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| | The body mass chart is a valuable instrument for checking when you've a healthy fat for your height. Just remember it's just a guide. You'll be able to furthermore choose any of the fat charts on this page to check if you're underweight, obese or merely right. The BMI chart has already performed the reckonings for you. It demonstrates the healthy, underweight, obese and obese grades for individual weights and heights. Only find the point where a fat meets the height.<br><br>If many of the population is overweight (according to the [http://safedietplans.com/bmi-chart bmi chart]) the error inside logic could be which the population is right and the bmi chart is wrong.<br><br>Strength Training: There is a great deal of information available on lifting weights and strength training, but bmi chart men being cautious to start this inside the "right" technique is significant as you receive older. Running Planet has completed a good job w/ laying out "The 8 rules of Strength Training". We have several advantageous videos on our Resources page.<br><br>Naturally, kids should, plus should, gain fat by the natural task of growth, but various kids go beyond that and place on excess fatty tissue; i.e. they become fat. Obesity is fast becoming a serious problem with todays youngsters, partially by the incorrect nutrition and eating too much of the wrong foods, plus partially by ignorance on behalf of the parents that have a misconception that puppy fat is a healthy and regular thing.<br><br>By filling in the height plus weight in an this calculator, an individual can know his BMI that enables him to deduce whether he is anorexic or not. While a healthy BMI is inside the range 19 - 25, a BMI index of 17.5 is considered to be an casual indicator of anorexia nervosa. However, this is not an accurate diagnosis for anorexia because certain individuals might have a low BMI but NOT be anorexic. Anorexia is a psychological condition which has to be diagnosed only after an in-depth emotional evaluation and laboratory tests, like, blood tests, electrocardiogram, plus bone density test.<br><br>BMI does not measure body fat directly bmi chart women, however, it relates closely to direct measures of body fat. For adults, BMI is interpreted while factors such as sex or age are not taken inside account.<br><br>After my son was born I weighed from the hospital at 192. That was following the baby was born. Because I was nursing, I lost the weight immediately. In 3 months I was back to 135, but then I stopped nursing. Since then I have gained back about 30 pounds, which puts me at 165. According to BMI (Body Mass Index) calculations, I am classified because "obese". Classifications are as follows: "Underweight", "Normal", "Overweight", and "Obese". BMI is calculated by the formula: fat (lb) / [height (in)]2 x 703. Divide your current fat by a height squared and then multiply by 703. The amount you come up with should be interpreted according to the following: 18.5 or below = Underweight, 18.4 - 24.9 = Normal, 25.0 - 29.9 = Overweight, 30.0 or above = Obese.<br><br>If you are thinking what the healthy weight is for a woman, then the BMI is the path to take. You could also check the circumference of your waist. If you believe you may be obese, then we should start eating healthy plus exercise frequently so which you can lose those pounds plus become the healthy, unique we. |
| [[Image:Dirac distribution CDF.svg|325px|thumb|The Heaviside step function, using the half-maximum convention]]
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| The '''Heaviside step function''', or the '''unit step function''', usually denoted by ''H'' (but sometimes ''u'' or ''θ''), is a [[continuous function|discontinuous]] [[Function (mathematics)|function]] whose value is [[0 (number)|zero]] for negative argument and [[1 (number)|one]] for positive argument.
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| It seldom matters what value is used for ''H''(0), since ''H'' is mostly used as a [[Distribution (mathematics)|distribution]]. Some common choices can be seen [[#Zero argument|below]].
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| The function is used in the mathematics of [[control theory]] and [[signal processing]] to represent a signal that switches on at a specified time and stays switched on indefinitely. It is also used in [[structural mechanics]] together with the [[Dirac delta function]] to describe different types of [[structural load]]s. It was named after the [[England|English]] [[polymath]] [[Oliver Heaviside]].
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| It is the [[cumulative distribution function]] of a [[random variable]] which is [[almost surely]] 0. (See [[constant random variable]].)
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| The Heaviside function is the [[integral]] of the [[Dirac delta function]]: ''H''′ = ''δ''. This is sometimes written as
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| :<math> H(x) = \int_{-\infty}^x { \delta(s)} \, \mathrm{d}s </math>
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| although this expansion may not hold (or even make sense) for ''x'' = 0, depending on which formalism one uses to give meaning to integrals involving ''δ''.
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| ==Discrete form==
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| An alternative form of the unit step, as a function of a discrete variable ''n'':
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| :<math>H[n]=\begin{cases} 0, & n < 0, \\ 1, & n \ge 0, \end{cases} </math>
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| where ''n'' is an [[integer]]. Unlike the usual (not discrete) case, the definition of ''H''[0] is significant.
