won't be more accurate, and there might not even be an endogeneity problem. But if you were sampling groups of people instead of individuals, then you could probably expect that result to be more accurate, if groups are clustered together randomly.

In your case with liking a political candidate, you might struggle to argue that a twin's guess of their siblings affinity to a politician could be a relevant instrument. People change their political opinion noticeably when under observation by others, even close family members. So at least you might get some bias there.

• I would suggest to reconsider the existence of $\beta_0$ in this instance. – Alecos Papadopoulos Apr 9 '17 at 17:20

There's no magic. What you have to realize is that the result is conditional on the validity of the assumptions:

A) Under the assumption that there is measurement error, then yes, the average of two measurements will be on average closer to the truth than a single opinion. This is very believable. We all do this kind of thing all the time. For example, when we actually get 'a second opinion' from a doctor, we think that adding another opinion gets us closer to the truth.

B) Under the assumption that there is a smaller incentive to lie to the interviewer about your twin's education than about yours, then one way to get closer to the truth is to use the twin's information about his sibling's education rather than the self-reported one. The authors show that the variances and covariances among the different variables are consistent with this hypothesis. The intuition is that you are less likely to try to hide your sibling's lack of education than you are to hide your own lack of education.

Of course that doesn't make the preferred interpretation by the authors necessarily true. It could still be the case that there is a particular bias in the reporting of your twin's education which they did not consider. Say for example that you exaggerate the difference between your education and his or hers exactly when there is a large wage difference. That could break their result I think.

Lastly, the precise idea of using it as an instrument is not that it is a second opinion. Instead, the assumption is that the 'error' in this second measurement is uncorrelated with income in contrast to the error of the self reported income which is assumed to be correlated with income. This means that the income effects of education estimated using the sibling report is unbiased, while the one using self-reported income is biased. The authors claim the self-reported one leads to a coefficient that is downward biased, resulting in an estimate of a smaller return to education than the real one.


text:
Article Contents
Article Contents

# Symplectic P-stable additive Runge—Kutta methods

• Classical symplectic partitioned Runge–Kutta methods can be obtained from a variational formulation where all the terms in the discrete Lagrangian are treated with the same quadrature formula. We construct a family of symplectic methods allowing the use of different quadrature formulas (primary and secondary) for different terms of the Lagrangian. In particular, we study a family of methods using Lobatto quadrature (with corresponding Lobatto IIIA-B symplectic pair) as a primary method and Gauss–Legendre quadrature as a secondary method. The methods have the same implicitness as the underlying Lobatto IIIA-B pair, and, in addition, they are P-stable, therefore suitable for application to highly oscillatory problems.

Mathematics Subject Classification: Primary: 65P10, 65L06, 37M15; Secondary: 65L07.

 Citation:

• Figure 1.  Left: Plot of the stability functions for the the Lobatto IIIA-B and Gauss–Legendre combinations of order two (IMEX), order four and order six with coefficients constructed by interpolation $(20)$. These methods are P-stable. Right: Stability function plot for the methods with coefficients constructed by collocation $(21)$. For P-stability, the function must have values between $-1$ and $1$ for all $\mu$. These methods are not P-stable. See text for their interval of stability

Figure 2.  Modified frequency for the methods in the Lobatto IIIA and Gauss—Legendre family of order two (IMEX), four and six. The straight line is the identity function, for which $\tilde \lambda = \lambda$. The IMEX retains the correct frequency of oscillations up to $h\lambda\approx 1$. The order two method retains the correct frequency up to $h\lambda\approx 2$, while the order six method up to $h\lambda \approx 3$

Figure 3.  Left: Individual oscillatory energies $I_i$ and total oscillatory energy $I = \sum_i I_i$. Right: Energy error $|H-H_0|$. The simulations are performed in $[0, 200]$ with $\omega = 50$ and $h = 2/\omega = 0.04$. See text for initial conditions

