formulasearchengine - User contributions [en]

Image-based modeling and rendering

2014-12-13T04:13:33Z

117.199.213.235: /* External links */

Greetings! I am Myrtle Shroyer. He used to be unemployed but now he is a pc operator but his promotion by no means arrives. To collect cash is what his family and him appreciate. Years ago we moved to North Dakota. my webpage: std home test ([http://test.gydch.com/praise/919726 sneak a peek at this web-site])

Comparison of analog and digital recording

2014-02-03T09:49:32Z

117.199.197.88: /* Noise and distortion */

{{about|correlation and dependence in statistical data||correlation (disambiguation)}}

In [[statistics]], '''dependence''' is any statistical relationship between two [[random variable]]s or two sets of [[data]]. '''Correlation''' refers to any of a broad class of statistical relationships involving dependence.

Familiar examples of dependent phenomena include the correlation between the physical [[human height|statures]] of parents and their offspring, and the correlation between the [[demand curve|demand]] for a product and its price. Correlations are useful because they can indicate a predictive relationship that can be exploited in practice. For example, an electrical utility may produce less power on a mild day based on the correlation between electricity demand and weather. In this example there is a [[causality|causal relationship]], because extreme weather causes people to use more electricity for heating or cooling; however, statistical dependence is not sufficient to demonstrate the presence of such a causal relationship (i.e., [[correlation does not imply causation]]).

Formally, ''dependence'' refers to any situation in which random variables do not satisfy a mathematical condition of [[independence (probability theory)|probabilistic independence]]. In loose usage, ''correlation'' can refer to any departure of two or more random variables from independence, but technically it refers to any of several more specialized types of relationship between [[conditional expectation|mean values]]. There are several '''correlation coefficients''', often denoted ''ρ'' or ''r'', measuring the degree of correlation. The most common of these is the [[Pearson product-moment correlation coefficient|Pearson correlation coefficient]], which is sensitive only to a linear relationship between two variables (which may exist even if one is a nonlinear function of the other). Other correlation coefficients have been developed to be more [[robust statistics|robust]] than the Pearson correlation – that is, more sensitive to nonlinear relationships.<ref>Croxton, Frederick Emory; Cowden, Dudley Johnstone; Klein, Sidney (1968) ''Applied General Statistics'', Pitman. ISBN 9780273403159 (page 625)</ref><ref>Dietrich, Cornelius Frank (1991) ''Uncertainty, Calibration and Probability: The Statistics of Scientific and Industrial Measurement'' 2nd Edition, A. Higler. ISBN 9780750300605 (Page 331)</ref><ref>Aitken, Alexander Craig (1957) ''Statistical Mathematics'' 8th Edition. Oliver & Boyd. ISBN 9780050013007 (Page 95)</ref> [[Mutual information]] can also be applied to measure dependence between two variables.

[[Image:Correlation examples2.svg|thumb|400px|right|Several sets of (''x'', ''y'') points, with the Pearson correlation coefficient of ''x'' and ''y'' for each set. Note that the correlation reflects the noisiness and direction of a linear relationship (top row), but not the slope of that relationship (middle), nor many aspects of nonlinear relationships (bottom). N.B.: the figure in the center has a slope of 0 but in that case the correlation coefficient is undefined because the variance of ''Y'' is zero.]]

==Pearson's product-moment coefficient==
{{Main|Pearson product-moment correlation coefficient}}

The most familiar measure of dependence between two quantities is the [[Pearson product-moment correlation coefficient]], or "Pearson's correlation coefficient", commonly called simply "the correlation coefficient". It is obtained by dividing the [[covariance]] of the two variables by the product of their [[standard deviation]]s. [[Karl Pearson]] developed the coefficient from a similar but slightly different idea by [[Francis Galton]].<ref name="thirteenways">J. L. Rodgers and W. A. Nicewander. [http://www.jstor.org/stable/2685263 Thirteen ways to look at the correlation coefficient]. The American Statistician, 42(1):59–66, February 1988.</ref>

The population correlation coefficient ρ''X,Y'' between two [[random variables]] ''X'' and ''Y'' with [[expected value]]s μ''X'' and μ''Y'' and [[standard deviation]]s σ''X'' and σ''Y'' is defined as:

:<math>\rho_{X,Y}=\mathrm{corr}(X,Y)={\mathrm{cov}(X,Y) \over \sigma_X \sigma_Y} ={E[(X-\mu_X)(Y-\mu_Y)] \over \sigma_X\sigma_Y},</math>

where ''E'' is the [[expected value]] operator, ''cov'' means [[covariance]], and, ''corr'' a widely used alternative notation for the correlation coefficient.

The Pearson correlation is defined only if both of the standard deviations are finite and both of them are nonzero. It is a corollary of the [[Cauchy–Schwarz inequality]] that the correlation cannot exceed 1 in [[absolute value]]. The correlation coefficient is symmetric: corr(''X'',''Y'') = corr(''Y'',''X'').

The Pearson correlation is +1 in the case of a perfect direct(increasing) linear relationship (correlation), −1 in the case of a perfect decreasing (inverse) linear relationship ('''anticorrelation'''),<ref>Dowdy, S. and Wearden, S. (1983). "Statistics for Research", Wiley. ISBN 0-471-08602-9 pp 230</ref> and some value between −1 and 1 in all other cases, indicating the degree of [[linear dependence]] between the variables. As it approaches zero there is less of a relationship (closer to uncorrelated). The closer the coefficient is to either −1 or 1, the stronger the correlation between the variables.

If the variables are [[statistical independence|independent]], Pearson's correlation coefficient is 0, but the converse is not true because the correlation coefficient detects only linear dependencies between two variables. For example, suppose the random variable ''X'' is symmetrically distributed about zero, and ''Y'' = ''X''2. Then ''Y'' is completely determined by ''X'', so that ''X'' and ''Y'' are perfectly dependent, but their correlation is zero; they are [[uncorrelated]]. However, in the special case when ''X'' and ''Y'' are [[bivariate Gaussian distribution|jointly normal]], uncorrelatedness is equivalent to independence.

