Workday Adaptive Planning Knowledge Center
FAQs for Sheets
How-to: Configure parameters that automatically update
Yes, you can do this by linking together your time parameters. You can link any time element, except for timespan, to a single period parameter.
Example: You have a report with three segments with separate time parameters that you want to set up so that update automatically changing one parameter will automatically update the other parameters.
To link parameters:
 1. Drag and drop the first time element to the parameter bar
 2. Then, drag and drop the other two time elements on top of the first parameter
 3. After adding the parameters, right-click on the Period parameter to verify that the elements are connected
 In Parameter Settings, several dynamic time options are available when you scroll to the top of the Initial Choice setting such as current month and last actuals month.
How-to: Calculate percent of sales for an account
You can use the Display as Percent report element to display results for multiple accounts.
Example: You have a revenue account called Book Sales want to know what Book COGS is as a percentage of Book Sales.
To calculate percent of sales:
 1. Click Display As and add the % of Account element to your report
 2. Right-click on the newly added % of Account element and select the Book Sales account as the denominator for the calculation
 3. Add any account that you want to see as % of Book Sales
How-to: Create a subtotal for different time periods from different versions
You can use the Custom Display As element to create a subtotal.
Example: You want to create a subtotal using the first six months a budget version and the last six months of a forecast version. Assuming that your report already has 2 segments set up (#1 first 6 months for the budget version and #2 last 6 months for the forecast version), we can set up a third segment that will contain our calculations for the subtotal.
To create a Custom subtotal:
 1. Add a new segment
 2. From the Calculations menu, add a Difference element to the new segment
 3. In the Difference Options, include the two versions that you want to use for the subtotal and make sure to offset the Subtract Version 6 months Backwards
 4. From the Calculations menu, add a Custom Calculation element below the difference element in the segment that sums the last 6 months
 - Because the difference element is offset, it will sum the first 6 months with the last 6 months
 5. From the Display As menu, add a Custom element to the bottom of the segment and include the formula below where "offset version" is the version offset in the Difference element
 - if(this.version.name = "offset version", -ACCT.this, ACCT.this)
In the steps above, we are using a workaround to make the difference element a sum instead. The reason we use the difference is because it allows us to operate with 2 different versions in a single calculation, where as it is impossible, currently, to formulaically refer to values in another version from you current version.
How-to: Create a variance between two different versions and time periods
You can create a report that shows the variance between Budget 2020 version for FY2020 and Budget 2021 version for FY2021 by offsetting the time for one of the versions forward or backward.
To create the report:
 1. Place both the Budget 1 and Budget 2 versions in one segment
 2. Add a 2020 Time element to the segment or Filter
 3. Right-click on the Budget 2 version and select Properties
 4. Shift the version forward by 12 months.
 - By shifting the time forward, the Budget 2 version will display data for 2021 when the Budget 2 version is displaying data for 2020
 5. Add a Difference element next to the versions.
 6. Right-click on the Difference element, select Properties and verify that the Difference element is creating the proper variance and that the Budget 2 version is shifted forward by 12 months.
The resulting report should give you 3 columns: one for Budget 2020, one for Budget 2021, and one for the variance between the two versions.
How-to: Remove total rows for accounts
Totals can't be removed for a parent account in Report Properties. When the option to "Show totals at bottom" is checked in Report Properties, the total for the parent account will be shown as a row at the bottom of the rollup. When you uncheck "Show totals at bottom," the totals will appear in the same row as the parent account at the top of the rollup. As a workaround to remove totals, you can remove totals by dragging each account to the report builder separately.
To remove totals:
 1. From Design Elements, add a custom header to the report, right-click to select Properties, and update the label to represent the parent account
 2. Drag and drop the accounts that rollup to the parent account that we didn't add to the report to prevent displaying its total
How-to: Reverse the sign for non-GL accounts in Reports
Because the reverse sign feature in reports only applies to GL accounts, you can use a custom calculation to reverse the sign for non-GL accounts in a matrix report.
Example 1:
 - Formula -1*ACCT.Example
 - Translation: Multiplies the account by -1 to reverse the sign for the account
Example 2:
 - Formula: if([Budget]<[Actuals], div(([Budget]-[Actuals])/[Actuals])*-1, div(([Budget]-[Actuals])/[Actuals]))
 - Translation: If the Budget value is less than Actuals, then take the variance and multiple by negative one, otherwise just take the variance
How-to: Create a rolling 12 month average report


Hooded Warbler Habitat Selection
January 1, 1993 by Gregory Gough
Male and female hooded warblers separate into different habitats in the non-breeding season. In the Yucatan Peninsula in Mexico long-running studies revealed that males occupy forest habitat while females are in the treefall gaps, forest edges, and other adjacent shrubby habitats.
small yellow bird
The key difference between the male and female habitats is the orientation of the vegetation. Males like their plant stems to be up and down while the females prefer their stems to be at an angle.
So ingrained is this preference that laboratory studies of hand-raised hooded warblers revealed that strips of black crepe paper arranged vertically were preferred by males whereas oblique arrangements were preferred by females.
But what would happen if the vegetation structure changed? In 1988, Hurricane Gilbert slammed into the study area and snapped off many a tree top.
In areas that had previously been the provenance of males, and had suffered significant changes to the vertical structure of the forest, females moved in. In areas that were relatively untouched the males remained.
This article summarizes the information in this scientific paper:
Morton, Eugene S., Van der Voort, M. and Greenberg, Russell S. 1993. How a warbler chooses its habitat: Field support for laboratory experiments. Animal Behaviour, 46: 47-53
Download scientific paper


This snapshot, taken on
Frequently Asked Questions
This page answers some questions which are most often asked about UK bank and public holidays. It is written in general terms only and should not be regarded as a complete and authoritative statement of the law. The entitlement to paid annual leave is contained in the provisions of the Working Time Regulations.
What are bank holidays?
Bank holidays are days in the whole or part of the UK on which banks may close for business. The law makes provision for certain payments to be deferred until the next appropriate day for this purpose.
Does this entitle employees to a holiday?
What rights do employees have on bank holidays?
Any right to time off or extra pay on bank holidays depends on the terms of an employee's contract of employment. Even when entitlements of this nature are not explicitly written down, they may sometimes be incorporated by custom and practice (for example, where they have become part of the customary terms of employment in a particular industry).
Does the Government have any plans to ensure that employers do not include bank holidays as part of the 20 days statutory annual leave entitlement?
See Holiday Entitlement page.
When are the bank holidays?
The expected dates of bank and public holidays in England, Wales, and Northern Ireland for 2005 to 2008 inclusive have been announced by the DTI. Following Devolution, dates for Scotland are a matter for the Scottish Executive.
There are currently 8 permanent bank and public holidays in England and Wales and Scotland and 10 in Northern Ireland. These include Christmas Day and Good Friday which, in England, Wales and Northern Ireland, are common law holidays - they are not specified by law as bank holidays but have become customary holidays because of common observance.
What happens when bank holidays fall on a weekend?
Substitute days are customarily appointed for all UK bank and public holidays which fall on a Saturday or Sunday. For some bank holidays, these substitute days are laid down in legislation. In other cases, they are appointed by Royal Proclamation (or Proclamation by the Secretary of State for Northern Ireland). The substitute day is normally the following Monday.
What happens to those workers who normally work weekends when certain bank holidays fall at a weekend i.e. Christmas?
Time off for the actual Christmas Day and Boxing Day would be determined by a worker's contract of employment which may have been explicitly agreed or incorporated by custom and practice.
Is there provision for special bank holidays?
Provisions in the legislation enable the dates of bank holidays to be changed or other holidays to be declared, for example to celebrate special occasions. The most recent examples of special bank holidays were for the Royal Wedding in 1981, the Millennium holiday in 1999 and the Queen's Golden Jubilee in 2002.


