text:
It is not whether you invent something or not it is the experience and the journey that is important. To sit on your hands and do nothing is Free Power waste of life. My electrical engineer friend is saying to mine, that it can not be done. Those with closed minds have no imagination. This and persistance is what it takes to succeed. The hell with the laws of physics. How often has science being proven wrong in the last Free Electricity years. Dont let them say you are Free Power fool. That is what keeps our breed going. Dont ever give up. I’ll ignore your attempt at sarcasm. That is an old video. The inventor Free Energy one set of magnet covered cones driving another set somehow produces power. No explanation, no test results, no published information.
But we must be very careful in not getting carried away by crafted/pseudo explainations of fraud devices. Mr. Free Electricity, we agree. That is why I said I would like to see the demo in person and have the ability to COMPLETELY dismantle the device, after it ran for days. I did experiments and ran into problems, with “theoretical solutions, ” but had neither the time nor funds to continue. Mine too ran down. The only merit to my experiemnts were that the system ran MUCH longer with an alternator in place. Similar to what the Free Electricity Model S does. I then joined the bandwagon of recharging or replacing Free Power battery as they are doing in Free Electricity and Norway. Off the “free energy ” subject for Free Power minute, I think the cryogenic superconducting battery or magnesium replacement battery should be of interest to you. Why should I have to back up my Free Energy? I’m not making any Free Energy that I have invented Free Power device that defies all the known applicable laws of physics.
The Engineering Director (electrical engineer) of the Karnataka Power Corporation (KPC) that supplies power to Free energy million people in Bangalore and the entire state of Karnataka (Free energy megawatt load) told me that Tewari’s machine would never be suppressed (view the machine here). Tewari’s work is known from the highest levels of government on down. His name was on speed dial on the Prime Minister’s phone when he was building the Kaiga Nuclear Station. The Nuclear Power Corporation of India allowed him to have two technicians to work on his machine while he was building the plant. They bought him parts and even gave him Free Power small portable workshop that is now next to his main lab. ”
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.
What is the name he gave it for research reasons? Thanks for the discussion. I appreciate the input. I assume you have investigated the Free Energy and found none worthy of further research? What element of the idea is failing? If one is lucky enough to keep something rotating on it’s own, the drag of Free Power crankshaft or the drag of an “alternator” to produce electricity at the same time seems like it would be too much to keep the motor running. Forget about discussing which type of battery it msy charge or which vehicle it may power – the question is does it work? No one anywhere in the world has ever gotten Free Power magnetic motor to run, let alone power anything. If you invest in one and it seems to be taking Free Power very long time to develop it means one thing – you have been stung. Free Energy’t say you haven’t been warned. As an optimist myself, I want to see it work and think it can. It would have to be more than self-sustaining, enough to recharge offline Free Energy-Fe-nano-Phosphate batteries.
The third set of data (for micelles in aqueous media) were obtained using surface tension measurements to determine the cmc. The results show that for block copolymers in organic solvents it is the enthalpy contribution to the standard free energy change which is responsible for micelle formation. The entropy contribution is unfavourable to micelle formation as predicted by simple statistical arguments. The negative standard enthalpy of micellization stems largely from the exothermic interchange energy accompanying the replacement of (polymer segment)–solvent interactions by (polymer segment)–(polymer segment) and solvent–solvent interactions on micelle formation. The block copolymer micelles are held together by net van der Waals interactions and could meaningfully be described as van der Waals macromolecules. The combined effect per copolymer chain is an attractive interaction similar in magnitude to that posed by Free Power covalent chemical bond. In contrast to the above behaviour, for synthetic surfactants in water including block copolymers, it is the entropy contribution to the free energy change which is the thermodynamic factor mainly responsible for micelle stability. Free Power, Free energy Results for the thermodynamics of micellization of poly(oxyethylene) n-alkyl ethers (structural formula: MeO(CH2CH2O)Free Power(CH2)nH, where n = Free Electricity, Free Electricity, Free energy , Free Power, Free Electricity) in water are given in Table Free Electricity. Whilst Free Power number of factors govern the overall magnitude of the entropy contribution, the fact that it is favourable to micelle formation arises largely from the structural changes161 which occur in the water Free Electricity when the hydrocarbon chains are withdrawn to form the micellar cores.
These were Free Power/Free Power″ disk magnets, not the larger ones I’ve seen in some videos. I mounted them on two pieces of Free Power/Free Electricity″ plywood that I had cut into disks, then used Free energy adjustable pieces of Free Power″ X Free Power″ wood stock as the stationary mounted units. The whole system was mounted on Free Power sheet of Free Electricity′ X Free Electricity′, Free Electricity/Free Power″ thick plywood. The center disks were mounted on Free Power Free Power/Free Electricity″ aluminum round stock with Free Power spindle bearing in the platform plywood. Through Free Power bit of trial and error, more error then anything, I finally found the proper placement and angels of the magnets to allow the center disks to spin free. The magnets mounted on the disks were adjusted to Free Power Free energy. Free Electricity degree angel with the stationary units set to match. The disks were offset by Free Electricity. Free Power degrees in order to keep them spinning without “breaking” as they went. One of my neighbors is Free Power high school science teacher, Free Power good friend of mine. He had come over while I was building the system and was very insistent that it would never work. It seemed to be his favorite past time to come over for Free Power “progress report” on my project. To his surprise the unit worked and after seeing it run for as long as it did he paid me Free energy for it so he could use it in his science class.
By the way, do you know what an OHM is? It’s an Englishman’s.. OUSE. @Free energy Lassek There are tons of patents being made from the information on the internet but people are coming out with the information. Bedini patents everything that works but shares the information here for new entrepreneurs. The only thing not shared are part numbers. except for the electronic parts everything is home made. RPS differ with different parts. Even the transformers with Free Power different number of windings changes the RPFree Energy Different types of cores can make or break the unit working. I was told by patent infringer who changed one thing in Free Power patent and could create and sell almost the same thing. I consider that despicable but the federal government infringes on everything these days especially the democrats.
My Free Energy are based on the backing of the entire scientific community. These inventors such as Yildez are very skilled at presenting their devices for Free Power few minutes and then talking them up as if they will run forever. Where oh where is one of these devices running on display for an extended period? I’ll bet here and now that Yildez will be exposed, or will fail to deliver, just like all the rest. A video is never proof of anything. Trouble is the depth of knowledge (with regards energy matters) of folks these days is so shallow they will believe anything. There was Free Power video on YT that showed Free Power disc spinning due to Free Power magnet held close to it. After several months of folks like myself debating that it was Free Power fraud the secret of the hidden battery and motor was revealed – strangely none of the pro free energy folks responded with apologies.

#### In most cases of interest there are internal degrees of freedom and processes, such as chemical reactions and phase transitions, which create entropy. Even for homogeneous “bulk” materials, the free energy functions depend on the (often suppressed) composition, as do all proper thermodynamic potentials (extensive functions), including the internal energy.

