Recent comments

popiol:

First off, the likelihood that your "inputs" will be "exact", in any "real world" case (measurements, and/or results from prior computations), is essentially zero. (A set of cases of order zero, to be exact.) So, for all practical purposes, one must consider all inputs to be inexact.

As for relative vs. absolute errors. The nature of present computer floating-point representations makes it such that the smallest possible errors (half a unit in the last place, 1/2 ulp) scales with the magnitude of the value (this is exactly true, when only considering the exponent part when determining "magnitude", this means there is a step function like behavior of the absolute minimal error). So the relative error is the most meaningful error measure, since even the absolute error scales almost exactly the same as the relative error.

Additionally, the nature of both the relative and absolute errors of division are precisely the same as for multiplication. (At least so long as division is done according to the IEEE specifications.) So, once again, your arguments for "only polynomials" based upon an ill-conceived appeal to present computer architecture, fails muster.

(Besides, are you aware of the issues with regard to numerical stability of polynomial computations? How about even the far simpler case of just summing a set of numbers? These issues further belie the argument for "only polynomials".)

Now, I'm not sure what to make of your comment about "the domain becomes a part of the range"... Any spline basis, including B-splines, maps from some domain into some, possibly other, range (just as with any function). However, since the "rational" part of Non-Uniform Rational B-splines (NURBs) is only about taking a ratio of B-splines, the modification, if you will, occurs wholly within the range, and has nothing whatsoever to do with the domain. The same is true if you simply want to look at is as replacing y(x) with u(x)/v(x).

On the other hand, you are certainly free to consider leaving this ratio like "reformulation" (y(x) → u(x)/v(x)) to a separate issue from "the approximation method (as long as it's a general method)", at least so long as facilities are provided for the appropriate restrictions on the ratio functions* (such as constraints on the sum of squares of the coefficients of the denominator functions). Given this proviso, I have no issue with separating this from the rest of the method. Just don't try to represent this choice as anything more than it is: a choice/preference.

David

* Actually, since any given problem, presented to your "solver", may have any number of additional constraints on the functions, and/or their coefficients, such facilities really should be provided as a part of a general "solver".

Can you please provide the citation for the study? I would like to read the paper.

I think the result is a little bias , I will agree with the result if they were also conduct in place like Africa
On crimes, don't forget about child molesters and kidnapping. Italian Mobs commited lots of crimes as well. Nazi killing of Jews is crime.
On Other note, a lots of black men are in Jail for crime that whites might not put in Jail for e.g drugs white kids use more drug than black. Blacks use weed but rest of the drugs are used by whites. I love all people white, yellow, purple. I believe that God created everyone black or white for a reason, and I believe we need each other.

I strongly applaud this very well reasoned post (except the embrace of vaccines, but that is immaterial to the point of the argument). The article indeed does not make sense.

Tadeusz,

Your math is a distinction without a difference (see below for why).

You are choosing to operate in an accelerated frame of reference rather than an inertial one.

Physics books discuss this all the time. You just don't like their approach. And, it appears, you don't understand it, even though it is based on Newton's laws.

The reason physicists prefer the standard approach is that it avoids introducing a fictitious centrifugal force. That force is fictitious because it is not exerted by any body. Centrifugal force arises in the planet's accelerated frame of reference to explain why the planet is stationary in that frame despite the gravitational force that the Sun exerts on it.

Here's the standard approach one more time:
A planet deviates from straight line motion because gravity exerts a centripetal force on it. That alone is sufficient to explain its motion in a two-body problem.

If you wish to work in an accelerated frame of reference (like that of the planet), that only complicates things, and it doesn't produce any difference in any experiment once the difference in reference frames is properly accounted for.

How do you account for the different reference frames? You add a fictitious force to account for the body's inertia in the accelerated frame. If that accelerated frame is due to a central force, as in planetary motion, the force to add is centrifugal. That's why it is a distinction without a difference.