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Guide to becoming a better manager with PINot a PI Client? Request a Demo
Have your employees completed the PI Behavioral Assessment? If not, use the Sending Assessments Guide to learn how to assess your employees and understand their drives, needs, and behaviors in the workplace. Then, come back here to learn about leveraging those results to develop your management capabilities.
All set? Now let's begin.
Here's your roadmap to using PI's tools to develop managers.
1. Manage people
Use these tools when:
- Entering a managerial role for the first time
- Managing a new employee
- Handling conflict between two employees
Whether you're a first time manager or one with years of experience, PI's Manager Development Chart provides you with actionable insights based on your behavioral drives. The chart includes a description of your natural strengths and respective caution areas to consider as a manager. There are also self-coaching tips provided to help you balance your most naturally occurring behavioral style in a variety of situations.
Here's how to generate the Manager Development Chart:
Have you ever managed two employees who just don't see eye to eye? Employee conflict can lead to decreased motivation, trust, and performance on a team.
The PI Relationship Guide is a tool designed specifically to mediate these conversations. Through awareness of employees' communication styles, strengths, cautions, and blockers, this guide can help you form better, more effective working relationships while minimizing personal squabbles.
Here's how to generate the 1:1 Relationship Guide:
Don't let different working styles get in the way of productivity. Reach out to your PI Champion to learn more about how the relationship guide can help you navigate those complex work relationships!
Are two employees not seeing eye to eye? Download their Relationship Guide and set up a meeting with them both. Here's a general framework for this conversation:
1. Start with Relationship Strengths – Open the conversation by exploring the strengths that the two recognize in each other. For example, " [Person 1] tell me something that [Person 2] does really well."
2. Move on to Relationship Cautions – Ask each employee to describe the conflict at hand without interrupting each other. If the conflict aligns with any of the cautions listed on the Relationship Guide, let the employees know that the conflict arose from a difference in their natural behaviorsthis often provides a sense of relief. If not, move on to step 3.
3. Give Relationship Tips – Using what you learned in the session and what you already know about the two employees, facilitate a conversation that explores actions they can each take based on the Relationship Tips section of the Relationship Guide. Remember that Relationship Strengths can be leveraged while planning these actions!
2. Manage expectations
Use the Management Strategy Guide when:
- Becoming a new manager for a team
- A new employee is added to the team
- Meetings with employees, such as 1 on 1s and Performance Reviews
A common pitfall for managers is thinking, "If I treat everyone how I want to be treated, I'll be a great manager." PI's Management Strategy Guide gives managers custom insights into how to manage others the way they want to be managed— no guesswork involved.
The guide identifies what management strategies will enable individuals to thrive, based on their behavioral preferences for workplace interactions, how they take action, respond to risk, and make decisions.
Here's how to generate the Management Strategy Guide:
Check out our Guide to Developing Individuals for more examples on when to use the Management Strategy Guide!
Print, download, or email a direct report's Management Strategy Guide to share with two people:
- The direct report
- The manager
(Both people should receive the same version of the Management Strategy Guide)
Have the manager and their direct report(s) work through the Management Strategy Guide exercise separately.
- The direct report should review page 1 and complete item 1 (Reflect) on page 2 as an assessment of their manager
- The manager should review page 1 and complete item 1 (Reflect) on page 2 as an assessment of themselves
Then, bring the two together for an action planning conversation. During this meeting, the manager and direct report will compare their responses from page 1 of the Management Strategy Guide to review both strengths and opportunities.
Finally, the manager & direct report will use items 2, 3, and 4 on page 2 of the Management Strategy Guide to build an action plan based on the discussion. Do this 1-2 times a year.
3. Manage growth
Use the Coaching Guide when:
- Aligning an employee's natural behaviors with your expectations of the role
- Preparing a new employee for the behavioral expectations of their role
- Coaching an employee towards better performance
Use the Coaching Guide to provide your employees with custom reflection questions based on their behaviors. These prompts will help them leverage their natural strengths for a given role—or identify areas of growth and actions to take to more closely meet the company's expectations for their role.
Consider what you are trying to achieve as a manager. Take into account the employee's situation. Is this a new employee? A low performer? High performer? Disengaged team member? This context, along with your intended outcome, will influence how you approach the conversation and identify specific actions to take to improve performance.
Here's how to generate a Coaching Guide:
- It is important that the employee come up with specific goals, and the solutions to take them to the next level. Support the employee in taking ownership of both the goal and the solution. Ask the employee where they think they have room for improvement. You may "know" the solution, but the idea is to get the employee to realize this on their own.
- Remember that the goal should be SMART (specific, measurable, achievable, relevant, and timely).
- Ask questions to help the employee come up with action items to accomplish their performance goal, such as, "What are some ways you could do that?"
- Here's an Employee Goals template that can help you get started.
- Follow up with the employee.
- Before the end of the meeting, agree to a follow-up plan. The follow up is an important but often forgotten step; work gets busy, and schedules become packed. Put time on your calendars now to check in later for progress, which can help keep both you and the employee accountable.
- Suggested check in dates are 30, 60, and 90 days out for short-term goals, or quarterly for longer-term goals.
When the employee's goal is attained with their current job, celebrate the accomplishment! Now it's time to look toward the future and what opportunities or career paths are available for the employee. Repeat this process with a future job in mind.
Use the Manager's Guide to Reference Profiles
General tips for managing employees for each of the 17 Reference Profiles.
PI's People Management Study
Discover the traits that most strongly correlate with great (and terrible) managers.

source: openbmb/Ultra-FineWeb


and comment more fully
CHAPTER 12 – The Arc
Why Arc was a game changer? Because it allowed explosion of all other GBs. The details would be explained below.
This is an important graph that you need to understand how Arc works.
The X axis is level of onwer's Arc that is being worked on
The Y axis is net cost of Arc (it means that total FPs required MINUS FPs earned by donor including donor's Arc bonus). This means total FPs required to complete GB after maximum FPs are harvested from rewards.
Different lines represent different Arc bonuses of donors. The better the donor bonus, the less the owner of GB has to pay for his GB because more FPs is coming back from the rewards.
Positive overall Y value means that GB owner must contribute to level GB, while negative value means that GB owner can actually profit from leveling a GB.
This graph assumes that GB owner works with 5 other donors that have the same arc value (different lines).
arc gb.jpg
The reason why you have such a graph pattern is because the reward although it is unknown, it appears to be linear, while total FPs of Arc is exponential (next level total FPs = previous level total FPs *1.025). During levels 0-10, the total FPs values are fixed, while rewards are small. This is why you have such an increase in cost. During levels 10-50, the exponential function is early stage and is overrun by linear function of rewards. While after lvl50, the exponential function (total FPs) explodes with respect to linear function (rewards), making GBs very pricey. You can appreciate the impact of the increasing rewards by noticing that after lvl10 the different color lines are further and further apart, while after lvl60 they start to come closer again becasue rewards become insignificant with respect to overall cost of GB.
The Arc increases to 30% in first ten levels, then by 1% to level 60, then for next 20 levels by 0.5% until 190% total, and then 0.1% per level afterwards.
In early spring 2016, we were able to develop this graph when our Arc's were just started to grow. We understood that if Inno made 1% per level or even 0.5% per level, we could have huge profits (we assumed that initial lvl20, lvl40, lvl60 pattern would follow and there was possibility that overall cost of GB would be negative). However, Inno correctly assigned 0.1% after lvl80, still theoretically possible to achieve a time when certain GBs levels become free of real cost, but limiting these levels to narrow range of 40-60 only when huge arc bonuses are provided as donors.
Notice that for "average" player who gets a little bit extra on top of his reward maybe 100% or 120% or 140%, the cost really increases with level. Majority of players will not be able to break through the "cheap" levels, and they will be stuck in expensive range lvl5-20 forever. Even if they do, starting from lvl 20-30, they will start to be heavily sniped as GB is much more attractive with rewards and this increasing the cost for the host again. This is basically 95-99% of all players. First, you need to get to higher level, and second you need donors with high arc to provide the combination that does the magic.
The costs pattern is not identical for each individual GB and that goes beyond of this topic, but it follows similar patterns.
Majority of average experienced players (unless they do not earn horrendous amounts of FPs) stop their GBs around lvl60-80. If you follow the teal line which represents the 100+90% arc (lvl80) donor, the line starts significantly creep up after owner of GB reached lvl60, and shoot up vertically after lvl80.The rule of thumb is that even with all 90% arcs, the lvl80 for most GBs costs about 1000 FPs, and that is often too much.
The reason players choose to take their arc from lvl60 to lvl80 is because there is a significant in GB leveling cost reduction from purple line (80%) to teal line (90%). It might appear initially that there is a little difference between 180% and 190% in sniping, but that is a big difference. If the sniping profits margins are small e.g. 10%, additional 10% might double the profit making the large investment into Arc reasonable. There are players that rush their Arc beyond 90%, but in reality that will not have a significant impact. In order to provide costs on such investments these players will have to hoard FPs left and right, snipe day and night, and employ an army of noobs that will feed Fps in variety of ways to them. This action is often driven by wanting to have highest GB in the ranking. The cost of leveling arc 80->180 lvl is about few million FPs, and that is just too pricey for 10% extra bonus for 99.999% players.
This graph also explains why levels 30-70 are so prone to sniping from outside. This is because the rewards are increasing significantly with respect to not so fast increasing total FPs making GB attractive to stealing what could have been used to level the GB, but then leaving the empty unfilled gap, and if it is done on correct GB, the GB owner is usually forced to cover the remaining.
The little Zig-Zaging of the function line is due to rounding to nearest "5fp" on GBs, and it has no significant effect overall.
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CHAPTER 13 – GvG HQ and Defense Bonus
One of most annoying thing that can happen is when an inexperienced member with trusted rights moves HQ, and that person has minimal understanding of the consequences and mechanism of HQ bonus distribution that can easily lead to your guild losing several additional sectors.
50% and especially 75% sectors are a deterrent. They can be killed by larger guilds pretty quickly, but in repetitive fights when filled with correct defense units especially when attacker is forced to go auto, it can cause significant damage to the attacker. 0% sectors are much more vunerable and easier to kill, and often attacker losses less than half of units than defender. An action from one person placing HQ correctly and understanding how 50% bonus is applied to sectors can often cause more damage to other guild than several fighters. That skill can give an edge when war is pretty even.
The specific age defense points are different to the Support Pool Bonus that guilds receive from guild level. However, they are linked by support factor.
(Support Pool Bonus + Total defense bonus from all defense GBs in guild) / Support Factor for specific age = Total defense points for specific age
> Support Pool Bonus
A guild receives these points for higher level. It is the number with a shield.
> Total defense bonus from all defense GBs in guild
Every defense GB contributes extra points on top of Support Pool Bonus. St. Basil contributes 3 points (for 1st 10 levels), Deal Castle contributes 3 points (for 1st 10 levels), and observatory contributes 10 points.
> Support factor
It is a number that is preset. They can be derived by solving the equation above when it is only the variable missing. It can be derived also from the ratio of support factors when you know total defense points for specific age. Also other numbers from that equation can be derived for example, you do not have to add all your defense GBs within the guild, but you can derive the total.2
I derived them previously, but I can be wrong if I do not remember them correctly. Please let me know if I got it wrong.
IA - 1.0
EMA - 1.5
HMA - 2.0
LMA - 3.0
CA - 4.0
InA - 6.0
PE - 8.0
ME - 10.0
CE - 12.0
TE - 14.0
TF - 16.0
AA - 16.0
> Total defense points for specific age
This is a total number of % that is redistributed to sectors as a defense.
For most (higher ages) the maximum % defense for HQ is 75% and other sectors is %50
Exceptions include (HQ/other sectors)
InA 25%/0% | EMA 35%/10% | HMA 45%/20% | LMA 55%/30% | CA 65%/40%
These lower values make sectors less stable and easier to take making it less attractive to older and larger guilds.
In our case = Support Pool Bonus (8540) + Total defense bonus from all defense GBs in guild (3092) = 11632 total bonus
Specific age (AA) total defense bonus = 11632 / 16 = 727 (%)
In other words, we can fill one HQ (75%) and 13 other sectors (13*50%=650%) total of 725% before next sectors will not have full bonus.
The defense bonus is distributed in concentric circles from HQ, which means the closest sectors to HQ have the priority to receiving it. Here is how priority of sectors would look like on these arrangements. If there is enough defense bonuses on HQ, it would spread to 1-away-from-HQ, if all sectors have enough bonus that are 1-away, then 2-away would receive defense bonus and so on.
On this image the


