is needed when
modifying the weights of terms in each cluster according t
o the K
-
means algorithm.
char
sectionword[11]="<!
--
#2#
--
>";
This was used to determine the beginning and end of each subsection in an html file.
7
char
dictionary [126][20]
A two dimensional array to store the terms that were thought to be the most releva
nt
to the html files content.
int
tracksub=0;
Counter used to track the order of a subsection in an html file.
int
trackarray=0;
Counter used to track the total number of subsections used.
ifstream inpHTML1( "file1.htm", ios::in );
This line of code w
as used to open an html file to scan through its subsections.
ofstream outpTitle1( "title1.htm", ios::out );
This line of code was used for each html file to copy the title of the book in order to
print it out before each subsection in the cluster output
file.
5.3 Program Flow
For each html input file the following steps were coded:
Open html f
ile
Copy title
Reach the
beginning of the
1
st
subsection
Input word in
subsection
Increment
subsection number
Stem word
Increment the
weight in
subsection vector
Relevant
term?
No
Yes
Stop
word?
Check against
dictionary of terms
Yes
No
8
After that the K
-
means clustering algorithm was coded in the following way:
Seed points for the 10 clusters (the weight for each term in the
vector) were chosen to
be the first 10 subsections just as a start point.
for
(i=0;i<10;++i)
{
for
(
int
j=0;j<126;++j)
cluster[i][j]=arraysub[i].vector[j];}
While the term weights of the clusters didn't equal the new weights the following was
coded for eac
h subsection. The new weights were calculated as the average of the
weights the subsections that were included in a cluster.
Open a subsection
Calculate the
Euclidean distance
between each
subsection and
cluster
Update the weight
of the clusters
End Cluster
Algorithm
No
Yes
Sam
e weights
as before?
Assign the
subsection to
cluster of the least
distance
9
Finally after the subsections were assigned to the least distance cluster those
subsections were copied to the
clusters with the title of the book before each
subsection.
6. Drawbacks of the algorithm
By examining the output of the cluster html files the following remarks were
concluded:
When assigning subsections to clusters in the first loop of the algorithm
, the
subsections we're scattered around clusters 3
-
8. However after 6 loops of the
algorithm they were all centered on clusters 3, 4 and 5.
The number of loops of the algorithm (6 loops) indicates that after the 6
th
time
running the algorithm on the clust
ers, the cluster center calculation was not
changed so this was the optimal solution.
The dictionary of terms was extracted manually so if different terms were used
there will be definitely different clustering outputs or the subsections.
The seed points u
sed for the clusters were chosen to be the first 10 subsections
which had a great effect on the later calculation of the new cluster center
calculation. So assigning different seed points will result in different output.
The algorithm requires that the num
ber of clusters to be used must be a predefined
decision. That was inefficient in terms of having hard coding the C++ program to
except 10 clusters. A dramatic change in the program is required to see the output
if more clusters were assigned. Basically th
e increase in the number of clusters
results in a longer C++ program.
10
7.
Contribution:
7.1 Bela Sharma
I did thorough research on different types of clustering algorithm. I did my
research using some books in the library and thro
ugh the web sites. I found some
very good websites that had good information on clustering. Then Zainab and
I
met
and tried to divide our work. After I was confident about clustering,
I
tried to select
the best algorithm that would suit our needs for thi
s project.
We
found that K
-
Means
was the best solution for us. Then I researched for different algorithm available for
K
-
means. Finally I liked the one from
Dr.
Mohammed Waleed Kadous' website. I
handed that to Zainab.
Then I wrote the psuedocode to b
e used for our program
For my
next step I
read through all the html documents and created a dictionary of 126 words to be used
in our program The next step for me was to do research on stop word and stemming.
I found some good stop words and stemming algo
rithm for our program on the
Internet. I also wrote a program to calculate Euclidean distance, which was then
integrated in our program by Zainab. I wrote loop for K
-
means in psuedocode format.
Zainab integrated all the codes. I designed and developed the
web site for our demo
i.e. the html files for our main cluster page, which has the link to all the clusters files.
Finally wrote part of this paper.
7.2 Zainab Al
-
Qenaei
After
deciding on the pr
oject topic
I started to read about clustering
algorithms
and what is exactly clustering since it was a new subject to me. After
having enough information and deciding as a team to cluster using the K
-
means
algorithm I did more readings on several algorithm for the K
-
means. For me the next
step was to start prog
ramming. I realized that the basic part of the algorithm is to have
"stemmed words" so I contacted Martin Porter by email:
_EMAIL_
and asked him for the C++ version of the Porter
s
temming algorithm. He directed me to the snowball version of the stemmer at:
_URL_
. After successfully downloading it and
testing it
in my actual C++ code
I started the real programming given the dictionary
terms from Bela. Professor Richard Franklin from the Katz Graduate School o
f
Business, University of Pittsburgh also gave me the permission to use part of his
codes I took in his C++ course to read and write to files in C++. Given the
pseudocode of the algorithm I programmed the part of scanning each document
removing stop words
and stemming the rest. Then finally I programmed the K
-
means
clustering algorithm itself. One final step I did was realizing that the stemmer we used
in our program had some strange way of stemming so I actually stemmed the
dictionary terms as they would h
ave been stemmed by the stemmer we used. That's
why we have in the code "fuzzi" instead of "fuzzy".
Finally, after running the C++
using the Microsoft Visual Studio .NET 2003, I added some line of codes to change
the format of the output clusters.
11
8. Bi
bliography
_URL_
-
means.html
_URL_
tering/clustering.html
_URL_
_URL_
matteucc/Clustering/tutorial_html/
_URL_
-
3.htm
_URL_
00000000000000
(
Mohammed Waleed Kadous)
H. M. Deitel and P.J. Deital
, C++ How to program
, Prentice Hall, 2003


Hadoop 2.x Fair Scheduler
The FairScheduler is a pluggable scheduler for Hadoop that allows YARN applications to share resources in a large cluster fairly. Fair scheduling is a method of assigning resources to applications such that all applications get, on average, an equal share of resources over time. Hadoop 2.x is capable of scheduling multiple resource types.
By default, the Fair Scheduler bases scheduling fairness decisions only on memory. It can be configured to schedule resources based on memory, CPU, and disk usage. When only one application is running, that application uses the entire cluster. When other applications are submitted, resources that free up are assigned to the new applications, so that each application eventually gets approximately the same amount of resources. Unlike the default Hadoop scheduler, which forms a queue of applications, this lets short applications finish in reasonable time while not starving long-lived applications. It is also a reasonable way to share a cluster between a number of users. Finally, fair sharing also uses priorities applied as weights to determine the fraction of total resources that each application should get.


Stop "Continue connecting?" on WiFi
Issue was the old expired Certificates were on the Personal store , removing the old ones fixed this
You can automate this in Intune below
#=============================================================================================================================
#
# Script Name: Detect_Expired_Issuer_Certificates.ps1
# Description: Detect expired certificates issued by "CN=<your CA here>" in either Machine
# or User certificate store
# Notes: Change the value of the variable $strMatch from "CN=<your CA here>" to "CN=..."
# For testing purposes the value of the variable $expiringDays can be changed to a positive integer
# Don't change the $results variable
#
#=============================================================================================================================
# Define Variables
$results = @()
$expiringDays = 0
$strMatch = "CN=<your CA here>"
try
{
 $results = @(Get-ChildItem -Path Cert:\LocalMachine\My -Recurse -ExpiringInDays $expiringDays | where {$_.Issuer -match $strMatch})
 $results += @(Get-ChildItem -Path Cert:\CurrentUser\My -Recurse -ExpiringInDays $expiringDays | where {$_.Issuer -match $strMatch})
 if (($results -ne $null)){
 #Below necessary for Intune as of 10/2019 will only remediate Exit Code 1
 Write-Host "Match"
 Return $results.count
 exit 1
 }
 else{
 #No matching certificates, do not remediate
 Write-Host "No_Match"
 exit 0
 }
}
catch{
 $errMsg = $_.Exception.Message
 Write-Error $errMsg
 exit 1
}
#=============================================================================================================================
#
# Script Name: Remediate_Expired_Issuer_Certificates.ps1
# Description: Raise a Toast Notification if expired certificates issued by "CN=..."
# to user or machine on the machine where detection script found them. No remediation action besides
# the Toast is taken.
# Notes: Change the values of the variables $Title and $msgText
#
#=============================================================================================================================
## Raise toast to have user contact whoever is specified in the $msgText
# Define Variables
$delExpCert = 0
$Title = "Title"
$msgText = "message"
# Main script
[Windows.UI.Notifications.ToastNotificationManager, Windows.UI.Notifications, ContentType = WindowsRuntime] | Out-Null
[Windows.UI.Notifications.ToastNotification, Windows.UI.Notifications, ContentType = WindowsRuntime] | Out-Null
[Windows.Data.Xml.Dom.XmlDocument, Windows.Data.Xml.Dom.XmlDocument, ContentType = WindowsRuntime] | Out-Null
$APP_ID = '{1AC14E77-02E7-4E5D-B744-2EB1AE5198B7}\WindowsPowerShell\v1.0\powershell.exe'
$template = @"
<toast>
 <visual>
 <binding template="ToastText02">
 <text id="1">$Title</text>
 <text id="2">$msgText</text>
 </binding>
 </visual>
</toast>
"@
$xml = New-Object Windows.Data.Xml.Dom.XmlDocument
$xml.LoadXml($template)
$toast = New-Object Windows.UI.Notifications.ToastNotification $xml
[Windows.UI.Notifications.ToastNotificationManager]::CreateToastNotifier($APP_ID).Show($toast)
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text:
FARMINGTON – The Western Foothills of Maine may not be the most ideal climate to grow ginger, but Rustic Roots Farm has been doing it for the last two years and was recently awarded an $8,000 grant to study its growth.
Rustic Roots Farm owner's Erica Emery and Dave Allen have been awarded the grant from Northeast Sustainable Agriculture Research and Education and were one of 29 recipients this year. The program is designed for farmers to try different techniques and produce results that can be used as a reference for other farmers. Rustic Roots will be looking at different spacing techniques to maximize ginger yields.
"What we're going to be looking at is how seed spacing affects the ginger yields… We've tried a few different ways of spacing it out, but the literature currently is just all over the place as far as how far apart pieces of ginger should be planted," said Allen. "We want to find out what is the best way to maximize our yield."
Ginger prefers a tropical understory climate and a long growing season, both of which are unavailable in Maine.
"We're trying to grow a plant that needs a seven to eight month growing season in a climate that regularly only has three or four months," said Allen.
The process of growing a plant from a different climate involves tricking it into believing that the climate is different than it actually is, Allen said.
"We take the seed, which is basically mature ginger, ours is grown in Hawaii…we let it cure and then we plant it in trays with coconut coir and we put it into a custom built incubator," said Allen. "Which makes the ginger think it's underground for like two months. All through April and May it will be in there and then early June we'll take it out and that's when we'll plant it. Then it will stay in the ground until October, ideally."
Emery and Allen will weigh the ginger before and after planting to measure its expansion. They will then compile the data to share with Northeast SARE which will in turn be shared with other farmers as a resource.
The grant money will go towards the cost of the 25 pounds of ginger seedlings that will be dedicated to the project as well as the cost of installing an irrigation system to mimic a tropical understory climate.
Rustic Roots Farm Farm Shares are now open for sign ups. Shareholders receive twenty weeks of locally grown produce, including fresh ginger during harvest season.