If we have a series of ''n'' measurements of ''X'' and ''Y'' written as ''xi'' and ''yi'' where ''i'' = 1, 2, ..., ''n'', then the ''sample correlation coefficient'' can be used to estimate the population Pearson correlation ''r'' between ''X'' and ''Y''. The sample correlation coefficient is written

:<math>
r_{xy}=\frac{\sum\limits_{i=1}^n (x_i-\bar{x})(y_i-\bar{y})}{(n-1) s_x s_y}
=\frac{\sum\limits_{i=1}^n (x_i-\bar{x})(y_i-\bar{y})}
{\sqrt{\sum\limits_{i=1}^n (x_i-\bar{x})^2 \sum\limits_{i=1}^n (y_i-\bar{y})^2}},
</math>

where x and y are the sample [[arithmetic mean|means]] of ''X'' and ''Y'', and ''s''''x'' and ''s''''y'' are the [[standard deviation#With sample standard deviation|sample standard deviations]] of ''X'' and ''Y''.

This can also be written as:
:<math>
r_{xy}=\frac{\sum x_iy_i-n \bar{x} \bar{y}}{(n-1) s_x s_y}=\frac{n\sum x_iy_i-\sum x_i\sum y_i}
{\sqrt{n\sum x_i^2-(\sum x_i)^2}~\sqrt{n\sum y_i^2-(\sum y_i)^2}}.
</math>

If ''x'' and ''y'' are results of measurements that contain measurement error, the realistic limits on the correlation coefficient are not −1 to +1 but a smaller range.<ref>{{cite journal|last=Francis|first=DP|coauthors=Coats AJ, Gibson D|title=How high can a correlation coefficient be?|journal=Int J Cardiol|year=1999|volume=69|pages=185–199|doi=10.1016/S0167-5273(99)00028-5|issue=2}}</ref>

For the case of a linear model with a single independent variable, the [[Coefficient of determination|coefficient of determination (R squared)]] is the square of r, Pearson's product-moment coefficient .

==Rank correlation coefficients==
{{Main|Spearman's rank correlation coefficient|Kendall tau rank correlation coefficient}}

[[Rank correlation]] coefficients, such as [[Spearman's rank correlation coefficient]] and [[Kendall's tau|Kendall's rank correlation coefficient (τ)]] measure the extent to which, as one variable increases, the other variable tends to increase, without requiring that increase to be represented by a linear relationship. If, as the one variable increases, the other ''decreases'', the rank correlation coefficients will be negative. It is common to regard these rank correlation coefficients as alternatives to Pearson's coefficient, used either to reduce the amount of calculation or to make the coefficient less sensitive to non-normality in distributions. However, this view has little mathematical basis, as rank correlation coefficients measure a different type of relationship than the [[Pearson product-moment correlation coefficient]], and are best seen as measures of a different type of [[association (statistics)|association]], rather than as alternative measure of the population correlation coefficient.<ref name="Yule and Kendall">Yule, G.U and Kendall, M.G. (1950), "An Introduction to the Theory of Statistics", 14th Edition (5th Impression 1968). Charles Griffin & Co. pp 258–270</ref><ref name="Kendall Rank Correlation Methods">Kendall, M. G. (1955) "Rank Correlation Methods", Charles Griffin & Co.</ref>

To illustrate the nature of rank correlation, and its difference from linear correlation, consider the following four pairs of numbers (''x'', ''y''):

:(0, 1), (10, 100), (101, 500), (102, 2000).

As we go from each pair to the next pair ''x'' increases, and so does ''y''. This relationship is perfect, in the sense that an increase in ''x'' is ''always'' accompanied by an increase in ''y''. This means that we have a perfect rank correlation, and both Spearman's and Kendall's correlation coefficients are 1, whereas in this example Pearson product-moment correlation coefficient is 0.7544, indicating that the points are far from lying on a straight line. In the same way if ''y'' always ''decreases'' when ''x'' ''increases'', the rank correlation coefficients will be −1, while the Pearson product-moment correlation coefficient may or may not be close to −1, depending on how close the points are to a straight line. Although in the extreme cases of perfect rank correlation the two coefficients are both equal (being both +1 or both −1) this is not in general so, and values of the two coefficients cannot meaningfully be compared.<ref name="Yule and Kendall"/> For example, for the three pairs (1, 1) (2, 3) (3, 2) Spearman's coefficient is 1/2, while Kendall's coefficient is 1/3.

==Other measures of dependence among random variables==

The information given by a correlation coefficient is not enough to define the dependence structure between random variables.<ref name="wilmottM.com">{{cite journal|authors=Mahdavi Damghani B.|title=The Non-Misleading Value of Inferred Correlation: An Introduction to the Cointelation Model|journal=Wilmott Magazine|year=2013|doi=10.1002/wilm.10252 }}</ref> The correlation coefficient completely defines the dependence structure only in very particular cases, for example when the distribution is a [[multivariate normal distribution]]. (See diagram above.) In the case of [[elliptical distribution]]s it characterizes the (hyper-)ellipses of equal density, however, it does not completely characterize the dependence structure (for example, a multivariate t-distribution's degrees of freedom determine the level of tail dependence).

[[Distance correlation]] and [[Brownian covariance]] / Brownian correlation <ref>Székely, G. J. Rizzo, M. L. and Bakirov, N. K. (2007). "Measuring and testing independence by correlation of distances", ''[[Annals of Statistics]]'', 35/6, 2769–2794. {{doi| 10.1214/009053607000000505}} [http://personal.bgsu.edu/~mrizzo/energy/AOS0283-reprint.pdf Reprint]
</ref><ref>Székely, G. J. and Rizzo, M. L. (2009). "Brownian distance covariance", ''Annals of Applied Statistics'', 3/4, 1233–1303. {{doi| 10.1214/09-AOAS312}} [http://personal.bgsu.edu/~mrizzo/energy/AOAS312.pdf Reprint]
</ref> were introduced to address the deficiency of Pearson's correlation that it can be zero for dependent random variables; zero distance correlation and zero Brownian correlation imply independence.

The [[correlation ratio]] is able to detect almost any functional dependency{{citation needed|date=August 2011}}{{clarify|reason=doesn't seem true for correlation ratio as defined in article of that name|date=August 2011}}, and the [[Entropy (information theory)|entropy]]-based [[mutual information]], [[total correlation]] and [[dual total correlation]] are capable of detecting even more general dependencies. These are sometimes referred to as multi-moment correlation measures{{citation needed |date=August 2011}}, in comparison to those that consider only second moment (pairwise or quadratic) dependence.

The [[polychoric correlation]] is another correlation applied to ordinal data that aims to estimate the correlation between theorised latent variables.

One way to capture a more complete view of dependence structure is to consider a [[copula (statistics)|copula]] between them.

