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# Closed Form of the following infinite series

I am working on Special Functions. I have the following infinite series:

$f(z)=\left(z + \displaystyle\frac{(\gamma)_1}{\Gamma(4)}\frac{z^2}{1!}+\displaystyle\frac{(\gamma)_2}{\Gamma(6)}\frac{z^3}{2!}+\displaystyle\frac{(\gamma)_3}{\Gamma(8)}\frac{z^4}{3!}+\cdots\right)$,

where $(\gamma)_n=(\gamma)(\gamma+1)\cdots(\gamma+n-1)$ and is called as Pochhammer symbol.

I tried to bring this series to a closed form as follows: \begin{eqnarray} f(z)&=&\sqrt{z}\left(\sqrt{z} + \displaystyle\frac{(\gamma)_1}{1!}\frac{(\sqrt{z})^3}{3!}+\displaystyle\frac{(\gamma)_2}{2!}\frac{(\sqrt{z})^5}{5!}+\displaystyle\frac{(\gamma)_3}{3!}\frac{(\sqrt{z})^7}{7!}+\cdots\right)\\ &=&\sqrt{z}\sum_{k=0}^{\infty}\frac{(\gamma)_k}{(1)_k}\frac{(\sqrt{z})^{2k+1}}{(2k+1)!} \end{eqnarray} Can this be reduced to a Confluent Hypergeometric Function (or any other closed form)? Also, for $\gamma=1$, I obtain $f(z)=\sqrt{z}\sinh(\sqrt{z})$.

Can anyone provide me any hint?

• Since $(2k+1)! = 4^k(1)_k(\frac32)_k$, the sum is the generalized hypergeometric function $z{}_1F_2\left(\gamma; 1,\frac32; \frac{z}{4}\right)$. – achille hui May 16 '18 at 9:50
• Thanks a lot! This helped very much. – user374063 May 17 '18 at 6:32

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# Subtle Distinction

1. Jul 10, 2006

### actionintegral

Friends,

In a recent post I said

"The speed of light is the same for all observers".

I meant unequivocally. With no exceptions. Always the same. No tricks or gimmicks.

But I was quickly corrected in triplicate!

'To be exact: The speed of light is the same for all inertial observers. There is a significant difference.'

If the difference is significant, then I need to understand it. Does this mean the speed of light can change for an observer?

2. Jul 10, 2006

### pmb_phy

Yes. When it is said that the speed of light is observer dependant it refers to the "coordinate speed of light." Consider an observer in a uniform g-field (or, equivalently, a uniformly accelerating frame of reference). The speed of light in the field will be a function of the location of a light packet in the field. If the observer is located at z = 0 then, for a g-field pointing in the -z direction, the speed of light will be a function of z. Einstein derived the expression for this speed of light and published it in 1907. As measured at z = 0 the speed of light is that measured by an inertial observer in flat spacetime.

Pete

3. Jul 10, 2006

### actionintegral

4. Jul 10, 2006

### George Jones

Staff Emeritus
Whenever I see the unqualified statement "The speed of light is the same for all observers.", I take it to mean the physical speed as measured by the measuring apparatus of the observer. With this take on this statement, it is true for all observers in both special and general relativity.

As Pete has pointed out, of the coordintate speed of light can change, but while coordinate speed is often easier to compute than physical speed, coordinate speed is less natural to measure than physical speed.

5. Jul 10, 2006

### pervect

Staff Emeritus
I tend to agree with George. The coordinate speed of light can change with regard to the obsever - the coordinate speed being defined as the rate of change of the distance coordinate with respect to the time coordinate in some chosen coordinate system.

However, when you measure the speed of light in a vacuum using properly set-up local clocks and local rulers (clocks and rulers located near the same point that the light is), you always get the same value, 'c'.

"Properly set up" means that the frame defined by the rulers isn't rotating, the rulers are all at right angles to each other, and that the rulers are Minkowski-orthogonal to the time vector defined by the clocks.

This follows from the fact that the geometry of space-time is always locally "flat", i.e. has the familiar Minkowski metric in some small area around a given point.

MTW expressses this by saying that the geometry of space-time is locally Lorentzian.

6. Jul 10, 2006

### bernhard.rothenstein

Have a look please at Edward A. Desloge and R.J.Philpott Am.J.Phys. 55 252 1987 Ch.VII

7. Jul 13, 2006

### Robert.Hipple

Hi Bernhard!

Fantastic!

I have been looking for a paper like this for quite some time. It forms a perfect pedagogical bridge between SR and GR.

Sincerely,
Robert

8. Jul 28, 2006

### MeJennifer

By the way, a common confusion is the difference between the speed of light and c.

The speed of light is not constant in all frames of reference but c is!

9. Jul 28, 2006

Staff Emeritus
Excuse me but what "frames of reference" are you speaking of here? Are you talking about media? Light can be made to "sit up and beg" with the right nonlinear media, but frames of reference?

10. Jul 28, 2006

### MeJennifer

For instance in a non-inertial frame of reference the speed of light is different, however c remains constant.

This is sometimes very confusing in discussions about the speed of light, in these cases it is often better not to use c at all.

Last edited: Jul 28, 2006
11. Jul 28, 2006

### pervect

Staff Emeritus
This doesn't have anyting to do about the issue of the speed of light in a media vs 'c'.

This issue has to do with how velocities are measured. People who rely on coordinates are usually the ones confused by this issue.

The physics is actually very simple - when you use local rulers and local clocks, the speed of light over a short path is always 'c'. This is true even in accelerated coordinate systems, though one has to pay attention to the "short" part of the above statement.

People often use coordinate systems to measure the "speed of light" and think of the speed as being measured by the rate of change of a distance coordinate with respect to a time coordinate. This is a fundamentally different defintion, for it uses coordinates to measure the speed, rather than local clocks and rulers.

[edits below]

An analogy might help. Suppose someone tells you "We have a naval ship, and it always travels in the sea at a constant velocity". Now,if you set up a lattitude/longitude coordinate system on the Earth, and measure how many degrees of longitude the ship moves in one hour. you would find that the ship moves faster and fasater as it gets closer and closer to the north pole. This is the coordinate based defintion of speed - one measured the coordinate of the ship (its longitude) and how fast it changes with time.

However, someone actually on the ship, measuring its velocity relative to the water, fnds that the speed of the ship really is constant, as you were informed of in the first place. So the confusion arised because of differences in defintions.

For this example, we are ignoring the issue of ocean currents - assuming that they are negligible. In relativity, of course, there are no "ether currents" to worry about.

In our naval example, the issue is how one defines distances and velocities. Using coordinates, as one gets closer and closer to the north pole, a minute of longitude (a coordinate measure) is not the same as a physical nautical mile in one's local coordinate system. The curvature of the Earth is responsible for this confusion, just as the curvature of space-time is what makes the "coordinate speed" of light vary.

One can set up a metric that gives physical distances on the Earth as a function of changes in coordinates - i.e. distances as a function of $\delta$ lattitude and $\delta$ longitude. This metric for the curved surface of the Earth is conceputally the same as Einstein's metric for space-time, except that Einstein's metric gives the invariant Lorentz interval, rather than the distance.

One can see that when the metric coefficients are diagonal and all equal to 1, physical distances correspond to coordinate distances.

You might ask "Can we set up a coordinate system so that the metric of the Earth is everywhere an identity matrix"?. The answer is no, and the reason this can't be done is because the Earth's surface is curved. Relativity says the same thing about space-time - in the presence of curvature near large masses, you can't make the metric coefficients equal to an identity matrix everywhere, though at any particular point you can "normalize" them so that coordinate distances are equal to physical distances (ruler distances) and coordinate times are equal to clock times.

Last edited: Jul 28, 2006


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## Linear Regression

### Introduction

A data model explicitly describes a relationship between predictor and response variables. Linear regression fits a data model that is linear in the model coefficients. The most common type of linear regression is a least-squares fit, which can fit both lines and polynomials, among other linear models.

Before you model the relationship between pairs of quantities, it is a good idea to perform correlation analysis to establish if a linear relationship exists between these quantities. Be aware that variables can have nonlinear relationships, which correlation analysis cannot detect. For more information, see Linear Correlation.

The MATLAB® Basic Fitting UI helps you to fit your data, so you can calculate model coefficients and plot the model on top of the data. For an example, see Example: Using Basic Fitting UI. You also can use the MATLAB `polyfit` and `polyval` functions to fit your data to a model that is linear in the coefficients. For an example, see Programmatic Fitting.

If you need to fit data with a nonlinear model, transform the variables to make the relationship linear. Alternatively, try to fit a nonlinear function directly using either the Statistics and Machine Learning Toolbox™ `nlinfit` function, the Optimization Toolbox™ `lsqcurvefit` function, or by applying functions in the Curve Fitting Toolbox™.

This topic explains how to:

• Perform simple linear regression using the `\` operator.

• Use correlation analysis to determine whether two quantities are related to justify fitting the data.

• Fit a linear model to the data.

• Evaluate the goodness of fit by plotting residuals and looking for patterns.

• Calculate measures of goodness of fit R2 and adjusted R2

### Simple Linear Regression

This example shows how to perform simple linear regression using the `accidents` dataset. The example also shows you how to calculate the coefficient of determination ${R}^{2}$ to evaluate the regressions. The `accidents` dataset contains data for fatal traffic accidents in U.S. states.

