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{{For|essential singularities of real valued functions|Classification of discontinuities}}
Online calculators are internet-based. It is pretty handy when you may be online plus require immediate computations done. The program is especially exact and powerful.<br><br>Over the last 100 years the average individual has gotten taller and tends to carry more muscle. The result is that BMI calculations tend to be a small bit off, many individuals can read higher than they absolutely are. However for most people the results are nevertheless very accurate. If you are truly tall or you are carrying a lot of muscle be prepared for the charts to tell you you are obese.<br><br>Whenever calculating how much fat to get rid of the most crucial number to learn is the Body Fat Percentage. This number informs you exactly how much of your body is fat, plus from there you can calculate how much is muscle, water, etc. For example, should you are a 586" female weighing 180 pounds and have a BP of 43%, then 77.4 pounds are fat, and 102.6 pounds are muscle, skeletal mass, plus water. We equally have a BMI of 28.2 - a little over the norm. Then you can figure out which if you would like your BF to be 23% - pretty perfect for a female - we need to lose 36 pounds of fat. The result: a weight of 144 pounds with a BP of 23%, that in turn provides we a BMI of 22.6, well in the usual range.<br><br>The [http://safedietplansforwomen.com/bmi-calculator bmi calculator women] is regarded as the many normal you will find, plus among the easiest to utilize. While you're losing fat, it can equally be fun to punch modern numbers into the fat reduction calculator from time to time to watch the BMI number go down. Especially pleasing is the day whenever a amount moves within the overweight range to the obese range, or from obese to normal!<br><br>For female with low activity that has a weight at 149lbs plus under, should try a 1,200 calorie diet to help their fat reduction. Women 150lbs to 164 lbs should have 1,400 calories; 165 to 184lbs 1,600 calories; and finally females over 185lbs must have 1,800 calories.<br><br>Once we learn your BF losing fat becomes a more streamlined task. In the example above which girl today knows she must lose 36 pounds of fat to receive to her goal. To make certain she doesn't lose any muscle mass inside the task, she'll join a strength training system, that usually also enable her to burn fat quicker.<br><br>In terms of its dodgy mathematics, the BMI is borderline junk science. But inside this regard, BMI is less egregious than Global Warming 'studies', in which almost all of the big-name 'researchers' cherry-pick, hide, or fabricate data. Click on the link for my long hub found on the topic.
 
[[File:Essential singularity.png|right|220px|thumb|Plot of the function exp(1/''z''), centered on the essential singularity at ''z''=0. The hue represents the [[Arg (mathematics)|complex argument]], the luminance represents the [[absolute value]]. This plot shows how approaching the essential singularity from different directions yields different behaviors (as opposed to a pole, which, approached from any direction, would be uniformly white).]]
[[File:Modell des Graphen von 6w=eˆ(1-6z) -Schilling XIV, 6 - 312- (2).jpg|thumb|Model illustrating essential singularity of a complex function 6w=exp(1/(6z))]]
 
In [[complex analysis]], an '''essential singularity''' of a function is a "severe" [[singularity (mathematics)|singularity]] near which the function exhibits extreme behavior.
 
The category ''essential singularity'' is a "left-over" or default group of singularities that are especially unmanageable: by definition they fit into neither of the other two categories of singularity that may be dealt with in some manner &ndash; [[removable singularity|removable singularities]] and [[pole (complex analysis)|pole]]s.
 
==Formal description==
Consider an [[open set|open subset]] ''U'' of the [[complex plane]] '''C'''. Let ''a'' be an element of ''U'', and ''f''&nbsp;:&nbsp;''U''&nbsp;\&nbsp;{''a''}&nbsp;→&nbsp;'''C''' a [[meromorphic function]]. The point ''a'' is called an ''essential singularity'' of the function ''f'' if the singularity is neither a [[pole (complex analysis)|pole]] nor a [[removable singularity]].
 
For example, the function ''f''(''z'') = ''e''<sup>1/''z''</sup> has an essential singularity at ''z'' = 0.
 
==Alternate descriptions==
 
Let ''a'' be a complex number, assume that ''f''(''z'') is not defined at ''a'' but is [[Analytic function|analytic]] in some region ''U'' of the complex plane, and that every [[Open set|open]] [[neighbourhood (mathematics)|neighbourhood]] of ''a'' has non-empty intersection with ''U''.
 
If both
:<math>\lim_{z \to a}f(z)</math> &nbsp; and &nbsp; <math>\lim_{z \to a}\frac{1}{f(z)}</math> &nbsp; exist, then ''a'' is a [[removable singularity]] of both ''f'' and 1/''f''.  
 
