|
|
| Line 1: |
Line 1: |
| {{Redirect|C-space|the art gallery|C-Space, Beijing}}
| | Pearl powder is a finely milled powder from quality freshwater pearls and its naturally compatible and easily absorbed by the skin and body. The vinegar can be applied directly to the affected area. One study suggests a novel method of testing multiple topical skin-lightening methods prior to initiating therapy, using UV-induced skin tanning. They're very natural, so lemons are a great way of bleaching the skin and helping to reduce the appearance of your acne scars. The reason is that the papaya extracts nourish the skin and also make it look better. <br><br>As a result, we should pay great attention to eat more fruits in spring, so as to make the skin moist and healthy. Less commonly, some Black women will develop a decrease in melanin or postinflammatory hypopigmentation in response to skin trauma (burns, etc. Try and look for a product which contains Alpha Arbutin, as this substance has had a very high success rate when whitening a variety of skin tones. It is highly important to know which was the cause which led to the apparition of your dark patches or brown spots in order to know how to treat them. It not only gradually whitens skin naturally, but your skin also becomes brighter and healthier without any harmful side effects. <br><br>Fill the tub with warm or hot water, strain the decoction and pour the herb liquid into the tub. One is the natural way of achieving the goal of fairness and other is the medicated methods which include different therapies and treatments. In addition, arsenic was used by women during the Elizabethan era (including the Queen, herself) in a mixture with vinegar and chalk to whiten their skin and prevent signs of aging. Many-a-times, one frustratingly discovers the image size has reduced substantially one the cropping is done and a large size print would ruin resolution. So many natural remedies for fair skin tone like massage with olive and almond oil on skin so they give shining and perfect fair skin. <br><br>Sugar with honey applied to our skin can exfoliate them just as well as the salons can. Even though they seem too traditional for the individuals of today, the effect is still as efficient as it was before. The cream is able to treat acne scars and aging spots. The results is an increase of the synthesis of the melanin and the rise of the pigmentation of the skin. We all know that all complexions are wonderful and it matters not which skin color you have, nevertheless for those who have neglected their pale skin color in the past when you had been some sort of sunshine worshipper and also you are somebody who wants some sort of brighter skin color there is nothing wrong within wanting a brighter skin. <br><br>Once they have fully dried, grind them to form a fine powder. Moreover, past biopsies of breast tumors have shown to have higher concentrations of metals like zinc, iron, chromium, and iron, just to name a few. An excellent natural hand cream contains ingredients that moisturize, soothe and nourish the skin. Lighten skin: the skin will burn and peel and have light skin, blue eyes, and either brown or blonde hair. It can also be removed from a regional drug store or alternatively is sold web-based from Online Canada Nearby.<br><br>If you adored this short article and you would certainly such as to obtain additional details pertaining to best skin bleaching products ([http://stylax.info/sitemap/ stylax.info]) kindly go to our web site. |
| {{other uses|PCI configuration space}}
| |
| | |
| In [[classical mechanics]], the parameters that define the configuration of a system are called ''[[generalized coordinates]],'' and the vector space defined by these coordinates is called the '''configuration space''' of the [[physical system]]. It is often the case that these parameters satisfy mathematical constraints, which means that the set of actual configurations of the system is a manifold in the space of generalized coordinates. This [[manifold]] is called the '''configuration manifold''' of the system.
| |
| | |
| ==Configuration spaces in physics==
| |
| | |
| ===Particle===
| |
| The position of a single particle moving in ordinary [[Euclidean space|Euclidean 3-space]] is defined by the vector '''r'''=(x, y, z), and therefore its ''configuration space'' is '''R'''<sup>3</sup>. If the particle is constrained to lie on a sphere, then its configuration space is the subset of coordinates in '''R'''<sup>3</sup> that define points on the sphere S<sup>2</sup>. | |
| | |
| For ''n'' particles the configuration space is '''R'''<sup>3''n''</sup>, or possibly the subspace where no two positions are equal.
| |
| | |
| An important problem in physics considers the set of all trajectories of a particle between two points, which is a configuration space that is also known as a [[function space]] ''M''. In [[quantum mechanics]] one [[path integral formulation|formulation]] uses ''histories'', or trajectories, as configurations.