“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
Figure Free Electricity. Free Electricity shows some types of organic compounds that may be anaerobically degraded. Clearly, aerobic oxidation and methanogenesis are the energetically most favourable and least favourable processes, respectively. Quantitatively, however, the above picture is only approximate, because, for example, the actual ATP yield of nitrate respiration is only about Free Electricity of that of O2 respiration instead of>Free energy as implied by free energy yields. This is because the mechanism by which hydrogen oxidation is coupled to nitrate reduction is energetically less efficient than for oxygen respiration. In general, the efficiency of energy conservation is not high. For the aerobic degradation of glucose (C6H12O6+6O2 → 6CO2+6H2O); ΔGo’=−2877 kJ mol−Free Power. The process is known to yield Free Electricity mol of ATP. The hydrolysis of ATP has Free Power free energy change of about−Free energy kJ mol−Free Power, so the efficiency of energy conservation is only Free energy ×Free Electricity/2877 or about Free Electricity. The remaining Free Electricity is lost as metabolic heat. Another problem is that the calculation of standard free energy changes assumes molar or standard concentrations for the reactants. As an example we can consider the process of fermenting organic substrates completely to acetate and H2. As discussed in Chapter Free Power. Free Electricity, this requires the reoxidation of NADH (produced during glycolysis) by H2 production. From Table A. Free Electricity we have Eo’=−0. Free Electricity Free Power for NAD/NADH and Eo’=−0. Free Power Free Power for H2O/H2. Assuming pH2=Free Power atm, we have from Equations A. Free Power and A. Free energy that ΔGo’=+Free Power. Free Power kJ, which shows that the reaction is impossible. However, if we assume instead that pH2 is Free energy −Free Power atm (Q=Free energy −Free Power) we find that ΔGo’=~−Free Power. Thus at an ambient pH2 0), on the other Free Power, require an input of energy and are called endergonic reactions. In this case, the products, or final state, have more free energy than the reactants, or initial state. Endergonic reactions are non-spontaneous, meaning that energy must be added before they can proceed. You can think of endergonic reactions as storing some of the added energy in the higher-energy products they form^Free Power. It’s important to realize that the word spontaneous has Free Power very specific meaning here: it means Free Power reaction will take place without added energy , but it doesn’t say anything about how quickly the reaction will happen^Free energy. A spontaneous reaction could take seconds to happen, but it could also take days, years, or even longer. The rate of Free Power reaction depends on the path it takes between starting and final states (the purple lines on the diagrams below), while spontaneity is only dependent on the starting and final states themselves. We’ll explore reaction rates further when we look at activation energy. This is an endergonic reaction, with ∆G = +Free Electricity. Free Electricity+Free Electricity. Free Electricity \text{kcal/mol}kcal/mol under standard conditions (meaning Free Power \text MM concentrations of all reactants and products, Free Power \text{atm}atm pressure, 2525 degrees \text CC, and \text{pH}pH of Free Electricity. 07. 0). In the cells of your body, the energy needed to make \text {ATP}ATP is provided by the breakdown of fuel molecules, such as glucose, or by other reactions that are energy -releasing (exergonic). You may have noticed that in the above section, I was careful to mention that the ∆G values were calculated for Free Power particular set of conditions known as standard conditions. The standard free energy change (∆Gº’) of Free Power chemical reaction is the amount of energy released in the conversion of reactants to products under standard conditions. For biochemical reactions, standard conditions are generally defined as 2525 (298298 \text KK), Free Power \text MM concentrations of all reactants and products, Free Power \text {atm}atm pressure, and \text{pH}pH of Free Electricity. 07. 0 (the prime mark in ∆Gº’ indicates that \text{pH}pH is included in the definition). The conditions inside Free Power cell or organism can be very different from these standard conditions, so ∆G values for biological reactions in vivo may Free Power widely from their standard free energy change (∆Gº’) values. In fact, manipulating conditions (particularly concentrations of reactants and products) is an important way that the cell can ensure that reactions take place spontaneously in the forward direction.

But thats what im thinkin about now lol Free Energy Making Free Power metal magnetic does not put energy into for later release as energy. That is one of the classic “magnetic motor” myths. Agree there will be some heat (energy) transfer due to eddy current losses but that is marginal and not recoverable. I takes Free Power split second to magnetise material. Free Energy it. Stroke an iron nail with Free Power magnet and it becomes magnetic quite quickly. Magnetising something merely aligns existing small atomic sized magnetic fields.
Any ideas on my magnet problem? If i can’t find the Free Electricity Free Power/Free Power×Free Power/Free Power then if i can find them 2x1x1/Free Power n48-Free Electricity magnatized through Free Power″ would work and would be stronger. I have looked at magnet stores and ebay but so far nothing. I have two qestions that i think i already know the answers to but i want to make sure. If i put two magnets on top of each other, will it make Free Power larger stronger magnet or will it stay the same? Im guessing the same. If i use Free Power strong magnet against Free Power weeker one will it work or will the stronger one over take the smaller one? Im guessing it will over take it. Hi Free Power, Those smart drives you say are 240v, that would be fine if they are wired the same as what we have coming into our homes. Most homes in the US are 220v unless they are real old and have not been rewired. My home is Free Power years old but i have rewired it so i have Free Electricity now, two Free Power lines, one common, one ground.
Historically, the term ‘free energy ’ has been used for either quantity. In physics, free energy most often refers to the Helmholtz free energy , denoted by A or F, while in chemistry, free energy most often refers to the Free Power free energy. The values of the two free energies are usually quite similar and the intended free energy function is often implicit in manuscripts and presentations.


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# Flaw in calculation of $\int x \, dx=x^2$

$$\int x\ dx=\int \underbrace{(1 + 1 + \cdots + 1)}_{x\text{ times}}\ dx=x^2$$ Is the algebra Ok? The professor said that the function looses continuity; could anybody explain that?

-
What does "$x$ times" mean when $x=\frac{1}{2}$? –  Thomas Andrews Sep 27 '12 at 20:01
Someone posted the question of where the error is in this argument a few weeks ago. I posted a reply. Maybe this isn't quite a duplicate question, but perhaps the same reply would work here. –  Michael Hardy Sep 27 '12 at 20:04
Even without losing continuity this remains wrong: Compare $$\sum_{k=1}^n k =\sum_{k=1}^n \underbrace{1+1+\ldots +1}_{n} = n^2??$$ –  Hagen von Eitzen Sep 27 '12 at 20:05
Is the problem written correctly? The integral result is wrong from the start. Was he trying to show that if you sum some set of rectangles you get the same results? Regardless, the title is wrong from the start. –  Amzoti Sep 27 '12 at 20:07

One big problem we have in integration notation is that we use the letter $x$ in a way that is inconsistent. When writing the sum:

$$f(n)=1+2+3+\cdots+n$$

we would never write:

$$f(n)=\sum_{n=1}^n n$$

Rather, we write it as:

$$f(n)=\sum_{k=1}^n k$$

Note that $k$ is not $n$ - $k$ is a value that varies from $1$ to $n$.

In the integral, it is wrong to treat the $x$ "inside" the integral as a constant. It is not - it is like $k$ in the sum above. Depending on how you are defining integrals (as anti-derivatives or as areas or whatever) the $x$ on the inside is not the same as the outside. So we'd never say:

$$\int_0^x f(x) \, dx$$

But rather we say:

$$\int_0^x f(t) \, dt$$

with definite integrals.

