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lodore
September 10th, 2006, 01:17 PM
Hi

this product does seem interesting to me.

1. can someone show me some screenshots?

2. does it create the snapshots in windows?

3. once i have created a snapshot do i just press a certain button at bottime and it comes up with the first defence recovery menu? then i just click on the working snapshot and im backing and running?

lodore

ps im not sure if i wanna trial it yet. i want to ask questions and see screenshots first.

vhick
September 10th, 2006, 01:53 PM
-{ Quote: "Hi

this product does seem interesting to me.

1. can someone show me some screenshots?

2. does it create the snapshots in windows?

3. once i have created a snapshot do i just press a certain button at bottime and it comes up with the first defence recovery menu? then i just click on the working snapshot and im backing and running?

lodore

ps im not sure if i wanna trial it yet. i want to ask questions and see screenshots first." }-

sir you go to the site and you can view the movie provide to it.;)

ErikAlbert
September 10th, 2006, 02:24 PM
1. Too much work to take screenshots. Take a backup of your actual system partition as precaution, install FDISR and look at the screens. Each action is supported by wizards.

2. Yes, FDISR stores all its snapshots (max. 10) in Windows, usually on system partition [C:]

3. Yes, on reboot FDISR shows a splash screen with F1-key and pause bar, before Windows starts.
The F1-key shows a list of all available snapshots (max. 10) and you can reboot in any of these snapshots.
The absolute minimum = 2 snapshots : primary snapshot for daily work and secondary snapshot as a rollback snapshot,
in case something goes wrong in the primary snapshot.
The primary snapshot can also be the rollback-snapshot, while the secondary snapshot can be the working snapshot.
It doesn't matter because each snapshot is independent.

stevetwc
September 21st, 2006, 04:21 PM
The working concept of FDISR is to copy all the files of current state into a special protected folder, and optionally compress it using NTFS compression. When you choose to boot into a different snapshots, basically, the directory structures are altered in the way that all files of current state will go into another folder, and the directory structure of the files in the snapshot that you are going to boot are restored into the proper structure and you will be able to boot into the new snapshot with almost no significant boot delay.

An example to explain this will be:

At Current State, you have:
C:\abc.txt
C:\123\def.txt

When you take a snapshot, it is stored in:
C:\$ISR\0\abc.txt C:\$ISR\0\123\def.txt

So, now you messed with your current state and it becomes:
C:\ghi.txt
C:\456\jkl.txt

At the boot screen, you choose to boot into the snapshot you took earlier, so the hard disk will look like this:
C:\abc.txt
C:\123\def.txt
C:\$ISR\1\ghi.txt C:\$ISR\1\456\jkl.txt

This is my own observation of how the program works, and I welcome any Leapfrog personnel to correct my mistake if there is any ;)

September 21st, 2006, 09:03 PM
Steve, I do not believe that the bootable snapshots are compressed in any way, they may be in a future version of FD. The snapshots may be smaller in size but that is because four files are NOT copied: the paging file, recycle bin, hibernate file, temp files. Like I have said many times in this forum, even the exceptions, with this excellent program, make sense.

ErikAlbert
September 21st, 2006, 09:39 PM
I thought NTFS compressed folders/files are in BLUE.
I don't see any FDISR folder in BLUE, they are all black.
I could be wrong, but as a newbie+ I can make mistakes.

stevetwc
September 21st, 2006, 11:13 PM
-{ Quote: "Steve, I do not believe that the bootable snapshots are compressed in any way, they may be in a future version of FD. The snapshots may be smaller in size but that is because four files are NOT copied: the paging file, recycle bin, hibernate file, temp files. Like I have said many times in this forum, even the exceptions, with this excellent program, make sense.

Please read the manual of the latest FDISR from Leapfrog website. It is stated that:

Ability to create a compressed snapshot using NTFS file compression for a significantly smaller snapshot.

I tried to take a snapshot and it is actually compressed.

stevetwc
September 21st, 2006, 11:15 PM
-{ Quote: "I thought NTFS compressed folders/files are in BLUE.
I don't see any FDISR folder in BLUE, they are all black.
I could be wrong, but as a newbie+ I can make mistakes." }-

If you are using the latest version yet you are able to see the blue colour, it is very obvious that either Windows is not protecting you from deleting system files or your system has been compromised ;D

ErikAlbert
September 22nd, 2006, 05:05 AM
-{ Quote: "If you are using the latest version yet you are able to see the blue colour, it is very obvious that either Windows is not protecting you from deleting system files or your system has been compromised ;D" }-
Where did you get your FDISR ? From Leapfrog or from Raxco ?
Raxco doesn't resell the Leapfrog version until it is tested and approved.
And no my system isn't compromised and my FDISR is working properly since I bought it.
Afaik the Leapfrog version has compression, but that's NOT an official version for public use, that's a test version for resellers without support.

Reve_Etrange
September 22nd, 2006, 06:43 AM
I'm trialing the I18N build from leapfrog, and the $ISR snapshot subfolders aren't compressed, and fully writeable. Used the wizard to make the secondary snapshot. My bad? RE ErikAlbert September 22nd, 2006, 06:52 AM -{ Quote: "I'm trialing the I18N build from leapfrog, and the$ISR snapshot subfolders aren't compressed, and fully writeable. Used the wizard to make the secondary snapshot.

RE" }-
I thought the compression wasn't automatic, you have to specify it, but I'm not interested in the Leapfrog version and don't visit the website either. I can wait until Raxco announces the new version of FDISR.
I'm not saying that Leapfrog version is bad, I just don't work with non-official versions.
FDISR is supposed to save ME and I'm not supposed to save FDISR.

September 22nd, 2006, 08:21 AM
Oh, ok, Steve, I didn't realize that you were using Leapfrog, they are one version ahead of Raxco.

stevetwc
September 22nd, 2006, 09:56 AM
-{ Quote: "Where did you get your FDISR ? From Leapfrog or from Raxco ?
Raxco doesn't resell the Leapfrog version until it is tested and approved.
And no my system isn't compromised and my FDISR is working properly since I bought it.
Afaik the Leapfrog version has compression, but that's NOT an official version for public use, that's a test version for resellers without support." }-

Obviously that is not a test version.

If you are lazy to register, you can get the exactly same file here.

Peter2150
September 22nd, 2006, 11:17 AM
-{ Quote: "Obviously that is not a test version.

If you are lazy to register, you can get the exactly same file here.

True enough, but what you can't get is any support.

Reve_Etrange
September 22nd, 2006, 11:48 AM
Anyway, how come that everything be writeable under the snapshots folders?

RE

stevetwc
September 22nd, 2006, 12:51 PM
-{ Quote: "Anyway, how come that everything be writeable under the snapshots folders?

RE" }-

I'm not sure which version you are using, but you can try the latest version from the link I provided. It is perfectly protecting the snapshot files. I even tried some brute force delete tools yet still cant delete it inside Windows.

Not really know what happened to your program, but you shouldnt be allowed to alter the snapshot or else that will have defeated the purpose of having snapshot.

stevetwc
September 22nd, 2006, 12:56 PM
-{ Quote: "True enough, but what you can't get is any support." }-

I do agree with you that software support is an essential part for a working solution. However, my personal preference has been to evaluate the quality of a software excluding its support. Because I do not like a poorly written software with a superior support service. Moreover, isnt the main purpose of using FDISR is to have immediate system recovery without tedious technical support? That's just my own opinion though ;D

Peter2150
September 22nd, 2006, 01:48 PM
-{ Quote: "I do agree with you that software support is an essential part for a working solution. However, my personal preference has been to evaluate the quality of a software excluding its support. Because I do not like a poorly written software with a superior support service. Moreover, isnt the main purpose of using FDISR is to have immediate system recovery without tedious technical support? That's just my own opinion though ;D" }-

Still why not be trialing what you can purchase today. Leapfrog isn't a retail seller, you need to go to the retail partners. I'd trial with their versions.

Reve_Etrange
September 22nd, 2006, 02:03 PM
I got an official version from another vendor. I don't know if this is ok to mention Raxco's competition here...
I18N is a prerequisite for me, and Raxco's latest version doesn't support it.
Cheers,

RE

ErikAlbert
September 22nd, 2006, 02:36 PM
One thing is sure : Raxco doesn't seem to be in hurry to release a new version of FDISR. I hope the developer included some improvements of our wish-list.

Peter2150
September 22nd, 2006, 03:04 PM
-{ Quote: "I got an official version from another vendor. I don't know if this is ok to mention Raxco's competition here...
I18N is a prerequisite for me, and Raxco's latest version doesn't support it.
Cheers,

RE" }-

Sure it is. This really isn't a Raxco forum, but Leapfrog. Kinda unusual.