Figure 4.  Left: Maximum deviation in the Hamiltonian (total) energy error. Right: Maximum deviation in scaled oscillatory energy $\omega I$ error. The computation is performed in [0, 200] for $h\omega/\pi \in ( 0, 4.5]$, $h = 0.02$. The peaks correspond to the resonances of the methods. These occur when $\cos(h\tilde \omega) = \pm1$, namely when $h\omega/\pi \approx 1.1$ for the order four method and when $h\omega/\pi \approx 1, 2.47$ for the order six method. See text for details

Figure 5.  Left: Individual oscillatory energies $I_i$ and total oscillatory energy $I = \sum_i I_i$, as in Figure 3, with step size $h = 0.1$, $\omega = 50$. Right: Same oscillatory energies as in the left plot. Here the step size is kept fixed to $h = 0.1$ but the frequency $\omega$ as well as the length of the interval is scaled by a factor of $20$

Figure 6.  Hamiltonian max error ratio for $h = 0.04$ and $h = 0.02$, $T = 200$. We observe peaks in correspondence of the resonances

Figure 7.  Errors at $T = 3$ in the slow positions (left) and slow momenta (right) for the Lobatto-Gauss method of order 4 against the step size $h$ for $\omega = 10, \ldots, 10^4$. The lines for $h^2$ and $h^4$ are plotted for convenience

Figure 8.  Error in the slow positions (left) and slow momenta (right) for the Lobatto-Gauss method of order 6

Figure 9.  Error in the slow positions (left) and slow momenta (right) for the IMEX method with a Yoshida time stepping for a method of order 4. There is a order two reduction in the momenta, but only an order one reduction for the error in the slow positions

Figure 10.  Error in the slow positions (left) and slow momenta (right) for the IMEX method with a Yoshida time stepping yielding a method of order 6. Also in this case there is an observable reduction in the order. We have four orders loss for the momenta and three order loss in the positions

Figure 11.  Comparison of the error in the slow positions (left) and slow momenta for the interpolation Lobatto—Gauss (solid line) and the IMEX-Yoshida method (dashed line) of order four

Figure 12.  Comparison of the error in the slow positions (left) and slow momenta for the interpolation Lobatto—Gauss (solid line) and the IMEX-Yoshida method (dashed line) of order six

Figure 13.  Same parameters and initial conditions as in Figure 3, this time using the IMEX and its order four and six implementation using the Yoshida technique. The Hamiltonian error (right) does not separate as clearly as the Lobatto-Gauss methods of corresponding order

Figure 14.  Comparison of the Hamiltonian error for the Lobatto-Gauss methods (left) and Yoshida methods of the same order (right), same parameters and initial conditions as in Figure 3, except for the step-size, $h = 0.005$. It is known that the Yoshida technique can lead to a large error constant in the leading error term

Figure 15.  Left: Maximum error in Hamiltonian (total) energy. Right: Maximum deviation in scaled oscillatory energy $\omega I$. Same parameters and initial conditions as in Figure 4, this time with the IMEX and its order four and six implementations using the Yoshida technique

Figure 16.  Same parameters and initial conditions as in Figure 5, this time with the IMEX and its order four and six implementations using the Yoshida technique

Figure 17.  Hamiltonian max error ratio for the IMEX and its higher order implementations with the Yoshida technique. Same initial conditions and parameters as in Figure 6