Indefinite integrals are similar oddities. The indefinite integral:

$$F(x) = \int f(x) \, dx$$

is, in a sense, lazy notation - we reuse the letter $x$ because we really mean $F$ and $f$ have the same domain, and $F'(x)=f(x)$ for all $x$ in that domain.

Add to that the obvious difficulty of defining what "$x$ times" means when $x$ is not an integer, and you'll see the error.

-

$$f(x)=\underbrace{(1 + 1 + \cdots + 1)}_{x\text{ times}}$$

You will note that $f$ is only defined for $x \in \mathbb{Z}^+$, i.e. at isolated points.

It is clear that

$$f(1)=1$$ $$f(2)=1+1=2$$ $$f(3)=1+1+1=3$$ etc.

however, a problem arises when we want to find $f(-1)$ or $f\left(\frac{1}{2}\right)$. It is because of this we are not able to integrate this, as it is not a continuous (or differentiable) function. What happens when we want to find $\int_0^1 f(x)\,dx$?

-
I think that in your definition, $f(1)=x$ should change to $f(1)=1$, $f(2)=1+1$ and so on. –  Emmad Kareem Sep 27 '12 at 20:29
@EmmadKareem Right. It's been a long day! –  Argon Sep 27 '12 at 20:36
Thanks for the clarification. As a side note, I know about long days! –  Emmad Kareem Sep 27 '12 at 20:41

The right hand side of the following is not using a mathematical notation:

$$\int x\ dx=\int \underbrace{(1 + 1 + \cdots + 1)}_{x\text{ times}}\ dx=x^2$$

Hence we are mixing a picture with very specific notations and this is leading to the confusion. Elaborating further on @Thomas Andrews answer (if I may),

$$\underbrace{(1 + 1 + \cdots + 1)}_{x\text{ times}}$$

can be repented by summation notation as follows:

$$x=\sum_{n=1}^x 1$$

Now you could represent the expression accurately by writing:

$$\int x\ dx=(\int \sum_{n=1}^x 1 dx=\int x\ dx)=\frac{x^2}{2}+C$$

-

format: plain


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# Merging ssu-align alignments

ssu-align is an HMM-based MSA tool for ribosome's small subunit (SSU) sequences. It's bundled with three SSU models:

• archaeal,
• bacterial
• eukaryotic

Approach Given a set of archaeal and bacterial sequences the tool will first identify the best model for each sequence and produce two separate alignments for archaea and bacteria, and the tool provides no merging functionality.

Rationale The underlying issue with SSU is the secondary structure, which results in: 1) indels; 2) pairwise point mutations (to maintain the secondary structure)

Problem While you can force it to use a single model for all sequences, aligning archaeal sequences to the bacterial model will produce poor results.

Solution? Nevertheless, the authors of GreenGenes claim that they've used ssu-align to produce two MSAs (one for archaea and bacteria) and build a joint phylogenetic tree using FastTree, but they say nothing about the way they've managed to merge the alignments. Am I missing some functionality from SSU-align?

Note Merging two giant MSAs using conventional tools, such as MAFFT, won't get me far.

P.S.

I've already tried contacting the authors of the GreenGenes paper, but the corresponding author hasn't responded.

I think this is more to do with tree building than alignment construction.

I believe the underlying issue is the 1) distribution of indels, this results in a blockwise deletion in the resulting phylogeny and 2) nucleotide saturation.

Indels Thus, for indels

Archaeal
XXXX----YYYYY
bacterial
----ZZZZYYYYY

The resulting phylogeny will be based on YYYYY and XXXX is ignored.

The alternative explanation is that the genetic distances involved have resulted in saturation of the nucleotide sequences. SSU has to be a nucleotide phylogeny and the level of reversion mutations over a vast amount of evolutionary time can become indistinguishable from random.

With regards the first point, you can replace the indels "-" with "N". This is a cheat to trick a tree building program into not discarding the indel. Model based tree building programs have no ability to create a genetic distance between a base pair and an indel, so this data is essentially discarded from the tree. Worse it will remove the site from phylogenetic inference - which can be a massive loss of data. Two notes one this,

• Some max. likelihood, Bayesian tree programs can avoid blockwise deletion, I don't know programmatically how they do this;

• In PAML the distribution of indels was modelled, it doesn't appear to have been widely adopted however, but might be of value.

Alternative The alternative method is really for protein genes and called "RY" coding, it might work on SSU because of the compensatory mutations involved in maintaining a secondary structure of the SSU.

Word of warning, the saturation may be so great, very little nucleotide point mutation is preserved. Essentially we are talking about preservation of phylogenetic signal across the origins of life ... and that is a very, very long time ago.


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• ### Fully gapped superconducting state in Au2Pb: a natural candidate for topological superconductor(1609.06186)

We measured the ultra-low-temperature specific heat and thermal conductivity of Au$_2$Pb single crystal, a possible three-dimensional Dirac semimetal with a superconducting transition temperature $T_c \approx$ 1.05 K. The electronic specific heat can be fitted by a two-band s-wave model, which gives the gap amplitudes $\Delta_1$(0)/$k_BT_c$ = 1.38 and $\Delta_2$(0)/$k_BT_c$ = 5.25. From the thermal conductivity measurements, a negligible residual linear term $\kappa_0/T$ in zero field and a slow field dependence of $\kappa_0/T$ at low field are obtained. These results suggest that Au$_2$Pb has a fully gapped superconducting state in the bulk, which is a necessary condition for topological superconductor if Au$_2$Pb is indeed one.
• ### Multi-wavelength emissions from the millisecond pulsar binary PSR J1023+0038 during an accretion active state(1312.0605)

March 3, 2014 astro-ph.HE
Recent observations strongly suggest that the millisecond pulsar binary PSR J1023+0038 has developed an accretion disk since 2013 June. We present a multi-wavelength analysis of PSR J1023+0038, which reveals that 1) its gamma-rays suddenly brightened within a few days in June/July 2013 and has remained at a high gamma-ray state for several months; 2) both UV and X-ray fluxes have increased by roughly an order of magnitude, and 3) the spectral energy distribution has changed significantly after the gamma-ray sudden flux change. Time variabilities associated with UV and X-rays are on the order of 100-500 seconds and 50-100 seconds, respectively. Our model suggests that a newly formed accretion disk due to the sudden increase of the stellar wind could explain the changes of all these observed features. The increase of UV is emitted from the disk, and a new component in gamma-rays is produced by inverse Compton scattering between the new UV component and pulsar wind. The increase of X-rays results from the enhancement of injection pulsar wind energy into the intra-binary shock due to the increase of the stellar wind. We also predict that the radio pulses may be blocked by the evaporated winds from the disk and the pulsar is still powered by rotation.


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# Homework Help: How do I solve for theta?

1. Mar 5, 2010

### Ryuk1990

1. The problem statement, all variables and given/known data

This is originally from a physics problem but it's more of a math question. How do I solve for theta?

