text:
# [R-sig-ME] Numerical methods used to compute correlation coefficients

Douglas Bates bates at stat.wisc.edu
Thu Apr 16 23:42:26 CEST 2009

On Thu, Apr 16, 2009 at 3:33 PM, H c <harlancampbell at gmail.com> wrote:
> Thank you for the detailed answer.  The reason I ask, is that I am
> attempting to fit a mixture of mixed models to a dataset using the standard
> EM approach.  Exceptionally, the mixed models have AR(1) correlation.  I
> have been able to do the math and arrive at maximum-likelihood solutions
> using an R implementation I wrote.  However, the step that numerically
> calculates the \phi correlation coefficient(currently using optimize()) is
> extremely computationally expensive and thus makes any implementation of the
> algorithm on a large dataset impossible.
> I have attempted a few things in order to speed up estimation including
> transforming the data and maximizing the profiled likelihood rather then the
> likelihood.  Unfortunately, no success.  I have also tried using nlminb()
> rather then optimize.  Still incredibly slow.
> Would you have any suggestions as to how one could numerically obtain
> maximum-weighted-likelihood estimates for correlation parameters in a
> reasonable amount of time?
> Any suggestions would be greatly appreciated.

I'm afraid I don't have any immediate suggestions.  As you have seen,
there is a great deal of difference between writing some equations and
getting a working algorithm that is both robust and effective.  I
spent a considerable amount of time working with the EM algorithm and
variations like the ECME algorithm or the calculation of gradients of
the log-likelihood function with respect to some of the parameters
(these calculations are related to the EM algorithm).  In fact, I
would say that some of the best mathematics I have done was in
obtaining "simple" expressions for these quantities.

Unfortunately I found that in the implementation the use of ECME or
the analytic gradient just slowed down the convergence on large
complex problems.  Once I discovered that I could work out why it
happened but it was a disappointment to do such wonderful mathematics
and discover that it was for naught.

>
>  Wed, Apr 15, 2009 at 3:30 PM, Douglas Bates <bates at stat.wisc.edu> wrote:
>>
>> On Wed, Apr 15, 2009 at 1:14 PM, H c <harlancampbell at gmail.com> wrote:
>>
>> > Thank you.  This  is exactly what I wanted to know.  Perhaps one last
>> > question.  Is there any particular reason to prefer  this optimization
>> > routine over another, such as "optimize()"?
>>
>> optimize() only handles scalar problems and you must define an
>> interval in which the optimum is to be found.
>>
>> I have used other unconstrained optimizers such as nlm() and optim()
>> but had trouble with both of those.  The original version of the nlme
>> package for S and S-PLUS used the ms() optimizer in S which was based
>> on some Fortran code by David Gay.  Initially that code could not be
>> used in R because it was not released under an open source license.
>> Eventually it was released to the public domain and I wrote the nlminb
>> interface code for R, primarily so I could use it as the optimizer in
>> the nlme and lme4 packages.
>>
>> Even this code by David Gay is far from ideal.  The development
>> version of the lme4 package factors out the evaluation of the deviance
>> function or the REML criterion from the optimization of these, so that
>> those who are interested can experiment with different optimizers and
>> see what works best in their problems.
>>
>> > On Wed, Apr 15, 2009 at 12:59 PM, Douglas Bates <bates at stat.wisc.edu>
>> > wrote:
>> >>
>> >> On Tue, Apr 14, 2009 at 12:02 PM, H c <harlancampbell at gmail.com> wrote:
>> >> > Thank you for the quick response.
>> >> > when I refer to "correlation parameters", I mean the "generally small
>> >> > set of
>> >> > parameters \lambda" that parametrize the \Lambda_{i}
>> >> > Variance-Covariance
>> >> > matrix.
>> >> > For example, one has time series data such that every subject has
>> >> > been
>> >> > observed at 4 time points.  One wishes to model this using an AR(1)
>> >> > correlation structure within the mixed model.
>> >> > the AR(1) is parametrized by a fixed parameter, \phi :
>> >> > lme(y~X, random=~1|ID, method="ML", data=data,
>> >> > correlation=corAR1(0.5,form=~X,fixed=FALSE))
>> >>
>> >> > Since there is no closed form solution for the maximum-likelihood
>> >> > estimate
>> >> > of \phi.  what numerical methods are used to arrive at the given
>> >> > estimate?
>> >> > Hopefully this has clarified my question.
>> >>
>> >> In the sense that I know what you mean by the correlation parameters.
>> >> I'm not sure how to characterize the numerical methods other than to
>> >> say that the deviance (negative twice the log-likelihood) or the
>> >> corresponding version of the REML criterion is expressed with respect
>> >> to an unconstrained parameter and the resulting function optimized
>> >> using optimization software within R (nlminb).  You can check the
>> >> definition of the corAR family to determine exactly how the
>> >> parameterization is defined.
>> >>
>> >> > Thanks again,
>> >> > Harlan
>> >> >
>> >> > On Tue, Apr 14, 2009 at 12:37 PM, Douglas Bates <bates at stat.wisc.edu>
>> >> > wrote:
>> >> >>
>> >> >> On Tue, Apr 14, 2009 at 9:20 AM, H c <harlancampbell at gmail.com>
>> >> >> wrote:
>> >> >> > I have have already posted the following question:  What numerical
>> >> >> > methods
>> >> >> > are used in nlme to estimate correlation parameters?
>> >> >> > I was referred to the Pinheiro and Bates book.  Unfortunately, on
>> >> >> > p.
>> >> >> > 202,
>> >> >> > section 5.1.1, under the title "Estimation and Computational
>> >> >> > Methods",
>> >> >> > no
>> >> >> > description on a numerical method is provided.  (When the data is
>> >> >> > transformed to work with the profiled likelihood(y->ystar), one
>> >> >> > needs
>> >> >> > the
>> >> >> > parameters that define Lambda.  How are these parameters
>> >> >> > estimated?)
>> >> >>
>> >> >> I'm not sure what you mean by "correlation parameters".  If you mean
>> >> >> the correlation parameters in the unconditional distribution of the
>> >> >> random effects then those are estimated by maximum likelihood (ML)
>> >> >> or
>> >> >> residual maximum likelihood (REML).  The profiled deviance or the
>> >> >> profiled REML criterion is evaluated with respect to a transformed
>> >> >> set
>> >> >> of parameters and this value is optimized.
>> >> >
>> >> >
>> >
>> >
>
>


text:
# DAVIDSTUTZ

## Matrix Decompositions Demonstrated in PHP

This article presents an application demonstrating common used matrix decompositions and their applications implemented in PHP.

Matrix decompositions are used in numerical analysis to solve a wide range of problems. Throuhgout a course of numerical analysis at university I found myself implementing some of the corresponding algorithms in PHP - which is a very unusual programming language for numerical purposes. I decided to put them together to form a small application demonstrating some common matrix decompositions and their usage. The project can be found on GitHub.

The following table gives an overview of the decompositions covered:

Decomposition Factorization Applicable for Runtime
LU $A = LU$ $A \in \mathbb{R}^{n \times n}$, $A$ regular $\mathcal{O}(\frac{1}{3}n^3)$
Cholesky $A = LDL^T$ $A \in \mathbb{R}^{n \times n}$, $A$ symmetric and positive definite $\mathcal{O}(\frac{1}{6}n^3)$
QR: Givens Rotations $A = QR$ $A \in \mathbb{R}^{m \times n}$ $\mathcal{O}(\frac{4}{3}n^3)$
QR: Householder Transformations $A = QR$ $A \in \mathbb{R}^{m \times n}$ $\mathcal{O}(\frac{2}{3}n^3)$

format: plain


text:
## Description

ZSoft Corp. is a software company in GaoKe Hall. And the workers in the hall are very hard-working. But the elevator in that hall always drives them crazy. Why? Because there is only one elevator in GaoKe Hall, while there are hundreds of companies in it. Every morning, people must waste a lot of time waiting for the elevator.

Hal, a smart guy in ZSoft, wants to change this situation. He wants to find a way to make the elevator work more effectively. But it’s not an easy job.

There are 31 floors in GaoKe Hall. It takes 4 seconds for the elevator to raise one floor. It means:

It costs (31-1)*4=120 seconds if the elevator goes from the 1st floor to the 31st floor without stop. And the elevator stops 10 second once. So, if the elevator stops at each floor, it will cost 30*4+29*10 = 410 seconds (It is not necessary to calculate the stopping time at 31st floor). In another way, it takes 20 seconds for the workers to go up or down one floor. It takes 30*20 = 600 seconds for them to walk from the 1st floor to the 31st floor. Obviously, it is not a good idea. So some people choose to use the elevator to get a floor which is the nearest to their office.

After thinking over for a long time, Hal finally found a way to improve this situation. He told the elevator man his idea: First, the elevator man asks the people which floors they want to go. He will then design a stopping plan which minimize the time the last person need to arrive the floor where his office locates. For example, if the elevator is required to stop at the 4th, 5th and 10th floor,the stopping plan would be: the elevator stops at 4th and 10th floor. Because the elevator will arrive 4th floor at 3*4 = 12 second, then it will stop 10 seconds, then it will arrive 10th floor at 3*4+10+6*4 = 46 second. People who want to go 4th floor will reach their office at 12 second, people who want to go to 5th floor will reach at 12+20 = 32 second and people who want to go to 10th floor will reach at 46 second. Therefore it takes 46 seconds for the last person to reach his office. It is a good deal for all people.

Now, you are supposed to write a program to help the elevator man to design the stopping plan,which minimize the time the last person needs to arrive at his floor.

## Input

The input consists of several testcases. Each testcase is in a single line as the following: n f1 f2 … fn

It means, there are totally n floors at which the elevator need to stop, and n = 0 means no testcases any more. f1 f2 … fn are the floors at which the elevator is to be stopped (n <= 30, 2 <= f1 < f2 … fn <= 31). Every number is separated by a single space.

## Output

For each testcase, output the time the last reading person needs in the first line and the stopping floors in the second line. Please note that there is a summary of the floors at the head of the second line. There may be several solutions, any appropriate one is accepted. No extra spaces are allowed.