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| The discrete-time unit impulse is the first difference of the discrete-time step
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| :<math> \delta\left[ n \right] = H[n] - H[n-1].</math>
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| This function is the cumulative summation of the [[Kronecker delta]]:
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| :<math> H[n] = \sum_{k=-\infty}^{n} \delta[k] \,</math>
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| where
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| :<math> \delta[k] = \delta_{k,0} \,</math> | |
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| is the [[degenerate distribution|discrete unit impulse function]]. | |
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| == Analytic approximations ==
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| For a [[Smooth function|smooth]] approximation to the step function, one can use the [[logistic function]]
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| :<math>H(x) \approx \frac{1}{2} + \frac{1}{2}\tanh(kx) = \frac{1}{1+\mathrm{e}^{-2kx}},</math>
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| where a larger ''k'' corresponds to a sharper transition at ''x'' = 0. If we take ''H''(0) = ½, equality holds in the limit:
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| :<math>H(x)=\lim_{k \rightarrow \infty}\frac{1}{2}(1+\tanh kx)=\lim_{k \rightarrow \infty}\frac{1}{1+\mathrm{e}^{-2kx}}.</math>
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| There are many other smooth, analytic approximations to the step function.<ref>{{MathWorld | urlname=HeavisideStepFunction | title=Heaviside Step Function}}</ref> Among the possibilities are:
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| :<math>\begin{align}
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| H(x) &= \lim_{k \rightarrow \infty} \left(\frac{1}{2} + \frac{1}{\pi}\arctan(kx)\right)\\
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| H(x) &= \lim_{k \rightarrow \infty}\left(\frac{1}{2} + \frac{1}{2}\operatorname{erf}(kx)\right)
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| \end{align}</math>
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| These limits hold [[pointwise]] and in the sense of [[distribution (mathematics)|distributions]]. In general, however, pointwise convergence need not imply distributional convergence, and vice-versa distributional convergence need not imply pointwise convergence.
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| In general, any [[cumulative distribution function]] (c.d.f.) of a [[continuous distribution|continuous]] [[probability distribution]] that is peaked around zero and has a parameter that controls for [[variance]] can serve as an approximation, in the limit as the variance approaches zero. For example, all three of the above approximations are c.d.f.s of common probability distributions: The [[logistic distribution|logistic]], [[Cauchy distribution|Cauchy]] and [[normal distribution|normal]] distributions, respectively.
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| ==Integral representations==
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| Often an [[integration (mathematics)|integral]] representation of the Heaviside step function is useful:
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| :<math>H(x)=\lim_{ \epsilon \to 0^+} -{1\over 2\pi i}\int_{-\infty}^\infty {1 \over \tau+i\epsilon} \mathrm{e}^{-i x \tau} \mathrm{d}\tau =\lim_{ \epsilon \to 0^+} {1\over 2\pi i}\int_{-\infty}^\infty {1 \over \tau-i\epsilon} \mathrm{e}^{i x \tau} \mathrm{d}\tau.</math>
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| == Zero argument ==
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| Since ''H'' is usually used in integration, and the value of a function at a single point does not affect its integral, it rarely matters what particular value is chosen of ''H''(0). Indeed when ''H'' is considered as a [[distribution (mathematics)|distribution]] or an element of <math>L^\infty</math> (see [[Lp space]]) it does not even make sense to talk of a value at zero, since such objects are only defined [[almost everywhere]]. If using some analytic approximation (as in the [[#Analytic approximations|examples above]]) then often whatever happens to be the relevant limit at zero is used.
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| There exist various reasons for choosing a particular value.
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| * ''H''(0) = ½ is often used since the [[graph of a function|graph]] then has rotational symmetry; put another way, ''H''-½ is then an [[odd function]]. In this case the following relation with the [[sign function]] holds for all ''x'':
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| :<math> H(x) = \tfrac{1}{2}(1+\sgn(x)).</math>
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| * ''H''(0) = 1 is used when ''H'' needs to be [[right-continuous]]. For instance [[cumulative distribution function]]s are usually taken to be right continuous, as are functions integrated against in [[Lebesgue–Stieltjes integration]]. In this case ''H'' is the [[indicator function]] of a [[closed set|closed]] semi-infinite interval:
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| :<math> H(x) = \mathbf{1}_{[0,\infty)}(x).\,</math>
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| : The corresponding probability distribution is the [[degenerate distribution]].