Linear regression models the relation between a dependent, or response, variable $y$ and one or more independent, or predictor, variables ${x}_{1},...,{x}_{n}$. Simple linear regression considers only one independent variable using the relation

`$y={\beta }_{0}+{\beta }_{1}x+ϵ,$`

where ${\beta }_{0}$ is the y-intercept, ${\beta }_{1}$ is the slope (or regression coefficient), and $ϵ$ is the error term.

Start with a set of $n$ observed values of $x$ and $y$ given by $\left({x}_{1},{y}_{1}\right)$, $\left({x}_{2},{y}_{2}\right)$, ..., $\left({x}_{n},{y}_{n}\right)$. Using the simple linear regression relation, these values form a system of linear equations. Represent these equations in matrix form as

`$\left[\begin{array}{c}{y}_{1}\\ {y}_{2}\\ ⋮\\ {y}_{n}\end{array}\right]=\left[\begin{array}{cc}1& {x}_{1}\\ 1& {x}_{2}\\ ⋮& ⋮\\ 1& {x}_{n}\end{array}\right]\left[\begin{array}{c}{\beta }_{0}\\ {\beta }_{1}\end{array}\right].$`

Let

`$Y=\left[\begin{array}{c}{y}_{1}\\ {y}_{2}\\ ⋮\\ {y}_{n}\end{array}\right],X=\left[\begin{array}{cc}1& {x}_{1}\\ 1& {x}_{2}\\ ⋮& ⋮\\ 1& {x}_{n}\end{array}\right],B=\left[\begin{array}{c}{\beta }_{0}\\ {\beta }_{1}\end{array}\right].$`

The relation is now $Y=XB$.

In MATLAB, you can find $B$ using the `mldivide` operator as `B = X\Y`.

From the dataset `accidents`, load accident data in `y` and state population data in `x`. Find the linear regression relation $y={\beta }_{1}x$ between the accidents in a state and the population of a state using the `\` operator. The `\` operator performs a least-squares regression.

```load accidents x = hwydata(:,14); %Population of states y = hwydata(:,4); %Accidents per state format long b1 = x\y```
```b1 = 1.372716735564871e-04 ```

`b1` is the slope or regression coefficient. The linear relation is $y={\beta }_{1}x=0.0001372x$.

Calculate the accidents per state `yCalc` from `x` using the relation. Visualize the regression by plotting the actual values `y` and the calculated values `yCalc`.

```yCalc1 = b1*x; scatter(x,y) hold on plot(x,yCalc1) xlabel('Population of state') ylabel('Fatal traffic accidents per state') title('Linear Regression Relation Between Accidents & Population') grid on```

Improve the fit by including a y-intercept ${\beta }_{0}$ in your model as $y={\beta }_{0}+{\beta }_{1}x$. Calculate ${\beta }_{0}$ by padding `x` with a column of ones and using the `\` operator.

```X = [ones(length(x),1) x]; b = X\y```
```b = 2×1 102 × 1.427120171726538 0.000001256394274 ```

This result represents the relation $y={\beta }_{0}+{\beta }_{1}x=142.7120+0.0001256x$.

Visualize the relation by plotting it on the same figure.

```yCalc2 = X*b; plot(x,yCalc2,'--') legend('Data','Slope','Slope & Intercept','Location','best');```

From the figure, the two fits look similar. One method to find the better fit is to calculate the coefficient of determination, ${R}^{2}$. ${R}^{2}$ is one measure of how well a model can predict the data, and falls between $0$ and $1$. The higher the value of ${R}^{2}$, the better the model is at predicting the data.

Where $\underset{}{\overset{ˆ}{y}}$ represents the calculated values of $y$ and $\underset{}{\overset{‾}{y}}$ is the mean of $y$, ${R}^{2}$ is defined as

`${R}^{2}=1-\frac{\sum _{i=1}^{n}{\left({y}_{i}-{\underset{}{\overset{ˆ}{y}}}_{i}\right)}^{2}}{\sum _{i=1}^{n}{\left({y}_{i}-\underset{}{\overset{‾}{y}}\right)}^{2}}.$`

Find the better fit of the two fits by comparing values of ${R}^{2}$. As the ${R}^{2}$ values show, the second fit that includes a y-intercept is better.

`Rsq1 = 1 - sum((y - yCalc1).^2)/sum((y - mean(y)).^2)`
```Rsq1 = 0.822235650485566 ```
`Rsq2 = 1 - sum((y - yCalc2).^2)/sum((y - mean(y)).^2)`
```Rsq2 = 0.838210531103428 ```

### Residuals and Goodness of Fit

Residuals are the difference between the observed values of the response (dependent) variable and the values that a model predicts. When you fit a model that is appropriate for your data, the residuals approximate independent random errors. That is, the distribution of residuals ought not to exhibit a discernible pattern.

Producing a fit using a linear model requires minimizing the sum of the squares of the residuals. This minimization yields what is called a least-squares fit. You can gain insight into the “goodness” of a fit by visually examining a plot of the residuals. If the residual plot has a pattern (that is, residual data points do not appear to have a random scatter), the randomness indicates that the model does not properly fit the data.

Evaluate each fit you make in the context of your data. For example, if your goal of fitting the data is to extract coefficients that have physical meaning, then it is important that your model reflect the physics of the data. Understanding what your data represents, how it was measured, and how it is modeled is important when evaluating the goodness of fit.

One measure of goodness of fit is the coefficient of determination, or R2 (pronounced r-square). This statistic indicates how closely values you obtain from fitting a model match the dependent variable the model is intended to predict. Statisticians often define R2 using the residual variance from a fitted model:

R2 = 1 – SSresid / SStotal

SSresid is the sum of the squared residuals from the regression. SStotal is the sum of the squared differences from the mean of the dependent variable (total sum of squares). Both are positive scalars.

To learn how to compute R2 when you use the Basic Fitting tool, see R2, the Coefficient of Determination. To learn more about calculating the R2 statistic and its multivariate generalization, continue reading here.

#### Example: Computing R2 from Polynomial Fits

You can derive R2 from the coefficients of a polynomial regression to determine how much variance in `y` a linear model explains, as the following example describes:

1. Create two variables, `x` and `y`, from the first two columns of the `count` variable in the data file `count.dat`:

```load count.dat x = count(:,1); y = count(:,2);```

2. Use `polyfit` to compute a linear regression that predicts `y` from `x`:

```p = polyfit(x,y,1) p = 1.5229 -2.1911 ```

`p(1)` is the slope and `p(2)` is the intercept of the linear predictor. You can also obtain regression coefficients using the Basic Fitting UI.

3. Call `polyval` to use `p` to predict `y`, calling the result `yfit`:

`yfit = polyval(p,x);`

Using `polyval` saves you from typing the fit equation yourself, which in this case looks like:

`yfit = p(1) * x + p(2);`
4. Compute the residual values as a vector of signed numbers:

`yresid = y - yfit;`

5. Square the residuals and total them to obtain the residual sum of squares:

`SSresid = sum(yresid.^2);`

6. Compute the total sum of squares of `y` by multiplying the variance of `y` by the number of observations minus `1`:

```SStotal = (length(y)-1) * var(y); ```

7. Compute R2 using the formula given in the introduction of this topic:

```rsq = 1 - SSresid/SStotal rsq = 0.8707```
This demonstrates that the linear equation ```1.5229 * x -2.1911``` predicts 87% of the variance in the variable `y`.

#### Computing Adjusted R2 for Polynomial Regressions

You can usually reduce the residuals in a model by fitting a higher degree polynomial. When you add more terms, you increase the coefficient of determination, R2. You get a closer fit to the data, but at the expense of a more complex model, for which R2 cannot account. However, a refinement of this statistic, adjusted R2, does include a penalty for the number of terms in a model. Adjusted R2, therefore, is more appropriate for comparing how different models fit to the same data. The adjusted R2 is defined as:

R2adjusted = 1 - (SSresid / SStotal)*((n-1)/(n-d-1))

where n is the number of observations in your data, and d is the degree of the polynomial. (A linear fit has a degree of 1, a quadratic fit 2, a cubic fit 3, and so on.)

The following example repeats the steps of the previous example, Example: Computing R2 from Polynomial Fits, but performs a cubic (degree 3) fit instead of a linear (degree 1) fit. From the cubic fit, you compute both simple and adjusted R2 values to evaluate whether the extra terms improve predictive power:

1. Create two variables, `x` and `y`, from the first two columns of the `count` variable in the data file `count.dat`:

```load count.dat x = count(:,1); y = count(:,2);```

2. Call `polyfit` to generate a cubic fit to predict `y` from `x`:

```p = polyfit(x,y,3) p = -0.0003 0.0390 0.2233 6.2779```

`p(4)` is the intercept of the cubic predictor. You can also obtain regression coefficients using the Basic Fitting UI.

