NTuft

The square root may be considered a multivalued function. Example 1: a=-2 a2=+4 Example 2: a=+2 a2=4 The square operation should be applied first once a number is input to evaluate the expression. In distinction from the algebra convention when solving for variables where the power is simply removed. Squaring of course gives a positive value. Once the square root is applied, plus/minus is appended in front of the operator, for the equivalent reason absolute value is used here. ; because there is ambiguity (multi-value) output from the square root... relation. Nothing in the question remarked about limiting the domain of input or codomain of output to ensure a single-valued function.

Around the SPONCH CaFe.

Hi Trurl, I found this slideshow presentation informative Prime numbers and the Riemann zeta function, Carl Wang-Erickson, Nov. 12, 2019: There is some difficult math, but if you go through the presentation I think it can clear up how the Riemann hypothesis points at a pattern in prime number's average, logarithmic distribution. I would like you to describe that to me. I think of the argument (angle) for a complex number as rotating around. Can you refer me to that document or paper, please? I haven't gone through links or the paper you've provided, and I don't much understand the odometer question, but I read you're working at cryptography applications, so I'll think about it.

I see splodge was banned as sockpuppet of JustJoe, but this mention opens up a line for investigation. The Moon and the Magnetotail, NASA.gov: emphasis added.

The issue with post numbering--there was a thread where you, Genady, and some others were discussing how you can put links to specific posts within threads inside a reply as a way to refer back to prior material. Discussion there about the issue with posts not being numbered, and you mentioned someone else had tried to explain it to you. This should probably be PM material, but, anyway, did you get around to where you can identify specific posts by their forum-wide post number? You can see that number is contained within a URL/web address that is attached to each post?? The time stamp at the top of a post is a hot-link on my computer. If you copy the link address and paste it the post number will be displayed. Other than that just saying thanks for reading and participating in my rambling speculation here.

Fair enough. Objection warranted.

@swansont, Using Weber's electrodynamics we can substitute masses for charges to get a description of gravitational force. By my read, it wouldn't need monopoles or point charges then -- the masses act like point charges. It does reduce to Newtonian gravity, and with Mach's principle the system is extended as Relational Dynamics by A.K.T. Assis. Any thoughts on that? I'm pro-particle. You want to discuss the science I brought up on that? It was an overture to your particle leanings, I thought you'd like to discuss the cosmology development and why we can't find magnetic monopoles. @studiot, I think you had the technical issue explained to you by someone else, too? You have it figured now? Thanks to you and @joigus for more input here, and keywords.. I'll try to follow up. You guys all sure know a lot.

There may be something brought to bear on this here, A novel equivalence relation in relativity (+1 @studiot), So the f0 is the 0-th and fk is the conventional. I don't have a handle on co-variant, contra-variant, vector indices or tensors here, I'd barely made a start on what I think is Einstein's vector convention. is the power gain/loss a boost? I ought to go through the sections I pointed at to get the details, but if you could explicate what this is saying I'd appreciate it; I don't even know what questions to ask. Referring to the equivalence relation in relativity cite, does it make sense that the E and B fields are conceptually lightlike objects? I think it's such that they're thought of as the medium in which it propagates. What about the dimensionality? When swansont said that it could be reverted to a v=0 frame and electrostatics could describe it I was thinking that was like going from 3-D to 2-D spacelike dimensions, and then lo-and-behold the next section I read goes into classical electrodynamics... Which is not correct, as electrostatics can be 3-D, but as soon as it is, I think there is the additional degree of freedom for rotation, which again is a relative motion that can induce the B field. And? I think that there was some back-and-forth about whether an interaction hinges on a relative motion, and I think magnetism does. I highly recommend the reading on equivalence relation in relativity, I don't have a good handle on relativity, and several readings of the initial pages are necessary. "...everything in physics is made up to make the math work out. ...in the end, everything we do is to make the math work out."

They're not entirely unrelated, though. Searching the respective wiki articles for the other's terms, "transformation" or "Lorentz force", has details [Transformation of other quantities; Relativistic form of the Lorentz force]. The E and B fields defined by Lorentz force do not have a timelike quantity so I think you're correct to say they're different from Lorentz transformation including time. Yes, the corrected distribution got in there with the edit. However, also from the wiki's, the Lorentz transformation can illustrate that what appears as a static electric charge and E field in a rest frame appears to be a moving charge with consequent current flow and induced B field from another frame in relative movement--it only becomes an electro-magnetic interaction with some relative velocity, either of the charge or the observer thereof.

