Rydberg formula: Difference between revisions

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:'''''Fractional integration''' redirects here. Not to be confused with [[Autoregressive fractionally integrated moving average]]
If you own a measuring tape, you are able to measure yourself to determine where you carry most of the excess fat on your body. Calculating your waist to hip ratio helps we determine not merely where we carry many of your fat, and how much of the risk a fat actually poses to a wellness.<br><br>What is Body Mass Index? Body Mass Index, more commonly acknowledged as "BMI", is an indicator of the amount of body fat a person has. The BMI really divides your weight by your height to provide you the body fat analysis. The better amount of body fat a individual carries, the more probably they are to have health related illnesses. "Weight for height" is an significant measurement because whenever you're in the ideal range of fat for height, you are able to anticipate to reside the longest lifetime possible with limited illnesses. When a person steps from this range, on either side; having too small fat or having too much weight, is whenever wellness problems occur.<br><br>But before you all breathe a sigh of relief and down a cheeseburger, bag of potato chips, along with a carton of moose tracks ice cream (yum), the research waist to height ratio leader did say which the research did not prove that obesity was harmless. Being obese or obese still carries an improved risk of heart disease, diabetes and certain types of cancers.<br><br>Diesel tuning involves rewriting the ECU maps to liberate a diesel engine's true potential. Dozens of settings that affect the performance of the car are improved in the remapping process. The purpose of ECU remapping is to achieve the the best possible force curve for automobile performance plus gas economy. At the same time, safety variables initially programmed into your ECU need to be respected in purchase to avoid any damage to the engine or drive train.<br><br>Skinfold Thickness Measurements - One of the simplest techniques to measurefat weight is the skin fold width measuring. A tool called a skinfold caliper is selected to pinch the skin, gathering a double layer to measure the underlying tissue. The caliper reads two measurements - cm and mm, with all the mean of the 2 taken. Thisfat weight measuring is selected on different anatomical regions of the body.<br><br>For years, it was assumed which those indicated because "overweight" based on the BMI were at a much high risk of dying from heart related conditions. But the new research [http://safedietplansforwomen.com/waist-to-height-ratio waist to height ratio] which the Mayo Clinic in Rochester, Minnesota, published indicates anything very different. In their research of 250,000 people with heart condition, those with a BMI which indicated obese status had less chance of dying from heart difficulties than those with a general BMI. And people with a general BMI were less probably to die than folks with low BMI. And as expected, severely overweight persons did have a higher incidence of death from heart-related condition.<br><br>In the night I would go for a 5km walk. Initially it would take me over an hr to cover the distance, yet because I got healthier plus my endurance increased I got quicker. Now I may do it in 45 minutes on a advantageous day. Although I find walking alone really boring and whenever I walk with a friend the speed seems to suffer.<br><br>Because BMI utilizes only height and weight, the BMI result for a lean, "buff" individual with a svelte waist will really end up inside the obese category. As an example, a guy who's 5-11, yet has a muscled physique, may weigh 200 pounds. This puts him in the obese category for BMI (27.9), despite the reality his body fat percentage could be exceptionally low.
 
{{Calculus|expanded=Specialized calculi}}
 
In [[fractional calculus]], an area of [[applied mathematics]], the '''differintegral''' is a combined  [[Differential operator|differentiation]]/[[integral operator|integration]] operator. Applied to a [[function (mathematics)|function]] &fnof;, the ''q''-differintegral of ''f'', here denoted by
:<math>\mathbb{D}^qf</math>
is the fractional derivative (if ''q'' > 0) or fractional integral (if ''q'' < 0).  If ''q'' = 0, then the ''q''-th differintegral of a function is the function itself. In the context of fractional integration and differentiation, there are several legitimate definitions of the differintegral.
 
==Standard definitions==
 
The three most common forms are:
 
*The [[Riemann–Liouville differintegral]]
:This is the simplest and easiest to use, and consequently it is the most often used. It is a generalization of the [[Cauchy formula for repeated integration]] to arbitrary order.
 
: <math>
\begin{align}
{}_a\mathbb{D}^q_tf(t) & = \frac{d^qf(t)}{d(t-a)^q} \\
& =\frac{1}{\Gamma(n-q)} \frac{d^n}{dt^n} \int_{a}^t (t-\tau)^{n-q-1}f(\tau)d\tau
\end{align}
</math>
 
*The [[Grunwald–Letnikov differintegral]]
:The Grunwald–Letnikov differintegral is a direct generalization of the definition of a [[derivative]].  It is more difficult to use than the Riemann–Liouville differintegral, but can sometimes be used to solve problems that the Riemann–Liouville cannot.
 
: <math>
\begin{align}
{}_a\mathbb{D}^q_tf(t) & = \frac{d^qf(t)}{d(t-a)^q} \\
& =\lim_{N \to \infty}\left[\frac{t-a}{N}\right]^{-q}\sum_{j=0}^{N-1}(-1)^j{q \choose j}f\left(t-j\left[\frac{t-a}{N}\right]\right)
\end{align}
</math>
 
*The [[Weyl differintegral]]
:This is formally similar to the Riemann–Liouville differintegral, but applies to [[periodic function]]s, with integral zero over a period.
 