| |
| | |
| ===Rigid body===
| |
| The set of coordinates that define the position of a reference point and the orientation of a coordinate frame attached to a rigid body in three dimensional space form its configuration space, often denoted '''R'''<sup>3</sup>xSO(3)---'''R'''<sup>3</sup> represents the coordinates of the origin of the frame attached to the body, and SO(3) represents the rotation matrices that define the orientation of this frame relative to a ground frame. A configuration of the rigid body is defined by six parameters, three from '''R'''<sub>3</sup> and three from SO(3), and is said to have six [[Degrees of freedom (mechanics)|degrees of freedom]].
| |
| | |
| In Robotics, ''configuration space'' refers to the set of positions reachable by a robot's [[end-effector]] considered to be a rigid body in three dimensional space.<ref>John J. Craig, '''Introduction to Robotics: Mechanics and Control''', 3rd Ed. Prentice-Hall, 2004</ref> Thus, the positions of the end-effector of a robot can be identified with the group of spatial rigid transformations, often denoted SE(3).
| |
| | |
| The joint parameters of the robot are used as generalized coordinates to define its configurations. The set of joint parameter values is called the ''joint space''. The robot's [[forward kinematics|forward]] and [[inverse kinematics]] equations define mappings between its configurations and its end-effector positions, or between joint space and configuration space. Robot [[motion planning]] uses these mappings to find a path in joint space that provides a desired path in the configuration space of the end-effector.
| |
| | |
| ===Phase space===
| |
| In Mechanics, the configuration of a system is considered to consist of its position and its velocity, or more generally its momentum. The set of velocities available to a system defines a plane tangent to its configuration manifold. Momentum vectors are linear functionals on the tangent plane, known as cotangent vectors. Thus, the set of position and momenta of a mechanical system forms the [[cotangent bundle]] of the configuration manifold.
| |
| | |
| This larger manifold is called the [[phase space]] of the system. The usual configuration space can be viewed as "half" of the [[phase space]] of a mechanical system.
| |
| | |
| == Configuration spaces in mathematics ==
| |
| [[File:Moebius Surface 1 Display Small.png|thumb|The configuration space of 2 not necessarily distinct points on the circle is the [[orbifold]] <math>T^2/S_2,</math> which is the [[Möbius strip]].]]
| |
| <!-- Deleted image removed: [[File:Topological III by Robert R. Wilson, at Harvard University.JPG|upright|thumb|The configuration space of 3 not necessarily distinct points on the circle <math>T^3/S_3,</math> is the above orbifold.]] -->
| |
| | |
| In [[mathematics]] a '''configuration space''' refers to a broad family of constructions closely related to the '''[[state space]]''' notion in physics. The most common notion of '''configuration space''' in mathematics <math>C_n X</math> is the set of ''n''-element subsets of a [[topological space]] <math>X</math>. This set is given a [[topological space|topology]] by considering it as the [[quotient space|quotient]] <math>C_n X = F_n X / \Sigma_n</math> where <math>F_n X = \{(x_1,\cdots,x_n) \in X^n : x_i \neq x_j \forall \ i \neq j \}</math> and <math>\Sigma_n</math> is the [[symmetric group]] acting by permuting the coordinates of <math>F_n X</math>. Typically, <math>C_n X</math> is called the configuration space of ''n'' unordered points in <math>X</math> and <math>F_n X</math> is called the configuration space of ''n'' ordered or coloured points in <math>X</math>; the space of ''n'' ordered not necessarily distinct points is simply <math>X^n.</math>
| |
| | |
| If the original space is a manifold, the configuration space of ''distinct,'' unordered points is also a manifold, while the configuration space of ''not necessarily distinct'' unordered points is instead an [[orbifold]].
| |
| | |
| Configuration spaces are related to [[braid theory]], where the [[braid group]] is considered as the [[fundamental group]] of the space <math>C_n \Bbb R^2</math>.
| |
| | |
| A configuration space is a type of [[classifying space]] or (fine) [[moduli space]]. In particular, there is a universal bundle <math> \pi\colon E_n\to C_n </math> which is a subbundle of the trivial bundle <math> C_n\times X^n\to C_n</math>, and which has the property that the fiber over each point <math> p\in C_n</math> is the ''n'' element subset of <math> X_n </math> classified by ''p''.
| |
| | |
| The homotopy type of configuration spaces is not [[homotopy invariant]] – for example, that the spaces <math>F_n \Bbb R^m</math> are not homotopic for any two distinct values of <math>m</math>. For instance, <math>F_n\Bbb R</math> is not connected, <math>F_n\Bbb R^2</math> is a <math>K(\pi,1)</math>, and <math>F_n \Bbb R^m</math> is simply connected for <math> m \geq 3</math>.