Risk analyses
Technology is evolving rapidly. What is the solution for the future today may be outdated the day after tomorrow. The Ingenium Risk Analysis team uses sensitivity analysis to map out the future risks of an energy project and proposes flexible solutions that are future-proof.
This flexibility can cover various aspects. For example, the fuel used - and the cost price evolution, availability, government support - is a crucial factor in the TCO for a particular energy solution. For example, heating a building solely on biogas carries a risk if the price of gas were to rise sharply in the future. However, heating networks are future-proof. While they usually use the recovery heat from waste plants today, in the future, they may also be fed by another heat source.
Another parameter is the possibility of renovating, repairing or expanding the installation in the future. Especially in large and complex projects, such as hospitals or buildings that are delivered as hulls, it is important to take account of functional changes and evolutions in the building volume during the initial design of the technical installations.
The concepts and scenarios proposed by Ingenium always take possible risks and evolutions into account. Calculating fluctuations in the price of raw materials or maintenance and scenarios for the evolution of the buildings from the start makes a project future-proof.


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What is the difference between a chisel plow and disc ripper? A chisel plow consists of a narrow and two-faced shovel to shuffle the upper layer of the soil, whereas a disc ripper's main task is to deep tillage using a metal disk.
Chisel plow and disk ripper- a set of complicated debate to win. Both are lawn maintenance tools with a plethora of differences that can blow your mind.
However, today we shall endeavor to explain the chisel plow vs disc facts and all the complications regarding these farming tools. And this composition will cover only the vital spikes which depend on my standpoints.
Chisel Plow Vs Disc Ripper
|Shattering is the prime task.
|Can break the compacted soil.
|Can reach at most 30 CM below the ground.
|Can reach at most 90 CM of the ground.
|Allows drainage and airflow less than a ripper.
|Allows drainage and airflow densely.
|Requires moist soil.
|Requires dry soil.
|Primary level tool.
|Advanced level tool.
Before jumping to the differences, we must inform you not to be confused with the question, chisel plow or disc harrow? or both of them.
A disc harrow is a piece of equipment to prepare the soil to throw the seeds and germination.
It is also advantageous for removing unnecessary weeds. Nonetheless, too much utilization of this tool breaks the soil structure that harms the plants from growing.
About the difference between chisel plow and ripper or disc ripper, the distinctions are challenging to express. Yet, have a look at the table below.
The design of both tools competes with many segments. Hence, to discuss chisel plow vs disc ripper, the first aspect is the design. The module of the disc ripper allows it to dig or go through the soil by 35 inches or 90 CM.
This means it can break the soil into pieces so that water and nutrients can reach the maximum level.
The blueprint of the chisel plow is utterly for the beginner farmer who is new to farming. The design allows the farmer to break the soil for the crops, which require low depth to spread the roots.
If we go for chisel plow vs disc ripper, you must choose the chisel for your learning period if you are a newcomer in this farming world.
In the case of a chisel plow, the actual size of the shanks is 12 inches. And, about the thickness of the shank is a minimum of 1.25 inches which causes exquisite ramifications on the soil. Furthermore, vertical free space is above 27 inches.
Both tools are for utilization, yet, we will still explain plow vs disc in this term. At first, the chisel plow, without any doubt, is a blessing for the farmers who are farming vegetables or dreaming of producing them.
The procedure of utilizing this tool is undemanding. However, it would help to connect the chisel plow with the tractor. A chisel plow can dig around 30 CM; hence, you need to dig it into the soil. While inserting the shovels, you must notice if the shovel is entering the soil correctly or not.
It is the most vital part of using a chisel plow. Once you insert the shovels correctly, you are ready to smear your soil by driving the tractor.
After the chisel plow, here comes the disc ripper. The primary task of the disk ripper is to till the soil deeply. And the utilization procedure is similar to the chisel plow.
First, you need to dig the large shovels of disk ripper into the soil. And start maneuvering the tractor. The disk ripper will do its job. And the harrow of the disc ripper will remove the weeds from the soil as needed for your new cultivation.
According to the application system and purposes, you must choose either a chisel plow or disc ripper. However, the disk ripper's primary task is to shatter the soil beneath the upper level, especially from 30 to 90 CM.
It can even reach the area where people with traditional, conservative, or reserved tools can't reach. As a result, the draining becomes proper. Moreover, soil can intake more nutrients than average systems.
When the term comes to the chisel plow vs disk, chisel plow is another vital tool for farmers. The design of the chisel plow allows the soil to break. But the soil must be moist. Moreover, it can only dig up to 30 CM. Hence, a chisel plow is applicable where folks do not require deep tillage.
The prices of the varieties of both tools differ entirely from size to size and brand to brand. Nonetheless, we can provide you with an assumption. The average price of an ordinary disc ripper is around $25000 for a used one and $65000 for a new one.
Due to the size and functions of a chisel plow, it costs less to own. You need to spend $45000 on a new one, and you can get a used one by spending less than $20000.
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Frequently Asked Questions (FAQs)
When would you use a disc Ripper?
The use of a disc ripper or a chisel plow utterly depends on your entire purpose. If you are planning to grow those plants that do not require plenty of depth, you must use a chisel plow.
But, if you are planning for long rooted plants, you must use a disc ripper for serving the plant a set of proper nutrition.
What is the purpose of a chisel plow?
The prime purpose of chisel plow is breaking or smearing the soil so that you can easily plant the short-rooted plant. And, the tillage of a chisel plow is at most 30 CM by the shovels. You can also use it as a beginner to the farming world.
How much horsepower do you need to pull a chisel plow?
The horsepower of a tractor is a prime factor for the chisel plow. Most importantly, the requirements of the horsepower depend on the size of the chisel plow.
If the chisel plow's size is small or has less shovels, it will require less horsepower. If the size and number of shovels increases, it will require more horsepower. However, the average requirement is _PHONE_ horsepower.
How fast should you pull a chisel plow?
Farming is a job of patience and control. If you desire to view maximum output, you must maintain a speed of 6 to 6.5 mph. If you speed up and cross the limit, the soil may not smear properly.
A chisel plow vs disc are incomparable. It is your purpose that will determine what you need. If you are a beginner landscaper and farming for those plants which require less depth to spread their roots, you must go for chisel low.
If it is not and you are growing those which require a profound depth in the soil, you ought to for a disc ripper.
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Enamored with the world of golf Jack pursued a degree in Golf Course Management at THE Ohio State University. This career path allowed him to work on some of the highest profile golf courses in the country! Due to the pandemic, Jack began Inside The Yard as a side hustle that quickly became his main hustle. Since starting the company, Jack has relocated to a homestead in Central Arkansas where he and his wife raise cattle and two little girls.

source: m-a-p/FineFineWeb


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Author Judith Barton of Streeter presented an amusing and informative program to members of the Mason Bluebonnet Study Club at the Richard Eckert Center on February 21. A timeline of how her children's book entitled "Too Many Chickens" became a reality was outlined in sometimes fun details, other times serious ones. It all began with her husband's love of raising birds. He ordered 25 chickens and built a house for them. Mrs. Barton said that most of the chickens turned out to be roosters, even the "bonus chicken".
Facinated by this growing story, Mrs. Barton who was a retired art teacher took pictures of the developing saga. The pictures painted a story in her mind.
As the chickens grew, the house became smaller. She said that she could hear them bumping around in there at night....too many chickens.
For a child's birthday present, Barton put together a story using the pictures with appropriate prose to describe each part of the life of the chickens.
Having taken a class on putting together homemade books, she put this first book together and put it in a drawer where it resided until her son took an interest and persuaded her to enhance it and self publish. With added prose and watercolor art depicting her original pictures, the book was published and is available at Benjie's Books and Gifts.
Hints were given on how to put together homemade books and where to find materials needed were given as a part of her program. She showed different types of covers that can be created out of ordinary things one can find around the house. She encouraged members to make their own books as gifts.
Attending Mrs. Barton's presentation were Edna Earle Benton, Maudi Bergmann, Mary Hemphill, Carol Jordan, Tanya Lamoreaux, Sabin Nelson, and hostess Betty Meyer.
The next meeting of the Mason Bluebonnet Study Club will be a study of Texas Heritage in Music. The group will meet in the Methodist Church parking lot on March 21 at 10:45 a.m. and carpool to Brady. Lunch will be at the Patio Cafe, then a guided tour of the Heart of Texas Country Music Museum will follow.


