text:
Equipped with the right applications, a computer can be of great help in virtually any domain of activity. When it comes to designing and precision, no other tool is as accurate as a computer. Moreover, specialized applications such as AutoCAD give you the possibility to design nearly anything ranging from art, to complex mechanical parts or even buildings.
Suitable for business environments and experienced users
After a decent amount of time spent installing the application on your system, you are ready to fire it up. Thanks to the office suite like interface, all of its features are cleverly organized in categories. At a first look, it looks easy enough to use, but the abundance of features it comes equipped with leaves room for second thoughts.
Create 2D and 3D objects
You can make use of basic geometrical shapes to define your objects, as well as draw custom ones. Needless to say that you can take advantage of a multitude of tools that aim to enhance precision. A grid can be enabled so that you can easily snap elements, as well as adding anchor points to fully customize shapes.
With a little imagination and patience on your behalf, nearly anything can be achieved. Available tools allow you to create 3D objects from scratch and have them fully enhanced with high-quality textures. A powerful navigation pane is put at your disposal so that you can carefully position the camera to get a clearer view of the area of interest.
Various export possibilities
Similar to a modern web browser, each project is displayed in its own tab. This comes in handy, especially for comparison views. Moreover, layouts and layers also play important roles, as it makes objects handling a little easier.
Sine the application is not the easiest to carry around, requiring a slightly sophisticated machine to properly run, there are several export options put at your disposal so that the projects itself can be moved around.
Aside from the application specific format, you can save as an image file of multiple types, PDF, FBX and a few more. Additionally, it can be sent via email, directly printed out on a sheet of paper, or even sent to a 3D printing service, if available.
To end with
All in all, AutoCAD remains one of the top applications used by professionals to achieve great precision with projects of nearly any type. It encourages usage with incredible offers for student licenses so you get acquainted with its abundance of features early on. A lot can be said about what it can and can't do, but the true surprise lies in discovering it step-by-step.

AutoCAD For Windows 10 Crack represents a major improvement over similar graphics programs and fills a unique niche in the CAD market. It uses a simple paradigm to create complex drawings of a wide variety of objects. It is designed to be intuitive to the operator and can be learned quickly.

In addition to the traditional 2-D drafting area, AutoCAD now offers a 3-D drawing capability, extending the capabilities of 2-D drafting beyond traditional 2-D drawing. AutoCAD LT, the free software, is offered for both Mac and PC platforms.

New and improved tools such as Multimedia Blocks, which allow the user to perform operations on videos and images, also have significantly enhanced capability in AutoCAD.

AutoCAD LT is an entirely new design and development platform. This product provides AutoCAD feature compatibility with AutoCAD LT 2010 along with the enhancements from AutoCAD LT 2009.

Most new AutoCAD functions in AutoCAD 2010 such as the 3-D modeling tool and ribbon-based interface were added to AutoCAD LT 2010. AutoCAD LT 2010 also includes a new 2-D drafting area that provides the user with a traditional 2-D workspace that is similar to a traditional 2-D drafting area in AutoCAD, with enhancements such as the ability to easily convert 2-D drawings to 3-D.

AutoCAD LT 2010 also introduces a new command line, and new scripting languages. Both of these tools are based on the same principles as AutoCAD (as opposed to the obsolete and less user friendly command line of previous releases). AutoCAD LT 2010 also comes with a Web-based application. A major new feature is the ability to perform site-based AutoCAD tasks that are accessed and controlled from a Web browser.

There are several versions of AutoCAD, including AutoCAD 2000, 2002, 2004, 2007 and 2010. AutoCAD LT is an entirely new product that is not compatible with previous versions of AutoCAD. AutoCAD 2010, in addition to being compatible with AutoCAD LT 2010, is also compatible with AutoCAD 2000, 2002, 2004, 2007 and AutoCAD LT 2009.

This article will briefly describe the differences between each of the Autodesk products, specifically between AutoCAD LT 2010 and AutoCAD 2010. You can access the AutoCAD LT 2010 help file for information on installing and using AutoCAD LT.

Here is a

## AutoCAD Crack With Serial Key [32|64bit]

2D drafting
ACIS
AEAW
Agfa
Affinity Designer
Affinity Photo
Alias Wavefront
Autodesk Civil 3D
Autodesk DWG Viewer
Autodesk FormIt
Autodesk Inventor
Autodesk Navisworks
Autodesk Revit
Autodesk Viewer
BIM
Castle Architect
CCP
DAEDALUS Design
Graphisoft Inventor
IFC-A
SAP Design Automation
Siemens NX
3D printing
UG

References

Autodesk – Official web site
Using AutoCAD to “Solve Problems”, an article by Joe Bowers from Cadalyst

Category:Computer-aided design software
Category:Computer-aided design software for Windows
Category:Computer-aided design software for Linux
Category:Computer-aided design software for macOS
Category:Computer-aided design software for Android
Category:Computer-aided design software for iOS
Category:Computer-aided design software for iOS
Category:Computer-aided design software for Windows Mobile the rapidly growing numbers of cases of such attacks, as well as the frequency of such attacks.

The original paper, which was published in July in the journal Environmental Science & Technology, was entitled “Nanoscale Rechargeable Zinc-Air Battery Using NiO Electrode and Metal-Organic Frameworks as Fasteners and Pore-Reforming Agent”. After months of edits and reviews, the paper was published on-line in August at Environmental Science & Technology under a new title: “Nanoscale Rechargeable Zinc-Air Battery Using NiO Electrode and Metal-Organic Frameworks as Fasteners and Pore-Reforming Agent”.

A series of emails between the authors and journal editors led to a
af5dca3d97

Use the generated key in Autocad.

Sdr:Industrial Design

References

Official Website

Category:Free software programmed in Java (programming language)
Category:3D graphics software

How to send data from one screen to another screen in android?

I want to send data from one activity to another activity in android. It is actually a login screen and I want to send the username and password to the other activity. But I am unable to do that. I have tried a lot but in vain.
Can anyone please tell me how to send data from one screen to another screen in android?

A:

You can use intent to send data from one activity to another:
Intent intent = new Intent(Intent.ACTION_VIEW);
intent.setClass(context, “path-to-your-other-activity”);
intent.putExtra(“key”, “value”);
context.startActivity(intent);

You can also use constructor Intent(ComponentName, Uri) to open another activity
Also, you can use putExtra() to send data from one activity to another as shown above.
This is how to read data from intent:
Bundle b = getIntent().getExtras();
if (b!= null) {
String value = b.getString(“key”);
}

You can get multiple data to put to intent from

Q:

Line integral along a straight line

I am doing a line integral problem:
$\int_{\gamma} f(z) dz$ where $\gamma$ is a line passing through the origin and through the point $z=1$.
The function is given by $f(z)= \sin z$
I know that $f'(z) =\cos z$
The problem seems to be quite simple. But I cannot figure it out.
Any help is much appreciated!

A:

To compute $\displaystyle \int_{\gamma} f(z) dz$ along the line $\gamma$, you can apply Green’s

## What’s New In?

What’s New?

Drawing automation (e.g., place tool, copy tool, etc.) is more intelligent than before, and drawing commands work better in the right context.

Symbol Bands are more intelligent and use fewer objects.

AutoCAD draws more accurately on vector-based files than ever before. AutoCAD draws more accurately on vector-based files than ever before.

There are improvements in the way objects are selected and placed on an object.

A new setting to select whether objects with optional entities are selected (added).

You can now draw in two ways: with a surface and without a surface.

Graphical improvements and enhancements

Graphical improvements and enhancements

The New Tabbed Drawing View, drawing Tab, now has “Set to Drawing” on the Drawing Tab to allow you to set the current drawing to the selected drawing.

The New Tabbed Drawing View, Drawing List Tab, now has “Newly added” on the Drawing List Tab to indicate that you are working on newly added drawings.

On a title block, you can now enter freehand text for any text boxes. You can also easily enter text at any size.

The edit options for dynamic text and dynamic annotation have been enhanced.

The ribbon new commands, Immediate and Set, have been moved to the right side of the ribbon.

Enhanced Design Review capabilities

Design Review enhancements

Design Review enhancements

User Interface

User Interface

The Control Panel has been updated with more intuitive, easily-navigable navigation.

The New Tabbed Drawing View has been updated, which is a more intuitive view of all your drawings.

Autodesk.AutoCAD.ViewPort now supports a new, intuitive view of all drawings that is more like your own design review system. You can also use the new tab system to navigate through different views of your drawings.

Assignments and Drawings

Assignments and Drawings

Assignments are now able to support:

Multiple parent files

Multiple views

Fixed layouts

Multiple drawing layouts

In addition to the existing feature of drawing number and view control on the drawing header, the new Assignments module supports the following new features.


text:
Question

Question 11(Multiple Choice)
(05.06 MC)
Using the graph of the function g(x) = log3 (x-4), what are the x-intercept and asymptote of g(x)?

The x-intercept is 3, and the asymptote is located at x = 4.
The x-intercept is 5, and the asymptote is located at x = 4.
The x-intercept is 4, and the asymptote is located at y = 5.
The x-intercept is 5, and the asymptote is located at y = 3.

