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What is Class Counter in Maths



In 2009 Dusa Macduff goes to a talk at the Numerical Sciences Exploration Foundation in Berkeley, California. The speaker was Katrin Wehrheim, who was then an associate teacher at the Massachusetts Establishment of Innovation. In his discourse, Wehrheim provoked the symplectic math local area to face blunders in basic strategies grew over 10 years sooner.  reviewed Macduff, who was one of Wehrheim’s doctoral proposal analysts.

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Barnard School mathematician Dusa Macduff battled for a really long time to address what she saw as holes in the underpinnings of symplectic calculation.

The test was private for Macduff. In 1999 he composed an overview article that depended on hazardous major methods by one more sets of mathematicians, Posse Liu and Pack Tian. Presently, after 10 years, Wehrheim was bringing up that Macduff’s paper – in the same way as other early papers in symplectic math – including Fukaya’s – had mistakes, specifically how to move from nearby to worldwide in the worldwide calculation of focuses. Subsequent to paying attention to Wehrheim, Macduff concluded that she would attempt to address any slip-ups.

“I had a terrible heart about what I composed in light of the fact that I knew some way or another it was not completely exact,” she said. “I commit errors, I comprehend individuals commit errors, yet on the off chance that I commit an error, I attempt to address it, and in the event that I can’t, it’s off-base.”

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Macduff and Wehrheim started work on a progression of papers that were brought up and fixed as missteps in Fukaya’s treatment of transversality. In 2012 Macduff and Wehrheim moved toward Fukaya with their interests. Following 16 years in which his work was ignored by the numerical local area, he was happy he was intrigued.

“In 2012 we got K. There was an unmistakable protest from Wehrheim. We were extremely glad to have this since it was the primary significant numerical reaction we got on our work.

To examine the protests, mathematicians framed a Google Gathering in mid 2012 that included Macduff, Wehrheim, Fukaya and Ono along with two of Fukaya’s later partners, Yong-gyun Gracious and Hiroshi Ohta. The conversation by and large follows this structure: Wehrheim and Macduff will bring up issues about Fukaya’s work. Fukaya and his associates would then compose long, itemized replies.

Whether those answers were agreeable relied upon who was understanding them. According to Fukaya’s perspective, his work on Qur’anic structures was finished and right all along. I don’t think there was anything missing,” he said.

Others clash. After the Google Gathering conversation finished, Fukaya and his associates posted a few papers on Quranic structures that together ran for in excess of 400 pages. Hofer feels that the length of Fukaya’s reactions is proof that Macduff and Wehrheim’s incitement was essential.

“By and large, [Fukaya’s approach] worked, however it required more clarification than was initially given,” he said. “I think Fukaya and Ono’s unique paper was a little north of 100 pages, and because of this conversation on the Google bunch they delivered a 270-page composition and a couple hundred pages making sense of the first outcomes. So certain. Obviously required explanation.”

Abujaid concurs that there was a slip-up in Fukaya’s unique work.Simultaneously, he feels that Qur’anic develops are by and large the correct method for managing transversality issues. He views the blunders in the 1996 paper as happening on the grounds that the symplectic math local area was not adequately evolved at an opportunity to audit the new work appropriately.

“The paper ought to have been refereed all the more cautiously. My perspective is that with a decent ref report of a few adjusts that the paper would have been faultless and everything looks great,” said Abujaid.

In August 2012, after a Google Gathering conversation, McDuff and Wehrheim posted an article they had started composition before the conversation definite ways of revising Fukaya’s methodology. He later refined and distributed that paper with two others, and plans to compose a fourth paper regarding the matter. In September 2012, Fukaya and his co-creators posted a portion of their reactions to the issues raised by Macduff and Wehrheim. To Fukaya, Macduff and Wehrheim’s papers didn’t propel this region essentially.

“It is my viewpoint that the papers he composed don’t contain new and significant thoughts. There is absolutely a few contrast from the previous papers of our own and others. Notwithstanding, the thing that matters is just on a little detail,” FukAya said in an email.

Hofer imagines that this understanding short sells the commitments of Macduff and Wehrheim. From his perspective, the pair accomplished something other than fix little specialized subtleties in Fukaya’s work – they tackled significant level issues with Fukaya’s methodology.

“They comprehended the various pieces well overall and how they cooperated, so you couldn’t simply say: ‘Here, assuming it’s risky, I fixed it locally,'” he said. “You should know where pretty much another issue would emerge. He grasped it at an exceptionally undeniable level.”

