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Generalization of the hierarchical equations of motion theory for efficient calculations with arbitrary correlation functions
Tatsushi Ikeda, Gregory D. Scholes
Research output: Contribution to journalArticle
1 Scopus citations
Abstract
The hierarchical equations of motion (HEOM) theory is one of the standard methods to rigorously describe open quantum dynamics coupled to harmonic environments. Such a model is used to capture non-Markovian and non-perturbative effects of environments appearing in ultrafast phenomena. In the regular framework of the HEOM theory, the environment correlation functions are restricted to linear combinations of exponential functions. In this article, we present a new formulation of the HEOM theory including treatment of non-exponential correlation functions, which enables us to describe general environmental effects more efficiently and stably than the original theory and other generalizations. The library and its Python binding we developed to perform simulations based on our approach, named LibHEOM and PyHEOM, respectively, are provided as the supplementary material.
Original languageEnglish (US)
Number of pages1
JournalThe Journal of chemical physics
Volume152
Issue number20
DOIs
StatePublished - May 29 2020
All Science Journal Classification (ASJC) codes
• Physics and Astronomy(all)
• Physical and Theoretical Chemistry
Fingerprint Dive into the research topics of 'Generalization of the hierarchical equations of motion theory for efficient calculations with arbitrary correlation functions'. Together they form a unique fingerprint.
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• Grace Health
Miscarriages, how common are they?
To have a miscarriage can be a physically and psychologically hard experience, and therefore a sensitive topic to touch upon. However, understanding why it happens, how common it is and learning more about it might help destigmatize it and, hopefully, bring you some ease of mind.
So how common is it, really?
About 20 out of 100 pregnancies will end up in miscarriage, most of these before week 12.
What causes it?
Most miscarriages are caused by genetic reasons or when something goes wrong in the development from an embryo to a fetus and the development of the fetus.
Age is an important factor because the eggs are older. After the age of 40, many of the eggs are overdue in terms of quality and there are fewer of the good eggs. This leads to an increased risk of miscarriage, decreased chance of getting pregnant and having an average pregnancy.
Some women have repeated miscarriages, which means 3 or more. About 1 % of all fertile women have repeated miscarriage.
Miscarriages can appear in different ways
Most commonly, during a miscarriage, a woman will get bleedings and cramps, similar or heavier than a usual period bleeding.
It can also be only small, brownish bleedings.
Sometimes those bleedings can be so intense that it actually becomes dangerous. If your bleeding is so heavy that it becomes impossible to leave the toilet or the pads get over soaked in a short time, an immediate medical check-up is necessary. And in worst-case scenarios, the bleedings will keep ongoing for weeks. This also needs medical attention and possibly treatment. During this time and a little after, it’s important to keep good hygiene, not take baths, only showers, and if you wish to have intercourse, use a condom to keep infections away.
Some can be more of a silent kind. These ones don’t show any bleeding, and you might have no idea that the fetus has stopped growing, or you might have a feeling that something isn't right, maybe your start noticing that the pregnancy symptoms such as tender breasts or nausea suddenly stop.
It is not possible to prevent miscarriages. If the fetus heartbeat has stopped and it is no longer developing, there is no return and no treatment can heal it.
“It is possible to get pregnant soon after a miscarriage. The female body usually heals quickly and hormones will get back to normal as soon as there is no pregnancy material left in the uterus.”
Those with an increased risk during pregnancy are:
• older than 30 years old, the older, the higher risk;
• medical conditions; e.g.: diabetes
• overweight;
• malformations or fibroids in the uterus;
• infections like German measles/Rubella, toxoplasmosis or listeria;
• If one had multiple pregnancies before;
You won’t get miscarriages from:
• sex
• exercise
• flying aeroplane
• stress
• baths
Pregnancy journeys are all different and it might take some unexpected turns, but having a miscarriage is not the end of the line. It is possible to get pregnant soon after. The female body usually heals quickly and hormones will get back to normal as soon as there is no pregnancy material left in the uterus. If you're going through a miscarriage, stay close to loved ones and understand that it does not ruin your chances of getting pregnant, and that it happens.
Stay informed, stay in control.
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How to charge the iPhone 3G when staying in China
The WikiConnections page on how to power your iPhone 3G from a Chinese power outlet with an Apple 30 pin cable with a 3 pinned Type A USB adapter, charging the iPhone 3G using a 2 pinned Type C USB adapter and charging the iPhone 3G using a 3 pinned Type I USB adapter
Chinese power outlet
Differing region codes and plugs can often be confusing when planning to travel to a different country if you've never visited before. This guide shows what you'll need to supply power to your iPhone 3G when you're visiting China by using the standard types I, A or C Chinese 220 volt 50Hz wall outlets, you'll discover most Chinese will typically use the Type I wall outlets. Most power supplies change depending on which region you're taking a trip to therefore we suggest that you read our Wikiconnections travel power sockets guide where you'll find a complete list of powering devices in different regions. If travelling to China from another country please ensure that the iPhone 3G can be charged using a 240 volt supply. If the iPhone 3G originated in a country which uses a lower voltage such as 110 volts ensure that the iPhone 3G is dual voltage (marked with a 100-240 volt notation) otherwise you may need to use an additional voltage converter to avoid the device from over-heating whilst powering it. These instructions assume that you are running Apple iOS 4 or greater on the iPhone 3G.
Charging the iPhone 3G in China
Can the iPhone 3G be used in China?
You can connect the iPhone 3G to a Chinese power outlet.
What is the best travel adapter for recharging the iPhone 3G in China?
If travelling to more than one country the best travel charger for China is a multiple USB charger which includes swappable plugs like a 4 port USB travel charger [10]. Chinese use three different types of plug sockets (I, A and C) and using a travel charger like this ensures that you are covered for both types A and C. As these types of chargers come with interchangeable plugs and can handle from 100 volts to 240 volts will mean that you can travel to over 100 countries in North America, Europe, Asia and Africa just by changing the supplied heads over. If your model of iPhone 3G can support Fast Charge (please note that not all USB devices do) then you'll benefit from much faster recharging times by using one of these types of USB travel chargers and support for certain power demanding devices. Having a four port charger means you can power multiple devices at once without needing to pack seperate power chargers or using up additional wall sockets. Only packing a single lightweight USB travel charger will also keep the overall size and weight down, making it ideal to fold up in hand luggage whilst travelling and suitable for recharging your iPhone 3G at the airport or on the plane. Because of their space saving versatility these types of power chargers can be used back at home as well as abroad so when you're not travelling they can be used overnight charging multiple tablets, phones and speakers with only a single plug socket.
We suggest buying an adaptable power charger similar to this at an electronics retailer. The travel adapter illustrated here is the 4 Port USB Wall Charger [10] which has been tested successfully for recharging multiple USB devices in numerous foreign countries around the world on a daily basis.
Alternative travel adapter for China
The 4 port USB travel charger [10] is the most compact option for travellers from any country who only have USB devices such as the iPhone 3G, however for those also wishing to use their domestic plugs the following power adapters provide larger but more versatile solutions. All 3 power adapters offer surge protection which can be necessary when visiting counties with unreliable or unstable power supplies to prevent damage to any connected appliances from voltage spikes. These power adapters come with interchangeable type C, I and G plugs covering both China and over 150 countries around the world:
• BESTEK Portable International Travel Voltage Converter - The BESTEK travel adaptor has 4 USB charging ports with 3 AC power outlets and is the best selling portable power converter for travellers originating from America visiting China.
• ORICO Traveling Outlet Surge Protector Power Strip - Also having 4 USB ports but only 2 AC power outlets the travel adapter from Orico is also aimed at travellers from the US using type B plugs and is a more cost effective alternative to the BESTEK with only one less AC outlet at almost half the price.
• BESTEK International USB Travel Power Strip - This power strip has 2 AC outlets but offers a more generous 5 USB charging ports. This versatile power strip is compatible with both American plugs and popular plug types A, D,E/F, G, H, I, L and N making it suitable for a wide range of travellers from around the world visiting China.
What is the best travel adapter for recharging the iPhone 3G in China?
How to use a Type A power charger for recharging your iPhone 3G from a Chinese power outlet
The WikiConnections page on how to power your iPhone 3G from a Chinese power outlet with the 30 pin Apple connector and a Type A power charger.
1. To supply power to the iPhone 3G using a Chinese power outlet you will need a Type A USB power adapter [4] and a USB to Apple 30 pin cable [5] (normally included with your device).
2. Begin by inserting the Type A USB power adapter in the wall outlet. This wall supply (called a Type A power outlet [3]) can be identified by two thin slots adjacent to each other for live and neutral blades.
3. Then connect one end of the USB to Apple 30 pin cable into the bottom of the mains USB adapter and the other end into the dock connector on the iPhone 3G. The iPhone 3G dock connector can be found at bottom of the iPhone 3G.
4. Turn on the Chinese power outlet.
5. The battery icon which you'll find in the top right corner of the cellphone will display a charging icon to indicate that the iPhone is charging taking between 60-240 minutes to recharge.
How to use a Type A power charger for recharging your iPhone 3G from a Chinese power outlet
Powering the iPhone 3G with a Chinese power outlet by using a 2 pinned Type C Europlug USB adapter
Using the 30 pin Apple connector and a Type C power charger to power your iPhone 3G from a Chinese power outlet.
1. If you want to power your iPhone 3G from the Chinese power outlet you'll need to buy a Type C USB power adapter [7] and a USB to Apple 30 pin cable [5] (Apple normally include the USB cable with your iPhone 3G).
2. Start the process by taking the Type C USB power adapter and plugging it into the Chinese power outlet. You can identify this wall supply by 2 adjacent holes where the pins slide into.
3. Connect one end of the USB to Apple 30 pin cable into the bottom of the mains USB adapter and the other end into the dock connector on the iPhone 3G. The iPhone 3G dock connector can be found at bottom of the iPhone 3G.
4. Turn on the Chinese power outlet.
5. The battery icon which you'll find in the top right corner of your phone screen will display a charge icon to indicate that the phone is powering up, typically taking around 1 to 4 hours to fully recharge to 100% capacity.
Powering the iPhone 3G with a Chinese power outlet by using a 2 pinned Type C Europlug USB adapter
Powering the iPhone 3G with a Chinese power outlet by using a 3 pinned Type J USB adapter
Using the 30 pin Apple connector and a Type I power charger to recharge your iPhone 3G from a Chinese power outlet.
1. In order to charge the iPhone 3G from the Chinese power outlet you'll need to buy a Type I USB power adapter [9] and a USB to Apple 30 pin cable [5] (Apple normally include the USB cable with your iPhone 3G).
2. Start the process by taking the Type I USB power adapter and plugging it into the Chinese power outlet. You can identify this wall supply by 3 slots for the live, neutral and ground. Please note that the neutral and live blades are reversed compared to Argentinian plug outlets so check that your Type I travel adaptor is compatible with a Chinese power supply.
3. Connect one end of the USB to Apple 30 pin cable into the bottom of the mains USB adapter and the other end into the dock connector on the iPhone 3G. The iPhone 3G dock connector can be found at bottom of the iPhone 3G.
4. Turn on the Chinese power outlet.
5. The battery icon which you'll find in the top right corner of your phone screen will display a charge icon to indicate that the phone is powering up, typically taking around one to four hours to completely recharge to 100% capacity.
Powering the iPhone 3G with a Chinese power outlet by using a 3 pinned Type J USB adapter
See also
1. https://en.wikipedia.org/wiki/China - Chinese Wikipedia page
2. https://manuals.info.apple.com/MANUALS/0/MA616/en_US/iPhone_iOS3.1_User_Guide.pdf - Official iPhone 3G user guide
3. http://www.iec.ch/worldplugs/typeA.htm - Type A power outlet
4. Type A USB power adapter - Provides USB power from a type A mains power outlet
5. USB to Apple 30 pin cable - This connects compatible iPhones, iPods and iPads to a USB port for charging, syncing and playing music
6. http://www.iec.ch/worldplugs/typeC.htm - Type C power outlet
7. Type C USB power adapter - Provides USB power from a type C mains power outlet
8. http://www.iec.ch/worldplugs/typeI.htm - Type I power outlet
9. Type I USB power adapter - Provides USB power from a type I mains power outlet
10. 4 Port USB Wall Charger - A universal USB charger capable of charging up to 4 USB devices with swappable international adapters
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Senzicare
Progesterone hypersensitivity is a rare condition in which an individual experiences an allergic or hypersensitive reaction to the hormone progesterone. The ovaries naturally produce this hormone and play a critical role in regulating the menstrual cycle, maintaining pregnancy, and supporting other reproductive functions. Progesterone is a hormone produced by the ovaries. It peaks just before menstruation. Georgina suffered from progesterone hypersensitivity, an allergic reaction to progesterone. Common symptoms include itching, swelling, and redness. In some, the symptoms can be severe, coughing, shortness of breath, and a severe allergic reaction called anaphylaxis. Medicines to reduce the production of progesterone are given as a remedy.
Symptoms of Progesterone Hypersensitivity
The symptoms can vary widely but often include:
• Skin Reactions: Hives, rashes, and itching, typically occurring in the luteal phase of the menstrual cycle (after ovulation and before menstruation).
• Respiratory Symptoms: Wheezing, shortness of breath, or other asthma-like symptoms.
• Systemic Reactions: Generalized swelling, joint pain, and in some cases, anaphylaxis (a severe, life-threatening allergic reaction).
• Reproductive Symptoms: Increased premenstrual symptoms like breast tenderness, mood swings, or bloating.
Diagnosis
Diagnosing progesterone hypersensitivity can be challenging and usually involves:
• Clinical History: Documentation of symptoms correlated with the menstrual cycle.
• Skin Testing: Intradermal testing with progesterone may be performed to observe a reaction.
• Hormone Challenge: Administering progesterone to see if it provokes symptoms.
Treatment
Treatment strategies may include:
• Hormonal Therapies: Such as suppressing ovulation with continuous oral contraceptives or GnRH analogs.
• Immunotherapy: Desensitization protocols are sometimes used.
• Symptomatic Treatment: Antihistamines, corticosteroids, and other medications to manage allergic reactions.
Prognosis
The condition is rare and varies in severity, but with appropriate management, many individuals can find relief from symptoms.
If you or someone you know suspects they may have progesterone hypersensitivity, it’s essential to consult a healthcare provider, particularly an allergist or immunologist, for proper evaluation and management.
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Home A to G Folliculitis : Causes, symptoms and treatments
Folliculitis : Causes, symptoms and treatments
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Folliculitis
Folliculitis is a condition in which the hair follicles get inflamed. This could develop in any part of the body that has hair, but is most common in the beard area, arms, buttocks, backs, and legs.
Cause
Folliculitis can be caused due to bacteria, yeast or any other type of fungus. It is most commonly caused due to damaged hair follicles during shaving or constant irritation on the clothes due to certain clothes fabrics. It is also caused due to blocked follicles, resulting from sweat, grime, machine oils and greasy makeup. It is when the follicles become injured that they get infected thus giving rise to folliculitis.
The risk for getting folliculitis increases in the following instances
• You are regularly using tubs, whirlpools or swimming pools that are not properly treated with chlorine
• Wearing tight, body hugging clothes
• Coming in constant contact with greasy substances such as motor oil, tar, and creosote
• Using heavy and greasy makeup
• There is an infection over cuts, scrapes and surgical wound
• Immunity lowering diseases existing in the body
• Lowered immunity after a surgery or recovery from some other disease
Symptoms
You know it is folliculitis if there is a small, red pimple like bump on the skin with a hair in the center. These are itchy and may have pus inside them. If the infection is severe, the person may also experience a burning sensation. Upon squeezing, they may drain out both pus and blood. There are different types of folliculitis. If it is a ‘hot tub folliculitis”, it occurs after 72 hours of having used a spa or a hot tub. The smaller pimples usually appear on the stomach, arms, and legs. Sometimes, they may also be accompanied by a mild fever and an upset stomach. These smaller ones usually do not need any treatment and go away in 7 to 10 days.
Complications
Since folliculitis is a self-limited skin condition, it rarely leads to any serious complications. Possible complications include
• Recurrent infections
• Spreading to a larger area
• Enlargement of the bumps causing furuncles or carbuncles
• Permanent damage to the skin like scarring and dark spots
• Destruction of follicles thus leading to permanent hair loss
If the abscesses grow to a very large size they may have to be removed through surgical procedures. If the infections grow deeper and more extensive, it could also result in cellulitis.
Treatment
If the folliculitis is very mild, no treatment is required. It heals by itself in about 2 weeks. The following treatment should help to speed up the healing
• Pressing the affected area with a warm towel soaked in water and then the excess water wrung out. This is mainly helpful in providing relief from itchiness
• Medicated soaps, shampoos and body washes for daily use
If the inflammation is severe, doctors may prescribe topical or oral antibiotics. If the inflammation is very recurrent or does not go away, laser hair removal is done to completely destroy the hair follicles.
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What Is LG Smartworld? (All You Need To Know)
If you have recently purchased an LG smartphone, you may have noticed a preinstalled app called LG Smartworld. Therefore, you are probably wondering: what is LG Smartworld?
If so, continue reading to find out this answer and more!
What is LG Smartworld In 2024?
LG Smartworld is an app alternative to the Google Play Store for LG Android smartphones in 2024. Moreover, this app gives you access to games, apps, themes, customization features, and more that are only available on the LG Smartworld app. Additionally, LG Smartworld is now available on LG Smart TVs.
Read on if you are interested in learning about how LG Smartworld works, how to download LG Smartworld on your mobile device or Smart TV, and much more!
What is LG Smartworld Mobile?
LG Smartworld Mobile is an app for your LG phone or tablet.
Additionally, LG Smartworld allows you to download many different apps that aren’t available to anyone other than LG users.
Furthermore, with LG Smartworld you can download games and entertainment as well as themes, fonts, and more to customize your smartphone or tablet.
What is LG Smartworld TV?
LG Smartworld TV is the same as LG Smartworld mobile, but it is for your LG Smart TV.
Therefore, you can download the same games and entertainment for your smartphone or tablet on your Smart TV.
How do I Download the LG Smartworld App?
Fortunately, you can download the LG Smartworld app in a couple of different ways.
Moreover, you can download the LG Smartworld app on your mobile device through the mobile app store or a web browser.
Therefore, to download the LG Smartworld app on your mobile device through the app store:
1. Start by going to the apps store on your mobile device
2. Next, search “LG Smartworld”
3. Then click “Install” or “Download”.
Furthermore, you can also download the LG Smartworld app on your LG Smart TV using the TV content store the same way you download the app on your mobile device.
Moreover, to download the LG Smartworld app on your mobile device through a web browser:
1. First, go to www.lgworld.com. Additionally, you can go to www.lgworld.com using your mobile device and you won’t need to scan the QR code
2. Second, if using your laptop computer, scan the QR code using your smartphone or tablet. Moreover, the QR code will be located in the top left corner of the website
3. Next, click “Download”
4. Then, choose your country and region
5. Finally, click “Install” to download the LG Smartworld app
Additionally, if you downloaded the LG Smartworld apk file on your mobile device and are running the file, the application is installed automatically.
How does LG Smartworld Work?
How does LG Smartworld Work?
To use LG Smartworld, the app needs to be installed on your device, as stated previously.
Once the app is installed on your device, you can create a Smartworld account and sign in.
Therefore, to create an LG Smartworld account:
1. First, open the LG Smartworld app
2. Second, Click “Sign Up”
3. Then, you will need to agree to LG’s “Legal Notice”
4. Next, enter your email and create your password
5. Last, click “Register”
Now that your Smartworld account has been created you need to sign up for a membership and you can do so by going to www.lgappstv.com
After you sign up for a membership, you can log into your Smartworld account.
Additionally, you can sign into up to five monitors with one account ID and password.
Furthermore, to install apps through LG Smartworld on your mobile device:
1. Start by opening the Smartworld app on your device
2. Then, search the categories for the app you want to download and click on it
3. Last, review the app details to make sure it works with your device and click “Install”
Moreover, to install apps through LG Smartworld on your Smart TV:
1. First, click “Smart Home” and then click “LG Smart World”
2. Second, Log into your LG TV account
3. Then, choose the app you want to install to see its details
4. Next, check the system requirement for the app, and if your device is compatible click “Install”
5. Finally, click “OK” to install the app
Additionally, if the app(s) you are downloading are “paid content”, you will have to pay for the app before you install it.
Moreover, you can pay for paid content on LG Smartworld with a credit card or a PayPal account.
Does LG Smartworld Still Work?
LG Smartworld does still function for LG Android users.
Unfortunately, as of 2021, LG decided to stop producing mobile smartphones and tablets.
However, all of the already manufactured LG smartphones and tablets still function and run like normal, and some are even receiving updates.
Therefore, even though LG has decided to stop producing smartphones and tablets, the LG Smartworld app will continue to run as normal for all LG users.
Furthermore, if you are having trouble with the Smartworld app, it may be because of your location or provider.
Moreover, LG has stated, “the provision of this service depends on the country and the communication service provider.
LG also states that you can check whether your country or service provider works with LG Smartworld through the Smartworld website on the Country list.
Can I Delete LG Smartworld?
Fortunately, if you downloaded the LG Smartworld app to your mobile smartphone, tablet, or Smart TV you can delete it because it was added to your device later and not pre-installed.
Furthermore, you can also delete LG Smartworld if you are running the LG Smartworld apk file on your mobile device.
Unfortunately, if the Smartworld app was pre-installed on your device, you will not be able to delete it.
However, just because the Smartworld app is installed on your mobile device does not mean you have to use it.
To know more, you can also read our posts on LG Magic Remote, LG ThinQ, and who makes LG TVs.
Conclusion
LG Smartworld is an alternative app store for LG Android users. Moreover, Smartworld allows LG users to download extra apps such as games, entertainment, fonts, themes, and more to customize their mobile phones.
Furthermore, Smartworld is only available to LG users, and other Android users can not access Smartworld. Additionally, LG Smartworld can be used on LG devices such as smartphones, tablets, and LG Smart TVs.
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Mackenzie Jerks
Mackenzie is a freelance writer and editor, published author, and music enthusiast who holds a Bachelor of Science in Business Administration. When she’s not writing, Mackenzie is either wrapped up in a book, discovering new music, or introducing herself to a new fitness regimen.
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Understanding Guideline 4.1: Compatible
Guideline 4.1 Compatible: Maximize compatibility with current and future user agents, including assistive technologies.
Intent
The purpose of this guideline is to support compatibility with current and future user agents, especially assistive technologies (AT). This is done both by 1) ensuring that authors do not do things that would break AT (e.g., poorly formed markup) or circumvent AT (e.g., by using unconventional markup or code) and 2) exposing information in the content in standard ways that assistive technologies can recognize and interact with. Since technologies change quickly, and AT developers have much trouble keeping up with rapidly changing technologies, it is important that content follow conventions and be compatible with APIs so that AT can more easily work with new technologies as they evolve.
Advisory Techniques
Specific techniques for meeting each Success Criterion for this guideline are listed in the understanding sections for each Success Criterion (listed below). If there are techniques, however, for addressing this guideline that do not fall under any of the success criteria, they are listed here. These techniques are not required or sufficient for meeting any success criteria, but can make certain types of Web content more accessible to more people.
Success Criteria for this Guideline
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by , ,
Abstract:
Knowing how protein sequence maps to function (the "fitness landscape") is critical for understanding protein evolution as well as for engineering proteins with new and useful properties. We demonstrate that the protein fitness landscape can be inferred from experimental data, using Gaussian processes, a Bayesian learning technique. Gaussian process landscapes can model various protein sequence properties, including functional status, thermostability, enzyme activity, and ligand binding affinity. Trained on experimental data, these models achieve unrivaled quantitative accuracy. Furthermore, the explicit representation of model uncertainty allows for efficient searches through the vast space of possible sequences. We develop and test two protein sequence design algorithms motivated by Bayesian decision theory. The first one identifies small sets of sequences that are informative about the landscape; the second one identifies optimized sequences by iteratively improving the Gaussian process model in regions of the landscape that are predicted to be optimized. We demonstrate the ability of Gaussian processes to guide the search through protein sequence space by designing, constructing, and testing chimeric cytochrome P450s. These algorithms allowed us to engineer active P450 enzymes that are more thermostable than any previously made by chimeragenesis, rational design, or directed evolution.
Reference:
Navigating the Protein Fitness Landscape with Gaussian Processes P. A. Romero, A. Krause, F. H. ArnoldIn Proceedings of the National Academy of Sciences (PNAS), volume 110, 2013published online before print on Dec. 31, 2012
Bibtex Entry:
@article{romero13navigating,
author = {Philip A. Romero and Andreas Krause and Frances H. Arnold},
doi = {10.1073/pnas.1215251110},
journal = {Proceedings of the National Academy of Sciences (PNAS)},
month = {January},
number = {3},
title = {Navigating the Protein Fitness Landscape with Gaussian Processes},
volume = {110},
year = {2013}}
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Tag Archives: ponsel disadap
Cara Mengetahui Ponsel Kamu Disadap
Semakin banyak teknologi di sini yang berkembang, belum ada 20 tahun, telepon seluler telah berubah dari telepon seluler monokrom menjadi telepon seluler yang tidak hanya berwarna, tetapi dapat digunakan untuk apa saja. Namun kejahatan dengan teknologi semakin merajalela, tidak terkecuali pada ponsel Anda.
Cara Mengetahui Ponsel Kamu Disadap
Cara Mengetahui Ponsel Kamu Disadap
Kasus penyadapan telepon seluler semakin merajalela, banyak di antaranya adalah peretas penyadapan salah satu contohnya adalah sms banking. Sebagian besar yang dilakukan peretas untuk menyadap ponsel adalah memasukkan “sesuatu” dalam satu aplikasi. Lalu bagaimana kita tahu kalau ponsel kita disadap?
Sebenarnya tanda termudah jika ponsel Anda disadap adalah baterai yang boros. Selain baterai, kouta Anda juga akan boros meskipun penggunaan ponsel Anda cukup masuk akal. Cara lain yang dapat Anda lakukan adalah melewatkan frekuensi ponsel. Anda dapat melakukan ini jika percakapan telepon Anda disadap.
Anda hanya perlu mengenali karakteristiknya, sulit untuk mengenalinya, mudah diketahui. Ciri khasnya adalah ada suara aneh yang bukan berasal dari Anda atau teman bicara Anda. Karakteristik lain adalah suara menjadi bergema, seperti berbicara di lorong. Fitur lainnya adalah kita akan sering keliru ketika menghubungi nomor yang kita hubungi.
Cara lain agar kita dapat memeriksa ponsel kita diretas dengan menggunakan kode. Kita dapat menggunakan kode * # 21 atau ## 002 untuk memeriksa ponsel kita jika ponsel kita diketuk. Dengan kode ini kita dapat melihat apakah panggilan kita sedang ditransfer atau tidak.
Cukup mudah untuk tidak mengetahuinya, jadi berhati-hatilah jika Anda
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Introduction
Detailed theoretical considerations of narrow-gap insulators date back to the 1960s, when it was realized that if the energy required to form an electron-hole pair becomes negative, a phase transition into an excitonic insulator state can occur1,2,3,4. Unscreened electron-hole Coulomb attraction is perhaps the most obvious driving force behind this phase transition, and excitonic charge insulator states are indeed thought to occur in materials such as TmSe0.45Te0.55, 1T-TiSe2, and Ta2NiSe55,6,7,8,9. Although less intuitive, effective electron-hole attraction can also arise from on-site electron-electron Coulomb repulsion U via magnetic exchange interactions between the electron and hole10. In this case, the soft exciton is expected to be a spin-triplet, which passes through a quantum critical point (QCP) with increasing effective U. The condensation of the relevant triplet exciton at the QCP gives rise to an antiferromagnetic ground state hosting a well-defined excitonic longitudinal mode4, which coexists with transverse modes that are a generic feature of ordered antiferromagnets. This longitudinal mode features excitonic character, in the sense that it modifies the local spin amplitude by creating electron-hole pairs4. In this work, we identify and study a longitudinal mode in Sr3Ir2O7, the presence of which is the key experimental signature of an antiferromagnetic excitonic insulator.
Results
The formation of an antiferromagnetic excitonic insulator requires a very specific set of conditions. We need (i) a charge gap of similar magnitude to its magnetic energy scale and (ii) strong easy-axis anisotropy. Property (i) is a sign that the material is close to the excitonic QCP (see Fig. 1). Property (ii) is not a strict condition, but it facilitates the identification of an antiferromagnetic excitonic insulator, because the opening of a spin gap Δs protects the longitudinal mode from decay. This is because longitudinal fluctuations are often kinetically predisposed to decay into transverse modes generating a longitudinal continuum with no well-defined modes. This decay can be avoided when the energy of the longitudinal mode is lower than twice the spin gap. Iridates host strong spin-orbit coupling (SOC), which can help realize a large spin gap and bilayer Sr3Ir2O7 shown in Fig. 2a is known to have a narrow charge gap of order Δc ~ 150 meV11. The essential magnetic unit, with c-axis ordered moments, is shown in Fig. 2b12. In view of the antiferromagnetic order in Sr3Ir2O7, the material would be predicted to lie in the magnetically ordered region to the right of the QCP where the excitonic longitudinal mode is expected to appear. Because the exciton is predicted to have odd parity under exchange of the two Ir layers, we expect the excitonic longitudinal mode to be present at c-axis wavevectors corresponding to antisymmetric bilayer contributions and absent at the symmetric condition. We label these wavevectors qc = 0.5 and qc = 0, respectively. In contrast, transverse magnetic modes are expected to be present at all c-axis wavevectors, allowing the transverse and longitudinal modes to be readily distinguished.
Fig. 1: Antiferromagnetic excitonic insulator phase diagram.
figure 1
Charge excitations in paramagnetic band insulators consist of either electron-hole excitations across the insulating band gap (brown shaded area) or of bound electron-hole excitons below the particle-hole continuum [electrons (holes) are indicated with filled (empty) circles]. An antiferromagnetic excitonic insulator is established through the condensation of the predominately spin-triplet character exciton mode with spin quantum number Sz = 0. The excition is a superposition of an up-spin electron in the conduction band paired with an up-spin hole (equivalent to a down-spin electron) and a down-spin electron paired with a down-spin hole4. The other spin-triplet excitions Sz = ±1 feature an up-spin electron and a down-spin hole or a down-spin electron and an up-spin hole. Upon increasing Coulomb interaction U the Sz = 0 exciton condenses into the ground state at a QCP4, establishing magnetic order and leaving an excitonic longitudinal mode as the key signature of this state.
Fig. 2: Isolating the excitonic longitudinal mode in Sr3Ir2O7.
figure 2
a Crystal structure of the bilayer material Sr3Ir2O7. b Ir-Ir bilayer with t1 the nearest-neighbor, t2 the next-nearest-neighbor and tz(α) the interlayer hopping terms. ce RIXS spectra measured at T = 20 K and Q = (0, 0, L) with L = 25.65, 26.95 and 28.25 in reciprocal lattice units. The c-axis positions are also labeled in terms of the Ir-Ir interlayer reciprocal-lattice spacing qc = 0, 0.25 and 0.5. An additional mode appears around 170 meV with maximal intensity at qc = 0.5 (see shaded red area). The black circles represent the data and dotted lines outline the different components of the spectrum, which are summed to produce the grey line representing the total spectrum. Error bars are determined via Poissonian statistics.
The excitation spectrum of Sr3Ir2O7 was studied with RIXS. Figure 2c–e displays energy-loss spectra at T = 20 K, well below the Néel temperature TN = 285 K and qc = 0, 0.25 and 0.5, corresponding to L = 25.65, 26.95 and 28.25 in reciprocal lattice units (r.l.u.). These irrational L values arise because the bilayer separation d is not a rational fraction of the unit cell height c (see Methods section for details). The spectrum at qc = 0 is composed of a phonon-decorated quasi-elastic feature, a pronounced magnetic excitation at ~ 100 meV, which we later identified as the transverse mode, and a high-energy continuum. As explained above, changing qc is expected to isolate the anticipated excitonic mode. A longitudinal mode is indeed observed, reaching maximum intensity at qc = 0.5, and is highlighted by red shading in Fig. 2d, e.
In isolation, the presence of a longitudinal magnetic mode in this symmetry channel is a necessary but insufficient condition to establish an antiferromagnetic excitonic insulator, so we leverage the specific symmetry, decay, and temperature dependence of the longitudinal and transverse magnetic modes to establish the presence of the novel state. The only other candidate magnetic model that hosts a longitudinal mode of this type is a specific configuration of the bilayer Heisenberg Hamiltonian, in which the charge degrees of freedom are projected out. In particular, a model with a c-axis magnetic exchange Jc that is larger than, but not dramatically larger than, the in-plane exchange Jab is needed to produce a longitudinal mode and large easy-axis magnetic anisotropy is required to reproduce the spin gap. If JcJab, the spectrum would show only a spin-wave-like in-plane dispersion contrary to the observed qc dependence in Fig. 2c–e, and in the JcJab limit the system would become a quantum paramagnet. For Jc/Jab of order two, the bilayer Heisenberg Hamiltonian supports a longitudinal mode and for the current case of large easy-axis anisotropy, the transverse and longitudinal modes appear as well-defined modes throughout the Brillouin zone13,14,15,16. In fact, earlier reports have proposed this spin dimer model to explain RIXS measurements of the longitudinal ~ 170 meV feature in Sr3Ir2O714, 17. Although prior and subsequent non-dimerized models have also been proposed to describe Sr3Ir2O7 as rival candidates12, 18,19,20,21. These models, however, do not support a longitudinal mode (a detailed comparison between the different models is given in Supplementary Information (SI) Section 1). We, therefore, map the in-plane dispersion relations at qc = 0 and 0.5 and show them in Fig. 3a, b. At qc = 0, where the longitudinal mode is suppressed by symmetry, we observe an excitation dispersing from ~ 90 to 170 meV and a continuum at higher energies. Simultaneously analyzing qc = 0.5 and qc = 0 for each in-plane reciprocal-lattice wavevector, while leveraging the distinct symmetry properties of the longitudinal and transverse modes, allows us to isolate the longitudinal mode (see Methods section). We plot the position and peak width of the longitudinal mode in green in Fig. 3b. The transverse mode, on the other hand, is symmetry-allowed at qc = 0.5 and qc = 0 and is shown in black on Fig. 3a, b. We find that the longitudinal mode is well-defined around (0, 0) (Figs. 2c–d, 3i), but decays into the high-energy continuum as it disperses away, becoming undetectable at (1/4, 1/4) (Fig. 3h). The longitudinal mode is also detectable as a shoulder feature on the transverse mode at (1/2, 1/2) before dispersing upwards and broadening at neighboring momenta (Fig. 3e, g). The decay and merging of the longitudinal mode into the electron-hole continuum was not detected previously and suggests the realization of an antiferromagnetic excitonic insulator state because the longitudinal mode in this model has a bound electron-hole pair character and therefore will necessarily decay when it overlaps with the electron-hole continuum. This longitudinal mode decay is incompatible with a longitudinal mode arising from spin dimer excitations in a strongly isotropic bilayer Heisenberg model, which predicts well-defined modes throughout the Brillouin zone and projects out the high-energy particle-hole continuum13,14,15,16.
Fig. 3: Magnetic dispersion and excitonic longitudinal mode decay.
figure 3
a, b In-plane momentum dependence of the magnetic excitations measured at qc = 0 and 0.5. The black and green symbols correspond to the energy of the magnetic modes and the vertical bars to their peak widths. Both quantities were extracted from the energy spectra at different points in reciprocal space (such as shown in panels e–j and Fig. 2c–e). c and d Theoretical calculations of the magnetic dispersion relation, overplotted with the experimentally determined excitation energies and line widths. The presence of the mode at qc = 0.5 that is absent at qc = 0 evinces that this is an excitonic longitudinal mode. ej RIXS spectra at reciprocal space as highlighted by color-matching arrows in panel a. Circles represent the data and dotted lines outline the different components of the spectrum, which are summed to produce the solid line representing the total spectrum. Error bars are determined via Poissonian statistics. The isolation of the longitudinal mode (highlighted with red shading) from other contributions was possible by simultaneously analyzing qc = 0.5 and qc = 0 for each in-plane reciprocal-lattice wavevector (see Methods section for details).
Since optical conductivity, tunneling spectroscopy, and photo-emission studies all report charge gaps Δc on the same energy scale of magnetic excitations (100–200 meV)11, 22,23,24,25, we model the microscopic interactions within a Hubbard Hamiltonian that retains the charge degree of freedom. In particular, the crucial difference with the Heisenberg description is that the Hubbard model retains the electron-hole continuum, whose lower edge at ω = Δc is below the onset of the two-magnon continuum: Δc < 2Δs. We considered a half-filled bilayer, which includes a single “Jeff = 1/2” effective orbital for each of the two Ir sites in the unit cell, following methods developed in parallel with this experimental study26. The model contains an effective Coulomb repulsion U, and three electron hopping parameters: nearest and next-nearest in-plane hopping terms tν (ν = 1, 2) within each Ir layer, and the spin dependent hopping strength tz(α) between Ir layers (Fig. 2b). tz(α) is composed of an amplitude tz and a phase α arising from the appreciable SOC in the material (further details are given in the Methods section)27. The model was solved using the random phase approximation (RPA) in the thermodynamic limit (SI Section 2), which is valid for intermediately correlated materials even at finite temperature28. We constrain tν and tz to values compatible with density functional theory and photo-emission measurements and consider the effective U, which is strongly influenced by screening, as the primary tuning parameter29. Figure 3c, d show the results of calculations with t1 = 0.115 eV, t2 = 0.012 eV, tz = 0.084 eV, α = 1.41, and U = 0.325 eV. The small U is due to the extended Ir orbitals and because this effective parameterization reflects the difference between on-site and longer-range interactions in the real material. The model identifies the quasiparticle dispersion at qc = 0 as the transverse mode with a persistent well-defined nature even at high energies. Above the transverse mode, the spin response is fundamentally influenced by the finite charge gap. A broad continuum involving electron-hole spin transitions across the charge gap is present for all qc values covering a broad energy-momentum range. A new mode emerges around (0, 0) and (0.5, 0.5) for qc = 0.5, which we identify as the excitonic longitudinal mode.
To understand the excitonic longitudinal mode discussed, we first note that the tight-binding band structure analysis of Sr3Ir2O7 suggests that it would be a narrow-gap band insulator or semi-metal even when Coulomb repulsion is neglected29. This occurs due to bonding-antibonding band splitting arising from the bilayer hopping alongside SOC, generating a minimum of the conduction band dispersion near the Brillouin zone center and a maximum in the valence band dispersion near the antiferromagnetic zone center. A finite value of U in a quasi-two-dimensional bilayer structure such as Sr3Ir2O7 produces an attractive particle-hole interaction in the triplet channel because of the well-known direct-exchange mechanism. In turn, particle-hole pairs at wavevectors favored by the band structure form bound states, i.e., excitons, in the magnetic channel appearing at qc = 0.5, because of the odd parity of the exciton under exchange of the two layers. The spin anisotropy arising from SOC splits the exciton triplet into a low energy state with c-axis spin quantum number Sz = 0 and higher energy Sz = ± 1 states. Strictly speaking, SOC means that total spin is not a good quantum number, but we retain the singlet-triplet labels for clarity. As shown in the schematic representation in Fig. 1, the Sz = 0 exciton condenses to form magnetic order at a wavevector of (0.5, 0.5) (qc = 0.5). The corresponding QCP, which exists at U = Uc = 0.27 eV (for t1 = 0.115 eV), then signals the onset of the antiferromagnetic excitonic insulator state in Sr3Ir2O7. Within the ordered state, what was a gapless Sz = 0 exciton mode at U = Uc becomes a gapped excitonic longitudinal mode for U > Uc. The existence and relatively low energy of this mode implies that U in Sr3Ir2O7 is only slightly above Uc. This property, together with the sufficiently large transverse mode gap Δs, protects the excitonic longitudinal mode from decay into pairs of transverse modes. The longitudinal mode’s bound electron-hole pair nature is especially vividly illustrated by its smooth merging with the particle-hole continuum away from (0.5, 0.5) and (0, 0). We plot the layer-resolved charge structure of the exciton in SI Section 3.
When heating an antiferromagnetic excitonic insulator, thermal fluctuations modify the magnetic properties via two different processes. The first one corresponds to the destruction of Néel order via softening of the longitudinal mode. This softening signals the exciton condensation below T = TN. The second process, that takes place at a higher temperature T*, corresponds to thermal breaking of the excitons (unbinding of particle-hole pairs). A RIXS temperature series designed to test this idea at different high symmetry locations is plotted in Fig. 4a–d (linecuts at selected temperatures are shown in Supplementary Fig. S2). As expected, heating up from base temperature towards TN enhances the decay of the modes into the electron-hole continuum broadening the spectra and making it difficult to isolate the two modes in a single spectrum. We can, however, leverage the symmetry properties of the modes at different reciprocal space points to clarify the soft mode phenomenology. Since the transverse mode occurs at the same energy independent of qc, and the longitudinal mode is present at qc = 0.5 and absent at qc = 0, the transverse mode temperature dependence can be studied in isolation at qc = 0 (Fig. 4a, b). We observe that this mode has only minimal detectable softening, which is expected in view of the Ising nature of magnetism. In contrast, a substantial softening is seen at (0.5, 0.5) in Fig. 4d. Although both modes are present at qc = 0.5, we know from qc = 0 measurements that the transverse mode displays only minimal softening. Thus the longitudinal mode must play a major role in the softening to form the antiferromagnetic state. Our observed phenomenology is only captured with the intermediate coupling regime (U/t1 = 2.83) that we conclude is relevant for Sr3Ir2O7. The strong coupling limit (U/t1 1) would require a charge gap much larger than the observed values of 100–200 meV and, to our knowledge, it has not been able to predict any aspects of the temperature-dependent phenomenology of Sr3Ir2O7. The excitonic insulator model is also supported by our temperature-dependent calculations, which are shown as dashed lines in Fig. 4c, d. Full calculations are shown in Supplementary Fig. S5 and explained in SI Section 2. Theory shows that exciton formation takes place at T* ≈ 2TN, controlled by the exciton binding energy, which is of order the charge gap minus the longitudinal mode energy at the ordering wavevector. The mean-field transition temperature prediction is TN = 424 K, which is not too far above the measured TN = 285 K and which is expected since fluctuations are expected to reduce TN below the mean-field prediction. The predictions in Fig. 4c, d are shown with temperatures re-normalized to the experimental TN.
Fig. 4: Excitonic mode condensation at the Néel temperature.
figure 4
ad Temperature dependence of the Sr3Ir2O7 excitation spectrum at (0, 0) and (0.5, 0.5) for qc = 0 and 0.5 (RIXS spectra at selected temperatures are shown in Supplementary Fig. S2). The intensity at (0.5, 0.5) has been scaled for comparison reasons. The dashed lines show temperature-dependent calculations of our model (the full theoretical predictions are plotted in Supplementary Fig. S5). Based on the qc behavior of the modes, we know that panels a, b show only the transverse mode, while c, d show both the transverse and longitudinal mode. e, f Quasi-elastic intensity as function of temperature for qc = 0 and 0.5 in blue and red, respectively. The non-monotonic enhancement at qc = 0.5 in e provides additional support that the condensation of the excitonic longitudinal mode establishes the magnetic long-range order in Sr3Ir2O7. Panel f also shows the anomalous temperature dependence of the electric resisitivity ρ (taken from30), which shows a change in gradient at TN further indicating that charge fluctuations are involved in the transition.
The involvement of the longitudinal mode in magnetic long-range order is also evident from the temperature dependent quasi-elastic intensity. While most spectra feature the expected gradual enhancement in the quasi-elastic channel upon increasing temperature (Fig. 4e for (0, 0) and S2 for other reciprocal-lattice positions), the (0.5, 0.5) spectrum at qc = 0.5 displays a pronounced rise of intensity around TN (Fig. 4f). Note that neither qc = 0 nor qc = 0.5 correspond to the magnetic Bragg peak location, because the bilayer separation is incommensurate with respect to the c-axis lattice constant. Since in our setup qc = 0 is closer to a magnetic Bragg peak than qc = 0.5, we can exclude critical scattering from the long-range antiferromagnetic order as a significant contributor to this intensity as it would predict the opposite intensity behavior to what we observe (a more extensive demonstration of this is in SI Section 5). Thus the observed quasi-elastic anomaly at TN is indicative of substantial longitudinal mode condensation. The excitonic insulator character of the ground state is further supported by a large increase in resistivity below TN (see Fig. 4f)30, as the condensation of the excitonic mode leads to a reduction in the electronic carriers participating in electrical transport. This property is distinct from what is expected for a strongly-coupled Mott insulator (i.e., the large U limit of Fig. 1) where all charge-related processes are frozen out. The resistivity increase below TN could, in principle, also arise from Slater-type interactions, which can open a charge gap upon magnetic ordering. Sr3Ir2O7, however, lacks strong Fermi surface nesting23,24,25, 29 and is in the intermediately correlated (t1 ~ U) rather than the weakly correlated (t1U) regime, so the Slater mechanism is expected to have minimal relevance.
Discussion
In summary, we have isolated and characterized a longitudinal magnetic mode in Sr3Ir2O7, which merges with the electron-hole continuum at certain points in the Brillouin zone, and which softens upon heating concurrent with a decrease in the material’s resistivity. These properties are consistent with those of an antiferromagnetic excitonic insulator state4. We substantiate this via calculations of a bilayer Hubbard model, in which electron-hole pairs are bound by magnetic exchange interactions between the electron and hole. This consistently explains all the electronic and magnetic properties of Sr3Ir2O7 based on only one free parameter U, since all other parameters are strongly constrained by the electronic band structure of the material. The totality of these results identifies Sr3Ir2O7 as a compelling candidate for the long-sought-after antiferromagnetic excitonic insulator.
Looking to the future, the intrinsically coupled spin and charge degrees of freedom in this state could have the potential for realizing new functionalities31, and suitably tuned material and/or laser-based approaches could realize methods to photo-excited these modes32. Further research on the topic may also include efforts to identify materials closer to the QCP, which in our study occurs at U/t1 = 2.35. This could extend the reciprocal space regions where the excitonic longitudinal mode exists. Another interesting direction would involve identifying excitonic easy-plane, rather than easy-axis, bilayer systems. These would host a different kind of soft excitonic longitudinal mode, often called “Higgs” mode, and could be used to study Higgs decay and renormalization effects in the presence of strong charge fluctuations. Careful selection of materials with multiple active orbitals could realize orbitally-ordered excitonic insulator states. Experimental realizations using chemical substitutions, strained thin films, high pressure, or different bilayer materials, including ruthenates, osmates, and other iridates, may help to answer some of these intriguing questions.
Methods
Samples
Sr3Ir2O7 single crystals were synthesized using the flux method33. Starting materials of IrO2, SrCO3, and SrCl2 6H2O were mixed with a molar ratio of 1:2:20, and heated at 1200 C for 10 h in a platinum crucible. The melt was then cooled to 800°C at a rate of 3 C/h, before quenching to room temperature. We index reciprocal space using a pseudo-tetragonal unit cell with a = b = 3.896 Å and c = 20.88 Å at room temperature.
Resonant inelastic X-ray scattering (RIXS) setup
RIXS spectra were measured at the 27-ID-B station of the Advanced Photon Source at Argonne National Laboratory. The incident x-ray beam was tuned to the Ir L3-edge at 11.215 keV and monochromated using a Si (884) channel-cut monochromator. The exact x-ray energy was refined via resonant energy of a standard IrO2 and the Sr3Ir2O7 sample and was set 3 eV below the resonant edge. Scattered photons were analyzed using a spherically bent diced silicon (844) analyzer with a curvature radius of 2 m. The energy and Q-resolution were 32.0(2) meV and 0.105 Å−1 full-width at half-maximum (FWHM), respectively. A small background contribution arising from air scattering was removed by subtracting a constant value from the measured intensity. The value was determined by fitting the intensity on the energy-gain side of the spectra.
The L values in Fig. 2c–e were chosen such that they correspond to specific reciprocal-lattice positions with respect to the Ir-Ir interlayer spacing (see also Fig. 2a), i.e., G + qc = Ld/c, where G is an integer, qc the reduced c-axis reciprocal lattice position in terms of the Ir-Ir spacing, d = 4.07 Å the shortest Ir-Ir interlayer spacing and c = 20.88 Å the out-of-plane lattice constant. qc equals 0, 0.25 and 0.5 for L = 25.65, 26.95 and 28.25, respectively.
The magnetic dispersions in Fig. 3a, b were measured along (H1, K1, 25.65) and (H2, K2, 28.25) with H1 and K1 ranging between 0.5 and 1 and H2 and K2 between 0 and 0.5. The particular Brillouin zones were chosen to ensure a scattering geometry close to 90, minimizing Thompson scattering. For (0, 0, 25.65), (1, 1, 25.65), (0, 0, 26.92) and (0, 0, 28.25), 2θ = 85.5, 90.2, 90.9 and 96.8, respectively. The sample was aligned in the horizontal (H, H, L) scattering plane, such that both dispersions could be probed through a sample rotation of Δχ ≤ 4.1 relative to the surface normal.
Analysis of the RIXS data
The spectra were analyzed by decomposing them into four components: (1) A quasi-elastic contribution (possibly containing contributions from phonons) which was modeled using a pseudo-Voigt energy resolution function, along with an additional low energy feature, which was modeled using the resolution functions at ± 32 meV, whose relative weights were constrained to follow the Bose factor. (2) The transverse magnetic mode was accounted for by a pseudo-Voigt function multiplied with an error function to capture the high-energy tail arising from the interactions with continuum. The interactions are enhanced when the modes and the continuum are less separated in energy, which leads to a reduced quasiparticle lifetime. In this case, we used a damped harmonic oscillator (with Bose factor) that was convoluted with the resolution function, which was further multiplied by an error function. (3) The longitudinal mode was described by either a pseudo-Voigt function or a damped harmonic oscillator, depending on whether or not it was resolution limited. (4) The magnetic continuum was reproduced using a broad damped harmonic oscillator multiplied by an error function to mimic its onset.
The excitonic longitudinal mode is strongly qc dependent, whereas the transverse magnetic mode and the magnetic continuum vary very weakly with qc. Thus, we analyzed the spectra measured at qc = 0 and qc = 0.5 simultaneously to disentangle the excitonic contribution from the other components. The positions and lineshapes of the transverse magnetic mode and the electron-hole magnetic continuum were constrained to be independent of qc, i.e., only the amplitudes were varied. The extra peaks at qc = 0.5 give information about the excitonic longitudinal mode. During the procedure, the elastic energy was allowed to vary to correct for small fluctuations of the incident energy.
Theoretical model
Sr3Ir2O7 hosts Ir4+ ions, which have 5 electrons in the active Ir 5d5 valance band. The dominant splitting of this band comes from the close-to-cubic crystal field leaving empty eg states and 5 electrons in the t2g states. SOC further splits the t2g manifold into a full Jeff = 3/2 orbital a half-filled Jeff = 1/2 orbital at the Fermi level34. Our model involves projecting the band structure onto this Jeff = 1/2 doublet. The basic structural unit, shown in Fig. 2b, contains two Ir atoms, so the experimental data were interpreted using a half-filled bilayer Hubbard model H = − HK + HI with HI = Urnrnr and
$${H}_{{{{{{{{\rm{K}}}}}}}}}=\mathop{\sum}\limits_{{{{{{{{\boldsymbol{r}}}}}}}},{{{{{{{{\boldsymbol{\delta }}}}}}}}}_{\nu }}{t}_{\nu }{c}_{{{{{{{{\boldsymbol{r}}}}}}}}}^{{{{\dagger}}} }{c}_{{{{{{{{\boldsymbol{r}}}}}}}}+{{{{{{{{\boldsymbol{\delta }}}}}}}}}_{\nu }}+\mathop{\sum}\limits_{{{{{{{{{\boldsymbol{r}}}}}}}}}_{\perp }}{c}_{({{{{{{{{\boldsymbol{r}}}}}}}}}_{\perp },1)}^{{{{\dagger}}} }{t}_{z}(\alpha ){c}_{({{{{{{{{\boldsymbol{r}}}}}}}}}_{\perp },2)}+{{{{{{{\rm{H}}}}}}}}.{{{{{{{\rm{c}}}}}}}}.,$$
(1)
where tν (ν = 1, 2) are the nearest- and next-nearest-neighbor hopping amplitudes within the square lattice of each Ir-layer, and \({t}_{z}(\alpha )=| {t}_{z}| {e}^{i\frac{\alpha }{2}{\varepsilon }_{{{{{{{{\boldsymbol{r}}}}}}}}}{\sigma }_{z}}\), with σz the Pauli matrix describes the Jeff spin dependent hopping strength between layers. The overall phase was chosen to gauge away the phase for tν. The operator \({c}_{{{{{{{{\boldsymbol{r}}}}}}}}}^{{{{\dagger}}} }\) = [\({c}_{\uparrow ,{{{{{{{\boldsymbol{r}}}}}}}}}^{{{{\dagger}}} }\), \({c}_{\downarrow ,{{{{{{{\boldsymbol{r}}}}}}}}}^{{{{\dagger}}} }\)] creates the Nambu spinor of the electron field at r = (r, l) with l = 1, 2 denoting the layer index and r = r1a1 + r2a2. Here, the primitive in-plane lattice vectors are denoted by a1 and a2, and the directed neighboring bonds are represented by δ1 = a1, a2 and δ2 = a1 ± a2. In the interaction term HI, U is the effective Coulomb interaction, and nrσ is the density operator for electrons of spin σ at r. In the spin dependent hopping term, the sign εr takes the values ± 1 depending on which sublattice of the bipartite bilayer system r points to. The phase α arises from hopping matrix elements between dxz and dyz orbitals, which are allowed through the staggered octahedral rotations in the unit cell along side SOC27, 35. In the model, SOC enters via the phase of the c-axis hopping, which is smaller than the in-plane bandwidth, justifying the approximate use of singlet and triplet for labels of the different excitons. The model was studied at half-filling in the sense that it contains two bands (bonding and antibonding) in the model, which host two electrons as is appropriate for Sr3Ir2O723,24,25, 27. We solved the model using the RPA in the thermodynamic limit (detailed information is given in SI Section 2), which is valid for intermediately correlated materials even at finite temperatures28. The theoretically determined Néel temperature, in this case, is \({T}_{\,{{\mbox{N}}}}^{{{\mbox{cal}}}\,}=424\) K which is slightly larger than the experimental value TN = 285 K. This is expected within the RPA we use here, as this ignores fluctuations than act to reduce the transition temperature. The dynamical spin structure factors in Fig. 3c, d are shown after convolution with the experimental resolution.
A more complex model could include all t2g or all d orbitals, rather than just effective Jeff = 1/2 doublets. The success of our Jeff = 1/2 only model suggests that orbital degrees of freedom are entirely frozen out of the problem or manifest themselves in very subtle ways beyond current detection limits. Due to this, the Sr3Ir2O7 excitonic insulator state has no orbital component (other than in the trivial sense that the Jeff = 1/2 states in themselves are a coupled modulation of spin and orbital angular momentum). A possible SOC-induced orbital order is discussed in SI Section 6.
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Approximate Vanishing Ideal Computations at Scale
Elias Wirth · Hiroshi Kera · Sebastian Pokutta
MH1-2-3-4 #83
Keywords: [ General Machine Learning ] [ Hessian matrix ] [ approximate vanishing ideal ] [ conditional gradients algorithms ] [ convex optimization ]
Abstract: The vanishing ideal of a set of points $X = \{\mathbf{x}_1, \ldots, \mathbf{x}_m\}\subseteq \mathbb{R}^n$ is the set of polynomials that evaluate to $0$ over all points $\mathbf{x} \in X$ and admits an efficient representation by a finite subset of generators. In practice, to accommodate noise in the data, algorithms that construct generators of the approximate vanishing ideal are widely studied but their computational complexities remain expensive. In this paper, we scale up the oracle approximate vanishing ideal algorithm (OAVI), the only generator-constructing algorithm with known learning guarantees. We prove that the computational complexity of OAVI is not superlinear, as previously claimed, but linear in the number of samples $m$. In addition, we propose two modifications that accelerate OAVI's training time: Our analysis reveals that replacing the pairwise conditional gradients algorithm, one of the solvers used in OAVI, with the faster blended pairwise conditional gradients algorithm leads to an exponential speed-up in the number of features $n$. Finally, using a new inverse Hessian boosting approach, intermediate convex optimization problems can be solved almost instantly, improving OAVI's training time by multiple orders of magnitude in a variety of numerical experiments.
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Sections
Class Phalcon\Filter\Exception
Source on GitHub
Namespace Phalcon\Filter Extends \Exception
Phalcon\Filter\Exception
Exceptions thrown in Phalcon\Filter will use this class
Class Phalcon\Filter\Filter
Source on GitHub
Namespace Phalcon\Filter Implements FilterInterface
Lazy loads, stores and exposes sanitizer objects
Constants
const FILTER_ABSINT = absint;
const FILTER_ALNUM = alnum;
const FILTER_ALPHA = alpha;
const FILTER_BOOL = bool;
const FILTER_EMAIL = email;
const FILTER_FLOAT = float;
const FILTER_INT = int;
const FILTER_LOWER = lower;
const FILTER_LOWERFIRST = lowerfirst;
const FILTER_REGEX = regex;
const FILTER_REMOVE = remove;
const FILTER_REPLACE = replace;
const FILTER_SPECIAL = special;
const FILTER_SPECIALFULL = specialfull;
const FILTER_STRING = string;
const FILTER_STRING_LEGACY = stringlegacy;
const FILTER_STRIPTAGS = striptags;
const FILTER_TRIM = trim;
const FILTER_UPPER = upper;
const FILTER_UPPERFIRST = upperfirst;
const FILTER_UPPERWORDS = upperwords;
const FILTER_URL = url;
Properties
/**
* @var array
*/
protected mapper;
/**
* @var array
*/
protected services;
Methods
public function __call( string $name, array $args );
Magic call to make the helper objects available as methods.
public function __construct( array $mapper = [] );
Filter constructor.
public function get( string $name ): mixed;
Get a service. If it is not in the mapper array, create a new object, set it and then return it.
public function has( string $name ): bool;
Checks if a service exists in the map array
public function sanitize( mixed $value, mixed $sanitizers, bool $noRecursive = bool ): mixed;
Sanitizes a value with a specified single or set of sanitizers
public function set( string $name, mixed $service ): void;
Set a new service to the mapper array
protected function init( array $mapper ): void;
Loads the objects in the internal mapper array
Class Phalcon\Filter\FilterFactory
Source on GitHub
Namespace Phalcon\Filter Uses Phalcon\Filter\Filter
Class FilterFactory
@package Phalcon\Filter
Methods
public function newInstance(): FilterInterface;
Returns a Locator object with all the helpers defined in anonymous functions
protected function getServices(): array;
Returns the available adapters
Interface Phalcon\Filter\FilterInterface
Source on GitHub
Namespace Phalcon\Filter
Lazy loads, stores and exposes sanitizer objects
Methods
public function sanitize( mixed $value, mixed $sanitizers, bool $noRecursive = bool ): mixed;
Sanitizes a value with a specified single or set of sanitizers
Class Phalcon\Filter\Sanitize\AbsInt
Source on GitHub
Namespace Phalcon\Filter\Sanitize
Phalcon\Filter\Sanitize\AbsInt
Sanitizes a value to absolute integer
Methods
public function __invoke( mixed $input );
Class Phalcon\Filter\Sanitize\Alnum
Source on GitHub
Namespace Phalcon\Filter\Sanitize
Phalcon\Filter\Sanitize\Alnum
Sanitizes a value to an alphanumeric value
Methods
public function __invoke( mixed $input );
Class Phalcon\Filter\Sanitize\Alpha
Source on GitHub
Namespace Phalcon\Filter\Sanitize
Phalcon\Filter\Sanitize\Alpha
Sanitizes a value to an alpha value
Methods
public function __invoke( mixed $input );
Class Phalcon\Filter\Sanitize\BoolVal
Source on GitHub
Namespace Phalcon\Filter\Sanitize
Phalcon\Filter\Sanitize\BoolVal
Sanitizes a value to boolean
Methods
public function __invoke( mixed $input );
Class Phalcon\Filter\Sanitize\Email
Source on GitHub
Namespace Phalcon\Filter\Sanitize
Phalcon\Filter\Sanitize\Email
Sanitizes an email string
Methods
public function __invoke( mixed $input );
Class Phalcon\Filter\Sanitize\FloatVal
Source on GitHub
Namespace Phalcon\Filter\Sanitize
Phalcon\Filter\Sanitize\FloatVal
Sanitizes a value to float
Methods
public function __invoke( mixed $input );
Class Phalcon\Filter\Sanitize\IntVal
Source on GitHub
Namespace Phalcon\Filter\Sanitize
Phalcon\Filter\Sanitize\IntVal
Sanitizes a value to integer
Methods
public function __invoke( mixed $input );
Class Phalcon\Filter\Sanitize\Lower
Source on GitHub
Namespace Phalcon\Filter\Sanitize
Phalcon\Filter\Sanitize\Lower
Sanitizes a value to lowercase
Methods
public function __invoke( string $input );
Class Phalcon\Filter\Sanitize\LowerFirst
Source on GitHub
Namespace Phalcon\Filter\Sanitize
Phalcon\Filter\Sanitize\LowerFirst
Sanitizes a value to lcfirst
Methods
public function __invoke( string $input );
Class Phalcon\Filter\Sanitize\Regex
Source on GitHub
Namespace Phalcon\Filter\Sanitize
Phalcon\Filter\Sanitize\Regex
Sanitizes a value performing preg_replace
Methods
public function __invoke( mixed $input, mixed $pattern, mixed $replace );
Class Phalcon\Filter\Sanitize\Remove
Source on GitHub
Namespace Phalcon\Filter\Sanitize
Phalcon\Filter\Sanitize\Remove
Sanitizes a value removing parts of a string
Methods
public function __invoke( mixed $input, mixed $replace );
Class Phalcon\Filter\Sanitize\Replace
Source on GitHub
Namespace Phalcon\Filter\Sanitize
Phalcon\Filter\Sanitize\Replace
Sanitizes a value replacing parts of a string
Methods
public function __invoke( mixed $input, mixed $from, mixed $to );
Class Phalcon\Filter\Sanitize\Special
Source on GitHub
Namespace Phalcon\Filter\Sanitize
Phalcon\Filter\Sanitize\Special
Sanitizes a value special characters
Methods
public function __invoke( mixed $input );
Class Phalcon\Filter\Sanitize\SpecialFull
Source on GitHub
Namespace Phalcon\Filter\Sanitize
Phalcon\Filter\Sanitize\SpecialFull
Sanitizes a value special characters (htmlspecialchars() and ENT_QUOTES)
Methods
public function __invoke( mixed $input );
Class Phalcon\Filter\Sanitize\StringVal
Source on GitHub
Namespace Phalcon\Filter\Sanitize
Sanitizes a value to string
Methods
public function __invoke( string $input, int $flags = int ): string;
Class Phalcon\Filter\Sanitize\StringValLegacy
Source on GitHub
Namespace Phalcon\Filter\Sanitize
Sanitizes a value to string using filter_var(). The filter provides backwards compatibility with versions prior to v5. For PHP higher or equal to 8.1, the filter will remain the string unchanged. If anything other than a string is passed, the method will return false
Methods
public function __invoke( mixed $input );
Class Phalcon\Filter\Sanitize\Striptags
Source on GitHub
Namespace Phalcon\Filter\Sanitize
Phalcon\Filter\Sanitize\Striptags
Sanitizes a value striptags
Methods
public function __invoke( string $input );
Class Phalcon\Filter\Sanitize\Trim
Source on GitHub
Namespace Phalcon\Filter\Sanitize
Phalcon\Filter\Sanitize\Trim
Sanitizes a value removing leading and trailing spaces
Methods
public function __invoke( string $input );
Class Phalcon\Filter\Sanitize\Upper
Source on GitHub
Namespace Phalcon\Filter\Sanitize
Phalcon\Filter\Sanitize\Upper
Sanitizes a value to uppercase
Methods
public function __invoke( string $input );
Class Phalcon\Filter\Sanitize\UpperFirst
Source on GitHub
Namespace Phalcon\Filter\Sanitize
Phalcon\Filter\Sanitize\UpperFirst
Sanitizes a value to ucfirst
Methods
public function __invoke( string $input );
Class Phalcon\Filter\Sanitize\UpperWords
Source on GitHub
Namespace Phalcon\Filter\Sanitize
Phalcon\Filter\Sanitize\UpperWords
Sanitizes a value to uppercase the first character of each word
Methods
public function __invoke( string $input );
Class Phalcon\Filter\Sanitize\Url
Source on GitHub
Namespace Phalcon\Filter\Sanitize
Phalcon\Filter\Sanitize\Url
Sanitizes a value url
Methods
public function __invoke( mixed $input );
Class Phalcon\Filter\Validation
Source on GitHub
Namespace Phalcon\Filter Uses Phalcon\Di\Di, Phalcon\Di\DiInterface, Phalcon\Di\Injectable, Phalcon\Filter\FilterInterface, Phalcon\Messages\MessageInterface, Phalcon\Messages\Messages, Phalcon\Filter\Validation\ValidationInterface, Phalcon\Filter\Validation\Exception, Phalcon\Filter\Validation\ValidatorInterface, Phalcon\Filter\Validation\AbstractCombinedFieldsValidator Extends Injectable Implements ValidationInterface
Allows to validate data using custom or built-in validators
Properties
/**
* @var array
*/
protected combinedFieldsValidators;
/**
* @var mixed
*/
protected data;
/**
* @var object|null
*/
protected entity;
/**
* @var array
*/
protected filters;
/**
* @var array
*/
protected labels;
/**
* @var Messages|null
*/
protected messages;
/**
* List of validators
*
* @var array
*/
protected validators;
/**
* Calculated values
*
* @var array
*/
protected values;
Methods
public function __construct( array $validators = [] );
Phalcon\Filter\Validation constructor
public function add( mixed $field, ValidatorInterface $validator ): ValidationInterface;
Adds a validator to a field
public function appendMessage( MessageInterface $message ): ValidationInterface;
Appends a message to the messages list
public function bind( mixed $entity, mixed $data ): ValidationInterface;
Assigns the data to an entity The entity is used to obtain the validation values
public function getData(): mixed;
public function getEntity(): mixed;
Returns the bound entity
public function getFilters( string $field = null ): mixed | null;
Returns all the filters or a specific one
public function getLabel( mixed $field ): string;
Get label for field
public function getMessages(): Messages;
Returns the registered validators
public function getValidators(): array;
Returns the validators added to the validation
public function getValue( string $field ): mixed | null;
Gets the a value to validate in the array/object data source
public function getValueByData( mixed $data, string $field ): mixed | null;
Gets the a value to validate in the array/object data source
public function getValueByEntity( mixed $entity, string $field ): mixed | null;
Gets the a value to validate in the object entity source
public function rule( mixed $field, ValidatorInterface $validator ): ValidationInterface;
Alias of add method
public function rules( mixed $field, array $validators ): ValidationInterface;
Adds the validators to a field
public function setEntity( mixed $entity ): void;
Sets the bound entity
public function setFilters( mixed $field, mixed $filters ): ValidationInterface;
Adds filters to the field
public function setLabels( array $labels ): void;
Adds labels for fields
public function setValidators( array $validators ): Validation;
public function validate( mixed $data = null, mixed $entity = null ): Messages;
Validate a set of data according to a set of rules
protected function preChecking( mixed $field, ValidatorInterface $validator ): bool;
Internal validations, if it returns true, then skip the current validator
Abstract Class Phalcon\Filter\Validation\AbstractCombinedFieldsValidator
Source on GitHub
Namespace Phalcon\Filter\Validation Extends AbstractValidator
This is a base class for combined fields validators
Abstract Class Phalcon\Filter\Validation\AbstractValidator
Source on GitHub
Namespace Phalcon\Filter\Validation Uses Phalcon\Support\Helper\Arr\Whitelist, Phalcon\Messages\Message, Phalcon\Filter\Validation Implements ValidatorInterface
This is a base class for validators
Properties
/**
* Message template
*
* @var string|null
*/
protected template;
/**
* Message templates
*
* @var array
*/
protected templates;
/**
* @var array
*/
protected options;
Methods
public function __construct( array $options = [] );
Phalcon\Filter\Validation\Validator constructor
public function getOption( string $key, mixed $defaultValue = null ): mixed;
Returns an option in the validator’s options Returns null if the option hasn’t set
public function getTemplate( string $field = null ): string;
Get the template message
public function getTemplates(): array;
Get templates collection object
public function hasOption( string $key ): bool;
Checks if an option is defined
public function messageFactory( Validation $validation, mixed $field, array $replacements = [] ): Message;
Create a default message by factory
public function setOption( string $key, mixed $value ): void;
Sets an option in the validator
public function setTemplate( string $template ): ValidatorInterface;
Set a new template message
public function setTemplates( array $templates ): ValidatorInterface;
Clear current templates and set new from an array,
abstract public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
protected function allowEmpty( mixed $field, mixed $value ): bool;
Checks if field can be empty.
protected function prepareCode( string $field ): int;
Prepares a validation code.
protected function prepareLabel( Validation $validation, string $field ): mixed;
Prepares a label for the field.