1. thongdat2
The x-intercept and the asymptote of g(x) are x = 5 and x = 4, respectively

### How to determine the x-intercept and asymptote of g(x)?

The equation of the function is given as:
g(x)  = log3 (x – 4)
Set the function to 0, to determine the x-intercept
log3 (x – 4) = 0
Express the function as an exponential function
x – 4 = 3^0
Evaluate the exponent
x – 4 = 1

format: plain


text:
Chapter 13

• Indications: upper extremity surgery (arm, elbow, forearm, wrist, hand)
• Landmarks: the clavicular head of the sternocleidomastoid muscle
• Equipment:
• A 5-cm, 22-gauge, short-bevel insulated needle
• Peripheral nerve stimulator
• Local anesthetic: 25–35 mL

###### Figure 13-1.

Insertion of the needle in the supraclavicular brachial plexus block. The needle is inserted lateral to the insertion of the clavicular head of the sternocleidomastoid muscle.

### General Considerations

The supraclavicular approach to the brachial plexus characteristically is associated with a rapid onset of anesthesia and a high success rate. The first percutaneous supraclavicular block was performed by Kulenkampff in Germany in 1911, reportedly on himself. A few months after, Hirschel described a method of brachial plexus with an axillary approach. In 1928, Kulenkampff and Persky published their experiences with a thousand blocks without apparent major complications.

Kulenkampff's technique required the patient to be in the sitting position. The needle insertion was above the midpoint of the clavicle in the direction of the spinous process of T2 or T3. Unfortunately, this medial orientation of the needle was associated with a risk of pneumothorax, which eventually became the reason for the supraclavicular block to fall into disfavor in many centers. Since then, many modifications to the original technique were proposed to decrease the risk for pneumothorax. The technique described in this chapter takes into account the location of the dome of the pleura to reduce the risk for pneumothorax.

The advantages of a supraclavicular technique over other brachial plexus block approaches are its rapid onset and complete and predictable anesthesia for entire upper extremity and particularly, hand surgery. The introduction of ultrasound guidance to regional anesthesia in the last decade has resulted in significant renewed interest in the clinical application of the supraclavicular block, as well as a greater understanding of its mechanics.

### Functional Anatomy

The supraclavicular block is often called the "spinal anesthesia of the upper extremity" because of its ubiquitous application for upper extremity surgery. The reasons for its high success rate are in its anatomic characteristics. The block is performed at the level of the distal trunks and origin of the divisions, where the brachial plexus is confined to its smallest surface area (Figure 13-2A). The three trunks carry the entire sensory, motor, and sympathetic innervation of the upper extremity, with the exception of the uppermost part of the medial side of the arm (T2). The densely packed divisions, in contrast, carry a similar amount of innervation in a slightly larger surface area, but there is a larger surface of absorption. Another important anatomic feature of the supraclavicular block is the presence of the subclavian artery in front of the lower trunk and its divisions (Figure 13-2B). To increase the chance of blocking C8-T1 dermatomes it may be beneficial to insert ...

Sign in to your MyAccess profile while you are actively authenticated on this site via your institution (you will be able to verify this by looking at the top right corner of the screen - if you see your institution's name, you are authenticated). Once logged in to your MyAccess profile, you will be able to access your institution's subscription for 90 days from any location. You must be logged in while authenticated at least once every 90 days to maintain this remote access.

Ok

## Subscription Options

### AccessAnesthesiology Full Site: One-Year Subscription

Connect to the full suite of AccessAnesthesiology content and resources including procedural videos, interactive self-assessment, real-life cases, 20+ textbooks, and more


text:
Want to ask us a question? Click here
Browse Questions
 Ad
0 votes

# If a be the edge-length of the unit cell, r be the radius of an atom, then for face centered cubic lattice, the correct relation is

Can you answer this question?

## 1 Answer

0 votes
$4r =\sqrt 2a$
Hence (B) is the correct answer.
answered Jun 5, 2014


text:
Order with confidence. The Effect of Nootropics on the Brain $23.65 at Amazon.com Millions of children and adults in America today struggle with mental fatigue, learning, reading & attention challenges. Much of this could be remedied if these individuals knew how to take care of their body and maximize their brain energy. Recommendation #11 Games Armodafinil is sort of a purified modafinil which Cephalon sells under the brand-name Nuvigil (and Sun under Waklert22). Armodafinil acts much the same way (see the ADS Drug Profile) but the modafinil variant filtered out are the faster-acting molecules23. Hence, it is supposed to last longer. as studies like Pharmacodynamic effects on alertness of single doses of armodafinil in healthy subjects during a nocturnal period of acute sleep loss seem to bear out; anecdotally, it’s also more powerful, with Cephalon offering pills with doses as low as 50mg. (To be technical, modafinil is racemic: it comes in two forms which are rotations, mirror-images of each other. The rotation usually doesn’t matter, but sometimes it matters tremendously - for example, one form of thalidomide stops morning sickness, and the other rotation causes hideous birth defects.) Amazon.com Store Card Top 10 Surprising Spices And Herbs That Boost** Brain Power Mindfulness May Help Diminish Cravings Article continues below Of the two, DHA helps preserve brain function. As for EPA, it helps fight inflammation that may cause the brain to age prematurely. I have been using a Alpha Brain with New Mood from Onnit. I take the Alpha Brain with my other vitamins in the morning with a glass of water followed by coffee and breakfast. I do experience the initial clarity and motivation that is normal with coffee what I have noticed since adding Alpha Brain is the duration of that clarity and motivation has gone further into the day. I have been on Alpha Brain for a month now. My overall quality of written work through the day has improved to equal what I produce in the morning from my initial caffein boost. I did try using Alpha Brain a few hours before sleep but I did not experience any increase in lucid dreaming. I started using New Mood at night prior to sleep. I am sleeping sounder (I do not know if that is the intended result) and when I look at my work load in the morning I do not experience the anxiety I used to feel. I have also noticed this combination has helped me react and think clearer in solving problems that arise during the day. The Ultimate List of Top 10 Home Remedies To Improve** Memory 5x: 11 - 13 June: 1 Supplements for the Brain 1 star Remember me Scutellaria baicalensis$18.75 MisterYouAreSoDumbCeretropic & Nootropics Depot Get Word of the Day daily email! With regard to research, the subject of Nootropics has seen an influx in persons looking for information such that, there is sufficient information on the subject for anyone that takes the time to find it. Children's Health How Citicoline Improves Memory (Mechanism) Just like there is no “one size fits all” for keto (or for any lifestyle), choosing the right nootropic for you depends on the specific outcome you are looking for — whether it be increased focus and concentration, improved mood or stress levels, or enhanced memory and overall brain health. The initial results are a shock: the mean effect of the magnesium citrate comes in at almost the exact same magnitude (-0.25) as had been estimated for the Magtein back in the original Noopept analysis (0.26), except the estimated average effect is negative, as in, the magnesium citrate was harmful, and statistically-significantly so. Huh? 2.0 out of 5 starsNegative: I noticed no difference. Patented Nootropic Powders Brain Attention™ Chewables Because the FDA considers smart drugs dietary supplements, they are not as closely regulated as stronger psychoactive drugs – or even food, for that matter. The government essentially determines whether or not an ingredient is generally considered safe – and stops there. Danica Russel says: noopeptImputed <- noopeptSecond (True,0.90),(True,0.40)] Daisy says If you are looking for an incredible brain booster to boost your brain and get rid of stress then Scholar’s Secret will be the best option for you. Within a low budget this nootropic is able to deliver you the best performance. The manufacturer of this brain booster used scientifically formulated blend which can improve the capacity of your memory and also enhance the clarity. Premium quality ingredients are used to make the nootropic the best one in the market. It is capable of increasing the alertness of your brain and also can increase the focus. If you have any mental disease like Alzheimer then it will help you to get rid of it. # effSz 0.09778545 0.09763823 0.09931263 -0.1895882 0.3907156 74.52276 The next cheap proposition to test is that the 2ml dose is so large that the sedation/depressive effect of nicotine has begun to kick in. This is easy to test: take much less, like half a ml. I do so two or three times over the next day, and subjectively the feeling seems to be the same - which seems to support that proposition (although perhaps I’ve been placebo effecting myself this whole time, in which case the exact amount doesn’t matter). If this theory is true, my previous sleep results don’t show anything; one would expect nicotine-as-sedative to not hurt sleep or improve it. I skip the day (no cravings or addiction noticed), and take half a ml right before bed at 11:30; I fall asleep in 12 minutes and have a ZQ of ~105. The next few days I try putting one or two drops into the tea kettle, which seems to work as well (or poorly) as before. At that point, I was warned that there were some results that nicotine withdrawal can kick in with delays as long as a week, so I shouldn’t be confident that a few days off proved an absence of addiction; I immediately quit to see what the week would bring. 4 or 7 days in, I didn’t notice anything. I’m still using it, but I’m definitely a little nonplussed and disgruntled - I need some independent source of nicotine to compare with! Power times prior times benefit minus cost of experimentation: (0.20×0.30×540)−41=−9(0.20 \times 0.30 \times 540) - 41 = -9. So the VoI is negative: because my default is that fish oil works and I am taking it, weak information that it doesn’t work isn’t enough. If the power calculation were giving us 40% reliable information, then the chance of learning I should drop fish oil is improved enough to make the experiment worthwhile (going from 20% to 40% switches the value from -$9 to +$23.8). Share Facebook Twitter Pinterest Diindolylmethane (DIM) Sorry, there was a problem. careers TruBrain is ridiculously over priced. I have been stacking pretty similar ingredients for the last 6 months and its cost me maybe \$100 total. L-methylfolate ★ STRESS & MOOD SUPPORT- Designed to increase your mental performance, promote positive mood, increase natural energy and ramp up your full mental potential. Feel your mind re-energize, combat stress, helping you stay alert and focused on your most important tasks. Brain function booster at its best! Flavouring & Sweeteners 30mg: 2 - 4 December: 1 Mechanism #1: Regulating The Activity Of Neurotransmitters Amphetamine (e.g., dextroamphetamine (enantiopure drug), lisdexamfetamine [an inactive prodrug]), methamphetamine (a substituted amphetamine)  – systematic reviews and meta-analyses report that amphetamine benefits a range of cognitive functions (e.g., inhibitory control, episodic memory, working memory, and aspects of attention) in the general population, and these effects are especially notable in individuals with ADHD.[28][30][31][33] A systematic review from 2014 noted that low doses of amphetamine also improve memory consolidation, in turn leading to improved recall of information in non-ADHD youth.[31] It also improves task saliency (motivation to perform a task) and performance on tedious tasks that require a high degree of effort.[30][32][33] The results of this meta-analysis cannot address the important issues of individual differences in stimulant effects or the role of motivational enhancement in helping perform academic or occupational tasks. However, they do confirm the reality of cognitive enhancing effects for normal healthy adults in general, while also indicating that these effects are modest in size. Improves Mood 37. Unno, K., Fujitani, K., Takamori, N., Takabayashi, F., Maeda, K., Miyazaki, H., . . . Hoshino, M. (2011). Theanine intake improves the shortened lifespan, cognitive dysfunction and behavioural depression that are induced by chronic psychosocial stress in mice. Free Radic Res, 45(8), 966-974. doi:10.3109/10715762.2011.566869 Nootropics Side Effects: In rats, injecting 300 μg/kg of Selank increased memory trace stability for one month [R]. Men Based upon a brief chat, they could direct you to the best psychic that could offer you one of the most exact reading for your requirements.   Follow us on Twitter Omega-3 has various types, amongst which DHA is essential. https://www.ncbi.nlm.nih.gov/pubmed/21036578 There are two different categories that nootropics fall into: synthetic (created in the lab) and natural (found in nature). Other nootropics can be considered “in-betweeners” and therefore fall within a spectrum of these two categories. summary(l1) Total Recall is a cutting-edge brain booster that is a combination of vitamins, minerals, cofactors, and botanicals specifically formulated to promote cognitive function naturally.* Our mental focus supplement formula includes Alpha Glycerol Phosphoryl Choline, Alpha Lipoic Acid, Vinpocetine, Benfotiamine, and Phosphatidylserine—everything you could possibly want to support your cognitive health is all right here in one convenient brain supplement.* Skip to content 10 Comments 6 Air Purifying Plants That Remove Impurities, Says NASA Decreases depression and tension Top 10 Qualia Mind In fact, studies show that caffeine can jump start short term memory. Gomez-Ramirez M, et al.The deployment of intersensory selective attention: a high-density electrical mapping study of the effects of theanine. Clin Neuropharmacol. 2007 Jan-Feb;30(1):25-38 81 ^ Geng J, Dong J, Ni H, Lee MS, Wu T, Jiang K, Wang G, Zhou AL, Malouf R (2010). "Ginseng for cognition". Cochrane Database Syst Rev (12): CD007769. doi:10.1002/14651858.CD007769.pub2. PMID 21154383. Ask New Question Immunity 1-8 Show Fineprints # MR6 MR1 MR2 MR4 MR3 MR5 MR7 MR8