How mathematicians assess the significance of mistakes in Fukaya’s 1996 paper and the commitments Wehrheim and Macduff made to address them mirrors a polarity in the manner we ponder the act of science.

“Arithmetic has two ideas,” Abuzaid said. “Arithmetic is this way: the money of math is thought. Also, science is the cash of arithmetic is verification. It is hard for me to say which side individuals stand on. My own perspective is: overwhelmingly significant in science is thought, And there’s proof to ensure that contemplations don’t wander off.”

Fukaya is a geometer with a sense to think in overgeneralized terms. Conversely, Wehrheim is prepared in examination, a field known for its thorough regard for specialized subtleties. In a profile for the MIT site Ladies in Math, she expressed that in math, “we don’t compose great papers any longer,” and looked at mathematicians who don’t tell the subtleties of their work to climbers who arrive at the top. Mountains without leaving snares on the way. “Somebody with little preparation would have not a chance of following it without tracking down a way for themselves,” she said.

These contrasting assumptions for what considers an adequate measure of detail in a proof caused a lot of pressure in the symplectic calculation local area around the protests of Macduff and Wehrheim. Abuzaid contends that it is essential to be shrewd while bringing up botches in crafted by another mathematician, and Wehrheim might not have been strategic enough in this. “Assuming that you present it as: ‘All that has preceded us is off-base and presently we will offer the right response,’ that is probably going to set off some kind of issue of need claims,” he said. .

Wehrheim declined different solicitations to be evaluated for this article, saying she “needs to stay away from additional politicization of the subject.” In any case, Macduff feels that he and Wehrheim had no real option except to be enabled to bring up the defects in Fukaya’s work: it was the best way to definitely stand out.

“It resembles being an informant,” she said. out with you. what’s more, not from individuals who can be off-base.”

Notwithstanding who gets the credit for fixing the issues with Fukaya’s paper, they have been fixed. In the beyond couple of years, on account of arithmetic, the debate encompassing his work has been settled.

These issues were felt and ultimately fixed,” Eliashberg said. “Perhaps it superfluously makes a ton of energy in certain gatherings, however generally speaking I think everything was dealt with and things will go on.”


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Cannot Add Custom Object to Navigation Menu in Community Salesforce




Navigation menus in Salesforce communities provide an easy way to quickly access the most important information. However, when attempting to add a custom object to the navigation menu of a community. Many users may find that it is not possible.

This article will explain why this cannot be done. And what alternatives exist for adding custom objects to your community’s navigation menu.


Salesforce communities are designed with specific features. That allow administrators to create customized user experiences. Navigation menus are one of these features. Allowing admins to specify which items are visible on the global navigation bar. So users can quickly navigate various pages in the community. While admins can modify existing navigation items such as Home Page and Contact Us.They cannot add new ones without additional development.

Reasons Why Custom Object Cannot Be Added To Navigation Menu:

The primary reason why custom objects cannot be added to the navigation menu of a community is due to security restrictions placed on Salesforce communities by Salesforce. Each object in a community must have explicit access set for any user who will view it. Without this, users could potentially access confidential information that was not intended for them, which could lead to serious security issues. As such, custom objects are not allowed in the navigation menus of communities as they do not have the same level of access control as other components within a community.

Alternatives for Adding Custom Objects to Navigation Menu:

Although it is not possible to add custom objects directly to a community’s navigation menu, there are alternatives that can be used to achieve the same result.

One option is to add custom pages or Visualforce pages that include components such as custom objects, formulas, and other features. These pages can then be added to the navigation menu, allowing users to access them without any additional development.

Another option is to create Lightning Components that contain your custom objects and add them to the navigation menu in a similar manner as with custom pages or Visualforce pages. This can provide an even more customized experience for your users.


Adding custom objects to a navigation menu in a Salesforce Community can be tricky. Custom objects may not appear in the page layout of your Community, so it is important to understand the limitations of Salesforce Communities when it comes to custom objects. This article will explain how to add a custom object to your Community navigation menu and how you can use the Community Builder feature to customize the look and feel of your Community.

How to Add a Custom Object to Navigation Menu in Salesforce Community:

1) In Setup, navigate to App Manager > Your App > Navigation Menus.

2) select the desired menu from the drop-down list (e.g. Global Navigation).

3) Click New Item in the action bar and select Custom Object from the drop-down list that appears.