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| * ''H''(0) = 0 is used when ''H'' needs to be [[left-continuous]]. In this case ''H'' is an indicator function of an [[open set|open]] semi-infinite interval:
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| :<math> H(x) = \mathbf{1}_{(0,\infty)}(x).\,</math>
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| == Antiderivative and derivative==
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| The [[ramp function]] is the [[antiderivative]] of the Heaviside step function: <math>R(x) := \int_{-\infty}^{x} H(\xi)\mathrm{d}\xi = x H(x).</math>
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| The [[distributional derivative]] of the Heaviside step function is the [[Dirac delta function]]:
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| <math> \tfrac{d H(x)}{dx} = \delta(x)</math>
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| == Fourier transform ==
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| The [[Fourier transform]] of the Heaviside step function is a distribution. Using one choice of constants for the definition of the Fourier transform we have
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| :<math> | |
| \hat{H}(s) = \lim_{N\to\infty}\int^N_{-N} \mathrm{e}^{-2\pi i x s} H(x)\,\mathrm{d}x = \frac{1}{2} \left( \delta(s) - \frac{i}{\pi}\mathrm{p.v.}\frac{1}{s} \right).
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| </math> | |
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| Here <math>\mathrm{p.v.}\frac{1}{s}</math> is the [[distribution (mathematics)|distribution]] that takes a test function <math>\varphi</math> to the [[Cauchy principal value]] of <math>\int^{\infty}_{-\infty} \varphi(s)/s\,\mathrm{d}s.</math> The limit appearing in the integral is also taken in the sense of (tempered) distributions.
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| ==Hyperfunction representation==
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| This can be represented as a [[hyperfunction]] as <math>H(x) = \left(\frac{1}{2\pi i}\log(z),\frac{1}{2\pi i}\log(z)-1\right)</math>.
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| ==See also==
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| * [[Rectangular function]]
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| * [[Step response]]
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| * [[Sign function]]
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| * [[Negative number]]
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| * [[Laplace transform]]
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| * [[Iverson bracket]]
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| * [[Laplacian of the indicator]]
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| * [[Macaulay brackets]]
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| * [[Sine integral]]
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| ==References==
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| {{Reflist}}
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| {{DEFAULTSORT:Heaviside Step Function}}
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| [[Category:Special functions]]
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| [[Category:Generalized functions]]
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The body mass chart is a valuable instrument for checking when you've a healthy fat for your height. Just remember it's just a guide. You'll be able to furthermore choose any of the fat charts on this page to check if you're underweight, obese or merely right. The BMI chart has already performed the reckonings for you. It demonstrates the healthy, underweight, obese and obese grades for individual weights and heights. Only find the point where a fat meets the height.
If many of the population is overweight (according to the bmi chart) the error inside logic could be which the population is right and the bmi chart is wrong.
Strength Training: There is a great deal of information available on lifting weights and strength training, but bmi chart men being cautious to start this inside the "right" technique is significant as you receive older. Running Planet has completed a good job w/ laying out "The 8 rules of Strength Training". We have several advantageous videos on our Resources page.
Naturally, kids should, plus should, gain fat by the natural task of growth, but various kids go beyond that and place on excess fatty tissue; i.e. they become fat. Obesity is fast becoming a serious problem with todays youngsters, partially by the incorrect nutrition and eating too much of the wrong foods, plus partially by ignorance on behalf of the parents that have a misconception that puppy fat is a healthy and regular thing.
By filling in the height plus weight in an this calculator, an individual can know his BMI that enables him to deduce whether he is anorexic or not. While a healthy BMI is inside the range 19 - 25, a BMI index of 17.5 is considered to be an casual indicator of anorexia nervosa. However, this is not an accurate diagnosis for anorexia because certain individuals might have a low BMI but NOT be anorexic. Anorexia is a psychological condition which has to be diagnosed only after an in-depth emotional evaluation and laboratory tests, like, blood tests, electrocardiogram, plus bone density test.
BMI does not measure body fat directly bmi chart women, however, it relates closely to direct measures of body fat. For adults, BMI is interpreted while factors such as sex or age are not taken inside account.
After my son was born I weighed from the hospital at 192. That was following the baby was born. Because I was nursing, I lost the weight immediately. In 3 months I was back to 135, but then I stopped nursing. Since then I have gained back about 30 pounds, which puts me at 165. According to BMI (Body Mass Index) calculations, I am classified because "obese". Classifications are as follows: "Underweight", "Normal", "Overweight", and "Obese". BMI is calculated by the formula: fat (lb) / [height (in)]2 x 703. Divide your current fat by a height squared and then multiply by 703. The amount you come up with should be interpreted according to the following: 18.5 or below = Underweight, 18.4 - 24.9 = Normal, 25.0 - 29.9 = Overweight, 30.0 or above = Obese.
If you are thinking what the healthy weight is for a woman, then the BMI is the path to take. You could also check the circumference of your waist. If you believe you may be obese, then we should start eating healthy plus exercise frequently so which you can lose those pounds plus become the healthy, unique we.