2. Relevant equations

400 - Tcos(theta) = 0

-200 + Tsin(theta) = 0

Using those equations, I need to solve for theta. Also, knowing that tan(theta) = sin(theta)/cos(theta) is supposed to be relevant to this.

3. The attempt at a solution

All I did was simplify the equations to 200 - Tcos(theta) + Tsin(theta) = 0

Not sure if that was a good idea or not but I'm suck.

2. Mar 5, 2010

### Staff: Mentor

Your equations can be rewritten as
Tsin(theta) = 200
Tcos(theta) = 400

Instead of adding equations to each other, what about dividing each side of one equation by the corresponding side of the other?

3. Mar 5, 2010

### rock.freak667

Place all the constants on one side of the equality for each of the equations.

Then remember that sin2θ+cosθ=1.

so something like R2sin2θ+R2cos2θ=1

4. Mar 5, 2010

### Ryuk1990

Do you mean as in like this?

tan(theta) = 200/400

Is this legal?

5. Mar 5, 2010

### Mentallic

Yes

You can even take a slower approach to solve the two simultaneous equations:

$$Tsin\theta=200$$ (1)

$$Tcos\theta=400$$ (2)

Re-arrange (1) : $$T=200csc\theta$$ (3)

Substitute (3) into (2) : $$200csc\theta cos\theta=400$$

Simplify : $$tan\theta=1/2$$

So yes, if you are convinced that substitution is a valid step in solving simultaneously, then the process of dividing both equations together is also.

6. Mar 6, 2010

### Staff: Mentor

Sure, it's legal, as long as T isn't 0, and I'm reasonably sure in this problem it isn't. Once you get a value for theta, then substitute into either of the original equations to find T.


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# On the fractional NLS equation and the effects of the potential well's topology

created by gallo on 10 May 2022

[BibTeX]

preprint

Inserted: 10 may 2022

Year: 2020

ArXiv: 2012.15665 PDF

Abstract:

In this paper we consider the fractional nonlinear Schr\"odinger equation $$\varepsilon{2s}(-\Delta)s v+ V(x) v= f(v), \quad x \in \mathbb{R}N$$ where $s \in (0,1)$, $N \geq 2$, $V \in C(\mathbb{R}^N,\mathbb{R})$ is a positive potential and $f$ is a nonlinearity satisfying Berestycki-Lions type conditions. For $\varepsilon>0$ small, we prove the existence of at least $\rm{cupl}(K)+1$ positive solutions, where $K$ is a set of local minima in a bounded potential well and $\rm{cupl}(K)$ denotes the cup-length of $K$. By means of a variational approach, we analyze the topological difference between two levels of an indefinite functional in a neighborhood of expected solutions. Since the nonlocality comes in the decomposition of the space directly, we introduce a new fractional center of mass, via a suitable seminorm. Some other delicate aspects arise strictly related to the presence of the nonlocal operator. By using regularity results based on fractional De Giorgi classes, we show that the found solutions decay polynomially and concentrate around some point of $K$ for $\varepsilon$ small.

Credits | Cookie policy | HTML 5 | CSS 2.1


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# Bug fix for mathtime.sty version 2 (1995/03/07)

We are in the final days of completing the typesetting of a complex
book, and this morning, I uncovered, and fixed, an error in
mathtime.sty, version 2 (1995/03/07), which is present in the June
1996 LaTeX2e distribution as

% ls -l latex2e/unpacked/mathtime.sty
-rw-rw-r--   1 beebe        8320 Dec 19  1995 latex2e/unpacked/mathtime.sty

The error appears in an earlier version of this file on our system too
(the one that came with the original version of the MathTime purchased
from Y&Y in October 1992).

Briefly, a couple of days ago, I switched from times.sty to
mathtime.sty, and was surprised to see a number of new overfull boxes
appear.  While fixing them this morning, I noticed that a line that
was previously correct was now overfull, and the cause appeared to be
an initial \boldmath $D$.  In the previous printing of the book with
times.sty, that D began the line; with mathtime.sty, it was preceded
by a small amount of space, which caused the line to be overfull.

Examination of mathtime.sty revealed the problem:  it says

\def\boldmath{\@nomath\unboldmath
...
\mathcode\+="202B
\mathversion{bold}
}

Notice that there is a missing percent on the last item in the
definition, which results in \boldmath getting a single space into the
end of its definition.

I've changed my personal copy of mathtime.sty (known as xmathtime.sty)

\def\boldmath{\@nomath\unboldmath
...
\mathcode\+="202B
\mathversion{bold}%
}

A similar error appears in the definition of \unboldmath:

\def\unboldmath{\@nomath\boldmath
...
\mathcode\+="2243
\mathversion{normal}
}

This should be changed to

\def\unboldmath{\@nomath\boldmath
...
\mathcode\+="2243
\mathversion{normal}%
}

Here is a small test file to demonstrate the error:

% -*-latex-*-
\documentclass[]{article}
\usepackage{mathtime}
\def\slug{\vrule width 3pt depth 0pt height 10pt}
\begin{document}
\slug\boldmath $D$\slug
\end{document}

The output of dv2dt on the .dvi file from this file says:

...
sr 655360 196608
r3 163840
fd1 18 10421504624 655360 655360 0 7 'cmmib10'
,,,

When I change mathtime to xmathtime (my patched version) in this test
file, and run LaTeX2e again, dv2dt then produces

...
sr 655360 196608
fd1 18 10421504624 655360 655360 0 7 'cmmib10'
...

The unwanted move-right command, r3 163840, has disappeared.

========================================================================
Nelson H. F. Beebe                  Tel: +1 801 581 5254
Center for Scientific Computing     FAX: +1 801 581 4148
Department of Mathematics, 105 JWB  Internet: beebe@math.utah.edu
University of Utah                  URL: http://www.math.utah.edu/~beebe
Salt Lake City, UT 84112, USA
========================================================================


text:
# [SOLVED] TypeError: only integer scalar arrays can be converted to a scalar index

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Error encountered is: "TypeError: only integer scalar arrays can be converted to a scalar index".
This error comes when we handle Numpy array in the wrong way using Numpy utility functions. The fix is to refer the documentation of the Numpy function and use the function correctly.

Error:

TypeError: only integer scalar arrays can be converted to a scalar index

Table of Content:

1. Solution
2. Case 1: Error with np.concatenate
3. Case 2: Error with np.ndindex
4. See source of error in Numpy source code

# Solution

The error you have faced is this:

TypeError: only integer scalar arrays can be converted to a scalar index

This means that the index you are using to refer to an array element is wrong. The index should always be an integer.

Despite this, due to flexibility of Python, you can use an array with one Interger element as an index. Internally, the array will be converted to a single Integer and will be used as an index.

This error is defined in Numpy library. So, you are using one of the functions in Numpy in a wrong way. You need to refer the Numpy documentation to confirm the API of the function which is giving an error.

You should be able to identify the issue. The most common issue is that a set of array needs to be passed as a list to a Numpy function. We will do not pass it as a list then, this error will be encountered.