The [[coefficient of determination]] generalizes the correlation coefficient for relationships beyond [[simple linear regression]].

==Sensitivity to the data distribution==

The degree of dependence between variables ''X'' and ''Y'' does not depend on the scale on which the variables are expressed. That is, if we are analyzing the relationship between ''X'' and ''Y'', most correlation measures are unaffected by transforming ''X'' to ''a'' + ''bX'' and ''Y'' to ''c'' + ''dY'', where ''a'', ''b'', ''c'', and ''d'' are constants. This is true of some correlation statistics as well as their population analogues. Some correlation statistics, such as the rank correlation coefficient, are also invariant to [[monotone function|monotone transformations]] of the marginal distributions of ''X'' and/or ''Y''.

[[Image:correlation range dependence.svg|300px|right|thumb|[[Pearson product moment correlation coefficient|Pearson]]/[[Spearman's rank correlation coefficient|Spearman]] correlation coefficients between ''X'' and ''Y'' are shown when the two variables' ranges are unrestricted, and when the range of ''X'' is restricted to the interval (0,1).]]Most correlation measures are sensitive to the manner in which ''X'' and ''Y'' are sampled. Dependencies tend to be stronger if viewed over a wider range of values. Thus, if we consider the correlation coefficient between the heights of fathers and their sons over all adult males, and compare it to the same correlation coefficient calculated when the fathers are selected to be between 165 cm and 170 cm in height, the correlation will be weaker in the latter case. Several techniques have been developed that attempt to correct for range restriction in one or both variables, and are commonly used in meta-analysis; the most common are Thorndike's case II and case III equations.<ref>{{cite book|last=Thorndike|first=Robert Ladd|title=Research problems and techniques (Report No. 3)|year=1947|publisher=US Govt. print. off.|location=Washington DC}}</ref>

Various correlation measures in use may be undefined for certain joint distributions of ''X'' and ''Y''. For example, the Pearson correlation coefficient is defined in terms of [[moment (mathematics)|moments]], and hence will be undefined if the moments are undefined. Measures of dependence based on [[quantile]]s are always defined. Sample-based statistics intended to estimate population measures of dependence may or may not have desirable statistical properties such as being [[bias of an estimator|unbiased]], or [[consistent estimator|asymptotically consistent]], based on the spatial structure of the population from which the data were sampled.

Sensitivity to the data distribution can be used to an advantage. For example, [[scaled correlation]] is designed to use the sensitivity to the range in order to pick out correlations between fast components of time series.<ref name = "Nikolicetal">Nikolić D, Muresan RC, Feng W, Singer W (2012) Scaled correlation analysis: a better way to compute a cross-correlogram. ''European Journal of Neuroscience'', pp. 1–21, {{DOI|10.1111/j.1460-9568.2011.07987.x }}</ref> By reducing the range of values in a controlled manner, the correlations on long time scale are filtered out and only the correlations on short time scales are revealed.

==Correlation matrices==

The correlation matrix of ''n'' random variables ''X''1, ..., ''X''''n'' is the ''n''  ×  ''n'' matrix whose ''i'',''j'' entry is corr(''X''''i'', ''X''''j''). If the measures of correlation used are product-moment coefficients, the correlation matrix is the same as the [[covariance matrix]] of the [[standardized variable|standardized random variables]] ''X''''i'' / σ (''X''''i'') for ''i'' = 1, ..., ''n''. This applies to both the matrix of population correlations (in which case "σ" is the population standard deviation), and to the matrix of sample correlations (in which case "σ" denotes the sample standard deviation). Consequently, each is necessarily a [[positive-semidefinite matrix]].

The correlation matrix is symmetric because the correlation between ''X''''i'' and ''X''''j'' is the same as the correlation between ''X''''j'' and ''X''''i''.

==Common misconceptions==

===Correlation and causality===
{{Main|Correlation does not imply causation}}
The conventional dictum that "[[correlation does not imply causation]]" means that correlation cannot be used to infer a causal relationship between the variables.<ref>{{cite journal | last=Aldrich | first=John | journal=Statistical Science | volume=10 | issue=4 | year=1995 | pages=364–376 | title=Correlations Genuine and Spurious in Pearson and Yule | jstor=2246135 | doi=10.1214/ss/1177009870}}</ref> This dictum should not be taken to mean that correlations cannot indicate the potential existence of causal relations. However, the causes underlying the correlation, if any, may be indirect and unknown, and high correlations also overlap with [[identity (mathematics)|identity]] relations ([[tautology (logic)|tautologies]]), where no causal process exists. Consequently, establishing a correlation between two variables is not a sufficient condition to establish a causal relationship (in either direction).

A correlation between age and height in children is fairly causally transparent, but a correlation between mood and health in people is less so. Does improved mood lead to improved health, or does good health lead to good mood, or both? Or does some other factor underlie both? In other words, a correlation can be taken as evidence for a possible causal relationship, but cannot indicate what the causal relationship, if any, might be.

=== Correlation and linearity ===

[[Image:Anscombe's quartet 3.svg|thumb|325px|right|Four sets of data with the same correlation of 0.816]]
The Pearson correlation coefficient indicates the strength of a linear relationship between two variables, but its value generally does not completely characterize their relationship. In particular, if the [[conditional expectation|conditional mean]] of ''Y'' given ''X'', denoted E(''Y''|''X''), is not linear in ''X'', the correlation coefficient will not fully determine the form of E(''Y''|''X'').

The image on the right shows [[scatterplot]]s of [[Anscombe's quartet]], a set of four different pairs of variables created by [[Francis Anscombe]].<ref>{{cite journal | last=Anscombe | first=Francis J. | year=1973 | title=Graphs in statistical analysis | journal=The American Statistician | volume=27 | pages=17–21 | jstor=2682899 | doi=10.2307/2682899}}</ref> The four ''y'' variables have the same mean (7.5), variance (4.12), correlation (0.816) and regression line (''y'' = 3 + 0.5''x''). However, as can be seen on the plots, the distribution of the variables is very different. The first one (top left) seems to be distributed normally, and corresponds to what one would expect when considering two variables correlated and following the assumption of normality. The second one (top right) is not distributed normally; while an obvious relationship between the two variables can be observed, it is not linear. In this case the Pearson correlation coefficient does not indicate that there is an exact functional relationship: only the extent to which that relationship can be approximated by a linear relationship. In the third case (bottom left), the linear relationship is perfect, except for one [[outlier]] which exerts enough influence to lower the correlation coefficient from 1 to 0.816. Finally, the fourth example (bottom right) shows another example when one outlier is enough to produce a high correlation coefficient, even though the relationship between the two variables is not linear.