# nootropics

The body makes key neurotransmitters such as dopamine, serotonin, GABA, acetylcholine and more.  Certain nutrients enhance the production and utilization of these neurotransmitters. Learn more about Mind Lab Pro® N-Acetyl L-Tyrosine DICTIONARYTHESAURUS Atomoxetine – can improve working memory and aspects of attention when used at an optimal dose.[33] Gingo Biloba Leaf (24% extract) Leave a comment View All Antioxidants >> Awakened Alchemy developed the Awaken nootropic brain supplement behind a highly qualified neuroscience team. They designed a very meticulous nootropic stack that not only improves various elements of cognitive functioning but also creates a very good sense of overall well being. Learn more about Mind Lab Pro® Vitamin B6 Not only that, but by choosing the right combinations, you can in fact optimize brain health to tackle debilitating problems we can all face at any age, such as stress, depression and mental fatigue. active mind pills|brain supplements after stroke active mind pills|brain supplements anxiety active mind pills|brain supplements apoaequorin
Legal | Sitemap


text:
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

I was browsing #rstats on Twitter recently and came across this question:

Neat problem, I’ll take a quick look. So I answered the tweet. But the more I’ve dwelt on the question, and looked at the replies, the more I think this would make a great exercise in an interview. It’s a simple enough problem, but how someone chooses to answer it tells you a lot about the kind of colleague they would be.

Example responses ranged from a literal reading of the question, which used R to solve the problem in a spreadsheat way. To others who arrived at an answer, but discarded some steps not required by R. (these steps may have only been included to fully explain the question.

So, fancy having a go yourself? Here’s the sample data:

library(tidyverse)

tibble(A = c(100, 50, 100, 50),
B = c(50, 100, 50, 100)) %>%
mutate(A_minus_B = A - B,
sign = if_else(A_minus_B > 0,
"positive",
"negative"))

What would you do? What would you want to see from a candidate if you asked them this at an interview?


text:
Original Problem

There are several points on a straight line, and you're standing at point 1. Your task is to get to the last point in the minimum number of jumps. There are two constraints on the jumps you can make:

1. the first and last jumps should be of size 1;
2. the absolute difference between the lengths of two consecutive jumps should be less than or equal to 1.

Return the minimum number of jumps you should make to get from the first point to the last one under the conditions given above.

Example

For n = 14, the output should be

minJumpToReachEnd(n) = 7.

Here's the fastest way to get to the last point:

JUMP LENGTHPOSITION
- 1
1 2
2 4
3 7
3 10
2 12
1 13
1 14

Input/Output

• [time limit] 4000ms (py)
• [input] integer points

The number of points.

Constraints:

5 ≤ points ≤ 109.

• [output] integer

The minimum required number of jumps.

## Solution

In order to minimize the number of jumps, it's necessary to increase the stepwidth as much as possible. I was thinking of this problem in 2D, drawing the current stepwidth on the y-axis. That means that for 5 jumps, we can reach a height of two at most:

When you think about it, you go up on the left, keep going and go down on the right side afterwards. So, the jump steps can be modeled like this, with the derivation of the final height:

$\begin{array}{rl} & 2\sum\limits_{k=1}^h k - h &\leq n - 1\\ \Leftrightarrow & h(h+1)-h &\leq n-1\\ \Leftrightarrow & h^2 & \leq n-1\\ \Rightarrow & h = \lfloor\sqrt{n-1}\rfloor \end{array}$

Okay, that's pretty cool. The number of elements we cover with this pattern is:

$s = 2\sum\limits_{k=1}^h k - h = h^2$

We know that the sum over the final height is less or equal to the required width, namely $$h^2\leq n$$. With 5 points, it was closed perfectly, but let's see how it looks with 9 points:

The gap is large enough to fill another $$h$$-block in. The number of such blocks can be calculated as:

$r = \left\lfloor \frac{n-1-s}{h} \right\rfloor$

The $$r h$$ value repairs the fact, that we initially reduced the double sum by $$h$$, as it's possible to have only one jump on the highest level and then back down. When we look at the graph of 6 points, we see a similar thing as with 9:

We still have one jump left, with a width $$< h$$, which can be added on the respective level when going down on the right. The gap-width is simply $$n-1-s-rh$$. In order to make this a binary value of 0 or 1, we divide the value by the maximum gap-width of $$h-1$$:

$g = \left\lceil \frac{n-1-s-rh}{h-1} \right\rceil= -\left\lfloor \frac{rh-n+1+s}{h-1} \right\rfloor$

That means that the final number of jumps is simply the number of jumps $$h$$ plus $$h$$ on the right, reduced by one for the upper level plus the boolean $$g$$ if a gap $$< h$$ is there plus $$r$$, the number of additional $$h$$ elements on the top:

$\begin{array}{rl} j &= 2h-1 + g + r\\ &= 2h-1 -\left\lfloor \frac{\left\lfloor \frac{n-1-h^2}{h} \right\rfloor\cdot h-n+1+h^2}{h-1} \right\rfloor + \left\lfloor \frac{n-1-h^2}{h} \right\rfloor \end{array}$

