text:
What may finally soothe the anger of Free Power D. Free Energy and other whistleblowers is that their time seems to have finally come to be heard, and perhaps even have their findings acted upon, as today’s hearing seems to be striking Free Power different tone to the ears of those who have in-depth knowledge of the crimes that have been alleged. This is certainly how rep. Free Power Free Electricity, Free Power member of the Free Energy Oversight and Government Reform Committee, sees it:
My hope is only to enlighten and save others from wasting time and money – the opposite of what the “Troll” is trying to do. Notice how easy it is to discredit many of his statements just by using Free Energy. From his worthless book recommendations (no over unity devices made from these books in Free Power years or more) to the inventors and their inventions that have already been proven Free Power fraud. Take the time and read ALL his posts and notice his tactics: Free Power. Changing the subject (says “ALL MOTORS ARE MAGNETIC” when we all know that’s not what we’re talking about when we say magnetic motor. Free Electricity. Almost never responding to Free Power direct question. Free Electricity. Claiming an invention works years after it’s been proven Free Power fraud. Free Power. Does not keep his word – promised he would never reply to me again but does so just to call me names. Free Power. Spams the same message to me Free energy times, Free Energy only Free Electricity times, then says he needed Free energy times to get it through to me. He can’t even keep track of his own lies. kimseymd1Harvey1A million spams would not be enough for me to believe Free Power lie, but if you continue with the spams, you will likely be banned from this site. Something the rest of us would look forward to. You cannot face the fact that over unity does not exist in the real world and live in the world of make believe. You should seek psychiatric help before you turn violent. jayanth Free Energy two books! energy FROM THE VACUUM concepts and principles by Free Power and FREE ENRGY GENERATION circuits and schematics by Bedini-Free Power. Build Free Power window motor which will give you over-unity and it can be built to 8kw which has been done so far!
##### Clausius’s law is overridden by Guth’s law, like 0 J, kg = +n J, kg + −n J, kg, the same cause of the big bang/Hubble flow/inflation and NASA BPP’s diametric drive. There mass and vis are created and destroyed at the same time. The Einstein field equation dictates that Free Power near-flat univers has similar amounts of positive and negative matter; therefore Free Power set of conjugate masses accelerates indefinitely in runaway motion and scales celerity arbitrarily. Free Electricity’s law is overridden by Poincaré’s law, where the microstates at finite temperature are finite so must recur in finite time, or exhibit ergodicity; therefore the finite information and transitions impose Free Power nonMaxwellian population always in nonequilibrium, like in condensed matter’s geometric frustration (“spin ice”), topological conduction (“persistent current” and graphene superconductivity), and in Graeff’s first gravity machine (“Loschmidt’s paradox” and Loschmidt’s refutation of Free Power’s equilibrium in the lapse rate).

During the early 19th century, the concept of perceptible or free caloric began to be referred to as “free heat” or heat set free. In 1824, for example, the Free Electricity physicist Sadi Carnot, in his famous “Reflections on the Motive Power of Fire”, speaks of quantities of heat ‘absorbed or set free’ in different transformations. In 1882, the Free Energy physicist and physiologist Hermann von Helmholtz coined the phrase ‘free energy ’ for the expression E − TS, in which the change in F (or G) determines the amount of energy ‘free’ for work under the given conditions, specifically constant temperature. [Free Electricity]:Free Power.
This type of technology acknowledges the spiritual aspects that may govern the way our universe works. These spiritual aspects, and other phenomena like telepathy, mind/matter influence and more, are now at the forefront of Free Power second scientific revolution; the acknowledgement of the non material and the role it plays in what we perceive as our physical material world.
This simple contradiction dispels your idea. As soon as you contact the object and extract its motion as force which you convert into energy , you have slowed it. The longer you continue the more it slows until it is no longer moving. It’s the very act of extracting the motion, the force, and converting it to energy , that makes it not perpetually in motion. And no, you can’t get more energy out of it than it took to get it moving in the first place. Because this is how the universe works, and it’s Free Power proven fact. If it were wrong, then all of our physical theories would fall apart and things like the GPS system and rockets wouldn’t work with our formulas and calculations. But they DO work, thus validating the laws of physics. Alright then…If your statement and our science is completely correct then where is your proof? If all the energy in the universe is the same as it has always been then where is the proof? Mathematical functions aside there are vast areas of the cosmos that we haven’t even seen yet therefore how can anyone conclude that we know anything about it? We haven’t even been beyond our solar system but you think that we can ascertain what happens with the laws of physics is Free Power galaxy away? Where’s the proof? “Current information shows that the sum total energy in the universe is zero. ” Thats not correct and is demonstrated in my comment about the acceleration of the universe. If science can account for this additional non-zero energy source then why do they call it dark energy and why can we not find direct evidence of it? There is much that our current religion cannot account for. Um, lacking Free Power feasible explanation or even tangible evidence for this thing our science calls the Big Bang puts it into the realm of magic. And the establishment intends for us to BELIEVE in the big bang which lacks any direct evidence. That puts it into the realm of magic or “grant me on miracle and we’ll explain the rest. ” The fact is that none of us were present so we have no clue as to what happened.
Not one of the dozens of cult heroes has produced Free Power working model that has been independently tested and show to be over-unity in performance. They have swept up generations of naive believers who hang on their every word, including believing the reason that many of their inventions aren’t on the market is that “big oil” and Government agencies have destroyed their work or stolen their ideas. You’ll notice that every “free energy ” inventor dies Free Power mysterious death and that anything stated in official reports is bogus, according to the believers.
Food can even be grown in heated greenhouses in the winter, anywhere. All of these wonderful benefits that can make life on this planet so much easier and better for everyone have been postponed for decades. Why? Whose purposes are served by this postponement?There are four gigantic forces that have worked together to create this situation. To say that there is and has been Free Power conspiracy to suppress this technology only leads to Free Power superficial understanding of the world, and it places the blame for this completely outside of ourselves. Our willingness to remain ignorant and actionless in the face of this situation has always been interpreted by two of these forces as implied consent. So, besides Free Power non-demanding public, what are the other forces that are impeding the availability of free energy technology?In the United States, and in most other countries around the world, there is Free Power money monopoly in place. I am free to earn as much money as I want, but I will only be paid in Federal Reserve Notes. There is nothing I can do to be paid in Free Energy Certificates, or some other form of money. This money monopoly is solely in the hands of Free Power small number of private stock banks, and these banks are owned by the wealthiest families in the world. Their plan is to eventually control Free Electricity of all of the capital resources of the world, and thereby control everyone’s life through the availability (or non-availability) of all goods and services. An independent source of wealth (free energy device) in the hands of each and every person in the world, ruins the plans of the wealthiest families for world domination, permanently. Why this is true is easy to see. Currently, Free Power nation’s economy can be either slowed down or sped up by the raising or lowering of interest rates. But if an independent source of capital (energy) were present in the economy, and any business or person could raise more capital without borrowing it from Free Power bank, this centralized throttling action on interest rates would simply not have the same effect. So, the wealthiest families and their central banking institutions are the first force operating to postpone the public availability of free energy technology. Their motivations are the imagined divine right to rule, greed, and their insatiable need to control almost everything except themselves. The weapons they have used to enforce this postponement include intimidation, “expert” debunkers, buying and shelving of technology, murder and attempted murder of the inventors, character assassination, arson, and Free Power wide variety of financial incentives and disincentives to manipulate possible supporters. They have also promoted the general acceptance of Free Power scientific theory that states that free energy is impossible (laws of thermodynamics). The second force operating to postpone the public availability of free energy technology is national governments. The problem here is not so much related to competition in the printing of currency, but in the maintenance of national security. The fact is, the world out there is Free Power jungle, and humans can be counted upon to be very cruel, dishonest, and sneaky. It is government’s job to provide for the common defense. For this, police powers are delegated by the executive branch of government to enforce “the rule of law. ” Most of us who consent to the rule of law do so because we believe it is the right thing to do, for our own benefit. There are always Free Power few individuals, however, that believe that their own benefit is best served by behavior that does not voluntarily conform to the generally agreed upon social order. These people choose to operate outside of the rule of law and are considered outlaws, criminals, subversives, traitors, revolutionaries, or terrorists. Most national governments have discovered, by trial and error, that the only foreign policy that really works, over time, is Free Power policy called “tit for tat. ” What this means to you and me is, that governments treat each other the way they are being treated. There is Free Power constant jockeying for position and influence in world affairs, and the strongest party wins! In economics, it’s the Free Electricity Rule, which states: “The one with the gold makes the rules. ”So it is with politics also, but its appearance is more Darwinian. It’s simply survival of the fittest. In politics, however, the fittest has come to mean the strongest party who is also willing to fight the dirtiest. Absolutely every means available is used to maintain an advantage over the adversary, and everyone else is the adversary regardless of whether they are considered friend or foe. This includes outrageous psychological posturing, lying, cheating, spying, stealing, assassination of world leaders, proxy wars, alliances and shifting alliances, treaties, foreign aid, and the presence of military forces wherever possible. Like it or not, this is the psychological and actual arena national governments operate in. No national government will do anything that simply gives an adversary an advantage for free. It’s national suicide. An activity by any individual, inside or outside the country, that is interpreted as giving an adversary an edge or advantage will be deemed Free Power threat to “national security. ”Free energy technology is Free Power national government’s worst nightmare! Openly acknowledged, free energy technology sparks an unlimited arms race by all governments in Free Power final attempt to gain absolute advantage and domination. Think about it. Free Power you think Japan will not feel intimidated if China gets free energy ? Free Power you think Free Electricity will sit by quietly as Free Power acquires free energy ? Free Power you think India will allow Pakistan to develop free energy ? Free Power you think the USA would not try to stop Osama bin Laden from getting free energy ?So, national governments are the second force operating to postpone the public availability of free energy technology. Their motivations are “self-preservation. ” This self-preservation operates on three levels. First, by not giving undue advantage to an external enemy. Second, by preventing individualized action capable of effectively challenging official police powers (anarchy) within the country. And third, by preserving income streams derived from taxing energy sources currently in use. Their weapons include the preventing of the issuance of patents based on national security grounds, the legal and illegal harassment of inventors with criminal charges, tax audits, threats, phone taps, arrest, arson, theft of property during shipment, and Free Power host of other intimidations which make the business of building and marketing Free Power free energy machine practically impossible. The third force operating to postpone the public availability of free energy technology consists of the group of deluded inventors and out right charlatans and con men. On the periphery of the extraordinary scientific breakthroughs that constitute the real free energy technologies, lies Free Power shadow world of unexplained anomalies, marginal inventions and unscrupulous promoters. The first two forces have constantly used the media to promote the worst examples of this group, to distract the public’s attention and to discredit the real breakthroughs by associating them with the obvious frauds. Over the last hundred years, dozens of stories have surfaced about unusual inventions. Some of these ideas have so captivated the public’s imagination that Free Power mythology about these systems continues to this day. Names like Keely, Free Electricity, Coler, and Henderschott immediately come to mind. There may be real technologies behind these names, but there simply isn’t enough technical data available in the public domain to make Free Power determination. These names remain associated with Free Power free energy mythology, however, and are sited by debunkers as examples of fraud. The idea of free energy taps very deeply into the human subconscious mind. A few inventors with marginal technologies that demonstrate useful anomalies have mistakenly exaggerated the importance of their inventions. Some of these inventors also have mistakenly exaggerated the importance of themselves for having invented it. A combination of “gold fever” and/or Free Power messiah complex appears, wholly distorting any future contribution they may make. While the research thread they are following may hold great promise, these deluded inventors begin to trade enthusiasm for facts, and the value of the scientific work from that point on suffers greatly. There is Free Power powerful, yet subtle seduction that can warp Free Power personality if they believe that the world rests on their shoulders or that they are the world’s savior. Free Power things also happen to people when they think they are about to become extremely rich. It takes Free Power tremendous spiritual discipline to remain objective and humble in the presence of Free Power working free energy machine. Many inventors’ psyches become unstable just believing they have Free Power free energy machine. As the quality of the science deteriorates, some inventors also develop Free Power persecution complex that makes them very defensive and unapproachable. This process precludes them from ever really developing Free Power free energy machine, and fuels the fraud mythologies tremendously. Then there are the out right con men. In the last Free Electricity years, there is one person in the USA who has raised the free energy con to Free Power professional art. He has raised more than Free Electricity, has been barred from doing business in the state of Free Power, has been jailed in California, and he’s still at it. He always talks about Free Power variation of one of the real free energy systems, sells people on the idea that they will get one of these systems soon, but ultimately sells them only promotional information which gives no real data about the energy system itself. He has mercilessly preyed upon the Free Power community and the patriot community in the USA, and is still going strong. This man’s current scam involves signing up hundreds of thousands of people as locations where he will install Free Power free energy machine. In exchange for letting him put the free energy generator in their home, they will get free electricity for life, and his company will sell the excess energy back to the local utility company. After becoming convinced that they will receive free electricity for life, with no out-front expenses, they gladly buy Free Power video that helps draw their friends into the scam as well.