These examples indicate that the correlation coefficient, as a summary statistic, cannot replace visual examination of the data. Note that the examples are sometimes said to demonstrate that the Pearson correlation assumes that the data follow a [[normal distribution]], but this is not correct.<ref name="thirteenways"/>

==Bivariate normal distribution==
If a pair (''X'', ''Y'') of random variables follows a [[bivariate normal distribution]], the conditional mean E(''X''|''Y'') is a linear function of ''Y'', and the conditional mean E(''Y''|''X'') is a linear function of ''X''. The correlation coefficient ''r'' between ''X'' and ''Y'', along with the [[Marginal distribution|marginal]] means and variances of ''X'' and ''Y'', determines this linear relationship:

:<math>
E(Y\mid X) = E(Y) + r\sigma_y\frac{X-E(X)}{\sigma_x},
</math>

where ''E(X)'' and ''E(Y)'' are the expected values of ''X'' and ''Y'', respectively, and σ''x'' and σ''y'' are the standard deviations of ''X'' and ''Y'', respectively.

==Partial correlation==
{{Main|Partial correlation}}
If a population or data-set is characterized by more than two variables, a [[partial correlation]] coefficient measures the strength of dependence between a pair of variables that is not accounted for by the way in which they both change in response to variations in a selected subset of the other variables.

==See also==
{{Commons category|Correlation and dependence}}
{{Portal|Statistics}}
<div style="-moz-column-count:3; column-count:3;">
* [[Association (statistics)]]
* [[Autocorrelation]]
* [[Canonical correlation]]
* [[Coefficient of determination]]
* [[Cointegration]]
* [[Cointelation]]
* [[Concordance correlation coefficient]]
* [[Cophenetic correlation]]
* [[Copula (probability theory)|Copula]]
* [[Correlation function]]
* [[Covariance and correlation]]
* [[Cross-correlation]]
* [[Ecological correlation]]
* [[Fraction of variance unexplained]]
* [[Genetic correlation]]
* [[Goodman and Kruskal's lambda]]
* [[Illusory correlation]]
* [[Interclass correlation]]
* [[Intraclass correlation]]
* [[Modifiable areal unit problem]]
* [[Multiple correlation]]
* [[Point-biserial correlation coefficient]]
* [[Quadrant count ratio]]
* [[Statistical arbitrage]]
* [[Subindependence]]
</div>

==References==
{{Reflist|colwidth=35em}}

==Further reading==
* {{cite book |author=Cohen, J., Cohen P., West, S.G., & Aiken, L.S. |year=2002 |title=Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed.) |publisher=Psychology Press |isbn= 0-8058-2223-2 }}
* {{springer|title=Correlation (in statistics)|id=p/c026560}}

==External links==
{{Wikiversity|Correlation}}
{{Wiktionary|correlation}}
{{Wiktionary|dependence}}
* [http://mathworld.wolfram.com/CorrelationCoefficient.html MathWorld page on (cross-) correlation coefficient(s) of a sample.]
* [http://peaks.informatik.uni-erlangen.de/cgi-bin/usignificance.cgi Compute Significance between two correlations] – A useful website if one wants to compare two correlation values.
*[http://www.mathworks.com/matlabcentral/fileexchange/20846 A MATLAB Toolbox for computing Weighted Correlation Coefficients]
* [http://www.docstoc.com/docs/3530180/Proof-that-the-Sample-Bivariate-Correlation-Coefficient-has-Limits-(Plus-or-Minus)-1 Proof that the Sample Bivariate Correlation Coefficient has Limits ±1]
* [http://nagysandor.eu/AsimovTeka/correlation_en/index.html Interactive Flash simulation on the correlation of two normally distributed variables.] Author: Juha Puranen.

{{Statistics}}

{{DEFAULTSORT:Correlation And Dependence}}
[[Category:Covariance and correlation]]
[[Category:Statistical dependence]]
[[Category:Dimensionless numbers]]

Testing and performance of IC engines

2014-01-26T13:33:38Z

117.199.183.55: /* Power and mechanical efficiency */

{{Financial risk types}}
'''[[Risk management]] in Indian banks''' is a relatively newer practice, but has already shown to increase efficiency in governing of these banks as such procedures tend to increase the corporate governance of a financial institution. In times of volatility and fluctuations in the market, financial institutions need to prove their mettle by withstanding the market variations and achieve sustainability in terms of growth and well as have a stable share value. Hence, an essential component of risk management framework would be to mitigate all the risks and rewards of the products and service offered by the bank. Thus the need for an efficient risk management framework is paramount in order to factor in internal and external risks.<ref>{{cite journal|coauthors=Srinivas Nallamothu & Fayaz Ahmed|title=Risk Management Framework for Indian Banks|url=http://www.coolavenues.com/know/fin/fayaz_1.php3}}</ref>

The financial sector in various economies like that of India are undergoing a monumental change factoring into account world events such as the ongoing Banking Crisis across the globe. The [[2007–present recession in the United States]] has highlighted the need for banks to incorporate the concept of Risk Management into their regular procedures. The various aspects of increasing global competition to [[Indian Banks]] by Foreign banks, increasing [[Deregulation]], introduction of innovative products, and financial instruments as well as innovation in delivery channels have highlighted the need for [[Indian Banks]] to be prepared in terms of risk management.<ref name="ijeronline">{{cite journal|coauthors=Dr. Krishn A. Goyal, Prof. Sunita Agrawal|title=RISK MANAGEMENT IN INDIAN BANKS: SOME EMERGING ISSUES|journal=IJER|date=December 2010|url=http://www.ijeronline.com/documents/volumes/vol1issue1/ijer2010010109.pdf}}</ref>

[[Indian Banks]] have been making great advancements in terms of technology, quality, as well as stability such that they have started to expand and diversify at a rapid rate. However, such expansion brings these banks into the context of risk especially at the onset of increasing Globalization and Liberalization. In banks and other financial institutions, risk plays a major part in the earnings of a bank. The higher the risk, the higher the return, hence, it is essential to maintain a parity between risk and return. Hence, management of [[Financial risk]] incorporating a set systematic and professional methods especially those defined by the [[Basel II]] becomes an essential requirement of banks. The more risk averse a bank is, the safer is their Capital base.<ref name="ijeronline" />