## Source

Asia Guangzhou 2003

## Solution

1. 电梯决定停在第k层时：要去 1..k 层的人应选择在这时下电梯，这样一定可以得到当前决策下的一个最优解。如图：

1. 电梯在第k层时，若要去 k+r 层的人选择在这时下电梯，则：要去k+1..k+r-1层的人也应选择在此时下电梯，这样一定可以得到当前决策下的一个最优解。如图：

f[i,j]表示电梯在第i层，电梯上有要去楼层最高的j个人时，电梯上的人全部到达各自楼层所需的最短时间

f[i,j] = min{ max(t1, t2) } (0<=k<=j)

t1 = f[i+1, k] + 电梯停留时间 + 电梯上升一层所用时间

t2 = max{ |d[l] – i| * 人爬一层楼所用时间 } ( k+1<=l<=j )

#include <iostream>
using std::cin;
using std::cout;
using std::endl;

#include <cstring>
using std::memset;

#include <algorithm>
using std::max;

#include <cmath>
using std::abs;

#include <limits>
using std::numeric_limits;

#include <vector>
using std::vector;

const int maxN = 30, maxF = 31;
const int ve = 4, st = 10, vw = 20; // 电梯上一层所需时间；电梯停一层所需时间；人走一层所需时间

int n, f[maxN + 1];

bool input()
{
cin >> n;
if (n==0) return false;

// 注意：f[1..n]中楼层数从高到底排列
for (int i = n; i>=1; --i)
cin >> f[i];

return true;
}

int dp[maxF + 1][maxN + 1], nextJ[maxF + 1][maxN + 1];

// 现在电梯在第currF层，第L到第R人离开电梯
// 函数返回这些离开电梯的人中最晚到达目的楼层所需的时间
int tLeave(int currF, int l, int r)
{
if (l>r)  return 0;
// 仅需考虑两端
return max(abs(currF-f[l]), abs(currF-f[r])) * vw;
}

// 现在电梯在第i层，电梯里本来有j个人，在要下电梯的人离开后还剩jj个人
// 函数返回这些留在电梯里的人中最晚到达目的楼层所需的时间
int tStay(int i, int j, int jj)
{
// 没人下电梯
if (j==jj)
return dp[i+1][jj] + ve;
// 所有人都离开电梯
else if (jj==0)
return 0;
// 第1层不计算电梯停留时间
else if (i==1)
return dp[i+1][jj] + ve;
//普通情况
else
return dp[i+1][jj] + ve + st;
}

void calculate()
{
// 边界：电梯在顶楼时所有人都必须下电梯
int topFloor = f[1];
for (int j = 1; j<=n; ++j)
dp[topFloor][j] = tLeave(topFloor,1,j);

for (int i = topFloor - 1; i>=1; --i)
for (int j = 1; j<=n; ++j)
{
dp[i][j] = numeric_limits<int>::max();
for (int jj = 0; jj <= j; ++jj)
{
// 取离开电梯的人和留下的人中的最晚到达者
int tmp = max(tStay(i,j,jj),tLeave(i,jj+1,j));
if (dp[i][j] > tmp)
{
dp[i][j] = tmp;
nextJ[i][j] = jj;
}
}
}
cout << dp[1][n] << endl;
}

void rebuildSolution()
{
vector<int> stops;
int j = nextJ[1][n], topFloor = f[1];
for (int i = 2; i<=topFloor; ++i)
if (nextJ[i][j]!=j)
{
stops.push_back(i);
j = nextJ[i][j];
if (j==0) break;
}

cout << stops.size();
for (int i = 0; i!=stops.size(); ++i)
cout << ' ' << stops[i];
cout << endl;
}

void solve()
{
memset(dp,0,sizeof(dp));
memset(nextJ,0,sizeof(nextJ));
calculate();
rebuildSolution();
}

int main()
{
while (input())
solve();
}


text:
Distance-transitive graph

The Biggs-Smith graph, the largest 3-regular distance-transitive graph.
 Graph families defined by their automorphisms distance-transitive ${\displaystyle {\boldsymbol {\rightarrow }}}$ distance-regular ${\displaystyle {\boldsymbol {\leftarrow }}}$ strongly regular ${\displaystyle {\boldsymbol {\downarrow }}}$ symmetric (arc-transitive) ${\displaystyle {\boldsymbol {\leftarrow }}}$ t-transitive, t ≥ 2 skew-symmetric ${\displaystyle {\boldsymbol {\downarrow }}}$ (if connected) vertex- and edge-transitive ${\displaystyle {\boldsymbol {\rightarrow }}}$ edge-transitive and regular ${\displaystyle {\boldsymbol {\rightarrow }}}$ edge-transitive ${\displaystyle {\boldsymbol {\downarrow }}}$ ${\displaystyle {\boldsymbol {\downarrow }}}$ ${\displaystyle {\boldsymbol {\downarrow }}}$ vertex-transitive ${\displaystyle {\boldsymbol {\rightarrow }}}$ regular ${\displaystyle {\boldsymbol {\rightarrow }}}$ (if bipartite) biregular ${\displaystyle {\boldsymbol {\uparrow }}}$ Cayley graph ${\displaystyle {\boldsymbol {\leftarrow }}}$ zero-symmetric asymmetric

In the mathematical field of graph theory, a distance-transitive graph is a graph such that, given any two vertices v and w at any distance i, and any other two vertices x and y at the same distance, there is an automorphism of the graph that carries v to x and w to y.

A distance transitive graph is vertex transitive and symmetric as well as distance regular.

A distance-transitive graph is interesting partly because it has a large automorphism group. Some interesting finite groups are the automorphism groups of distance-transitive graphs, especially of those whose diameter is 2.

Distance-transitive graphs were first defined in 1971 by Norman L. Biggs and D. H. Smith, who showed that there are only 12 finite trivalent distance-transitive graphs. These are:

Graph name Vertex count Diameter Girth Intersection array
complete graph K4 4 1 3 {3;1}
complete bipartite graph K3,3 6 2 4 {3,2;1,3}
Petersen graph 10 2 5 {3,2;1,1}
Graph of the cube 8 3 4 {3,2,1;1,2,3}
Heawood graph 14 3 6 {3,2,2;1,1,3}
Pappus graph 18 4 6 {3,2,2,1;1,1,2,3}
Coxeter graph 28 4 7 {3,2,2,1;1,1,1,2}
Tutte–Coxeter graph 30 4 8 {3,2,2,2;1,1,1,3}
Graph of the dodecahedron 20 5 5 {3,2,1,1,1;1,1,1,2,3}
Desargues graph 20 5 6 {3,2,2,1,1;1,1,2,2,3}
Biggs-Smith graph 102 7 9 {3,2,2,2,1,1,1;1,1,1,1,1,1,3}
Foster graph 90 8 10 {3,2,2,2,2,1,1,1;1,1,1,1,2,2,2,3}

Independently in 1969 a Russian group led by Georgy Adelson-Velsky showed that there exist graphs that are distance-regular but not distance-transitive. The only graph of this type with degree three is the 126-vertex Tutte 12-cage. The smallest distance-regular graph that is not distance-transitive is the Shrikhande graph. Complete lists of distance-transitive graphs are known for some degrees larger than three, but the classification of distance-transitive graphs with arbitrarily large vertex degree remains open.

The simplest asymptotic family of examples of distance-transitive graphs is the Hypercube graphs. Other families are the folded cube graphs and the square rook's graphs. All three of these families have arbitrarily high degree.

References

Early works
• Adel'son-Vel'skii, G. M.; Veĭsfeĭler, B. Ju.; Leman, A. A.; Faradžev, I. A. (1969), "An example of a graph which has no transitive group of automorphisms", Doklady Akademii Nauk SSSR, 185: 975–976, MR 0244107.
• Biggs, Norman (1971), "Intersection matrices for linear graphs", Combinatorial Mathematics and its Applications (Proc. Conf., Oxford, 1969), London: Academic Press, pp. 15–23, MR 0285421.
• Biggs, Norman (1971), Finite Groups of Automorphisms, London Mathematical Society Lecture Note Series, 6, London & New York: Cambridge University Press, MR 0327563.
• Biggs, N. L.; Smith, D. H. (1971), "On trivalent graphs", Bulletin of the London Mathematical Society, 3 (2): 155–158, doi:10.1112/blms/3.2.155, MR 0286693.
• Smith, D. H. (1971), "Primitive and imprimitive graphs", The Quarterly Journal of Mathematics. Oxford. Second Series, 22 (4): 551–557, doi:10.1093/qmath/22.4.551, MR 0327584.
Surveys
• Biggs, N. L. (1993), "Distance-Transitive Graphs", Algebraic Graph Theory (2nd ed.), Cambridge University Press, pp. 155–163, chapter 20.
• Van Bon, John (2007), "Finite primitive distance-transitive graphs", European Journal of Combinatorics, 28 (2): 517–532, doi:10.1016/j.ejc.2005.04.014, MR 2287450.
• Brouwer, A. E.; Cohen, A. M.; Neumaier, A. (1989), "Distance-Transitive Graphs", Distance-Regular Graphs, New York: Springer-Verlag, pp. 214–234, chapter 7.
• Cohen, A. M. Cohen (2004), "Distance-transitive graphs", in Beineke, L. W.; Wilson, R. J., Topics in Algebraic Graph Theory, Encyclopedia of Mathematics and its Applications, 102, Cambridge University Press, pp. 222–249.
• Godsil, C.; Royle, G. (2001), "Distance-Transitive Graphs", Algebraic Graph Theory, New York: Springer-Verlag, pp. 66–69, section 4.5.
• Ivanov, A. A. (1992), "Distance-transitive graphs and their classification", in Faradžev, I. A.; Ivanov, A. A.; Klin, M.; et al., The Algebraic Theory of Combinatorial Objects, Math. Appl. (Soviet Series), 84, Dordrecht: Kluwer, pp. 283–378, MR 1321634.


text:
# create command

Syntax

sketch edge create keyword

Primary keywords:

Create an edge or a set of edges.

automatic

Automatically create edges from a background geometry present in a set. The background geometry usually represents an imported CAD geometry (e.g., a DXF or STL files).

by-points i1 i2 <keyword>

Create an edge between two points with the IDs i1 and ID i2.

Add one or more control points at locations v2, a 2D coordinate vector ($$x, y$$). If given, this keyword must precede all other keywords. If edge type is not specified, by default the edge becomes a polyline with vertices at the control points. To change edge type, use Type keyword.

group s1 <slot s2 >

Assign the created edge the group name s1 (in slot s2 if provided, in the slot named Default if not).

ratio f

Set the ratio f (a number between 0.1 and 10.1), which is used to distribute zone lengths along the edge (each zone will be f of the size of the zone preceding it). This setting automatically propagates across dependent edges of regular blocks while Ratio-Isolate is false.

ratio-isolate b

The option only applies to the edges which form regular (3- or 4-sided) blocks.

Set the flag to control ratio propagation. Ratio settings propagate when false (the default). If set true a ratio assignment on this edge will not propagate to dependent edges.

size i

Set the number of zones on the edge. This setting automatically propagates across dependent edges of regular blocks.

type keyword

Specify the curve type of the edge.

arc
polyline
simple

This is the default type (a line).

spline


text:
Driver Easy 5.0.9

A guide to uninstall Driver Easy 5.0.9 from your computer

Driver Easy 5.0.9 is a Windows application. Read more about how to remove it from your PC. It was developed for Windows by Easeware. More information on Easeware can be seen here. You can read more about on Driver Easy 5.0.9 at . Usually the Driver Easy 5.0.9 application is placed in the C:\Program Files\Easeware\DriverEasy directory, depending on the user's option during setup. The complete uninstall command line for Driver Easy 5.0.9 is C:\Program Files\Easeware\DriverEasy\unins000.exe. Driver Easy 5.0.9's main file takes about 2.51 MB (2636656 bytes) and is named DriverEasy.exe.

The following executables are installed together with Driver Easy 5.0.9. They take about 4.49 MB (4713120 bytes) on disk.

• DriverEasy.exe (2.51 MB)
• Easeware.CheckScheduledScan.exe (38.86 KB)
• Easeware.ConfigLanguageFromSetup.exe (16.36 KB)
• Easeware.DriverInstall.exe (387.36 KB)
• unins000.exe (1.31 MB)
• UnRAR.exe (247.36 KB)
...click to view all...

This info is about Driver Easy 5.0.9 version 5.0.9 only. If you are manually uninstalling Driver Easy 5.0.9 we advise you to verify if the following data is left behind on your PC.