\frac{3}{4} |z_i|^2 Im \frac{\sqrt{\pm D}}{b+2z_i^3} = \frac{3}{4} |z_i|^2 Im \frac{\sqrt{\pm D}}{2az_i -b} $$
Now we can sum over the roots and get $$ A = \frac{1}{4} Im \left(\sqrt{\pm D} \sum \frac{|z_i|^2}{2az_i -b} \right) $$ and we are letf with expressing the sum in the brackets as a function on $a$ and $b$.
My algebra gives $$ \sum \frac{|z_i|^2}{2az_i -b} = \frac{\pm \sum \frac{b}{|z_i|^2}}{b^3 + 4a^3b} $$ but I do not see any easy way to deal with the expression $\sum \frac{1}{z_i \bar z_i}$. Of course one can solve the cubic equation and work it out, but there should be an easier way.
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It seems to me that the question is fully Russian: Dima, Igor, Wadim and Kassabov. – Wadim Zudilin Nov 23 '11 at 11:47
Sorry, but I am not russian :) – kassabov Nov 23 '11 at 12:05
What is the prizinal polynomial? – Igor Rivin Nov 23 '11 at 14:00
igor: I've meant original – kassabov Nov 23 '11 at 14:16
_USER_: I was conjecturing that, but my ignorance is deep, so there might have been some associated polynomial I was not aware of :) – Igor Rivin Nov 23 '11 at 16:24
For $t$ real, the area determined by the roots of $x^3-x^2+tx-t=(x-1)(x^2+t)$ is either $\sqrt{t}$ or $0$ according as $t \gt 0$ or $t \lt 0.$ At first that made me think that there is no hope. But now I think that maybe the polar coordinates of the coefficients are better to look at. One can go back and forth after a fashion using $\arctan.$ Another thought is that given $x^3+ax^2+bx+c$ one should work with $a^6$,$b^3$ and $c^2$ to account for the effect of scaling.
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Rotisserie Grilling Sample: Charcoal vs Gas
It's I wrote a Cookbook week on DadCooksDinner!
To whet your whistle, here's a sample section from Rotisserie Grilling. I let my inner food geek run wild, and explore the science of rotisserie. Enjoy!
—Start Excerpt—
Sidebar: Charcoal vs. Gas
The cheapest charcoal grill browns meat better than most gas grills. Why?
Warning! Science content ahead. If you want to skip it, the summary is: Meat browns as meat juices are exposed to heat and evaporate. Dry heat browns better than wet heat because the extra water has to evaporate before the meat will start to brown. Burning charcoal is dry heat. Burning gas releases water, making wet heat. Therefore, charcoal browns meat better than gas.
Starting science content. My wife, the high school chemistry teacher, made sure I have the science correct. She says you better not skip ahead. There will be a quiz.
Why is dry heat better than wet heat? The Maillard reaction.
The Maillard reaction occurs when sugars and amino acids are exposed to heat in a dry environment; the result is browning and the release of water. "The result is browning" is shorthand for complex chemical interactions that scientists are still figuring out. The sugars caramelize, interact with the amino acids, and produce all sorts of flavor compounds. Those flavor compounds are what make the browned crust on a roast so delicious.
Meat is full of protein fibers and meat juices. When meat is cooked, the heat tightens the muscle fibers, and they squeeze juices out of the meat. The meat juices are full of sugars and amino acids, and when they reach the surface of the meat, they are exposed to heat. That starts the Maillard reaction. As the juices brown, they release more water. That extra water slows down the Maillard reaction until it evaporates, and browning starts again.
Water prevents browning. Meat needs to be cooked at 350°F or higher to evaporate the water fast enough to keep the browning reaction going, and higher temperatures are better. Boiled meat is gray, without any browning at all, because it is covered with water. This is why recipes recommend patting food dry before cooking; any extra water slows down browning until it evaporates.
Now we get to charcoal versus gas. (Finally!)
Charcoal is wood heated in an oxygen free environment. When all the water in the wood has evaporated, you are left with carbon. When carbon is burned, it produces heat, carbon dioxide, and a little carbon monoxide. That's our dry heat – no water.
Gas is either propane or methane (also known as natural gas). When gas is burned, it produces heat, carbon dioxide, and water. That water is the problem – it needs to be evaporated by the heat of the grill before the Maillard reaction will start.
Now for the good news: a rotisserie helps browning, whether you use gas or charcoal. Escaping juices roll around the surface of the meat, spreading the sugars and amino acids so the Maillard reaction can do its thing. Yes, a charcoal grill with a rotisserie browns better than a gas grill with a rotisserie. But, a gas grill with a rotisserie browns about as well as a charcoal grill without a rotisserie. If you have a gas grill, don't give up – the rotisserie will still help.
End Science content. You can keep reading now.
If you want a gas grill that browns as well as a charcoal grill, you need more heat, to help evaporate the extra water. This means more burners, especially infrared burners, which do a great job of generating heat. But that makes the grill more expensive. It's tough to beat a cheap kettle grill filled with charcoal.
Don't get me wrong; I use both charcoal and gas grills. In a perfect world, I would use charcoal all the time. However…gas grills are so convenient. They're easy to light and provide constant, even heat as long as you don't run out of gas. There are no worries about charcoal burning down and cooling off; there's no need to add extra coals every hour. In the middle of February, when every trip to the grill involves shoveling snow, I love that extra convenience.
—End of excerpt—
The book:
Rotisserie Grilling by Mike Vrobel
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An annotation that designates that an annottee should not be referred to after type checking (which includes macro expansion).
Examples of potential use: 1) The annottee can only appear in the arguments of some other macro that will eliminate it from the AST during expansion. 2) The annottee is a macro and should have been expanded away, so if hasn't, something wrong has happened. (Comes in handy to provide better support for new macro flavors, e.g. macro annotations, that can't be expanded by the vanilla compiler).
Value Params
the error message to print during compilation if a reference remains after type checking
class Object
trait Matchable
class Any


Part IV – Plane detection, a first step to implementing panorama hotspots
In order to be able to detect hotspots under the mouse, the first thing we need to do is find some way to detect which plane the mouse is currently over and what the local x,y coordinates of the mousecursor are in the local space of that plane.
Instead of providing all the theoretical background I want to try and make it conceptually clear how we can do this. So let go of the mouse coordinates for a moment and take a look at our untransformed starting cube we discussed in a previous post:
The Cube
We can see that a cube is nothing more than a space enclosed by 6 planes. We can even specify the equations for these planes:
The Cube Planes
The plane numbers correspond to how we have defined our planes in the panoramas these past examples. Contained within this cube is the set of all (x,y,z) coordinates with an absolute value for x, y and z less or equal to 1. In addition for the coordinates that lie exactly within a plane of the cube, 'special' equations hold. For example for plane 0 we could say that Math.abs(x) <= 1 AND Math.abs (y) <= 1, which is the same as saying that for all points in plane 0, Math.abs(x) <= Math.abs(z) AND Math.abs (y) <= Math.abs(z). But this is true for plane 2 as well, so how do we differentiate between these two planes? Simple, check the sign of z. If z < 0 and Math.abs(x) <= Math.abs(z) and Math.abs (y) <= Math.abs (z), or even shorter, if z < 0 and Math.abs(x) >= z and Math.abs (y) >= z, we are dealing with points in plane 0.
It gets even better, if the planes are closer or further away from the origin (0,0,0) and in effect the cube is smaller or larger, this will still hold. In order words seeing the z instead of -1 and 1 in the example equations above means that these equations hold for planes parallel to our planes as well. And we can write these kind of equations for each plane. So given any point you can tell in which plane (or rather quadrant) the point lies by looking at "the sign of the coordinate having the largest absolute value" (from page 142 from Mathematics for 3d Game Programming and Computer Graphics).
Visually this means that given any point contained in the cube you cannot only tell in which plane it lies, but in which quadrant as well. In other words if you view a cube as 6 pyramids put together, you know in which 'pyramid' a point lies by looking at "the sign of the coordinate having the largest absolute value".
The Cube Pyramids
(A cube's content split into 6 pyramids)
So the next problem presents itself: when we are pointing at a certain pixel in our cube, what is it's coordinate? We can calculate the coordinate by pointing a vector in the direction of our mouse pointer and see where it intersects one of the 6 planes. But how do we calculate the direction of the vector based on the position of the mouse pointer?
Remember the information we discussed in an earlier post about relating the field of view, wall size and wall distance (projection plane distance)?:
projectionplane_distance = (wallsize/2) / tan (fov_in_radians * 0.5)
Visually:
Calculating the field of view
The area within the rectangle on the wall, is the area of our 3d space actually visible on the screen.
(Note that we are using the same field of vision horizontally as we are vertically, like it has been in our panorama's all this time)
What this did in effect, was given a wall size (stage size in pixels), and a field of vision, calculate the projection plane distance.
Once we have a projection plane distance, we could pick a point in the visible area of our 3d space, in other words a point on our stage, in other words at a certain distance in pixels from the center of the wall/stage, and calculate what the angle of a vector towards that point on the wall would be:
First for the angle alpha which represents the angle between a vector pointing straight at the screen and the mouse x position:
projectionplane_distance = x_offset_from_center / tan (alpha) =>
projectionplane_distance * tan (alpha) = x_offset_from_center =>
tan (alpha) = x_offset_from_center / projectionplane_distance =>
alpha = atan (x_offset_from_center / projectionplane_distance)
The x_offset_from_center is the difference between the center of the stage and the mouse x in pixels.
Of course the mouse position does not only present an offset across the x axis but across the y axis as well:
We can see the same formula applies, however instead of the projectionplane_distance we need to use pythagoras on the plane distance and the mouse y offset from the center, to calculate the length of our adjacent, which gives us the following y angle:
beta = atan (y_offset_from_center / sqrt (projectionplane_distance^2 + x_offset_from_center^2))
So now, given any vector that goes through our camera and points at the center of the screen, we can create a vector that points at the pixel under our mouse by rotating it by the calculated angles.
rotatedvector = [0 0 z].rotateY (alpha).rotateX(beta)
Visually:
Pick whatever you want for z for example [0 0 -1] or [0 0 -10] or whatever. As long as x and y are zero and we are pointing away from the camera.
So now we have rotated vector, what can we do with it?
If we view our rotated vector as a point, we can determine in what quadrant of the cube we are. However we are faced with another problem. The principle that "the sign of the coordinate having the largest absolute value" determines that quadrant only works for an unrotated cube. And we are constantly rotating our cube as we are looking around in our panorama. So we have to 'undo' the rotation of the cube on our rotated vector, which gives us the vector we would have had if we were able to point at the same spot in the unrotated cube and use that one to determine in which quadrant (is quadrant actually the right term or should it be pyramid?) our vector lies:
_lastX = _canvas._xmouse;
_lastY = _canvas._ymouse;
var lDeltaXFromCenter:Number = _lastX - _viewportWidthDiv2;
var lDetaYFromCenter:Number = _lastY - _viewportHeightDiv2;
//tan (alpha) = opposite/adjacent
var lXAngleFromCameraToMouseX:Number = Math.atan(lDeltaXFromCenter / _projectionPlaneDistance);
var lYAngleFromCameraToMouseY:Number = Math.atan(lDetaYFromCenter / Math.sqrt((lDeltaXFromCenter * lDeltaXFromCenter) + (_projectionPlaneDistance * _projectionPlaneDistance)));
StageUtil.printScreen ("Mouse angles:" + lXAngleFromCameraToMouseX + "|" + lYAngleFromCameraToMouseY);
StageUtil.printScreen ("Pan/tilt angles:" + _pan + "|" + _tilt);
//now create a center point vector which points at the mouse coordinates by rotating it by our deduced angles
var lCenterPointVector:Point3D = new Point3D(0, 0, -1);
var lMatrix:IdentityMatrix3D = new IdentityMatrix3D();
lMatrix.rotateX (lYAngleFromCameraToMouseY); //is in radians
lMatrix.multiplyVector (lCenterPointVector);
lMatrix.rotateY (lXAngleFromCameraToMouseX); //is in radians
lMatrix.multiplyVector (lCenterPointVector);
//undo cube rotation
lMatrix.rotateX ( -_tilt * _toRadians);
lMatrix.multiplyVector (lCenterPointVector);
lMatrix.rotateY ( -_pan * _toRadians);
lMatrix.multiplyVector (lCenterPointVector);
var x:Number = Math.abs (lCenterPointVector.x);
var y:Number = Math.abs (lCenterPointVector.y);
var z:Number = Math.abs (lCenterPointVector.z);
var lPlane:Number = null;
if (z >= x && z >= y) {
 if (lCenterPointVector.z < 0) {
 lPlane = 0;
 } else {
 lPlane = 2;
 }
} else if (x >= y && x >= z) {
 if (lCenterPointVector.x < 0) {
 lPlane = 3;
 }