== Risk Ratio ==
Risk ratio would be defined as the ratio of the probability of an issue occurring as against to an issue not occurring.<ref name="pmid14695382">{{cite journal |author=Sistrom CL, Garvan CW |title=Proportions, odds, and risk |journal=Radiology |volume=230 |issue=1 |pages=12–9 |date=January 2004 |pmid=14695382 |doi=10.1148/radiol.2301031028 |url=http://radiology.rsnajnls.org/cgi/pmidlookup?view=long&pmid=14695382}}</ref>

:<math>RR= \frac {p_\text{issue occurring}}{p_\text{issue not occurring}} </math>

== Total Impact of Risk ==
Total impact of the risk (TIR) occurring would entail as the impact (I), the risk would cause multiplied by the Risk Ratio. It is essentially how much a bank would be impacted in the chance that the risk did occur. This essentially helps ascertain what is the total value of their investments that may be subject to risk and how it would impact them.<ref>ART, RiskAoA, RiskPath, SCHRAM</ref>
:<math>TIR= I\times RR </math>

== Risk and Reward ==
The ratio is in simplest terms calculated by dividing the amount of profit the trader expects to have made when the position is closed (i.e. the reward) by the amount he or she stands to lose if the price moves in the unexpected direction (i.e. the risk).

To calculate the total risk ensuing with the total expected return, a favored method is the use of variance or standard deviation. The larger the variance, the larger the standard deviation, the more uncertain the outcome. The standard deviation, E is a measure of average difference between the expected value and the actual value of a random variable (or unseen state of nature).

:<math> E = \sqrt{\sum P(n-X)^2} </math>

Here, n stands for a possible outcome, x stands for the expected outcome and P is the probability (or likelihood) of the difference between n and X occurring.<ref>{{cite book|title=Fundamental Analysis Workbook|publisher=National Stock Exchange of India Limited}}</ref>

== Types of Risk ==
[[File:Risk in Banking.jpg|thumb|Types of Risks in Banking]]
The term '''''Risk''''' and the types associated to it would refer to mean financial risk or uncertainty of financial loss. The [[Reserve Bank of India]] guidelines issued in Oct. 1999 has identified and categorized the majority of risk into three major categories assumed to be encountered by banks. These belong to the clusters:<ref>{{cite journal|title=Trend and Progress of Banking in India|journal=Reserve Bank of India|year=1996–97, 1998–99, 2001–02 and 2002–03}}</ref>

*[[Credit Risk]]
*[[Market Risk]]
*[[Operational Risk]]

The type of risks can be fundamentally subdivided in primarily of two types, i.e. Financial and Non-Financial Risk. Financial risks would involve all those aspects which deal mainly with financial aspects of the bank. These can be further subdivided into Credit Risk and Market Risk. Both Credit and Market Risk may be further subdivided.

Non-Financial risks would entail all the risk faced by the bank in its regular workings, i.e. [[Operational Risk]], [[Strategic Risk]], [[Funding Risk]], [[Political Risk]], and [[Legal Risk]].<ref name="ijeronline" />

== See also ==
*[[Risk management tools]]
*[[Probabilistic risk assessment]]

== References ==
{{Reflist}}

{{Financial risk}}

[[Category:Risk]]
[[Category:Banking in India]]
[[Category:India Education Program]]

Apsidal precession

2013-12-25T06:13:25Z

117.199.179.51: /* Long-term climate */

In the [[mathematics|mathematical]] field of [[differential geometry]], a '''calibrated manifold''' is a [[Riemannian manifold]] (''M'',''g'') of dimension ''n'' equipped with a [[differential form|differential ''p''-form]] ''φ'' (for some 0 ≤ ''p'' ≤ ''n'') which is a '''calibration''' in the sense that
* ''φ'' is closed: d''φ'' = 0, where d is the [[exterior derivative]]
* for any ''x'' ∈ ''M'' and any oriented ''p''-dimensional subspace ''ξ'' of T''x''''M'', ''φ''|''ξ'' = ''λ'' vol''ξ'' with ''λ'' ≤ 1. Here vol''ξ'' is the volume form of ''ξ'' with respect to ''g''.
Set ''G''''x''(''φ'') = { ''ξ'' as above : ''φ''|''ξ'' = vol''ξ'' }. (In order for the theory to be nontrivial, we need ''G''''x''(''φ'') to be nonempty.) Let ''G''(''φ'') be the union of ''G''''x''(''φ'') for ''x'' in ''M''.

The theory of calibrations is due to R. Harvey and B. Lawson and others. Much earlier (in 1966) [[Edmond Bonan]] introduced [[G2 manifold|G2-manifold]] and [[Spin(7)-manifold]], constructed all the parallel forms and showed that those manifolds were Ricci-flat. [[Quaternion-Kähler manifold]] were simultaneously studied in 1965 by [[Edmond Bonan]] and Vivian Yoh Kraines and they constructed the parallel 4-form.

==Calibrated submanifolds==

A ''p''-dimensional submanifold ''Σ'' of ''M'' is said to be a '''calibrated submanifold''' with respect to ''φ'' (or simply ''φ''-calibrated) if T''Σ'' lies in ''G''(''φ'').

A famous one line argument shows that calibrated ''p''-submanifolds minimize volume within their homology class. Indeed, suppose that ''Σ'' is calibrated, and ''Σ'' ′ is a ''p'' submanifold in the same homology class. Then

:<math>\int_\Sigma \mathrm{vol}_\Sigma = \int_\Sigma \varphi = \int_{\Sigma'} \varphi \leq \int_{\Sigma'} \mathrm{vol}_{\Sigma'}</math>

where the first equality holds because ''Σ'' is calibrated, the second equality is [[Stokes' theorem]] (as ''φ'' is closed), and the third equality holds because ''φ'' is a calibration.

==Examples==

* On a [[Kähler manifold]], suitably normalized powers of the [[Kähler form]] are calibrations, and the calibrated submanifolds are the [[complex submanifold]]s.
* On a [[Calabi-Yau manifold]], the real part of a holomorphic volume form (suitably normalized) is a calibration, and the calibrated submanifolds are [[special Lagrangian submanifold]]s.
* On a [[G2 manifold|G2-manifold]], both the 3-form and the Hodge dual 4-form define calibrations. The corresponding calibrated submanifolds are called associative and coassociative submanifolds.
* On a [[Spin(7)-manifold]], the defining 4-form, known as the Cayley form, is a calibration. The corresponding calibrated submanifolds are called Cayley submanifolds.