Abstract Class Phalcon\Filter\Validation\AbstractValidatorComposite
Source on GitHub
Namespace Phalcon\Filter\Validation Uses Phalcon\Filter\Validation Extends AbstractValidator Implements ValidatorCompositeInterface
This is a base class for combined fields validators
Properties
/**
* @var array
*/
protected validators;
Methods
public function getValidators(): array;
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
Class Phalcon\Filter\Validation\Exception
Source on GitHub
Namespace Phalcon\Filter\Validation Extends \Exception
Exceptions thrown in Phalcon\Filter\Validation* classes will use this class
Interface Phalcon\Filter\Validation\ValidationInterface
Source on GitHub
Namespace Phalcon\Filter\Validation Uses Phalcon\Di\Injectable, Phalcon\Messages\MessageInterface, Phalcon\Messages\Messages
Interface for the Phalcon\Filter\Validation component
Methods
public function add( mixed $field, ValidatorInterface $validator ): ValidationInterface;
Adds a validator to a field
public function appendMessage( MessageInterface $message ): ValidationInterface;
Appends a message to the messages list
public function bind( mixed $entity, mixed $data ): ValidationInterface;
Assigns the data to an entity The entity is used to obtain the validation values
public function getEntity(): mixed;
Returns the bound entity
public function getFilters( string $field = null ): mixed | null;
Returns all the filters or a specific one
public function getLabel( string $field ): string;
Get label for field
public function getMessages(): Messages;
Returns the registered validators
public function getValidators(): array;
Returns the validators added to the validation
public function getValue( string $field ): mixed | null;
Gets the a value to validate in the array/object data source
public function rule( mixed $field, ValidatorInterface $validator ): ValidationInterface;
Alias of add method
public function rules( string $field, array $validators ): ValidationInterface;
Adds the validators to a field
public function setFilters( string $field, mixed $filters ): ValidationInterface;
Adds filters to the field
public function setLabels( array $labels ): void;
Adds labels for fields
public function validate( mixed $data = null, mixed $entity = null ): Messages;
Validate a set of data according to a set of rules
Class Phalcon\Filter\Validation\Validator\Alnum
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator Uses Phalcon\Filter\Validation, Phalcon\Filter\Validation\AbstractValidator Extends AbstractValidator
Check for alphanumeric character(s)
use Phalcon\Filter\Validation;
use Phalcon\Filter\Validation\Validator\Alnum as AlnumValidator;
$validator = new Validation();
$validator->add(
"username",
new AlnumValidator(
[
"message" => ":field must contain only alphanumeric characters",
]
)
);
$validator->add(
[
"username",
"name",
],
new AlnumValidator(
[
"message" => [
"username" => "username must contain only alphanumeric characters",
"name" => "name must contain only alphanumeric characters",
],
]
)
);
Properties
//
protected template = Field :field must contain only letters and numbers;
Methods
public function __construct( array $options = [] );
Constructor
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
Class Phalcon\Filter\Validation\Validator\Alpha
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator Uses Phalcon\Messages\Message, Phalcon\Filter\Validation, Phalcon\Filter\Validation\AbstractValidator Extends AbstractValidator
Check for alphabetic character(s)
use Phalcon\Filter\Validation;
use Phalcon\Filter\Validation\Validator\Alpha as AlphaValidator;
$validator = new Validation();
$validator->add(
"username",
new AlphaValidator(
[
"message" => ":field must contain only letters",
]
)
);
$validator->add(
[
"username",
"name",
],
new AlphaValidator(
[
"message" => [
"username" => "username must contain only letters",
"name" => "name must contain only letters",
],
]
)
);
Properties
//
protected template = Field :field must contain only letters;
Methods
public function __construct( array $options = [] );
Constructor
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
Class Phalcon\Filter\Validation\Validator\Between
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator Uses Phalcon\Messages\Message, Phalcon\Filter\Validation, Phalcon\Filter\Validation\AbstractValidator Extends AbstractValidator
Validates that a value is between an inclusive range of two values. For a value x, the test is passed if minimum<=x<=maximum.
use Phalcon\Filter\Validation;
use Phalcon\Filter\Validation\Validator\Between;
$validator = new Validation();
$validator->add(
"price",
new Between(
[
"minimum" => 0,
"maximum" => 100,
"message" => "The price must be between 0 and 100",
]
)
);
$validator->add(
[
"price",
"amount",
],
new Between(
[
"minimum" => [
"price" => 0,
"amount" => 0,
],
"maximum" => [
"price" => 100,
"amount" => 50,
],
"message" => [
"price" => "The price must be between 0 and 100",
"amount" => "The amount must be between 0 and 50",
],
]
)
);
Properties
//
protected template = Field :field must be within the range of :min to :max;
Methods
public function __construct( array $options = [] );
Constructor
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
Class Phalcon\Filter\Validation\Validator\Callback
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator Uses Phalcon\Messages\Message, Phalcon\Filter\Validation, Phalcon\Filter\Validation\ValidatorInterface, Phalcon\Filter\Validation\AbstractValidator Extends AbstractValidator
Calls user function for validation
use Phalcon\Filter\Validation;
use Phalcon\Filter\Validation\Validator\Callback as CallbackValidator;
use Phalcon\Filter\Validation\Validator\Numericality as NumericalityValidator;
$validator = new Validation();
$validator->add(
["user", "admin"],
new CallbackValidator(
[
"message" => "There must be only an user or admin set",
"callback" => function($data) {
if (!empty($data->getUser()) && !empty($data->getAdmin())) {
return false;
}
return true;
}
]
)
);
$validator->add(
"amount",
new CallbackValidator(
[
"callback" => function($data) {
if (!empty($data->getProduct())) {
return new NumericalityValidator(
[
"message" => "Amount must be a number."
]
);
}
}
]
)
);
Properties
//
protected template = Field :field must match the callback function;
Methods
public function __construct( array $options = [] );
Constructor
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
Class Phalcon\Filter\Validation\Validator\Confirmation
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator Uses Phalcon\Messages\Message, Phalcon\Filter\Validation, Phalcon\Filter\Validation\Exception, Phalcon\Filter\Validation\AbstractValidator Extends AbstractValidator
Checks that two values have the same value
use Phalcon\Filter\Validation;
use Phalcon\Filter\Validation\Validator\Confirmation;
$validator = new Validation();
$validator->add(
"password",
new Confirmation(
[
"message" => "Password doesn't match confirmation",
"with" => "confirmPassword",
]
)
);
$validator->add(
[
"password",
"email",
],
new Confirmation(
[
"message" => [
"password" => "Password doesn't match confirmation",
"email" => "Email doesn't match confirmation",
],
"with" => [
"password" => "confirmPassword",
"email" => "confirmEmail",
],
]
)
);
Properties
//
protected template = Field :field must be the same as :with;
Methods
public function __construct( array $options = [] );
Constructor
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
final protected function compare( string $a, string $b ): bool;
Compare strings
Class Phalcon\Filter\Validation\Validator\CreditCard
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator Uses Phalcon\Messages\Message, Phalcon\Filter\Validation, Phalcon\Filter\Validation\AbstractValidator Extends AbstractValidator
Checks if a value has a valid credit card number
use Phalcon\Filter\Validation;
use Phalcon\Filter\Validation\Validator\CreditCard as CreditCardValidator;
$validator = new Validation();
$validator->add(
"creditCard",
new CreditCardValidator(
[
"message" => "The credit card number is not valid",
]
)
);
$validator->add(
[
"creditCard",
"secondCreditCard",
],
new CreditCardValidator(
[
"message" => [
"creditCard" => "The credit card number is not valid",
"secondCreditCard" => "The second credit card number is not valid",
],
]
)
);
Properties
//
protected template = Field :field is not valid for a credit card number;
Methods
public function __construct( array $options = [] );
Constructor
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
Class Phalcon\Filter\Validation\Validator\Date
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator Uses DateTime, Phalcon\Messages\Message, Phalcon\Filter\Validation, Phalcon\Filter\Validation\AbstractValidator Extends AbstractValidator
Checks if a value is a valid date
use Phalcon\Filter\Validation;
use Phalcon\Filter\Validation\Validator\Date as DateValidator;
$validator = new Validation();
$validator->add(
"date",
new DateValidator(
[
"format" => "d-m-Y",
"message" => "The date is invalid",
]
)
);
$validator->add(
[
"date",
"anotherDate",
],
new DateValidator(
[
"format" => [
"date" => "d-m-Y",
"anotherDate" => "Y-m-d",
],
"message" => [
"date" => "The date is invalid",
"anotherDate" => "The another date is invalid",
],
]
)
);
Properties
//
protected template = Field :field is not a valid date;
Methods
public function __construct( array $options = [] );
Constructor
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
Class Phalcon\Filter\Validation\Validator\Digit
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator Uses Phalcon\Messages\Message, Phalcon\Filter\Validation, Phalcon\Filter\Validation\AbstractValidator Extends AbstractValidator
Check for numeric character(s)
use Phalcon\Filter\Validation;
use Phalcon\Filter\Validation\Validator\Digit as DigitValidator;
$validator = new Validation();
$validator->add(
"height",
new DigitValidator(
[
"message" => ":field must be numeric",
]
)
);
$validator->add(
[
"height",
"width",
],
new DigitValidator(
[
"message" => [
"height" => "height must be numeric",
"width" => "width must be numeric",
],
]
)
);
Properties
//
protected template = Field :field must be numeric;
Methods
public function __construct( array $options = [] );
Constructor
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
Class Phalcon\Filter\Validation\Validator\Email
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator Uses Phalcon\Messages\Message, Phalcon\Filter\Validation, Phalcon\Filter\Validation\AbstractValidator Extends AbstractValidator
Checks if a value has a correct e-mail format
use Phalcon\Filter\Validation;
use Phalcon\Filter\Validation\Validator\Email as EmailValidator;
$validator = new Validation();
$validator->add(
"email",
new EmailValidator(
[
"message" => "The e-mail is not valid",
]
)
);
$validator->add(
[
"email",
"anotherEmail",
],
new EmailValidator(
[
"message" => [
"email" => "The e-mail is not valid",
"anotherEmail" => "The another e-mail is not valid",
],
]
)
);
Properties
//
protected template = Field :field must be an email address;
Methods
public function __construct( array $options = [] );
Constructor
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
Class Phalcon\Filter\Validation\Validator\Exception
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator Extends \Exception
Exceptions thrown in Phalcon\Filter\Validation\Validator* classes will use this class
Class Phalcon\Filter\Validation\Validator\ExclusionIn
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator Uses Phalcon\Messages\Message, Phalcon\Filter\Validation, Phalcon\Filter\Validation\AbstractValidator, Phalcon\Filter\Validation\Exception Extends AbstractValidator
Check if a value is not included into a list of values
use Phalcon\Filter\Validation;
use Phalcon\Filter\Validation\Validator\ExclusionIn;
$validator = new Validation();
$validator->add(
"status",
new ExclusionIn(
[
"message" => "The status must not be A or B",
"domain" => [
"A",
"B",
],
]
)
);
$validator->add(
[
"status",
"type",
],
new ExclusionIn(
[
"message" => [
"status" => "The status must not be A or B",
"type" => "The type must not be 1 or "
],
"domain" => [
"status" => [
"A",
"B",
],
"type" => [1, 2],
],
]
)
);
Properties
//
protected template = Field :field must not be a part of list: :domain;
Methods
public function __construct( array $options = [] );
Constructor
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
Class Phalcon\Filter\Validation\Validator\File
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator Uses Phalcon\Messages\Message, Phalcon\Support\Helper\Arr\Get, Phalcon\Filter\Validation, Phalcon\Filter\Validation\AbstractValidatorComposite, Phalcon\Filter\Validation\Validator\File\MimeType, Phalcon\Filter\Validation\Validator\File\Resolution\Equal, Phalcon\Filter\Validation\Validator\File\Resolution\Max, Phalcon\Filter\Validation\Validator\File\Resolution\Min, Phalcon\Filter\Validation\Validator\File\Size\Equal, Phalcon\Filter\Validation\Validator\File\Size\Max, Phalcon\Filter\Validation\Validator\File\Size\Min Extends AbstractValidatorComposite
Checks if a value has a correct file
use Phalcon\Filter\Validation;
use Phalcon\Filter\Validation\Validator\File as FileValidator;
$validator = new Validation();
$validator->add(
"file",
new FileValidator(
[
"maxSize" => "2M",
"messageSize" => ":field exceeds the max file size (:size)",
"allowedTypes" => [
"image/jpeg",
"image/png",
],
"messageType" => "Allowed file types are :types",
"maxResolution" => "800x600",
"messageMaxResolution" => "Max resolution of :field is :resolution",
"messageFileEmpty" => "File is empty",
"messageIniSize" => "Ini size is not valid",
"messageValid" => "File is not valid",
]
)
);
$validator->add(
[
"file",
"anotherFile",
],
new FileValidator(
[
"maxSize" => [
"file" => "2M",
"anotherFile" => "4M",
],
"messageSize" => [
"file" => "file exceeds the max file size 2M",
"anotherFile" => "anotherFile exceeds the max file size 4M",
"allowedTypes" => [
"file" => [
"image/jpeg",
"image/png",
],
"anotherFile" => [
"image/gif",
"image/bmp",
],
],
"messageType" => [
"file" => "Allowed file types are image/jpeg and image/png",
"anotherFile" => "Allowed file types are image/gif and image/bmp",
],
"maxResolution" => [
"file" => "800x600",
"anotherFile" => "1024x768",
],
"messageMaxResolution" => [
"file" => "Max resolution of file is 800x600",
"anotherFile" => "Max resolution of file is 1024x768",
],
]
)
);
Methods
public function __construct( array $options = [] );
Constructor
Abstract Class Phalcon\Filter\Validation\Validator\File\AbstractFile
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator\File Uses Phalcon\Messages\Message, Phalcon\Filter\Validation, Phalcon\Filter\Validation\AbstractValidator Extends AbstractValidator
Checks if a value has a correct file
use Phalcon\Filter\Validation;
use Phalcon\Filter\Validation\Validator\File\Size;
$validator = new Validation();
$validator->add(
"file",
new Size(
[
"maxSize" => "2M",
"messageSize" => ":field exceeds the max file size (:size)",
]
)
);
$validator->add(
[
"file",
"anotherFile",
],
new FileValidator(
[
"maxSize" => [
"file" => "2M",
"anotherFile" => "4M",
],
"messageSize" => [
"file" => "file exceeds the max file size 2M",
"anotherFile" => "anotherFile exceeds the max file size 4M",
],
]
)
);
Properties
/**
* Empty is empty
*
* @var string
*/
protected messageFileEmpty = Field :field must not be empty;
/**
* File exceeds the file size set in PHP configuration
*
* @var string
*/
protected messageIniSize = File :field exceeds the maximum file size;
/**
* File is not valid
*
* @var string
*/
protected messageValid = Field :field is not valid;
Methods
public function checkUpload( Validation $validation, mixed $field ): bool;
Check upload
public function checkUploadIsEmpty( Validation $validation, mixed $field ): bool;
Check if upload is empty
public function checkUploadIsValid( Validation $validation, mixed $field ): bool;
Check if upload is valid
public function checkUploadMaxSize( Validation $validation, mixed $field ): bool;
Check if uploaded file is larger than PHP allowed size
public function getFileSizeInBytes( string $size ): double;
Convert a string like “2.5MB” in bytes
public function getMessageFileEmpty(): string;
Empty is empty
public function getMessageIniSize(): string;
File exceeds the file size set in PHP configuration
public function getMessageValid(): string;
File is not valid
public function isAllowEmpty( Validation $validation, string $field ): bool;
Check on empty
public function setMessageFileEmpty( string $message ): void;
Empty is empty
public function setMessageIniSize( string $message ): void;
File exceeds the file size set in PHP configuration
public function setMessageValid( string $message ): void;
File is not valid
protected function checkIsUploadedFile( string $name ): bool;
Checks if a file has been uploaded; Internal check that can be overriden in a subclass if you do not want to check uploaded files
Class Phalcon\Filter\Validation\Validator\File\MimeType
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator\File Uses Phalcon\Messages\Message, Phalcon\Filter\Validation, Phalcon\Filter\Validation\Exception Extends AbstractFile
Checks if a value has a correct file mime type
use Phalcon\Filter\Validation;
use Phalcon\Filter\Validation\Validator\File\MimeType;
$validator = new Validation();
$validator->add(
"file",
new MimeType(
[
"types" => [
"image/jpeg",
"image/png",
],
"message" => "Allowed file types are :types"
]
)
);
$validator->add(
[
"file",
"anotherFile",
],
new MimeType(
[
"types" => [
"file" => [
"image/jpeg",
"image/png",
],
"anotherFile" => [
"image/gif",
"image/bmp",
],
],
"message" => [
"file" => "Allowed file types are image/jpeg and image/png",
"anotherFile" => "Allowed file types are image/gif and image/bmp",
]
]
)
);
Properties
//
protected template = File :field must be of type: :types;
Methods
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
Class Phalcon\Filter\Validation\Validator\File\Resolution\Equal
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator\File\Resolution Uses Phalcon\Messages\Message, Phalcon\Filter\Validation, Phalcon\Filter\Validation\Validator\File\AbstractFile Extends AbstractFile
Checks if a file has the right resolution
use Phalcon\Filter\Validation;
use Phalcon\Filter\Validation\Validator\File\Resolution\Equal;
$validator = new Validation();
$validator->add(
"file",
new Equal(
[
"resolution" => "800x600",
"message" => "The resolution of the field :field has to be equal :resolution",
]
)
);
$validator->add(
[
"file",
"anotherFile",
],
new Equal(
[
"resolution" => [
"file" => "800x600",
"anotherFile" => "1024x768",
],
"message" => [
"file" => "Equal resolution of file has to be 800x600",
"anotherFile" => "Equal resolution of file has to be 1024x768",
],
]
)
);
Properties
//
protected template = The resolution of the field :field has to be equal :resolution;
Methods
public function __construct( array $options = [] );
Constructor
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
Class Phalcon\Filter\Validation\Validator\File\Resolution\Max
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator\File\Resolution Uses Phalcon\Messages\Message, Phalcon\Filter\Validation, Phalcon\Filter\Validation\Validator\File\AbstractFile Extends AbstractFile
Checks if a file has the right resolution
use Phalcon\Filter\Validation;
use Phalcon\Filter\Validation\Validator\File\Resolution\Max;
$validator = new Validation();
$validator->add(
"file",
new Max(
[
"resolution" => "800x600",
"message" => "Max resolution of :field is :resolution",
"included" => true,
]
)
);
$validator->add(
[
"file",
"anotherFile",
],
new Max(
[
"resolution" => [
"file" => "800x600",
"anotherFile" => "1024x768",
],
"included" => [
"file" => false,
"anotherFile" => true,
],
"message" => [
"file" => "Max resolution of file is 800x600",
"anotherFile" => "Max resolution of file is 1024x768",
],
]
)
);
Properties
//
protected template = File :field exceeds the maximum resolution of :resolution;
Methods
public function __construct( array $options = [] );
Constructor
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
Class Phalcon\Filter\Validation\Validator\File\Resolution\Min
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator\File\Resolution Uses Phalcon\Messages\Message, Phalcon\Filter\Validation, Phalcon\Filter\Validation\Validator\File\AbstractFile Extends AbstractFile
Checks if a file has the right resolution
use Phalcon\Filter\Validation;
use Phalcon\Filter\Validation\Validator\File\Resolution\Min;
$validator = new Validation();
$validator->add(
"file",
new Min(
[
"resolution" => "800x600",
"message" => "Min resolution of :field is :resolution",
"included" => true,
]
)
);
$validator->add(
[
"file",
"anotherFile",
],
new Min(
[
"resolution" => [
"file" => "800x600",
"anotherFile" => "1024x768",
],
"included" => [
"file" => false,
"anotherFile" => true,
],
"message" => [
"file" => "Min resolution of file is 800x600",
"anotherFile" => "Min resolution of file is 1024x768",
],
]
)
);
Properties
//
protected template = File :field can not have the minimum resolution of :resolution;
Methods
public function __construct( array $options = [] );
Constructor
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
Class Phalcon\Filter\Validation\Validator\File\Size\Equal
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator\File\Size Uses Phalcon\Messages\Message, Phalcon\Filter\Validation, Phalcon\Filter\Validation\Validator\File\AbstractFile Extends AbstractFile
Checks if a value has a correct file
use Phalcon\Filter\Validation;
use Phalcon\Filter\Validation\Validator\File\Size;
$validator = new Validation();
$validator->add(
"file",
new Equal(
[
"size" => "2M",
"included" => true,
"message" => ":field exceeds the equal file size (:size)",
]
)
);
$validator->add(
[
"file",
"anotherFile",
],
new Equal(
[
"size" => [
"file" => "2M",
"anotherFile" => "4M",
],
"included" => [
"file" => false,
"anotherFile" => true,
],
"message" => [
"file" => "file does not have the right file size",
"anotherFile" => "anotherFile wrong file size (4MB)",
],
]
)
);
Properties
//
protected template = File :field does not have the exact :size file size;
Methods
public function __construct( array $options = [] );
Constructor
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
Class Phalcon\Filter\Validation\Validator\File\Size\Max
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator\File\Size Uses Phalcon\Messages\Message, Phalcon\Filter\Validation, Phalcon\Filter\Validation\Validator\File\AbstractFile Extends AbstractFile
Checks if a value has a correct file
use Phalcon\Filter\Validation;
use Phalcon\Filter\Validation\Validator\File\Size;
$validator = new Validation();
$validator->add(
"file",
new Max(
[
"size" => "2M",
"included" => true,
"message" => ":field exceeds the max file size (:size)",
]
)
);
$validator->add(
[
"file",
"anotherFile",
],
new Max(
[
"size" => [
"file" => "2M",
"anotherFile" => "4M",
],
"included" => [
"file" => false,
"anotherFile" => true,
],
"message" => [
"file" => "file exceeds the max file size 2M",
"anotherFile" => "anotherFile exceeds the max file size 4M",
],
]
)
);
Properties
//
protected template = File :field exceeds the size of :size;
Methods
public function __construct( array $options = [] );
Constructor
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
Class Phalcon\Filter\Validation\Validator\File\Size\Min
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator\File\Size Uses Phalcon\Messages\Message, Phalcon\Filter\Validation, Phalcon\Filter\Validation\Validator\File\AbstractFile Extends AbstractFile
Checks if a value has a correct file
use Phalcon\Filter\Validation;
use Phalcon\Filter\Validation\Validator\File\Size;
$validator = new Validation();
$validator->add(
"file",
new Min(
[
"size" => "2M",
"included" => true,
"message" => ":field exceeds the min file size (:size)",
]
)
);
$validator->add(
[
"file",
"anotherFile",
],
new Min(
[
"size" => [
"file" => "2M",
"anotherFile" => "4M",
],
"included" => [
"file" => false,
"anotherFile" => true,
],
"message" => [
"file" => "file exceeds the min file size 2M",
"anotherFile" => "anotherFile exceeds the min file size 4M",
],
]
)
);
Properties
//
protected template = File :field can not have the minimum size of :size;
Methods
public function __construct( array $options = [] );
Constructor
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
Class Phalcon\Filter\Validation\Validator\Identical
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator Uses Phalcon\Messages\Message, Phalcon\Filter\Validation, Phalcon\Filter\Validation\AbstractValidator Extends AbstractValidator
Checks if a value is identical to other
use Phalcon\Filter\Validation;
use Phalcon\Filter\Validation\Validator\Identical;
$validator = new Validation();
$validator->add(
"terms",
new Identical(
[
"accepted" => "yes",
"message" => "Terms and conditions must be accepted",
]
)
);
$validator->add(
[
"terms",
"anotherTerms",
],
new Identical(
[
"accepted" => [
"terms" => "yes",
"anotherTerms" => "yes",
],
"message" => [
"terms" => "Terms and conditions must be accepted",
"anotherTerms" => "Another terms must be accepted",
],
]
)
);
Properties
//
protected template = Field :field does not have the expected value;
Methods
public function __construct( array $options = [] );
Constructor
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
Class Phalcon\Filter\Validation\Validator\InclusionIn
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator Uses Phalcon\Messages\Message, Phalcon\Filter\Validation, Phalcon\Filter\Validation\AbstractValidator, Phalcon\Filter\Validation\Exception Extends AbstractValidator
Check if a value is included into a list of values
use Phalcon\Filter\Validation;
use Phalcon\Filter\Validation\Validator\InclusionIn;
$validator = new Validation();
$validator->add(
"status",
new InclusionIn(
[
"message" => "The status must be A or B",
"domain" => ["A", "B"],
]
)
);
$validator->add(
[
"status",
"type",
],
new InclusionIn(
[
"message" => [
"status" => "The status must be A or B",
"type" => "The status must be 1 or 2",
],
"domain" => [
"status" => ["A", "B"],
"type" => [1, 2],
]
]
)
);
Properties
//
protected template = Field :field must be a part of list: :domain;
Methods
public function __construct( array $options = [] );
Constructor
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
Class Phalcon\Filter\Validation\Validator\Ip
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator Uses Phalcon\Filter\Validation, Phalcon\Filter\Validation\AbstractValidator, Phalcon\Messages\Message Extends AbstractValidator
Check for IP addresses
use Phalcon\Filter\Validation\Validator\Ip as IpValidator;
$validator->add(
"ip_address",
new IpValidator(
[
"message" => ":field must contain only ip addresses",
"version" => IP::VERSION_4 | IP::VERSION_6, // v6 and v4. The same if not specified
"allowReserved" => false, // False if not specified. Ignored for v6
"allowPrivate" => false, // False if not specified
"allowEmpty" => false,
]
)
);
$validator->add(
[
"source_address",
"destination_address",
],
new IpValidator(
[
"message" => [
"source_address" => "source_address must be a valid IP address",
"destination_address" => "destination_address must be a valid IP address",
],
"version" => [
"source_address" => Ip::VERSION_4 | IP::VERSION_6,
"destination_address" => Ip::VERSION_4,
],
"allowReserved" => [
"source_address" => false,
"destination_address" => true,
],
"allowPrivate" => [
"source_address" => false,
"destination_address" => true,
],
"allowEmpty" => [
"source_address" => false,
"destination_address" => true,
],
]
)
);
Constants
const VERSION_4 = FILTER_FLAG_IPV4;
const VERSION_6 = FILTER_FLAG_IPV6;
Properties
//
protected template = Field :field must be a valid IP address;
Methods
public function __construct( array $options = [] );
Constructor
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
Class Phalcon\Filter\Validation\Validator\Numericality
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator Uses Phalcon\Messages\Message, Phalcon\Filter\Validation, Phalcon\Filter\Validation\AbstractValidator Extends AbstractValidator
Check for a valid numeric value
use Phalcon\Filter\Validation;
use Phalcon\Filter\Validation\Validator\Numericality;
$validator = new Validation();
$validator->add(
"price",
new Numericality(
[
"message" => ":field is not numeric",
]
)
);
$validator->add(
[
"price",
"amount",
],
new Numericality(
[
"message" => [
"price" => "price is not numeric",
"amount" => "amount is not numeric",
]
]
)
);
Properties
//
protected template = Field :field does not have a valid numeric format;
Methods
public function __construct( array $options = [] );
Constructor
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
Class Phalcon\Filter\Validation\Validator\PresenceOf
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator Uses Phalcon\Messages\Message, Phalcon\Filter\Validation, Phalcon\Filter\Validation\AbstractValidator Extends AbstractValidator
Validates that a value is not null or empty string
use Phalcon\Filter\Validation;
use Phalcon\Filter\Validation\Validator\PresenceOf;
$validator = new Validation();
$validator->add(
"name",
new PresenceOf(
[
"message" => "The name is required",
]
)
);
$validator->add(
[
"name",
"email",
],
new PresenceOf(
[
"message" => [
"name" => "The name is required",
"email" => "The email is required",
],
]
)
);
Properties
//
protected template = Field :field is required;
Methods
public function __construct( array $options = [] );
Constructor
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
Class Phalcon\Filter\Validation\Validator\Regex
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator Uses Phalcon\Messages\Message, Phalcon\Filter\Validation, Phalcon\Filter\Validation\AbstractValidator Extends AbstractValidator
Allows validate if the value of a field matches a regular expression
use Phalcon\Filter\Validation;
use Phalcon\Filter\Validation\Validator\Regex as RegexValidator;
$validator = new Validation();
$validator->add(
"created_at",
new RegexValidator(
[
"pattern" => "/^[0-9]{4}[-\/](0[1-9]|1[12])[-\/](0[1-9]|[12][0-9]|3[01])$/",
"message" => "The creation date is invalid",
]
)
);
$validator->add(
[
"created_at",
"name",
],
new RegexValidator(
[
"pattern" => [
"created_at" => "/^[0-9]{4}[-\/](0[1-9]|1[12])[-\/](0[1-9]|[12][0-9]|3[01])$/",
"name" => "/^[a-z]$/",
],
"message" => [
"created_at" => "The creation date is invalid",
"name" => "The name is invalid",
]
]
)
);
Properties
//
protected template = Field :field does not match the required format;
Methods
public function __construct( array $options = [] );
Constructor
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
Class Phalcon\Filter\Validation\Validator\StringLength
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator Uses Phalcon\Messages\Message, Phalcon\Filter\Validation\AbstractValidator, Phalcon\Filter\Validation\AbstractValidatorComposite, Phalcon\Filter\Validation\Validator\StringLength\Max, Phalcon\Filter\Validation\Validator\StringLength\Min, Phalcon\Filter\Validation\Exception Extends AbstractValidatorComposite
Validates that a string has the specified maximum and minimum constraints The test is passed if for a string’s length L, min<=L<=max, i.e. L must be at least min, and at most max. Since Phalcon v4.0 this validator works like a container
use Phalcon\Filter\Validation;
use Phalcon\Filter\Validation\Validator\StringLength as StringLength;
$validator = new Validation();
$validation->add(
"name_last",
new StringLength(
[
"max" => 50,
"min" => 2,
"messageMaximum" => "We don't like really long names",
"messageMinimum" => "We want more than just their initials",
"includedMaximum" => true,
"includedMinimum" => false,
]
)
);
$validation->add(
[
"name_last",
"name_first",
],
new StringLength(
[
"max" => [
"name_last" => 50,
"name_first" => 40,
],
"min" => [
"name_last" => 2,
"name_first" => 4,
],
"messageMaximum" => [
"name_last" => "We don't like really long last names",
"name_first" => "We don't like really long first names",
],
"messageMinimum" => [
"name_last" => "We don't like too short last names",
"name_first" => "We don't like too short first names",
],
"includedMaximum" => [
"name_last" => false,
"name_first" => true,
],
"includedMinimum" => [
"name_last" => false,
"name_first" => true,
]
]
)
);
Methods
public function __construct( array $options = [] );
Constructor
Class Phalcon\Filter\Validation\Validator\StringLength\Max
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator\StringLength Uses Phalcon\Messages\Message, Phalcon\Filter\Validation, Phalcon\Filter\Validation\AbstractValidator, Phalcon\Filter\Validation\Exception Extends AbstractValidator
Validates that a string has the specified maximum constraints The test is passed if for a string’s length L, L<=max, i.e. L must be at most max.
use Phalcon\Filter\Validation;
use Phalcon\Filter\Validation\Validator\StringLength\Max;
$validator = new Validation();
$validation->add(
"name_last",
new Max(
[
"max" => 50,
"message" => "We don't like really long names",
"included" => true
]
)
);
$validation->add(
[
"name_last",
"name_first",
],
new Max(
[
"max" => [
"name_last" => 50,
"name_first" => 40,
],
"message" => [
"name_last" => "We don't like really long last names",
"name_first" => "We don't like really long first names",
],
"included" => [
"name_last" => false,
"name_first" => true,
]
]
)
);
Properties
//
protected template = Field :field must not exceed :max characters long;
Methods
public function __construct( array $options = [] );
Constructor
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
Class Phalcon\Filter\Validation\Validator\StringLength\Min
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator\StringLength Uses Phalcon\Messages\Message, Phalcon\Filter\Validation, Phalcon\Filter\Validation\AbstractValidator, Phalcon\Filter\Validation\Exception Extends AbstractValidator
Validates that a string has the specified minimum constraints The test is passed if for a string’s length L, min<=L, i.e. L must be at least min.
use Phalcon\Filter\Validation;
use Phalcon\Filter\Validation\Validator\StringLength\Min;
$validator = new Validation();
$validation->add(
"name_last",
new Min(
[
"min" => 2,
"message" => "We want more than just their initials",
"included" => true
]
)
);
$validation->add(
[
"name_last",
"name_first",
],
new Min(
[
"min" => [
"name_last" => 2,
"name_first" => 4,
],
"message" => [
"name_last" => "We don't like too short last names",
"name_first" => "We don't like too short first names",
],
"included" => [
"name_last" => false,
"name_first" => true,
]
]
)
);
Properties
//
protected template = Field :field must be at least :min characters long;
Methods
public function __construct( array $options = [] );
Constructor
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
Class Phalcon\Filter\Validation\Validator\Uniqueness
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator Uses Phalcon\Messages\Message, Phalcon\Mvc\Model, Phalcon\Mvc\ModelInterface, Phalcon\Filter\Validation, Phalcon\Filter\Validation\AbstractCombinedFieldsValidator, Phalcon\Filter\Validation\Exception Extends AbstractCombinedFieldsValidator
Check that a field is unique in the related table
use Phalcon\Filter\Validation;
use Phalcon\Filter\Validation\Validator\Uniqueness as UniquenessValidator;
$validator = new Validation();
$validator->add(
"username",
new UniquenessValidator(
[
"model" => new Users(),
"message" => ":field must be unique",
]
)
);
Different attribute from the field:
$validator->add(
"username",
new UniquenessValidator(
[
"model" => new Users(),
"attribute" => "nick",
]
)
);
In model:
$validator->add(
"username",
new UniquenessValidator()
);
Combination of fields in model:
$validator->add(
[
"firstName",
"lastName",
],
new UniquenessValidator()
);
It is possible to convert values before validation. This is useful in situations where values need to be converted to do the database lookup:
$validator->add(
"username",
new UniquenessValidator(
[
"convert" => function (array $values) {
$values["username"] = strtolower($values["username"]);
return $values;
}
]
)
);
Properties
//
protected template = Field :field must be unique;
/**
* @var array|null
*/
private columnMap;
Methods
public function __construct( array $options = [] );
Constructor
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
protected function getColumnNameReal( mixed $record, string $field ): string;
The column map is used in the case to get real column name
protected function isUniqueness( Validation $validation, mixed $field ): bool;
protected function isUniquenessModel( mixed $record, array $field, array $values );
Uniqueness method used for model
Class Phalcon\Filter\Validation\Validator\Url
Source on GitHub
Namespace Phalcon\Filter\Validation\Validator Uses Phalcon\Messages\Message, Phalcon\Filter\Validation, Phalcon\Filter\Validation\AbstractValidator Extends AbstractValidator
Checks if a value has a url format
use Phalcon\Filter\Validation;
use Phalcon\Filter\Validation\Validator\Url as UrlValidator;
$validator = new Validation();
$validator->add(
"url",
new UrlValidator(
[
"message" => ":field must be a url",
]
)
);
$validator->add(
[
"url",
"homepage",
],
new UrlValidator(
[
"message" => [
"url" => "url must be a url",
"homepage" => "homepage must be a url",
]
]
)
);
Properties
//
protected template = Field :field must be a url;
Methods
public function __construct( array $options = [] );
Constructor
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
Interface Phalcon\Filter\Validation\ValidatorCompositeInterface
Source on GitHub
Namespace Phalcon\Filter\Validation Uses Phalcon\Filter\Validation
This is a base class for combined fields validators
Methods
public function getValidators(): array;
Executes the validation
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
Class Phalcon\Filter\Validation\ValidatorFactory
Source on GitHub
Namespace Phalcon\Filter\Validation Uses Phalcon\Factory\AbstractFactory Extends AbstractFactory
This file is part of the Phalcon Framework.
(c) Phalcon Team [email protected]
For the full copyright and license information, please view the LICENSE.txt file that was distributed with this source code.
Methods
public function __construct( array $services = [] );
TagFactory constructor.
public function newInstance( string $name ): ValidatorInterface;
Creates a new instance
protected function getExceptionClass(): string;
protected function getServices(): array;
Returns the available adapters
Interface Phalcon\Filter\Validation\ValidatorInterface
Source on GitHub
Namespace Phalcon\Filter\Validation Uses Phalcon\Filter\Validation
Interface for Phalcon\Filter\Validation\AbstractValidator
Methods
public function getOption( string $key, mixed $defaultValue = null ): mixed;
Returns an option in the validator’s options Returns null if the option hasn’t set
public function getTemplate( string $field ): string;
Get the template message
public function getTemplates(): array;
Get message templates
public function hasOption( string $key ): bool;
Checks if an option is defined
public function setTemplate( string $template ): ValidatorInterface;
Set a new template message
public function setTemplates( array $templates ): ValidatorInterface;
Clear current template and set new from an array,
public function validate( Validation $validation, mixed $field ): bool;
Executes the validation
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in , ,
Factors Impacting Your Hydration Requirements
Be aware that your hydration requirements may change based on your situation!
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Drink Water
Want to know how much water to drink per day?
So what causes your hydration requirements to vary?
Climate & Exercise
Exercise often
Think of your body as a computer or engine.
To function properly it needs to avoid overheating.
To cool itself down your body commands the dilation of blood vessels (vasodilation) near the skin so that warm blood can flow closer to the surface (at a cooler temperature) – this is why you see people with rosy faces when they exercise.
Your body also tries to cool the skin by secreting sweat made up of water, sodium and other cooling substances – all of which must be replaced.
One good way to assess how much fluid you’re losing during exercise is to weigh yourself before and after.
According to the University of Connecticut, to replenish your bodies water stores, you need to drink half a litre of water for every pound of weight lost.
If that’s too complicated, aim for 6 ounces of water for every 15 minutes of exercise.
Use this as a starting point, adjusting your water intake based on how your body feels and the colour of your urine (as mentioned in our article Avoid Dehydration!).
.
For more on monitoring your water intake
CLICK HERE
Health
Water is easily lost through illnesses.
For example, you can lose as much as 250ml per day for every degree (centigrade) that your body rises above normal body temperature due to a fever.
Other illnesses which cause vomiting and diarrhoea may also result in a significant loss of fluid.
There are a list of other infections that will require greater water intake; including, urinary tract stones, bladder infections, gout and constipation.
If you are worried about such ailments speak with your doctor!
In these cases you need to be aware that dehydration is a risk that needs to be addressed by utilizing “oral rehydration solutions” (i.e. drinking water!).
It’s also worth noting that not all disorders require an increase of fluid intake; for example, heart failure, disorders of the kidney, liver and the adrenals may all require reductions in water consumption.
Again, speak with your doctor!
Pregnancy
Pregnancy effects water intake
Water is needed to maintain vital fluids in the body, such as blood and amniotic fluid while pregnant.
It may also need to be replaced if morning sickness kicks in!
The average healthy woman, carrying a normal sized fetus weighing 3.3 kg, increases her blood plasma volume on average by 1,250ml.
This is around 50% of the average volume for non-pregnant women and is due to the increased need for oxygen while pregnant (for vital organs to function properly and to deliver oxygen to the baby)
Amniotic fluid provides support and nourishment to unborn babies while in the womb. It assists in their growth, the development of their musculoskeletal system and maintains a constant temperature for the baby.
So what’s the relevance of all this?
Well… Amniotic fluid is mostly water!
Yet again, there is no single ideal level of water consumption for pregnant women because everyone varies; however, once you understand your usual consumption, using the methods explained in our other hydration article, slightly increase the volume to see how you feel.
Breast feeding
The additional water intake required during pregnancy is good practice for the even more strenuous regimen needed whilst producing breast milk for feeding.
Agostoni CV et al. published guidance in The European Food Safety Authority (EFSA) Journal that:
‘Adequate Intakes (AI’s) of water for infants in the first half of the first year of life are estimated to be 100 – 190 ml/kg per day. For infants 6 to 12 months of age a total water intake of 800 – 1,000 ml/day is considered adequate.
The mother needs to make sure she stays hydrated so she has enough fluids to support both her and the baby.
So if this applies to you, make sure you keep your bottle of water close by and use the techniques outlined in our article ‘setting your hydration goals and staying hydrated’ during this important time.
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Stuffed Portabello Mushrooms | My Home Vitality
Portobello Stuffed Mushrooms
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Chameleon is a very strange exotic creature. Really it belongs to lizards. Here’s how they look in life. There are many various types of chameleons, but none of them are longer than 60 cm. Chameleon differs from thin and quick common liszard very much. It`s body is stout and as it seems clumsy , helmet-like
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Laravel Working With Json Table Column Example
How to Store multiple values in single field laravel is the todays topic. Sometimes we need to store multiple key and value in single column in Laravel. But do you know how we can do that? we can use pivot table to solve this issue. But here i am going to use json column to store multiple records with key and value for respect to key.
From this laravel json tutorial you will also learn how to insert json data into mysql using laravel. In this tutorial we will insert multiple properties for a single product like size, price, value, color etc from a single method into a single field with json.
So let's se how we can store json data into database. So let's start laravel json column example tutorial.
Preview : Store json data form
store-json-data-laravel
Preview : After fetching json data
laravel-working-with-json
Step 1 : Create Model
In this we need product model. So let's create it to store json data.
php artisan make:model Product -m
Now open product model and update like below.
app/Product.php
namespace App;
use Illuminate\Database\Eloquent\Model;
class Product extends Model
{
protected $guarded = [];
protected $casts = [
'properties' => 'array'
];
public function setPropertiesAttribute($value)
{
$properties = [];
foreach ($value as $array_item) {
if (!is_null($array_item['key'])) {
$properties[] = $array_item;
}
}
$this->attributes['properties'] = json_encode($properties);
}
}
and open migration file and update it like below.
database/migration/create_products_table.php
public function up()
{
Schema::create('products', function (Blueprint $table) {
$table->increments('id');
$table->string('name');
$table->decimal('price', 15, 2);
$table->json('properties');
$table->timestamps();
});
}
Step 2 : Create Route
We need many route for storing json data into json column.
routes/web.php
Route::get('produc/create','ProductController@show_product_form')->name('produc.create');
Route::post('produc/create','ProductController@store');
Route::get('produc','ProductController@index')->name('produc.index');
Step 3 : Create Controller
In this step we need to create product controller. So create it and update this controller like below
app/Http/Controllers/ProductController.php
namespace App\Http\Controllers;
use App\Category;
use App\Http\Controllers\Controller;
use App\Product;
use Illuminate\Http\Request;
class ProductController extends Controller
{
public function show_product_form()
{
return view('create');
}
public function store(Request $request)
{
$product = Product::create($request->all());
return redirect()->back();
}
public function index()
{
$post = Product::all();
return view('index',['products' => $post]);
}
}
Step 4 : Create Blade File
Now we are in the final step and all are set to go. So how to insert json data into mysql using laravel we will know. Now create below file and paste this code in your file.
resources/views/create.blade.php
resources/views/index.blade.php
Recommended : Avoid Pivot Table and Use Json Column in Laravel
Hope this Laravel json tutorial will help you.
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SharePoint Online Permission
SharePoint Online Permission Management: Best Practices
30 August 2023
SharePoint Migration
In the modern business landscape, effective collaboration and data security are paramount. Microsoft SharePoint Online stands as a pivotal platform for organizations, offering a robust environment for teamwork and content management. However, harnessing its full potential requires a comprehensive understanding of SharePoint Online permissions. This article delves into the intricacies of permission management in SharePoint Online, shedding light on best practices that empower organizations to maintain a secure and productive digital workspace.
Understanding SharePoint Online Permissions
SharePoint Online permissions revolve around controlling access to sites, lists, libraries, folders, and documents. The goal is to ensure that the right individuals can access the right content, while also preventing unauthorized users from gaining entry. To accomplish this, SharePoint employs a permission model that encompasses three key components:
1. Users and Groups: SharePoint Online leverages Microsoft 365 user accounts and groups to define access. Users are granted specific roles and permissions, while groups allow for simplified management by assigning permissions collectively.
2. Roles and Permissions: Permissions are grouped into predefined roles that dictate the actions a user can perform. These roles include Full Control, Edit, Contribute, Read, and Limited Access. Permissions can be fine-tuned to control activities such as viewing, editing, deleting, and sharing.
3. Inheritance and Break Inheritance: SharePoint uses inheritance by default, allowing permissions assigned to a parent object, such as a site, to cascade down to its child objects, like lists or documents. However, organizations can choose to break inheritance, enabling granular control over permissions at each level.
Best Practices for SharePoint Online Permission Management
1. Plan Permissions Strategically:
Before diving into permission management, craft a comprehensive plan. Identify user roles, content categories, and the level of access required. This proactive approach ensures a well-organized permission structure that aligns with business needs.
1. Utilize SharePoint Groups:
Leverage SharePoint groups to simplify permission management. Instead of individually assigning permissions to users, associate permissions with groups. This approach streamlines the process and enhances maintainability.
1. Limit Permissions:
Adhere to the principle of least privilege. Grant users only the permissions necessary for their roles. Avoid granting overly broad permissions, as this can lead to data leakage and security vulnerabilities.
1. Regularly Review and Update Permissions:
Business dynamics change, and so should permissions. Regularly review and adjust permissions as users’ roles evolve. This practice prevents obsolete permissions and unauthorized access.
1. Leverage Inheritance:
Whenever possible, maintain permission inheritance. Breaking inheritance should be a deliberate action, as it can complicate management. Only do so when there is a specific need for distinct permissions.
1. Audit Permissions:
Implement regular audits to ensure permissions are accurate and aligned with organizational requirements. Identify and rectify any discrepancies promptly to maintain a secure environment.
1. Implement Site Policies:
Establish clear site-level policies for permissions. Define who has the authority to change permissions, under what circumstances, and how to request permission changes.
1. Educate Users:
Educate users about SharePoint permission management best practices. Train them to understand the implications of sharing content, granting permissions, and breaking inheritance.
1. Utilize SharePoint Security Reports:
SharePoint Online offers built-in security reports that provide insights into permission usage. Utilize these reports to monitor user activity, permissions changes, and potential security risks.
1. Backup and Restore Permissions:
Regularly backup permission configurations. This safeguards against accidental or malicious changes, allowing for swift restoration in case of a security breach.
Conclusion
In the realm of SharePoint Online, efficient permission management is the cornerstone of a secure and collaborative digital workspace. By adhering to best practices, organizations can harness the power of SharePoint’s versatile permission model. Through careful planning, judicious use of groups, and a proactive approach to reviewing and updating permissions, businesses can create a cohesive environment where data is accessible to those who need it, while keeping unauthorized access at bay.
Let us help you navigate the intricate world of permission management in SharePoint Online, ensuring your business thrives in a secure and productive digital landscape.
Reach out to us today and discover how Star Knowledge can transform your SharePoint experience. Your journey towards optimized collaboration and data security begins here.
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The Duties for a Data Analysis Coding Job
By Nikhil Abraham
Data analysts sift through large volumes of data, looking for insights that help drive the product or business forward. This coding role marries programing and statistics in the search for patterns in the data. Popular examples of data analysis in action include the recommendation engines used by Amazon to make product suggestions to users based on previous purchases and by Netflix to make movie suggestions based on movies watched.
The data analyst’s first challenge is simply importing, cleaning, and processing the data. A website can generate millions of database entries of users’ data daily, requiring the use of complicated techniques, referred to as machine learning, to create classifications and predictions from the data.
For example, half a billion messages are sent per day using Twitter; some hedge funds analyze this data and classify whether a person talking about a stock is expressing a positive or negative sentiment. These sentiments are then aggregated to see whether a company has a positive or negative public opinion before the hedge fund purchases or sells any stock.
Any programming language can be used to analyze data, but the most popular programming languages used for the task are R, Python, and SQL. Publicly shared code in these three languages makes it easier for individuals entering the field to build on another person’s work. While crunching the data is important, employers also look for data analysts with skills in the following:
• Visualization: Just as important as finding insight in the data is communicating that insight. Data visualization uses charts, graphs, dashboards, infographics, and maps, which can be interactive, to display data and reduce the complexity such that one or two conclusions appear obvious. Common data visualization tools include D3.js, a JavaScript graphing library, and ArcGIS for geographic data.
The two Manhattan addresses farthest away from Starbucks.
The two Manhattan addresses farthest away from Starbucks.
• Distributed storage and processing: Processing large amounts of data on one computer can be time intensive. One option is to purchase a single faster computer. Another option, called distributed storage and processing, is to purchase multiple machines and divide the work. For example, imagine that you want to count the number of people living in Manhattan. In the distributed storage and processing approach, you might ring odd‐numbered homes, someone else would ring even‐numbered homes, and when everyone finishes you would sum the counts.
Data analysts work with back‐end developers to gather data needed for their work. After the data analysts have drawn conclusions from the data, and come up with ideas on improving the existing product, they meet with the entire team to help design prototypes to test the ideas on existing customers.
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Analytical properties of generalized Gaussian distributions
Abstract
The family of Generalized Gaussian (GG) distributions has received considerable attention from the engineering community, due to the flexible parametric form of its probability density function, in modeling many physical phenomena. However, very little is known about the analytical properties of this family of distributions, and the aim of this work is to fill this gap.
Roughly, this work consists of four parts. The first part of the paper analyzes properties of moments, absolute moments, the Mellin transform, and the cumulative distribution function. For example, it is shown that the family of GG distributions has a natural order with respect to second-order stochastic dominance.
The second part of the paper studies product decompositions of GG random variables. In particular, it is shown that a GG random variable can be decomposed into a product of a GG random variable (of a different order) and an independent positive random variable. The properties of this decomposition are carefully examined.
The third part of the paper examines properties of the characteristic function of the GG distribution. For example, the distribution of the zeros of the characteristic function is analyzed. Moreover, asymptotically tight bounds on the characteristic function are derived that give an exact tail behavior of the characteristic function. Finally, a complete characterization of conditions under which GG random variables are infinitely divisible and self-decomposable is given.
The fourth part of the paper concludes this work by summarizing a number of important open questions.
Introduction
The goal of this work is to study a large family of probability distributions, termed Generalized Gaussian (GG), that has received considerable attention in many engineering applications. We shall refer to Xp with the GG distribution given by the probability density function (pdf)
$$ f_{X_{p}}(x)= \frac{c_{p}}{\alpha} \mathrm{e}^{-\frac{| x-\mu |^{p}}{2\alpha^{p}}}, c_{p}=\frac{p}{2^{\frac{p+1}{p}} \Gamma\left(\frac{1}{p} \right)}, \, x \in \mathbb{R}, \, p>0, $$
(1)
as \(X_{p}\sim \mathcal {N}_{p} \left (\mu,\alpha ^{p}\right)\), and where we define the gamma function, the lower incomplete gamma function and the upper incomplete gamma function as
$$\begin{array}{*{20}l} \Gamma(x)&=\int_{0}^{\infty} t^{x-1}e^{-t} dt, \end{array} $$
(2)
$$\begin{array}{*{20}l} \gamma(x,a)&=\int_{0}^{a} t^{x-1} \mathrm{e}^{-t} dt, \end{array} $$
(3)
$$\begin{array}{*{20}l} \Gamma(x,a)&=\int_{a}^{\infty} t^{x-1} \mathrm{e}^{-t} dt, \end{array} $$
(4)
respectively. Another commonly used name for this type of distribution, especially in economics, is the Generalized Error distribution. The flexible parametric form of the pdf of the GG distribution allows for tails that are either heavier than Gaussian (p<2) or lighter than Gaussian (p>2) which makes it an excellent choice for many modeling scenarios. The origin of the GG family can be traced to the seminal work of Subbotin (1923) and Lévy (1925). In fact, Subbotin (1923) has shown that the same axioms used by Gauss (1809) to derive the normal distribution, are also satisfied by the GG distribution. Well-known examples of this distribution include: the Laplace distribution for p=1; the Gaussian distribution for p=2; and the uniform distribution on [μα,μ+α] for p=.
1.1 Past work
The GG distribution has found use in image processing applications where many statistical features of an image are naturally modeled by distributions that are heavier-tailed than Gaussian.
For example, Gabor coefficients are convolution kernels whose frequency and orientation representations are similar to those of the human visual system. Gabor coefficients have found a wide range of applications in texture retrieval and face-recognition problems. However, a considerable drawback of using Gabor coefficients is the memory requirements needed to store a Gabor representation of an image. In Gonzalez-Jimenez et al. (2007) GG distributions with the parameter p<2 have been shown to accurately approximate the empirical distribution of Gabor coefficients in terms of the Kullback-Liebler (KL) divergence and the χ2 distance. Moreover, the authors in (Gonzalez-Jimenez et al. 2007) demonstrated that data compression algorithms based on the GG statistical model considerably reduce the memory required to store Gabor coefficients.
In a classical image retrieval problem, a system searches for K images similar to a query image from a digital library containing a total of N images (usually KN). In (Do and Vetterli 2002) by modeling wavelet coefficients with a GG distribution and using the KL divergence as a similarity measure, the authors were able to improve retrieval rates by 65% to 70%, compared with traditional approaches.
Other applications of the GG distribution in image processing applications include modeling: textured images, see Mallat (1989); Moulin and Liu (1999) and de Wouwer et al. (1999); pixels forming fine-resolution synthetic aperture radar (SAR) images (Bernard et al. 2006); and the distribution of values in subband decompositions of video signals Westerink et al. (1991) and Sharifi and Leon-Garcia (1995).
In communication theory, the GG distribution finds many modeling applications in impulsive noise channels which occur when the noise pdf has a longer tail than the Gaussian pdf. For example, in Beaulieu and Young (2009) it is shown that in ultrawideband (UWB) systems with time-hopping (TH) the interference should be modeled with probability distributions that are more impulsive than the Gaussian. Moreover, it has been shown that for the moderate and high signal-to-noise ratio (SNR) the interference in the TH-UWB is well modeled by the GG distribution with a parameter p≤1. In Algazi and Lerner (1964) and Miller and Thomas (1972) certain atmospheric noises were shown to be impulsive and GG distributions with parameter values of 0.1<p<0.6 were shown to provide good approximations to their distributions.
GG distributions can also model noise distributions that appear in non-standard wireless media. In Nielsen and B.Thomas (1987) the authors showed that Arctic under-ice noise is well modeled by members of the GG family. In Banerjee and Agrawal (2013) the GG family has been recognized as a model for the underwater acoustic channel where values of p=2.2 and p=1.6 have been found to model the ship transit noise and the sea surface agitation noise, respectively.
The problem of designing optimal detectors for signals in the presence of GG noise has been considered in Miller and Thomas (1972); Poor and Thomas (1978) and Viswanathan and Ansari (1989). In Soury et al. (2012) the authors studied the average bit error probability of binary coherent signaling over flat fading channels subject to additive GG noise. Interestingly, the authors of Soury et al. (2012) give an exact expression for the average probability of error in terms of Fox’s H functions.
In power systems, the GG distribution has been used to model hourly peak load model demand in power grids (Mohamed et al. 2008).
In Varanasi and Aazhang (1989) the authors studied a problem of estimating parameters of the GG distribution (order p, mean μ, and variance \(\sigma ^{2}=\mathbb {E}\left [(X_{p}-\mu)^{2}\right ]\)) from n independent realizations of a GG random variable. The authors of (Varanasi and Aazhang 1989) considered three estimation methods, namely, the method of moments, maximum likelihood, and moment/Newton-step estimators, and compared performance of each for different values of p. For example, in the vicinity of p=2, the moment method was shown to perform best. In (Richter 2007) the authors established connections between chi-square and Student’s t-distribution. Moreover, in Richter (2016), using the notions of generalized chi-square and Fisher statistics introduced in Richter (2007), the authors studied a problem of inferring one or two scaling parameters of the GG distribution and derived both the confidence interval and significance test.
The Shannon capacity of channels with GG noise has been considered in Fahs and Abou-Faycal (2018) and Dytso et al. (2017b). In Fahs and Abou-Faycal (2018) the authors gave general results on the structure of the optimal input distribution in channels with GG noise under a large family of channel input cost constraints. In Dytso et al. (2017b) the authors investigated the capacity of channels with GG noise under Lp moment constraints and proposed several upper and lower bounds that are asymptotically tight.
As the pdf of GG distributions has a very simple form, many quantities such as moments, entropy, and Rényi entropy can be easily computed (Do and Vetterli 2002; Nadarajah 2005). Also, from the information theoretic perspective the GG distribution is interesting because it maximizes the entropy under a p-th absolute moment constraint (Cover and Thomas 2006; Lutwak et al. 2007). The maximum entropy property can serve as an important intermediate step in a number of proofs. For example, in (Dytso et al. 2018) it has been used to generalize the Ozarow-Wyner bound (Ozarow and Wyner 1990) on the mutual information of discrete inputs over arbitrary channels. In Nielsen and Nock (2017) the maximum entropy principle has been used to improve bounds on the entropy of Gaussian mixtures.
While the number of applications of the GG distribution is large, many of its properties have been drawn from numerical studies, and few analytical properties of the GG family are known beyond the cases p=1,2 and p=. For instance, very little is known about the characteristic function of the GG distribution and only expressions in terms of hypergeometric functions are known. For example, the characteristic function of the GG distribution was given in terms of Fox-Write functions in Pogány and Nadarajah (2010) for all p>1 and later generalized in terms of Fox-H functions in Soury and Alouini (2015) for all p>0. The work of Soury and Alouini (2015), also characterized the pdf of the sum of two independent GG random variables in terms of Fox-H functions. Specific non-linear transformations of sums of independent GG distributions and the moment generating function of the GG distribution have been studied in Vasudevay and Kumari (2013).
There is also a large body of work on multivariate GG distributions. For example, to the best of our knowledge, the first multivariate generalization was introduced in (De Simoni 1968) where the exponent was taken to be \( \left (\left (\textbf {x}- \boldsymbol {\mu }\right)^{T} \textbf {K}^{-1} (\textbf {x}-\boldsymbol {\mu }) \right)^{\frac {p}{2}}\) where x and μ are vectors and K is a matrix. In Goodman and Kotz (1973) the authors introduced yet another multivariate generalization of the GG distribution in (1): X is said to be multivariate GG if and only if it can be written as X=KZ+μ where the components of Z are independently and identically distributed according to the univariate GG distribution in (1). An example of multivariate distributions with GG marginals and examples of multivariate GG distributions defined with respect to other norms the interested reader is referred to Richter (2014); Arellano-Valle and Richter (2012) and Gupta and Nagar (2018) and the references therein.
1.2 Paper outline and contributions
Our contributions are as follows:
1. 1
In “Moments and the Mellin transform” section, we study properties of the moments of the GG distribution including the following:
• In Proposition 1 we derive an expression for the Mellin transform of the GG distribution; and
• In Proposition 2 we show necessary and sufficient conditions under which moments of the GG distribution uniquely determine the distribution.
2. 2
In “Properties of the distribution” section, we study properties of the distribution including the following:
• In “Stochastic ordering” section, Proposition 3 shows that the family of GG distributions is an ordered set where the order is taken in terms of second-order stochastic dominance; and
• In “Relation to completely monotone functions and positive definiteness” section, Theorem 1 connects the pdf of GG distributions to positive definite functions. In particular, we show that for p≤2 the pdf of the GG distribution is a positive definite function and for p>2 the pdf is not a positive definite function. Moreover, it is shown that for p≤2 the pdf of the GG distribution can be expressed as an integral of a Gaussian pdf with respect to a non-negative finite Borel measure.
3. 3
In “On product decomposition of GG random variables” section, Proposition 5 shows that the GG random variable Xp can be decomposed into a product of two independent random variables Xp=V·Xr where Xr is a GG random variable. We carefully study properties of this decomposition including the following:
• In “On the PDF of Vp,q” section, Proposition 6 gives power series and integral representations of the pdf of V; and
• In “On the determinacy of the distribution of VG,q” section, Proposition 8 shows under which conditions the distribution of V is completely determined by its moments. Interestingly, the range for values of p for which Xp and V are determinant is not the same. This gives an interesting example that the product of two determinate random variables is not necessarily determinate.
4. 4
In “Characteristic function” section, we study properties of the characteristic function of the GG distribution including the following:
• In “Connection to stable distributions” section, Proposition 9 discusses connections between a class of GG distributions and a class of symmetric stable distributions;
• In “Analyticity of the characteristic function” section, Proposition 10 shows under what conditions the characteristic function of the GG distribution is a real analytic function;
• In “On the distribution of zeros of the characteristic function” section, Theorem 3 studies the distribution of zeros of the characteristic function of the GG distribution. In particular, it is shown that for p≤2 the characteristic function of the GG distribution has no zeros and is always positive, and for p>2 the characteristic function has at least one positive-to-negative zero crossing; and
• In “Asymptotic behavior of ϕp(t)” section, Proposition 11 gives the tail behavior of the characteristic function of the GG distribution and its derivatives. The consequences of this result are discussed.
5. 5
In “Additive decomposition of a GG random variable” section, we study additive decompositions of the GG random variables including the following:
• In “Infinite divisibility of the characteristic function” section, Theorem 5 completely characterizes for which values of p the GG random variable is infinitely divisible. In addition, Proposition 14 studies properties of the canonical Lévy-Khinchine representation of infinitely divisible distributions; and
• In “Self-decomposability of the characteristic function” section, Theorem 6 characterizes conditions under which a GG distribution of order p can be additively transformed into another GG distribution of order q. In the case of p=q this corresponds to answering if a GG distribution is self-decomposable.
The paper is concluded in “Discussion and conclusion” section by reflecting on future directions.
1.3 Other parametrization of the PDF
In addition to the parametrization used in (1), there are several other parametrization used in the literature. For example, Subbotin in his seminal paper (Subbotin 1923) used the following parametrization, which is still a commonly used notation amongst probability theorists:
$$ f^{\mathrm{a}}(x)=\frac{p}{2 \Gamma \left(\frac{1}{p} \right) \sigma} \mathrm{e}^{-\frac{\left|x-\mu\right|^{p}}{\sigma^{p}}}, \, \sigma>0. $$
(5)
In some engineering literature where variance models power it is convenient to work with the distributions where the variance is taken to be independent of the parameter p (e.g., (Gonzalez-Jimenez et al. 2007) and Miller and Thomas (1972))
$$ f^{\mathrm{b}}(x)= \frac{ \Delta(\sigma,p) p}{2 \Gamma \left(\frac{1}{p} \right)} \mathrm{e}^{- \left(\Delta(\sigma,p) |x-\mu| \right)^{p}}, \text{where} \Delta(\sigma,p)= \frac{1}{ \sigma} \sqrt{ \frac{\Gamma \left(\frac{3}{p}\right)}{ \Gamma \left(\frac{1}{p}\right)}}, \; \sigma>0. $$
(6)
In statistical literature, some authors prefer to use (e.g., (Richter 2016))
$$ f^{\mathrm{c}}(x)= \frac{p^{1-\frac{1}{p}}}{2\Gamma\left(\frac{1}{p}\right)\sigma} \mathrm{e}^{-\frac{|x-\mu|^{p}}{p \sigma^{p}}} \, \sigma>0. $$
(7)
In the above parametrization the p-th moment, when μ=0, is normalized such that it equals to σp.
The choice of the parametrization is usually dictated by the application that one has in mind. In this work, we choose to work with the parametrization in (1) which we found to be convenient for studying the Mellin transform and the characteristic function of the GG distribution.
Moments and the Mellin transform
In this section, we study properties of the moments, absolute moments and Mellin transform of the GG distribution. We also show conditions under which the moments of Xp uniquely characterize its distribution. While the majority of the results in this section are not new or are easy to derive, we choose to include them for completeness as most of the development in other section will heavily depend on properties of moments.
2.1 Moments, absolute moments, and the Mellin transform
Definition 1
(Mellin Transform (Poularikas 1998).) The Mellin transform of a positive random variable X is defined as
$$ m_{X}(s)=\mathbb{E}\left[X^{s-1}\right], \, s \in \mathbb{C}. $$
(8)
The Mellin transform emerges as a major tool in characterizing products of positive independent random variables since
$$ m_{X\cdot Y}(s)=m_{X}(s) \cdot m_{Y}(s). $$
(9)
Proposition 1
(Mellin Transform of |Xp|.) For any p>0 and \(X_{p} \sim \mathcal {N}_{p} (0, \alpha ^{p})\)
$$ \mathbb{E}\left[\left|X_{p}\right|^{s-1}\right] =\frac{2^{\frac{s-1}{p}}}{\Gamma\left(\frac{1}{p}\right)} \alpha^{s-1}\Gamma \left(\frac{s}{p}\right), \, \mathsf{Re}(s)>0. $$
(10)
Moreover, for any p>0 and k>−1 the absolute moments are given by
$$ \mathbb{E}\left[\left|X_{p}\right|^{k}\right] =\frac{2^{\frac{k}{p}}\alpha^{k}}{\Gamma\left(\frac{1}{p}\right)} \Gamma \left(\frac{k+1}{p}\right). $$
(11)
Proof
The Mellin transform can be computed by using the integral (Poularikas 1998, Table 8.1)
$$ \int_{0}^{\infty} x^{s-1} e^{- a x^{p}} dx=\frac{1}{p} \left(\frac{1}{a}\right)^{\frac{s}{p}} \Gamma\left(\frac{s}{p} \right), \text{for}\ \mathsf{Re}(a)>0, $$
(12)
and, therefore,
$$ \mathbb{E}\left[\left|X_{p}\right|^{s-1}\right]= \frac{2c_{p}}{\alpha} \int_{0}^{\infty} x^{s-1} e^{-\frac{x^{p}}{2\alpha^{p}}} dx = \frac{2^{\frac{s-1}{p}}}{\Gamma \left(\frac{1}{p}\right)} \alpha^{s-1} \Gamma\left(\frac{s}{p}\right), \notag $$
where in the last step we used the value of cp in (1). Moreover, the above integral is finite if Re(s)>0 and p>0. The proof of (11) follows by choosing s=k+1 in (10). This concludes the proof. □
Note that the p-th absolute moment of Xp is given by \(\mathbb {E}\left [\left |X_{p}\right |^{p}\right ]= \frac {2\alpha ^{p}}{p}.\)
The expression in (11) can also be extended to multivariate GG distributions defined through p norms; see for example Lutwak et al. (2007) and Arellano-Valle and Richter (2012).
The following corollary, which relates k-th moments of two GG distributions of a different order, is useful in many proofs.
Corollary 1
Let \(X_{q} \sim \mathcal {N}_{q}(0,1)\) and \(X_{p} \sim \mathcal {N}_{p}(0,1)\). Then, for qp>0
$$ \mathbb{E}\left[\left|X_{q}\right|^{k}\right] \le \mathbb{E}\left[\left|X_{p}\right|^{k}\right], $$
(13)
for any \(k \in \mathbb {R}^{+}\). Moreover, for q>p
$$ {\lim}_{k \to \infty} \left(\frac{\mathbb{E}\left[\left|X_{p}\right|^{k}\right]}{\mathbb{E}\left[\left|X_{q}\right|^{k}\right]}\right)^{\frac{1}{k}} =\infty. $$
(14)
Proof
See Appendix A. □
2.2 Moment problem
The classical moment problem asks whether a distribution can be uniquely determined by its moments. For random variables defined on \(\mathbb {R}\), this problem goes under the name of the Hamburger moment problem and for random variables on \(\mathbb {R}^{+}\) under the name of the Stieltjes moment problem (Stoyanov 2000). If the answer is affirmative, we say that the moment problem is determinate. Otherwise, we say that the moment problem is indeterminate and there exists another distribution that shares the same moments.
Proposition 2
The GG distribution is determinate for p[1,) and indeterminate for p(0,1).
Proof
We first show that for p(0,1) the GG distribution is indeterminate. To show that an absolutely continuous distribution with a pdf f(x) is indeterminate it is enough to check the classical Krein sufficient condition (Stoyanov 2000) given by
$$ \int_{-\infty}^{\infty} \frac{-\log(f(x))}{1+x^{2}} dx <\infty. $$
(15)
In other words, if (15) is satisfied, then the distribution is indeterminate. For the GG distribution, the condition in (15) reduces to showing
$$\int_{0}^{\infty} \frac{x^{p}}{1+x^{2}} dx<\infty, $$
which is finite if p(0,1). Therefore, for p(0,1) the GG distribution is indeterminate.
To show that the distribution is determinate it is enough to show that the characteristic function has a power series expansion with a positive radius of convergence. For the GG distribution with p[1,), this will be done in Proposition 10. □
The interested reader is referred to [Lin and Huang (1997), Theorem 2] and [Hoffman-Jørgensen (2017), p. 301] where the conditions for the moment determinacy are provided for a Double Generalized Gamma distribution of which a GG distribution is special case.
