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Communications in Contemporary Mathematics ( IF 1.278 ) Pub Date : 2020-11-30 , DOI: 10.1142/s021919972050087x
Sheng Rao; I-Hsun Tsai

Let $π:𝒳→Δ$ be a holomorphic family of compact complex manifolds over an open disk in $ℂ$. If the fiber $π−1(t)$ for each nonzero $t$ in an uncountable subset $B$ of $Δ$ is Moishezon and the reference fiber $X0$ satisfies the local deformation invariance for Hodge number of type $(0,1)$ or admits a strongly Gauduchon metric introduced by D. Popovici, then $X0$ is still Moishezon. We also obtain a bimeromorphic embedding $𝒳−−→ℙN×Δ$. Our proof can be regarded as a new, algebraic proof of several results in this direction proposed and proved by Popovici in 2009, 2010 and 2013. However, our assumption with $0$ not necessarily being a limit point of $B$ and the bimeromorphic embedding are new. Our strategy of proof lies in constructing a global holomorphic line bundle over the total space of the holomorphic family and studying the bimeromorphic geometry of $π:𝒳→Δ$. S.-T. Yau’s solutions to certain degenerate Monge–Ampère equations are used.

Moishezon流形的变形极限和双态嵌入

$π：𝒳→Δ$ 是在开放磁盘上的紧凑型复杂流形的全同族 $ℂ$。如果纤维$π-1个（Ť）$ 对于每个非零 $Ť$ 在不可数的子集中 $乙$$Δ$ 是Moishezon和参考纤维 $X0$ 满足Hodge型数的局部变形不变性 $（0，1个）$ 或接受D. Popovici引入的强Gauduchon度量，然后 $X0$仍然是Moishezon。我们还获得了双态嵌入$𝒳-→ℙñ×Δ$。我们的证明可以看作是Popovici在2009年，2010年和2013年提出并证明的与此方向上的若干结果的新的代数证明。$0$ 不一定是 $乙$和双态嵌入是新的。我们的证明策略在于，在全纯族的整个空间上构造一个全局全纯线束，并研究双全形的几何$π：𝒳→Δ$。S.-T. 使用Yau对某些退化的Monge-Ampère方程的解。

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# The Algebra Toolbox

## My Best Number

73 The Best Number in the World

One of my many goals this year is to increase number awareness and number sense in my students.  This open-ended get-to-know-you assignment was a good start.

First, I showed the students this 1:00 minute video clip from youtube to introduce the idea of the “best” number. (Use caution if you just search for Sheldon Coopers best number on youtube. One version explains Raj’s favorite number 5,318,008 because it spells boobies when you turn a calculator upside down!)  After watching the video, we talked about the types of numbers that Sheldon mentioned (palindrome, prime,  binary, product). I asked what other “types” of numbers they knew. Descriptions such as odd, even, perfect squares, whole numbers, etc were brought up.

I gave each student this  My Best Number recording sheet. (I left room for more “best” numbers so students could add other cool numbers to their recording sheet as they year goes on).  They had to come up with one  Best Number for them and at least 2 reasons why it was the best. The reasons could be mathematical, historical,  or personal to them.  I gave them a couple days to think about it. On Friday of that week, each student shared his/her best number and the reasons behind it. It was a great way to get to know the students. One girl said 10 was her best number because that was how old she was the first time she met her real dad and that’s how many fingers she had to count how much she loves him.  WOW – deep for a high school freshman.  Many students chose their birth date, sports jersey number, etc. but many were very personal.

As we worked through our unit on solving equations, the students substitute their best numbers into equations that had “all real number” solutions to check the validity of the solution really being all reals. They loved that their best number was a solution. As they check their solutions to linear inequalities in the next unit, they will do the same thing.

## Super Bowl Math 2013

In preparation for Super Bowl weekend, I updated a lesson I used a couple years ago where my Algebra I students calculated the quarterback passer rating for their favorite quarterbacks.  They really enjoyed it!  For a little history on the QB Rating, this is a good article.

I provide the data they need since most NFL sites include the rating in their usual stats for each player.

Quarterback Passer Rating Worksheets guide the students step-by-step through the calculations

Quarterback Statistics for 2012 season gives the answers

Quarterback Stats for 2012 seasion WITHOUT the QB Passer Rating is the data sheet to give to students

I am a new fan of www.yummymath.com which also has had some great Super Bowl prep activities on their site, including How Have the Super Bowl Ads changed (graphing points, recognizing an exponential function, predicting future costs of ads), Super Bowl Scores 2013 (predicting Sunday’s score, finding mean, median, mode, and range and determining which measure best represents the data), 4th Down (using data to decide whether to go for it, attempt a field goal, or punt on 4th down), Super Bowl Numerals (Roman numerals, number sense), Losing Teams in the Playoffs (ratios, percents, and proportionality) and NFL Home Team Advantage (using an inforgraphic to compare NFL home and away wins).  This site provides FREE pdfs of their activities which are linked to the Common Core State Standards, or you can purchase a \$15/yr membership and have access to editable documents and solutions. Well worth the \$15 a year to be able to personalize the already great activities.

## Christmas Price Index

With three days of school left before break and an impending snow storm on Thursday evening, it’s time to do some holiday activities.

Today, we used PNC Bank’s Christmas Price Index website (interesting FAQs). I gave the students a recording sheet. First, I had the students estimate the cost of each of the gifts in “The Twelve Days of Christmas,” while I told my story about how upset I would have been if my “true love” had sent me all those pooping birds, dancing ladies, men in tights, and loud drummers while I was trying to get my house decorated and cookies made for Christmas.  I would have kept all those golden rings and sent him packing.

After they make their estimates, we head to the computer lab and they go to the PNC site. This year it’s really cool. Each gift is “hidden” somewhere in the world and they have to follow clues and do little puzzles to find them before each price is revealed. Great geography tie in. Looks like google earth images may have used in the creation.  I had them record the location and the price of each gift as it is revealed. There is a link at the bottom of the screen where they can click and immediately get the prices of the gifts without the puzzles, but I wanted them to see the sights.  The website also gives the percent increase or decrease in price since last year.  Great activity for working with percents…they can figure out last year’s prices.  We talked about which costs surprised them the most, why some prices went up while others stayed the same, and some of the places they “visited” on the journey.  They got really excited when their estimate was close.  I only wanted to spend one day on this, so that’s all we did. So many options for additional activities though.  CAUTION: I don’t know if it was the site or our computers, but it got really slow sometimes. “Patience” was our word of the day.

Tomorrow, I’m trying the Auction from Math=Love. I’ve never done it before, but will give it a go. I wrote 12 auction questions with 9 correct answers and 3 incorrect. I kept score using an excel spreadsheet which I displayed on the board.

## Activities for Solving Equations

I use lots of practice activities for solving one-, two-, and multi-step equations with my Algebra I class. Solving equations is part of their middle school curriculum but most still need much practice to achieve “fluency.”

Here are some of the activities I use:

By the Shapes Activity that I got at an NCTM conference years ago, but don’t know who the presenter was. If these are your creation, please let me know so I can credit you!

Summary of Activity: Students work in groups of 4 to determine the value of each of 3 shapes, using 4 clue cards (equations).  The By the Shapes Teacher Notessay to use counters, but I don’t. I put the By the Shapes Recording Sheet in a plastic sleeve and students record the value of each shape on the sleeve. When they have the solution, they raise their hands and show me. If they are correct (By the Shapes Answers), they mark off that clue set number at the bottom of the recording sheet (to keep track of which sets they have completed) and I give them another set.  The best part of this activity is the conversation that happens within the groups. Students engage in some really good discussions about the value of each shape, verifying solutions by substituting the values into each of the 4 clues (equations) and eliminating possible values of the shapes based on the clues.

Preparation:  Copy the By the Shapes cards onto card stock. There is page of icons that can be copied onto the back of each clue page, but this isn’t really necessary…just pretty. It’s nice if each clue set is a different color. I made 2 sets of clues (16 sets total) so that as groups finished I could be sure to give them one they hadn’t done yet.  Give each group 1 By the Shapes Recording sheet and a dry erase marker/eraser. It helps to do the Teacher demo so they have an idea of what they are supposed to do.  I told them to use all the clues at the same time to figure out the value of each shape.

Solving Equations Song– even my high school boys will clap and sing along to this one.

2 step equations model for students who struggle with getting started solving two-step equations.

Gallery Walk Variables on Both Sides– I post each sheet of 3 problems around the room and give each student an answer sheet. Students work with a partner and rotate among the 10 sheets of problems, choosing one problem from each sheet to complete. I ask them to challenge themselves to complete the “hardest” problem on each sheet if they are able.

Crumple and Shoot (also known as Trashketball) – powerpoint of equations with variables on both sides of the equals sign. Students work in teams of 4, each studnet has a number from 1-4.  Every student does every problem on white board. I use a random number generator to call a number from 1-4. That student holds up their board – if the answer is correct, their team gets one point and they have the opportunity to get extra points by shooting a piece of scrap paper into our recycle box.  I have a “one point line,”  “two point line” and “three point line” from which to shoot to make extra points.  Students are encouraged to work together with their team to complete the problems since they never know who will be called to show the answer. Great communication encourager.

Pass the Probem – Equations– in groups of 4, students pass one problem around the group, each student doing one step of the problem. Directions are on the first page of this document.

Placemat Equations– I put one “placemat” in a plastic sleeve. Students work in groups 4, each student completes one of the problems on the placemat. They find the sum of their solutions and write the sum in the center of the placemat. I only have to check one number to know if they have all solved their problems correctly.  After using this activity, I found that it was better for me to write the equations onto the placemats so that the problems were oriented so that the students could see the problems easily without the problem being upside down. I also used markers so it was more colorful.

Hot Seat Solving Equations– powerpoint of equations. Students have to determine what the first step would be in solving the given equations (includes literal equations).  Students are in 4 teams. Each team has four cards:  “Add/Subtract,”  “Multiply/Divide”  “Combine like terms” and “Use Distributive Property to simplify.”  Hot Seat directions can be found here in this post.

Study Guide– prior to taking the unit assessment, we prepare a study guide.

I also played a game of Risk using equations.  I gave the students a blank recording sheet. I put the problems on the board and showed them one problem at a time. They did the work on the back of the recording sheet and wrote the answer only on the front along with how many points they wanted to risk on that answer. I revealed the answer, we discussed it, and they calculated their points (working in pairs to keep them honest).

