Dini–Lipschitz criterion: Difference between revisions

Latest revision as of 19:25, 11 December 2014

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What exactly tends to make pumpkin so super? The strong antioxidants identified as carotenoids give this food its super status. Carotenoids have the capability to ward off the danger of various sorts of cancer and heart disease, along with, cataracts and macular degeneration. Follow Us On Twitter contains further concerning when to ponder it. Dr. Pratt mentions several other illness fighting super foods in his book as nicely, but we are most interested in pumpkin due to the fact of the year-round availability and ease of use in canned kind.

How can we add this wonder meals to our diets by way of out the year? Take benefit of the rewards and fantastic taste of pumpkin with the following delicious Pumpkin Recipes.

Any day Pumpkin Pancakes

2-1/two cups flour

1 cup of buttermilk

1 tsp. salt

2-1/4 tsp. Go is a staggering library for extra resources about the meaning behind it. soda

two tsp. baking powder

1/2 cup of pumpkin

Measure flour into bowl and add dry ingredients. Stir in buttermilk and add pumpkin. Mix Nicely. Cook on hot griddle or skillet till golden brown.

Pumpkin Spiced Muffins

1/3 cup butter or margarine, softened

1 cup brown sugar

two eggs

1 cup pumpkin

1/4 cup milk

2 cups flour

two tsp. baking powder

1 tsp. cinnamon

1/2 tsp. ginger

1/4 tsp. ground cloves

1/4 tsp. salt

1/four tsp. baking soda

Preheat oven to 350 degrees F. In a large bowl cream butter with brown sugar. Beat in eggs, then

pumpkin and milk. In a little bowl combine flour, baking powder, spices, salt and baking soda. Add to the creamed mixture. Bake for 20 to 25 minutes..