•  [1] E. Celledoni and E. H. Høyseth, The averaged Lagrangian method, J. Comput. Appl. Math., 316 (2017), 161-174.  doi: 10.1016/j.cam.2016.09.047. [2] G. J. Cooper and A. Sayfy, Additive Runge–Kutta methods for stiff ordinary differential equations, Math. Comp., 40 (1983), 207-218.  doi: 10.1090/S0025-5718-1983-0679441-1. [3] E. Hairer, C. Lubich and G. Wanner, Geometric Numerical Integration, Structure-Preserving Algorithms for Ordinary Differential Equations, Springer Series in Computational Mathematics, Springer, 2010. [4] L. Jay, Specialized partitioned additive Runge–Kutta methods for systems of overdetermined DAEs with holonomic constraints, SIAM J. Numer. Anal., 45 (2007), 1814-1842.  doi: 10.1137/060667475. [5] L. Jay, Structure preservation for constrained dynamics with super partitioned additive Runge–Kutta methods, SIAM J. Sci. Comput., 20 (1998), 416-446.  doi: 10.1137/S1064827595293223. [6] L. O. Jay and L. R. Petzold, Highly oscillatory systems and periodic stability, Technical Report, Army High Performance Computing Research Center, Stanford, CA, (1995), 95–105. [7] J. E. Marsden and M. West, Discrete mechanics and variational integrators, Acta Numerica, 10 (2001), 357-514.  doi: 10.1017/S096249290100006X. [8] R. I. McLachlan and A. Stern, Modified trigonometric integrators, SIAM J. Numer. Anal., 52 (2014), 1378-1397.  doi: 10.1137/130921118. [9] R. I. McLachlan, Y. Sun and P. S. P. Tse, Linear stability of partitioned Runge-Kutta methods, SIAM J. Numer. Anal., 49 (2011), 232-263.  doi: 10.1137/100787234. [10] F. Pfeil, A Higher Order IMEX Method for Solving Highly Oscillatory Problems, Master's thesis, University of Bergen, Norway, June 2019. [11] A. Sandu and M. Günther, A generalized-structure approach to additive Runge–Kutta methods, SIAM J. Numer. Anal., 53 (2015), 17-42.  doi: 10.1137/130943224. [12] A. Stern and E. Grinspun, Implicit-explicit variational integration of highly oscillatory problems, Multiscale Model. Simul., 7 (2009), 1779-1794.  doi: 10.1137/080732936. [13] G. M. Tanner, Generalized Additive Runge–Kutta Methods for Stiff Odes, PhD thesis, University of Iowa, 2018. [14] T. Wenger, S. Ober-Blöbaum and S. Leyendecker, Variational integrators of mixed order for dynamical systems with multiple time scales and split potentials, ECCOMAS Congress 2016, 2016. doi: 10.7712/100016.1920.10163. [15] T. Wenger, S. Ober-Blöbaum and S. Leyendecker, Construction and analysis of higher order variational integrators for dynamical systems with holonomic constraints, Adv. Comput. Math., 43 (2017), 1163-1195.  doi: 10.1007/s10444-017-9520-5. [16] H. Yoshida, Construction of higher order symplectic integrators, Phys. Lett. A, 150 (1990), 262-268.  doi: 10.1016/0375-9601(90)90092-3. [17] A. Zanna, A family of modified trigonometric integrators for highly oscillatory problems, FoCM, Barcelona, 2017. [18] M. Zhang and R. D. Skeel, Cheap implicit symplectic integrators, Appl. Numer. Math., 25 (1997), 297-302.  doi: 10.1016/S0168-9274(97)00066-4.

Figures(17)


text:
+0

# Solving system of equation with elimination and substitution help.

-1
134
1
+123

4. Solve the following system of equations:

3 + 2x - y = 0,

-3 - 7y = 10x

by using substitution, and by elimination.

Feb 24, 2019

#1
+5766
+1

$$2x - y = -3\\ 10x+7y = -3$$

$$\text{substitution}\\ y = 2x+3\\ 10x+7(2x+3) = -3\\ 24x+ 21=-3\\ 24x=-24\\ x=-1, y = 1\\ --\\ \text{elimination}\\ \text{subtract 5x the first equation from the second}\\ 12y=12\\ y=1,~x=-1$$

.
Feb 24, 2019

#1
+5766
+1
$$2x - y = -3\\ 10x+7y = -3$$
$$\text{substitution}\\ y = 2x+3\\ 10x+7(2x+3) = -3\\ 24x+ 21=-3\\ 24x=-24\\ x=-1, y = 1\\ --\\ \text{elimination}\\ \text{subtract 5x the first equation from the second}\\ 12y=12\\ y=1,~x=-1$$


text:
# Opus Heat

This test case has been proposed by Annabelle Le-Hyaric and Michel Fouquembergh formerly at AIRBUS.