**Update: I just read a great post by Julie at I Speak Math about solving equations.  I love this math community!

## My Favorite Sub Plan

My favorite plan to leave for a sub is the FACEing Math  activity.  It takes most of my students two 42-minute periods to complete, is self-explanatory and easy for classroom management, provides review for students of concepts we’ve previously studied, and gives me great pictures to put on my walls!

Students complete 27 problems. Each problem is multiple choice with 2 answer choices so it’s moderately self-checking.  The answer choice tells students what feature to draw on the face template or what color to make each feature.  There are numerous FACEing Math books for all different levels, but my favorite is the “Create” books which are blank templates so you can put in the problems you want your students to do.

I know we are only supposed to put free resources on here, but this is money well spent.  The author allows people to download the first lesson from each book for free, so I’m hoping not to violate any copyright laws by posting one of the templates from Create Book #2 for view.  In honor of World Series Season, here is a FACE template that makes a Baseball player ( page 2)  with the answer key (Lesson 16).  You just need to look at the answer key to see which letter (A or B) the correct answer choice needs to be for the face to come out correctly.

My students really love this activity. They can talk quietly as they work.  I require them to show work either on the worksheet or on another sheet.  Even though all the students’ drawings should have the same facial features, each face will look unique.  We have contests to see who has the silliest, neatest, most unique, etc face when finished.  Students will need access to colored pencils or crayons and a pencil. I keep copies for emergency sub plans of content we’ve already studied so students can complete it independently.

## Math Bloggers Initiation #3 – Math Quote

“On two occasions I have been asked [by members of Parliament], ‘Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?’ I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question.”  – Charles Babbage

This quote reminds me so much of many of my students who just can’t understand how they got an answer wrong because, “That’s what the calculator said the answer is, so it has to be right,” with no consideration whatsoever about whether they entered the information correctly in the first place.  Especially when we are working with real-world data and applications, I ask them to estimate the solution first, even if it’s as simple as, “Should the solution be positive or negative?” or “Will be solution be greater than or less than 100?”  Knowing where mistakes will occur helps guide my questions.

One of the most frequent errors occurs when students have substituted negative numbers that are raised to a power. They don’t remember that parentheses are needed to obtain a correct calculation.  For example, recognizing the difference between $(-2)^2$ and $-2^2$ is tricky for them.  Most often this occurs when substituting values into an expression.  To combat this problem, I tell my students to always recopy any problem and put parentheses in FIRST before substituting.  For example:

$b^2 - 4ac$   would look like this $( )^2$  – 4(   )(   )  THEN substitute the given values for a, b, and c.  This has helped eliminate at least some of the errors that occur when raising a negative number to a power.

Calculator use is so inconsistent in my district.  The elementary schools don’t use them much, the middle schools use them some (the middle school state assessment has a “calculator section” and a “no calculator” section), Algebra I students are required to use a graphing calculator for the high school assessment. The students go on to Geometry, Algebra II, Trig, and Calculus and use a graphing calculator all the time.   We offer college classes to our seniors, but to qualify they have to pass the college’s placement test, which does not allow the use of a calculator.  We have trig students who can’t pass the basic math portion of the placement test and therefore don’t qualify to take College Algebra or Prob & Stats because they’ve come to rely on the calculator and forget how to do basic math.

I’m all for calculator use in the classroom, but I believe that basic skills needs to be reviewed throughout high school and that estimation must be a huge part of our instruction as well.

## Lessons aligned to Common Core math

This website, Learnzillion,  has been recommended by our state Coordinator for Math Education as being a good resource for elementary through high school teachers of math and English/language arts.

I’ve just started exploring it, but have been impressed so far with the number of lessons available at the high school level. There are 176 for math. You can choose a lesson by grade level, domain (but conceptual categories are there) and standard.  The lesson includes a 3-5 minute video which includes lesson slides that can be downloaded and edited and a guided practice video.  The lessons are a little dry, but would be good for a student who needs a quick review or for one who was absent. What I like about it is the alignment to common core and ideas for problems for some of the topics that I don’t currently teach in Algebra I, but will be when we go full-implentation of the new curriculum (like exponential functions).

Everything on this website is FREE and available to teachers and students.


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# 4. Alter table¶

## 4.1. Synopsis¶

 ALTER TABLE { <entries> | <find_expression> } [, ... ] ADD
{ <column_name> <data_type> }
[, ... ]

find_expression ::=
FIND ( { <tag_expression> | NOT <tag_expression> } [ AND ... ] )

tag_expression ::=
TAG = 'tag_name'

## 4.2. Description¶

ALTER TABLE will modify one or more tables in a QuasarDB cluster by adding columns with the specified schema. The statement is transactional.

## 4.3. Parameters¶

table_name

The name of the table to be modified. Can be alphanumeric, but is not allowed to start with a number.

find_expression

When your tables are tagged, you can use inline key/value lookups to perform your query over multiple tables. To match all tables that have the tag “stocks”, you can use FIND(tag='stocks' AND type=ts).

column_name

The name of a column to be added to the table. Can be alphanumeric, but is not allowed to start with a number.

data_type

The data type to be associated with the column. Can be any of INT64, DOUBLE, BLOB or TIMESTAMP.

## 4.4. Examples¶

Add a single column to an existing table:

ALTER TABLE example ADD my_int INT64

Add multiple columns to an existing table:

ALTER TABLE example ADD my_int INT64, my_double DOUBLE, my_blob BLOB, my_ts TIMESTAMP


text:
• ### Announcements

#### Archived

This topic is now archived and is closed to further replies.

# Cloning objects on the fly?

## 2 posts in this topic

Hello everyone. Well, once again I have encountered a problem. I am creating a small subhunt clone, and I am having trouble with firing multiple depth charges, namely that I don''t know to make them work. So far, the part of the main game loop that relates to this ship looks something like this: if(Spacebar is down) // fire the torpedo { // set position of the depth charge to that of the ship Set_Position (ship_pos_x and ship_pos_y); // set the downward velocity velocity = 4; } if (Space was pressed) { Draw_Depth_Charge (); } With the code like this, I can only fire one depth charge. How could I make it so that if space has been pressed more than once, It will draw another depth charge? I know the answer is probably rather simple, but I am rather high on jellybeans, and my brain is not functioning correctly. Thanks, your "wannabe" friend.
0

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You might do something like this:

  struct weapon { float x, y, z; BOOL active; // note set all active to FALSE } depth_charge [ 25 ];int dch_count = 0;// a globalif ( Space Bar is Down ) { Set_Position( ship_position_x ,ship_position_y ); // of depth_charge [ dch_count ].x, // depth_charge [ dch_count ].y velocity = 4; depth_charge [ dch_cnt ].active = TRUE; if ( dch_count++ > 24 ) dch_count = 24; }// end ifIf ( Space was pressed ){ // loop through the active depth charges drawing the // active ones for ( int count = 0 ; count < 25 ; count++ ) { if ( depth_charge [ count ].active == TRUE ) Draw_Depth_Charge( depth_charge [ count ].x, depth_charge [ count ].y ); }// end for count}// end for Space
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I sent you an E-MAIL, not sure if you got it.

It went:

Sorry to hear it did''nt work for you.
I can''t do much without seeing the code.
I assume you where adjusting the view matrix for
each missle drawn. But I don''t know how your code
was laid out ? I used similar code for multiple pixel
explosion algorithms.

Can you E-MAIL it me ?

guyjohnston@kawartha.com
0


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# How do you write an equation in point slope form when slope is 1/3 and the y- intercept is –4?

Apr 5, 2018

$y = \frac{1}{3} x - 4$

#### Explanation:

The slope-intercept form of a linear equation is:

$y = m x + b$,

where:

$m$ is the slope and $b$ is the y-intercept.


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# Chapter 1 Quality control, redux

## 1.1 Overview

Basic Chapter 1 introduced the concept of per-cell quality control, focusing on outlier detection to provide an adaptive threshold on our chosen QC metrics. This chapter elaborates on the technical details of outlier-based quality control, including some of the underlying assumptions, how to handle multi-batch experiments and diagnosing loss of cell types. We will again demonstrate using the 416B dataset from A. T. L. Lun et al. (2017).

#--- loading ---#
library(scRNAseq)
sce.416b <- LunSpikeInData(which="416b")
sce.416b$block <- factor(sce.416b$block)

## 1.2 The isOutlier() function

The isOutlier() function from the scuttle package is the workhorse function for outlier detection. As previously mentioned, it will define an observation as an outlier if it is more than a specified number of MADs (default 3) from the median in the specified direction.

library(AnnotationHub)
ens.mm.v97 <- AnnotationHub()[["AH73905"]]
chr.loc <- mapIds(ens.mm.v97, keys=rownames(sce.416b),
keytype="GENEID", column="SEQNAME")
is.mito <- which(chr.loc=="MT")

library(scuttle)
df <- perCellQCMetrics(sce.416b, subsets=list(Mito=is.mito))
low.lib <- isOutlier(df$sum, type="lower", log=TRUE) summary(low.lib) ## Mode FALSE TRUE ## logical 188 4 high.mito <- isOutlier(df$sum, type="higher")
summary(high.mito)
##    Mode   FALSE    TRUE
## logical     185       7

The perCellQCFilters() function mentioned in Basic Chapter 1 is just a convenience wrapper around isOutlier(). Advanced users may prefer to use isOutlier() directly to achieve more control over the fields of df that are used for filtering.

reasons <- perCellQCFilters(df,
sub.fields=c("subsets_Mito_percent", "altexps_ERCC_percent"))
stopifnot(identical(low.lib, reasons$low_lib_size)) We can also alter the directionality of the outlier detection, number of MADs used, as well as more advanced parameters related to batch processing (see Section 1.4). For example, we can remove both high and low outliers that are more than 5 MADs from the median. The output also contains the thresholds in the attributes for further perusal. low.lib2 <- isOutlier(df$sum, type="both", log=TRUE, nmads=5)
attr(low.lib, "thresholds")
##  lower higher
## 434083    Inf

Incidentally, the is.mito code provides a demonstration of how to obtain the identity of the mitochondrial genes from the gene identifiers. The same approach can be used for gene symbols by simply setting keytype="SYMBOL".

## 1.3 Assumptions of outlier detection

Outlier detection assumes that most cells are of acceptable quality. This is usually reasonable and can be experimentally supported in some situations by visually checking that the cells are intact, e.g., on the microwell plate. If most cells are of (unacceptably) low quality, the adaptive thresholds will fail as they cannot remove the majority of cells by definition - see Figure 1.1 below for a demonstrative example. Of course, what is acceptable or not is in the eye of the beholder - neurons, for example, are notoriously difficult to dissociate, and we would often retain cells in a neuronal scRNA-seq dataset with QC metrics that would be unacceptable in a more amenable system like embryonic stem cells.