3. Call `polyval` to use the coefficients in `p` to predict `y`, naming the result `yfit`:

`yfit = polyval(p,x);`

`polyval` evaluates the explicit equation you could manually enter as:

`yfit = p(1) * x.^3 + p(2) * x.^2 + p(3) * x + p(4);`

4. Compute the residual values as a vector of signed numbers:

`yresid = y - yfit;`

5. Square the residuals and total them to obtain the residual sum of squares:

`SSresid = sum(yresid.^2);`

6. Compute the total sum of squares of `y` by multiplying the variance of `y` by the number of observations minus `1`:

```SStotal = (length(y)-1) * var(y); ```

7. Compute simple R2 for the cubic fit using the formula given in the introduction of this topic:

```rsq = 1 - SSresid/SStotal rsq = 0.9083```

8. Finally, compute adjusted R2 to account for degrees of freedom:

```rsq_adj = 1 - SSresid/SStotal * (length(y)-1)/(length(y)-length(p)) rsq_adj = 0.8945```
The adjusted R2, 0.8945, is smaller than simple R2, .9083. It provides a more reliable estimate of the power of your polynomial model to predict.

In many polynomial regression models, adding terms to the equation increases both R2 and adjusted R2. In the preceding example, using a cubic fit increased both statistics compared to a linear fit. (You can compute adjusted R2 for the linear fit for yourself to demonstrate that it has a lower value.) However, it is not always true that a linear fit is worse than a higher-order fit: a more complicated fit can have a lower adjusted R2 than a simpler fit, indicating that the increased complexity is not justified. Also, while R2 always varies between 0 and 1 for the polynomial regression models that the Basic Fitting tool generates, adjusted R2 for some models can be negative, indicating that a model that has too many terms.

Correlation does not imply causality. Always interpret coefficients of correlation and determination cautiously. The coefficients only quantify how much variance in a dependent variable a fitted model removes. Such measures do not describe how appropriate your model—or the independent variables you select—are for explaining the behavior of the variable the model predicts.

### Fitting Data with Curve Fitting Toolbox Functions

The Curve Fitting Toolbox software extends core MATLAB functionality by enabling the following data-fitting capabilities:

• Linear and nonlinear parametric fitting, including standard linear least squares, nonlinear least squares, weighted least squares, constrained least squares, and robust fitting procedures

• Nonparametric fitting

• Statistics for determining the goodness of fit

• Extrapolation, differentiation, and integration

• Dialog box that facilitates data sectioning and smoothing

• Saving fit results in various formats, including MATLAB code files, MAT-files, and workspace variables


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# Synopsis: Finding strength in small places

X-ray diffraction reveals why some nanostructured metals are stronger than others.

Pulling, rolling, or bending a metal such as steel introduces dislocations in its structure that allow it to absorb energy under stress and resist fracture. Scientists and engineers have tried to find a similar process to toughen nanocrystalline metals, as these materials are prone to fracture despite their ultrahigh strength and hardness.

Writing in Physical Review Letters, Yinmin Wang and colleagues at Lawrence Livermore National Laboratory, in collaboration with researchers at Ames Laboratory and Argonne National Laboratory, all in the US, present experiments on specific ways in which nanostructured metals deform under stress.

Wang et al. prepared bulk pieces of nanocrystalline nickel and cobalt, which have similar grain sizes but different crystal structures. Each metal contained a large number of nanograins (“domains”) with a different crystalline orientation than those around them. With synchrotron x-ray diffraction and electron microscopy, Wang et al. tracked changes in the structure and defect accumulations within the domains in response to tensile (pulling) stress.

In the experiments, cobalt proved to be more resistant to fracture than nickel. Wang et al. suggest that this is because the domains in cobalt reorient, or “twin”, more easily than those in nickel, thus offering an effective strain-hardening mechanism. However, they note that even for cobalt the twinning mechanism is less effective for grains smaller than $15$ nanometers, which may be one reason why truly nanoscale materials are so resistant to toughening. – Jessica Thomas

More Features »

### Announcements

More Announcements »

## Subject Areas

Materials Science

Magnetism

## Next Synopsis

Superconductivity

## Related Articles

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### Synopsis: A Crystal Ball for 2D Materials

Researchers predict new two-dimensional materials whose structures differ from their three-dimensional counterparts. Read More »

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### Viewpoint: Electron Pulses Made Faster Than Atomic Motions

Electron pulses have shattered the 10-femtosecond barrier at which essentially all atomic motion is frozen in materials. Read More »

Condensed Matter Physics

### Focus: Ultrafast Switch with Organic Crystal

An organic crystal was switched between paraelectric and ferroelectric states in a picosecond. Similar materials could eventually serve as extremely fast digital switches. Read More »


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Centrum Astronomii
Wydział Fizyki, Astronomii i Informatyki Stosowanej, Uniwersytet Mikołaja Kopernika

## TeV Gamma-Ray Observations of the Binary Neutron Star Merger GW170817 with H.E.S.S.

Abramowski A., Aharonian F., Backes M., Balzer A., Becherini Y., Becker Tjus J., Berge D., Bernlöhr K., Böttcher M., Boisson C., i 134 współautor(ów), w tym z CA, Katarzyński K., Rudak B.
2017

We search for high-energy gamma-ray emission from the binary neutron star merger GW170817 with the H.E.S.S. Imaging Air Cherenkov Telescopes. The observations presented here have been obtained starting only 5.3 hr after GW170817. The H.E.S.S. target selection identified regions of high probability to find a counterpart of the gravitational-wave event. The first of these regions contained the counterpart SSS17a that has been identified in the optical range several hours after our observations. We can therefore present the first data obtained by a ground-based pointing instrument on this object. A subsequent monitoring campaign with the H.E.S.S. telescopes extended over several days, covering timescales from 0.22 to 5.2 days and energy ranges between 270 {GeV} to 8.55 {TeV}. No significant gamma-ray emission has been found. The derived upper limits on the very-high-energy gamma-ray flux for the first time constrain non-thermal, high-energy emission following the merger of a confirmed binary neutron star system.

###### Słowa kluczowe
Gamma Rays: General, Gravitational Waves


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# ni oxidation number

For #Ni(CO)_4#, we break the #Ni-CO# bond and we get #Ni^0# #+4xx""^(-):C-=O^+#.And thus nickel has a formal oxidation state of #"ZERO".#. Coordination number of Ni in [Ni(C2O4)3]4- is (a) 3 (b) 6 (c) 4 (d) 2. Share Tweet Send [Deposit Photos] Nickel is a chemically low-active metal, with a silvery-white color. ; When oxygen is part of a peroxide, its oxidation number is -1. . It is possible to remove a fifth electron to form another the $$\ce{VO_2^{+}}$$ ion with the vanadium in a +5 oxidation â¦ Author links open overlay panel Xian-Zhu Fu a Ying-Jie Zhu b Qing-Chi Xu a Jun Li a Jia-Hong Pan c Jeff-Qiang Xu a Jing-Dong Lin a Dai-Wei Liao a. 2. The sum of the charges is a compound is always 0. CO3 has a -2 charge. Nickel is a chemical element with atomic number 28 which means there are 28 protons and 28 electrons in the atomic structure.The chemical symbol for Nickel is Ni. Oxidation number, also called oxidation state, the total number of electrons that an atom either gains or loses in order to form a chemical bond with another atom.. Each atom that participates in an oxidation-reduction reaction is assigned an oxidation number that reflects its ability to acquire, donate, or share electrons. For example, the oxidation number of Na + is +1; the oxidation number of N 3-is -3. Hence the oxidation state of Nickel is 0. The sum of oxidation numbers of all elements is zero. Average oxidation numbers of Ni in the nickel oxide samples estimated by different methods when the âNi in LiCoO 2 â model structure is used for the FEFF calculations: (1) the XANES-based method, (2) the coordination number-based method, (3) the bond length-based method with a single bond valence parameter and a single NiâO bond length, and (4) the bond length-based method â¦ It is classified as a basic metal oxide. In almost all cases, oxygen atoms have oxidation numbers of -2. JIPMER 1999: The oxidation number of nickel in K4[Ni(CN)4] is: (A) -2 (B) -1 (C) 2 (D) 0. Nickel can have a charge of either 2+ or 3+. So, x + 0 = 0; x = 0. Let x be the oxidation number of Ni in Ni(CO) 4. q = the charge on the complex. :0: N :0: :0: This problem has been solved! Carefully, insert coefficients, if necessary, to make the numbers of oxidized and reduced atoms equal on the two sides of each redox couples. P can be either +3or+5 In this case it must be +5 or it wouldn't work out with the rest. -1 for each Cl, +2 for Ni. Nickel(II) oxide is the chemical compound with the formula NiO.It is the principal oxide of nickel. Several million kilograms are produced annually of varying quality, mainly as an intermediate in the production of nickel alloys. Calculating Oxidation Numbers. Hence, x=0. An oxidation number can be assigned to a given element or compound by following the following rules. I believe the lower first ionisation energy can account for the increased tendency of Ni to do SET but I don't know how best to explain why all the additional oxidation states are available to Ni â¦ So Ni must have a +2 charge. Common oxidation states. To find the oxidation number of