Folders remaining:
• C:\Program Files\Easeware\DriverEasy

The files below are left behind on your disk when you remove Driver Easy 5.0.9:
• C:\Program Files\Easeware\DriverEasy\ar\Easeware.DriverInstall.resources.dll
• C:\Program Files\Easeware\DriverEasy\cs\Easeware.DriverInstall.resources.dll
• C:\Program Files\Easeware\DriverEasy\da\Easeware.DriverInstall.resources.dll
• C:\Program Files\Easeware\DriverEasy\de\Easeware.DriverInstall.resources.dll
• C:\Program Files\Easeware\DriverEasy\DriverEasy.exe
• C:\Program Files\Easeware\DriverEasy\Easeware.CheckScheduledScan.exe
• C:\Program Files\Easeware\DriverEasy\Easeware.ConfigLanguageFromSetup.exe
• C:\Program Files\Easeware\DriverEasy\Easeware.Driver.Backup.dll
• C:\Program Files\Easeware\DriverEasy\Easeware.Driver.Core.dll
• C:\Program Files\Easeware\DriverEasy\Easeware.DriverInstall.exe
• C:\Program Files\Easeware\DriverEasy\el-GR\Easeware.DriverInstall.resources.dll
• C:\Program Files\Easeware\DriverEasy\es-AR\Easeware.DriverInstall.resources.dll
• C:\Program Files\Easeware\DriverEasy\fr\Easeware.DriverInstall.resources.dll
• C:\Program Files\Easeware\DriverEasy\HardwareInfo\HardwareInfo.dll
• C:\Program Files\Easeware\DriverEasy\HardwareInfo\HardwareInfo64.dll
• C:\Program Files\Easeware\DriverEasy\hu\Easeware.DriverInstall.resources.dll
• C:\Program Files\Easeware\DriverEasy\Interop.WUApiLib.dll
• C:\Program Files\Easeware\DriverEasy\it\Easeware.DriverInstall.resources.dll
• C:\Program Files\Easeware\DriverEasy\ko\Easeware.DriverInstall.resources.dll
• C:\Program Files\Easeware\DriverEasy\nl\Easeware.DriverInstall.resources.dll
• C:\Program Files\Easeware\DriverEasy\pl\Easeware.DriverInstall.resources.dll
• C:\Program Files\Easeware\DriverEasy\pt-BR\Easeware.DriverInstall.resources.dll
• C:\Program Files\Easeware\DriverEasy\uk\Easeware.DriverInstall.resources.dll
• C:\Program Files\Easeware\DriverEasy\unins000.exe
• C:\Program Files\Easeware\DriverEasy\UnRAR.exe
• C:\Program Files\Easeware\DriverEasy\zh-CN\Easeware.DriverInstall.resources.dll

Use regedit.exe to manually remove from the Windows Registry the keys below:
• HKEY_LOCAL_MACHINE\Software\Microsoft\Windows\CurrentVersion\Uninstall\DriverEasy_is1

How to uninstall Driver Easy 5.0.9 from your PC with Advanced Uninstaller PRO

Driver Easy 5.0.9 is an application released by the software company Easeware. Sometimes, users choose to uninstall it. Sometimes this is hard because removing this by hand takes some skill regarding Windows program uninstallation. The best EASY procedure to uninstall Driver Easy 5.0.9 is to use Advanced Uninstaller PRO. Here are some detailed instructions about how to do this:

1. If you don't have Advanced Uninstaller PRO on your PC, add it. This is a good step because Advanced Uninstaller PRO is a very useful uninstaller and all around utility to optimize your system.

2. Run Advanced Uninstaller PRO. It's recommended to take some time to get familiar with the program's interface and number of functions available. Advanced Uninstaller PRO is a very useful system optimizer.

3. Click on the General Tools category

4. Activate the Uninstall Programs feature

5. A list of the applications installed on your PC will appear

6. Scroll the list of applications until you find Driver Easy 5.0.9 or simply click the Search feature and type in "Driver Easy 5.0.9". If it is installed on your PC the Driver Easy 5.0.9 application will be found very quickly. Notice that after you click Driver Easy 5.0.9 in the list of applications, some data about the program is made available to you:

• Safety rating (in the lower left corner). The star rating explains the opinion other users have about Driver Easy 5.0.9, ranging from "Highly recommended" to "Very dangerous".
• Reviews by other users - Click on the Read reviews button.
• Details about the application you want to uninstall, by clicking on the Properties button.
For example you can see that for Driver Easy 5.0.9:

• The software company is: http://www.drivereasy.com/
• The uninstall string is: C:\Program Files\Easeware\DriverEasy\unins000.exe
7. Click the Uninstall button. A confirmation page will show up. Confirm the uninstall by clicking the Uninstall button. Advanced Uninstaller PRO will then remove Driver Easy 5.0.9.

8. After uninstalling Driver Easy 5.0.9, Advanced Uninstaller PRO will ask you to run an additional cleanup. Click Next to go ahead with the cleanup. All the items of Driver Easy 5.0.9 that have been left behind will be found and you will be able to delete them. By uninstalling Driver Easy 5.0.9 with Advanced Uninstaller PRO, you can be sure that no Windows registry items, files or folders are left behind on your system.

Your Windows system will remain clean, speedy and ready to run without errors or problems.


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# Can most programs (except the IO part) be re-written as a sequence of matrix operations?

I got this idea recently. If we do not consider the data IO part of software, imagine the data is in the memory and we need to come out with some decision (which product to recommend to a user, how to render the 3D world in a game) by processing the data in memory. All of these tasks could be done through a sequence (probably a graph) of matrix and vector operations, such as multiply, add, sum, etc.

For instance, I used to work for a car pool company, there was a piece of code to decide which car should respond to user. That logic was implemented with c++ stl containers and flow controls like if/else/break. Then I realized that it can be re-written as logistic regression (the business logic is stored in the linear predictive model) , with certain precision.

In this sense, matrix operation is a programming language by itself.

Can anyone share any thoughts here? Is there any introductory discussion wiki that I can read ?

• You should define your "matrix operation language" more precisely. More concretely, how do you achieve a (possibly unbounded) loop in that? E.g. how do you perform a certain operation until a certain condition is false? Note that, when you have a way to perform arbitrary loops, you need only very basic arithmetic operations to simulate any program. If you did not already, you should read some introductory material about Turing completeness and computability. – chi Sep 27 '19 at 15:53

If you regard the output of a program as a function of its input then matrices can be used to represent some programs, namely those where the output is a linear function of the input. So a program that takes two arguments $$a$$ and $$b$$ and returns $$a+b$$ and $$a-b$$ could be represented by the matrix

$$\begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}$$

But most programs are not linear functions. For example, if the program instead returns $$a^2+b^2$$ and $$a^2-b^2$$ how will you represent that as a matrix ?


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MATLAB Bode Plot
 MATLAB Bode Plot All MATLAB Articles MATLAB's Nyquist Command In order to prevent spam, users must register before they can edit or create articles.

## 1 Introduction

This article is on the topic of creating Bode plots in MATLAB. The quick answer is use the bode command. However, the bode command has several options and the plots generated by the bode command are not easily reformatted. The default formatting of most MATLAB plots is good for analysis but less than ideal for dropping into Word and PowerPoint documents or even this website. As a result this article presents an alternative that requires more lines of code but offers the full formatting flexibility of the generic plot command.

## 2 MATLAB's Bode Command

The basic bode command is as follows

 >> bode(LTI_SYS)

where

The bode command will automatically call gcf which will put the bode plot on the current figure. If no figure exists then one is created by gcf.

If you wish to specify the frequency points at which LTI_SYS is plotted then create a frequency vector using logspace or linspace as follows

 >> freqVec = logspace(-1, 3, 5000);
>> bode(LTI_SYS, freqVec * (2*pi))

where

• freqVec is a vector of 5000 frequencies, in Hz, spaced evenly on a log scale from 10-1 to 103
• pi is a MATLAB constant equal to the value of $LaTeX: \pi$ and in this case it is used to convert freqVec to rad/sec as it is passed to the bode command

In order to get the magnitude and phase at each frequency point the bode command must be called with output arguments such as

 >> [mag, phase] = bode(LTI_SYS);

or

 >> [mag, phase] = bode(LTI_SYS, freqVec * (2*pi));

where

• mag is the magnitude (not in dB) at each point in freqVec
• phase is the phase (in degrees) at each point in freqVec

The mag and phase variables must come out as 3D arrays. Assuming LTI_SYS is SISO then the commands below will convert mag and phase into the vectors you would expect

 >> mag = mag(:);
>> phase = phase(:);
>> mag = db(mag);                               % to get the magnitude in 20log dB

### 2.1 Issues with the bode command

The main issue with the bode command is reformatting of the plot. The bode command appears to use a normal semilogx plot and then apply patches ro something similar to the figure. This can lead to odd behavior when attempting to create multi-line titles, reformat line widths or font sizes, etc. The normal relationship of axes to figure is just not quite present.

## 3 Manually create a bode plot

Since the bode command will return a magnitude and phase a bode plot can be created manually. It is done in this fashion

 >> freqVec = logspace(-1, 3, 5000);

>> [mag, phase] = bode(LTI_SYS, freqVec * (2*pi));

 >> figure;
>> subplot(2, 1, 1)
>> semilogx(freqVec, db(mag(:)))
>> subplot(2, 1, 2)
>> semilogx(freqVec, phase(:))

### 3.1 Example Honeywell GG530 MEMS Rate Gyro

Honeywell GG5300 MEMS Rate Gyro Plant

The Honeywell GG5300 Three Axis MEMS Rate Gyro is advertised as being for "Missiles & Munitions." The datasheet available on Honeywell's website states

 Bandwidth @ 90 deg phase 100 Hz typical

The typical sensor model would have the following parameters

 $LaTeX: \omega_n=100$ Hz, $LaTeX: \zeta=\frac{1}{\sqrt{2}}$, $LaTeX: K=1$

The sensor has a scale factor (Volts per radian) that we are ignoring for now. (The scale factor here is just a gain. External electronics can make this scale factor whatever is convenient.) Using the parameters in the above table a transfer function can be formed in MATLAB with the following commands

 >> wn = 100 * (2*pi);
>> z = 1/sqrt(2);
>> K = 1;
>> GG5300 = tf(K * [wn^2], [1, 2*z*wn, wn^2]);

The resulting frequency response for a single axis is

Honeywell GG5300 MEMS Gyro Sensor Model

For most models each axis can be modelled with an identical transfer function.


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# Functoriality of infinite loop space machines?

If $$C$$ is a symmetric monoidal category, then $$BC$$ is canonically an algebra over a certain $$E_\infty$$ operad, but if $$F: C \to D$$ is a symmetric monoidal functor then (as far as I can see) $$BF: BC \to BD$$ is not a map of algebras over that operad (unless all the morphisms $$(Fx) \otimes (Fy) \to F(x \otimes y)$$ are identities).

Because of this I struggle to associate a spectrum map between the two spectra arising from $$BC$$ and $$BD$$ by infinite loop space theory, I can only see how to get a zig-zag where the wrong-way map is a weak equivalence. For most practical purposes that's just as good, but nevertheless I wonder: are any of the "well known" infinite loop space machines functorial on the nose, with respect to symmetric monoidal functors?

Here is a nice gentle old-fashioned answer. Symmetric monoidal categories are functorially equivalent as symmetric monoidal categories to permutative (symmetric strict monoidal) categories, and those are functorially equivalent (essentially the same as) algebras over a certain $$E_{\infty}$$ operad $$\mathcal{P}$$, known nowadays as the categorical Barratt-Eccles operad, in Cat. Since $$B$$ is product preserving it gives a functor from $$\mathcal P$$-algebras in Cat to $$B\mathcal P$$-algebras in Top. That gives $$B$$ as a functor from symmetric monoidal categories to algebras over an $$E_\infty$$ operad. That goes back, at least in outline, to my 1974 paper $$E_{\infty}$$ spaces, group completions, and permutative categories".
Again in outline, by two recent papers, the same argument works equivariantly for (genuine) symmetric monoidal $$G$$-categories, which give genuine $$G$$-spectra for finite groups $$G$$ via infinite loop $$G$$-space machines. See Equivariant iterated loop space theory and permutative $$G$$-categories http://www.math.uchicago.edu/~may/PAPERS/GM3.pdf and Symmetric monoidal $$G$$-categories and their strictification http://www.math.uchicago.edu/~may/PAPERS/AddCat1.pdf}.