If
:<math>\lim_{z \to a}f(z)</math> &nbsp; exists but &nbsp; <math>\lim_{z \to a}\frac{1}{f(z)}</math> &nbsp; does not exist, then ''a'' is a [[zero (complex analysis)|zero]] of ''f'' and a [[pole (complex analysis)|pole]]  of 1/''f''.
 
Similarly, if
:<math>\lim_{z \to a}f(z)</math> &nbsp; does not exist but &nbsp; <math>\lim_{z \to a}\frac{1}{f(z)}</math> &nbsp; exist, then ''a'' is a pole of ''f'' and a zero of 1/''f''.
 
If neither
:<math>\lim_{z \to a}f(z)</math> &nbsp;  nor &nbsp; <math>\lim_{z \to a}\frac{1}{f(z)}</math> &nbsp; exists, then ''a'' is an essential singularity of both ''f'' and 1/''f''.
 
Another way to characterize an essential singularity is that the [[Laurent series]] of ''f'' at the point ''a'' has infinitely many negative degree terms (i.e., the [[principal part]] of the Laurent series is an infinite sum).
 
The behavior of holomorphic functions near their essential singularities is described by the [[Casorati–Weierstrass theorem]] and by the considerably stronger [[Picard's great theorem]]. The latter says that in every neighborhood of an essential singularity ''a'', the function ''f'' takes on ''every'' complex value, except possibly one, infinitely many times.
 
==References==
{{refbegin}}
*{{citeweb|url=http://mathworld.wolfram.com/EssentialSingularity.html|title=Essential Singularity at Mathworld|accessdate=18 February 2008}}
*Lars V. Ahlfors; ''Complex Analysis'', McGraw-Hill, 1979
*Rajendra Kumar Jain, S. R. K. Iyengar; ''Advanced Engineering Mathematics''. Page 920. Alpha Science International, Limited, 2004. ISBN 1-84265-185-4
{{refend}}
 
== External links ==
* '' [http://demonstrations.wolfram.com/AnEssentialSingularity/ An Essential Singularity]'' by [[Stephen Wolfram]], [[Wolfram Demonstrations Project]].
* [http://planetmath.org/encyclopedia/EssentialSingularity.html Essential Singularity on Planet Math]
*[http://www.encyclopediaofmath.org/index.php/Essential_singular_point Essential singularity] at [http://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]
 
[[Category:Complex analysis]]

Latest revision as of 19:28, 28 December 2014

Online calculators are internet-based. It is pretty handy when you may be online plus require immediate computations done. The program is especially exact and powerful.

Over the last 100 years the average individual has gotten taller and tends to carry more muscle. The result is that BMI calculations tend to be a small bit off, many individuals can read higher than they absolutely are. However for most people the results are nevertheless very accurate. If you are truly tall or you are carrying a lot of muscle be prepared for the charts to tell you you are obese.

Whenever calculating how much fat to get rid of the most crucial number to learn is the Body Fat Percentage. This number informs you exactly how much of your body is fat, plus from there you can calculate how much is muscle, water, etc. For example, should you are a 586" female weighing 180 pounds and have a BP of 43%, then 77.4 pounds are fat, and 102.6 pounds are muscle, skeletal mass, plus water. We equally have a BMI of 28.2 - a little over the norm. Then you can figure out which if you would like your BF to be 23% - pretty perfect for a female - we need to lose 36 pounds of fat. The result: a weight of 144 pounds with a BP of 23%, that in turn provides we a BMI of 22.6, well in the usual range.

The bmi calculator women is regarded as the many normal you will find, plus among the easiest to utilize. While you're losing fat, it can equally be fun to punch modern numbers into the fat reduction calculator from time to time to watch the BMI number go down. Especially pleasing is the day whenever a amount moves within the overweight range to the obese range, or from obese to normal!

For female with low activity that has a weight at 149lbs plus under, should try a 1,200 calorie diet to help their fat reduction. Women 150lbs to 164 lbs should have 1,400 calories; 165 to 184lbs 1,600 calories; and finally females over 185lbs must have 1,800 calories.

Once we learn your BF losing fat becomes a more streamlined task. In the example above which girl today knows she must lose 36 pounds of fat to receive to her goal. To make certain she doesn't lose any muscle mass inside the task, she'll join a strength training system, that usually also enable her to burn fat quicker.

In terms of its dodgy mathematics, the BMI is borderline junk science. But inside this regard, BMI is less egregious than Global Warming 'studies', in which almost all of the big-name 'researchers' cherry-pick, hide, or fabricate data. Click on the link for my long hub found on the topic.

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