Ni in {eq}\rm Ni(CN)_4^{2-}{/eq}: Let the oxidation number of Ni be x.. Electron Configuration 0 0. [1] This does have a general quantum chemical explanation. Still have questions? So 4 CO x 2 e- = 8 e- in total. Expert Answer: CO is a neutral ligand hence there will be no charge on metal. The oxidation number of hydrogen is +1 when it is combined with a nonmetal as in CH 4, NH 3, H 2 O, and HCl. Assign an oxidation number of -2 to oxygen (with exceptions). What is oxidation number of ni in ni(co4 Electron Configuration and Oxidation States of Nickel. The oxidation number of nickel in nickel(II) carbonate is +2. Isotopes Therefore, x+4(0)=0. so 3 oxygens X-2for the oxidation # = -6. so Ni2 has to be eqal to -6. since their are two atoms -6/2 =-3 The neutral CO molecules donate 2 electrons each. Palladium conversely only shuttles between (0) and (II) in a standard cross-coupling reaction. Expert Answer 100% (3 ratings) We first work out the charge of the PO_4-group. Let the oxidation number of Ni in K 4 [Ni(CN) 4] = x. Chemistry, 06.12.2020 20:20 taylor5384. The oxidation number of nickel is +2. Write down the transfer of electrons. Additionally, it has -2, â1, 0, +1, +2, +3, and +4, as its oxidation numbers. The oxidation state of an atom is a measure of the degree of oxidation of an atom. All Questions Ask Doubt. it should be equal to 0. Oxidation Number: The number that is assigned to an element to indicate the loss or gain of electrons by an atom of that element is called as the oxidation number. Nickel, chemical element, ferromagnetic metal of Group 10 (VIIIb) of the periodic table, markedly resistant to oxidation and corrosion. #"Oxidation number"# is the charge left on the central atom when all the bonding pairs of electrons are removed, with the charge devolved to the most electronegative atom. Related Questions & Answers: What Is The Use Of A Concave Mirror: Why Do Organisms Need To Take Food Short Answer: view the full answer Answered by Ramandeep | 22nd Feb, 2019, 10:47: AM. In the coordination compound, K4[Ni(CN)4], the oxidation state of nickel is Coordination Compounds In the coordination compound, K 4 [Ni(CN) 4], the oxidation state of nickel is. The oxidation number of sodium in the Na + ion is +1, for example, and the oxidation number of chlorine in the Cl-ion is -1. Based upon that oxidation number, an electronic configuration is also given but note that for more exotic compounds you should view this as a guide only. Put the value into the formula. Because #Ni(CO)_4# is quite volatile, its formation forms the basis for â¦ The oxidation number of a monatomic ion equals the charge of the ion. There are 3 Nickel (Ni) atoms, 2 Phosphorus (P) atoms, and 8 Oxygen (O) atoms. In compounds, fluorine is assigned a â1 oxidation number; oxygen is usually assigned a â2 oxidation number (except in peroxide compounds [where it is â1] and in binary compounds with fluorine [where it is positive]); and hydrogen is usually assigned a +1 oxidation number (except when it exists as the hydride ion, H â, in which case rule 2 prevails). charge on the complex is 0, the sum of oxidation states of all elements in. What is the oxidation number of Ni in Ni(CO)4 ? Hence, The oxidation number for nickel is zero in tetracarbonyl nickel. The positive oxidation state is the total number of electrons removed from the elemental state. The charge on CO group is 0. Lv 7. CO3 has a charge of 2-, so Ni has an oxidation number of 2+ 0 0. electron1. Silvery white, tough, and harder than iron, nickel is widely familiar because of its use in coinage but is more important as the pure metal or in the form of alloys. Thus, the oxidation number of Ni in Ni(CO) 4. is 0. It is zero. Check Answer and Solution for above Chemistry question - Tardigrade These oxidation states add up to eight, which is exactly the number of electrons that typically make up the outer (valence) shell â where chemistry happens. The oxidation number of â¦ In Nico4 What Is The Oxidation Number Of Ni. Question: What Is The Oxidation Number Of Nitrogen In The Nitrate Ion? 1 × 4 + x × (â1) × â¦ We need to calculate the oxidation number of nickel in tetracarbonyl nickel. Ni atom attached with four carbonyl ligands with overall zero charge on the complex has zero oxidation state.Let oxidation state of Ni be X. Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to â¦ Common Oxidation state of Nickel is +2. The oxidation number of simple ions is equal to the charge on the ion. Maximum oxidation state: $\mathrm{+V}$. Any free element has an oxidation number equal to zero. Show more. See the answer. Since the overall. 5 years ago. There are a few exceptions to this rule: When oxygen is in its elemental state (O 2), its oxidation number is 0, as is the case for all elemental atoms. Nickel (Ni) Oxidation Number. Oxidation state of nickel in Nickel tetracarbonyl can be calculated easily. So the oxidation number is Ni^(2+) oxygen's oxidation # is almost always -2 . 3. The sum of the oxidation states within a compound or ion must equal the overall charge. The usual oxidation number of hydrogen is +1. Using formula of oxidation. Identify which reactants are being oxidized (the oxidation number increases when it reacts) and which are being reduced (the oxidation number goes down). Where, x = The oxidation number of of Ni. Oxidation states of nickel and reactions with it Physical and chemical properties of nickel. There is no oxidation number for compounds. The oxidation number of nickel nitrate is +2 for Ni, +5 for N, -2 for O in Ni(NO3)2. In a complex sum of oxidation states is always equal to charge on the complex.Also CO is a neutral ligand, means having zero charge.Then sum of oxidations in Ni(CO)4 is as X+4*0=0 OR X=0 Hence oxidation state of Ni is zero It is defined as being the charge that an atom would have if all bonds were ionic. 1 0. The oxidation number of a free element is always 0. The atoms in He and N 2, for example, have oxidation numbers of 0. 8 times 2- = net charge of 16- from Oxygen atoms. Show transcribed image text. Nickel oxyhydroxides with various oxidation states prepared by chemical oxidation of spherical Î²-Ni(OH) 2. They are positive and negative numbers used for balancing the redox reaction. Electron configuration of Nickel is [Ar] 3d8 4s2. In Ni(CO)4 what is the oxidation number of Ni? In compounds of nickel (where known), the most common oxidation numbers of nickel are: 2 . Minimum oxidation state $\mathrm{-III}$. So PO_4=+5+4*(-2)=-3, so it's PO_4^(3-) There are 2 PO_4^(3-)'s for a total charge of -6 To balance that, the three Ni's must have a charge of +2 each. Possible oxidation states are +2,3. 4. Uncombined elements have an oxidation state of 0. Best Answer This is a coordination compound and there are certain rules for naming the coordination complexes.Let us first recaptulate the rules: In the ionic complex,we name the cation species followed by anion. The oxidation number of cyanide ion is -1. Asked by jaideepsnatu | 21st Feb, 2019, 04:04: PM. If Nickel has a charge of 2+, 3 times 2+ = 6+ total net charge of Nickel. 0 â1 +1 +2; Answer. Arthur. For monoatomic ions, the oxidation number always has the same value as the net charge corresponding to the ion. Oxygen has an oxidation number (charge) of 2- by default. The mineralogical form of NiO, bunsenite, is very rare.Other nickel(III) oxides have been claimed, for example: Ni 5 years ago.


text:
# Determine the Value of 'K' for Which the Following Function is Continuous at X = 3 F(X)=(X+3)2−36/X−3 - Mathematics

Sum

Determine the value of 'k' for which the follwoing function is continuous at x = 3

f(x) = {(((x+3)^2-36)/(x-3),  x != 3), (k,  x =3):}

#### Solution

Given f(x) is continuous at x = 3

:. lim_(x->3) f(x)= k

lim_(x-> 3) ((x+3)^2 - 36)/(x-3) = k

lim_(x->3) ((x+3)^2 - 6^2)/(x-3) = k

lim_(x->3) ((x+3+6)(x+3-6))/(x-3) = k

lim_(x->3) ((x - 3)(x + 9))/(x-3)

lim_(x->3) (x + 9) = 3 + 9

k = 12

Is there an error in this question or solution?


text:
# Spearman correlation

## Spearman rank correlation

The Spearman correlation coefficient (or Spearman’s $$\rho$$) measures rank correlation between two variables.

Assuming monotonicity, the Spearman’s $$\rho$$ will take values between $$-1$$ and $$1$$, representing completely opposite or identical ranks, respectively1.

Due to the dependance on ranks, the Spearman’s $$\rho$$ is used for ordinal value, although discrete and continous values are possible.

If we consider a dataset of size $$n$$, and $$X_i, Y_i$$ as the scores, we can then calculate the ranks as $$\operatorname{R}({X_i}), \operatorname{R}({Y_i})$$, and $$\rho$$ as

$r_s = \rho_{\operatorname{R}(X),\operatorname{R}(Y)} = \frac{\operatorname{cov}(\operatorname{R}(X), \operatorname{R}(Y))} {\sigma_{\operatorname{R}(X)} \sigma_{\operatorname{R}(Y)}},$

Here $$\rho$$ is the Pearson correlation coefficient, but applied to the rank variables, $$\operatorname{cov}(\operatorname{R}(X), \operatorname{R}(Y))cov(R(X),R(Y))$$ is the covariance of the rank variables, $$\sigma_{\operatorname{R}(X)}$$ and $$\sigma_{\operatorname{R}(Y)}$$ are the standard deviations of the rank variables.

If all the ranks are distinct integers, the simplified form can be applied

$r_s = 1 - \frac{6 \sum d_i^2}{n(n^2 - 1)},$

where $$d_i = \operatorname{R}(X_i) - \operatorname{R}(Y_i)$$ is the difference between the two ranks of each observation, $$n$$ is the number of observations.

1. Assuming no repeated ranks. ↩


text:
# Kishori Konwar and Prakash Nayarana Moorthy: A Layered Architecture for Erasure-Coded Consistent Distributed Storage

Friday, April 7, 2017 - 1:00pm to 2:30pm
Location:
32-G631
Speaker:
Kishori Konwar and Prakash Nayarana Moorthy
Biography:
MIT