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# sampcov: Sample Covariance (biased) In coxjohn/Lab1Intro: Lab1Intro

## Description

Returns a (biased) covariance matrix for a data matrix

## Usage

 1 sampcov(x, varnames = NULL)

## Arguments

 x a data set varnames a list of variable names

## Details

Accepts a data set and creates a $p\times p$ covariance matrix, where p is the number of variables. The function also accepts variable names that will be used to lable the columns of the matrix. These results are biased, as they use $\frac1n$ in the definition of the variance, rather than $\frac1n-1$.

## Examples

 1 sampcov(data, c("WEIGHT", "LENGTH", "DENSITY"))

coxjohn/Lab1Intro documentation built on Jan. 26, 2020, 4:10 a.m.


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On my way home at 17:15 along Dandenong road, it had been drizzling and the road was wet and the streetlights were on. A white Magna (from memory, Victorian registration ###-###) drove up from Greta St, barely slowed, then turned sharply left into Dandenong road approximately 1m in front of me, I braked heavily and nearly slid into the rear of the car. The driver then slowed and as I drew alongside (yelling loudly), his left indicators came on and he turned left into the service lane! Again I had to brake heavily, this time to avoid being hit by the left-hand side of the vehicle. I continued up Dandenong road and then saw that he had turned into the sports oval so I followed and asked the driver why he had nearly run into me twice. He claimed that he hadn’t seen me, I pointed out that I was wearing a fluorescent yellow Netti jacket and had both front and rear flashing lights and that he can’t have been looking if he couldn’t see me. He claimed that I needed better lights, my comment was that maybe he should either try looking, or removing the exceptionally dark window tint that covered all side and rear windows of his vehicle. At this he wound the window up and ignored me, I shouted that maybe next time if he killed someone he might pay a little more attention, at this he wound the window down, again told me to get some lights and said “OK, you’ve said your piece, get lost”.

Refs: Originally in my bike incidents page.


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## anonymous one year ago Calculate the discriminant to determine the number of real roots. y = x2 + 3x + 9 How many real roots does the equation have? A. two real roots B. no real roots C. one real root D. no solution to the equation

1. anonymous

@LynFran

2. amoodarya

$\sqrt{b^2-4ac}=\sqrt{3^2-4*9*1}$

3. anonymous

so A there are two real roots?

4. SolomonZelman

Ok, I will tell you this. The discriminant for any quadratic in a form of: $$\color{black}{ \displaystyle y=a{\rm x}^2+b{\rm x}+c }$$ is: $$\large\color{black}{ \displaystyle {\rm D}=\sqrt{b^2-4ac} }$$

5. SolomonZelman

So, if the discriminant is: an integer - then you can factor the quadratic a real number (not 0, and not integer) - then you just have 2 real roots. an imaginary number (that results from a negative in a square root) - then no real roots, rather, only 2 imaginary roots.

6. anonymous

for people that see this in the future its B


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ISO 10645

Nuclear Energy - Light Water Reactors - Calculation of the Decay Heat Power in Nuclear Fuels

active, Most Current


text:
Health Care Service Corporation Phone Number, Where Is The Wave House Tiktok Located, Introduction To Machine Tools, Parmesan Mousse Recipe, Tonymoly The Chok Chok Green Tea Watery Eye Cream Review, Kitchenaid Yeast Roll Recipe, Knowledge And Curriculum Syllabus, 100 Critical Thinking Questions, Pulsar N450 For Sale, " />

binomial probability examples

The probability of success is 1 minus the probability of failure that is P(S) = 1- p. Finally, all Bernoulli experiment is independent of each other, and the success’ probability does not alter from experiment to experiment. By using the YES/ NO survey, we can check whether the number of persons views the particular channel. × (½)4× (½)1 = 5/32. 1! The binomial distribution model is an important probability model that is used when there are two possible outcomes (hence "binomial"). Solution: (a) The repeated tossing of the coin is an example of a Bernoulli trial. = p \cdot p \cdot (1-p) \\ Each question has five possible answers with one correct answer per question. Success = "Rolling a 6 on a single die" Define the probability … In a situation in which there were more than two distinct outcomes, a multinomial probability model might be appropriate, but here we focus on the situation in which the outcome is dichotomous. The variable ‘n’ states the number of times the experiment runs and the variable ‘p’ tells the probability of any one outcome. Therefore the probability of getting a correct answer in one trial is $$p = 1/5 = 0.2$$It is a binomial experiment with $$n = 20$$ and $$p = 0.2$$.$$P(\text{student answers 15 or more}) = P( \text{student answers 15 or 16 or 17 or 18 or 19 or 20}) \\ = P(15) + P(16) + P(17) + P(18) + P(19) + P(20)$$Using the binomial probability formula$$P(\text{student answers 15 or more}) = \displaystyle{20\choose 15} 0.2^{15} (1-0.2)^{20-15} + {20\choose 16} 0.2^{16} (1-0.2)^{20-16} \\ \quad\quad\quad\quad\quad + \displaystyle {20\choose 17} 0.2^{17} (1-0.2)^{20-17} + {20\choose 18} 0.2^{18} (1-0.2)^{20-18} \\ \quad\quad\quad\quad\quad + \displaystyle {20\choose 19} 0.2^{19} (1-0.2)^{20-19} + {20\choose 20} 0.2^{20} (1-0.2)^{20-20}$$$$\quad\quad\quad\quad\quad \approx 0$$Conclusion: Answering questions randomly by guessing gives no chance at all in passing a test. In a binomial experiment, you have a number $$n$$ of independent trials and each trial has two possible outcomes or several outcomes that may be reduced to two outcomes.The properties of a binomial experiment are:1) The number of trials $$n$$ is constant.2) Each trial has 2 outcomes (or that can be reduced to 2 outcomes) only: "success" or "failure" , "true" or "false", "head" or "tail", ...3) The probability $$p$$ of a success in each trial must be constant.4) The outcomes of the trials must be independent of each other.Examples of binomial experiments1) Toss a coin $$n = 10$$ times and get $$k = 6$$ heads (success) and $$n - k$$ tails (failure).2) Roll a die $$n = 5$$ times and get $$3$$ "6" (success) and $$n - k$$ "no 6" (failure).3) Out of $$n = 10$$ tools, where each tool has a probability $$p$$ of being "in good working order" (success), select 6 at random and get 4 "in good working order" and 2 "not in working order" (failure).4) A newly developed drug has probability $$p$$ of being effective.Select $$n$$ people who took the drug and get $$k$$ "successful treatment" (success) and $$n - k$$ "not successful treatment" (failure). is a combination. For example, if we toss a coin, there could be only two possible outcomes: heads or tails, and if any test is taken, then there could be only two results: pass or fail. Success must be for a single trial. Example 2 A fair coin is tossed 5 times. = 120. Example 2: For the same question given above, find the probability of: Solution: P (at most 2 heads) = P(X ≤ 2) = P (X = 0) + P (X = 1). Suppose a die is thrown randomly 10 times, then the probability of getting 2 for anyone throw is ⅙. Now, if we throw a dice frequently until 1 appears the third time, i.e., r = three failures, then the probability distribution of the number of non-1s that arrived would be the negative binomial distribution. Binomial Probability Function Example: What is the probability of rolling exactly two sixes in 6 rolls of a die? . Because the card is replaced back, it is a binomial experiment with the number of trials $$n = 10$$There are 26 red card in a deck of 52. For example, if a six-sided die is rolled 10 times, the binomial probability formula gives the probability of rolling a three on 4 trials and others on the remaining trials. Required fields are marked *. = 21 \)Substitute$$P(5 \; \text{"6" in 7 trials}) = 21 (1/6)^5 (5/6)^{2} = 0.00187$$, Example 4A factory produces tools of which 98% are in good working order. Binomial probabilities – examples (calculator) Once you have determined that an experiment is a binomial experiment, then you can apply either the formula or technology (like a TI calculator) to find any related probabilities. The 1 is the number of opposite choices, so it is: n−k. Hence = \dfrac{1 \times 2 \times 3 \times 4 \times 5}{(1 \times 2 \times 3)(1 \times 2)} = 10 \)Substitute$$P(3 \; \text{heads in 5 trials}) = 10 (0.5)^3 (0.5)^{2} = 0.3125$$, eval(ez_write_tag([[728,90],'analyzemath_com-large-mobile-banner-1','ezslot_12',700,'0','0']));Example 3A fair die is rolled 7 times, find the probability of getting "$$6$$ dots" exactly 5 times.Solution to Example 3This is an example where although the outcomes are more than 2, we interested in only 2: "6" or "no 6".The die is rolled 7 times, hence the number of trials is $$n = 7$$.In a single trial, the outcome of a "6" has probability $$p = 1/6$$ and an outcome of "no 6" has a probability $$1 - p = 1 - 1/6 = 5/6$$The probability of having 5 "6" in 7 trials is given by the formula for binomial probabilities above with $$n = 7$$, $$k = 5$$ and $$p = 1/6$$$$\displaystyle P(5 \; \text{heads in 7 trials}) = \displaystyle {7\choose 5} (1/6)^5 (1-5/6)^{7-5} \\ = \displaystyle {7\choose 5} (1/6)^5 (5/6)^{2}$$Use formula for combinations to calculate\( \displaystyle {7\choose 5} = \dfrac{7!}{5!(7-5)!}

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# Educational things (part 1)

Soon the Feb long challenge starts, and I decided to share the most amazing things for me in this blog:

**1.**Min_25’s blog: https://min-25.hatenablog.com the ideas are of high-level there
**2.**The k-th ordered statistics queries with an update of the next type:
l r x y

  For i=l..r

If a[i] == x

a[i] = y

a[i], y <= N

**3.**My problem idea:

Given a permutation of length N and Q queries to it:

1. Swap(p[x], p[y])
2. Tell how many pairs of elements between l and r have differs with the value equals to K

NOTES-

Problem 1. K is the same for all queries

Problem 2. K is different for each query

11 Likes

Constraints, please? Although it’s meant for discussion.
But as of now, I know O(Q*N) soln

1 Like

Let’s have 3e5 everywhere

1 Like

Bump.

Random Quote -
“We are all born ignorant, but one must work hard to remain stupid.” ~ Benjamin Franklin

3 Likes

The complexity of the solution for the second problem O((N + Q) sqrt(N))

1 Like

So far… The solution for the second problem is SQRT-decomposition

Let’s split our array into \sqrt{N} blocks, each of the length \sqrt{N}. And for each block let’s store own sqrt-decomposition. Do you see how the queries and updates can be processed?

The third problem:

Let’s notice that all elements are unique, what it gives us

### Subproblem 1:

K is fixed, the answer is no more than N, we can store the values = 1 in the points (X, Y), where |p[x] - p[y]| = K. Do you see how to do updates and queries in quick O(log^2) time?
Consider the summation on sub-matrix [L..R, L..R]

### Subproblem 2:

Imagine we solve the problem without updates, then if we somehow know all the elements in the range l..r then we can find the answer by (set \& (set < < k)).count() if you’re familiar with C++ bitset. We can find the set with the Mo’s algorithm, don’t forget that there is boosted Mo’s algorithm with Hilbert order.