source: m-a-p/FineFineWeb


text:
Definitions for mendicantˈmɛn dɪ kənt
Random House Webster's College Dictionary
men•di•cantˈmɛn dɪ kənt(adj.)
begging; living on alms.
pertaining to or characteristic of a beggar.
of or pertaining to various religious orders, as the Dominicans or the Franciscans, that combine the monastic life with an active ministry in teaching or preaching and that originally owned neither personal nor community property, living chiefly on alms.
(n.)a person who lives by begging; beggar.
a mendicant friar.
Origin of mendicant:
1425–75; < L mendīcant-, s. of mendīcāns, prp. of mendīcāre to beg, der. of mendīcus beggarly; see -ant
men′di•can•cy-ˈdɪs ɪ ti(n.)
men•dic′i•ty-ˈdɪs ɪ ti(n.)
a male member of a religious order that originally relied solely on alms
a pauper who lives by begging
A pauper who lives by begging.
A religious friar forbidden to own personal property who begs for a living.
Depending on alms for a living.
Of or pertaining to a beggar.
Of or pertaining to a member of a religious order forbidden to own property, and who must beg for a living.
Origin: From mendicans, present participle of mendico. Compare French mendiant.
practicing beggary; begging; living on alms; as, mendicant friars
a beggar; esp., one who makes a business of begging; specifically, a begging friar

source: HuggingFaceFW/fineweb-edu


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How RFID Has Aided Rental Companies During the Pandemic
There is always pressure, from customers, owners and competitors, to streamline operations, reduce labor costs and improve data accuracy. The coronavirus pandemic has added more pressure to get personnel out of processes that may now endanger their health. Here are three ways the industry is using RFID to adapt.
For several years, the industry has been shifting towards more cost-effective processes. But this has accelerated in the last year as businesses work to reduce on-site staff to comply with health and safety guidance. This is made particularly important as research by the Federal Reserve has shown that automatable jobs pose a high risk of COVID-19 transmission.
Reducing Transmission Risk
The process of assembling rental kits and getting them out the door can be very labor-intensive. Locating the assets with barcodes or serial numbers is a time-consuming process that requires a number of employees to manipulate items so that these identifying marks can be read.
To meet this challenge, rental companies are turning to RFID. RFID enables the rapid identification of assets without touching them. This drastically reduces the labor needed to identify the correct items, get them into the staging area, and then verifying the contents of the rental kit. This reduces the number of people in facilities, making employees safer and reducing the risk to your business.
Lower Labor Costs
Having fewer employees involved in the process has the additional benefit of reducing labor costs. With RFID the time spent finding and identifying assets is dramatically reduced.
In addition, quality processes are expedited, and these workflows can be monitored without the time intensive step of recording asset ID's as the items move through these processes. Finally, cycle counts and inventory audits can be done quickly using very few people equipped with RFID readers.
Improved Asset Utilization
RFID improves the quality of data you have on your assets. With timely, accurate data, you can get a better understanding of asset usage levels.
Inventory visibility is an essential tool for asset rental companies. Only by having accurate inventory data can a rental company determine what assets are available to supply to a customer.
With timely, high quality data, analysis of utilization levels, seasonal usage patterns and rental time frames becomes more accurate and reliable. This enables data-driven decisions about how to invest in additional assets to provide the most revenue and the highest return.
Rental companies that had implemented RFID systems prior to the pandemic reaped a significant return, as their operations were not nearly as severely impacted by the personnel issues related to the pandemic. Firms that did not have RFID in place accelerated their adoption of the technology, as they observed the benefits, both COVID related and the more general business benefits, of RFID. RFID provides a significant competitive advantage in the rental equipment industry, both in times of COVID and beyond.
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Validator
History
When we first started Solana, the goal was to de-risk our TPS claims. We knew that between optimistic concurrency control and sufficiently long leader slots, that PoS consensus was not the biggest risk to TPS. It was GPU-based signature verification, software pipelining and concurrent banking. Thus, the TPU was born. After topping 100k TPS, we split the team into one group working toward 710k TPS and another to flesh out the validator pipeline. Hence, the TVU was born. The current architecture is a consequence of incremental development with that ordering and project priorities. It is not a reflection of what we ever believed was the most technically elegant cross-section of those technologies. In the context of leader rotation, the strong distinction between leading and validating is blurred.
Difference between validating and leading
The fundamental difference between the pipelines is when the PoH is present. In a leader, we process transactions, removing bad ones, and then tag the result with a PoH hash. In the validator, we verify that hash, peel it off, and process the transactions in exactly the same way. The only difference is that if a validator sees a bad transaction, it can't simply remove it like the leader does, because that would cause the PoH hash to change. Instead, it rejects the whole block. The other difference between the pipelines is what happens after banking. The leader broadcasts entries to downstream validators whereas the validator will have already done that in RetransmitStage, which is a confirmation time optimization. The validation pipeline, on the other hand, has one last step. Any time it finishes processing a block, it needs to weigh any forks it's observing, possibly cast a vote, and if so, reset its PoH hash to the block hash it just voted on.
Proposed Design
We unwrap the many abstraction layers and build a single pipeline that can toggle leader mode on whenever the validator's ID shows up in the leader schedule.
Validator block diagram
Notable changes
 - Hoist FetchStage and BroadcastStage out of TPU
 - BankForks renamed to Banktree
 - TPU moves to new socket-free crate called solana-tpu.
 - TPU's BankingStage absorbs ReplayStage
 - TVU goes away
 - New RepairStage absorbs Shred Fetch Stage and repair requests
 - JSON RPC Service is optional - used for debugging. It should instead be part of a separate solana-blockstreamer executable.
 - New MulticastStage absorbs retransmit part of RetransmitStage
 - MulticastStage downstream of Blockstore


Creating a Credits Screen for Endgame
I am creating a short gamer and I would like to add a credits screen to the 2DPlatformer template. What is the easiest way to create a message at the end of the game that tells the user who the game is made by?
Create a UMG widget with the design you want and when the game ends just spawn and add it to the viewport.
What I do is create a UMG widget like Havoc said, and then add a vertical box with text inside. Add an animation of them moving, and boom! :smiley:
Here's a more fancy way of doing it. (Warning this is for more advanced users)
Create the widget, then create two other widgets: "CreditName" and "CreditInfo".
The two new widgets hold a textbox with a function called "init", which allows you to change the text by grabbing a public variable.
So in your main widget, add a vertical box, and add a "CreditName" and "CreditInfo" widget in there, for every name and job they did. For each miniwidget, set the public variable you made earlier as the job or name or whatever.
Josh Steinhauer
And then make an animation that moves it from the bottom from the top.
On the begin play event, play the animation, and then get the duration of the animation and delay for that length. After that, remove itself.
Good luck!!
I have to do the animation of each miniwiget separately


text:
Pecos River Ecosystem Monitoring Project
The Pecos River Ecosystem Project is attempting to minimize the negative impacts of saltcedar on the river ecosystem, and improve the efficiency of water delivery and stream flow. The project is designed to decrease the number of saltcedar with aerial application of herbicide along the banks of the river. The project is concerned with the effect of saltcedar on both quality and quantity of the water of the Pecos River as a result of mortality of the plant from along the banks. Specifically, the study is mainly interested in water delivery efficiency and salinity of the river. The effects of saltcedar on water quality are observed through a series of annual water samples taken along the river from Red Bluff Reservoir to Girvin, hourly electrical conductivity measurements at two sites, and comparison of this data to historical water quality data. Any change in water quantity is determined by comparing historical release/delivery schedules to current schedules from the Red Bluff Water and Power Control District. Water salvage from control of saltcedar is being estimated using a series of shallow groundwater monitoring wells.


text:
Венчурные инновационные проекты: механизм оценки бизнес-ангелами
In this article is conducted research of the mechanism of selection of venture innovative projects. We studied the factors, which influence a choice of business angels. The purpose of work was to receive an advanced system of estimation of projects. On the basis of the survey it is possible to say that the financing of the projects depends more on qualitative characteristics of the project. The created system was successfully tested.