Motivated by emerging applications to the \emph{edge computing} paradigm, we introduce a two-layer erasure-coded fault-tolerant distributed storage system offering atomic access for read and write operations. In edge computing, clients interact with an edge-layer of servers that is geographically near; the edge-layer in turn interacts with a back-end layer of servers. The edge-layer provides low latency access and temporary storage for client operations, and uses the back-end layer for persistent storage. Our algorithm, termed Layered Data Storage (LDS) algorithm, offers several features suitable for edge-computing systems, works under asynchronous message-passing environments, supports multiple readers and writers, and can tolerate $f_1 < n_1/2$ and $f_2 < n_2/3$ crash failures in the two layers having $n_1$ and $n_2$ servers, respectively. We use a class of erasure codes known as regenerating codes for storage of data in the back-end layer. The choice of regenerating codes, instead of popular choices like Reed-Solomon codes, not only  optimizes the cost of back-end storage, but also helps in optimizing communication cost of read operations, when the value needs to be recreated all the way from the back-end. The two-layer architecture permits a modular  implementation of atomicity and erasure-code protocols; the implementation of erasure-codes is mostly limited to interaction between the two layers. We prove liveness and atomicity of LDS, and also compute performance costs associated with read and write operations. In a system with $n_1 = \Theta(n_2), f_1 = \Theta(n_1), f_2 = \Theta(n_2)$, the write and read costs are respectively given by $\Theta(n_1)$ and $\Theta(1) + n_1\mathcal{I}(\delta > 0)$. Here $\delta$ is a parameter closely related to the number of write operations that are concurrent with the read operation. The cost of persistent storage in the back-end layer is $\Theta(1)$. The impact of temporary storage is minimally felt in a multi-object system running $N$ independent instances of \calc, where only a small fraction of the objects undergo concurrent accesses at any point during the execution. For the multi-object system, we identify a condition on the rate of concurrent writes in the system such that the overall storage cost is dominated by that of persistent storage in the back-end layer, and is given by $\Theta(N)$.


text:
Mathias Brandewinder on .NET, F#, VSTO and Excel development, and quantitative analysis / machine learning.
12. December 2010 17:00

I recently began playing with ASP.NET MVC (never too late), and so far I really enjoy it. One aspect I really appreciate is its testability – I can write fairly straightforward unit tests to verify that the application behaves as I believe it should, as well as make sure I understand what is going on.

One point which got me stumped was how to test for authorization. A controller, or some of its methods, can be decorated with the attribute [Authorize], restricting users who can access the method by role or name. In the default ASP.NET MVC 2 template, when a user isn’t authorized to a specific area, he gets re-directed to the LogOn method on the AccountController.

So far so good. However, I ran into unexpected issues when I attempted to unit test that. Suppose there are two roles in our web application, Chicken and Pigs, and that we have a Controller that leads to a pigs-only area of the web site:

[Authorize(Roles = "Pig")]
public class PigsOnlyController : Controller
{
public ActionResult Index()
{
return View("Index");
}
}

My first thought was to mock the ControllerContext and do something along these lines:

[Test]
public void OnlyPigsShouldAccessIndex()
{
var context = new Mock<ControllerContext>();
context.SetupGet(p => p.HttpContext.Request.IsAuthenticated).Returns(true);
context.Setup(p => p.HttpContext.User.IsInRole("Pig")).Returns(true);

var controller = new PigsOnlyController();
controller.ControllerContext = context.Object;

// check what controller.Index() returns
}

However, while the web application itself behaved properly (Users in the Pig role get to the Index page, whereas Chicken get redirected to the Logon page), the test wasn’t doing what I expected: both Pigs and Chicken were happily reaching the Pigs-Only area.

As is often the case, I found out why on StackOverflow; the reason is that the re-direction is not the responsibility of the Controller. If the controller is properly decorated, the Index method won’t even be invoked, and where the call gets redirected to is handled in a different part.

So how do you unit test this behavior? In this case, we trust the framework to handle the redirection, so the only functionality we need to ascertain is that the Controller has the proper attribute.

Instead of validating the redirection, we can verify that the Controller class has an Authorize attribute, with the proper roles specified:

[Test]
public void ControllerShouldAuthorizePigsButNotChicken()
{
var information = typeof(PigsOnlyController);
var attributes = information.GetCustomAttributes(typeof(AuthorizeAttribute), false);
Assert.AreEqual(1, attributes.Length);

var authorization = attributes[0] as AuthorizeAttribute;
var authorizedRoles = authorization.Roles;

var roles = authorizedRoles.Split(',');
Assert.IsTrue(roles.Contains("Pig"));
Assert.IsFalse(roles.Contains("Chicken"));
}

I am not totally happy with the hard-coded strings “Pig” and “Chicken” in the test, but I don’t see a way around it; maybe it’s a sign that this test is more of an integration test than a unit test? If you know of a better way to test for that aspect, I am all ears!

20. May 2010 06:43

I gave a quick Firestarter talk at the San Francisco .Net user group yesterday about .less. .less (‘dot-less’) is an open source .Net library, which extends the functionality of CSS (it works with your existing CSS files), adding features like variables, using a syntax close to CSS. If you find that working with CSS causes some teeth-grinding , you should probably have a look!

6. November 2009 15:48

When I decided to have a 2-level horizontal menu for my professional webpage in ASP.NET, it came as a surprise to me that this wasn’t completely straightforward. I expected the standard  ASP menu control to support this, but found out that this wasn’t the case.

Fortunately, I came across a post by Peter Kellner, describing how he implemented that for the Silicon Valley Code Camp website, which was pretty much what I envisioned.

The one issue I had with his implementation, however, was that the second level menu uses multiple data sources. The Master Page handles the top-level menu, but each page contains a reference to the specific datasource used to populate the sub-menu. As a result, if you decide to add a page, you need to manually add to that page some code to define what sub-menu should show up, which is cumbersome.

The ideal solution for a lazy developer like me would be to have all the menus handled in the Master Page, so that when you add a new page to your website, you just need to add it to the Sitemap, and the right menu and sub-menu shows up.

More...

#### Need help with F#?

The premier team for
F# training & consulting.


text:
Various exercises related to the computation of areas of surfaces of revolution.

Find the surface area of the solid formed by revolving $y=2x$ on $[0,1]$ about the $x$-axis.
Find the surface area of the solid formed by revolving $y=x^2$ on $[0,1]$ about the $y$-axis.
To compute the integral, you will need to make a substitution like $u = 1 + 4x^2$ or something similar.
Find the surface area of the solid formed by revolving $y=x^3$ on $[0,1]$ about the $x$-axis.
To compute the integral, you will need to make a substitution like $u = 1 + 9 x^4$ or something similar.

### Sample Exam Questions

Give an integral formula for the area of the surface generated by revolving the curve $y = \ln x$ between $x=1$ and $x=2$ about the $y$-axis. Explain your answer. You do not need to evaluate the integral.
$\displaystyle \int _1^2 2 \pi \sqrt {x^2+1} ~ dx$ $\displaystyle \int _1^2 2 \pi (\ln x) \frac {\sqrt {x^2+1}}{x} ~ dx$ $\displaystyle \int _1^2 \frac {2 \pi }{x} \sqrt {1 + (\ln x)^2} ~ dx$ $\displaystyle \int _1^2 \frac {1}{2 \pi \sqrt {x^2+1}} ~ dx$ $\displaystyle \int _1^2 2 \pi (\ln x) \frac {x}{\sqrt {x^2+1}} ~ dx$ $\displaystyle \int _1^2 \frac {2 \pi x}{\sqrt {1 + (\ln x)^2}} ~ dx$
The curve $y = \frac {x^2}{8}$ between $x=0$ and $x = 3$ is revolved around the $y$-axis. Compute the surface area of the resulting surface.
$\displaystyle \frac {31 \pi }{6}$ $\displaystyle \frac {41 \pi }{6}$ $\displaystyle \frac {61 \pi }{6}$ $\displaystyle \frac {71 \pi }{6}$ $\displaystyle \frac {91 \pi }{6}$ none of the above


text:
# Make animated particle object start animation from the beginning when emitted?

So I made a sphere which rotates and scales and changes color. I wanna use it as a particle, which I can do.

So now I have a stream of spheres which rotate and scale in perfect sync. What I want is each sphere to begin rotating and scaling (from its own frame 1) at the moment it's duplicated.

A stream of spheres each growing and scaling sequentially.

How do I get an object to wait until the particle system duplicates it before animating?

• In my imagination there's a place to check [x] instatiate with offset from global timeline and furthermore [x] use a new instance of material so it only changes its own color. Ahh. Imagining. – ball2000 Oct 21 '14 at 23:55
• So... what I'm gonna end up doing for my rocket exhaust, is just have the rocket drag an actual train of my beautiful exhaust objects out of the ground using "Follow Path" and try to have them spin at just the right speed so each differently-colored traincar seems like new exhaust instead of part a moving train. Because particles made me cry. Yes I've seen the rocket exhaust examples they aren't the 'look' I want. – ball2000 Oct 22 '14 at 2:34
• Turned out ok ball2000.net/rocket.html (do people read these?) – ball2000 Oct 22 '14 at 7:45
• Some people do. BI or cycles? I'm thinking of particle lifetime in cycles to distort uv mapping. – sambler Oct 22 '14 at 8:02
• I tried cycles yesterday and I just couldn't even. So I guess it's Bl :) @sambler – ball2000 Oct 22 '14 at 8:41

I'm sorry to say that this feature, which was started on in 2011, was "nearly complete" in 2013 yet still seems like a distant dream. Some of the changes necessary for these updates were dependent on the dependency graph update, though. The depsgraph branch has had a lot of progress lately. Perhaps reading about dependencies will explain why things like this don't presently work out of the box; e.g. why you still can't "animate everything" as the 2.5 project advertised.