Add
Adds a license key to the set of keys of a particular type.
Syntax
Key Add(string key)
Parameter
Specify the following parameter when using this method:
Parameter Description
key
The license key string to add to the set.
Return value
The added license key object.
Exceptions
Add may throw one of the following exceptions:
 - ApplicationException if the license key has expired, is invalid, or is a non-FIPS 140 key on a system that requires FIPS 140 keys.
 - ArgumentException if the parameter is null or empty or if the key already exists.


text:
The domestic liner MS-21 will receive a system for monitoring the state of structures. Nikolay Lvov, General Director of the company-developer of the system NIC "IRT", announced this.
According to him, the state of the composite wing on the MS-21 will be monitored in real time. "We have signed a roadmap and a plan, now the terms of reference for the implementation of the system on MS-21 are being developed", – said the head of the company.
The monitoring system is a set of miniature sensors of various physical nature (sensors of acoustic emission, deformation, temperature, corrosion, etc.), which are installed in the structure of aircraft and carry out a comprehensive measurement of various parameters of their condition. The received information is processed using a specially created software package and displayed in an accessible form on the laptop of an aviation technician. The system detects the beginning of the appearance of defects in the structure, their development, the appearance of cracks and informs about a possible violation of the integrity of structures.
MS-21 is a medium-haul civil aircraft under development with a capacity of 163 to 211 passengers. At the end of 2021, the aircraft received a basic type certificate, in December it made its first flight with a Russian composite wing.
It was expected that at the first stage the aircraft would be delivered to customers with PW1400 engines, later they would have a choice between PW and Russian PD-14. But in the current situation, there is no longer any alternative to the PD-14. MS-21 with a domestic engine is now being tested, he has already made more than 100 successful flights.


text:
The restoration of optical images, as well as the unfolding of spectroscopic and other data that have been convolved with a window function or an instrumental impulse response, can be viewed as the solution of an integral equation. Solution of such an integral equation when the data are corrupted by noise or experimental error is treated as the problem of finding an estimate that is a linear functional of the data and minimizes the mean squared error between the true solution and itself. The estimate depends on assumptions about the spectral densities of the images and the noise, the choice of which is discussed. Coherent optical processing and digital processing are described.
CARL W. HELSTROM, "Image Restoration by the Method of Least Squares," J. Opt. Soc. Am. 57, 297-303 (1967)


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An automatic accompaniment generator for infinite melodies, applied to a simple mapping of the decimal digits of π to an A–harmonic-minor scale.
module PiMelody where
import Data.List
data MelodyNote = Gs | A | B | C' | D' | E' | F' | Gs' | A' | B'
deriving (Eq, Show, Enum)
type Melody = [MelodyNote] -- Assume simple all-quavers rythm.
piMelody :: Melody
piMelody = map toEnum piDigits
data Chord = Am | Dm | C | G7 | E
deriving (Eq, Show, Enum)
type Composition = [(Melody, Chord)]
-- (Infinite) list of pairs: a melody chunk, and what chord to go with it.
chordMNotes :: Chord -> [MelodyNote] -- Without suspensions.
chordMNotes Am = [A, C', E', A']
chordMNotes Dm = [A, D', F', A']
chordMNotes E = [Gs, B, D', E', Gs', B', F'] -- Minor dominant may also be diminished-7th.
chordMNotes C = [C', E']
chordMNotes G7 = [B, D', F', B']
resolves :: Chord -> [Chord]
resolves E = [Am, E] -- Dominants should resolve to their tonic, if at all.
resolves G7 = [C, G7, Am, E] -- For major dominant, allow also resolving to minor parallels.
resolves _ = [Am.. E] -- Non-dominant chord can resolve to anything.
accompany :: Melody -> Composition -- Choose suitable chords for a melody.
accompany melody = acc Am melody
where acc :: Chord -> Melody -> Composition
acc lastChord (n1:n2:ml) -- Try to find a chord that fits over two melody notes
| (Just nextChord) -- and works with the previous (possibly dominant) chord.
<- find (\ch -> all('elem' chordMNotes ch) [n1,n2]) $ resolves lastChord
= ([n1,n2], nextChord) : acc nextChord ml
-- If two melody notes don't fit in one chord, use two.
| (Just c1) <- find ((n1'elem'). chordMNotes) $ resolves lastChord
, (Just c2) <- find ((n2'elem'). chordMNotes) $ resolves c1
= ([n1], c1) : ([n2], c2) : acc c2 ml
piDigits :: [Int] -- Infinite list of decimal digits of π. Algorithm taken from:
-- Jeremy Gibbons, "Unbounded Spigot Algorithms for the Digits of Pi";
-- The Mathematical Association of America 2005.
piDigits = map fromInteger $ g(1,0,1,1,3,3)
where g(q,r,t,k,n,l) = if 4*q+r-t


text:
ISIS/Base is the successor of the DOS program ChemBase. ISIS/Base is a Methuselah of a program. The first version was developed in1989. It needs constant effort by MDL because it serves a dual purpose. It is the client for ISIS/Host, and it is a stand-alone chemical database system for the PC or Macintosh.
I once calculated that MDL would have to charge 500'000 USD for ISIS/Base, if you compare it on functionality with what was sold in 1984. Today, the industrial price is around 1000 USD and 300 USD for academic users.
ISIS/Base was formed not by MDL programmers, but by MDL users. This is the reason that ISIS/Base is one of the best programs for single user who want to manage chemical structures, reactions and data on the PC.
Its main uses are:
Field Type Definition in ISIS/Base
Fixed Text Text of a specified number of alphanumeric characters. A fixed-text field can store any number of characters up to the maximum number specified in its definition. However, no fixed-text field can contain more than 80 characters. (For example, MDL-000001 is the maximum number of characters that can be entered for a fixed-text field that has been defined to have a 10 character length.)
Variable Text Alphanumeric text of an unlimited length (limited solely by computer memory).
Integer For PC and Macintosh systems, the value of an integer may range from -_PHONE_ to +_PHONE_.
Real A real number, such as 1.50. The decimal-place precision of the number varies with computer systems.
Range A range of real-number values, such as 2.0 - 3.5. The decimal-place precision of the number varies with computer systems.
Date The date format (such as day/month/year) specified in your windowing software configuration file(s).
Sketch An ISIS/Draw sketch.
Structure A molecule (including a 3D structure, reactant, or product). You can have multiple structure fields in your database, but each field must have a unique name.
Reaction A chemical reaction. You can have multiple reaction fields in your database, but each field must have a unique name.
Parent Parent fields do not store data. Instead, parent fields point to one or more fields that store related data. For this reason, the parent field name should be representative of the types of data that the lower-level fields will store. For example, is the parent field for journal and author. ISIS/Base displays parent field names in brackets to distinguish them from other fields.
The calculated field type only applies to remote databases and cannot be selected as a field type in a local database.
You need ISIS/Draw to draw structures. ISIS/Draw is free of charge for academic and private use. Instead of drawing structures you can download structures from many sources on the Internet, or convert them to Molfiles using the conversion programs ConSystant & Chemeleon provided with ISIS/Base.
For moe information go to MDL® ISIS/Base.


text:
Beliefs and performance
The cognitions, or thought processes, in which an athlete engages may be critical to performance. A 1996 study by Williams and Leffingwell, Cognitive strategies in sport and exercise psychology, found several assumptions underlie the use of cognitive-behavioral inventions:
- Cognitions can affect athletic performance.
- These thought processes can be changed.
- This change can influence behavioral change, and therefore, improve performance.
They identified several areas of irrational beliefs that may affect an athlete's performance. In particular, they indicated that perfectionist demands may cause a poor self-concept or feelings of inadequacy, which increase the likelihood of failure. However, they distinguish between perfectionist demands and perfectionist desires indicating that a perfectionist desire, which is achievable and not judgmental, may increase the likelihood of success. Other irrational beliefs include:
- Considering failure a catastrophe
- Basing self-worth on achievement
- Focusing on fairness in competition
- Generalizing from a single performance to overall competence


text:
Planet Palooza mBot Automation Weeks I & II Combined
June 21 @ 9:00 am - June 26 @ 12:00 pm| $130
June 14, 2021
June 21, 2021
June 28, 2021
July 5, 2021
In this accelerated week of activities, Campers will learn to work with NASA planetary data to upload, sort, analyze, calculate, and respond to research questions using spreadsheets. They will explore relevant science data related to planetary geography, weather, climate, and physics as aligned with Next Generation Science Standards.
With the guidance of a camp facilitator available during the day, campers will use the data gathered from their research activities to build and program an mBot Educational Robot Kit (or similar device) to showcase the knowledge gained throughout the week.
This camp is most appropriate for students in 9th grade or higher.
Planets: Venus, Mercury, Earth, Uranus, Mars, Saturn, Jupiter, Neptune