Pete

Reve_Etrange
September 23rd, 2006, 09:41 AM
-{ Quote: "I'm not sure which version you are using, but you can try the latest version from the link I provided. It is perfectly protecting the snapshot files. I even tried some brute force delete tools yet still cant delete it inside Windows.

Not really know what happened to your program, but you shouldnt be allowed to alter the snapshot or else that will have defeated the purpose of having snapshot." }-
Could it be that I added special privilieges to my windows account? Like, those needed for system debugger and likes?
Or some service I disabled?
How are the snapshots files protected exactly?

RE

stevetwc
September 23rd, 2006, 04:25 PM
-{ Quote: "Could it be that I added special privilieges to my windows account? Like, those needed for system debugger and likes?
Or some service I disabled?
How are the snapshots files protected exactly?

RE" }-

The protection is similar to the protection of "System Volume Information" folder under your system root.

Reve_Etrange
September 24th, 2006, 11:47 AM
How can I check that this mechanism is working properly on my box, without actually deleting important files of course?

Peter2150
September 24th, 2006, 12:05 PM
-{ Quote: "How can I check that this mechanism is working properly on my box, without actually deleting important files of course?" }-

Hi Reve

I lost track. Exactly what mechanism are you wanting to check.

Pete

Reve_Etrange
September 24th, 2006, 03:00 PM
I'm not supposed to be able to delete files under the snapshot folders, yet I can. Either it comes from a bug in build 169 from SPursuit (sounds weird to me), or there's something on my PC that I enabled or disabled, so that I can now delete things the average user cannot.

Steve mentionned the protection of System Volume Information: what is it based on exactly? I mean, I could try and delete files in that folder, to prove that there's really something wrong on my machine (thus proving that LeapFrog isn't the culprit), but I'm none too willing to harm my system doing so.

Is it clearer? Maybe I'm thinking backwards or something here <:-.

RE

Peter2150
September 24th, 2006, 07:51 PM
-{ Quote: "I'm not supposed to be able to delete files under the snapshot folders, yet I can. Either it comes from a bug in build 169 from SPursuit (sounds weird to me), or there's something on my PC that I enabled or disabled, so that I can now delete things the average user cannot.

Steve mentionned the protection of System Volume Information: what is it based on exactly? I mean, I could try and delete files in that folder, to prove that there's really something wrong on my machine (thus proving that LeapFrog isn't the culprit), but I'm none too willing to harm my system doing so.

Is it clearer? Maybe I'm thinking backwards or something here <:-.

RE" }-

If you can get into actual files in the snapshot folders something is indeed wrong. Time to test SPursit techsuppot.

Pete

Reve_Etrange
September 25th, 2006, 04:48 AM
I sent them an email last friday afternoon, hope to get an answer in the next few days.

RE


text:
• UnkleRhaukus
Use partial fractions or the convolution theorem and the table of Laplace transforms, to find functions of $$t$$ which have the following Laplace transforms. (b) $\frac{p+2}{2p^2+p-1}$
Mathematics

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Poster
Asymptotically Unbiased Instance-wise Regularized Partial AUC Optimization: Theory and Algorithm
HuiYang Shao · Qianqian Xu · Zhiyong Yang · Shilong Bao · Qingming Huang

@
The Partial Area Under the ROC Curve (PAUC), typically including One-way Partial AUC (OPAUC) and Two-way Partial AUC (TPAUC), measures the average performance of a binary classifier within a specific false positive rate and/or true positive rate interval, which is a widely adopted measure when decision constraints must be considered. Consequently, PAUC optimization has naturally attracted increasing attention in the machine learning community within the last few years. Nonetheless, most of the existing methods could only optimize PAUC approximately, leading to inevitable biases that are not controllable. Fortunately, a recent work presents an unbiased formulation of the PAUC optimization problem via distributional robust optimization. However, it is based on the pair-wise formulation of AUC, which suffers from the limited scalability w.r.t. sample size and a slow convergence rate, especially for TPAUC. To address this issue, we present a simpler reformulation of the problem in an asymptotically unbiased and instance-wise manner. For both OPAUC and TPAUC, we come to a nonconvex strongly concave min-max regularized problem of instance-wise functions. On top of this, we employ an efficient solver that enjoys a linear per-iteration computational complexity w.r.t. the sample size and a time-complexity of $O(\epsilon^{-1/3})$ to reach a $\epsilon$ stationary point. Furthermore, we find that the min-max reformulation also facilitates the theoretical analysis of generalization error as a byproduct. Compared with the existing results, we present new error bounds that are much easier to prove and could deal with hypotheses with real-valued outputs. Finally, extensive experiments on several benchmark datasets demonstrate the effectiveness of our method.


text:
# Combination Theorem for Continuous Mappings/Topological Ring/Product Rule

## Theorem

Let $\struct{S, \tau_{_S}}$ be a topological space.

Let $\struct{R, +, *, \tau_{_R}}$ be a topological ring.

Let $f,g : \struct{S, \tau_{_S}} \to \struct{R, \tau_{_R}}$ be continuous mappings.

Let $f * g : S \to R$ be the mapping defined by:

$\forall x \in S: \map {\paren{f * g}} x = \map f x * \map g x$

Then

$f * g : \struct{S, \tau_{_S}} \to \struct{R, \tau_{_R}}$ is continuous.

## Proof

By definition of a topological ring, $\struct{R, *, \tau_{_R}}$ is a topological semigroup.

From Product Rule for Continuous Mappings to Topological Semigroup, $f * g : \struct{S, \tau_{_S}} \to \struct{R, \tau_{_R}}$ is a continuous mapping.

$\blacksquare$


text:
# Math 479 – Fall 2018: Training Workouts

Below are all of the Training Workouts for Math 479 – Fall 2018 to date. For the most recent Training Workout and additional information see the Math 479 Home Page.

Welcome!

Welcome to Math 479, where great mathematicians are born!  I will post intriguing activities, course announcements, and other exciting information here throughout the semester.  Check back frequently. Below are links to some resources we will be using in the course.

Training Workout #1 – Due Thursday, Aug 30, 2018
• Obtain and organize the following required items for the course. Bring the first two to class with you from now on along with your copy of Zeitz.
• Problem Training Notebook – Record all of your work for problems that require it in this notebook.
• Must-Know Notebook – This can be a separate notebook or a section in the Problem Training Notebook.
• Training Log I put a copy of the Training Log spreadsheet in the Dropbox folder that you share with me (if you haven’t already installed and accepted my shared folder invitation, do that now.) It is due once per week on Tuesday before 6:00pm, and it should cover everything you did for the problem solving course from Tuesday thru Monday inclusive of the previous week. See the sample spreadsheet for examples.
• Work the 30 problems from the problem set you were given in class. If you want to try it under the timed conditions that sixth, seventh, and eighth graders have available, give yourself 40 minutes. Then when you are finished, try to answer the ones you didn’t finish in time. Calculators are not allowed on these problems.
Hand in just the answers you obtained on this set of problems on the official Assignment Answer Form from the link below. Label the form “Training Workout #1” and put your name on it. You can keep the questions. Show your work in your Problem Training Notebook.
• Read: both of the Prefaces in the textbook (pg ix-xiii)
Training Workout #2 – Due Tuesday, Sept 4, 2018
• Hand in the second set of thirty problems you were given in class. Note that you should show your work (for problems you don’t solve in your head) in your Training Notebook. Write your answers on the official Answer form below, and hand that in as discussed in class. Be sure to label it “Training Workout #2” in the upper right hand corner.
• Read the MATHCOUNTS allowable forms of answers page. In particular, you don’t want to lose points for a answer that is correct but isn’t in the right form. For example, if the answer is supposed to be a common fraction, it has to be a reduced fraction, not a mixed number, or a decimal, or a non-reduced fraction. Also for questions where it ask you to find, say, the value of $x$, if the answer is three, don’t write $x=3$ for your answer; just write $3$.
• Hand in your Training Log. Save your updated Training Log spreadsheet by saving it in your Dropbox folder before the start of Tuesday’s class. Make sure it is up to date each week at that time.
• Read Section 1.1 in the textbook.
Training Workout #3 – Thursday, Sept 6, 2018
• Hand in the problem set I gave you in class. As usual, you may keep the problems and should hand in your answers on the official Answer Form linked to below. Remember to try to solve the problems elegantly as quickly and cleverly as possible with as little computation, calculators, algebra, paper and pencil as possible.
• Read Chapter 1.2 in Zeitz. In particular, read carefully Example 1.2.1. This is a very instructive and enlightening example!
Training Workout #4 – Tuesday, Sept 11, 2018
• USAMTS!

Start Working on USAMTS Year 30 Round 1! This is it, team! The first actual official math competition of the season!