Implemented in JavaScript, the following code can be brought up:

function minJumpToReachEnd(n) {
n--;
var h = Math.floor(Math.sqrt(n));
var r = Math.floor(n / h - h);
var g = Math.floor((h * (h + r) - n) / (h - 1));
return 2 * h - 1 - g + r;
}

As there are these nasty floor-functions, it's hard to come up with a simplification. But when we look at the pattern generated by this function, we see the following: $$3,4,4,5,5,5,6,6,6,7,7,7,7,8,8,8,8, ...$$. Looking up this pattern, we'll see that it's a well known series, namely A000267 - just shifted by two. The formula for the number of jumps then can be simplified to:

$j = \left\lfloor \sqrt{4 \cdot (n - 2) + 1} \right\rfloor = \left\lfloor \sqrt{4n - 7} \right\rfloor$

Now the implementation is much prettier:

minJumpToReachEnd = n => Math.floor(Math.sqrt(4 * n - 7))

In order to get the idea, I present some more jump patterns with the $$n-1-h^2$$ gaps in it:

#2:

#3:

#4:

#5:

#6:

#7:

#8:

#9:

#10:

« Back to problem overview


text:
# The origin of the period-$2T/7$ quasi-breathing in disk-shaped Gross-Pitaevskii breathers

### Submission summary

 As Contributors: Vanja Dunjko · Maxim Olshanii Preprint link: scipost_202108_00053v2 Date accepted: 2022-02-02 Date submitted: 2021-11-16 04:38 Submitted by: Dunjko, Vanja Submitted to: SciPost Physics Academic field: Physics Specialties: Atomic, Molecular and Optical Physics - Theory Approaches: Theoretical, Computational

### Abstract

We address the origins of the quasi-periodic breathing observed in [Phys. Rev.\ X vol. 9, 021035 (2019)] in disk-shaped harmonically trapped two-dimensional Bose condensates, where the quasi-period $T_{\text{quasi-breathing}}\sim$~$2T/7$ and $T$ is the period of the harmonic trap. We show that, due to an unexplained coincidence, the first instance of the collapse of the hydrodynamic description, at $t^{*} = \arctan(\sqrt{2})/(2\pi) T \approx T/7$, emerges as a `skillful impostor' of the quasi-breathing half-period $T_{\text{quasi-breathing}}/2$. At the time $t^{*}$, the velocity field almost vanishes, supporting the requisite time-reversal invariance. We find that this phenomenon persists for scale-invariant gases in all spatial dimensions, being exact in one dimension and, likely, approximate in all others. In $\bm{d}$ dimensions, the quasi-breathing half-period assumes the form $T_{\text{quasi-breathing}}/2 \equiv t^{*} = \arctan(\sqrt{d})/(2\pi) T$. Remaining unresolved is the origin of the period-$2T$ breathing, reported in the same experiment.

Published as SciPost Phys. 12, 092 (2022)

### List of changes

1. Fixed Eq. (2) to address Referee 2's requested change 1, namely, we removed the proportionality constant $C$ and instead used the proportionality symbol $\propto$. Also, we removed the braces.

2. Corrected a typo in the second equation in Eq. (5), namely the missing velocity field after the del operator on the left-hand side. This was Referee 1's requested change 1 and Referee 2's requested change 2.

3. The power-law equation of state is now numbered as Eq. (8).

4. After Eq. 8 (formerly 7), we clarified that the Damski-Chandrasekhar shock wave solution is approximate and valid at the initial stages of propagation.

5. Right before Eq. (12) (formerly 11), we explained that $V_{\text{inner}}(t) \equiv \dot{R}_{\text{inner}}(t)$ and
$V_{\text{outer}}(t) \equiv \dot{R}_{\text{outer}}(t)$. This addresses Referee 2's requested change 12.

6. Right after Eq. (12) (formerly 11), fixed the notation of the limit of delta t, as reqested by Referee 2's requested change 4.

7. After Eq. (12), we added an explanation of why Eq. (9) (formerly 8) is an approximate solution of Eq. (6) for d>1, as reqested by Referee 2's requested change 3.

8. In Eq. (12) (formerly 12), in the last equation, corrected 'for $R_{\text{outer}}$' to read 'for $r>R_{\text{outer}}$'. This was Referee 2's requested change 5.

9. After Eq. (17) (formerly 16), we added an explanation that $N$, the number of particles, is a volume integral over $n(r,t)$. This addresses Referee 2's requested change 7.

10. We added a substantial amount of detail to the proof of Statemet 5, that the single-valuedness of the velocity field implies that the velocity at the origin is zero. This addresses Referee 2's requested change 8.

11. In the expression for $1/r$, below Eq. (24) (formerly 23), we replaced all appeances of $R_{\text{inner}}(t)$ by $\bar{R}_{\text{inner}}(t)$. This addresses Referee 2's requested change 9.

12. In the caption to to Fig. 1, we corrected the way we refer to Eqs. (29) and (35) (formerly 28 and 34). This addresses one part of Referee 2's requested change 10.

13. At the end of the caption to Fig. 1, we added an explanation of why the hydrodynamical equations cannot be propagated past $t^{∗}$. This addresses the other part of Referee 2's requested change 10.

14. In the text of Statement 7, we clarified that the statement holds for power-law equations of state. This addresses one part of Referee 2's requested change 11.

15. In the text of Statement 8, we also clarified that the statement holds for power-law equations of state. This addresses the other part of Referee 2's requested change 11.

16. After the second displayed equation in Sec. 12, we added a statement explaining that the relevant velocity scale to compare the velocity field with is the initial speed of sound. This addresses Referee 2's requested change 6.

17. Near the end of the page where Sec. 12 begins, we corrected $2T/7 = 0.296\ldots \times T$ to $2T/7 = 0.286\ldots \times T$. This addresses Referee 1's requested change 2.

18. In the caption of Fig. 2, we changed the description of lines from 'dotted' and 'dashed' to 'short-dashed' and 'long-dashed'. This addresses Referee 2's requested change 13.

19. At the end of Sec. 12, we wrote down the Gross-Pitaevskii equation, with an explanation of the relevant parameters. We emphasized that the healing length and the number of particles were chosen to be close to the values they had in the ENS experiment [Phys. Rev. X vol. 9, 021035 (2019)]. This addresses Referee 2's requested change 15.

20. At the end of Sec. 12, we added a sentence explaining why we decided against attempting to introduce a quantum-mechanical analogue of the local velocity. This addresses Referee 2's requested change 14.

### Submission & Refereeing History

#### Published as SciPost Phys. 12, 092 (2022)

You are currently on this page

Resubmission scipost_202108_00053v2 on 16 November 2021
Submission scipost_202108_00053v1 on 20 August 2021

## Reports on this Submission

### Report

I am satisfied with the revision and support for publication.

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -

### Author:  Maxim Olshanii  on 2022-01-03  [id 2062]

(in reply to Report 2 on 2021-12-12)
Category:
remark

We are grateful to the Referee 2 for all the help with the manuscript.

### Report

It is my impression that the points raised in my first report have been adequately taken into account in the revised manuscript. I have no further "urgent" comments.

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -

### Author:  Maxim Olshanii  on 2022-01-03  [id 2063]

(in reply to Report 1 on 2021-11-21)
Category:
remark

Without all the hard work by the Referee 1, this article would not happen: thank you.


text:
# Emulation architecture¶

So far, the data transmission and reception were simulated by LabView functions. In this section, the data modulation and demodulation are carried out by EL470 satellite modems. These modems are configured to operate in compliance with the DVB-S standard, i.e., performing data encapsulation, data encoding and QPSK modulation. Moreover, the satellite channel is implemented by using a vector signal transceiver (VST) integrated with a LabView programming environment.

Figure 1 shows the architecture used to evaluate the satellite channel emulator performance. Computer A generates IP packets that are send out to Modem A in order to communicate with Modem B. Modem A represents a hub modem which transmits a QPSK signal through the satellite link. Subsequently, the QPSK signal is processed by the VST which represents the satellite channel. According to a given $Eb/No$ value, white gaussian noise is added to the signal, furthermore, the transmission through the VST output is delayed to emulate the typical satellite latency.

Finally, the delayed noisy signal is received by Modem B where the signal is demodulated, error correcting is performed and data is recovered in order to send to Modem B.

Figure 1. Emulation architecture

# Device description¶

## Newtec EL470¶

The modem EL470, which is accord with the DVBS or DVBS2 standards, is one of the most advanced satellite modems. Its principal function is to transmit and receive the IP streams over satellite. Its advantages include the direct connection to IP network infrastructures via a single auto-switching Gigabit Ethernet interface and the possibility to use multiple encapsulation protocols. Its maximum rate can reach 133Mbit/s.

The main characteristics are shown in the following table:

Table 1. EL470 main characteristics

## Ethernet switch CISCO 2811¶

Cisco 2811 series integrated services routers are capable of grouping data, security, voice and wireless services into a readable system, providing adequate network performance for the wired or wireless connections.