==Definitions via transforms==
 
Recall the [[continuous Fourier transform]], here denoted <math> \mathcal{F}</math> :
 
:<math> F(\omega) =  \mathcal{F}\{f(t)\} = \frac{1}{\sqrt{2\pi}}\int_{-\infty}^\infty f(t) e^{- i\omega t}\,dt </math>
 
Using the continuous Fourier transform, in Fourier space, differentiation transforms into a multiplication:
 
:<math>\mathcal{F}\left[\frac{df(t)}{dt}\right] = i \omega \mathcal{F}[f(t)]</math>
 
So,  
 
:<math>\frac{d^nf(t)}{dt^n} = \mathcal{F}^{-1}\left\{(i \omega)^n\mathcal{F}[f(t)]\right\}</math>
 
which generalizes to
 
:<math>\mathbb{D}^qf(t)=\mathcal{F}^{-1}\left\{(i \omega)^q\mathcal{F}[f(t)]\right\}.</math>
 
Under the [[Laplace transform]], here denoted by <math> \mathcal{L}</math>, differentiation transforms into a multiplication
 
:<math>\mathcal{L}\left[\frac{df(t)}{dt}\right] = s\mathcal{L}[f(t)].</math>
 
Generalizing to arbitrary order and solving for ''D''<sup>''q''</sup>''f''(''t''), one obtains
:<math>\mathbb{D}^qf(t)=\mathcal{L}^{-1}\left\{s^q\mathcal{L}[f(t)]\right\}.</math>
 
==Basic formal properties==
 
''Linearity rules''
:<math>\mathbb{D}^q(f+g)=\mathbb{D}^q(f)+\mathbb{D}^q(g)</math>
:<math>\mathbb{D}^q(af)=a\mathbb{D}^q(f)</math>
 
''Zero rule''
:<math>\mathbb{D}^0 f=f \, </math>
 
''Product rule''
 
:<math>\mathbb{D}^q_t(fg)=\sum_{j=0}^{\infty} {q \choose j}\mathbb{D}^j_t(f)\mathbb{D}^{q-j}_t(g)</math>
 
In general, ''composition (or [[semigroup]]) rule''
:<math>\mathbb{D}^a\mathbb{D}^{b}f = \mathbb{D}^{a+b}f</math>
is '''not satisfied'''. See Property 2.4 (page 75) in the book A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations. (Elsevier, 2006).
 
==Some basic formulae==
 
:<math>\mathbb{D}^q(t^n)=\frac{\Gamma(n+1)}{\Gamma(n+1-q)}t^{n-q}</math>
:<math>\mathbb{D}^q(\sin(t))=\sin \left( t+\frac{q\pi}{2} \right) </math>
:<math>\mathbb{D}^q(e^{at})=a^q e^{at}</math>
 
== See also ==
* [[Fractional-order integrator]]
 
==References==
* "An Introduction to the Fractional Calculus and Fractional Differential Equations", by Kenneth S. Miller, Bertram Ross (Editor), John Wiley & Sons; 1 edition (May 19, 1993). ISBN 0-471-58884-9.
 
* "The Fractional Calculus; Theory and Applications of Differentiation and Integration to Arbitrary Order (Mathematics in Science and Engineering, V)", by Keith B. Oldham, Jerome Spanier, Academic Press; (November 1974). ISBN 0-12-525550-0.
 
* "Fractional Differential Equations. An Introduction to Fractional Derivatives, Fractional Differential Equations, Some Methods of Their Solution and Some of Their Applications",  (Mathematics in Science and Engineering, vol. 198), by Igor Podlubny, Academic Press (October 1998). ISBN 0-12-558840-2.
 
* "Fractals and Fractional Calculus in Continuum Mechanics", by A. Carpinteri (Editor), F. Mainardi (Editor), Springer-Verlag Telos; (January 1998). ISBN 3-211-82913-X.
 
* [http://www.worldscibooks.com/mathematics/p614.html Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models.] by F. Mainardi, Imperial College Press, 2010. 368 pages.
 
* [http://www.springer.com/physics/complexity/book/978-3-642-14002-0 Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media.] by V.E. Tarasov, Springer, 2010. 450 pages.
 
* [http://www.springer.com/physics/theoretical,+mathematical+%26+computational+physics/book/978-3-642-33910-3 Fractional Derivatives for Physicists and Engineers] by V.V. Uchaikin, Springer, Higher Education Press, 2012, 385 pages.
 