We consider a 2D model representative of the neighboring of an electronic component submitted to a cooling air flow. It is described by four geometrical domains in $\mathbb{R}^2$ named $\Omega_i,i=1,2,3,4$, see figure. We suppose the velocity $\vec{v}$ is known in each domain --- for instance in $\Omega_4$ it is the solution of previous Navier-Stokes computations. --- The temperature $T$ of the domain $\Omega = \cup_{i=1}^4 \Omega_i$ is then solution of heat transfer equation :

$$$\label{eq:1} \rho C_i \Big( \frac{\partial T}{\partial t} + \vec{v} \cdot \nabla T \Big) - \nabla \cdot \left( k_i \nabla T \right) = Q_i,\quad i=1,2,3,4$$$

where $t$ is the time and in each sub-domain $\Omega_i$, $\rho C_i$ is the volumic thermal capacity, $k_i$ is the thermal conductivity. $k_1$ and $k_2$ are parameters of the model.

ICs dissipate heat, so the volumic heat dissipated $Q_1$ and $Q_2$ are also parameters of the model, while $Q_3=Q_4=0$.

One should notice that the convection term in heat transfer equation may lead to spatial oscillations which can be overcome by Petrov-Galerkin type or continuous interior penalty stabilization techniques.

Integrated circuits (ICs) (domains $\Omega_1$ and $\Omega_2$ ) are respectively soldered on PCB at $\mathbf{x1}=(e_{Pcb}, h_1)$ and $\mathbf{x_2}=(e_{Pcb}, h_2)$. They are considered as rectangles with width $e_{IC}$ and height $h_{IC}$. The printed circuit board (PCB) is a rectangle $\Omega_3$ of width $e_{PCB}$ and height $h_{PCB}$. The air(Air) is flowing along the PCB in domain $\Omega_4$. Speed in the air channel $\Omega_4$ is supposed to have a parabolic profile function of $x$ coordinate. Its expression is simplified as follows (notice that $\vec{v}$ is normally solution of Navier-Stokes equations; the resulting temperature and velocity fields should be quite different from that simplified model), we have for all $0 \leq y \leq h_{PCB}$

$$$\label{eq:2} \begin{array}[c]{rl} e_{Pcb} + e_{Ic} \leq x \leq e_{Pcb} + e_a, & \displaystyle \vec{v} = -V(x-(e_{Pcb}+e_{Ic}))(x-(e_{Pcb}+e_a))\vec{y}\\ e_{Pcb} \leq x \leq e_{Pcb} + e_{Ic}, & \vec{v} = 0 \end{array}$$$

where V is a parameter of the model.

The medium velocity $\vec{v}_i = \vec{0}, i=1,2,3$ in the solid domains $\Omega_i, i=1,2,3$.

## 1. Boundary conditions

We set

• on $\Gamma_1\cup\Gamma_3$, a zero flux (Neumann-like) condition

$$$\label{eq:10} -k_i\ \nabla T \cdot \vec{n}_i\ =\ 0;$$$
• on $\Gamma_2$, a heat transfer (Robin-like) condition

$$\label{eq:7} -k_4\ \nabla T \cdot \vec{n}_4\ =\ h(T-T_0);$$

where $h$ is a parameter of the model

• on $\Gamma_4$ the temperature is set (Dirichlet condition)

$$$\label{eq:11} T\ = T_0;$$$
• on other internal boundaries, the coontinuity of the heat flux and temperature, on $\Gamma_{ij} = \Omega_i \cap \Omega_j \neq \emptyset$

$$$\label{eq:6} \begin{array}{rl} T_i &= T_j \\ k_i\ \nabla T \cdot \vec{n}_i &= -k_j\ \nabla T \cdot \vec{n}_j. \end{array}$$$

## 2. Initial condition

At $t=0s$, we set $T = T_0$.

## 3. Outputs

The output is the mean temperature $s_1(\mu)$ of the hottest IC

$$$\label{eq:3} s_1(\mu) = \frac{1}{e_{IC} h_{IC}} \int_{\Omega_2} T$$$

## 4. Parameters

The table displays the various fixed and variables parameters of this test-case.