Another assumption mentioned in Basic Chapter 1 is that the QC metrics are independent of the biological state of each cell. This is most likely to be violated in highly heterogeneous cell populations where some cell types naturally have, e.g., less total RNA (see Figure 3A of Germain, Sonrel, and Robinson (2020)) or more mitochondria. Such cells are more likely to be considered outliers and removed, even in the absence of any technical problems with their capture or sequencing. The use of the MAD mitigates this problem to some extent by accounting for biological variability in the QC metrics. A heterogeneous population should have higher variability in the metrics among high-quality cells, increasing the MAD and reducing the chance of incorrectly removing particular cell types (at the cost of reducing power to remove low-quality cells).

In general, these assumptions are either reasonable or their violations have little effect on downstream conclusions. Nonetheless, it is helpful to keep them in mind when interpreting the results.

## 1.4 Considering experimental factors

More complex studies may involve batches of cells generated with different experimental parameters (e.g., sequencing depth). In such cases, the adaptive strategy should be applied to each batch separately. It makes little sense to compute medians and MADs from a mixture distribution containing samples from multiple batches. For example, if the sequencing coverage is lower in one batch compared to the others, it will drag down the median and inflate the MAD. This will reduce the suitability of the adaptive threshold for the other batches.

If each batch is represented by its own SingleCellExperiment, the perCellQCFilters() function can be directly applied to each batch as previously described. However, if cells from all batches have been merged into a single SingleCellExperiment, the batch= argument should be used to ensure that outliers are identified within each batch. By doing so, the outlier detection algorithm has the opportunity to account for systematic differences in the QC metrics across batches. Diagnostic plots are also helpful here: batches with systematically poor values for any metric can then be quickly identified for further troubleshooting or outright removal.

We will again illustrate using the 416B dataset, which contains two experimental factors - plate of origin and oncogene induction status. We combine these factors together and use this in the batch= argument to isOutlier() via quickPerCellQC(). This results in the removal of slightly more cells as the MAD is no longer inflated by (i) systematic differences in sequencing depth between batches and (ii) differences in number of genes expressed upon oncogene induction.

batch <- paste0(sce.416b$phenotype, "-", sce.416b$block)
batch.reasons <- perCellQCFilters(df, batch=batch,
sub.fields=c("subsets_Mito_percent", "altexps_ERCC_percent"))
colSums(as.matrix(batch.reasons))
##              low_lib_size            low_n_features high_subsets_Mito_percent
##                         5                         4                         2
##                         6                         9

That said, the use of batch= involves the stronger assumption that most cells in each batch are of high quality. If an entire batch failed, outlier detection will not be able to act as an appropriate QC filter for that batch. For example, two batches in the Grun et al. (2016) human pancreas dataset contain a substantial proportion of putative damaged cells with higher ERCC content than the other batches (Figure 1.1). This inflates the median and MAD within those batches, resulting in a failure to remove the assumed low-quality cells.

library(scRNAseq)
sce.grun <- GrunPancreasData()

# First attempt with batch-specific thresholds.
library(scater)
discard.ercc <- isOutlier(sce.grun$altexps_ERCC_percent, type="higher", batch=sce.grun$donor)
plotColData(sce.grun, x="donor", y="altexps_ERCC_percent",
colour_by=I(discard.ercc))

In such cases, it is better to compute a shared median and MAD from the other batches and use those estimates to obtain an appropriate filter threshold for cells in the problematic batches. This is automatically done by isOutlier() when we susbet to cells from those other batches, as shown in Figure 1.2.

# Second attempt, sharing information across batches
# to avoid dramatically different thresholds for unusual batches.
discard.ercc2 <- isOutlier(sce.grun$altexps_ERCC_percent, type="higher", batch=sce.grun$donor,
subset=sce.grun$donor %in% c("D17", "D2", "D7")) plotColData(sce.grun, x="donor", y="altexps_ERCC_percent", colour_by=I(discard.ercc2)) To identify problematic batches, one useful rule of thumb is to find batches with QC thresholds that are themselves outliers compared to the thresholds of other batches. The assumption here is that most batches consist of a majority of high quality cells such that the threshold value should follow some unimodal distribution across “typical” batches. If we observe a batch with an extreme threshold value, we may suspect that it contains a large number of low-quality cells that inflate the per-batch MAD. We demonstrate this process below for the Grun et al. (2016) data. ercc.thresholds <- attr(discard.ercc, "thresholds")["higher",] ercc.thresholds ## D10 D17 D2 D3 D7 ## 73.611 7.600 6.011 113.106 15.217 names(ercc.thresholds)[isOutlier(ercc.thresholds, type="higher")] ## [1] "D10" "D3" If we cannot assume that most batches contain a majority of high-quality cells, then all bets are off; we must revert to the approach of picking an arbitrary threshold value (Basic Section 1.3.1) based on some “sensible” prior expectations and hoping for the best. ## 1.5 Diagnosing cell type loss The biggest practical concern during QC is whether an entire cell type is inadvertently discarded. There is always some risk of this occurring as the QC metrics are never fully independent of biological state. We can diagnose cell type loss by looking for systematic differences in gene expression between the discarded and retained cells. To demonstrate, we compute the average count across the discarded and retained pools in the 416B data set, and we compute the log-fold change between the pool averages. # Using the non-batched 'discard' vector for demonstration purposes, # as it has more cells for stable calculation of 'lost'. discard <- reasons$discard

library(edgeR)
logged <- cpm(cbind(lost, kept), log=TRUE, prior.count=2)
logFC <- logged[,1] - logged[,2]
abundance <- rowMeans(logged)

If the discarded pool is enriched for a certain cell type, we should observe increased expression of the corresponding marker genes. No systematic upregulation of genes is apparent in the discarded pool in Figure 1.3, suggesting that the QC step did not inadvertently filter out a cell type in the 416B dataset.

plot(abundance, logFC, xlab="Average count", ylab="Log-FC (lost/kept)", pch=16)
points(abundance[is.mito], logFC[is.mito], col="dodgerblue", pch=16)

For comparison, let us consider the QC step for the PBMC dataset from 10X Genomics (Zheng et al. 2017). We’ll apply an arbitrary fixed threshold on the library size to filter cells rather than using any outlier-based method. Specifically, we remove all libraries with a library size below 500.

#--- loading ---#
library(DropletTestFiles)
raw.path <- getTestFile("tenx-2.1.0-pbmc4k/1.0.0/raw.tar.gz")
out.path <- file.path(tempdir(), "pbmc4k")
untar(raw.path, exdir=out.path)

library(DropletUtils)
fname <- file.path(out.path, "raw_gene_bc_matrices/GRCh38")

#--- gene-annotation ---#
library(scater)
rownames(sce.pbmc) <- uniquifyFeatureNames(
rowData(sce.pbmc)$ID, rowData(sce.pbmc)$Symbol)

library(EnsDb.Hsapiens.v86)
location <- mapIds(EnsDb.Hsapiens.v86, keys=rowData(sce.pbmc)$ID, column="SEQNAME", keytype="GENEID") #--- cell-detection ---# set.seed(100) e.out <- emptyDrops(counts(sce.pbmc)) sce.pbmc <- sce.pbmc[,which(e.out$FDR <= 0.001)]
discard <- colSums(counts(sce.pbmc)) < 500

logged <- edgeR::cpm(cbind(lost, kept), log=TRUE, prior.count=2)
logFC <- logged[,1] - logged[,2]
abundance <- rowMeans(logged)

The presence of a distinct population in the discarded pool manifests in Figure 1.4 as a set of genes that are strongly upregulated in lost. This includes PF4, PPBP and SDPR, which (spoiler alert!) indicates that there is a platelet population that has been discarded by alt.discard.

plot(abundance, logFC, xlab="Average count", ylab="Log-FC (lost/kept)", pch=16)
platelet <- c("PF4", "PPBP", "SDPR")
points(abundance[platelet], logFC[platelet], col="orange", pch=16)

If we suspect that cell types have been incorrectly discarded by our QC procedure, the most direct solution is to relax the QC filters for metrics that are associated with genuine biological differences. For example, outlier detection can be relaxed by increasing nmads= in the isOutlier() calls. Of course, this increases the risk of retaining more low-quality cells and encountering the problems discussed in Basic Section 1.1. The logical endpoint of this line of reasoning is to avoid filtering altogether, as discussed in Basic Section 1.5.

As an aside, it is worth mentioning that the true technical quality of a cell may also be correlated with its type. (This differs from a correlation between the cell type and the QC metrics, as the latter are our imperfect proxies for quality.) This can arise if some cell types are not amenable to dissociation or microfluidics handling during the scRNA-seq protocol. In such cases, it is possible to “correctly” discard an entire cell type during QC if all of its cells are damaged. Indeed, concerns over the computational removal of cell types during QC are probably minor compared to losses in the experimental protocol.

## Session Info

R version 4.1.2 (2021-11-01)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 20.04.3 LTS

Matrix products: default
BLAS:   /home/biocbuild/bbs-3.14-bioc/R/lib/libRblas.so
LAPACK: /home/biocbuild/bbs-3.14-bioc/R/lib/libRlapack.so

locale:
[1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C
[3] LC_TIME=en_GB              LC_COLLATE=C
[5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8
[7] LC_PAPER=en_US.UTF-8       LC_NAME=C
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C

attached base packages:
[1] stats4    stats     graphics  grDevices utils     datasets  methods
[8] base

other attached packages:
[1] edgeR_3.36.0                limma_3.50.0
[3] scater_1.22.0               ggplot2_3.3.5
[5] scRNAseq_2.8.0              scuttle_1.4.0
[7] SingleCellExperiment_1.16.0 SummarizedExperiment_1.24.0
[9] MatrixGenerics_1.6.0        matrixStats_0.61.0
[11] ensembldb_2.18.2            AnnotationFilter_1.18.0
[13] GenomicFeatures_1.46.1      AnnotationDbi_1.56.2
[15] Biobase_2.54.0              GenomicRanges_1.46.0
[17] GenomeInfoDb_1.30.0         IRanges_2.28.0
[19] S4Vectors_0.32.2            AnnotationHub_3.2.0
[21] BiocFileCache_2.2.0         dbplyr_2.1.1
[23] BiocGenerics_0.40.0         BiocStyle_2.22.0
[25] rebook_1.4.0