# Not passing as list
array1, array2, ..., arrayN

# Passing as list
(array1, array2, ..., arrayN)

# Case 1: Error with np.concatenate

Consider the following code snippet:

import numpy as np
a = np.zeros((1,2))
np.concatenate(a,a)

Using the above code snippet, we can reproduce the error. The error is as follows:

Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "<__array_function__ internals>", line 6, in concatenate
TypeError: only integer scalar arrays can be converted to a scalar index

The solution is to use the array as a list:

np.concatenate((a,a))

Now, consider this Python code:

import numpy as np

a = [1,2]
np.concatenate(a,a)

This code looks simple and has an issue as well. The issue is different and is that a is a list. The error will be as follows:

Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "<__array_function__ internals>", line 6, in concatenate
TypeError: 'list' object cannot be interpreted as an integer

np.concatenate accepts Numpy arrays.

# Case 2: Error with ndindex

We can get the same error with ndindex function of Numpy library.

Consider the following Python code:

import numpy as np
opengenus = np.ndindex(np.random.rand(128,128))

Error:

Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "/usr/local/lib64/python3.6/site-packages/numpy/lib/index_tricks.py", line 640, in __init__
strides=_nx.zeros_like(shape))
File "/usr/local/lib64/python3.6/site-packages/numpy/lib/stride_tricks.py", line 103, in as_strided
array = np.asarray(DummyArray(interface, base=x))
File "/usr/local/lib64/python3.6/site-packages/numpy/core/_asarray.py", line 85, in asarray
return array(a, dtype, copy=False, order=order)
TypeError: only integer scalar arrays can be converted to a scalar index

Note the error is same so the fix is same:

Fix:

np.ndindex(np.random.rand(128,128).shape)

Output:

<numpy.ndindex object at 0x7f1fe5f3cfd0>

# See source of error in Numpy source code

This error comes from this function in Numpy source code (File: numpy/core/src/multiarray/number.c):

File:

numpy/core/src/multiarray/number.c

Code snippet from the Numpy code file:

static PyObject *
array_index(PyArrayObject *v)
{
if (!PyArray_ISINTEGER(v) || PyArray_NDIM(v) != 0) {
PyErr_SetString(PyExc_TypeError,
"only integer scalar arrays can be converted to a scalar index");
return NULL;
}
return PyArray_GETITEM(v, PyArray_DATA(v));
}

array_index is used whenever we refer to array index in Numpy. The function array_index is used as follows in the same file.

NPY_NO_EXPORT PyNumberMethods array_as_number = {
.nb_subtract = array_subtract,
.nb_multiply = array_multiply,
.nb_remainder = array_remainder,
.nb_divmod = array_divmod,
.nb_power = (ternaryfunc)array_power,
.nb_negative = (unaryfunc)array_negative,
.nb_positive = (unaryfunc)array_positive,
.nb_absolute = (unaryfunc)array_absolute,
.nb_bool = (inquiry)_array_nonzero,
.nb_invert = (unaryfunc)array_invert,
.nb_lshift = array_left_shift,
.nb_rshift = array_right_shift,
.nb_and = array_bitwise_and,
.nb_xor = array_bitwise_xor,
.nb_or = array_bitwise_or,

.nb_int = (unaryfunc)array_int,
.nb_float = (unaryfunc)array_float,
.nb_index = (unaryfunc)array_index,


text:
One possible drawback with high level languages such as Python, is that it’s difficult to understand what happens behind the scene when code is executed.

While it’s true that most Python developers probably don’t care about the dirty details of the Python Virtual Machine, some basic knowledge of this hidden side of the language can always be useful, especially when performance starts to enter the game.

## Python is an interpreted language (isn’t it?)

Unlike « pure » programming languages such as C or C++ (who said Assembly?), Python is an interpreted language, running on a Virtual Machine (VM).

I’m actually talking about the standard implementation of Python, called CPython (not to be confused with « Cython », which is something else), but there are other versions of Python, like PyPy or Jython, with completely different implementations. Let’s focus on CPython anyway, as it’s what most Python developers use by default.

So, (C)Python is an interpreted language, which is the main reason why it’s considered as a slow language, compared to compiled languages such as C or even Java.

Actually this is not completely true: Python code is always compiled, not into native machine language but into bytecode, which is in turn interpreted by the Python Virtual Machine. Python bytecode is the internal representation of a Python program, and it’s what you can find inside .pyc files, which are produced when you execute a Python script.

## A tour of Python bytecode

To understand Python bytecode, one has to understand first how the Python VM works.

The Python VM is a stack based virtual machine, which means its working memory is structured as a stack.

If you ever owned a calculator such as the HP-48, you probably already know what is a stack machine. With the HP-48, to make a simple computation such as 2 * (12 + 42), you had to use a syntax called RPN (Reverse Polish Notation), and enter something weird like 2 12 42 + *, which means:

• Push « 2 » on the stack
• Push « 12 » on the stack
• Push « 42 » on the stack
• Add the two numbers at the top of the stack (i.e. 12 and 42), and replace them with the result (i.e. 54)
• Multiply the two numbers at the top of the stack (i.e. 2 and 54), and replace them with the result
• In the end, you have only the result on the stack (i.e. 108)

The Python VM works exactly the same way, so Python bytecode contains a set of instructions operating on a stack.

Let’s define a trivial Python function:

def f(x, y, z):
return x * (y + z)

The bytecode produced by this function can be displayed thanks to the built-in dis module:

>>> import dis
>>> dis.dis(f)
10 BINARY_MULTIPLY
11 RETURN_VALUE

Here is the meaning of this bytecode display:

• The first column shows the line number in the source code.
• The second column is the address of the instruction.
• The third column is the operation code name (or opcode).
• The fourth column is the operation parameter.
• The fifth column (inside parentheses) gives the meaning of the parameter, related to the source code.

As you can see, this bytecode is quite similar to the RPN example above:

• The LOAD_FAST instruction pushes a variable (here a function parameter) on the stack.
• The BINARY_ADD instruction pops two values from the top of the stack, adds them, and pushes the results on the stack.
• The BINARY_MULTIPLY instruction does what you guess.
• And at last, RETURN_VALUE returns the remaining value which is on top of the stack.

There are around 120 different bytecode instructions, which are listed in the Python documentation.

Now let’s see a slightly more complex function, printing the n first integers:

def print_seq(n):
for i in xrange(n):
print i

The bytecode produced by this function is the following:

  2           0 SETUP_LOOP              25 (to 28)
9 CALL_FUNCTION            1
12 GET_ITER
>>   13 FOR_ITER                11 (to 27)
16 STORE_FAST               1 (i)

22 PRINT_ITEM
23 PRINT_NEWLINE
24 JUMP_ABSOLUTE           13
>>   27 POP_BLOCK
31 RETURN_VALUE

You can easily understand how it works thanks to the documentation, but here are some comments:

There is an additional column in the display, containing the >> symbol. This indicates that the instruction is a destination of a jump from some other instruction.

CALL_FUNCTION 1 means that there is a function to call with one positional argument, to be found on the top of the stack. The name of the function itself is a value on the stack, pushed by the instruction LOAD_GLOBAL.

We can see that print produces built-in bytecode instructions (PRINT_ITEM and PRINT_NEWLINE), as it’s a special keyword, not a real function.