==References==
<references />
*{{citation | first =Edmond| last =Bonan |authorlink=Edmond Bonan| title =Structure presque quaternale sur une variété différentiable| journal = C. R. Acad. Sci. Paris | volume =261| year = 1965 | pages =5445–5448}}.
*{{citation | first =Edmond| last =Bonan |authorlink=Edmond Bonan| title = Sur les variétés riemanniennes à groupe d'holonomie G2 ou Spin(7)| journal = C. R. Acad. Sci. Paris | volume =262| year = 1966 | pages = 127–129}}.
* {{citation | first = M. | last = Berger | title = Quelques problemes de geometrie Riemannienne ou Deux variations sur les espaces symetriques compacts de rang un| journal = Enseignement Math.| volume = 16 | year = 1970 | pages = 73–96 }}.
* {{citation | first = Kenneth A.| last = Brakke | title = Minimal cones on hypercubes | journal = J. Geom. Anal.| year = 1991 | pages = 329–338 (§6.5)}}.
* {{citation | first = Kenneth A.| last = Brakke | title = Polyhedral minimal cones in R4 | journal = | year = 1993}}.
* {{citation | first = Georges | last = de Rham | title = On the Area of Complex Manifolds. Notes for the Seminar on Several Complex Variables| publisher=Institute for Advanced Study, Princeton, NJ|year=1957–1958 }}.
* {{citation | first = Herbert | last = Federer | title = Some theorems on integral currents| journal = Trans. AMS | volume = 117 | year = 1965 | pages = 43–67 | doi = 10.2307/1994196 | jstor = 1994196 | publisher = Transactions of the American Mathematical Society, Vol. 117}}.
* {{citation | title= Riemannian Holonomy Groups and Calibrated Geometry|series=Oxford Graduate Texts in Mathematics|first=Dominic D.|last= Joyce|authorlink=Dominic Joyce|publisher=Oxford University Press|location= Oxford|isbn= 978-0-19-921559-1|year=2007}}.
* {{citation|title=Spinors and Calibrations|last=Harvey|first= F. Reese|publisher=Academic Press|year=1990|isbn=978-0-12-329650-4}}.
*{{citation | first =Vivian Yoh | last = Kraines | title = Topology of quaternionic manifolds
| journal = Bull. Amer. Math. Soc| volume =71,3, 1 | year = 1965 | pages = 526–527}}.
* {{citation | first = Gary | last = Lawlor | title = Proving area minimization by directed slicing | journal = Indiana U. Math. J. | volume = 47 | year = 1998 | pages = 1547–1592}}.
* {{citation | first = Lawlor, Gary | last = Morgan, Frank | title = Curvy slicing proves that triple junctions locally minimize area | journal = J. Diff. Geom. | volume = 44 | year = 1996 pages = 514–528}}.
* {{citation | first = Lawlor, Gary | last = Morgan, Frank | title = Paired calibrations applied to soap films, immiscible fluids, and surfaces or networks minimizing other norms| journal = Pac. J Math. | volume = 166 | year = 1994 pages = 55–83}}.
* {{citation | first = R. C. | last = McLean | title = Deformations of calibrated submanifolds | journal = Communications in Analysis and Geometry | volume = 6 | year = 1998 | pages = 705–747}}.
* {{citation | first = Frank | last = Morgan | title = Area-minimizing surfaces, faces of Grassmannians, and calibrations| journal = Amer. Math. Monthly | volume = 95 | year = 1988 | pages = 813–822 | doi = 10.2307/2322896 | jstor = 2322896 | issue = 9 | publisher = The American Mathematical Monthly, Vol. 95, No. 9}}.
* {{citation | first = Frank | last = Morgan | title = Calibrations and new singularities in area-minimizing surfaces: a survey In "Variational Methods" (Proc. Conf. Paris, June 1988), (H. Berestycki J.-M. Coron, and I. Ekeland, Eds.)| journal = Prog. Nonlinear Diff. Eqns. Applns | volume = 4 | year = 1990 | pages = 329–342}}.
* {{citation|title=Geometric Measure Theory: a Beginner's Guide|last=Morgan|first= Frank |publisher=4th ed. Academic Press, London|year=2009}}.
* {{citation | first = Dao Trong | last = Thi | title = Minimal real currents on compact Riemannian manifolds| journal = Izv. Akad. Nauk. SSSR Ser. Mat| volume = 41 | year = 1977 | pages = 807–820}}.
* {{citation | first = Le Hong | last = Van | title = Relative calibrations and the problem of stability of minimal surfaces | journal = Lecture Notes in Mathematics, Springer-Verlag, New York | volume = 1453 | year = 1990 | pages = 245–262}}.
* {{citation | first = W. | last = Wirtinger | title = Eine Determinantenidentität und ihre Anwendung auf analytische Gebilde und Hermitesche Massbestimmung| journal = Monatsh. Math. Phys. | volume = 44 | year = 1936 | pages = 343–365 (§6.5) | doi = 10.1007/BF01699328}}.

[[Category:Differential geometry]]
[[Category:Riemannian geometry]]
[[Category:Structures on manifolds]]

Diffusion capacitance

2013-10-06T11:31:24Z

117.199.194.157:

In [[mathematics]], the '''Silverman–Toeplitz theorem''', first proved by [[Otto Toeplitz]], is a result in [[summability theory]] characterizing [[Matrix (mathematics)|matrix]] summability methods that are regular. A regular matrix summability method is a matrix transformation of a [[convergent sequence]] which preserves the [[Limit of a sequence|limit]].

An [[infinite matrix]] <math>(a_{i,j})_{i,j \in \mathbb{N}}</math> with [[complex number|complex]]-valued entries defines a regular summability method [[if and only if]] it satisfies all of the following properties
:<math>\lim_{i \to \infty} a_{i,j} = 0 \quad j \in \mathbb{N}</math> (every column sequence converges to 0)
:<math>\lim_{i \to \infty} \sum_{j=0}^{\infty} a_{i,j} = 1</math> (the row sums converge to 1)
:<math>\sup_{i} \sum_{j=0}^{\infty} \vert a_{i,j} \vert < \infty</math> (the absolute row sums are bounded).