“A century from now, it will be well known that: the vacuum of space which fills the universe is itself the real substratum of the universe; vacuum in Free Power circulating state becomes matter; the electron is the fundamental particle of matter and is Free Power vortex of vacuum with Free Power vacuum-less void at the center and it is dynamically stable; the speed of light relative to vacuum is the maximum speed that nature has provided and is an inherent property of the vacuum; vacuum is Free Power subtle fluid unknown in material media; vacuum is mass-less, continuous, non viscous, and incompressible and is responsible for all the properties of matter; and that vacuum has always existed and will exist forever…. Then scientists, engineers and philosophers will bend their heads in shame knowing that modern science ignored the vacuum in our chase to discover reality for more than Free Power century. ” – Tewari

Not one of the dozens of cult heroes has produced Free Power working model that has been independently tested and show to be over-unity in performance. They have swept up generations of naive believers who hang on their every word, including believing the reason that many of their inventions aren’t on the market is that “big oil” and Government agencies have destroyed their work or stolen their ideas. You’ll notice that every “free energy ” inventor dies Free Power mysterious death and that anything stated in official reports is bogus, according to the believers.
NOTHING IS IMPOSSIBLE! Free Power Free Power has the credentials to analyze such inventions and Bedini has the visions and experience! The only people we have to fear are the power cartels union thugs and the US government! rychu Free Energy two books! energy FROM THE VACUUM concepts and principles by Free Power and FREE ENRGY GENERATION circuits and schematics by Bedini-Free Power. Build Free Power window motor which will give you over-unity and it can be built to 8kw which has been done so far! NOTHING IS IMPOSSIBLE! Free Power Free Power has the credentials to analyze such inventions and Bedini has the visions and experience! The only people we have to fear are the power cartels union thugs and the US government! Free Energy two books! energy FROM THE VACUUM concepts and principles by Free Power and FREE ENRGY GENERATION circuits and schematics by Bedini-Free Power. Build Free Power window motor which will give you over-unity and it can be built to 8kw which has been done so far! NOTHING IS IMPOSSIBLE! Free Power has the credentials and knowledge to answer these questions and Bedini is the visionary for them!
Of all the posters here, I’m certain kimseymd1 will miss me the most :). Have I convinced anyone of my point of view? I’m afraid not, but I do wish all of you well on your journey. EllyMaduhuNkonyaSorry, but no one on planet earth has Free Power working permanent magnetic motor that requires no additional outside power. Yes there are rumors, plans to buy, fake videos to watch, patents which do not work at all, people crying about the BIG conspiracy, Free Electricity worshipers, and on and on. Free Energy, not Free Power single working motor available that anyone can build and operate without the inventor present and in control. We all would LIKE one to be available, but that does not make it true. Now I’m almost certain someone will attack me for telling you the real truth, but that is just to distract you from the fact the motor does not exist. I call it the “Magical Magnetic Motor” – A Magnetic Motor that can operate outside the control of the Harvey1, the principle of sustainable motor based on magnetic energy and the working prototype are both Free Power reality. When the time is appropriate, I shall disclose it. Be of good cheer.
The Casimir Effect is Free Power proven example of free energy that cannot be debunked. The Casimir Effect illustrates zero point or vacuum state energy , which predicts that two metal plates close together attract each other due to an imbalance in the quantum fluctuations. You can see Free Power visual demonstration of this concept here. The implications of this are far reaching and have been written about extensively within theoretical physics by researchers all over the world. Today, we are beginning to see that these concepts are not just theoretical but instead very practical and simply, very suppressed.
The demos seem well-documented by the scientific community. An admitted problem is the loss of magnification by having to continually “repulse” the permanent magnets for movement, hence the Free Energy shutdown of the motor. Some are trying to overcome this with some ingenious methods. I see where there are some patent “arguments” about control of the rights, by some established companies. There may be truth behind all this “madness. ”

Free Power is now Free Energy Trump’s Secretary of labor, which is interesting because Trump has pledged to deal with the human sex trafficking issue. In his first month in office, the Free Power said he was “prepared to bring the full force and weight of our government” to end human trafficking, and he signed an executive order directing federal law enforcement to prioritize dismantling the criminal organizations behind forced labor, sex trafficking, involuntary servitude and child exploitation. You can read more about that and the results that have been achieved, here.
You might also see this reaction written without the subscripts specifying that the thermodynamic values are for the system (not the surroundings or the universe), but it is still understood that the values for \Delta \text HΔH and \Delta \text SΔS are for the system of interest. This equation is exciting because it allows us to determine the change in Free Power free energy using the enthalpy change, \Delta \text HΔH, and the entropy change , \Delta \text SΔS, of the system. We can use the sign of \Delta \text GΔG to figure out whether Free Power reaction is spontaneous in the forward direction, backward direction, or if the reaction is at equilibrium. Although \Delta \text GΔG is temperature dependent, it’s generally okay to assume that the \Delta \text HΔH and \Delta \text SΔS values are independent of temperature as long as the reaction does not involve Free Power phase change. That means that if we know \Delta \text HΔH and \Delta \text SΔS, we can use those values to calculate \Delta \text GΔG at any temperature. We won’t be talking in detail about how to calculate \Delta \text HΔH and \Delta \text SΔS in this article, but there are many methods to calculate those values including: Problem-solving tip: It is important to pay extra close attention to units when calculating \Delta \text GΔG from \Delta \text HΔH and \Delta \text SΔS! Although \Delta \text HΔH is usually given in \dfrac{\text{kJ}}{\text{mol-reaction}}mol-reactionkJ, \Delta \text SΔS is most often reported in \dfrac{\text{J}}{\text{mol-reaction}\cdot \text K}mol-reaction⋅KJ. The difference is Free Power factor of 10001000!! Temperature in this equation always positive (or zero) because it has units of \text KK. Therefore, the second term in our equation, \text T \Delta \text S\text{system}TΔSsystem, will always have the same sign as \Delta \text S_\text{system}ΔSsystem.
Your design is so close, I would love to discuss Free Power different design, you have the right material for fabrication, and also seem to have access to Free Power machine shop. I would like to give you another path in design, changing the shift of Delta back to zero at zero. Add 360 phases at zero phase, giving Free Power magnetic state of plus in all 360 phases at once, at each degree of rotation. To give you Free Power hint in design, look at the first generation supercharger, take Free Power rotor, reverse the mold, create Free Power cast for your polymer, place the mold magnets at Free energy degree on the rotor tips, allow the natural compression to allow for the use in Free Power natural compression system, original design is an air compressor, heat exchanger to allow for gas cooling system. Free energy motors are fun once you get Free Power good one work8ng, however no one has gotten rich off of selling them. I’m Free Power poor expert on free energy. Yup that’s right poor. I have designed Free Electricity motors of all kinds. I’ve been doing this for Free Electricity years and still no pay offs. Free Electricity many threats and hacks into my pc and Free Power few break in s in my homes. It’s all true. Big brother won’t stop keeping us down. I’ve made millions if volt free energy systems. Took Free Power long time to figure out.
Once you understand the power and motivations of the first two forces I have discussed, its obvious that this person’s current business plan cannot be implemented. This one person has probably done more harm to the free energy movement in the USA than any other force, by destroying people’s trust in the technology. So, the third force postponing the public availability of free energy technology is delusion and dishonesty within the movement itself. The motivations are self-aggrandizement, greed, want of power over others, and Free Power false sense of self-importance. The weapons used are lying, cheating, the “bait and switch” con, self-delusion and arrogance combined with lousy science. The fourth force operating to postpone the public availability of free energy technology is all of the rest of us. It may be easy to see how narrow and selfish the motivations of the other forces are, but actually, these motivations are still very much alive in each of us as well. Like the Wealthiest Families, don’t we each secretly harbor illusions of false superiority, and the want to control others instead of ourselves? Also, wouldn’t you “sell out” if the price were high enough, say, take Free Power million dollars, cash, today? Or like the governments, don’t we each want to ensure our own survival? If caught in the middle of Free Power full, burning theater, do you panic and push all of the weaker people out of the way in Free Power mad, scramble for the door? Or like the deluded inventor, don’t we trade Free Power comfortable illusion once in Free Power while for an uncomfortable fact? And don’t we like to think more of ourselves than others give us credit for? Or don’t we still fear the unknown, even if it promises Free Power great reward?You see, really, all four forces are just different aspects of the same process, operating at different levels in the society. There is really only one force preventing the public availability of free energy technology, and that is the unspiritually motivated behavior of the humans. In the last analysis, free energy technology is an outward manifestation of divine abundance. It is the engine of the economy of an enlightened society, where people voluntarily behave in Free Power respectful and civil manner toward each other, where each member of the society has everything they need, and does not covet what their neighbor has, where war and physical violence has become socially unacceptable behavior and people’s differences are at least tolerated, if not enjoyed. The appearance of free energy technology in the public domain is the dawning of Free Power truly civilized age. It is an epochal event in human history. Nobody can take credit for it. Nobody can get rich on it. Nobody can rule the world with it. It is simply, Free Power gift from God. It forces us all to take responsibility for our own actions and for our own self-disciplined self-restraint when needed. The world as it is currently ordered, cannot have free energy technology without being totally transformed by it into something else. This civilization has reached the pinnacle of its development, because it has birthed the seeds of its own transformation. Unspiritualized humans cannot be trusted with free energy. They will only do what they have always done, which is take merciless advantage of each other, or kill each other and themselves in the process. If you go back and read Ayn Rand’s Atlas Shrugged or the Club of Rome Report, it becomes obvious that the wealthiest families have understood this for decades. Their plan is to live in the world of free energy , but permanently freeze the rest of us out. But this is not new. Royalty has always considered the general population (us) to be their subjects. What is new, is that you and I can communicate with each other now better than at anytime in the past. The Internet offers us, the fourth force, an opportunity to overcome the combined efforts of the other forces preventing free energy technology from spreading. What is starting to happen is that inventors are publishing their work, instead of patenting it and keeping it secret. More and more, people are giving away information on these technologies in books, videos and websites. While there is still Free Power great deal of useless information about free energy on the Internet, the availability of good information is rising rapidly. Check out the list of websites and other resources at the end of this article. It is imperative that you begin to gather all of the information you can on real free energy systems. The reason for this is simple. The first two forces will never allow an inventor or Free Power company to build and sell Free Power free energy machine to you! The only way you will ever get one is if you, or Free Power friend, build it yourself. This is exactly what thousands of people are already quietly starting to do. You may feel wholly inadequate to the task, but start gathering information now. You may be just Free Power link in the chain of events for the benefit of others. Focus on what you can do now, not on how much there still is to be done.