So, the total complexity is O(Q (N^(2/3) + N/64)), I haven’t seen such complexities before

Feel free to ask questions, I can add links to the algorithms I mentioned. Also, to explain the things more clearly.

I’m stupid

@whzzt suggested simple O(Q sqrt(N) + Q N / 64) solution for the third problem.

Let’s store the bitsets of all elements on the prefixes, i.e. the set of first \sqrt{n} elements, the first 2*\sqrt{n} elements and so on.

When you need to answer the query, just take 2 bitsets, operate with not more than 2*\sqrt{n} elements. Fir the update we should go with updating all of the prefix bitsets.

So, query is K*(the \ size \ of \ block)+N/64, and update is N/K,

We can find the optimal K:

K+N/64 \approx N/K

Better to choose K \approx 64-sqrt{N}

//


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#### See the full image with a free trial.

Read an issue on 9 Apr 1913 in Adelaide, South-Australia and find what was happening, who was there, and other important and exciting news from the times. You can also check out other issues in The Adelaide Advertiser.

## How to Find What You Are Looking for on This Page

We use Optical Character Recognition (OCR) technology to make the text on a newspaper image searchable. Below is the OCR data for 9 Apr 1913 Adelaide Advertiser in Adelaide, South-Australia. Because of the nature of the OCR technology, sometimes the language can appear to be nonsensical. The best way to see what’s on the page is to view the newspaper page.