I can see the utilitarian argument, but if there were some non-contingent, non-interacting "field" isn't it possible that our observations or reality is contingent in a way that couldn't necessarily be measured? I know that's a mushy, philosophical-religio-mystical question, but I don't see physics as "made up", rather that it's trying to develop a description.. To me, the explanatory power for theory is deficient if it's not encompassing reality, even if utility wouldn't require a complete understanding. Lorentz force,

Injuries to diplomats is a limited hangout, a cover for two-way signals surveillance or injection technology.

Yes, thank you. Yes, should say increases expression. Certainly yes there is the assumption that LDL receptors are involved in LDL-C clearance. The interpretation to end the abstract from the authors is like what you suggest. It could be decreased production VLDL->IDL->LDL is sensed and signals upregulation of expression of receptors, seeing that the diets step down both fat% and SFA%: 34%(15%)[0,0], 29%(9%)[-5%,-6%], 25%(6%)[-9%,-9%]. I presume both numbers are % of total energy, and the latter not a %SFA of total fat, as that seems implausible.

Indeed this is a complicated topic. I did not read the paper either, and should have and parsed it, instead of posting the "rah-rah" blog write-up. This was a feeding study on humans, which is important as I think the usual rodent studies want to draw a parallel between a small-bodied herbivore and a large-bodied omnivore with a large gallbladder and a large brain-body ratio which brain is a cholesterol dependent construction. I don't think most any conlcusions on mechanisms of metabolism can be extended to humans, but the basic results may point toward what are conserved mechanisms. It looks to me that the Lipoproteins work alongside chylomicrons in the distribution and metabolism of fats. This is complicated by fats being both structural components and energetic substrates. Lipoproteins go from Very-Low Density packages distributed by the liver to Intermediate-Density, to Low-Density as they unload fatty acid cargo at peripheral tissue, dependent on binding of the Lipoprotein receptors. There is data that reducing SFA content in the diet reduces expression of LDL receptors (Reducing saturated fat intake is associated with increased levels of LDL receptors on mononuclear cells in healthy men and women). Some knowledgeable people have taken evidence that the LDL receptor is saturated at very low levels as license to start statins without real indications. Again, there ought to be due diligence and it's lacking on my part here as well, but for one the materials and methods would need an investigation as to whether this saturation level is an in vitro type of tissue study or in the context of connected running metabolism. It's noteworthy that the study linked above looked at mononuclear cells, since I'm rather certain there are human population studies that show a decrease in all cause mortality and in particular suicides and infectious disease death correlating with higher levels of LDL. I suppose what I find most interesting about the 3 egg/day result is that estimates are that cholesterol is metabolized on the order of 1g generated by the liver per day(Ed.: with losses, I'd bet, as bile salts of cholesterol+taurine/glycine excreted]. Usual estimates are that 20% of that may come from diet, but I would speculate that that may largely be tied to average egg intake. Going from 0 eggs/d to 3/day, with a conservative estimate of 200mg cholesterol per egg, shifts the burden on the liver from ~1g/day production to .4g/day, yet there is what looks like a non-significant increase in total cholesterol; it looks like the metabolism simply shifted to acommodate the increased ingestion (assuming 100% assimilation and utilization). There is increasing evidence (especially if you buy into the write-ups, hook-line-and-sinker) that would exonerate SFA intake from causative in CVD. It seems to have been scapegoated in the context of metabolic syndrome or metabolic disease. I would just point out the French paradox as an entry into the topic. Energy balance, the interplay between intake and expenditure, is probably more important than trying to leverage metabolic mechanisms, which are complex and seemingly geared to account for and accomodate just about any diet. You seem to point at Calorie-Restricted-Optimal-Nutrition, which I second has merit; studies on monkeys are even by visible appearance alarming in comparing overfeeding to CR. That said, the Optimal-Nutrition end requires some knowledge and application: being wary of anti-nutrients (say trans-fats, and likely some lectins or phytochemicals) and saturating would be bottlenecks(chokepoints) on metabolism by finding adequate mineral, vitamin, and vitamin-like substance sources. Ok now you're "trolling" for a free online physical! J/k I'm skeptical of the "Lipid hypothesis", but I know it still holds by and large in the mainstream. Which is preferred out on the science boards here at SF.net. Going into these details does seem somewhat natural from the context of the OP, but it's also a generalization of a specific question... Anyway perhaps welcome to SF, OP; not much context on what you want assessed and expecting readers to watch a video is a forlorn hope, and diverging into related topics is almost a given if you cease any follow-up or specifications on the topic at hand.