The main characteristics are shown in the following table:

Table 2. Cisco2811 main characteristics

## NI PXIe-8135¶

This embedded controller consists of a quad-core Intel Core i7-3610QE processor and all the I/O standards. It integrates standard I/O features in a single unit by the compact packaging technology. Combining with other NI compatible chassis, it can be a completely compatible computer.

The main characteristics are shown in the following table:

Table 3. NI PXIe-8135 main characteristics

## NI PXle-5644R¶

A new type of instrumentation that assembles a vector signal generator and vector signal analyzer with FPGA-based real-time signal processing and control has been developed, and the NI PXIe-5644R vector signal transceivers are part of it. Thanks to this software-designed approach, a VST could have the flexibility of software defined radio architecture with RF instrument class performance.

The main characteristics are shown in the following table:

Table 3. NI PXIe-5644R main characteristics

## FSV signal and spectrum analyzer¶

The FSV signal and spectrum analyzer is widely used for signals to develop, product, install and service in the RF systems. It offers the digital modulation analysis for the measurements which can reach 160MHz analysis bandwidth.

# Modem configuration¶

The modems are configured for using DVB-S in a Single Channel Per Carrier (SCPC) scheme, i.e., the forward and return links uses DVB-S and there is no Demand Assigned Multiple Access (DAMA) since only one terminal is sending out data over the carrier.

The modem configuration interface is accessed via a web browser using the IP address as can be seen in Figures 2 and 3. The interface allows users to select the modulator/demodulator parameters such as the carrier frequency, the symbol rate, the modulation, etc.

Figure 2. Modem A configuration

Figure 3. Modem B configuration

Modem A whose IP address is 192.168.88.100 is configured with the following parameters:
• Modulator
• Carrier frequency: 1.75 GHz
• Symbol rate: 2 Mbauds
• Modulation: QPSK
• Coding rate: ¾
• Roll-off factor: 0.35
• Output power: -35 dBm
• Demodulator
• Carrier frequency: 1.50 GHz
• Symbol rate: 2 Mbauds
• Modulation: QPSK
• Coding rate: ¾
• Roll-off factor: 0.20
• Output power: -35 dBm
Modem B whose IP address is 192.168.88.101 is configured with the following parameters:
• Modulator
• Carrier frequency: 1.50 GHz
• Symbol rate: 2 Mbauds
• Modulation: QPSK
• Coding rate: ¾
• Roll-off factor: 0.35
• Output power: -35 dBm
• Demodulator
• Carrier frequency: 1.75 GHz
• Symbol rate: 2 Mbauds
• Modulation: QPSK
• Coding rate: ¾
• Roll-off factor: 0.20
• Output power: -35 dBm

Furthermore, the configuration interface provides graphic tools to monitor the modem status. For instance, the IP throughput, the carrier-to-noise ratio at the demodulator input and the received output power are plotted as shown in Figure 4.

Figure 4. Modem status


text:
# Case Study: Martin’s Renovating

Saturday, April 9, 2011
By dreeves

This is an interesting case study. Martin put $5k at risk on a very conservative goal — spending at least 8 hours a week on a house renovation project for a total of 249 hours by May 5. He actually signed the contract on Oct 21, right before he started shooting up above his yellow brick road. He maintained a blazing pace until the holidays. Then sometime in January he hit the 249 hours, making his$5k safe, and you can see what happened to his productivity since then:

I’d say it’s time for a new commitment contract!

Tags: , , ,


text:
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]

# 18. Embedded Mode

Embedded Mode in Calc provides an alternative to copying numbers and formulas back and forth between editing buffers and the Calc stack. In Embedded Mode, your editing buffer becomes temporarily linked to the stack and this copying is taken care of automatically.

 [ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]

## 18.1 Basic Embedded Mode

To enter Embedded mode, position the Emacs point (cursor) on a formula in any buffer and press M-# e (calc-embedded). Note that M-# e is not to be used in the Calc stack buffer like most Calc commands, but rather in regular editing buffers that are visiting your own files.

Calc normally scans backward and forward in the buffer for the nearest opening and closing formula delimiters. The simplest delimiters are blank lines. Other delimiters that Embedded Mode understands are:

1. The TeX and LaTeX math delimiters ', ', ', and ';
2. Lines beginning with \begin' and \end';
3. Lines beginning with @' (Texinfo delimiters).
4. Lines beginning with .EQ' and .EN' (eqn delimiters);
5. Lines containing a single %' or .\"' symbol and nothing else.

See section 18.5 Customizing Embedded Mode, to see how to make Calc recognize your own favorite delimiters. Delimiters like ' can appear on their own separate lines or in-line with the formula.

If you give a positive or negative numeric prefix argument, Calc instead uses the current point as one end of the formula, and moves forward or backward (respectively) by that many lines to find the other end. Explicit delimiters are not necessary in this case.

With a prefix argument of zero, Calc uses the current region (delimited by point and mark) instead of formula delimiters.

With a prefix argument of C-u only, Calc scans for the first non-numeric character (i.e., the first character that is not a digit, sign, decimal point, or upper- or lower-case e') forward and backward to delimit the formula. M-# w (calc-embedded-word) is equivalent to C-u M-# e.

When you enable Embedded mode for a formula, Calc reads the text between the delimiters and tries to interpret it as a Calc formula. It's best if the current Calc language mode is correct for the formula, but Calc can generally identify TeX formulas and Big-style formulas even if the language mode is wrong. If Calc can't make sense of the formula, it beeps and refuses to enter Embedded mode. But if the current language is wrong, Calc can sometimes parse the formula successfully (but incorrectly); for example, the C expression atan(a[1])' can be parsed in Normal language mode, but the atan won't correspond to the built-in arctan function, and the a[1]' will be interpreted as a' times the vector [1]'!

If you press M-# e or M-# w to activate an embedded formula which is blank, say with the cursor on the space between the two delimiters ', Calc will immediately prompt for an algebraic entry.

Only one formula in one buffer can be enabled at a time. If you move to another area of the current buffer and give Calc commands, Calc turns Embedded mode off for the old formula and then tries to restart Embedded mode at the new position. Other buffers are not affected by Embedded mode.

When Embedded mode begins, Calc pushes the current formula onto the stack. No Calc stack window is created; however, Calc copies the top-of-stack position into the original buffer at all times. You can create a Calc window by hand with M-# o if you find you need to see the entire stack.

For example, typing M-# e while somewhere in the formula n>2' in the following line enables Embedded mode on that inequality:

 We define $F_n = F_(n-1)+F_(n-2)$ for all $n>2$.

The formula n>2 will be pushed onto the Calc stack, and the top of stack will be copied back into the editing buffer. This means that spaces will appear around the >' symbol to match Calc's usual display style:

 We define $F_n = F_(n-1)+F_(n-2)$ for all $n > 2$.

No spaces have appeared around the +' sign because it's in a different formula, one which we have not yet touched with Embedded mode.

Now that Embedded mode is enabled, keys you type in this buffer are interpreted as Calc commands. At this point we might use the "commute" command j C to reverse the inequality. This is a selection-based command for which we first need to move the cursor onto the operator (>' in this case) that needs to be commuted.

 We define $F_n = F_(n-1)+F_(n-2)$ for all $2 < n$.

The M-# o command is a useful way to open a Calc window without actually selecting that window. Giving this command verifies that 2 < n' is also on the Calc stack. Typing 17 RET would produce:

 We define $F_n = F_(n-1)+F_(n-2)$ for all $17$.

with 2 < n' and 17' on the stack; typing TAB at this point will exchange the two stack values and restore 2 < n' to the embedded formula. Even though you can't normally see the stack in Embedded mode, it is still there and it still operates in the same way. But, as with old-fashioned RPN calculators, you can only see the value at the top of the stack at any given time (unless you use M-# o).

Typing M-# e again turns Embedded mode off. The Calc window reveals that the formula 2 < n' is automatically removed from the stack, but the 17' is not. Entering Embedded mode always pushes one thing onto the stack, and leaving Embedded mode always removes one thing. Anything else that happens on the stack is entirely your business as far as Embedded mode is concerned.

If you press M-# e in the wrong place by accident, it is possible that Calc will be able to parse the nearby text as a formula and will mangle that text in an attempt to redisplay it "properly" in the current language mode. If this happens, press M-# e again to exit Embedded mode, then give the regular Emacs "undo" command (C-_ or C-x u) to put the text back the way it was before Calc edited it. Note that Calc's own Undo command (typed before you turn Embedded mode back off) will not do you any good, because as far as Calc is concerned you haven't done anything with this formula yet.

 [ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]

## 18.2 More About Embedded Mode

When Embedded mode "activates" a formula, i.e., when it examines the formula for the first time since the buffer was created or loaded, Calc tries to sense the language in which the formula was written. If the formula contains any TeX-like \' sequences, it is parsed (i.e., read) in TeX mode. If the formula appears to be written in multi-line Big mode, it is parsed in Big mode. Otherwise, it is parsed according to the current language mode.