Dsastat Syntax
DsaStat Syntax
DsaStat uses the following syntax:
Imagem dsastat [/loglevel:{INFO|TRACE|DEBUG}] [/output:{SCREEN|FILE|BOTH}] [/s:ServerName[PortNumber][;ServerName[PortNumber]...]] [/t:{TRUE|FALSE}] [/sort:{TRUE|FALSE}] [/p:PageSize] [/scope:{BASE|ONELEVEL|SUBTREE}] [/b:SearchPath] [/filter:LdapFilter] [/gcattrs:{[LDAPAttributes[Attribute;Attribute...]]| [ObjectClass]|[Auto]|[All]} [/u:UserName] [/pwd:Password] [/d:Domain
Parameters
/loglevel:{INFO|TRACE|DEBUG}
Specifies the extent of logging that is performed during execution. The default option is INFO.
/output:{SCREEN|FILE|BOTH}
Specifies where the results of DsaStat are displayed. If FILE is selected, the output is saved to a file named Dsastat.log.nnnnn. The default option is BOTH.
/s: ServerName[PortNumber][;ServerName[PortNumber]...]
Specifies the names of the servers on which the comparison is performed. Separate each server name with a semicolon (;). The server name can be appended with the TCP/IP port number. If PortNumber is 3268, the comparison is performed against the global catalog of that server. The default port number is the default LDAP port (389).
/t:{TRUE|FALSE}
Specifies whether to perform a statistics comparison or a full-content comparison. Setting /t: to TRUE performs a statistical comparison. Setting /t: to FALSE performs a full-content comparison. The default is TRUE. The statistical comparison merely counts the objects. It does not compare the attributes of the objects that have been retrieved from the domain controllers and it ignores the /gcattrs parameter. A full-content comparison retrieves every object with attribute values and performs a comparison of the attributes of the same object from different domain controllers.
/sort:{TRUE|FALSE}
Determines whether the search operations are performed with sorting based on object GUID. Setting /sort: to TRUE performs sorted queries. Setting /sort: to FALSE does not perform sorted queries. The default value is FALSE. Performing a sorted query by setting this option to TRUE has a negative impact on performance; however, it complements the full-content comparison because it ensures that objects are returned in nearly the same order from different servers and improves the performance of full-content comparison.
/p: PageSize
Sets the number of entries to be returned per page for ldap_search operation. The valid range for PageSize is 1-999. The default value is 64. If the directory objects are large (such as user objects with many of their attributes populated with values), it is advisable to use a smaller page size.
/scope:{BASE|ONELEVEL|SUBTREE}
Specifies the extent of scope for the search operation. The default option is SUBTREE.
/b: SearchPath
Sets the distinguished name of the base search path. This allows DsaStat to perform the comparison against any subtree of the directory.
/filter: LdapFilter
Sets LDAP filter used in the LDAP search operation. The filter must conform to LDAP search syntax as specified in RFC 2254. The default filter is (objectclass=*).
/gcattrs:{[LDAPAttributes[Attribute;Attribute...]]| [ObjectClass]|[Auto]|[All]}
Specifies attributes to be returned from search. This option is used only if the comparison parameter /t is set to FALSE: LDAPAttributes specifies any LDAP attribute available. Multiple attributes may be specified separated by semicolons. ObjectClass specifies that no attributes be displayed. Auto specifies that only the attributes replicated to the global catalog be displayed. All specifies that all attributes contained in an object be displayed
/u: UserName
Specifies the user name to use for the query.
/pwd: Password
Specifies the password to use for authenticating the user name. Must be used with the /u parameter.
/d: Domain
Specifies the domain to use for authenticating the user name. Must be used with the /u parameter.
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text:
As a DJ, there are many ways to make a positive impact on the music scene. From hosting events and organizing music festivals to creating your music, there are plenty of opportunities to influence the music scene positively. Here are some tips to help you make a positive impact.
Host Events and Music Festivals
Hosting events and music festivals is a great way to make a positive impact on the music scene. These events can provide an opportunity for local artists to showcase their work, and can also be a hub for people to connect and enjoy music.
Create Your Music
Creating your music can be a great way to make a positive impact on the music scene. Whether you're producing beats, writing lyrics, or creating music videos, you can add your unique sound and style to the music scene. Don't be afraid to take risks and explore different genres and styles.
Support Local Artists
Supporting local artists is a great way to make a positive impact on the music scene. Seek out local artists and attend their shows, or purchase their music and merchandise. Music producers supporting local music, you can help them progress and make their mark on the music scene.
Promote Music Education
Promoting music education is another great way to make a positive impact on the music scene. Whether you're teaching classes or volunteering at local schools, you can help to foster a love of music and encourage young people to get involved in the music scene.
Promoting diversity is essential for making a positive impact on the music scene. Make sure to include different perspectives and genres in your music selection and events, and support artists from all backgrounds. Don't be afraid to challenge yourself to think outside of the box and break the mold.
Participate in Music Conferences
Attending music conferences is another great way to make a positive impact on the music scene. You can meet other artists and industry professionals, share ideas and gain valuable insight into the latest trends. You can also learn about the latest technology and techniques for producing music.
Get Involved with Local Charities
Getting involved with local charities is a great way to make a positive impact on the music scene. Whether you're hosting fundraising events, donating proceeds from shows, or offering your services as a DJ, your efforts can help to make a difference in your community.
Share Your Knowledge
Sharing your knowledge is a great way to make a positive impact on the music scene. Whether you're writing blog posts, giving interviews, or making tutorials, you can help to inspire and educate others. It's also a great way to build relationships and connect with other artists.


Support Site for The Unemployed & Underemployed
Tuesday July 29th 2014
Find the error, its impossible
maths pic
Find the error, its impossible:
Did you know that 80% of UCDS students could not find the error above?
Forward this to at least 5 people with the title 'Find the error, it's impossible',
and when you click 'Send', the answer will be right in front of your eyes!
Reader Feedback
34 Responses to "Find the error, its impossible"
 1. Misy says:
 What is the answer?
 2. Laurence says:
 Okay, the fact that you said that 20% of the students solved it contradicts the fact that you said the error is impossible to find. If someone found the error, then it's not impossible.
 I have a hint that this question is just another way for someone to chain posts.
 There are some riddles like these that do have answers, but I believe this is just another one that's a waste of time.
 3. Barbara says:
 Only error I see is there's no ' in the word it's in "its impossible"…
 4. Shego13524 says:
 Also, I think there should be a semicolon instead of a comma… But I agree with the fact that it's not impossible due to the 20% of people who did find it… Although that data wasn't in the version they got, was it?
 5. max field says:
 There are a few errors, depending upon what kind of problem for which one is looking. One is that the series of numbers should begin with zero. Another is that there should either be a period or a semicolon where the first comma is. I use periods after "error" and after "impossible." Another problem is that "its," as used in the sentence should is "it is," so there should be an apostrophe as in "it's." Those UCDS students aren't very bright, are they?
 6. Colter says:
 The answer is "impossible"
 It says to find the error above; when you look above you'll notice it states "Find the error, ITS IMPOSSIBLE". The numbers are all in chronological order so there is no error there, and the data referring to the UCDS students is worthless. It's one of those trick questions were learn to solve in grade school. Hope this helps, happy holidays!
 7. Ashley says:
 The answer is NOTHING…because when you click SEND, NOTHING is right in front of your eyes!!!
 8. Josh says:
 The answer is its (its impossible). It should be it's. The error is an error of grammar. If you look closely in the text for what title to use when forwarding this on to 5 people, the apostrophe is present on the it's. Therefore being right in front of your eyes when you email it.
 9. nidger says:
 Find the error, its IMPOSSIBLE..
 the answer is IMPOSSIBLE.. nothing to do with the numbers..or how its spelt..
 it is or it's must be a statement..!!!
 10. Pretty Boy says:
 The "Error" here is that the numbers do not start from '0′ but from the number '1′… '0′ (Zero) is a number too and it must be the first in the row… simple… :)
 11. David says:
 The error is in grammar. supposed to be IT'S instead of ITS.
 12. Robert Wakeford says:
 I've been looking on the web for the answer to this and it seems about 50/50 as to whether the answer is 'grammer' or 'nothing'.
 Personally I like the grammer answer.
 13. Jeff says:
 Its simple…There is no "0″ to start…The row of numbers should start with "0″.
 14. Jeff says:
 Its simple…There is no "0″ to start…The row of numbers should start with "0″. Also meaning Nothing..which stats about seeing it when u forward. You see nothing or zero.
 15. Jeff says:
 Error #2
 The answer has NOTHING to do with the numbers, and it isn't a grammatical or punctual error. The error itself is in syntax. The title states that it is impossible, yet it says 80% of UCSD students could NOT solve it. Therefore, 20% HAVE solved it, meaning it is in fact NOT impossible. There's the error.
 16. jb says:
 well email says it's "ALMOST" impossibleso therefore the answer does not have anything to do with the wording. If there is an error it has to be something else. It may be the apostrophe that's missing from the word (it's).
 17. keeks says:
 totally agree with Jeff… the error in the mail is inconsistency when it says it's impossible at first and then that 20% people could find the error :)
 18. MCFLeetwood says:
 Hi – Actually if done correctly using a font where the lower case L looks like the number one, then when you forward and click send it goes from reading l23456789l0l1l2l3l4l5l6l7l8l920
 to L23456789L0L1L2L3L4L5L6L7L8L920
 I have tried this several times changing fonts, but never got the JEST behind it. I must be amoung the 20% with bad Grammer lol – MC
 19. mojorisin1970 says:
 There is NO error in the sequence of numbers, its not impossible. Therefore, it is possible. Hope this helped
 20. Alex says:
 The answer is in the first sentence..
 The error is stating that Its (It's) impossible. The fact that it has been solved by any percentage, means that it is possible. If the problem was impossible, then it would be 100% of the students.
 Find the error, its impossible..
 error = impossible
 21. david l says:
 LOL!! Ya'll should try looking up UCDS!! LOL!! The whole idea is to make everyone think as hard as all of you did and completely miss the obvious.
 22. Melanie says:
 A lot of you are right, but just not completely. See above website for Wikianswers.
 23. Jim says:
 the answer is very simple :find the error ….the word error is all you have to find….thats it…
 24. Jim says:
 said another way…..find waldo….what do you do…you look for waldo hidden somewhere on the page…
 25. gigi says:
 The Error is the the sentence of:
 "Find the error, its impossible"
 there are some reasons why they are:
 #1 after error there is suppose to be a period
 #2 Its should be "It's" and therefor It's would have to be capital
 #3 theres no period
 #4 impossible is suppose to be capital
 26. Michael B says:
 I guess it is impossible to find an error where no error exists. Interesting that 20% of the students found an error. Is this the 20% that failed?
 27. Clark says:
 Not sure where most of you went to school but, in Ohio, we studied GRAMMAR, not 'grammer' and the challenging sentence does, indeed, contain errors in GRAMMAR and punctuation.
 28. Alex says:
 Find the error. "It's impossible".
 29. eddie says:
 The error is the actual words "The Error". That's what they are looking for here.
 30. GRoblich Magflurg says:
 It's grammatical it should read Find the error. It's impossible. Use of full stops.
 31. Andrew says:
 The answer is rather overlooked, and would not be very obvious to anyone who did not attend the school. (or were overly obsessive, as I am.)
 Most look to the grammatical error as the 'all in all error' but one other thing struck me. I asked myself 'who's this 80%' and did a Google search for UCDS… it's a developmental school, where as UCSD is a highly prestigious school. Now if you think about this being delivered to people attending the University of California San Diego, not noticing the error in the school's initials sounds a lot more of a 'Ohhhhhhh, dang it!' than "oh, 'its' should have an apostrophe."
 The likely hood of someone mistyping UCSD as UCDS is far less likely, as it has a fairly large connection to most people, far more than its versus it's.
 Of course, with how often this has gone around the internet it's been changed over and over again. I tried to look to the earliest I could find, and all of them had UCDS. Which was later corrected. Thought it was odd that no one has pointed that out.
 Of course, I'm not always right, so it could be grammatical, I simply see it more likely being a misspelling of the school.