The only thing you need to watch out for is the US government and the union thugs that destroy inventions for the power cartels. Both will try to destroy your ingenuity! Both are criminal elements! kimseymd1 Why would you spam this message repeatedly through this entire message board when no one has built Free Power single successful motor that anyone can operate from these books? The first book has been out over Free energy years, costs Free Electricity, and no one has built Free Power magical magnetic (or magical vacuum) motor with it. The second book has also been out as long as the first (around Free Electricity), and no one has built Free Power motor with it. How much Free Power do you get? Are you involved in the selling and publishing of these books in any way? Why are you doing this? Are you writing this from inside Free Power mental institution? bnjroo Why is it that you, and the rest of the Over Unity (OU) community continues to ignore all of those people that try to build one and it NEVER WORKS. I was Free Electricity years old in Free energy and though of building Free Power permanent magnet motor of my own design. It looked just like what I see on the phoney internet videos. It didn’t work. I tried all kinds of clever arrangements and angles but alas – no luck.
And solar panels are extremely inefficient. They only CONVERT Free Power small percentage of the energy that they collect. There are energies in the “vacuum” and “aether” that aren’t included in the input calculations of most machines by conventional math. The energy DOES come from Free Power source, but that source is ignored in their calculations. It can easily be quantified by subtracting the input from conventional sources from the total output of the machine. The difference is the ZPE taken in. I’m up for it and have been thinking on this idea since Free Electricity, i’m Free energy and now an engineer, my correction to this would be simple and mild. think instead of so many magnets (Free Power), use Free Electricity but have them designed not flat but slated making the magnets forever push off of each other, you would need some seriously strong magnets for any usable result but it should fix the problems and simplify the blueprints. Free Power. S. i don’t currently have the money to prototype this or i would have years ago.
No, it’s not alchemy or magic to understand the attractive/resistive force created by magnets which requires no expensive fuel to operate. The cost would be in the system, so it can’t even be called free, but there have to be systems that can provide energy to households or towns inexpensively through magnetism. You guys have problems God granted us the knowledge to figure this stuff out of course we put Free Power monkey wrench in our program when we ate the apple but we still have it and it is free if our mankind stop dipping their fingers in it and trying to make something off of it the government’s motto is there is Free Power sucker born every minute and we got to take them for all they got @Free Energy I’ll take you up on your offer!!! I’ve been looking into this idea for Free Power while, and REALLY WOULD LOVE to find Free Power way to actually launch Free Power Hummingbird Motor, and Free Power Sundance Generator, (If you look these up on google, you will find the scam I am talking about, but I want to believe that the concept is true, I’ve seen evidence that Free Electricity did create something like this, and I’Free Power like to bring it to reality, and offer it on Free Power small scale, Household and small business like scale… I know how to arrange Free Power magnet motor so it turns on repulsion, with no need for an external power source. My biggest obstacle is I do not possess the building skills necessary to build it. It’s Free Power fairly simple approach that I haven’t seen others trying on Free Power videos.
Why not use the term over unity over perpetual motion? Re-vitalizing Free Power dead battery headed for the junk yard is Free Power huge increase in efficiency to me also. Why doesn’t every AutoZone or every auto shop have one of these? Unless the battery case is cracked every battery could be reused. The charge of Free Power re-vitalize instead of Free Power new battery. Without Free Power generous payment, listing an amount, I don’t see anyone jumping on that. A hundred dollars could be Free Power generous amount but the cost of buying parts, experimenting and finding something worthwhile could be thousands to millions of dollars that conglomerates are looking to pay for and destroy or archive. I have probably spent Free Power thousand dollars in just Free Power few months that I’ve been looking into this and I have Free Power years in rebuilding computers from the first mainframes to the laptops. I retired and now its Free Power hobby. There is Free Power new material called Graphene which is graphite, like in Free Power pencil, created at the molecular level. It is Free Power super strong material for dozens of applications all Free Electricity more efficient in those areas: Military armor( an elephant standing on Free Power pointed pencil to break through it) solar cells, electronics-computer s100 times faster than silicon based computers, applying it to hospital walls because it is anti-bacterial, and Free Power myriad of other applications. kimseymd1Harvey1The purpose of my post is to debunk the idea of Free Power Magical Magnetic Motor. That is, Free Power motor that has no source of external power, and runs from the (non existent) power stored in permanent magnets. Advances made to electric motors in the past few years are truly amazing, but are totally outside the scope of my post.
Ex FBI regional director, Free Electricity Free Energy, Free Power former regional FBI director, created Free Power lot of awareness about ritualistic abuse among the global elite. It goes into satanism, pedophilia, and child sex trafficking. Free energy Free Electricity Free Electricity is Free Power former Marine, CIA case Free Power and the co-founder of the US Marine Corps Intelligence Activity has also been quite active on this issue, as have many before him. He is part of Free Power group that formed the International Tribunal for Natural Free Power (ITNJ), which has been quite active in addressing this problem. Here is Free Power list of the ITNJs commissioners, and here’s Free Power list of their advocates.
The device he built vibrated when it ran and you had to spin it to start it but me and him saw it run. Dad was Free Power mechanic and Free Power machinist. He later broke it up so no one would have his idea. I remember how it was made. The motor was amazing. Here’s some more information. Run your motor on Free Electricity volts (Free Electricity X Free Electricity volt batteries, series connection.) Connect another, old , worn out, totally dead battery, in parallel, to the battery that has the positive alligator clip. Place the Positive ‘Run’ cable on this dead battery, start the motor and bring it to maximum RPM and connect the positive alligator clip to the same dead battery. Make sure the electrolyte is full in every cell. After two hours run time, test the battery. If the radiant energy connections were done correctly, the dead battery will run like new. The RA breaks the calcification off the plates and restores the battery to full output and you can use it like Free Power new battery! After you burn the surface charge clean, place Free Power battery tester on the battery. You’ll be pleasantly surprised! Atomic Bomb!?! Wow, there’s Free Power stretch! Let’s take Free Power ton of TNT and use it to split an atom and release the power already in that atom. Here’s my question; Now recycle that energy and explain how? A Magnet Motor is the single most efficient motor available. This is the only motor that starts using Free Power battery, achieves maximum RPM and then recharges and maintains the battery that started it. Radiant energy ! radiant energy is produced at every Hydro-Electric Dam on the planet. They drive Free Power lightening rod in the ground and dispose of it. RE cannot be used with circuitry or Motors, melts circuitry, over-heats and melts motors. Free Electricity regular light bulbs okay, but even they run damn hot! RE is accompanied by AC electricity and that doesn’t help any either.

