Rational zeta series: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
en>Jsondow
→‎Elementary series: Corrected "integer" to "positive integer"
en>Rjwilmsi
m →‎References: Added 1 doi to a journal cite using AWB (10222)
 
Line 1: Line 1:
'''Planck force''' is the derived unit of [[force]] resulting from the definition of the base [[Planck units]] for time, length, and mass. It is equal to the natural unit of [[momentum]] divided by the natural unit of time.
Paleo diet recipes are good for those who are looking for a diet that promotes health and gives results quickly. Nonetheless, this really is easier said than undertaken. From 185 lb he has over the years managed to bring his weight down to 145. A recent study published in the European Journal of Clinical Nutrition indicates the Paleo diet is twice as effective as other diets for promoting weight loss and reducing belly fat. Many people use it as it seems like the quickest way to lose weight. <br><br>We drive ourselves harder in the community of others. - Mix arugula, spinach, bacon bits, blackberries, egg bits, walnuts, cinnamon and nutmeg. Ancient diet for optimal health enjoy delicious breakfast, lunch and dinner Paleo Recipes. These benefits could expand the health claims now permitted to be identified by the FDA. Fat takes a long time to digest and keeps us feeling full longer. <br><br>The reason for this is because the cows are free to roam around and eat all the grass. "I saw the difference in my body, my energy and my mental clarity. Specifically diabetes, obesity, high blood pressure, depression, and high cholesterol. Today, it appears to be a staple of the American diet. The process of preparing this type of apparently complicated checking seafood dinner is not that mind dazzling. <br><br>His photos quickly went viral, with admirers of his sleek physique warring with fans who expressed concern that the NBA's Most Valuable Player had shredded too much fat. This diet basically consumed lots of fruits and veggies and also lots of protein rich food. When we do feel hungry, we usually also feel panic or anxiety. For example, you ought to refrain from eating farm-raised animals or genetically-altered create. He ate fruits and vegetables, which grew in abundance. <br><br>Or at least the leftover carcass of a wolf-pack kill. I don't recall the exact number of recipes, but they do have several paleo diet cake recipes. Regardless, of the primitive place of shelter Caveman was constantly looking for food. As you may have already observed, the Paleo Diet plan includes consuming an average volume of various meats, seafood, chicken, plenty of vegetables and fat (from resources like grape & grape oil), little fruits and nut products. No wonder that anti obesity solutions form a billion dollar business worldwide. <br><br>Those cave men and women led very different lives than we do today. Desserts are put together from fruits like bananas and berries. "Base your diet on garden vegetables, especially greens, lean meats, nuts and seeds, little starch, and no sugar. It is not an easy thing to have new ideas for meal and having lack of options but there are still some good choices from the paleo diet which might be used. The Paleo diet burns body fat, builds immune system and increase overall level of energy.<br><br>Should you adored this short article and also you would want to be given guidance regarding [http://gritsandgroceries.info/ paleo cookie recipe] kindly go to our web site.
 
:<math>F_\text{P} = \frac{m_\text{P} c}{t_\text{P}} = \frac{c^4}{G} = 1.21027 \times 10^{44} \mbox{ N.}</math>
 
==Other derivations==
 
The Planck force is also associated with the equivalence of gravitational potential energy and electromagnetic energy<ref>{{cite web |title=Gravity and the Photon |work=HyperPhysics |publisher=Georgia State University |url=http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/blahol.html#c2 |accessdate=2012-09-12}}</ref> and in this context it can be understood as the force that confines a self-gravitating mass to half its [[Schwarzschild radius]]:
 
:<math>F_\text{P} = \frac{G m^2}{r_\text{G}^2} </math>,
:<math>r_\text{G} = \frac{r_\text{s}}{2} = \frac{G m}{c^2}.</math>,
 
where ''G'' is the [[gravitational constant]], ''c'' is the [[speed of light]], ''m'' is any mass and ''r''<sub>G</sub> is half the Schwarzschild radius, ''r''<sub>s</sub>, of the given mass.
Since the dimension of force is also a ratio of energy per length, the Planck force can be calculated as energy divided by half the Schwarzschild radius:
 