Note that Calc does not change the current language mode according to what it finds. Even though it can read a TeX formula when not in TeX mode, it will immediately rewrite this formula using whatever language mode is in effect. You must then type d T to switch Calc permanently into TeX mode if that is what you desire.

Calc's parser is unable to read certain kinds of formulas. For example, with v ] (calc-matrix-brackets) you can specify matrix display styles which the parser is unable to recognize as matrices. The d p (calc-show-plain) command turns on a mode in which a "plain" version of a formula is placed in front of the fully-formatted version. When Calc reads a formula that has such a plain version in front, it reads the plain version and ignores the formatted version.

Plain formulas are preceded and followed by %%%' signs by default. This notation has the advantage that the %' character begins a comment in TeX, so if your formula is embedded in a TeX document its plain version will be invisible in the final printed copy. See section 18.5 Customizing Embedded Mode, to see how to change the "plain" formula delimiters, say to something that eqn or some other formatter will treat as a comment.

There are several notations which Calc's parser for "big" formatted formulas can't yet recognize. In particular, it can't read the large symbols for sum, prod, and integ, and it can't handle =>' with the righthand argument omitted. Also, Calc won't recognize special formats you have defined with the Z C command (see section 8.8.7.6 User-Defined Compositions). In these cases it is important to use "plain" mode to make sure Calc will be able to read your formula later.

Another example where "plain" mode is important is if you have specified a float mode with few digits of precision. Normally any digits that are computed but not displayed will simply be lost when you save and re-load your embedded buffer, but "plain" mode allows you to make sure that the complete number is present in the file as well as the rounded-down number.

Embedded buffers remember active formulas for as long as they exist in Emacs memory. Suppose you have an embedded formula which is pi to the normal 12 decimal places, and then type C-u 5 d n to display only five decimal places. If you then type d n, all 12 places reappear because the full number is still there on the Calc stack. More surprisingly, even if you exit Embedded mode and later re-enter it for that formula, typing d n will restore all 12 places because each buffer remembers all its active formulas. However, if you save the buffer in a file and reload it in a new Emacs session, all non-displayed digits will have been lost unless you used "plain" mode.

In some applications of Embedded mode, you will want to have a sequence of copies of a formula that show its evolution as you work on it. For example, you might want to have a sequence like this in your file (elaborating here on the example from the "Getting Started" chapter):

 The derivative of ln(ln(x)) is (the derivative of ln(ln(x))) whose value at x = 2 is (the value) and at x = 3 is (the value)

The M-# d (calc-embedded-duplicate) command is a handy way to make sequences like this. If you type M-# d, the formula under the cursor (which may or may not have Embedded mode enabled for it at the time) is copied immediately below and Embedded mode is then enabled for that copy.

 The derivative of ln(ln(x))

and press M-# d with the cursor on this formula. The result is

 The derivative of ln(ln(x)) ln(ln(x))

with the second copy of the formula enabled in Embedded mode. You can now press a d x RET to take the derivative, and M-# d M-# d to make two more copies of the derivative. To complete the computations, type 3 s l x RET to evaluate the last formula, then move up to the second-to-last formula and type 2 s l x RET.

Finally, you would want to press M-# e to exit Embedded mode, then go up and insert the necessary text in between the various formulas and numbers.

The M-# f (calc-embedded-new-formula) command creates a new embedded formula at the current point. It inserts some default delimiters, which are usually just blank lines, and then does an algebraic entry to get the formula (which is then enabled for Embedded mode). This is just shorthand for typing the delimiters yourself, positioning the cursor between the new delimiters, and pressing M-# e. The key sequence M-# ' is equivalent to M-# f.

The M-# n (calc-embedded-next) and M-# p (calc-embedded-previous) commands move the cursor to the next or previous active embedded formula in the buffer. They can take positive or negative prefix arguments to move by several formulas. Note that these commands do not actually examine the text of the buffer looking for formulas; they only see formulas which have previously been activated in Embedded mode. In fact, M-# n and M-# p are a useful way to tell which embedded formulas are currently active. Also, note that these commands do not enable Embedded mode on the next or previous formula, they just move the cursor. (By the way, M-# n is not as awkward to type as it may seem, because M-# ignores Shift and Meta on the second keystroke: M-# M-N can be typed by holding down Shift and Meta and alternately typing two keys.)

The M-#  (calc-embedded-edit) command edits the embedded formula at the current point as if by  (calc-edit). Embedded mode does not have to be enabled for this to work. Press M-# M-# to finish the edit, or M-# x to cancel.

 [ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]

## 18.3 Assignments in Embedded Mode

The :=' (assignment) and =>' ("evaluates-to") operators are especially useful in Embedded mode. They allow you to make a definition in one formula, then refer to that definition in other formulas embedded in the same buffer.

An embedded formula which is an assignment to a variable, as in

 foo := 5

records 5 as the stored value of foo for the purposes of Embedded mode operations in the current buffer. It does not actually store 5 as the "global" value of foo, however. Regular Calc operations, and Embedded formulas in other buffers, will not see this assignment.

One way to use this assigned value is simply to create an Embedded formula elsewhere that refers to foo, and to press = in that formula. However, this permanently replaces the foo in the formula with its current value. More interesting is to use =>' elsewhere:

 foo + 7 => 12

See section 14.5 The Evaluates-To Operator, for a general discussion of =>'.

If you move back and change the assignment to foo, any =>' formulas which refer to it are automatically updated.

 foo := 17 foo + 7 => 24

The obvious question then is, how can one easily change the assignment to foo? If you simply select the formula in Embedded mode and type 17, the assignment itself will be replaced by the 17. The effect on the other formula will be that the variable foo becomes unassigned:

 17 foo + 7 => foo + 7

The right thing to do is first to use a selection command (j 2 will do the trick) to select the righthand side of the assignment. Then, 17 TAB DEL will swap the 17 into place (see section 12.1 Selecting Sub-Formulas, to see how this works).

The M-# j (calc-embedded-select) command provides an easy way to operate on assigments. It is just like M-# e, except that if the enabled formula is an assignment, it uses j 2 to select the righthand side. If the enabled formula is an evaluates-to, it uses j 1 to select the lefthand side. A formula can also be a combination of both:

 bar := foo + 3 => 20

in which case M-# j will select the middle part (foo + 3').

The formula is automatically deselected when you leave Embedded mode.

Another way to change the assignment to foo would simply be to edit the number using regular Emacs editing rather than Embedded mode. Then, we have to find a way to get Embedded mode to notice the change. The M-# u or M-# = (calc-embedded-update-formula) command is a convenient way to do this.

 foo := 6 foo + 7 => 13

Pressing M-# u is much like pressing M-# e = M-# e, that is, temporarily enabling Embedded mode for the formula under the cursor and then evaluating it with =. But M-# u does not actually use M-# e, and in fact another formula somewhere else can be enabled in Embedded mode while you use M-# u and that formula will not be disturbed.

With a numeric prefix argument, M-# u updates all active =>' formulas in the buffer. Formulas which have not yet been activated in Embedded mode, and formulas which do not have =>' as their top-level operator, are not affected by this. (This is useful only if you have used m C; see below.)

With a plain C-u prefix, C-u M-# u updates only in the region between mark and point rather than in the whole buffer.

M-# u is also a handy way to activate a formula, such as an =>' formula that has freshly been typed in or loaded from a file.

The M-# a (calc-embedded-activate) command scans through the current buffer and activates all embedded formulas that contain :=' or =>' symbols. This does not mean that Embedded mode is actually turned on, but only that the formulas' positions are registered with Embedded mode so that the =>' values can be properly updated as assignments are changed.

It is a good idea to type M-# a right after loading a file that uses embedded =>' operators. Emacs includes a nifty "buffer-local variables" feature that you can use to do this automatically. The idea is to place near the end of your file a few lines that look like this:

 --- Local Variables: --- --- eval:(calc-embedded-activate) --- --- End: ---

where the leading and trailing ---' can be replaced by any suitable strings (which must be the same on all three lines) or omitted altogether; in a TeX file, %' would be a good leading string and no trailing string would be necessary. In a C program, /*' and */' would be good leading and trailing strings.

When Emacs loads a file into memory, it checks for a Local Variables section like this one at the end of the file. If it finds this section, it does the specified things (in this case, running M-# a automatically) before editing of the file begins. The Local Variables section must be within 3000 characters of the end of the file for Emacs to find it, and it must be in the last page of the file if the file has any page separators. See section Local Variables in Files' in the Emacs manual.

Note that M-# a does not update the formulas it finds. To do this, type, say, M-1 M-# u after M-# a. Generally this should not be a problem, though, because the formulas will have been up-to-date already when the file was saved.

Normally, M-# a activates all the formulas it finds, but any previous active formulas remain active as well. With a positive numeric prefix argument, M-# a first deactivates all current active formulas, then actives the ones it finds in its scan of the buffer. With a negative prefix argument, M-# a simply deactivates all formulas.