== References ==
* Toeplitz, Otto (1911) "[http://matwbn.icm.edu.pl/ksiazki/pmf/pmf22/pmf2219.pdf ''Über die lineare Mittelbildungen.'']" ''Prace mat.-fiz.'', '''22''', 113–118 (the original paper in [[German language|German]])
* Silverman, Louis Lazarus (1913) "On the definition of the sum of a divergent series." University of Missouri Studies, Math. Series I, 1–96

{{DEFAULTSORT:Silverman-Toeplitz theorem}}
[[Category:Theorems in analysis]]
[[Category:Summability methods]]
[[Category:Summability theory]]

Blood volume

2013-09-24T08:10:40Z

117.199.210.250: /* Humans */

Let <math>G(V,E)</math> be a [[graph (mathematics)|graph]] and <math>M</math> a [[Matching (graph theory)|matching]] in <math>G</math>. A vertex <math>v\in V(G)</math> is said to be '''saturated''' by <math>M</math> if there is an edge in <math>M</math> incident to <math>v</math>. A vertex <math>v\in V(G)</math> with no such edge is said to be '''unsaturated''' by <math>M</math>. We also say that <math>M</math> '''saturates''' <math>v</math>.<ref>[http://planetmath.org/?op=getobj&from=objects&id=4735 Saturate]. [[PlanetMath]].</ref>

==See also==
* [[Hall's marriage theorem]]
* [[Bipartite matching]]

==References==
{{reflist}}

[[Category:Matching]]

Neutrino oscillation

2012-08-24T07:30:45Z

117.199.154.125: /* Two neutrino case */

== primary sector ==

With these encounters with [http://www.nrcil.net/fancybox/lib/rakuten_LV_133.html ルイヴィトン財布モノグラム] Luo Feng [http://www.nrcil.net/fancybox/lib/rakuten_LV_123.html ルイヴィトンパドロック] himself, [http://www.nrcil.net/fancybox/lib/rakuten_LV_14.html メンズルイヴィトン] and no pride. 'the sheer vastness of the universe, the fate of the special, there are adventures, and [http://www.nrcil.net/fancybox/lib/rakuten_LV_111.html バックルイヴィトン] certainly there are many. really good ...... will combine everything, use good, in [http://www.nrcil.net/fancybox/lib/rakuten_LV_97.html ルイヴィトン中古通販] order to become a masterpiece strong.' Luo Feng illegal channels, 'as long as the earth tens Qianxiu In 'I can officially become the main industry [http://www.nrcil.net/fancybox/lib/rakuten_LV_120.html ルイヴィトンのキーケース] of. By the time I will be able to carry out the laws of perception of a rapid increase. ' primary sector, real outbreak. Feng Luo do now, is to give his foundation is growing fast, [http://www.nrcil.net/fancybox/lib/rakuten_LV_137.html ルイヴィトンショルダーバッグ] so that when the main Yanfeng sector can achieve strikingly terrible burst of strength! ...... that is over half gone. control room meteorite ink asterisk, Feng Luo and Dylan stood in the control room. 'immediately [http://www.nrcil.net/fancybox/lib/rakuten_LV_73.html ルイヴィトンアクセサリー] began shuttling the universe, into the solar system.' 'Countdown, 10 ...... 9 ...... 8 ...... 7 ...... 6 ...... 5 ...... 4 ...... 3 ...... 2 ...... 1!'
相关的主题文章：
<ul>

<li>[http://www.bmwclassics.co.uk/cgi-bin/gb/guestbook.cgi http://www.bmwclassics.co.uk/cgi-bin/gb/guestbook.cgi]</li>

<li>[http://bbs.520.io/forum.php?mod=viewthread&tid=317911&fromuid=80983 http://bbs.520.io/forum.php?mod=viewthread&tid=317911&fromuid=80983]</li>

<li>[http://pswa.moo.jp/kaigi/joyful.cgi http://pswa.moo.jp/kaigi/joyful.cgi]</li>

</ul>

== but also did not hear the conversation of those two. ==

Natural. Galaxy even though you said. Give them alive is a great kindness. ' Luo Feng nodded: 'For their punishment is simple ......' Luo Feng said a pass, but it is to let the snow under the eyes blink Yong, Wang did not seem to think [http://www.nrcil.net/fancybox/lib/rakuten_LV_24.html ルイヴィトン帽子] God would want Chuzhe Deng [http://www.nrcil.net/fancybox/lib/rakuten_LV_53.html ルイヴィトンミニバッグ] heir disposal Galaxy actually means. 'Understand?' Luo Feng Road. ...... fire cut the afternoon, after both Hu find any, [http://www.nrcil.net/fancybox/lib/rakuten_LV_29.html ルイヴィトンマフラー] by air condensed into a rope tied to live could not move, all fell to the ground. The surface of the heart is more anxious panic panic, they both looked not far Luo Feng, snow Yong. Can even [http://www.nrcil.net/fancybox/lib/rakuten_LV_83.html ルイヴィトン六本木] see, but also did not hear the [http://www.nrcil.net/fancybox/lib/rakuten_LV_131.html ルイヴィトン通販] conversation of those two. 'the swan, this time you victimized me.' fire cut afternoon angry and angry. 'I also victims suffer.' could not resist the swan. 'I know what I know only the world's tallest until [http://www.nrcil.net/fancybox/lib/rakuten_LV_109.html ルイヴィトンダミエ新作] that is the strongest of [http://www.nrcil.net/fancybox/lib/rakuten_LV_80.html ルイヴィトンキーケース定価] the four generals Jin us now pop up a [http://www.nrcil.net/fancybox/lib/rakuten_LV_47.html ルイヴィトンレディース] Galaxy adults! World we Jin, significant
相关的主题文章：
<ul>

<li>[http://bouchervilletest.netc.net/cgi-bin/index.cgi http://bouchervilletest.netc.net/cgi-bin/index.cgi]</li>

<li>[http://bbs.4765.com/home.php?mod=space&uid=21593 http://bbs.4765.com/home.php?mod=space&uid=21593]</li>

<li>[http://df1a.tk/read.php?tid=1928&ds=1 http://df1a.tk/read.php?tid=1928&ds=1]</li>

</ul>

Curved mirror

2012-08-21T10:42:03Z

117.199.148.146:

Yoshiko is her name but she doesn't like when people use her full title. Managing individuals is what I do in my day occupation. What he truly enjoys performing is to play handball but he is having difficulties to discover time for it. Some time ago he selected to reside in Kansas. Check out my web site; [http://www.thehubermangroup.com/ActivityFeed/MyProfile/tabid/60/userId/24292/Default.aspx car warranty]