 Name Description Range Units $k_1$ thermal conductivity $[1,3$] $W \cdot m^{-1} \cdot K^{-1}$ $k_2$ thermal conductivity $[1,3$] $W \cdot m^{-1} \cdot K^{-1}$ $h$ transfer coefficient $[0.1,5$] $W \cdot m^{-2} \cdot K^{-1}$ $Q_1$ heat source $[10^4, 10^{6}$] $W \cdot m^{-3}$ $Q_1$ heat source $[10^4, 10^{6}$] $W \cdot m^{-3}$ $V$ Inflow rate $[1,30$] $m^2 \cdot s^{-1}$
 Name Description Nominal Value Units $t$ time $[0, 500$] $s$ $T_0$ initial temperature $300$ $K$ IC Parameters $\rho C_{IC}$ heat capacity $1.4 \cdot 10^{6}$ $J \cdot m^{-3} \cdot K^{-1}$ $e_{IC}$ thickness $2\cdot 10^{-3}$ $m$ $h_{IC} = L_{IC}$ height $2\cdot 10^{-2}$ $m$ $h_{1}$ height $2\cdot 10^{-2}$ $m$ $h_{2}$ height $7\cdot 10^{-2}$ $m$ PCB Parameters $k_3 = k_{Pcb}$ thermal conductivity $0. 2$ $W \cdot m^{-1} \cdot K^{-1}$ $\rho C_{3}$ heat capacity $2 \cdot 10^{6}$ $J \cdot m^{-3} \cdot K^{-1}$ $e_{Pcb}$ thickness $2\cdot 10^{-3}$ $m$ $h_{Pcb}$ height $13\cdot 10^{-2}$ $m$ Air Parameters $T_0$ Inflow temperature $300$ $K$ $k_4$ thermal conductivity $3 \cdot 10^{-2}$ $W \cdot m^{-1} \cdot K^{-1}$ $\rho C_{4}$ heat capacity $1100$ $J \cdot m^{-3} \cdot K^{-1}$ $e_{a}$ thickness $4\cdot 10^{-3}$


text:
# Least-squares data fitting and POLYFIT

Nick Trefethen, 1st October 2011

(Chebfun example stats/LeastSquares.m)

In Matlab, a standard command for least-squares fitting by a polynomial to a set of discrete data points is POLYFIT. The polynomial returned by POLYFIT is represented in Matlab's usual manner by a vector of coefficients in the monomial basis.

In Chebfun, there is an overloaded POLYFIT command in the domain class that does the same thing, except that the polynomial is returned as a chebfun rather than a coefficient vector. Here is an example:

npts = 100;
x = linspace(-1,1,npts);
y = 1./(1+25*x.^2) + 1e-1*randn(1,npts);
f = polyfit(x,y,10,domain(-1,1));
plot(x,y,'xk','markersize',12)
hold on, plot(f,'r','linewidth',2)
title('Discrete polynomial least-squares fit','fontsize',16)

Chebfun also has a POLYFIT command in the chebfun class, and this is for continuous rather than discrete polynomial least-squares fitting. For example, here is a least-squares fit to a jagged function:

f = chebfun('abs(x+.2)-.5*sign(x-.5) ','splitting','on');
r = polyfit(f,10);
hold off, plot(f,'k',r,'r','linewidth',2)
title('Continuous polynomial least-squares fit','fontsize',16)


text:
# Feedback on my first Python program- Guess the number

## Recommended Posts

Hello everyone. I am a C++ and a C# programmer but I was bored recently so I decided to play around with Python for a little while. Here is my first Python program which is a simple little guess the number application. Any feedback would be greatly appreciated (Things I did wrong, things I could do better, things that I could have done easier, ect). Here is the code:
import random

def PlayGame(): pass
Guess=0
try:
print
Guess=int(raw_input("Enter a number between 1 and 10: "))
except ValueError:
print
print "Oops not a number! Try Again!"
if Guess<pNum:
print
print "Too Low"
pTries+=1
elif Guess>pNum:
print
print "Too High"
pTries+=1
else:
pTries+=1
print
print "You got it in "+str(pTries)+" tries!"
PA=""
while PA!="y" and PA!="n":
print
PA=raw_input("Play again (y/n): ")
if PA=="y":
PlayGame()
elif PA=="n":
print
print "See you again soon!"
return
else:
print
print "Please enter Y or N"
return

def PlayGame():
print "Welcome to Guess a number!"
Tries=0
mNum=random.randrange(1,10)

PlayGame()
print
print("The End!")
print
print("Created by Donald May")

Any feedback would be great, thanks :).