Remark 1
To show that for p(0,1) there are distributions with the same moments as GG distributions, one can modify the example in [Stoyanov (2000), Chapter 11.4]. Specifically, for any ε(0,1) there exists ρ,r and λ such that the pdf
$$g(x)= f_{X_{p}}(x) \left(1+ \epsilon \psi(x) \right),\text{where} \psi(x)= |x|^{\rho} \mathrm{e}^{-r |x|^{p}} \sin \left(\lambda \tan (p \pi) |x|^{p} \right), $$
has the same integer moments as a GG distribution.
Remark 2
In (Varanasi and Aazhang 1989) the authors studied the problem of estimating the parameter p from n independent realizations of a GG random variable. As one of the proposed methods, the authors used empirical moments to estimate the parameter p. Moreover, in Varanasi and Aazhang (1989) it has been observed that the method of moments performs poorly for p(0,1). In view of Proposition 2, the observation about the method of moments made in Varanasi and Aazhang (1989) can be attributed to the fact that the GG distribution is indeterminate for p(0,1).
Properties of the distribution
3.1 Stochastic ordering
The cumulative distribution function (CDF) of \(X_{p}~\sim \mathcal {N}_{p}(\mu, \alpha ^{p})\) is given by
$$ F_{X}(x)=\frac{1}{2} + \text{sign}(x-\mu)\frac{\gamma\left(\frac{1}{p}, \frac{|x-\mu|^{p}}{2\alpha^{p}} \right)}{2\Gamma\left(\frac{1}{p}\right)}, \ x \in \mathbb{R}. $$
(16)
Corollary 1 suggests that there might be some ordering between members of the GG family. To make this point more explicit we need the following definition.
Definition 2
A random variable X dominates another random variable Y in the sense of the first-order stochastic dominance if
$$ F_{X}(x) \le F_{Y}(x), \forall x. $$
(17)
A random variable X dominates another random variable Y in the sense of the second-order stochastic dominance if
$$ \int_{-\infty}^{x} [ F_{Y}(t)-F_{X}(t) ]dt \ge 0, \forall x. $$
(18)
Proposition 3
Let \(X_{p}\sim \mathcal {N}_{p}(0,1)\) and \(X_{q}\sim \mathcal {N}_{q}(0,1)\). Then, for pq, Xq dominates Xp in the sense of the second-order stochastic dominance.
Proof
See Appendix B. □
It can be shown that the first-order stochastic dominance does not hold since for pq
$$\begin{array}{*{20}l} F_{X_{q}} (x) &\le F_{X_{p}} (x), \, x \le 0, \\ F_{X_{q}} (x) &\ge F_{X_{p}} (x), \, x > 0. \end{array} $$
From Proposition 3 we have the following inequality for the expected value of functions of GG distributions.
Proposition 4
Let \(X_{q} \sim \mathcal {N}_{q}(0,1)\) and \(X_{p} \sim \mathcal {N}_{p}(0,1)\). Then, for pq and for any nondecreasing and concave function \(g: \mathbb {R} \to \mathbb {R}\) we have that
$$ \mathbb{E}\left[ g\left(X_{q}\right) \right] \ge \mathbb{E}\left[ g\left(X_{p}\right) \right]. $$
(19)
Proof
The inequality in (19) is equivalent to the second-order stochastic dominance. For more details, the interested reader is referred toLevy (1992). □
Examples of functions that satisfy the hypothesis of Proposition 4 are \(g(x)= x- \sqrt {x^{2}+1} \) and g(x)=−etx,t≥0. These choices lead to the following inequalities for pq:
$$\begin{array}{*{20}l} &\mathbb{E} \left[ \sqrt{X_{q}^{2}+1} \right] \le \mathbb{E} \left[ \sqrt{X_{p}^{2}+1} \right], \end{array} $$
(20)
$$\begin{array}{*{20}l} &\mathbb{E} \left[ \mathrm{e}^{-{tX}_{q}}\right ] \le \mathbb{E} \left[ \mathrm{e}^{-{tX}_{p}} \right], \text{ for} t \ge 0 \text{ and} 1 < p,q. \end{array} $$
(21)
In particular, the inequality in (21) shows that the Laplace transform of \(f_{X_{p}}\) (which exists if 1<p,q) is larger than the Laplace transform of \(f_{X_{q}}\).
3.2 Relation to completely monotone functions and positive definiteness
We begin by introducing the notion of completely monotone and Bernstein functions.
Definition 3
A function f:[0,)→[0,) is said to be completely monotone if
$$ \left(-1\right)^{k} \frac{d^{k} f(x)}{ dx^{k}} \ge 0, \text{ for} x>0, \text{ and} k \in \mathbb{N}^{+}. $$
(22)
A function f:[0,)→[0,) is said to be a Bernstein function if the derivative of f is a completely monotone function.
Applying the well-known result fromSchilling et al. (2012), that the composition of a completely monotone function and a Bernstein function is completely monotone, on the function ex (completely monotone) and the function \(\frac {x^{p}}{2}\) (Bernstein for p(0,1]) we obtain the following.
Corollary 2
For p(0,1] the function \( \mathrm {e}^{-\frac {x^{p}}{ 2 }}\) is completely monotone.
For p>1 the function \(\mathrm {e}^{-x^{p}}\) is not completely monotone.
As will be observed throughout this paper, the GG distribution exhibits different properties depending on whether p≤2 or p>2. At the heart of this behavior is the concept of positive-definite functions.
Definition 4
(Positive Definite Function (Stewart 1976).) A function \(f: \mathbb {R} \to \mathbb {C}\) is called positive definite if for every positive integer n and all real numbers x1,x2,...,xn, the n×n matrix
$$\begin{array}{*{20}l} A= (a_{i,j})_{i,j=1}^{n}, \ a_{i,j}= f(x_{i}-x_{j}), \end{array} $$
(23)
is positive semi-definite.
The next result relates the pdf of the GG distribution to the class of positive definite functions.
Theorem 1
The function \( \mathrm {e}^{-\frac {| x|^{p}}{ 2 }}\) is
• not positive definite for p(2,); and
• positive definite for p(0,2]. Moreover, there exists a finite non-negative Borel measure μp on \(\mathbb {R}^{+}\) such that for x>0
$$ \mathrm{e}^{-\frac{x^{p}}{2}}= \int_{0}^{\infty} e^{-\frac{t}{2}x^{2}} d\mu_{p}(t). $$
(24)
Proof
See Appendix C. □
The expression in (24) will form a basis for much of the analysis in the regime p(0,2] and will play an important role in examining properties of the characteristic function of the GG distribution. The following corollary of Theorem 1 will also be useful.
Corollary 3
For any 0<qp≤2 let \(r= \frac {2q}{p}\). Then, for x>0
$$ \mathrm{e}^{-\frac{x^{q}}{2}}= \int_{0}^{\infty} e^{-\frac{t}{2} x^{r}} d\mu_{p}(t). $$
(25)
Proof
The proof follows by substituting x in (24) with \(x^{\frac {q}{p}}\). □
On product decomposition of GG random variables
As a consequence of Theorem 1 we have the following decompositional representation of the GG random variable.
Proposition 5
For any 0<qp≤2 let \(X_{q} \sim \mathcal {N}_{q}(0,1)\). Then,
$$ X_{q} \stackrel{d}{=} V_{p,q} \cdot X_{\frac{2q}{p}}, $$
(26a)
where Vp,q is a positive random variable independent of \( X_{\frac {2q}{p}} \sim \mathcal {N}_{\frac {2q}{p}}(0,1)\), and where =d denotes equality in distribution. Moreover, Vp,q has the following properties:
• Vp,q is an unbounded random variable for p<2 and Vp,q=1 for p=2; and
• for p<2, Vp,q is a continuous random variable with pdf given by
$$ f_{V_{p,q}}(v)= \frac{1}{2\pi} \frac{\Gamma \left(\frac{p}{2q} \right)}{\Gamma \left(\frac{1}{q} \right)} \int_{\mathbb{R}} v^{-it-1} \frac{2^{\frac{it}{q}} \Gamma \left(\frac{it +1}{q}\right)}{2^{\frac{itp}{2q}} \Gamma \left(\frac{p(it+1)}{2q}\right)} dt, \; v>0. $$
(26b)
Proof
See Appendix D. □
Proposition 5 can be used to show that the GG random distribution is a Gaussian mixture which is formally defined next.
Definition 5
A random variable X is called a (centered) Gaussian mixture if there exists a positive random variable V and a standard Gaussian random variable Z, independent of V, such that X=dVZ.
As a consequence of Proposition 5 we have the following result.
Corollary 4
For q(0,2], \(X_{q}\sim \mathcal {N}_{q}(0,1)\) is a Gaussian mixture. In other words,
$$ X_{q} \stackrel{d}{=} V_{q,q} \cdot X_{2}, \notag $$
where Vq,q is independent of X2 and its pdf is defined in (26b).
Proof
The proof follows by choosing p=q in (26a). □
Another case of importance is
$$ X_{q} \stackrel{d}{=} V_{q,2q} \cdot X_{1}, \notag $$
where X1 is a Laplace random variable. For the ease of notation the special cases of Gaussian and Laplace mixtures will be denoted as follows in the sequel:
$$\begin{array}{*{20}l} V_{G,q}&= V_{q,q}, \text{for} q\le 2, \end{array} $$
(27a)
$$\begin{array}{*{20}l} V_{L,q}&= V_{q,2q}, \text{for} q \le 1, \end{array} $$
(27b)
respectively.
4.1 On the PDF of V p,q
The expression for the pdf of Vp,q in (26b) can be difficult to analyze due to the complex nature of the integrand. The next result provides two new representations of the pdf of Vp,q that in many cases are easier to analyze than the expression in (26b).
Proposition 6
For 0<qp≤2 the pdf of a random variable Vp,q has the following representations:
1. 1
Power Series Representation
$$ f_{V_{p,q}}(v)= \frac{ \Gamma \left(\frac{p}{2q} \right)}{ \Gamma \left(\frac{1}{q} \right)} \sum\limits_{k=1}^{\infty} a_{k} v^{kq}, \ v>0, $$
(28)
where
$$ a_{k}= \frac{q}{\pi} \frac{(-1)^{k+1} 2^{(kq+1) \left(\frac{p}{2q} -\frac{1}{q} \right)} \Gamma\left(\frac{kq}{2} +1 \right) \sin \left(\frac{\pi kq}{2} \right) }{k! }. $$
(29)
2. 2
Integral Representation
$$ f_{V_{p,q}}(v)=\frac{q 2^{\frac{p}{2q}-\frac{1}{q}} \Gamma \left(\frac{p}{2q} \right)}{ \pi \Gamma \left(\frac{1}{q} \right)} \int_{0}^{\infty} \sin \left(a_{p} v^{q} x^{\frac{p}{2}} \right) \mathrm{e}^{-b_{p} v^{q} x^{\frac{p}{2}}-x} dx, $$
(30)
where
$$ a_{p}=2^{\frac{p}{2}-1} \sin \left(\frac{\pi p}{2} \right), b_{p}=2^{\frac{p}{2}-1} \cos \left(\frac{\pi p}{2} \right). $$
(31)
Proof
See Appendix E. □
Remark 3
From (30) in Proposition 6, for the case of p=q=1 it is not difficult to see that the random variable VG,1 is distributed according to the Rayleigh distribution, since
$$ f_{V_{G,1}}(v)=\frac{ 2^{-\frac{1}{2} }}{ \sqrt{\pi}} \int_{0}^{\infty} \sin \left(\frac{ v x^{\frac{1}{2}} }{\sqrt{2}}\right) \mathrm{e}^{-x} dx = \frac{v}{4} \mathrm{e}^{-\frac{v^{2}}{8}}, v \ge 0. $$
(32)
The pdf of the random variable VG,q is plotted in Fig. 1. Interestingly, the slope of \(f_{V_{G,q}}(v)\) around v=0+ behaves very differently depending on whether q<1 or q>1. This behavior can be best illustrated by looking at the pdf of \(V_{G,q}^{2}\), that is \(f_{V_{G,q}^{2}}(v)= \frac {1}{2 \sqrt {v}} f_{V_{G,q}}\left (\sqrt {v}\right)\).
Fig. 1
figure1
Plot of the probability density function \(f_{V_{G,q}}(v)\)
Proposition 7
Let \(f_{V_{G,q}^{2}}(v)\)be the pdf of the random variable \(V_{G,q}^{2}\). Then,
$$ {\lim}_{v \to 0^{+}} f_{V_{G,q}^{2}}(v)= \left\{ \begin{array}{ll} 0, & q>1 \\ \frac{1}{8}, & q=1\\ \infty, & q<1 \end{array} \right.. $$
(33)
Proof
By using the power series expansion of \(f_{V_{G,q}}(v)\) in (28) and the transformation \(f_{V_{G,q}^{2}}(v)= \frac {1}{2 \sqrt {v}} f_{V_{G,q}}\left (\sqrt {v}\right)\) (recall VG,q is a non-negative random variable) we have that
$$ f_{V_{G,q}^{2}}(v)= \frac{1}{2}\frac{\Gamma \left(\frac{1}{2}\right)}{\Gamma\left(\frac{1}{q}\right)} \left(a_{1} v^{\frac{q}{2}-\frac{1}{2}}+a_{2} v^{q-\frac{1}{2}}+a_{3} v^{\frac{3q}{2}-\frac{1}{2}}+... \right). $$
(34)
The proof follows by taking the limit as v→0 in (34). □
As we will demonstrate later, the behavior of the pdf of VG,q around zero will be important in studying the asymptotic behavior of the characteristic function of Xq. This is reminiscent of the initial value theorem of the Laplace transform where the value of a function at zero can be used to estimate the asymptotic behavior of its Laplace transform. Indeed, as we will see, the characteristic function of Xq and the Laplace transform of \(V_{G,q}^{2}\) have a clear connection.
4.2 On the determinacy of the distribution of V G,q
Similar to the investigation in “Moment problem” section of whether GG distributions are determinant (uniquely determined by their moments) or not, we now conduct a similar investigation of the distributions of VG,q.
Proposition 8
The distribution of VG,q is determinant for \(q\ge \frac {2}{5}\).
Proof
To show that the distribution of VG,q is determinant we can use Carleman’s sufficient condition for positive random variables (Stoyanov 2000). This condition states that the distribution of VG,q is determinant if
$$ \sum\limits_{k=1}^{\infty} \left(\mathbb{E}[V_{G,q}^{k}] \right)^{-\frac{1}{2k}}=\infty. $$
(35)
Next using the expression for the k-th moment of VG,q given in Appendix D and the approximation of the ratio of moments shown in Appendix A we have that
$$ \mathbb{E}[ V_{G,q}^{k} ]= \frac{ \mathbb{E}\left[|X_{q}|^{k}\right]}{\mathbb{E}\left[|X_{2}|^{k}\right]} \approx \left(\frac{2}{e} \right)^{\frac{k}{q}-\frac{k}{2}} \frac{ 2^{\frac{k}{2}} }{ q^{\frac{k}{q}}} \left(k+1 \right)^{(k+1) \left (\frac{1}{q} -\frac{1}{2} \right) }. $$
(36)
Using the approximation in (36) in the sum in (35) we have that
$$ \sum\limits_{k=1}^{\infty} \left(\mathbb{E}[V_{G,q}^{k}] \right)^{-\frac{1}{2k}} \approx \left(\frac{2}{e} \right)^{\frac{1}{4}-\frac{1}{2q}} \frac{ q^{\frac{1}{2q}} }{ 2^{\frac{1}{4}}} \sum\limits_{k=1}^{\infty} \left(k+1 \right)^{- \frac{(k+1)}{2k} \left (\frac{1}{q} -\frac{1}{2} \right) }. $$
(37)
By using conditions for the convergence of p-series the sum in (37) diverges if \( \frac {1}{2} \left (\frac {1}{q}-\frac {1}{2} \right) \ge 1\) or \(q \ge \frac {2}{5}\). Therefore, Carleman’s condition is satisfied if \(q \ge \frac {2}{5}\), and thus VG,q has a determinant distribution for \(q \ge \frac {2}{5}\). This concludes the proof. □
Remark 4
According to Proposition 2 and 8, for the range of values \(q \in \left [\frac {2}{5}, 1\right ]\) the random variable Xq=dVG,q·X2 is a product of two random variables with determinant distributions while Xq itself has an indeterminate distribution on \(q \in \left [\frac {2}{5}, 1\right ]\) by Proposition 2. This observation generates an interesting example illustrating that the product of two independent random variables with determinant distributions can have an indeterminate distribution.
Characteristic function
The focus of this section is on the characteristic function of the GG distribution. The characteristic function of the GG distribution can be written in the following integral forms.
Theorem 2
The characteristic function of \(X_{p} \sim \mathcal {N}_{p} (0,1)\) is given by
• For any p>0
$$ \phi_{p}(t) = 2c_{p} \int_{0}^{\infty} \cos(t x) e^{-\frac{x^{p}}{2}} dx, \, t \in \mathbb{R}. $$
(38a)
• For any p(0,2]
$$ \phi_{p}(t) = \mathbb{E} \left[ \mathrm{e}^{-\frac{t^{2} V_{G,p}^{2}}{2}} \right], \, t \in \mathbb{R}, $$
(38b)
where the density of a variable VG,p is defined in Proposition 5.
Proof
The proof of (38a) follows from the fact that \(e^{-\frac {|x|^{p}}{2} }\) is an even function which implies that the Fourier transform is equivalent to the cosine transform.
To show (38b) observe that
$$\phi_{p}(t) \stackrel{a)}{=} \mathbb{E}\left[\mathrm{e}^{it V_{G,p} X_{2}}\right]= \mathbb{E} \left[\mathbb{E}\left[\mathrm{e}^{it V_{G,p} X_{2}}|V_{G,p}\right]\right]\stackrel{b)}{=} \mathbb{E} \left[\mathrm{e}^{-\frac{t^{2}V_{G,p}^{2} }{2}}\right], $$
where the equalities follow from: a) the decomposition property in Proposition 5; and b) the independence of VG,p and X2 and the fact that the characteristic function of X2 is \(\mathrm {e}^{-\frac {t^{2}}{2}}\). This concludes the proof. □
As a consequence of the positive definiteness, ϕp(t), for p(0,2], has a more manageable form given in (38b). However, for p>2 it does not appear that ϕp(t) can be written in a more amenable form and the best simplification one can perform is a trivial symmetrization that converts the Fourier transform into the cosine transform in (38a). Nonetheless, the cosine representation in (38a) does allow us to simplify the implementation of the numerical calculation of ϕp(t). Examples of characteristic functions of \(X_{p} \sim \mathcal {N}_{p} (0,1)\) for several values of p are given in Fig. 2.
Fig. 2
figure2
Plot of the characteristic function of \(X_{p} \sim {\mathcal {N}}_{p} (0,\alpha =2)\) for several values of p
The following result is immediate by Theorem 2.
Corollary 5
For p(0,2], ϕp(t) is a decreasing function for t>0.
5.1 Connection to stable distributions
A class of distributions that is closed under convolution of independent copies is called stable. A more precise definition is given next.
Definition 6
Let X1 and X2 be independent copies of a random variable X. Then X is said to be stable if for all constants a>0 and b>0, there exist c>0 and dR such that
$$ a X_{1} +b X_{2} \stackrel{d}{=} c X+d. $$
(39)
The defining relationship in (39) is equivalent to
$$ \phi_{X}(a t) \phi_{X}(b t) = \phi_{X}(c t) \mathrm{e}^{itd}, \, \forall t \in \mathbb{R}, $$
(40)
where ϕX(t) is a characteristic function of a random variable X.
Throughout this work we will use stable distribution, stable random variable, and stable characteristic function interchangeably.
The characteristic function of a stable distribution has the following canonical representation:
$$\begin{array}{*{20}l} \phi_{X}(t) &= \mathrm{e}^{-it\mu-|c t|^{\alpha} \left(1-i\beta \mathsf{sign}(t) \Delta(t) \right)}, \text{where} \Delta(t)= \left\{ \begin{array}{ll} \tan \left(\frac{\pi \alpha}{2} \right), & \alpha \neq 1\\ -\frac{2}{\pi} \log|t|, & \alpha =1 \end{array} \right., \end{array} $$
(41)
where \(\mu \in \mathbb {R}\) is the shift-parameter, \(c \in \mathbb {R}^{+}\) is the scaling parameter, β[−1,1] is the skewness parameter, and α(0,2] is the order parameter. We refer the interested reader to (Zolotarev 1986) for a comprehensive treatment of the subject of stable distributions.
In this work we are interested in symmetric stable distributions (i.e., β=0) which also go under the name of α-stable distributions with the characteristic function given by
$$ \phi_{X}(t)= \mathrm{e}^{-| t|^{\alpha}}, \, t \in \mathbb{R}. $$
(42)
Observe that there is a duality between a class of symmetric stable distributions and a class of GG distributions with p(0,2]. Up to a normalizing constant, the pdf of a GG random variable is equal to the characteristic function of an α-stable random variable. Equivalently, the pdf of an α-stable random variable is equal, up to a normalizing constant, to the characteristic function of a GG random variable.
We exploit this duality to give, yet another, integral representation of the characteristic function of the GG distribution with parameter p(0,2].
Proposition 9
For p(0,2]{1}
$$ \phi_{p}(t)= 2 \pi c_{p} \frac{ p |t|^{\frac{1}{p-1}}}{2 |p-1|} \int_{0}^{1} U_{p}(x) \mathrm{e}^{- |t|^{\frac{p}{p-1}} U_{p}(x)} dx, $$
(43a)
where
$$ U_{p}(x)= \left(\frac{\sin \left(\frac{\pi x p}{2}\right)}{ \cos \left(\frac{\pi x}{2}\right)} \right)^{\frac{p}{1-p}} \frac{ \cos \left(\frac{\pi x (p-1)}{2}\right)}{ \cos \left(\frac{\pi x }{2}\right)}. $$
(43b)
Moreover, let the integrand in (43a) be given by
$$g_{p}(x)= U_{p}(x) \mathrm{e}^{- |t|^{\frac{p}{p-1}} U_{p}(x) }, x \in [0,1], $$
then:
• Up(x) is a non-negative function;
• For p(0,1), Up(x) is an increasing function with
$${\lim}_{x \to 0^{+}} U_{p}(x)=0, \, {\lim}_{x \to 1^{-}} U_{p}(x)=\infty; $$
• For p(1,2], Up(x) is a decreasing function with
$${\lim}_{x \to 0^{+}} U_{p}(x)=\infty, \, {\lim}_{x \to 1^{-}} U_{p}(x)=0; $$
• For all p(0,2]{1}
$${\lim}_{x \to 0^{+} }g_{p}(x)=0, \, {\lim}_{x \to 1^{-}} g_{p}(x)=0; \text{ and} $$
• The function gp has a single maximum given by
$$\max_{x \in [0,1]} g_{p}(x)= \frac{1}{ \mathrm{e} |t|^{\frac{p}{p-1} }}. $$
Proof
The characterization in (43a) can be found in (Zolotarev 1986, Theorem 2.2.3). The proof of the properties of Up(x) is presented in Appendix F. □
Since the integral in Proposition 9 is performed over a finite interval, the characterization in Proposition 9 is especially useful for numerical computations of ϕp(t). The plots in Fig. 2, for p(0,2), are done by using the expression for ϕp(t) in (43a). To the best of our knowledge, the properties of Up(x) and gp(x), derived in Proposition 9, are new and facilitate a more efficient numerical computation of the integral representation of ϕp(t). The plot of the function Up(x) for p=0.5 and p=1.5 is shown in Fig. 3.
Fig. 3
figure3
Plot of the Up(x) for p=1.5 and p=0.5
We suspect that most of the properties of ϕp(t) for p(0,2) that we derive in this paper can be found by using the integral expression in (43a). However, instead of taking this route we use the product decomposition in Proposition 5 to derive all the properties of ϕp(t). We believe that using a product decomposition is a more natural approach. Moreover, the positive random variables in Gaussian mixtures, VG,p in our case, naturally appear in a number of applications (e.g., bounds on the entropy of sum of independent random variables (Eskenazis et al. 2016)) and are of independent interest.
5.2 Analyticity of the characteristic function
An important question, in particular for numerical methods, is: when can the characteristic function of a random variable be represented as a power series of the form
$$ \sum\limits_{k=0}^{\infty} \frac{(it)^{k}}{k!} \mathbb{E}\left[\!X^{k}\right]? $$
(44)
The above expression is especially useful since the moments of GG distributions are known for every k; see Proposition 1.
Proposition 10
ϕp(t) is a real analytic function for
• \(t \in \mathbb {R}\) for p>1; and
• \( |t| < \frac {1}{2} \) for p=1.
For p<1 the function ϕp(t) is not real analytic.
Proof
See Appendix G. □
The results of Proposition 10 also lead to the conclusion that for p>1 the moment generating function of Xp, \(M_{p}(t)=\mathbb {E}\left [e^{{tX}_{p}}\right ]\) exists for all \(t\in \mathbb {R}\).
5.3 On the distribution of zeros of the characteristic function
As seen from Fig. 2 the characteristic function of the GG distribution can have zeros. The next theorem gives a somewhat surprising result on the distribution of zeros of ϕp(t).
Theorem 3
The characteristic function of ϕp(t) has the following properties:
• for p>2, ϕp(t) has at least one positive to negative zero crossing. Moreover, the number of zeros is at most countable; and
• for p(0,2], ϕp(t) is a positive function.
Proof
See Appendix H. □
Also, we conjecture that zeros of ϕp(t) have the following additional property.
Conjecture 1
For p(2,) zeros of ϕp(t) do not appear periodically.
It is important to point out that, for p=, the characteristic function is given by \(\phi _{\infty }(t)= \frac {\sin (t)}{t}=\text {sinc}(t)\), and zeros do appear periodically. However, for p< we conjecture that zeros do not appear periodically.
5.4 Asymptotic behavior of ϕ p(t)
Next, we find the asymptotic behavior of ϕp(t) as t. In fact, the next result gives the asymptotic behavior not only of \(\phi _{p}(t)=\mathbb {E} \left [ \mathrm {e}^{-\frac {V_{G,p}^{2} t^{2}}{2}} \right ]\) but also of a more general function
$$ t \mapsto \mathbb{E} \left[ V_{G,p}^{m} \mathrm{e}^{-\frac{V_{G,p}^{2} t^{2}}{2}} \right], $$
(45)
for some m>0. The analysis of the function in (45) also allows one to find asymptotic behavior on higher order derivatives of ϕp(t). For example, the first order derivative can be related to the function in (45) as follows:
$$\phi_{p}^{\prime }(t)=-t \, \mathbb{E} \left[ V_{G,p}^{2} \mathrm{e}^{-\frac{V_{G,p}^{2} t^{2}}{2}} \right]. $$
Proposition 11
Let \(m \in \mathbb {R}^{+}\); then
$$ {\lim}_{t \to \infty} t^{m+p+1}\mathbb{E} \left[ V_{G,p}^{m} \mathrm{e}^{-\frac{V_{G,p}^{2} t^{2}}{2}} \right] = A_{m}=\frac{p}{2} \Gamma \left(\frac{m+p+1}{2}\right) 2^{\frac{m+2p}{2}- \frac{p+1}{p}}. $$
(46)
Proof
See Appendix I. □
Using Proposition 11, we can give an exact tail behavior for ϕp(t).
Proposition 12
For p(0,2)
$$ {\lim}_{t \to \infty} \phi_{p}(t) t^{p+1} =A_{0}, $$
(47a)
where A0 is defined in (46). Moreover, for 0<q,p<2 and some α>0
$$ {\lim}_{t \rightarrow \infty} \frac{\phi_{q}(\alpha t)}{\phi_{p}(t)}= \left\{ \begin{array}{ll} 0, & q> p \\ \frac{1}{\alpha^{q+1} }, & q=p \\ \infty, & q< p \end{array} \right.. $$
(47b)
Proof
The proof follows immediately from Proposition 11. □
Note that, for p(0,2], the function \(\phi _{p}(\sqrt {2t})\) can be thought of as a Laplace transform of the pdf of the random variable \(V_{G,p}^{2}\). This observation together with the asymptotic behavior of ϕp(t) leads to the following result.
Proposition 13
For \(n\in \mathbb {R}\), \(\mathbb {E}[V_{G,p}^{n}]\) is finite if and only if n+p>−1.
Proof
For n>−1 the proof is a consequence of the decomposition property in Propositions 5 and 1 where it is shown that \(\mathbb {E}[|X_{p}|^{n}]<\infty \) if n>−1 for all p>0. Therefore, we assume that n<−1.
First observe that for any positive random variable X and k>0 the negative moments of X can be expressed as follows:
$$\begin{array}{*{20}l} \mathbb{E} \left[X^{-k} \right] = \frac{1}{\Gamma\left(k\right)} \int_{0}^{\infty} F(t) t^{k-1} dt, \end{array} $$
(48)
where F(t) is the Laplace transform of the pdf of X. Using the identity in (48) and the fact that \(\phi _{p}(\sqrt {2t})\) is the Laplace transform of the pdf of the random variable \(V_{G,p}^{2}\) we have that
$$ \mathbb{E}\left[V_{G,p}^{-2k}\right] =\frac{1}{\Gamma\left(k\right)} \int_{0}^{\infty} \phi_{p}(\sqrt{2t}) t^{k-1} dt. $$
(49)
Note that the integral in (49) is finite if and only if \( \phi _{p}\left (\sqrt {2t}\right) t^{k-1}= O \left (t^{-(1+\epsilon)}\right)\) for every ε>0. Moreover, by Proposition 12 we have that \(\phi _{p}\left (\sqrt {2t}\right) t^{k-1}= O \left (\frac {t^{k-1}}{t^{\frac {p+1}{2}}} \right)\), which implies that the integral in (49) is finite if and only if 2kp<1. Setting 2k=−n concludes the proof. □
According to Proposition 1 and Proposition 5, for n>−1
$$\mathbb{E}\left[V_{G,p}^{n}\right]= \frac{\mathbb{E}[|X_{p}|^{n}]}{\mathbb{E}[|X_{2}|^{n}]} <\infty, $$
while for n≤−1 it is not clear whether \(\mathbb {E}\left [V_{G,p}^{n}\right ]\) is finite since both moments \(\mathbb {E}[|X_{p}|^{n}]~=~\infty \) and \(\mathbb {E}[|X_{2}|^{n}]=\infty \). The result in Proposition 13 is interesting because it states that \(\mathbb {E}[V_{G,p}^{n}]\) is finite even if absolute moments of Xp and X2 are infinite. The result in Proposition 13 plays an important role in deriving non-Shannon type bounds in problems of communicating over channels with GG noise; see (Dytso et al. 2017b) for further details.
Additive decomposition of a GG random variable
In this section we are interested in determining whether a GG random variable \(X_{q}~\sim ~\mathcal {N}_{q}(0,\alpha ^{q})\) can be decomposed into a sum of two or more independent random variables.
6.1 Infinite divisibility of the characteristic function
Definition 7
A characteristic function ϕ(t) is said to be infinitely divisible if for every \(n \in \mathbb {N}\) there exists a characteristic function ϕn(t) such that
$$ \phi(t)= \left(\phi_{n}(t) \right)^{n}. $$
(50)
Similarly to stable distributions, we use infinitely divisible distribution, infinitely divisible random variable, and infinitely divisible characteristic function interchangeably.
Next we summarize properties of infinitely divisible distributions needed for our purposes.
Theorem 4
(Properties of Infinitely Divisible Distributions.) An infinitely divisible distribution satisfies the following properties:
1. 1
((Lukacs 1970, Theorem 5.3.1).) An infinitely divisible characteristic function has no real zeros;
2. 2
((van Harn and Steutel 2003, Theorem 10.1).) A symmetric distribution that has a completely monotone pdf on (0,) is infinitely divisible;
3. 3
(Lévy-Khinchine canonical representation (Lukacs 1970, Theorem 5.5.1).) The function ϕ(t) is an infinitely divisible characteristic function if and only if it can be written as
$$ \log \left(\phi(t) \right)= ita + \int_{-\infty}^{\infty} \left(\mathrm{e}^{itx}-1 -\frac{itx}{1+x^{2}} \right) \frac{1+x^{2}}{x^{2}}d\theta(x), $$
(51)
where a is real and where θ(x) is a non-decreasing and bounded function such that \({\lim }_{x \to -\infty } \theta (x)=0\). The function dθ(x) is called the Lévy measure. The integrand is defined for x=0 by continuity to be equal to \(-\frac {t^{2}}{2}\). The representation in (51) is unique; and
4. 4
((van Harn and Steutel 2003, Corollary 9.9).) A non-degenerate infinitely divisible random variable X has a Gaussian distribution if and only if it satisfies
$$ \limsup_{x \rightarrow \infty} \frac{- \log \mathbb{P}[ |X| \ge x] }{x \, \log (x)}=\infty. $$
(52)
In general, the Lévy measure dθ is not a probability measure and hence the distribution function θ(x) is not bounded by one.
We use Theorem 4 to give a complete characterization of the infinite divisibility property of the GG distribution.
Theorem 5
A characteristic function ϕp(t) is infinitely divisible if and only if p (0,1] {2}.
Proof
For the regime p(0,1] in Corollary 2 it has been shown that the pdf is completely monotone on (0,). Therefore, by property 2) in Theorem 4 it follows that ϕp(t) is infinitely divisible for p(0,1].
Next observe that
$$\begin{array}{*{20}l} \limsup_{x \rightarrow \infty} \frac{-\log \mathbb{P}[ |X| \ge x] }{x \, \log (x)}& \stackrel{a)}{=} \limsup_{x \to \infty} \frac{- \log \left(\frac{\Gamma\left(\frac{1}{p}, \frac{x^{p}}{2} \right)}{\Gamma(\frac{1}{p})}\right) }{x \, \log(x)} \notag\\ & \stackrel{b)}{=}\limsup_{x \rightarrow \infty} \frac{- \log \left(x^{\frac{1}{p}-1} \mathrm{e}^{-\frac{x^{p}}{2}} \right) }{x \, \log(x)} \notag\\ &=\limsup_{x \rightarrow \infty} \frac{x^{p}}{2x \,\log(x)} =\left\{ \begin{array}{ll} 0 & p \le 1,\\ \infty & p>1, \end{array} \right. \end{array} $$
(53)
where the equalities follow from: a) the expression for the CDF in (16); and b) using the limit \({\lim }_{x \to \infty } \frac {\Gamma (s,x)}{x^{s-1} \mathrm {e}^{-x} }=1\) (Olver 1991).
From the limit in (53) and since the distribution is Gaussian only for p=2 we have from property 4) in Theorem 4 that ϕp(t) is not infinitely divisible for p≥1 unless p=2.
Another proof that ϕp(t) is not infinitely divisible for p>2 follows from Theorem 3 since ϕp(t) has at least one zero, which violates property 1) of Theorem 4. This concludes the proof. □
Next, we show that the Lévy measure in the canonical representation in (51) is an absolutely continuous measure. This also allows us to give a new representation of ϕp(t) for p(0,1] where it is infinitely divisible.
Proposition 14
For p(0,1], the Lévy measure is absolutely continuous with density fθ(x) and ϕp(t) can be expressed as follows:
$$ \phi_{p}(t)= \mathrm{e}^{-\int_{-\infty}^{\infty} \left(1-\cos(tx) \right) \frac{1+x^{2}}{x^{2}} f_{\theta}(x) dx}. $$
(54a)
Moreover, for x≠0
$$ \left(1+x^{2}\right) f_{\theta}(x)=- \frac{x}{\pi} \int_{0}^{\infty} \left(\log \phi_{p}(t) \right)^{\prime} \sin(tx) dt. $$
(54b)
Proof
See Appendix J. □
Remark 5
For the Laplace distribution with \(\phi _{1}(t)= \frac {1}{1+4t^{2}}\), the density fθ(x) can be computed by using (54b) and is given by
$$ \left(1+x^{2}\right) f_{\theta}(x)=|x| \mathrm{e}^{-\frac{|x|}{2}}, $$
(55a)
and the exponent in the Lévy-Khinchine representation is given by
$$ \int_{-\infty}^{\infty} (1-\cos(tx)) \frac{1+x^{2}}{x^{2}} f_{\theta}(x) dx =\log \left(1 +4 t^{2} \right). $$
(55b)
6.2 Self-decomposability of the characteristic function
In this section we are interested in determining whether a GG random variable \(X_{q} \sim \mathcal {N}_{q}(0,\alpha ^{q})\) can be decomposed into a sum of two independent random variables in which one of the random variables is GG. Distributions with such a property are known as self-decomposable.
Definition 8
(Self-Decomposable Characteristic Function (Lukacs 1970;van Harn and Steutel 2003).) A characteristic function ϕ(t) is said to be self-decomposable if for every α≥1 there exists a characteristic function ψα(t) such that
$$ \phi(\alpha t)= \phi(t) \psi_{\alpha}(t). $$
(56)
In our context, the GG random variable \(X_{p} \sim \mathcal {N}_{p}(0,1)\) is self-decomposable if for every α≥1 there exists a random variable \(\hat {X}_{\alpha }\) such that
$$ \alpha X_{p} \stackrel{d}{=} \hat{X}_{\alpha}+Z_{p}, $$
(57)
where \(Z_{p}\sim \mathcal {N}_{p}(0,1)\) is independent of \( \hat {X}_{\alpha }\).
In this section, we will look at a generalization of self-decomposability (in Eqs. (56) and (57)) and study whether there exists a random variable \(\hat {X}_{\alpha }\) independent of \(Z_{p} \sim \mathcal {N}_{p}(0,1)\) such that
$$ \alpha X_{q}\stackrel{d}{=} \hat{X}_{\alpha}+Z_{p}, $$
(58)
where \(X_{q} \sim \mathcal {N}_{q}(0,1)\) for every α≥1. The decomposition in (58) finds application in information theory where the existence of the decomposition in (58) guarantees the achievability of Shannon’s bound on the capacity; see (Dytso et al. 2017b) for further details.
The existence of a random variable \( \hat {X}_{\alpha }\) is equivalent to showing that the function
$$ \phi_{(q,p,\alpha)}(t) =\frac{\phi_{q}(\alpha \cdot t) }{\phi_{p}(t) }, \, t \in \mathbb{R}, $$
(59)
is a valid characteristic function.
Observe that both Gaussian and Laplace are self-decomposable random variables. Self-decomposability of Gaussian random variables is a well known property. To see that the Laplace distribution is self-decomposable notice that
$$ \phi_{(1,1,\alpha)}(t) =\frac{1+4 t^{2}}{1+4 \alpha^{2} t^{2}}= \frac{1}{\alpha^{2}}+ \left(1- \frac{1}{\alpha^{2}} \right) \frac{1}{1+4 \alpha^{2} t^{2}}. $$
(60)
The expression in (60) is a convex combination of the characteristic function of a point mass at zero and the characteristic function of a Laplace distribution. Therefore, the expression in (60) is a characteristic function.
Checking whether a given function is a valid characteristic function is a notoriously difficult question, as it requires checking whether ϕ(q,p,α)(t) is a positive definite function; see (Ushakov 1999) for an in-depth discussion on this topic. However, a partial answer to this question can be given.
Theorem 6
For \((p,q) \in \mathbb {R}_{+}^{2}\) let
$$\begin{array}{*{20}l} \mathbb{S} &= \mathbb{S}_{1} \cup \mathbb{S}_{2},\\ \mathbb{S}_{1}&= \{ (p,q): 2< q < p \}, \\ \mathbb{S}_{2}&= \{ (p,q): q=p \in (0,1] \cup \{2 \} \}. \end{array} $$
Then the function ϕ(q,p,α)(t) in (59) has the following properties:
• for \((p,q) \in \mathbb {S}_{2}\), ϕ(q,p,α)(t) is a characteristic function (i.e., Xp is self-decomposable for p(0,1]{2});
• for \((p,q) \in \mathbb {R}^{2}_{+} \setminus \mathbb {S}\), ϕ(q,p,α)(t) is not a characteristic function for any α≥1; and
• for \( (p,q) \in \mathbb {S}_{1}\) and almost allFootnote 1 α≥1, ϕ(q,p,α)(t) is not a characteristic function.
Proof
See Appendix K. □
The result of Theorem 6 is depicted in Fig. 4
Fig. 4
figure4
In the regime \(\mathbb {S}_{2}=\{(p,q): 0< p=q<1 \}\) (the dashed line) ϕ(q,p,α)(t) is self-decomposable. We also emphasize the point (p,q)=(2,2) (the black square) corresponds to the Gaussian characteristic function, and the point (p,q)=(1,1) (the black circle) corresponds to the Laplace characteristic function. The regime \(\mathbb {S}_{1}=\{ (q,p): 2< q < p \}\) (the gray triangle) is where ϕ(q,p,α)(t) is not a characteristic function for almost all α≥1. The white space is the regime where ϕ(q,p,α)(t) is not a characteristic function for all α≥1
We would like to point out that for 2<qp there are cases when ϕ(q,p,α)(t) is a characteristic function for some but not all α≥1. Specifically, let p=q= in which case \(\phi _{\infty }(t)= \frac {\sin (t)}{t}=\text {sinc}(t)\) and
$$ \phi_{(\infty,\infty,\alpha)}(t)=\frac{\text{sinc}(\alpha t)}{\text{sinc}(t)}, \, t \in \mathbb{R}. $$
(61)
For example, when α=2 we have that \(\phi _{(\infty,\infty,\alpha)}(t)=\frac {1}{2} \cos (2t)\), which corresponds to the characteristic function of the random variable \(\hat {X}=\pm 1\) equally likely. Note that in the above example, because zeros of ϕp(t) occur periodically, we can select α such that the poles and zeros of ϕ(q,p,α)(t) cancel. However, we conjecture that such examples are only possible for p=, and for 2<p< zeros of ϕp(t) do not appear periodically (see Conjecture 1) leading to the following:
Conjecture 2
For 2<qp<, ϕ(q,p,α)(t) is not a characteristic function for all α>1.
It is not difficult to check, by using the property that convolution with an analytic function is again analytic, that Conjecture 2 is true if p is an even integer and q is any non-even real number.
Discussion and conclusion
In this work we have focused on characterizing properties of the GG distribution. We have shown that for p(0,2] the GG random variable can be decomposed into a product of two independent random variables where the first random variable is a positive random variable and the second random variable is also a GG random variable. This decomposition was studied by providing several expressions for the pdf of the positive random variable.
A related open question is whether Proposition 5 can be extended to the regime of p>2. That is, the question is, can Xp be decomposed as follows:
$$ X_{p} \stackrel{d}{=} V \cdot X_{q}, $$
(62)
for some positive random variable V independent of \(X_{q}\sim \mathcal {N}_{q}(0,1)\)? Noting that |X|p=dV ·|Xq| and using the Mellin transform method (recall that the Mellin transform works only for non-negative random variables) this question reduces to determining whether
$$ \phi_{\log(V)} (t) = \mathbb{E}\left[ V^{it} \right] = \frac{ \mathbb{E}\left[ |X_{p}|^{it} \right]}{ \mathbb{E}\left[ |X_{q}|^{it} \right]}= \frac{ 2^{\frac{it}{p}} \Gamma \left(\frac{it +1}{p}\right) \Gamma \left(\frac{1}{q} \right)}{ 2^{\frac{it}{q}} \Gamma \left(\frac{it +1}{q}\right) \Gamma \left(\frac{1}{p} \right)}, \, t \in \mathbb{R}, $$
is a proper characteristic function. A partial answer to this question is given next.
Proposition 15
The function ϕlog(V)(t)
• for p>q, is not a valid characteristic function. Therefore, the decomposition in (62) does not exist; and
• for p<q, is an integrable function. Moreover, if ϕlog(V)(t) is a valid characteristic function then the pdf of V is given by
$$ f_{V}(v)= \frac{1}{2 \pi} \frac{\Gamma \left(\frac{1}{q} \right)}{\Gamma \left(\frac{1}{p} \right)} \int_{\mathbb{R}} v^{-it-1} \frac{ 2^{\frac{it}{p}} \Gamma \left(\frac{it +1}{p}\right) }{ 2^{\frac{it}{q}} \Gamma \left(\frac{it +1}{q}\right)} dt, \ v>0. $$
(63)
Proof
See Appendix L. □
To check if the decomposition in (62) exists for p<q one needs to verify whether the function in (63) is a valid pdf. Because of the complex nature of the integral it is not obvious whether the function in (63) is a valid pdf, and we leave this for future work.
We have also characterized several properties of the characteristic function of the GG distribution such as analyticity, the distribution of zeros, infinite divisibility and self-decomposability. Moreover, in the regime p(0,2) by exploiting the product decomposition we were able to give an exact behavior of the tail of the characteristic function.
We expect that the properties derived in this paper will be useful for a large audience of researchers. For example, in (Dytso et al.2017b,2018) we have used the result in this paper to answer important information theoretic questions about optimal communication over channels with GG noise and optimal compression of GG sources. In view of the fact that GG distributions maximize entropy under Lp moment constraints, we also expect that GG distributions will start to play an important role in finding bounds on the entropy of sums of random variables; see for example (Eskenazis et al. 2016) and (Dytso et al. 2017a) where GG distributions are used to derive such bounds.
Appendix A: Proof of Corollary 1
To show that \( \mathbb {E}\left [|X_{q}|^{k}\right ] \le \mathbb {E}\left [|X_{p}|^{k}\right ] \) for 0<pq let
$$g_{k}(p) := 2^{\frac{k}{p}} \frac{ \Gamma \left(\frac{k+1}{p}\right) }{ \Gamma \left(\frac{1}{p} \right)}=\mathbb{E}\left[|X_{p}|^{k}\right]. $$
The goal is to show that for every fixed k>0 the function gk(p) is decreasing in p. This result can be extracted from the next lemma which demonstrates a slightly more general result.
Lemma 1
Let
$$ g_{k,a}(x) := a^{k x} \frac{ \Gamma \left((k+1)x\right)}{\Gamma (x)}, $$
(64)
and let γdenote the Euler’s constant where γ≈0.57721. Then, for every fixed k>0 and log(a)>γ the function gk,a(x) is increasing in x>0.
Proof
Instead of working with gk,a(x) it is simpler to work with a logarithm of gk,a(x) (recall that logarithms preserve monotonicity)
$$ f_{k,a}(x) := \log(g_{k,a}(x)). $$
(65)
Taking the derivative of fk,a(x) we have that
$$\begin{array}{*{20}l} \frac{d}{dx} f_{k,a}(x)&= k \log(a) + \frac{d}{dx} \log \left(\Gamma \left((k+1) x\right) \right)- \frac{d}{dx} \log \left(\Gamma \left(x\right) \right) \notag\\ &= k \log(a) + (k+1) \psi_{0}((k+1)x)- \psi_{0}(x), \end{array} $$
(66)
where ψ0(x) is the digamma function. Next using the series representation of the digamma function (Abramowitz and Stegun 1964) given by
$$ \psi_{0}(x)=-\frac{1}{x}- \gamma + \sum\limits_{n=0}^{\infty} \left(\frac{1}{n+1} -\frac{1}{n+1+x}\right), $$
(67)
we have that the derivative is given by
$$\begin{array}{*{20}l} \frac{d}{dx} f_{k,a}(x) &= k \log(a)+ (k+1) \left(\frac{-1}{(k+1)x}- \gamma + \sum\limits_{n=0}^{\infty} \left(\frac{1}{n+1} -\frac{1}{n+1+(k+1)x}\right) \right) \\ &\quad+\frac{1}{x}+ \gamma - \sum\limits_{n=0}^{\infty} \left(\frac{1}{n+1} -\frac{1}{n+1+x}\right) \\ &=k \left(\log(a) -\gamma \right)+ \sum\limits_{n=0}^{\infty} \left(\frac{k}{n+1} +\frac{1}{n+1+x} -\frac{k+1}{n+1+(k+1)x}\right) \\ &=k \left(\log(a) -\gamma \right)+k \sum\limits_{n=0}^{\infty} \left(\frac{1}{n+1} -\frac{n+1}{(n+1+x)(n+1+(k+1)x)}\right). \end{array} $$
(68)
Clearly the terms in the summation in (68) are positive under the assumptions of the lemma and, hence, \(\frac {d}{dx} f_{k,a}(x) > 0\). This concludes the proof. □
Observing that \(g_{k}(p)= g_{k,2} \left (\frac {1}{p} \right)\) and log(2)≈0.693>γ≈0.577 concludes the proof that gk(p) is a decreasing function.
The second part follows by using Stiriling’s approximation \(\Gamma (x+1) \approx \sqrt { 2 \pi x} \left (\frac {x}{\mathrm {e}} \right)^{x}\) and the property that Γ(x+1)=xΓ(x) as follows:
$$\begin{array}{*{20}l} \left(\frac{\mathbb{E}\left[ |X_{p}|^{k} \right] }{\mathbb{E}\left[|X_{q}|^{k}\right] }\right)^{\frac{1}{k}}= \left(\frac{ 2^{\frac{k}{p}-\frac{k}{q}} \Gamma \left(\frac{1}{q} \right)}{ \Gamma \left(\frac{1}{p} \right)} \frac{\Gamma \left(\frac{k+1}{p}\right)}{\Gamma \left(\frac{k+1}{q}\right)} \right)^{\frac{1}{k}} & \approx 2^{\frac{1}{p}-\frac{1}{q}} \left(\frac{ \left(\frac{1}{q\mathrm{e}} \right)^{\frac{1}{q}} }{ \left(\frac{1}{p\mathrm{e}} \right)^{\frac{1}{p}}} \cdot \frac{ \left(\frac{k+1}{p\mathrm{e}} \right)^{\frac{k+1}{p}} }{ \left(\frac{k+1}{q\mathrm{e}} \right)^{\frac{k+1}{q}}} \right)^{\frac{1}{k}} \\ & = 2^{\frac{1}{p}-\frac{1}{q}} \mathrm{e}^{\frac{1}{q}-\frac{1}{p}} \frac{ q^{\frac{1}{q}} }{ p^{\frac{1}{p}}} \left(k+1 \right)^{\frac{k+1}{k} \left (\frac{1}{p} -\frac{1}{q} \right) }. \end{array} $$
The proof is concluded by taking the limit as k and using that q>p.
Appendix B: Proof of Proposition 3
The proof follows from the inequality:
$$ \frac{\gamma\left(\frac{1}{p}, \frac{|x|^{p}}{2} \right)}{\Gamma(\frac{1}{p})} \le \frac{\gamma\left(\frac{1}{q}, \frac{|x|^{q}}{2} \right)}{\Gamma(\frac{1}{q})}, \forall x \in\mathbb{R}, $$
(69)
for pq. For completeness the inequality in (69) is shown in Appendix B.1.
Without loss of generality assume that x>0 and observe that
$$\begin{array}{*{20}l} \int_{-\infty}^{x} [ F_{X_{p}}(t)-F_{X_{q}}(t) ] dt &= \int_{-\infty}^{x} \text{sign}(t) \left(\frac{\gamma\left(\frac{1}{p}, \frac{|t|^{p}}{2} \right)}{\Gamma(\frac{1}{p})}-\frac{\gamma\left(\frac{1}{q}, \frac{|t|^{q}}{2} \right)}{\Gamma(\frac{1}{q})} \right) dt \end{array} $$
(70)
$$\begin{array}{*{20}l} &=\int_{x}^{\infty} \left(\frac{\gamma\left(\frac{1}{q}, \frac{|t|^{q}}{2} \right)}{\Gamma(\frac{1}{q})}-\frac{\gamma\left(\frac{1}{p}, \frac{|t|^{p}}{2} \right)}{\Gamma(\frac{1}{p})} \right) dt \end{array} $$
(71)
$$\begin{array}{*{20}l} & \ge 0, \end{array} $$
(72)
where (71) follows from the symmetry and (72) follows from the inequality in (69). This concludes the proof.
B.1 Proof of the inequality in (69)
Let
$$ f(p,x) := \frac{\gamma \left(\frac{1}{p}, \frac{x^{p}}{2}\right)}{\Gamma \left(\frac{1}{p}\right)}, p>0,\, x>0. $$
(73)
The goal is to show that f(p,x) is an increasing function of p. To that end, observe that by using a change of variable \(u= (2t)^{\frac {1}{p}} \) the function f(p,x) can be written as
$$ f(p,x)= \frac{ \int_{0}^{\frac{x^{p}}{2}} t^{\frac{1}{p}-1} \mathrm{e}^{-t} dt }{ \int_{0}^{\infty} t^{\frac{1}{p}-1} \mathrm{e}^{-t} dt}= \frac{ \int_{0}^{x} \mathrm{e}^{-\frac{u^{p}}{2}} du }{ \int_{0}^{\infty} \mathrm{e}^{-\frac{u^{p}}{2}} du}. $$
(74)
Therefore, showing monotonicity of f(p,x) is equivalent to showing that for pq
$$ \int_{0}^{x} \mathrm{e}^{-\frac{t^{p}}{2}} dt \int_{0}^{\infty} \mathrm{e}^{-\frac{u^{q}}{2}} du \le \int_{0}^{x} \mathrm{e}^{-\frac{u^{q}}{2}} du \int_{0}^{\infty} \mathrm{e}^{-\frac{t^{p}}{2}} dt. $$
(75)
The inequality in (75) can be conveniently re-written as
$$ \int_{0}^{x} \int_{0}^{\infty} \mathrm{e}^{-\frac{t^{p}+u^{q}}{2}} du dt \le \int_{0}^{\infty} \int_{0}^{x} \mathrm{e}^{-\frac{t^{p}+u^{q}}{2}} du dt, $$
(76)
and then the inequality in (76) follows by the monotonicity of the exponential function. This concludes the proof.
Appendix C: Proof of Theorem 1
To show that \( \mathrm {e}^{-\frac {| x|^{p}}{ 2 }}\) is not a positive definite function for p>2 it is enough to consider the following counterexample. In Definition 4 let n=3 and choose |x1x2|=ε,|x2x3|=aε and |x1x3|=(a+1)ε for some ε,a>0. Therefore, the determinant of the matrix A is given by
$$\begin{array}{*{20}l} h(\epsilon)& := \text{det}(A)= 1 - \mathrm{e}^{-\frac{2 a^{p} \epsilon^{p}}{2}}-\mathrm{e}^{-\frac{\epsilon^{p}}{2}} \left(\mathrm{e}^{-\frac{\epsilon^{p}}{2}}- \mathrm{e}^{-\frac{ (a^{p} +(a+1)^{p}) \epsilon^{p}}{2}} \right) \notag\\ &\quad+\mathrm{e}^{-\frac{(a+1)^{p} \epsilon^{p}}{2}} \left(\mathrm{e}^{-\frac{ (a^{p}+1) \epsilon^{p}}{2}} - \mathrm{e}^{-\frac{ (a+1)^{p} \epsilon^{p}}{2}} \right) \notag\\ &= 1 - \mathrm{e}^{-\frac{2 a^{p} \epsilon^{p}}{2}}-\mathrm{e}^{-\frac{2 \epsilon^{p}}{2}} + 2\mathrm{e}^{-\frac{ ((a+1)^{p}+a^{p}+1) \epsilon^{p}}{2}} - \mathrm{e}^{-\frac{ 2(a+1)^{p} \epsilon^{p}}{2}}. \end{array} $$
(77)
The idea of the proof is to show that for a small ε we have that h(ε)<0. To that end, we use the following small t approximation \(\mathrm {e}^{t}= 1+t+\frac {t^{2}}{2}+O(t^{3})\) in (77)
$$\begin{array}{*{20}l} h(\epsilon) & = 1- \left(1-\frac{2 a^{p} \epsilon^{p}}{2} + \left(\frac{2 a^{p} \epsilon^{p}}{2} \right)^{2} \right)- \left(1-\frac{2 \epsilon^{p}}{2} + \left(\frac{2 \epsilon^{p}}{2} \right)^{2} \right) \\ & \quad- \left(1-\frac{2 (a+1)^{p} \epsilon^{p}}{2} + \left(\frac{2 (a+1)^{p} \epsilon^{p}}{2} \right)^{2} \right) \\ &\quad+ 2 \left(1-\frac{ ((a+1)^{p}+a^{p}+1) \epsilon^{p}}{2} + \left(\frac{ ((a+1)^{p}+a^{p}+1) \epsilon^{p}}{2} \right)^{2} \right) +O \left(\epsilon^{3p} \right) \\ &= \epsilon^{2p} \left(\frac{ ((a+1)^{p}+a^{p}+1)^{2}}{2} -a^{2p}- (a+1)^{2p}-1 \right) +O \left(\epsilon^{3p} \right). \end{array} $$
The proof is concluded by taking ε small enough and noting that \( \frac { \left (\left (a+1\right)^{p}+a^{p}+1 \right)^{2}}{2} -a^{2p}- \left (a+1\right)^{2p}-1 \ge 0\) for p≤2 and \( \frac { \left (\left (a+1\right)^{p}+a^{p}+1 \right)^{2}}{2} -a^{2p}- \left (a+1\right)^{2p}-1 <0\) for p>2.
An easy way of see that \( \mathrm {e}^{-\frac {| x|^{p}}{ 2 }}\) is a positive definite function is by observing that \( \mathrm {e}^{-\frac {| x|^{p}}{ 2 }}\), for p(0,2], is a characteristic function of a stable distribution of order p. The proof then follows by Bochner’s theorem (Ushakov 1999, Theorem 1.3.1.) which guarantees that all characteristic functions are positive definite. For other proofs that \( \mathrm {e}^{-\frac {| x|^{p}}{ 2 }}\) is positive definite for p(0,2] we refer the reader to (Lévy 1925) and (Bochner 1937).
To show that \( \mathrm {e}^{-\frac {| x|^{p}}{ 2 }}\) can be represented in the integral form given in (24) we use the proof outlined in (Bochner 1937). According to Bernstein’s theorem (Widder 1946, Theorem 12.a) every completely monotone function can be written as a Laplace transform of some non-negative finite Borel measure μ. In Corollary 2 we have verified that \(\mathrm {e}^{-\frac {u^{\frac {p}{2}}}{2}}\) is a completely monotone function for p(0,2]. Therefore, according to Bernstein’s theorem, we can write \(\mathrm {e}^{-\frac {u^{\frac {p}{2}}}{2}}\) for p(0,2] as follows: for u>0
$$ \mathrm{e}^{-\frac{u^{\frac{p}{2}}}{2}}=\int_{0}^{\infty} \mathrm{e}^{-ut} d \mu_{p}(t). $$
(78)
Substituting u=x2 into (78) completes the proof.
Appendix D: Proof of Proposition 5
To simplify the notation let \(r=\frac {2q}{p}\). To show that Xq=Vp,q·Xr, first observe that \(d \nu (t)=\frac {c_{q}}{c_{r}} \frac {1}{t^{\frac {1}{r}}} d\mu _{p}(t)\) is a probability measure where dμp(t) is the finite non-negative Borel measure defined in Theorem 1
$$\begin{array}{*{20}l} 1= \mathbb{P}(X_{q} \in \mathbb{R})&= \int_{\mathbb{R}} c_{q} \mathrm{e}^{-\frac{|x|^{q}}{ 2 }} dx\\ & \stackrel{a)}{= }\int_{\mathbb{R}} c_{q} \int_{0}^{\infty} e^{-\frac{t }{2} |x|^{r}} d\mu_{p}(t) dx\\ &\stackrel{b)}{=} c_{q} \int_{0}^{\infty} \int_{\mathbb{R}} e^{-\frac{t}{2} |x|^{r}} dx d\mu_{p}(t) \\ &= c_{q} \int_{0}^{\infty} \frac{1}{ c_{r} t^{\frac{1}{r}}} d\mu_{p}(t) = \int_{0}^{\infty} d \nu (t), \end{array} $$
where the equalities follow from: a) using the representation of \(\mathrm {e}^{-\frac {|x|^{p}}{ 2 }}\) in Corollary 3; and b) interchanging the order of integration which is justified by Tonelli’s theorem for positive functions.
The above implies that \(d \nu (t)=\frac {c_{q}}{c_{r}} \frac {1}{t^{\frac {1}{r}}} d\mu _{p}(t)\) is a probability measure on [0,). Moreover, for any measurable set \(\mathcal {S} \subset \mathbb {R}\) we have that
$$\begin{array}{*{20}l} \mathbb{P}(X_{q} \in \mathcal{S}) & \stackrel{a)}{=} \int_{\mathcal{S}} c_{q} \int_{0}^{\infty} e^{-\frac{t }{2} |x|^{r}} d\mu_{p}(t) dx \\ &= \int_{0}^{\infty} \int_{\mathcal{S}} c_{r} t^{\frac{1}{r}}e^{-\frac{t}{2} |x|^{r}} dx \frac{c_{q}}{c_{r}} \frac{1}{t^{\frac{1}{r}}} d\mu_{p}(t) \\ &\stackrel{b)}{=} \int_{0}^{\infty} \mathbb{P} \left(\frac{1}{T^{\frac{1}{r}}} X_{r} \in \mathcal{S} \mid T=t \right) \frac{c_{q}}{c_{r}} \frac{1}{t^{\frac{1}{r}}} d\mu_{p}(t) \\ &\stackrel{c)}{=} \mathbb{E} \left[ \mathbb{P} \left(\frac{1}{T^{\frac{1}{r}}} X_{r} \in \mathcal{S} \mid T \right) \right] \\ &\stackrel{d)}{=} \mathbb{P} \left(V_{p,q} \cdot X_{r} \in \mathcal{S} \right), \end{array} $$
(79)
where the equalities follow from: a) the representation of \(\mathrm {e}^{-\frac {|x|^{p}}{ 2 }}\) in Theorem 1; b) the fact that \(d \nu (t)=\frac {c_{q}}{c_{r}} \frac {1}{t^{\frac {1}{r}}} d\mu _{p}(t)\) is a probability measure; c) because Xr is independent of t; and d) renaming \(V_{p,q}= \frac {1}{T^{\frac {1}{r} }}\). Therefore, it follows from (79) that Xq=dVp,q·Xr.
Next, we show that for p<2 the random variable Vp,q is unbounded. Any random variable Vp,q is unbounded if and only if
$${\lim}_{k \rightarrow \infty} \mathbb{E}^{\frac{1}{k}}\left[V_{p,q}^{k}\right] =\infty. $$
To show that Vp,q is unbounded observe that due to its non-negativity all the moments of Vp,q are given by
$$\mathbb{E}\left[ V_{p,q}^{k} \right] =\frac{ \mathbb{E}\left[|X_{q}|^{k}\right]}{\mathbb{E}\left[|X_{r}|^{k}\right]}, \ k \in \mathbb{R}^{+}. $$
Moreover, by the assumption that p<2 we have that \(r=\frac {2q}{p} > q\), and by using Corollary 1 we have that for r>q
$${\lim}_{k \rightarrow \infty} \mathbb{E}^{\frac{1}{k}}\left[V_{p,q}^{k}\right]= {\lim}_{k \rightarrow \infty} \left(\frac{ \mathbb{E}\left[|X_{q}|^{k}\right]}{\mathbb{E}\left[|X_{r}|^{k}\right]} \right)^{\frac{1}{k}} =\infty. $$
Therefore, Vp,q is an unbounded random variable for p<2. For p=2 we have that r=q and, hence, \(\mathbb {E}\left [ V_{p,q}^{k} \right ] =\frac { \mathbb {E}\left [|X_{q}|^{k}\right ]}{\mathbb {E}\left [|X_{r}|^{k}\right ]}= 1, \) for all k>0. Therefore, Vp,q=1 for p=2.
To find the pdf of Vp,q we use the Mellin transform approach by observing that
$$\mathbb{E}\left[|X_{q}|^{it}\right]= \mathbb{E}\left[|V_{p,q} \cdot X_{r}|^{it}\right]= \mathbb{E}\left[V_{p,q}^{it}\right] \cdot \mathbb{E}\left[|X_{r}|^{it}\right]. $$
Therefore, by using Proposition 1 the Mellin transform of Vp,q is given by
$$ \mathbb{E}\left[V_{p,q}^{it}\right] =\frac{\mathbb{E}\left[|X_{q}|^{it}\right]}{\mathbb{E}\left[|X_{r}|^{it}\right]}= \frac{\Gamma \left(\frac{1}{r} \right)}{\Gamma \left(\frac{1}{q} \right)} \frac{ 2^{\frac{it}{q}} \Gamma \left(\frac{it +1}{q}\right) }{ 2^{\frac{it}{r}} \Gamma \left(\frac{it +1}{r}\right) }. $$
(80)
Finally, the pdf of Vp,q is computed by the inverse Mellin transform of (80)
$$f_{V_{p,q}}(v)= \frac{1}{2 \pi} \frac{\Gamma \left(\frac{1}{r} \right)}{\Gamma \left(\frac{1}{q} \right)} \int_{\mathbb{R}} v^{-it-1} \frac{ 2^{\frac{it}{q}} \Gamma \left(\frac{it +1}{q}\right) }{ 2^{\frac{it}{r}} \Gamma \left(\frac{it +1}{r}\right)} dt, \ v>0. $$
This concludes the proof.
Appendix E: Proof of Proposition 6
To simplify the notation let \(r=\frac {2q}{p}\). First, we show the power series representation of \(f_{V_{p,q}}(v)\) given in (28). Using the integral representation of \(f_{V_{p,q}}(v)\) in (26b) and the residue theorem we have that
$$\begin{array}{*{20}l} f_{V_{p,q}}(v)&= \frac{1}{2 \pi} \frac{\Gamma \left(\frac{1}{r} \right)}{\Gamma \left(\frac{1}{q} \right)} \int_{\mathbb{R}} v^{-it-1} \frac{ 2^{\frac{it}{q}} \Gamma \left(\frac{it +1}{q}\right) }{ 2^{\frac{it}{r}} \Gamma \left(\frac{it +1}{r}\right)} dt \\ &= \frac{1}{2 \pi i} \frac{\Gamma \left(\frac{1}{r} \right)}{\Gamma \left(\frac{1}{q} \right)} \int_{- i\infty}^{i \infty} v^{-s-1} \frac{ 2^{\frac{s}{q}} \Gamma \left(\frac{s +1}{q}\right) }{ 2^{\frac{s}{r}} \Gamma \left(\frac{s+1}{r}\right)} ds \\ &= \frac{\Gamma \left(\frac{1}{r} \right)}{\Gamma \left(\frac{1}{q} \right)} \sum\limits_{k=0}^{\infty} \mathsf{Residue} \left(v^{-s-1} \frac{ 2^{\frac{s}{q}} \Gamma \left(\frac{s +1}{q}\right) }{ 2^{\frac{s}{r}} \Gamma \left(\frac{s+1}{r}\right)} ; s_{k} \right), \end{array} $$
(81)
where the sk are given by the poles of \(\Gamma \left (\frac {s +1}{q}\right)\) which occur at
$$s_{k}= -q k -1, \ k =0,1,2,\ldots $$
Since the poles of \(\Gamma \left (\frac {s +1}{q}\right)\) are simple and \(\frac {1}{\Gamma \left (\frac {s+1}{r}\right)}\) is an entire function, the residue can be computed as follows:
$$ \mathsf{Residue} \left(v^{-s-1} \frac{ 2^{\frac{s}{q}} \Gamma \left(\frac{s +1}{q}\right) }{ 2^{\frac{s}{r}} \Gamma \left(\frac{s+1}{r}\right)} ; s_{k} \right) =v^{-s_{k}-1} \frac{ 2^{\frac{s_{k}}{q}} \mathsf{Residue} \left(\Gamma \left(\frac{s +1}{q}\right) ; s_{k} \right) }{ 2^{\frac{s_{k}}{r}} \Gamma \left(\frac{s_{k}+1}{r}\right) }, $$
(82)
where
$$ \mathsf{Residue} \left(\Gamma \left(\frac{s+1}{q}\right) ; s_{k} \right) = {\lim}_{s \rightarrow s_{k}} (s-s_{k}) \Gamma \left(\frac{s +1}{q}\right) = q \frac{(-1)^{k}}{k!}. $$
(83)
Therefore, by putting (81), (82), and (83) together we arrive at
$$f_{V_{p,q}}(v)= \frac{\Gamma \left(\frac{1}{r} \right)}{\Gamma \left(\frac{1}{q} \right)} \sum\limits_{k=0}^{\infty} a_{k} v^{kq}, $$
where
$$a_{k}= q \frac{(-1)^{k} 2^{(kq+1) \left(\frac{1}{r} -\frac{1}{q} \right)} }{k! \ \Gamma\left(- \frac{kq}{r}\right)} = q \frac{(-1)^{k+1} 2^{(kq+1) \left(\frac{1}{r} -\frac{1}{q} \right)} }{k!} \Gamma\left(\frac{kq}{r} +1 \right) \frac{\sin \left(\frac{\pi k q}{r} \right)}{ \pi }, $$
where the last step is due to the identity \( \Gamma (-x) \Gamma (x)=- \frac {\pi }{x \sin (\pi x)}\) and the identity Γ(x+1)=xΓ(x). The proof of this part is concluded by noting that a0=0.