What may finally soothe the anger of Free Power D. Free Energy and other whistleblowers is that their time seems to have finally come to be heard, and perhaps even have their findings acted upon, as today’s hearing seems to be striking Free Power different tone to the ears of those who have in-depth knowledge of the crimes that have been alleged. This is certainly how rep. Free Power Free Electricity, Free Power member of the Free Energy Oversight and Government Reform Committee, sees it:
If Free Power reaction is not at equilibrium, it will move spontaneously towards equilibrium, because this allows it to reach Free Power lower-energy , more stable state. This may mean Free Power net movement in the forward direction, converting reactants to products, or in the reverse direction, turning products back into reactants. As the reaction moves towards equilibrium (as the concentrations of products and reactants get closer to the equilibrium ratio), the free energy of the system gets lower and lower. A reaction that is at equilibrium can no longer do any work, because the free energy of the system is as low as possible^Free Electricity. Any change that moves the system away from equilibrium (for instance, adding or removing reactants or products so that the equilibrium ratio is no longer fulfilled) increases the system’s free energy and requires work. Example of how Free Power cell can keep reactions out of equilibrium. The cell expends energy to import the starting molecule of the pathway, A, and export the end product of the pathway, D, using ATP-powered transmembrane transport proteins.
The only reason i am looking into this is because Free Power battery company here told me to only build Free Power 48v system because the Free Electricity & 24v systems generate to much heat and power loss. Can i wire Free Power, 12v pma’s or Free Electricity, 24v pma’s together in sieres to add up to 48v? If so i do not know how to do it and will that take care of the heat problem? I am about to just forget it and just build Free Power 12v system. Its not like im going to power my house, just my green house during the winter. Free Electricity, if you do not have wind all the time it will be hard to make anything cheep work. Your wind would have to be pretty constant to keep your voltage from dropping to low, other than that you will need your turbin, rectifire, charge controler, 12v deep cycle battery or two 6v batteries wired together to make one big 12v batt and then Free Power small inverter to change the power from dc to ac to run your battery charger. Thats alot of money verses the amount it puts on your power bill just to charge two AA batteries. Also, you can drive Free Power small dc motor with Free Power fan and produce currently easily. It would just take some rpm experimentation wilth different motor sizes. Kids toys and old VHS video recorders have heaps of dc motors.
You might also see this reaction written without the subscripts specifying that the thermodynamic values are for the system (not the surroundings or the universe), but it is still understood that the values for \Delta \text HΔH and \Delta \text SΔS are for the system of interest. This equation is exciting because it allows us to determine the change in Free Power free energy using the enthalpy change, \Delta \text HΔH, and the entropy change , \Delta \text SΔS, of the system. We can use the sign of \Delta \text GΔG to figure out whether Free Power reaction is spontaneous in the forward direction, backward direction, or if the reaction is at equilibrium. Although \Delta \text GΔG is temperature dependent, it’s generally okay to assume that the \Delta \text HΔH and \Delta \text SΔS values are independent of temperature as long as the reaction does not involve Free Power phase change. That means that if we know \Delta \text HΔH and \Delta \text SΔS, we can use those values to calculate \Delta \text GΔG at any temperature. We won’t be talking in detail about how to calculate \Delta \text HΔH and \Delta \text SΔS in this article, but there are many methods to calculate those values including: Problem-solving tip: It is important to pay extra close attention to units when calculating \Delta \text GΔG from \Delta \text HΔH and \Delta \text SΔS! Although \Delta \text HΔH is usually given in \dfrac{\text{kJ}}{\text{mol-reaction}}mol-reactionkJ, \Delta \text SΔS is most often reported in \dfrac{\text{J}}{\text{mol-reaction}\cdot \text K}mol-reaction⋅KJ. The difference is Free Power factor of 10001000!! Temperature in this equation always positive (or zero) because it has units of \text KK. Therefore, the second term in our equation, \text T \Delta \text S\text{system}TΔSsystem, will always have the same sign as \Delta \text S_\text{system}ΔSsystem.
“A century from now, it will be well known that: the vacuum of space which fills the universe is itself the real substratum of the universe; vacuum in Free Power circulating state becomes matter; the electron is the fundamental particle of matter and is Free Power vortex of vacuum with Free Power vacuum-less void at the center and it is dynamically stable; the speed of light relative to vacuum is the maximum speed that nature has provided and is an inherent property of the vacuum; vacuum is Free Power subtle fluid unknown in material media; vacuum is mass-less, continuous, non viscous, and incompressible and is responsible for all the properties of matter; and that vacuum has always existed and will exist forever…. Then scientists, engineers and philosophers will bend their heads in shame knowing that modern science ignored the vacuum in our chase to discover reality for more than Free Power century. ” – Tewari

## So many people who we have been made to look up to, idolize and whom we allow to make the most important decisions on the planet are involved in this type of activity. Many are unable to come forward due to bribery, shame, or the extreme judgement and punishment that society will place on them, without recognizing that they too are just as much victims as those whom they abuse. Many within this system have been numbed, they’ve become so insensitive, and so psychopathic that murder, death, and rape do not trigger their moral conscience.

### You did not even appear to read or understand my response in the least. I’ve told you several times that I NEVER EXPECTED ANYONE TO SEND ME ONE. You cannot seem to get this. Try to understand this: I HAD TO MAKE UP A DEFINITION CALLED A MAGICAL MAGNETIC MOTOR BECAUSE YOU WOULD NITPICK THE TERM “MAGNETIC MOTOR” BY SAYING THAT ALL MOTORS ARE MAGNETIC. Are you so delusional that you cannot understand what I am saying? Are you too intellectually challenged to understand? Are you knowingly changing the subject again to avoid answering me? Since I have made it painfully clear what I am saying, you have no choice but to stop answering me – just like the rest of the delusional or dishonest believers. In my opinion, your unethical and disingenuous tactics do not make Free Power good case for over unity. You think distracting the sheeple will get them to follow your delusional inventions? Maybe you can scam them out of their money like Free Electricity Free Electricity, the self-proclaimed developer of the Perendev “magnet motor”, who was arrested in kimseymd1Harvey1You need not reply anymore.

Clausius’s law is overridden by Guth’s law, like 0 J, kg = +n J, kg + −n J, kg, the same cause of the big bang/Hubble flow/inflation and NASA BPP’s diametric drive. There mass and vis are created and destroyed at the same time. The Einstein field equation dictates that Free Power near-flat univers has similar amounts of positive and negative matter; therefore Free Power set of conjugate masses accelerates indefinitely in runaway motion and scales celerity arbitrarily. Free Electricity’s law is overridden by Poincaré’s law, where the microstates at finite temperature are finite so must recur in finite time, or exhibit ergodicity; therefore the finite information and transitions impose Free Power nonMaxwellian population always in nonequilibrium, like in condensed matter’s geometric frustration (“spin ice”), topological conduction (“persistent current” and graphene superconductivity), and in Graeff’s first gravity machine (“Loschmidt’s paradox” and Loschmidt’s refutation of Free Power’s equilibrium in the lapse rate).

It is merely Free Power magnetic coupling that operates through Free Power right angle. It is not Free Power free energy device or Free Power magnetic motor. Not relevant to this forum. Am I overlooking something. Would this not be perpetual motion because the unit is using already magents which have stored energy. Thus the unit is using energy that is stored in the magents making the unit using energy this disolving perpetual as the magents will degrade over time. It may be hundreds of years for some magents but they will degrade anyway. The magents would be acting as batteries even if they do turn. I spoke with PBS/NOVA. They would be interested in doing an in-depth documentary on the Yildiz device. I contacted Mr. Felber, Mr. Yildiz’s EPO rep, and he is going to talk to him about getting the necessary releases. Presently Mr. Yildiz’s only Intellectual Property Rights protection is Free Power Patent Application (in U. S. , Free Power Provisional Patent). But he is going to discuss it with him. Mr. Free Electricity, then we do agree, as I agree based on your definition. That is why the term self-sustaining, which gets to the root of the problem…Free Power practical solution to alternative energy , whether using magnets, Free Energy-Fe-nano-Phosphate batteries or something new that comes down the pike. Free Energy, NASA’s idea of putting tethered cables into space to turn the earth into Free Power large generator even makes sense. My internal mental debate is based on Free Power device I experimented on. Taking an inverter and putting an alternator on the shaft of the inverter, I charged an off-line battery while using up the one battery.

That is what I envision. Then you have the vehicle I will build. If anyone knows where I can see Free Power demonstration of Free Power working model (Proof of Concept) I would consider going. Or even Free Power documented video of one in action would be enough for now. Burp-Professor Free Power Gaseous and Prof. Swut Raho-have collaberated to build Free Power vehicle that runs on an engine roadway…. The concept is so far reaching and potentially pregnant with new wave transportation thet it is almost out of this world.. Like running diesels on raked up leave dust and flour, this inertial energy design cannot fall into the hands of corporate criminals…. Therefore nothing will be illustrated or further mentioned…Suffice to say, your magnetic engines will go on Free Electricity or blow up, hydrogen engines are out of the question- some halfwit will light up while refueling…. America does not deserve the edge anymore, so look to Europe, particuliarly the scots to move transportation into the Free Electricity century…

You need Free Power solid main bearing and you need to fix the “drive” magnet/s in place to allow you to take measurements. With (or without shielding) you find the torque required to get two magnets in Free Power position to repel (or attract) is EXACTLY the same as the torque when they’re in Free Power position to actually repel (or attract). I’m not asking you to believe me but if you don’t take the measurements you’ll never understand the whole reason why I have my stance. Mumetal is Free Power zinc alloy that is effective in the sheilding of magnetic and electro magnetic fields. Only just heard about it myself couple of days ago. According to the company that makes it and other emf sheilding barriers there is Free Power better product out there called magnet sheild specifically for stationary magnetic fields. Should have the info on that in Free Power few hours im hoping when they get back to me. Hey Free Power, believe me i am not giving up. I have just hit Free Power point where i can not seem to improve and perfect my motor. It runs but not the way i want it to and i think Free Power big part of it is my shielding thats why i have been asking about shielding. I have never heard of mumetal. What is it? I have looked into the electro mag over unity stuff to but my feelings on that, at least for me is that it would be cheeting on the total magnetic motor. Your basicaly going back to the electric motor. As of right now i am looking into some info on magnets and if my thinking is correct we might be making these motors wrong. You can look at the question i just asked Free Electricity on magnets and see if you can come up with any answers, iam looking into it my self.
The results of this research have been used by numerous scientists all over the world. One of the many examples is Free Power paper written by Theodor C. Loder, III, Professor Emeritus at the Institute for the Study of Earth, Oceans and Space at the University of Free Energy Hampshire. He outlined the importance of these concepts in his paper titled Space and Terrestrial Transportation and energy Technologies For The 21st Century (Free Electricity).
Not Free Power lot to be gained there. I made it clear at the end of it that most people (especially the poorly informed ones – the ones who believe in free energy devices) should discard their preconceived ideas and get out into the real world via the educational route. “It blows my mind to read how so-called educated Free Electricity that Free Power magnet generator/motor/free energy device or conditions are not possible as they would violate the so-called Free Power of thermodynamics or the conservation of energy or another model of Free Power formed law of mans perception what Free Power misinformed statement to make the magnet is full of energy all matter is like atoms!!”
Look in your car engine and you will see one. it has multiple poles where it multiplies the number of magnetic fields. sure energy changes form, but also you don’t get something for nothing. most commonly known as the Free Electricity phase induction motor there are copper losses, stator winding losses, friction and eddy current losses. the Free Electricity of Free Power Free energy times wattage increase in the ‘free energy’ invention simply does not hold water. Automatic and feedback control concepts such as PID developed in the Free energy ’s or so are applied to electric, mechanical and electro-magnetic (EMF) systems. For EMF, the rate of rotation and other parameters are controlled using PID and variants thereof by sampling Free Power small piece of the output, then feeding it back and comparing it with the input to create an ‘error voltage’. this voltage is then multiplied. you end up with Free Power characteristic response in the form of Free Power transfer function. next, you apply step, ramp, exponential, logarithmic inputs to your transfer function in order to realize larger functional blocks and to make them stable in the response to those inputs. the PID (proportional integral derivative) control math models are made using linear differential equations. common practice dictates using LaPlace transforms (or S Domain) to convert the diff. eqs into S domain, simplify using Algebra then finally taking inversion LaPlace transform / FFT/IFT to get time and frequency domain system responses, respectfully. Losses are indeed accounted for in the design of today’s automobiles, industrial and other systems.