And why is that added force considered fictitious? The real force is centripetal, and it has a reaction (or paired force), namely the gravitational force that the planet exerts on the sun in a planetary motion situation. The fictitious centrifugal force has no reaction force because it is not exerted by any body. Therefore there is no body on which the reaction force can act.

In other words, you think you have discovered something new, but you have only found a more complicated way to analyze a situation that produces no new predictions--even though you think Uranus is proving your point.

You're almost right about one thing: These conclusions are "so obvious, that no one discusses them anymore." Text books address them all the time, and I have given my own explanation here in a few different ways.

I have no plans to discuss this further, because I think I've explained this well enough for everyone else reading this thread.

I notice you have added a new post, repeating your misguided claim. I will not comment on that.

I suggest you move your writings to AristotelianMechanicsBlog.com and GeocentricUniverseBlog.com.

Here's a book review for you: The View From the Center of the Universe.

Fred Bortz

The Galilean principle says that any body tends to continue its rectilinear uniform motion at a constant speed. In the contemporary physics this Galilean principle is called the momentum conservation principle. The momentum as a vector parameter has a magnitude (the magnitude of motion) and direction. Therefore the Galilean principle means that every body tends to preserve the parameters of the motion vector: the direction and the magnitude. Each change of any of these parameters by the act of an external force (actio) causes a tendency (reactio) for preservation of the hitherto direction and velocity of motion. Therefore during the deceleration and acceleration acts the inertia force

whereas during the orbital motion acts the centrifugal force which is also an inertia force.

Both forces (1) and (2) result directly from the above Galilean principle. The differences between them are only that:
? (1) is the tendency to preserve the magnitude of velocity (a=dv/dt) with a parallel direction of the acting force, "actio", to the direction of the body’s motion
? (2) is the tendency to preserve the direction of motion with the angle of 90° between the vector of the force, "actio", and the body’s motion vector
A homogenous body with mass m in its rectilinear uniform motion at constant speed v has the momentum equal

The situation becomes complicated in the case of a heterogeneous celestial body. The whole momentum (impulse) of a real existing heterogeneous celestial body needs to be calculated by integration of momentum of all its material points

Therefore the whole momentum p of a real existing heterogeneous celestial body is a vector sum of all moments of all its parts of different densities:

From the (5) a direct conclusion can be drawn that the Galilean principle is distributed on particular parts of a real non-homogenous celestial body proportionally to their densities. Each change of velocity or the motion’s direction of the non-homogenous celestial body causes tensions in its interior and in the case of non-rigid bodies such as terrestrial or gas planets, relative shifts of the parts of different densities. It means that reducing the non-homogenous celestial body from the equation (5) to the case of the body from (3) as a material point is mathematically forbidden as the vector sum of momentum cannot be substituted with an arithmetical sum. It means that transformation of accelerates reference frame to inertial reference frame, where orbital centrifugal force does not exist is mathematically prohibited. Through this transformation the whole information concerning the internal structure of the celestial body and stress in its interior is lost. Each true non-homogenous body during every rotation becomes a centrifuge which means that the so called weightlessness state on the orbit is only an approximation (with the exclusion of density differences). A proof for that are the phenomena observed at the ISS, which are erroneously called a microgravity. In reality they are differences of the orbital centrifugal force caused by differences in densities of particular parts of the station. The proof for that every planet on the orbit around the Sun acts exactly as an ordinary centrifuge are the infrared photographs of Uranus taken in 1994÷2003.

The biggest harms for science are caused by these theories, which are assented for so obvious, that no one discusses them anymore.

Tadeusz Tumalski

The problem of numerical stability is that sometimes small errors propagate into large errors. Subtraction increases only the relative error, while doesn't change the absolute error. When the input is exact, the output is exact. It's not the case with exponentiation or division. Of course, the result of those operations is as exact as possible, but even a small error on the input can cause a large error on the output.