Adelaide Advertiser (Newspaper) - April 9, 1913, Adelaide, South Australia National Library of Australia the land and the produces. Mkt filing wheat in discussion at Kadina. The weighing of wheat in. Bolk a. Not met with the support of the chamber of Commerce hut several branches of the agricultural Bureau Are still anxious to toe the system Given a trial. At the March meeting of the Scadina Branch the Hon. Dec rotary or. K. J. Riyo Drew attention to the fact that other countries could produce wheat at a less co t than waa the Case with Australia., and it was therefore essential that the get of transferring the wheat from the Field to the Mills of the older countries should be kept Ohlow As possible. At the annual Congress of the agricultural Bureau m 19j2 the following Resolution had been Pas de that this Cong res Argea the Adru Ory Board of agriculture to take any Steps Ufa Ich Are necessary a order to bring about the system of weigh a wheat by the Load Over Ile had entered into communication with the agricultural department of Victoria and new South Wales with regard to this matter and had received the following re plies from director of agriculture. Vic sir in reply to tour letter Nola tire to the weighing of wheat in bulk i have to state that the system adopted at the ports of Williamstown port Mel Bourne and Geelong is the a Beni ii received at the ports sex country station in truckloads calculated to average 12 bags to the ton this is for the guard s in formation when making up trains the including Contente Are then weighed by sworn weigher and the Tare of the truck which is painted on the sides of each added to the weight of the covers reckoned at 3 quarters Rachis deducted from the Gross weight. Following thi3 the weights Tare truck number and other de Tail Are entered on a special form and forwarded to the clerical staff who enter the Gross and net weigh together with All details contained on the waybill on a right certificate which & issued to the Childer and. If required a copy of Une � b supplied to the Farmer at the sending nation. The freight be charged for at per ton of actual weight and the shippers pay the producers on three weights and a thar go of 6 immediately rectified by reference to the automatic Register each Atie Dan As previously stated is a sworn Man and his duties at the ports mentioned consist Only of weighing and entering the slip the weight tickets &c., being attended to by from under Secretary of. Department of. Agriculture. New. South Waey. Sir. J i have the Honor to acknowledge receipt of your letter asking for information regard ing the system of weighing wheat in bulk by Means of Weighbridges at railway Sta Tion or other centres and in reply advise Yon that Weighbridges in this state Are under the control of the railway com missioners who Only instal them at rail a Way stations where the Teafile warrants i same. As a Rule the commissioners re Auire that the output from a station shall lie so less than 10,000 bags of wheat in a it had been stated that the. Approximate Cost of installing we go badges capable of weighing from 10 tons to 12 tons would be �100. In South Australia there were Over 100 railway stations from which in season 10,000 or More bags of wheat Are tracked. A approximate estimate 1 Obj the wheat re eyed into railway Yards from Farmers j teams at someof1 the nations on the Western system gave the Fol lowing figures Wallaroo 140 000 bags Moonta 113,000 Snow town 06,000 Pake Ville. 62,000 Kadina 51 000 Green s Pla m West 49.000 Bute 37,000 Willa Mulka. 30,000 Melton 31,000. He was of opinion that the installation of Weighbridges at each of the stations mentioned would prove a profitable investment and consider Abl reduce the Cost of handling the wheat. It was not unusual in a Busy wheat Yard for teams to have to i wait hours before they could be unloaded. Or. Sorrel said auctioneer expects that private arrange ment Wal be made far a Aale. " messes elder Smith & co. Sold the machinery Stock and other things at Satin factory prices. Burra sheep show., it has Long been a desire amongst those interested in the Burra show particularly in the Merino sheep Clasa that something would be. Devised to. Bring in As competitors the Best breeders of South Australia. It has been Felt that Burra was an outside Centre where a Strong com petition should be established. Burra has been one of the first societies Iii initiate prizes for pens of five rams and of five ewes and the valuable Silver Tea set presented by or. M. Hawker will it is Toped attract Competition from the Best breeders of that robust Type of Merino that has made the Burra District famous. The conditions have not been finally decided. A show with exhibitors like messes. Sandland Koo owie Duffield trustees Koonook hawkers East Bun Garee. Dungaree and North Dungaree Canovie proprietor.,. Murray Bros. Cap Peede Mortlock Martindale. Bowman mount Bryane. Bowman wan Dillah. A. Gebhardt Mac erode. Gebhardt Sokoto. Pearse the gum Mcbride the Gap Hope Wolta Wolt Brooks Boe Ono Ecollins Luc indal Melrose Ulo Loo Collins Collinsville and sir s. J. Way Kad lung a of comparatively easy Access to Burra would arouse inter state interest. Autumn Early Raine followed by sane Bury weather have resulted in a capital growth of herbage on reserved pastures or among the stubble and even m the open coun try the Promise of Early feed has been excellent in Many places. Many Farmer now would like to see another Good general rain recorded and the autumn feed would then be carried on finely. As it is the Rains have proved of immense advantage and have enabled the owners to Kui by cultivation and grazing the wholesale Germina Tion of weeds on the Fallows. In the lower North the Start of the season has been auspicious and As or. H. N. Thomas of Auburn who visited me City on Mon Day Pat it As far a that District is concerned the Early feed a better than it has been for sheep for Western Australia. A consignment of 40 English Leicester ram Bra by or. A. Francis of Hilly Fields Dashwood Gully were hipped by the Ingarra on saturday to the order of or. A. W. Edgar of Gin Gin Western i Australia. I big Elton. April 7.-a Public knee ten was held on saturday evening in the Institute to consider the advice Bilitz of erecting a sheep dip at River ton and also concerning the uniform system of Letri Pitrat on of stallions. Or. J. P. Schalt presided Over a Small attendance. After considerable discussion it was decided to interview messes. Bagot shakes & Lewis with regard to a Slect dip at their yank. It Wou d be impossible to give a guarantee the number of sheep that would be available for dipping. A motion was carried in favor of uniform registration of Sta this time j of the monthly meeting of the i committee of the mount Gambier a. Aid h. Society was held on saturday afternoon last there being a Large attendance of members in the absence of the president through illness. Or. J. Bot Tell occupied the chair. Officers were elected As follow Secretary or. J. A. Shep Pard re elected . A. Smyth. Neil me Arthur. And e. A. Price were elected to fill the vacancies in the general committee messes. W. F. Brooke and e. J. Price were added to the horticultural committee and Are. F. Crouch to the pastoral committee. The executive com Mittee was reappointed. With the addition of or. P. Krummel. I if you Are Yon requiring watches ? we guarantee our watches a we onry Tock Unes tin know can be thoroughly relied on. We Stock them in Gold Silver and Metal for ladles and gents in a big Range it prices to suit the requirements of everyone. Abo Many new designs in wristlet watches. V " Are you requiring up to Date jewellery ? our stocks comprise All the newest and most bean Fol designs of engagement Kings neck lets bangles brooches Cameo goods earrings fie., lines that will last a lifetime. We import direct from the manufacturers and manufacture co customers can depend on getting the very latest styles at the very lowest prices possible. Dainty wedding gifts ? if so we will be very pleased to submit our Beautiful Range of goods to you. We guarantee our qualities the goods Are up to Date and consist of the latest styles in. Copper Ware electroplated Are clocks Sterling silverware Pewter Are cased goods. Your inspection is invited by j. M. Wendt jeweller 8b optician 76 Rundle St 24,26,28 Arcade Raab the Domo. A Kow per joke Rte Babb Cosam sep Aba. To. To cheap to fact 9 to bid at Boot Hall the Price of other Solpa Cicai. On thousands of Tearnen n the state ate the Domo Erny dry. Write for Bat of tee style. Gabon. Elfae a. �1 M. 4 a.16. A .30. �5 to & �. s. A 4. .c7.m it �. 105 a. W. Dobbie & co., Ltd. A Meh Lack vols a eats. A. ,".tfoe i hot Day can be obtained Attlio " vegetarian cafe ?. 8. Wat Ooth St debt Fob ? 1/. Bead Tua specimen Wrom Lonhi and to Oatts soap. Kock Chicken Pic Taree vegetables Gex Tana Tait coff Aad wait. The Mot i changed oar. _ _ Pauai. . Chamber of manufactures. A meeting of the Council of the South australian chamber of manufactures was held on tuesday under the chairmanship of the president or. Arthur Hill. It was resolved that the chamber should act As a commission for South Australia m connection with the victorian All austra Lian inhibition to be held in Melbourne during the present year. To request was received from the italian Consul hat the chamber would Supply exhibits of South australian a Rodu to for the colonial agricultural Institute at Flo rence. It was resolved to Forward the request to the government. The following were appointed a com Mittee to make in connection with the South australian chamber of manufactures exhibition to be held in 1915 messes. Arthur Hill president. M. Simpson Thompson e. C. Vardon w. W. Feb Woodi c. Alle Yelland and g Cleland v be new zealand Ahu or. C. Allen said he noticed that the new zealand minister of customs and Marine was in Melbourne conferring with the Munster of Trade and customs or. Tudor m regard to a reciprocity treaty Between Australia and new zealand. It would be a splendid Opportunity he urged for any member of the chamber who exported goods to new zealand to try and get a preference. Or. A f. Cleland said a preference would be of value to him in his business. There was a preferential duty for wine from South Africa but the australian manufacturers got no such preference. A a consequence the australian wine exported to new zealand had fallen off by about 20,000 Gallons whilst the South african Trade had. Increased by j 10,000 Australia ought certainly to be on the same footing As South Africa. He proposed that a sub committee should be appointed to Send a preliminary letter calling attention to the value of a preferential duty on wine and Ohve Oil and to enquire into further exports from the state. The president and messes. Allen Penn and Cleland were appointed a sub committee. The rowing Rad big. 1 to the editor sr have read with interest everything that has appeared in your columns recently Anent the inter state eight selection t of Crews. I for one cordially undone the action of Butterworth and Abbott a i fail to see1 How they could act otherwise than they did. When or. Nichols elected the eight of which they were stroke and even respectively he selected them with that definite end m View and not a Young gladiators open for any Challenge. To accept their services for a specific eight and then divert there from that object to sait the wishes of the Murray Bridge or any Ether Crews was bad generalship on the part of or. 2��ehoife. It is Only those who deserve tyranny who eur Brit tamely to it. As none of the Crew of which messes. Butterworth and Abbott were members had done anything to make them submit to the tyrannical ruling of either or. Nicholls or or. Auld they did what any sane per son would do resigned. The thing for messes. Auld and Nicholls to do that i can Sec is to Send in their resignations As or. Grayson did when he found he could not handle his eight. With the latter gentleman i think the drawing of lot Between messes. Whyte and the other Disputant whose name i cannot re Call would have solved that difficulty. With regard to the Murray Bridge Chal Lenge it should never have been taken a curiously for As i before observed the men were engaged to Tow in the inter state eight and not open for Challenge. The Murray Bridge Crew had their Chance of nomination the same As the others. Why did they not apply singly or As a whole the Faur thing is for messes. Auld and Nicholls to ask the last Crew of which messes. Abbott and Butterworth Are Mem bets to reconsider their resignations and whether or not they do so at All events let the deadlock occur rather than select men who failed in getting nominations Wuen they Naa tue Chanee. I am a. Fred. Jackson. Walkerville april 7, 1913. Sovereigns 3ielted. A jeweller s bankruptcy. Alleged effect of Early Clos ing act. Disclosures reveal no the transactions of j a bankrupt jeweller were made in the Ade Laide insolvency court before his Honor or. Commissioner Russell s.m-, on tues Day during the investigation of charges against Horatio Daniel Robson of o con Nell Street North Adelaide. At the pre Vious hearing of the ease the accountant s report showed that the debtor attributed is insolvency to the effect of the Early losing act. Or. J. H. Haslam appeared for the insolvent and or. R. Ingleby for receiver and William George Church the opposing creditor. It. Ingle by said charges had been Laid by the opposing creditor and also with the approval of the court by the official receiver act ing for the general body of creditors. Edward Alfred Anstey said the insolvent was indebted to his firm for �36 17/. He was indebted for the whole of that sum on August 29, 1912, the Date of the first meet ing of creditors of which the witness was elected chairman. At that meeting the insolvent suggested that1 he should he allowed to continue in business another six months and promised to pay �20 a month into or. Herbert Solomon s hands for division among the creditors strictly speaking the witness believed the Sugges Tion Carne from the insolvent s solicitor. The creditors passed a Resolution adopting the suggestion and the meeting was adjourned for six months. A meeting of creditors was held in january at which k was decided that the debtor should declare his insolvency. Herbert Solomon practitioner of the supreme court said he acted for the debtor at the first meeting of creditors. The Deb Tor had not paid him any Money for division among the creditors. A Bill of Sale Over the furniture and Stock in Trade and building was in the witness s name. All these had been sold and the Gross realisation was nearly �400. Cross examined the witness said about f 375 on the Bill of Sale was advanced by or. Isaacs m 1910. Subsequently on i two occasions there had been advances by j the witness of �150 and �100, making Ai total of �625. The interest was rate of 15 per cent. The insolvent had paid off in account of principal and in j Terpst about �320. At the. Time of the fico and meeting of creditors there was due from him approximately �490. There i had been nothing about tits insolvent to Lead the witness to suppose that he i was dishonest or would deceive his Credi Tor. J or. Haslam do that the Early closing act has been and is As the insolvent state the main reason of his failure he How ref the Bis a a taking i Book and � believe that to be the cause. I will Yon also that is your be if from f i your knowledge of other cases i have been informed by other jewellers that it. Has affected them seriously. Gay. A j creditor said that the mall suburban jewellers had been pre judicially affected by the act and could not get Money any be examined the witness said no part of e �.�0 Iii off Ose from the proceeds in insurance policy. % a r -., i to a Tite witness Esti mated roughly that about �300 net was one to. Him from the insolvent at the pre sent Date. He would just about get Back the principal. The advances were mostly Cash. The insolvent said he started business on his own account in Jorth Adelaide in May 1907. Hib capital1 at the Start was �55. One of the insolvent s books that containing the daily entries was missing it having been Burnt in the fire at his . Tea slam was it your practice " to we sovereigns for to in urn for the i tire of jewellery yes. 1 " in infringe men.1. Of the coinage act is it not it is the practice among manufacturing jewel �t�1 be the qty laity of the so Verdin Gold?-22 Carat Worth 20/ actually. Answering further questions by or. Has a Lam. The insolvent stated that at the time he1 obtained the Bill of Gale he was being pressed by his creditors. He valued his household furniture at. That time at i�300, i he paid a Vav Ali the Money he receive in premises. The Money from the insulin i company about recouped him for i loss on the Stock. He received �25 in respect to the docs of customers Good., he gave to the customers approximated the value of their goods destroyed. He received �214 altogether in respect of the fire. The fire resulted in a dead Lof to him of �125. The Rami Scrioner did Yon it receive and value in the shape of melted Gold or Silver no i could not sort it out. Did Yon not get anything Hack i sent a tub of dirt to Melbourne and got �1 1 for to. Were any precious Otoles among fit j no Thev were in the Safe. J or. the electric cars Tan to Prospect what did you find a falling off of he Prospect Trade. Everyone m o Connell Street noticed it. When did you notice the effect of the Early closing act just after the fire. Up to the time the act came into open Tion when was the majority of your Busi Ness done on saturday afternoons and evenings and Niter. 6 the week. My business was moot Lvin repair the commissioner have you any ides where that business has gone into the town. " it � the at it a Fiaai Commonwealth and Papua. or a Maud By"�Efle-tadfomeaaaiyto�10at-jrj01fceasaiaaie Iii Minir turn 9�/ rat of interest on Sta 9 ?".�." Deposit of a deposits up to de out of in Jumana b13 Deff bos hts int. Oor Wraa lh-7e17nr9x 10 a monetary and commercial. Tuesday evening. At the meetings of shareholders of the various Large banking institutions of great Britain held at the beginning of the year the chairmen Are reported to have Given exhaustive summaries of the conditions ruling during 1912. The Prosperity of banking is acknowledged to be so closely Allied to that of Trade and industries that it is of the utmost importance remarked the London Finan Cial news in its special banking Supply agent that those responsible for the direction of Banks should keep themselves fully acquainted with the changes continually taking place and with the conditions governing the different businesses with which they Are in relations. It is very evident that Bank managements Are fully alive to the necessities of the Case and the addresses which Are regularly made to shareholders Bear evidence of very careful study and a close first hand knowledge of what is going on both in great Britain and abroad where banking interests Are continually growing in importance. References were of course very generally made to the great activity of Trade the labor unrest and to the necessity of again making Large depreciation allowances. The Gold Reserve ques Tion however was the chief subject dealt wich by sir. E. Holden at the meeting of the London City and m Dland Bank and also by sir Felix schuster at the Union meeting. Thev immense quantities of Gold absorbed by India again called for comment and in spite of the world production valued at about �100,000,000, i it seems that thet Gold reserves of the various nations Are generally quite stationary while t the liabilities have in creased to a considerable extent. Sir Felix schuster called attention to the desire express red by the president of the Reich Bank to raise their Gold Reserve from the present figure of some \ �40,000,000 cd -�60,000,000 or even �75,000,000, if possible by a gradual process and coupled with the great t Trade demands and the possibility of Large requirements on chinese account,1 when the " currency comes to be reorganised " there the Outlook is for very keen com petition for the Metal for some time to come. " the following table gives the Gold holdings of the principal european Central Banka at the � beginning of this year land in 1912. J Gold holdings. J i Jan. 2,1913. Jan. 4,1912. England.�31,300,000 �34,421,000 France 127,766,000 126,836,000 Germany. 38,832,00 -36,388,000 russia.158,374,000 143,290,000 Austria Hungary 50,398,000 53,827,000 Spain. 17,489,000 16,717,000 Italy 42,619,000 " 40,785,000 Netherlands 13,481,000 11,462,000 Belgium. 7,658,000 6,645,000 Switzerland. 6,939,000 ,6,449,000 .sweden.5,570,000r 4,727,000 Norway. 2,316,000 2,192,000total. 502,742,000, 483,732000 austra asian Wool exports. I australasian Wool exports from july 1, 1912, to March 31, 1913, Accord no to statistics compiled by messes. Dalgety & co amount to 2,262,189 Bales compared with " 2,030,166 Bales for the corresponding period of last year a decrease of 232,022 Bales the decrease solar As the Commonwealth Vas concerted totalled 257,284 Bales who e new zealand showed an increase of 25,261 Bales South Australia s Bures the to Date total 161 3s4 Bales a decrease of 10,293 Bales on the figures for the Corre pending Pend of lat season the food ins is a Oum Miry of the movements of each state and new zealand for the period referred in the past three year increase. 1�12 13. 1311-12. Be Creuse. L�lo-11 state. Bales. Bales. Bales. Baie Victoria. 