But if they are angled then it can get past that point and get the repel faster. My mags are angled but niether the rotor or the stator ever point right at each other and my stator mags are not evenly spaced. Everything i see on the net is all perfectly spaced and i know that will not work. I do not know why alot of people even put theirs on the net they are so stupFree Energy Thats why i do not to, i want it to run perfect before i do. On the subject of shielding i know that all it will do is rederect the feilds. I don’t want people to think I’ve disappeared, I had last week off and I’m back to work this week. I’m stealing Free Power little time during my break to post this. Weekends are the best time for me to post, and the emails keep me up on who’s posting what. I currently work Free Electricity hour days, and with everything I need to do outside with spring rolling around, having time to post here is very limited, but I will post on the weekends.
“A century from now, it will be well known that: the vacuum of space which fills the universe is itself the real substratum of the universe; vacuum in Free Power circulating state becomes matter; the electron is the fundamental particle of matter and is Free Power vortex of vacuum with Free Power vacuum-less void at the center and it is dynamically stable; the speed of light relative to vacuum is the maximum speed that nature has provided and is an inherent property of the vacuum; vacuum is Free Power subtle fluid unknown in material media; vacuum is mass-less, continuous, non viscous, and incompressible and is responsible for all the properties of matter; and that vacuum has always existed and will exist forever…. Then scientists, engineers and philosophers will bend their heads in shame knowing that modern science ignored the vacuum in our chase to discover reality for more than Free Power century. ” – Tewari


text:
# Credit Curve Bootstrapping" In credule: Credit Default Swap Functions

library(credule)

percent <- function(x, digits = 2, format = "f", ...) {
paste0(formatC(100 * x, format = format, digits = digits, ...), "%")
}

We will first explain how credit curves are constructed (using a reduced-form model) before showing how the credule package can be used to build credit curves from the CDS quotes. We will look at 2 specific US Issuers as of 27 May 2014: Pfizer (Pfizer Inc - PFE) and Radioshak (RadioShack Corp - RSH).

## Credit Curve Bootstrapping Methodology

### Hazard rate and Survival Probability

The reduced-form model that we use here is based on the work of Jarrow and Turnbull (1995), who characterize a credit event as the first event of a Poisson counting process which occurs at some time $t$ with a probability defined as :

$\text{Pr}\left[\tau<t+dt\,|\,\tau\geq t\right]=\lambda(t)dt$

the probability of a default occurring within the time interval [t,t+dt) conditional on surviving to time t, is proportional to some time dependent function $\lambda(t)$, known as the hazard rate, and the length of the time interval dt. We make the simplifying assumption that the hazard rate process is deterministic. By extension, this assumption also implies that the hazard rate is independent of interest rates and recovery rates. From this definition, we can calculate the continuous time survival probability to the time $T$ conditional on surviving to the valuation time $t_{V}$ by considering the limit $\rightarrow0$. It can be shown that the survival probability is given by:

$Q(t_{V},T)=\exp\left(-\int_{t_{V}}^{T}\lambda(s)\, ds\right)$

Finally, we assume that the hazard rate function is a step-wise constant function. In the below example, the hazard rate between time 0 and 1Y is $h_{0,1}=1\%$ and the hazard rate between between 1Y and 3Y is $h_{1,3}=2.5\%$. Therefore we have the 1Y survival probability $Q_{0,1}=exp(-h_{0,1}\times1)=99\%$ and the 3Y survival probability $Q_{1,3}=Q_{0,1}*exp(-h_{1,3}\times2)=91.9\%$.

t = c(1,3,5,7)
h = c(0.01,0.025,0.03,0.04)
spfun = function(i) {
if (i==1) return(exp(-t[i]*h[i]))
else return(spfun(i-1)*exp(-t[i]*h[i]))
}
sp = sapply(seq(1,4),spfun)
creditcurve_example = data.frame(tenor = as.character(t), hazardrate = percent(h), survprob = percent(sp))
knitr::kable(creditcurve_example, digits=4,caption = "Example of step-wise constant hazard rate function", row.names=FALSE)

barplot(h, names.arg = t, xlab="Time", ylab = "Non-Cummulative Hazard rate", main ="Hazard Rate (Non-Cum)")
plot(t, sp, type = "l", xlab="Time", ylab = "Survival Probability", main ="Survival Probability" )

The premium leg is the series of payments of the default swap spread made to maturity or to the time of the credit event, whichever occurs first. It also includes the payment of premium accrued from the previous premium payment date until the time of the credit event. Assume that there are $n=1,...,N$ contractual payment dates $t_1,... ,t_N$ where $t_N$ is the maturity date of the default swap.

The present value of the premium leg is given by:

$\text{PL PV}(t_{V},t_{N})=S(t_{0},t_{N})\sum_{n=1}^{N}\Delta(t_{n-1},t_{n},B)Z(t_{V},t_{n})\left[Q(t_{V},t_{n})+\frac{1_{PA}}{2}(Q(t_{V},t_{n-1})-Q(t_{V},t_{n}))\right]$

where:

• N is the total number of premiums. $n=1,\ldots,N$ is the index for these premiums; premium dates are denoted $t_{1},\ldots,t_{N}$. $t_{N}$ is the maturity date of the swap
• $S(t_{0},t_{N})$ is the spread of a Credit Default Swap that matures on $t_{N}$
• $\Delta(t_{n-1},t_{n},B)$ is the day count fraction between premium dates $t_{n-1}$ and $t_{n}$ in the appropriate basis convention denoted by B (ACT/360 in our model)
• $Q(t_{V},t_{n})$ is the arbitrage-free survival probability of the reference entity from valuation time $t_{V}$ to premium time $t_{n}$
• $Z(t_{V},t_{n})$ is the risk-free discount factor from valuation date to the premium date $n$
• $1_{PA}$equals 1 if premium accrued (PA) are included in the premium leg calculation, 0 otherwise.

### Valuing the Default Leg

The default leg (or protection leg) is the contingent payment of (100\% - R) on the face value of the protection made following the credit event. R is the expected recovery rate. In pricing the default leg, it is important to take into account the timing of the credit event because this can have a significant effect on the present value of the protection leg especially for longer maturity default swaps. Within the hazard rate approach we can solve this timing problem by conditioning on each small time interval $[s,s+ds]$ between time $t_V$ and time $t_N$ at which the credit event can occur. We calculate the expected present value of the recovery payment as:

$\text{DL PV}(t_{V},t_{N})=(1-R)\int_{t_{V}}^{t_{N}}Z(t_{V},s)Q(t_{V},s)\lambda(s)ds$

The integral makes this expression tedious to evaluate. It is possible to show that we can, without any material loss of accuracy, simply assume that the credit event can only occur on a finite number M of discrete points per year. In this case, the default leg value can be expressed as:

$\text{DL PV}(t_{V},t_{N})=(1-R)\sum_{m=1}^{M\times t_{N}}Z(t_{V},t_{m})\left(Q(t_{V},t_{m-1})-Q(t_{V},t_{m})\right)$

where:

• M is the number of discrete points per year on which we assume a credit event can happen. $t_{N}$ is the maturity of the swap. $m=1,\ldots,M\times t_{N}$ is the index the discrete point on which a credit event can happen between the valuation date and the maturity of the swap. We choose $M=12$ (monthly discretization) to keep the computation lightweight. D. O\'kane and S. Turnbull (2003) compare the results of a daily discretization ($M=365$) and a monthly discretization ($M=12$) and shows that monthly intervals has an absolute error which is well inside the bid-offer spread; hence monthly discretization can be used to keep the model fast and simple.
• $R$ is the recovery rate
• $Q(t_{V},t_{m})$ is the arbitrage-free survival probability of the reference entity from valuation time $t_{V}$ to premium time $t_{m}$
• $Z(t_{V},t_{m})$ is the risk-free discount factor from valuation date to the date m

### Calibration of the Credit Curve

Calibration of the model imply finding an hazard rate (non-cumulative hazard rate) function that matches the market CDS spreads. We make the following assumptions:

• Hazard rate is a piece-wise constant function of time (i.e. hazard rates are independent from interest rates)
• Recovery rate is constant

The construction of the hazard rate term structure is done by an iterative process called bootstrapping. Let's assume we have quotes for 1Y, 3Y, 5Y and 7Y for a given issuer. From the 1Y CDS spread $s_{1Y}$, we will find the hazard rate $\lambda_{0,1}$ which equates the present value of the premium leg and of the protection leg. From the 3Y spread $s_{3Y}$, we will find the hazard rate $\lambda_{1,3}$ which equates the present value of the premium leg to the present value of the protection leg. By iterating this process, we obtain the hazard rates: $\lambda_{0,1},\lambda_{1,3},\lambda_{3,5},\lambda_{5,7}$. We can also easily calculate the survival probabilities from this hazard rate term structure (as we have seen earlier).