an improved
 MCF model based CAD flow that performs aggressive
 optimizations, such as topology and wire style
 optimization, to reduce the energy and switch area of
 FPGA global routing architectures. The experiments show
 that when compared to traditional mesh architecture,
 the optimized FPGA routing architectures achieve up to
 10\% to 15\% energy savings and up to 20\% switch area
 savings in average for a set of seven benchmark
 circuits.",
 acknowledgement = ack-nhfb,
 articleno = "13",
 journal-URL = "_URL_
 keywords = "FPGA; global routing; low power",
}
@Article{Huang:2009:OPR,
 author = "Shih-Hsu Huang and Chia-Ming Chang and Yow-Tyng Nieh",
 title = "Opposite-phase register switching for peak current
 minimization",
 journal = j-TODAES,
 volume = "14",
 number = "1",
 pages = "14:1--14:??",
 month = jan,
 year = "2009",
 CODEN = "ATASFO",
 DOI = "_URL_
 ISSN = "_PHONE_ (print), _PHONE_ (electronic)",
 bibdate = "Mon Jan 26 18:12:50 MST 2009",
 bibsource = "_URL_
 _URL_
 abstract = "In a synchronous sequential circuit, huge current
 peaks are often observed at the moment of clock
 transition (since all registers are clocked). Previous
 works focus on reducing the number of switching
 registers. However, even though the switching registers
 are the same, different combinations of switching
 directions still result in different peak currents.
 Based on that observation, in this article, we propose
 an ECO (engineering change order) approach to minimize
 the peak current by considering the switching
 directions of registers. Our approach is well suitable
 for reducing the peak current in IC testing.
 Experimental data consistently show that our approach
 works well in practice.",
 acknowledgement = ack-nhfb,
 articleno = "14",
 journal-URL = "_URL_
 keywords = "IC testing; Logic synthesis; peak current; sequential
 circuit synthesis",
}
@Article{Lin:2009:SCD,
 author = "Yen-Chun Lin and Li-Ling Hung",
 title = "Straightforward construction of depth-size optimal,
 parallel prefix circuits with fan-out 2",
 journal = j-TODAES,
 volume = "14",
 number = "1",
 pages = "15:1--15:??",
 month = jan,
 year = "2009",
 CODEN = "ATASFO",
 DOI = "_URL_
 ISSN = "_PHONE_ (print), _PHONE_ (electronic)",
 bibdate = "Mon Jan 26 18:12:50 MST 2009",
 bibsource = "_URL_
 _URL_
 abstract = "Prefix computation is used in various areas and is
 considered as a primitive operation. Parallel prefix
 circuits are parallel prefix algorithms on the
 combinational circuit model. The depth of a prefix
 circuit is a measure of its processing time; smaller
 depth implies faster computation. The size of a prefix
 circuit is the number of operation nodes in it. Smaller
 size implies less power consumption, less VLSI area,
 and less cost. A prefix circuit with $n$ inputs is
 depth-size optimal if its depth plus size equals $2 n -
 2$. A circuit with a smaller fan-out is in general
 faster and occupies less VLSI area. To be of practical
 use, the depth and fan-out of a prefix circuit should
 be small. In this paper, a family of depth-size
 optimal, parallel prefix circuits with fan-out 2 is
 presented. This family of prefix circuits is easier to
 construct and more amenable to automatic synthesis than
 two other families of the same type, although the three
 families have the same minimum depth among all
 depth-size optimal prefix circuits with fan-out 2. The
 balanced structure of the new family is also a merit.",
 acknowledgement = ack-nhfb,
 articleno = "15",
 journal-URL = "_URL_
 keywords = "Depth-size optimal; fan-out; parallel prefix
 circuits",
}
@Article{Kahng:2009:LAA,
 author = "Andrew B. Kahng and Chul-Hong Park and Puneet Sharma
 and Qinke Wang",
 title = "Lens aberration aware placement for timing yield",
 journal = j-TODAES,
 volume = "14",
 number = "1",
 pages = "16:1--16:??",
 month = jan,
 year = "2009",
 CODEN = "ATASFO",
 DOI = "_URL_
 ISSN = "_PHONE_ (print), _PHONE_ (electronic)",
 bibdate = "Mon Jan 26 18:12:50 MST 2009",
 bibsource = "_URL_
 _URL_
 abstract = "Process variations due to lens aberrations are to a
 large extent systematic, and can be modeled for
 purposes of analyses and optimizations in the design
 phase. Traditionally, variations induced by lens
 aberrations have been considered random due to their
 small extent. However, as process margins reduce, and
 as improvements in reticle enhancement techniques
 control variations due to other sources with increased
 efficacy, lens aberration-induced variations gain
 importance. For example, our experiments indicate that
 delays of most cells in the Artisan TSMC 90nm library
 are affected by 2--8\% due to lens aberration.
 Aberration-induced variations are systematic and depend
 on the location in the lens field. In this article, we
 first propose an aberration-aware timing analysis flow
 that accounts for aberration-induced cell delay
 variations. We then propose an aberration-aware
 timing-driven analytical placement approach that
 utilizes the predictable slow and fast regions created
 on the chip due to aberration to improve cycle time. We
 study the dependence of our improvement on chip size,
 as well as use of the technique along with field
 blading which allows partial reticle exposure. We
 evaluate our technique on two testcases, {\em AES\/}
 and {\em JPEG\/} implemented in 90nm technology. The
 proposed technique reduces cycle time by 4.322\% (80ps)
 at the cost of 1.587\% increase in trial-routed
 wirelength for AES. On JPEG, we observe a cycle time
 reduction of 5.182\% (132ps) at the cost of 1.095\%
 increase in trial-routed wirelength.",
 acknowledgement = ack-nhfb,
 articleno = "16",
 journal-URL = "_URL_
 keywords = "design for manufacturing; Layout; lithography; timing
 yield",
}
@Article{Chien:2009:SMV,
 author = "Chih-Da Chien and Cheng-An Chien and Jui-Chin Chu and
 Jiun-In Guo and Ching-Hwa Cheng",
 title = "A {252Kgates\slash 4.9Kbytes SRAM\slash 71mW}
 multistandard video decoder for high definition video
 applications",
 journal = j-TODAES,
 volume = "14",
 number = "1",
 pages = "17:1--17:??",
 month = jan,
 year = "2009",
 CODEN = "ATASFO",
 DOI = "_URL_
 ISSN = "_PHONE_ (print), _PHONE_ (electronic)",
 bibdate = "Mon Jan 26 18:12:50 MST 2009",
 bibsource = "_URL_
 _URL_
 abstract = "This article proposes a low-cost, low-power
 multistandard video decoder for high definition (HD)
 video applications. The proposed design supports
 multiple-standard (JPEG baseline, MPEG-1/2/4 Simple
 Profile (SP), and H.264 Baseline Profile (BP)) video
 decoding through interactive parsing control and common
 parameter bus interface. In order to reduce hardware
 cost, the shared adder-based structure and reusable
 data management are proposed to achieve hardware
 sharing and reduce internal memory size, respectively.
 In addition, the proposed design is optimized through
 reducing memory bandwidth by increasing both data reuse
 amount and burst length of memory access as well as
 eliminating cycle overhead in data access for
 supporting HD video decoding with single AHB-based SDR
 memory. The proposed 252Kgates/4.9kB/71mW/0.13$\mu$m
 multi-standard video decoder reduces 72\% in gate count
 and 87\% in power consumption as compared to the
 state-of-the-art design, when operating at 120MHz for
 real-time HD1080 video decoding with single AHB-based
 SDR memory.",
 acknowledgement = ack-nhfb,
 articleno = "17",
 journal-URL = "_URL_
 keywords = "H.264; MPEG; Video decoder",
}
@Article{Reviriego:2009:EED,
 author = "Pedro Reviriego and Juan Antonio Maestro",
 title = "Efficient error detection codes for multiple-bit upset
 correction in {SRAMs} with {BICS