##### Share on other sites
Your code looks pretty good. Here are two minor recommendations:

1) The first definition of the "PlayGame()" function isn't needed.

2) Instead of using recursion (AskNum calling AskNum calling AskNum...), you might want to use a while loop. I doubt the player would ever fill the stack, but I think it would be a better practice, in this case.

- Mike

##### Share on other sites
Thanks. I didn't even think about the stack, good point.

I originally had a while loop but I replaced it becuase I figured this way would be better.


text:
# Newton Raphson Method with Line Search

1. Jul 10, 2013

### brunnels

I am developing a code that uses Newton's method to optimize a functional W:ℝ6→ℝ
Because the functional is poorly represented by a quadratic, convergence is slow. Therefore I've implemented a line search using two methods: the secant method and the backtracking method (with the Armijo condition)
My problem is that the line search produces a factor of zero. When plotting
W(x + α Δx) $\ \ \ \ \$ α$\in$[-1,1]
as a function of $\alpha$, it is clear that α=0 is a minimizer. I can't understand why this would be the case.


text:
# Basic LaTeX Document

Published May 26, 2022  -  By Marco Garosi

Any $\TeX$ — and thus $\LaTeX$ — document should have some basic elements to work properly. TeX documents should indeed provide some basic yet fundamental information on the document in order to be successfully compiled. This note gives a basic “skeleton” that you may use as a starting point for any (La)TeX document.

## A book with not-too-small text

Following is the code to produce a book using font-size of 11 points (11 pt.). Standard size in LaTeX is 10 points. Also, it defines the paper to be A4 size (210 x 297 millimiters), which is the main type of paper in Europe. American fellows should just delete that instruction, since their typical sheet is called a letter and is slightly different. Pay attention to sheet format!

documentclass[a4paper,11pt]{book}

\usepackage[T1]{fontenc} % font encoding
\usepackage[utf8]{inputenc} % input encoding - important for non-english languages. It allows you to use accented letters directly from your keyboard, without having to use weird commands
\usepackage[your-lang-here]{babel} % hyphenation rules. You should put your language - if supported by babel - between the square brackets. Example: \usepackage[italian]{babel}

\title{Book title}
\date{\today}

\begin{document}

\frontmatter % initial content
\maketitle % makes the title with the information given above

\end{document}


text:
# Microcontroller I/O configuration

I have been using PIC microcontrollers and have been using MikroC for the programming but I am little bit confused about the ports. On a PIC16F84A the port is defined in mikroC as TRISA = 0xFF, and a bit of the port can be accessed by PORTA.f0. But for other microcontrollers in the series a different code is used. For example, TRISIO = 0xFF.

Can you please explain to me how I can know the code for accessing the ports that applies for every microcontroller out there? Also the input for a PIC is 1 and output is 0, and for Atmel the input 0 and output 1 which I found confusing if someone can explain?

• Please consider making your question title more specific, as it stands "Help with microcontrollers" could be any one of a thousand questions. Bear in mind others who come along with the same problem and would never find this question due to a bad title. It's also considered bad to ask two questions in one post, better to ask seperate questions so that each answer can be voted on it's merits. – Martin Jul 9 '13 at 9:03

Try looking at the header files you're using, or like Scott Seidman mentioned the compiler datasheet

Microcontrollers datasheet aren't always going to have the exact variable names used in program (maybe in MPLAB) but most likely not in 3rd-party IDE like MikroC

MikroC Manual for PIC12, 16 and 18

You just have to read the datasheet of each microcontroller that you are using. Which is something you should do for every device that you are using, anyway.

• The question has much more to do with how the individual compiler sets up each uC than with the uC itself. – Scott Seidman Jul 9 '13 at 10:39

I don't use MikroC, which looks like a fine compiler, but many compilers put all the chip-related info into a header file which is compiled into your code via an #include statement, or some such.