• Get the USAMTS Year 30 Round 1 Problems!
• Read all of the problems carefully now! That will load them into your brain and allow ideas to simmer to the surface.
• Start working on them now. Record your progress in your logs as you go.
• Write up a brief (one or two paragraphs per problem) initial progress report to hand in on Tuesday in class. For each of the five problems you should give your initial impressions, and discuss which strategies or problem solving mindsets from Zeitz you think might be helpful as a possible initial approach. If you solve any, don’t hand in your solution, just discuss what problem solving strategies, if any, you used.
• Be patient! Be confident! Don’t give up easily!!

Rules: This will be a major consideration in determining your grade in this course, similar to a take-home exam (except that you have more than five weeks to work on it!). We will follow the contest rules stated at the website. You can use reference books, online math references (that don’t involve asking another human being), calculators, Maple, spreadsheets, Geogebra, mechanical models, rulers, protractors, etc. to solve these problems. The only thing you cannot do is discuss the problem with anyone either directly or indirectly. You can not ask me questions about the problems to clarify the problem statement and so on, but you can ask me to explain Playbook facts, general mathematical terminology, theorems, etc.

These five problems will be due on Monday, October 15, 2018 at 8pm by placing a pdf of your solutions in your Dropbox folder. Note that Note that unless you are still in high school or middle school, you should hand these solutions in to me, not submit them to the USAMTS competition! Do not write more than one solution on a single sheet of paper (a single problem solution can be on multiple sheets of paper). Neatness counts for this training workout. LaTeX solutions are required. You should use the official LaTeX template provided at the bottom of that page at the USAMTS website. I will answer any LaTeX or Overleaf questions you have. Problem number one can be easily typed in LaTeX using a table or matrix. Including figures or diagrams from Geogebra or Asymptote to help your exposition is highly encouraged.

If you are currently in high school, in addition to handing in your solutions to me as stated above, you must also officially register for the USAMTS contest itself at the USAMTS website (do that now), and submit your official solutions to them as an official participant.

I will grade it according to the rules of the USAMTS contest. In particular, rule #14 says “Each solution will be given a score of 0, 1, 2, 3, 4, or 5. Solutions will be graded both on mathematical correctness and on writing style.” No solutions will be graded before the due date of October 16.

Game on!! Go Scranton Mathletes!

Training Workout #5 – Thursday, Sept 13, 2018
• Solve the 8 problem set I gave you in class. As usual, you may keep the problems and should hand in your answers on the official Answer Form linked to below.  If you want to take it under contest conditions, give youself 40 minutes. Do not use a calculator or computer. Be sure to log your efforts in the training log.
• Continue working on USAMTS Round One. Be sure to log your efforts in the training log.
• Read the MATHCOUNTS Vocabulary Handout – linked to below. Write down any terms that you don’t know and either look them up or ask me about them at the start of class.
Training Workout #6 – Tuesday, Sept 18, 2018
• Solve the 8 problem set I gave you in class. As usual, you may keep the problems and should hand in your answers on the official Answer Form linked to below.  If you want to take it under contest conditions, give youself 40 minutes. Do not use a calculator or computer. Be sure to log your efforts in the training log.
• USAMTS Round One. Continue working on Round 1 Problems that you haven’t solved. Hand in a draft of your attempted solution to at least one of the problems #2-5 (not #1). It can be either handwritten or typed in LaTeX. Be sure to log your efforts in the training log.
• Read Over Sections 2.1-2.3 In Zeitz. You don’t need to work all of the examples but familiarize yourself with the material.
Training Workout #7 – Thursday, Sept 20, 2018
• Solve as many of the 8 problems in the set I gave you in class as you can. As usual, you may keep the problems and should hand in your answers on the official Answer Form linked to below.  If you want to take it under contest conditions, give youself 40 minutes and no calculator. Be sure to log your efforts in the training log.
• Continue working on USAMTS Round One. Be sure to log your efforts in the training log.
• Look over Section 3.1 in Zeitz You don’t have to work through all of his examples, but you certainly should if you have time.
Training Workout #8 – Tuesday, Sept 25, 2018
• Solve the Logic Problem from the 2017 Admissions Test that I gave you in class. Prove your answers. You can hand this in on paper either handwritten or typed.
• Finish reading Section 3.1 in Zeitz You don’t have to work through all of his examples, but you certainly should if you have time.
Training Workout #9 – Thursday, Sept 27, 2018
• Solve as many of the 8 problems on the Training Workout 9 pdf that is in your Dropbox folder. As usual, you may keep the problems and should hand in your answers on the official Answer Form linked to below.  If you want to take it under contest conditions, give youself 40 minutes and no calculator. Be sure to log your efforts in the training log.
• Hand in your first draft of USAMTS Round One. Solve as many problems as you can. Any correct solutions that are not replaced by a future submission will be given bonus points for being submitted early. Write up your solutions in $\LaTeX$ using the formatting template recommended by USAMTS. Place your pdf in your Dropbox folder, labeled “USAMTS Round 1 draft 1- NAME.pdf” where NAME is replaced by your name. If you use Overleaf to do $\LaTeX$ you can start your document by doing the following.
1. Login to Overleaf. If you don’t have an Overleaf account, you can create one for free.
3. Click on the Menu icon in the upper left hand corner of the Overleaf screen.
4. Choose the “Copy Project” to make an editable copy for your solution. Give it the project name “USAMTS Round 1 draft 1 – NAME” where NAME is your name or nickname. Tell it to create the copy. When it does you will be able to edit that project.
If all goes well you should be in business. Save the pdf of your draft in your Dropbox folder.
• Be sure to update your Training Logs. Keep a record of your hours that you put into training. It is a large facter in determining your course grade.
Training Workout #10 – Tuesday, Oct 2, 2018
• Solve the Rock, Paper, Scissors Problem that I gave you in class. Prove your answers. You can hand this in on paper either handwritten or typed.
• Continue working on USAMTS Round 1. – it is due on October 15, which is only two weeks away.
• Start reading Section 3.2 in Zeitz You don’t have to work through all of his examples, but you certainly should if you have time.
• Update your Training Log. – it is due once per week, before class on Tuesday.
Training Workout #11 – Thursday, Oct 4, 2018
• Solve the ten question set that is in your Dropbox folder. You do not have to prove your answers. Hand this in on the official answer sheet linked to below.
• Continue working on USAMTS Round 1. – it is due on October 15, which is less than two weeks away.
• Finish reading Section 3.2 in Zeitz You don’t have to work through all of his examples, but you certainly should if you have time.
Training Workout #12 – Thursday, Oct 11, 2018
• Continue working on USAMTS Round 1. – it is due on October 15.
• Answer the Stair Climbing Olympics Problem – that I gave you in class. Prove your answers. You can hand it in on paper in class, either handwritten or typed.
• Start reading Section 3.3 in Zeitz You don’t have to work through all of his examples, but you certainly should if you have time.
USAMTS Round 1 Due – MONDAY, Oct 15, 2018
• Hand in your solution to 2018 USAMTS Round One. Put a pdf of your latexed solutions in your Dropbox folder before 8pm on Monday, October 15, 2018. I will collect all solutions at that time. High school students should also submit their solutions online officially to USAMTS. College students should only submit them to me. This will count as your first exam, so partial results will be given partial credit. Game on!
• Finish reading Section 3.3 in Zeitz. You don’t have to work through all of his examples, but you certainly should if you have time. It’s great stuff!
Training Workout #14 – Thursday, Oct, 2018
• Solve the 8 problem set I gave you in class. As usual, you may keep the problems and should hand in your answers on the official Answer Form linked to below. If you want to take it under contest conditions, give youself 40 minutes. Do not use a calculator or computer. Be sure to log your efforts in the training log.
• Start reading Section 3.4 in Zeitz. You don’t have to work through all of his examples, but you certainly should if you have time. It’s great stuff!
Training Workout #15 – Tuesday, Oct 23, 2018
• USAMTS Round 2!

Start Working on USAMTS Year 30 Round 2! This is it, team! The next actual official math competition of the season!

• Get the USAMTS Year 30 Round 2 Problems!
• Read all of the problems carefully now! That will load them into your brain and allow ideas to simmer to the surface.
• Start working on them now. Record your progress in your logs as you go.
• Write up a brief (one or two paragraphs per problem) initial progress report to hand in on Tuesday in class. For each of the five problems you should give your initial impressions, and discuss which strategies or problem solving mindsets from Zeitz you think might be helpful as a possible initial approach. If you solve any, don’t hand in your solution, just discuss what problem solving strategies, if any, you used.
• Be patient! Be confident! Don’t give up easily!!

Rules: This will be a major consideration in determining your grade in this course, similar to a take-home exam (except that you have more than five weeks to work on it!). We will follow the contest rules stated at the website. You can use reference books, online math references (that don’t involve asking another human being), calculators, Maple, spreadsheets, Geogebra, mechanical models, rulers, protractors, etc. to solve these problems. The only thing you cannot do is discuss the problem with anyone either directly or indirectly. You can not ask me questions about the problems to clarify the problem statement and so on, but you can ask me to explain Playbook facts, general mathematical terminology, theorems, etc.