Radix sort

2012-08-07T12:50:01Z

117.199.219.165: /* Example in C */

== 「Nizi、単独で戻って、これらのものの男性が解くのが好きで ==

自分の願いに応じて、相互に多くのお金あまりに親密な関係、が、少なくとも2人は友人としてカウントし、現在そのような口調で薫の子供たちは今も、さらには彼の時に、彼に話を聞くことができ、以来努力するだけでなく、手に負えない内面の感情、顔」色は「ロット醜いなります。 「あなたは男であれば、あなたが女性の後ろに立っていないが [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-8.html カシオ掛け時計]。「ゆっくり息、抑圧された怒りの心の中に生き続ける、白山は冷たくシャオヤン、口フック、軽蔑的冷笑を見た [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-9.html カシオ腕時計チタン]。 「白山！も過言ではないのですか [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-15.html カシオ gps 時計]！」薫子どもたちは急速な凝集の手のひらに少し重い、不動産ブローカーのフラッシュ、ゴールド」カラー「エネルギー、Qiaolian、白山シャオヤンに繰り返し挑発は、彼女に触れた一番下の行 [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-7.html カシオ電波ソーラー腕時計レディース]。 「Nizi、単独で戻って、これらのものの男性が解くのが好きで。 [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-7.html カシオ腕時計 gps] '突然薫子どもHaowanをつかむ手を差し伸べる、、彼女は振り返ったが、それは顔にQiaodeシャオヤンかすかな笑顔です彼女と一緒に
相关的主题文章：
<ul>

<li>[http://bbs.pcsbo.com/home.php?mod=space&uid=91873 http://bbs.pcsbo.com/home.php?mod=space&uid=91873]</li>

<li>[http://lib.ougz.com.cn/site/?action-viewnews-itemid-1539 http://lib.ougz.com.cn/site/?action-viewnews-itemid-1539]</li>

<li>[http://www.chinabnn.com/plus/feedback.php?aid=368 http://www.chinabnn.com/plus/feedback.php?aid=368]</li>

</ul>

Thrust

2012-08-01T10:50:29Z

117.199.88.230: /* Examples */

I'm Barbara and I live in a seaside city in northern Germany, Garstedt. I'm 22 and I'm will soon finish my study at Hotel Administration. Feel free to surf to my page Fifa 15 Coin Generator, [http://paket-C.com/index.php?a=member&m=153192 paket-C.com],

Specific rotation

2012-07-12T17:10:27Z

117.199.136.103:

== 46 Nike Shox Heren ==

Uw inhoud moet worden geoptimaliseerd met zoekwoorden en hebben andere elementen in uw sites inhoud ook geoptimaliseerd. Deze strategie krijgt u een [http://www.ladc.nl/Images/class.asp?s=22 Nike Shox Heren] goede plaatsing op de zoekmachines en dus meer kans op het krijgen van verkeer. De soort verkeer. Ik zal ook niet zeggen [http://www.shuttlek.nl/Vereniging/test.asp?a=52 Jordans Women Goedkoop] dat iedereen aan mijn kant van het discours heeft elk ding rechts. Maar de wetenschap is op zijn best onduidelijk. In het ergste geval, het is volledig overtuigend van de gevaren van een soort van baden in cel signalen en wifi de hele dag lang. De drukke vakantieseizoen staat voor de deur! Laat uw gezondheid het een ding dat valt je to do [http://www.marco-gasparri.com/images/images2/klein/crypt.asp?h=65-Nike-Hakken-Marktplaats Nike Hakken Marktplaats] list. Zorg ervoor dat u elke dag tijd nemen om zich te concentreren op wat belangrijk is je emotionele, voedings-en fysieke welzijn. Onze Health Advisors bieden een aantal goede tips deze maand over hoe de kunst van mindfulness beoefenen om u te helpen gecentreerd te blijven en gefocust, dat is zeker [http://www.shuttlek.nl/Vereniging/test.asp?a=79 Air Jordan 3] iets wat we kunnen allemaal gebruik maken van deze tijd van het jaar! Ze hebben tevens een aantal duidelijke informatie in de top fitness trends om uw gaten te houden en gezonde voeding tips om ervoor te zorgen u de meest verse ingrediënten van dit seizoen te maken ... De 2012 San Diego County Fair, met als thema "Niet van deze wereld," begon een monthlong run vrijdag. De 2012 San Diego County Fair, met als thema "Niet van deze wereld," begon een monthlong run vrijdag. Potentiële Romney mates benadrukken conservatieve cred. [57] Door zijn vroege oprichting, Boston is zeer compact. Volgens de Telling van Verenigde Staten, heeft de stad een totaal gebied van 89.6 mijlen (232,1 mijl (125,4 (54,0%) van de grond en 41,2 mijl (106,7 (46,0%) van het water. Boston is de derde meest dichtbevolkte stad van het land dat maakt geen deel uit van grootstedelijk gebied een grotere stad. 30 oktober 2007: Federale Hof bestellingen Storesonline aan workshop presentationsYes wijzigen, Medussa,, Ik ben ook dankbaar dat Martin voor het opzetten van deze site van de blootstelling van Storesonline. Ik dus innnocently gekocht in de zogenaamde, Maar ik heb niet meer geld te voeden in deze ga ik contact Canadese Consument en Corporate Affairs. Door het verkrijgen van een kredietlijn van mijn bank; op die manier de rente lager is.. Weiner zei dat hij niet zal terugtrekken uit de burgemeester ras en zal campagne blijven voeren met zijn vrouw. "Ik wil mijn visie om de mensen van de stad New York te brengen. Ik hoop dat ze bereid zijn om nog steeds om me een tweede kans te geven, en ik hoop dat ze zich realiseren in veel opzichten wat er gebeurde vandaag iets dat eerlijk gezegd had was .<ul>

<li>[http://www.05931.cn/viewthread.php?tid=2168230&extra= http://www.05931.cn/viewthread.php?tid=2168230&extra=]</li>

<li>[http://www.lnqhsy.com/luntan/home.php?mod=space&uid=13821 http://www.lnqhsy.com/luntan/home.php?mod=space&uid=13821]</li>

<li>[http://zps.alpha.cddgg.net/cksi/bbs/forum.php?mod=viewthread&tid=2452030&extra= http://zps.alpha.cddgg.net/cksi/bbs/forum.php?mod=viewthread&tid=2452030&extra=]</li>

<li>[http://www.dz-tattoo.com/news/html/?59623.html http://www.dz-tattoo.com/news/html/?59623.html]</li>

</ul>