I wonder if it matters if it's intentional or malicious. A stoic line would be that one can only control their responses, or that one can stifle any unreasonable emotional reaction, if there is self-mastery. Nonetheless, if something "gets your goat" I think it helps you see yourself--why or how am I identified with this point of contention that leads to negative emotion or reaction? I agree with a line of argument that says the truth hurts. That dis-confirming information is interpreted by the brain as physical injury. I don't know how scientifically founded that is, but I do think there are studies on cognitive biases in political opinion where people presented with information dis-confirmatory to their belief have pain centers light up. I also think the issue of whether you're thinking with your adipose or your blood is at play. I'm not so sure we can really control what impressions we make on others. Being able to be externally considerate always and internally considerate never is an equation for happiness. Being able to control the impressions we make on others would be quite a skill... But is there a need for it? Perhaps stepping on people's corns can create a friction, create some difficulty to make a change that wouldn't be possible another way. It only make sense and is reasonable I think to be respectful here, I think we'd hope we understand each other and are working on things together. Yet if you think it's necessary to correct with dis-confirming information, it's going to bring the pain, and oftentimes I think it's done with a flair or presentation that might be taken personally, or as an insult, when in reality it's done in good humor (at least for the rest of the readers).

Can you explain more about the extra dimensions? It seems as though some results did not fit, so you postulate these ED orbitals. Does your geometric model remain planar? You mention that P level is stacked on the z-axis(coming out of the page), PL over PR, one over another -- so is it more like PL - QL PL \ QL \ \ PR \ QR PR QL once you get to P+Q level? Not sure I understand your diagrams... Then you on to hexagrams and decagons (plus two orbitals in the center). Is the geometry planar?? I think this is interesting. I think the shell model can accomodate geometric nucleus structure. You start with a 4 (2 proton-2 neutron), add 6s or 8s, then 10s or 12s.. I think you could really gain something (and maybe lose the extra dimensions) from reading this write-up on another geometrical model for nuclear structure: I'll try to get through the rest. MOON-HECT-Keplerian-ATOM-Periodicity.pdf

Very well, and that can be a metric. It'd be an issue of myopathy, broadly speaking, over time, but overall I think it is a low-incidence reported side effect.

Here's a link to a blog post discussing a controlled feeding study (2017) looking at effects of egg consumption on blood cholesterol: Three Eggs a Day = Doping for Your Heart Health: Larger LDL & HDL, Increased Efflux and Transport + More Benefits @Nutrition4Health, I did not watch the video; would you clarify about what the claims are that are being made? Is he claiming that eating eggs leads to cholesterol absorption and then sustained, circulating high cholesterol levels? Because I think that is bogus. From what I understand, the number of particles, which relates to whether LDL and HDL are small and dense vs. large and fluffy, is an issue--it can be differentiated by an NMR lipid profile. Per Cleveland (U.S.) Clinic recommendations I believe an [Ed.: NMR profile for particle quantifying/sizing should be added], an ApoB level [and also see cited study re:ApoAII], and of course circulating triglycerides are recommended to get a good picture (check recommendations, this is not advice). The cholesterol intake from egg consumption is in my opinion offset by the choline (or lecithin) content of eggs facilitating healthy fat metabolism. What seems to be more well established is that dietary saturated fat intake leads to increased LDL levels, which for some people may be problematic. The cholesterol hypothesis, roughly speaking, is that (LDL) cholesterol becoming oxidized and deposited in the endothelium is the mechanism of development for atherosclerosis. I do not think it is still held that dietary cholesterol is the main part of the mechanism, rather that the interplay between dietary fat and endogenous cholesterol metabolism can lead to oxidation and deposition of cholesterol plaques. The susceptibility to oxidation/inappropriate deposition I think is tied to the particle size... As an aside, @exchemist, I do not think olive oil should be eschewed, as I think MUFA and PUFA are not shown to increase LDL "cholesterol". But yes perhaps control total fat intake--although Mediterranean ratio of <=30-40% total kCal I think is good... Again, IMO, traditional statins are very problematic in interrupting mevalonate->cholesterol, because it's then interferring with everything downstream in the steroid pathways (and muscle pain, weakness, and atrophy are underreported), let alone that cholesterol is a structural component in animal cell membranes. Perhaps look into psyllium husk, berberine, niacin (nicotinic acid) for cholesterol lowering? And do address choline/lecithin via eggs, liver, or perhaps a lecithin supplement for various things; or if you want to take statins for their anti-inflammatory and CVD protective effects it may be worthwhile investigating increasing dietary cholesterol. You may want an NMR lipid profile before even concluding that your levels are telling the tale, because the particle size/density may be more important. Friendly advice, not medical, and I should re-acquaint myself with the current literature, or any new evidence on the matter.