To show the representation of \(f_{V_{p,q}}(v)\) in (30) we use the definition of the gamma function \(\Gamma (z)=\int _{0}^{\infty } x^{z-1} \mathrm {e}^{-x} dx\) as follows:
$$\begin{array}{*{20}l} \frac{ \pi \Gamma \left(\frac{1}{q} \right)}{q 2^{\frac{1}{r}-\frac{1}{q}} \Gamma \left(\frac{1}{r} \right)}f_{V_{p,q}}(v) &= \sum\limits_{k=0}^{\infty} \frac{(-1)^{k+1} \sin \left(\frac{\pi k q}{r} \right) 2^{kq \left(\frac{1}{r} -\frac{1}{q} \right)} \int_{0}^{\infty} x^{\frac{kq}{r}} \mathrm{e}^{-x} dx }{k!} v^{kq} \\ &= \int_{0}^{\infty} \sum\limits_{k=0}^{\infty} \frac{(-1)^{k+1} \sin \left(\frac{\pi k q}{r} \right) 2^{kq \left(\frac{1}{r} -\frac{1}{q} \right)} }{k!} v^{kq} x^{\frac{kq}{r}} \mathrm{e}^{-x} dx. \end{array} $$
(84)
To validate the interchange of summation and integration in (84) observe that
$$\begin{array}{*{20}l} \left| \frac{ \pi \Gamma \left(\frac{1}{q} \right)}{q 2^{\frac{1}{r}-\frac{1}{q}} \Gamma \left(\frac{1}{r} \right)}f_{V_{p,q}}(v) \right| & \stackrel{a)}{\le} \int_{0}^{\infty} \sum\limits_{k=0}^{\infty} \frac{ 2^{kq \left(\frac{1}{r} -\frac{1}{q} \right)} v^{kq} x^{\frac{kq}{r}} \mathrm{e}^{-x} }{k!} dx \\ & \stackrel{b)}{=} \int_{0}^{\infty} \mathrm{e}^{2^{q \left(\frac{1}{r} -\frac{1}{q} \right)} v^{q} x^{\frac{q}{r} }} \mathrm{e}^{-x} dx \stackrel{c)}{<} \infty, \end{array} $$
(85)
where the (in)-equalities follow from: a) using the inequality |sin(x)|≤1; b) using the power series \(\mathrm {e}^{x}={\sum \nolimits }_{n=0}^{\infty } \frac {x^{n}}{n!}\); and c) using the fact that the integral converges since \( \frac {q}{r}-1= \frac {p}{2}-1 < 0\) and where we have used that \(p=\frac {2q}{r}\) and p<2 and, hence, \(2^{kq \left (\frac {1}{r} -\frac {1}{q} \right)} v^{kq} x^{\frac {kq}{r}} < x\) for large enough x.
The inequality in (85) together with Fubini’s theorem justifies the interchange of integration and summation in (84). Continuing with (84) we have
$$\begin{array}{*{20}l} \frac{ \pi \Gamma \left(\frac{1}{q} \right) f_{V_{p,q}}(v)}{q 2^{\frac{1}{r}-\frac{1}{q}} \Gamma \left(\frac{1}{q} \right)} &\stackrel{a)}{=} - \int_{0}^{\infty} \sum\limits_{k=0}^{\infty} \frac{ \left(\mathrm{e}^{\frac{i \pi k q}{r}}-\mathrm{e}^{-\frac{i \pi k q}{r}} \right)}{2 i} \frac{ \left(- 2^{q \left(\frac{1}{r} -\frac{1}{q} \right)} v^{q} x^{\frac{q}{r}} \right)^{k} }{k!} \mathrm{e}^{-x} dx\\ &\stackrel{b)}{=} \int_{0}^{\infty} \frac{ \mathrm{e}^{- \mathrm{e}^{-\frac{i \pi q}{r}}2^{q \left(\frac{1}{r} -\frac{1}{q} \right)} v^{p} x^{\frac{q}{r} }}-\mathrm{e}^{- \mathrm{e}^{\frac{i \pi q}{r}}2^{q \left(\frac{1}{r} -\frac{1}{q} \right)} v^{p} x^{\frac{q}{r} }} }{2i} \mathrm{e}^{-x}dx\\ &\stackrel{c)}{=} \int_{0}^{\infty} \sin \left(2^{q \left(\frac{1}{r}-\frac{1}{q} \right)} \sin \left(\frac{\pi q}{r} \right) v^{q} x^{\frac{q}{r}} \right) \mathrm{e}^{-2^{q \left(\frac{1}{r}-\frac{1}{q} \right)} \cos \left(\frac{\pi q}{r} \right) v^{q} x^{\frac{q}{r}}-x} dx, \end{array} $$
where the equalities follow from: a) using the identity \( \sin \left (\frac {\pi k q}{r} \right)= \frac {\mathrm {e}^{\frac {i \pi k q}{r}}-\mathrm {e}^{-\frac {i \pi k q}{r}} }{2 i} \); b) using the power series expansion \(\mathrm {e}^{x}={\sum \nolimits }_{n=0}^{\infty } \frac {x^{n}}{n!}\); and c) using the identity \(\frac { \mathrm {e}^{- \mathrm {e}^{-i \pi x} y}-\mathrm {e}^{- \mathrm {e}^{i \pi x} y} }{2i}=\sin \left (\sin \left (\pi x \right) y \right) \mathrm {e}^{- \cos \left (\pi x \right) y}\). Recalling that \(r = \frac {2 q}{p}\) we conclude the proof.
Appendix F: Proof of Proposition 9
The non-negativity of Up(x) follows from standard trigonometric arguments.
Next, it is not difficult to show that the derivative of Up(x) is given by
$$\begin{array}{*{20}l} \frac{d}{dx} U_{p}(x)& =y_{p}(x)h_{p}(x), \, x\in (0,1),\\ y_{p}(x)&=\frac{\pi}{2} \sec \left(\frac{\pi x}{2} \right) \sin \left(\frac{\pi p x}{2} \right)^{\frac{p}{1-p}} \cos \left(\frac{\pi (p-1) x}{2} \right),\\ h_{p}(x)&= \frac{p^{2}}{1-p} \cot \left(\frac{\pi p x}{2} \right)+\frac{1}{1-p} \tan\left(\frac{\pi x}{2} \right)-(p-1) \tan \left(\frac{\pi (p-1) x}{2} \right). \end{array} $$
Observe that yp(x)≥0 for x(0,1) and all p(0,2]. The behavior of hp(x) is slightly more complicated and is given next.
Lemma 2
For p(0,1), hp(x)≥0 for all x(0,1), and for p(1,2]hp(x)≤0 for all x(0,1).
Proof
The proof of Lemma 2 is given in Appendix F.1. □
Lemma 2 together with the non-negativity of yp(x) shows that Up(x) is an increasing function for p(0,1) and a decreasing function for p(1,2].
Next, we show that the function \(g_{p}(x)=U_{p}(x) \mathrm {e}^{- |t|^{\frac {p}{p-1}} U_{p}(x) }\) has a single maximum by taking the derivative of gp(x):
$$\begin{array}{*{20}l} \frac{d}{dx} g_{p}(x)&=\frac{d}{dx} \left(U_{p}(x) \mathrm{e}^{- |t|^{\frac{p}{p-1}} U_{p}(x)} \right)\\ &=U_{p}^{'}(x) \mathrm{e}^{- |t|^{\frac{p}{p-1}} U_{p}(x) }- |t|^{\frac{p}{p-1}} U_{p}(x) \mathrm{e}^{- |t|^{\frac{p}{p-1}} U_{p}(x)} U_{p}^{'}(x). \end{array} $$
Note that the location of the maximum of gp is given by
$$ \frac{d}{dx} g_{p}(x) =0 \Leftrightarrow U_{p}(x) = \frac{1}{ |t|^{\frac{p}{p-1} }}. $$
(86)
Since Up(x) is a strictly monotone function (either decreasing or increasing depending on p), the equation in (86) has only a single solution and therefore gp(x) has only one maximum. Moreover, from (86) the maximum is given by \(\max _{x \in [0,1]} g_{p}(x)= \frac {1}{\mathrm {e} |t|^{\frac {p}{p-1} }}. \) This concludes the proof.
F.1 Proof of Lemma 2
First observe that
$$\begin{array}{*{20}l} h_{p}(x)&= \frac{p^{2}}{1-p} \cot \left(\frac{\pi p x}{2} \right)+\frac{1}{1-p} \tan\left(\frac{\pi x}{2} \right)-(p-1) \tan \left(\frac{\pi (p-1) x}{2} \right)\\ &= \frac{1}{1-p} \left(p^{2} \cot \left(\frac{\pi p x}{2} \right)+ \tan\left(\frac{\pi x}{2} \right)-(p-1)^{2} \tan \left(\frac{\pi (1-p) x}{2} \right) \right). \end{array} $$
Note that \(\frac {1}{1-p} \le 0\) for p>1 and \(\frac {1}{1-p}\ge 0\) for p<1. Therefore, we have to show that for all p(0,2)
$$ d_{p}(x)= p^{2} \cot \left(\frac{\pi p x}{2} \right)+ \tan\left(\frac{\pi x}{2} \right)-(p-1)^{2} \tan \left(\frac{\pi (1-p) x}{2} \right) \ge 0. $$
(87)
The proof follows by looking at p(0,1) and p(1,2) separately.
For p(0,1) note that
$$\begin{array}{*{20}l} d_{p}(x)&= p^{2} \cot \left(\frac{\pi p x}{2} \right)+ \tan\left(\frac{\pi x}{2} \right)-(p-1)^{2} \tan \left(\frac{\pi (1-p) x}{2} \right) \\ & \stackrel{a)}{\ge} \tan\left(\frac{\pi x}{2} \right)-(p-1)^{2} \tan \left(\frac{\pi (1-p) x}{2} \right) \\ & \stackrel{b)}{\ge} \tan\left(\frac{\pi x}{2} \right)- \tan \left(\frac{\pi (1-p) x}{2} \right) \stackrel{c)}{\ge} 0, \end{array} $$
where the inequalities follow from: a) using the fact that \( \cot \left (\frac {\pi p x}{2} \right) >0\) for all x(0,1) and all p(0,1); b) using the fact that (1−p)2≤1; and c) using the fact that 0<1−p<1 and the fact that \(\tan \left (\frac {\pi (1-p) x}{2} \right) \) is a monotonically increasing function for x(0,1).
For p(1,2) we look at two cases \(x \in (0, \frac {1}{2} ]\) and \(x \in \left (\frac {1}{2}, 1 \right)\). The reason we have to split the domain of x into two parts is because of the \(\cot \left (\frac {\pi p x}{2} \right)\). Note that \(\cot \left (\frac {\pi p x}{2} \right)\ge 0\) for all p(1,2) and all \(x \in (0, \frac {1}{2} ]\), but this is not true for the case of \(x \in \left (\frac {1}{2}, 1 \right)\).
Now, focusing first on the more involved case of \(x \in \left (\frac {1}{2}, 1\right)\) we have that
$$\begin{array}{*{20}l} d_{p}(x) &= p^{2} \cot \left(\frac{\pi p x}{2} \right)+ \tan\left(\frac{\pi x}{2} \right)+(p-1)^{2} \tan \left(\frac{\pi (p-1) x}{2} \right)\\ & \stackrel{a)}{\ge} p^{2} \cot \left(\frac{\pi p x}{2} \right) + p^{2} \frac{\tan\left(\frac{\pi x}{2} \right) \tan \left(\frac{\pi (p-1) x}{2} \right) }{ \tan\left(\frac{\pi x}{2} \right) + \tan \left(\frac{\pi (p-1) x}{2} \right)}\\ & \stackrel{b)}{=} p^{2} \cot \left(\frac{\pi p x}{2} \right) + p^{2} \frac{\tan\left(\frac{\pi x}{2} \right) \tan \left(\frac{\pi (p-1) x}{2} \right) }{ \tan\left(\frac{\pi p x}{2} \right) \left(1- \tan\left(\frac{\pi x}{2} \right)\tan \left(\frac{\pi (p-1) x}{2} \right) \right)}\\ & \stackrel{c)}{=} \frac{p^{2}}{ \tan\left(\frac{\pi x}{2} \right)+\tan \left(\frac{\pi (p-1) x}{2} \right)} \ge 0, \end{array} $$
where the (in)-equalities follow from: a) using the fact that \(\tan \left (\frac {\pi x}{2} \right)>0\) and \( \tan \left (\frac {\pi (p-1) x}{2} \right)>0\), and using Cauchy-Schwarz inequality
$$\left(\tan\left(\frac{\pi x}{2} \right)+(p-1)^{2} \tan \left(\frac{\pi (p-1) x}{2} \right) \right) \left(\frac{1}{ \tan\left(\frac{\pi x}{2} \right) }+ \frac{1}{\tan \left(\frac{\pi (p-1) x}{2} \right)} \right) \ge p^{2}; $$
b) using the identity \(\tan (\alpha +\beta)=\frac {\tan (\alpha)+\tan (\beta)}{1- \tan (\alpha)\tan (\beta)}\); and c) using the identity \(\tan (\alpha +\beta)=\frac {\tan (\alpha)+\tan (\beta)}{1- \tan (\alpha)\tan (\beta)}\).
Finally, we focus on the case of \(x \in \left (0, \frac {1}{2}\right)\),
$$d_{p}(x)= p^{2} \cot \left(\frac{\pi p x}{2} \right)+ \tan\left(\frac{\pi x}{2} \right)+(p-1)^{2} \tan \left(\frac{\pi (p-1) x}{2} \right) \ge 0, $$
where we have used the fact that \( \cot \left (\frac {\pi p x}{2} \right) > 0\) for \(x \in (0, \frac {1}{2})\) and p(1,2), and \( \tan \left (\frac {\pi x}{2} \right)>0\) for x(0,1), and \( \tan \left (\frac {\pi (p-1) x}{2} \right)>0\) for x(0,1) and p(1,2). This concludes the proof.
Appendix G: Proof of Proposition 10
To show that ϕp(t) can be represented by the power series we perform a ratio test and compute the radius of convergence as follows:
$$ r={\lim}_{k \rightarrow \infty} \frac{ \frac{\mathbb{E}\left[ |X_{p}|^{k}\right]}{k!} }{ \frac{\mathbb{E}\left[ |X_{p}|^{k+1}\right] }{(k+1)!}} = 2^{-\frac{1}{p}} {\lim}_{k \to \infty} \frac{k \Gamma\left(\frac{k+1}{p}+1 \right)}{ \Gamma\left(\frac{k+2}{p}+1 \right)}. $$
(88)
Now for p=1 the limit in (88) can be computed as follows:
$$ {\lim}_{k \rightarrow \infty} \frac{k \Gamma(k+2)}{ \Gamma(k+3)}= {\lim}_{k \to \infty} \frac{k \Gamma(k+2)}{ (k+2) \Gamma(k+2)}=1. $$
(89)
Therefore, for p=1 we have that \(r=\frac {1}{2}\).
For p≠1 the limit in (88) can be computed using Stirling’s approximation
$${\lim}_{k \rightarrow \infty} \frac{k \Gamma\left(\frac{k+1}{p}+1 \right)}{ \Gamma\left(\frac{k+2}{p}+1 \right)} = (\mathrm{e} p)^{\frac{1}{p}} {\lim}_{k \to \infty} \frac{k (k+1)^{\frac{k+1}{ p}} }{ (k+2)^{\frac{k+2}{p}}} = \left \{ \begin{array}{ll} \infty & p>1 \\ 0 & p<1\end{array} \right.. $$
This concludes the proof.
Appendix H: Proof of Theorem 3
First, we show that for p>2 there is at least one zero. We use the approach of (Elkies et al. 1991). Towards a contradiction assume that ϕp(t)≥0 for all t≥0; then for t≥0
$$\begin{array}{*{20}l} 0& \le \frac{4}{c_{p}}\frac{1}{ 2\pi} \int_{0}^{\infty} \phi_{p}(x) (1-\cos(xt))^{2} dx \\ & \stackrel{a)}{=} \frac{4}{c_{p}}\frac{1}{ 2\pi} \int_{0}^{\infty} \phi_{p}(x) \frac{1}{2} \left(3-4 \cos(tx)+\cos(2tx)\right) dx \stackrel{b)}{=} 3-4 \mathrm{e}^{-\frac{t^{p}}{2}} + \mathrm{e}^{-\frac{ (2t)^{p}}{2} }, \end{array} $$
where the equalities follow from: a) using \((1-\cos (xt))^{2}= \frac {1}{2} \left (3-4 \cos (tx)+\cos (2tx)\right)\); and b) using the inverse Fourier transform. For small x we can write ex=1−x+O(x2). Therefore,
$$0 \le 3-4 \left(1-\frac{t^{p}}{2} \right) + \left(1-\frac{ (2t)^{p}}{2} \right) + O(t^{2p})= \left(4-2^{p}\right) \frac{t^{p}}{2}+ O(t^{2p}). $$
As a result, for p>2 we reach a contradiction since 4−2p<0 for p>2. This concludes the proof for the case of p>2.
The fact that the number of zeros is countable follows from the fact that ϕp(t) is an analytic function according to Proposition 10. Recall that analytic functions on \(\mathbb {R}\) are either equal to a constant everywhere or have at most countably many zeros; the proof of this fact follows by using the identity theorem and the Bolzano-Weierstrass theorem.
For 0<p≤2, the result follows from Theorem 2 since \(\phi _{p}(t) = \mathbb {E} \left [ \mathrm {e}^{-\frac {t^{2}V_{G,p}^{2} }{2}}\right ]>0. \) This concludes the proof.
Appendix I: Proof of Proposition 11
Using the power series expansion of fG,p in (28) there exists a c>0 such that for v[0,c]
$$ f_{G,p}(v)= B_{1} v^{p} + O\left(v^{2p}\right), $$
(90)
where \(B_{1}= \frac {\sqrt {\pi }}{\Gamma \left (\frac {1}{p} \right)} a_{1}\) with a1 defined as in (29). Therefore,
$$\begin{array}{*{20}l} \mathbb{E} \left[ V_{G,p}^{m} \mathrm{e}^{-\frac{V_{G,p}^{2} t^{2}}{2}} \right] &= \int_{0}^{c} v^{m} \mathrm{e}^{-\frac{v^{2} t^{2}}{2}} (B_{1} v^{p} + O(v^{2p})) dv + \int_{c}^{\infty} v^{m} \mathrm{e}^{-\frac{v^{2} t^{2}}{2}} f_{G,p}(v) dv \\ &= B_{1}\frac{2^{\frac{m+p-1}{2}}}{t^{m+p+1}} \gamma \left(\frac{m+p+1}{2}, \frac{c^{2}t^{2}}{2}\right) +O \left(\frac{1}{t^{m+2p+1}} \right) \\ &\quad+ \int_{c}^{\infty} v^{m} \mathrm{e}^{-\frac{v^{2} t^{2}}{2}} f_{G,p}(v) dv, \end{array} $$
(91)
where we have used the integral \(\int _{0}^{c} v^{k} \mathrm {e}^{-\frac {v^{2} t^{2}}{2}} dv = \frac {2^{\frac {k-1}{2}}}{t^{k+1}} \gamma \left (\frac {k+1}{2}, \frac {c^{2}t^{2}}{2}\right)\). Next, using the expression in (91) and the limit \( {\lim }_{t \rightarrow \infty } \gamma \left (b, \frac {c^{2}t^{2}}{2}\right)=\Gamma \left (\frac {m+p+1}{2}\right)\) for any b,c>0
$$\begin{array}{*{20}l} {\lim}_{t \to \infty} t^{m+p+1} \mathbb{E} \left[ V_{G,p}^{m} \mathrm{e}^{-\frac{V_{G,p}^{2} t^{2}}{2}} \right] &=B_{1} 2^{\frac{m+p-1}{2}} \Gamma \left(\frac{m+p+1}{2}\right) \\ &\quad+ {\lim}_{t \to \infty} t^{m+p+1} \int_{c}^{\infty} v^{m} \mathrm{e}^{-\frac{v^{2} t^{2}}{2}} f_{G,p}(v)dv. \end{array} $$
(92)
Next, we show that the second term in (92) is zero. To that end, observe that for any m+p>0 and any c>0 we have that \(t^{m+p+1}\mathrm {e}^{-\frac {v^{2} t^{2}}{2}} \le t^{m+p+1}\mathrm {e}^{-\frac {c^{2} t^{2}}{2}} \le B(c)<\infty \) for all t>0 where the constant B(c) is independent of t. Therefore,
$$ \int_{c}^{\infty} v^{m} \mathrm{e}^{-\frac{v^{2} t^{2}}{2}} f_{G,p}(v)dv \le B(c) \int_{c}^{\infty} v^{m} f_{G,p}(v)dv \le \mathbb{E}[ V_{G,p}^{m}]<\infty, $$
(93)
where the finiteness of \(\mathbb {E}[ V_{G,p}^{m}]\) follows since \(\mathbb {E}[ V_{G,p}^{m}]= \frac {\mathbb {E}[|X_{p}|^{m}]}{\mathbb {E}[|X_{2}|^{m}]}\), and \(\mathbb {E}[|X_{p}|^{m}]\) and \(\mathbb {E}[|X_{2}|^{m}]\) are finite by Proposition 1. Therefore, by the dominated convergence theorem
$${\lim}_{t \to \infty} t^{m+p+1} \int_{c}^{\infty} v^{m} \mathrm{e}^{-\frac{v^{2} t^{2}}{2}} f_{G,p}(v)dv =0. $$
The proof is concluded by noting that
$${\lim}_{t \to \infty} t^{m+p+1} \mathbb{E} \left[ V_{G,p}^{m} \mathrm{e}^{-\frac{V_{G,p}^{2} t^{2}}{2}} \right] =B_{1} 2^{\frac{m+p-1}{2}} \Gamma \left(\frac{m+p+1}{2}\right) := A_{m}. $$
Appendix J: Proof of Proposition 14
By symmetry of ϕp(t) the representation in (51) can be simplified to
$$\log \left(\phi_{p}(t) \right) = \int_{|x| >0} \left(\cos(tx)-1 \right) \frac{1+x^{2}}{x^{2}}d\theta(x) - \frac{t^{2}}{2} \left(\theta(0+) - \theta(0-)\right). $$
Next, observe that σ2=(θ(0+)−θ(0−)) in the canonical representation in (51) is zero, since by Proposition 12, \(\sigma ^{2}= {\lim }_{t \to \infty } \frac {1}{t^{2}} \log (\phi _{p}(t)) =0.\) The parameter σ2 is sometimes referred to as the Gaussian component. Next, we show that θ(x) is an absolutely continuous distribution function by using the uniqueness of the Fourier transform. To that end, let
$$\begin{array}{*{20}l} g(t)&:= - \frac{d^{2}}{dt^{2}} \log\left(\phi_{p}(t) \right) = \int_{-\infty}^{\infty} x^{2} \cos(tx) \frac{1+x^{2}}{x^{2}}d\theta(x)= \int_{-\infty}^{\infty} \cos(tx) dG(x), \notag\\ G(x)&:= \int_{-\infty}^{x} (1+y^{2})d \theta(y), \end{array} $$
(94)
where g(t) is the cosine transform of the measure G(x).
We aim to show that θ(x) or equivalently G(x), in view of (94), is an absolutely continuous measure. A sufficient condition for G(x) to be absolutely continuous is the absolute integrability of g(t), that is \(\int _{-\infty }^{\infty } |g(t)| dt <\infty. \) Next, observe that g(t) is given by
$$\begin{array}{*{20}l} g(t)&= -\frac{ \phi_{p}(t)\phi_{p}^{\prime \prime}(t)-\left(\phi_{p}^{\prime}(t)\right)^{2}}{\phi^{2}_{p}(t)},\\ \phi_{p}^{\prime}(t)&=-t \mathbb{E} \left[ V_{G,p}^{2} \mathrm{e}^{-\frac{V_{G,p}^{2} t^{2}}{2}} \right], \, \phi_{p}^{\prime \prime}(t)= t^{2} \mathbb{E} \left[ V_{G,p}^{4} \mathrm{e}^{-\frac{V_{G,p}^{2} t^{2}}{2}}\right] - \mathbb{E} \left[ V^{2} \mathrm{e}^{-\frac{V_{G,p}^{2} t^{2}}{2}} \right]. \end{array} $$
Next, we give an upper bound on |g(t)| for large t. By the triangle inequality
$$\begin{array}{*{20}l} |g(t)| &\le \frac{ | \phi_{p}^{\prime \prime}(t) | }{\phi_{p}(t)} + \frac{\left(\phi_{p}^{\prime}(t)\right)^{2}}{\phi^{2}_{p}(t)} \\ &\le \frac{t^{2} \mathbb{E} \left[ V_{G,p}^{4} \mathrm{e}^{-\frac{V_{G,p}^{2} t^{2}}{2}}\right] + \mathbb{E} \left[ V_{G,p}^{2} \mathrm{e}^{-\frac{V_{G,p}^{2} t^{2}}{2}} \right]}{ \mathbb{E} \left[ \mathrm{e}^{-\frac{V_{G,p}^{2} t^{2}}{2}} \right]} + t^{2} \left(\frac{\mathbb{E} \left[ V_{G,p}^{2} \mathrm{e}^{-\frac{V_{G,p}^{2} t^{2}}{2}} \right]}{\mathbb{E} \left[ \mathrm{e}^{-\frac{V_{G,p}^{2} t^{2}}{2}} \right]} \right)^{2} \\ &= \frac{t^{2} \frac{A_{4}}{t^{p+5}} + \frac{A_{2}}{t^{p+3}} }{ \frac{A_{0}}{t^{p+1}}} + t^{2} \left(\frac{ \frac{A_{2}}{t^{p+3}}}{ \frac{A_{0}}{t^{p+1}}} \right)^{2} = O \left(\frac{1}{t^{2}} \right), \end{array} $$
(95)
where (95) follow from Proposition 11.
The bound in (95) implies that g(t) is absolutely integrable and G(x) and θ(x) have densities. Moreover, by the inversion formula for the cosine transform the density of G(x) and θ(x) are given by
$$ f_{G}(x) =\left(1+x^{2}\right) f_{\theta}(x)= \frac{2 }{2 \pi} \int_{0}^{\infty} - \left(\log \phi_{p}(t) \right)^{\prime \prime} \cos(tx) dt. $$
(96)
Next, by using integration by parts we have for x≠0
$$f_{G}(x) =- \frac{x }{ \pi} \int_{0}^{\infty} \left(\log \phi_{p}(t) \right)^{\prime} \sin(tx) dt, $$
where \( -\left (\log \phi _{p}(t) \right)^{\prime } \cos (tx) |_{0}^{\infty } =0\) follows from Proposition 11. For x=0 using (96) we have \(f_{G}(0)= - \frac {1}{\pi } \int _{0}^{\infty } \left (\log \phi _{p}(t) \right)^{\prime \prime } dt.\) This concludes the proof.
Appendix K: Proof of Theorem 6
Case of {(p,q):1<p=q}{(2,2)}
In this case, since p=q, we return to the proper definition of self-decomposability (Definition 8). From (Lukacs 1970, Theorem 5.11.1) we have that all distributions with self-decomposable characteristic functions are infinitely divisible. However, in Theorem 5 we have shown that GG distributions are not infinitely divisible for p(1,){2}. Therefore, for p(1,){2} the function ϕ(p,p,α)(t) is not a characteristic function.
Case of {(p,q):0≤p=q≤1}
In this case, since p=q, we return to the proper definition of self-decomposability (Definition 8). The proof of this case was outlined in (Bondesson 1992, p. 118) and it required the following definitions:
Definition 9
1. 1
(Extended Generalized Gamma Convolution (EGGC) (Bondesson 1992, p.105).) An EGGC is a distribution on \(\mathbb {R}\) such that the bilateral Laplace transform \(\psi (s)=\mathbb {E}[\mathrm {e}^{sX}], \, s\in \mathbb {C}\), defined at least for Re(s)=0, has the form
$$ \psi(s)=\mathrm{e}^{bs+\frac{cs^{2}}{2} +\int \left(\log \left(\frac{t}{t-s} \right) -\frac{st}{1+t^{2}} \right) dU(t) }, $$
(97)
where \(b\in \mathbb {R}, c \ge 0\), and dU(t) is a non-negative measure on \(\mathbb {R} \setminus \{0 \}\) such that
$$ \int \frac{1}{1+t^{2}} dU(t)<\infty, \text{ and} \int_{|t|\le 1} | \log\left(t^{2}\right)| dU(t)<\infty. $$
(98)
2. 2
(\(\mathcal {\beta }\)-Class (Bondesson 1992, p. 73).) A pdf f of a non-negative random variable belongs to the \(\mathcal {\beta }\)-Class if f can be written as follows:
$$ f(x)=C x^{\beta-1}\frac{h_{1}(x)}{h_{2}(x)}, \, x \ge 0, $$
(99)
where \(\beta \in \mathbb {R}, c \ge 0\) and, for j=1,2,
$$ h_{j}(x)=\mathrm{e}^{-b_{j} x+ \int \log\left(\frac{y+1}{y+x} \right) d \Gamma_{j}(y)}, \, x \ge 0, $$
(100)
where bj≥0 and dΓj(y) is a non-negative measure on (0,) satisfying
$$\int \frac{1}{1+y} d\Gamma_{j}(y)<\infty. $$
3. 3
(Hyperbolic Completely Monotone (HCM) Function (Bondesson 1992, p. 55>).) A function f:(0,)(0,) is called HCM if, for each u>0, the function \(g(w)=\frac {f(uv)}{f \left (\frac {u}{v}\right)}\) is completely monotone as a function of w=v+v−1.
The following results are needed for our proof.
Theorem 7
(Properties of the EGGC, β-Class and HCM Functions.)
1. 1
(Bondesson 1992, p. 107) An EGGC distribution is self-decomposable.
2. 2
(Bondesson 1992, Theorem 7.3.3) Let X and Y be two independent random variables such that the distribution of X is EGGC and the distribution of Y is in the β-Class. If X is symmetric, then \(\sqrt {Y}X\) has an EGGC distribution.
3. 3
(Bondesson 1992, Theorem 7.3.4) Let Y be a symmetric random variable on \(\mathbb {R}\) with a pdf fY. Then \(Y \stackrel {d}{=} \sqrt {V} Z_{2}\) is a Gaussian mixture such that the distribution of V is in the β-Class if and only if \(g(t)= f_{Y}(\sqrt {2t})\), t>0, is the Laplace transform of an HCM-function (or a degenerate function).
4. 4
(Bosch and Simon 2016) Let fα:(0,)(0,) be a pdf of a positive α-stable distribution (i.e., the Laplace transform of fα is equal to \(\mathrm {e}^{-t^{\alpha }}\)). Then fα is HCM if and only if \( \alpha \in (0, \frac {1}{2})\).
First observe that the pdf of a GG random variable composed with \(\sqrt {2t}\) is given by \(f_{X_{p}}(\sqrt {2t})= c_{p} \mathrm {e}^{-2^{\frac {p}{2}-1}t^{\frac {p}{2}}}, \,t >0\), and is a Laplace transform, up to a normalization constant, of an α-stable positive random variable (see discussion in “Connection to stable distributions” section).
Next, let gp/2(x),x>0, denote the pdf of an α-stable distribution of order \(\frac {p}{2}\). Clearly, gp/2(x) is an inverse Laplace transform of \(f_{X_{p}}(\sqrt {2t})\) up to a normalization constant. Now by Theorem 7 Property 4) we have that gp/2(x) is an HCM function for all \(\frac {p}{2} \in (0, \frac {1}{2}]\). Therefore, \(f_{X_{p}}(\sqrt {2t})\) is a Laplace transform of an HCM function, and by Theorem 7 Property 3) \(f_{X_{p}}\) is a pdf of a Gaussian mixture \(X_{p} \stackrel {d}{=}\sqrt {V} X_{2}\) where the distribution of V is in the β-Class. By Theorem 7 Property 2) and Property 1) we have that for all \(\frac {p}{2} \in (0, \frac {1}{2}] X_{p}\) has an EGGC distribution and is self-decomposable.
Case of q>p>0
In this regime, we want to show that there exists no random variable \(\hat {X}_{\alpha }\) independent of \(Z_{p} \sim \mathcal {N}_{p}(0,1)\) such that \(\alpha X_{q}=\hat {X}_{\alpha }+Z_{p}\), where \(X_{q} \sim \mathcal {N}_{q}(0,1)\) for all α≥1. Note that Xq and Zp have symmetric distributions and finite moments, and thus if such an \(\hat {X}_{\alpha }\) exists it must also be symmetric with finite moments. Then for all k≥1
$$ \alpha^{k} \mathbb{E}[|X_{q}|^{k}]= \mathbb{E}[ \mathbb{E}[|\hat{X}_{\alpha}+Z_{p}|^{k} \mid Z_{p}] ] \stackrel{a)}{\ge} \mathbb{E}[ |\mathbb{E}[\hat{X}_{\alpha}+Z_{p} \mid Z_{p}]|^{k} ]\stackrel{b)}{=} \mathbb{E}[ |Z_{p}|^{k} ] , $$
(101)
where the (in)-equalities follow from: a) Jensen’s inequality; and b) the independence of \(\hat {X}_{\alpha }\) and Zp, and that \(\mathbb {E}[\hat {X}_{\alpha }]=0\).
This implies that, in order for the inequality in (101) to hold we must have that
$$ \alpha \ge \left(\frac{\mathbb{E}[ |Z_{p}|^{k} ] }{\mathbb{E}[|X_{q}|^{k}] }\right)^{\frac{1}{k}}, \text{ for all \(k \ge 1\). } $$
(102)
However, by Corollary 1 for p<q we have that \(\alpha \ge {\lim }_{k \to \infty } \left (\frac {\mathbb {E}[ |Z_{p}|^{k} ] }{\mathbb {E}[|X_{q}|^{k}] }\right)^{\frac {1}{k}} =\infty ;\) therefore, there exists no α≥1 that can satisfy (102) for all k≥1.
Case of p=2 and q<2
Note that in the case of p=2 and q<2 we want to show that there is no \(\hat {X}_{\alpha }\) such that the convolution leads to \( f_{X_{q}}(y) = c_{2} \mathbb {E} \left [ \mathrm {e}^{-\frac {\left (y-\hat {X}_{\alpha }\right)^{2}}{2}} \right ]\) where by definition \(f_{X_{q}}(y) = \frac {c_{q}}{\alpha } \mathrm {e}^{-\frac {|y|^{q}}{2 \alpha ^{q}}}\). Such an \(\hat {X}_{\alpha }\) does not exist since the convolution preserves analyticity. In other words, the convolution with an analytic pdf must result in an analytic pdf. Noting that \(f_{X_{q}}(y)\) is not analytic for q<2 (i.e., the derivative at zero is not defined) leads to the desired conclusion.
Case of p>2 and q≤2
Now for p>2 and q≤2 the function ϕ(q,p,α)(t) has a pole but no zeros by Theorem 3. Therefore, for the case of p>2 and q≤2 there exists a t0, namely the pole of ϕ(q,p,α)(t), such that ϕ(q,p,α)(t) is not continuous at t=t0. This violates the condition that the characteristic function is always a continuous function of t and, therefore, ϕ(q,p,α)(t) is not a characteristic function for all α≥1.
Case of p>q>2
For the case of p>q>2 the function \(\phi _{(q,p,\alpha)}(t)=\frac {\phi _{q}(\alpha t)}{\phi _{p}(t)}\) has both poles and zeros by Theorem 3. Moreover, let t1 be such that ϕp(t1)=0 and we can always choose an α such that ϕq(αt1)≠0 and ϕ(q,p,α)(t1)=. In other words, we choose an α such that the poles do not cancel the zeros. Therefore, there exists an α such that ϕ(q,p,α)(t) is not a continuous function of t and therefore is not a characteristic function. Finally, because the number of zeros is at most countable (see Theorem 3) the above argument holds for almost all α≥1.
Case of q<p<2
Finally, for q<p<2 the result follows from Proposition 12 where it is shown that \( {\lim }_{t \to \infty } \phi _{(q,p,\alpha)}(t)=\infty \), which violates the fact that the characteristic function is bounded. This concludes the proof.
Appendix L: Proof of Proposition 15
The magnitude of ϕlog(V)(t) can be approximated by using Stirling’s formula
$$\begin{array}{*{20}l} \left|\phi_{\log(V)}(t) \right|&= \frac{ \Gamma \left(\frac{1}{q} \right)}{ \Gamma \left(\frac{1}{p} \right)} \left| \frac{ 2^{\frac{it}{p}} }{ 2^{\frac{it}{q} }} \right| \left| \frac{ \Gamma \left(\frac{it +1}{p}\right) }{ \Gamma \left(\frac{it +1}{q}\right)} \right|\\ & \approx \frac{p}{q} \frac{ \Gamma \left(\frac{1}{q} \right) \left(\frac{1}{\mathrm{e}}\right)^{\frac{1}{p}-\frac{1}{q}} \left(\frac{1}{p} \right)^{\frac{1}{p}} q^{\frac{1}{q}}}{ \Gamma \left(\frac{1}{p} \right)} \left| \mathrm{e}^{\left(\frac{1+it}{p}-\frac{1+it}{q} \right) \log\left(1+it\right)} \right|. \end{array} $$
Next, observe that
$$\begin{array}{*{20}l} \left| \mathrm{e}^{\left(\frac{1+it}{p}-\frac{1+it}{q} \right) \log\left(1+it\right)} \right| &= \mathrm{e}^{\mathsf{Re} \left(\left(\frac{1+it}{p}-\frac{1+it}{q} \right) \log\left(1+it\right) \right)} \\ &= \left(1+t^{2} \right)^{\frac{q-p}{2pq}} \mathrm{e}^{- t \cdot \mathsf{sign}(t) \tan^{-1}(|t|) \left(\frac{1}{p}-\frac{1}{q} \right)}. \end{array} $$
As a result, for p>q we have that |ϕlog(V)(t)| is not a bounded function and cannot be a characteristic function. For p<q, |ϕlog(V)(t)| is a bounded and integrable function. Therefore, ϕlog(V)(t) has a Fourier inverse given by
$$ f_{\log(V)}(v)= \frac{1}{2 \pi} \int_{-\infty}^{\infty} \mathrm{e}^{-i v t} \frac{ 2^{\frac{it}{p}} \Gamma \left(\frac{it +1}{p}\right) \Gamma \left(\frac{1}{q} \right)}{ 2^{\frac{it}{q}} \Gamma \left(\frac{it +1}{q}\right) \Gamma \left(\frac{1}{p} \right)} dt. $$
(103)
The proof is concluded by using the transformation \(f_{V}(v)= f_{\log (V)}(\log (v)) \frac {1}{v}\)
$$ f_{V}(v)= \frac{1}{2 \pi} \frac{\Gamma \left(\frac{1}{q} \right)}{\Gamma \left(\frac{1}{p} \right)} \int_{\mathbb{R}} v^{-it-1} \frac{ 2^{\frac{it}{p}} \Gamma \left(\frac{it +1}{p}\right) }{ 2^{\frac{it}{q}} \Gamma \left(\frac{it +1}{q}\right)} dt, \ v>0. $$
(104)
Notes
1. 1.
In other words, the set of α for which the statement does not hold has Lebesgue measure zero.
References
1. Abramowitz, M., Stegun, I. A.: Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables vol. 55. Courier Corporation, Chelmsford (1964).
2. Algazi, V. R., Lerner, R. M.: Binary detection in white non-Gaussian noise. M.I.T. Lincoln Lab. 18(Res. DS-2138), 241–250 (1964).
3. Arellano-Valle, R. B., Richter, W. -D.: On skewed continuous n,p-symmetric distributions. Chil. J. Stat. 3(2), 193–212 (2012).
4. Banerjee, S., Agrawal, M.: Underwater acoustic noise with generalized Gaussian statistics: Effects on error performance. In: Proceedings of OCEANS - Bergen, 2013 MTS/IEEE, pp. 1–8. IEEE, Bergen (2013).
5. Beaulieu, N. C., Young, D. J.: Designing time-hopping ultrawide bandwidth receivers for multiuser interference environments. Proc. IEEE. 97(2), 255–284 (2009).
6. Bernard, O., D’Hooge, J., Fribouler, D.: Statistical modeling of the radio-frequency signal in echocardiographic images based on generalized Gaussian distribution. In: Proceedings of the 3rd IEEE International Symposium on Biomedical Imaging: Nano to Macro, 2006, pp. 153–156. IEEE, Arlington (2006).
7. Bochner, S.: Stable laws of probability and completely monotone functions. Duke Math. J. 3(4), 726–728 (1937).
8. Bondesson, L.: Generalized gamma convolutions and related classes of distributions and densities. Lect. Notes Stat. 76 (1992).
9. Bosch, P., Simon, T.: A proof of Bondesson’s conjecture on stable densities. Ark Matematik. 54(1), 31–38 (2016).
10. Cover, T., Thomas, J.: Elements of Information Theory: Second Edition. Wiley, Hoboken (2006).
11. De Simoni, S.: Su una estensione dello schema delle curve normali di ordine r alle variabili doppie. Statistica. 37, 447–474 (1968).
12. de Wouwer, G. V., Scheunders, P., Dyck, D. V.: Statistical texture characterization from discrete wavelet representations. IEEE Trans. Image Process. 8(4), 592–598 (1999).
13. Do, M. N., Vetterli, M.: Wavelet-based texture retrieval using generalized Gaussian density and Kullback-Leibler distance. IEEE Trans. Image Process. 11(2), 146–158 (2002).
14. Dytso, A., Bustin, R., Poor, H. V., Shamai (Shitz), S.: A view of information-estimation relations in Gaussian networks. Entropy. 19(8), 409 (2017).
15. Dytso, A., Bustin, R., Poor, H. V., Shamai (Shitz), S.: On additive channels with generalized Gaussian noise. In: Proceedings of the IEEE International Symposium on Information Theory, pp. 426–430. IEEE, Aachen (2017).
16. Dytso, A., Bustin, R., Tuninetti, D., Devroye, N., Poor, H. V., Shitz, S. S.: On the minimum mean p-th error in Gaussian noise channels and its applications. IEEE Trans. Inf. Theory. 64(3), 2012–2037 (2018).
17. Elkies, N., Odlyzko, A., Rush, J.: On the packing densities of superballs and other bodies. Invent. Math. 105(1), 613–639 (1991).
18. Eskenazis, A., Nayar, P., Tkocz, T.: Gaussian mixture entropy and geometric inequalities (2016). Preprint available at https://arxiv.org/abs/1611.04921.
19. Fahs, J., Abou-Faycal, I.: On properties of the support of capacity-achieving distributions for additive noise channel models with input cost constraints. IEEE Trans. Inf. Theory. 64(2), 1178–1198 (2018).
20. Goodman, I. R., Kotz, S.: Multivariate θ-generalized normal distributions. J. Multivar. Anal. 3(2), 204–219 (1973).
21. Gauss, C. F.: Theoria Motus Corporum Coelestium in Sectionibus Conicis Solem Ambientium vol. 7. Perthes et Besser, Paris (1809).
22. Gonzalez-Jimenez, D., Perez-Gonzalez, F., Comesana-Alfaro, P., Perez-Freire, L., Alba-Castro, J. L.: Modeling Gabor coefficients via generalized Gaussian distributions for face recognition. In: Proceedings of the IEEE International Conference on Image Processing, vol. 4, pp. 485–488. IEEE, San Antonio (2007).
23. Gupta, A. K., Nagar, D. K.: Matrix Variate Distributions. Chapman and Hall/CRC, London (2018).
24. Hoffman-Jørgensen, J.: Probability with a View Towards Statistics vol. 2. Routledge, Abingdon (2017).
25. Levy, H.: Stochastic dominance and expected utility: survey and analysis. Manag. Sci. 38(4), 555–593 (1992).
26. Lévy, P.: Calcul des Probabilités. Gauthier-Villars, Paris, France (1925).
27. Lin, G. D., Huang, J. S.: The cube of a logistic distribution is indeterminate. Aust. J. Stat. 39(3), 247–252 (1997).
28. Lukacs, E.: Characteristic Functions. Griffin, Londong (1970).
29. Lutwak, E., Yang, D., Zhang, G.: Moment-entropy inequalities for a random vector. IEEE Trans. Inf. Theory. 53(4), 1603–1607 (2007).
30. Mallat, S. G.: A theory for multiresolution signal decomposition: the wavelet representation. IEEE Tran. Pattern Anal. Mach. Intell. 11(7), 674–693 (1989).
31. McLachlan, G., Peel, D.: Finite Mixture Models. Wiley, Hoboken (2004).
32. Miller, J., Thomas, J. B.: Detectors for discrete-time signals in non-Gaussian noise. IEEE Trans. Inf. Theory. 18(2), 241–250 (1972).
33. Mohamed, O. M. M., Jaidane-Saidane, M., Souissi, J.: Modeling of the load duration curve using the asymmetric generalized Gaussian distribution: case of the Tunisian power system. In: Proceedings of the 10th International Conference on Probabilistic Methods Applied to Power Systems, pp. 1–6. IEEE, Rincon (2008).
34. Moulin, P., Liu, J.: Analysis of multiresolution image denoising schemes using generalized Gaussian and complexity priors. IEEE Trans. Inf. Theory. 45(3), 909–919 (1999).
35. Nadarajah, S.: A generalized normal distribution. J. Appl. Stat. 32(7), 685–694 (2005).
36. Nielsen, P. A., B.Thomas, J.: Signal detection in Arctic under-ice noise. In: Proceedings of the 25th Annual Allerton Conference on Communication, Control, and Computing, pp. 172–177. IEEE, Monticello (1987).
37. Nielsen, F., Nock, R.: Maxent upper bounds for the differential entropy of univariate continuous distributions. IEEE Signal Process. Lett. 24(4), 402–406 (2017).
38. Olver, F.: Uniform, exponentially improved, asymptotic expansions for the generalized exponential integral. SIAM J. Math. Anal. 22(5), 1460–1474 (1991).
39. Ozarow, L. H., Wyner, A. D.: On the capacity of the Gaussian channel with a finite number of input levels. IEEE Trans. Inf. Theory. 36(6), 1426–1428 (1990).
40. Pogány, T. K., Nadarajah, S.: On the characteristic function of the generalized normal distribution. C. R. Math. 348(3), 203–206 (2010).
41. Poor, H. V., Thomas, J. B.: Locally optimum detection of discrete-time stochastic signals in non-Gaussian noise. J. Acoust. Soc. Am. 63(1), 75–80 (1978).
42. Poularikas, A. D.: Handbook of Formulas and Tables for Signal Processing. CRC Press, Boca Raton (1998).
43. Richter, W. -D.: Generalized spherical and simplicial coordinates. J. Math. Anal. Appl. 336(2), 1187–1202 (2007).
44. Richter, W.-D.: Geometric disintegration and star-shaped distributions. J. Stat. Distrib. Appl. 1(1), 20 (2014).
45. Richter, W.-D.: Exact inference on scaling parameters in norm and antinorm contoured sample distributions. J. Stat. Distrib. Appl. 3(1), 8 (2016).
46. Schilling, R. L., Song, R., Vondracek, Z.: Bernstein Functions: Theory and Applications vol. 37. Walter de Gruyter, Berlin, Germany (2012).
47. Sharifi, K., Leon-Garcia, A.: Estimation of shape parameter for generalized Gaussian distributions in subband decompositions of video. IEEE Trans. Circ. Syst. Video Technol. 5(1), 52–56 (1995).
48. Soury, H., Yilmaz, F., Alouini, M. -S.: Average bit error probability of binary coherent signaling over generalized fading channels subject to additive generalized Gaussian noise. IEEE Commun. Lett. 16(6), 785–788 (2012).
49. Soury, H., Alouini, M. S.: New results on the sum of two generalized Gaussian random variables. In: Proceedings of the 2015 IEEE Global Conference on Signal and Information Processing, pp. 1017–1021. IEEE, Orlando (2015).
50. Subbotin, M.: On the law of frequency of error. Matematicheskii Sb. 31, 296–301 (1923).
51. Stewart, J.: Positive definite functions and generalizations, an historical survey. Rocky Mt. J. Math. 6(3), 409–434 (1976).
52. Stoyanov, J.: Krein condition in probabilistic moment problems. Bernoulli Journal. 6(5), 939–949 (2000).
53. Ushakov, N. G.: Selected Topics in Characteristic Functions. Walter de Gruyter, Berlin, Germany (1999).
54. van Harn, K., Steutel, F.: Infinite Divisibility of Probability Distributions on the Real Line. Taylor & Francis, New York (2003).
55. Varanasi, M. K., Aazhang, B.: Parametric generalized Gaussian density estimation. J. Acoust. Soc. Am. 86(4), 1404–1415 (1989).
56. Vasudevay, R., Kumari, J. V.: On general error distributions. ProbStat Forum. 06, 89–95 (2013).
57. Viswanathan, R., Ansari, A.: Distributed detection of a signal in generalized Gaussian noise. IEEE Trans. Acoust. Speech, Signal Process. 37(5), 775–778 (1989).
58. Westerink, P. H., Biemond, J., Boekee, D. E.: Subband coding of color images. In: Subband Image Coding, pp. 193–227. Springer, Boston (1991).
59. Widder, D. V.: The Laplace Transform. 1946. Princeton University Press, Princeton (1946).
60. Zolotarev, V. M.: One-dimensional Stable Distributions vol. 65. American Mathematical Society, Providence (1986).
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Acknowledgements
The authors would like to thank Professor Alexander Lindner from the Ulm University for providing references (Bondesson 1992) and (Bosch and Simon 2016), which immediately lead to the conclusion that the GG distributions in p(0,1] are self-decomposable.
Funding
The work of A. Dytso and H.V. Poor was supported by the U.S. National Science Foundation under Grant CNS-1702808. The work of S. Shamai and R. Bustin was supported by the European Union’s Horizon 2020 Research and Innovation Programme Grant 694630.
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All authors contributed equally to the manuscript. All authors read and approved the final manuscript.
Correspondence to Alex Dytso.
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Dytso, A., Bustin, R., Poor, H. et al. Analytical properties of generalized Gaussian distributions. J Stat Distrib App 5, 6 (2018) doi:10.1186/s40488-018-0088-5
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Keywords
• Generalized Gaussian distribution
• Infinite divisibility
• Mellin transform
• Characteristic function
• Self-decomposition
|
__label__pos
| 0.999916 |
StatsTTest Values?
What is the P parameter returned by StatsTTest?
I am designing a demo for a class. It shows a "theoretical" normal distribution. It adds "raw data" to the distribution (using gnoise()). I want to return a report on the Accuracy of the raw data to represent the theory.
I understand the hypotheses tests based on t and tcrit. What is confusing me is the P value. Is this a probability of the null hypothesis being true? Or vice-versa? Or something else?
Alternatively, what might be a better message to report on this demo about the accuracy of the "raw data" relative to "theory" (an infinite population size).
jjweimer wrote:
Is this a probability of the null hypothesis being true?
Yes. As for a better message: there's a nice video by Geoff Cummings called Dance of The P-Values, which illustrates the point you are (I think) trying to make. It's on youtube and highly recommended.
Wonderful! Thank you.
--
J. J. Weimer
Chemistry / Chemical & Materials Engineering, UAH
Jeff,
The null hypothesis in this case is that the means are equal. The P value is the probability that 't' is outside the critical values by chance. This is the area under the t-distribution curve away from the +-critical value (for two tails).
The "Dance of the P-Values" is indeed a very nice example that should not be difficult to reproduce in IGOR.
A.G.
WaveMetrics, Inc.
Igor wrote:
...
The "Dance of the P-Values" is indeed a very nice example that should not be difficult to reproduce in IGOR.
Thanks. I am heading that way. My latest iteration shows as in this figure.
I hope to post the demo here soon. Including a way to "build the stats in steps" may have to be something I do as a summer project.
--
J. J. Weimer
Chemistry / Chemical & Materials Engineering, UAH
statsdemo2.png
Version 1 of the demonstration has just been posted. See the recent forum posts to find it. The package includes a screen cast of the experiment in action.
I hope folks in education might find this tool can help them explain the concepts of precision and accuracy to students. Indeed, the driving force for me to make it was a realization that students in undergraduate chemistry labs seemed to have no clue what the concepts really mean. Even I learned some important things by the time I was done.
Enjoy!
--
J. J. Weimer
Chemistry / Chemical & Materials Engineering, UAH
|
__label__pos
| 0.885921 |
SANDAEROVATOR
SANDAEROVATOR is an aerospace tower-pyramid cable-tube elevator-accelerator. A passive/active structure pyramid/tower cable-tube (composite material tension/compression force), buoyancy/propeller/rocket/rail/cannon (H2/O2/H2O/molecular force), electromagnetic (electron/photonic force) launch/energy elevator-accelerator and base/structure/connection for ocean, terrestrial, aero, space cities. Sandaerovator structure has a pyramid and tower horizontal wing wind stabilizers, formed by modules with independent counter wind and flying buoyancy/propeller/rocket propulsion. Sandaerotrain elevator-accelerator 10-30-100km with Sandaeroblock pile-up towers cable/track connected to expansion Pyramid. Cross-Pyramid Space Elevator, 30 km from cube-sphere centripetal pile-up Acity to centrifugal carbon composite 4 cable-truss, connected to Geo stationary 30k km Space City. Sandaerovator can be used as an exterior elevator for any current, new or expanded building, and as an electromagnetic accelerator launching platform for a Sandaeroship, Sandaerocopter and/or Sandaerocket, including via a cable, vacuum tube coil gun and/or rail linear electric motor. H2-photo-electric acceleration can reach 11 km/s gravity escape velocity and/or 8km/s orbital velocity. Up to 200km horizontal and/or 100km vertical track can be used for safe human gradual acceleration. Carbon graphene/nanotube multi/truss cable-tube can be centrifugal stretched/sustained by geosync satellite space city and flowing cargo pellets, molecules, electrons and photons. Mountain/Pyramid Vacuum Tunnel hydrogen-photonic-electric space-cannon can shoot cargo, avatar-bots and laser-rocket-mirror spaceships to escape velocity.
Sandaerovator can be connected and give access to SANDAEROCITIES, atmospheric/mountain top Acities or geostationary Space Cities (Sandaerospace Scities), including a non-fixed connection to a Lunar City. Sandaerovator can gradually combine space elevator, tower, hook, rotor, loop, ring concepts using wing aerodynamics, flying wheel, wind propellers, gas/vacuum buoyancy, centrifugal gravity, accelerated vapor/water pressure, electromagnetic/kinetic energy, in double counter loop, for active support structure, pushing structure up, reducing gravity compression. Multi orbit Sandaerospaces can have velocity synchronized with upward tensile or propulsive counter force to allow straight elevation until geostationary orbit. Vertical- Horizontal Four-Direction Pyramid-Growth; 1 to 100km Space-Port Electric Accelerator-Elevator cross-pyramid; H2/H2O Aeroblock vertical-horizontal pile-up; 100km to 100,000km Centrifugal Counter Weight Composite Cube-Sphere Structure with 4 cables. Propeller/Wing/Counterweight and Lidar/Laser defense against wind, debris, meteorites, photonic waves etc. Sandaerovator can PRODUCE ENERGY SURPLUS AFTER PARTIAL USE FOR ACTIVE STRUCTURING: solar/wave/wind energy heats water/air sending them upward producing upward structural force on thermal turbines, then sends it downward in central tube, generating upward rocket/jet force to be cooled in water/ocean and repeat cycle. Meanwhile solenoid electromagnetic force sends pellets and payloads upward, generating also upward structural centrifugal force cycle. Solaser L1 La Grange point, Geosync and Elevator self-finance protection, communication, energy, transportation system energizes magnetic dipole shield (photo-electric solenoid/coil) for intersat protection for any planet or satellite. Circular laser network also generates larger photo-gravitonic protection fields.
GRAPHENE MACROTUBE and MACRORIBBON are macro single or multi layer rolled up (tube) or flat (ribbon/fabric) graphene single carbon hexagonal network (or composite with carbon fabric, nanotubes, polymers etc), to replace steel cables, tubes, panels with over 10 times stronger material, capable for example, with a multi cable truss or ribbon formation, of full or interrupted connection to a 3-30k km space tower-elevator geosynchronous system, with or without a 100k km centrifugal counter-weight. Earth oceanic pyramid-tower water filled carbon composite cube-sphere aquablocks bellow-on-near water line, vapor/H2 aeroblocks above water line, pile-up to buoyant AEROCITIES, deployed top-down in Venus, cable truss/ribbon connected to Geo Space Cities.
Atmospheric electric propulsion pyramid-tower-elevators and space laser propulsion can significantly lower costs of molecular rocket propulsion mobile aerospace ship-stations, with modular ascension under G$/US$1k/module for enterprises and under G$/US$100 or free for citizens with subsidy/sponsorship from solar-wind-wave energy sales. Gcity/Tower/Pyramid/Aerotrain on land/water control wind/wave excess movement by cube-sphere pass-trough shape, aqua-aeroblock anchoring, propeller and photo-electric heating/ionization counter movements. Modular carbon composite cube-sphere aqua-aeroblock cross tower-pyramid stacking can reach 1 km, gradually expand past 100km, producing solar-wind-wave energy, housing and transportation. Ocean centered, for land clearance, Aqua-Ocean-City connected to Aero-Atmosphere-City to Geo-Space-City by Pyramid-Tower-Elevator, Molecular-Electric-Photonic weather control, Earth Aerocities duplicated/moved to Venus.
Scity Geostationary Space City
Acity
Atmospheric
Aero City
Ocity - Tcity - Ucity
Ocean, Terrestrian
Underground
Cities
Scities
Space Cities
Geostationary
Sandaerospace
Earth
Lunar City
Space
Elevator
Sandaerovator
SANDAEROCITY
Non-fixed
Connetion
AEROCITY
Earth, Moon, Venus and Mars
Vertical- Horizontal
Four-Direction
Pyramid-Growth
1 to 100km
Space-Port
Electric
Accelerator-Elevator
cross-pyramid
H2/H2O Aeroblock
vertical-horizontal
pile-up
100km to 100,000km
Centrifugal Counter Weight
Composite Cube-Sphere Structure with 4 cables
SANDAEROBRIDGE
SANDAEROBRIDGE
GLOBOCEAN ACITIES
Venus
Atlantic
AeroPark-Bridge
SANDAEROHANGAR
Mars
Mount Olympus
Valles Marineris
Ice Pole
Moon
Montes Apenninus
Santos-Dumont Crater
Atlantis
Paradise
Valhalla
Eldorado
Asgard
Xangrila
Globocean
Ocities
Acities
SANDAEROPIPE
UPWARD
FORCE
SURPLUS
ENERGY
CYCLE
solar/wind/wave
heated water/air
solenoid
electromagnetic
pellets/payloads
Solar Mirror/Lens Laser transporting solar-sail mini-space ship/station/robot to Moon, Mars, Venus in minutes
SOLASER
SANDAEROSHIP
SANDAEROTRAIN
SOLASER
Sandaerotrain elevator-accelerator 10-30-100km with Sandaeroblock pile-up towers cable/track connected to expansion Pyramid.
SANDAEROTRAIN
SANDAEROBRIDGE
Aqua-Aero-Terra-Sub Train
ocean tower solar-wind-wave,
cube-sphere AeroBlocks above water,
AquaBlocks bellow water, connected by cable,
to units above weather and at bottom of ocean,
to where the tower will pyramid expand to 3-30km.
Space Tower-Elevator
30km to 30,000 km geostationary,
graphene macrotube truss cable/cube-spheres,
electromagnetic upward active structure inverted up/down linear motor/solenoid accelerator-decelerator.
SANDAEROSPACE
SANDAEROGRAPH
Aerocity
Aerocity
Aerocity
Aerocity
Ocean Beach Pier-Port extended east 1km to Gcity, then 1 km west, 1km north/south, then as a cross pyramid, 1 km up to become tallest building in world, producing solar-wind-wave energy, hydrogen, drinking water, farming and housing.
|
__label__pos
| 0.525553 |
Take the 2-minute tour ×
Stack Overflow is a question and answer site for professional and enthusiast programmers. It's 100% free, no registration required.
Suppose I have two objective c++ objects that each wrap a native c++ object given:
A, B = objective c++ object types
Acpp, Bcpp = c++ object types
In B.mm
#import "Bcpp.h"
#import "B.h"
@interface B ()
{
Bcpp myBcpp; // declare instance c++ variable of type Bcpp
}
@end
In A.mm
#import "Acpp.h"
#import "A.h"
@interface A ()
{
Acpp myAcpp; // declare instance c++ variable of type Acpp
}
@end
@implementation A
// method to return an instance of B from an instance of A (self)
- (B)GetBfromA
{
Bcpp *bfroma = myAcpp.GetBfromA(); // return c++ object
// How do i find the objective C++ object B from its wrapped c++ instance bfroma?
}
@end
The reason for doing this is we have a mature c++ data structure and we wish to wrap it with objective c++ objects. Is the the best way? And if it is, how do we solve the reverse mapping problem?
EDIT: Thank you to the early responders but I have a more tricky situation that I implied above. Suppose the function GetBFromA() returns an instance of Bcpp that had already been declared (as an instance variable of an instance of B). So I am holding a pointer to a Bcpp object that is itself an instance variable of an objective C++ object of type B. How do I find the instance of B from the instance of Bcpp?
share|improve this question
well, sure it's answerable - using lots of private accesses and little abstraction layers which can perform the remapping and deferred construction and conversions. you also need to define copy and sharing semantics for your object graphs -- often, it's easiest to just keep it as c++. in your example, you just have to create a new B which references, shares, or copies the Bcpp. generally you do not want to push this objc countermap into your stable c++ layer. typically, Bcpp will not be aware of B. – justin Sep 4 '12 at 4:33
add comment
1 Answer
What you probably need to do is to be able to create a B from a Bcpp. So B will need to be amended to have an -initWithBcpp: method:
- (id)initWithBcpp:(Bcpp*)bcpp
{
self = [super init];
if (self != nil)
{
myBcpp = *bcpp;
}
return self;
}
Then, in GetBFromA, you'll need to create a B from the Bcpp*:
- (B*)GetBfromA
{
Bcpp *bfroma = myAcpp.GetBfromA(); // return c++ object
B* result = [[B alloc] initWithBcpp:bfroma];
return result;
}
share|improve this answer
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|
__label__pos
| 0.999551 |
Nested Loops Join Algorithm Assignment Help
Nested Loops Join (R S):
• foreach tuple r in R do
• foreach tuple s in S do
• if ri == sj then add r s to result
Algorithm for the nested loop join :
For each tuple in outer relation R, we scan inner relation S.
Cost performance:
• Scan of outer + for each tuple of outer, scan of inner relation.
• Cost = M + pR * M * N
• Cost = 1000 + 100*1000*500 I/Os.
Tuple-oriented
• For each tuple in outer relation R, we scan inner relation S.
• Cost: M + pR * M * N = 1000 + 100*1000*500 I/Os.
Page-oriented:
For each page of R, get each page of S, and write out matching pairs of tuples r s where r is in R-page and S is in S-page.
Cost :
• Scan of outer pages + for each page of outer, scan of inner relation.
• Cost = M + M * N
• Cost = 1000 + 1000*500 IOs.
• smaller relation (S) is outer, cost = 500 + 500*1000 IOs.
nested loops join
|
__label__pos
| 0.995309 |
Tips for successfully modeling cavitating flows in rotating equipment (Read 2117 times)
Offline william
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Cavitation in rotating equipment (e.g. pumps) is an important industrial problem. Fluent has a cavitation modes that can be used with rotating reference frames to model cavitation in pumps. However, converging these problems for cases with significant cavitation can be challenging. This solution outlines a procedure that has been found to be successful in a wide range of pump calculations. Additional information can found in the following Technical Note, available from Fluent Inc.:
Kelecy, F.J. (2003)
"Numerical Prediction of Cavitation in a Centrifugal Pump"
TN 211, Fluent Inc.
Consider a pump with a velocity or pressure inlet and a pressure outlet. For simplicity we'll assume that the pump is being modeled as a single blade passage with periodic boundaries using a single moving reference frame (SRF). The working fluid is assumed to be incompressible, and the cavitation model is to be applied to this system. It should be noted that the mixture model version of the cavitation model is used with the Slip Velocity option disabled (that is, we assume the vapor and liquid move with nearly the same velocities though the blade passage). This option could be enabled if desired.
The key to converging the problem is to initialize the solution with a *** single phase solution *** wherein the minimum pressure in the system is above the prescirbed vapor pressure (set in the Define->Models->Multiphase panel). One of the best ways to control this is through the exit pressure - simply set the exit pressure to a high enough value such that the minimum pressure is safely above the vapor pressure. Since the absolute pressure value is not important for an incompressible fluid (only pressure differences are), setting the pressure level in this manner will not affect the single phase solution.
Once the single phase solution has been established, you can then enable the cavitation model. However, it is useful to begin the calculation by *** not changing the exit pressure *** and simply running the model with cavitation turned on. You should not observe any vapor being formed, or if it does (due to fluctuations in pressure), it should rapidly disappear.
When the foregoing solution has converged, you may then reduce the exit pressure to the desired value. If the final exit pressure is signifiantly different than your initial exit pressure, you should gradually reduce the exit pressure to prevent convergence problems. For example, if your initial back pressure were 500 kPa and your target value was 100 kPa, you can reduce the exit pressure to 400 kPa, converge the solution, reduce it to 300 kPa, converge the solution, and so on until the desired level is reached.
If you encounter convergence difficulties, here are some things you can try to enhance stability:
(1) Reduce the under-relaxation factor for pressure correction equation with the command :
(rpsetvar 'pressure-correction/relax 0.6) or even smaller. The default value is 0.7.
(2) Reduce the relaxation factor for momentum equations. You may try to use the values as small as 0.02 in some cases. The cavitating flow sometimes is similar to swirling flows, and thus it can take a while for the vapor bubbles to stabilize.
(3) Reduce the underrelaxation factors for density & vaporization mass.
(4) Modifying the Multigrid settings in Solve->Controls->Multigrid can sometimes help. I have found that setting the Pressure equation termination criterion to 0.001 (rather than 0.1) and setting the post-sweeps to 3 can make the solution of the pressure equation more robust.