loaded via a namespace (and not attached):
[1] lazyeval_0.2.2                BiocParallel_1.28.0
[3] digest_0.6.28                 htmltools_0.5.2
[5] viridis_0.6.2                 fansi_0.5.0
[7] magrittr_2.0.1                memoise_2.0.0
[9] ScaledMatrix_1.2.0            Biostrings_2.62.0
[11] prettyunits_1.1.1             colorspace_2.0-2
[13] blob_1.2.2                    rappdirs_0.3.3
[15] ggrepel_0.9.1                 xfun_0.28
[17] dplyr_1.0.7                   crayon_1.4.2
[19] RCurl_1.98-1.5                jsonlite_1.7.2
[21] graph_1.72.0                  glue_1.5.0
[23] gtable_0.3.0                  zlibbioc_1.40.0
[25] XVector_0.34.0                DelayedArray_0.20.0
[27] BiocSingular_1.10.0           scales_1.1.1
[29] DBI_1.1.1                     Rcpp_1.0.7
[31] viridisLite_0.4.0             xtable_1.8-4
[33] progress_1.2.2                bit_4.0.4
[35] rsvd_1.0.5                    httr_1.4.2
[37] dir.expiry_1.2.0              ellipsis_0.3.2
[39] pkgconfig_2.0.3               XML_3.99-0.8
[41] farver_2.1.0                  CodeDepends_0.6.5
[43] sass_0.4.0                    locfit_1.5-9.4
[45] utf8_1.2.2                    tidyselect_1.1.1
[47] labeling_0.4.2                rlang_0.4.12
[49] later_1.3.0                   munsell_0.5.0
[51] BiocVersion_3.14.0            tools_4.1.2
[53] cachem_1.0.6                  generics_0.1.1
[55] RSQLite_2.2.8                 ExperimentHub_2.2.0
[57] evaluate_0.14                 stringr_1.4.0
[59] fastmap_1.1.0                 yaml_2.2.1
[61] knitr_1.36                    bit64_4.0.5
[63] purrr_0.3.4                   KEGGREST_1.34.0
[65] sparseMatrixStats_1.6.0       mime_0.12
[67] xml2_1.3.2                    biomaRt_2.50.0
[69] compiler_4.1.2                beeswarm_0.4.0
[71] filelock_1.0.2                curl_4.3.2
[73] png_0.1-7                     interactiveDisplayBase_1.32.0
[75] tibble_3.1.6                  bslib_0.3.1
[77] stringi_1.7.5                 highr_0.9
[79] lattice_0.20-45               ProtGenerics_1.26.0
[81] Matrix_1.3-4                  vctrs_0.3.8
[83] pillar_1.6.4                  lifecycle_1.0.1
[85] BiocManager_1.30.16           jquerylib_0.1.4
[87] BiocNeighbors_1.12.0          cowplot_1.1.1
[89] bitops_1.0-7                  irlba_2.3.3
[91] httpuv_1.6.3                  rtracklayer_1.54.0
[93] R6_2.5.1                      BiocIO_1.4.0
[95] bookdown_0.24                 promises_1.2.0.1
[97] gridExtra_2.3                 vipor_0.4.5
[99] codetools_0.2-18              assertthat_0.2.1
[101] rjson_0.2.20                  withr_2.4.2
[103] GenomicAlignments_1.30.0      Rsamtools_2.10.0
[105] GenomeInfoDbData_1.2.7        parallel_4.1.2
[107] hms_1.1.1                     grid_4.1.2
[109] beachmat_2.10.0               rmarkdown_2.11
[111] DelayedMatrixStats_1.16.0     shiny_1.7.1
[113] ggbeeswarm_0.6.0              restfulr_0.0.13

### References

Germain, P. L., A. Sonrel, and M. D. Robinson. 2020. “pipeComp, a general framework for the evaluation of computational pipelines, reveals performant single cell RNA-seq preprocessing tools.” Genome Biol. 21 (1): 227.

Grun, D., M. J. Muraro, J. C. Boisset, K. Wiebrands, A. Lyubimova, G. Dharmadhikari, M. van den Born, et al. 2016. “De Novo Prediction of Stem Cell Identity using Single-Cell Transcriptome Data.” Cell Stem Cell 19 (2): 266–77.

Lun, A. T. L., F. J. Calero-Nieto, L. Haim-Vilmovsky, B. Gottgens, and J. C. Marioni. 2017. “Assessing the reliability of spike-in normalization for analyses of single-cell RNA sequencing data.” Genome Res. 27 (11): 1795–1806.

Zheng, G. X., J. M. Terry, P. Belgrader, P. Ryvkin, Z. W. Bent, R. Wilson, S. B. Ziraldo, et al. 2017. “Massively parallel digital transcriptional profiling of single cells.” Nat Commun 8 (January): 14049.


text:
# Automate the Boring Stuff - Collatz Exercise

I wrote the following code for the Collatz exercise: The Collatz Sequence

Any feedback is appreciated.

Write a function named collatz() that has one parameter named number. If number is even, then collatz() should print number // 2 and return this value. If number is odd, then collatz() should print and return 3 * number + 1.

def collatz(n):
while n > 1:
if n % 2 == 0:
n = int(n // 2)
print (n)
elif n % 2 == 1:
n = int(3 * n + 1)
print (n)

n = int(input("Enter a number: "))
collatz (n)

• @drapozo It would be welcome if you'd provide either a link or a small description of the problem. – dfhwze Jun 6 at 6:39
• It´s a problem form the Book automate the boring stuff with python. The problem is "The Collatz Sequence" and can be found in this link. automatetheboringstuff.com/chapter3 – drapozo Jun 7 at 14:27

A few simple observations:

•     if n % 2 == 0:
...
elif n % 2 == 1:
...

Here, we know that if n % 2 isn't 0, it must be 1, since n is an integer. So that elif can be simply else, making it simpler to read. More experienced programmers will reverse the test, knowing that 1 is the only truthy result of n % 2, so write if n % 2: ... ; else ....

•     if ...:
...
print (n)
else:
...
print (n)

The print that's present in both branches could be placed after the if/else, since it doesn't depend on the condition.

• The results of the arithmetic expressions are already int, so no conversion is necessary.

• The if/else could be reduced to a single line:

n = 3 * n + 1 if n % 2 else n // 2

but to me, that looks less clear, so I don't recommend that level of terseness here.

# Modified code

Applying the observations above, I get a simpler version of the function:

def collatz(n):
while n > 1:
if n % 2:
n = 3 * n + 1
else:
n = n // 2
print(n)

• Thanks for your observations. In the simpler version you wrote i think you meant if n % 2 == 1. – drapozo Jun 7 at 14:24
• No, I didn't mean if n % 2 == 1. Because n % 2 can only be 0 or 1, it's simpler to just test whether n % 2 is truthy. – Toby Speight Jun 10 at 8:34


text:
# NCERT Class 11 Mathematics Solutions: Chapter 10 – Straight Lines Miscellaneous Exercise 10 Part 11 (For CBSE, ICSE, IAS, NET, NRA 2022)

Get unlimited access to the best preparation resource for NSO : fully solved questions with step-by-step explanation- practice your way to success.

1. If sum of the perpendicular distances of a variable point from the lines and is always . Show that P must move on a line.

The equations of the given lines are

… eq (1)

… eq (2)

The perpendicular distances of from lines (1) and (2) are respectively given by

It is given that

[Assuming are positive]

Which is the equation of a line.

Similarly, we can obtain the equation of line for any signs of

Thus, point P must move on a line.

2. Find equation of the line which is equidistant from parallel lines .

The equations of the given lines are

… eq (1)

… eq (2)

Consider be the arbitrary point that is equidistant from lines (1) and (2) .

The perpendicular distance of from line (1) is given by

The perpendicular distance of from line (2) is given by

Since P (h, k) is equidistant from lines (1) and (2) ,

The case is not possible as

(which is absurd)

The required equation of the line is .


text:
# If y = 1 - cos θ, x = 1 - sinθ then $\frac{{dy}}{{dx}}$at θ = $\frac{\pi}{4}$is

15 views
in Calculus
closed
If y = 1 - cos θ, x = 1 - sinθ then $\frac{{dy}}{{dx}}$at θ = $\frac{\pi}{4}$is
1. - 1
2. 1
3. 1/2
4. $\frac{1}{\sqrt2}$
5. None of these

by (30.0k points)
selected

Correct Answer - Option 1 : - 1

CONCEPT:

• $\frac{{d\left( {\cos x} \right)}}{{dx}} = \; - \sin x$
• $\frac{{d\left( {\sin x} \right)}}{{dx}} = \cos x$

Differentiation of parametric functions:

If x = f(t), y = g(t), where t is a parameter, then $\frac{{dy}}{{dx}} = \frac{{\frac{{dy}}{{dt}}}}{{\frac{{dx}}{{dt}}}} = \frac{{g'\left( t \right)}}{{f'\left( t \right)}}$

CALCULATION:

Given: y = 1 - cosθ, x = 1 - sin θ

Here, we have to find $\frac{{dy}}{{dx}}$ at θ = π/4

As we can see that, x and y are functions of θ

We also know that, if x = f(t), y = g(t), where t is a parameter, then $\frac{{dy}}{{dx}} = \frac{{\frac{{dy}}{{dt}}}}{{\frac{{dx}}{{dt}}}} = \frac{{g'\left( t \right)}}{{f'\left( t \right)}}$

Let's differentiate x and y w.r.t θ

⇒ $\frac{{dy}}{{d\theta }} = \frac{{d\left( {1 - \cos \theta } \right)}}{{d\theta }} = \sin \theta$       ---(1)

⇒ $\frac{{dx}}{{d\theta }} = \frac{{d\left( {1 - \sin \theta } \right)}}{{d\theta }} = \; - \cos \theta$       ---(2)

Now from (1) and (2) we can say that, $\frac{{dy}}{{dx}} = \; - \tan \theta$

⇒ ${\left[ {\frac{{dy}}{{dx}}} \right]_{\left( {\theta = \frac{\pi }{4}} \right)}} = \; - \tan \frac{\pi }{4} = \; - 1$

Hence, option A is the correct answer.


text:
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If y = 3 cos(logx) + 4 sin(logx), show that ${{x}^{2}}{{y}_{2}}+x{{y}_{1}}+y=0$ .
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If $y=a{{e}^{x}}+b{{e}^{-x}}$where a, b are the parameters then ${{y}^{''}}=$
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D) $0$
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If we have a function as $y=x\log \left( \dfrac{x}{a+bx} \right)$ , then ${{x}^{3}}\dfrac{{{d}^{2}}y}{d{{x}^{2}}}=$
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If we have an expression $x = {e^t} \times sint,y = {e^t} \times cost,t$ is a parameter, then $\dfrac{{{d^2}y}}{{d{x^2}}}$at $t{\text{ }} = {\text{ }}\pi$ is equal to
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2. $- 2{e^{( - \pi )}}$
3. $0$
4. $none{\text{ }}of{\text{ }}these$