These five problems will be due on Monday, November 26, 2018 at 8pm by placing a pdf of your solutions in your Dropbox folder. Note that unless you are still in high school or middle school, you should hand these solutions in to me, not submit them to the USAMTS competition! Do not write more than one solution on a single sheet of paper (a single problem solution can be on multiple sheets of paper). Neatness counts for this training workout. LaTeX solutions are required. You should use the official LaTeX template provided at the bottom of that page at the USAMTS website. I will answer any LaTeX or Overleaf questions you have. Problem number one can be easily typed in LaTeX using a table or matrix. Including figures or diagrams from Geogebra or Asymptote to help your exposition is highly encouraged.

If you are currently in high school, in addition to handing in your solutions to me as stated above, you must also officially submit your official solutions to USAMTS as an official participant.

I will grade it according to the rules of the USAMTS contest. In particular, rule #14 says “Each solution will be given a score of 0, 1, 2, 3, 4, or 5. Solutions will be graded both on mathematical correctness and on writing style.” No solutions will be graded before the due date of November 26.

Game on!! Go Scranton Mathletes!

• Try to solve one or two problems from the set I gave you in class – That is practice for the upcoming VTRMC contest we will be taking next Saturday. If you want to get use to exam timing, give yourself 2.5 hours and see how many problems you can answer correctly in that time.
Training Workout #16 – Thursday, Oct 25, 2018
• Solve the 8 problem set in your Dropbox folder. As usual, you may keep the problems and should hand in your answers on the official Answer Form linked to below.  If you want to take it under contest conditions, give youself 40 minutes. Do not use a calculator or computer. Be sure to log your efforts in the training log.
• Continue working on USAMTS Round Two. Be sure to log your efforts in the training log.
Training Workout #17 – Saturday, Oct 27, 2018
• VTRMC!!! Participate in the 2018 VTRMC Competition, this Saturday, October 27, 2018 in room LSC 233 from 9:30am-noon. Show up between 9:00-9:15am to register and get settled. We will go to lunch afterwards. This counts as an exam in the course. Get plenty of rest the night before and hydrate before the contest itself. Game on!
• Continue working on USAMTS Round Two. Be sure to log your efforts in the training log.
Training Workout #18 – Thursday, Nov 1, 2018
• Solve the 8 problem set in your Dropbox folder. As usual, you may keep the problems and should hand in your answers on the official Answer Form linked to below.  If you want to take it under contest conditions, give youself 40 minutes. Do not use a calculator or computer. Be sure to log your efforts in the training log.
• Continue working on USAMTS Round Two. Be sure to log your efforts in the training log.
• Finish reading Section 3.4 and read over Section 4.1 in Zeitz. As usual you don’t have to work through all of the problems but if you have time, you should. It’s great stuff!
Training Workout #19 – Tuesday, November 6, 2018
• Solve the problem for Training Workout 19 that is in your Dropbox folder. Write up your proof (handwritten is ok, but LaTeX is c)
• Hand in a first draft of USAMTS Round Two. Solve as many problems as you can, but you don’t have to hand in something for every problem on this draft. Write up your solutions in $\LaTeX$ using the formatting template recommended by USAMTS. Place your pdf in your Dropbox folder, labeled “USAMTS Round 2 draft 1- NAME.pdf” where NAME is replaced by your name. If you use Overleaf to do $\LaTeX$ you can start your document by doing the following.
1. Login to Overleaf. If you don’t have an Overleaf account, you can create one for free.
3. Click on the Menu icon in the upper left hand corner of the Overleaf screen.
4. Choose the “Copy Project” to make an editable copy for your solution. Give it the project name “USAMTS Round 2 draft 1 – NAME” where NAME is your name or nickname. Tell it to create the copy. When it does you will be able to edit that project.
If all goes well you should be in business. Save the pdf of your draft in your Dropbox folder.
• Be sure to update your Training Logs. Keep a record of your hours that you put into training. It is a large facter in determining your course grade.
Training Workout #20 – Thursday, Nov 8, 2018
• Solve the 8 problem set I gave you in class. As usual, you may keep the problems and should hand in your answers on the official Answer Form linked to below.  If you want to take it under contest conditions, give youself 40 minutes. Do not use a calculator or computer. Be sure to log your efforts in the training log.
• Continue working on USAMTS Round Two. Be sure to log your efforts in the training log.
• Finish reading Section 4.1 in Zeitz. As usual you don’t have to work through all of the problems but if you have time, you should. It’s great stuff!
Training Workout #21 – Tuesday, Nov 13, 2018
• Answer the 2015 Admissions Test problem I gave you in class. Write up your solution by hand or LaTeX and hand it in on paper in class on Tuesday. Be sure to log your efforts in the training log.
• Continue working on USAMTS Round Two. Be sure to log your efforts in the training log.
• Start reading Section 4.2 in Zeitz. As usual you don’t have to work through all of the problems but if you have time, you should. It’s great stuff!
Training Workout #22 – Tuesday, Nov 20, 2018
• Update your Training Logs! Some of them are getting behind and out of date. These are an important component of your course grade (it’s either this or your Putnam score.)
• Solve the Mathical Card Game problem that is in your Dropbox folder. As usual, you should prove all of your answers. You can write or type your solutions and hand them in in class on Tuesday.
• Solve the 8 problem set I gave you in class on Tuesday. As usual, you may keep the problems and should hand in your answers on the official Answer Form linked to below. If you want to take it under contest conditions, give youself 40 minutes. Do not use a calculator or computer.
• Continue working on USAMTS Round Two. Be sure to log your efforts in the training log.
• Start reading Section 4.3 in Zeitz. As usual you don’t have to work through all of the problems but if you have time, you should. It’s great stuff!
USAMTS Round 2 Due – MONDAY,November 26, 2018
• Hand in your solution to 2018 USAMTS Round Two. Put a pdf of your latexed solutions in your Dropbox folder before 8pm on Monday, November 26, 2018. I will collect all solutions at that time. High school students should also submit their solutions online officially to USAMTS. College students should only submit them to me. This will count as your third exam, so partial results will be given partial credit. Game on!
• Finish reading Section 4.3 in Zeitz. You don’t have to work through all of his examples, but you certainly should if you have time. It’s great stuff!
Training Workout #24 – Thursday, Nov 29, 2018
• Solve the eight problems in the Training Workout 24 pdf in your Dropbox folder As usual, you may keep the problems and should hand in your answers on the official Answer Form linked to below. If you want to take it under contest conditions, give youself 10 minutes per pair of questions. Do not use a calculator or computer for anything.
• Update your Training Logs! Some of them are getting behind and out of date. These are an important component of your course grade (it’s either this or your Putnam score.)
PUTNAM! – Saturday, Dec 1, 2018
• Take the 2018 Putnam contest from 10:00am-6:00pm, Saturday, Dec 1, in the LSC 233. Just bring pencils, pens, and erasers. Get sleep the night before. Hydrate. Don’t eat anything strange for breakfast. Study your Must-Know facts. Study your problem solving strategies and plan a mental checklist for using them if you get stuck. Be sure to log your efforts in the training log. Lunch is on the math department at a local restaurant. This counts as Part I of your Final Exam. Game on!
Training Workout #26 – Thursday, Dec 1, 2018
• Hand in your Must-Know Notebook – Get your Must-Know Notebook organized and up to speed and bring that to class to hand in to be graded. Neatness counts. See the syllabus below for details.
• Hand in your Problem Training Notebook – Get your Problem Training Notebook organized and up to speed and bring that to class to hand in to be graded. Neatness does not count. See the syllabus below for details.
• Solve and hand in at least one problem from USAMTS Round 3. – USAMTS Round 3 is now available. I also made an Overleaf template for you to type your solutions. You can hand in any problem, including problem #1, but you don’t have to hand in problem #1 if, say, you hand in problem #2 instead.

Since this is an active contest I cannot tell you if your solutions are correct or not. But if you hand in more than one solution, each solution that has significant progress can be used to make up for a class you missed during the semester when computing your final grade.

Final Exam Part 2 – Thursday, Dec 13, 2018
• Study for Part 2 of your Final Exam. – It will be held in our usual classroom on Thursday, December 13, 2018 at 5:15 pm. Know your Must-know facts inside and out.
• Finish updating your Training Log Spreadsheets. – The will be graded as part of your course grade.  Make sure they are up to date by the time of the Final Exam.


text:
Skipping if and while statements despite being true

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So i'm getting ready to wrap up a few features and start my web page design and something bad happens. My if and while statement don't work. All they needed to do was check if a condition was true and they keep skipping it. I tried "If (true), while(true), for(true)" and nothing works. I know that bool variable that they check is true. I put a break point right before the if/while statements are activated and I  know when the bool value is turned to true. I watched this variables and it said it was true. Why is this happening? Has anyone ever encountered a problem like this and how do you fix it?