The latest update I can find in the same vein is that Lukas wrote a patch that allows you to use a particle's age to update a shader.

The best thing you can do to participate right now with in-progress projects like this is to get in contact with the specific developers that are working on the relevant infrastructures, and show them the problem you're trying to solve. Let them know you're interested, try their test branches, test out experimental versions, etc, and if you're feeling bold, look at their code.

• Anything more on this yet? – VRM Oct 16 '15 at 20:14
• Lukas's blog hasn't been updated since 2012. You could dig through his twitter and find clues that he's still interested, but that doesn't guarantee activity. twitter.com/lukastoenne – Wray Bowling Oct 23 '15 at 15:22

If you are up to a lot of work this is possible in Blender. You will need to create a group of objects (your spheres). Each sphere will become a particle and emitted in reverse order, you can adjust the order but just be mindful that by default it is last created first emitted.

Giving each particle a particular property - in my example a different color but you might change or offset an animation. This is when you make the calculations to time everything to the particle emissions.

In my example I have 8 spheres to be emitted over 24 frames (1 every 3 frames). Maybe someone can give you a better example of how to change the color on larger sets... Offset animated color change over many objects?

I recently did this with a butterfly animation that has 1200 butterflies.

Because the flapping of the wings is looped over 10 frames I required 10 butterflies in the group offset by 1 frame. I then created 3 particles so that not all of the butterflies took off together. As I didn't want the butterflies to be flapping whilst landed I removed the cyclic animation and manually repeated the flapping from after particle launch. Prior to particle launch I slowed the flapping of some and turned the flapping off for others. I then timed and rendered the 3 particles separately giving each particles their own seed value.

But yes a magic button that can "Use Animation of object as starting life of particle" will be a nice feature.

It's probably too late but I just did a similar thing with butterflies. I made a butterfly, animated it with shapekeys, changed the min & max values of the keys to -1 & 1, then I added a keyframe for the shapekey on frame 0 (you do not care about the value). In the graph editor I added a 'sinus' modifier on the key value and voilà, the butterfly moves the wings in a loop. The magic thing with this method is that you can now use the butterfly as a particle, the loop won't be sync for all the butterflies since the movement of the wings is not hardcoded but calculated (I think).

Only one butterfly & only one particle system, but many many variations...

I didn't tested it, but if it works for shapekey values, it should also work for bone rotations, or translations.

Now I'm trying to make them landed at start and fly away when a dummy comes close to them...

I think you would need multiple particle systems with each firing at the desired frame. Set each one for the object you want for that particle system. If it set to start and stop on frame 10, only one object will emit at 10. You just need to time the emitter so it comes out right. You can fine tune the frame to 3 decimal places.

• – ball2000 Oct 30 '14 at 9:31
• Oh wait, that's multiple emitters but you said multiple systems... Nope, no different with multiple 'systems' – ball2000 Oct 30 '14 at 9:32


text:
# Fermi nuclear model

1. Jun 30, 2011

### Sebastian

1. The problem statement, all variables and given/known data

This question is about the Fermi nuclear model (see Das & Ferbel page 56 or http://www.e12.physik.tu-muenchen.de/stud/vorlesungen/fabbietti/WS2007/Lecture3.pdf" [Broken]). Let the nucleon mass be $m$, the number of nucleons be $A$ and the number of protons be $Z$. Assume a hypothetical situation where the only difference between the proton and the neutron is that the proton has magnetic moment $\mu_p$ and the neutron has magnetic moment $\mu_n$. The nucleus is placed in a magnetic field $B$. Assume also that the protons and neutrons may align the directions of their magnetic moments such that energy is minimized.

A. Find a formula connecting the Fermi energy of the protons with that of the neutrons.
B. Find a formula connecting the Fermi momentum of the protons with that of the neutrons.

2. Relevant equations

I think the binding energy of a nucleon should be $-\mu B$. However, I don't see how to continue from here.


text:
# Why does this give me an "Ambiguous paths to For Each in xxxxxx"

I am utterly confused by getting this error and have tried everything... what's wrong?

Hi ClausS,

Notice the arrows that say "Cycle". They are pointing the wrong way on the second and third foreach. Switch them with the arrows that don't have text and it will work.

Regards,


text:
WIKISKY.ORG
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# π Sgr (Albaldah)

Contents

### Images

DSS Images   Other Images

### Related articles

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Lithium and rotation in F and G dwarfs and subgiantsLithium abundances have been determined in 127 F and G Pop I stars basedon new measurements of the equivalent width of the lambda 6707 ÅLi I line from their high resolution CCD spectra. Distances and absolutemagnitudes of these stars have been obtained from the HipparcosCatalogue and their masses and ages derived, enabling us to investigatethe behaviour of lithium as a function of these parameters. Based ontheir location on the HR diagram superposed on theoretical evolutionarytracks, the sample of the stars has been chosen to ensure that they havemore or less completed their Li depletion on the main sequence. A largespread in the Li abundances is found at any given effective temperatureespecially in the already spun down late F and early G stars. Thisspread persists even if the Li-dip'' stars that have evolved from themain sequence temperature interval 6500-6800 K are excluded. Stars inthe mass range up to 2 M/Msun when divided into threemetallicity groups show a linear correlation between Li abundance andmass, albeit with a large dispersion around it which is not fullyaccounted for by age either. The large depletions and the observedspread in Li are in contrast to the predictions of the standard stellarmodel calculations and suggest that they are aided by non-standardprocesses depending upon variables besides mass, age and metallicity.The present study was undertaken to examine, in particular, the effectsof rotation on the depletion of Li. No one-to-one correlation is foundbetween the Li abundance and the present projected rotational velocity.Instead the observed abundances seem to be dictated by the rotationalhistory of the star. However, it is noted that even this interpretationis subject to the inherent limitation in the measurement of the observedLi EQW for large rotational velocities.Table 1 is only available in electronic form at the CDS via anonymousftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/409/251 Observations of H3 in the Diffuse Interstellar MediumSurprisingly large column densities of H+3 havebeen detected using infrared absorption spectroscopy in seven diffusecloud sight lines (Cygnus OB2 12, Cygnus OB2 5, HD 183143, HD 20041, WR104, WR 118, and WR 121), demonstrating that H+3is ubiquitous in the diffuse interstellar medium. Using the standardmodel of diffuse cloud chemistry, our H+3 columndensities imply unreasonably long path lengths (~1 kpc) and lowdensities (~3 cm-3). Complimentary millimeter-wave, infrared,and visible observations of related species suggest that the chemicalmodel is incorrect and that the number density ofH+3 must be increased by 1-2 orders of magnitude.Possible solutions include a reduced electron fraction, an enhanced rateof H2 ionization, and/or a smaller value of theH+3 dissociative recombination rate constant thanimplied by laboratory experiments. Line-strength indices and velocity dispersions for 148 early-type galaxies in different environmentsWe have derived high quality line-strength indices and velocitydispersions for a sample of 148 early-type galaxies in differentenvironments. The wavelength region covered by the observations (lambda=~ 4600 to 6600 Å) includes the Lick/IDS indices Hβ,Mg1, Mg2, Mgb, Fe5015, Fe5270, Fe5335, Fe5406,Fe5709, Fe5782, NaD, TiO1 and TiO2. The data areintended to address possible differences of the stellar populations ofearly-type galaxies in low- and high-density environments. This paperdescribes the sample properties, explains the data reduction andpresents the complete list of all the measurements. Most galaxies of thesample (85%) had no previous measurements of any Lick/IDS indices andfor 30% of the galaxies we present first-time determinations of theirvelocity dispersions. Special care is taken to identify galaxies withemission lines. We found that 62 per cent of the galaxies in the samplehave emission lines, as measured by the equivalent width of the [OIII]5007Å line, EW[OIII] > 0.3 Å. Tables 5 and 6 are onlyavailable in electronic form at the CDS via anonymous ftp tocdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/ A+A/395/431. They are also available via ftp atftp.mpe.mpg.de in the directory people/dthomas/Beuing02 or via WWW atftp://ftp.mpe.mpg.de/people/dthomas/Beuing02. UBVRIJH photometry of two new luminous δ Scuti stars and the discovery of δ Scuti pulsation in the most evolved Ap star knownTime-series photometry of the Hipparcos variable stars HD 199434 and21190 is reported. Both stars are pulsators of the δ Scuti type.Reclassifications of the MK types of the stars, based on newspectrograms, are given. HD 21190 is found to be F2III SrEuSi:, makingit the most evolved Ap