That was just to clarify a little the thing about computer architecture. Forget it, I see that this conversation won't get us anywhere. The range modification bothers me more. Now, I understand why you claim that it's not a domain transformation. I forgot that a B-spline transforms a function into a curve first. This is where the domain becomes a part of the range. However, it is still a problem reformulation, and thus it can be done independently of the approximation method (as long as it's a general method). It doesn't matter so much, but it's a way I prefer to look at it. It will matter when I start to implement it, and this is why I want to keep things tidy.

I AM A 22 YEAR OLD GIRL/LADY WHATEVER YOU WANT TO CALL ME,AND I LOVE OLDER MEN.
THEY ARE MORE ATTENTIVE,MORE CARING AND JUST MORE!!!!!

I WAS WORKING IN SCOTLAND ABOUT A YEAR AGO WHEN I WAS 21 AND I DATED A GUY 53...HE LOOKED LIKE HE WAS 35,AND HE WAS SOOOO GORGEOUSE,AND GENEROUS. BUT IF YOU ARE A YOUNGER GIRL LOOKING TO DATE AN OLDER GUY...YOU HAVE TO BE MATURE ENOUGH.....THEY DONT LIKE CHILDISH HANGUPS...

The only reason scientific studies have ever "shown" that blacks are linked to apes is because of the ulterior motives of whites and other non-blacks who don't like blacks. It has nothing to do with scientific research, it's just that whites and others want to dehumanize blacks for the sake of declaring supremacy over them, and justifying crimes against them.

90% of crimes in the americas, europe, australia, etc. are not committed by blacks. If any of you dog raping white supremacist fucks would look at the Justice Bureau stats, white males according to stats kill, kidnap and rape more than any other race of men in those countries and any country where whites reside in the millions. White men lead in crimes against children across the board, including but not limited to, child abuse, child molestation and child kidnapping.

There is no unbiased research available to prove that blacks are closely related to apes, so all research on this subject is invalid, like the opinions of those who agree with those findings. Blacks can't swim? Bullshit, most of the blacks I know swim very well. Weak statements made on unfounded theories made by racists is not fact, but opinion that racists want to justify by disguising it as fact.

IQ tests are about as accurate as this study, meaning it's not very. So the "point" that blacks have low IQ's is weak. Even though IQ studies aren't accurate, they STILL didn't show all that much of a difference at certain ages, and that was with every race.

Africa is NOT a country, it's a continent, and to the whites and non-blacks saying that, that just proves how unintelligent and mentally un-evolved you are.

Many East Indians have african blood in them. If any of you idiots would look at their history, there was a time when arabs had africans as slaves. There was a lot of mix breeding involved as a result. Many east indians have similar features to blacks but are ashamed to admit that. That's to the idiot that made the comment about east indians.

The bone structure of apes and caucasians match more than that of blacks. Apes have similar skull structure to whites, as well as thin lips, flat buttocks, and straight fur/hair, and under that fur they are pink. Who fits that description more, blacks or whites? Answer: whites.

To the idiot that had the comment "Your writing is rediculous", you're a joke. First of all, there are no E's in the word RIDICULOUS, asshole, and second your entire paragraph was poorly written garbage that my 9 year old niece could proofread and rewrite better than you did.

At the guy "Patterns", I take it you've never been to India, or Thailand, where you can't even walk down the street after 7 pm. You've made asinine assumptions about an entire race without focusing on the negatives of others and therefore in your weak mind that justifies seeing blacks as inferior. I take it that even if predominantly black areas weren't dangerous that you'd find something to justify your hatred for blacks.

All in all, just about everyone who commented here is an ass, and has proven my point that inferiority is not a race, but a mindset.

You may need another boyfriend. When people decide to give up sex, they aren't thinking of their partner, they're thinking of themselves (personal issues). Trust me, fixing other people doesn't work. Move on.

I love it Fred. Please keep the lessons coming.

ben