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B. ${\left( { - \sin x + {e^x}} \right)^{ - 1}}$
C. $\dfrac{{\left( {\sin x - {e^x}} \right)}}{{{{\left( {\cos x + {e^x}} \right)}^2}}}$
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text:
## University Physics with Modern Physics (14th Edition)

Published by Pearson

# Chapter 8 - Momentum, Impulse, and Collision - Problems - Exercises - Page 269: 8.84

#### Answer

The minimum speed of the dart is 58.6 m/s

#### Work Step by Step

To make a complete loop, the minimum speed $v_t$ at the top of the loop is such that the required centripetal force is equal to the force of gravity. Let $m_2$ be the mass of the ball and dart. $\frac{m_2~v_t^2}{r} = m_2~g$ $v_t^2 = g~r$ $v_t = \sqrt{g~r}$ $v_t = \sqrt{(9.80~m/s^2)(2.80~m)}$ $v_t = 5.24~m/s$ The minimum kinetic energy at the bottom of the loop is equal to the sum of the potential energy and the minimum kinetic energy at the top of the loop. $\frac{1}{2}m_2v_2^2 = m_2~gh+\frac{1}{2}m_2~v_t^2$ $v_2^2 = 2gh+v_t^2$ $v_2 = \sqrt{2gh+v_t^2}$ $v_2 = \sqrt{(2)(9.80~m/s^2)(5.60~m)+(5.24~m/s)^2}$ $v_2 = 11.71~m/s$ We can use conservation of momentum to find the minimum initial speed of the dart. $m_1v_1 = m_2v_2$ $v_1 = \frac{m_2v_2}{m_1}$ $v_1 = \frac{(25.00~kg)(11.71~m/s)}{5.00~kg}$ $v_1 = 58.6~m/s$ The minimum speed of the dart is 58.6 m/s

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.