Open the header file, and scan it for port information.


text:
Under the auspices of the Computational Complexity Foundation (CCF)

REPORTS > DETAIL:

### Paper:

TR21-107 | 20th July 2021 14:02

#### Classification of OBDD size for monotone 2-CNFs

TR21-107
Authors: igor razgon
Publication: 23rd July 2021 09:08
Keywords:

Abstract:

We introduce a new graph parameter called linear upper maximum induced
matching width \textsc{lu-mim width}, denoted for a graph $G$ by $lu(G)$.
We prove that the smallest size of the \textsc{obdd} for $\varphi$,
the monotone 2-\textsc{cnf} corresponding to $G$, is sandwiched
between $2^{lu(G)}$ and $n^{O(lu(G))}$.
The upper bound is based on a combinatorial statement that might
be of an independent interest.
We show that the bounds in terms of this parameter are best possible.

The new parameter is closely related to two existing parameters:
linear maximum induced matching width (\textsc{lmim width}) and linear symmetric induced matching width
(\textsc{lsim width}). We prove that \textsc{lu-mim width} lies strictly in between these two
parameters, being dominated by \textsc{lsim width} and dominating \textsc{lmim width}.
We conclude that neither of the two existing parameters can be used instead of \textsc{lu-mim width}
to characterize the size of \textsc{obdd}s for monotone $2$-\textsc{cnf}s and this justifies introduction
of the new parameter.

ISSN 1433-8092 | Imprint


text:
Volume 2, Issue 4
Numerical Solutions to Bean's Critical-State Model for Type-II Superconductors

Int. J. Numer. Anal. Mod., 2 (2005), pp. 479-488.

Published online: 2005-02

Cited by

Export citation
• Abstract

In this paper we study the numerical solution for an $p$-Laplacian type of evolution system $H_t + \nabla \times [|\nabla \times H|^{p-2} \nabla \times H] = F (x, t)$, $p > 2$ in two space dimensions. For large $p$ this system is an approximation of Bean's critical-state model for type-II superconductors. By introducing suitable transformation, the system is equivalent to a nonlinear parabolic equation. For the nonlinear parabolic problem we obtain the numerical solution by combining approximation schemes for the linear equation and the nonlinear semigroup. The convergence and stability of the scheme are proved. Finally, a numerical experiment is presented.

• Keywords

approximation of Bean's critical-state model, numerical solutions.

35Q60, 35K50, 65M60

• BibTex
• RIS
• TXT
@Article{IJNAM-2-479, author = {}, title = {Numerical Solutions to Bean's Critical-State Model for Type-II Superconductors}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2005}, volume = {2}, number = {4}, pages = {479--488}, abstract = {

In this paper we study the numerical solution for an $p$-Laplacian type of evolution system $H_t + \nabla \times [|\nabla \times H|^{p-2} \nabla \times H] = F (x, t)$, $p > 2$ in two space dimensions. For large $p$ this system is an approximation of Bean's critical-state model for type-II superconductors. By introducing suitable transformation, the system is equivalent to a nonlinear parabolic equation. For the nonlinear parabolic problem we obtain the numerical solution by combining approximation schemes for the linear equation and the nonlinear semigroup. The convergence and stability of the scheme are proved. Finally, a numerical experiment is presented.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/942.html} }
TY - JOUR T1 - Numerical Solutions to Bean's Critical-State Model for Type-II Superconductors JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 479 EP - 488 PY - 2005 DA - 2005/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/942.html KW - approximation of Bean's critical-state model, numerical solutions. AB -

In this paper we study the numerical solution for an $p$-Laplacian type of evolution system $H_t + \nabla \times [|\nabla \times H|^{p-2} \nabla \times H] = F (x, t)$, $p > 2$ in two space dimensions. For large $p$ this system is an approximation of Bean's critical-state model for type-II superconductors. By introducing suitable transformation, the system is equivalent to a nonlinear parabolic equation. For the nonlinear parabolic problem we obtain the numerical solution by combining approximation schemes for the linear equation and the nonlinear semigroup. The convergence and stability of the scheme are proved. Finally, a numerical experiment is presented.

W. Wei & H.-M. Yin. (1970). Numerical Solutions to Bean's Critical-State Model for Type-II Superconductors. International Journal of Numerical Analysis and Modeling. 2 (4). 479-488. doi:
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