chromebook Shenanigans displays url on webpage lower left-hand side on my end. Perhaps right-click, copy link address, paste it and it'll be at end of url.

couldn't add edit to #1229842, so for what it's worth here, if you hover over the time stamp on a post the last # in the url (e.g. in your post above #1229844) looks like the post number over the whole forum.

I suppose I quibbled, "Accept this definition from wikipedia." And your stance is, "That is unacceptable." It was on the issue that I'd missed a point you were emphasizing about Fields, but I didn't see the point, and wanted to wave it away and make do with a "group", though I didn't define the group operation well, either. I grant your recent echoed point. I am out walking the dog in the... p-1ark!... and uncertain on which end is the wiener, in natural casing, and which end is gauging the walking. So I think it is a confusion of the mathematical theory and matematical modeling, which is nuanced, but I think it is good. I had premised that I wanted to take as granted the sets and their field axioms. In going in to describe the problem in situ, I think there needs to be a failure of the commutator. My work-up is not formally acceptable or explicit. I think that commutative multiplication can describe energy being added to a particle. I think the failure of the commutator to allow addition can describe the phenomena discussed. I do not think it is too far afield to have your wiener and walk it, too, if on a lattice gauge the spacing in the physics field is bringing together the interactions that are described by the operations that characterize the mathematical field. The book recommended Thursday is in the mail. +1 over there. Ought to walk before you run, and a group is more basic than a field, so maybe start there? Perhaps you have some thoughts on the set to generate a group? I need to study the Lagrangian formalism, among other things. And be more precise in my terms and work-up to be taken seriously... Tread carefully.

In TQFT, for Wilson loops the expectation value does not change under smooth deformations..They are gauge invariant. By Wick rotations obects from thermal physics, exp(βH), are related to quantum physics, exp(−iH T).. Polyakov loop is "thermal analogue" to Wilson loop.. An imaginary temporal compactification, length of β=1/T(emp.), leads to topologically nontrivial loops around the compact direction known as Polyakov loops. Those loops (assuming the group center change of basis is not trivial) are gauge dependent, Ok. I read your questions on TQFT, and those and the leads to "functorials", etc., look interesting. Interesting formulation. Thanks for this, article, too, but they make statements with caveats, so I wouldn't conclude it's unsolvable.

I'll repeat the distinction between the two. So addition and multiplication, multiplicative inverse, and effectively two nullary operations would be an equivalent way to define the field. I think I posited those, though I called addition non-commutative for the reasons I explained. You seemed to argue earlier that wasn't a field--was it a problem with the operations I was proposing? Feel free to give up. -1

What I had in mind was a discrepancy in the trace -- a Wilson loop is functional if the perimeter measure is correct, whereas a Polyakov loop implies the area between confined states is what's needed (fuzzy re-hash). I think it's related to confinement and chiral symmetry breaking. I'll follow up on what you've mentioned. I shouldn't have asked the last leading question, Glueballs. Would you explain what about it makes you think it "is considered to be the toughest problem around concerning physics?" I thought it was the conceptual or theoretical mathematical description of what has been pretty well established physically. So the back and forth between Physico-Mathematics, Mathematical-Physics; it does exist!

@joigus, So does area-law confinement imply Polyakov loops to you? As opposed to Wilson loops being based on perimeter? Is the issue that glueballs need to have a prediction made about their lower mass bound?

-1 to 1st Lt post. +1 @TheVat's response. Antenna/transceiver in the near-field vs. far-field for a satellite? Two-way street--this is a function of supercomputing power, and the U.S. and PRC lead the world, and are close competitors as far as I know. At least the mass of data is analyzed and distilled before intel assessment I reckon. FBI can hack back TOR layers and are dismissing cases without prejudice to not disclose the method. @Alex_Krycek, "I want to believe." Tic-tac shape noted. Cf. orb over Mosul.