413,o57 616,18 -127,411 4&3,3il j s. Wales 7�/.u17 81s,210 �8.193 i ,0u 1 Queensland �uu,o�4 21/,o60 16,996 197,w2 is aus Ulia ,j84 171,0/7 m,b2 w Vul italia w.j5 72, As b.t/23 70, 02 Tasmania. 21,o2s 17.6j6 of 3,032 ,818 australian totals. 1,587,235 1,814,57� -257,281 1,782.939 n. Zealand 442,871" 417,110 2o,361 Australasia totals. 2,030,166 2.262,189 -232,023 2,305,401 the Iya Tiona Bank of Australasia the returns of Tae National Bank of Australasia or me Quarter ended March 31 Are As follow.-Liamauaanotes not bearing in Eitt , Bills in circulation not bearing interest�4, 8/8 bal ances due to other Banks �16,907 6/11, be to its by the Crown not bearing Inte rest �,887 7/8, by Ocner persons not be aim interest �81,885 7/4l bearing Inte rest �1,639,094 13/1�2,487,060 0/5, total s�2,577,359 3/8. Assets com �34s,391 12/10 australian notes �140,432 13/10 landed and other property �78,625 18/7, notes and bylis of other Banks �18,257 18/ balances due by other Banks �8,253 5/7r amount of All debts due to the Bank �154,331 -6/6 total �2,448,292 15/4. Amount of the capital Stock paid up. At the close of the Quarter ended March 31, 1913. �1,498,220 rate of the last dividend declared to the shareholders preference 6 per cent per annul Ordinary 6 percent per annul amount of the last dividend declared preference �9.173 8/, Ordinary �35,773 41 amount of the reserved profits exclusive of such dividend at the time of declaring such dividend �419,412 18/3. The Bank of new South Wales. The returns of the Bank of new South Wales for the Quarter ended March 31 Are As follow liabilities notes in circulation not bearing interest�5,040 18/6 Bills m circulation not bearing interest�1,243 7/2 balances due to other Banks �9,698 8/10 deposits bearing interest �576,892 6/8, government accounts �8,461 10/9, not bearing interest �242,405 6/3, government accounts �124,052 5/5�951,811 9/1 total �867,796 3/6. , �492,682 13/4 australian notes �33,782 government securities �2,3571 10/10 landed property �24,500 notes and Bills of other Banks �30 balances due from o Cher Banks �36,459 16/3 amount of All debts due to the Bank �1,041,163 12/9 total �1,652,189 13/2. Amount of the capital Stock paid up at the close of the Quarter ended March 31, 1913, �3,253,540 rate of last dividend declared to the shareholders 10 per cent per annul amount of the last dividend declared �150,000 amount of reserved profits at the time of declaring such dividend �2,085.000. " a Paradox in of. An interesting explanation of the Rise in prices of crude Oil and its by products is says the London financial news i supplied from America. The Advance is attributed partly to the dissolution of the Standard Oil Trust. At first sight it would appear ridiculous to that the resumption of Competition among the subsidiaries of the Trust would Lead to an in crease in prices but it will be seen that there is something in the suggestion. Under upon from 3/7tov3/8 per Bushel and Steamer parcels 3/8j to 39 per Bushel for prompt delivery. The Sydney Market is some what unsettled owing to the strike but no material change in values has been mentioned. If the difficulties continue a weakening in rates maybe looked for. As it will be impossible to bring supplies from the country or to make shipments. To Day s buying limits for Farmers. Lots in the country were based upon3/7 Pei Bushel on ticks Darling Harbor or 3/81 per Bushel for parcels. Floor and mall offal. ? �8. 5a per Bushel Tor local Trade lots delivered usual. Terms the Market is �8 17/6 per ton fore let in City brands and �8 12/6-per ton for country Brand � Muf offal is still reported by manufacturers to be going but freely at 1/2 per. Bushel. Delivered usual Terrish. For par�els7 not Ori try Bcka port Adelaide the quotation is 1/1 per Bushel. Reseller for delivery during the next six months quote 12d. Per Bushel on trucks mile end. " Barley and Oats. Jt j there Are no fresh developing Nib in connection with tile markets for Barley a Udo Oats refrain., from operating trans actions Are going through at Jaie crates Melbourne reports j that Earley stocks in that Market Are substantially in excess.-. Of ? weather a gents up Bueno area agent week ago reduced estimate wheat surplus 1,809,000 quarters Makarc his figure now about 15,000,000 quarters for season. Other Cable received in Liverpool confirm this. Weather conditions favourable for maize.-. Russia weather in Southern Region is unfavourable Ever Frost without Snow being experienced fears of crop damage increased. Supt ifs about As recently. Offers of wheat Inore in evidence. Feol poor Quality prevents business. Roumania weather is frosty shortage of 40 per cent wheat acreage confirmed indicating crop about 6j million quarters compared Vith 11,000,000 quarters Normal. Bulgaria and Turkey Short crops also expected Here. Hungary a weather Milder after Frost. Latif sown wheat Condit on i favourable and acreage Short France weather conditions continue favourable complaints m Ich fewer supplies native wheat rather moderate Good demand expected for foreign. Go Marv crop reports now mostly favourable supplies of wheat fair but not heavy. Export demand continues. Italy weather and crop reports mostly favourable. Markets firm fresh buying inactive. United kingdom weather seasonable favourable for ploughing sowing crop Outlook improved. North. Africa Algeria and Tunis favourable a Morocco better v y Dairy produce owing chiefly to the weaker Market for butter m the Eastern states where sup plies have largely increased As the result of the late rams local prices eased about a Penny per Pound at to Day s auctions. Offerings of stores and dairies showed an increase on previous sales but the demand was Good. Beet factory and Creamery sorts sold at from had to 14d., per la. Best separators at from lord. To Lold. Per lb., and store lines 8d. To 9d. Per in. There was rather an easing in the demand for eggs on tuesday and prices backed a half Penny per dozen Hen Selling at 1/3 per dozen and Duck at l/3�\per dozen. Canned fish. Notwithstanding that the season is Over when the demand for canned fish is. At its Best steady orders continue to come for Ward and if the Winter Trade in these goods is As Active As it was last year carry Over stocks will be very Light. London mail advices of a month ago referring to these goods Saide the excellent values of j s of Salmon has largely increased the de Mand and the position is much stronger. There Are now few if any Sellers except at an Advance of 9d. To 1/ per Case above the lowest Point. Tins is not surprising having regard to the value offered in this popular sure which is. Still some shillings per Case cheaper than 1 la. Flat tins which Are scarce. The email Supply and con sequent High Price a a British Columbia fish m 1 la. Tall tins diverts attention to the Best brands of red Alaska which Are Well Worth extra notice. The Supply of choicest lobsters in both j and 1 la. Flat Tine is very Small and prices Are the highest known to that in some districts the goods Are unsaleable. One or two shippers have issued their quotations for new season crayfish. These show an Advance of 5/ per Case Over last years rates an increase More or less expected As the apply particularly of Sia to season was not equal to the demand until the last few months when the fishing improved considerably. Whether the Staat higher Range of aloes will materially affect ? a mrs Tifin remains to be average Copper prices. It f. H. Snow advises the receipt of Grani giving the following average prices for Copper for March Standard Hopper �65 8/9 per ton Best selected cop per �70 16/3 per ton american electro Lytic Copper 14.713 cents per wheat feed Grams produce in. Wheat . Farmers lots in the country Are based upon 3 7i to 3/7? per Bushel on trucks. Port Adelaide or 3/7 to 3/7j per Bushel at the chief outposts. Par cels 3/9 to 3/9 per Bushel b., port Adelaide. City brands �8 17/6, country brands �8 12/6 per ton delivered in Adelaide. Bran and Pollard Millers prices for Trade Lote delivered in Adelaide usual terms 1/2 per Bushel. Hay.-�2 13/ for wheaten shaved delivered m Adelaide. Chaff per ton of 2,240 la parcels trucks mile end railway Staffon �3 5/. Bags extra delivered �3 15/ to �3 17/6, half extra. Export �4 per ton Leb. Nominal. Oats algerian Farmers lots in the country 1/11 to 2/ pee Bushel on trucks port Adelaide. I peas Duns buying once from far mers 3/7 to 3/8 per Bushel. trucks port Adelaide 7/6 per dozen. Potatoes local �7 co �8 per ton in the Market mount Gambier pinkeye and snowflakes �5 12/6. Redskins �6 2/6, on trucks at the mount Millicent redskins �6 5/, trucks Mil cent victorian car mens �7 to �7 5/, on wharf port Ade Laide and pinkeye �6 10/ to �6 15/, on trucks. Me end. Brown globes and Brown Spanish �8 m the Market mount Gam Biers �6 10/, at the mount. Honey at auction from 2jd to 3d. Per la. For prime. . 5jd. Per la. Best mixed soft shells. 4jd. To 5d. Per la. Ker Nels 1/2� per la. factory cured sides Lod. To lid. Per in. Hams lid. To 12d per at auction .-6 d. To 7�d per la. Err tuesday s Market guaranteed fresh Hen 1/3 Duck 1/3j. Butter tuesday s Market Best fac tory Ard Creamery la d. To 14d.Best separators Lud. To 11jd. Store lines 8d. To 9d. Mcglew & co .�-?."?Gram buyer Export. A okla in -�78hio a utter state . Melbourne april 8. was firm at 3/81 to 3/9. There were enquiries to Coyer april contracts at 3/91. Parcels were reduced 5/ to �5 10/. Flour �8 15/. and Pollard �5,10/. Barley was Dull English 3/9 to 4/3 Cape 2/9 to 8/3 Oats were inactive with Busi Ness in Algern milling at 2/5 to 2/5j, feed 2/1 to 2/3. Mai 4/2 to 4/3. Peas Dun 4/ to 4/1. Chaff was steady at �3 to �3 15/. Hay Manger �5 10/ to �0". Straw prime victorian 37/6 to 40/, a rail tas Manian 57/6 to 67/6, sex wharf. ". Market produced potatoes were Filmer with Hight supplies Carmens �510/ to �5 15/ Brownell. �5 15/ to �6 pinkeye je4 10/ to �5 special to�5 a. Onions were easier a �6 10/ to �6 15/. In j3� 4�t�a , 7/3 Bra Bagg 8/ to 8/3 or spot and saes were made to arrive per Janus at equal to Aooie 7/0 delivered. Their were moderate saes of Ceylon team clothes Pega were strongly held. Canary seed sold of spot at "�35 i. Sydney april 8. was Dull country lots 3/7$, sex trucks and City parcels were Worth 3/8. Tile strike is still seriously i restricting business and those houses which have victorian representatives Are j Lul filing Many of their country orders from the Southern m february of shipment i and june was at a standstill and Large business a done a j March shipment beanbags 300 changing hands at 6/9 slings and about 100 Boles april shipment at t 6/6. Corn sacks were sold to Brisbane at 6/8 delivered. In metals Cement was firm following o the action of the minister in cancelling orders for import transaction in a included the Sale of 373 packages of Ceylon at lord Dairy of cheese and butter were accumulating As the area of distribution is restricted to the City and suburbs. Eggs were the Only commodity the Supply of which was curtailed by the strike. New Laid were quoted at 2/. To 2/3, Case eggs 1/5 to 1/8. Feedstuff?.-chaff,further advanced Vic Toria and South australian wheaten Selling at from �6 to �65/ victorian and tas Mardan oaten a from �5 10/ to �5 15/. 1 Market were easier owing to the inability of merchants to get orders away into the country. Tasmanian redskins were Selling at �8, Bismarck and Brownell �7 10/ to �7 15/ up to Sites to 7 5/1 the Steamer Alden brought about 2,600 bags the Best of which were to be had at. �7. Tasmanian turnips were quoted atx�3 a v.4 a Adelaide i Ait prod toe pm it kit. 1 Mes is a. W. Sandford & co. Reported on april 8 the Trade was Well represented at to Day auction and nor Ensins quantities were Cata Fop Leif. Prices for butter receded further in empathy with toe weaker Narket in the East the was or Burner conned not Only to Fae tones but to fairies and Eer orators As Well though store and collect lots1 maintained late rates. Best fac tory and Mcrea Nety butter fresh in prints realised hid. To 1/2 . Second Grade factories. Oct. To lord. Cboin a up aerators and dairies ism. To lit i medium Zulj fix Quality lots. Sid to la store and Collet tors 8d. To sa., Arconi in to con Dit Tai and Quality. quantities received to Dor he a further increase. And paces weakened in Trifid new Laid Ben sell ire at 1/3 per dozen Ducie 1/3. Clearease continues to be effected of Allm Crnin nor Onmon Forward and Vaines re firm at late ratesvi., a. To 73d. Per la. For Large to Leaf. fair Trade a a cinch recorded in his line. Prime Clear extracted. Quit Tine at 23d. Per la. Beeswax a Strong demand at Froin 1/1 to 1/2. Almonds. There is no quotable alteration Brandis by inst Sid mixed not shells. 444\to 6dhard to ,8id bulk 74.live new catalogue was submitted and cleared at fair prices while for Quality lots the to Idine a especially keen. Grid table weight though for a few poor Quality Turkey the prices were not of gco4 l. ? j. / the Adelaide chilled butter and produce com Pany reported april 8 butter the Sodden drop in values in Eastern states bras reflected at our Market to Day. Supplies in All " trades Are ample for Trade wants. demand but anything under is weak and neglected. London cables a Dull Market for choicest australian at 106/ to 110/, Melbourne and Sydney advise having reduced their rates in sympathy with London notations. By auction . Creamery and Apo to Choice factory prints 124 to 1/2 Oto binary Fae tones prime dairies and separators 104 to1/ fair dairies stores and collectors84 to end. Eggs the broken Hill strike is Tatlong fair quantities from Northern districts on this Market. Export Dall local Trade Only fair. Fresh Hen 1/3. Duck 1/4. Cheese diet and steady at 8j4 to 7 d. For Good to prune new makes in Large to Small matured 744 to parcels arriving from Eastern states who Are now a. Prime factors ended rides 9j4 to 10$d. Middles. 10j4 to Uri barns. 104 to 1/. Lard bulk 714 packets sj4 Honey steady at 244 to 2j4 for prime dear liquid dark tainted and. Inferior lid. To 21. Beeswax 1/2 to 1/3. Brandis almonds Sid. Mixed soft Beds 54 kernels 1/1 to 1/2. Live poultry Market is flooded with Light stuff. Quality Birds however Are in Strong demand at Good rates j prime pens table roosters 2/10 to 2/7 medium i do., 1/5 to 1/10 Light cockerel 1/ to 1/3 mixed i pens. 1/5 to 1/10. Bens 1/5 to 2/1 ducks. 1/ to 2/3 geese 3/5 to 4/s turkeys. Cd. To Laid. Per lb., lire Weicht for fair to prime thirds pigeons 54. Messes. Murphy it Kame reported on april 87 continued Fine weather has greatly assisted to increase butter production supplies Are there fore coming in More freely. Many of the nor ? them areas arc opening no and consignments of butter Are arriving for the. The increased supplies together with easier values throughout Tea australian Market have been reflected Here and prices have eased for choicest qualified. Choice Standard brands of factory butter Are sell ins at from. In to 3ft second Grade Facto. Front Lod. To Tif Jav pastors and1 to Fairir. Test of. Ila. To 1/ scares and mixed dairies from Sid. To 9d. Supplies of eggs show a farther increase. The. Arrival to Day being considerably in Advance of last week s quantities. Values sve therefore sed ii Eli guaranteed Nev Laid Ben uses seeing at a i Ordinary 1/s Duck eggs. 1/3 per Boscn. Cheese value remain unaltered. Scary Trade is going through new make Selling at 7d. Per la matured d. Some difficulty is Espe Rieneck in securing sufficient supplies of Bacon to meet the brisk demand and the tendency is to wards higher prices prime factory cured Side Are Selling at Tom Lud. To lord. Middles from. Lod. To lid. Rolls from d. To 9jd. Hams from Lod. To 1/ lard from 6 d. To 7�d. For bladder and Case lot. All consignment of Boner cleared at 2d. Per la. Tor Choice. Dangers of the Abiotic i what explorers have to pack. I i no class of Pioneer runs greater risks than the Arctic or Antarctic explorer. The path to the poles abound.-, avs a writer in Pearson s weekly with death traps cunningly set by nature Ever ready to envelope the intrepid traveller just As Cap Tain Scott and has comrades were Over whelmed by an Antarctic blizzard one of the greatest and Ever present dangers that beset the Arctic traveller is that of Drifting ice floes Polar currents and the Ere Smire of the Waves pack and pile these Uge masses of ice upon one another until they will Tower Twenty or thirty feet above the water. Through these dangerous obstacles the explorer s vessel has to push its Way week after week trusting to Providence and skilful navigation to make its Way unscathed Bat there is Little Hope for the vessel and its Crew should one of those furious tem pests arise for which the Arctic seas Are noted then these massive ice blocks Aro thrown against each other until they Are crushed into dust whilst Waves Rise like toners and break Over the hoes in hugs greenish waterfalls sooner or later the frail vessel is swamped by the Mountain Ous Waves or the vessel comes Between two floes of ice at the moment they strike together. The jagged knife like edges of the bergs splinter the Hull like to to Wood and tha Craft with it human freight is crushed. In the final dash when the exploration party leaves the expedition vessel to Cross the Fields of ice and Snow with Sledge and Sony there Are Many treacherous traps of iat Oxe to avoid there is for instance the deadly Crevasse which has claimed innumerable victims in the history of Polar exploration. These crevasses Are formed by swollen Mountain streams and torrents cutting gullies deep into the ground Over the tops of these fissures and driven Snow slowly collects until Bridge like layers Are formed in appearance they do not differ from the solid Snow covered ground and it is Here that their danger Les the explorer with his heavily Laden Sledge drives across these deceptive carpets of Snow and the ground gives beneath their weight and the party is into the torrent hundreds of feet below. A Sledge party Are endeavouring to sur mount a Imo Mainous ice Peak freshly covered with Snow. The new Snow has not had time to freeze to the icy surface underneath and Here Hes a serious danger. Ii disturbed to any great extent this1 new covering glides in a mass Down the Moun Tain 6ide, carrying m its flight the Hap less explorers who in their helplessness Are probably precipitated Down a Crevasse or carried Over some icy precipice. These masses of moving Snow can quit comfortably Swallow up sledges dogs and passengers a nerve trying ordeal through which explorers often have to go is making their was through ice covered fjords these a narrow paths bounded on each Side by towering Walls of jabbed ice. Every few minutes a. Map of this glittering cry Sipl crashes downwards on to the narrow path. It is impossible to Tell when and where these masses of Nee will fall and the tra Vellers have to take the ask of being crushed by one of these Small avalanches. The eskimos who Are an exceedingly superstitious race genuinely believe that these Falls m the ice valleys Are governed by ome special Providence. They travel through them m deadly fear of being crushed from above or their sledges pierced i by masses of ice m some miraculous Man Ner darting no from below j another of nature s death traps again Sec which Arctic travellers have to guard is def Ting Snow the str is earned along and Over the Edge of an ice crag or precipice where it freezes into apparently i solid i Earth in reality it is merely a deceptive Cornice quite unable Cesar the Atra a of ledge or Man. Be explore St Edde Asor rag to surmount an ice Mountain at the top of which these cornices Are Genei ally to be found unthinkingly travels on to Joan of these overhanging Nasses not noticing that it ends abruptly in apace the unsupported Snow collapses under his i weight and the unfortunate traveller is hurled to his death on the jagged ice Rock a j hundreds of feet below _ second sight. Al Singleton do Yon believe m second sight. Kederly yes. All women have 1 Iti Singleton is Ait possible Kederly i it is. Every time one woman Pat a another m the Street they both turn to get a Colond sight of what the other has acid stomach and dyspep3�a cd Ltd. Food we i Tab a hot j1�ox to g naked Rotim rhe letter which is herewith published in full resulted from an announcement la ode of oui la dip dailies of the Renus. Able curative properties of by sugared Nesia in the treatment of stomach at i my the Cau a of practical y All forma of. So a Mach trouble 6, farm to race. H go Road Chauvell Heath by sex. D a sir i have suffered Foi some months from dyspepsia and acidity of the Otoi Naeini and have find All sorts of Patent As veil As doctor s medicines with no effect. See ing a doctor s statement in one Urf the daily Pap to about the marvels of visit rated Mig Tinesia i got a Small bottle from the local chemist and am glad to that it has done me More Good than and Chin of i have even tried. Food to me was like a hot Aron to a naked wound but inca i have taken Bis rated magnesia i pm now enjoy my food without bad after effects w. Doughty. A drag Luty s experience is doubtless that of thousands of others who have obtained Relief and cure of Sto Naoh trouble Frere the use of by surfed magnesia where medicines Ami advertised remedies live fe.le. It Fadtra who suffer from stomach trouo1. In my form to hould get a Little Bis rated magnesia from their chemists at no a half a teaspoonful m a Quarter of a Glass of warm or cold water after eat ing will almost immediately Reeve the severest Pun. A this is the Overland a pedal