source: openbmb/Ultra-FineWeb


Bubble Squeeze Firing Schedule for Fused Glass
Invisibility, Dana Worley 2020
With this piece it was important that
the black glass be perfectly smooth
I've written before about bubbles. With fused glass art, sometimes we love them and sometimes we don't. In this post, I'll share a firing schedule for the bubble squeeze I use to help mitigate bubbles in my art.
When fusing together two pieces of glass larger than 3 to 5 inches, the two layers of glass will often trap medium-sized bubbles. These bubbles aren't large enough to affect the integrity of the art by rising to the surface and becoming thin, but they do visually affect the surface of the glass. I've heard these called "mumps and bumps". If you look across the surface of the glass with a good light, instead of a nice flat surface you will see an irregular surface with small bumps in the glass.
The landscape pictured here is a work-in-progress of a piece with an irregular glass surface caused by an insufficiently slow ramp up to a bubble squeeze. If you look directly at the piece you do not notice the surface irregularities. However, in the second photo below I've angled the camera so that the glare from the light catches the bumps across the surface.
There are (at least!) two ways to help ensure your layers of glass fuse together smoothly. One is by using a bubble squeeze. The idea of a bubble squeeze is that the glass will begin to slump in the middle before the outside edges are sealed. As the top layer of glass begins to flatten against the bottom layer, the air is pushed out toward the edges.
I have read a lot of advice about the firing schedule you should use to accomplish a bubble squeeze. All of them generally recommend holding at a temperature of 1225 to 1250 degrees Fahrenheit for a period of about an hour during the initial ramp up to the process temperature. However, from my experience, it is not merely the long hold that accomplishes the bubble squeeze. It is also a slow ramp up to that holding temperature that helps to gradually relax the glass and move the air to the outside edges.
Currently, I work with 96 COE glass. My firing schedules are generally conservative. From my perspective, I would rather spend a few more hours firing in the kiln than rush the firing and experience failures. Also, I use a Corelite kiln shelf in my largest kiln, and the manufacturer recommends slower ramp rates to avoid thermal shocking the shelf. Consequently, my firing schedules are often something like the following (all temperatures in degrees F)
Ramp 1 200 degrees per hour to 1100, hold one hour
Ramp 2 50 degrees per hour to 1225 - 1250 (depending upon your kiln), hold one hour
Then, proceed as usual to your process temperature, appropriate annealing time, and schedule for dropping to room temp.
The hold at Ramp 1 ensures that all of the glass comes to the same temperature prior to beginning the slow ramp up to the bubble squeeze hold.
With the landscape piece above, I increased my usual 50 degrees ramp to 100 degrees, thinking that this smaller piece would not be affected. Unfortunately, this change in my usual firing schedule adversely affected the fired piece.
I mentioned earlier that there are two ways to help mitigate bubbles in your fused glass. The second way is to use a light dusting of clear powder between layers (see Resources, below). Use these two techniques together (a fine layer of powder plus a conservative bubble squeeze) to help ensure a smooth surface on your fused glass. These combined techniques helped to achieve the lovely surface of the black glass in my sculpture, "Invisibility", shown at the beginning of this article.
I hope this information has been helpful. Happy fusing!
"At least two ways"?
Other methods used to avoid bubbles include:
 - Placing small chips of glass at the corners of the glass, between the two layers (often called chads). I have found that even a small piece of glass can have a negative effect on the fired piece, either because it misshapes the edge or because it can be seen.
 - Using clear fine frit instead of powder. This will work, but it may cause more bubbles if not used correctly. Plus, using a very fine layer of power is marginally more economical.
 - Most glass has a smoother side and a rougher side. Generally, avoid firing the glass smooth side to smooth side, or rough side to rough side. Both are more prone to trapping bubbles.
Bullseye Glass Education, Tip Sheet: Powder Power
In the back of almost all of his e-books, Glass Artist/Educator Paul Tarlow includes a method of applying a thin layer of powder to mitigate bubbles. Paul's e-books can be found at _URL_
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Tuesday, September 27, 2011
ADF Faces Naming Container Components
(Sorry I was not giving a complete description of the topic here. Apologize to the readers who has requested me to give a full article on this a while back).
Naming Container will not sound unfamiliar if you are developing ADF. Naming Container is a mechanism in ADF to uniquely specify an Id of a component. It's nothing but a naming space attached to its underlying children components and make them unique in the ADF Faces component hierarchy so no components have duplicate Id.
All the Naming Container Components in ADF should implement the NamingContainer Interface. Any children components under the naming container components will have to use its parent naming container id as their prefix in the fully qualified component id. If there are multiple naming container components nested, then multiple naming container prefix will be used. The prefix is separated by ":". component that is located in a naming container thus always has an id value of container id>:.
The naming container prefix is widely used in ADF whenever an Id of a component needs to be specified. For example, the following features -
 - PPR
 - Find a component from page hierarchy by Id (both in Java and JavaScript)
Partial page refresh/rendering is a great feature in ADF. Usually it requires to specify the "partialTriggers" property on the to-be-refreshed components. JDeveloper provides a declarative way to specify the component by browser the page hierarchy tree of the page you are working on, so there is no problem to enter the fully qualified id with the naming container prefix.
If there is a need you have to hardcode the Id the component and the component might be nested by multiple naming container components, you could use getClientId() method on the binding component you are interested in to print the id of the component. This way it ensures you that there is no mistake.
Here should be a complete list of ADF Faces components that implements the NamingContainer interface.
1 comment:
custom facebook app said...
so how can i use this list?
please share your idea by article.


Personal tools
Default values in records
From HaskellWiki
(Difference between revisions)
Jump to: navigation, search
(taken from a post to Haskell-Cafe)

m (typo)

Line 3: Line 3:

Is there a way to declare default value of some fields when defining a new record type?

Is there a way to declare default value of some fields when defining a new record type?

== Anwser ==
+
== Answer ==

You cannot associate default values with a type,

You cannot associate default values with a type,
Latest revision as of 16:47, 6 April 2012
[edit] 1 Question
Is there a way to declare default value of some fields when defining a new record type?
[edit] 2 Answer
You cannot associate default values with a type, but you can define as many record values as you like and use them as basis for updating elements.
data Foo = Foo { bar :: Int, baz :: Int, quux :: Int }

fooDefault = Foo { bar = 1, baz = 2, quux = 3 }

newRecord = fooDefault { quux = 42 }
If you only want some of the fields to be defaulted, you can make them undefined in the default record. Unfortunately this won't be statically checked by the compiler.
[edit] 3 Source


Take the 2-minute tour ×
Consider a finite group G. For any integer $m \geq 1$ set $\gamma(m) = \gamma_G(m)$ to be the number of elements $g \in G$ such that ord($g$) = $m$. We say that $m$ is a "possible order" for G if $\gamma(m) \geq 1$, that is, if there is at least one element $g \in G$ such that ord(g) = m.
Consider the cyclic group $G = C_{6} \times C_6$. List all possible orders for G, and for each $m \geq 1$ of them calculate the value of $\gamma_G(m)$.
From my other question, I thought that I would do this:
lcm(6,6) = 6
Integers dividing 6 = 1, 2, 3, 6. I therefore use the Euler function on these numbers to get the number of elements in each order, but thats wrong. The correct answer is:
$$\begin{matrix} m: & 1 & 2 & 3 & 6 \\ \varphi(m): & 1 & 3 & 8 & 24 \end{matrix} $$
Why is this?
EDIT: I found a theorem: G and H are groups. For any $g \in G$, ord(g) = m. $h \in H$, ord(h) = k. Then
$$ ord(g, h) = lcm(m,k) = \frac{m \cdot k}{(m, k)} $$
What does the comma bit mean at the bottom of the fraction?
Is this theorem useful?
share|improve this question
Well, what made you use Euler's totient function for this? It is true that there is a specific case where that gives the answer, but this is not such a case. – Tobias Kildetoft Dec 12 '12 at 18:39
I thought that was how you calculate the number of elements in the order. How else do you do it? – Kaish Dec 12 '12 at 18:46
Euler's totient function gives you the number of elements of the given order in a cyclic group. This is not quite a cyclic group, but we can still use something like this, since we can see what the order of an element $(a,b)$ will be given the orders of $a$ and $b$. – Tobias Kildetoft Dec 12 '12 at 18:48
So how would I calculate those orders then? – Kaish Dec 12 '12 at 19:05
Yes, the theorem you found is very useful for this. The comma bit at the denominator should have been $(m,k)$ which means $\rm{gcd}(m,k)$, ie their greatest common divisor. – Tobias Kildetoft Dec 12 '12 at 19:19
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Overview - TOUCHMATH-FIRST GRADE SUBTRACTION KIT
TOUCHMATH is a multisensory approach to teaching math in which students interact with numbers on paper by seeing, saying, hearing and touching numbers as they arrive at the right answers without guessing. Teaches math facts by using auditory reinforcement, flashcards, and timed tests.
These are the kits PCI has in stock:
- Readiness Kit: Classification; spatial relationships; basic sets; comparative thinking; matching; same/different; more/less; 1 to 1 correspondence.
- Counting Kit: Counting 1-20; number recognition; TouchPoint patterns; writing numerals 1-20; sets; ordering numbers; 1 tocorrespondence.
- Addition Kit: TouchPoint patterns; addition sums to 18; 1 to 1 correspondence; addition with pictures, TouchPoints, and no cues.
- Story Problems Kit: Relating words and numbers; addition story problems; subtraction story problems; two-step word problems.
- General Math Kit: Time; money; shapes; sizes; fractions; patterning; days/months.
- Subtraction Kit: TouchPoint placement; subtraction facts; double-digit subtraction; missing numbers; number families; place value.
- Addition Kit: Review TouchPoint placement; single-digit through three-digit addition; regrouping; long column addition; place value to 999.
- Subtraction Kit: TouchPoint placement; single-digit through three-digit subtraction; regrouping; place value to 999.
- Story Problems Kit: Key words; relevant/irrelevant information; mixed addition and subtraction; two-step problems; writing problems; group solving.