Edited by LAURENT*

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Yes I've encountered this several times. In all cases it was caused by me messing something up.

Please post the code, otherwise we have no way of helping out.

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All they needed to do was check if a condition was true and they keep skipping it. I tried "If (true), while(true), for(true)" and nothing works.

You missed the obvious test of removing the test all together, although I don't think it makes any difference.

As it all makes no sense from a logic perspective, and we know a computer is a very logic-driven device, there is only one conclusion you can draw: Your hypothesis is wrong.

In other words, the "if" does get taken, it does whatever is in the "then" part, but for some reason, that has no or not enough effect.
You can try to run through it with a debugger to find the spot where it reverts your 'then' code, close inspection after a few hours doing something else also often works.

As VildNinja said already, if you want our help, we need some code lines to look at.

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Drop a breakpoint in your debugger, step through the code one line at a time and verify every value is what you expect.

It is extremely rare for the underlying systems to get this wrong, and it does occasionally happen on newly-released platforms and systems, but sometimes (extremely rarely) the tools will be wrong. After you have verified in your debugger that you haven't messed up the logic -- and you almost certainly have -- then step through the assembly and double check again.

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Also, try doing a full rebuild. Helps in a depressingly large number of cases of completely messed up behavior.

http://www.gamedev.net/topic/682628-visual-studios-2010-debugger-variable-doesnt-update/#entry5312556

I tried that, it still didn't work. From what I observed I didn't initialize a bool variable HOWEVER it always true by default for some reason. Even in the very early stages of the program's execution as soon as  this bool value is declared it is true and I didn't even set it. I'm like 'awesome bools are automatically true upon being declared". Tracking the bool variable and it behavior shows it remains consistent because I changed it to see if the variable wasn't updating for debug. I need time to prepare my code example. It ain't easy getting spot on info that help you to help me.

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From what I observed I didn't initialize a bool variable HOWEVER it always true by default for some reason.

bool has three states: false, true, and undefined. I believe VC++ compiler treats 0 as false, 1 as true, and anything else is undefined, however Visual Studio might treat undefined as true (because it's not 0) thus causing this confusion. I'd suggest to set it explicitly to true right before the loop - it should enter your loop.

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Okay..... Don't get ma

From what I observed I didn't initialize a bool variable HOWEVER it always true by default for some reason.

bool has three states: false, true, and undefined. I believe VC++ compiler treats 0 as false, 1 as true, and anything else is undefined, however Visual Studio might treat undefined as true (because it's not 0) thus causing this confusion. I'd suggest to set it explicitly to true right before the loop - it should enter your loop.

I just set it explicitly and well..... it worked. Why does this debugger keep lying to me? Why! I've read around the web a bit and came to the conclusion that I should get my program to work first then clean up everything later including initializing the uninitialized. I didn't follow it at first but later I ended up creating variables for ideas that flopped and were worthless. So I just try to get a feature to work and clean up the mess later right after it works. (sigh) my conclusions are always wrong. shit.

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What would the following code print? (This is compiled with VC++ 2015 in Debug mode with default project settings)

  bool f;

// watch window says:
// f	true (204)	bool
// see that "204"?
// this boolean is stored as a byte in memory, so it has 256 possible values, only two of which are true and false.
// That's 1/128th chance that the bool will even act as a boolean, regardless of not knowing its value!

if (f == false)
{
printf("first case\n"); // not printed
}
if (f == true)
{
printf("second case\n"); // not printed either.  But clearly a bool is either true or false, right?  WRONG.
}
if (f) // this is the same as (f != 0)
{
printf("third case\n");
}

Edited by Nypyren

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From what I observed I didn't initialize a bool variable HOWEVER it always true by default for some reason.

bool has three states: false, true, and undefined. I believe VC++ compiler treats 0 as false, 1 as true, and anything else is undefined, however Visual Studio might treat undefined as true (because it's not 0) thus causing this confusion. I'd suggest to set it explicitly to true right before the loop - it should enter your loop.

Numerically zero is false and non-zero is true regardless of type. On the die T/F is a check against zero. This is true of the language, not dependent on VS. If a bool is not defined and its memory contains a non-zero value then it will evaluate as true.

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On the die T/F is a check against zero

Explicit comparison to true compares to 1, thus if it was garbage value it will give unexpected results.

	bool val;
memset(&val, 5, sizeof(val)); // simulate garbage value

if (val == true) // VC++ generates cmp eax,1
cout << "true" << endl;
else if (val == false)
cout << "false" << endl;
else
cout << "undefined" << endl; // this gets printed

Edited by Zaoshi Kaba

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I just set it explicitly and well..... it worked. Why does this debugger keep lying to me? Why! I've read around the web a bit and came to the conclusion that I should get my program to work first then clean up everything later including initializing the uninitialized. I didn't follow it at first but later I ended up creating variables for ideas that flopped and were worthless. So I just try to get a feature to work and clean up the mess later right after it works. (sigh) my conclusions are always wrong. shit.

.

Yeah.... it's like near-zero work to initialize variables, and saves on lots of possible headaches.  Also, asserts are your friend.

(There are certain languages where uninitialized variables are more clearly defined.  Like C#.  C++ is not one of those languages.)

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On the die T/F is a check against zero

Explicit comparison to true compares to 1, thus if it was garbage value it will give unexpected results.

	bool val;
memset(&val, 5, sizeof(val)); // simulate garbage value

if (val == true) // VC++ generates cmp eax,1
cout << "true" << endl;
else if (val == false)
cout << "false" << endl;
else
cout << "undefined" << endl; // this gets printed

Ah. That's true, I forget that people still do (x == bool) instead of just using the value directly. Looking back up, it looks like Nypyren already covered it.

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bool f;

if (f == false) {
printf("first case\n"); // not printed
}
if (f == true) {
printf("second case\n"); // not printed either. But clearly a bool is either true or false, right? WRONG.
}

This is actually a fun case in C++.

Here is the relevant line from the c++ standard: "Using a bool value in ways described by this International Standard as “undefined,” such as by examining the value of an uninitialized automatic object, might cause it to behave as if it is neither true nor false".

I had quoted it earlier today for another discussion thread, but it applies here. It is one of the fun little quirks of undefined behavior. When you enter the realm of undefined behavior, all kinds of weird things can happen. The most scary of all is when it looks like it works okay, because you don't know when or if it will ever behave differently, a silent landmine in your code waiting to blow up.

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I didn't see your code but IIRC the last time I had such a hair-pulling situation I had mistakenly ended the if statement with a semi-colon before the curly braces. Like so:
if ( a == b );
{
//blah
}

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So i'm getting ready to wrap up a few features and start my web page design and something bad happens. My if and while statement don't work. All they needed to do was check if a condition was true and they keep skipping it. I tried "If (true), while(true), for(true)" and nothing works. I know that bool variable that they check is true. I put a break point right before the if/while statements are activated and I  know when the bool value is turned to true. I watched this variables and it said it was true. Why is this happening? Has anyone ever encountered a problem like this and how do you fix it?

So there are two problems here: Your code is not working the way you want it to and the debugger isn't working the way you want it to.

So let's deal with the major and actual problem first. Can you post the code so we can see it? And tell you exactly what's wrong and why?

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## Saturday, May 18, 2019

Note that xT denotes the transpose of x, and Ax < b means that the inequality is taken element-wise over the vectors Ax and b. The above objective function is convex if and only if H is positive- semidefinite. The quadprog function expects a problem of the above form, defined by the parameters fH; f; A; b; Aeq; beq; l; u; x0; H and f are required, the others are optional (empty matrix [])

General Formula
Example

rewrite pattern above

Code in matlab

clc;clear all;close all;
H = diag([1; 0]);
f = [3; 4];
A = [-1 -3; 2 5; 3 4];
b = [-15; 100; 80];
l = zeros(2,1);
Aeq = [];
Beq = [];
u = [];
x0 = [];
options = optimset('Algorithm','interior-point-convex');

Output

>> x

x =

0.0000
5.0000

>> fval

fval =

20.0000

>>

We can verify3 that x = 0; y = 5, with an optimal value 20.


text:
# Preprints

A full list is also available, with details of how to submit relevant papers and how to acknowledge INI.