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-{{context|date=May 2012}}
-In [[financial mathematics]], a '''distortion risk measure''' is a type of [[risk measure]] which is related to the [[cumulative distribution function]] of the [[rate of return|return]] of a [[financial portfolio]].
-== Mathematical definition ==
-The function <math>\rho_g: L^p \to \mathbb{R}</math> associated with the [[distortion function]] <math>g: [0,1] \to [0,1]</math> is a ''distortion risk measure'' if for any [[random variable]] of gains <math>X \in L^p</math> (where <math>L^p</math> is the [[Lp space|L<sup>p</sup> space]]) then
-: <math>\rho_g(X) = -\int_0^1 F_{-X}^{-1}(p) d\tilde{g}(p) = \int_{-\infty}^0 \tilde{g}(F_{-X}(x))dx - \int_0^{\infty} g(1 - F_{-X}(x)) dx</math>
-where <math>F_{-X}</math> is the cumulative distribution function for <math>-X</math> and <math>\tilde{g}</math> is the dual distortion function <math>\tilde{g}(u) = 1 - g(1-u)</math>.<ref name="PortfolioOpt"/>
-If <math>X \leq 0</math> [[almost surely]] then <math>\rho_g</math> is given by the [[Choquet integral]], i.e. <math>\rho_g(X) = -\int_0^{\infty} g(1 - F_{-X}(x)) dx.</math><ref name="PortfolioOpt">{{cite doi|10.1007/978-0-387-77439-8_25}}</ref><ref name="Wirch">{{cite web|title=Distortion Risk Measures: Coherence and Stochastic Dominance|author=Julia L. Wirch|author2=Mary R. Hardy|url=http://pascal.iseg.utl.pt/~cemapre/ime2002/main_page/papers/JuliaWirch.pdf|format=pdf|accessdate=March 10, 2012}}</ref>  Equivalently, <math>\rho_g(X) = \mathbb{E}^{\mathbb{Q}}[-X]</math><ref name="Wirch"/> such that <math>\mathbb{Q}</math> is the [[probability measure]] generated by <math>g</math>, i.e. for any <math>A \in \mathcal{F}</math> the [[sigma-algebra]] then <math>\mathbb{Q}(A) = g(\mathbb{P}(A))</math>.<ref name="PropertiesDRM">{{cite doi|10.1007/s11009-008-9089-z}}</ref>
+Feel of the word pumpkin and photos of jack-o-lanterns and whipped cream covered Thanksgiving pies will almost certainly pop into your thoughts. Pumpkin is traditionally regarded as a holiday food and is a staple in our kitchen pantries and freezers in the course of that festive time of the year. However, did you know that pumpkin now heralded as one particular of the Super Foods?<br><br>According to Dr. Steven Pratt, author of SuperFoods Rx: Fourteen Foods That Will Modify Your Life, Well, pumpkin is 1 of the most nutritionally useful foods known to man. Moreover, its economical, offered year round in canned form, extremely easy to incorporate into recipes, high in fiber, low in calories, and packs an abundance of disease fighting nutrients.<br><br>What exactly tends to make pumpkin so super? The strong antioxidants identified as carotenoids give this food its super status. Carotenoids have the capability to ward off the danger of various sorts of cancer and heart disease, along with, cataracts and macular degeneration. [http://about.me/bakingcupsglass Follow Us On Twitter] contains further concerning when to ponder it. Dr. Pratt mentions several other illness fighting super foods in his book as nicely, but we are most interested in pumpkin due to the fact of the year-round availability and ease of use in canned kind.<br><br>How can we add this wonder meals to our diets by way of out the year? Take benefit of the rewards and fantastic taste of pumpkin with the following delicious Pumpkin Recipes.<br><br>Any day Pumpkin Pancakes<br><br>2-1/two cups flour<br><br>1 cup of buttermilk<br><br>1 tsp. salt<br><br>2-1/4 tsp. [http://about.me/sitewindowxir Go] is a staggering library for extra resources about the meaning behind it. soda<br><br>two tsp. baking powder<br><br>1/2 cup of pumpkin<br><br>Measure flour into bowl and add dry ingredients. Stir in buttermilk and add pumpkin. Mix Nicely. Cook on hot griddle or skillet till golden brown.<br><br>Pumpkin Spiced Muffins<br><br>1/3 cup butter or margarine, softened<br><br>1 cup brown sugar<br><br>two eggs<br><br>1 cup pumpkin<br><br>1/4 cup milk<br><br>2 cups flour<br><br>two tsp. baking powder<br><br>1 tsp. cinnamon<br><br>1/2 tsp. ginger<br><br>1/4 tsp. ground cloves<br><br>1/4 tsp. salt<br><br>1/four tsp. baking soda<br><br>Preheat oven to 350 degrees F. In a large bowl cream butter with brown sugar. Beat in eggs, then<br><br>pumpkin and milk. In a little bowl combine flour, baking powder, spices, salt and baking soda. Add to the creamed mixture. Bake for 20 to 25 minutes..<br><br>If you beloved this posting and you would like to get additional facts regarding [http://people.tribe.net/knottygovernor414 Articles On Health] kindly pay a visit to our own internet site.
-=== Properties ===
-In addition to the properties of general risk measures, distortion risk measures also have:
-# ''Law invariant'': If the distribution of <math>X</math> and <math>Y</math> are the same then <math>\rho_g(X) = \rho_g(Y)</math>.
-# ''Monotone'' with respect to first order [[stochastic dominance]].
-## If <math>g</math> is a [[concave function|concave]] distortion function, then <math>\rho_g</math> is monotone with respect to second order stochastic dominance.
-# <math>g</math> is a [[concave function|concave]] distortion function if and only if <math>\rho_g</math> is a [[coherent risk measure]].<ref name="PortfolioOpt"/><ref name="Wirch"/>
-== Examples ==
-* [[Value at risk]] is a distortion risk measure with associated distortion function <math>g(x) = \begin{cases}0 & \text{if }0 \leq x < 1-\alpha\\ 1 & \text{if }1-\alpha \leq x \leq 1\end{cases}.</math><ref name="Wirch"/><ref name="PropertiesDRM"/>
-* [[Conditional value at risk]] is a distortion risk measure with associated distortion function <math>g(x) = \begin{cases}\frac{x}{1-\alpha} & \text{if }0 \leq x < 1-\alpha\\ 1 & \text{if }1-\alpha \leq x \leq 1\end{cases}.</math><ref name="Wirch"/><ref name="PropertiesDRM"/>
-* The negative [[expected value|expectation]] is a distortion risk measure with associated distortion function <math>g(x) = x</math>.<ref name="PortfolioOpt"/>
-== See also ==
-* [[Risk measure]]
-* [[Coherent risk measure]]
-* [[Deviation risk measure]]
-* [[Spectral risk measure]]
-== References ==
-{{reflist}}
-*{{cite journal|last=Wu|first=Xianyi|coauthors=Xian Zhou|title=A new characterization of distortion premiums via countable additivity for comonotonic risks|journal=Insurance: Mathematics and Economics|date=April 7, 2006|volume=38|issue=2|pages=324–334|url=http://www.sciencedirect.com/science/article/pii/S016766870500123X|accessdate=March 14, 2012}}
-[[Category:Mathematical finance]]
-[[Category:Financial risk]]

Dini–Lipschitz criterion: Difference between revisions

Latest revision as of 19:25, 11 December 2014

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