star known. Its Strömgren photometricindices support the peculiar spectral type. It is also one of the mostevolved δ Scuti stars known. Its combined Ap-δ Scuti naturemakes it an important test of models of pulsation in peculiar starsrecently developed by Turcotte et al., although it is more extreme thanany model they examined. Physical parameters of both stars are estimatedfrom Strömgren and Hβ photometry, and Hipparcos absolutemagnitudes. We attempt mode identifications based on amplitude ratiosand phase differences from our photometry. The dominant pulsation of HD21190 may be an overtone radial mode. The model fits for HD 199434 areeven less satisfactory, but favour an l=2 mode. Given the good qualityand wavelength coverage of our data, the poor results from theapplication of the photometric theory of mode identification may callinto question the use of that technique. Catalogue of Apparent Diameters and Absolute Radii of Stars (CADARS) - Third edition - Comments and statisticsThe Catalogue, available at the Centre de Données Stellaires deStrasbourg, consists of 13 573 records concerning the results obtainedfrom different methods for 7778 stars, reported in the literature. Thefollowing data are listed for each star: identifications, apparentmagnitude, spectral type, apparent diameter in arcsec, absolute radiusin solar units, method of determination, reference, remarks. Commentsand statistics obtained from CADARS are given. The Catalogue isavailable in electronic form at the CDS via anonymous ftp tocdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcar?J/A+A/367/521 Research Note Hipparcos photometry: The least variable starsThe data known as the Hipparcos Photometry obtained with the Hipparcossatellite have been investigated to find those stars which are leastvariable. Such stars are excellent candidates to serve as standards forphotometric systems. Their spectral types suggest in which parts of theHR diagrams stars are most constant. In some cases these values stronglyindicate that previous ground based studies claiming photometricvariability are incorrect or that the level of stellar activity haschanged. Table 2 is only available in electronic form at the CDS viaanonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/367/297 The proper motions of fundamental stars. I. 1535 stars from the Basic FK5A direct combination of the positions given in the HIPPARCOS cataloguewith astrometric ground-based catalogues having epochs later than 1939allows us to obtain new proper motions for the 1535 stars of the BasicFK5. The results are presented as the catalogue Proper Motions ofFundamental Stars (PMFS), Part I. The median precision of the propermotions is 0.5 mas/year for mu alpha cos delta and 0.7mas/year for mu delta . The non-linear motions of thephotocentres of a few hundred astrometric binaries are separated intotheir linear and elliptic motions. Since the PMFS proper motions do notinclude the information given by the proper motions from othercatalogues (HIPPARCOS, FK5, FK6, etc.) this catalogue can be used as anindependent source of the proper motions of the fundamental stars.Catalogue (Table 3) is only available at the CDS via anonymous ftp tocdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strastg.fr/cgi-bin/qcat?J/A+A/365/222 On the Variability of A6 to F9 SupergiantsHipparcos Satellite photometry of A6 to F9 supergiants reveals theiractivity. A few are especially quiescient. A0-A5II stars are examinedto help connect this study with that of earlier supergiants. Ca II activity and rotation in F-K evolved starsCa II H and K high resolution observations for 60 evolved stars in thefield and in 5 open clusters are presented. From these spectrachromospheric fluxes are derived, and a homogeneous sample of more than100 giants is built adding data from the literature. In addition, formost stars, rotational velocities were derived from CORAVELobservations. By comparing chromospheric emission in the cluster starswe confirm the results of Pasquini & Brocato (1992): chromosphericactivity depends on the stellar effective temperature, and mass, whenintermediate mass stars (M ~ 4 Msun) are considered. TheHyades and the Praesepe clump giants show the same level of activity, asexpected from stars with similar masses and effective temperatures. Adifference of up to 0.4 dex in the chromospheric fluxes among the Hyadesgiants is recorded and this sets a clear limit to the intrinsic spreadof stellar activity in evolved giants. These differences in otherwisevery similar stars are likely due to stellar cycles and/or differencesin the stellar initial angular momentum. Among the field stars none ofthe giants with (V-R)o < 0.4 and Ia supergiants observedshows a signature of Ca II activity; this can be due either to the realabsence of a chromosphere, but also to other causes which preclude theappearance of Ca II reversal. By analyzing the whole sample we find thatchromospheric activity scales linearly with stellar rotational velocityand a high power of stellar effective temperature: F'k ~Teff7.7 (Vsini)0.9. This result can beinterpreted as the effect of two chromospheric components of differentnature: one mechanical and one magnetic. Alternatively, by using theHipparcos parallaxes and evolutionary tracks, we divide the sampleaccording to the stellar masses, and we follow the objects along anevolutionary track. For each range of masses activity can simply beexpressed as a function of only one parameter: either theTeff or the angular rotation Omega , with laws F'k~ Omega alpha , because angular velocity decreases witheffective temperature along an evolutionary track. By using theevolutionary tracks and the observed Vsini we investigate the evolutionof the angular momentum for evolved stars in the range 1-5Msun. For the 1.6-3 solar mass stars the data are consistentwith the IOmega =const law while lower and higher masses follow a lawsimilar to IOmega 2=const, where I is the computed stellarmomentum of inertia. We find it intriguing that Vsini remains almostconstant for 1Msun stars along their evolution; if a similarbehavior is shared by Pop II stars, this could explain the relativelyhigh degree of activity observed in Pop II giants. Finally, through theuse of models, we have verified the consistency of the F'k ~Omega alpha and the IOmega beta = Const lawsderived, finding an excellent agreement. This representation, albeitcrude (the models do not consider, for instance, mass losses) representsthe evolution of Ca II activity and of the angular momentum in asatisfactory way in most of the portion of HR diagram analyzed.Different predictions could be tested with observations in selectedclusters. Based on observations collected at ESO, La Silla. Tables 1-3are only available in electronic form at the CDS via anonymous ftp tocdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/Abstract.html A Second Catalog of Orbiting Astronomical Observatory 2 Filter Photometry: Ultraviolet Photometry of 614 StarsUltraviolet photometry from the Wisconsin Experiment Package on theOrbiting Astronomical Observatory 2 (OAO 2) is presented for 614 stars.Previously unpublished magnitudes from 12 filter bandpasses withwavelengths ranging from 1330 to 4250 Å have been placed on thewhite dwarf model atmosphere absolute flux scale. The fluxes wereconverted to magnitudes using V=0 for F(V)=3.46x10^-9 ergs cm^-2 s^-1Å^-1, or m_lambda=-2.5logF_lambda-21.15. This second catalogeffectively doubles the amount of OAO 2 photometry available in theliterature and includes many objects too bright to be observed withmodern space observatories. The Tokyo PMC catalog 90-93: Catalog of positions of 6649 stars observed in 1990 through 1993 with Tokyo photoelectric meridian circleThe sixth annual catalog of the Tokyo Photoelectric Meridian Circle(PMC) is presented for 6649 stars which were observed at least two timesin January 1990 through March 1993. The mean positions of the starsobserved are given in the catalog at the corresponding mean epochs ofobservations of individual stars. The coordinates of the catalog arebased on the FK5 system, and referred to the equinox and equator ofJ2000.0. The mean local deviations of the observed positions from theFK5 catalog positions are constructed for the basic FK5 stars to comparewith those of the Tokyo PMC Catalog 89 and preliminary Hipparcos resultsof H30. The Angular Momentum of Main Sequence Stars and Its Relation to Stellar ActivityRotational velocities are reported for intermediate-mass main sequencestars it the field. The measurements are based on new, high S/N CCDspectra from the Coudé Feed Telescope of the Kitt Peak NationalObservatory. We analyze these rotation rates for a dependence on bothmass and age. We compare the average rotation speeds of the field starswith mean velocities for young stars in Orion, the Alpha Persei cluster,the Pleiades, and the Hyades. The average rotation speeds of stars moremassive than $\sim1.6$ \msun\experience little or no change during theevolutionary lifetimes of these stars on the zero age main sequence orwithin the main sequence band. Less massive stars in the range betwee n1.6\msun\ and 1.3\msun\ also show little decline in mean rotation ratewhile they are on the main sequence, and at most a factor of 2 decreasein velocity as they evolve off the main sequence. The {\it e}-foldingtime for the loss of angular momentum b y the latter group of stars isat least 1--2 billion years. This inferred characteristic time scale forspindown is far longer than the established rotational braking time forsolar-type stars with masses below $\sim1.3$ \msun. We conclude from acomparison of the trends in rotation with trends in chromospheric andcoronal activity that the overall decline in mean rotation speed alongthe main sequence, from $\sim2$ \msun\ down to $\sim1.3$ \msun, isimposed during the pre-main sequence phase of evolution, and that thispattern changes little thereafter while the star resides on the mainsequence. The magnetic activity implicated in the rotational spindown ofthe Sun and of similar stars during their main sequence lifetimes mus ttherefore play