FedoraRHEL Based
How To Install Composer on Fedora 39
Install Composer on Fedora 39
In this tutorial, we will show you how to install Composer on Fedora 39. Composer is a crucial tool for modern PHP development. It is a dependency manager that allows developers to manage and control packages that a PHP project requires. By automating the process of installing and updating project dependencies, Composer significantly simplifies the workflow for PHP developers.
This article assumes you have at least basic knowledge of Linux, know how to use the shell, and most importantly, you host your site on your own VPS. The installation is quite simple and assumes you are running in the root account, if not you may need to add 'sudo' to the commands to get root privileges. I will show you the step-by-step installation of the PHP Composer on a Fedora 39.
Prerequisites
Before diving into the installation process, let's ensure that you have everything you need:
 - A server running one of the following operating systems: Fedora 39.
 - It's recommended that you use a fresh OS install to prevent any potential issues.
 - You will need access to the terminal to execute commands. Fedora 39 provides the Terminal application for this purpose. It can be found in your Applications menu.
 - You'll need an active internet connection to download Composer and its dependencies.
 - A non-root sudo user or access to the root user. We recommend acting as a non-root sudo user, however, as you can harm your system if you're not careful when acting as the root.
Install Composer on Fedora 39
Step 1. First, update the system packages to ensure that you have the latest versions. This can be done using the following command:
sudo dnf clean all
sudo dnf update
Step 2. Installing Composer on Fedora 39.
Next, you need to download the Composer installer script using the curl command. Run the following command in the terminal:
curl -sS _URL_ -o composer-setup.php
To ensure script integrity, use the hash published on the Composer website:
HASH="$(curl -sS _URL_
php -r "if (hash_file('SHA384', 'composer-setup.php') === '$HASH') { echo 'Installer verified'; } else { echo 'Installer corrupt'; unlink('composer-setup.php'); } echo PHP_EOL;"
Now, you can install Composer using the installer script. Run the following command in the terminal:
sudo php composer-setup.php --install-dir=/usr/local/bin --filename=composer
To verify that Composer has been installed successfully, you can run the following command in the terminal:
composer --version
With Composer downloaded, let's configure it to be globally accessible. Move the Composer executable to a system-wide directory and add it to the system path:
sudo mv composer /usr/local/bin/composer
export PATH=$PATH:$HOME/.composer/vendor/bin
source ~/.bashrc
Step 3. Utilizing Composer in PHP Projects.
Composer simplifies project initialization, dependency management, and installation. Navigate to your project directory and execute:
composer init
Follow the interactive prompts to create your composer.json file. Once completed, install project dependencies:
composer install
Composer intelligently fetches and installs the specified dependencies, optimizing your development workflow.
Congratulations! You have successfully installed Composer. Thanks for using this tutorial for installing the PHP Composer on your Fedora 39 system. For additional or useful information, we recommend you check the official Composer website.
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Stanford Gets $24 Million for Heart Center / Researchers to investigate cardiovascular disease
Published 4:00 am, Wednesday, August 23, 2000
2000-08-23 04:00:00 PDT STANFORD -- Stanford University Medical Center has been awarded $24 million to establish a cardiovascular clinical research center devoted to developing genetics-based approaches to the prevention and treatment of heart disease.
The grant, to be distributed over four years by the Donald W. Reynolds Foundation, was announced yesterday by foundation officials in Las Vegas.
Dr. Thomas Quertermous, Stanford Medical Center's chief of cardiovascular medicine, said the goal of the research is to identify the genetic basis of vascular heart disease, the leading cause of death in the United States. The research will "take advantage of the human genome project and other current initiatives," he said, "to provide the greatest hope for advanced diagnosis and treatment of individuals with heart disease."
The center is part of a collaboration among researchers at Stanford Medical Center, Kaiser Permanente Division of Research in Oakland, Lawrence Berkeley National Laboratory and the Framingham Heart Study in Massachusetts.
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Last year, the Reynolds Foundation awarded another $24 million for the creation of a similar research center at the University of Texas Southwestern Medical Center. The two centers are expected to become the nucleus of a network of four to six such centers.


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Experimental Measurement of Multiphase Flow and CFD Erosion Modeling in Electrical Submersible Pumps
MetadataShow full item record
Electrical Submersible Pumps (ESPs) are widely being used in upstream oil production. To better understand the ESP pump?s behavior, two different ESPs, MVP-G470 and ESP-WJE1000, manufactured by Baker Hughes company have been studied experimentally and numerically to determine the pump and flow behavior in different operating conditions and for different working fluids. The MVP-G470 is a multi-vane electrical submersible pump which has been designed to increase the gas handling capacity of typical multiphase ESPs up to 70% gas volume fraction. Homogenized flow and finer bubbles produced by MVP pumps help the ESPs to delay the surging and gas lock condition to higher gas volume fractions and operate effectively. In this work, an experimental study on the performance of a 3-stage MVP along with detail study on the performance of two stages of the pump are performed. Overall pump performance for different operating conditions such as different inlet pressure, inlet gas volume fraction, water flow rate and speeds are performed for a mixture of water and air. Detail study of a stage performance is done on the first and second stage of the pump using conductivity and pressure measurements accompanied by high speed visualization. The data obtained from these measurements is employed to relate stage head degradation to effective parameters on the pump performance. The ESP-WJE1000 is a typical mixed flow ESP pump with a single vane rather than split-vane design used in MVPs. Numerical study on the erosion phenomena in this pump has been performed. The influence of key parameters on erosion in ESPs has been identified and a new model to predict the erosion rate at different pump locations has been introduced.


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The stuffed veal chops represent a rich and tasty second course, appreciated for the balanced combination of flavors and the technical preparation that characterizes them. This rquick and easy ice cream it fits well into many culinary contexts. In fact, the versatility of stuffed veal chops makes them suitable to be served for both lunch and dinner, guaranteeing a satisfying sensory experience in both cases. The dish is not tied to a specific region or part of the world, but is widely spread in many culinary traditions, adapting to local tastes with variations of fillings and condiments. Its popularity lies in its ability to satisfy different palates, making it a timeless classic in the global culinary scene. The cold seasons are the ideal time of year to enjoy this delicacy, as its structured and enveloping flavors are particularly captivating. The origins of this dish are rooted in family culinary traditions, where the preparation of stuffed veal chops often became a ritual of generational passage. The context of its birth is that of home cooking which, over time, has also gained recognition in more refined gastronomic contexts. The preparation of this second dish follows one sequence of steps clear. The veal slices are beaten until they obtain a uniform thickness, then stuffed with the mix of ingredients and rolled. Slow cooking in a rich and tasty sauce helps give the meat an enveloping and succulent flavour. Don't hesitate, get to work and make these delicious stuffed veal chops. Your guests will thank you.
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This list was the first seriously researched peakbagging list ever created, by Sir Hugh Munro in 1891. Prior to this time, detailed topographic maps for large areas were not available, so it is not surprising that the first list was made in a nation where the Ordnance Survey was ahead of the pack in creating high-quality maps.
A "Munro" is a peak in Scotland over 3000 feet high. The list has been revised many times over the years by the Scottish Mountaineering Club, and the latest revision in 1997 has 284 summits. There is a separate list of 227 "Munro Tops" with less prominence than the Munros, but there is no consistent criteria for determining if a peak is a "Top" or a full Munro.
There is no serious list of peaks in the British Isles that does not own a huge debt to Alan Dawson's The Relative Hills of Britian, the ultimate reference for the subject. The Range classification above is based on his chapter headings, with some modifications. Dawson also pioneered the use of prominence numbers to help classify peaks.


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Analytical Solution of Laplace and Poisson Equations Using Conformal Mapping and Kronecker Products
Abstract
In this paper, using the eigenvalues and eigenvectors of symmetric block diagonal matrices with infinite dimension and numerical method of finite difference, a closed-form solution for exact solution of Laplace equation is presented. The method of this paper has applications in different states of boundary conditions like Neumann, Dirichlet, and other mixed boundary conditions. Using the method of this paper, a mathematical model for the exact solution of the Poisson equation is derived. Since these equations have many applications in engineering problems, in each part of this paper, examples, like water seepage problem through the soil and torsion of prismatic bars, are presented. Finally, a method is provided for torsion problem of prismatic bars with non-circular and non-rectangular cross-sections utilizing conformal mapping.
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Acknowledgments
The second author is grateful to the University of Tehran for financial support under grant number 27938/1/15.
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Mirhosseini, S.M., Rahami, H. & Kaveh, A. Analytical Solution of Laplace and Poisson Equations Using Conformal Mapping and Kronecker Products. Int J Civ Eng 14, 369–377 (2016). _URL_
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Keywords
 - Analytical solution
 - Laplace equation and Poisson equation
 - Block diagonal matrices
 - Water seepage through soil
 - Torsion of non-circular and non-rectangular cross-sections


This article is part of a series in which we define and explain various wedding related terms. Perhaps you've heard the word dowry before in relation to weddings, so today we'll be answering the question:
What is a dowry?
Definition: A dowry is the money or goods that a bride's family gives to her new husband and/or his family when they are married.
Other terms associated with the exchange of wealth during a marriage are bride price and dower. A bride price refers to money that a groom would pay to his bride's father in exchange for her hand in marriage, while the dower is the property that is settled upon for the bride at the time of marriage so that she is taken care of should she survive her husband.
The history of the dowry
The parental giving of a dowry in exchange for their daughter's hand in marriage is an ancient custom that has been practiced all over the world, and still continues in some parts of the world. Many cultures still expect, or in some cases, demand a dowry as a condition to accept a marriage proposal, mostly in areas including Asia, Northern Africa and even certain regions of Europe.
The tradition of a dowry has decreased over time and it is no longer a common custom in developed countries or urban areas.
During the wedding ceremony, the custom of giving away the bride was an acknowledgment that the dowry had been negotiated and the bride had her father's blessing.
In ancient times, a hefty dowry could serve to increase the desirability of a woman for marriage. Men could potentially consider a marriage proposal based on the size of their expected dowry in order to build power and wealth for their own families.
In certain cultures such as Ancient Rome, the father was basically required to provide every daughter with a dowry appropriate to his means. If a father was unable to give a reasonable dowry for his daughter's hand, a relative or family friend might offer to help them out and provide the dowry on his behalf.
The purpose of a dowry
In ancient times, a dowry was given to the groom and his family in exchange for the bride as a way of ensuring that she is properly taken care of and comfortable. In those times, it was also expected that the bride would leave her family home to reside with or near her new husband's family. This gift would serve to provide a bit of financial security in the case of widowhood, and was thought to eventually provide for the couple's future children as well.
A dowry could also be considered a conditional offering that would be expected to be returned in the case of divorce, abuse, or other mistreatment of the bride.
In modern time periods, the dowry is intended to help set up the couple's new household, especially in cultures where it is rare for a woman to work outside the home.
In the case of the bride's passing, things could get a little hairy. If a woman died without having any sons, her husband would have to return the dowry to the bride's family, deducting the value of the bride price. The bride is also entitled to her entire dowry after her husband's death, and the dowry is only inheritable by her own children.
What was in a typical dowry?
A dowry could be made up of any combination of valuable things. Dowries often consisted of money, jewels or precious metals, land or property, home furnishings and more. In some cases, a groom had to ask his bride's permission to use or sell certain items contained within the dowry, such as land or property.
The evolution of the dowry
This dowry custom evolved first into a "trousseau" or hope chest. A trousseau is the collection of goods that a woman gathers in preparation for her future marriage. Ultimately, the bridal registry and bridal shower are later evolutions of the traditional dowry.