We can also see that return None is implicitly added at the end of the function, if it has nothing to return.

## Inside the Python VM

To finish this overview, let’s look into the virtual machine in more details.

As the name « CPython » implies, the Python VM is written in C, so in the end every single bytecode instruction is interpreted by a bunch of C code.

The core of the VM is the function PyEval_EvalFrameEx, defined in Python/ceval.c, which executes a single bytecode instruction. This function is basically a big switch on the opcode, and each bytecode instruction is implemented inside a case block.

Here is for instance the C implementation of the BINARY_ADD instruction:

TARGET(BINARY_ADD) {
PyObject *right = POP();
PyObject *left = TOP();
PyObject *sum;
if (PyUnicode_CheckExact(left) &&
PyUnicode_CheckExact(right)) {
sum = unicode_concatenate(left, right, f, next_instr);
/* unicode_concatenate consumed the ref to v */
}
else {
Py_DECREF(left);
}
Py_DECREF(right);
SET_TOP(sum);
if (sum == NULL)
goto error;
DISPATCH();
}

This code just takes the parameters from the stack, and calls PyNumber_Add function, which is defined this way:

#define NB_SLOT(x) offsetof(PyNumberMethods, x)

PyObject *
{
PyObject *result = binary_op1(v, w, NB_SLOT(nb_add));
if (result == Py_NotImplemented) {
PySequenceMethods *m = v->ob_type->tp_as_sequence;
Py_DECREF(result);
if (m && m->sq_concat) {
return (*m->sq_concat)(v, w);
}
result = binop_type_error(v, w, "+");
}
return result;
}

As Python is a dynamic language, this function makes no assumption about the type of the parameters. The real work is delegated to another function, binary_op1, which is a generic function to perform a binary operation on a pair of objects:

#define NB_BINOP(nb_methods, slot) \
(*(binaryfunc*)(& ((char*)nb_methods)[slot]))

static PyObject *
binary_op1(PyObject *v, PyObject *w, const int op_slot)
{
PyObject *x;
binaryfunc slotv = NULL;
binaryfunc slotw = NULL;

if (v->ob_type->tp_as_number != NULL)
slotv = NB_BINOP(v->ob_type->tp_as_number, op_slot);
if (w->ob_type != v->ob_type &&
w->ob_type->tp_as_number != NULL) {
slotw = NB_BINOP(w->ob_type->tp_as_number, op_slot);
if (slotw == slotv)
slotw = NULL;
}
if (slotv) {
if (slotw && PyType_IsSubtype(w->ob_type, v->ob_type)) {
x = slotw(v, w);
if (x != Py_NotImplemented)
return x;
Py_DECREF(x); /* can't do it */
slotw = NULL;
}
x = slotv(v, w);
if (x != Py_NotImplemented)
return x;
Py_DECREF(x); /* can't do it */
}
if (slotw) {
x = slotw(v, w);
if (x != Py_NotImplemented)
return x;
Py_DECREF(x); /* can't do it */
}
Py_RETURN_NOTIMPLEMENTED;
}

And that’s not finished! The actual addition function depends on the type of the parameters, so if we assume that the parameters are float numbers, this addition is implemented by the following function:

static PyObject *
{
double a,b;
CONVERT_TO_DOUBLE(v, a);
CONVERT_TO_DOUBLE(w, b);
a = a + b;
PyFPE_END_PROTECT(a)
return PyFloat_FromDouble(a);
}

Got it! We can at last see our addition, done by the line a = a + b !

Now you probably see why numeric computation done in pure Python code is far slower than in C, and why you should use numpy if performance is a concern for you!


text:
# If 22.15mL of 0.100M sulfuric acid is required to neutralize 10.0mL of lithium hydroxide solution, what is the molar concentration of the base? How would I approach this problem?

## ${H}_{2} S {O}_{4}$ (aq) + 2LiOH(aq) $\rightarrow$ $L {i}_{2} S {O}_{4}$ + $2 {H}_{2} O$

Nov 29, 2015

$\text{0.443 M}$

#### Explanation:

Your strategy when it comes to neutralization reactions is to use the balanced chemical equation to help you determine how many moles of each reactant must be present in solution in order for complete neutralization to take place.

In your case, the balanced chemical equation looks like this

${\text{H"_2"SO"_text(4(aq]) + color(red)(2)"LiOH"_text((aq]) -> "Li"_2"SO"_text(4(aq]) + 2"H"_2"O}}_{\textrm{\left(l\right]}}$

Notice that you have a $1 : \textcolor{red}{2}$ mole ratio between sulfuric acid and lithium hydroxide. This tells you that the reaction will always consume $\textcolor{red}{2}$ times more moles of lithium hydroxide than moles of sulfuric acid.

Now, the problem provides you with the molarity and volume of the sulfuric acid solution, which is one way of providing with the number of moles of sulfuric acid, since

$\textcolor{b l u e}{\text{molarity" = "moles of solute"/"liters of solution}}$

If you determine the number of moles of sulfuric acid present in the initial solution, you can sue the aforementioned mole ratio to figure out how many moles of lithium hydroxide would be needed in order to make sure that all the moles of acid are neutralized.

So, the number of moles of sulfuric acid will be

$\textcolor{b l u e}{c = \frac{n}{V} \implies n = c \cdot V}$

$n = {\text{0.100 M" * 22.15 * 10^(-3)"L" = "0.002215 moles H"_2"SO}}_{4}$

This means that you'd need

0.002215 color(red)(cancel(color(black)("moles H"_2"SO"_4))) * (color(red)(2)" moles LiOH")/(1color(red)(cancel(color(black)("mole H"_2"SO"_4)))) = "0.00443 moles LiOH"

Now all you need to do is use the volume of the solution to figure out the solution's molarity

c = "0.00443 moles"/(10.0 * 10^(-3)"L") = color(green)("0.443 M")

So remember, chemical reactions are all about mole ratios. As far as solutions are concerned, start by focusing on moles, the use molarity and volume to help you find what you need.


text:
Browse Questions

# In Bohr series of lines of hydrogen spectrum,third line from the red end corresponds to which one of the following inner orbit jumps of electron of Bohr orbit in atom of hydrogen

$\begin{array}{1 1}(a)\;4\to 1&(b)\;2\to 5\\(c)\;3\to 2&(d)\;5\to 2\end{array}$

The emission is in visible (VIBGYOR) region.Thus Balmer series is either (c) or (d).In (c) only one emission .The third line will be in the jump from 5 to 12.
Hence (d) is the correct answer.

+1 vote


text:
# Why is standard reduction potential an intensive property?

My book says that

Since the number of electrons lost must equal the number gained, the half-reactions must be multiplied by integers as necessary to achieve the balanced equation. However, the value of e° is not changed when a half-reaction is multiplied by an integer. Since a standard reduction potential is an intensive property (it does not depend on how many times the reaction occurs), the potential is not multiplied by the integer required to balance the cell reaction.

However, I do not understand why the reduction potential is unaffected by the number of mols. If you have a greater number of mols of the metal, doesn't that allow for a greater potential difference?