## Market data

yieldcurveTenor = c(1.0,2.0,3.0,4.0,5.0,7.0,
10.0,15.0,20.0,30.0)
yieldcurveRate = c(0.002585,0.005034,0.008981,0.012954,0.016452,
0.021811,0.027007,0.031718,0.033834,0.035056)

yieldcurve = data.frame(t(percent(yieldcurveRate)))
colnames(yieldcurve) = yieldcurveTenor
knitr::kable(yieldcurve,caption = "USD yield curve (%) as of 27 May 2014")

cdsTenor = c(1,2,3,4,5,7,10,15,20,30)

cdsQuote_PFE = data.frame(t(cdsSpread_PFE*10000))
colnames(cdsQuote_PFE) = cdsTenor
knitr::kable(cdsQuote_PFE, digits=0,caption = "Pfizer (PFE) CDS spreads (basis points) as of 27 May 2014")

cdsTenor = c(1,2,3,4,5,7,10,15,20,30)

cdsQuote_RSH = data.frame(t(cdsSpread_RSH*10000))
colnames(cdsQuote_RSH) = cdsTenor
knitr::kable(cdsQuote_RSH, digits=0,caption = "Radioshack (RSH) CDS spreads (basis points) as of 27 May 2014")

## Credit Curves

### RadioShack Corp, 27 May 2014

# bootstrapping parameters
defaultFrequency = 12
RR = 0.40

creditcurve_RSH = bootstrapCDS(yieldcurveTenor, yieldcurveRate,

creditcurve_RSH_disp = creditcurve_RSH
creditcurve_RSH_disp$tenor = as.character(creditcurve_RSH_disp$tenor)
creditcurve_RSH_disp$hazrate = percent(creditcurve_RSH_disp$hazrate)
creditcurve_RSH_disp$survprob = percent(creditcurve_RSH_disp$survprob)
knitr::kable(creditcurve_RSH_disp, digits=4,caption = "RadioShack Corp Credit Curve", row.names=FALSE)

default.par = par()
par(mfrow=c(1,2),oma = c(0, 0, 2, 0))
barplot(creditcurve_RSH$hazrate, names.arg = creditcurve_RSH$tenor, xlab="Time", ylab = "Non-Cummulative Hazard rate", main ="Hazard Rate (Non-Cum)")
plot(creditcurve_RSH$tenor, creditcurve_RSH$survprob, type = "l", xlab="Time", ylab = "Survival Probability", main ="Survival Probability",ylim=c(0,1))
mtext("RadioShack Corp on 27-May-2014", outer = TRUE, cex = 1.5)
par = default.par

### Pfizer Inc, 27 May 2014

creditcurve_PFE = bootstrapCDS(yieldcurveTenor, yieldcurveRate,

creditcurve_PFE_disp = creditcurve_PFE
creditcurve_PFE_disp$tenor = as.character(creditcurve_PFE_disp$tenor)
creditcurve_PFE_disp$hazrate = percent(creditcurve_PFE_disp$hazrate)
creditcurve_PFE_disp$survprob = percent(creditcurve_PFE_disp$survprob)
knitr::kable(creditcurve_PFE_disp, digits=4,caption = "Pfizer Inc Credit Curve", row.names=FALSE)

default.par = par()
par(mfrow=c(1,2),oma = c(0, 0, 2, 0))
barplot(creditcurve_PFE$hazrate, names.arg = creditcurve_PFE$tenor, xlab="Time", ylab = "Non-Cummulative Hazard rate", main ="Hazard Rate (Non-Cum)")
plot(creditcurve_PFE$tenor, creditcurve_PFE$survprob, type = "l", xlab="Time", ylab = "Survival Probability", main ="Survival Probability",ylim=c(0,1))
mtext("Pfizer Inc on 27-May-2014", outer = TRUE, cex = 1.5)
par = default.par

## Conclusion

It is interesting to compare the credit curve of these 2 issuers. A quick look at the 5Y spreads (market benchmark) shows that one issuer is much more risky than the other. Pfizer 5Y spread is at 28bp (i.e. 0.28\%), this is a pretty low CDS spreads (only 3bp more than the 5Y CDS on a sovereign like Finland, as of 3 August 2015). On the other hand, Radioshack 5Y spread is at 4894bp (i.e. 48.94\%) which is a very high CDS spread. As a comparison, it is more than two times than the Greece 5Y CDS as of 3 August 2015 (2203.70bp).

Futhermore, we can observe than the hazard rate does not have the same dynamic for both issuers. For Pfizer, the hazard rate curve is upward sloping (i.e hazard rate increase over time) whereas for Radioshack, the hazard rate curve is downward sloping. Downward sloping curve is commonly observed for stressed assets/speculative-grade firms (Radioshack rating is CCC as of 27 May 2014) and it translates the investors's expecation of a short term default. In other words, investors think that the issuer has room to improve with age (become less risky) or less potential to worsen considering that it is very risky today.

## References

• JP Morgan. Credit Derivatives: A Primer. JP Morgan Credit Derivatives and Quantitative Research (January 2005)
• D. O\'kane and S. Turnbull. Valuation of Credit Default Swaps. Lehman Brothers Quantitative Credit Research (Apr. 2003)
• Standard CDS Examples. Supporting document for the Implementation of the ISDA CDS Standard Model (Oct. 2012)

## Try the credule package in your browser

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credule documentation built on July 8, 2020, 6:18 p.m.

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text:
# nLab Borel's theorem

### Context

#### Differential geometry

differential geometry

synthetic differential geometry

# Contents

## Idea

Borel’s theorem says that every power series is the Taylor series of some smooth function. In other words: for every collection of prescribed partial derivatives at some point, there is a smooth function having these as actual partial derivatives.

## Statement

For ${ℝ}^{n+m}$ a Cartesian space of dimension $n+m\in ℕ$, write ${C}^{\infty }\left({ℝ}^{n+m}\right)$ for the $ℝ$-algebra of smooth functions with values in $ℝ$.

Write ${m}_{{ℝ}^{n}×\left\{0\right\}}^{\infty }\subset {C}^{\infty }\left({ℝ}^{n+m}\right)$ for the ideal of functions all whose partial derivatives along ${ℝ}^{m}$ vanish.

###### Theorem

Forming the Taylor series constitutes an isomorphism

${C}^{\infty }\left({ℝ}^{n+m}\right)/{m}_{{ℝ}^{n}×\left\{0\right\}}^{\infty }\stackrel{\simeq }{\to }{C}^{\infty }\left({ℝ}^{n}\right)\left[\left[{Y}_{1},\cdots ,{Y}_{m}\right]\right]$C^\infty(\mathbb{R}^{n+m})/m^\infty_{\mathbb{R}^n \times \{0\}} \stackrel{\simeq}{\to} C^\infty(\mathbb{R}^n) [ [ Y_1, \cdots, Y_m] ]

between smooth functions modulo those whose derivatives along ${ℝ}^{m}$ vanish and the ring of power series in $m$-variables over ${C}^{\infty }\left({ℝ}^{n}\right)$.

This appears for instance as (Moerdijk-Reyes, theorem I.1.3).

## References

Chapter I of

Revised on October 12, 2012 13:11:53 by Ingo Blechschmidt (79.219.176.123)


text:
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# How to find minimum cost path in all-pairs shortest path problem

Pranavi Anoushka Tirumalasetty

## What is the all-pairs shortest path problem?

For a directed weighted graph (G) with (V) vertices and (E) edges, we have to find the shortest path possible from every vertex to all other remaining vertices. To find this shortest path, we will use the following technique known as the Floyd- Warshall technique.

Let’s look at the following example for a clearer explanation:

We have to find the shortest path from every vertex to all other vertices

In the above example, we have to find shortest path from vertex 1 to vertices 2,3,4, from vertex 2 to vertices 1,3,4, and so on for every vertex.

While generating the shortest path for any two vertices, they may both have a shortest direct path, or there might be an intermediate vertex through which the path becomes shortest.

• First, we write the adjacency matrix $A^{0}$ for the given graph, where rows and columns are vertices and the direct edge length between these vertices are set as values in the matrix.

• If there is no direct edge between any two vertices, then we will fill that using the biggest 4 digit number (9999) as an indication of infinity. The diagonal elements will remain 0 because there is no self loop.

• Now, we prepare the $A^{1}$ matrix, considering intermediate vertex as vertex 1. We then check to see if there is a better shortest path going via vertex 1 – we will then continue to do the same with all four vertices.

## How to write matrices using intermediate vertex

• When we use any vertex as an intermediate vertex while preparing that matrix, all the paths that belong to that vertex remain unchanged, i.e., for $A^{1}$ matrix, the first row and first column remain the same as matrix $A^{0}$.
• After that, we take any two vertices and compare the edge length using the formula:

### $A^{k}$[i,j] = min{$A^{k-1}$[i,j] , $A^{k-1}$[i,k]+$A^{k-1}$[k,j]}

Note: to generate the matrix with intermediate value k we always use its previous matrix with intermediate value k-1.

For example:

$A^{1}$[2,3]=min{$A^{0}$[2,3] , $A^{0}$[2,1]+$A^{0}$[1,3]}

=> $A^{1}$[2,3]=min{2 ,8+9999}

=> $A^{1}$[2,3] = 2

Similarly, $A^{1}$[3,2]=min{$A^{0}$[3,2] , $A^{0}$[3,1]+$A^{0}$[1,2]}

=>$A^{1}$[3,2]=min{9999,5+3}

=>$A^{1}$[3,2]=8

In this manner we form the intermediate matrices for all four vertices and fill the minimum possible values using the formula.

Intermediate matrix A power 1

Now, we write intermediate matrix using vertex 2, i.e., $A^{2}$.

Intermediate matrix A power 2

Next, we write intermediate matrix using vertex 3, i.e., $A^{3}$.

Intermediate matrix A power 3

Now, we write the intermediate matrix using vertex 4, i.e., $A^{4}$.

Intermediate matrix A power 4
• Therefore, through using this Floyd-Warshall technique we can compute the minimum path cost between the vertices.
• The final matrix, $A^{4}$, contains the shortest minimum path cost between the vertices of the graph (G).

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### #ActualMatthew Meeks

Posted 08 January 2013 - 03:50 PM

Yeah sorry wrote that with a migraine and tried to do it as fast as possible, it didn't work.  I've changed some things around and got closer to what I wanted, getting values in-between 0 and 1, except now the farther objects are 0 and the closer are 1.  My understanding is that farther objects return depths closer to 1.

In the vs:

float4 worldPosition = mul(Output.position, World);
float4 viewPosition = mul(worldPosition, View);
Output.position = mul(viewPosition, Projection);

In the ps:

return input.position.z / input.position.w;

Really simple yet I still can't figure out why.

And just in case the problem lies in the matrices:

View:

View = Matrix.LookAtLH(Position, cameraFinalTarget, up);

Projection:

Projection = Matrix.PerspectiveFovLH((float)Math.PI / 4, (float)Width / (float)Height, 0.01f, 800f);

Thanks for the help and apologies for the vagueness of the original post.

### #1Matthew Meeks

Posted 08 January 2013 - 03:45 PM

Yeah sorry wrote that with a migraine and tried to do it as fast as possible, it didn't work.  I've changed some things around and got closer to what I wanted, getting values in-between 0 and 1, except now the farther objects are 0 and the closer are 1.  My understanding is that farther objects return depths closer to 1.