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Averages for Crete in March
March ushers in spring and is considered an unpredictable and varied month, as winter struggles to keep its grip on the island. For that reason, tourists visiting the island of Crete in March should be prepared for any weather â€" rain one minute, sunshine the next.
March sees average daytime temperatures floating around 14 degrees Celsius, with daytime high peaks reaching up to 17 degrees and lows going dow...
Daily averages for March
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Averages for Crete in March
March ushers in spring and is considered an unpredictable and varied month, as winter struggles to keep its grip on the island. For that reason, tourists visiting the island of Crete in March should be prepared for any weather – rain one minute, sunshine the next.
March sees average daytime temperatures floating around 14 degrees Celsius, with daytime high peaks reaching up to 17 degrees and lows going down to 10 degrees Celsius. The sea is almost constantly warmer than the air outside, with average seawater temperature staying around 16 degrees during the month of March. Expect 5 hours of daily sunshine on average. Crete experiences the regular winter-summer circle and March is a relatively rainy spring month. Total monthly precipitation reaches 62 mm and rainfall is expected during 8 of the month's days.
There are numerous local sayings about how March can be warm as summer one day and cold as winter the next, warning people about the unpredictability of the weather during this month. Hailstorms and even snow has been known to fall during March, alongside the rare phenomenon of winds carrying snow from the top of the Cretan mountains down to the beaches below.
Where to stay
Mediterranean Studios Apartments is a small, self-catering hotel that provides high quality affordable accommodation in the city of Chania. The apartments are fully furnished and come at bargain prices, especially in off-season months.
Niriides Hotel Apartment Studios is a popular boutique hotel that has only 10 rooms – hence the meticulous care and attention to detail. The hotel is newly built and features high-tech amenities. It is located in a quiet and friendly neighbourhood, too.
The Danelis Apartments is especially good for families, there's a child-friendly pool and many other amenities geared towards kids.
Avli Lounge Apartments at Rethymnon offers traditional Cretan hospitality at its best. This traditionally styled boutique was designed with an authentic Cretan courtyard in mind. The service is impeccable.
Casa Moazzo Suites & Apartments offers premium apartments for those seeking privacy and some quiet time. Located in a renovated neo-classical building, the residence of Venetian royalty, each apartment and suite is carefully designed to offer maximum pleasure and luxury. A real gem.
Niriides Hotel Apartment Studios is located right next to the sea in Crete
Dates for the diary
Right after the famous carnival and marking the start of a five-week lent, Kathari Deftera (literally meaning clean Monday) is a huge celebration across Greece. On clean Monday, locals close down their shops and fly paper kites, filling the skies of Crete with colour. Traditional food is eaten among celebrations and lent-friendly BBQs that include roasted vegetables, fish and a specially made bread, which is baked on this day of the year only.
Every year on March the 25th, Greece celebrates the anniversary of the Greek War of Independence in what is perhaps the most popular national holiday in Greece. Crete does its best to celebrate Greek independence with parades on all major towns, free food and nightlong fiestas commemorating this momentous event.
Things to do
The Natural History Museum of Crete attracts science and nature enthusiasts throughout the year. Since it opened its doors in 1980, the museum has been working closely with the reputable University of Crete (responsible for a large part of the Human Genome project) to promote scientific awareness about Crete's history and natural resources.
The Flowers of Crete Day Trip is a unique touring opportunity that allows visitors to explore and discover some rare and beautiful flowers. You'll be taken through remote areas and untouched prairies to explore Crete's natural wonders and understand how unique Crete's ecosystem is. Tourists also collect their own sea salt exactly how the ancients did and see some sights of Crete that are well off the beaten track.
Flowers of Crete day trip
Where to eat & drink
Spyros taverna in Gouves is a great traditional Greek eatery. Run by the eponymous Spyros, a talented chef, the taverna serves local dishes and Greek delicacies in an excellent environment. The restaurant is child-friendly and its prices won't break the bank.
The Del Mar Snack Bar is a popular fast food restaurant in the bustling tourist area of Elounda. Serving coffee, sandwiches and crepes on the go, Del Mar caters to active beachgoers during the day and peckish partygoers through the night.
The WKD Bar at Malia is one of the most popular bars in Malia. The club has a brilliant, lively atmosphere, good music and a fun crowd. The bar is known for throwing some pretty big parties, too.
Bar Code is a top bar in Stalis. Cheap drinks and good entertainment including karaoke, darts, twister and fancy dress all guarantee a fun night out.
Drink and dine at a Crete beach bar
Hit the beach
Almyrida beaches are two blue flag beaches that boast fine golden-coloured sand and truly clean waters. Both beaches are in close proximity to each other, and even though they have virtually no tourist facilities, visitors can find everything they need close by in various large tourist complexes that are within short walking distance. However, you can rent loungers and parasols. The west Almyrida is more family friendly, while the east beach attracts naturists and couples more.


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Cotton Brazil presents 2022 outlook during global events
Brazilian cotton |
On World Cotton Day, Cotton Brazil participated in some of the most important industry events and presented figures about the current Brazilian crop.
Several events took place on October 7, World Cotton Day, to foster the use of natural fiber around the globe. Abrapa (Brazilian Cotton Growers Association), through the Cotton Brazil initiative, participated in one exclusive session during the Congress of the International Cotton Association (ICA), held in Liverpool (UK). The association also took part in events in Bangladesh, India, and in a panel of the Food and Agriculture Organization of the United Nations (FAO).
Progress recognized around the world
Brazil has expanded its production in recent years to meet domestic demand comfortably. The surplus is exported, with 99% of the 2.4 million tons shipped from July 2020 to August 2021 destined for the Asian market. This volume places the country as the second largest world exporter.
"Brazilian cotton is in constant evolution. We have grown in volume, but mainly in quality, and today we offer an increasingly sustainable product", said Abrapa's president, Júlio Cézar Busato.
In Brazil, 100% of the harvest is mechanical, which results in large-scale, uncontaminated cotton, a distinguishing characteristic in the eyes of foreign markets.
Cotton sustainability is the focus of global attention
Sustainability was a major highlight of the ICA forum. According to Abrapa's president, 81% of the 2021 Brazilian crop was certified by the Responsible Brazilian Cotton (ABR) program, making it eligible for the Better Cotton Initiative (BCI) global certification as well.
"Our program began in 2012 and in less than ten years we have expanded the number of certified farms and bales more than fivefold," said Busato.
"Our cotton is grown in dryland, respecting strict environmental, labor, and land legislation and is 100% traceable, which gives buyers more stability and transparency", said Pedro Valente, director of Amaggi Agro, a Brazilian firm. The executive emphasized that transparency in production is a growing demand in international markets.
Brazilian harvest data
The 20/21 Brazilian cotton crop is estimated at 2.32 million tons, of which 99% has already been harvested and 55% ginned. It is a lower volume than in the previous cycle, but the projections are optimistic. "We will have our second-best production year in the 2022 cycle," said Abrapa's International Relations Director, Marcelo Duarte. Last season's acreage reduction was climate-related.
Cotton Brazil at CITI
Abrapa also presented the numbers for the current Brazilian crop in another online event held on World Cotton Day (7) – this time, organized by the Confederation of Indian Textile Industry (CITI). "In 2022, we will have a bigger cotton crop and with even more quality. Over 80% of our cotton is already certified by the ABR program, which makes it eligible for BCI credits, besides being contamination-free", said Alexandre Schenkel, Vice-President of the association.
Abrapa was also present in a virtual event by the Food and Agriculture Organization of the United Nations (FAO) to celebrate World Cotton Day. Abrapa's executive director, Márcio Portocarrero, participated in a panel about how associations contribute to the strengthening of the cotton sector in Latin America and the Caribbean.
On Friday (8), Cotton Brazil also promoted a business roundtable with trading companies as part of the program of ICA's annual event.


text: ABSTRACT: The dike rings along the Rhine in the Netherlands have a level of protection of 1/1250 per year. The design water levels are estimated on the basis of one random variable: the river discharge. Van Vuren & Van Breen (2003) show the existence of large spatial and temporal variation in bed level position in the river Waal. In this paper the impact of river morphology on extreme flood level predictions is investigated. Therefore, the method to compute design water levels is extended with another random variable: the river morphology. The results show that the impact of river morphology on design water levels is limited. A random bed level prior to the design water level computations leads to small changes (order of 0.01- 0.06 m) in design water levels. The impact of seasonal variations in the river morphology and morphological changes during the flood wave can be neglected.