Look at the unit volt. 1 volt = 1 joule per coulomb. If the number of moles is doubled, the coulombs are doubled, as is the number of joules. Think of the volt as the driving force behind an individual electron in an electrochemical system.

• Good answer. This question is just another example of how physics is dropping the ball by continuing to use outdated units in which coulomb and mole exist as separate units, just reporting electrical potential in J per mole and current in mol per s, etc. – Curt F. Jun 19 '15 at 17:00

Basically, Imagine that you have a waterfall that is 100 meters high, and 50 meters long, this scenario makes reduction potential an intensive property: now let's say that you have two of the said waterfall--you will have in total (when put side by side) a larger waterfall that is 100 meters high, and 100 meters long. You do not need to multiply it by two because the your "potential" (usually determined by height in physics) is unchanged.

I'll take a shot at this, so don't insta-hate me. :)

The best way I think I can show you this through is an example. Say we have 2 apples in one bin and 3 oranges in another bin. Assuming the $\ce{E}$ is the difference of the apples and the oranges you get $1.00$.

Even if we doubled the apples and the oranges the difference would be the same. In other words no matter the quantity the voltage will be equivalent.

Now, you might be thinking: what if we just double the apples. Well it doesn't matter because we can consider apples and oranges as reactants to a apple-orange pie. So the more apples we have: it would just be excess.

Take a look at this. Explains it beautifully.


text:
+1.617.933.5480

# Q: Econometrics; BLUE Estimators

I need help understanding how to solve this question.

Use the BLUE estimator to estimate the slope and intercept in:
ln(housing expenditure) = Bo + B1 * ln(income) + v.

I have all of the data in an excel file, but do not know how to use the data to solve this problem. I have found estimates for the slo...

Ok, here's what you're going to do. Right now, you have two rows: Housing Expenditure and Income. Let's say you have these in columns A and B. You need to create two new rows where they are the natural log of Housing Expenditures and Income. This is easy. Go to cell C2 and type in =ln(A2). Go to cell D2 and type in =ln(B2)

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text:
OSCSTAT

Oscillator Status Register 1
Name:
OSCSTAT
Offset:
0xEDB
Reset:
Access:
 Bit7 6 5 4 3 2 1 0 EXTOR HFOR MFOR LFOR SOR ADOR PLLR AccessRO RO RO RO RO RO RO Resetq q q q q q q

## Bit 7 – EXTOR: EXTOSC (external) Oscillator Ready bit

ValueDescription
1 The oscillator is ready to be used
0 The oscillator is not enabled, or is not yet ready to be used

## Bit 6 – HFOR: HFINTOSC Oscillator Ready bit

ValueDescription
1 The oscillator is ready to be used
0 The oscillator is not enabled, or is not yet ready to be used

## Bit 5 – MFOR: MFINTOSC Oscillator Ready bit

ValueDescription
1 The oscillator is ready to be used
0 The oscillator is not enabled, or is not yet ready to be used

## Bit 4 – LFOR: LFINTOSC Oscillator Ready bit

ValueDescription
1 The oscillator is ready to be used
0 The oscillator is not enabled, or is not yet ready to be used

## Bit 3 – SOR: Secondary (Timer1) Oscillator Ready bit

ValueDescription
1 The oscillator is ready to be used
0 The oscillator is not enabled, or is not yet ready to be used

1 The oscillator is ready to be used
0 The oscillator is not enabled, or is not yet ready to be used
1 The PLL is ready to be used
0 The PLL is not enabled, the required input source is not ready, or the PLL is not locked.


text:
NIPS 2018
Sun Dec 2nd through Sat the 8th, 2018 at Palais des Congrès de Montréal
Paper ID: 2992 Variational Learning on Aggregate Outputs with Gaussian Processes

### Reviewer 1

In this paper, the authors propose a general framework of aggregated observation models using Gaussian process with variational methods for inference. They focus on the Poisson link function in exponential family for counts data and derive some lower bounds for optimization using variational inference, Taylor expansion and Jensen's inequality. They apply the methods on synthetic data and Malaria Atlas data to show the performance. In this work, the authors try to predict the labels for individuals while only aggregated labels are available. This problem is studied in Ref. [13, 14, 20]. In this work, the authors extend previous works to exponential family and bring in Gaussian process which can derive uncertainty. Overall, I think this is a good paper. The theorems and experiments are comprehensive and solid. The extension to use Poisson distribution can be useful for count data and the usage of Gaussian process enables one to get the uncertainty. The paper is well-written. Below are some suggestions which I think can make the paper more clear. 1. For equation (7) in line 145, please define what is z. 2. For equation (6) in line 144, please reformulate the equation. Currently, there exists \prod_{i=1}^{N_a} but i does not appear in the equation. 3. In variational inference, the authors choose the variational posterior $q(f) = \int p(f|u)q(u)du$, which shares the conditional distribution $p(f|u)$ with the prior definition. Though the authors have presented that in line 156, I prefer the authors to discuss their choice of variational posterior $q(f)$ before presenting the lower bound in line 149. 4. In Section 4. Experiments, it seems that the authors compare their methods VBAgg with two other approaches Nystrom and NN. Could the authors provide reference for Nystrom and NN and explain more about the formulation of these two approaches? In practice, how can one know the 'population' $p^a_i$ in line 113? Could the authors explain more about how they get $p^a_i$ in line 264? Could $p^a_i$ be treated as parameters to learn as well? Note: I have read the feedback. Thanks.


text:
# Can I use the Coulomb Counting Method to estimate the SOC of a battery being charged by PV panels?

I have seen a couple questions about Coulomb Counting, but I have not found anything defining an "outside source" providing the current to the battery, this questions might be close, How to estimate Li Ion Battery SOC?.

I am wondering if what I am doing is possible in order to produce a simple SoC estimation of a lithium ion battery being charged by PV panels. The lithium ion battery is basically an energy storage system, maybe something like a Tesla power wall.

I am using the Coulomb Counting equation (Section 3.2.1 of the paper, https://www.hindawi.com/journals/isrn/2013/953792/). I have implemented the equation in the following way:

soc = soc[-1] + ((irradiance * self.solar_panel_size)/(pv_volt))/(c*60)*dt

Units

• irradiance: W/m^2 (changes between 0 and 1000 depending on time of day)
• solar_panel_size: m^2
• pv_volt: Volts
• c: Amp-hours (60 is to convert Amp-hours into Amp-minutes)
• dt: Minutes

I believe the typical size for a solar panel is about 1.635m^2 (https://us.sunpower.com/how-many-solar-panels-do-you-need-panel-size-and-output-factors). I also believe the voltage coming from the solar panel changes with the irradiance, but I am hoping maybe 5 volts would be a good number to use for pv_volt (https://www.altestore.com/howto/solar-panels-pv-and-voltages-a98/).

Things I am assuming:

• Not taking into account cycling, inefficiencies, temperature, different charge rates depending on SoC
• Assuming a linear charging rate

I am trying to use the equation for a battery with a rating of 8kWh and power rating of 2kW. The battery can be fully charged/discharged in 4 hours (I know a battery would never be charged "100%", or discharged to "0%", but for the sake of simplicity, I want to assume this is the case). I would think that at 1000 W/m^2 irradiance, based on my equation, the SoC would increase by 25% in 1 hour.