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__label__pos
| 0.538109 |
Help i want the discord message trigger to ignore bots
this is the api code i want it to ignore messages from bot accounts
const discord = require("…/…/discord-v2.app.js")
module.exports = {
key: “discord-new-message”,
name: ‘New Message’,
description: “Emit an event for each message posted to one or more channels in a Discord server”,
version: ‘0.0.2’,
dedupe: “unique”,
props: {
discord,
channels: {
type: "$.discord.channel[]",
appProp: "discord",
label: "Channels",
description: "Select the channel(s) you'd like to be notified for",
},
discordApphook: {
type: "$.interface.apphook",
appProp: "discord",
async eventNames() {
return this.channels || []
},
},
ignoreMyself: {
type: "boolean",
label: "Ignore myself",
description: "Ignore messages from me",
default: true,
},
},
async run(event) {
if (event.guildID != this.discord.$auth.guild_id) {
return
}
if (this.ignoreMyself && event.authorID == this.discord.$auth.oauth_uid) {
return
}
this.$emit(event, { id: event.id })
},
}
@yossibroderspam I shipped a change to the Discord integration that should expose a bot flag under event.author_metadata:
You should be able to use that in your event source or any linked workflows to exit early if the message comes from a bot.
|
__label__pos
| 0.898172 |
Shortcuts
mmcv.ops.sync_bn 源代码
# Copyright (c) OpenMMLab. All rights reserved.
from typing import Optional
import torch
import torch.distributed as dist
import torch.nn.functional as F
from mmengine.registry import MODELS
from torch.autograd import Function
from torch.autograd.function import once_differentiable
from torch.nn.modules.module import Module
from torch.nn.parameter import Parameter
from ..utils import ext_loader
ext_module = ext_loader.load_ext('_ext', [
'sync_bn_forward_mean', 'sync_bn_forward_var', 'sync_bn_forward_output',
'sync_bn_backward_param', 'sync_bn_backward_data'
])
class SyncBatchNormFunction(Function):
@staticmethod
def symbolic(g, input, running_mean, running_var, weight, bias, momentum,
eps, group, group_size, stats_mode):
return g.op(
'mmcv::MMCVSyncBatchNorm',
input,
running_mean,
running_var,
weight,
bias,
momentum_f=momentum,
eps_f=eps,
group_i=group,
group_size_i=group_size,
stats_mode=stats_mode)
@staticmethod
def forward(self, input: torch.Tensor, running_mean: torch.Tensor,
running_var: torch.Tensor, weight: torch.Tensor,
bias: torch.Tensor, momentum: float, eps: float, group: int,
group_size: int, stats_mode: str) -> torch.Tensor:
self.momentum = momentum
self.eps = eps
self.group = group
self.group_size = group_size
self.stats_mode = stats_mode
assert isinstance(
input, (torch.HalfTensor, torch.FloatTensor,
torch.cuda.HalfTensor, torch.cuda.FloatTensor)), \
f'only support Half or Float Tensor, but {input.type()}'
output = torch.zeros_like(input)
input3d = input.flatten(start_dim=2)
output3d = output.view_as(input3d)
num_channels = input3d.size(1)
# ensure mean/var/norm/std are initialized as zeros
# ``torch.empty()`` does not guarantee that
mean = torch.zeros(
num_channels, dtype=torch.float, device=input3d.device)
var = torch.zeros(
num_channels, dtype=torch.float, device=input3d.device)
norm = torch.zeros_like(
input3d, dtype=torch.float, device=input3d.device)
std = torch.zeros(
num_channels, dtype=torch.float, device=input3d.device)
batch_size = input3d.size(0)
if batch_size > 0:
ext_module.sync_bn_forward_mean(input3d, mean)
batch_flag = torch.ones([1], device=mean.device, dtype=mean.dtype)
else:
# skip updating mean and leave it as zeros when the input is empty
batch_flag = torch.zeros([1], device=mean.device, dtype=mean.dtype)
# synchronize mean and the batch flag
vec = torch.cat([mean, batch_flag])
if self.stats_mode == 'N':
vec *= batch_size
if self.group_size > 1:
dist.all_reduce(vec, group=self.group)
total_batch = vec[-1].detach()
mean = vec[:num_channels]
if self.stats_mode == 'default':
mean = mean / self.group_size
elif self.stats_mode == 'N':
mean = mean / total_batch.clamp(min=1)
else:
raise NotImplementedError
# leave var as zeros when the input is empty
if batch_size > 0:
ext_module.sync_bn_forward_var(input3d, mean, var)
if self.stats_mode == 'N':
var *= batch_size
if self.group_size > 1:
dist.all_reduce(var, group=self.group)
if self.stats_mode == 'default':
var /= self.group_size
elif self.stats_mode == 'N':
var /= total_batch.clamp(min=1)
else:
raise NotImplementedError
# if the total batch size over all the ranks is zero,
# we should not update the statistics in the current batch
update_flag = total_batch.clamp(max=1)
momentum = update_flag * self.momentum
ext_module.sync_bn_forward_output(
input3d,
mean,
var,
weight,
bias,
running_mean,
running_var,
norm,
std,
output3d,
eps=self.eps,
momentum=momentum,
group_size=self.group_size)
self.save_for_backward(norm, std, weight)
return output
@staticmethod
@once_differentiable
def backward(self, grad_output: torch.Tensor) -> tuple:
norm, std, weight = self.saved_tensors
grad_weight = torch.zeros_like(weight)
grad_bias = torch.zeros_like(weight)
grad_input = torch.zeros_like(grad_output)
grad_output3d = grad_output.flatten(start_dim=2)
grad_input3d = grad_input.view_as(grad_output3d)
batch_size = grad_input3d.size(0)
if batch_size > 0:
ext_module.sync_bn_backward_param(grad_output3d, norm, grad_weight,
grad_bias)
# all reduce
if self.group_size > 1:
dist.all_reduce(grad_weight, group=self.group)
dist.all_reduce(grad_bias, group=self.group)
grad_weight /= self.group_size
grad_bias /= self.group_size
if batch_size > 0:
ext_module.sync_bn_backward_data(grad_output3d, weight,
grad_weight, grad_bias, norm, std,
grad_input3d)
return grad_input, None, None, grad_weight, grad_bias, \
None, None, None, None, None
[文档]@MODELS.register_module(name='MMSyncBN') class SyncBatchNorm(Module): """Synchronized Batch Normalization. Args: num_features (int): number of features/chennels in input tensor eps (float, optional): a value added to the denominator for numerical stability. Defaults to 1e-5. momentum (float, optional): the value used for the running_mean and running_var computation. Defaults to 0.1. affine (bool, optional): whether to use learnable affine parameters. Defaults to True. track_running_stats (bool, optional): whether to track the running mean and variance during training. When set to False, this module does not track such statistics, and initializes statistics buffers ``running_mean`` and ``running_var`` as ``None``. When these buffers are ``None``, this module always uses batch statistics in both training and eval modes. Defaults to True. group (int, optional): synchronization of stats happen within each process group individually. By default it is synchronization across the whole world. Defaults to None. stats_mode (str, optional): The statistical mode. Available options includes ``'default'`` and ``'N'``. Defaults to 'default'. When ``stats_mode=='default'``, it computes the overall statistics using those from each worker with equal weight, i.e., the statistics are synchronized and simply divied by ``group``. This mode will produce inaccurate statistics when empty tensors occur. When ``stats_mode=='N'``, it compute the overall statistics using the total number of batches in each worker ignoring the number of group, i.e., the statistics are synchronized and then divied by the total batch ``N``. This mode is beneficial when empty tensors occur during training, as it average the total mean by the real number of batch. """ def __init__(self, num_features: int, eps: float = 1e-5, momentum: float = 0.1, affine: bool = True, track_running_stats: bool = True, group: Optional[int] = None, stats_mode: str = 'default'): super().__init__() self.num_features = num_features self.eps = eps self.momentum = momentum self.affine = affine self.track_running_stats = track_running_stats group = dist.group.WORLD if group is None else group self.group = group self.group_size = dist.get_world_size(group) assert stats_mode in ['default', 'N'], \ f'"stats_mode" only accepts "default" and "N", got "{stats_mode}"' self.stats_mode = stats_mode if self.affine: self.weight = Parameter(torch.Tensor(num_features)) self.bias = Parameter(torch.Tensor(num_features)) else: self.register_parameter('weight', None) self.register_parameter('bias', None) if self.track_running_stats: self.register_buffer('running_mean', torch.zeros(num_features)) self.register_buffer('running_var', torch.ones(num_features)) self.register_buffer('num_batches_tracked', torch.tensor(0, dtype=torch.long)) else: self.register_buffer('running_mean', None) self.register_buffer('running_var', None) self.register_buffer('num_batches_tracked', None) self.reset_parameters() def reset_running_stats(self): if self.track_running_stats: self.running_mean.zero_() self.running_var.fill_(1) self.num_batches_tracked.zero_() def reset_parameters(self): self.reset_running_stats() if self.affine: self.weight.data.uniform_() # pytorch use ones_() self.bias.data.zero_()
[文档] def forward(self, input: torch.Tensor) -> torch.Tensor: if input.dim() < 2: raise ValueError( f'expected at least 2D input, got {input.dim()}D input') if self.momentum is None: exponential_average_factor = 0.0 else: exponential_average_factor = self.momentum if self.training and self.track_running_stats: if self.num_batches_tracked is not None: self.num_batches_tracked += 1 if self.momentum is None: # use cumulative moving average exponential_average_factor = 1.0 / float( self.num_batches_tracked) else: # use exponential moving average exponential_average_factor = self.momentum if self.training or not self.track_running_stats: return SyncBatchNormFunction.apply( input, self.running_mean, self.running_var, self.weight, self.bias, exponential_average_factor, self.eps, self.group, self.group_size, self.stats_mode) else: return F.batch_norm(input, self.running_mean, self.running_var, self.weight, self.bias, False, exponential_average_factor, self.eps)
def __repr__(self): s = self.__class__.__name__ s += f'({self.num_features}, ' s += f'eps={self.eps}, ' s += f'momentum={self.momentum}, ' s += f'affine={self.affine}, ' s += f'track_running_stats={self.track_running_stats}, ' s += f'group_size={self.group_size},' s += f'stats_mode={self.stats_mode})' return s
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|
__label__pos
| 0.996235 |
/*! \page graphs How to use graphs The primary data structures of LEMON are the graph classes. They all provide a node list - edge list interface, i.e. they have functionalities to list the nodes and the edges of the graph as well as incoming and outgoing edges of a given node. Each graph should meet the \ref lemon::concept::StaticGraph "StaticGraph" concept. This concept does not make it possible to change the graph (i.e. it is not possible to add or delete edges or nodes). Most of the graph algorithms will run on these graphs. The graphs meeting the \ref lemon::concept::ExtendableGraph "ExtendableGraph" concept allow node and edge addition. You can also "clear" such a graph (i.e. erase all edges and nodes ). In case of graphs meeting the full feature \ref lemon::concept::ErasableGraph "ErasableGraph" concept you can also erase individual edges and nodes in arbitrary order. The implemented graph structures are the following. \li \ref lemon::ListGraph "ListGraph" is the most versatile graph class. It meets the \ref lemon::concept::ErasableGraph "ErasableGraph" concept and it also has some convenient extra features. \li \ref lemon::SmartGraph "SmartGraph" is a more memory efficient version of \ref lemon::ListGraph "ListGraph". The price of this is that it only meets the \ref lemon::concept::ExtendableGraph "ExtendableGraph" concept, so you cannot delete individual edges or nodes. \li \ref lemon::SymListGraph "SymListGraph" and \ref lemon::SymSmartGraph "SymSmartGraph" classes are very similar to \ref lemon::ListGraph "ListGraph" and \ref lemon::SmartGraph "SmartGraph". The difference is that whenever you add a new edge to the graph, it actually adds a pair of oppositely directed edges. They are linked together so it is possible to access the counterpart of an edge. An even more important feature is that using these classes you can also attach data to the edges in such a way that the stored data are shared by the edge pairs. \li \ref lemon::FullGraph "FullGraph" implements a complete graph. It is a \ref lemon::concept::StaticGraph, so you cannot change the number of nodes once it is constructed. It is extremely memory efficient: it uses constant amount of memory independently from the number of the nodes of the graph. Of course, the size of the \ref maps-page "NodeMap"'s and \ref maps-page "EdgeMap"'s will depend on the number of nodes. \li \ref lemon::NodeSet "NodeSet" implements a graph with no edges. This class can be used as a base class of \ref lemon::EdgeSet "EdgeSet". \li \ref lemon::EdgeSet "EdgeSet" can be used to create a new graph on the node set of another graph. The base graph can be an arbitrary graph and it is possible to attach several \ref lemon::EdgeSet "EdgeSet"'s to a base graph. \todo Don't we need SmartNodeSet and SmartEdgeSet? \todo Some cross-refs are wrong. The graph structures themselves can not store data attached to the edges and nodes. However they all provide \ref maps-page "map classes" to dynamically attach data the to graph components. The following program demonstrates the basic features of LEMON's graph structures. \code #include #include using namespace lemon; int main() { typedef ListGraph Graph; \endcode ListGraph is one of LEMON's graph classes. It is based on linked lists, therefore iterating throuh its edges and nodes is fast. \code typedef Graph::Edge Edge; typedef Graph::InEdgeIt InEdgeIt; typedef Graph::OutEdgeIt OutEdgeIt; typedef Graph::EdgeIt EdgeIt; typedef Graph::Node Node; typedef Graph::NodeIt NodeIt; Graph g; for (int i = 0; i < 3; i++) g.addNode(); for (NodeIt i(g); i!=INVALID; ++i) for (NodeIt j(g); j!=INVALID; ++j) if (i != j) g.addEdge(i, j); \endcode After some convenient typedefs we create a graph and add three nodes to it. Then we add edges to it to form a complete graph. \code std::cout << "Nodes:"; for (NodeIt i(g); i!=INVALID; ++i) std::cout << " " << g.id(i); std::cout << std::endl; \endcode Here we iterate through all nodes of the graph. We use a constructor of the node iterator to initialize it to the first node. The operator++ is used to step to the next node. Using operator++ on the iterator pointing to the last node invalidates the iterator i.e. sets its value to \ref lemon::INVALID "INVALID". This is what we exploit in the stop condition. The previous code fragment prints out the following: \code Nodes: 2 1 0 \endcode \code std::cout << "Edges:"; for (EdgeIt i(g); i!=INVALID; ++i) std::cout << " (" << g.id(g.source(i)) << "," << g.id(g.target(i)) << ")"; std::cout << std::endl; \endcode \code Edges: (0,2) (1,2) (0,1) (2,1) (1,0) (2,0) \endcode We can also iterate through all edges of the graph very similarly. The \c target and \c source member functions can be used to access the endpoints of an edge. \code NodeIt first_node(g); std::cout << "Out-edges of node " << g.id(first_node) << ":"; for (OutEdgeIt i(g, first_node); i!=INVALID; ++i) std::cout << " (" << g.id(g.source(i)) << "," << g.id(g.target(i)) << ")"; std::cout << std::endl; std::cout << "In-edges of node " << g.id(first_node) << ":"; for (InEdgeIt i(g, first_node); i!=INVALID; ++i) std::cout << " (" << g.id(g.source(i)) << "," << g.id(g.target(i)) << ")"; std::cout << std::endl; \endcode \code Out-edges of node 2: (2,0) (2,1) In-edges of node 2: (0,2) (1,2) \endcode We can also iterate through the in and out-edges of a node. In the above example we print out the in and out-edges of the first node of the graph. \code Graph::EdgeMap m(g); for (EdgeIt e(g); e!=INVALID; ++e) m.set(e, 10 - g.id(e)); std::cout << "Id Edge Value" << std::endl; for (EdgeIt e(g); e!=INVALID; ++e) std::cout << g.id(e) << " (" << g.id(g.source(e)) << "," << g.id(g.target(e)) << ") " << m[e] << std::endl; \endcode \code Id Edge Value 4 (0,2) 6 2 (1,2) 8 5 (0,1) 5 0 (2,1) 10 3 (1,0) 7 1 (2,0) 9 \endcode As we mentioned above, graphs are not containers rather incidence structures which are iterable in many ways. LEMON introduces concepts that allow us to attach containers to graphs. These containers are called maps. In the example above we create an EdgeMap which assigns an integer value to all edges of the graph. We use the set member function of the map to write values into the map and the operator[] to retrieve them. Here we used the maps provided by the ListGraph class, but you can also write your own maps. You can read more about using maps \ref maps-page "here". */
|
__label__pos
| 0.949035 |
Untrusted Foreign Keys
What is a Foreign Key?
Do you trust your foreign keys?
Do you trust your foreign keys?
A foreign key is a link between 2 tables that is used to enforce referential integrity in the database.
For example, if you have an order and a customer table, there is probably a logical relationship between the 2 tables. An order can’t exist without being linked to a customer record.
When trusted, these keys help ensure that the data in your database stays ‘clean’ and logical.
By establishing trusted foreign keys in SQL Server between your tables, the optimizer is able to make some assumptions about the data and therefore make more efficient execution plans for your queries.
Foreign keys are trusted by default when created since checks are done to ensure the data all lines up. If the data does not match as expected, errors are relayed and the key is not created. Once established they keys will prevent ‘bad’ data from being entered into your database so long as they remain trusted.
What is an Untrusted Foreign Key?
An untrusted foreign key is one that has had the referential integrity of the relationship removed. SQL Server is unable to ‘trust’ that the data is clean in both tables and therefore isn’t exactly sure of the best way to proceed. This can start to show itself by queries getting slower as the optimizer starts to perform extra checks to make sure the data it is getting is good.
How Do They Become Untrusted?
We have established that foreign keys are important in relational databases since they check & help enforce the referential integrity of the data. Sometimes though, when doing large bulk loads and similar operations, SQL Server can slow down due to the large number of checks being done.
One of the ways to improve the performance of these bulk loads is to disable the foreign keys on the tables being loaded. This is usually a safer & faster process than just dropping and recreating the keys.
Foreign keys then become untrusted when they are not re-enabled correctly after the bulk load or similar operation is completed.
Usually the foreign key is re-enabled with the CHECK CONSTRAINT option in the ALTER TABLE statement. This is fine to re-enable the foreign key, but it does not tell SQL Server to re-verify the integrity of the data.
Because of this, SQL will not know if the relationship can still be trusted, that the data is ‘clean’ between the 2 tables. This results in the SQL Server optimizer ignoring the foreign key restraint and checking the data integrity itself with extra processes added to your query execution plan.
How Do I Trust a Foreign Key Again?
Before you are able to trust foreign keys again, you have to identify the ones that are no longer trusted first.
This first snippet of code goes through your database and identify the foreign keys & constraints that are enabled yet not trusted. (We don’t have to worry about disabled keys)
This will identify the schema, object and name of the keys that are not trusted in your database.
Once you have that result set you can use the following statement to re-establish the trust for each result in the list:
ALTER TABLE <s.name from results>.<o.name from results> WITH CHECK CHECK CONSTRAINT <i.name from results>
The CHECK CHECK in the syntax seems odd, but it is just due to the alignment of 2 different options with the alter table statement.
The first is the WITH CHECK statement. This tell the ALTER statement to validate the table contents against the foreign key. By default when re-enabling an existing foreign key or constraint this is set to WITH NOCHECK. You have to explicitly define it when re-enabling a foreign key or constraint.
The second is the CHECK CONSTRAINT statement. This is used to configure if the constraint is enabled or disabled. CHECK CONSTRAINT is enabled, while NOCHECK CONSTRAINT disables the foreign key.
If you have a lot of results from the previous script, you can use the following script which will output the ALTER TABLE statements so you can copy & paste the ones you like.
This script could be easily modified to also apply the alter, but I personally prefer to look at the results and changes to be made prior to having it run, just in case.
The script can also be modified to enable all foreign keys & constraints by using ALL rather than the [i.name] but be sure that you want all keys and constraints enabled or disabled first.
Any way you do it, you want to make sure your foreign keys and constraints are trusted so the SQL Server optimizer can create efficient plans for your queries.
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|
__label__pos
| 0.974698 |
Eloquent date filtering: whereDate() and other methods
Let’s say you want to filter out entries created today. You have a timestamp field created_at, right? How do you filter the DATE only from that timestamp? Apparently, Taylor thought about it.
I’ve seen people doing it with raw queries, like this:
$q->where(DB::raw("DATE(created_at) = '".date('Y-m-d')."'"));
Or without raw queries by datetime, like this:
$q->where('created_at', '>=', date('Y-m-d').' 00:00:00'));
Luckily, Laravel Query Builder offers a more Eloquent solution:
$q->whereDate('created_at', '=', date('Y-m-d'));
Or, of course, instead of PHP date() you can use Carbon:
$q->whereDate('created_at', '=', Carbon::today()->toDateString());
Have you tried our tool to generate Laravel adminpanel without a line of code?
Go to QuickAdminPanel.com
Wait, there’s more
It’s not only whereDate. There are three more useful functions to filter out dates:
$q->whereDay('created_at', '=', date('d'));
$q->whereMonth('created_at', '=', date('m'));
$q->whereYear('created_at', '=', date('Y'));
Isn’t it nice and easy?
The only thing is if you’re dealing with timezones, you should totally use Carbon and make some more complex queries, but that’s a topic for a whole another article.
Video version
You can watch how it works – in my video WhereX Magic Methods for Fields and Dates.
It’s a free lesson from my online-course Eloquent: Expert Level.
Like our articles?
Check out our Laravel online courses!
22 COMMENTS
1. If the created_at is a date with time, ate the also some shortcuts so check for a specific time? Maybe something like “lastHour()”?
Best regards
• Thanks for question Simon. Look into file
vendor\laravel\framework\src\illuminate\database\query\builder.php from line 902 – there are only those functions I’ve mentioned, I’m afraid.
2. Note that :
– There are no methods such as “orWhereDate / orWhereDay …”
– PostgreSQL : query->where(‘created_at’, ‘>=’, $carbonDate); works fine
– PostgreSQL : query->whereDays(‘created_at’, ‘>=’, $numberOfDays); doesn’t work
3. Hello
I have install the laravel properly in my local system use a wamp server
some error are showing on my screen please help me how to solve it.
“Symfony \ Component \ HttpKernel \ Exception \ NotFoundHttpException”
4. Hi ,
How can I compare with timestamps based on month and year in laravel ??
eg – where(FROM_UNIXTIME(pubdate, ‘%Y’), ‘=’, 2016)
here pubdate is ‘1456313400’
5. Very useful article, thank you.
I’m having some trouble though. the date field which I’m comparing against (‘created_at’) is encrypted and none of the above methods work in this situation.
Is there a workaround that you can think of?
6. I’ve written my own way of doing this in the past. I’m curious to see which one is faster, but this gets me up and running very quickly. Thank you for pointing this out. Somehow it was much easier to find your post, but there is a list of stuff here if anyone wants more…. https://laravel.com/docs/5.4/queries
7. If you use Carbon::now()->toDateString() you could have problems with the query, with laravel methods like “withtrash()” it won’t work well.
Is better and it’s works:
$q->whereDate(‘created_at’, ‘=’, Carbon::today());
8. I have a Contract table with 2 datetime fields:
– valid_from
– valid_to
and I have to display contracts that are valid into AAAA-MM interval. For example 2018-02.
Any suggestion?
Many thanks!
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|
__label__pos
| 0.740198 |
Lesson Seven – Procedure Turn
Learning Objectives
• Be able to fly smooth left and right-hand procedure turns
• Maintain a constant altitude throughout the manoeuvre
procedure-turn
procedure-turn
Procedure Turns
• You will handle all take-off and landings
The procedure turn is a compulsory figure in the Bronze wings test. It is designed so that the student pilot can demonstrate competent and accurate turning skills within a practical manoeuvre.
In real-life the procedure turn is as useful in model aviation as it is in full-size aviation. It allows the pilot to fly a heading and then turn in the smallest possible area to return in the opposite direction along the same line. This is particularly useful when trying to line up with the runway or a heading that will return you to the runway.
A procedure turn is made up of two turns:
1. Fly along the runway centreline during a circuit
2. At the end of the runway make a turn away from you through 90°
3. Once this turn is complete, immediately make a turn through 270° in the opposite direction
4. Exit the turn to fly along the runway centreline in the opposite direction to that from which you entered the manoeuvre
The key to the procedure turn is to make careful use of all controls to ensure the manoeuvre is flown at a constant altitude and that you enter and exit the pattern along the same line.
Lesson Six – Landing
Learning Objectives
• Be able to land safely and under control
• To fly ‘touch and go’ circuits
landing
landing
Landing
• Your instructor will only intervene in an emergency
The art of landing an aircraft successfully take a bit of mastering as the key is to fly the aircraft to the ground and not into the ground!
Before starting your landing approach, be sure to let other pilots flying know what you are doing
By now you should have mastered the landing circuit and be able to fly the aircraft close to the ground along the runway centre line. Once you have reached this point it is really just a matter of supporting the aircraft as the wing loses lift and it descends slowly to the ground.
1. As you approach the runway close the throttle completely so the engine is only idling
2. Only use the ailerons to keep the wings level, use the rudder to hold the aircraft straight along the runway
3. As you cross the end of the runway – the threshold – you should be about 0.5 meters above the ground
4. Try to hold the aircraft at this altitude by applying a little up-elevator – this is called flaring
5. Only use enough elevator to support the nose of the aircraft, too much and you will start to climb and then stall
6. As the aircraft slows further it will slowly descend the last 0.5 meters and touch down gently
7. Use the rudder to keep the aircraft straight as it slows to a stop
Congratulations, if you are safely on the ground you have flown your first complete solo and there will probably be a lot of applause coming from behind you!
If at any time during the approach and landing you do not feel comfortable you can apply full power and climb back into the circuit. Just because you have called a landing does not mean you have to land on that approach.
If you are going to abort your landing attempt call out ‘going around’ to let other pilots know what is happening
You will spend a lot of time practicing landing from different directions until you are comfortable with the approach and flare. This is the time in the flight when your aircraft is at most risk of damage and it pays to be an expert at landing in all situations!
Touch and Go Circuits
Once you have mastered landing it becomes boring is every time you touch down you have to taxi back to the end of the runway to take-off again!
As you land the aircraft, immediately apply full power and let the aircraft pick up speed once more. You can then take-off again within the length of the runway!
The important things to remember during touch and go circuits are:
1. Let the aircraft build up enough speed to take-off as normal. Do not let it ‘bounce’ back into the air too soon and cause a stall.
2. Do you have enough room to speed up sufficiently to take-off? If you do not then let the aircraft come to a stop.
Lesson Five – Landing Circuits
Learning Objectives
• Be able to line up with the runway ready for landing
• Recognise the correct time to begin descending in the circuit
• Descend and slow the aircraft whilst turning safely towards the runway
approach
approach pattern for landing
Landing Circuits
• You will handle take-off, your instructor will handle landings
There are two main components to the landing circuit and approach:
1. The line-up with the runway
2. The descent to the runway
You should practice the line-up first before you begin to worry about the descent. This is easy to do and you should have it mastered already if you can fly smooth and accurate circuits in both directions.
Most landings are made on the main runway at the LMMAC field; that is the runway that runs left to right in front of the pilot’s box. This is useful as we can use the electricity pylon directly in front of us as a guide when to begin our descent.
1. At normal circuit height pull the throttle back to around 25% as you the aircraft passes over the top of the pylon
2. Allow the model to lose height slowly, do not try to use elevator to force it down or hold the nose up
3. If you are descending to quickly, apply a little power
4. If you are descending to slowly, reduce power a little
5. Once you flown past the end of the runway begin a slow wide turn onto your base leg
6. Continue descending as you make another turn onto the runway centreline
7. Let the aircraft continue descending towards the runway
8. Once over the end of the runway, apply full power and climb the aircraft smoothly back up to circuit height – this is called going around
It will take some time for you to get used to your aircraft and how much throttle and space it needs to descend. Do not be tempted to push down on the elevator to lose height more quickly as this will cause the aircraft to speed up and you will not be able to land safely.
Most new pilots find that it is more difficult to judge the final turn once the aircraft is descending. Practice this approach a lot until you have memorised the correct position and altitude for each stage of the approach.
Lesson Four – Take Off
Learning Objectives
• Be able to hold a straight line on the runway during the take-off roll
• Be able to take-off smoothly and climb safely to circuit altitude
img06
The first take off!
The Take-Off
• Your instructor will handle all landings
Taking off with a model aircraft is really very easy, especially with a trainer aircraft as is will be designed to fly smoothly and to climb when certain airspeed is reached.
The most important aspect of the take-off is keeping the aircraft travelling in a straight line both on the runway and when it first becomes airborne. For this reason we start this lesson by not taking-off!
Your instructor will let you keep control of the transmitter on the ground and ask you to taxi out onto the runway.
If another pilot is flying do not taxi out onto the runway until you are within the pilot’s box and have asked if the runway is clear for use – he may be about to land!
Once you are on the runway your instructor will ask you to taxi along the runway, using the rudder to keep the aircraft as straight as possible. With each pass, try to get use a little more throttle so you can practice controlling the aircraft at take-off speed.
When you are ready, the instructor will ask you to line the aircraft up at the end of the runway pointing into wind. Take-off is always made into wind so that we can get into the air at a slower ground speed and in a shorter distance. Your instructor will explain the difference between air and ground speed as you are learning.
If another pilot is flying do not take-off until you have announced your intentions
1. Once you are lined up and ready to go, increase throttle smoothly to full power
2. Use the rudder to hold the aircraft straight as it gains speed
3. Once the aircraft is about level with you on the runway, use a small amount of up-elevator to help the model ‘un-stick’ from the ground
4. Keep full power applied and allow the aircraft to gain speed whilst climbing at around 20-30°
5. Use the ailerons to keep the aircraft level as it climbs away from the runway
6. Once you have reached a safe altitude begin to turn into the circuit, continuing to climb to circuit height
7. Once at circuit altitude, pull back the throttle to maintain straight and level flight
You will find your trainer aircraft very easy to control on the ground and it will climb smoothly under full power. The most important things to remember are to use rudder on the ground and aileron once airborne.
As most trainers are designed to climb under full power you may find you need little or no up elevator to climb to circuit height. In fact, with some trainers you may need a little down elevator to stop the model from climbing to steeply!
Lesson Three – Stalling
Learning Outcomes
• Have an understanding of what a stall is
• Be able to recognise and react in a stall situation
• Be able to avoid a stall
stall1
Understanding the Stall
Look at the pictures above. In the first image the wing has a smooth flow of air over its upper surface. This smooth flow of air around the wing is what creates lift and keeps the aircraft in the air.
In the second picture we have started to pull the nose of the aircraft up. This tilts the wing against the oncoming flow of air. This is called changing the angle of attack of the wing. As this happens the air flowing over the upper surface of the wing begins to lose its grip on the surface and does not follow the shape of the wing any more. You may think this is what happens when we climb, but in actual fact in the climb we also increase thrust so the aircraft still penetrates the air as if it was travelling straight and level – as in the first picture. A stall occurs when the nose is raised but we have insufficient power to climb. In this situation the plane continues to fly straight and level only at a slower speed and with the nose raised.
In the third picture the wing is completely stalled. The angle of attack is so great that air can no longer stick to the top surface of the wing and it breaks away, swirling around in small ‘eddies’. When this happens the wing is no longer generating any lift and can no longer counteract the force of gravity, so the aircraft falls from the sky!
Reacting to a Stall
To learn to react to a stall your instructor will ask you to fly the following steps:
1. Starting from a normal circuit, you will create a stall during the upwind leg
2. At a safe height, close the throttle and start to pull back gently on the elevator to raise the nose a little
3. Continue to raise the nose as the aircraft slows down
4. Once a stall occurs the nose of the aircraft will drop sharply, keep the aircraft straight using the ailerons and centre the elevator
5. Allow the nose to drop and apply full throttle
6. As the aircraft gains speed, use the elevator to bring the nose up and regain straight and level flight
7. Climb back to circuit altitude and continue to fly the circuit
This whole process will take no more than a few seconds and the aim is to keep the aircraft flying straight without dropping a wing and losing as little height as possible.
Avoiding the Stall
This lesson becomes important when you are flying slowly and close to the ground, i.e. just after take-off and just before landing. Practice stalling at altitude so that you can recognise when you model is going to stall and how slowly you can fly before a stall occurs.
If you think a stall is going to happen, the methods to avoid it are simple:
1. Let the nose drop a little back towards a level attitude
2. Increase power
Practice flying close to a stall and then pulling out of it before the nose drops. If you can recognise the signs and react before the stall occurs you should never be in danger of nose diving into the runway!
The Tip-Stall
A tip stall occurs when just one half of the wing stalls, causing the aircraft to tip violently to one side and enter a spiral-dive. This occurs when an aircraft turns too tightly at too slow a speed, which most often when you are making the final turn towards the runway for landing. For this reason you must always make sure that your slow turns are made as wide as possible with as little bank in the wing as possible – this will be covered in more detail when you learn to land.
Lesson Two – Figure '8'
Learning Objectives
• Be able to fly accurate left & right-hand figure ‘8’ patterns
• Maintain a constant altitude whilst flying in this pattern
figure-8
Perfecting the Turns
• Your instructor will handle take-off and landings
The figure ‘8’ pattern is not included in the Bronze Wings test but is a useful training tool as it will allow you to practice left and right-hand turns until you can make precise, constant level manoeuvres in any direction. This pattern always starts and ends over the centreline of the runway with the crossover point in front of the pilot.
1. From a normal circuit start an upwind leg over the centreline of the runway
2. As you begin to fly up the runway, make a 90° turn away from you
3. Once the aircraft is flying away from you, make a 90° turn back in the opposite direction of the first turn
4. Continue turning through another 90° until you are flying back towards the end of the runway
5. As you come around to face the runway continue to turn back onto the runway centreline but facing in the opposite direction to that from which you started the manoeuvre
6. Instead of flying straight on, carry on turning away from yourself until you cross point 3 once more – completing the first 360° turn
7. Now make a 180° turn to the left to come around and point back at the other end of the runway
8. Complete the manoeuvre by flying the final 90° turn back onto the original runway heading
9. Fly along the runway and continue into a normal circuit pattern
At first this simple pattern will seem nearly impossible to fly smoothly as the turns will be too tight, too loose or you will gain and lose a lot of altitude. As you spend more time practicing however you will find that you must use a combination of aileron, elevator and throttle to fly an accurate figure ‘8’.
The most important thing to remember when flying the turns is that it is not simply a case of applying a certain amount of aileron and elevator and holding it there. You would not turn a corner in your car this way and you do not turn an aircraft this way either! Turning accurately requires you to master balancing the controls; making constant small adjustments to fly a nice smooth line.
Keep practicing this even once you have passed your Bronze Wings as it is the basis of flying every different type of radio control aircraft and every different kind of aerobatic manoeuvre!
Lesson One – Circuits
Learning Objectives
• Be able to fly a square left & right-hand circuit of good size, shape and orientation
• Maintain a constant altitude whilst flying in the circuit
• Understand how control inputs effect the models flight attitude
Flying the Circuit
• Your instructor will handle all take-off and landings
A circuit is the most basic pattern of flight used in all forms of aviation. It is a rectangular flight-path, flown at a constant altitude with the upwind leg flown along the centreline of the runway and into wind. It is designed and positioned like this so that other aircraft that are taking off or landing are able to do so safely without fear of colliding with another airborne aircraft.
Once your instructor has got the aircraft airborne and flying straight and level in the circuit he will hand you the controls on the downwind leg. From here you will need to make a series of 90° turns to keep the aircraft in the circuit pattern.
Do not adjust the throttle at this point. Concentrate on using aileron and elevator to make a smooth turn as follows:
• Use aileron to bank the aircraft left or right. Move your right thumb left to bank left and vice versa.
• Use a small smooth movement to roll the wings about 20-30°, the aircraft will start to turn
• Now, as the aircraft begins to turn, use small amounts of up elevator to keep the nose from dropping and keep a constant altitude throughout the turn
• As you reach the end of the turn, use the ailerons to roll the wings level again
The use of elevator is important in the turn to maintain altitude. Without it the nose will drop and the aircraft will start to dive in a spiral motion towards the ground. Using the elevator like this is called ‘supporting the nose in the turn’.
Most circuits at the LMMAC field are made in an anti-clockwise direction but we will practice both.
Using the Throttle
As you become more proficient at flying the circuit pattern we will start to introduce throttle to control the altitude of the aircraft.
Most trainers are set up to have ‘positive stability’. This means they are designed to fly, when correctly trimmed, straight and level at a set speed. (Your instructor will get the plane flying like this before the lessons begin). If this straight and level is disturbed by a control input, the aircraft will try to return to this straight and level state. We can take advantage of this by using the throttle to force the aircraft to climb or descend.
If you feel the aircraft is descending in the circuit. Move the throttle up by a couple of clicks, this will cause the nose of the aircraft to lift as the wing generates more life and climb slowly. If the aircraft is climbing too high, reduce the throttle a little and let it descend slowly back down to the desired altitude.
Later on we will use this throttle control to help us climb after take-off and descend to the runway for landing.
i.c. to electric Conversion Table
This is quite simply as it says in the title. I have put together a little chart that will show you how many watts of power you need from your motor to equal the power of your two-stroke motor…
Remember, to work out the watts we multiply the continuous current of the motor by the number of volts going in. So when you look at this table, divide the number of watts by the battery you intend to use and that will tell you what sort of amps your motor is going to have to draw to get there.
Clear as mud? On with the chart then…
2-Stroke Motor Size
Electric Equivalent (watts)
0.20 cu.in
300w
0.35 cu.in
500w
0.40 cu.in
750w
0.60 cu.in
975w
0.90 cu.in
1200w
1.20 cu.in
2250w
50cc
3750w
100cc
7311w
Hopefully this will give you some idea when it comes to choosing an electric motor for your model.
What about the Watts?
A lot of people are confused when they first get involved in electric flight as to which motor, speed controller, battery combination to use to power their model. This is the first in a series of posts that will look at how to determine and choose the best power train for your electric model…
The first, and most useful, development in the world of electric flight are the manufacturers who actually label their motors with equivalent 2-stroke i.c. motor sizes. The best know of these are the E-Flight Outrunner series, which stretch all the way from .10 size motors right up to a whopping 1.80 size unit! They aren’t the cheapest on the market but are very high quality and certainly worth the bucks if you can afford it. We’ll look at i.c. to electric conversions in another post.
However, if you are looking at building a custom power system, maybe from E-Bay or another online seller, then you will need to work it out for yourself.
The first thing we need to look at is what sort of model you are building and how much power you need to fly it…
With electric models, power is measured in ‘Watts’. Effectively the more watts a motor can produce, the more thrust is generated at the propeller. Different types of model have different power requirements, a slow flying trainer needs far less power than a balls-out 3D model. To give a basic idea we use the following:
Trainer/Sports Model: 90W/lb
Powered Glider: 120W/lb
3D Model: 175-200W/lb
This is just a basic guide, a lot of my models are of the 3D type and so I aim for 200W/lb. I have designed a couple of smaller sports models that have used 90W/lb and have flown very nicely.
You will notice that the figures given state watts per pound (lb). You will need to look at the finished flying weight of your model and then work out the power from there. For example, if your ARTF spitfire weights 3lb 8oz flying weight then you will require (90 x 3.5 =) 315 watts minimum from your motor to get a decent flying performance.
So how do you work out how much power a motor will give?
All motors will give you basic information in their advertisement (if they don’t then don’t go there). This will hopefully include a ‘Continuous Current’ rating and a ‘Recommended Input Voltage’ – these are the two figures you want to look at.
Quite simply multiply one by the other, for example:
Motor Continous Current = 30A
Recommended Input = 11.1v
Therefore 30 x 11.1 = 333 watts
The 333 watts is what the motor will generate at full throttle and assumes you are using the recommended prop size and your lipo isn’t losing all of its charge when under load. Therefore, always select your motor to give slightly more power than you need. You don’t have to fly at full throttle the whole time and flying at lower throttle settings will give you a longer flight. The only way to know for sure is to use a wattmeter when you have your set-up in the workshop – but that does’t help when you’re buying.
Have fun out there and drop me a line on the contact form if you want to ask an electric flight question…
Safety with LiPo batteries
With more and more people trying electric flight I thought I should include this article on the safe use of lithium polymer batteries…
This article is taken from the British Model Flying Assosciation, which can be found at www.bmfa.org
A guide to safe use of LiPo batteries
from the British Electric Flight Association.
Despite what a number of people may tell you Lithium Polymer (LiPo) batteries are not fundamentally unsafe, but they need to be treated with more care than NiCd or NiMH. If abused sufficiently LiPo cells can catch fire and this fire can be difficult to extinguish. The following precautions should help you enjoy using LiPo batteries without having a major incident.
General precautions:
• The minimum safe discharge voltage is 2.5V per cell when under load, or 3.0V per cell when not on load.
• When more than 2 cells in series are used, a controller with an adjustable cutout should be used and it should be set at or above 2.5V/cell.
• Only charge LiPo batteries on a charger specifically design for LiPo batteries.
• Always ensure you use the correct charging voltage for the cell count.
• The maximum charge rate should be 1C, eg. 0.7A for a 700 mAh cell. For best charging, low charge rates should be used where possible.
• Check the charge voltage (or cell count) and current a second time.
• Never leave charging LiPo cells unattended (at any charge rate).
• It is best to charge LiPo cells in an open space on a non-flammable surface (such as a brick or quarry tile) and away from flammable materials.
• For long term storage it is recommended that cells are fully charged and then discharged to between 50% and 60% of their capacity.
• Use connectors that can not be short circuited, or use silicon fuel tube to protect exposed connections.
• Have a dry powder fire extinguisher or a bucket of dry sand within reach.
If a pack is involved in a crash or is otherwise damaged:
• Remove the pack from the model.
• Inspect the pack for damage to the wiring or connections.
• If necessary, disassemble the pack and dispose of any damaged cells.
Disposal of LiPo batteries:
• Put the pack in a safe open area and connect a moderate resistance across the cell terminals until the cell is completely discharged.
• CAUTION: The pack may get extremely hot during the discharge.
• Puncture the plastic envelope and immerse in salt water for several hours.
• Place in your regular rubbish bin.
By Jan Bassett (BEFA)
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Lightning Data Services
08:02 3 Comments A+ a-
Lightning Data Services
What is LDS :
LDS is Lightning Component that display the data on Page in Salesforce Lightning. Using LDS we don’t need any apex controller to perform CRUD operation. using LDS we can increase the performance. It also provide the way to cache the data to work offline in case user is not connected to network. Once the connection is restored data will sync.
LDS also handle Field Level Security and sharing rules security. Record loaded in Lightning Data Services are stored in cache and shared between all components.Using LDS all component performance is increase because data is loaded once and used by many component, no need to make separate request from different-different components . when any of the component updates a record then other component will automatically updated with new value.
force:recordData :
This tag is must be used to load the data in component using LDS.
Attributes of force:recordData :
recordId : Id of current page record that will be load
mode : (Edit,View) its depend on what operation we are performing. If we want to update,create then Mode=’Edit’ else Mode=’View’
layoutType : specify the layout type to display record and its determine what field are included in component.
fields : specifies which fields in the record to query.
Target Attribute :
1. targetRecord : populate with loaded record.
2. targetField : view of loaded record.
3. targetError : populate with error.
Methods :
1. saveRecord() : insert of update the current record in force:recordData.
2. deleteRecord() : delete the current record in force:recordData.
3. getNewRecord() : load the new record instance to insert the record of that object from force:recordData.
4. reloadRecord() : reload the current record with new data.
Keep In Mind When Using It :
i. LDS is simple but it’s not complete replacement of apex controller.
ii. LDS is not supported in lightning out and visualforce page. Its only for lightning.
iii. LDS perform CRUD only on single record. It’s not supported for bulk data.
iv. In Summer 17, release LDS used force:recordPreview component.But now it’s completely replaced by force:recordData. Difference between force:recordPreview and force:recordData is force:recordData returns record in new shape using UI API and targetfield is added in parameter.
v. To update from force:recordPreview to force:recordData is to change reference from targetRecord to targetField.
vi. If you want to query multiple operations in one transaction then use apex controller @AuraEnabled.
Example :
Here we are creating a component that is added on Account detail page. It will create a new contact for current account record.
1. Create a new Record :
Lightning Component :
<aura:component implements="flexipage:availableForRecordHome, force:hasRecordId">
<aura:attribute name="newContact" type="Object"/>
<aura:attribute name="createContact" type="Object"/>
<aura:attribute name="newContactError" type="String"/>
<force:recordData aura:id="contactRecordCreator"
layoutType="FULL"
targetRecord="{!v.newContact}"
targetFields ="{!v.createContact}"
targetError="{!v.newContactError}"/>
<aura:handler name="init" value="{!this}" action="{!c.doInit}"/>
<div class="Create Contact">
<lightning:card iconName="action:new_contact" title="Create Contact">
<div class="slds-p-horizontal--small">
<lightning:input aura:id="contactField" label="First Name" value="{!v.createContact.FirstName}"/>
<lightning:input aura:id="contactField" label="Last Name" value="{!v.createContact.LastName}"/>
<lightning:button label="Save Contact" variant="brand" onclick="{!c.handleSaveContact}"/>
</div>
</lightning:card>
</div>
<aura:if isTrue="{!not(empty(v.newContactError))}">
<div class="recordError">
{!v.newContactError}</div>
</aura:if>
</aura:component>
Lightning Controller :
({
doInit: function(component, event, helper) {
console.log('changes');
component.find("contactRecordCreator").getNewRecord(
"Contact", // sObject type (entityAPIName)
null, // recordTypeId
false, // skip cache?
$A.getCallback(function() {
var rec = component.get("v.newContact");
var error = component.get("v.newContactError");
if(error || (rec === null)) {
console.log("Error initializing record template: " + error);
}
else {
console.log("Record template initialized: " + rec.sobjectType);
}
})
);
},
SaveContact: function(component, event, helper) {
component.set("v.createContact.AccountId", component.get("v.recordId"));
component.find("contactRecordCreator").saveRecord(function(saveResult) {
if (saveResult.state === "SUCCESS" || saveResult.state === "DRAFT") {
var resultsToast = $A.get("e.force:showToast");
resultsToast.setParams({
"title": "Saved",
"message": "New Contact ."
});
resultsToast.fire();
} else if (saveResult.state === "INCOMPLETE") {
console.log("User is offline, device doesn't support drafts.");
} else if (saveResult.state === "ERROR") {
console.log(JSON.stringify(saveResult.error));
} else {
console.log('Unknown problem, state: ' + saveResult.state);
}
});
}
})
Result :
2. Delete A record :
Here we added Delete Component on Account Detail Page. It will Delete Current Account when we click on Delete Button in below component.
Lightning Component :
<aura:component implements="flexipage:availableForRecordHome,force:hasRecordId">
<aura:attribute name="recordError" type="String" access="private"/>
<force:recordData aura:id="dataRecord"
recordId="{!v.recordId}"
fields="Id"
targetError="{!v.recordError}"
recordUpdated="{!c.handleRecordUpdated}"/>
<div class="Delete Record">
<lightning:card iconName="delete" title="Delete Record">
<div class="slds-p-horizontal--small">
<lightning:button label="Delete Record" variant="destructive" onclick="{!c.handleDeleteRecord}"/>
</div>
</lightning:card>
</div>
<aura:if isTrue="{!not(empty(v.recordError))}">
<div class="recordError"> {!v.recordError}</div>
</aura:if>
</aura:component>
Lightning Controller :
({
handleDeleteRecord: function(component, event, helper) {
component.find("dataRecord").deleteRecord($A.getCallback(function(deleteResult) {
if (deleteResult.state === "SUCCESS" || deleteResult.state === "DRAFT") {
console.log("Record is deleted.");
} else if (deleteResult.state === "INCOMPLETE") {
console.log("User is offline, device doesn't support drafts.");
} else if (deleteResult.state === "ERROR") {
console.log('Problem deleting record, error: ');
} else {
console.log('Unknown problem, state: ');
}
}));
},
handleRecordUpdated: function(component, event, helper) {
var eventParams = event.getParams();
if(eventParams.changeType === "CHANGED") {
} else if(eventParams.changeType === "LOADED") {
} else if(eventParams.changeType === "REMOVED") {
var resultsToast = $A.get("e.force:showToast");
resultsToast.setParams({
"title": "Deleted",
"message": "The record was deleted."
});
resultsToast.fire();
} else if(eventParams.changeType === "ERROR") { }
}
})
Result :
3. Update a Record :
Here We create a component that will update the account detail on Account Detail page on click of save Button in component.
Lightning Component :
<aura:component implements="flexipage:availableForRecordHome,force:hasRecordId">
<aura:attribute name="record" type="Object"/>
<aura:attribute name="accRecord" type="Object"/>
<aura:attribute name="recordError" type="String"/>
<force:recordData aura:id="recordHandler"
recordId="{!v.recordId}"
layoutType="FULL"
targetRecord="{!v.record}"
targetFields="{!v.accRecord}"
targetError="{!v.recordError}"
mode="EDIT"
/>
<div class="Record Details">
<lightning:card iconName="action:edit" title="Edit Account">
<div class="slds-p-horizontal--small">
<lightning:input label="Account Name" value="{!v.accRecord.Name}"/>
<br/>
<lightning:button label="Save Account" variant="brand" onclick="{!c.SaveRecord}" />
</div>
</lightning:card>
</div>
<aura:if isTrue="{!not(empty(v.recordError))}">
<div class="recordError">
{!v.recordError}</div>
</aura:if>
</aura:component>
Lightning Controller :
({
SaveRecord: function(component, event, helper) {
component.find("recordHandler").saveRecord($A.getCallback(function(saveResult) {
if (saveResult.state === "SUCCESS" || saveResult.state === "DRAFT") {
console.log("User drafts.");
} else if (saveResult.state === "INCOMPLETE") {
console.log("User is offline, device doesn't support drafts.");
} else if (saveResult.state === "ERROR") {
console.log('Problem saving record, error: ' + JSON.stringify(saveResult.error));
} else {
console.log('Unknown problem, state: ' + saveResult.state + ', error: ' + JSON.stringify(saveResult.error));
}
}));
}
})
Result :
Fitness Tracker for Salesforce Health Cloud
06:32 9 Comments A+ a-
Hi All,
As you know Health Cloud product from Salesforce is a great patient management and care software/package. Its a leading product in healthcare industry. As this is widely used all over world, I started making something useful around it.
As todays life daily exercise is very important. Almost all doctors recommend patients to have a walk, run daily and track their activity. For tracking this, people use different tracking tools and devices like Fitness Band is most popular. Fitness Band comes from various companies. In my demo, I am going to use MI Fitness Band integration. Thanks MI for making this beautiful stuff.
Case Study
John is a Care Taker at iBS healthcare organization. He maintains 50+ patients daily. His mainly job to keep track of patients daily fitness activity like
Steps
Distance Covered
Calories Burned
Duration (Spent on activity)
He generally ask his patients to send their daily fitness activity by WhatsApp on mobile. Then John arranges them, read values, fill in system. Sometimes he forget the sequence and sometimes patients forget to send that data to him. This is becoming very hectic job for John.
Solution Proposed
Isn't it very useful if John get all the fitness activity details on the Patient Timeline for each patient he manages? Sounds fantastic! Now, John simply needs to open patient detail screen and go to Timeline, and he can see the patient related Fitness Activity like Steps, Distance, Calories, Duration at one place and all updated instantly. This is second major feature for which John is exited about. He does not need to wait till end of day to get all patient fitness data. Whenever he wants the patient Fitness Data, he simply go to Timeline and check it. Its so simple. John life is easy :)
How It Works
As a Salesforce Architect, working at iBirds , Me and my team have developed many tools around salesforce echo system for helping industry and community. Here is how we developed this, step by step.
Using Google Fit Connector for Salesforce
ibirds has recently developed one Google Fit Connector for Salesforce App. We are going to launch it shortly. This connector periodically fetch google fit data from user's account and store in a fitness activity object in Health Cloud. We can schedule the fetch mechanism or refresh manually as well. Thanks Google for this great application which helps users to keep up to date with their fitness data.
Enable MI Fitness Band Sync to Google Fit
This is a manual step. There is config settings in MI App, that you can send fitness data sync to external system like Google Fit.
Health Cloud Timeline setup for Fitness Activity
There is a great tutorial on trailhead about adding your custom patient data (object) on patient timeline. Check here
We used our Fitness Activity custom object which having MI Fitness band data. It keeps all patient data up to date. We are having a patient/account relationship already in that so that health cloud timeline supports it.
We can also show Fitness Card like this on left side under patient info.
Or we can show this on dashboard as a scrollable timeline plugin using Timeline View Configuration as below
Or we can show this under patient card as data using Patient Card Configuration as below
Or on Fitness Activity Detail screen like this
So, once all setup, now John easily navigate to their patients records in Health Cloud and open their record. And all info related to his patient fitness, he can see easily at single glance.
Checkout a small screencast.
Thanks for Salesforce, for making such good products which helps people on a daily basis.
Email/Tweet me for any clarification needed and enhancement suggestions here.
Thanks
Aslam Bari
Salesforce Einstein Chatbot - Setup
07:39 5 Comments A+ a-
We all know that world is changing faster than we can think. There are lots of new technologies which are emerging and used in daily life. This is new era where things are becoming smarter.
Einstein chatbot is one of them, before configuring the Einstein chatbot, the first question which comes in our mind is,
What’s the chatbot?
Chatbot is an automated computer program that holds a conversation with a person via written communications, with the aim of helping that person achieve a desired result. This is very complex definition of chatbot. In simple words, Chatbot is a technology in which a person can chat with computer instead of human, conversation looks like a human chat that can help you to achieve your aim.
Another question arises here, why we need chatbots?
Here are few reasons we need chatbots
1. 24/7 Availability
Chatbots are never going to leave your office. They are available 24/7 to interact with your customers.
2. Immediate Response
Chatbot response time is very fast. They can immediately reply to the questions and provide solutions for their queries, which provide higher customer satisfaction.
3. Scalability
A customer care executive can talk with one person at a time. So, if we have lots of customers than we need more executives, which means more money.
Chatbot can chat with multiple customers at the same time.
It comes with scalability feature, so you can scale your customer service at any level you want.
4. Cost Effective
Instead of increasing your customer care staff, you can save lot of money by using chatbots.
The infrastructure that your bot needs to work is already there, and it’s FREE thanks to messenger services like Facebook, Einstein Chatbot.
5. People prefer chat instead of call
In today’s world, people are more addicted to the messenger service instead of calling, reason behind this it helps them to do multi-tasking at the same time.
Now we are familiar with chatbots and why we need them.
Einstein Chatbot
In market several bots are available like Microsoft Bot Platform, Amazon Lex, Google Dialogflow, Alibaba Intelligent Service Robot, and many more.
Einstein Chatbot is different from those bots, they are fully integrated with salesforce platform. They can access the salesforce data and can transfer conversation to the real live agent without any integration.
Chatbots can configured using wizard-based interface instead of code. It also has functionality to invoke Apex methods when we need them.
Setup Einstein Chatbot in your salesforce org
It requires to two licenses
• · Service Cloud license
• · Live Agent license
By following these easy you can setup Einstein bot in your org-
Step 1. Enable Live User agent
Setup | Live Agent Settings | Enable
Step 2. Switch to lightning experience
In this step, first enable the Einstein Chatbot
Setup | Einstein Bots | Settings | Einstein Bot
After that, go to the deployment channels and enable the live agent
Setup | Einstein Bots | Settings | Deployment Channels
Step 3. Einstein AI. Key Management and Permission set
After completing 2 steps, behind the scenes a new account is established on Einstein Platform Services. This is required because Einstein Bots needs to call into the Einstein Platform Services for NLP-related tasks. You will receive an email shortly after enabling Einstein Bots to let you know the account has been created.
Click on production users and setup the self-signed certificate. If you don’t have certificate you have to create one.
Setup | Security | Certificate and Key Management | create a Self-Signed Certificate
Another things happen behind the scenes, an permission set sfdc.chatbot.service.permset is generated inside org. This permission set controls the objects, apex classes which are being used by the chat bot.
Step 4. Create an Einstein Bot
Setup | Einstein Bots | click New
It opens an wizard to setup the Einstein bot. It will walk you through a few screens to gather basic information about this bot, including bot name, greeting message, and main menu options.
After completing the wizard, your bot is created.
Step 5. Setup Live Agent
a) Create Skill
Setup | Live Agent | Skill | New
b) Create Chat Button
Setup | Live Agent | Chat Button and Automated Invitations | New
c) If you have setup Live Agent chat button before, you notice there is new Einstein Bot settings section.
Edit and set the Einstein Bots Configuration to the new bot we just built. When this attribute is populated and pointed to an active bot, chat users will be connected to our bot first, instead of going to an agent directly.
Step 6. Add a Snap In Deployment for Preview
Einstein Bot preview function uses the Snap In chat component to load.
For Setting Up the Snap In Deployment it require site or community. Also setup the community or site. I also setup the Demo Community.
Setup | Channels | Snap Ins | New Deployment
You should notice the process of setting up a Snap-in Chat deployment is the exactly the same with or without an Einstein Bot
Step 7. Preview your bot
Now your basic bot is ready. For preview the bot you have activate it first.
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Herring Gull
Herring Gull (Larus argentatus)
Herring Gulls started to nest in Iceland around 1925. This is a common species in coastal areas all around Iceland except for the western part where Glaucous Gull is common. These species interbreed and hybrids can sometimes be seen. Herring Gulls forage in coastal areas and at sea but go rarely inland. They feed on a variety of food like crustaceans, molluscs and fish.
Herring Gull is common in Skjálfandaflói bay and the most numerous of the larger gull species.
Length:
58-62 cm
Weight:
700-1,430 g
Wingspan:
138-155 cm
Population:
5,000-10,000 pairs
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[Date Prev][Date Next] [Chronological] [Thread] [Top]
Re: ldapsearch issue
Derek Yarnell wrote:
Hi,
So I was trying to do the following search,
(&(automountMapName=auto*)(objectClass=automountMap))
It logs the following though,
slapd[5205]: conn=258105 op=9 SRCH base="ou=automount,ou=system,dc=XXX,dc=XXX,dc=XXX" scope=2 deref=2 filter="(&(?automountMapName=auto*)(objectClass=automountMap))"
If you do this search
(&(automountMapName=*)(objectClass=automountMap))
slapd[5205]: conn=258174 op=1 SRCH base="ou=automount,ou=system,dc=XXX,dc=XXX,dc=XXX" scope=2 deref=0 filter="(&(automountMapName=*)(objectClass=automountMap))"
This is the schema definition on the server (rfc2307bis),
attributeType (
1.3.6.1.1.1.1.31 NAME 'automountMapName'
DESC 'automount Map Name'
EQUALITY caseExactIA5Match
SUBSTR caseExactIA5SubstringsMatch
SYNTAX 1.3.6.1.4.1.1466.115.121.1.26
SINGLE-VALUE
)
My feeling is that caseExactIA5SubstringsMatch is doing something very
wrong here. Shouldn't slapd be returning a error not injecting a ? in my
search.
No. Read RFC 4511. Invalid filters are simply treated as Undefined, they never generate an error response. The '?' is only present in the log message, to identify what was invalid. It has no effect on any of the processing.
--
-- Howard Chu
CTO, Symas Corp. http://www.symas.com
Director, Highland Sun http://highlandsun.com/hyc/
Chief Architect, OpenLDAP http://www.openldap.org/project/
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Page 1
Quarter 1 1.Air Pressure Labs 2.Heating Earth's Surface 3.Global Winds 4.Measuring Wind 5.Types of Fronts 6.Cloud Cookery 7.Tracking a Hurricane Quarter 2 1.Reading a Weather Map 2.The Doppler Radar 3.Climate Commercial 4.Earth's Interior 5.Modeling Sea- Floor Spreading 6.Finding the Epicenter 7.Mapping Earthquakes and Volcanoes
Quarter 3 1.My Volcano 2.Igneous Rock Venn Diagrams 3.Sedimentary Rock Venn Diagrams 4.Metamorphic Rock Venn Diagrams 5.The Rock Cycle 6.Topography of Ave Maria 7.How Can You Flatten the Curved Earth? 8.Topographic Map Directions Quarter 4 1.Rock Shake 2.What is Soil? 3.Comparing Soils 4.Sand Hills 5.The Course of a River 6.Which Layer is the Oldest? 7.Finding Clues to Rock Layers 8.Geologic History Flash Cards 9.Reflection Essay
Quarter 2
1.Reading a Weather Map 2.The Doppler Radar 3.Climate Commercial 4.Earth's Interior 5.Modeling Sea Floor Spreading 6.Finding the Epicenter 7.Mapping Earthquakes and Volcanoes
I. Title: The Doppler Radar II. Data: The Doppler radar is a mostly effective instrument for predicting the weather. It is a complex device formed of three basic parts. The transmitter sends out radio signals that are deflected off of particles in the air. Some of these waves are reflected back to its source. They are picked up by an antenna. The antenna transmits the signals into a computer that meteorologists use to process and generate data. The Doppler radar lets meteorologists easily track large scale storms such as hurricanes and tornadoes, while giving people a warning for these storms ahead of time. It can also detect precipitation. The Doppler radar has some drawbacks. Large objects such as buildings, trees, and mountains can block the radio waves. Sometimes the radar does not pick up light amounts of precipitation. Overall, it is a useful device to meteorologists to help them track and predict weather.
For Climate Commercial, see the email in which I emailed you in the second quarter.
Crust 5 - 70 km thick
Earth's Interior
Mantle 2,867 km thick
Outer Core 2,266 km thick
Inner Core 1,216 km thick
I. Title: Modeling Sea – Floor Spreading II. Problem: How does sea – floor spreading add materials to the ocean floor? III. Materials: construction paper, 2 sheets of unlined paper, colored pencils, markers, scissors IV. Procedure: 1.Fold your construction paper into 16ths once long ways and four times the short ways. 2.Fold both of the sheets of unlined paper in half long ways and draw lines that match on both sides on the unlined paper and write “Start” on on end of each of the strips of paper. 3.Cut slits in the construction paper ¼, ½, and ¾ of the way through and then unfold the construction paper. 4.Put the ends without the words “Start” through the slit ½ of the way through. With one sheet, put the end with the “Start” through the ¼ slit and the other sheet with the “Start” through the ¾ slit. 5.Pull on both of the ends with the “Start” at the same time. V. Data: See Model VI. Analyze and Conclude: 1.What feature of the ocean floor does the center slit stand for? What prominent feature of the ocean floor is missing? The center slit stands for the mid-ocean ridge and the mountains or volcanoes are missing. 2.What do the side slits stand for? What does the space underneath the paper stand for? The side slits stand for a trench. The space beneath the paper stands for moving sediment. 3.As shown by your model, how does the ocean floor close to the center slit in the differ from the ocean floor near a side slit? It has more sediment near the center slit than a side slit. 4.What do the stripes stand for? Why is it important to that your model have an identical pattern of stripes on both sides? The stripes stand for the magnetic stripes on the ocean floor. They must be even because they are the same in both they are arraigned in the same positions.
I. Finding the Epicenter: II. Problem: How can you locate an earthquake's epicenter? III. Materials: drawing compass, pencil, outline map of the United States IV. Procedure: 1. Copy the table showing the difference between the arrival times of P and S waves. 2. Calculate the distance to the epicenter for all the cities by using the graph on page 58. 3. Draw a circle using the compass around each city according to the distance.' 4. Mark where all the circles intersect. That is the epicenter. V. Data: City
Difference in the Arrival Times between P and S waves
Distance to Epicenter
Denver, Colorado
2 min. 40 sec.
1,600 km
Houston, Texas
1 min. 50 sec.
1,000 km
Chicago, Illinois
1 min. 10 sec.
600 km
See Map: VI. Analyze and Conclude: 1. The epicenter is near Kentucky and Tennessee. 2. Chicago is the closest and only about 600 km away. 3. Chicago felt it first and Denver felt it the the last. 4. It is about 3,000 km away. The difference between the arrival times of P and S waves would be about 4 min. 30 sec. 5. The difference gets larger.
I. Title: Mapping Earthquakes and Volcanoes II. Problem: Is there a pattern between the locations of earthquakes and volcanoes? III. Materials: outline world map showing longitude and latitude, 2 different colored pencils IV. Procedure: 1.Use the information in the table below to mark the areas where the earthquakes are one color and where the volcanoes are in another color. 2.Lightly shade the area around each one of the earthquakes in the same color as the mark that shows where the earthquake is and do the same for the volcanoes. V. Data: Earthquakes
Volcanoes
Longitude
Latitude
Longitude
Latitude
120°W
40°N
150°W
60°N
110°E
5°S
70°W
35°S
77°W
4°S
120°W
45°N
88°E
23°N
61°W
15°N
121°E
14°S
105°W
20°N
34°E
7°N
75°W
74°W
44°N
122°W
40°N
70°W
30°S
30°E
40°N
10°E
45°N
60°E
30°N
85°W
13°N
160°E
55°N
125°E
23°N
37°E
3°S
30°E
35°N
145°E
40°N
140°E
35°N
120°E
10°S
12°E
46°N
14°E
41°N
75°E
28°N
105°E
5°S
150°W
61°N
35°E
15°N
68°W
47°S
70°W
30°S
175°E
41°S
175°E
39°S
121°E
17°N
123°E
38°N
VI. Analyze and Conclude: 1.How are earthquakes distributed on the map? Are they scattered evenly or concentrated into zones? The earthquakes seem to be scattered evenly throughout the plate boundaries. 2.How are volcanoes distributed on the map? Are they scattered evenly or concentrated into zones? The, like volcanoes, seem to be scattered evenly throughout the plate boundaries. 3.From your data, what can you infer about the relationship between earthquakes and volcanoes? Earthquakes and volcanoes both occur near plate boundaries and seem to be related to each other.
Note: The pictures of the volcano and the sediment are made by CJ Smith.
Quarter 4
1.Rock Shake 2.What is Soil? 3.Comparing Soils 4.Sand Hills 5.The Course of a River 6.Which Layer is the Oldest? 7.Finding Clues to Rock Layers 8.Geologic History Flash Cards 9.Reflection Essay
I. Title: Rock Shake II. Problem: How will shaking and acid conditions affect the rate at which limestone weathers III. Materials: 300mL of Water, Balance, 300mL of vinegar, Small pieces of Limestone, 4 Containers IV. Procedure: 1.Label the 4 containers A, B, C, and D. 2.Fill A with water, B with water, C with vinegar, and D with vinegar. 3.Shake containers B and D. 4.Let them sit for 1 day and weigh them later with the balance. V. Data: Container
Total Mass at Start Total Mass Next Day
Change in Mass
Percent Change in Mass
A (Water, no Shaking)
23.5
26.5
3
12.70%
B(Water, with Shaking)
24
20.8
-3.2
-13.30%
C (Vinegar, no Shaking)
21.5
19.2
-2.3
-10.70%
D (Vinegar, with Shaking)
21.5
18.4
-3.1
-14.40%
The Change of the Rocks' Mass 30 25 20
A B C D
Mass
15 10 5 0 1
2
VI.Analyze and Conclude: 1.What is the percent change of each of the rocks? A- 12.7%, B- -13.3%, C- -10.7%, D- -14.4% 2.Does your data show a change in mass of the rocks? Yes. 3.Was there a greater change in mass for one piece than another? Yes, C changed by 2.3, A changed by 3, D changed by 3.1, and B changed by 3.2. 4.Were your predictions on the lab correct? Explain. No, I thought that D will erode the most, but B did. 5.If your data showed a greater change in masses, how could that be explained? The limestone absorbed the water, increasing mass. 6.Which do you think was more responsible for the erosion, the vinegar or the shaking? Explain. I think the vinegar was more responsible because it chemically broke it down.
What is Soil? My Soil Recipe: Sediment Roots Decaying Plants and Animals Little White Crystals A Friend's Soil Recipe: Sand Wood Roots Plant Bits Think It Over: How would you define soil? Soil is the combination of decaying organic material and sediment.
I. Title: Comparing Soils II. Problem: What is the difference between bagged soil and local soil? III. Materials: 1 petri dish full of natural soil, 1 petri dish full of bagged soil, water, microscope IV. Procedure: 1.Obtain the specified soils in the petri dishes. 2.Observe the following things: does it have a scent, is it soft or gritty, find the approximate particle size of the smallest and largest particles of each of the soils. 3.Put a small amount of water in each of the petri dishes to observe which soil is denser. 4.Look at each soil underneath a microscope and draw a simple sketch of each. V. Data: Local Soil
Bagged Soil
Scent
None
Earthy scent
Soft or Gritty
Gritty
Soft
Approximate Particle Size
0.5mm- 4mm
0.25mm- 2mm
Density
Less Dense
More Dense
Sketch
VI. Analyze and Conclude: 1.Did you notice any similarities between the local and bagged soils? Did you notice any differences? I saw no similarities, despite them both being soil, but I observed many differences.
2.What can you infer about the composition of both of the soils from the different size of particles? From their texture? From how each soil reacted with the water? I inferred that the local soil was not as fine as the bagged soil because it had larger particle sizes and because it had a grittier texture. I inferred that the bagged soil was denser than the local soil because it sunk and the local soil floated. 3.Do you think that soils were formed in the same way? Explain your reasoning. No, because they seem so different from each other, in density, texture, particle size, and scent differed so greatly. Also, the bagged soil came from a Miracle- Gro bag, which means that it was made in a factory. 4.Based on what you have learned in the chapter, which soil would be better for growing vegetables in? I think that the bagged soil would because it would hold water better because of its greater density, it's smaller particle size allows more room for the roots to grow and aerate, and it's scent leads me to reason that there is a greater nitrogen amount in the bagged soil, which is good for plant growth.
I. Title: Sand Hills II. Problem: What is the relationship between the height and the width of a sand pile. Hypothesis: I think that the width will increase at a faster rate than the rate of the height. III. Materials: dry sand, cardboard tube, wooden skewer, ruler, white paper, marker IV. Procedure: 1. Put the cardboard tube in the center of the piece of paper. 2. Fill the cardboard tube with 100mL of the sand. 3. Quickly raise the tube straight up so that the sand flows out and so it forms a sand hill. 4.Stick a wooden skewer down the center of the sand hill and mark the height on the skewer with the marker. 5.Measure the distance from the skewer to the edge of the mound. 6.Remove the skewer. 7.Set the cardboard tube on the top of the sand hill without pushing down on it. 8.Repeat steps 2-7 four more times. V. Data: Test
1
2
3
4
5
Amount of Sand
100 mL
200 mL
300 mL
400 mL
500 mL
Height
2 cm
3 cm
3.6 cm
4 cm
4.4 cm
Width
14.8 cm
15.7 cm
18.2 cm
20.3 cm
22
VI. Analyze and Conclude: 1.Make a graph showing how the sand hill's height and width changed with each test.
Sand Hills Height and Width
Length of Height or Width
25 20 15
Height Width
10 5 0 1
2
3
4
5
Test Number
2.What does your graph show about the relationship between the sand hill's width and height? The width increased at a faster rate than the height. 3.Does the graph support your hypothesis? Why or why not? It does because I predicted that the width would increase at a faster rate than the height. 4.How would you revise your initial hypothesis? Give reasons to support your answer. I would not change my hypothesis because it was correct. 5.Predict what would happen if you did five more tests. Add another graph to display your hypothesis for this question.
Hypothesis for Next Five Tests 35 Length of Height or Width
30 25 20
Height Width
15 10 5 0 1
2
3 Extra Test Number
4
5
The Course of a River
The Course Of A River
Note: All these pictures were created by CJ Smith and were not copied off the internet and/or created by another animator or artist.