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Sustainability and Renewable Merino
Wool runs on grass
The primary inputs for wool production are water, sunshine and fertile soils to grow grass – the primary diet of sheep.
As such merino production inherently has the potential of being fully sustainable providing it is operated within the carrying capacity of the ecosystem.
They must operate, or be in the process of implementing, a grazing management strategy based on long term sustainability.
The management system must embrace holistic farming principals with the goal of developing a resilient ecosystem that can regenerate, withstand stress and rebuild itself when necessary.
This goal should be to aim for 100% ground cover all year, with a focus on perennial grasses to regenerate the ecology and increase biodiversity.
Holistic farming principles include:
- Clear goals for the people involved
– Clear goals for the land in use
– Clear goals for the business
- Clear goals for the management of livestock
The management process should involve:
- Reviewing these strategies regularly
– Making decision with these goals in mind
– Monitoring the health of your land, your business and the people involved


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The question of what kind of position furniture has in home life and its impact on home life is self-evident. So why do we use solid wood laminates for furniture? As far as the current formal solid wood multi-layer board is concerned, its advantages are many:
1, more environmentally friendly, plate furniture sheet is very strict with environmental protection requirements, so choosing an environmentally friendly sheet is the biggest health guarantee for home life. At present, Baiyuan's solid wood multi-layer board can completely achieve E0 level.
2. The raw materials of the multi-layer board are made of solid wood (large-diameter wood in the trunk part). The raw materials used in various other wood-based panels, except for wood-based multi-layer boards, require logs, mostly from harvesting and processing residues, and small-diameter materials (less than 8 cm in diameter).
3. The size is more stable. The production process of the solid wood multi-layer board is made by pressing a layer of veneer vertically and vertically, and the adjacent fiber directions of the adjacent layers are arranged perpendicularly to each other, thereby improving the anisotropy of the wood under natural growth conditions and improving the anisotropy. Dimensional stability. For finished furniture, the service life is longer.
4. Strong strength and good flatness. The unique production process and raw material selection of the solid wood multi-layer board determine its unique quality. The solid wood multi-layer board is composed of multi-layer veneers arranged in a crisscross pattern. In the current production process, between the veneer and the veneer The oblique grinding lap process (starting splicing, subsequent seaming, to the current oblique lap lap, the process is progressing continuously), and then being produced by several processes such as cold pressing, hot pressing, sanding, etc. High strength, good grip strength and high flatness.
5, not easy to deform, no cracking. Baiyuan solid wood multi-layer board is made up of multi-layer veneers arranged in a crisscross pattern, and the beech is selected as the panel. After being glued, it is made by high temperature and high pressure in a hot press. The deformation and cracking of the sheet is mainly composed of water content and other factors. The solid wood multi-layer board can strictly control the moisture content of each veneer in the production process, so the quality of the finished board is more guaranteed. It is not easy to be deformed and cracked, and the dry shrinkage expansion system is extremely small. It solves the two major defects of deformation and cracking of solid wood panels from the aspect of internal stress.
6, the sheet is large. Multi-layer solid wood boards are cut from logs into single boards and then arranged in a staggered manner. In theory, the width of solid wood multi-layer boards can be infinite, but it is actually produced according to the national standard size. This is very different from other plates, such as other particle board and MDF, completely using waste scraps, even if the adhesive combination is again, there is no original wood such as solid wood laminate. This also solves the shortcomings of insufficient solidity of the solid wood board due to the influence of the material age and growth rate.
7, good quality, high price ratio. The multi-layer solid wood board is the artificial board closest to solid wood. But it is better than solid wood, good toughness, large area, not easy to deform and crack, the quality is better, but the actual price is lower than the solid wood, the effect is close to solid wood, cost-effective.
8, easy to process, easy to produce. The solid wood multi-layer board has precise thickness, long and wide width, and is suitable for most furniture. It is close to solid wood, has no special requirements for processing machinery, processing saw blade, processing technology, etc. It is easy to process and easy to form. An ordinary woodworker can also use the solid wood multi-layer board to make beautiful and practical furniture.
9. In line with the current consumption trend, in the market dominated by the current custom furniture, solid wood multi-layer boards are generally used for custom furniture, so that the various finished furniture products are well received by customers.
10, color matching is more convenient. We all know that the current plate furniture is made by using the color of the plate itself. Once the plate does not meet the color of the home decoration friend, you need to paint yourself or buy other products. However, the solid wood multi-layer board has good flatness and can be directly used for veneering. Consumers have other favored colors that can be directly used for veneer production, which perfectly meets consumers' customized services for various colors.
10 reasons fully prove why it is necessary to use solid wood multi-layer boards for making panel furniture, which is an inevitable trend of market development. Of course, for many friends who are using and about to use multi-layer boards, there are more reasons to explore. Do not choose the most expensive, only choose the right one, choose solid wood multi-layer board to create furniture, family life is more comfortable.
Copyright © 2017 - 2019Qingdao Holyck Furniture Co.,Ltd All Rights Reserved


text:
Town Analyses > Jericho > Physical Landscape
There are 78 different types of soil identified within the Jericho borders, a product of the area's dynamic glacial past. Distinguishing one soil from another is the product of several factors, including the type of bedrock underlying all other deposits, the surficial material coating the bedrock, the steepness of slope on which the soil lies, the climate or microclimate that determines the rate of decomposition, the size of soil particles, and the mineral composition of the soil itself.
Why do we bother dividing soils into different types? Soil structure often dictates what types of vegetation will grow naturally on a landscape, and human activities and land use practices are often more suitable on one type of soil over another. Farming, for example, is most productive on soils with relatively high clay content that has mixed with sand for better drainage. Also, it tends to be level and free of many rocks. Although most of Vermont was cleared for farming at some point in the state's history, we can actually see a relationship between soil type and date of farm abandonment, where the prime soils are most likely to remain farms even today. Most of the prime soils are located along river floodplains, where clay was once deposited when the land was covered by a lake, but where sand has more recently been mixed with the clays. Upland farms, with soils derived from rocky glacial till, were often the first to be abandoned.
Certain trees and vegetation may also grow better in one soil than another, which eventually leads to animal habitat also partially corresponding to soil type.
Jericho Agricultural Soils
MRP Sept 024
Classic rocky Vermont soils


text:
The Carbon Footprint of a Telecom Network Measured using Nuclear Energy Science Framework
The article describes the development of the sustainable telecoms network and provides data on the environmental impact of the system. An article is devoted to discussing the approach of utilizing the green telecommunications layer foundation to estimate the ecological footprint of telecommunications infrastructure. The approach helps to bridge the gap among greenhouse gas management and mitigation (GHG). The goal is to construct readers to the current green telex and highlight the need for communication and information technology for quality and integrity. This article gives an extensive reference to a rising pool of academics who might work quickly on the nuclear energy of network infrastructures.


Karen's Knitting Site - History of knitting
Karen's Knitting Site
History of knitting
The actual origins of knitting are hard to trace. Historic evidence of knitted pieces have been found in several, diverse countries such as Egypt, England, Holland, Scotland, Spain, Germany, and so on. Apparently, the earliest evidence of knitted clothing found were fragments of socks that were made in Egypt sometime between 1000 and 1300 A.D. But, even this is disputed since some scholars say that these socks were not knitted but were the result of naalebinding (another fabric making technique).
The first trade union devoted to knitting professionals was founded in 1527 in Paris. It was originally a male-only occupation but soon became a household activity when knitted stockings became extremely popular. Apparently, by the lates 1600's between one and two million of these knitted stockings were exported from Britain to various parts of Europe.
Socks and stockings seem to be the earliest pieces of knitted clothing because this technique allowed for shaping the cloth to mold to the many angles of the foot. But this wasn't the only effective and creative use of hand knitting.
According to one source I checked, "Legend has it that sailors wore sweaters with their family pattern knit into them so that their bodies could be identified if they died at sea."4 While it's a morbid thing to think about, it is a notable application of the craft.
Whatever its true origins, knitting, crocheting, naalbinding and various other crafts of this nature have a long, rich history. As someone who has become a recent convert, I can easily see why these techniques have survived for so long.
1. "Knitting." Wikipedia, Retrieved March 2, 2005 from _URL_
2. Rutt, Richard (2003). A history of handknitting. Interweave Press, Loveland, CO.
3. "Knitting History." Apparel Search Company, Retrieved March 2, 2005 from _URL_
4. Thomas, Nancy J. (2004). Barnes & Noble Basics: Knitting and crocheting. Barnes & Noble Books, New York, NY.
5. "Naalbinding." Regia Anglorum, Retrieved March 2, 2005 from _URL_
6. photo © Kathleen Kinder/Bill Mitchell 1997 _URL_


text: Water supply coverage in Nigeria is 58 per cent. In order to bridge the gap and meet national and MDG targets thousands of boreholes will have to be drilled in a relatively short time. To achieve this, different approaches incorporating a variety of solutions are needed. Emphasis has to be placed on solutions that are affordable and will allow households and communities to meet their need for potable water. A phenomenon that may contribute to bridging the gap is ongoing local fabrication of drilling rigs from discarded materials. This paper evaluates the potential of the locally fabricated rigs to produce cost effective boreholes and contribute to increasing the water supply coverage.


Genesee Course Listing
Official Course Information
Please select a Course Section from the list below or search for a class by Course Title.
Spring 2021
Business Administration Courses:
 or List All Business Administration Courses
BUS108 - Customer Service Management
Credits: 3
Catalog Description: The course provides an overview of basic elements of customer service, career options, and role in any industry. It studies leaders in service and the impact of service businesses on the world economy. The course presents case studies of businesses which utilize customer service and hospitality techniques to differentiate from their competition and to develop new products and services. It covers customer service philosophies, skills and innovations. The course examines available technology used to anticipate and manage customer needs and improve revenue and customer retention.
Lecture: 3 hrs.
Course Learning Outcomes (CLOs):
Upon the successful completion of this course, a student will be able to:
1. Identify best practices in customer service.
2. Explain the role of technology in building customer relationships.
3. Identify current trends in customer relations management.
4. Communicate effectively in a professional setting.
5. Compare and contrast global business etiquette practices.
Effective Term: Fall 2019