| |
| | |
| It used to be an open question whether there were examples of ''compact'' manifolds which were homotopic but had non-homotopic configuration spaces: such an example was found only in 2005 by Longoni and Salvatore. Their example are two three-dimensional [[lens space]]s, and the configuration spaces of at least two points in them. That these configuration spaces are not homotopic was detected by [[Massey product]]s in their respective universal covers.<ref>{{citation|last1= Salvatore| first1=Paolo| last2=Longoni| first2=Riccardo| title=Configuration spaces are not homotopy invariant| journal= Topology |volume= 44| year=2005|issue= 2|pages=375–380|doi= 10.1016/j.top.2004.11.002}}</ref> | |
| | |
| ==See also==
| |
| *[[Feature space]] (topic in pattern recognition)
| |
| *[[Parameter space]]
| |
| *[[Phase space]]
| |
| *[[State space (physics)]]
| |
| | |
| == References ==
| |
| <references/>
| |
| | |
| ==External links==
| |
| * [http://www.overcomingbias.com/2008/04/conf-space.html Intuitive Explanation of Classical Configuration Spaces].
| |
| *''[http://ford.ieor.berkeley.edu/cspace'' Interactive Visualization of the C-space for a Robot Arm with Two Rotational Links] from [[UC Berkeley]].
| |
| * [http://www.youtube.com/watch?v=SBFwgR4K1Gk&list=UUswRb5tFvit2fXAiZtwpYuA&index=1&feature=plcp Configuration Space Visualization] from [[Free University of Berlin]]
| |
| | |
| {{DEFAULTSORT:Configuration Space}}
| |
| [[Category:Classical mechanics]]
| |
| [[Category:Manifolds]]
| |
| [[Category:Topology]]
| |
Pearl powder is a finely milled powder from quality freshwater pearls and its naturally compatible and easily absorbed by the skin and body. The vinegar can be applied directly to the affected area. One study suggests a novel method of testing multiple topical skin-lightening methods prior to initiating therapy, using UV-induced skin tanning. They're very natural, so lemons are a great way of bleaching the skin and helping to reduce the appearance of your acne scars. The reason is that the papaya extracts nourish the skin and also make it look better.
As a result, we should pay great attention to eat more fruits in spring, so as to make the skin moist and healthy. Less commonly, some Black women will develop a decrease in melanin or postinflammatory hypopigmentation in response to skin trauma (burns, etc. Try and look for a product which contains Alpha Arbutin, as this substance has had a very high success rate when whitening a variety of skin tones. It is highly important to know which was the cause which led to the apparition of your dark patches or brown spots in order to know how to treat them. It not only gradually whitens skin naturally, but your skin also becomes brighter and healthier without any harmful side effects.
Fill the tub with warm or hot water, strain the decoction and pour the herb liquid into the tub. One is the natural way of achieving the goal of fairness and other is the medicated methods which include different therapies and treatments. In addition, arsenic was used by women during the Elizabethan era (including the Queen, herself) in a mixture with vinegar and chalk to whiten their skin and prevent signs of aging. Many-a-times, one frustratingly discovers the image size has reduced substantially one the cropping is done and a large size print would ruin resolution. So many natural remedies for fair skin tone like massage with olive and almond oil on skin so they give shining and perfect fair skin.
Sugar with honey applied to our skin can exfoliate them just as well as the salons can. Even though they seem too traditional for the individuals of today, the effect is still as efficient as it was before. The cream is able to treat acne scars and aging spots. The results is an increase of the synthesis of the melanin and the rise of the pigmentation of the skin. We all know that all complexions are wonderful and it matters not which skin color you have, nevertheless for those who have neglected their pale skin color in the past when you had been some sort of sunshine worshipper and also you are somebody who wants some sort of brighter skin color there is nothing wrong within wanting a brighter skin.
Once they have fully dried, grind them to form a fine powder. Moreover, past biopsies of breast tumors have shown to have higher concentrations of metals like zinc, iron, chromium, and iron, just to name a few. An excellent natural hand cream contains ingredients that moisturize, soothe and nourish the skin. Lighten skin: the skin will burn and peel and have light skin, blue eyes, and either brown or blonde hair. It can also be removed from a regional drug store or alternatively is sold web-based from Online Canada Nearby.
If you adored this short article and you would certainly such as to obtain additional details pertaining to best skin bleaching products (stylax.info) kindly go to our web site.