Search preprint archive
Authors Title Attachments
JF Rodrigues Reaction-diffusion: From systems to nonlocal equations in a class of free boundary problems
VA Galaktionov On higher-order viscosity approximations of one-dimensional conservation laws
Y Du On a free boundary problem arising from population biology
H-D Cao; G Tian; X Zhu Kähler-Ricci solitons on compact manifolds with $c_1({\it M}) > 0$
OC Schnürer Neumann and second boundary value problems for Hessian and Gauss curvature flows
X Ma Christoffel-Minkowski problem I: Hessian equations on $S^n$


text:
# Finite representations and programming languages Countably inifite

I'm going over some of the pre-requisite math regarding Automata theory, and finite representations.

• If ∑ is a finite alphabet the set of all strings over the alphabet (∑*) is countably infinite.

• The set of all possible languages over an alphabet ∑ is uncountably infinite.

How can the set of languages possible from ∑ be uncountably infinite, yet the possible application of that alphabet to a language be countably infinite?

Can I ask those replying to not use too much complex notation, as I'm not a mathematics wizz.

• Do you understand the difference between countable infinite and uncountable infinite, or is there only one kind of infinite in your mind? Do you have a vague idea of how this distinction came to be (cf. Cantor)? – delnan Mar 4 '14 at 23:43
• Thanks. I kind of get the idea of uncountably infinite. It essentially is a set that cannot be indexed, like a set of real numbers, because say the possible number of incremental steps between say 1.0 and 2.0 is immeasurably infinite. – Andrew S Mar 4 '14 at 23:49
• "Immeasurably infinite" is not a technical term AFAIK (if it is, disregard the following). If by that you mean that there's a (countably or not) infinite number of steps between 1 and 2, then you've fallen into the trap of underestimating infinity. The real number interval [1;2] is indeed uncountable, but the rationals in the same interval are countable, despite there being a (countably) infinite number of them and no discrete steps! – delnan Mar 4 '14 at 23:56

Here is a simpler situation highlighting the difference. The set of finite binary strings is countable. The set of infinite binary strings is uncountable.

Another example: the set of numbers with finite decimal expansion is countable. The set of numbers with infinite decimal expansion is uncountable.

The reason that the number of languages is uncountable is that you have infinitely many choices: for each word, you can decide whether it's in the language or not. That's why it's like that infinite binary string considered above.

• The first two arguments are not convincing, an infinite set of binary strings is countable just infinitely, 0, 1, 10, 11, .....infinity (correctly me if I'm wrong,which I probably am). However, I like your last example. – Andrew S Mar 5 '14 at 1:42
• The set of all finite strings is countable - that's 0, 1, 10, 11, ... The set of all infinite strings is uncountable. You can't even write any of them, since they're all infinite. Examples can be $0^\omega$ (infinitely many zeroes), $(01)^{\omega}$ (a repeating pattern), $1010^210^310^410^5\dots$ (a non-repeating pattern), and many, many more. Uncountably more. More than you can describe. – Yuval Filmus Mar 5 '14 at 1:52
• @AndrewS, you are considering finite binary strings. Check out Cantor's diagonal argument to see the crucial difference. – vonbrand Mar 5 '14 at 1:53
• Thanks so much folks I'll now sleep tonight (well a little bit). – Andrew S Mar 5 '14 at 2:06
• I don't think this answer provides a valuable intuition. 1) There are non-trivial countable sets of infinite strings, e.g. represented by Turing machines or Büchi automata. 2) The rational numbers contain such that have infinite decimal expansions, yet the set is countable. 3) The property of "having infinitely many choices" is too vague to be useful. – Raphael Mar 5 '14 at 7:14

Questions of the form "how can" are always hard to answer as they ask for intuition. The intuition here is: uncountable means "too many" in way. Why are there "much more" objects of one kind than of the other kind? Well, they just are.

Make sure you understand the facts.

1. Given a finite set $$\Sigma$$, construct the bijection to $$\mathbb{N}$$ for the set of all (finite) strings over $$\Sigma^*$$.

Hint: $$\Sigma^n$$ is finite, so combining a generalised numbering of $$\Sigma^n$$ with $$n$$ should work.\

2. Show that the set of all tuples of naturals, i.e. $$\mathbb{N}^+ = \bigcup_{i \geq 1} \mathbb{N}^i$$, is countable.

Hint: Construct the bijection for $$\mathbb{N}^i$$ first (cf. Cantor) and combine those, again using $$i$$.

3. Show that the power set of $$\mathbb{N}$$, i.e. $$2^{\mathbb{N}}$$, is uncountable.

Hint: Use diagonalisation.

If you have done this, you have all the tools to show for instance that

• all algorithmic (or, more generally, finitely represented) concepts are countable but
• the set of all functions over naturals or reals or ... is uncountable.


text:
Sales Toll Free No: 1-855-666-7446

# Amplitude of a Wave

Top
 Sub Topics Have you ever observed the water waves while traveling on the boat? The energy the wave has, makes the boat to move from a point to another. So after reading there lies a question that might wonder you. What is that getting transferred water or energy? Its actually energy that gets transferred from a point to another that actually makes your boat move to your destiny and the water will be in its own place. This energy which a wave carries depends on the amplitude. Tsunami waves carrying higher energy. Its all because of its greater amplitude.

## What is the Amplitude of a Wave?

The amplitude is that which gives the distance from center to either crust or trough of a wave. It is expressed in meters (m). The larger the amplitude is, the more energy it carries.

## Amplitude of a Wave Formula

The Amplitude Formula is given by,
A = $\frac{D}{f}$
where,
D is the distance traveled by the wave and
f is the frequency of the wave.

## Amplitude of a Sound Wave

A sound wave has compressions and rarefaction. The peak tells about the compression and the trough about rarefaction. The greater the distance between peaks and troughs the larger will be the amplitude of the wave.

Amplitude has lot more to say about loudness and volume of sound. Just as bigger waves crash on beach with more force than smaller waves bigger waves stimulate our ear drum and cilia with greater volume than another sound wave.A sound wave carrying greater volume is said to have greater sound pressure level (SPL). It is expressed in decibels.

## Amplitude of a Sine Wave

The amplitude of sine wave equation is given as
y(t) = A sin($\omega$ t + $\phi$ )
where,
A is the amplitude of the sine wave,
$\omega$ is the angular frequency.

The angular frequency is given as
$\omega$ =2 $\pi$ f
where,
f is the frequency,
t is the varying parameter,
$\phi$ is the phase change.

## Amplitude of a Light Wave

The amplitude of light tells about how intense or bright a light wave is relative to other light waves of same wavelength. It gives an idea of how much energy a wave carries. If light from star A is brighter than star B carrying same wavelength. It tells that star A has larger amplitude comparatively.

## How to find the Amplitude of a Wave?

Lets go through same examples on amplitude of a wave:

### Solved Examples

Question 1: Calculate the amplitude of the wave that travels a distance of 50 m carrying a frequency of 100 Hz.
Solution:

Given: Distance D = 50 m, frequency f = 100 Hz

The amplitude of wave is given by
A = $\frac{D}{f}$
= $\frac{50\ m}{100\ Hz}$
= 0.5 decibels.

Question 2: A sine wave is represented by y = 4 sin $\omega$ t. what is its amplitude?
Solution:

The sine wave is expressed in the form y = A sin $\omega$ t
Hence the amplitude is A = 4.


text:
# American Institute of Mathematical Sciences

July  2017, 37(7): 3531-3544. doi: 10.3934/dcds.2017151

## Topological stability from Gromov-Hausdorff viewpoint

 Instituto de Matemática, Universidade Federal do Rio de Janeiro, P. O. Box 68530, 21945-970 Rio de Janeiro, Brazil

Received  February 2017 Revised  March 2017 Published  March 2019

Fund Project: Work partially supported by CNPq from Brazil.

We combine the classical Gromov-Hausdorff metric [5] with the $C^0$ distance to obtain the $C^0$-Gromov-Hausdorff distance between maps of possibly different metric spaces. The latter is then combined with Walters's topological stability [11] to obtain the notion of topologically GH-stable homeomorphism. We prove that there are topologically stable homeomorphism which are not topologically GH-stable. Also that every topological GH-stable circle homeomorphism is topologically stable. Afterwards, we prove that every expansive homeomorphism with the pseudo-orbit tracing property of a compact metric space is topologically GH-stable. This is related to Walters's stability theorem [11]. Finally, we extend the topological GH-stability to continuous maps and prove the constant maps on compact homogeneous manifolds are topologically GH-stable.

Citation: Alexanger Arbieto, Carlos Arnoldo Morales Rojas. Topological stability from Gromov-Hausdorff viewpoint. Discrete & Continuous Dynamical Systems - A, 2017, 37 (7) : 3531-3544. doi: 10.3934/dcds.2017151
##### References:

show all references

##### References:
Topologically but not topologically GH-stable homeomorphism
Isometric stability in $S^1$ implies topological stability
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text:
org.apache.commons.math3.optimization.general

• All Implemented Interfaces:

Deprecated.
As of 3.1 (to be removed in 4.0).