Embedded mode has two symbols, Active' and ~Active', which it puts next to the major mode name in a buffer's mode line. It puts Active' if it has reason to believe that all formulas in the buffer are active, because you have typed M-# a and Calc has not since had to deactivate any formulas (which can happen if Calc goes to update an =>' formula somewhere because a variable changed, and finds that the formula is no longer there due to some kind of editing outside of Embedded mode). Calc puts ~Active' in the mode line if some, but probably not all, formulas in the buffer are active. This happens if you activate a few formulas one at a time but never use M-# a, or if you used M-# a but then Calc had to deactivate a formula because it lost track of it. If neither of these symbols appears in the mode line, no embedded formulas are active in the buffer (e.g., before Embedded mode has been used, or after a M-- M-# a).

Embedded formulas can refer to assignments both before and after them in the buffer. If there are several assignments to a variable, the nearest preceding assignment is used if there is one, otherwise the following assignment is used.

 x => 1 x := 1 x => 1 x := 2 x => 2

As well as simple variables, you can also assign to subscript expressions of the form var_number' (as in x_0), or var_var' (as in x_max). Assignments to other kinds of objects can be represented by Calc, but the automatic linkage between assignments and references works only for plain variables and these two kinds of subscript expressions.

If there are no assignments to a given variable, the global stored value for the variable is used (see section 14.1 Storing Variables), or, if no value is stored, the variable is left in symbolic form. Note that global stored values will be lost when the file is saved and loaded in a later Emacs session, unless you have used the s p (calc-permanent-variable) command to save them; see section 14.3 Other Operations on Variables.

The m C (calc-auto-recompute) command turns automatic recomputation of =>' forms on and off. If you turn automatic recomputation off, you will have to use M-# u to update these formulas manually after an assignment has been changed. If you plan to change several assignments at once, it may be more efficient to type m C, change all the assignments, then use M-1 M-# u to update the entire buffer afterwards. The m C command also controls =>' formulas on the stack; see section 14.5 The Evaluates-To Operator. When you turn automatic recomputation back on, the stack will be updated but the Embedded buffer will not; you must use M-# u to update the buffer by hand.

 [ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]

## 18.4 Mode Settings in Embedded Mode

Embedded Mode has a rather complicated mechanism for handling mode settings in Embedded formulas. It is possible to put annotations in the file that specify mode settings either global to the entire file or local to a particular formula or formulas. In the latter case, different modes can be specified for use when a formula is the enabled Embedded Mode formula.

When you give any mode-setting command, like m f (for fraction mode) or d s (for scientific notation), Embedded Mode adds a line like the following one to the file just before the opening delimiter of the formula.

 % [calc-mode: fractions: t] % [calc-mode: float-format: (sci 0)]

When Calc interprets an embedded formula, it scans the text before the formula for mode-setting annotations like these and sets the Calc buffer to match these modes. Modes not explicitly described in the file are not changed. Calc scans all the way to the top of the file, or up to a line of the form

 % [calc-defaults]

which you can insert at strategic places in the file if this backward scan is getting too slow, or just to provide a barrier between one "zone" of mode settings and another.

If the file contains several annotations for the same mode, the closest one before the formula is used. Annotations after the formula are never used (except for global annotations, described below).

The scan does not look for the leading % ', only for the square brackets and the text they enclose. You can edit the mode annotations to a style that works better in context if you wish. See section 18.5 Customizing Embedded Mode, to see how to change the style that Calc uses when it generates the annotations. You can write mode annotations into the file yourself if you know the syntax; the easiest way to find the syntax for a given mode is to let Calc write the annotation for it once and see what it does.

If you give a mode-changing command for a mode that already has a suitable annotation just above the current formula, Calc will modify that annotation rather than generating a new, conflicting one.

Mode annotations have three parts, separated by colons. (Spaces after the colons are optional.) The first identifies the kind of mode setting, the second is a name for the mode itself, and the third is the value in the form of a Lisp symbol, number, or list. Annotations with unrecognizable text in the first or second parts are ignored. The third part is not checked to make sure the value is of a legal type or range; if you write an annotation by hand, be sure to give a proper value or results will be unpredictable. Mode-setting annotations are case-sensitive.

While Embedded Mode is enabled, the word Local appears in the mode line. This is to show that mode setting commands generate annotations that are "local" to the current formula or set of formulas. The m R (calc-mode-record-mode) command causes Calc to generate different kinds of annotations. Pressing m R repeatedly cycles through the possible modes.

LocEdit and LocPerm modes generate annotations that look like this, respectively:

 % [calc-edit-mode: float-format: (sci 0)] % [calc-perm-mode: float-format: (sci 5)]

The first kind of annotation will be used only while a formula is enabled in Embedded Mode. The second kind will be used only when the formula is not enabled. (Whether the formula is "active" or not, i.e., whether Calc has seen this formula yet, is not relevant here.)

Global mode generates an annotation like this at the end of the file:

 % [calc-global-mode: fractions t]

Global mode annotations affect all formulas throughout the file, and may appear anywhere in the file. This allows you to tuck your mode annotations somewhere out of the way, say, on a new page of the file, as long as those mode settings are suitable for all formulas in the file.

Enabling a formula with M-# e causes a fresh scan for local mode annotations; you will have to use this after adding annotations above a formula by hand to get the formula to notice them. Updating a formula with M-# u will also re-scan the local modes, but global modes are only re-scanned by M-# a.

Another way that modes can get out of date is if you add a local mode annotation to a formula that has another formula after it. In this example, we have used the d s command while the first of the two embedded formulas is active. But the second formula has not changed its style to match, even though by the rules of reading annotations the (sci 0)' applies to it, too.

 % [calc-mode: float-format: (sci 0)] 1.23e2 456.

We would have to go down to the other formula and press M-# u on it in order to get it to notice the new annotation.

Two more mode-recording modes selectable by m R are Save (which works even outside of Embedded Mode), in which mode settings are recorded permanently in your Emacs startup file ~/.emacs' rather than by annotating the current document, and no-recording mode (where there is no symbol like Save or Local in the mode line), in which mode-changing commands do not leave any annotations at all.

When Embedded Mode is not enabled, mode-recording modes except for Save have no effect.

 [ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]

## 18.5 Customizing Embedded Mode

You can modify Embedded Mode's behavior by setting various Lisp variables described here. Use M-x set-variable or M-x edit-options to adjust a variable on the fly, or put a suitable setq statement in your ~/.emacs' file to set a variable permanently. (Another possibility would be to use a file-local variable annotation at the end of the file; see section Local Variables in Files' in the Emacs manual.)

While none of these variables will be buffer-local by default, you can make any of them local to any embedded-mode buffer. (Their values in the *Calculator*' buffer are never used.)

The calc-embedded-open-formula variable holds a regular expression for the opening delimiter of a formula. See section Regular Expression Search' in the Emacs manual, to see how regular expressions work. Basically, a regular expression is a pattern that Calc can search for. A regular expression that considers blank lines, $', and $$' to be opening delimiters is "\\\\|^\n\\|\\$\\$?". Just in case the meaning of this regular expression is not completely plain, let's go through it in detail. The surrounding " "' marks quote the text between them as a Lisp string. If you left them off, set-variable or edit-options would try to read the regular expression as a Lisp program. The most obvious property of this regular expression is that it contains indecently many backslashes. There are actually two levels of backslash usage going on here. First, when Lisp reads a quoted string, all pairs of characters beginning with a backslash are interpreted as special characters. Here, \n changes to a new-line character, and \\ changes to a single backslash. So the actual regular expression seen by Calc is \\|^ (newline) \|\$\$?'. Regular expressions also consider pairs beginning with backslash to have special meanings. Sometimes the backslash is used to quote a character that otherwise would have a special meaning in a regular expression, like $', which normally means "end-of-line," or ?', which means that the preceding item is optional. So \$\$?' matches either one or two dollar signs.

The other codes in this regular expression are ^', which matches "beginning-of-line," \|', which means "or," and \', which matches "beginning-of-buffer." So the whole pattern means that a formula begins at the beginning of the buffer, or on a newline that occurs at the beginning of a line (i.e., a blank line), or at one or two dollar signs.

The default value of calc-embedded-open-formula looks just like this example, with several more alternatives added on to recognize various other common kinds of delimiters.

By the way, the reason to use ^\n' rather than ^$' or \n\n', which also would appear to match blank lines, is that the former expression actually "consumes" only one newline character as part of the delimiter, whereas the latter expressions consume zero or two newlines, respectively. The former choice gives the most natural behavior when Calc must operate on a whole formula including its delimiters. See the Emacs manual for complete details on regular expressions. But just for your convenience, here is a list of all characters which must be quoted with backslash (like \$') to avoid some special interpretation: . * + ? [ ] ^ $\'. (Note the backslash in this list; for example, to match \[' you must use "\\\\\\[". An exercise for the reader is to account for each of these six backslashes!) The calc-embedded-close-formula variable holds a regular expression for the closing delimiter of a formula. A closing regular expression to match the above example would be "\\'\\|\n$\\|\\$\\$?". This is almost the same as the other one, except it now uses \'' ("end-of-buffer") and \n\$' (newline occurring at end of line, yet another way of describing a blank line that is more appropriate for this case).