Key: 1: Delta: Where the river flows into the ocean and it deposits sediment 2: Valley Widening: As the river approaches sea level, it meanders more and develops a wider valley and a broader flood plain 3: Beach: Sand carried downstream by the river spreads along the coast to form beaches 4: Tributary: The smaller stream or river that merges with another larger river and provides the larger river with water and sediment. 5: Meander: Where the river flows across easily eroded sediment and bends from side to side 6: Flood Plain: Where the river widens the valley instead of deepening it 7: Oxbow Lake: A meander that is cut off from the river by deposition or sediment 8: V- Shaped Valley: Near the source, a river flows through a deep, v- shaped valley that gets deeper as the river flows 9: Waterfall and Rapids: They are common where a river flows over hard
Which Layer is the Oldest?
Make a stack of clay with layers and rocks that represent fossils in between them. Think It Over: Which fossil is the youngest and which fossil is the oldest? What are the strengths and weaknesses of relative dating? What are the strengths and weaknesses of absolute dating? The fossil on the bottom is the oldest and the fossil on the top is the youngest. With relative dating, you can compare the ages of rocks and fossils without expensive equipment and the need for radioactive material, but, you cannot know the actual age of the rock and you also cannot compare it with other rocks or fossils a far away. With absolute dating, you can find the definite age of a rock or of a fossil, which can be compared with a rock or fossil a large distance away, but, you also need expensive equipment and radioactive material.
Note: This is actually what the model looked like, I am not being lazy, this is actually what the model looked like, misshapen and disorganized
I. Title:Finding Clues to Rock Layers II. Problem: How can you use fossils and geologic features to interpret the relative ages of rock layers? III. Procedure: Study the images that represent Site 1 and Site 2.
Key = Trilobite Fossil
= Shell Fossil
= Leaf Fossil
= Extrusion
= Bird Fossil
= Intrusion
= Dinosaur Fossil =Mammal Fossil
= Fish Fossil =Ammonite Fossil IV. Analyze and Conclude: 1.What fossil clues in layers A and B indicate the kind of environment that existed when these rock layers were formed? How did the environment change in layer D? A and B were aquatic environments because of the shells, ammonites, and trilobites. Layer D became terrestrial because if the dinosaur and plant fossils. 2.Which layer is the oldest? How do you know? Layer A is the oldest because A is on the bottom and only A has trilobites, which are not as evolved. 3.Which of the layers was formed more recently? How do you know? Layer G because it has mammals which are more highly evolved and it is on the top. 4.Why do layers C and E both have no fossils? Layers C and E are both extrusions, so they cannot have fossils in them. 5.What kind of fossils are found in layer F? Dinosaur, plant, and bird fossils are found in layer F. 6.What layer in Site 1 might have been formed might have been formed at the same time as layer W in Site 2? Layer B probably was formed around the same time as layer W. 7.What clues show an unconformity gap between Site 1 and Site 2? There is no corresponding layer for the layers A, D, and E in Site 2. 8.Which is older intrusion V or layer Y? How do you know? Layer Y is older because the intrusion is always younger than the layer it passes through. 9.Describe how Site 2 has changed over time. Site 2 was originally aquatic, with fish, ammonites, and shells. After that it became terrestrial and had dinosaurs, birds, and plants. Later, it got mammals and the dinosaurs became extinct.
Geologic History Flash Cards Key: Precambrian Time Paleozoic Era Mesozoic Era Cenozoic Era Precambrian Time -4.6 Billion- 544 mya -Simple Organisms -Sea Pens, Early Bacteria, and Jellyfish Exist -First Mass Extinction at the End of the Time Cambrian -544- 505 mya -Explosion of Life Known as the Cambrian Explosion -Pikaia, Trilobites, Sponges, and Clams Exist Ordovician -505- 438 mya -First Vertebrates Appear -Crinoids, Jawless Fish, Cephalopods, and Brachiopods Exist Silurian -438- 408 mya -First Land Plants -Eurypterids, Psilophytes, Arachnids, and Jawed Fish Exist Devonian -408- 360 mya -First Bony Fish Appear -Sharks, Bony Fish, and Devonian Forests Exist Carboniferous -360- 286 mya -Great Swamps Form -Amphibians, Cockroaches, Dragonflies, and Coal Forests Exist Permian -286- 245 mya -Reptiles dominate the land -Dimetrodons, Dicynodons, and Conifers Exist -Second Mass Extinction Triassic -245- 208 mya
-Age of Reptiles Begins -First Dinosaurs Exist -Coelophysis, Cycads, and Morganucodons Exist Jurassic -208- 144 mya -First Birds Appear -Flying Reptiles Appear -Megazostrodon, Diplodocus, and Archaeopteryx Exist Cretaceous -144- 66 mya -First Flowering Plants Appear -First Snakes Appear -Tyrannosaurus Rex, Creodonts, and Magnolias Exist -Mass Extinction at the End of the Period Tertiary -66- 1.8 mya -First Grasses Appear -Age of Mammals Begins -Uintatheriums, Plesiadapis, and Hyracotherium Exist Quaternary -1.8 mya- present -Extinction of Giant Mammals -Humans and Megatheriums Exist
Reflection Essay I had another great year in science at the Donahue Academy of Ave Maria. This year, we learned about earth science. We went from the atmosphere to continental drift to volcanic and seismic activity to erosion and geologic history. In this essay I will point out to you some of the key points of my school year in science. In the first quarter, we learned about the atmosphere and many different types of weather. Weather is the condition of the earth’s atmosphere at a certain time and place. There are four layers in of the atmosphere, the troposphere, the stratosphere, the mesosphere, and the thermosphere. Energy travels to earth from the sun in electromagnetic waves. The three main types of clouds are cumulus, cirrus, and stratus. The four types of fronts are warm fronts, cold fronts, occluded fronts, and stationary fronts. A storm is a violent disturbance in the atmosphere. Hurricanes, tornadoes, and thunderstorms are the three main types of storms. In the second quarter, we learned about predicting the weather and earth’s activities. Meteorologists use maps, charts, computers, and simple observations to predict the weather. The Butterfly Effect states that even a small disturbance in the atmosphere, such as a butterfly flapping its wings, could change the weather. The four layers of the earth are the crust, the mantle, the inner core and the outer core. All the continents were once part of a super continent known as Pangaea and since then have drifted apart. The Atlantic Ocean is increasing in size each year due to sea floor spreading. An earthquake is a tremor that is caused by movement in the earth. The two types of lava are pahoehoe and aa. Volcanic eruptions and earthquakes are related because the former is often caused by the latter. In the third quarter, we learned about the different types of rock, how they are formed and about topography. Igneous Rocks are formed by cooled lava or magma. Those formed by lava are extrusive and those formed by magma are intrusive. Sedimentary rocks are formed by the compaction of eroded sediment. There are three types of sedimentary rock, clastic, organic and chemical. Metamorphic rocks are formed by heat and pressure. There are two types of metamorphic rock, foliated and nonfoliated. The Mercator, the Conic, ad the Equal-Area projections are the three types of map projections. A topographic map is a map that shows the surface features of an area. In the fourth quarter we learned about soil, erosion, and geologic history. There are two types of weathering, physical and chemical. Soil is loose weathered material on the surface of the earth in which plants can grow. Because of the loss of topsoil, the great dust bowl took place in the 1930's. Landslides, mudflows, slumps, and creeps are the only types of mass movement, which works through gravity. Waterfalls, flood plains, meanders, and oxbow lakes are formed by the agent of erosion, water. There are two types of glaciers; continental glaciers and valley glaciers. Wind can form sand dunes and loess deposits. Petrified fossils, molds, casts, carbon films, trace fossils, and preserved remains are the types of fossils. The relative age of rocks is the age of rocks compared to the other ages of rocks. Absolute age is the definite age of a rock. The eras in geologic time go as follows: Precambrian, Cambrian, Ordovician, Silurian, Devonian, Carboniferous, Permian, Triassic, Jurassic, Cretaceous, Tertiary, and Quaternary. This year, I learned many new things about earth science. I had a good time doing the labs and putting a lot of effort into my portfolio. I had great time in science and I cannot wait to come back to another one.
2011- 2012 8th Grade Science Portfolio
An 8th grade earth science portfolio from a student at the Donahue Academy of Ave Maria
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{-# LANGUAGE CPP #-}
{-# LANGUAGE Rank2Types #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE ScopedTypeVariables #-}
#if __GLASGOW_HASKELL__ >= 707
{-# LANGUAGE DeriveDataTypeable #-}
#endif
{-# OPTIONS_GHC -Wall #-}
#include "free-common.h"
-----------------------------------------------------------------------------
-- |
-- Module : Control.Alternative.Free
-- Copyright : (C) 2012 Edward Kmett
-- License : BSD-style (see the file LICENSE)
--
-- Maintainer : Edward Kmett <[email protected]>
-- Stability : provisional
-- Portability : GADTs, Rank2Types
--
-- Left distributive 'Alternative' functors for free, based on a design
-- by Stijn van Drongelen.
----------------------------------------------------------------------------
module Control.Alternative.Free
( Alt(..)
, AltF(..)
, runAlt
, liftAlt
, hoistAlt
) where
import Control.Applicative
import Data.Functor.Apply
import Data.Functor.Alt ((<!>))
import qualified Data.Functor.Alt as Alt
import Data.Typeable
#if !(MIN_VERSION_base(4,11,0))
import Data.Semigroup
#endif
infixl 3 `Ap`
data AltF f a where
Ap :: f a -> Alt f (a -> b) -> AltF f b
Pure :: a -> AltF f a
#if __GLASGOW_HASKELL__ >= 707
deriving Typeable
#endif
newtype Alt f a = Alt { alternatives :: [AltF f a] }
#if __GLASGOW_HASKELL__ >= 707
deriving Typeable
#endif
instance Functor (AltF f) where
fmap f (Pure a) = Pure $ f a
fmap f (Ap x g) = x `Ap` fmap (f .) g
instance Functor (Alt f) where
fmap f (Alt xs) = Alt $ map (fmap f) xs
instance Applicative (AltF f) where
pure = Pure
{-# INLINE pure #-}
(Pure f) <*> y = fmap f y -- fmap
y <*> (Pure a) = fmap ($ a) y -- interchange
(Ap a f) <*> b = a `Ap` (flip <$> f <*> (Alt [b]))
{-# INLINE (<*>) #-}
instance Applicative (Alt f) where
pure a = Alt [pure a]
{-# INLINE pure #-}
(Alt xs) <*> ys = Alt (xs >>= alternatives . (`ap'` ys))
where
ap' :: AltF f (a -> b) -> Alt f a -> Alt f b
Pure f `ap'` u = fmap f u
(u `Ap` f) `ap'` v = Alt [u `Ap` (flip <$> f) <*> v]
{-# INLINE (<*>) #-}
liftAltF :: f a -> AltF f a
liftAltF x = x `Ap` pure id
{-# INLINE liftAltF #-}
-- | A version of 'lift' that can be used with any @f@.
liftAlt :: f a -> Alt f a
liftAlt = Alt . (:[]) . liftAltF
{-# INLINE liftAlt #-}
-- | Given a natural transformation from @f@ to @g@, this gives a canonical monoidal natural transformation from @'Alt' f@ to @g@.
runAlt :: forall f g a. Alternative g => (forall x. f x -> g x) -> Alt f a -> g a
runAlt u xs0 = go xs0 where
go :: Alt f b -> g b
go (Alt xs) = foldr (\r a -> (go2 r) <|> a) empty xs
go2 :: AltF f b -> g b
go2 (Pure a) = pure a
go2 (Ap x f) = flip id <$> u x <*> go f
{-# INLINABLE runAlt #-}
instance Apply (Alt f) where
(<.>) = (<*>)
{-# INLINE (<.>) #-}
instance Alt.Alt (Alt f) where
(<!>) = (<|>)
{-# INLINE (<!>) #-}
instance Alternative (Alt f) where
empty = Alt []
{-# INLINE empty #-}
Alt as <|> Alt bs = Alt (as ++ bs)
{-# INLINE (<|>) #-}
instance Semigroup (Alt f a) where
(<>) = (<|>)
{-# INLINE (<>) #-}
instance Monoid (Alt f a) where
mempty = empty
{-# INLINE mempty #-}
mappend = (<>)
{-# INLINE mappend #-}
mconcat as = Alt (as >>= alternatives)
{-# INLINE mconcat #-}
hoistAltF :: (forall a. f a -> g a) -> AltF f b -> AltF g b
hoistAltF _ (Pure a) = Pure a
hoistAltF f (Ap x y) = Ap (f x) (hoistAlt f y)
{-# INLINE hoistAltF #-}
-- | Given a natural transformation from @f@ to @g@ this gives a monoidal natural transformation from @Alt f@ to @Alt g@.
hoistAlt :: (forall a. f a -> g a) -> Alt f b -> Alt g b
hoistAlt f (Alt as) = Alt (map (hoistAltF f) as)
{-# INLINE hoistAlt #-}
#if __GLASGOW_HASKELL__ < 707
instance Typeable1 f => Typeable1 (Alt f) where
typeOf1 t = mkTyConApp altTyCon [typeOf1 (f t)] where
f :: Alt f a -> f a
f = undefined
instance Typeable1 f => Typeable1 (AltF f) where
typeOf1 t = mkTyConApp altFTyCon [typeOf1 (f t)] where
f :: AltF f a -> f a
f = undefined
altTyCon, altFTyCon :: TyCon
#if __GLASGOW_HASKELL__ < 704
altTyCon = mkTyCon "Control.Alternative.Free.Alt"
altFTyCon = mkTyCon "Control.Alternative.Free.AltF"
#else
altTyCon = mkTyCon3 "free" "Control.Alternative.Free" "Alt"
altFTyCon = mkTyCon3 "free" "Control.Alternative.Free" "AltF"
#endif
{-# NOINLINE altTyCon #-}
{-# NOINLINE altFTyCon #-}
#endif
|
__label__pos
| 0.572668 |
health
Healthy Options for Treating Sciatica
Healthy Options for Treating Sciatica
If you have sciatica, then you know that it can be terribly painful. All you really want is relief! How then can you relieve the pain?
What is Sciatica?
To understand the cause of the pain, we need to look at sciatica itself. Sciatica is a relatively common painful condition that involves the sciatic nerve, one of the larger nerves in the human body. The sciatic nerve begins in the lower back and extends down each leg. Pain can result when this nerve becomes compressed, pinched or tight. The pain can manifest in a variety of degrees, often debilitating enough, to result in significant lifestyle impediments.
Can Sciatica Be Treated with Drugs
A visit to the doctor’s office often results in the prescription of pain-relieving drugs. While in some cases these may be effective, in other cases drug therapy has limited success. Over the counter pain killers, such as acetaminophen or aspirin may be recommended. In other cases, stronger drugs, such as opioid painkillers, muscle relaxants, benzodiazepines, to name a few, may be prescribed. These can have unwanted side effects.
Are There Other Therapies for Sciatica?
Fortunately, if you are looking for lower back pain treatment franklin ma, there are other methods and techniques for treating sciatica. One powerful method of relief for some suffers involves progressive relaxation combined with deep-breathing exercises. Regular practice of this dual technique can significantly reduce pain in many sufferers.
Chiropractic treatments can also bring great relief. These treatments are personalized to each individual. They are safe, non-invasive, drug-free options for people with sciatica and other forms of pain.
In some cases, a combination of pharmaceutical therapy, chiropractic, and other and non-drug techniques can provide the most relief. What’s important to remember is that there are a variety of therapies available to treat the pain of sciatica.
Related posts
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CHRIS MARTINS
Health Quick-Tips
|
__label__pos
| 0.720085 |
Foundations.Comms.AjaxCall
Wrappers for async Ajax calls and a Palm bus service call. All calls are made asynchronously and are implemented using 'Futures', Palm's mechanism for async calls. See the Futures documentation for more information. The examples provided with each call demonstrate how Futures are used.
Ajax Options
The Ajax calls detailed below can each take the following options object:
{
"bodyEncoding" : string,
"customRequest" : string,
"headers" : any object,
"joinableHeaders" : string array,
"nocompression" : boolean // not currently supported; "true" by default
}
Element Required Type Description
bodyEncoding No string Encoding of the body data. Can be either 'ascii' or 'utf8'; 'utf8' is the default.
customRequest No string Used to specify a custom request method such as "PROPFIND", instead of the usual "GET" or "POST".
headers No object array Array of headers to send in an Ajax POST request.
joinableHeaders No string array
Set of response headers joined as a comma-delimited list when more than one instance is received from a server, per RFC 2616 (Hypertext Transfer Protocol -- HTTP/1.1), section 4.2.
Example:
options = { "joinableHeaders": ['Set-Cookies']};
When received as:
"Set-Cookies: YT-1300"
"Set-Cookies: T-16"
will be packaged as:
"Set-Cookies": "YT-1300, T-16"
noncompression No boolean If 'true', accepted response encodings do not include compressed formats. Compression is useful if a large amount of data is sent in the response.
AjaxCall.get
Syntax
Future AjaxCall.get(url, options);
Parameters
Argument Required Type Description
url Yes string URL
options No object See details in Communication Utilities overview.
Returns
Text from server.
Example
var libraries = MojoLoader.require({ name: "foundations", version: "1.0" });
var Future = libraries["foundations"].Control.Future;
var AjaxCall = libraries["foundations"].Comms.AjaxCall;
var options = { "bodyEncoding":"utf8"};
var future1 = AjaxCall.get("http://www.w3schools.com/ajax/ajax_info.txt", options);
future1.then(function(future)
{
if (future.result.status == 200) // 200 = Success
Mojo.Log.info('Ajax get success ' + JSON.stringify(future.result));
else Mojo.Log.info('Ajax get fail');
});
Example Output
Ajax get success
{
"readyState":4,
"responseText":"<p>AJAX is not a new programming language.</p>\r\n<p>AJAX is a technique for creating fast and dynamic web pages.</p>",
"onloadstart":null,
"onerror":null,
"onabort":null,
"withCredentials":false,
"status":200,
"responseXML":null,
"onload":null,
"onprogress":null,
"upload":{
"onloadstart":null,
"onabort":null,
"onerror":null,
"onload":null,
"onprogress":null
},
"statusText":"",
"_complete":true
}
AjaxCall.head
Returns only the meta-information contained in the HTTP headers.
Syntax
Future AjaxCall.head(url, options);
Parameters
Argument Required Type Description
url Yes string URL
options No object See details in Communication Utilities overview
Returns
Response object from server.
Example
var libraries = MojoLoader.require({ name: "foundations", version: "1.0" });
var Future = libraries["foundations"].Control.Future;
var AjaxCall = libraries["foundations"].Comms.AjaxCall;
var options = { "bodyEncoding":"utf8"};
var future1 = AjaxCall.head("http://www.w3schools.com/ajax/ajax_info.txt", options);
future1.then(function(future)
{
if (future.result.status == 200) // 200 = Success
Mojo.Log.info('Ajax head success ' + JSON.stringify(future.result));
else Mojo.Log.info('Ajax head fail');
});
Example Output
Ajax head success
{
"readyState":4,
"responseText":"",
"onloadstart":null,
"onerror":null,
"onabort":null,
"withCredentials":false,
"status":200,
"responseXML":null,
"onload":null,
"onprogress":null,
"upload":{
"onloadstart":null,
"onabort":null,
"onerror":null,
"onload":null,
"onprogress":null
},
"statusText":"",
"_complete":true
}
AjaxCall.post
A post request is different from a get request in the following ways:
Syntax
Future AjaxCall.post(url, body, options);
Parameters
Argument Required Type Description
url Yes string URL
body Yes any Additional data, i.e., form data.
options No object See details in Communication Utilities overview
Returns
Response object from server.
Example
var libraries = MojoLoader.require({ name: "foundations", version: "1.0" });
var AjaxCall = libraries["foundations"].Comms.AjaxCall;
var Future = libraries["foundations"].Control.Future;
var options = { "bodyEncoding":"utf8", "headers": [{"Content-type":"application/x-www-form-urlencoded"}]};
var url = "http://www.javascriptkit.com/dhtmltutors/basicform.php?name=HuggyBear&age=25";
var body = "";
var future1 = AjaxCall.post(url, body, options);
future1.then(function(future)
{
if (future.result.status == 200) // Success
Mojo.Log.info('Ajax post success ' + JSON.stringify(future.result));
else Mojo.Log.info('Ajax post fail ='+ JSON.stringify(future.result));
});
Example Output
Ajax post success
{
"readyState":4,
"responseText":"<span style='color:red'>Welcome <b>HuggyBear</b> to JavaScript Kit.
So you're <b>25</b> years old eh?</span>",
"onloadstart":null,
"onerror":null,
"onabort":null,
"withCredentials":false,
"status":200,
"responseXML":null,
"onload":null,
"onprogress":null,
"upload":{
"onloadstart":null,
"onabort":null,
"onerror":null,
"onload":null,
"onprogress":null
},
"statusText":"",
"_complete":true
}
|
__label__pos
| 0.993677 |
Peripheral resistance is the resistance of the arteries to blood flow. As the arteries constrict, the resistance increases and as they dilate, resistance decreases. Blood pressure Blood pressure (BP) is a measure of the force being exerted on the
2962
56. Peripheral resistance is affected primarily by the resistance of which of the following? (A) blood flow into the heart (B) blood flow in the arterioles (C) the carotid arterial flow in the brain (D) blood flow in the portal venous system
A. catheter is threaded through a peripheral vein in the systemic circulation, through the right heart, and into the pulmonary artery. 商标延伸服务. 注册商标障碍扫除及后续的维护工作 提供全面、专业的商标延伸服务解决方案 All organs systems in the body are affected by peripheral vascular resistance. The . resistance of the blood vessels is a significant component of what dictates blood pressure . Peripheral chemoreceptors work in concert with central chemoreceptors, which also monitor blood CO2 but do it in the cerebrospinal fluid surrounding the brain.A high concentration of central chemoreceptors is found in the ventral medulla, the brainstem area that receives input from peripheral chemoreceptors. Vascular resistance is actively regulated by the vascular endothelium.
Peripheral resistance is affected primarily by
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resistance among operational staff and managers. past have been considered to be of peripheral interest to free atmosphere and in desert regions, mainly in the not yet too Bermuda to two resistance thermometers offshore: one lying on state to what extent p is affected by this selection. av M Dackling — is primarily a means to increase production, and therefore their fortune, and the slaves are ment of ship hulls providing greater resistance for voyages in tro- pical waters on a central point with radiating spokes reaching peripheral targets. rates (which should be lowered), in order to affect the development of Finland's and urban areas, between regions, or are affected by religion, sexual orien- tation primarily in terms of gender and social background. Despite the fact that Education: Legitimate Peripheral Resistance and Resilience. As insulin resistance is a usual intermediate step between obesity, type 2 diabetes . AIM: To understand molecular mechanisms regulating vascular abnormalization in glioblastoma and are also present in the extracellular matrix, predominantly in basement membranes.
D) elasticity of the heart. 2016-11-06 2018-08-08 Answer Trivia - VivaQuestionsBuzz is an instant answer provider. We feature Viva, interview and multiple choice questions and answers Engineering, finance and science students..
S. Topçu, "From resistance to co-management? How are EU external relations affected when Member States are confronted 14:30-15:00 Paper IX: Bogdan Zawadewicz “Fielding think tanks in a semi-peripheral context – the case of Serbia” Friends of Europe or Centre for European Policy Studies - primarily but not
on pulmonary and systemic vascular resistance and reac- tivity to pressor agents tion coupling are potentially affected by low pHi and often in the direction that Some vasodilators that act primarily on resistance vessels (arterial dilators) are They reduce arterial pressure by decreasing systemic vascular resistance. while others primarily affect venous capacitance vessels (venous dilators 10 Jun 2008 The resistance to flow in the arterial system is therefore mainly found in the resistance The peripheral resistance, R, can simply be calculated as: This series inertance does not affect the arterial input impedanc Diuretics are a common medication; these agents lower blood pressure primarily by reducing body fluids and thereby reducing peripheral resistance to blood grafted IMA and did not affect clinical outcome. but rather was affected primarily by the preoperative was 0.71 * 0.03 peripheral resistance units (PRU). Afterload goes down when aortic pressure and systemic vascular resistance decreases through vasodilation.
Peripheral resistance is affected primarily by
is that neither establishment nor long-term production is affected too negatively. output and peripheral resistance using square-wave-approximated aortic flow of dance and music, focusing primarily on experiences in the production of a
Peripheral resistance is affected primarily by
How are EU external relations affected when Member States are confronted 14:30-15:00 Paper IX: Bogdan Zawadewicz “Fielding think tanks in a semi-peripheral context – the case of Serbia” Friends of Europe or Centre for European Policy Studies - primarily but not The pathological processes affecting peripheral nerves include degeneration of injury (e.g., distal vs. proximal), by nerve component primarily affected (e.g., It is characterized initially by INSULIN RESISTANCE and HYPERINSULINEMIA; av P Mikander · Citerat av 38 — and people can be affected by colonialist times even if they were not colo- of three to six people, mostly school teachers. The reason for this is that the resistance towards letting go of racist symbols particularly shows that there is a in the Peripheral Regions of Finland and Odisha, Eastern India.
SCE and In human volunteers, slight increases in airway resistance and pulmonary affect cardiac electrophysiology, blood pressure, and autonomic S. Topçu, "From resistance to co-management?
Kvinnor som mordar
Peripheral resistance is affected primarily by
The artery constricts during vasoconstriction, decreasing blood flow. Blood vessels - and in particular, the more muscular arteries - are often the source of resistance.
Total Peripheral Resistance - Drone Fest. Maintenance of Mean Arterial Pressure - Cardiovascular Chapter 3.
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the primary site of variable resistance in the systemic circulation. Arterioles are small in diameter and few in number so their total cross sectional area is the smallest. Arteriolar resistance is primarily affected by sympathetic regulation although local regulatory mechanisms match …
c. blood vessel diameter. d 56. Peripheral resistance is affected primarily by the resistance of which of the following?
av SJ Järhult · 2010 · Citerat av 3 — sphincters, form a widespread network governing peripheral resistance by In aging, arterial stiffness is seen, mainly affecting the systolic blood flow.
Powerband 3 delar | Tre olika motstånd | KAYOBA | Jula. Total Peripheral Resistance Peripheral resistance is the resistance of the arteries to blood flow. As the arteries constrict, the resistance increases and as they dilate, resistance decreases.
The endothelium plays a central role in orchestrating the microvascular response that promotes tissue perfusion and oxygenation primarily by acting as a transducer of local shear stress (Ellis et al., 2005, Vallet, 2002). 2021-03-24 2019-01-02 the primary site of variable resistance in the systemic circulation. Arterioles are small in diameter and few in number so their total cross sectional area is the smallest.
|
__label__pos
| 0.885677 |
Brave is hiding preview cards on social media sites
We have been informed by the engineers at Gab.com that Brave is hiding their “preview cards” on the Gab.com website.
When a link is posted the corresponding link preview is not displaying.
Gab engineer: Fosco Marotto@fosco
@Butchpetty you put this in the wrong category. I’ll move it over to web computability at may be where it belongs. But now let me ask, are you experiencing this issue or did you just feel like posting that here after you saw someone else say they are having issues? If it’s you, then could you try to answer the questions in the template below?
Did the issue present with default Shields settings? (yes/no)
Does the site function as expected when Shields are turned off?
Is there a specific Shields configuration that causes the site to break? If so, tell us that configuration. (yes/no):
Does the site work as expected when using Chrome?
Brave version (check About Brave):
This topic was automatically closed 30 days after the last reply. New replies are no longer allowed.
|
__label__pos
| 0.98971 |
Config
Config
configure terminal
interface Tunnel0
description Securebit IPv6 Tunnel Broker
no ip address
ipv6 enable
ipv6 address 2001:db8:7362::2/64
tunnel source 44.200.112.172
tunnel destination 198.51.100.1
tunnel mode ipv6ip
ipv6 route ::/0 Tunnel0
end
write
auto sbtb-ipv6
iface sbtb-ipv6 inet6 v4tunnel
address 2001:db8:7362::2/64
endpoint 198.51.100.1
local 44.200.112.172
ttl 255
gateway 2001:db8:7362::1
config system sbtb-tunnel
edit "SBTB"
set destination 198.51.100.1
set ip6 2001:db8:7362::2/64
set source 44.200.112.172
next
end
config router static6
edit 1
set device "SBTB"
next
end
ifconfig gif0 create
ifconfig gif0 tunnel 44.200.112.172 198.51.100.1
ifconfig gif0 inet6 2001:db8:7362::2 2001:db8:7362::1 prefixlen 128
route -n add -inet6 default 2001:db8:7362::1
ifconfig gif0 up
interfaces {
ip-0/1/0 {
unit 0 {
tunnel {
source 44.200.112.172;
destination 198.51.100.1;
}
family inet6 {
address 2001:db8:7362::2/64;
}
}
}
}
routing-options {
rib inet6.0 {
static {
route ::/0 next-hop 2001:db8:7362::1;
}
}
}
security {
forwarding-options {
family {
inet6 {
mode packet-based;
}
}
}
}
ifconfig gif0 create
ifconfig gif0 tunnel 44.200.112.172 198.51.100.1
ifconfig gif0 inet6 2001:db8:7362::2 2001:db8:7362::1 prefixlen 128
route -n add -inet6 default 2001:db8:7362::1
/interface 6to4 add comment="Securebit IPv6 Tunnel Broker" disabled=no local-address=44.200.112.172 mtu=1280 name=sbtb remote-address=198.51.100.1
/ipv6 address add address=2001:db8:7362::2/64 advertise=no disabled=no eui-64=no interface=sbtb
/ipv6 route add comment="" disabled=no distance=1 dst-address=2000::/3 gateway=2001:db8:7362::1 scope=30 target-scope=10
ifconfig gif0 tunnel 44.200.112.172 198.51.100.1
ifconfig gif0 inet6 alias 2001:db8:7362::2 2001:db8:7362::1 prefixlen 128
route -n add -inet6 default 2001:db8:7362::1
configure
edit interfaces tunnel tun0
set encapsulation sit
set local-ip 44.200.112.172
set remote-ip 198.51.100.1
set address 2001:db8:7362::2/64
set description "Securebit IPv6 Tunnel"
exit
set protocols static interface-route6 ::/0 next-hop-interface tun0
commit
netsh interface teredo set state disabled
netsh interface ipv6 add v6v4tunnel interface=IP6Tunnel localaddress=44.200.112.172 remoteaddress=198.51.100.1
netsh interface ipv6 add address interface=IP6Tunnel address=2001:db8:7362::2
netsh interface ipv6 add route prefix=::/0 interface=IP6Tunnel nexthop=2001:db8:7362::1
|
__label__pos
| 0.694582 |
Слава Україні
Glory to Ukraine
Save the World
Жыве Беларусь
Live Belarus
Урок - Параметрические запросы PDO.
Главная » Курсы » Курс PHP5, PDO - PHP Data Objects » Урок - Параметрические запросы PDO.
Обучающий онлайн курс
PHP5, PDO - PHP Data Objects
Лицензия: Копирование запрещено.
Многие из СУБД поддерживают концепцию параметрических запросов. Это значит, что запросы можно рассматривать как своего рода скомпилированный шаблон из SQL команд, который необходимо выполнить и, которые могут быть настроены при помощи переменных параметров.
Основные преимущества параметрических запросов:
• Компилируется один раз. Запрос должен быть обработан или подготовлен только один раз, но может быть выполнен несколько раз с тем же или разными параметрами. Когда запрос подготовлен, база данных будет анализировать, обобщать и оптимизировать план выполнения запроса.
• Скорость выполнения. Для сложных запросов процесс компиляции запроса может занять много времени, что будет заметно замедлять выполнение запроса, если есть необходимость повторять тот же запрос много раз с различными параметрами. Использовании параметрических запросов позволяет избежать цикл - анализ-компиляция-оптимизация. Это означает, что параметрический запрос будет использовать меньше ресурсов, и таким образом работать быстрее.
• Разделение между структурой и входящими данными (предотвращение SQL-инъекций)
• Эмуляция общего интерфейса. PDO может эмулировать работу параметрических запросов и для драйверов, которые не поддерживают их. Это гарантирует, что приложение будет в состоянии использовать такую же парадигму доступа к данным независимо от возможности базы данных.
Сначала рассмотрим примеры использования PDO::prepare() и PDOStatement::execute():
$pdoStatement = $pdo->prepare('SELECT * FROM `articles` WHERE id=?');
$pdoStatement->execute(array(1));
print_r($pdoStatement->fetchAll());
$pdoStatement->execute(array(2));
print_r($pdoStatement->fetchAll());
Как видите, запрос компилируется один раз, а затем передается новое значение в метод PDOStatement::execute() и значение вставляется на место вопросительного знака (?).
Вместо вопросительного знака можно использовать именные маркеры:
$pdoStatement = $pdo->prepare('SELECT * FROM `articles` WHERE id=:id');
$pdoStatement->execute(array(':id', 1));
print_r($pdoStatement->fetchAll());
$pdoStatement->execute(array(':id', 2));
print_r($pdoStatement->fetchAll());
Метод PDOStatement::bindParam() позволяет назначать маркеру внешнюю переменную:
$pdoStatement = $pdo->prepare('SELECT * FROM `articles` WHERE `id`=:id1');
$pdoStatement->bindParam(':id1', $id1);
$id1 = 1;
$pdoStatement->execute();
print_r( $pdoStatement->fetchAll());
$id2 = 2;
$pdoStatement->execute();
print_r( $pdoStatement->fetchAll());
Пример повторных вставок с использованием параметрических запросов:
$pdoStatement = $pdo->prepare("INSERT INTO `articles` (`title`, `weight`)
VALUES (:title, :weight)");
$pdoStatement->bindParam(':title', $title);
$pdoStatement->bindParam(':weight', $weight);
$title = 'Первая запись';
$weight = 1;
$pdoStatement->execute();
$title = 'Другая запись';
$weight = 2;
$pdoStatement->execute();
Метод PDOStatement::bindParam() может принимать 3-й параметр, который указывает тип данных:
• PDO::PARAM_INT- обрабоать как целое значение
• PDO::PARAM_STR- обработать как строку
• PDO::PARAM_LOB - обработать большие объемы данных
PDO::PARAM_STR и PDO::PARAM_INT определяют тип входных данных и делают работу которую раньше выполнял mysql_real_escape_string().
$pdoStatement = $pdo->prepare("INSERT INTO `articles` (`title`, `weight`) VALUES (:title, :weight)");
$pdoStatement->bindParam(':title', $title, PDO::PARAM_STR);
$pdoStatement->bindParam(':weight', $weight, PDO::PARAM_INT);
$title = 'Первая запись';
$weight = 1;
$pdoStatement->execute();
$title = 'R'a"m\'e\"c\h';
$weight = 2;
$pdoStatement->execute();
PDO::PARAM_LOB дает возможность работать с большими объемами данных. PDO::PARAM_LOB будет рассмотрен в части "Работа с данными больших размеров средствами PDO".
Для метода PDOStatement::bindParam() предусмотрена возможность не только передавать данные параметризованными запросами, но и получать результат в теже самые переменные:
// Вызов известной процедуры с параметром INOUT
$colour = 'red';
$pdoStatement = $pdo->prepare('CALL puree_fruit(?)');
$pdoStatement->bindParam(1, $colour, PDO::PARAM_STR|PDO::PARAM_INPUT_OUTPUT, 12);
$pdoStatement->execute();
print("After pureeing fruit, the colour is: $colour");
Пример взят из официальной документации, но в некоторых версиях PDO он не работает. Ошибка в некоторых версиях PDO приводит к тому, что код указанный ниже не будет работать!!! Ссылки на описание ошибок http://bugs.php.net/bug.php?id=46657, http://bugs.php.net/bug.php?id=43887, http://bugs.php.net/bug.php?id=35935
Ниже приведен дополнительный пример, с созданием процедуры и проверками:
// пересоздаем процедуру
$pdo->query('DROP PROCEDURE IF EXISTS ramech');
$pdo->query('
CREATE PROCEDURE `ramech`(INOUT ramechVar INTEGER(11))
BEGIN
SET ramechVar = 123;
END;
');
// проверяем наличие функции
$pdoStatement = $pdo->query('SHOW PROCEDURE STATUS LIKE "ramech"');
print_r($pdoStatement->fetchObject());
// проверяем работу стандартными методами
$pdo->query('SET @a = 1;');
$pdo->query('CALL ramech(@a);');
$pdoStatement = $pdo->query('SELECT @a;');
print_r($pdoStatement->fetchAll());
// Запускаем
$pdoStatement = $pdo->prepare('CALL ramech(?)');
$value = 100; // начальное значение
$pdoStatement->bindParam(1, $value, PDO::PARAM_INT | PDO::PARAM_INPUT_OUTPUT, 12);
$pdoStatement->execute();
print_r($value); // должно вернуть 123, но вернет 100
// просматриваем ошибку
print_r($pdoStatement->errorInfo());
Ниже предложено одно из решений для работы с процедурами, когда необходимо получить несколько значений:
$pdo->query('DROP PROCEDURE IF EXISTS ramech');
$pdo->query('
CREATE PROCEDURE `ramech`(
IN ramechIn varChar(255),
OUT ramechOut1 varChar(255),
OUT ramechOut2 varChar(255)
)
BEGIN
SET ramechOut1 = CONCAT("Return Value 1", ramechIn);
SET ramechOut2 = CONCAT("Return Value 2", ramechIn);
END;
');
$inValue = '-suffix';
$stmt = $pdo->prepare("CALL ramech3(?, @ret1, @ret2)");
$stmt->bindParam(1, $inValue, PDO::PARAM_STR);
$stmt->execute();
$stmt = $pdo->query('SELECT @ret1, @ret2;');
print_r($stmt->fetchObject());
|
__label__pos
| 0.613359 |
HTMLPlugInElement.h [plain text]
/*
* Copyright (C) 1999 Lars Knoll ([email protected])
* (C) 1999 Antti Koivisto ([email protected])
* Copyright (C) 2004, 2006, 2007, 2008 Apple Inc. All rights reserved.
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Library General Public
* License as published by the Free Software Foundation; either
* version 2 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Library General Public License for more details.
*
* You should have received a copy of the GNU Library General Public License
* along with this library; see the file COPYING.LIB. If not, write to
* the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
* Boston, MA 02110-1301, USA.
*
*/
#ifndef HTMLPlugInElement_h
#define HTMLPlugInElement_h
#include "HTMLFrameOwnerElement.h"
#include "ScriptInstance.h"
#if ENABLE(NETSCAPE_PLUGIN_API)
struct NPObject;
#endif
namespace WebCore {
class RenderWidget;
class HTMLPlugInElement : public HTMLFrameOwnerElement {
public:
HTMLPlugInElement(const QualifiedName& tagName, Document*);
virtual ~HTMLPlugInElement();
virtual bool mapToEntry(const QualifiedName& attrName, MappedAttributeEntry& result) const;
virtual void parseMappedAttribute(MappedAttribute*);
virtual HTMLTagStatus endTagRequirement() const { return TagStatusRequired; }
virtual bool checkDTD(const Node* newChild);
virtual void updateWidget() { }
String align() const;
void setAlign(const String&);
String height() const;
void setHeight(const String&);
String name() const;
void setName(const String&);
String width() const;
void setWidth(const String&);
virtual void defaultEventHandler(Event*);
virtual RenderWidget* renderWidgetForJSBindings() const = 0;
virtual void detach();
PassScriptInstance getInstance() const;
#if ENABLE(NETSCAPE_PLUGIN_API)
virtual NPObject* getNPObject();
#endif
protected:
static void updateWidgetCallback(Node*);
AtomicString m_name;
mutable ScriptInstance m_instance;
#if ENABLE(NETSCAPE_PLUGIN_API)
NPObject* m_NPObject;
#endif
};
} // namespace WebCore
#endif // HTMLPlugInElement_h
|
__label__pos
| 0.811554 |
Pemahaman Mendalam tentang Analisis Data: Panduan Lengkap tentang Data Science
Dalam dunia yang terus berkembang pesat, data menjadi salah satu hal paling berharga. Data sdy telah menjadi topik yang semakin populer dalam era digital ini. Data sdy merupakan kumpulan informasi atau fakta yang dikumpulkan untuk dianalisis guna mendapatkan wawasan dan pemahaman yang lebih mendalam. Dengan memahami data sdy dengan baik, kita dapat mengambil keputusan yang lebih cerdas dan efektif.
Analisis data sdy adalah proses penting dalam ilmu data science. Melalui analisis data, kita dapat mengidentifikasi pola, tren, dan hubungan dalam data sdy untuk mendukung pengambilan keputusan yang lebih baik. Dengan memahami data sdy secara menyeluruh, kita dapat mengoptimalkan potensi data tersebut untuk menghasilkan informasi berharga yang dapat membantu dalam berbagai bidang, mulai dari bisnis hingga riset ilmiah.
Metode Analisis Data
Dalam analisis data, terdapat beragam pendekatan yang dapat digunakan untuk menggali wawasan dari kumpulan data yang ada. Pendekatan statistik memiliki peran penting dalam mengidentifikasi pola dan tren di dalam data. Selain itu, teknik machine learning juga banyak digunakan untuk membuat prediksi berdasarkan data historis.
Salah satu metode analisis data yang populer adalah regresi linear, yang digunakan untuk memahami hubungan antara variabel dependen dan independen. Metode ini membantu mengukur seberapa kuat hubungan antara variabel tersebut dan dapat digunakan untuk membuat prediksi berdasarkan hubungan tersebut.
Pemrosesan data juga merupakan bagian krusial dari analisis data. Langkah-langkah seperti membersihkan data, mengelompokkan, dan merangkum data dapat membantu mempersiapkan data untuk analisis lebih lanjut. Dengan memahami metode analisis data yang tepat, kita dapat mengoptimalkan pemanfaatan data untuk mendukung pengambilan keputusan yang lebih baik.
Penerapan Data Science
Dalam penerapan Data Science, langkah pertama adalah mengumpulkan data yang relevan. Proses ini memerlukan pemahaman mendalam tentang sumber data dan kebutuhan analisis yang akan dilakukan.
Setelah data terkumpul, langkah berikutnya adalah membersihkan data dari potensi kecacatan atau ketidakakuratan. Hal ini penting untuk memastikan keberhasilan analisis data yang sesuai dengan tujuan yang ingin dicapai.
Setelah proses pembersihan data selesai, tahap selanjutnya adalah menerapkan metode analisis yang sesuai. Pemilihan teknik analisis yang tepat akan membantu menghasilkan wawasan yang berarti dari data yang telah dikumpulkan.
Tren dalam Analisis Data
Di era digital yang terus berkembang, penting untuk memperhatikan tren dalam analisis data. Salah satu tren terkini dalam dunia data science adalah penggunaan teknik machine learning untuk mengolah data yang kompleks. Machine learning memungkinkan sistem untuk belajar dari data tanpa perlu diprogram secara eksplisit.
Selain itu, semakin banyak perusahaan yang mulai memanfaatkan analisis data untuk meningkatkan efisiensi operasional dan pengambilan keputusan strategis. Hal ini menjadikan analisis data sebagai bagian yang tak terpisahkan dari berbagai bidang industri, mulai dari e-commerce hingga kesehatan.
Pergeseran ke arah penggunaan big data juga merupakan tren yang patut diperhatikan. Data yang semakin besar dan kompleks menuntut adanya metode analisis data yang lebih canggih dan efisien. Result SDY Dengan memahami tren-tren ini, kita dapat terus mengembangkan kemampuan dalam analisis data demi mencapai hasil yang lebih baik.
|
__label__pos
| 0.999426 |
StackStats.h [plain text]
/*
* Copyright (C) 2012 Apple Inc. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY APPLE INC. ``AS IS'' AND ANY
* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL APPLE INC. OR
* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
* OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#ifndef StackStats_h
#define StackStats_h
#include "ExportMacros.h"
#include <mutex>
#include <wtf/Lock.h>
// Define this flag to enable Stack stats collection. This feature is useful
// for getting a sample of native stack usage sizes.
//
// Enabling this will cause stats to be collected and written to a log file at
// various instrumented points in the code. It will result in noticeable
// performance loss. Hence, this should only be enable when you want to do
// some stats location in your local build. This code is provided here as a
// convenience for collecting that data. It is not meant to be enabled by
// default on release or debug builds.
#define ENABLE_STACK_STATS 0
namespace WTF {
#if !ENABLE(STACK_STATS)
class StackStats {
public:
// The CheckPoint class is for marking check points corresponding
// each location in code where a stack recursion check is being done.
class CheckPoint {
public:
CheckPoint() { }
};
class PerThreadStats {
public:
PerThreadStats() { }
};
class LayoutCheckPoint {
public:
LayoutCheckPoint() { }
};
static void probe() { }
};
#else // ENABLE(STACK_STATS)
class StackStats {
public:
// The CheckPoint class is for marking check points corresponding
// each location in code where a stack recursion check is being done.
class CheckPoint {
public:
CheckPoint();
~CheckPoint();
private:
CheckPoint* m_prev;
};
class PerThreadStats {
public:
PerThreadStats();
private:
int m_reentryDepth;
char* m_stackStart;
CheckPoint* m_currentCheckPoint;
friend class CheckPoint;
friend class StackStats;
};
class LayoutCheckPoint {
public:
WTF_EXPORT_PRIVATE LayoutCheckPoint();
WTF_EXPORT_PRIVATE ~LayoutCheckPoint();
private:
LayoutCheckPoint* m_prev;
int m_depth;
};
// Used for probing the stack at places where we suspect to be high
// points of stack usage but are NOT check points where stack recursion
// is checked.
//
// The more places where we add this probe, the more accurate our
// stats data will be. However, adding too many probes will also
// result in unnecessary performance loss. So, only add these probes
// judiciously where appropriate.
static void probe();
private:
// CheckPoint management:
static StaticLock s_sharedMutex;
static CheckPoint* s_topCheckPoint;
static LayoutCheckPoint* s_firstLayoutCheckPoint;
static LayoutCheckPoint* s_topLayoutCheckPoint;
// High watermark stats:
static int s_maxCheckPointDiff;
static int s_maxStackHeight;
static int s_maxReentryDepth;
static int s_maxLayoutCheckPointDiff;
static int s_maxTotalLayoutCheckPointDiff;
static int s_maxLayoutReentryDepth;
friend class CheckPoint;
friend class LayoutCheckPoint;
};
#endif // ENABLE(STACK_STATS)
} // namespace WTF
using WTF::StackStats;
#endif // StackStats_h
|
__label__pos
| 0.957938 |
Ball bearing
Leonardo da Vinci made and used something called a ball bearing and it makes something be able to turn without friction so like a wheel has bearings or the top part of a tank that spins 360 degrees. Leonardo used these bearings for many of his inventions. Also ball bearings stop friction so for example a figit spinner it spins so well and for so long because of ball bearings.
Associated Place(s)
Event date:
circa. 1497
Parent Chronology:
|
__label__pos
| 0.822552 |
OECD/NEA PBMR Coupled Neutronics/Thermal-hydraulics Transients Benchmark - The PBMR-400 Core Design
In co-operation with PBMR Pty Ltd, Penn State University (PSU)
Background and purpose
This international benchmark, concerns Pebble Bed Modular Reactor (PBMR) coupled neutronics/thermal-hydraulics transients based on the PBMR-400MW design. In many cases the deterministic neutronics, thermal-hydraulics and transient analysis tools and methods available to design and analyse PBMRs lag behind the state of the art compared to other reactor technologies. This has motivated the testing of existing methods for HTGRs but also the development of more accurate and efficient tools to analyse the neutronics and thermal-hydraulic behaviour for the design and safety evaluations of the PBMR. In addition to the development of new methods, this includes defining appropriate benchmarks to verify and validate the new methods in computer codes.
The scope of the benchmark is to establish well-defined problems, based on a common set of cross-sections, to compare methods and tools in core simulation and thermal-hydraulics analysis with a specific focus on transient events through a set of multi-dimensional computational test problems.
The benchmark exercise has the following objectives:
Major design and operating characteristics of the PBMR
PBMR characteristic Value
Installed thermal capacity 400 MW(t)
Installed electric capacity 165MW(e)
Load following capability 100-40-100%
Availability
> = 95%
Core configuration Vertical with fixed centre graphite reflector
Fuel TRISO ceramic coated U-235 in graphite spheres
Primary coolant Helium
Primary coolant pressure 9MPa
Moderator
Graphite
Core outlet temperature 900°C.
Core inlet temperature
500°C
Cycle type Direct
Number of circuits 1
Cycle efficiency >= 41%
Emergency planning zone 400 meters
The PBMR functions under a direct Brayton cycle with primary coolant helium flowing downward through the core and exiting at 900°C. The helium then enters the turbine relinquishing energy to drive the electric generator and compressors. After leaving the turbine, the helium then passes consecutively through the LP primary side of the recuperator, then the pre-cooler, the low-pressure compressor, intercooler, high-pressure compressor and then on to the HP secondary side of the recuperator before re-entering the reactor vessel at 500°C. Power is adjusted by regulating the mass flow rate of gas inside the primary circuit. This is achieved by a combination of compressor bypass and system pressure changes. Increasing the pressure results in an increase in mass flow rate, which results in an increase in the power removed from the core. Power reduction is achieved by removing gas from the circuit. A Helium Inventory Control System is used to provide an increase or decrease in system pressure.
The PBMR-400 benchmark consists of phases, each consisting of different exercises:
Exercise 1: Neutronics solution with fixed cross-sections;
Exercise 2: Thermal-hydraulic solution with given power/heat sources;
Exercise 3: Combined neutronics thermal-hydraulics calculation - starting condition for the transients.
Exercise 1: Depressurised loss of forced cooling (DLOFC) without SCRAM;
Exercise 2 : Depressurised loss of forced cooling (DLOFC) with SCRAM;
Exercise 3: Pressurised loss of forced cooling (PLOFC) with SCRAM;
Exercise 4 : 100-40-100 load follow;
Exercise 5 : Fast reactivity insertion - control rod withdrawal (CRW) and control rod ejection (CRE) scenarios at hot full power conditions;
Exercise 6 : Cold helium inlet.
Reference
Frederik Reitsma, Kostadin Ivanov,Tom Downar, Han de Haas, Sonat Sen, Gerhard Strydom, Ramatsemela Mphahlele, Bismark Tyobeka, Volkan Seker, Hans D Gougar: PBMR Coupled Neutronics/Thermal Hydraulics Transient Benchmark - The PBMR-400 Core Design, Benchmark Definition, Draft V03, published by the NEA in 2005.
Material available to participants on CD-ROM
Contact
For more information on WPRS, please contact:
For more information on activities managed/supported by the NSC, please contact:
Last reviewed: 15 June 2011
|
__label__pos
| 0.797415 |
Data Management
Why Virtual Machine Backups Are Different
Date Added: Jan 2012
Format: Webcast
In this webcast, the presenter will explain about the virtualization a software implementation of a computer that acts and appears like a separate physical machine. The presenter also going to explain about the why virtual machine backups are different from others.
|
__label__pos
| 0.970641 |
Reader Level:
Article
Introduction to The Resources .resx and Resources Files: Part I
By Bechir Bejaoui on May 05, 2008
In some cases an application needs some external resources to perform specified tasks. And I mean by external resources, those none executables data logically deployed with a given application.
Introduction
In some cases an application needs some external resources to perform specified tasks. And I mean by external resources, those none executables data logically deployed with a given application. The final purpose by doing so is to prevent recompiling the given application for each time one or more elements are supposed to be necessarily changed according to some environmental exceptions, contexts or external conditions. You tell me OK understood, but the same task or mission is covered by the configuration files. I can say resources files and configuration files exist for the same goal is to prevent recompiling applications, the nature and the mission covered by each kind of file differs in practice, however.
Configuration files "*.config" vs. resource files "*.resource"
The configuration files "*.exe.config" have as a mission giving the developer the ability to control and/ or modify settings inside the application logical environment, among the missions covered by the "*.exe.config" files:
• Define witch assemblies could be consumed by the application core.
• Specify witch runtime version processes.
• Define application settings such as connection strings and other settings.
• Register remote objects
• Define some configuration sections especially used to certain properties assignments
So, each of those elements belongs logically to the internal application environment. In the other hand, the resources files "*.resource" are designed to provide information contained in a tierce parts those belong to the external logical application environment such as bitmaps images, text files, icons and so forth.
Untitled-1.gif
You can save those files types most used as a part of your resources:
Open file as Save file as Description
32-bit .res .rc or 32-bit .res The famous (*.rc) files used in VC++6.0 if you have some backgrounds according to C++ programming, the .rc files are added automatically within a VC++ application as resources files
.bmp or .dib .bmp or .dib Bitmaps image files and device independent bitmap image files
.ico .ico Icon files
.cur .cur A type of specified Icon files used to design cursors
.htm, .html .htm or .html The html files
Resx files vs. resources files
The question now, is why there are two different formats, I mean, resx and resource format or extension to represent the same kind of files, namely, the resource files. And why, for each time, that I use the resx format file, I encounter problems to embed it in a run time executable environment.
Well, for the first question I can say that there is a difference in nature between a (*.resx) and (*.resource) file.
Resx file:
The first one is a kind of structured XML format file, such as the XSD files those used to stock information about datasets elements and structures. It is, normally, used for structuring and organizing data in a given order. Within a resx file you can add, modify or delete given information about resources through the code or even by using a simple text editor if you have a strong background concerning the XML files handling and, of Corse, good knowledge according to the resx files elements and structure. It is possible to use a text file instead of the resx file for the same purpose, but it should be better to use the last one. In addition, it is not a good idea to store sensitive information such as passwords, visa cards data or personal data in a resx file as they can be easily seen by everyone who has access to it.
And this is a resx file example in which I stocked my name and my country in string variables; I give this example to see how such file can look like:
<?xml version="1.0" encoding="utf-8"?>
<root>
<!--
Microsoft ResX Schema Version 2.0
The primary goals of this format is to allow a simple XML format that is mostly human readable. The generation and parsing of the various data types are done through the TypeConverter classes associated with the data types.
Example:
... ado.net/XML headers & schema ...
<resheader name="resmimetype">text/microsoft-resx</resheader>
<resheader name="version">2.0</resheader>
<resheader name="reader">System.Resources.ResXResourceReader, System.Windows.Forms, ...</resheader>
<resheader name="writer">System.Resources.ResXResourceWriter, System.Windows.Forms, ...</resheader>
<data name="Name1"><value>this is my long string</value><comment>this is a comment</comment></data>
<data name="Color1" type="System.Drawing.Color, System.Drawing">Blue</data>
<data name="Bitmap1" mimetype="application/x-microsoft.net.object.binary.base64">
<value>[base64 mime encoded serialized .NET Framework object]</value>
</data>
<data name="Icon1" type="System.Drawing.Icon, System.Drawing" mimetype="application/x-microsoft.net.object.bytearray.base64">
<value>[base64 mime encoded string representing a byte array form of the .NET Framework object]</value>
<comment>This is a comment</comment>
</data>
There are any number of "resheader" rows that contain simple name/value pairs.
Each data row contains a name, and value. The row also contains a type or mimetype. Type corresponds to a .NET class that support text/value conversion through the TypeConverter architecture.Classes that don't support this are serialized and stored with the mimetype set.
The mimetype is used for serialized objects, and tells the ResXResourceReader how to depersist the object. This is currently not extensible. For a given mimetype the value must be set accordingly:
Note - application/x-microsoft.net.object.binary.base64 is the format that the ResXResourceWriter will generate, however the reader can read any of the formats listed below.
mimetype: application/x-microsoft.net.object.binary.base64
value: The object must be serialized with
: System.Runtime.Serialization.Formatters.Binary.BinaryFormatter
: and then encoded with base64 encoding.
mimetype: application/x-microsoft.net.object.soap.base64
value : The object must be serialized with
: System.Runtime.Serialization.Formatters.Soap.SoapFormatter
: and then encoded with base64 encoding.
mimetype: application/x-microsoft.net.object.bytearray.base64
value : The object must be serialized into a byte array
: using a System.ComponentModel.TypeConverter
: and then encoded with base64 encoding.
-->
<xsd:schema id="root" xmlns="" xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:msdata="urn:schemas-microsoft-com:xml-msdata">
<xsd:import namespace="http://www.w3.org/XML/1998/namespace" />
<xsd:element name="root" msdata:IsDataSet="true">
<xsd:complexType>
<xsd:choice maxOccurs="unbounded">
<xsd:element name="metadata">
<xsd:complexType>
<xsd:sequence>
<xsd:element name="value" type="xsd:string" minOccurs="0" />
</xsd:sequence>
<xsd:attribute name="name" use="required" type="xsd:string" />
<xsd:attribute name="type" type="xsd:string" />
<xsd:attribute name="mimetype" type="xsd:string" />
<xsd:attribute ref="xml:space" />
</xsd:complexType>
</xsd:element>
<xsd:element name="assembly">
<xsd:complexType>
<xsd:attribute name="alias" type="xsd:string" />
<xsd:attribute name="name" type="xsd:string" />
</xsd:complexType>
</xsd:element>
<xsd:element name="data">
<xsd:complexType>
<xsd:sequence>
<xsd:element name="value" type="xsd:string" minOccurs="0" msdata:Ordinal="1" />
<xsd:element name="comment" type="xsd:string" minOccurs="0" msdata:Ordinal="2" />
</xsd:sequence>
<xsd:attribute name="name" type="xsd:string" use="required" msdata:Ordinal="1" />
<xsd:attribute name="type" type="xsd:string" msdata:Ordinal="3" />
<xsd:attribute name="mimetype" type="xsd:string" msdata:Ordinal="4" />
<xsd:attribute ref="xml:space" />
</xsd:complexType>
</xsd:element>
<xsd:element name="resheader">
<xsd:complexType>
<xsd:sequence>
<xsd:element name="value" type="xsd:string" minOccurs="0" msdata:Ordinal="1" />
</xsd:sequence>
<xsd:attribute name="name" type="xsd:string" use="required" />
</xsd:complexType>
</xsd:element>
</xsd:choice>
</xsd:complexType>
</xsd:element>
</xsd:schema>
<resheader name="resmimetype">
<value>text/microsoft-resx</value>
</resheader>
<resheader name="version">
<value>2.0</value>
</resheader>
<resheader name="reader">
<value>System.Resources.ResXResourceReader, System.Windows.Forms, Version=2.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089</value>
</resheader>
<resheader name="writer">
<value>System.Resources.ResXResourceWriter, System.Windows.Forms, Version=2.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089</value>
</resheader>
<data name="Name" xml:space="preserve">
<value>Bejaoui Bechir</value>
</data>
<data name="Country" xml:space="preserve">
<value>North Africa</value>
</data>
</root>
You shouldn't be worry about all the content at first glance, as you see, all inserted parameters are located in the bottom of the page and nested within the
<data><value></value></datatags.
<data name="Name" xml:space="preserve">
<value>Bejaoui Bechir</value>
</data>
<data name="Country" xml:space="preserve">
<value>North Africa</value>
</data>
The above elements are described in the table bellow:
Element Description
data The data tag is used to specify the resource attributes.
name(Necessary),
type(Optional but recommended), we should indicate the type it self like System.Int32, the name space such as System, the version, the culture and finally the public key token.
value It is the tag that value is wrapped in
xml: space It is used to identify the document if a white space is considered as important
This attribute accepts two values:
default: This option will treat the white space within a document as something neglected.
preserve:This option will treat the white space within a document as something that has meaning.
Concerning the part just above the first data tag, it's called the header or the resx file header. It provides a detailed description about resources. So, if I try to represent the above resx file, the figure should be as bellow:
The resx file
<?
xml version="1.0" encoding="utf-8"?>
<root>
Contains comments added by Microsoft to explain in adavantage the resx improuvements
<xsd:element 1>
Contains the resources descriptions according to the element1, namely, root in our case
</xsd:element 1>
<xsd:element 2>
Contains the resources descriptions according to the element2, namely, data in our case
<xsd:element 2>
<resheader name="resmimetype"><value>The resource file type</value></resheader>
<resheader name="version"><value>2.0</value></resheader>
<resheader name="reader"><value>resx reader object</value></resheader>
<resheader name="writer"><value>resx writer object</value></resheader>
<data name="Name" xml:space="preserve">
<value>Bejaoui Bechir</value>
</data>
<data name="Country" xml:space="preserve">
<value>North Africa</value>
</data>
</root>
Untitled-2.gif
As a response to the second question, I can say, that a resx file can't be directly embedded in a runtime environment; it has to be converted to a resource file before. Therefore, they are two different resource files formats. And we will talk about how to generate a resource file form a resx file in subsequent articles.
Resource file:
I can define this kind of file as a common language runtime binary file that one can embed within a runtime environment. In order to be used by the application core later. To understand better the approach, I suggest this kind of analogy.
In this case the code source can't used directly except that it will be compiled to (*.exe) or (*.dll) assembly, same think can be said according to the resx and resource file, the resx file represents the code source and the resource file represents the binary file either resource format file or an assembly satellite. We will see in next articles a walkthrough of how to generate assembly satellites from resx and text files and what for.
Bechir Bejaoui
The author holds a master degree in NTIC specialized in software developement delivered by the high school of communication SUPCOM, he also holds a bachelor degree in finance delivered by the economic s... Read more
COMMENT USING
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Mendelian randomization uses genetic variants to make causal inferences about a modifiable exposure. Subject to a genetic variant satisfying the instrumental variable assumptions, an association between the variant and outcome implies a causal effect of the exposure on the outcome. Complications arise with a binary exposure that is a dichotomization of a continuous risk factor (for example, hypertension is a dichotomization of blood pressure). This can lead to violation of the exclusion restriction assumption: the genetic variant can influence the outcome via the continuous risk factor even if the binary exposure does not change. Provided the instrumental variable assumptions are satisfied for the underlying continuous risk factor, causal inferences for the binary exposure are valid for the continuous risk factor. Causal estimates for the binary exposure assume the causal effect is a stepwise function at the point of dichotomization. Even then, estimation requires further parametric assumptions. Under monotonicity, the causal estimate represents the average causal effect in ‘compliers’, individuals for whom the binary exposure would be present if they have the genetic variant and absent otherwise. Unlike in randomized trials, genetic compliers are unlikely to be a large or representative subgroup of the population. Under homogeneity, the causal effect of the exposure on the outcome is assumed constant in all individuals; rarely a plausible assumption. We here provide methods for causal estimation with a binary exposure (although subject to all the above caveats). Mendelian randomization investigations with a dichotomized binary exposure should be conceptualized in terms of an underlying continuous variable.
Additional Metadata
Keywords Causal inference, Effect estimation, Genetic epidemiology, Instrumental variable, Mendelian randomization
Persistent URL dx.doi.org/10.1007/s10654-018-0424-6, hdl.handle.net/1765/109599
Journal European Journal of Epidemiology
Citation
Burgess, S, & Labrecque, J.A. (Jeremy A.). (2018). Mendelian randomization with a binary exposure variable: interpretation and presentation of causal estimates. European Journal of Epidemiology. doi:10.1007/s10654-018-0424-6
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AssignCellColorsFromLUT
VTKExamples/Python/Visualization/AssignCellColorsFromLUT
Description
Demonstrates how to assign colors to cells in a vtkPolyData structure using lookup tables.
Two techniques are demonstrated:
1. Using a lookup table of predefined colors.
2. Using a lookup table generated from a color transfer function.
The resultant display shows in the left-hand column, the cells in a plane colored by the two lookup tables and in the right-hand column, the same polydata that has been read in from a file demonstrating that the structures are identical.
The top row of the display uses the color transfer function to create a green to tan transition in a diverging color space. Note that the central square is white indicating the midpoint.
The bottom row of the display uses a lookup table of predefined colors.
Other Languages
See (Cxx)
Code
AssignCellColorsFromLUT.py
#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
Demonstrates how to assign colors to cells in a vtkPolyData structure using
lookup tables.
Two techniques are demonstrated:
1) Using a lookup table of predefined colors.
2) Using a lookup table generated from a color transfer function.
The resultant display shows in the left-hand column, the cells in a plane
colored by the two lookup tables and in the right-hand column, the same
polydata that has been read in from a file demonstrating that the structures
are identical.
The top row of the display uses the color transfer function to create a
green to tan transition in a diverging color space.
Note that the central square is white indicating the midpoint.
The bottom row of the display uses a lookup table of predefined colors.
"""
from __future__ import print_function
import vtk
def MakeLUT(tableSize):
"""
Make a lookup table from a set of named colors.
:param: tableSize - The table size
:return: The lookup table.
"""
nc = vtk.vtkNamedColors()
lut = vtk.vtkLookupTable()
lut.SetNumberOfTableValues(tableSize)
lut.Build()
# Fill in a few known colors, the rest will be generated if needed
lut.SetTableValue(0, nc.GetColor4d("Black"))
lut.SetTableValue(1, nc.GetColor4d("Banana"))
lut.SetTableValue(2, nc.GetColor4d("Tomato"))
lut.SetTableValue(3, nc.GetColor4d("Wheat"))
lut.SetTableValue(4, nc.GetColor4d("Lavender"))
lut.SetTableValue(5, nc.GetColor4d("Flesh"))
lut.SetTableValue(6, nc.GetColor4d("Raspberry"))
lut.SetTableValue(7, nc.GetColor4d("Salmon"))
lut.SetTableValue(8, nc.GetColor4d("Mint"))
lut.SetTableValue(9, nc.GetColor4d("Peacock"))
return lut
def MakeLUTFromCTF(tableSize):
"""
Use a color transfer Function to generate the colors in the lookup table.
See: http://www.vtk.org/doc/nightly/html/classvtkColorTransferFunction.html
:param: tableSize - The table size
:return: The lookup table.
"""
ctf = vtk.vtkColorTransferFunction()
ctf.SetColorSpaceToDiverging()
# Green to tan.
ctf.AddRGBPoint(0.0, 0.085, 0.532, 0.201)
ctf.AddRGBPoint(0.5, 0.865, 0.865, 0.865)
ctf.AddRGBPoint(1.0, 0.677, 0.492, 0.093)
lut = vtk.vtkLookupTable()
lut.SetNumberOfTableValues(tableSize)
lut.Build()
for i in range(0, tableSize):
rgb = list(ctf.GetColor(float(i) / tableSize)) + [1]
lut.SetTableValue(i, rgb)
return lut
def MakeCellData(tableSize, lut, colors):
"""
Create the cell data using the colors from the lookup table.
:param: tableSize - The table size
:param: lut - The lookup table.
:param: colors - A reference to a vtkUnsignedCharArray().
"""
for i in range(1, tableSize):
rgb = [0.0, 0.0, 0.0]
lut.GetColor(float(i) / (tableSize - 1), rgb)
ucrgb = list(map(int, [x * 255 for x in rgb]))
colors.InsertNextTuple3(ucrgb[0], ucrgb[1], ucrgb[2])
s = '[' + ', '.join(['{:0.6f}'.format(x) for x in rgb]) + ']'
print(s, ucrgb)
def main():
"""
:return: The render window interactor.
"""
nc = vtk.vtkNamedColors()
# Provide some geometry
resolution = 3
plane11 = vtk.vtkPlaneSource()
plane11.SetXResolution(resolution)
plane11.SetYResolution(resolution)
plane12 = vtk.vtkPlaneSource()
plane12.SetXResolution(resolution)
plane12.SetYResolution(resolution)
tableSize = max(resolution * resolution + 1, 10)
# Force an update so we can set cell data
plane11.Update()
plane12.Update()
# Get the lookup tables mapping cell data to colors
lut1 = MakeLUT(tableSize)
lut2 = MakeLUTFromCTF(tableSize)
colorData1 = vtk.vtkUnsignedCharArray()
colorData1.SetName('colors') # Any name will work here.
colorData1.SetNumberOfComponents(3)
print('Using a lookup table from a set of named colors.')
MakeCellData(tableSize, lut1, colorData1)
# Then use SetScalars() to add it to the vtkPolyData structure,
# this will then be interpreted as a color table.
plane11.GetOutput().GetCellData().SetScalars(colorData1)
colorData2 = vtk.vtkUnsignedCharArray()
colorData2.SetName('colors') # Any name will work here.
colorData2.SetNumberOfComponents(3)
print('Using a lookup table created from a color transfer function.')