4) Enter a label for your new item, such as “My Custom Object”.

5) From the object type picklist, select your custom object.

6) Select “Active” to make it available in your Community.

7) Click Save to add the item to the menu.

Customizing Your Navigation Menu in Community Builder:

1) Navigate to Setup > Communities Settings > Community Builder.

2) Select the desired theme from the list and click Edit next to it.

3) Select Navigation Menus from the left-hand pane and choose Global Navigation from the drop-down list at the top of this page.

4) Drag and drop any items you want to add or remove from your navigation menu, including custom objects.

5) Customize the look and feel by setting colors, tokens, fonts and more.

6) Click Save to save your changes.


Adding a custom object to a navigation menu in Salesforce Community is possible with the help of App Manager and Community Builder. With these tools you can easily add or remove items from your Navigation Menu, customize its look and feel, and make sure that all users have access to the objects they need. With just a few clicks, you can ensure that your Community is up-to-date with everything it needs!


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A Step-by-Step Guide on Resolving Issues with Corrupt PST Files



Corrupt PST files

Corrupt PST files can be a major cause of concern when trying to access important data.

In the following guide, we will discuss 10 step-by-step methods to fix corrupt PST files.

1. Run Scanpst –

This is Microsoft’s inbuilt utility for scanning and repairing corrupted Outlook PST files. To run this tool, open your Control Panel and select Mail. Double-click on the Scanpst shortcut or search for it in your C:\Program Files\Microsoft Office folder. Once you have launched the tool, click “Browse” to locate your corrupted PST file, then click “Start” to begin scanning. If any errors are detected, choose “Repair” to repair them automatically.

2. Use a Third-Party Tool –

If the Scanpst utility does not resolve the issue, you can use third-party PST recovery software for repairing corrupt Outlook files. These tools are designed to repair severely corrupted PST files and can also be used to recover deleted emails. Before choosing particular software, make sure it is compatible with your version of Outlook and offers all the features you need.

3. Create a New Data File –

If all else fails, you may have to create an entirely new data file in Outlook and manually import your old messages into it. This process will require downloading Microsoft’s Import/Export Wizard or any other such tool that supports the migration of Outlook data files between different versions.

4. Run an Antivirus Scan –

Sometimes, the corruption of PST files can be caused by a virus infection. To check whether this is the case with your file, run a full system scan using antivirus software and delete all malicious items detected.

5. Use Outlook’s Inbox Repair Tool –

Outlook has its own inbuilt repair tool that helps resolve issues related to corrupt PST files. To use this tool, open the Microsoft Office folder on your computer and select “Scanpst” or “Inbox Repair Tool” (depending on your version of Outlook). Once launched, choose your corrupted PST file and click “Start” or “Repair” to begin the repair process.

6. Try Different Compression Formats –

If you are unable to open your Outlook PST file, try saving it in different compression formats such as ZIP or RAR. This can help reduce the size of the files and make them easier to access.

7. Install Updates –

Outlook periodically releases new updates that may be able to resolve issues with corrupt PST files. Therefore, make sure that you have the latest version of Microsoft Office installed on your computer before attempting any repair work.

8. Repair Windows Registry Entries –

Corrupt registry entries can also cause problems with Outlook data files so it is important to check for any damaged or missing entries in the Windows registry and repair them.

9. Use a Data Recovery Tool –

If all else fails, you may have to use a data recovery tool to recover any lost or deleted emails from your corrupted PST file. There are many such tools available on the internet and some of them can even be used to recover emails from Outlook’s Offline Storage Table (OST) files.

10. Consult a Professional –

If none of the above methods work, it is time to consult a professional for help. A certified technician will be able to analyze your computer and determine the exact cause of the issue with your PST file before recommending an appropriate solution.


The above steps should help you fix any issues with your Outlook PST files. However, if the corruption is severe and none of these methods work, it may be necessary to consult a professional for assistance. In such cases, it is important to ensure that you choose an experienced technician who can offer reliable solutions at reasonable costs.

These 10 steps should offer you assistance in resolving issues with corrupt PST files, but if you are still unable to repair them then it is best to consult a professional. The experts have the skills and knowledge required to fix your Outlook data files without further damaging them.

By following the above-mentioned steps, you should be able to resolve any issues with corrupt PST files. However, if all of these solutions fail, it’s best to consult a professional technician or IT expert for help in recovering your lost data.


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