* "Physics of Fractal Operators", by Bruce J. West, Mauro Bologna, Paolo Grigolini, Springer Verlag; (January 14, 2003). ISBN 0-387-95554-2
 
* ''Operator of fractional derivative in the complex plane'', by Petr Zavada, Commun.Math.Phys.192, pp.&nbsp;261–285,1998. {{doi|10.1007/s002200050299}} (available [http://www.springerlink.com/content/2xbape94pk99k75a/  online] or as the [http://arxiv.org/abs/funct-an/9608002 arXiv preprint])
 
* ''Relativistic wave equations with fractional derivatives and pseudodifferential operators'', by Petr Zavada, Journal of Applied Mathematics, vol. 2, no. 4, pp.&nbsp;163–197, 2002. {{doi|10.1155/S1110757X02110102}} (available [http://www.hindawi.com/GetArticle.aspx?doi=10.1155/S1110757X02110102&e=cta online] or as the [http://arxiv.org/abs/hep-th/0003126 arXiv preprint])
 
==External links==
* [http://mathworld.wolfram.com/FractionalCalculus.html MathWorld – Fractional calculus]
*[http://mathworld.wolfram.com/FractionalDerivative.html MathWorld – Fractional derivative]
* Specialized journal: [http://www.diogenes.bg/fcaa/ Fractional Calculus and Applied Analysis]
* Specialized journal: [http://fds.ele-math.com/ Fractional Dynamic Systems (FDS)]
* Specialized journal: [http://www.nonlinearscience.com/journal_2218-3892.php Communications in Fractional Calculus] (ISSN 2218-3892)
* http://www.nasatech.com/Briefs/Oct02/LEW17139.html
* http://unr.edu/homepage/mcubed/FRG.html
* [http://www.tuke.sk/podlubny/fc_resources.html Igor Podlubny's collection of related books, articles, links, software, etc. ]
* Podlubny, I., Geometric and physical interpretation of fractional integration and fractional differentiation. [http://www.diogenes.bg/fcaa/ Fractional Calculus and Applied Analysis], vol.&nbsp;5, no.&nbsp;4, 2002, 367&ndash;386. (available as [http://www.tuke.sk/podlubny/pspdf/pifcaa_r.pdf original article], or [http://arxiv.org/abs/math.CA/0110241 preprint at Arxiv.org])
 
[[Category:Fractional calculus]]
[[Category:Generalizations of the derivative]]
[[Category:Linear operators in calculus]]

Latest revision as of 19:52, 6 December 2014

If you own a measuring tape, you are able to measure yourself to determine where you carry most of the excess fat on your body. Calculating your waist to hip ratio helps we determine not merely where we carry many of your fat, and how much of the risk a fat actually poses to a wellness.

What is Body Mass Index? Body Mass Index, more commonly acknowledged as "BMI", is an indicator of the amount of body fat a person has. The BMI really divides your weight by your height to provide you the body fat analysis. The better amount of body fat a individual carries, the more probably they are to have health related illnesses. "Weight for height" is an significant measurement because whenever you're in the ideal range of fat for height, you are able to anticipate to reside the longest lifetime possible with limited illnesses. When a person steps from this range, on either side; having too small fat or having too much weight, is whenever wellness problems occur.

But before you all breathe a sigh of relief and down a cheeseburger, bag of potato chips, along with a carton of moose tracks ice cream (yum), the research waist to height ratio leader did say which the research did not prove that obesity was harmless. Being obese or obese still carries an improved risk of heart disease, diabetes and certain types of cancers.

Diesel tuning involves rewriting the ECU maps to liberate a diesel engine's true potential. Dozens of settings that affect the performance of the car are improved in the remapping process. The purpose of ECU remapping is to achieve the the best possible force curve for automobile performance plus gas economy. At the same time, safety variables initially programmed into your ECU need to be respected in purchase to avoid any damage to the engine or drive train.

Skinfold Thickness Measurements - One of the simplest techniques to measurefat weight is the skin fold width measuring. A tool called a skinfold caliper is selected to pinch the skin, gathering a double layer to measure the underlying tissue. The caliper reads two measurements - cm and mm, with all the mean of the 2 taken. Thisfat weight measuring is selected on different anatomical regions of the body.

For years, it was assumed which those indicated because "overweight" based on the BMI were at a much high risk of dying from heart related conditions. But the new research waist to height ratio which the Mayo Clinic in Rochester, Minnesota, published indicates anything very different. In their research of 250,000 people with heart condition, those with a BMI which indicated obese status had less chance of dying from heart difficulties than those with a general BMI. And people with a general BMI were less probably to die than folks with low BMI. And as expected, severely overweight persons did have a higher incidence of death from heart-related condition.

In the night I would go for a 5km walk. Initially it would take me over an hr to cover the distance, yet because I got healthier plus my endurance increased I got quicker. Now I may do it in 45 minutes on a advantageous day. Although I find walking alone really boring and whenever I walk with a friend the speed seems to suffer.

Because BMI utilizes only height and weight, the BMI result for a lean, "buff" individual with a svelte waist will really end up inside the obese category. As an example, a guy who's 5-11, yet has a muscled physique, may weigh 200 pounds. This puts him in the obese category for BMI (27.9), despite the reality his body fat percentage could be exceptionally low.

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