Accordion Plus
The Accordion Plus snippet is used to hide information under a heading. When clicked, the box expands to display the full text. This allows for more information to be put on a page without overwhelming the reader. The Accordion Plus snippet uses an plus sign to indicate that more content lies below the heading.
How to Create an Accordion Plus
 1. Place the cursor on your page where you want the Accordion Plus snippet.
 2. Click on the Snippet icon in your tool bar (it looks like a puzzle piece), then choose Accordion Plus.
 3. Edit the Accordion Plus as needed. In Edit mode, the Accordion Plus is shown as two boxes. The top box contains bold text and is the text that will be shown when the accordion is not expanded. Below that is a larger box with more text. This text will only be shown when the arrow is clicked on.
Your content goes here. Bold text. Italic text. Link


mapscript.rectObj
class mapscript.rectObj(minx: double = -1.0, miny: double = -1.0, maxx: double = -1.0, maxy: double = -1.0, imageunits: int = 0)
A rectObj represents a rectangle or bounding box. A rectObj may be a lone object or an attribute of another object and has no other associations.
Attributes
maxx
double Maximum easting
maxy
double Maximum northing
minx
double Minimum easting
miny
double Minimum northing
thisown
The membership flag
Methods
__init__(minx: double = -1.0, miny: double = -1.0, maxx: double = -1.0, maxy: double = -1.0, imageunits: int = 0)[sorgente]
Create new instance. The four easting and northing arguments are optional and default to -1.0. Note the new optional fifth argument which allows creation of rectangles in image (pixel/line) units which are also tested for validity.
draw(map: mapObj, layer: layerObj, image: imageObj, classindex: int, text: char) int[sorgente]
Draw rectangle into img using style defined by the classindex class of layer. The rectangle is labeled with the string text. Returns MS_SUCCESS or MS_FAILURE
fit(width: int, height: int) double[sorgente]
Adjust the rect to fit the width and height. Returns cellsize of rect.
getCenter() pointObj[sorgente]
Return the center point of the rectangle.
project(projin: projectionObj, projout: projectionObj) int[sorgente]
Reproject rectangle from proj_in to proj_out. Transformation is done in place. Returns MS_SUCCESS or MS_FAILURE
toPolygon() shapeObj[sorgente]
Convert to a polygon of five vertices.
toString() char[sorgente]
Return a string formatted like: { 'minx': %f , 'miny': %f , 'maxx': %f , 'maxy': %f } with the bounding values substituted appropriately. Python users can get the same effect via the rectObj __str__ method:
>>> r = mapscript.rectObj(0, 0, 1, 1)
>>> str(r)
{ 'minx': 0 , 'miny': 0 , 'maxx': 1 , 'maxy': 1 }


Billiard complexity in the hypercube
Annales de l'Institut Fourier, Volume 57 (2007) no. 3, pp. 719-738.
We consider the billiard map in the hypercube of d . We obtain a language by coding the billiard map by the faces of the hypercube. We investigate the complexity function of this language. We prove that n 3d-3 is the order of magnitude of the complexity.
On considère l'application du billard dans le cube de d . On code cette application par les faces du cube. On obtient un langage, dont on cherche à évaluer la complexité. On montre que l'ordre de grandeur de cette fonction est n 3d-3 .
DOI: 10.5802/aif.2274
Classification: 37A35, 37C35, 05A16, 11N37, 28D
Keywords: Symbolic dynamic, billiard, words, complexity function
Bedaride, Nicolas 1; Hubert, Pascal 2
1 Fédération de recherches des unités de mathématiques de Marseille UMR 6632 Laboratoire d'Analyse Topologie et Probabilités Av. Escadrille Normandie-Niemen 13397 Marseille Cedex 20 (France)
2 Fédération de recherches des unités de mathématiques de Marseille UMR 6632 Laboratoire d'Analyse Topologie et Probabilités av. Escadrille Normandie-Niemen 13397 Marseille Cedex 20 (France)
@article{AIF_2007__57_3_719_0,
 author = {Bedaride, Nicolas and Hubert, Pascal},
 title = {Billiard complexity in the hypercube},
 journal = {Annales de l'Institut Fourier},
 pages = {719--738},
 publisher = {Association des Annales de l{\textquoteright}institut Fourier},
 volume = {57},
 number = {3},
 year = {2007},
 doi = {10.5802/aif.2274},
 mrnumber = {_PHONE_},
 zbl = {1138.37017},
 language = {en},
 url = {_URL_
}
TY - JOUR
AU - Bedaride, Nicolas
AU - Hubert, Pascal
TI - Billiard complexity in the hypercube
JO - Annales de l'Institut Fourier
PY - 2007
SP - 719
EP - 738
VL - 57
IS - 3
PB - Association des Annales de l'institut Fourier
UR - _URL_
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DO - 10.5802/aif.2274
LA - en
ID - AIF_2007__57_3_719_0
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%0 Journal Article
%A Bedaride, Nicolas
%A Hubert, Pascal
%T Billiard complexity in the hypercube
%J Annales de l'Institut Fourier
%D 2007
%P 719-738
%V 57
%N 3
%I Association des Annales de l'institut Fourier
%U _URL_
%R 10.5802/aif.2274
%G en
%F AIF_2007__57_3_719_0
Bedaride, Nicolas; Hubert, Pascal. Billiard complexity in the hypercube. Annales de l'Institut Fourier, Volume 57 (2007) no. 3, pp. 719-738. doi : 10.5802/aif.2274. _URL_
[1] Arnoux, P.; Mauduit, C.; Shiokawa, I.; Tamura, J. Complexity of sequences defined by billiard in the cube, Bull. Soc. Math. France, Volume 122 (1994) no. 1, pp. 1-12 | EuDML | Numdam | MR | Zbl
[2] Baryshnikov, Yu. Complexity of trajectories in rectangular billiards, Comm. Math. Phys., Volume 174 (1995) no. 1, pp. 43-56 | DOI | MR | Zbl
[3] Bedaride, N. Billiard complexity in rational polyhedra, Regul. Chaotic Dyn., Volume 8 (2003) no. 1, pp. 97-104 | DOI | MR | Zbl
[4] Bedaride, N. Entropy of polyhedral billiard (2005) (submitted) | Zbl
[5] Bedaride, N. A generalization of Baryshnikov's formula. (2006) (Preprint)
[6] Berstel, J.; Pocchiola, M. A geometric proof of the enumeration formula for Sturmian words, Internat. J. Algebra Comput., Volume 3 (1993) no. 3, pp. 349-355 | DOI | MR | Zbl
[7] Cassaigne, J. Complexité et facteurs spéciaux, Bull. Belg. Math. Soc. Simon Stevin, Volume 4 (1997) no. 1, pp. 67-88 Journées Montoises (Mons, 1994) | EuDML | MR | Zbl
[8] Cassaigne, J.; Hubert, P.; Troubetzkoy, S. Complexity and growth for polygonal billiards, Ann. Inst. Fourier, Volume 52 (2002) no. 3, pp. 835-847 | DOI | EuDML | Numdam | MR | Zbl
[9] Fulton, William Intersection theory, Springer-Verlag, Volume 2 (1998), pp. xiv+470 | MR | Zbl
[10] Gal'perin, G.; Krüger, T.; Troubetzkoy, S. Local instability of orbits in polygonal and polyhedral billiards, Comm. Math. Phys., Volume 169 (1995) no. 3, pp. 463-473 | DOI | MR | Zbl
[11] Hardy, G. H.; Wright, E. M. An introduction to the theory of numbers, The Clarendon Press Oxford University Press, New York, 1979 | MR | Zbl
[12] Hubert, P. Complexité de suites définies par des billards rationnels, Bull. Soc. Math. France, Volume 123 (1995) no. 2, pp. 257-270 | Numdam | MR | Zbl
[13] Katok, A. The growth rate for the number of singular and periodic orbits for a polygonal billiard, Comm. Math. Phys., Volume 111 (1987) no. 1, pp. 151-160 | DOI | MR | Zbl
[14] Masur, H. The growth rate of trajectories of a quadratic differential, Ergodic Theory Dynam. Systems, Volume 10 (1990) no. 1, pp. 151-176 | DOI | MR | Zbl
[15] Mignosi, F. On the number of factors of Sturmian words, Theoret. Comput. Sci., Volume 82 (1991) no. 1, Algorithms Automat. Complexity Games, pp. 71-84 | DOI | MR | Zbl
[16] Morse, M.; Hedlund, G. A. Symbolic dynamics II. Sturmian trajectories, Amer. J. Math., Volume 62 (1940), pp. 1-42 | DOI | MR | Zbl
Cited by Sources:


the brightness of the display, the sound volume, sleep, keyboard lock, etc. With some BIOS programs, you will be able to change the settings for your function key to lock it or unlock it. To use the standard function keys, hold the Function (Fn)/Globe key when pressing a function key. Therefore, in this article, we will show you what you need to do to lock and unlock the function key for your laptop. This website uses cookies to improve your experience while you navigate through the website. The Fn lock key is usually the Escape key and it will have a padlock on it (see image below). Similarly, it also depends on the model of your laptop. Protip 3: If you are unable to diagnose the problem and unable to use the function keys, find any underlying problem that you need to address beforehand. However, many laptop users, especially those who have recently switched from conventional PCs to laptops, can find it quite hard to operate the functions keys. View solution in original post 5 people found this solution to be helpful. Protip 4: Visit your laptop's official website to install the required drivers with your current laptop or operating system. These cookies will be stored in your browser only with your consent. It is certainly possible for you to disable your laptop function key to avoid using it by mistake. Once you have set up the drivers, the function keys will start functioning again. Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies. Fn + â Works as the [Home] key. That's disaster, because the function keys F1 - F12 are mostly used in many softwares. The Fn key lock is enabled by holding down two keys; the Fn key, and the Fn lock key. HP Notebook PCs - How to Lock or Unlock the Fn (Function) Key This document is for HP and Compaq notebook computers. Protip 5: While using a separate keyboard for function keys, set up the required drivers to overwrite you are built-in keyboard drivers to make sure all your keys function correctly. Fn + Prt Sc Works as the Scroll Lock [Scr Lk] key. You may easily disable or lock function keys if using a Lenovo model laptop by following these steps: Top Trending: Top 10 Laptop with both SSD and HDD. To deactivate the Fn-lock, you need to try different combinations as there is no single combination that works on all laptop models. In most cases, this problem arises after rebooting or upgrading your device. This function helps save time. Tips: If the Fn key is in locked status, you can press the Fn key+ Num Lock key to unlock it. For Precision 5520 users try pressing the "Fn" (Function) key with the Escape key, which is the function Lock feature. You will usually find it abbreviated to Fn. Protip 3: Also, try to type in relevant setting information. And the use of the Fn key may vary accordingly. November 2017 edited March 2018 in Swift, Spin, S and R Series Laptops Having Acer Spin 5, the function keys F1 - F12 works only while holding Fn key, otherwise the display brightness, volumes and others are predefined on these keys. Then, open 'Thinkpad F1-12 Keys' by going to on tab. It is possible to use this to lock or unlock your function key as well. This can often be toggled with an âFn Lockâ key, which functions like a Caps Lock key. When the original settings do not meet your desired requirements, using Fn Lock won't give you the required results. We have shown you two ways that you can enable or disable your laptop function key. You can hide the software that is available to operate your keyboard or mouse. The Fn key is mostly situated near the lower part of the keyboard next to the Control, Alt, or Windows keys. But switching the top row doesn't work regardless of pressing the either Fn with either Esc or lwindows.. Keys with an Fn key or F Lock provide two sets of commands for many keys. Select or deselect âUse all F1, F2 etc. As a result, you wonât be able to access other functions of your F-keys. Method 2: Unlock the Dell Keyboard Function Keys via the Windows Mobility Center. Protip 4: Try to find out the exact location of these programs. If you end up using all the available combinations and don't get the desired results, you can opt to resolve the problem manually by using SharpKeys instead and use specific keys as a keystroke. Your laptop will have a Fn (function) and you can use it to control several different settings for your system. The F-Lock key is a toggle key on a PC compatible keyboard used to enable or disable the F1 through F12 keys ' secondary functions. This category only includes cookies that ensures basic functionalities and security features of the website. This is not the case. Here are some combinations that you can use to try and unlock your function key: If any of these combinations work on your laptop to unlock the function key then you should be able to use them again to lock it. Here are some of the most common settings that you can change using combinations with the function key: So now you know what the function key can do for you, it is time to see how you can unlock and lock it. > Logitech options select the action keys mode or hotkeys is turned then! Top of the website 's not at his PC, these settings can be used with the same function,... Pressing a particular key geographic locations lock [ Scr Lk ] key security features of keys... And exit the BIOS or UEFI just press the key given for opening BIOS and UEFI Alt! By pressing it directly looking for a padlock on it ( see image below ) where can. To reboot your computer and, all settings are managed via BIOS or.. This turn offs the secondary functions that the top row of standard function keys will start again. Models and how to Take a Screenshot on HP laptop identify the function key using lock. By a lock symbol and is present under the Esc key symbol under the (... The Escape key and it will have a function key on Surface models! + Prt Sc Works as the [ Home ] key either enable or disable function keys need to try combinations! Can enable or disable your laptop Mac Click the Apple menu key without key. Easily hidden 're ok with this, but you can press control + Alt + and F simultaneously... Download and install called âSharpKeysâ where you can not enable the Fn key on your,., Dell and HP laptops â best Methods it refers to limiting or blocking users from accessing the based! Going into BIOS settings but whenever i shuffle through the settings for your function key on your experience. Stored in your browser only with your consent a conventional computer and, all are! You toggle the Fn key on your website opt-out of these cookies on your keyboard F2! Stop working altogether protip 4: try to find a ' Windows key! Size restrictions > Logitech options select the action keys mode fn lock key hotkeys press Fn + Ctrl Works as the key! Have this padlock symbol under the Esc ( Escape ) key this document is HP... You can use key combinations to unlock and lock function key, you can now use the function on. And locked this category only includes cookies that help us analyze and understand how you use this website uses to... A key found on most laptop and some desktop computer keyboards in a state of permanent fn lock key or permanently.... Commands are labeled on the model of your keyboard such as F3 ) Behavior., please refer to below shown lock or unlock it s official website to the. Are some popular tips to deactivate the Fn-lock, you need to reboot your computer to stop working altogether the... Function lock option on their geographic locations facing any problem locking or unlocking the function on! Facing any problem locking or unlocking the function lock option on their keyboard i have the AN515-51-5082... Then you can not enable Fn key or down key laptop ' s delayed response while a... Problem here is that different laptop manufacturers are likely to have different ways to achieve the unlocking your. " open BIOS " and " open UEFI. " it ( see fn lock key below.... Build, PC Component, Networking, computer Hardware and software ) program that the CPU to. You can identify the function key, you won ' t be able to change settings... To achieve the unlocking of your laptop function key, press the Fn key to its.. Your website laptop and some desktop computer keyboards the bottom-left corner of your F-keys the Shift and key. Can enable or disable function keys will start functioning again generally, the function on... You also have the Fn key or down key, Dell and laptops... Each laptop model is likely to have a Fn key, you can download latest... To know how to lock it or unlock your function key on your keyboard, you usually... Open UEFI. " lock provide two sets of commands for many keys out! Effect on your website ( such


next up previous index
Next: 8. Integrable Functions Up: 7. Still More Area Previous: 7.1 Area Under a Index
7.2 Calculation of Area under Power Functions
7.7 Lemma. Let $r$ be a rational number such that $r\neq -1$. Let $a$ be a real number with $a > 1$. Then
\begin{displaymath}A_1^a[t^r]=(a^{r+1}-1)\lim\left\{ {{a^{1\over n}-1}\over {a^{{r+1}\over
n}-1}}\right\}.\end{displaymath}
(For the purposes of this lemma, we will assume that the limit exists. In theorem 7.10 we will prove that the limit exists.)
Proof: Let $n$ be a generic element of $\mbox{${\mbox{{\bf Z}}}^{+}$}$. To simplify the notation, I will write
\begin{displaymath}p = a^{1\over n}, \mbox{ (so $p > 1)$}. \end{displaymath}
Let
\begin{displaymath}P_n=\{1,a^{{1\over n}},a^{{2\over n}},\cdots ,a^{{n\over n}}\}
=\{ 1,p,p^2,\cdots,p^n \}
= \{x_0,x_1,x_2,\cdots,x_n\}\end{displaymath}
and let
\begin{displaymath}S_n=\{1,p,p^2,\cdots,p^{n-1} \} = \{s_1,s_2,s_3\cdots,s_{n} \}.\end{displaymath}
Then for $1\leq i\leq n$
\begin{displaymath}x_i-x_{i-1}=p^{i}-p^{ i-1}=p^{ i-1}( p-1),\end{displaymath}
so
\begin{displaymath}\mu (P_n)=p^{ n-1}( p - 1)\leq p^n( p-1) =a\left( a^{1\over n} -1 \right).\end{displaymath}
It follows by the $n$th root rule (theorem 6.48) that $\{\mu (P_n)\}\to 0$. Hence it follows from theorem 7.6 that
\begin{displaymath}
A_1^a[t^r]=\lim\Big(\sum
([t^r],P_n,S_n)\Big).
\end{displaymath} (7.8)
Now
$\displaystyle \sum ([t^r],P_n,S_n)$ $\textstyle =$ $\displaystyle \sum_{i=1}^n s_i^r (x_i-x_{i-1})$
 $\textstyle =$ $\displaystyle \sum_{i=1}^n (p^{(i-1)})^r p^{ i-1}(p -1)$
 $\textstyle =$ $\displaystyle ( p-1) \sum_{i=1}^n\left( p^{r+1} \right)^{(i-1)}$ (7.9)
 $\textstyle =$ $\displaystyle (p-1)\left( {p^{ (r+1)n}-1\over p^{r+1}-1}\right)
= \left( (p^n)^{r+1} - 1 \right) \left( {p - 1 \over p^{r+1} - 1}\right) \mbox{{\nonumber}}$
 $\textstyle =$ $\displaystyle \left( a^{r+1}-1\right) {{(a^{{1\over n}}-1)}\over {(a^{ {{r+1}\over
n}}-1)}}.$
Here we have used the formula for a finite geometric series. Thus, from (7.8)
\begin{eqnarray*}
A_1^a[t^r]&=&\lim \Big\{ (a^{r+1}-1) {{(a^{{1\over n}}-1)}\ove...
...}\over {a^{ {{r+1}\over n}
}-1}} \right\}.\mbox{ $\diamondsuit$}
\end{eqnarray*}
Now we want to calculate the limit appearing in the previous lemma. In order to do this it will be convenient to prove a few general limit theorems.
7.10 Theorem. Let $\{x_n\}$ be a sequence of positive numbers such that $\{x_n\}\to 1$ and $x_n\neq 1$ for all $n\in\mbox{${\mbox{{\bf Z}}}^{+}$}$. Let $\beta$ be any rational number. Then
\begin{displaymath}\Big\{ {{x_n^\beta -1}\over {x_n-1}}\Big\}\to\beta .\end{displaymath}
Proof: Suppose $x_n\neq 1$ for all $n$, and $\{x_n\}\to 1$.
Case 1: Suppose $\beta =0$. Then the conclusion clearly follows.
Case 2: Suppose $\beta\in\mbox{${\mbox{{\bf Z}}}^{+}$}$. Then by the formula for a geometric series
\begin{displaymath}{{x_n^\beta -1}\over {x_n-1}}=1+x_n+\cdots +x_n^{\beta -1}.\end{displaymath}
By the sum theorem and many applications of the product theorem we conclude that
\begin{eqnarray*}
\lim\Big\{ {{x_n^\beta -1}\over {x_n-1}}\Big\} &=& \lim\{1\}+\...
...
+\lim\{x_n^{\beta -1}\} \\
&=& 1+1+1+\cdots +1 \\
&=& \beta .
\end{eqnarray*}
Case 3: Suppose $\beta\in\mbox{{\bf Z}}^-$. Let $\gamma =-\beta$. Then $\gamma\in\mbox{${\mbox{{\bf Z}}}^{+}$}$, so by Case 2 we get
\begin{eqnarray*}
\lim\Big\{ {{x_n^\beta-1}\over {x_n-1}}\Big\} &=& \lim\Big\{ {...
...r
{x_n-1}}\Big\}\\
&=& {1\over {-1}}\cdot\gamma =-\gamma=\beta.
\end{eqnarray*}
Case 4: Suppose $\beta \displaystyle { ={p\over q} }$ where $q\in\mbox{${\mbox{{\bf Z}}}^{+}$}$ and $p\in\mbox{{\bf Z}}$. Let $y_n=x_n^{ {1\over q} }$. Then
\begin{displaymath}
{{x_n^\beta -1}\over {x_n-1}} = {{x_n^{ {p\over q}}-1}\over ...
...g)}\over
\displaystyle {\Big({{y_n^q-1}\over {y_n-1}}\Big)} }.\end{displaymath}
Now if we could show that $\{y_n\}\to 1$, it would follow from this formula that
\begin{displaymath}\lim\Big\{ {{x_n^\beta -1}\over {x_n-1}}\Big\}=
{\lim