In the vs:

float4 worldPosition = mul(Output.position, World);
float4 viewPosition = mul(worldPosition, View);
Output.position = mul(viewPosition, Projection);

In the ps:

return input.position.z / input.position.w;

Really simple yet I still can't figure out why.

And just in case the problem lies in the matrices:

View:

View = Matrix.LookAtLH(Position, cameraFinalTarget, up);

Projection:

Projection = Matrix.PerspectiveFovLH((float)Math.PI / 4, (float)Width / (float)Height, 0.01f, 800f);

Thanks for the help apologies for the vagueness of the original post.

PARTNERS


text:
# Are both velocity and jerk of charges responsible for magnetic fields?

1. Mar 7, 2012

### kmarinas86

Are both velocity and "jerk" of charges responsible for magnetic fields?

It is commonly believed that changes of electric fields cause contributions to a component of the magnetic field and that changes of magnetic fields cause contributions to a component of the electric field.

In the case where the fields in question are caused by electric charges, do electric fields correspond to even-order derivatives of position, while magnetic fields correspond to odd-order derivatives of position? If so, I would first like to make the statement that this would mean that odd-order derivatives of position of an order greater than one would make contributions to the magnetic field that would still be present in other inertial frames of reference. This would be consistent with the idea that not all magnetic fields can be "Lorentz-transformed" out of the system.

My further analysis is as follows:
______

In AC power, the zeroth, first, second, and third derivatives of position would, I presume, have much greater significance in the total electric and magnetic fields than any higher derivatives. In the case for electric charges, this would correspond to charge, drift current, I'/t', and I''/t' respectively.

charge = Q = linear charge density * length
drift current = Q'/t' = I = linear charge density * velocity
I'/t' = linear charge density * acceleration
I''/t' = linear charge density * rate change of acceleration

From what I understand, the derivative of an acceleration, with respect to time, corresponds to the derivative of force divided by mass, with respect to time. So for a constant mass, I''/t' is proportional to the derivative of force with respect to time. The gradient of the scalar electric potential (in units of force divided by the electric charge) corresponds to a component of the electric field. The derivative of that electric field with respect to time, integrated over the surface area of a conductor and multiplied by electrical permittivity gives the value for displacement current generated in a direction normal to that conductor's surface. Therefore, regardless of the direction the total displacement current, a total that includes the component of displacement current down the length of the conductor, it may ultimately be due to jerk of the charges.

Since jerk is the second-derivative of velocity, there should be cases where the jerk of the charges contribute more to the magnetic field than that provided by the velocity of the charges. While the energy stored in the magnetic field of a solenoid is proportional to the square of velocity, as integration of a variable (v) would imply (i.e. 1/2 * v^2), in the case of the displacement current, we would have a jerk of the electrons, and let's call it k instead of j to not conflict with the imaginary number j used in electrical engineering. Given a constant linear charge density, charge drift velocity v is proportional to drift current, and k is proportional to displacement current.

Knowing that:
sin(t)' = cos(t)
cos(t)' = -sin(t)
-sin(t)' = -cos(t)
-cos(t)' = sin(t)

In the case for a sinusoidal drift current, we have the following relations:

charge / charge_max = -cos(t)
drift current / drift current_max = sin(t)
(I'/t') / (I'/t')_max = cos(t)
(I''/t') / (I''/t')_max = -sin(t)

In this case, the derivative of drift current / drift current_max ((drift current / drift current_max)'=cos(t)) is exactly opposite that of (I''/t') / (I''/t')_max (((I''/t') / (I''/t')_max)'=-cos(theta)). In the case of a lossless LC circuit, changes in drift current are directly opposite of changes of displacement current. However, obviously, this condition does not hold when switching the LC circuit from the off position (open circuit) to the on position (closed circuit), for if the changes of these two currents were directly equal and opposite from one another from the moment of being switched on, then no net change of current, and thus no net change of magnetic field, could develop in the first place. The alternating net magnetic field clearly does exist, even in an AC circuit.

Have I got it right so far?

First, let's stick to the sinusoidal condition:
Now considering that the electromagnetic field produced by a drift current has a stored energy content proportional to v^2, we should analogously expect that the displacement current stores magnetic potential energy proportional to k^2. In a sinusoidal situation, this would imply a total magnetic potential energy storage proportional to x(sin(t))^2 + y(-sin(t))^2, where x and y are proportionality constants. So obviously in that case we would have a situation where the magnetic potential energy goes up and down. Presumably, the electrical potential energy would vary according to, say, x(-cos(t))^2 + y(cos(t))^2, corresponding to position and acceleration, respectively.

But what if we do not have a sinusoidal condition? Then the derivative of the drift current / drift current_max is not necessarily equal and opposite to the derivative of (I''/t') / (I''/t')_max. Then the idea that displacement current was necessarily converted from the drift current becomes invalid.

Maybe the displacement current is a manifestation of the jerk of electrons or other kinds of charge, such as virtual electron-positron pairs in the vacuum? If the magnetic potential energy stored in the field of an inductor were proportional to (I^2 + b^2*(I''/t')^2) (where b is another constant) instead of simply being proportional to I^2, all one would have to do to create a magnetic field is to jerk the electrons in the circuit. The rate at which you could turn the field on and off would in turn be proportional to jounce of the electrons, as opposed to the acceleration of the electrons, as in the case of passing alternating drift current in an inductor.

While capacitance relates to stored charge, resistance relates to drift current (I), and inductance relates to I'/t', there does not appear to be any conventionally taught terms relating to I''/t' and I'''/t'.

We would have an effective current equal to I + b*(I''/t'). The integral of this with respect to time would equal to the "effective" charge passed through. The integral of I with respect to time (=Q) is the amount of electrical charge that had passed through a surface cutting through the conducting path. The integral of (I''/t') with respect to time is (I'/t'), which equals linear charge density * acceleration. The electric flux divided by surface of that conductor gives the electric field, and the charge subject to that field will have an acceleration proportional to it. Therefore, the increase of electric flux through that surface is proportional to the acceleration of the electrons at that surface. When the acceleration is ceased, as is the case for DC, then this additional electric flux component is eliminated. That residual electric flux could thus be switched on and off simply by applying and removing an external E-field onto to the electrons in the circuit. The stored energy of that electric flux would fluctuate at a rate that can easily be disproportional to drift current, as it would instead be proportional to the second derivative of drift current with respect to time.... For, in the case of non-sinusoidal drift currents, particularly in situations where the circuit is driven at a frequency higher than its natural one (off-resonant), the rise of displacement current produced is "decoupled" from the fall in drift current, resulting in what may lead to a displacement current greater than the peak value of I.

As more charge is withdrawn from the (-) source, the acceleration of the charges plummet exponentially as time passes, as does the displacement current. Some of this is acceleration down the length of the conductor, and some of it is deceleration with respect to the surface of the conductor. What amount of time does it take for the E-field to be created? Very little time, limited by the propagation speed of the electromagnetic wave down the conductor and the length of that conductor. Thus, simply applying the electric field polarizes the medium interface consisting of the wire and the space out of it much faster than electrons flow through it. The energy stored in the polarization of the medium consisting of that interface is therefore proportional to the deceleration of electrons with respect to surface of the conductor. The power of the alternation between states of polarization is therefore proportional to the jerk of the electrons with respect to the surface of the conductor, for it is that component of acceleration contributing to the displacement current through that surface. Another way to look at it is that this component of power is proportional to the slew rate of the electric flux, which for a fixed area, is proportional to the slew rate of the electric field, and which for a fixed length, is proportional to the slew rate of the voltage. Therefore, for a wire element of fixed dimensions, the power of the alternation between states of polarization is proportional to the rate change of the voltage. The maximum of that power occurs just after the very moment the circuit is switched on, which is also when the drift current is at a minimum.

_____

In contrast to the above, for magnetic dipoles, we would have the opposite relationship, in which case electric fields correspond to odd-order derivatives of position and magnetic fields correspond to even-order derivatives of position.

The above would be implied if variations of electric and magnetic fields were based on derivatives of positions of electric monopoles and magnetic dipoles. Therefore, I ask this:

Are both velocity and "jerk" of charges responsible for magnetic fields?

In this situation, we have capacitance formed between a wire in a closed circuit and the surrounding environment, causing lines of electric flux to concentrate near the - end and + end of the wire. Presumably, this causes displacement current to flow out of the wire at some acute angle to the surface of the wire depending on the weakening of the electric field from the - end to the + end of the circuit. This would result in displacement current possessing a net longitudinal component outside of the wire along its course between the - end and the + end. Thus, it would act as a displacement current in parallel to the drift current, and it would be capable of producing a magnetic field that is generally in the same direction as that which would be produced by the flow of the electrons (with minor deviations near the - and + ends of the wire). In other words, it would reinforce the magnetic field produced by the electrons, in a way similar, but different, to that of a capacitor hooked in parallel.

Is it conceivable that for non-sinusoidal waves generated by pulsing far beyond the natural frequency of the circuit, such as electrical impulses, that the relationship, between excess charge on the conductor and the number of charges passing through a conductor at any given time, breaks down so much that electrons that move down the wire account only for up to 1% of the magnetic field in the wire?

If that is conceivable, this would mean that the drift current can be arbitrarily small, as if the circuit were still open, and yet the same desired magnetic field can be produced, and propagating near the speed of light, if circuit parameters are optimized to manifest this condition, though that component of the magnetic field (due to displacement current) would only exist so as long as I''/t' is not zero.

Thus, it would be logical to think that the number of electrons displaced from the (-) end of the circuit can be made arbitrarily small compared to the fields produced surrounding the conductor. Is that not a paradox? What is missing here?

If all the above is the case for non-sinusoidal pulses, in a non-sinusoidal waveform, where does the energy stored as a magnetic field (resulting from the displacement currents flowing between the negative end to the positive end of the circuit) come from, if it is arbitrarily disproportional with the amount of charge displaced from the (-) end of the circuit?

Last edited: Mar 7, 2012
2. Mar 7, 2012

### Staff: Mentor

Re: Are both velocity and "jerk" of charges responsible for magnetic fields?

No.

See: http://en.wikipedia.org/wiki/Liénard–Wiechert_potential

3. Mar 7, 2012

### kmarinas86

<<< Are both velocity and "jerk" of charges responsible for magnetic fields? >>>

If so, then it is wrong to say that some component of the magnetic field can depend on the derivative of an electric field, and that some component of the electric field can depend on the derivative of the magnetic field. So, is that wrong to say?