I think my main issue is the "PV portion" of my equation, right now it basically depends on the size and voltage of the PV panel, I am not sure if I can do it this way, or if there is a more "optimal" way.

If I can use the Coulomb Counting equation as I am using it, then I guess my question is, what values can I realistically use for c and pv_volt to obtain a "realistic" SoC rate at every time interval?

• If you can measure charge (and discharge) current rather than involve voltage in any way you are liable to get a superior result. LiIon ENERGY charge efficiency at various states of charge is high but varies. Whereas CURRENT charge efficiency is extremely high - typically over 99% when new and INCREASES with use. So current based coulomb counting can be very effective. || I may be wrong BUT the paper seems to be an immense step backwards. Direct current measurement is easy and low cost with modern componentry (and was hardly less so in 2013 when the paper was published. ... – Russell McMahon Oct 15 '20 at 1:31
• ... PV panel efficiency, irradiance, panel area, assumed panel voltage, .... are far less certain measures than measure current. || If you are wanting a "how will my panel do" measure then something like (irradiance/1000) x Imp /Battery_Ah is a good measure of SOC change. I varies about linearly with irradiance for most of the charge range. See PV panel curves for typical results. || More can be said if wanted. – Russell McMahon Oct 15 '20 at 1:35
• It depends on the C charge discharge design intent. if C>>1 then charge dissipation in the battery ESR’s (more than 1 RC//R2C2) will reduce the energy stored in equivalent capacitance by E=I^2*ESR * t , which is why the V vs I battery slopes are non-linear. But it can be made to work with constraints – Tony Stewart EE75 Oct 15 '20 at 4:45
• Also your last link erroneously states the nominal voltage too low for each Voc. It should be between <70% to 82% of Voc for 100 to 1000W/m^2 input for MPT and you must use a MPPT controller incl. a battery charge manager. – Tony Stewart EE75 Oct 15 '20 at 4:51
• For a 1.6m^2 panel, 5V will be an inappropriate choice of PV voltage : look up the MPPT voltage for that panel. – user_1818839 Oct 15 '20 at 8:14

## 1 Answer

If you can measure charge (and discharge) current rather than involve voltage in any way you are liable to get a superior result.

LiIon ENERGY charge efficiency at various states of charge is high but varies and decreases at increasingly high levels of SOC.

Whereas, CURRENT charge efficiency is extremely high - typically over 99% when new and INCREASES with use. So current based coulomb counting can be very effective.

I may be wrong BUT the paper seems to be an immense step backwards. Direct current measurement is easy and low cost with modern componentry (and was hardly less so in 2013 when the paper was published.
1 ... PV panel efficiency, irradiance, panel area, assumed panel voltage, .... are far less certain measures than measure current. || If you are wanting a "how will my panel do" measure then something like (irradiance/1000) x Imp /Battery_Ah is a good measure of SOC change. I varies about linearly with irradiance for most of the charge range. See PV panel curves for typical results. More can be said if wanted. – Russell McMahon♦ 8 hours ago

For the equation you suggested, what would be some common values for Imp and Battery_Ah? Because if I assume 1000 for irradiance (sun is at its highest), Imp for one panel is 5A, and Battery_Ah is 200, for 1 hour of charging, SOC would only increase by 0.025%. I feel I may be using the equation wrong, or I may be missing something.

Sorry, I did not put a % in there - which is misleading. ie it will change by 0.025 (where 1 is full) or 2.5%.

Imp is whatever the manufacturer says it is at maximum power point.
eg at say Imp=5A and Vmp = 18V panel will give Wmp = 5 x 18 = 90 Watt.

If you use that to charge a 12V battery in 1000 W/m^2 insolation then it will give you slightly over 5A (as Vpanel will be clamped to 12V (rather than 18V) and Ipanel will be slightly above Imp as Isc is > Imp and at 12V the panel is moving towards Isc.

Note that Imp < Isc is not an error as V will be 0 at SC.
Similarly Voc > Vmp

A PWM controller regulates current (or stops it) by applying variable duty cycle PWM so Ibattery <= Ipanel_max. A "12V" panel usually has Vmp = 18V (as that allows a lead acid battery to be boost charged) so a PWM controller will "waste" the energy between Vpanel and Vbat.

A MPPT controller tries to operate the panel at optimum power point for the current insolation = Vmp_current and Imp_current giving Wmp_current (where current varies with current insolation, panel temperature, panel cleanliness, ... .
THEN it converts the energy to battery optimum ay typically 90%+ efficiency - usually using a buck converter.

What does "one sun" = 1000 W/m^2 mean and imply?

Crucially important: While 1000 W/m^2 insolation is termed "one sun" this is just a measurement unit and is NOT the amount of insolation expected at midday. It happens that in many locations midday insolation is ABOUT 1 sun, but this varies with location, atmospheric conditions, time of year, ... . Altitude also has an effect. Some locations on earth have up to about 1.3 sun = 1300 W/m^2 under optimum conditions.

So, using "1 sun" = 1000 W/m^2 as an assumption when determining panel output is often a useful approximation it is not a consistently reliable one.

• Agreed except “waste” is more like matching impedance to open circuit to match Z=Voc/Isc=Vmpt/Impt – Tony Stewart EE75 Oct 15 '20 at 12:30
• For Imp, can I assume there is more than on PV panel in series to increase the amps provided by the PV system? For example, if each panel provides 5A (or slightly over as you mentioned with your example), can I assume 8 panels in parallel and bump up my Ipanel to somewhere around 40A? – W. Churchill Oct 16 '20 at 5:12
• @W.Churchill No assumptions needed. For identical (or at least equal voltage) panels in parallel Imp (I max power) = sum of the Imp's for each panel. For (ideally) identical panels in series Imp is the Imp of one panel OR the Imp of the lowest Imp panel and Vmp (V max power) is the sum of the Vmps of all panels. – Russell McMahon Oct 16 '20 at 11:34


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# Math Help - cant integrate system of equations

1. ## cant integrate system of equations

...(1)

...(2)

...(3)

...(4)

...(5)

...(6)

I've got to this point after performing some asymptotics, and can't see anyway of integrating (2) - (6) since they are all coupled, could someone please confirm that this is not possible for me please?

Thanks in advance!

2. Originally Posted by hunkydory19
...(1)

...(2)

...(3)

...(4)

...(5)

...(6)

I've got to this point after performing some asymptotics, and can't see anyway of integrating (2) - (6) since they are all coupled, could someone please confirm that this is not possible for me please?

Thanks in advance!
physics. I have NO idea what this means. What are the dependent variables? What does it mean to integrate a system of equations?

3. Originally Posted by Drexel28
physics. I have NO idea what this means. What are the dependent variables? What does it mean to integrate a system of equations?
it's just a bunch of coupled ODEs, but sorry but i think i hear the phone

4. Personally I think it would help a lot if you put all that stuff in terms of x, y, and z's and a, b, and c's then if all you want is a solution, push it through Mathematica's NDSolve or even DSolve.