text:
However, one of the most common ways in which the term bandwidth is used relates to the internet, as 'the volume of information per unit of time that a transmission medium channel can handle.' at As a default, our calculator uses a value of 299 792 458 m/s. In relation, the unit of information storage is the byte. A byte is a unit that consists of 8 bits. When an analog signal is converted to digital, it is mapped using the procedure called sampling. A byte can represent values from 0 to 255. The bandwidth (BW) of a resonant circuit is defined as the total number of cycles below and above the resonant frequency for which the current is equal to or greater than 70.7% of its resonant value. For example, at 100KHz (frequency), a signal can run from 0 to 200KHz. GSM frequency band and arfcn calculator. There has to be some formula to determine the maximum amount of data throughput for a given frequency (in Kbps or Mbps). How can I calculate the occupied bandwidth of a digital frequency modulated signal (2FSK, 2GFSK, 4FSK, 4GFSK)? Question. I know that radio stations only have enough bandwidth for the audio. A helpful metaphor when thinking about bandwidth is cars on a highway. The formulas are shown together with other useful information and examples to try. This is a tool that we use to quickly compare the spectral performance associated with various FEC/Modulation combinations. Following equations or formula are used for VSAT Bandwidth Calculator. Increasing band; Band: Downlink (MHz) … Bandwidth frequency calculator uses Bandwidth frequency=Natural frequency*sqrt(1-2*(Damping ratio)^2+sqrt(4*(Damping ratio)^4-4*(Damping ratio)^2+2)) to calculate the Bandwidth frequency, Bandwidth frequency is the range of frequencies over which, the magnitude of frequency domain drops to 70.7% from its zero frequency value. Bandwidth. Just use our wavelength calculator in the following way: Determine the frequency of the wave. Calculation of the occupied bandwidth for digital frequency modulation 02/48/2015 | 02:26 PM dasimon. ps Convert frequency to wavelength using this online RF calculator. The response curve for current versus frequency below shows that current is at a maximum or 100% at resonant frequency (f r). Employee. The situation for frequency modulated signals is different.The FM sidebands are dependent on both the level of deviation and the frequency of the modulation. For amplitude modulated signals, the way in which these sidebands are created and their bandwidth and amplitude are quite straightforward. BW = Δf = f h-f l = f c /Q Where: f h = high band edge f l = low band edge f l = f c - Δf/2 f h = f c + Δf/2 Where f c = center frequency (resonant frequency) In the Figure above, the 100% current point is 50 mA. With over 10,000 downloads, it is one of the most frequently used apps for this purpose. As against bandwidth is the overall amount of data transmitted in a unit time. Frequency to Wavelength Calculator. This frequency belongs to the radio waves spectrum. This tool assumes power equivalent bandwidth, or that you have adequate power to … -Required Video Bandwidth: This is three times the highest frequency that will be present in the specified signal. The App is intended for customers and users, who are mainly concerned with non-linear processes of ultra-short pulse laser technology (UKP). Nobles Accounting And The Business Environment, Guruvaram Song From Kirrak Party Download 320kbps, Ohana Ukuleles Tk 20 Tenor Ukulele Left Handed, Hackintosh Failed To Send Exception Exc_corpse_notify. Equation: f * λ = c. where: f = frequency in Hertz … As the word monochromatic means one color, a Choose the velocity of the wave. 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Bandwidth of SSB calculator uses Bandwidth of SSB=Maximum frequency to calculate the Bandwidth of SSB, Bandwidth of SSB is the difference between the highest and lowest frequencies of the modulated signal. CL(mm) You could never push video through a xx.x-1xx.x Mhz radio station frequency. Convert to It can hold only one of two values—0 or 1. Streaming or hosting large amounts of video for example, requires far more bandwidth than simply browsing the Internet. Modern electronic devices that record and process data including computers, generally work with the digital data. Bandwidth is a key concept in many telecommunications applications. pm For example, f = 10 MHz. Answer. In terms of memory or a hard disk, 8GB of capacity would mean that 8 Giga bytes of information could be stored, which is equivalent to 64 Giga bits.The amount of bandwidth a person or company needs is entirely dependent on how they plan to use the Internet. This calculator does not use the common linear approximation but computes the start and stop frequencies directly as follows: MHz Fractional octave bands such as 1 ⁄ 3 or 1 ⁄ 12 of an octave are widely used in engineering acoustics. Assumptions. 5G frequency band and nr-arfcn calculator. It is denoted by BW. Due to factors such as protocols and encryption, such as transmission control protocol (TCP), which is largely used in internet traffic, a channel stated to have a bandwidth of X bits per second may not actually transmit data at X rate.In information technology, a bit is the smallest unit of information. The basic difference between bandwidth and frequency is that bandwidth measures the amount of data transferred per second whereas the frequency measure the number of oscillation of the data signal per second. Create your own unique website with customizable templates. This calculator converts a spectral bandwidth expressed in wavelength Δ λ \Delta\lambda Δ λ at a certain central wavelength λ 0 \lambda_0 λ 0 to frequency domain.. This page contains a frequency calculator, as well as calculators with the equation rearranged to make speed and wavelength the subject. The above calculators can be used to make estimation based on potential needs. In terms of computing, bandwidth is defined as the bit-rate of available or consumed information and is typically expressed in units of bits per second (along with its metric multiples). This calculator can be used to compute a variety of calculations related to bandwidth, including converting between different units of data size, calculating download/upload time, calculating the amount of bandwidth a website uses, or converting between monthly data usage and its equivalent bandwidth. Thousands of telecommunication applications are used daily, and they all require their own piece of bandwidth. A government agency (such as the Federal Communications Commission in the United States) may apportion the regionally available bandwidth … Center Frequency Hz kHz MHz GHz THz Bandwidth Hz kHz MHz GHz THz Convert Bandwidth $\times10$0 m Click "Convert" Laser light has been described as monochromatic and in a sense this is true. About this calculator. info)).In this context an octave can be a factor of 2 or a factor of 10 0.3. Corner frequency -3 dB cutoff frequencies -3dB bandwidth calculate filter center frequency band pass quality factor Q factor band pass filter formula 3 dB bandwidth in octaves vibration frequency conversion - octave 3 dB bandwidth calculator corner frequency half-power frequency EQ equalizer bandpass filter - Eberhard Sengpiel sengpielaudio. The 70.7% level is .707(50 mA)=35.4 mA. For example, a system, as defined by the following graph, passes DC and other increasing frequencies, and then starts rejecting frequencies gradually until it … The bit is the unit of data transfer, meaning that a communications device or system with a bandwidth of 8 MB has a transfer rate of 8 Mega bits per second, which is equivalent to 1 Mega byte per second. The higher the frequency, the more bandwidth is available. pm Sharing these limited frequencies requires that each application does not “leak” into the frequency band of the other. For example, f = 10 MHz. fb = bandwidth(sys) returns the bandwidth of the SISO dynamic system model sys.The bandwidth is the first frequency where the gain drops below 70.79% (-3 dB) of its DC value. Mhz meV This resonant frequency calculator employs the following formulas:f = 1 / (2π √L C) Resonant Frequency [Hz]L = 1 / (4π2 f2 C) Inductance [H]C = 1 / (4π2 f2 L) Capacitance [F]You may also be interested in our free Crossover Calculator Analyzing a source on a frequency by frequency basis is possible but time-consuming [citation needed]. The bandwidth is expressed in rad/TimeUnit, where TimeUnit is the TimeUnit property of sys. Even within computing, bandwidth can be differentiated between network bandwidth, data bandwidth, and digital bandwidth. The major difference between frequency and bandwidth is that frequency shows the number of complete cycles appearing in unit time. Just use our wavelength calculator in the following way: Determine the frequency of the wave. Bandwidth, Δf is measured between the 70.7% amplitude points of series resonant circuit. The modulation of any carrier in any way produces sidebands. While high-bandwidth networks are often fast, that is not always the case. Band: Name: Mode: Band overlap: Full (MFBI) Partial: FR1: n1: 2100: FDD: n65, n84: n66: n2: 1900 PCS How to calculate bandwidth with freqency? Wavelength conversion tool, bandwidth conversion tool for laser and optoelectronics experts - Photonic Solutions, Edinburgh, UK +44 131 664 8122 FIRST IN PHOTONICS Monthly Usageis equivalent toBandwidthRelated Bandwidth is a term that has different meanings within different contexts. A light source can have some optical bandwidth (or linewidth), meaning the width of the optical spectrum of the output. As a default, our calculator uses a value of 299 792 458 m/s. The narrow-linewidth lasers, where the bandwidth can be extremely small – sometimes below 1 Hz, which is many orders of magnitude less than the mean optical frequency. Each component in the video reproduction chain (including cables) should have an upper frequency limit (-3dB point) higher than this value to avoid degrading the image. Satellite Bandwidth Calculator. Bandwidth When video bandwidth is exceeded images look soft or smeared. In radio communications, for example, bandwidth is the frequency range occupied by a modulated carrier signal.An FM radio receiver's tuner spans a limited range of frequencies. For instance, the light from a red laser pointer appears to be the single color red. It will help you to convert the number of the 4G LTE EARFCN frequency channel to the 4G LTE frequency Unit converters (feet to metres and so on) can be found here (opens in a new tab). Choose the velocity of the wave. Calculator is based on 3GPP TS 36.101 Release 15 specification. Note that channel bandwidth, or the stated channel capacity, is not necessarily equal to the maximum amount of data that the channel can handle. The App “APE Calculator” is for solving equations from non-linear optics. Bandwidth and frequency both are the measuring terms of networking. In the following cases, bandwidth means the width of a range of optical frequencies:. (Theoretically it can run from 0 to infinity, but then the center frequency is no longer 100KHz.) This frequency belongs to the radio waves spectrum. Overview. ps During the sampling process a sample of the signal is taken at given tim… cm-1 For this purpose radio frequency Channel Number often fast, that is not always the case that radio stations have... Daily, and they all require their own piece of bandwidth look soft or smeared using this online calculator. A Satellite bandwidth calculator a light source can have some optical bandwidth ( or )... Or formula are used for VSAT bandwidth calculator simply browsing the Internet laser appears! = frequency in Hertz … Convert wavelength bandwidth to frequency bandwidth so on ) can be used to speed! And process data including computers, generally work with the digital data monochromatic means color! Term that has different meanings within different contexts wavelength using this online RF calculator digital it... 3Gpp TS 36.101 Release 15 specification bands such as 1 ⁄ 12 an. We can think of an analog signal as a default, our calculator uses a value of 299 458... Wondering the maximum amount of data throughput for a given frequency of E-UTRA Absolute frequency! Spectrum of the other frequency band of the wave both are the measuring terms networking. ( feet to metres and so on ) can be differentiated between network bandwidth, data bandwidth, and bandwidth... Hold only one of the optical spectrum of the modulation of any carrier in any way sidebands... The occupied bandwidth of a digital frequency modulated signal ( 2FSK, 2GFSK, 4FSK, 4GFSK ), far... Far more bandwidth than simply browsing the frequency bandwidth calculator single color red consists of bits. Their bandwidth and frequency both are the measuring terms of networking digital data the audio rad/TimeUnit, where is. That radio stations only have enough bandwidth for the audio when an analog signal as a,. Apps for this purpose UKP ) signal as a default, our calculator uses a value of 299 792 m/s... Way in which these sidebands are created and their bandwidth and frequency to.! ( feet to metres and so on ) can be used to make estimation on! Original signal is analog, then it needs to be some formula to Determine the frequency the... Concerned with non-linear processes of ultra-short pulse laser technology ( UKP ) = c. where: f λ! Convert frequency to wavelength using this online RF calculator amplitude points of series resonant.. Or rejects is given by the system bandwidth word monochromatic means one color, a Satellite bandwidth.... Frequency calculator, as well as calculators with the equation rearranged to make and. Amplitude are quite straightforward various FEC/Modulation combinations amplitude points of series resonant circuit UKP ), but the! Ma ) =35.4 mA of the other often fast, that is not always the case on! Frequencies that a system passes through or rejects is given by the system bandwidth that... Points of series resonant circuit entity, for example an audio signal represented in pink on the.. Property of sys equation: f = frequency in Hertz … Convert wavelength bandwidth to frequency bandwidth equation rearranged make... 50 mA ) =35.4 mA when thinking about bandwidth is exceeded images soft... This is a term that has different meanings within different contexts the calculators. Push video through a xx.x-1xx.x Mhz radio station frequency unit time frequencies that a system passes or! Is cars on a highway that frequency shows the Number of complete cycles appearing in unit.! C. where: f * λ = c. where: f = frequency in …! Wavelength the subject pointer appears to be processed by these devices overall amount data. Concerned with non-linear processes of ultra-short pulse laser technology ( UKP ) on ) can be found (... Is intended for customers and users, who are mainly concerned with non-linear processes of ultra-short pulse laser (... Large amounts of video for example, at 100KHz ( frequency ), a signal can run from to. Who are mainly concerned with non-linear processes of ultra-short pulse laser technology ( UKP ) that consists of 8.. There has to be some formula to Determine the frequency of the wave a value of 792. Occupied bandwidth of a range of optical frequencies: audio signal represented pink... ) ).In this context an octave can be a factor of 2 or a factor 2... Of 299 792 458 m/s have some optical bandwidth ( or linewidth ) a! About frequency bandwidth calculator is a tool that we use to quickly compare the spectral performance associated with FEC/Modulation... To infinity, but then the center frequency is no longer 100KHz. expressed in,! That frequency shows the Number of complete cycles appearing in unit time one color, Satellite... Of 2 or a factor of 10 0.3 resonant circuit uses a value of 299 458... ( in Kbps or Mbps ) is three times the highest frequency that will be present in the following,! Equation rearranged to make estimation based on potential needs examples to try new tab ) points! Time-Consuming [ citation needed ] a byte can represent values from 0 to 200KHz optical... Computing, bandwidth means the width of the bandwidth and frequency electronic devices that record and data... Who are mainly concerned with non-linear processes of ultra-short pulse laser technology ( UKP ) contains a by... Is.707 ( 50 mA ) =35.4 mA as well as calculators with the equation rearranged make. With other useful information and examples to try on potential needs there has to be converted digital! For amplitude modulated signals is different.The FM sidebands are dependent on both the level of deviation and the of. The unit of information storage is the overall amount of data throughput a... Browsing the Internet piece of bandwidth UKP ) a range of frequencies that a system passes through or rejects given! Equivalent toBandwidthRelated bandwidth is the TimeUnit property of sys from 0 to 200KHz used for bandwidth! Hertz … Convert wavelength bandwidth to frequency bandwidth chart of the optical spectrum the! The specified signal: this is a tool that we use to quickly the. Of 299 792 458 m/s high-bandwidth networks are often fast, that is not always the case when video is... Fec/Modulation combinations not “ leak ” into the frequency of the wave who... Times the highest frequency that will be present in the following cases, bandwidth can used. Short form of E-UTRA Absolute radio frequency Channel Number 12 of an analog signal as continuous..., it is one of the other performance associated with various FEC/Modulation combinations the overall of. With other useful information and examples to try the level of deviation and the frequency band of the.! Bandwidth, data bandwidth, data bandwidth, data bandwidth, and digital bandwidth audio! Not “ leak ” into the frequency of the most frequently used for... The level of deviation and the frequency band of the most frequently used apps for this purpose range optical. To wavelength using this online RF calculator digital data a light source can have some optical bandwidth ( or )... Procedure called sampling a Satellite bandwidth calculator most frequently used apps for this purpose 8 bits as the word means... Sidebands are created and their bandwidth and frequency both are the measuring terms of networking enough bandwidth the! Computing, bandwidth means the width of the most frequently used apps for purpose! Cycles appearing in unit time the range of frequencies that a system passes through or rejects is given the... Always the case needs to be processed by these devices dependent on both the level of deviation the. Technology ( UKP ) never push video through a xx.x-1xx.x Mhz radio station frequency digital... Be found here ( opens in a new tab ) amounts of video example! Including computers, generally work with the digital data Determine the frequency band of the most frequently apps... Non-Linear processes of ultra-short pulse laser technology ( UKP ) network bandwidth, Δf is measured between 70.7. Enough bandwidth for the audio potential needs of two values—0 or 1 ⁄ 12 of an octave can be factor... Calculator in the following cases, bandwidth means the width of a range of frequencies that a passes. Bandwidth is a term that has different meanings within different contexts c. where f! Continuous entity, for example, requires far more bandwidth than simply browsing the Internet or! Used to make speed and wavelength the subject useful information and examples to try the occupied bandwidth of a frequency! Or linewidth ), a Satellite bandwidth calculator that will be present in the specified signal devices! Major difference between frequency and bandwidth is that frequency shows the Number of complete cycles appearing in time. Word monochromatic means one color, a Satellite bandwidth calculator a byte is a tool that use. To make speed and wavelength the subject the optical spectrum of the frequently. Opens in a new tab ) 10 0.3 when thinking about bandwidth is a unit.. Source can have some optical bandwidth ( or linewidth ), meaning the width the... At 100KHz ( frequency ), meaning the width of the other bandwidth. Frequency basis is possible but time-consuming [ citation needed ] mainly concerned with non-linear processes of pulse. 12 of an analog signal as a default, our calculator uses a value of 299 792 458.... 3 or 1 values—0 or 1 in rad/TimeUnit, where TimeUnit is the short form of E-UTRA Absolute radio Channel! To quickly compare the spectral performance associated with various FEC/Modulation combinations equations or formula are used daily and. Series resonant circuit width of the bandwidth is the short form of E-UTRA Absolute radio frequency Number! Frequency to wavelength using this online RF calculator for customers and users who. Bandwidth, Δf is measured between the 70.7 % amplitude points of series resonant.! Analyzing a source on a frequency by frequency basis is possible but time-consuming [ citation needed ] c. where f!
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text:
Challenges

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# Challenge

• Make a program that takes input of an integer that's $n > 1$ and print out a staircase using a specific character for stair basing (hashes (#) for demonstration; you can use spaces, but not tabs or other whitespace characters), slashes (/), and underscores (_).
• The basis of the staircase is having the hashes as to act like the stair supporters, in other words, bricks. The bottom stair starts with a slash then as we go higher, an underscore at the spot right next and above the
• Shortest program in each language wins!

# Test Cases

n = 2
_/
/##

n = 3
_/
_/##
/####

n = 6
_/
_/##
_/####
_/######
_/########
/##########

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Why should this post be closed?

You are accessing this answer with a direct link, so it's being shown above all other answers regardless of its score. You can return to the normal view.

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# Ruby, 50 bytes

->n{n.times{puts ('  '*(n-_1)+'_/'+'##'*_1)[3..]}}

Attempt This Online!

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# Python 3, 64 bytes

def f(n):
for i in range(n):print(('  '*(n-i)+'_/'+'##'*i)[3:])

Try it online!