@Deprecated
Available choices of update formulas for the β parameter in NonLinearConjugateGradientOptimizer.

The β parameter is used to compute the successive conjugate search directions. For non-linear conjugate gradients, there are two formulas to compute β:

• Fletcher-Reeves formula
• Polak-Ribière formula
On the one hand, the Fletcher-Reeves formula is guaranteed to converge if the start point is close enough of the optimum whether the Polak-Ribière formula may not converge in rare cases. On the other hand, the Polak-Ribière formula is often faster when it does converge. Polak-Ribière is often used.

Since:
2.0
Version:
$Id: ConjugateGradientFormula.java 1422230 2012-12-15 12:11:13Z erans$
• ### Method Detail

• #### values

Deprecated.
Returns an array containing the constants of this enum type, in the order they are declared. This method may be used to iterate over the constants as follows:
System.out.println(c);

Returns:
an array containing the constants of this enum type, in the order they are declared


text:
# Let $\{G,*\}$ and $\{G',\circ\}$ be groups, prove that $S$ forms a group under the product operation

$\{G,*\}$ is a group with identity element $e$, and $\{G',\circ\}$ is a group with identity element $e'$. Let $S=G\times G'$. Define the “product” of pairs of elements $(a,a'),(b,b')\in S$ by $(a,a')(b,b')=(a\circ b,a'*b')$

Prove that $S$ is a group under the “product” operation.

My first thoughts on the problem was that how can we prove that $a\circ b\in G$ and $a'*b'\in G'$ and thus that $S$ is closed under the "product" operation. The problem is, I can't seem to find a way to do so. The fact that $a*b\in G,\forall a,b\in G$ doesn't seem to give any information about whether $a\circ b\in G,\forall a,b\in G$. Any help with regards to closure would be helpful. Hopefully I can use that help to figure out associativity, identity and inverse for myself.

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Surely the question as posted contains a typo, as $\circ$ is not even defined on $G.$ –  user17794 Aug 6 '12 at 3:49
@TimDuff: I think that's what OP is confused about. –  Kris Aug 6 '12 at 3:53

I switch the group operation symbol. I used $(G, \circ)$ and $(G', *)$.

Let $\cdot$ be the product operation on $G \times G'$. That is $(a,b)\cdot (a',b') = (a \circ a', b * b')$. Clearly $G \times G'$ is closed under the $\cdot$ since $a \circ a' \in G$ and $b * b' \in G'$.

$\cdot$ is associative. Suppose $a, a', a'' \in G$ and $b,b', b'' \in G'$. Then

$(a,b) \cdot ((a',b') \cdot (a'', b'')) = (a,b) \cdot (a' \circ a'', b' * b'') = (a \circ (a' \circ a''), b * (b' * b''))$

using the associativity of $\circ$ and $*$, you have

$= ((a \circ a') \circ a'', (b * b') * b'') = (a \circ a', b * b') \cdot (a'', b'') = ((a,b) \cdot (a',b')) \cdot (a'', b'')$

Thus associativity has been shown.

Similarly using individual operations you can show that $(e, e')$ is the identity of the product group. I leave it you to figure out what the inverse would be.

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Are you sure you are not making a mistake when you say that $a \circ a' \in G$? I think that it should be $a \circ b \in G$ under your (switched) notation. –  KingOliver Aug 6 '12 at 5:10
@jmi4 I believe this typo should only affect the second paragraph. It is fixed now. –  William Aug 6 '12 at 5:39

I believe you need only show that for $a,b \in G, \, c,d \in G' \Rightarrow (a*b, c\circ d) \in G \times G'$.

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You got me by a minute William –  KingOliver Aug 6 '12 at 3:54
I think you got the product operation written down incorrectly. It is supposed to be $(a,a')(b,b')=(a\circ b,a'*b')$ not $(a,a')(b,b')=(a*b,a'\circ b')$ –  E.O. Aug 6 '12 at 3:59
@E.O. $\circ$ is not an operation on $G$ so what you wrote doesn't make sense. –  Vectk Aug 6 '12 at 4:23
@E.O. the OP wrote the groups as $(G,*)$ and $(G', \circ)$ therefore my answer is correctly written. Regards. –  KingOliver Aug 6 '12 at 4:25
@Brian that is what I thought too, but since the book I am using seems to have 2 other questions based on the same binary operator I was not sure. –  E.O. Aug 6 '12 at 4:38


text:
SEARCH HOME
 Math Central Quandaries & Queries
 Question from Ann, a parent: You have 3 fish weighing a total of 21 lbs. The largest fish weighs twice as much as the second fish and the third fish weighs half the amount of the second fish. So how much does the third fish weigh? My answer is 3 lbs., however I don't know how to prove my answer. Can you help. Thank You

Hi Ann,

If the third fish weighs 3 lbs. then that is half the weight of the second fish so the second fish weighs 6 lbs. The largest fish weighs twice as much as the second fish so it weighs 12 lbs. Hence the total weight is

3 + 6 + 12 = 21 lbs.

I don't however think that this is what the teacher wants. The teacher wants to know how you arrived at the answer of 3 lbs. I expect that the teacher is looking for something like this.

Suppose the third fish weighs $x$ lbs. That is half the weight of the second fish so the second fish weighs $2x$ lbs. ....

Continue by expressing the weight of the first fish in terms of $x.$ Add the three weights and set the result equal to 21 lbs. Solve this equation for $x.$

Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.


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NCERT Solutions for Class 12 Biology Chapter 5 Principles of Inheritance and Variation PDF – eSaral

# NCERT Solutions for Class 12 Biology Chapter 5 Principles of Inheritance and Variation PDF

Hey, are you a class 12 student and looking for ways to download NCERT Solutions for Class 12 Biology Chapter 5 Principles of Inheritance and Variation PDF? If yes. Then read this post till the end.

In this article, we have listed NCERT Solutions for Class 12 Biology Chapter 5 Principles of Inheritance and Variation in PDF that are prepared by Kota’s top IITian Faculties by keeping Simplicity in mind.

If you want to learn and understand class 12 Biology Chapter 5 “Principles of Inheritance and Variation” in an easy way then you can use these solutions PDF.

NCERT Solutions helps students to Practice important concepts of subjects easily. Class 12 Biology solutions provide detailed explanations of all the NCERT questions that students can use to clear their doubts instantly.

If you want to score high in your class 12 Biology Exam then it is very important for you to have a good knowledge of all the important topics, so to learn and practice those topics you can use eSaral NCERT Solutions.

In this article, we have listed NCERT Solutions for Class 12 Biology Chapter 5 Principles of Inheritance and Variation PDF that you can download to start your preparations anytime.

So, without wasting more time Let’s start.

Question 1: Mention the advantages of selecting pea plant for experiment by Mendel.

Solution. Mendel selected pea plants to carry out his study on the inheritance of characters from parents to offspring.

He selected a pea plant because of the following features.

(a) Peas have many visible contrasting characters such as tall/dwarf plants, round/wrinkled seeds, green/yellow pod, purple/white flowers, etc.

(b) Peas have bisexual flowers and therefore undergo self pollination easily. Thus, pea plants produce offsprings with same traits generation after generation.

(c) In pea plants, cross pollination can be easily achieved by emasculation in which the stamen of the flower is removed without affecting the pistil.

(d) Pea plants have a short life span and produce many seeds in one generation.

Question 2: Differentiate between the following −

(a) Dominance and Recessive

(b) Homozygous and Heterozygous

(c) Monohybrid and Dihybrid.

Solution. (a) Dominance and Recessive

(b) Homozygous and Heterozygous

(c) Monohybrid and Dihybrid

Question 3: A diploid organism is heterozygous for 4 loci, how many types of gametes can be produced? Solution. Locus is a fixed position on a chromosome, which is occupied by a single or more genes. Heterozygous organisms contain different alleles for an allelic pair. Hence, a diploid organism, which is heterozygous at four loci, will have four different contrasting characters at four different loci.

For example, if an organism is heterozygous at four loci with four characters, say Aa, Bb, Cc, Dd, then during meiosis, it will segregate to form 8 separate gametes.

If the genes are not linked, then the diploid organism will produce 16 different gametes. However, if the genes are linked, the gametes will reduce their number as the genes might be linked and the linked genes will be inherited together during the process of meiosis.

Question 4: Explain the Law of Dominance using a monohybrid cross.

Solution. Mendel’s law of dominance states that a dominant allele expresses itself in a monohybrid cross and suppresses the expression of recessive allele. However, this recessive allele for a character is not lost and remains hidden or masked in the progenies of $F_{1}$ generation and reappears in the next generation

For example, when pea plants with round seeds (RR) are crossed with plants with wrinkled seeds (rr), all seeds in $\mathrm{F}_{1}$ generation were found to be round (Rr). When these round seeds were self fertilized, both the round and wrinkled seeds appeared in $\mathrm{F}_{2}$ generation in $3: 1$ ratio. Hence, in $\mathrm{F}_{1}$ generation, the dominant character (round seeds) appeared and the recessive character (wrinkled seeds) got suppressed, which reappeared in $\mathrm{F}_{2}$ generation.