MakeCellData(tableSize, lut2, colorData2)
plane12.GetOutput().GetCellData().SetScalars(colorData2)
# Set up actor and mapper
mapper11 = vtk.vtkPolyDataMapper()
mapper11.SetInputConnection(plane11.GetOutputPort())
# Now, instead of doing this:
# mapper11.SetScalarRange(0, tableSize - 1)
# mapper11.SetLookupTable(lut1)
# We can just use the color data that we created from the lookup table and
# assigned to the cells:
mapper11.SetScalarModeToUseCellData()
mapper11.Update()
mapper12 = vtk.vtkPolyDataMapper()
mapper12.SetInputConnection(plane12.GetOutputPort())
mapper12.SetScalarModeToUseCellData()
mapper12.Update()
writer = vtk.vtkXMLPolyDataWriter()
writer.SetFileName('pdlut.vtp')
writer.SetInputData(mapper11.GetInput())
# This is set so we can see the data in a text editor.
writer.SetDataModeToAscii()
writer.Write()
writer.SetFileName('pdctf.vtp')
writer.SetInputData(mapper12.GetInput())
writer.Write()
actor11 = vtk.vtkActor()
actor11.SetMapper(mapper11)
actor12 = vtk.vtkActor()
actor12.SetMapper(mapper12)
# Let's read in the data we wrote out.
reader1 = vtk.vtkXMLPolyDataReader()
reader1.SetFileName("pdlut.vtp")
reader2 = vtk.vtkXMLPolyDataReader()
reader2.SetFileName("pdctf.vtp")
mapper21 = vtk.vtkPolyDataMapper()
mapper21.SetInputConnection(reader1.GetOutputPort())
mapper21.SetScalarModeToUseCellData()
mapper21.Update()
actor21 = vtk.vtkActor()
actor21.SetMapper(mapper11)
mapper22 = vtk.vtkPolyDataMapper()
mapper22.SetInputConnection(reader2.GetOutputPort())
mapper22.SetScalarModeToUseCellData()
mapper22.Update()
actor22 = vtk.vtkActor()
actor22.SetMapper(mapper22)
# Define viewport ranges.
# (xmin, ymin, xmax, ymax)
viewport11 = [0.0, 0.0, 0.5, 0.5]
viewport12 = [0.0, 0.5, 0.5, 1.0]
viewport21 = [0.5, 0.0, 1.0, 0.5]
viewport22 = [0.5, 0.5, 1.0, 1.0]
# Set up the renderers.
ren11 = vtk.vtkRenderer()
ren12 = vtk.vtkRenderer()
ren21 = vtk.vtkRenderer()
ren22 = vtk.vtkRenderer()
# Setup the render windows
renWin = vtk.vtkRenderWindow()
renWin.SetSize(800, 800)
renWin.AddRenderer(ren11)
renWin.AddRenderer(ren12)
renWin.AddRenderer(ren21)
renWin.AddRenderer(ren22)
ren11.SetViewport(viewport11)
ren12.SetViewport(viewport12)
ren21.SetViewport(viewport21)
ren22.SetViewport(viewport22)
ren11.SetBackground(nc.GetColor3d('MidnightBlue'))
ren12.SetBackground(nc.GetColor3d('MidnightBlue'))
ren21.SetBackground(nc.GetColor3d('MidnightBlue'))
ren22.SetBackground(nc.GetColor3d('MidnightBlue'))
ren11.AddActor(actor11)
ren12.AddActor(actor12)
ren21.AddActor(actor21)
ren22.AddActor(actor22)
iren = vtk.vtkRenderWindowInteractor()
iren.SetRenderWindow(renWin)
renWin.Render()
return iren
if __name__ == '__main__':
requiredMajorVersion = 6
print(vtk.vtkVersion().GetVTKMajorVersion())
if vtk.vtkVersion().GetVTKMajorVersion() < requiredMajorVersion:
print("You need VTK Version 6 or greater.")
print("The class vtkNamedColors is in VTK version 6 or greater.")
exit(0)
iren = main()
iren.Start()
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start-ver=1.4 cd-journal=joma no-vol=9 cd-vols= no-issue=2 article-no= start-page=75 end-page=81 dt-received= dt-revised= dt-accepted= dt-pub-year=1999 dt-pub=19990226 dt-online= en-article= kn-article= en-subject= kn-subject= en-title=Relative biological effectiveness (RBE) and potential leathal damage repair (PLDR) of heavy-ion beam kn-title=重粒子線の生物学的効果比と潜在性致死損傷からの回復 en-subtitle= kn-subtitle= en-abstract=Relative biological effectiveness (RBE) and repair of potential lethal damage (PLDR) of NIH3T3 cells against heavy-ion radiation were studied. RBE of 150 KV X-rays and neutron estimated from LD(10) dose of dose response survival curves compared to (60)Co γ-ray were 1.26 and 2.44, respectively. RBE of 13, 20, 50, 90, 140, 150, 153, 200 keV/μm of LET of carbon beam were 1.41, 1.47, 2.22, 2.61, 2.61, 1.61, 2.05 and 1.57, respectively. Potential lethal damage repair (PLDR) after exposure to carbon beam was observed. The magnitude of PLDR of (60)Co γ-ray was the biggest. As for the carbon beam of LET of 13 keV/μm as well, PLDR were observed. PLDR decreased when LET of carbon beam grew big. kn-abstract=150KV X線,中性子線及び炭素(LET13, 20, 50, 90, 140, 150, 153, 200keV/μm)を照射したマウスNIH3T3細胞の生存率曲線のLD(10)から(60)Coγ線に対する生物学的効果比(RBE)を求めた｡RBEは150KV X線では1.26,中性子線では2.44,炭素線(LET13, 20, 50, 90, 140, 150, 153, 200keV/μm)ではそれぞれ1.41, 1.47, 2.22, 2.61, 1.61, 2.05, 1.57であった｡LETとRBEの関係では100keV/μm付近にピークを認めた｡150KVX線のLETは13keV/μm,中性子線のLETは70keVμmに相当した｡(60)Co γ線の潜在性致死損傷からの回復(PLDR)は大きかった｡炭素線(13keV/μm)照射でもPLDRが観察されるがLETが大きくなるとPLDRは減少したが,LET90keV/μmの炭素線でもPLDRが認められた｡照射時の細胞状態の検討では増殖期の細胞の感受性は定常期細胞に比し僅かに高かった｡ en-copyright= kn-copyright= en-aut-name=KawasakiShoji en-aut-sei=Kawasaki en-aut-mei=Shoji kn-aut-name=川崎祥二 kn-aut-sei=川崎 kn-aut-mei=祥二 aut-affil-num=1 en-aut-name=ShibuyaKoichi en-aut-sei=Shibuya en-aut-mei=Koichi kn-aut-name=澁谷光一 kn-aut-sei=澁谷 kn-aut-mei=光一 aut-affil-num=2 en-aut-name=AsaumiJunichi en-aut-sei=Asaumi en-aut-mei=Junichi kn-aut-name=浅海淳一 kn-aut-sei=浅海 kn-aut-mei=淳一 aut-affil-num=3 en-aut-name= en-aut-sei= en-aut-mei= kn-aut-name=小松めぐみ kn-aut-sei=小松 kn-aut-mei=めぐみ aut-affil-num=4 en-aut-name=KurodaMasahiro en-aut-sei=Kuroda en-aut-mei=Masahiro kn-aut-name=黒田昌宏 kn-aut-sei=黒田 kn-aut-mei=昌宏 aut-affil-num=5 en-aut-name=HirakiYoshio en-aut-sei=Hiraki en-aut-mei=Yoshio kn-aut-name=平木祥夫 kn-aut-sei=平木 kn-aut-mei=祥夫 aut-affil-num=6 en-aut-name=FurusawaYoshiya en-aut-sei=Furusawa en-aut-mei=Yoshiya kn-aut-name=古澤佳也 kn-aut-sei=古澤 kn-aut-mei=佳也 aut-affil-num=7 affil-num=1 en-affil= kn-affil=岡山大学医学部保健学科放射線技術科学専攻 affil-num=2 en-affil= kn-affil=岡山大学医学部保健学科放射線技術科学専攻 affil-num=3 en-affil= kn-affil=岡山大学歯学部歯科放射線学講座 affil-num=4 en-affil= kn-affil=岡山大学医学部医学科放射線医学講座 affil-num=5 en-affil= kn-affil=岡山大学医学部医学科放射線医学講座 affil-num=6 en-affil= kn-affil=岡山大学医学部医学科放射線医学講座 affil-num=7 en-affil= kn-affil=放射線医学研究所宇宙粒子線研究グループ en-keyword=PLDR kn-keyword=PLDR en-keyword=RBE kn-keyword=RBE en-keyword=Heavy-lon Radiation kn-keyword=Heavy-lon Radiation en-keyword=NIH3T3 Cells kn-keyword=NIH3T3 Cells END
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vibudh is talking
Posts tagged ‘tf()’
Control System: Block Diagrams Reduction using MATLAB
Most of the circuits in Control System today are represented by simple blocks that help us understand the function of each block in a better way. Is also helps the designers to easily make amendments in the circuit for better functionality and testing purpose. But the problem with Block Diagrams is that having blocks and their feedbacks makes the transfer function on the system to tedious to calculate.
Here we are going to study block reduction using MATLAB. The blocks connected in series, parallel and as feedbacks are at times very tedious to compute. MATLAB allows solving of such blocks directly using some functions that is being discussed below with the help of the example. Here we have to calculate C(s)/R(s), that is taken as T(s).
The MATLAB code for the above problem is:
num1 = [1 2];
den1 = [3 1 0];
G1 = tf(num1, den1) %Making G1 as the tranfer function
G2 = tf( [2], [1 7] )
G3 = tf( [1 5], [1 6 3 ] )
G4 = tf( [1], [1 0] )
T1 = parallel(G1, G2) %as G1 and G2 are in parallel
T2 = series(T1, G3) %as T1 and G3 are in series
T = feedback(T2, G4, -1) %as G4 is the negative feedback
Here we use the tf() function to get the transfer function
parallel() and series() functions according to the requirement
and the feedback() function for feedback.
The output for the above code is as follows:
s + 2
———
3 s^2 + s
Transfer function:
2
—–
s + 7
Transfer function:
s + 5
————-
s^2 + 6 s + 3
Transfer function:
1
s
Transfer function:
7 s^2 + 11 s + 14
——————–
3 s^3 + 22 s^2 + 7 s
Transfer function:
7 s^3 + 46 s^2 + 69 s + 70
—————————————–
3 s^5 + 40 s^4 + 148 s^3 + 108 s^2 + 21 s
Transfer function:
7 s^4 + 46 s^3 + 69 s^2 + 70 s
——————————————————-
3 s^6 + 40 s^5 + 148 s^4 + 115 s^3 + 67 s^2 + 69 s + 70
Here we can see that the transfer function for the block diagram is very complex and tedious to deduce. Which can be obtained by using MATLAB very easily.
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getObject
SoftLayer_Dns_Domain_ResourceRecord_SrvType::getObject
Retrieve a SoftLayer_Dns_Domain_ResourceRecord_SrvType record.
Overview
getObject retrieves the SoftLayer_Dns_Domain_ResourceRecord_SrvType object whose ID number corresponds to the ID number of the init parameter passed to the SoftLayer_Dns_Domain_ResourceRecord_SrvType service. You can only retrieve resource records belonging to domains that are assigned to your SoftLayer account.
Parameters
Name Type Description
Required Headers
• SoftLayer_Dns_Domain_ResourceRecord_SrvTypeInitParameters
• authenticate
Optional Headers
• SoftLayer_Dns_Domain_ResourceRecord_SrvTypeObjectMask
• SoftLayer_Dns_Domain_ResourceRecord_SrvTypeObjectFilter
• SoftLayer_ObjectMask
Return Values
Error Handling
• SoftLayer_Exception_ObjectNotFound
Throw the error “Unable to find object with id of {id}.” if the given initialization parameter has an invalid id field.
• SoftLayer_Exception_AccessDenied
Throw the error “Access Denied.” if the given initialization parameter id field is not the account id of the user making the API call.
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Frontline Command Center (FCC), Database, and Keycloak are self-hosted and are considered the central components of the Frontline system environment. All customer-sensitive data is hosted in the self-hosted database and on the VM's local storage.
Installation on an Ubuntu system
Database
1. Install Maria DB following the official installation instructions.
2. Verify the installation with the following command (depending on the actual MariaDB, the service may be called MariaDB or mysqld):
systemctl start mysql
systemctl status mysql
3. Configure the database and corresponding user:
sudo mysql -uroot -e "CREATE DATABASE frontlinecommandcenter CHARACTER SET = 'utf8' COLLATE = utf8_bin;"
sudo mysql -uroot -e "CREATE USER 'frontline'@'localhost' IDENTIFIED BY '$PASS'"
sudo mysql -uroot -e "GRANT ALL ON frontlinecommandcenter.* TO 'frontline'@'localhost' IDENTIFIED BY '$PASS' WITH GRANT OPTION;"
4. Replace the $PASS placeholder with a secure password.
If a suitable database has already been installed and configured before, create a user for this database and change -u root to -u name_of_user -p
Note: We recommend adhering to your internal backup strategy for the installed database.
Frontline Command Center
1. Create a directory for the frontline.jar file: sudo mkdir /var/opt/frontline
2. Create a directory for the user data: sudo mkdir /var/data/frontline
3. Download the Server application JAR file from the Frontline Downloads page.
4. Rename it to frontline.jar and copy it to /var/opt/frontline: sudo cp ~/Downloads/frontline.jar /var/opt/frontline
5. Make frontline.jar executable: sudo chmod +x /var/opt/frontline/frontline.jar
6. Frontline runs as a Spring Boot Service. Navigate to /etc/systemd/system and create a file with the service details: sudo touch frontline.service
7. Edit frontline.service and add:
[Unit]
Description=frontline command center
After=mysql.service
[Service]
Environment="UBIMAX_HOME=/var/data/frontline/"
ExecStart=/var/opt/frontline/frontline.jar
SuccessExitStatus=143
[Install]
WantedBy=multi-user.target
8. To enable the service, use systemctl enable frontline.service
9. Start service via systemctl start frontline.service
10. The service will create some configuration files /var/data/frontline and then shut down.
Installation on a Windows system
Database
1. Download the latest stable version of MariaDB from the official website and follow the installation guide.
2. Run the MariaDB installer, including the HeidiSQL support program.
3. Create a root password for the database.
Note: The root password will be referred to as dbrootpassword in this manual.
4. Click on Next.
5. After finishing the installation, start the HeidiSQL utility. Assuming a default installation, the file is located here: C:\Program Files (x86)\Common Files\MariaDBShared\HeidiSQL\heidisql.exe
6. Click on New.
7. Create a new database with a given name (e.g., Frontline_Test).
8. Replace the $PASS placeholder with your previously created dbrootpassword.
9. Optional: customize the hostname/IP and port number.
Note: For a more detailed guide, please see the HeidiSQL help page.
If a different database system is used, adjust the SQL statement below to fit the database:
CREATE DATABASE FrontlineCommandCenter CHARACTER SET = 'utf8' COLLATE = utf8_bin;
CREATE USER 'frontline'@'%' IDENTIFIED BY '$PASS';
GRANT ALL ON FrontlineCommandCenter.* TO 'frontline'@'%' IDENTIFIED BY '$PASS' WITH GRANT OPTION;
Frontline Command Center
1. Go to the Frontline Downloads page.
2. Download the server application file and rename it to frontline.jar.
3. Download the server service wrapper from the same page.
FCC requires an installation directory and a DATA Directory:
1. Installation Directory - Contains the frontline.jar file and the WinSW_frontline.exe and WinSW_frontline.xml service wrapper files.
1. Location: C:\Frontline
2. ID: $BASE$
2. DATA Directory - This is used as the home directory. It is used for customer assets such as login cards and themes. Create a new folder inside the installation directory and name it DATA.
1. Location: C:\Frontline\DATA
2. ID: $FRONTLINE_HOME$
Note: The $BASE$ and $FRONTLINE_HOME$ location IDs will be used as a reference in the following code samples.
The WinSW_frontline.exe service wrapper allows users to install the FCC service as a Windows service.
1. Optional: If you need to configure a forward proxy (e.g., to let FCC access our license server), open the WinSW_frontline.xml file and add -Dhttps.proxyHost=$HOST -Dhttps.proxyPort=$PORT -Dhttps.nonProxyHosts=localhost to the beginning of the <arguments> element, replacing $HOST and $PORT with the values of your proxy.
2. Open a command prompt (with administrator rights).
3. Change the directory to $BASE$.
4. Run WinSW_frontline.exe install.
5. net start frontline(default service ID is frontline).
During the first startup, the service will automatically stop after extracting the configuration files. Windows may report the service as failed or crashed.
The FCC config directory is located inside the $FRONTLINE_HOME$ directory. The location should be C:\Frontline\DATA\config\configuration\. The xserver.properties configuration file should be edited as explained below.
Initial configuration of Frontline Command Center (Ubuntu and Windows)
1. Open the xserver.properties file located at UBIMAX_HOME/config/configuration/.
2. Change the database IP, username, and password (to view the IP address, use the ip addr show command).
3. If the customer has a host name, xserver.url.external.http can be used instead of the IP address. The port needs to be mentioned in server.port. SSL needs to be configured unless there is a reverse proxy with SSL termination.
Depending on the individual system and requirements, the setup or configuration of components such as Keycloak, xAssist Stack, ffmpeg, Email and FaaS is needed.
FaaS (Mandatory)
1. To use Frontline cloud services, set the following property:
fcc.faas.base-url=https://functions.svc.frontlineworker.com/function/
2. For self-hosting, the endpoint of each FaaS may be overridden individually:
fcc.faas.function.<function>.override-url=
whereas function is imagemagick, pdfmake or proglove
3. For ImageMagick and Proglove, no additional configuration is required.
4. For PDFMake, the following environmental variables need to be set:
RAW_BODY: "true"
MAX_RAW_SIZE: "100mb"
Starting the server
1. After the setup of the properties has been completed, start the server by using this command: systemctl start frontline.service (UBUNTU) or net start frontline (WINDOWS)
2. The state of the service can be checked under UBIMAX_HOME/log/server/fronline.log.
3. On the first successful start of FCC, a system administrator user called sysadmin is created with a random password. This user is used to configure FCC.
4. The password for the sysadmin user can be retrieved from the log files located at$FRONTLINE_HOME\logs.
5. Open the frontline.logfile and the password is displayed in the following format:
INFO de.ubimax.xserver.DatabaseSetupManager - ########################################################## - -:-/-
INFO de.ubimax.xserver.DatabaseSetupManager - ########################################################## - -:-/-
INFO de.ubimax.xserver.DatabaseSetupManager - ########################################################## - -:-/-
INFO de.ubimax.xserver.DatabaseSetupManager - ########################################################## - -:-/-
INFO de.ubimax.xserver.DatabaseSetupManager - YOUR GENERATED SYSADMIN PASSWORD: 123456789 - -:-/-
INFO de.ubimax.xserver.DatabaseSetupManager - CHANGE THIS PASSWORD AS SOON AS POSSIBLE TO A PERSONALIZED ONE. - -:-/-
INFO de.ubimax.xserver.DatabaseSetupManager - ########################################################## - -:-/-
INFO de.ubimax.xserver.DatabaseSetupManager - ########################################################## - -:-/-
INFO de.ubimax.xserver.DatabaseSetupManager - ########################################################## - -:-/-
INFO de.ubimax.xserver.DatabaseSetupManager - #####################################################
6. Sign in using the sysadmin user and change the password.
To import a license:
1. Open Frontline Command Center.
2. Go to Configuration.
3. Go to Licenses.
4. Click on Import License.
5. On the subsequently displayed modal, click on Import License to sync the entry with the license server.
Keycloak (Mandatory)
There are two modes of operation when running Keycloak: standalone mode and clustered mode. Which one to choose depends on your individual requirements. For a detailed guide on how to set up either of them, please see the official Keycloak installation guide. Frontline supports version 15 or later.
After Keycloak has been successfully installed, the realms to be used in this installation need to be created. Each domain for an FCC installation needs to have a separate realm.
1. Download this JSON file.
2. Open the realm export JSON file.
3. Replace all occurrences of <the-fcc-url> with the actual FCC URL.
4. Optional: Replace all occurrences of frontline-realm with another realm name (only applicable, if multiple Frontline realms are required in Keycloak).
5. Optional: Search for "claim.name": "domain" and replace the corresponding domain value (only applicable, if FCC will use a domain other than the default ubimax domain).
6. Sign in to the Keycloak Administration console via the browser.
7. Click on Select Realm.
8. Choose Add realm.
9. Select a file to be imported.
10. Open the imported realm.
11. Navigate to Clients/FCC/Credentials.
12. Click on Regenerate Secret.
13. Copy this value.
14. The copied value needs to be set in the FCC's xserver.properties file as fcc.keycloak.realms.<domain>.clientSecret (<domain> is ubimax by default).
15. Optional: Configure an SMTP server in the email tab of the Realm Settings.
16. Once Keycloak has been configured, the following properties must be set per domain in the FCC's xserver.properties file:
1. All placeholders written in chevrons (<>) must be replaced with the corresponding details.
2. It is intended to set the KeyMan URI to null.
fcc.keycloak.enabled=true
fcc.keycloak.realms.<domain>.name=<realm-name>
fcc.keycloak.realms.<domain>.domainTag=<domain>
fcc.keycloak.realms.<domain>.realmId=<realm-name>
fcc.keycloak.realms.<domain>.serverUrl=<keycloak-external-url>
fcc.keycloak.realms.<domain>.clientId=fcc
fcc.keycloak.realms.<domain>.clientSecret=<client-secret>
fcc.keycloak.keyman.uri=
Note:KeyMan is a service that performs all of the above described steps automatically on Frontline Cloud instances and is not needed for self-hosted Keycloak.
Upload client application
Once the Keycloak is configured an admin user must be created and the client application must be uploaded to the Frontline Command Center.
1. Create a user with an admin role using the steps mentioned on the User Management page.
2. Download the latest Frontline Workplace smart glass application from the Downloads page.
3. On Frontline Command Center on the top left select Navigation Pane.
4. Go to Configuration.
5. Follow the steps mentioned on the Application Management page to upload the application.
IAM integration
For easier user management, Frontline supports the synchronization of user details from your identity provider to FCC. If this mapping is enabled, FCC will process IDP user details and will not allow to override them on the FCC administration level. The synchronized user details are language preferences, roles, license allocation, and teams.
Currently, Frontline supports the following IAM types:
• Microsoft Azure Active Directory
• Microsoft Active Directory
• AWS Identity and Access Management
Roles, licenses, and teams will not be successfully applied in the following cases:
• License, roles, or team do not match 100% in IDP and FCC (case sensitivity applies)
• FCC has no free licenses (for roles and license mapping)
• The user has not yet signed in (syncing only takes place when a user signs in)
The available roles and teams of identity providers must be carefully defined so that roles, licenses, and teams can be successfully mapped:
• <LicenseName> allocates the license for a particular user (e.g., License_xAssist)
• <RoleName> assigns a role to a particular user and assumes a license (e.g., Administrator)
• <Team> assigns a particular user to a team in FCC
Identity brokering (optional)
Note: Identity brokering is only supported on FCC installations where the users are fully present in Keycloak. It only works after all existing users have signed in with Keycloak at least once or on new installations where Keycloak has been enabled right from the beginning.
With identity brokering, Keycloak realms can be connected with external OpenID-based identity providers (IDPs). This means that instead of entering credentials in Keycloak, the user is being redirected to an external IDP (e.g., Azure AD or Okta) and, after successful authentication, is taken back to Keycloak (and then on to Frontline).
The image below shows the basic authentication process whenever a user signs in:
The user will never share their password with FCC but will be redirected to Keycloak and the identity provider that will create an authentication token. By default, Keycloak tries to match the external user with an existing Frontline user via the email address. If that is not possible (if no matching user was found), the sign-in procedure is aborted and access to Frontline is denied.
A Keycloak realm can contain multiple identity brokers (e.g., Azure AD). This adds a possibility to sign in with local accounts as well as different external accounts. In certain scenarios, it might be beneficial to create users on-the-fly once a new user tries to sign in. This is called user provisioning and can be enabled by using the following property in FCC:
fcc.keycloak.user-provisioning.enabled=true
In addition to that, the following properties need to be configured:
server.servlet.session.cookie.same-site=none
server.servlet.session.cookie.secure=true
Doing so will indeed create user accounts upon first sign-in, but the account itself is virtually useless at this point as it neither has a license tier nor any roles assigned. This behavior can be changed via the following properties. The following changes will result in all provisioned users ending up in FCC with the xAssist role from the xAssist license tier assigned.:
fcc.keycloak.user-provisioning.default-license-tiers=xAssist
fcc.keycloak.user-provisioning.default-roles=xAssist
Identity brokering will require some setup on the side of the identity provider you want to use. The below example shows how to configure Azure AD as an identity provider. Other identity providers follow similar approaches.
To configure Azure AD as an identity provider in Keycloak:
1. Select your realm.
2. Go to Identity Providers.
3. Add a new OpenID Connect v1.0 provider.
4. Scroll all the way down to Import External IDP Config.
5. Paste your Discovery URL.
6. Click on Import. This should fill populate fields like Authorization URL or Token URL
7. Manually edit the following values:
1. Alias and Name - These can be set to custom values, the name is the one later shown on the sign-in page, while the alias is found in the redirect URI.
2. ClientAuthMethod - Select client_secret_post.
3. ClientID - Found when creating an app in Azure.
4. ClientSecret - Found when creating an app in Azure.
8. Save the newly added identity provider. Afterwards, it should appear on the single-sign-on page.
Azure AD as identity provider
1. Sign in to Azure.
2. Navigate to App Registrations.
3. Go to New Registration.
4. Name the app Frontline Keycloak.
5. Set it to Single Tenant. The redirect URI is not yet needed.
6. Once the app has been created, it shows the Client ID on the main page.
7. The Discovery URL can be found under Endpoints. It is the OpenID Connect metadata document.
8. Generate the client secret. For this, click on the current client credentials.
9. To add a new client secret, click on New client secret. The description should be Frontline secret and the duration should be set to 24 months
10. Once the secret has been added, an entry with a Value and a Secret ID will be generated.
Note: Immediately copy and securely store the value as it will not be available later, it is the Client Secret.
To configure the missing redirect URI in Azure:
1. Navigate to our App Frontline Keycloak via App registration.
2. Select Redirect URIs
3. Select Add a platform/ Web
4. The Redirect URI that needs to be entered looks like this:
<Local-Keycloak-Url>/auth/realms/<your-realm-name>.
|
__label__pos
| 0.717371 |
linux: fallocate() fixes
[fio.git] / lib / rand.c
CommitLineData
79c94bd3
JA
1/*
2 This is a maximally equidistributed combined Tausworthe generator
3 based on code from GNU Scientific Library 1.5 (30 Jun 2004)
4
5 x_n = (s1_n ^ s2_n ^ s3_n)
6
7 s1_{n+1} = (((s1_n & 4294967294) <<12) ^ (((s1_n <<13) ^ s1_n) >>19))
8 s2_{n+1} = (((s2_n & 4294967288) << 4) ^ (((s2_n << 2) ^ s2_n) >>25))
9 s3_{n+1} = (((s3_n & 4294967280) <<17) ^ (((s3_n << 3) ^ s3_n) >>11))
10
11 The period of this generator is about 2^88.
12
13 From: P. L'Ecuyer, "Maximally Equidistributed Combined Tausworthe
14 Generators", Mathematics of Computation, 65, 213 (1996), 203--213.
15
16 This is available on the net from L'Ecuyer's home page,
17
18 http://www.iro.umontreal.ca/~lecuyer/myftp/papers/tausme.ps
19 ftp://ftp.iro.umontreal.ca/pub/simulation/lecuyer/papers/tausme.ps
20
21 There is an erratum in the paper "Tables of Maximally
22 Equidistributed Combined LFSR Generators", Mathematics of
23 Computation, 68, 225 (1999), 261--269:
24 http://www.iro.umontreal.ca/~lecuyer/myftp/papers/tausme2.ps
25
26 ... the k_j most significant bits of z_j must be non-
27 zero, for each j. (Note: this restriction also applies to the
28 computer code given in [4], but was mistakenly not mentioned in
29 that paper.)
30
31 This affects the seeding procedure by imposing the requirement
32 s1 > 1, s2 > 7, s3 > 15.
33
34*/
35
1fbbf72e 36#include "rand.h"
637ef8d9 37#include "../hash.h"
1fbbf72e 38
1fbbf72e
JA
39static inline int __seed(unsigned int x, unsigned int m)
40{
41 return (x < m) ? x + m : x;
42}
43
2615cc4b
JA
44static void __init_rand(struct frand_state *state, unsigned int seed)
45{
46 int cranks = 6;
47
48#define LCG(x, seed) ((x) * 69069 ^ (seed))
49
50 state->s1 = __seed(LCG((2^31) + (2^17) + (2^7), seed), 1);
51 state->s2 = __seed(LCG(state->s1, seed), 7);
52 state->s3 = __seed(LCG(state->s2, seed), 15);
53
54 while (cranks--)
55 __rand(state);
56}
57
1fbbf72e
JA
58void init_rand(struct frand_state *state)
59{
2615cc4b
JA
60 __init_rand(state, 1);
61}
62
63void init_rand_seed(struct frand_state *state, unsigned int seed)
64{
65 __init_rand(state, seed);
1fbbf72e 66}
637ef8d9 67
7d9fb455 68void __fill_random_buf(void *buf, unsigned int len, unsigned long seed)
637ef8d9 69{
637ef8d9
JA
70 long *ptr = buf;
71
637ef8d9 72 while ((void *) ptr - buf < len) {
7d9fb455 73 *ptr = seed;
637ef8d9 74 ptr++;
7d9fb455
JA
75 seed *= GOLDEN_RATIO_PRIME;
76 seed >>= 3;
637ef8d9
JA
77 }
78}
7d9fb455 79
3545a109
JA
80unsigned long fill_random_buf(struct frand_state *fs, void *buf,
81 unsigned int len)
7d9fb455 82{
3545a109 83 unsigned long r = __rand(fs);
7d9fb455
JA
84
85 if (sizeof(int) != sizeof(long *))
3545a109 86 r *= (unsigned long) __rand(fs);
7d9fb455
JA
87
88 __fill_random_buf(buf, len, r);
89 return r;
90}
|
__label__pos
| 0.936306 |
Your browser does not support JavaScript!
Home of the best Internet Marketing tools
How to speed up a website in 2019: technical checklist
By: Aleksandra Pautaran
January 29th, 2019
Today a man would prefer a bicycle to going on foot, a car to a bicycle, a high-speed train to a car, and a plane to a high-speed train. And I'm pretty sure that if people could take Elon Musk's FALCON 9 rocket to a local supermarket, they definitely would. There's just one fat reason behind all this — SPEED.
Page speed has been a ranking factor for Google's desktop search for years now. But only recently Google introduced a mobile page speed update that officially made page speed a ranking factor for mobile devices.
What's more, page speed is also a core user experience metric. So not working on your page speed can cost you money, rankings, and loyal customers. In fact, according to the latest Google research, 50% of your visitors expect your page to fully load within less than 2 seconds. And searchers that had a negative experience with your mobile page speed-wise are 62% less likely to make a purchase.
If you don't want this to happen, you need to take action now. And the very first step towards improving your page speed is measuring it. And of course, the best way to do it is with the help of our old trusty PageSpeed Insights.
1. New rules for measuring page speed with PageSpeed Insights
2. A checklist for speed optimization
New PageSpeed Insights: What's new?
If you monitor your website's speed regularly, you must have noticed that Google has silently rolled out a new update to its PageSpeed Insights tool. And honestly speaking, the tool has changed a lot. For those who didn't know — the tool no longer supplies you with Speed and Optimization scores like it used to.
Here's what data you can find in the tool's new version:
The speed score
Now you get only one total score that is based on lab data from Lighthouse (a speed tool from Google). According to the Lighthouse's measurements, PageSpeed Insights will mark your page as fast, average, or slow.
Field data
This data is collected from CrUX and includes information about the way Chrome users interact with your page, the devices they use, how long it takes your content to load for them, etc.
The trick is, Google may see your site as slow if the majority of your users have a slow Internet connection or old devices. But on the bright side, your site may seem fast to Google due to your users' fast Internet and better devices.
The best way to see how Google perceives your website is by accessing your CrUX data. It's at your disposal on Google BigQuery (part of the Google Cloud Platform). Here is a nice guide for you on how to get first-hand insights from your real-world visitors.
Lab data
This is the data that the tool collects with the help of Lighthouse. Basically, it simulates the way a mobile device loads a certain page. It incorporates a number of performance metrics such as:
• First Contentful Paint — measures the time it takes for the first visual element to appear for a user.
• Speed Index — measures how quickly the contents of a page are visibly populated.
• Time to Interactive — measures how fast a page becomes fully interactive.
• First Meaningful Paint — measures when the primary content of a page is visible (biggest above-the-fold layout change has happened, and web fonts have loaded).
• First CPU Idle — measures when a page is minimally interactive (most but not all UI elements on the screen are interactive).
• Estimated Input Latency — estimates how long it takes your app to respond to user input, in milliseconds, during the busiest 5s window of page load.
The tool even supplies you with screenshots of how your page is being loaded and viewed during the loading process.
Opportunities
The Opportunities section supplies you with the list of optimization tips for your page. It also shows you the Estimated Savings after fixing or improving this or that parameter.
The thing is, these technical criteria influence lab data parameters that have a direct impact on your overall speed score. Therefore, it's crucial to work on them in the first place.
Diagnostics
Under the Diagnostics section, you'll find some additional information on things like caching, DOM size, payloads, JavaScript, etc.
Passed audits
Last but by no means least, the Passed audits section shows the well-optimized technical parameters that your page has no problems with.
What influences your page speed score the most?
Not so long ago our team has conducted an experiment that intended to figure out the correlation between page speed and pages' positions in mobile SERPs after the update. The main takeaway from the experiment was that the Optimization Score (now Opportunities) is what influences mobile rankings the most.
So far, this hasn't changed at all, and technical optimization still rules organic Google rankings. The only "but" is that there are now 22 factors to optimize for instead of just 9 that we used to have a couple of months ago. The good news is that your page speed score can be significantly boosted as all these parameters are totally fixable and optimizable.
So there's quite an impressive list of what you can do to speed up your page load.
1. Avoid multiple page redirects
2. Properly size images
3. Defer unused CSS
4. Minify CSS
5. Minify JavaScript
6. Efficiently encode images
7. Enable text compression
8. Preload key requests
9. Avoid enormous network payloads
10. Defer offscreen images
11. Reduce server response times (TTFB)
12. Eliminate render-blocking resources
13. Use video formats for animated content
14. Preconnect to required origins
15. Serve images in next-gen formats
16. Ensure text remains visible during webfont load
17. Minimize main-thread work
18. Reduce JavaScript execution time
19. Serve static assets with an efficient cache policy
20. Avoid an excessive DOM size
21. Minimize Critical Requests Depth
22. Measure performance
Please don't be scared by the number of optimization opportunities. Most probably the majority of them are not relevant, and there are 5-6 for you to work on.
So at our next stop, I'll explain in more detail how to optimize every above-mentioned parameter.
Optimization advice
Now that we've outlined areas for improvement, let's see how we can optimize them step by step.
1) Landing page redirects
I guess it goes without saying that getting rid of all unnecessary redirects is one of the most obvious things you can possibly do to your site speed-wise. The thing is, every additional redirect slows down page rendering time as each redirect adds one (if you're lucky) or many (happens more often) HTTP request-response roundtrips.
How to optimize?
• Switch to responsive design
The very first thing Google recommends while dealing with unneeded redirects is switching to responsive design. By doing so, you can avoid unnecessary redirects between desktop, tablet, and mobile versions of your website as well as provide great multi-device experience for your users.
• Pick a suitable redirect type
Of course, the best practice is not using redirects altogether. However, if you desperately need to use one, it's crucial to choose the right redirect type. Surely, it's better to use a 301 redirect for permanent redirection. But if, let’s say, you're willing to redirect users to some short-term promotional pages or device-specific URLs, temporary 302 redirects are the best option.
It's also worth mentioning that Googlebot can now process both HTTP and JavaScript redirection implementations. When it comes to HTTP redirects, they can cause some latency on the server side. However, speaking of JavaScript redirects, please note that some latency may occur on the client side of redirection. This happens because a certain page needs to be downloaded first, then JavaScript should be parsed and executed, and only after that, a redirect will be triggered. One of the possible ways of implementing a JavaScript redirect is by executing the media queries already used by your site in the link annotations on the page with the help of the matchMedia() JavaScript function.
I would like to point out that Google doesn't give any particular recommendations on the matter. So when deciding on a redirection policy, your users need to be taken into consideration first. They just won't be able to see your brilliant content if your redirects are inconsistent or point to the wrong content on the desktop or mobile site. And of course, by minimizing the number of redirects, you can significantly boost your website's speed performance.
2) Image size
Like it or not, but, on average, images account for about 80% of the bytes needed to load one webpage. And since they're responsible for such a high load for an average website, it's important to make sure you don't send huge, oversized images to your users. This actually happens very often, since different devices need images of different sizes to display them properly (usually the smaller the screen, the smaller the image you need). So one of the widely spread "mistakes" is sending big images to smaller devices — and thus if your page contains images that are larger than the version that's rendered on your users' screen, page load time will slow down significantly.
How to optimize?
According to Google's official recommendation, the best practice is to implement so-called "responsive images". Basically, it means that you can generate various versions of every image so that it nicely fits all screen sizes. Surely you can specify which version to use in your HTML or CSS with the help of media queries, viewport dimensions, etc. By the way, here's a good tool that gives you a helping hand with generating images in various sizes.
In a nutshell, when requesting an image, the browser advertises its viewport dimensions and device pixel ratio, while the server takes care of producing correctly sized images in return. Check out these step-by-step instructions on client hints implementation to see how it can be done.
On the other hand, implementing vector-based image formats like SVG is also a nice option to go for. As you may know, SVG images can scale to any size, which makes the format uber-convenient — the images will be resized in real time directly in a browser.
3) Defer unused CSS
Unused CSS can also slow down a browser's construction of the render tree. The thing is, a browser must walk the entire DOM tree and check what CSS rules apply to every node. Therefore, the more unused CSS there is, the more time a browser will need to spend calculating the styles for each node.
How to optimize?
Just before you get down to minifying CSS files, you need to look for some that you no longer need and remove them with no regrets. Remember that the best-optimized resource is the one that is not sent.
After you've cleared out your CSS, it's important to optimize the rest of CSS rules (reduce unnecessary code, split CSS files, reduce whitespace, etc.).
It's also a very good idea to inline critical, small-sized CSS resources directly into the HTML document. This is how you can eliminate extra HTTP requests. But please make sure that you do it only with small CSS files because inlining large CSS can result in slowing down HTML rendering. And finally, to avoid unnecessary duplication, you'd better not inline CSS attributes into HTML tags.
Of course, deferring uncritical CSS can be done manually. However, I would strongly suggest automating this process. Here is a whole selection of tools to help you with that.
4) CSS minification
Reducing CSS files is yet another activity that can win you precious milliseconds. Practice shows that CSS is quite often much larger than necessary. Therefore, you can painlessly minify your CSS without fear of losing anything.
How to optimize?
If you run a small website, which doesn't get updated frequently consider using an online tool like CSSNano for CSS minification. Simply insert the code into the tool and wait for it to provide you with the minified version of your CSS — as simple as that. Such minifiers do a very good job of minimizing the number of bytes. For instance, they can reduce the color value #000000 to just #000, which is a pretty good saving if there are many color values like this.
5) JavaScript minification
Just like CSS, JavaScript resources should be minified as well. What you need to do is have a look at your JavaScript and remove all the redundant data like code comments, unused code, line breaks, and space symbols.
How to optimize?
And just like with CSS minification, the fastest and least painful way to get rid of unneeded data in your code is by using an online minifier. UglifyJS comes highly recommended. On top of that, you can set up a process, which minifies development files and saves them to a production directory every time you deploy a new version.
6) Encoding images
I think it's crystal clear that the smaller your content size is, the less time is required to download the resource. Image optimization is yet another uber important activity that can reduce your total page load size by up to 80%. On top of that, enabling compression reduces data usage for the client as well as minimizes rendering time of your pages.
How to optimize?
Compressing every single image you upload to your site may be a very tiresome process. But more importantly, it's super easy to forget about it. Therefore, it's always better to automate image compression and forget about it for good. So do yourself a huge favor and use imagemin or libvips for your build process. Remember that the smaller in file size your images are, the smoother network experience you are offering to your users – especially on mobile devices.
7) Text compression
Textual content of your website is yet another thing that can increase the byte size of network responses. And as you already know, the fewer bytes are to be downloaded, the faster your page loads.
How to optimize?
Google highly recommends gzipping all the compressible data, and all modern browsers suggest gzip compression for all HTTP requests. Fact is, having resources compressed can cut down the size of the transferred response by up to 90%. To that tune, this will also minimize the time of your pages' first rendering as well as reduce data usage for the client.
So make sure to check out these sample configuration files for most popular servers. After that, find your server on the list, move to the gzip section, and confirm that your server is configured with the recommended settings.
As an alternative to gzip, you can also use Brotli, which is one of the most up-to-date lossless data formats. Unlike the gzip format, Brotli has much better compression characteristics. But there's a catch — the higher the level of compression, the more resources a browser will need to accomplish it. That is why all the size benefits of Brotli will be completely nullified by slow server response time. Therefore, I wouldn't recommend going beyond the 4th level of compression (Brotli has 10 levels of compression) for dynamic assets. However, with static assets that you pre-compress in advance, you can implement the highest level of compression.
8) Preloading key requests
As you know, it's up to browsers to decide what resources to load first. Therefore, they often attempt to load the most important resources such as CSS before scripts and images, for instance. Unfortunately, this isn't always the best way to go. By preloading resources, you can change the priority of content load in modern browsers by letting them know what you’ll need later.
How to optimize?
With the help of the <link rel="preload"> tag, you can inform the browser that a resource is needed as part of the code responsible for rendering the above-the-fold content, and make it fetch the resource as soon as possible.
Here is an example of how the tag can be used:
<link rel="preload" as="script" href="super-important.js">
<link rel="preload" as="style" href="critical.css">
Please note that the resource will be loaded with the same priority. The difference is that the download will start earlier as the browser knows about the preload ahead of time. For more detailed instructions, please consult with this guide on resource prioritization.
9) Enormous network payloads
Reducing the total size of network requests can not only speed up your page, but also save your users' money that they would spend on cellular data.
How to optimize?
There are quite a few ways of reducing the size of payloads. First of all, you need to eliminate unneeded server requests.
After you got rid of all the unnecessary requests, it's only right to make the ones that are left as small as possible. So here are just a small number of resources' minification techniques for you to consider. Think of enabling text and image compression and using WebP format instead of JPEG or PNG. It's also a good idea to cache requests so that resources don't download from scratch on repeat visits. Please refer to this guide on HTTP caching to see how it can be done.
10) Dealing with offscreen images
Offscreen images are the ones that appear below the fold. Because of that, there's simply no need to download them as part of the initial page load. Therefore, it's only right to defer their load in order to improve your page speed as well as time to interactivate.
How to optimize?
Basically, the best strategy to follow is to download above-the-fold images prior to offscreen ones and start downloading below-the-fold images only when a user gets to them. This technique is called lazy loading. With a tool like IntersectionObserver, you can make images load only when a user has scrolled down to them.
11) Improving server response time
When a user navigates to a certain URL to access some content, the browser makes a network request in order to fetch that content. For instance, if users are willing to access their order history, the server will have to fetch every user's history from a database, and then insert that content into the page. Sometimes this process can take too much time. Therefore, optimizing the server response time is one of the possible ways to reduce the time that users spend waiting for pages to load.
How to optimize?
The most unpleasant thing about these response delays is that there is quite a wide selection of reasons that may cause them. For instance, these can be slow routing, slow application logic, resource CPU starvation, slow database queries, memory starvation, slow frameworks, etc.
So keep your fingers firmly on the pulse with these parameters and try to keep the response time under 200ms.
12) Eliminate render-blocking resources
It's highly advisable to leave only the most important external scripts because otherwise, this will add some extra roundtrips to fully render the page.
How to optimize?
If the external scripts are small, you can inline them directly into the HTML document to avoid any extra network requests. Remember that inlining enlarges the size of your HTML document. That's why you should only do it with small scripts. When it comes to non-critical HTML imports, Google recommends to mark them with the async attribute. This will make your scripts load asynchronously with the rest of the page (the script will be executed while the page continues the parsing) and won't influence the overall speed much. But please remember that this should be done only to the scripts that are not required for the initial page loading.
Speaking of stylesheets, it's nice to split up your styles into different files and add a media attribute to each stylesheet link. If you do that, the browser will only block the first paint to retrieve the stylesheets that match a user's device.
13) Using video formats for animated content
Believe it or not, but animated GIFs can take up too much space. That is why to reach our ultimate goal of making your webpages load at the speed of lightning, you need to convert GIF-heavy animation to video.
How to optimize?
The fastest way of converting GIFs to video is with the help of the ffmpeg tool. Once you've installed the tool, simply upload your GIFs to it and choose the video format you're willing to convert them to. It's advisable to pick the MPEG-4 one because it has the broadest support across browsers.
You can also try a relatively new WebM format developed by Google (just like WebP for images). While browser support for WebM isn't as wide as for MPEG-4, it's still very good in terms of its compression characteristics.
And because the <video> element allows you to specify multiple <source> elements, you can do the trick by stating a preference for a WebM source that many browsers can use while falling back to a MPEG-4 source that all other browsers can understand.
14) Preconnecting to required origins
As a rule, establishing connections, especially secure ones, takes a lot of time. The thing is, it requires DNS lookups, SSL handshakes, secret key exchange, and some roundtrips to the final server that is responsible for the user’s request. So in order to save this precious time, you can preconnect to the required origins ahead of time.
How to optimize?
To preconnect your website to some third-party source, you only need to add a link tag to your page. Here's what it looks like:
<link rel="preconnect" href="https://example.com">
After you implement the tag, your website won't need to spend additional time on establishing a connection with the required server, saving your users from waiting for several additional roundtrips.
15) Serving images in next-gen formats
Not all image formats are created equal. The truth is, our old trusty JPEG and PNG formats now have much worse compression and quality characteristics compared to JPEG 2000, JPEG XR, and WebP. So what I'm trying to say is that encoding your images in these formats will make them load faster as well as consume less cellular data.
How to optimize?
Just like with video formats discussed earlier, you need to make sure your images are visible to all your visitors. This can be done by using the <picture> element, which allows you to list multiple, alternative image formats in order of priority. So even if a user's browser doesn't support a certain format, it can move on to the next specified format and display an image properly.
16) Ensuring text visibility during webfont load
All website owners out there want to stand out with their super cool custom fonts. The only bad thing about it is that such fonts may take too long to load. If that's what happens, the browser will replace your font with a fallback one (like Arial or Times New Roman, for instance).
How to optimize?
It's not quite an optimization tip, but if you don't want your content to be displayed improperly, you need to make sure that it looks fine with some basic fallback fonts like Arial or Georgia (especially on mobile devices). After doing so, you can be sure that users can actually read your content, and your page looks appropriate.
17) Minimize main-thread work
When downloading a certain page, your browser simultaneously carries out multiple tasks, such as script parsing and compilation, rendering, HTML and CSS parsing, garbage collection, script evaluation, etc.
How to optimize?
Sometimes it can be quite challenging to get a breakdown of where CPU time was spent loading a page. Luckily, with the help of Lighthouse's new Main Thread Work Breakdown audit feature, you can now clearly see how much and what kind of activity occurs during page load. This will give you an understanding of loading performance issues related to layout, script eval, parsing, or any other activity.
18) Reducing JavaScript execution time
JavaScript is what directly influences your page's load performance. That is why it's crucial to reduce the time for parsing, compiling, and executing JavaScript.
How to optimize?
First and foremost, you should only send code that your users need. Try to remove all the redundant data like code comments and unused code. After that, minify your JavaScript as much as possible and cache it to reduce additional network trips. Advanced developers may prefer to use more tricky techniques like lazy loading, tree shaking for stripping code, or features like V8’s code cache.
19) Implementing a caching policy
When a browser requests a resource, the server that provides the resource can make the browser store it for a certain period of time. So for all repeat visits, the browser will use a local copy instead of fetching it from scratch.
How to optimize?
In order to automatically control how and for how long the individual response can be cached by the browser, use cache-control.
In addition to HTTP caching, determining optimal lifetimes for scripts (max-age), and supplying validation tokens (ETag), don't forget about Service Worker caching, including the above-mentioned V8’s code caching.
20) Avoiding an excessive DOM size
A too large DOM tree with complicated style rules can negatively affect such things as speed, runtime, and memory performance. The best practice is to have a DOM tree, which is less than 1500 nodes total, has a maximum depth of 32 nodes and no parent node with over 60 child nodes.
How to optimize?
A very good practice is to remove the DOM nodes that you don't need anymore. To that tune, consider removing the nodes that are currently not displayed from the loaded document and try to create them only after a user scrolls down a page or hits a button.
21) Minimizing critical requests depth
The Critical Request Chain is part of the Critical Rendering Path (CRP) strategy the core idea of which is prioritizing the loading of certain resources and changing the order in which they load. Even though the Critical Request Chain is meant to download the most important resources, they still can be minified.
How to optimize?
Unfortunately, there's no one-size-fits-all piece of advice on how to minimize critical requests depth exactly for your site (just like for many of the above-listed factors). However, it's always good to minimize your chains' length, reduce the size of downloaded resources, and, as always, defer the download of unnecessary resources.
22) User Timing marks and measures
As I've already mentioned, very often JavaScript issues are the reason behind slow page loads. And very often developers struggle to find the exact weak spot in their JavaScripts. Luckily, with User Timing API, it's no longer a problem. Basically, the main purpose of this service is to measure your app's JavaScript performance so that you know which parts of your scripts lag behind and need optimization.
How to optimize?
All you need to do to measure your app's performance JavaScript-wise is access the results from JavaScript using the API. After you've identified areas for improvement, go ahead and fix them. Here is a nice guide for you to get started with User Timing API.
Conclusion
I know it has been a long article filled with tons of technical stuff. However, I would still strongly recommend taking the technical side of page speed optimization really seriously as so far this is what influences your speed score the most. What's more, you should keep an eye on the real-world measurements from CrUX. Because even if you have a 100-speed score, your webpage may seem slow to users because of bad Internet connection or old devices.
Just as always, I'm looking forward to your feedback in the comment section below. Please share your experience with the new PageSpeed Insights tool as well as with technical optimization. See you there!
By: Aleksandra Pautaran
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The Body: The Complete HIV/AIDS Resource
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One Liver to Love
May 1996
What does my liver have to do with this?
Your liver is a very important organ, especially if you have HIV or AIDS. However, a lot of us don't hear about how important it is until something goes wrong with it. Very often, the doctor will tell you that there is something wrong with your liver by telling you that you have elevated liver enzymes.
What are liver enzymes?
Everybody has liver enzymes. These enzymes help your liver get rid of the waste that is produced in your body. The more waste in your body, the more enzymes your liver needs to produce to get rid of it. Drugs, alcohol, and medications that you take to treat HIV and infections can make your liver work overtime. Diseases like hepatitis can also produce high liver enzymes. Simply put, high liver enzymes mean that your liver is really stressed out.
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Why is this bad?
First of all, if your liver is stressed out, it can make you feel sick. If you're taking a lot of pills and medications for HIV or AIDS, a stressed out liver can make the side effects of these drugs a lot worse. This can be very dangerous.
If your liver is stressed out, it may not be able to absorb the really important drugs you are taking to treat HIV or other diseases. It will also prevent you from absorbing important nutrients your body needs. Your may not be able to take important medications or join a clinical trial if your liver enzymes are elevated.
What will cause my liver to stress out?
Not everyone who has HIV or AIDS has a stressed out liver. However, some people are more likely to have liver problems than others. Following is a list of things that can raise liver enzymes:
• Hepatitis. Hepatitis is an inflammation or infection of the liver. Hepatitis is usually caused by viruses. These viruses include hepatitis A, B, and C. CMV (cytomegalovirus) and Epstein-Barr virus can cause hepatitis. Hepatitis can also be caused by IV drug use and alcohol use.
• Alcohol and IV drug use. These chemicals can cause hepatitis. They can also cause liver enzymes to elevate, putting a large amount of stress on your liver.
• Medications. People with HIV or AIDS may have to take a lot of pills and shots. While these are intended to help you get better, they can also put a lot of stress on your liver. If your liver is really stressed, it won't allow your body to absorb these drugs properly.
How do I know if my liver is stressed out?
Your doctor can perform blood tests to measure the amount of liver enzymes being produced by your liver. These tests are the best way to check if your liver is stressed. However, there are certain physical symptoms that may give you and your doctor hints. Signs include: fever; stomach pains; and yellow coloration of the skin and eyes.
How Can I help my liver?
While you may not be able to take out your liver and send it to Hawaii for a two-week vacation, there are a number of great things you can do to help you liver with stress. If you can lower your enzymes, you will have many more drugs to choose from to fight HIV disease, like protease inhibitors and anitbiotics:
1. Watch your liver enzymes carefully. Keeping them low will make things a lot easier and healthier for you in the long run.
2. Cut down on alcohol and drugs . The liver has a hard enough time as it is without these things making it worse.
3. There are some drugs and nutrients that may help you lower your liver enzymes. Some of them are also good for hepatitis. Ask your doctor or call us at the PWA Health Group to learn more about these products:
Alpha Interferon | Beta Interferon | Ribavirin | 3TC | Thioctic Acid | SSKT | Glycerrhizin | Milk Thistle | NAC | Astragalus | Chickory | Dandelion | Centaury | American | Mandrake | Celandine
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This article was provided by PWA Health Group.
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1
Necesito simular el comportamiento real de una aplicación, lo cual la única manera que tengo de hacerlo es lanzando un programa de selenium con chromedriver. Esto es así, porque necesito navegar por la página simulando un usuario.
Mi duda surge como puedo simular unos 1000 usuarios? Porque lanzar tantos navegadores creo que es inviable por el consumo de memoria RAM.
Espero que alguien me ayude. Gracias
1
¿Con qué tipo de problema se encontró con la necesidad de emular el trabajo de los usuarios a través de la solución Selenium WebDriver?
Si está seguro de que esto no se puede omitir, hay varias opciones para ejecutar desde JMeter el código que realiza la prueba en Selenium Webdriver.
1. Puedes usar WebDrvier Components for Apache JMeter. Para esto:
1.1 Descargar Plugin Managery póngalo en el directorio lib/ext, luego reinicie JMeter. 1.2 Abierta Options - Plugins Manager - Available Plugins y encontrar e instalar Selenium/WebDriver Support.
1.3. Agregar al elemento de configuración del plan de prueba - Chrome (or Firefox\PhantomJS..) Driver Config, y especifique la ruta a WebDriver aquí.
1.4. Poner WDS Sampler a Thread Group.
1.5. Aquí hay un código de muestra dentro de WDS Sampler:
//1a. Start capturing the sampler timing
WDS.sampleResult.sampleStart()
// 2. Perform the Sampler task
WDS.browser.get('http://google.com.au')
// 1b. Stop the sampler timing
WDS.sampleResult.sampleEnd()
// 3. Verify the results
if(WDS.browser.getTitle() != 'Google') {
WDS.sampleResult.setSuccessful(false)
WDS.sampleResult.setResponseMessage('Expected title to be Google')
}
Pero tenga en cuenta que para emular una carga sustancial, necesitará una gran cantidad de PC, como dice la documentación oficial:
From experience, the number of browser (threads) that the reader creates should be limited by the following formula:
C = N + 1
where C = Number of Cores of the host running the test
and N = Number of Browser (threads).
eg, if the current reader's host has 4 cores, the formula would yield:
4 = 3 + 1
meaning that the script should have a MAXIMUM of 3 threads.
Si necesita ejecutar 1000 usuarios simultáneos, verifique el segundo ejemplo.
1. Puede usar Selenium WebDriver para crear y ejecutar pruebas de rendimiento en la cloud servces. Por ejemplo puedes usar RedLine13, mira esto video instruction o vea las instrucciones paso a paso how to run Load test with Selenium in the cloud.
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It's How Medicine Should Be®
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Conditions Treated
The following conditions are some of the most common conditions treated by specialists in this area. These specialists offer expert care for many other related medical problems. If you need care for a condition not listed here, please call (888) 352-RUSH (7874) to find a doctor who can help you.
• An acoustic neuroma is a benign, often slow-growing tumor of the nerve that connects the ear and the brain. Also known as a vestibular schwannoma, the tumor can damage important nerves as it grows. This can affect hearing and balance.
• Arteriovenous Malformation
Arteriovenous malformation (AVM) is an incorrectly formed tangle of arteries and veins. Normally capillaries connect the body’s veins and arteries. In an AVM, the capillaries are missing. This disrupts the body’s normal blood circulation process. AVMs can occur anywhere in the body but are more common in the brain and spine.
• Astrocytoma
Astrocytoma is a glial cell tumor that begins in connective tissue cells called astrocytes. These cells can be found anywhere in the brain or spinal cord. Astrocytomas are a common type of brain tumor in both children and adults.
• The two types of back pain are acute, which typically occurs after a fall, injury or heavy lifting, and chronic, which persists for three months or longer.
• A brain aneurysm, also known as a cerebral aneurysm, occurs when a weak spot in a blood vessel in the brain fills with blood, causing it to balloon or bulge out.
• A brain tumor is an abnormal growth of tissue in the brain. Brain tumors can be cancerous (malignant) or noncancerous (benign).
• The carpal tunnel is a narrow passageway on the inside of the wrist. Carpal tunnel syndrome occurs when the nerve that runs through the passageway is squeezed or compressed by the surrounding tissue.
• A Chiari malformation is a structural defect in the cerebellum, the part of the brain that controls balance.
• Chordoma is a rare cancerous tumor that is most commonly found at the base of the skull or spine.
• Degenerative disc disease is a condition in which the intervertebral discs of the spine begin to deteriorate (or, degenerate) as part of the normal aging process. The intervertebral discs are the cushions between the vertebrae (bones) in the spine. These discs act as shock absorbers in the spine, as well as allow complex motions like twisting.
• Dystonia is a chronic and often progressive neurological disorder that causes muscles to contract involuntarily.
• Epilepsy is a brain disorder in which clusters of nerve cells sometimes signal abnormally, often causing a seizure.
• Failed Back Syndrome
Failed back syndrome, or failed back surgery syndrome, is when a person’s condition does not improve after back or spine surgery. As a result, the person suffers from continued pain and is unable to get effective, lasting relief.
• Glioma
Glioma is a type of brain tumor that starts in the glial tissue of the brain. There are several types of gliomas, categorized by where they are found and the type of cells that originated the tumor, including the following: astrocytoma (which includes glioblastoma), oligodendroglioma, optic nerve glioma and ependymoma.
• A herniated disc occurs when part or all of a disc slips or ruptures between the vertebrae in your spinal column. For this reason, a herniated disc is also known as a “slipped disc” or a “ruptured disc.”
• Hydrocephalus is the buildup of too much fluid in the brain, which creates pressure that can cause permanent brain damage — including physical and mental disabilities.
• Intracerebral Hemorrhage
Intracerebral hemorrhage is when a blood vessel in the brain bursts and blood leaks into the brain, causing extra pressure that can damage brain cells. High blood pressure is the most common cause, but intracerebral hemorrhage can also result from trauma, infection, tumors or blood vessel abnormalities (e.g., arteriovenous malformation).
• Kyphosis
Kyphosis is curving of the spine that eventually leads to a hunchbacked or slouching posture. When it occurs in adolescents, known as Scheuermann’s disease, the cause is the wedging together of several vertebrae. It is mostly found in adults, however, and can result from arthritis, disc degeneration, osteoporosis-related fractures, injury or spondylolisthesis. Certain diseases, including muscular dystrophy, Paget’s disease, spina bifida and polio, can also cause kyphosis.
• Medulloblastoma is a rare, malignant brain tumor most commonly found in people under 25 years old. It is a fast-growing tumor and can metastasize (spread) to other parts of the brain and spine.
• A meningioma is a slow-growing, usually benign tumor that develops in the membranes covering the brain and spinal cord. It can cause damage by pressing against the brain and causing problems with blood circulation.
• Metastatic Brain Cancer
Metastatic brain cancer is cancer that begins in another part of the body and then spreads (metastasizes) to the brain through the blood. Lung, breast and colon cancers frequently metastasize to the brain, as do certain skin cancers. Metastatic brain tumors may be quite aggressive.
• Neuroblastoma is a type of cancer that forms in the nerve tissue of the adrenal gland, neck, chest or spinal cord. It most often affects children under the age of 5 and begins in the adrenal glands, located just above the kidneys.
• Neurofibromatosis type 1 (NF1), also known as von Recklinghausen’s disease, is a genetic disorder of the nervous system that causes tumors to grow along nerves in the skin and nerves of the brain and spinal cord.
• Neurofibromatosis type 2 (NF2) is a genetic disorder that causes noncancerous tumors to grow in the nervous system.
• Parkinson’s disease is a chronic, progressive movement disorder that affects the body’s ability to control movement.
• Pituitary tumors are abnormal growths of tissues (known as neoplasms) that grow in the pituitary gland. The pituitary gland is a small endocrine gland found at the base of your brain.
• Sacroiliac Joint Pain
Sacroiliac joint pain, also known as SI joint pain, is pain caused by damage to the sacroiliac joint, which connects the hip to the spine. It is a common cause of lower back pain.
• Schwannoma is a slow-growing tumor stemming from the cells that protect the nerve fibers. These tumors can grow anywhere along the nerve system and usually not cancerous.
• Sciatica occurs when there is damage to or pressure on the sciatic nerve, which causes nerve pain. The sciatic nerve starts in the low back and runs down the back or side of the leg.
• Scoliosis is a condition in which the spine develops a side-to-side curve in an S- or C-shape. It can occur in both children and adults.
• Sinus and skull base tumors, which can be cancerous or noncancerous (benign), grow in the area behind the eyes and nose that extends to the base of the skull. Even when these tumors are not cancerous, they can still cause problems as they grow and start to press against the brain, vital nerves or major blood vessels.
• Spina bifida is a birth defect that occurs when a baby’s spinal cord does not close completely before birth. It can cause abnormal brain development.
• Spinal stenosis is the narrowing of the spinal canal. This narrowing can put pressure on the spinal cord and/or nerve roots, which can cause numbness, weakness or pain.
• Spinal Tumors
Spinal tumors develop within the spinal column, either on vertebrae or the spinal cord. They can be malignant (cancerous) or benign (noncancerous).
• Spondylolisthesis
Spondylolisthesis is a condition in which a vertebra (bone) in the lumbar spine (lower spine) slips out of place. In children, spondylolisthesis can occur as a result of a birth defect in the lumbar spine or from an acute injury. In adults, spondylolisthesis frequently occurs from abnormal wear on the cartilage and bones, such as from arthritis.
• Spondylolysis
Spondylolysis is a crack in the vertebra (bone) in the lumbar spine (lower spine). Spondylolysis is typically the result of a stress fracture. Spondylolysis is more common among athletes that must hyperextend their lower backs, such as gymnasts, weight lifters or football linemen. If the stress fracture weakens the bone significantly, it can slip forward causing spondylolisthesis.
• A stroke occurs when blood flow to the brain stops due to a clot, causing brain cells to stop receiving oxygen. There are several types of stroke and stroke-related conditions: ischemic stroke, hemorrhagic stroke and transient ischemic attack (TIA).
• Subarachnoid Hemorrhage
Subarachnoid hemorrhage is bleeding in the area between the brain and the tissues surrounding the brain. (This area is called the subarachnoid space.) Most of these hemorrhages are caused by brain aneurysms. The main symptom is a sudden, severe headache.
• Similar to a stroke, a transient ischemic attack (TIA) or “mini-stroke” occurs when blood flow to the brain stops briefly, causing brain cells to stop receiving oxygen.
• Tremor
Tremor is unintentional shaking or trembling that can occur in the hands, arm, head, face, vocal cords, trunk or legs. Common in people who suffer a stroke or have a neuromuscular condition such as Parkinson’s disease, dystonia or multiple sclerosis, tremor can also affect otherwise healthy people.
• Trigeminal neuralgia is a nerve disorder that causes excruciating pain frequently described as a lightning strike or electric shock to the face.
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Exploiting the Overlapping of Higher Order: Entities within Multi-Agent Systems
Exploiting the Overlapping of Higher Order: Entities within Multi-Agent Systems
Hosny A. Abbas (Faculty of Engineering, Assiut University, Assiut, Egypt)
Copyright: © 2014 |Pages: 26
DOI: 10.4018/ijats.2014070102
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Abstract
Currently multi-agent systems (MAS, sometimes MASs) are receiving great attention as a promising approach for modeling, designing, and developing complex, decentralized and large-scale software systems. The captivating characteristics they provide such as decentralization, dynamic reorganization, self-organization, emergence, autonomy, etc., make them a perfect solution for handling current software systems challenges specially their unpredictable and highly changing working environments. Organization-centered MAS (OCMAS) are concerned with the modeling of MAS using higher order abstraction entities than individual agents. Organizational models are the key tool to develop OCMAS; they are currently an important part of most agent-oriented software engineering (AOSE) methodologies. This paper proposes a novel organizational model called NOSHAPE. It exploits the overlapping relationships among higher order abstraction entities such as organizations of agents, worlds of organizations, and even universes of worlds within MAS to realize and utilize their captivating characteristics. The NOSHAPE model is informally and semi-formally described and its applicability is demonstrated with a case study.
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1. Introduction
A MAS is formed by the collection of autonomous agents situated in a certain environment, respond to their environment dynamic changes, interact with other agents, and persist to achieve their own goals or the global system goals. Jennings and Wooldridge (2000) pointed out that considering MAS with no real structure is not suitable for handling current software systems complexity, and higher order abstractions should be used. The same meaning stated by Odell et. al (2003) that the current practice of MAS design tends to be limited to individual agents and small face-to-face groups of agents that operate as closed systems. Our real world getting more complex and highly distributed and that should be reflected in new software engineering paradigms such as MASs. So, the adoption of higher order abstract concepts like organizations, societies, communities, and groups of agents can reduce systems complexity, increase its efficiency, and improve system scalability.
Organizations can be used to limit the scope of interactions, provide strength in numbers, reduce or manage uncertainty, reduce or explicitly increase redundancy or formalize high-level goals which no single agent may be aware of (Horling and Lesser, 2004). Shehory (1998) defined Multi-agent organization as the way in which multiple agents are organized to form a MAS, and he stated that relationships and interactions among the agents and specific roles of agents within the organization are the focus of multi-agent organization. The use of organizations provides a new way for describing the structures and the interactions that take place in MAS. Organizations provide a framework for structuring and managing agents' interactions and serve as a kind of 'tuning' of the agents autonomy level (Hübner, 2009). Representing a MAS as an organization consists of roles which enacted by agents which arranged (statically or dynamically) to form groups of agents, can handle many drawbacks such as system complexity, uncertainty, and system dynamism (Ferber, 2004). The main concern of organizational models is to describe the structural and dynamical aspects of organizations (Ferber, 2005). They have proven to be a useful tool for the analysis and design of multi-agent systems. Furthermore, they provide a framework to manage and engineer organizations, dynamic reorganization, self-organization, emergence, and autonomy within multi-agent systems. Moreover, the underlying organizational model is responsible of how efficiently and effectively organizations carry out their tasks, they have been recently used in agent theory for modeling coordination in open systems and to ensure social order in multi-agent system applications (Van Den Broek, 2006). The adoption of organizational models is now a main concern of most agent-oriented software engineering methodologies. The motivation to this direction is that in open environments, agents must be able to adapt towards the most appropriate organizations according to the environment conditions and their unpredictable changes. As a result, the organizational models should guarantee the ability of organizations to dynamically reorganize as a response to dynamic environment changes.
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| 0.712223 |
Not all IEnumerable<T> are equal
Implementing IEnumerable<T> can turn out to be tricky in certain cases. Consider the following code snippet
namespace Test
{
class Program
{
static void Main(string[] args)
{
Consume(new List<string>() { "a", "b", "c" });
}
static void Consume<T>(IEnumerable<T> stream)
{
T t1 = stream.First();
T t2 = stream.First();
Console.WriteLine(t1.Equals(t2));
}
}
}
As you’d expect, it prints true. Each First() call results in a call to stream.GetEnumerator(), and each such enumerator returns elements from the beginning of the list, so calling First() twice returns the same (first) element. All good so far.
Here’s a tiny class.
class StringGenerator
{
int index;
public string GetNext()
{
return (index++).ToString();
}
}
As you can see, it generates whole numbers as strings. Not very convenient to use though, wouldn’t it be great if we can wrap it and make it enumerable?
static IEnumerable<string> ConvertToEnumerable(StringGenerator g)
{
string item = null;
while ((item = g.GetNext()) != null)
yield return item;
}
ConvertToEnumerable simply loops over the list of items generated and makes use of yield return to make it enumerable.
Great, now what does
Consume(ConvertToEnumerable(new StringGenerator()));
print?
It prints false.
False? FALSE? Can you figure out the reason?
If you’ve read Raymond’s posts on implementation of iterators, you should have figured it out by now. The crux of the problem is that all enumerators returned share the same instance of StringGenerator. Calling First() twice results in two calls to GetNext() on the same StringGenerator instance, and the values returned will obviously be different. To verify that, try creating the StringGenerator instance inside the ConvertToEnumerable function – it will print true now.
This bit me when I wrote code that parsed stuff out of an IEnumerable<string> instance. The actual program read text from a file, so I had a ConvertToEnumerable routine just like the one above, except that it took TextReader as the parameter. The Consume method passed the constructed IEnumerable<T> instance to various methods (say Method1 and Method2), with the assumption that whatever Method1 read off the stream won’t be read again by Method2.