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text:
# Eulers formula proof power series

On Euler’s Number e Avery I. McIntosh [email protected] power series de nition, but that’s another story). This formula is usually.. a Mathematical Intelligencer poll voted Euler’s identity. The key objects of Euler’s proof are power series. Intuitive Understanding Of Euler's Formula.

### EULER: CONTINUED FRACTIONS AND DIVERGENT SERIES (AND

Reading Classics: Euler 1 Notes by Steven Miller2 March 7,. 2.4 Euler’s Proof of Euler’s Line. 3.1 Power Series Review.

Euler's formula & Euler's identity. recognizing function from Taylor series. Worked example: recognizing function from Taylor series.

### euler-maclaurin summation formula - University of Connecticut

Today, I'll prove Euler's Pentagonal Number Theorem and show how he used it to find recurrence formulae for the sum of $$n$$'s positive divisors and the partitions of.This argument gives a geometric statement of the left hand side of the Euler's formula. Power Series. a constant will not be a rigorous proof of Euler's formula.

MATH 473: EULER’S FORMULA Here is Euler’s Formula Proposition 1. If xis a real number, and i= p 1, then eix= cosx+ isinx: Idea of proof. The Taylor series of the.What is Special in Euler. formula for the derivative occurs for a=e. The next step is the observation that the exponential function e^x has a power series.These proofs do not require Euler's formula so there is no. in a proof of the Euler formula for. on recognizing series parallel graphs. Proof.

### Basic theory of the gamma function derived from Euler’s

Euler's Product Formula. One has the following equality of formal power series in q: (12.4) Proof. Classical Partition Function and Euler's Product Formula 39.

### Basel problem | Math Wiki | FANDOM powered by Wikia

On Euler’s Pentagonal. although he was unable to find a rigorous proof until 1750. He also noted that the coefficients of reciprocal power series are.The Basel problem was the. Leonhard Euler was the first one to. We will first demonstrate this approach and then give a rigorous proof. The power series for the.This Euler number is a. This definition has the particularly simple series. "Bernoulli and Euler Polynomials and the Euler-Maclaurin Formula.".

Power Series Solution of a Differential Equation • Approximation by Taylor. Use a power series to solve the differential. given by Euler’s Method for 13.

### On Euler’s Pentagonal Theorem - MathPages

One could provide answers based on a wide range of definitions of $\exp$, $\cos$, and $\sin$ (e.g., via differential equations, power series, Lie theory, inverting integrals, infinite sums, infinite products, complex line integrals, continued fractions, circular functions, and even Euclidean geometry) as well as offering Euler's formula up as a tautology based on a definition.

### Reading Classics: Euler 1 - Williams College

I was trying to prove Euler's formula in complex. comparing is an accurate proof of the formula. only applies to power series so we can.Euler's formula, named after Leonhard Euler,. Here is a proof of Euler's formula using power series expansions as well as basic facts about the powers of i:[5].

Power Series, Maclaurin Series. Proof of Wallis's Formula from Euler's Product Formula. 2. From first principles Euler's equation from the rate of change.

### Euler Equation - BrainMass

• EULER’S FORMULA: ζ(2. Here is an alternative proof for evaluating ζ(2) given by Euler a few years. Replace arcsint in the integrand by its power series and.

### Infinitude of Primes Via Euler's Product Formula

Lemma 2 (Euler). For a positive integer k, the zeta function ζ(x) = P ∞ n=1 1 x satisﬁes ζ(2k) = (−1)k−1(2π)2kb 2k 2(2k)! (9) Euler proved this identity by comparing two diﬀerent power series expansions of xcotx. A more elementary proof is given in Papadimitriou’s paper, and is described in a very accessible way in the article by T. Apostol [Ap].To derive (1) Euler introduced the power series x+ x2 22 + x3 32 +. Euler’s idea was based on an audacious generalization of Newton’s formula for.

7.4 Cauchy-Euler Equation 551 The method of proof is mathematical induction. 2 i Quadratic formula complex roots. Cauchy-Euler Substitution.Euler’s formula The purpose of this. about power series allows us to diﬀerentiate it term by term to ﬁnd that d dt ez(t) = X. A more elegant proof can be.

### A Famous Infinite Series - ptrow.com

SERIES TRANSFORMATION FORMULAS OF EULER TYPE,. We also evaluate in a closed form certain power series with harmonic numbers. Proof. In formula.

### Euler’s formula - UCB Mathematics

IIn analysis, Euler developed the idea of power series, in particular for the exponential function ex. The notation e. Proof of Euler’s Polyhedral Formula.

### Complex exponentials: Euler’s formula - The Live Toad

THE SUM OF ONE SERIES Euler and Bernoulli summation methods of. (Euler method) does not present strict proof. expansion of a function sin into power series.