Question 5: Define and design a test – cross?

Solution. Test cross is a cross between an organism with unknown genotype and a recessive parent. It is used to determine whether the individual is homozygous or heterozygous for a trait.

If the progenies produced by a test cross show $50 \%$ dominant trait and $50 \%$ recessive trait, then the unknown individual is heterozygous for a trait. On the other hand, if the progeny produced shows dominant trait, then the unknown individual is homozygous for a trait.

Question 6: Using a Punnett square, work out the distribution of phenotypic features in the first filial generation after a cross between a homozygous female and a heterozygous male for a single locus.

Solution. In guinea pigs, heterozygous male with black coat colour (Bb) is crossed with the female having white coat colour (bb). The male will produce two types of gametes, $\mathrm{B}$ and $\mathrm{b}$, while the female will produce only one kind of gamete, $\mathrm{r}$. The genotypic and phenotypic ratio in the progenies of $F_{1}$ generation will be same i.e., $1: 1$.

Question 7.When a cross in made between tall plants with yellow seeds (TtYy) and tall plant with green seed (TtYy), what proportions of phenotype in the offspring could be expected to be

(a) Tall and green.

(b) Dwarf and green.

Solution. A cross between tall plant with yellow seeds and tall plant with green seeds will produce

(a) three tall and green plants

(b) one dwarf and green plant

Question 8 Two heterozygous parents are crossed. If the two loci are linked what would be the distribution of phenotypic features in $\mathrm{F}_{1}$ generation for a dihybrid cross?

Solution. Linkage is defined as the coexistence of two or more genes in the same chromosome. If the genes are situated on the same chromosome and lie close to each other, then they are inherited together and are said to be linked genes.

For example, a cross between yellow body and white eyes and wild type parent in a Drosophila will produce wild type and yellow white progenies. It is because yellow bodied and white eyed genes are linked. Therefore, they are inherited together in progenies.

Question 9: Briefly mention the contribution of T.H. Morgan in genetics.

Solution. Morgan’s work is based on fruit flies (Drosophila melanogaster). He formulated the chromosomal theory of linkage. He defined linkage as the co-existence of two or more genes in the same chromosome and performed dihybrid crosses in Drosophila to show that linked genes are inherited together and are located on X-chromosome. His experiments have also proved that tightly linked genes show very low recombination while loosely linked genes show higher recombination.

Question 10: What is pedigree analysis? Suggest how such an analysis, can be useful.

Solution. Pedigree analysis is a record of occurrence of a trait in several generations of a family. It is based on the fact that certain characteristic features are heritable in a family, for example, eye colour, skin colour, hair form and colour, and other facial characteristics. Along with these features, there are other genetic disorders such as Mendelian disorders that are inherited in a family, generation after generation. Hence, by using pedigree analysis for the study of specific traits or disorders, generation after generation, it is possible to trace the pattern of inheritance. In this analysis, the inheritance of a trait is represented as a tree, called family tree. Genetic counselors use pedigree chart for analysis of various traits and diseases in a family and predict their inheritance patterns. It is useful in preventing hemophilia, sickle cell anemia, and other genetic disorders in the future generations.

Question 11: How is sex determined in human beings?

Solution. Human beings exhibit male heterogamy. In humans, males (XY) produce two different types of gametes, $X$ and $Y$. The human female ( $X X$ ) produces only one type of gametes containing $X$ chromosomes. The sex of the baby is determined by the type of male gamete that fuses with the female gamete. If the fertilizing sperm contains $X$ chromosome, then the baby produced will be a girl and if the fertilizing sperm contains $Y$ chromosome, then the baby produced will be a boy. Hence, it is a matter of chance that determines the sex of a baby. There is an equal probability of the fertilizing sperm being an $X$ or $Y$ chromosome. Thus, it is the genetic make up of the sperm that determines the sex of the baby.

Question 12:A child has blood group O. If the father has blood group A and mother

blood group B, work out the genotypes of the parents and the possible genotypes of the other offsprings.

Solution. The blood group characteristic in humans is controlled by three set of alleles, namely, $I^{A}, I^{B}$, and i. The alleles, $I^{A}$ and $I^{B}$, are equally dominant whereas allele, i, is recessive to the other alleles. The individuals with genotype, $\mathrm{I}^{\mathrm{A}} \mathrm{I}^{\mathrm{A}}$ and $\mathrm{I}^{\mathrm{A}} \mathrm{i}$, have blood group A whereas the individuals with genotype, $\left.\left.\right|^{B}\right|^{B}$ and $I^{B}$ i, have blood group $B$. The persons with genotype $\left.\left.\right|^{A}\right|^{B}$ have blood group $A B$ while those with blood group $O$ have genotype ii

Hence, if the father has blood group A and mother has blood group B, then the possible genotype of the parents will be

Father Mother

A cross between homozygous parents will produce progeny with AB blood group.

A cross between heterozygous parents will produce progenies with AB blood group $\left(\mathrm{A}^{\mathrm{A}} \mathrm{B}^{\mathrm{B}}\right)$ and $\mathrm{O}$ blood group (ii)

Question 13: Explain the following terms with example

(a) Co-dominance

(b) Incomplete dominance

Solution. (a) Co-dominance

Co-dominance is the phenomenon in which both the alleles of a contrasting character are expressed in heterozygous condition. Both the alleles of a gene are equally dominant. ABO blood group in human beings is an example of co-dominance. The blood group character is controlled by three sets of alleles, namely, $\mathrm{I}^{A}, \mathrm{I}^{\mathrm{B}}$, and $\mathrm{i}$. The alleles, $\mathrm{I}^{\mathrm{A}}$ and $\mathrm{I}^{\mathrm{B}}$, are equally dominant and are said to be codominant as they are expressed in AB blood group. Both these alleles do not interfere with the expression of each other and produce their respective antigens. Hence, $A B$ blood group is an example of co-dominance.

2. Incomplete dominance

Incomplete dominance is a phenomenon in which one allele shows incomplete dominance over the other member of the allelic pair for a character. For example, a monohybrid cross between the plants having red flowers and white flowers in Antirrhinum species will result in all pink flower plants in $\mathrm{F}_{1}$ generation. The progeny obtained in $\mathrm{F}_{1}$ generation does not resemble either of the parents and exhibits intermediate characteristics. This is because the dominant allele, $R$, is partially dominant over the other allele, r. Therefore, the recessive allele, $r$, also gets expressed in the $F_{1}$ generation resulting in the production of intermediate pink flowering progenies with Rr genotype.

Question 14: What is point mutation? Give one example.

Solution. Point mutation is a change in a single base pair of DNA by substitution, deletion, or insertion of a single nitrogenous base. An example of point mutation is sickle cell anaemia. It involves mutation in a single base pair in the beta-globin chain of haemoglobin pigment of the blood. Glutamic acid in short arm of chromosome II gets replaced with valine at the sixth position.

Question 15: Who had proposed the chromosomal theory of inheritance?

Solution. Sutton and Boveri proposed the chromosomal theory of inheritance in 1902. They linked the inheritance of traits to the chromosomes.

Question 16: Mention any two autosomal genetic disorders with their symptoms.

Solution. Two autosomal genetic disorders are as follows.

1. Sickle cell Anaemia

It is an autosomal linked recessive disorder, which is caused by point mutation in the beta-globin chain of haemoglobin pigment of the blood. The disease is characterized by sickle shaped red blood cells, which are formed due to the mutant haemoglobin molecule. The disease is controlled by $\mathrm{Hb}^{\mathrm{A}}$ and $\mathrm{Hb}^{\mathrm{S}}$ allele. The homozygous individuals with genotype, $\mathrm{Hb}^{\mathrm{S}} \mathrm{Hb}^{\mathrm{S}}$, show the symptoms of this disease while the heterozygous individuals with genotype, $\mathrm{Hb}^{\mathrm{A}} \mathrm{Hb}^{\mathrm{S}}$, are not affected. However, they act as carriers of the disease.

Symptoms

Rapid heart rate, breathlessness, delayed growth and puberty, jaundice, weakness, fever, excessive thirst, chest pain, and decreased fertility are the major symptoms of sickle cell anaemia disease. (b) Down’s syndrome

It is an autosomal disorder that is caused by the trisomy of chromosome 21.

Symptoms

The individual is short statured with round head, open mouth, protruding tongue, short neck, slanting eyes, and broad short hands. The individual also shows retarded mental and physical growth.