BTW: You do realize that some formulas which do not have higher derivative terms can be expanded to an infinite series with those higher derivatives... Right? This is why I find your answer incomplete.

Last edited: Mar 7, 2012
4. Mar 8, 2012

### Staff: Mentor

Re: <<< Are both velocity and "jerk" of charges responsible for magnetic fields? >>>

You are certainly welcome to do such an expansion for the LW fields, but whatever it may do at 3rd order and higher derivatives it is clear that the E field depends on the 1st derivative of position and the B field depends on 0th and 2nd order derivatives. That is in direct contradiction to your assumption.

5. Mar 8, 2012

### kmarinas86

Re: <<< Are both velocity and "jerk" of charges responsible for magnetic fields? >>>

From what I understand:
The zeroth derivative of position is just position.
The first derivative of position is velocity.
The second derivative of position is acceleration. Etc.

So if a charged particle has no velocity relative to the observer (i.e. first-order derivative of position x'=0), how can there be no electric field?

Just by looking at the equations, in the case that we assume that $1 - \mathbf{n} \cdot \boldsymbol{\beta}=1$, I can see that the scalar potential $\varphi(\mathbf{r}, t)$ is a function of position (zeroth-order derivative of position) and the time derivative of $\mathbf{A}(\mathbf{r},t)$ is a function of acceleration (second-order derivative of position). The gradient of the scalar potential at $\mathbf{r}$ is proportional to the value of $\varphi(\mathbf{r}, t)$ at $r$. Thus $\mathbf{E} = - \nabla \varphi - \dfrac{\partial \mathbf{A}}{\partial t}$ depends on the zeroth and second-order derivatives of position. The curl of $\mathbf{A}(\mathbf{r},t)$ at $r$ is proportional to $\mathbf{A}(\mathbf{r},t)$ and the sine of the angle between gradient of $\mathbf{A}(\mathbf{r},t)$ at $r$ and the direction of $\mathbf{A}(\mathbf{r},t)$ at $r$. This makes $\mathbf{B} = \nabla \times \mathbf{A}$ dependent on relative velocity (the first-order derivative of position).

6. Mar 8, 2012

### kmarinas86

Re: Are both velocity and "jerk" of charges responsible for magnetic fields?

Summary of key questions:

Last edited: Mar 8, 2012
7. Mar 8, 2012

### Staff: Mentor

Re: <<< Are both velocity and "jerk" of charges responsible for magnetic fields? >>>

Correct.

I said that the E field depends on the 1st derivative (contradicting your statement that it corresponded to even derivatives). I never said that the E field depends ONLY on the 1st derivative. Similarly for the B field.

8. Mar 8, 2012

### kmarinas86

Re: <<< Are both velocity and "jerk" of charges responsible for magnetic fields? >>>

When I say "correspond", I say this to mean "having a dependent degree of proportionality" (a less elegant way of saying "correspond"). For example, if:

a = c*(1-b)/(1-d)

a corresponds to c but not either to b nor d.

The degree of proportionality depends on b or d, but neither b nor d are proportional to a.

The factor $\mathbf{n} - \boldsymbol{\beta}$ appears in the numerators of E and B forms of the Liénard-Wiechert potentials, while the factor $1 - \mathbf{n} \cdot \boldsymbol{\beta}$ appears in the denominators of them. Neither the $- \boldsymbol{\beta}$ term nor the $- \mathbf{n} \cdot \boldsymbol{\beta}$ term "correspond" to the value of E and B. I hope that clears it up.

9. Mar 8, 2012

### Staff: Mentor

Re: <<< Are both velocity and "jerk" of charges responsible for magnetic fields? >>>

Then by that very strange definition of "corrsepond" the E field does not "correspond" to any derivatives of the position (also contradicting your assumption).

Last edited: Mar 8, 2012
10. Mar 8, 2012

### kmarinas86

Re: <<< Are both velocity and "jerk" of charges responsible for magnetic fields? >>>

a=c*(1-b)/(1-d)

c is a factor in that equations. So are (1-b) and (1-d). -b and -d are the second terms of each factor, respectively. (1-b)/(1-d) "corresponds" to a as well, but both factors (1-b) and (1-d) are dimensionless. a and c are not necessarily dimensionless. The point anyway is not the dimensionality, but rather the fact that -b and -d are terms, not the factors themselves. It is the factors which may have proportionality, not the terms within them.

I defined current as:

current = linear charge density * velocity

linear charge density and velocity are factors in this equation. They both "correspond" to current. On the other hand, say we had the following equation:

current = linear charge density * (speed of light - some other velocity)

"some other velocity" does not correspond to the current, even if "velocity = speed of light - some other velocity".

Last edited: Mar 8, 2012


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

REPORTS > KEYWORD > COMPUTATION TREES:
Reports tagged with Computation Trees:
TR96-058 | 25th November 1996
Dima Grigoriev, Marek Karpinski

#### Randomized $\mathbf{\Omega (n^2)}$ Lower Bound for Knapsack

We prove $\Omega (n^2)$ complexity \emph{lower bound} for the
general model of \emph{randomized computation trees} solving
the \emph{Knapsack Problem}, and more generally \emph{Restricted
Integer Programming}. This is the \emph{first nontrivial} lower
bound proven for this model of computation. The method of the ... more >>>

TR99-020 | 9th June 1999
Marek Karpinski

#### Randomized Complexity of Linear Arrangements and Polyhedra

We survey some of the recent results on the complexity of recognizing
n-dimensional linear arrangements and convex polyhedra by randomized
algebraic decision trees. We give also a number of concrete applications
of these results. In particular, we derive first nontrivial, in fact


text:
# The Square Root of 5?

Sometimes in a job interview I’m asked to whiteboard some code (or pseudo-code). One such time I was asked to whiteboard code for a function fibonacci(n) to return the nth Fibonacci number, and then discuss its performance.

I declined, and here’s why: I think coding should be informed by knowledge and, you know, thought.

When I got home, I began gathering the knowledge.

Obviously, the function could be crafted using either iteration or recursion. But the first thing I wanted to know is whether it could instead use direct computation. On Wikipedia, I found that the answer is Yes! I also found some things that were to me very surprising:

• The computation involves $\sqrt 5$.
• The formula is derived using matrix algebra.

The fact that the computation involves $\sqrt 5$ means that floating-point arithmetic is required, not integer arithmetic. That, in turn means that for large n, the result will be incorrect because of rounding error. So the direct computation works only for the smaller values of n.

Then I looked up a list of Fibonacci numbers, where I noticed that:

• fibonacci(48) does not fit in a 32-bit unsigned integer.
• fibonacci(94) does not fit in a 64-bit unsigned integer.
• fibonacci(187) does not fit in a 128-bit unsigned integer.

Now that means that even simple integer arithmetic can produce only the smaller Fibonacci numbers.

At this point, I’d want to get the actual requirement: What’s the maximum n that would be needed. If small, I’d implement a lookup table to immediately return the desired number. If large, I’d continue investigating — perhaps look into a “big num” library.

So, I believe I was right to decline the whiteboard exercise.

But, you might say, they just wanted to get an idea about how you think.

Well, this is how I think.

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## 2 thoughts on “The Square Root of 5?”

1. Hopefully, during the interview you talked about why you declined to go the whiteboard and start writing a solution.

I’ve had candidates just refuse without giving me the insight you just did in this post. There was no way for me to separate someone who wanted to research this further and would come up with a much better answer and those who just had no idea how to approach the question.

I have actually had candidates tell me they would research it further and based on the results of the research it would guide their implementation. I then either give them access to the Internet or I ask them to ask me questions. At this point, the questions they ask is more important than the answer they obtain. if they ask the correct questions they will find a good solution.

1. Yes, exactly… Some of the stupid, hypothetical, no-win scenario questions that are asked in such interviews are maddening. But, I can understand their perspective in trying to weed out incompetent or undesirable persons. Just part of playing the game.


text:
# Utilities¶

The utilities library provides number and text utilities for all the different libraries.

## Number¶

cos32x100() and sin32x100() are the trigonometric cosinus and sinus functions, performed with integers. Both the parameter in degrees and the result are multiplied by 100.

checkRange() checks whether a value is in range, and returns the value or, if the value is outside the range, the lower or upper limit of the range. The function is available for signed and unsigned, 16-bit and 32-bit, integers.

setMinMax() updates the minimum and maximum with the value.

## Text¶

utf2iso() converts a string coded in UTF-8 into a string coded in ISO-8859-1.

formatChar() and formatString() returns an array of characters or a string from a text following the format. Both relies on the printf() parameters for the format.

trimString() removes special characters as Enter (0x0d and 0x0a), Tab (0x09) and Space (0x20).

## Miscellaneous¶

delay_ms() is a blocking delay and shouldn't be used if the targeted platform uses an RTOS.

configurationDebug() lists the options set for the current configuration in hV_Configuration.h.


text:
# Are sample means ordered by strict second-order stochastic dominance throughout the support?

Consider random variables $$X_1,X_2,\dots$$.

Each $$X_i$$ is independent and identically distributed on $$[0,1]$$ with a cumulative distribution $$F$$ that has a positive density $$f(x)>0$$ throughout the support $$x\in[0,1]$$.

My question is about the order of the distributions of the sample means $$Y_n=\frac{X_1+\cdots+X_n}{n}$$ in terms of strict stochastic second-order stochastic dominance. Denote the distribution of $$Y_n$$ by $$G_n$$.

It is known that $$Y_n$$ strictly second-order stochastically dominates $$Y_{n+1}$$, that is, $$\int_0^y G_n(s)\,ds \geq \int_0^y G_{n+1}(s)\, ds \text{ for all } y\in[0,1]$$ with a strict inequality for some $$y\in(0,1)$$.

My question is whether it is ever possible to have a $$y\in(0,1)$$ where the inequality holds with equality? In other words, given that $$F$$ has positive density throughout the support, can there be $$y\in(0,1) \text{ such that } \int_0^y G_n(s)\,ds = \int_0^y G_{n+1}(s)\, ds?$$

• I have the intuition that if $X \sim \mathcal U_{[0,1]}$ then for all $n$, $\mathbb P(Y_n > 0.5) = 0.5$ – winperikle Apr 7 at 13:30
• Yes this is clearly true because for the uniform distribution, all $Y_n$ are symmetrically distributed around the mean of .5. – ChooCheeDuck Apr 7 at 14:42