The calc-embedded-open-word and calc-embedded-close-word variables are similar expressions used when you type M-# w instead of M-# e to enable Embedded mode.

The calc-embedded-open-plain variable is a string which begins a "plain" formula written in front of the formatted formula when d p mode is turned on. Note that this is an actual string, not a regular expression, because Calc must be able to write this string into a buffer as well as to recognize it. The default string is "%%% " (note the trailing space).

The calc-embedded-close-plain variable is a string which ends a "plain" formula. The default is " %%%\n". Without the trailing newline here, the first line of a "big" mode formula that followed might be shifted over with respect to the other lines.

The calc-embedded-open-new-formula variable is a string which is inserted at the front of a new formula when you type M-# f. Its default value is "\n\n". If this string begins with a newline character and the M-# f is typed at the beginning of a line, M-# f will skip this first newline to avoid introducing unnecessary blank lines in the file.

The calc-embedded-close-new-formula variable is the corresponding string which is inserted at the end of a new formula. Its default value is also "\n\n". The final newline is omitted by M-# f if typed at the end of a line. (It follows that if M-# f is typed on a blank line, both a leading opening newline and a trailing closing newline are omitted.)

The calc-embedded-announce-formula variable is a regular expression which is sure to be followed by an embedded formula. The M-# a command searches for this pattern as well as for =>' and :=' operators. Note that M-# a will not activate just anything surrounded by formula delimiters; after all, blank lines are considered formula delimiters by default! But if your language includes a delimiter which can only occur actually in front of a formula, you can take advantage of it here. The default pattern is "%Embed\n\$$% .*\n\$$*", which checks for %Embed' followed by any number of lines beginning with %' and a space. This last is important to make Calc consider mode annotations part of the pattern, so that the formula's opening delimiter really is sure to follow the pattern.

The calc-embedded-open-mode variable is a string (not a regular expression) which should precede a mode annotation. Calc never scans for this string; Calc always looks for the annotation itself. But this is the string that is inserted before the opening bracket when Calc adds an annotation on its own. The default is "% ".

The calc-embedded-close-mode variable is a string which follows a mode annotation written by Calc. Its default value is simply a newline, "\n"`. If you change this, it is a good idea still to end with a newline so that mode annotations will appear on lines by themselves.

 [ << ] [ >> ] [Top] [Contents] [Index] [ ? ]

This document was generated by XEmacs Webmaster on October, 2 2007 using texi2html


text:
# Decomposition as a product of irreducible elements

One can prove that if $A$ is a noetherian ring and an integral domain then we can write every $a\not\in A ^\times$, $a\neq0$, as a product of finite irreducible elements.

So I am looking for an example of a ring $A$, such there exist at least one irreducible element and there exist $a\not\in A^\times$ that we can't decomposed as a finite product of irreducible elements.

I tried to look at $\mathcal{C}^0(\mathbb{R},\mathbb{R})$ but it doesn't seen to work ($f$ inversible $\iff$ $f$ does not vanish).

Any help will be greatly appreciate

The ring of holomorphic functions on $\mathbb C$ is a domain with elements which are divisible by infinitely many different primes.
There are indeed irreducible elements, namely those functions of the form $x-\alpha$ for $\alpha\in \mathbb C$.


text:
# Solving a second-order equation using Laplace Transforms

I'm trying to solve this second order differential equation using Laplace Transform. The Laplace transform of the equation is as follows:

$$I(s) = \frac{E}{s^2+ \frac{R}{L}s + \frac{1}{LC}}$$

I'm having trouble trying to bring it back to the time domain. Should I be using partial fractions with quadratic factors or is there a easier method to go abut this? Any help would be much appreciated.

-
Yes, you should be using partial fraction decomposition and then reverse the Laplace transform. You might as well use $A=R/L$ and $B=1/(LC)$ if it helps you in the intermediate steps. –  anon Feb 7 '12 at 10:54

$$s^2+\frac{R}{L}s+\frac{1}{LC}=(s+\alpha)^2+\beta^2$$
$$\alpha=\frac{R}{2L} \qquad \beta=\sqrt{\frac{1}{LC}-\frac{R}{2L}}.$$
So, when $\frac{1}{LC}>\frac{R}{2L}$ you will recognize an exponentially decaying sine wave. When $\frac{1}{LC}=\frac{R}{2L}$ you will get just an exponential decay. When $\frac{1}{LC}<\frac{R}{2L}$ you will get an exponential decay multiplied by a hyperbolic cosine. All this can be deduced from the table I linked at the beginning of this answer.


text:
• The exclusive charmonium production process in $\bar{p}p$ annihilation with an associated $\pi^0$ meson $\bar{p}p\to J/\psi\pi^0$ is studied in the framework of QCD collinear factorization. The feasibility of measuring this reaction through the $J/\psi\to e^+e^-$ decay channel with the PANDA (AntiProton ANnihilation at DArmstadt) experiment is investigated. Simulations on signal reconstruction efficiency as well as the background rejection from various sources including the $\bar{p}p\to\pi^+\pi^-\pi^0$ and $\bar{p}p\to J/\psi\pi^0\pi^0$ reactions are performed with PandaRoot, the simulation and analysis software framework of the PANDA experiment. It is shown that the measurement can be done at PANDA with significant constraining power under the assumption of an integrated luminosity attainable in four to five months of data taking at the maximum design luminosity.
• Simulation results for future measurements of electromagnetic proton form factors at \PANDA (FAIR) within the PandaRoot software framework are reported. The statistical precision with which the proton form factors can be determined is estimated. The signal channel $\bar p p \to e^+ e^-$ is studied on the basis of two different but consistent procedures. The suppression of the main background channel, $\textit{i.e.}$ $\bar p p \to \pi^+ \pi^-$, is studied. Furthermore, the background versus signal efficiency, statistical and systematical uncertainties on the extracted proton form factors are evaluated using two different procedures. The results are consistent with those of a previous simulation study using an older, simplified framework. However, a slightly better precision is achieved in the PandaRoot study in a large range of momentum transfer, assuming the nominal beam conditions and detector performance.
• This document illustrates the technical layout and the expected performance of the Micro Vertex Detector (MVD) of the PANDA experiment. The MVD will detect charged particles as close as possible to the interaction zone. Design criteria and the optimisation process as well as the technical solutions chosen are discussed and the results of this process are subjected to extensive Monte Carlo physics studies. The route towards realisation of the detector is outlined.
• ### Indication of a deeply bound compact K-pp state formed in the pp -> p Lambda K+ reaction at 2.85 GeV(1002.3526)

Feb. 18, 2010 nucl-ex
We have analyzed data of the DISTO experiment on the exclusive pp -> p Lambda K+ reaction at 2.85 GeV to search for a strongly bound compact K-pp (= X) state to be formed in the pp -> K+ + X reaction. The observed spectra of the K+ missing-mass and the p Lambda invariant-mass with high transverse momenta of p and K+ revealed a broad distinct peak with a mass M_X = 2265 +- 2 (stat) +- 5 (syst) MeV/c2 and a width Gamma_X = 118 +- 8 (stat) +- 10 (syst) MeV.
• ### DISTO data on Kpp(0912.5116)

Dec. 28, 2009 hep-ex
The data from the DISTO Collaboration on the exclusive pp -> p K+ Lambda production acquired at T_p = 2.85 GeV have been re-analysed in order to search for a deeply bound K- pp (= X) state, to be formed in the binary process pp -> K+ X. The preliminary spectra of the DeltaM_{K+} missing-mass and of the M_{p Lambda} invariant-mass show, for large transverse-momenta of protons and kaons, a distinct broad peak with a mass M_X = 2265 +- 2 MeV/c^2 and a width Gamma_X = 118 +- 8 MeV/c^2.
• ### K$^-$ Meson Production in the Proton-Proton Reaction at 3.67 GeV/c(nucl-ex/9910010)

Oct. 11, 1999 nucl-ex
The total cross section of the reaction $pp\to ppK^+K^-$ has been determined for proton--proton reactions with $p_{beam}=3.67 GeV/c$. This represents the first cross section measurement of the $pp \to ppK^-K^+$ channel near threshold, and is equivalent to the inclusive $pp\to ppK^-X$ cross section at this beam momentum. The cross section determined at this beam momentum is about a factor 20 lower than that for inclusive $pp\to ppK^+X$ meson production at the same CM energy above the corresponding threshold. This large difference in the $K^+$ and $K^-$ meson inclusive production cross sections in proton-proton reactions is in strong contrast to cross sections measured in sub-threshold heavy ion collisions, which are similar in magnitude at the same energy per nucleon below the respective thresholds.


text:
0

# Is the quotient of two nonzero numbers never a rational number?

Wiki User

2011-08-23 01:36:47

The quotient of two nonzero integers is the definition of a rational number. There are nonzero numbers other than integers (imaginary, rational non-integers) that the quotient of would not be a rational number.

If the two nonzero numbers are rational themselves, then the quotient will be rational. (For example, 4 divided by 2 is 2: all of those numbers are rational).

Wiki User

2011-08-23 01:36:47
Study guides

20 cards

➡
See all cards
3.8
1793 Reviews