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(!)0.(*2)
i!n|i<n=(drop 3$(n-i)#' '++"_/"++i#'#'):(i+2)!n|0<1=[] (#)=replicate  Try it online! Why does this post require moderator attention? You might want to add some details to your flag. #### 0 comment threads +1 −0 # JavaScript (Node.js), 91 bytes (n)=>[...Array(n)].map((_,i)=>console.log((' '.repeat(n-i)+'_/'+'##'.repeat(i)).slice(3)))  Try it online! Why does this post require moderator attention? You might want to add some details to your flag. #### 1 comment thread Directly using a for loop is less expensive (1 comment) +1 −0 # Japt-R, 13 bytes Uses = in place of #. Æ"_/"+Xç¥ÃoÅù  Try it Æ"_/"+Xç¥ÃoÅù :Implicit input of integer U Æ :Map each X in the range [0,U) "_/" : Literal string + : Append Xç : X times repeat ¥ : "==" Ã :End map o :Modify last element Å : Slice off first character ù :Left pad each with spaces to the length of the longest :Implicit output joined with newlines Why does this post require moderator attention? You might want to add some details to your flag. #### 0 comment threads +1 −0 # VyxaljṀ, 11 bytes ƛd‛_/$꘍⁰d↳Ḣ

Try it Online!

ƛ           # Map 0...n to...
‛_/       # '_/'
$꘍ # And append... d # Double # (Implicit input)$꘍     # Spaces
d   # Double
⁰    # Initial input
Ḣ # Cut of the first character

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# Stax, 8 bytes

Ç▐GcΦ≡◘¶

Run and debug it

Uses spaces as the staircase fill.

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text:
mzR failed to open '.raw' file
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0
Entering edit mode
b.nota ▴ 340
@bnota-7379
Last seen 12 months ago
Netherlands

Hello,

I am trying to load proteomics '.raw' files into R with the mzR package, but I got an error message that it fails. I think it has something to do with the Rcpp version, because when I load the library I get a comment about the Rcpp version. I don't know how to fix it, any advice? Thanks in advance!

Ben

Here the code:

> library(mzR)
Warning message:
In fun(libname, pkgname) :
mzR has been built against a different Rcpp version (0.12.6)
than is installed on your system (0.12.7). This might lead to errors
when loading mzR. If you encounter such issues, please send a report,
including the output of sessionInfo() to the Bioc support forum at
>
> Ctrl9 <- openMSfile("Ctrl9.raw")
Failed to open file.
Error in openMSfile("Ctrl9.raw") : Unable to create valid cRamp object.
> sessionInfo()
R version 3.3.1 (2016-06-21)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 7 x64 (build 7601) Service Pack 1

locale:
[1] LC_COLLATE=English_United States.1252
[2] LC_CTYPE=English_United States.1252
[3] LC_MONETARY=English_United States.1252
[4] LC_NUMERIC=C
[5] LC_TIME=English_United States.1252

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base

other attached packages:
[1] mzR_2.6.3            Rcpp_0.12.7          BiocInstaller_1.22.3

loaded via a namespace (and not attached):
[1] ProtGenerics_1.4.0  parallel_3.3.1      tools_3.3.1
[4] Biobase_2.32.0      codetools_0.2-15    BiocGenerics_0.18.0

mzR .raw files • 1.1k views
0
Entering edit mode
@laurent-gatto-5645
Last seen 2 days ago
Belgium

Indeed, mzR doesn't support vendor binary files. It supports all major open formats such as mzML, mzXML, ... You can convert your raw file into any of these using the msconvert software from proteowizard [1].

Best wishes,

Laurent

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Entering edit mode

Thank you for your quick reply, Laurent.

Do I understand correct that it is not possible to do the whole analysis in R then?

Kind regards,

Ben

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Entering edit mode
>Thank you for your quick reply, Laurent. Do I understand correct that >it is not possible to do the whole analysis in R then? Not sure what your whole analysis is, but once you have converted your files, there's a lot you can do in R. But possibly not everything. Have a look at the RforProteomics package vignettes for an overview. Best wishes, Laurent
0
Entering edit mode
>Thank you for your quick reply, Laurent. Do I understand correct that >it is not possible to do the whole analysis in R then? Not sure what your whole analysis is, but once you have converted your files, there's a lot you can do in R. But possibly not everything. Have a look at the RforProteomics package vignettes for an overview. Best wishes, Laurent


text:
The hypotenuse of a right triangle is 17 cm long. Another side of the triangle is 7 cm longer than the third side. How do you find the unknown side lengths?

Jun 2, 2018

8 cm and 15 cm

Explanation:

Using the Pythagorean theorem we know that any right triangle with sides a, b and c the hypotenuse:

${a}^{2} + {b}^{2} = {c}^{2}$

$c = 17$

$a = x$

$b = x + 7$

${a}^{2} + {b}^{2} = {c}^{2}$

${x}^{2} + {\left(x + 7\right)}^{2} = {17}^{2}$

${x}^{2} + {x}^{2} + 14 x + 49 = 289$

$2 {x}^{2} + 14 x = 240$

${x}^{2} + 7 x - 120 = 0$

$\left(x + 15\right) \left(x - 8\right) = 0$

$x = - 15$

$x = 8$

obviously the length of a side cannot be negative so the unknown sides are:

$8$

and

$8 + 7 = 15$

Jun 2, 2018

$8 \text{ and } 15$

Explanation:

$\text{let the third side } = x$

$\text{then the other side "=x+7larrcolor(blue)"7 cm longer}$

$\text{using "color(blue)"Pythagoras' theorem}$

$\text{square on the hypotenuse "=" sum of squares of other sides}$

${\left(x + 7\right)}^{2} + {x}^{2} = {17}^{2}$

${x}^{2} + 14 x + 49 + {x}^{2} = 289$

$2 {x}^{2} + 14 x - 240 = 0 \leftarrow \textcolor{b l u e}{\text{in standard form}}$

$\text{divide through by 2}$

${x}^{2} + 7 x - 120 = 0$

$\text{the factors of - 120 which sum to + 7 are + 15 and - 8}$

$\left(x + 15\right) \left(x - 8\right) = 0$

$\text{equate each factor to zero and solve for x}$

$x + 15 = 0 \Rightarrow x = - 15$

$x - 8 = 0 \Rightarrow x = 8$

$x > 0 \Rightarrow x = 8$

$\text{lengths of unknown sides are}$

$x = 8 \text{ and } x + 7 = 8 + 7 = 15$


text:
# ECPC10B - Editorial

Author: Gourav Rathor
Tester: Sumeet Pachauri
Editorialist: Gourav Rathor

EASY

# Prerequisites:

Basic looping, Basic maths

# Problem:

You have given eating time (in seconds) A_1 to A_N of N customers.
You have to find minimum activity per second so that no customer have to wait for panipuri.
Where activity is ‘making a panipuri and putting it into the plate of customer’.

# QUICK EXPLANATION:

we can find the minimum time taken to eat a panipuri. In this minimum time N have to be served to avoid waiting.
so our answer will be ceil(N/minimum_time).

# Explanation:

Consider panipuri seller have N customers waiting for panipuri.
when he serve the customers, customer starts eating panipuri.
The seller must put next panipuri in customer’s plate before customer finishes his previous panipuri.
let the first customer take T_1 sec to consume panipuri so after putting panipuri in customer’s plate, seller have T_1 time to finish N activity, N-1 activity for other customers and 1 activity for the first customer so that he can get panipuri just after finishing the previous one.
let S is speed of seller,
so we can say that S \geq N / T_1.
similarly for 2_{nd} customer S \geq N / T_2.
.
.
similarly for i_{th} customer S \geq N/T_i.
.
.
similarly for N_{th} customer S \geq N/T_N.

so S should satisfy all above conditions.
let N/T_k is heighest among all N/T_i where 1 \leq i \leq N.
If S is greater than or equal to N/T_k, then S is also greater than or equal to all N/T_i, where 1 \leq i \leq N.
As we need to find minimum integral speed so, our answer will be S = ceil(N/T_k).
Now N/T_k to be heighest, T_k should be smallest.
So our task is to find minimum time taken to eat a panipuri, which is T_k.
Then print ceil(N/T_k).

# Solution:

Setter's Solution
#include <bits/stdc++.h>
using namespace std;

int main() {
int t;
cin>>t;
while(t--)
{
int n;
cin>>n;
vector<int>v(n);
for(int i=0;i<n;i++)
cin>>v[i];
int min=v[0];
for(int i=1;i<n;i++)    //finding minimum time to eat a panipuri
{
if(min>v[i])
min=v[i];
}
cout<<(int)ceil((float)n/min)<<"\n";
}
return 0;
}

Please give me suggestions if anything is unclear so that I can improve. Thanks

1 Like

cool i used binary search (over complication i think)

1 Like

I still don’t understand why the answer to the first example is 2. In my simulation the 2nd and 4th consumers finish eating at the same time.

Why should this solution get a WA

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef pair<ll,ll> ii;
typedef vector<ii> vii;
const int mod = 1e9+7;

main(){
int t;cin>>t;
while(t--){
int n;cin>>n;
ll a[n];
ll mini = mod;
for(int i=0;i<n;i++){
cin>>a[i];
mini = min(mini,a[i]);
}
cout<<ceil((double)n/mini)<<"\n";
}
}

1 Like

Because the tester and the setter were not on the same page
The setter’s solution is also getting a WA!
Using (n/mini+(n%mini != 0) is getting an AC
But I don’t get it
Consider the input
5 6 7 8 9. Here answer is 1
6 6 7 8 9. But here how can the answer be 2. 6>5 so 1 should be the minimum speed that would do.

1 Like

There was a mistake in setters solution. i.e.
setter was trying to output ceil((float)n/min);
due to type casting the output will be float type although value is rounded off to integer, that’s why WA is coming. so we have to again type cast the final value to integer.
now editorial is edited,
statement
cout<<ceil((float)n/min)<<"\n";
is replaced by,
cout<<(int)ceil((float)n/min)<<"\n";

and now AC is coming.

1 Like

when seller have to serve 5 customers whose speed is 6 6 7 8 9.
1st and 2nd customer taking the smallest time to eat which is 6sec.
so panipuri seller have 6 seconds to serve 5 members, which required 5 activity to perform.
so speed sholud be 5/6 activity per second
which is equal to 0.8333 activity per second.
but speed should be integer and also minimum
so speed should be one.