text:
The First Congregational Church, at the corner of Hampden and Pleasant Streets in Holyoke, around 1910. Image from Holyoke: Past and Present Progress and Prosperity (1910).
The church in 2017:
Holyoke's First Congregational Church was established in 1799, as the Third Congregational Church of West Springfield. At the time, West Springfield encompassed the present-day towns of Agawam and Holyoke. The latter was variously known as the Third Parish or Ireland Parish, and was only sparsely settled, with most of its population was located along Northampton Street. The church had only 11 members when it was established, and shared space with the First Baptist Church. Not until 1834 did the Congregational church move into a building of its own, upon the completion of a modest Greek Revival-style church near the corner of Northampton and Dwight Streets.
Holyoke was incorporated as a separate municipality in 1850, and the church became the First Congregational Church of Holyoke. Around the same time, the new town was undergoing a rapid transformation from a small farming community into a major industrial center. However, most of this new development was along the banks of the Connecticut River, far removed from the church on Northampton Street. Despite a significant growth in Holyoke's population, the church actually declined in membership during this time, with many parishioners leaving to join the newly-established Second Congregational Church, with its more convenient location at the corner of High and Dwight Streets.
Faced with this decline, along with a revolving door of pastors throughout the 1870s and 1880s, the church finally decided to relocate closer to downtown Holyoke. In 1886, the church purchased this lot at the corner of Hampden and Pleasant Streets, and by the end of the following year it had completed a chapel on the site, which is visible on the far right side of both photos. Although still located some distance from downtown Holyoke, the new church was situated in the midst of a new upscale residential development, and within just a few years its membership had more than doubled, from 64 at the time of the 1887 move, to around 160 by 1890.
Church services were held in this chapel until 1894, when the church building itself was completed. The new church was the work of prominent Holyoke architect George P. B. Alderman, and featured a Romanesque-style design that was common for churches of this period. The exterior was primarily brick, with brownstone trim, and included common Romanesque elements such as rounded arches, asymmetrical facades, and a mix of towers and turrets of varying heights. The overall design bore some resemblance to the new Second Congregational Church, which had been completed almost a decade earlier on Maple Street, although that church had been constructed entirely of brownstone instead of brick.
Throughout the 20th century, the First Congregational Church underwent a series of mergers and name changes. In 1961, it became First United Congregational Church after a merger with the German Reformed Church, and then in 1973 it became Grace United Church after merging with Grace Church. The members of Grace United continued to worship here until 1995, when the church merged with the Second Congregational Church, becoming the United Congregational Church of Holyoke. Following this merger, most religious services were held at the former Second Congregational building on Maple Street, but the church retained ownership of the former First Congregational building here on Pleasant Street, which was repurposed as the E. B. Robinson Ecumenical Mission Center. The church still owns the property today, and the historic building is still standing with few exterior changes since the first photo was taken, although it appears to vacant as of the 2017 photo.


Phase plane
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Template:Differential equations
In applied mathematics, in particular the context of nonlinear system analysis, a phase plane is a visual display of certain characteristics of certain kinds of differential equations; a coordinate plane with axes being the values of the two state variables, say (x, y), or (q, p) etc. (any pair of variables). It is a two-dimensional case of the general n-dimensional phase space.
The phase plane method refers to graphically determining the existence of limit cycles in the solutions of the differential equation.
The solutions to the differential equation are a family of functions. Graphically, this can be plotted in the phase plane like a two-dimensional vector field. Vectors representing the derivatives of the points with respect to a parameter (say time t), that is (dx/dt, dy/dt), at representative points are drawn. With enough of these arrows in place the system behaviour over the regions of plane in analysis can be visualized and limit cycles can be easily identified.
The entire field is the phase portrait, a particular path taken along a flow line (i.e. a path always tangent to the vectors) is a phase path. The flows in the vector field indicate the time-evolution of the system the differential equation describes.
In this way, phase planes are useful in visualizing the behaviour of physical systems; in particular, of oscillatory systems such as predator-prey models (see Lotka–Volterra equations). In these models the phase paths can "spiral in" towards zero, "spiral out" towards infinity, or reach neutrally stable situations called centres where the path traced out can be either circular, elliptical, or ovoid, or some variant thereof. This is useful in determining if the dynamics are stable or not.[1]
Other examples of oscillatory systems are certain chemical reactions with multiple steps, some of which involve dynamic equilibria rather than reactions that go to completion. In such cases one can model the rise and fall of reactant and product concentration (or mass, or amount of substance) with the correct differential equations and a good understanding of chemical kinetics.[2]
Example of a linear system
A two-dimensional system of linear differential equations can be written in the form:[1]
which can be organized into a matrix equation:
where A is the 2 × 2 coefficient matrix above, and x = (x, y) is a coordinate vector of two independent variables.
Such systems may be solved analytically, for this case by integrating:[3]
although the solutions are implicit functions in x and y, and are difficult to interpret.[1]
Solving using eigenvalues
More commonly they are solved with the coefficients of the right hand side written in matrix form using eigenvalues λ, given by the determinant:
and eigenvectors:
The eigenvalues represent the powers of the exponential components and the eigenvectors are coefficients. If the solutions are written in algebraic form, they express the fundamental multiplicative factor of the exponential term. Due to the nonuniqueness of eigenvectors, every solution arrived at in this way has undetermined constants c1, c2,... cn.
The general solution is:
where λ1 and λ2 are the eigenvalues, and (k1, k2), (k3, k4) are the basic eigenvectors. The constants c1 and c2 account for the nonuniqueness of eigenvectors and are not solvable unless an initial condition is given for the system.
The above determinant leads to the characteristic polynomial:
which is just a quadratic equation of the form:
("tr" denotes trace) and
The explicit solution of the eigenvalues are then given by the quadratic formula:
Eigenvectors and nodes
The eigenvectors and nodes determine the profile of the phase paths, providing a pictorial interpretation of the solution to the dynamical system, as shown next.
Classification of equilibrium points of a linear autonomous system.[1] These profiles also arise for non-linear autonomous systems in linearized approximations.
The phase plane is then first set-up by drawing straight lines representing the two eigenvectors (which represent stable situations where the system either converges towards those lines or diverges away from them). Then the phase plane is plotted by using full lines instead of direction field dashes. The signs of the eigenvalues will tell how the system's phase plane behaves:
 - If the signs are opposite, the intersection of the eigenvectors is a saddle point.
 - If the signs are both positive, the eigenvectors represent stable situations that the system diverges away from, and the intersection is an unstable node.
 - If the signs are both negative, the eigenvectors represent stable situations that the system converges towards, and the intersection is a stable node.
The above can be visualized by recalling the behaviour of exponential terms in differential equation solutions.
Repeated eigenvalues
This example covers only the case for real, separate eigenvalues. Real, repeated eigenvalues require solving the coefficient matrix with an unknown vector and the first eigenvector to generate the second solution of a two-by-two system. However, if the matrix is symmetric, it is possible to use the orthogonal eigenvector to generate the second solution.
Complex eigenvalues
Complex eigenvalues and eigenvectors generate solutions in the form of sines and cosines as well as exponentials. One of the simplicities in this situation is that only one of the eigenvalues and one of the eigenvectors is needed to generate the full solution set for the system.
See also
External links
fr:Méthode du plan de phase pl:Metoda płaszczyzny fazowej ru:Метод фазовой плоскости


text: With the phase out of conventional CFC and HCFC refrigerants, air conditioning and heat pump systems will have to be redesigned to accommodate new replacement refrigerants. An important component in these systems is the expansion device. Short tube orifices are a common expansion device used on residential sized air conditioners and heat pumps in the United States. The design for optimum performance of these systems requires predicting correct flow characteristics through short tube orifices for a given set of operating conditions. Very little data are available on how these new replacement refrigerants will perform in short tube orifices relative to conventional refrigerants. This paper presents the results of an experimental study to evaluate the flow characteristics of HFC-134a flowing through short tube orifices in heat pump systems. Three types of measurements were made during this study: mass flow tests, pressure distribution inside the orifice, and flow visualization. Measured data were analyzed and discussed as a function of operating variables and short tube geometry. In general, the variables (upstream pressure, subcooling, and quality, and orifice diameter and length) affecting two-phase flow through orifices with HFC-134a were the same as those found with HCFC- 22. For operating saturation temperatures upstream of the orifices of 45.4°C, the mass flow produced with HFC-134a varied from 16 to 23 percent less than that for HCFC-22 under choked flow conditions. Choked flow conditions for HFC-134a were typically established when downstream pressures were reduced below the saturation pressure corresponding to the inlet temperature. The flow rate was strongly dependent on the upstream pressure and upstream subcooling/quality, but it was insensitive to downstream flow conditions. As the inlet quality increased from 0 percent to 5 percent, a sharp drop in flow was measured due to a large increase in void fraction at the entrance of the short tube. Pressure distribution data indicated the presence of a vena contracta and metastable flow near the orifice entrance.