only a minor role in determining the rotation rates ofthe intermediate mass stars, either because a solar-like dynamo is weakor absent, or else the geometry of the magnetic field is appreciablyless effective in removing angular momentu m from these stars. (SECTION:Stars) A catalogue of [Fe/H] determinations: 1996 editionA fifth Edition of the Catalogue of [Fe/H] determinations is presentedherewith. It contains 5946 determinations for 3247 stars, including 751stars in 84 associations, clusters or galaxies. The literature iscomplete up to December 1995. The 700 bibliographical referencescorrespond to [Fe/H] determinations obtained from high resolutionspectroscopic observations and detailed analyses, most of them carriedout with the help of model-atmospheres. The Catalogue is made up ofthree formatted files: File 1: field stars, File 2: stars in galacticassociations and clusters, and stars in SMC, LMC, M33, File 3: numberedlist of bibliographical references The three files are only available inelectronic form at the Centre de Donnees Stellaires in Strasbourg, viaanonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5), or viahttp://cdsweb.u-strasbg.fr/Abstract.html MSC - a catalogue of physical multiple starsThe MSC catalogue contains data on 612 physical multiple stars ofmultiplicity 3 to 7 which are hierarchical with few exceptions. Orbitalperiods, angular separations and mass ratios are estimated for eachsub-system. Orbital elements are given when available. The catalogue canbe accessed through CDS (Strasbourg). Half of the systems are within 100pc from the Sun. The comparison of the periods of close and widesub-systems reveals that there is no preferred period ratio and allpossible combinations of periods are found. The distribution of thelogarithms of short periods is bimodal, probably due to observationalselection. In 82\% of triple stars the close sub-system is related tothe primary of a wide pair. However, the analysis of mass ratiodistribution gives some support to the idea that component masses areindependently selected from the Salpeter mass function. Orbits of wideand close sub-systems are not always coplanar, although thecorresponding orbital angular momentum vectors do show a weak tendencyof alignment. Some observational programs based on the MSC aresuggested. Tables 2 and 3 are only available in electronic form at theCDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/Abstract.html The Pulkovo Spectrophotometric Catalog of Bright Stars in the Range from 320 TO 1080 NMA spectrophotometric catalog is presented, combining results of numerousobservations made by Pulkovo astronomers at different observing sites.The catalog consists of three parts: the first contains the data for 602stars in the spectral range of 320--735 nm with a resolution of 5 nm,the second one contains 285 stars in the spectral range of 500--1080 nmwith a resolution of 10 nm and the third one contains 278 stars combinedfrom the preceding catalogs in the spectral range of 320--1080 nm with aresolution of 10 nm. The data are presented in absolute energy unitsW/m(2) m, with a step of 2.5 nm and with an accuracy not lower than1.5--2.0%. Chemical composition of the components of the binary Am star β AurNot Available Chemical Abundances for F and G Luminosity Class II StarsAbstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1995AJ....110.2425L&db_key=AST Vitesses radiales. Catalogue WEB: Wilson Evans Batten. Subtittle: Radial velocities: The Wilson-Evans-Batten catalogue.We give a common version of the two catalogues of Mean Radial Velocitiesby Wilson (1963) and Evans (1978) to which we have added the catalogueof spectroscopic binary systems (Batten et al. 1989). For each star,when possible, we give: 1) an acronym to enter SIMBAD (Set ofIdentifications Measurements and Bibliography for Astronomical Data) ofthe CDS (Centre de Donnees Astronomiques de Strasbourg). 2) the numberHIC of the HIPPARCOS catalogue (Turon 1992). 3) the CCDM number(Catalogue des Composantes des etoiles Doubles et Multiples) byDommanget & Nys (1994). For the cluster stars, a precise study hasbeen done, on the identificator numbers. Numerous remarks point out theproblems we have had to deal with. SANTIAGO 91, a right ascension catalogue of 3387 stars (equinox J2000).The positions in right ascension of 3387 stars belonging to the Santiago67 Catalogue, observed with the Repsold Meridian Circle at Cerro Calan,National Astronomical Observatory, during the period 1989 to 1994, aregiven. The average mean square error of a position, for the wholeCatalogue, is +/-0.009 s. The mean epoch of the catalogue is 1991.84. The position corrections of 1400 stars observed with PA II in San Juan.Not Available Second astrolabe catalogue of Santiago.Positions for 350 FK5 and 164 FK5 Extension stars as determined with theDanjon astrolabe of Santiago and differences astrolabe-catalogue aregiven for Equinox J2000.0 and for the mean observation epoch of eachstar. The average mean error in alpha is +/-0.005s and +/-0.07" indelta. The mean epoch of observation of the catalogue is J1979.96. The second Quito astrolabe catalogueThe paper contains 515 individual corrections {DELTA}α and 235corrections {DELTA}δ to FK5 and FK5Supp. stars and 50 correctionsto their proper motions computed from observations made with theclassical Danjon astrolabe OPL-13 at Quito Astronomical Observatory ofEcuador National Polytechnical School during a period from 1964 to 1983.These corrections cover the declination zone from -30deg to +30deg. Meanprobable errors of catalogue positions are 0.047" in αcosδand 0.054" in δ. The systematic trends of the catalogue{DELTA}αalpha_cosδ,{DELTA}αdelta_cosδ,{DELTA}δalpha_, {DELTA}δdelta_ arepresented for the observed zone. Corrections to the right ascension to be applied to the apparent places of 1217 stars given in "The Chinese Astronomical Almanach" for the year 1984 to 1992.Not Available Santiago Fundamental Catalogue - A catalogue of 1105 FK5 stars (equinox J2000.0)The positions in right ascension and declination of 1105 FK5 stars,observed with a Meridian Circle during the period 1979 to 1991, aregiven. The average mean square error of a position, for the wholecatalog, is +/- 0.009 s in right ascension and +/- 0.10 arcsec indeclination. The mean epoch of the catalog is 1983.148. CA II H and K measurements made at Mount Wilson Observatory, 1966-1983Summaries are presented of the photoelectric measurements of stellar CaII H and K line intensity made at Mount Wilson Observatory during theyears 1966-1983. These results are derived from 65,263 individualobservations of 1296 stars. For each star, for each observing season,the maximum, minimum, mean, and variation of the instrumental H and Kindex 'S' are given, as well as a measurement of the accuracy ofobservation. A total of 3110 seasonal summaries are reported. Factorswhich affect the ability to detect stellar activity variations andaccurately measure their amplitudes, such as the accuracy of the H and Kmeasurements and scattered light contamination, are discussed. Relationsare given which facilitate intercomparison of 'S' values with residualintensities derived from ordinary spectrophotometry, and for convertingmeasurements to absolute fluxes. The stellar temperature scale for stars of spectral types from O8 to F6 and the standard deviation of the MK spectral classificationEmpirical effective temperature of 211 early-type stars found in aprevious investigation (Kontizas and Theodossiou, 1980; Theodossiou,1985) are combined with the effective temperatures of 313 early-typestars from the literature. From these effective temperatures of a totalnumber of 524 early-type stars of spectral types from O8 to F6 a newstellar temperature scale is developed along with the standard deviationof the MK spectral classification. JHKLM standard stars in the ESO systemA list of 199 standard stars suitable for the ESO standard photometricsystem at JHKLM is given. Faint stars (although brighter than K = 7.7)to be used on larger telescopes are included. This list is based on ananalysis of all infrared photometric observations carried out at LaSilla from 1979 until 1989 inclusive. The accuracy of the data (about0.02 mag. at J, H, K, L, and M) is similar to the one achieved at SAAOand CTIO. Comparisons with these systems, as well as with the AAO andMSSO systems, are made: it is shown that the ESO system is very close tothe other ones, with the exception of CTIOs. Near-IR imaging and spectroscopy of GGD27 - IRSSeeing limited near-IR imaging photometry and polarimetry of the IRreflection nebula GGD27 - IRS are presented in order to investigate thesource's peculiar morphology and detail its photometric and polarimetricproperties. IRS2, previously thought to be the source of illumination ofthe nebula, is shown to be a bright knot of emission at the apex of thenorthern lobe of the bipolar-shaped nebula. It is inferred from theobserved polarimetric pattern and from evidence from narrow-band imagingand 3-micron spectroscopy that the source of illumination of much of thenebula, and therefore the source of the associated bipolar molecularoutflow, is an unseen stellar object situated approximately 3 arcsec SWof IRS2. Estimates of the optical depth and visual extinction in theregion are also presented. It is proposed that the nebula/outflow isaligned close to the plane of the sky and both a large-scale'interstellar' disk and small-scale 'circumstellar' disk or envelopeobscure the central illuminating source from direct view. Physical data of the fundamental stars.Not Available
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 Constellation: Sagittarius Right ascension: 19h09m45.80s Declination: -21Â°01'25.0" Apparent magnitude: 2.89 Distance: 134.953 parsecs Proper motion RA: 0 Proper motion Dec: 0 B-T magnitude: 3.296 V-T magnitude: 2.903

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 Proper Names Albaldah   (Edit) Bayer π Sgr Flamsteed 41 Sgr HD 1989 HD 178524 TYCHO-2 2000 TYC 6295-282-1 USNO-A2.0 USNO-A2 0675-31855712 BSC 1991 HR 7264 HIP HIP 94141 → Request more catalogs and designations from VizieR