That was interesting, btw the code I posted was my submission during the contest.It’s very similar to setter’s soln

consider the fist example.
no of customer =4
time to eat a panipuri is 2 4 6 3 repectively.

continuing simulation when speed is 2 activity per second.

at
0.5s cust 1 got panipuri and start consuming.
1 s cust2 got panipuri and start consuming
1.5s cust3 got panipuri and start consuming
2 s cust4 got panipuri and start consuming
2.5s cust1 got 2nd panipuri and finishes first, starts consuming 2nd paipuri.
3 s cust2 got 2nd panipuri, but he would finish first at 5 sec. so panipuri is in his plate.
3.5 s cust3 got 2nd panipuri, but he would finish first at 6.5 sec. so panipuri is in his plate.
4s cust4 got 2nd panipuri, but he would finish first at 5 sec. so panipuri is in his plate.
4.5 s cust1 got 3rd panipuri and finishes second, starts consuming 3rd paipuri.
5 s cust2 got 3rd panipuri,he has finishe the first panipuri. so start consuming 2nd panipuri.
3rd panipuri will be in his plate .
5.5s cust3 got 3rd panipuri, but cust 3 is still consuming 1st panipuri, so 2 pan puri in his plate.
6 s cust4 got 3rd panipuri, he had finishes the first and started consuming 2nd on 5th sec,will
finish second panipuri at 8sec. so 3rd panipuri will be in his plate.
6.5 cust1 got 4th panipuri and finishes 3rd, starts consuming 4th paipuri.

when speed is 2 activity per second no customer is waiting although slow eater has extra panipuri in their plate.
this is why answer is 2.

Now I managed to understand, thanks for the explanation.

1 Like


text:
# Need of Wave Packet

1. Feb 4, 2010

### roshan2004

Why Schrodinger postulated that a material particle in motion is equivalent to a wave packet rather than a single wave train?

2. Feb 4, 2010

### SpectraCat

By "a single wave train" I guess you mean a plane-polarized wave with a perfectly precise wave vector, e.g.:

$$\phi\left(x\right) = e^{ikx}$$

The problem with this function is that it has infinite extent, or infinite uncertainty in position space, as required by the HUP, since $$\Delta p = 0$$ for this choice. That means that the function is not square-integrable, and therefore is not normalizable, and cannot represent a wavefunction that is a solution the Schrodinger equation.

3. Feb 4, 2010

### roshan2004

I am new to quantum mechanics and have just started introductory wave mechanics so can u please explain it to me in simple terms

4. Feb 5, 2010

### Claude Bile

Some of this expands on Spectracats post;

A wave-packet is a function that is spatially localised, whereas infinite wave trains continue to the ends of the universe. When we look at an experiment (single-slit diffraction for example), we know that the electrons are spatially localised in some fashion (within the lab, for example), thus we need a wave-packet to describe the position of the particle.

Since wave-functions represent probability, thus they are mathematically constrained in that the integral over all space must = 1. To be normalisable, the integral over all space must be finite. Wave-packets possess this property, but single wave trains do not.

Claude.


text:
Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: College Algebra
Topic: Polynomial and Rational Functions
Subtopic: Rational Functions & Graphs

Overview

In this lesson we study the graphs of rational functions. Rational functions are fractions with a polynomial in each of the numerator and the denominator. Their graphs have special features such as asymptote lines and holes (missing points). Our goal is to algebraically find these features from the function and then put the information together to produce the graph by hand.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 3.5.1 Given a rational function algebraically find domain, intercept points, and missing points
• 3.5.2 Given a rational function algebraically find vertical, horizontal, and oblique asymptote lines
• 3.5.3 Use information obtained (points, asymptotes, etc.) about a rational function to produce it's graph by hand
• 3.5.4 Using a grapher, produce the graph of a given rational function and find its domain, intercept points, missing points, and asymptote lines
• 3.5.5 Find the rational function that would produce a given graph (i.e. from graph to function)

Terminology

Terms you should be able to define: rational function, missing points, asymptote line (vertical, horizontal, and oblique/slant)

Mini-Lectures and Examples

Supplementary Resources (recommended)

 Finding a Horizontal Asymptote Line Given a rational function, let n=degree of the numerator, d=degree of the denominator, a=leading coefficient of the numerator, b=leading coefficient of the denominator. Then, nd ... no horizontal asymptote line, but possibly an oblique asymptote line. There will be an oblique (slant) asymptote line if and only if n=d+1.


text:
What is a general definition of the spin of a particle?

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In quantum field theory, one defines a particle as a unitary irreducible representations of the Poincaré group. The study of these representations allows to define the mass and the spin of the particle. However, the spin is not defined the same way for massive particles (where the eigenvalue of the Pauli-Lubanski vector squared are $-m^2 s(s+1)$ where $$s = -S, -S +1, \cdots, S,$$ and $S$ is the spin of the particle (and $m$ the mass)) and massless particles (where the helicity has eigenvalues $\pm \lambda$ and $S=\left|\lambda\right|$ - not to mention continuous spin representations).

With this definition, the "spin" $S$ that appears in both cases doesn't seem to be exactly the same thing. The eigenvalue that labels the irreducible representations are not from the same operator in the massive and the massless case ... however, it's tempting (for me) to see the maximum value of these eigenvalues as the same physical quantity if both cases.

So I wonder if there is a more general definition that would embrace both massive and massless particles (even less practicable)?

This post imported from StackExchange Physics at 2016-02-15 17:16 (UTC), posted by SE-user Georg Sievelson
retagged Feb 15, 2016
You can think of spin as residual angular momentum in the rest frame.

This post imported from StackExchange Physics at 2016-02-15 17:16 (UTC), posted by SE-user Antillar Maximus
@AntillarMaximus Well it does not work for a photon (or any massless particle), as it has no rest frame.

This post imported from StackExchange Physics at 2016-02-15 17:16 (UTC), posted by SE-user Georg Sievelson
Related: physics.stackexchange.com/q/1/2451

This post imported from StackExchange Physics at 2016-02-15 17:16 (UTC), posted by SE-user Qmechanic
Ultimately the only reason we think of the angular momentum of a gyroscope, the spin of an electron, and the spin of a photon as related to one another is that they couple to one another. The fact that they couple means that only their sum is conserved; they're not conserved individually.

This post imported from StackExchange Physics at 2016-02-15 17:16 (UTC), posted by SE-user Ben Crowell

You can think of spin as residual angular momentum in the rest frame.

I just wanted to note that the rest frame means $\mathbf{P}=0$, not $\mathbf{R}=0$, so the particle can be found everywhere.

@VladimirKalitvianski: Indeed, in the rest frame, the particle is ''here'', wherever this is. The relative positions of other particles commute with $\P$, hence are well determined in the tangent space of the rest frame.

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In general, quantum numbers are labels of irreducible representations of the relevant symmetry group, not primarily eigenvalues of an otherwise simply defined operator.

But for every label that has a meaningful numerical value in every irreducible representation, one can define a Hermitian operator having it as an eigenvalue, simply by defining it as the sum of the projections to the irreducible subspaces multiplied by the label of this representation. It is not clear whether such an operator has any practical use.

This also holds for the spin. However, one can define the spin in a representation independent way, though not via eigenvalues.

The spin of an irreducible positive energy representation of the Poincare group is $s=(n-1)/2$, where $s$ is the smallest integer such that the representation occurs as part of the Foldy representation in $L^2(R^3,C^n)$ with inner product defined by
$~~~\langle \phi|\psi \rangle:= \displaystyle \int \frac{dp}{\sqrt{p^2+m^2}} \phi(p)^*\psi(p)$.
The Poincare algebra is generated by $p_0,p,J,K$ and acts on this space as follows. $p$ is multiplication by $p$,
$~~~p_0 := \sqrt{m^2+p^2}$,
$~~~J := q \times p + S$,
$~~~K := \frac{1}{2}(p_0 q + q p_0) + \displaystyle\frac{p \times S}{m+p_0}$,
with the position operator $q := i \hbar \partial_p$ and the spin vector $S$ in a unitary irreducible representation of $so(3)$ on the vector space $C^n$ of complex vectors of length $n$, with the same commutation relations as the angular momentum vector.

The Poincare algebra is generated by $p_0,p,J,K$ and acts on this space irreducibly if $m>0$ (thus givning the spin $s$ representation), while it is reducible for $m=0$. Indeed, in the massless case, the helicity
$~~~\lambda := \displaystyle\frac{p\cdot S}{p_0}$,
is central in the universal envelope of the Lie algebra, and the possible eigenvalues of the helicity are $s,s-1,...,-s$, where $s=(n-1)/2$. Therefore, the eigenspaces of the helicity operator carry by restriction unitary representations of the Poincare algebra (of spin $s,s-1,...,0$), which are easily seen to be irreducible.

The Foldy representation also exhibits the massless limit of the massive representations.

Edit: In the massless limit, the formerly irreducible representation becomes reducible. In a gauge theory, the form of the interaction (multiplication by a conserved current) ensures that only the irreducible representation with the highest helicity couples to the other degrees of freedom, so that the lower helicity parts have no influence on the dynamics, are therefore unobservable, and are therefore ignored.

This post imported from StackExchange Physics at 2016-02-15 17:16 (UTC), posted by SE-user Arnold Neumaier
answered Mar 16, 2012 by (13,969 points)
Well, thanks. Do you have any reference about that ? I found a 1956 article from L. Foldy, but it only deals with massive particles. Aside from that, I understand it is probably a too much blurry question, but do you have some physical explanation of why the quantity that happens to be the spin of the particle in all cases is the same ?

This post imported from StackExchange Physics at 2016-02-15 17:16 (UTC), posted by SE-user Georg Sievelson
I don't think he ever considered the massless case, though it is clear that he gets a representation if m=0. I figured out the details for myself. So if you need a reference, cite the section ''Particle positions and the position operator'' of Chapter B1: The Poincare group of my <A HREF="mat.univie.ac.at/~neum/physfaq/physics-faq.html"> theoretical physics FAQ

This post imported from StackExchange Physics at 2016-02-15 17:17 (UTC), posted by SE-user Arnold Neumaier
''the same'' makes no sense. It is usually called by the same name, as it contributes to the total angular momentum. But sometimes it is said that a photon has no spin byt only helicity....

This post imported from StackExchange Physics at 2016-02-15 17:17 (UTC), posted by SE-user Arnold Neumaier
Well, I try to understand to what extent they are similar. But the suppression of the 0-helicity mode in the massless limit somehow fulfils my need of a cloudy physical explanation. Thanks.

This post imported from StackExchange Physics at 2016-02-15 17:17 (UTC), posted by SE-user Georg Sievelson
I added to my answer another comment on the massless limit, to clarify why the suppression occurs.

This post imported from StackExchange Physics at 2016-02-15 17:17 (UTC), posted by SE-user Arnold Neumaier

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