:<math>F_\text{P} = \frac{m c^2}{\frac{Gm}{c^2}}=\frac{c^4}{G}.</math>
 
As mentioned above, Planck force has a unique association with the [[Planck mass]]. This unique association also manifests itself when force is calculated as any energy divided by the reduced [[Compton wavelength]] (reduced by 2π) of that same energy:
:<math>F = \frac{m c^2}{\frac{\hbar}{m c}} = \frac{m^2 c^3}{\hbar}.</math>
 
Here the force is different for every mass (for the electron, for example, the force is responsible for the [[Schwinger effect]] (see page 3 here [http://prst-ab.aps.org/pdf/PRSTAB/v5/i3/e031301]). It is Planck force only for the Planck mass (approximately 2.18 &times; 10<sup>-8</sup>&nbsp;kg). This follows from the fact that the [[Planck length]] is a reduced Compton wavelength equal to half the Schwarzschild radius of the Planck mass:
 
:<math>\frac{\hbar}{m_\text{P} c} = \frac{G m_\text{P}}{c^2}</math>
 
which in turn follows from another relation of fundamental significance:
 
:<math>c \hbar = G m_\text{P}^2.</math>
 
==General relativity==
 
Planck force is often useful in scientific calculations as a ratio of electromagnetic energy per gravitational length. Thus for example it appears in the [[Einstein field equations]], describing the properties of a gravitational field surrounding any given mass:
 
:<math>G_{\mu\nu}=8\pi\frac{G}{c^4} T_{\mu\nu}</math>
 
where <math>G_{\mu\nu}</math> is the [[Einstein tensor]] and <math>T_{\mu\nu}</math> is the [[energy–momentum tensor]].
 
== Notes and references==
{{Reflist|2}}
 
 
{{Planck's natural units}}
{{Portal bar|Physics}}
 
[[Category:Units of force]]
[[Category:Natural units|Force]]

Latest revision as of 15:46, 8 June 2014

Paleo diet recipes are good for those who are looking for a diet that promotes health and gives results quickly. Nonetheless, this really is easier said than undertaken. From 185 lb he has over the years managed to bring his weight down to 145. A recent study published in the European Journal of Clinical Nutrition indicates the Paleo diet is twice as effective as other diets for promoting weight loss and reducing belly fat. Many people use it as it seems like the quickest way to lose weight.

We drive ourselves harder in the community of others. - Mix arugula, spinach, bacon bits, blackberries, egg bits, walnuts, cinnamon and nutmeg. Ancient diet for optimal health enjoy delicious breakfast, lunch and dinner Paleo Recipes. These benefits could expand the health claims now permitted to be identified by the FDA. Fat takes a long time to digest and keeps us feeling full longer.

The reason for this is because the cows are free to roam around and eat all the grass. "I saw the difference in my body, my energy and my mental clarity. Specifically diabetes, obesity, high blood pressure, depression, and high cholesterol. Today, it appears to be a staple of the American diet. The process of preparing this type of apparently complicated checking seafood dinner is not that mind dazzling.

His photos quickly went viral, with admirers of his sleek physique warring with fans who expressed concern that the NBA's Most Valuable Player had shredded too much fat. This diet basically consumed lots of fruits and veggies and also lots of protein rich food. When we do feel hungry, we usually also feel panic or anxiety. For example, you ought to refrain from eating farm-raised animals or genetically-altered create. He ate fruits and vegetables, which grew in abundance.

Or at least the leftover carcass of a wolf-pack kill. I don't recall the exact number of recipes, but they do have several paleo diet cake recipes. Regardless, of the primitive place of shelter Caveman was constantly looking for food. As you may have already observed, the Paleo Diet plan includes consuming an average volume of various meats, seafood, chicken, plenty of vegetables and fat (from resources like grape & grape oil), little fruits and nut products. No wonder that anti obesity solutions form a billion dollar business worldwide.

Those cave men and women led very different lives than we do today. Desserts are put together from fruits like bananas and berries. "Base your diet on garden vegetables, especially greens, lean meats, nuts and seeds, little starch, and no sugar. It is not an easy thing to have new ideas for meal and having lack of options but there are still some good choices from the paleo diet which might be used. The Paleo diet burns body fat, builds immune system and increase overall level of energy.

Should you adored this short article and also you would want to be given guidance regarding paleo cookie recipe kindly go to our web site.

Retrieved from "https://en.formulasearchengine.com/index.php?title=Rational_zeta_series&oldid=241650"