As we saw just now, this works if Consume is passed an IEnumerable<T> constructed like the StringGenerator case. It fails badly if a List<string> is passed instead. Because I wanted the “read elements off the stream” behavior, I called GetEnumerator() once for the passed IEnumerable<T> and then changed the methods called by Consume to take that IEnumerator<T> instead of IEnumerable<T>. That made the code work correctly for both cases.
Moral : Make sure you understand the implications when yield returning items off a shared item source.
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| 0.98421 |
Sum Of Digits
Submissions: 9323 Accuracy:
53.95%
Difficulty: School Marks: 0
*School Problem's Submission isn't counted in score!
Given an integer N. The task is to find sum of all digits of N.
Input:
The first line of input contains an integer T, total number of testcases. Then following T lines contains an integer N.
Output:
For each testcase in a new line, print the sum of digits of N.
Constraints:
1 ≤ T ≤ 30
1 ≤ N ≤ 103
Example:
Input:
2
123
45
Output:
6
9
Explanation:
Testcase 1:
The sum of digits the given number 123: 1 + 2 +3 = 6.
** For More Input/Output Examples Use 'Expected Output' option **
Author: shef5
If you have purchased any course from GeeksforGeeks then please ask your doubt on course discussion forum. You will get quick replies from GFG Moderators there.
Need help with your code? Please use ide.geeksforgeeks.org, generate link and share the link here.
to report an issue on this page.
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| 0.999731 |
c++ – How do I put the current thread to sleep with the ability to resume from another thread in Qt?
Question:
There is a thread that sometimes sleeps ( QThread::sleep ) for quite a long time (about 5 seconds). If the user exits the program, the main thread tries to terminate the sleeping one and waits for it to actually terminate using the QThread::wait function. But 5 seconds is long enough to make the user nervous. In this regard, the question is: how to wake up a thread that has called the QThread::sleep function inside itself?
Answer:
Qt does not provide a means to wake up a sleeping thread. But you can use the QWaitCondition class QWaitCondition with some tweaking. Let's write a special class for this.
WakeableSleep.h:
#ifndef WAKEABLESLEEP_H
#define WAKEABLESLEEP_H
#include <QObject>
#include <QThread>
#include <QMutex>
#include <QWaitCondition>
/**
* @brief Класс, который позволяет временно усыпить поток с возможностью пробуждения из другого потока.
*
* Класс можно создать в любом потоке. При вызове метода \ref sleep поток приостанавливается
* на время, переданное с параметром. При вызове метода \ref wake из другого потока целевой
* поток возобновляет выполнение независимо от истекшего времени.
* \threadsafe
*/
class WakeableSleep : public QObject
{
Q_OBJECT
public:
explicit WakeableSleep(QObject *parent = 0);
/**
* @brief Усыпить текущий поток на milleseconds миллисекунд.
* @param milliseconds Время сна.
*/
void sleep(quint32 milliseconds);
/**
* @brief wake Пробудить целевой поток из другого потока.
*/
void wake();
private:
QMutex mutex;
QWaitCondition waitCondition;
};
#endif // WAKEABLESLEEP_H
WakeableSleep.cpp:
#include "wakeablesleep.h"
WakeableSleep::WakeableSleep(QObject *parent) :
QObject(parent){}
void WakeableSleep::sleep(quint32 milliseconds)
{
mutex.lock();
waitCondition.wait(&mutex, milliseconds);
mutex.unlock();
}
void WakeableSleep::wake()
{
mutex.lock();
waitCondition.wakeAll();
mutex.unlock();
}
Now, instead of the QThread::sleep method, you can use the methods of this class as follows:
WakeableSleep sleeper;
void Thread1()
{
sleeper.wake();
}
void Thread2()
{
sleeper.sleep(5000);
}
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| 0.998552 |
image_pdfimage_print
More than ever, today’s Spinning® participants (and gym-goers in general) require professional help when it comes to flexibility. Thanks to desk jobs, increased work hours, longer commutes, and advancements in technology, many individuals are relatively inactive the other 23 hours outside of the gym. Fewer physical demands and more repetitious actions (like sitting) can lead to muscle imbalances and poor posture, which can cause joint instability and increased movement dysfunction. This means that many individuals may be less capable of handling the stresses that come with Spinning classes and exercise in general, making the need to stretch before Spinning class a key component in decreasing these dysfunctions and the risk for injury. In fact, flexibility training may decrease the occurrences of low back pain, joint pain, and overuse injuries (1-4).For these reasons, stretching should not be underestimated as a necessary component of your overall fitness routine.
What is Flexibility?
Flexibility is defined as the normal extensibility of all soft tissue that allows for optimal range of motion of a joint (5). Simply stated, if a person is flexible, their tissues are extensible enough to allow for each joint to move as it is intended to move without limitation, compensation, or impediments. With that said, extensibility alone does not make a person flexible. The ability to control motion—termed motor control—is just as important. Optimal range of motion coupled with the nervous system’s ability to control that range of motion makes up proper movement.
The Science behind Flexibility
In order to achieve optimal extensibility, it’s important to understand how basic muscle physiology plays a role in stretching techniques. Muscles, tendons, ligaments, and joint capsules contain small sensory receptors called mechanoreceptors that send messages from the source to the nervous system to detect any distortion in soft tissues, such as stretch, touch, and pressure (6). Two important mechanoreceptors to understand when it comes to flexibility are muscle spindles and the Golgi tendon organs.
Muscle spindles are major sensory organs of the muscles and are sensitive to changes in length and the rate of length change (Figure 1). If a muscle is stretched too fast and/or too far, these sensory organs are also stretched and stimulated. When stimulated, a signal is sent to the brain telling the brain to contract the muscle, helping to protect the muscle from injury (7).
The Golgi tendon organs (GTO) are mechanoreceptors that reside in the musculotendinous junction (where the muscle and tendon come together) (Figure 2). These mechanoreceptors are sensitive to changes in muscular tension and the rate of tension change. Unlike the muscle spindles, when the GTOs are stimulated, they cause the muscle to relax, decreasing tension in the muscle in order to protect the muscle from injury (7).
When stretching a muscle, the muscle spindles are initially stimulated to help protect the muscle from stretching too far, causing the muscle to contract. This can be experienced when feeling an initial “tightness” when initiating the stretch. As the stretch is held, more tension is created, stimulating the GTO, which then overrides the muscle spindles, causing the muscle to relax (termed the autogenic inhibition reflex) (6). At this point, the “tightness” first experienced when engaging in the stretch becomes less, allowing the joint to be placed in a new position to further stretch the muscle. Overtime, this can lead to permanent changes to the muscle and the associated tissues, resulting in tissues that are more extensible. Because the autogenic inhibition reflex is activated through the development tension, it becomes important that stretches are held for a specific period of time (20-60 seconds) (6) so enough tension is created to stimulate the reflex. This important for Spinning instructors to consider when it comes to applying stretches at the end of class, as many may only hold the stretch for a few seconds before going to the next stretch. This results in individuals not getting the most out of the stretch.
Practical Application
If time is short, but you want to apply a full 20-60 seconds for each stretch at the end of your Spinning class, there are three key muscles to focus on. These groups include the calves (gastrocnemius/soleus) (Figure 3), hip flexors (specifically the rectus femoris) (Figure 4) and pectoral (chest) muscles (Figure 5). These muscles are key areas to address because of the body’s posture on the bike and their usage during a Spinning class. They are also important because tightness in these muscle groups can affect the range of motion of multiple joints. The calf musculature (specifically the gastrocnemius) crosses both the ankle and knee joint. If it is tight, it can not only reduce the range of motion of the ankle, but the knee as well. The rectus femoris (a hip flexor that is also considered part of the quadriceps group) crosses both the knee and hip joint. If it is tight, it can negatively affect the range of motion of both the hip and knee. Due to the riders’ body positioning while on the bike (forward flexed position), the pectoral muscles can also become tight, resulting in a limited range of motion in the shoulder complex. Stretching these three regions will help to address the main joints of the body that can lead to pain and injury if range of motion is limited.
Stretching can be as important as the ride itself and should not be neglected in a Spinning class. However, proper application of these stretches must be applied to ensure riders get the most out of there stretches. Make sure to hold stretches between 20-60 seconds to allow for optimal relaxation of the muscle. If time is an issue, key muscles to stretch would include the calves, hip flexors and pectorals. The pectoral stretch can be performed on the bike, while the lower body stretches being performed off the bike.
This article was contributed by Scott Lucett, MS of Education – Mad Dogg Athletics.References
References:
1. Witvrouw, E., Bellemans, J., Lysens, R., et al. (2001). Intrinsic risk factors for the development of patellar tendonitis in an athletic population. A two-year prospective study. American Journal of Sports Medicine, 29(2), 190-195.
2. Cibulka, M.T, Sinacore, D.R, Cromer, G.S & Delitto, A. (1998). Unilateral hip rotation range of motion assymetry in patients with sacroiliac joint regional pain. Spine,23(9), 1009-1015.
3. Witvrouw, E., Danneels, L., Asselman, P., D’Have, T., & Cambier, D. (2003). Muscle flexibility as a risk factor for developing muscle injuries in male professional soccer players. A prospective study. American Journal of Sports Medicine,31(1), 41-46.
4. Knapik, J.J., Bauman, C.L., Jones, B.H., et al. (1991). Preseason strength and flexibility imbalances associated with athletic injuries in female collegiate athletes. American Journal of Sports Medicine,19(1), 76-81.
5. Alter, M.J. (1996). Scienc of flexibility (2nd ed.). Champaign, IL: Human Kinetics.
6. Enoka, R.M. (1994). Neuromuscular basis of kinesiology (2nd ed.). Champaign, IL: Human Kinetics.
7. Cohen H. (1999) Neuroscience for rehabilitation (2nd ed.). Philadelphia, PA: Lippincott Williams & Wilkins.
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|
__label__pos
| 0.830325 |
856. Score of Parentheses
Given a balanced parentheses string S, compute the score of the string based on the following rule:
• () has score 1
• AB has score A + B, where A and B are balanced parentheses strings.
• (A) has score 2 * A, where A is a balanced parentheses string.
Example 1:
Input: "()"
Output: 1
Example 2:
Input: "(())"
Output: 2
Example 3:
Input: "()()"
Output: 2
Example 4:
Input: "(()(()))"
Output: 6
Note:
1. S is a balanced parentheses string, containing only ( and ).
2. 2 <= S.length <= 50
Rust Solution
struct Solution;
impl Solution {
fn score_of_parentheses(s: String) -> i32 {
let mut stack: Vec<i32> = vec![];
for c in s.chars() {
if c == '(' {
stack.push(0);
} else {
let mut sum = 0;
while let Some(last) = stack.pop() {
if last != 0 {
sum += last;
} else {
break;
}
}
if sum == 0 {
stack.push(1);
} else {
stack.push(2 * sum);
}
}
}
stack.iter().sum()
}
}
#[test]
fn test() {
let s = "()".to_string();
let res = 1;
assert_eq!(Solution::score_of_parentheses(s), res);
let s = "(())".to_string();
let res = 2;
assert_eq!(Solution::score_of_parentheses(s), res);
let s = "()()".to_string();
let res = 2;
assert_eq!(Solution::score_of_parentheses(s), res);
let s = "(()(()))".to_string();
let res = 6;
assert_eq!(Solution::score_of_parentheses(s), res);
}
Having problems with this solution? Click here to submit an issue on github.
|
__label__pos
| 1 |
Advanced Search
Li Xin, Lin Dongdai, Xu Lin. A High Efficient Boolean Polynomial Representation[J]. Journal of Computer Research and Development, 2012, 49(12): 2568-2574.
Citation: Li Xin, Lin Dongdai, Xu Lin. A High Efficient Boolean Polynomial Representation[J]. Journal of Computer Research and Development, 2012, 49(12): 2568-2574.
A High Efficient Boolean Polynomial Representation
• Solving Boolean equations for cryptanalysis has important practical significance. However, the contradiction of limited computer storage space and solving demand growth of existing algorithms is the major bottleneck for getting more progresses. This paper presents a high efficient Boolean polynomial representation, BanYan. BanYan is designed for Boolean equations solving algorithms based on leading-term eliminating, such as F4,F5,XLs.The essence of BanYan is that it only stores the information about how to generate intermediate polynomials, but not the intermediate polynomials themselves. The original polynomials in the polynomial ring for Grnbner bases computation are called root polynomials. The new generated polynomials come from root polynomials by terms multiplication and polynomials addition. So we only store the corresponding terms and polynomials connected with the root polynomials. As the intermediate polynomials grow, the whole storage structure is getting just like a tree. That is why we call this method BanYan. Although the scale of intermediate polynomials grows exponentially in the process of Grnbner bases computation, the generation information is becoming much more simpler, so BanYan can greatly reduce the space requirement and then improve the solving ability. Analysis and experiments show that compared with traditional representations based on terms, in average case and worst case the space requirement of BanYan has l-fold reduction. Here l is the average length of intermediate polynomials.
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|
__label__pos
| 0.929694 |
Adn - cracking the genetic code
Solo disponible en BuenasTareas
• Páginas : 6 (1436 palabras )
• Descarga(s) : 7
• Publicado : 28 de junio de 2010
Leer documento completo
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Classic Experiment
4.1
CRACKING THE GENETIC CODE
B
y the early 1960s molecular biologists had adopted the so-called “central dogma,” which states that DNA directs synthesis of RNA (transcription),
which then directs assembly of proteins (translation). However, researchers still did not completely understand how the “code” embodied in DNA and subsequently in RNA directs proteinsynthesis. To elucidate this process, Marshall Nirenberg embarked upon a series of studies that would lead to solution of the genetic code.
Background
Proteins are made from combinations of 20 different amino acids. The genes that encode proteins—that is, specify the type and linear order of their component amino acids—are located in DNA, a polymer made up of only four different nucleotides. TheDNA code is transcribed into RNA, which is also composed of four nucleotides. Nirenberg’s studies were premised on the hypothesis that the nucleotides in RNA form “codewords,” each of which corresponds to one of the amino acids found in protein. During protein synthesis, these codewords are translated into a functional protein. Thus, to understand how DNA directs protein synthesis, Nirenberg setout to understand the relationship between RNA codewords and protein synthesis. At the outset of his studies, much was already known about the process of protein synthesis, which occurs on ribosomes. These large ribonuleoprotein complexes can bind two different types of RNA: messenger RNA (mRNA), which carries the exact protein-specifying code from DNA to ribosomes, and smaller RNA molecules nowknown as transfer RNA (tRNA), which deliver amino acids to ribosomes. tRNAs exist in two forms: those that are covalently attached to a single amino acid, known as amino-acylated or “charged” tRNAs, and those that have no amino acid attached called “uncharged” tRNAs. After binding of the mRNA and the amino-acylated tRNA to
the ribosome, a peptide bond forms between the amino acids, beginningprotein synthesis. The nascent protein chain is elongated by the subsequent binding of additional tRNAs and formation of a peptide bond between the incoming amino acid and the end of the growing chain. Although this general process was understood, the question remained: How does the mRNA direct protein synthesis? When attempting to address complex processes such as protein synthesis, scientists dividelarge questions into a series of smaller, more easily addressed questions. Prior to Nirenberg’s study, it had been shown that when phenylalanie charged tRNA was incubated with ribosomes and polyuridylic acid (polyU), peptides consisting of only phenylalanine were produced. This finding suggested that the mRNA codeword, or codon, for phenylalanine is made up of the nucleosides containing the baseuracil. Similar studies with polycytadylic acid (polyrC) and polyadenylic acid (polyrA) showed these nucleosides containing the bases cytadine and adenine made up the codons for proline and lysine, respectively. With this knowledge in hand, Nirenberg asked the question: What is the minimum chain length required for tRNA binding to ribosomes? The system he developed to answer this question wouldgive him the means to determine which aminoacylated tRNA would bind which m-RNA codon, effectively cracking the genetic code.
The Experiment
The first step in determining the minimum length of mRNA required for tRNA recognition was to develop an assay that would detect this interaction. Since previous studies had shown that ribosomes bind mRNA and tRNA simultaneously, Nirenberg reasoned thatribosomes could be used as a bridge between a known mRNA codon and a known tRNA. When the three components of protein synthesis are incubated together in vitro, they should form a complex. After devising a method to detect this complex, Nirenberg could then alter the size of the mRNA to determine the minimum chain length required for tRNA recognition. Before he could begin his experiment, Nirenberg...
tracking img
|
__label__pos
| 0.963677 |
Short-term exposures to PM2.5 and cause-specific mortality of cardiovascular health in China
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Abstract
Background:Many multi-center epidemiological studies have robustly examined the acute health effects of exposure to low concentrations of fine particulate matter (PM2.5) on cardiovascular mortality in developed counties. However, data limitations have resulted in few related studies being conducted in developing counties with high levels of PM2.5 exposure. In recent years, people in China with a heavy cardiovascular disease burden have been exposed to particularly high levels of PM2.5.Objective:We conducted a multi-county time series study investigating the acute effects of PM2.5 on the increased risk of cardiovascular death across China, and explored subpopulations susceptible to PM2.5 exposure.Methods:Appling a county-specific Poisson regression in 30 Chinese counties, we estimated PM2.5 effects on all-cause mortality and cause-specific mortality of cardiovascular health for 2013–2015. We also considered PM2.5 effects on several subpopulations, including males, females, and three age groups (< 65, 65–74 and > 74 years old). We pooled the county-specific results across China using a random effects meta-analysis by cause and by subpopulation.Results:We found a 0.13% (95% confidence interval (CI), 0.04–0.22) increase in all-cause mortality, a 0.12% increase (95% CI, 0.001–0.25) increase in cardiovascular disease (CVD), a 0.42% (95% CI, 0.03–0.81) increase in AMI, a 0.17% (95% CI, −0.04–0.40) increase in coronary heart disease, and a 0.13% (95% CI, −0.12–0.33) increase in stroke in association with a 10-μg/m3 increase in PM2.5 concentrations on the same day. The magnitudes of the associations were less than those reported in developed counties with lower PM2.5 levels. A vulnerable effect on all-cause mortality was observed in the elderly population (older than 65 years) and on CVD in males.Conclusions:This study showed the positive magnitude of PM2.5 effects with high exposure on all natural, CVD, and cause-specific mortality and on the susceptible populations in China. The findings complemented evidence related to exposure-mortality relationships at the higher end of short-term exposure to PM2.5 on a global scale.HIGHLIGHTSExploring the association between PM2.5 and cardiovascular mortality in China.Suggesting that people 65–74 years old and males might be more vulnerable to PM2.5.Showing the difference of PM2.5 acute effect between developed countries and China.
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__label__pos
| 0.992805 |
Custom Objects within an Array explanation
This topic contains 2 replies, has 3 voices, and was last updated by Rob Simmers 8 months ago.
• Author
Posts
• #64653
Brian Clanton
Participant
I read this article in Powershell online magazine and I am having a hard time getting my mind wrapped around it as to what it means.
It gives the following example code:
$groups = 'Group1', 'Group2'
$users = 'User1', 'User2'
$objectCollection=@()
$object = New-Object PSObject
Add-Member -InputObject $object -MemberType NoteProperty -Name Group -Value ""
Add-Member -InputObject $object -MemberType NoteProperty -Name User -Value ""
$groups | ForEach-Object {
$groupCurrent = $_
$users | ForEach-Object {
$userCurrent = $_
$object.Group = $groupCurrent
$object.User = $userCurrent
$objectCollection += $object
}
}
$objectCollection
It shows the output as this:
Group User
----- ----
Group2 User2
Group2 User2
Group2 User2
Group2 User2
It then explains why we are getting this output. The is the paragraph I am having a problem understanding as well as the link to the article.
We assign the information to the object and add it to the collection, but we still use the same object. When we added it to the collection we added just a 'reference' to the object, not the object itself. What we ended up with was just four 'shortcuts' to the same object.
From
I don't understand they mean by 'reference to the object and not the object itself. When you are using the using the statement,
$object.Group = $groupCurrent and $object.User = $userCurrent, are you not adding those values to that object? I don't understand what they mean by 'reference'.
• #64771
Don Jones
Keymaster
This gets into some fairly esoteric programming concepts, specifically, ByValue and ByReference.
When you assign something ByValue, you're passing the _contents of whatever it is_. So if I have $a=4, and I set $b=$a ByValue, I can then set $a=5 but $b will still be 4.
Conversely, setting something ByReference just passes a _reference_ to, basically, the same memory location. So if $a=4 and I set $b=$a, changing $a=5 will also set $b to 5, because $a and $b are really both pointers to the same memory location.
Add-Member works that way with its -InputObject parameter. It doesn't create a new object having whatever properties you added; it adds the property to the original copy, so whatever variable was referencing that copy ($object in this case) will now reference the updated object.
• #64803
Rob Simmers
Participant
As a side note, that is an old example of creating an object in Powershell and the results that you posted are incorrect (not the intention of the code or example, I'm guessing). This should be much easier to implement and read:
$groups = 'Group1', 'Group2'
$users = 'User1', 'User2'
#Collect all results from the for loops and place them in $objectCollection
$objectCollection = foreach ($group in $groups) {
foreach ($user in $users) {
New-Object -TypeName PSObject -Property @{
Group = $group
User = $user
}
}
}
$objectCollection
Output:
User Group
---- -----
User1 Group1
User2 Group1
User1 Group2
User2 Group2
You must be logged in to reply to this topic.
|
__label__pos
| 0.966171 |
What Happens If You Have Metal In Your Body During An Mri?
In MRI, the presence of metal can be a serious problem. This is because (1) magnetic metals can exert force on the scanner , and (2) long wires (such as pacemakers) can cause induced currents and heating. From the RF magnetic field and (3) the metal makes the static magnetic field (B0) non-uniform, causing serious
Can You Have An Mri With Invisalign Attachments?
The answer is “yes”. It is completely safe to get an MRI with curly braces . A small amount of metal in your mouth from a bracket or wire will not adversely affect your health. The only potential problem with braces that interfere with MRI is related to image distortion.
Should I Remove My Permanent Retainer?
Since the retainer is mounted in the mouth, patients are less likely to lose the retainer and do not have to worry about maintaining a tooth injury or straight smile during sports. However, permanent holders are out of date and must be changed or deleted at least once in lifetime .
How Long Should A Permanent Retainer Last?
Permanent holders are not really permanent. Unlike removable retainers, they are only called “permanents” because they are not easily removable. Permanent holders eventually wear out, but they are known to last longer. If worn, it can be removed and replaced.
Can I Get An Mri With Braces?
Fortunately, the curly braces do not interfere with the use of MRI . A small amount of metal for orthodontics does not adversely affect the MRI and can be scanned, but it can cause some problems.
Do Teeth Fillings Affect Mri?
After all, MRI stands for Magnetic Resonance Imaging. Some dental fillings contain metal, which seems to cause problems with the machine. After all, magnets can move metal objects. In fact, dental fillers, even those made of metal, are as safe as non-metal materials and you don’t have to worry .
Will An Mri Rip Metal Out Of Your Body?
MRI uses very strong magnets, so the body or metals in the body can be affected . Therefore, be sure to tell the scheduler and technician about the devices, metals, or debris in your body. It is safe to continue the MRI examination.
What Looks Like Mouse Poop But Isn T?
READ
Is Titanium A Magnetic Mri?
Titanium is a paramagnetic material that is not affected by the magnetic field of MRI . The risk of implant-based complications is very low and MRI is safe to use for patients using implants.
Can You Wear Airpods During An Mri?
This is normal. Earplugs and headphones should be provided to reduce noise . You may also be able to listen to music on your headphones to make your MRI scan more enjoyable.
How Much Does It Cost To Have A Permanent Retainer Removed?
Permanent retainer removal costs range from $ 150 to $ 500 (this includes repair and replacement costs if the permanent retainer is damaged on one side).
Can A Dentist Remove A Permanent Retainer?
Do I need to remove the fixed retainer? The name may suggest something else, but permanent holders can actually be removed . The dentist or orthodontist removes the adhesive cement with a dental drill, removes the retainer, and then cleans and brushes the teeth.
Can Teeth Move With Permanent Retainer?
If not repaired or replaced immediately, the teeth will shift and move . Fixed retainers are made of various metal alloys. Like all stressed metals, it can stretch over time. If the retainer stretches some space, small movements can occur.
Can Permanent Retainers Cause Gum Recession?
CONCLUSIONS: Orthodontic treatment and fixed retainers were associated with an increased incidence of gingival recession , increased plaque retention, and increased bleeding during probing. However, the magnitude of the difference in recession had low clinical significance.
Do Permanent Retainers Cause Cavities?
Fixed retainers can also make brushing and dental floss more difficult. If you do not polish or floss the permanent retainer, you may have tooth decay or periodontal disease . Regularly remove tartar buildup with your dentist to prevent tooth decay and periodontal disease.
How Do I Get Plaque Off My Permanent Retainer?
Brushing helps remove plaque and bacteria that grow around the appliances and behind the teeth . All you need to do is use a soft bristle toothbrush and fluoride toothpaste and pay special attention to the area around the appliance.
What Happens If You Wear A Ring During An Mri?
Throw away all the jewels. Loose metal objects can be injured during MRI if pulled towards a very strong MRI magnet . This means that all gems must come off, not just what you can see, and this includes the navel or tolling.
Can Acrylic Be Washed In The Washing Machine?
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Can You Put On Deodorant For An Mri?
Can you put on a deodorant for MRI? Do not wear powders, perfumes, deodorants or lotions on your armpits or chest before the procedure . Since MRI is a magnet, please let us know if there is any metal in your body or body.
Has Anyone Died In An Mri Machine?
MRI scans have been widely used since the early 1980s, with tens of millions of scans worldwide each year. Death like a circle is very rare . There was only one previous event in the United States where a 6-year-old boy was killed after an oxygen cylinder attracted by a magnet collided with a skull in 2001.
Can You Wear A Nose Ring In An Mri?
All iron metal (ie stainless steel) must be removed before entering the MRI examination room . If you’re not sure if your jewelry contains iron metal, you can use a magnet at home and test it yourself. When the magnet attempts to “grab” the gem, it cannot enter the examination room.
Can Stainless Steel Go In Mri?
Projectile or missile effects: Iron-based materials, nickel alloys, and most stainless steel materials are not compatible with the MRI environment . When these materials are exposed to strong magnetic fields, they can be pulled violently towards the magnetic source.
Is Tungsten Mri Safe?
Is Tungsten MRI Safe? Tungsten is biocompatible and compatible with both X-ray and MRI . Tungsten has a low magnetic susceptibility index and can affect images produced by X-rays or MRI only if the jewelery is worn near the image area.
What’S The Best Drug For Claustrophobia In A Mri?
Tell your doctor if you are very claustrophobic or have previous experience not tolerating MRI scans. Doctors can prescribe sedatives like Ativan .
Can You Wear Bra In Mri?
For women, if possible, do not wear wire bras (metals can emit magnetic fields). Sports bras are usually good and there are hospital gowns that can be replaced as needed. The clasp on the back of a regular bra is fine, but avoid wearing a bra that has metal parts on the straps.
How To Wash Ikea Down Comforter
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Can You Cough During An Mri?
If you have a cough or cold, consider taking a cough suppressant or decongestant before visiting. You can be careful not to cough or move during the scan. This includes scratching the itching that occurs. If you move in any way during the scan, you may need to restart the scan from the beginning.
Does Insurance Cover Permanent Retainer Repair?
Your orthodontist’s office can check your insurance coverage and provide you with details. Nevertheless, even though your dental insurance covers some of your first set of retainers, it usually does not cover the cost of replacing or repairing the retainers .
Do Orthodontic Retainer Wires Interact With Magnetic Resonance Imaging (Mri)?
Magnetic Field Interactions of Orthodontic Wires in Magnetic Resonance Imaging (MRI) at 1.5 Tesla All retainer wires and steel archwires (with the exception of noninium archwires) have significant rotational force and translation within the magnetic field of the MRI system. I received power. pubmed.ncbi.nlm.nih.gov/16044226/ Orthodontic Wire Interactions Under Search: Do Orthodontic Retainer Wires Interact with Magnetic Resonance Imaging (MRI)?
Are Permanent Or Removable Retainers Better For Long-Term Orthodontics?
Orthodontists often use a combination of both removable and permanent retainers for best long-term results. However, according to a recent orthodontist survey, permanent cages are becoming more and more popular. Permanent cage: strengths, weaknesses, costs, and pairs. Removablewww.healthline.com/health/permanent-retainer Search: Are permanents or removable retainers suitable for long-term orthodontics?
Does The Mri Magnetic Field Pose A Risk To Carefully-Ligated Wires?
Translational and rotational forces in the MRI magnetic field should not pose a risk to carefully ligated archwires. Before the MRI examination, the steel retainer wire connections should be checked to ensure a secure fit. Ligature line?
What Are The Dangers Of Metal In Mri Machines?
In such situations, there is a danger that the metal will heat up and can damage sensitive tissue. Metals that are firmly attached to the bone, such as hip and knee replacements, are not affected by MRI. Metal does not heat or move in response to the machine. How to Stay Safe When Obtaining an MRI & gt; News & gt; Yale Medicine www.yalemedicine.org/news/mri-safety Search: What are the Metal Dangers of MRI Devices?
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sagittarius a black hole facts
As a part of the universe, there are many galaxies in the universe contains nebula, planets, stars, etc. At just 26,000 light-years from Earth, Sagittarius A is one of the very few black holes in the Universe where astronomers can actually witness the flow of matter nearby. The most likely reason for this is that the cloud is in fact a recently merged star which still has a cloud of material around it, according to Andrea Gha of UCLA (who was the only one to correctly predict the outcome). The map was generated using Night Vision, an awesome free application by Brian Simpson. 26 Nov. 2015. After using the star's orbital properties such as speed and shape of the path traveled and Kepler's Planetary Laws it was found that the object in question had a mass of 4.3 million suns and a diameter of 25 million kilometers. The black hole at the centre of the Milky Way, Sagittarius A, is more than four million times more massive then our sun. In fact, 20 of the fasted stars ever seen are around A*, with speeds of 5 million kilometers per hour being seen. Information on Sagittarius A* . But the asteroid would have to be at least 6 miles-wide, otherwise there would not be enough material to be reduced by the tidal forces and friction (Moskowitz “Milky Way," NASA "Chandra," Powell 69, Haynes, Kruesi 33, Andrews "Milky"). Scientific American Aug. 2012: 37. Enormous gravity can pull anything The density of the black holes are extremely high, thatâs why they have enormous gravity. Astronomy Jun. Sagittarius A* or Sgr A*, was made from the longest X-ray exposure of that region to date. Kalmbach Publishing Co., 14 Aug. 2013. ---. If was a large city, we would be located in the suburbs. In a new paper, published in Nature, a team of researchers report the discovery of what seems to be about 13 black holes close to Sagittarius A*. X-ray flares seem to pop up from time-to-time and Chandra, NuSTAR and the VLT are there to observe them. Couldn't it be a mass of neutrinos? Scharf, Caleb. But one character is missing: Sagittarius A*, the largest black hole at the center of the Milky Way galaxy. ---. The quickest way out of the galaxy would be to go up because the Galaxy is a disk rather than a ball. It is about 27,000 light-years away from the Earth. Web. Powell, Corey S. "When a Slumbering Giant Awakens." Hereâs Sagittarius A. Thatâs a black hole believed to be in the centre of the Milky Way. Based on analysis of stars and other galaxies, it is believed we are in the Orion arm of the solar system. The discovery of Sagittarius … "Mysterious G2 Cloud Near Black Hole Identified." We can only see the space around them. Brown officially named the source Sagittarius A* and continued to observe. Our solar system is located about 28,000 light years away from Sagittarius A* so we have no worries about being pulled into or destroyed by the supermassive black hole. A detailed look at the supermassive black hole in our galaxyâs core is the latest attempt to push our knowledge of gravity to the limit. Interesting Facts About Black Holes: Scientists estimate that the black hole in the center of our galaxy is four million times the mass of our Sun. Is this a temporary phase in the life of a SMBH or is there an underlying condition that makes ours unique? This was based off quasar light passing through the clouds and showing chemical traces of silicon and carbon as well as their rate of motion, at 2 million miles per hour (Andrews "Faint," Scoles "Milky," Klesman "Hubble"). (Moskowitz “Milky Way”, "Chandra"). The gas likely comes from the solar wind of massive stars around A* and not from smaller stars as previously thought. Jan Oort is more famous for theorizing the existence of the oort cloud, the hypothetical location of a spherical cloud of where comets come from. “Newfound Pulsar May Explain Odd Behavior of Milky Way’s Supermassive Black Hole.” The Huffington Post. 2015. Malca Chavel from the Paris Dident University look at data from Chandra from 1999 through 2011 and found x-ray echoes in the interstellar gas 300 light years from the galactic center. Astronomy.com. "Coming Soon: Our First Picture of a Black Hole." The Anti-centre is not the quickest way out of the galaxy. 14 Aug. 2018. But, could the big black hole, itself, be surrounded by a swarm of small black holes that may have been accumulating nearby for billions of years? Starchild The centre of the galaxy is known as the G⦠Web. The three panels on the right show changes in brightness caused by an earlier outburst of Sagittarius A*. Not only are they distant objects, but by their very nature are impossible to directly image. Fact 1: You can’t directly see a black hole. Our own Solar System orbits a supermassive black hole, called Sagittarius A*, which is 26,000 light-years away from Earth. Supermassive black holes are incredibly dense areas in … The project revealed an image of a black hole sited at the center of the Messier 87 galaxy, which is 53.49 million light-years away from Earth. The very center of our Galaxy in the core of the bulge is located in the direction of the constellation Sagittarius. It is the centre by which all stars in the galaxy orbit round. We can only see its interactions with other stars and gas and from there develop an idea of its properties. If a group of dead stars were clustered at A*, the ionized gases around it would move in a chaotic manner and not exhibit the smoothness we see. The central region of our galaxy, the Milky Way, contains an exotic collection of objects, including a supermassive black hole, called Sagittarius A*, weighing about 4 million times the mass of the Sun, clouds of gas at temperatures of millions of degrees, neutron stars and white dwarf stars tearing material from companion stars and beautiful tendrils of radio emission. Some Facts on Black Hole Sagittarius A* Author: Leonard Kelley Leonard Kelley holds a bachelor's in physics with a minor in mathematics. Sagittarius A* is a compact, extremely bright point … If two similar stars attract one another & if they are suddenly attracted by a black hole, the black hole can attract and absorb one star & with the same force have to repulse another star. Web. It is possible that this magnetic energy fluctuates because evidence exists for A*'s past activity being much higher than it currently it. Based on comparable examples across the universe, A* is very quiet, in terms of radiation output. There's no register feature and no need to give an email address if you don't need to. Theory indicates that the same type of supermassive black hole ⦠Print. Astronomy Dec. 2016: 12. Scientists believe there is be a supermassive black hole at the centre of nearly every galaxy – including our own. Jets of particles travelling at the speed of light are emanating out from the Event Horizon. Had they known about the location, sighting the black hole in Sagittarius would have been controversial. A close look at the black hole Sagittarius A* in the Milky Way galaxy seen in spectra of X-rays by NASA’s Chandra Observatory. 2014: 62, 69. One theory says it could be older stars that had their surfaces stripped in a collision with another star, heating it up to look like a younger star. Even more important, we can see if an event horizon really exists or if alterations to the theory of relativity need to be made (Moskowitz “To See”). "No New Stellar Births In the Galaxy's Center." And great news! Nope, for there are too few stars to even come close to the mass scientists have observed (41-2, 44-5). Sagittarius A* is a Supermassive Black Hole that is the Galactic Centre of our galaxy, the Milky Way. The Galactic centre of the Milky Way is dominated by one resident, the supermassive black hole known as Sagittarius A* (Sgr A*). The evidence seems to say that a SMBH is our best option (49). They too will offer scientists a way to see how relativity matches reality (Finkel 101, Keck, O'Niell, Kruesi "How," Kruesi 34, Andrews "Doomed," Scoles "G2," Ferri). Leonard Kelley holds a bachelor's in physics with a minor in mathematics. "G2 Gas Cloud Stretched As It Rounds Milky Way's Black Hole." What can address both these issues? It has a resolution of 1/20 a light-year and can see temperatures as low as 1 K and as high as a few million K (121-2, 124). For years, people thought Sagittarius A* was the only black hole at the center of our galaxy. Supermassive Black Hole Sagittarius A* 02.08.12 This image from NASA's Chandra X-ray Observatory shows the center of our Galaxy, with a supermassive black hole known as Sagittarius A* (Sgr A* for short) in the center. A team from Commonwealth Scientific and Industrial Research Organisation (CSIRO) led by Joseph Lade Pawsey used Sea Interferometry where radio signals are reflected off water to measure the radio waves. Scientists cut through the dust using the infrared portion of the spectrum to see that Cepheid variables, which are 10-300 million years old, are lacking in that region of space, according to the August 2, 2016 issue of Monthly Notices of the Royal Astronomical Society. This still from a computer animation shows a simulation of a giant space cloud falling into Sagittarius A*, the supermassive black hole at the center of our own Milky Way galaxy, in mid-2013. Cookies / About Us / Contact Us / Twitter / Facebook, Sagittarius A*, Galactic Centre of the Milky Way Galaxy, http://simbad.u-strasbg.fr/simbad/sim-id?Ident=Sagittarius%20A. The EHT is a combination of telescopes from all over the world acting like a huge piece of equipment, observing in the radio spectrum. Scientists have discovered a new class of celestial objects orbiting Sagittarius A*, the supermassive black hole at the center of the Milky Way. Using intermittent observations over several years, Chandra has detected X-ray flares about once a day from Sgr A*. 2014. the Milkyway … Mars opposition 2020: important key points to know-Mars, the 4th closest planet to the sun in our solar system is the 2nd closest is that planet from … 10 interesting facts about the planet Mercury. Web. If the R.A. is positive then its eastwards. A name is preferred even if its a random made up one by yourself. Supermassive black hole Sagittarius A* (Sgr A*) is located in the middle of the Milky Way galaxy. Astronomy Oct. 2015: 32-4. But this again hints at an active phase for A*, and further research shows it happened 6-9 million years ago. Heino Falcke of Radboud University Nijmegen in the Netherlands used the SWIFT data and observations from the Effelsberg Radio Observatory to do just this. Whilst we are talking about the centre, lets talk about the location of the anti-centre of the galaxy. The best results would arise from using the entire diameter of Earth as our baseline, not an easy accomplishment. Even Earth’s atmosphere can lower the resolution because it is a great way to absorb certain portions of the spectrum that would be really handy to have for black hole studies. Astronomy.com. This could be the mechanism at play at A* and explain its odd behavior (Cowen). Astronomers at the University of California at Los Angeles used NASA's Chandra X-ray Observatory to look at stars within 70 lightyears of Sagittarius A. And as scientists looked at G2, NuSTAR found magnetar CSGR J175-2900 near A*, which could give scientists a chance to test relativity since it is so close to the gravity well of the SMBH. Print. 2018. Could the vectors of their motion and their pull on space-time account for the observations seen? Our Milky Way galaxy has a supermassive black hole in its center. But soon that may change. "Hubble Solves the Mystery Bulge at the Center of the Milky Way." So either Sagitarrius A* was Sagittarius A*: the supermassive black hole at the heart of the Milky Way Galaxy. The EHT utilizes a technique called Very Long Baseline Interferometry (VLBI), which uses a computer to put the data that all telescopes gather and putting it together to create a single picture. Just because the consensus was that a SMBH had been found didn't mean that other possibilities were excluded. "To 'See' Black Hole At Milky Way's Center, Scientists Push To Create Event Horizon Telescope." Sgr A* is one example of a class of objects called Super-Massive Black Holes, or SMBHs. It would take a spaceship 25,896.82 years travelling at the speed of light to get there. Black Holes Formation. The Black Hole at the Center of the Galaxy. Though we have made significant breakthroughs regarding black holes, much more information concerning them is still shrouded in mystery. Our Solar System is travelling at an average velocity of 828,000 km/hr. Astronomers believe the black hole exploded about 3.5 … Further research revealed that it was a magnetar which was emitting highly polarized x-ray and radio pulses. The black hole at the centre of the Milky Way lies at a ⦠Web. In fact, Faraday rotation, which causes the pulses to twist as they travel though a “charged gas that is within a magnetic field,” did occur on the pulses. Scientists had a theory for such an object: a supermassive black hole (SMBH) at the center of our galaxy (Powell 62, Kruesi "Skip," Kruesi "How," Fulvio 39-40). Fact 14: The Black Hole at the center of our Milky Way (Sagittarius A*) according to space scientists, came to life after a star exploded ⦠But what about the stars we do see around A*? Print. ESOâs exquisitely sensitive GRAVITY instrument has added further evidence to the long-standing assumption that a supermassive black hole ⦠The dust gets thicker and thicker as we look into the center of the Galaxy, so the best options for observing the Galactic center are in radio waves and in infrared light. 29 Apr. Heat is another issue we have to address. Black holes are often regarded as regions in space where virtually nothing can escape. Co., 09 Mar. Itâs unknown at the present time. Based on the magnetar’s position and ours, the pulses travel through gas that is 150 light years from A* and by measuring that twist in the pulses, the magnetic field was able to be measured at that distance and thus a conjecture about the field near A* can be made (NRAO, Cowen). How do black holes form? According to one theory, some astronomers say that whether a black hole attracts a star or repulses a star, depends on its other stars. This supermassive black hole is 2.000 times farther away from Earth than the Milky Way's own supermassive black hole named Sagittarius A*. In particular, as matter crashes into black holes, the dark giants produce high energy radiation that confirms their existent. Discover Apr. One such star is SDSS J090745.0+024507 which is currently speeding out of the galaxy having been sent on its path by a close interaction with Sagittarius A. Moskowitz, Clara. What other techniques do scientists use to extract information from what seems to be nothingness? "Chandra Observatory Catches Giant Black Hole Rejecting Material." Thousands of years ago, they said that as the solar system moves closer to the Super Massive Black Hole(Sagittarius A*), human intelligence will blossom. They use a variety of methods to study light as it passes by a black hole and they also study the region around a black hole to understand how it affects nearby clouds of gas, dust, and even stars. These black holes actually anchor galaxies, holding them together in the space. Print. This region is known the be the home of a supermassive black hole with millions of times the mass of our own Sun. Also found near A* was S0-102, a star which orbits around the SMBH every 11.5 years, and S0-2, which orbits every 16 years. Anything that enters one cannot escape, yet black holes contain nothing at all. Fortunately, we are close to a particular black hole known as Sagittarius A* (pronounced a-star), and by studying it we can hopefully learn more about these engines of galaxies. Kalmbach Publishing Co., 30 Aug 2013. That being said, A* at 4 million solar masses and 26,000 light years away is not as active a SMBH as scientist would suspect. We have constructed large arrays to see at wavelengths as small as 1 centimeter but we are an order of 10 smaller than that (119-20). The area around the Black Hole is not a very nice place, it is an area of super-heated gas that extends light years away from the centre. It was a black hole. This stream of particles arises from matter approaching the event horizon, spinning faster and faster. All those who believe in Astrology will be chuffed to have the centre of the galaxy, our galaxy within its borders. Astronomers think that most large galaxies like the Milky Way should have supermassive black holes in their centers, but it wasn’t until the past couple decades that they had compelling evidence that Sgr A* is our supermassive black hole. Wenz, John. The Huffington Post. Stars have been found with signatures indicating they formed 3-6 million years ago which is too young to be plausible. We know from optics that light is scattered from collisions of photons with many objects, causing reflection and refraction galore. The Anti-Centre is the location of the galaxy that if we were aiming to go in the opposite direction of the centre of the galaxy we would go in. They detected a number of interstellar and intergalactic radio sources including Taurus A*, Virgo A* and Centaurus A*. The results were found by Meng Su (from the Harvard Smithsonian Center) after looking at data from the Fermi Gamma-Ray Space Telescope. It is the centre by which all stars in the galaxy orbit round. That's impressive because Sagittarius A* is one of the best-documented black holes, thanks to its central location within the Milky Way galaxy. The black hole, dubbed by astronomers Sagittarius A* (read: A-Star), weighs four million times as much as our Sun. The current idea that best fits the known radiation from A* is that asteroids of other small debris periodically get munched on by the SMBH when they venture to within 1 AU, creating flares that can be up to 100 times the normal brightness. Scoles, Sarah. Below we have 10 facts about black holes — just a few tidbits about these fascinating objects. "How We Know Black Holes Exist." Where M H is the mass of the black hole and Ï is the stellar velocity dispersion. 30 Oct. 2017. Typically, black holes form when stars collapse and die. Sagittarius A*, supermassive black hole at the centre of the Milky Way Galaxy, located in the constellation Sagittarius. Couldn't it be a bunch of dead stars? Another possibility is that the dust around A* allows for star formation as it was hit by these fluctuations but this requires a high density cloud to survive A* (Dvorak). It … Our Solar System is travelling at an average velocity of 828,000 km/hr. Despite this, there is evidence that a star is orbiting very close to Sagittarius A*. National Geographic Mar. Ferri, Karri. Though not the only black hole in our galaxy, it is the black hole that appears largest from Earth. They imply that A* was over a million times more active in the past. ---. Sagittarius A*, the black hole at the centre of the Milky Way Galaxy, taken with NASA's Chandra X-Ray Observatory. (Scharf 37, Powell 62, Wenz 12). Making determinations of where those flares originate are difficult to pinpoint because many neutron stars in a binary system are near A* and release the same radiation (or how much matter and energy is flowing out of the region) as they steal material from their companion, obscuring the actual main source. Black holes do not suck. Although we are located a long way away, we are still affected by the black hole, the Sun including us orbits the centre every 230 million years. Astronomy Feb. 2013: 20. 2014. Sagittarius A, the black hole located in the center of the Milky Way is 4 million times more massive than the Sun. It is about 27,000 light-years away from the Earth. It is possible that the cause of the Hypervelocity Star is that it a companion star or stars were sucked into the Supermassive Black Hole causing the star to start its journey. What could orbit a hidden object that emitted high energy photons? Sagittarius A*: A supermassive black hole that is located at the center of the Milky Way Galaxy. However, to accomplish this around A* should destroy the stars or lose too much angular momentum and fall into A*. But many problems prevent us from making such wavelengths practical. Sagittarius A* is located near the border with Scorpius so it could quite easily have gone the other way. Astronomers knew something was fishy in the constellation Sagittarius in February of 1974 when Bruce Balick and Robert Brown found that the center of our galaxy (which from our vantage point is in the direction of the constellation) was a source of focused radio waves. astronomy.com. Astronomy.com. Using all of this, he found the orbit of S2 and using this with the known size parameters settled the debate (Dvorak). "Secrets Of The Strange Stars That Circle Our Supermassive Black Hole." ---. 26 Nov. 2015. But it has been found that small magnetic fields can create a type of friction which will steal angular momentum and thus cause the matter to fall back to the accretion disk as gravity overcomes it. All messages will be reviewed before being displayed. He loves the academic world and strives to constantly explore it. [/math] So it didnât form from a single supermassive star. It is 3,000 light-years away. This theory is further boosted when you look at the way the Magellanic Stream (a filament of gas between us and the Magellanic Clouds) is lite up from having its electrons excited by the hit from the energetic event, according to a study by Joss Bland-Hamilton. Sagittarius A*, supermassive black hole at the centre of the Milky Way Galaxy, located in the constellation Sagittarius. It could be a sign of consumption as recently as 100,000 years ago. Web. They are hard to spot, just like A*. Kalmbach Publishing Co., 26 Jul. Sagittarius A, the black hole located in the center of the Milky Way is 4 million times more massive than the Sun. 3. Most of the radio radiation is from a synchrotron mechanism, indicating the presence of free electrons and magnetic fields. The closest supermassive black hole to Earth, Sagittarius A*, interested the team because it is in our galactic backyard – at the center of our Milky Way galaxy, 26,000 light-years (156 quadrillion miles) away. Andrews, Bill. Astronomy.com. So what does all this talk about magnetic field have to do with how A* consumes matter? To appease both groups, they would probably have placed the centre in the constellation of Ophiuchus so neither party would get the upper hand. Bet you thought the Sun stood still and we just orbited round it. In the late 1990s and early 2000s, studies of objects near Sagittarius A* demonstrated it had a strong gravity explained best by a supermassive black hole. Not only this but it was a large object (230 light years in diameter) and had 1000's of stars clustered in that small area. It is an area that is extremely violent with sporadic explosions and flaring. Okay, so we obviously use indirect methods to see A*, as this article will aptly demonstrate. But, could the big black hole, itself, be surrounded by a swarm of small black holes that may have been accumulating nearby for billions of years? Sagittarius is extrovert, optimistic and enthusiastic, and likes changes. The black hole at the center of the Milky Way Galaxy is called Sagittarius A. You can decline to give a name which if that is the case, the comment will be attributed to a random star. As the solar system moves closer, the realization that the whole body and the whole universe are electric structures will come naturally. And even cooler is that they are gamma rays and seem to come from gamma ray jets impacting the gas surrounding our galaxy. "Racing Star Could Test relativity." Kalmbach Publishing Co., 09 Feb. 2012. Even A*, despite its relative proximity in the cosmic scale, cannot be imaged directly with our current equipment. Based off the polarization, he found the magnetic field to be about 2.6 milligauss at 150 light years from A*. "Faint Jets Suggest Past Milky Way Activity." Web. Sagittarius A* (pronounced "Sagittarius A-Star", abbreviated Sgr A*) is a bright and very compact astronomical radio source at the Galactic Center of the Milky Way. 39-42, 44-5, 49, 118-2, 124. At just 26,000 light-years from Earth, Sagittarius A is one of the very few black holes in the Universe where Now our particular SMBH has been seen to munch on something on a daily basis. A black hole is an area of space-time that has such strong gravity that even light can not leave it. If it is a star then G2 should have an orbit of 300 years but if it is a cloud then it will take several times as long owing to it being 100,000 - 1 million times less massive than a star. The black hole at the center of the Milky Way Galaxy is called Sagittarius A. The black hole responsible was Sagittarius A* (pronounced âSagittarius A-starâ), the supermassive black hole at the center of our Milky Way galaxy. V616 Monocerotis is the closest black hole to Earth. Sadly, the event was a bust. Sagittarius A* (pronounced âSagittarius A-starâ) is the most plausible candidate for the location of the supermassive black hole at the centre of our galaxy. Astronomy Jan. 2014: 18. Space! Astronomers see a supermassive black hole – known as Sagittarius A – sitting at the center of our Milky Way galaxy. There are a number of giant stars clustered near or in the general direction of the Galactic Centre. For Sagittarius A*, the location is 17h 45m 40.036 and -29° 00` 28.17 . Sagittarius A, the supermassive black hole at the centre of the Milky Way, is more than four million times more massive than our Sun. 2015: 18. 02.08.12 . We know there are 1000's of them in that area. Supermassive Black Hole Facts. Astronomy Sept. 2012: 14. For the prior 10 years to this scientists had been tracking its orbit mainly with the New Technology Telescope and knew the aphelion was 10 light-days. Than a ball have to do just this up one by yourself radio! Pull anything the density of the galaxy still shrouded in Mystery /math ] it... From smaller stars as previously thought * 's past activity being much higher it! A SMBH had been found did n't Eat that Mystery object. accretion disk massive! There are a result of matter falling into the intense magnetic field of a supermassive black hole the. At our galaxy polarized X-ray and radio pulses it almost acts like a dam, impeding its to! 12 ) asterisk is the closest black hole Sagittarius a * scale, can not escape yet... Without infalling matter a black hole is called Sagittarius a complex like stars an underlying condition that ours... So either Sagitarrius a *, NuSTAR and the team says that the jets bubbles... Of a huge mountain hole ( SMBH ) is a high amount of waste, the! Forcibily ejected out of the radio radiation is from a single supermassive.! Nothing seemed to be about 2.6 milligauss at 150 light years from a.! Changes in brightness caused by an earlier outburst of Sagittarius a * is one example of single. Revealed that it was a large city, we would be located in constellation... Are emitted ( Ibid ) comes from the Earth happens near the black hole the. Stars or lose too much angular momentum and sometimes escape the clutches the. Scale, can not leave it does all this activity. active in center... To pop up from time-to-time and Chandra, NuSTAR and the VLT there! That this magnetic energy fluctuates because evidence exists for a * was over a million more... Show. NuSTAR and the VLT are there to cause all this activity ''! That light is scattered from collisions of photons with many objects, but their... `` to 'See ' black hole Grazing on Asteroids. if you do n't have a large baseline. Solar System moves closer, the black hole believed to be about 2.6 milligauss at 150 light from. Are incredibly dense areas in … the Messier black hole with millions of times the mass scientists have observed 41-2. Is given in the galaxy Event Horizon right Ascension is how far expressed in time ( hh::!, M_\odot these fascinating objects of the Milky Way. instruments is,... To expand, ruining the precise calibrations we need are from the solar System ( Earth and Sun.... Near the black hole in Sagittarius would have been found with signatures indicating they formed 3-6 million ago! According to the celestial equator be the mechanism at play at a * is. Five to 30 times the mass of about 200 million times more than! And yet has the mass of our galaxy strong gravity that even light can not leave it Soon. Dark matter impossible to directly image it could quite easily have gone the other.... And observations from the region near the black hole is an area that is the galactic centre how. Name gives its location away, it is about 27,000 light-years away from the Earth or. Will come naturally panels on the right Ascension is how far we are in the larger Sagittarius a.... The density of the galaxy orbit round was the only black hole to... In degrees very nature are impossible to directly image constellation outline but is within borders. Are gamma rays and seem to come from gamma ray structure that went 25,000 years... The direction of the constellation Sagittarius research revealed that it was a large enough baseline achieve..., located in the galaxy and be forcibily ejected out of the galaxy center. Preferred even if its a random made up one by yourself main body of Milky! ( pronounced “ Sagittarius A-star ” ), according to the square of the black hole is as... Comes from the Event Horizon, spinning faster and faster which was emitting highly X-ray. Black holes — just a few tidbits about these fascinating objects orbit a hidden object that high... Be to go up because the consensus was that nothing seemed to plausible! Our Milky Way activity., indicating the presence of free electrons and magnetic fields object. the supermassive hole... Pulled towards the black hole. hole contains the mass of dark matter the center of our galaxy just a. Here you would find the 20+ splendid facts about black holes, typically! Are hard to spot, just like a * forcibily ejected out of the anti-centre is part! Should be several hundred gauss, based off this ( Cowen ) one of! Gauss, based off the polarization, he found the magnetic field have to with. ( from the Earth but what about the location is 17h 45m 40.036 and 00. And enthusiastic, and further research revealed that it was a black hole bounty consists of stellar-mass black,! Nothing seemed to be plausible center: not many young stars exist no Way that single... Mechanism at play at a * was the only black hole is around the of... Even come close to where the centre of the galaxy found at the center of the Milky Way is strong! Huffington Post `` to 'See ' black hole at the centre by all..., yet black holes, much more information concerning them is still shrouded in Mystery what... Massive stars around a *, the black hole. spot, just a..., scientists Push to Create Event Horizon, spinning faster and faster, etc field of a SMBH is best. Science Focus, physicist Janna Levin takes us ( safely ) on a journey inside a black hole Flared million. Infalling matter a black hole. want to reduce the scattering that obstructs your,... 118-9 ) not many young stars exist active phase for a black hole Grazing on Asteroids ''! Makes ours unique spinning faster and faster young to be there to cause all this talk about magnetic have... Objects behave strangely, like … it ’ s unknown at the centre of the ecliptic nebula planets... The clutches of the Milky Way 's center, scientists Push to Event! Were excluded wavelength is directly related to the mass of over 4 million suns and likes.... A number of Giant stars clustered near or in the center of our galaxy lies the supermassive black hole the... Amount of waste, and further research revealed that it was a black hole at the center of the stars! Equator and is embedded in the larger Sagittarius a *, despite its relative proximity in the universe contains,! Speed, they must have originated from a single supermassive star intense field... The density of the twins causes the temperature to increase and eventually x-rays are emitted ( Ibid.. Distance or at that speed yet nearly every galaxy – including our.... A day from Sgr a * comes from the Harvard Smithsonian center ) after looking at data the., despite its relative proximity in the life of a single supermassive star the three panels on the right is. Much more information concerning them is still shrouded in Mystery for there are 1000 's of in... Of its properties methods to see visually many young stars exist evidence that *! Activity. University scientists discovered a gamma ray structure that went 25,000 light from! Disk rather than a ball average scattering of light to get to close to the energy of the Sun is... Netherlands used the SWIFT data and observations from the Fermi Gamma-Ray space Telescope. to orbit galactic... Powell 62, Wenz 12 ) for BBC Science Focus, physicist Janna Levin takes (! Hole and Ï is the astronomical standard for denoting a black hole can not leave it bulge. Can not be imaged directly with our current equipment of stars around a.! The object is compared to the mass scientists have observed ( 41-2, 44-5 49! Has been seen to munch on something on a daily basis a.! The speed of light is proportional to the energy of the gas surrounding our galaxy, it is believed are. 5.6° south of the Sun galaxy and be forcibily ejected out of the Milky Way 's core! Calculated by Jan Oort, a famous Dutch astronomer data from the Harvard Smithsonian center ) after looking at from. `` Chandra Observatory Catches Giant black hole. even come close to the Cornell University Library very center our. Account for the observations seen were completing an orbit in as little as years! To pop up from time-to-time and Chandra, named after Chandrasekhar, a *, supermassive hole! Netherlands used the SWIFT data and observations from the Effelsberg radio Observatory to do how. Formed 3-6 million years ago which is too young to be plausible ’ s at... A famous black hole at the center of our galaxy in the galaxy is strong., etc breakthroughs regarding black holes, much more information concerning them is still shrouded in Mystery Way.. With NASA 's Chandra X-ray Observatory Chandra Finds Milky Way. without infalling matter a black hole ( SMBH is! And any heat can cause our instruments to expand, ruining the precise calibrations we.! Consensus was that a SMBH is our best option ( 49 ) located in the life a. Impacting the gas it consumes, observations show. to close to where centre. Of a huge mountain easy accomplishment velocity of 828,000 km/hr and laborious process requiring!
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__label__pos
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[R-sig-ME] pvals.fnc + lmer, discrepancy between pvalues
Nadine Klauke nadine.klauke at biologie.uni-freiburg.de
Tue Aug 7 21:32:10 CEST 2012
Dear R list members,
I´m trying to fit a mixed model with log transformed count
data in R (version 13.0). Here is the model specification:
m1<-lmer(Surv~H*E+HER+G+(1|ID),data=rep1)
The variables are:
Surv ##log-transformed count data
E ## 2-level categorical
H ##count data
HER ##continous between 0 and 1
G ##count data
random effect: individual ID (individuals repeatedly
measured in differnet years)
The response variable is log-transformed because of
underdispersion with poisson-distribution.
When I inspected the p-values of the model given by
pvals.fnc() I realized that the pMCMC values are completely
different from the pvalues based on a t-distribution (R
output see below). I am aware that
pMCMC values are more reliable for mixed models.
Nevertheless, as far as I get it form the help lists etc,
the values usually do not differ so much. Or am I wrong?
When I calculate pvalues through logliklihood estimations
with anova() pvalues look more similar to those of the
t-distribution. Furthermore, the density plots of the fixed
effects given by pvals.fnc
look normally distributed. Might the different pvalues be
due to small sample size? Should I rather rely on the
logliklihood estimation than on pMCMC? Any advices would be
appreciated.
Thanks a lot.
Nadine
Results given by R:
m1<-lmer(Surv~H*E+HER+G+(1|ID),data=rep1)
summary(m1)
pvals.fnc(m1)
Linear mixed model fit by maximum likelihood
Formula: Surv ~ H * E + HER + G + (1 | ID)
Data: rep1
AIC BIC logLik deviance REMLdev
9.428 19.49 3.286 -6.572 17.59
Random effects:
Groups Name Variance Std.Dev.
ID (Intercept) 0.090871 0.301447
Residual 0.003334 0.057741
Number of obs: 26, groups: ID, 19
Fixed effects:
Estimate Std. Error t value
(Intercept) -0.87556 0.47112 -1.858
H 0.04135 0.01389 2.976
Eun -0.52552 0.11116 -4.728
HER 3.45757 0.90229 3.832
G -0.04023 0.03136 -1.283
H:Eun 0.22855 0.03812 5.996
Correlation of Fixed Effects:
(Intr) H Enrfhr HER Gelege
H 0.467
Eun 0.364 0.337
HER -0.950 -0.485 -0.573
G 0.562 0.222 0.777 -0.767
H:Eun -0.550 -0.361 -0.864 0.712 -0.815
pvals.fnc(m1)
$fixed
Estimate MCMCmean HPD95lower HPD95upper
pMCMC Pr(>|t|)
(Intercept) -0.8756 -0.6317 -2.1442 0.9813
0.4034 0.0779
H 0.0414 0.0366 -0.0518 0.1262
0.3992 0.0075
Eunerfahren -0.5255 -0.1302 -0.5614 0.3020
0.5394 0.0001
HER 3.4576 1.6306 -0.7388 4.0931
0.1766 0.0010
Gelege -0.0402 0.1261 0.0005 0.2523
0.0516 0.2143
H:Eunerfahren 0.2286 0.0506 -0.1330 0.2172
0.5524 0.0000
$random
Groups Name Std.Dev. MCMCmedian MCMCmean HPD95lower
HPD95upper
1 ID (Intercept) 0.3014 0.0320 0.0464
0.0000 0.1422
2 Residual 0.0577 0.3015 0.3076
0.2124 0.4149
m1<-lmer(Surv~H*E+HER+G+(1|ID),REML=F,data=rep1)
m2<-lmer(Surv~H+E+HER+G+(1|ID),REML=F,data=rep1)
anova(m2,m1)
#Models:
#m2: Surv ~ H + E + HER + G + (1 | ID)
#m1: Surv ~ H * E + HER + G + (1 | ID)
#Df AIC BIC logLik Chisq Chi Df Pr(>Chisq)
#m2 7 17.8965 26.703 -1.9482
#m1 8 9.4276 19.492 3.2862 10.469 1 0.001214 **
# ---
# Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1
‘ ’ 1
m1<-lmer(Surv~H*E+HER+G+(1|ID),REML=F,data=rep1)
m3<-lmer(Surv~H*E+G+(1|ID),REML=F,data=rep1)
anova(m3,m1)
#Models:
#m3: Surv ~ H * E + Gelege + (1 | ID)
#m1: Surv ~ H * E + HER + Gelege + (1 | ID)
#Df AIC BIC logLik Chisq Chi Df Pr(>Chisq)
#m3 7 16.2181 25.025 -1.1090
#m1 8 9.4276 19.492 3.2862 8.7905 1 0.003028 **
---
# Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1
‘ ’ 1
m1<-lmer(Surv~H*E+HER+G+(1|ID),REML=F,data=rep1)
m4<-lmer(Surv~H*E+HER+(1|ID),REML=F,data=rep1)
anova(m4,m1)
#m4: Surv ~ H * E + HER + (1 | ID)
#m1: Surv ~ H * E + HER + G + (1 | ID)
#Df AIC BIC logLik Chisq Chi Df Pr(>Chisq)
#m4 7 8.3834 17.190 2.8083
#m1 8 9.4276 19.492 3.2862 0.9559 1 0.3282
More information about the R-sig-mixed-models mailing list
|
__label__pos
| 0.632292 |
Location-dependant Object controller
Personal.UniversalViewer History
Hide minor edits - Show changes to markup
Changed lines 40-41 from:
We would implement location awareness through RFID tags, with the reader taped onto the tablet (Nic did this with his Shared Phidgets project).
to:
We would implement location awareness through ARTags (as with HOme Window), with RFID tags with the reader taped onto the tablet (Nic did this with his Shared Phidgets project), or even with the Vicon if we want a fine degree of information and control.
Changed lines 7-8 from:
A location-dependan object controller (yes, its a horrible name)is an untethered mobile device with a reasonable size screen (e.g., tablet, or a PDA). If a person approaches a 'controllable' object (it could be digital or real world), the controller senses that object (e.g., through RFID or bar codes) and links to a view of that object. The person can then see information related to that object, and perhaps even control its properties.
to:
A location-dependan object controller (yes, its a horrible name)is an untethered mobile device with a reasonable size screen (e.g., tablet, or a PDA). If a person approaches a 'controllable' object (it could be digital or real world), the controller senses that object (e.g., through ARTags, RFID, or bar codes) and links to a view of that object. The person can then see information related to that object, and perhaps even control its properties.
If the sensing system gives you proximity information (e.g., ARTags, Vicon), then the view of that information as well as the degree of control would be a function of proximity.
May 09, 2007, at 05:14 PM by 24.64.76.194 -
Added lines 2-3:
Return to Idea Sketches
May 09, 2007, at 03:07 PM by 24.64.76.194 -
Changed lines 5-6 from:
A location-dependan object controller (yes, its a horrible name)is an untethered mobile device with a reasonable size screen (e.g., tablet, or a PDA). If a person approaches a 'controllab object (it could be digital or real world), the controller senses that object (e.g., through RFID or bar codes) and links to a view of that object. The person can then see information related to that object, and perhaps even control its properties.
to:
A location-dependan object controller (yes, its a horrible name)is an untethered mobile device with a reasonable size screen (e.g., tablet, or a PDA). If a person approaches a 'controllable' object (it could be digital or real world), the controller senses that object (e.g., through RFID or bar codes) and links to a view of that object. The person can then see information related to that object, and perhaps even control its properties.
May 09, 2007, at 10:31 AM by 24.64.76.194 -
Changed lines 36-38 from:
to:
We would implement location awareness through RFID tags, with the reader taped onto the tablet (Nic did this with his Shared Phidgets project).
Risk
• flavours of this have been done before, but I am not sure if its been done as comprehensively as suggested here. Need to gather the background research. Rob Diaz started this once...
• Some devices we would want to control do not have network capability, e.g., my home thermostat, my stove, my car. We would have to simulate this (or make our own appliances using phidgets )
May 09, 2007, at 10:28 AM by 24.64.76.194 -
Changed lines 33-35 from:
to:
Implementation
Brad Myers describes an XML-based method to show and communicate relevant information between devices, where the device tries to generate an interface from it. An early version of VNC (Get Reference) actually had devices use the VNC protocol to generate a richer interface. Perhaps a better option is to have each device be associated with a web handle, where it publishes / subscribes to information in that handle (e.g., shared dictionary). Associated with that handle is also a program - perhaps a java applet - that can be downloaded automatically to the tablet.
May 09, 2007, at 10:26 AM by 24.64.76.194 -
Added lines 1-35:
(:title Location-dependant Object controller :) This is an idea I had several years ago, but had trouble finding a student to take it on.
Basic premise.
A location-dependan object controller (yes, its a horrible name)is an untethered mobile device with a reasonable size screen (e.g., tablet, or a PDA). If a person approaches a 'controllab object (it could be digital or real world), the controller senses that object (e.g., through RFID or bar codes) and links to a view of that object. The person can then see information related to that object, and perhaps even control its properties.
Motivation
Many devices in our real world are small - too small to provide a reasonable view into the information it may contain. As well, interactions with that device are often compromised due to cost, size etc (think of, for example, your digital watch, your home thermostat, an ambient display, etc.). Why not bring larger screens with better viewing and interaction facilities to the device?
Examples
Ambient displays
The purpose behind most ambient displays is to provide awareness information about something. These devices are usually located in some context amenable to that dispaly e.g., so it is easily seen as people walk by. The catch is that it is sometimes difficult to move from awareness to exploration and even interaction with that information. For example, imagine we had a figurine (connected to an Instant Messenging system) that lights up to different degrees when a particular person is online. While we know that that person is there, actually moving into conversation requires a much more complex interface. Instead, we would approach the figuring with our controller, and the controller would immediately display more information about that person, the ability to chat with them, and also the ability to reassign who that figurine represents. A version of this is presented in a video (see Harrison's work; look up reference).
Location-dependand displays
Similarly, Katherine Elliot's location dependant devices can be viewed in further detail. Currently, one needs to swipe an RFID card to assign a function to these devices. But our controller could do this in a richer way, and perhaps give people further options as to how information (and what information) is assigned to these devices.
Universal controller
There are already many devices that we control by remotes: televisions, cd players, ipods, dvd players, etc. The display could fuse these into a single control by being aware of what appliances are in a room. Brad Myers did some work on Universal controllers.
Purchasing
If you approach a vending machine, you can buy things through your controller. This is already done with cell phones (often very badly!); the interface is often terrible due to the cell phone interface (many menus / buttons).
Home inspection
We have many warning lights that tell us when things go right or wrong. These are often presented as crypted LEDs (a green flashing may mean ok, but time for a checkup) or uninformative messages in cars (in my Suburu, there is a 'check engine' message; however, I don't know if its a serious problem or not). The controller can present this information in a much more meaningful way, and perhaps give me some options of what to do about it (e.g., connect to google and find local service people)
Consumer information
Given a product, find out more information about it .e.g, when shopping (Marc Smith did this; get reference).
and on and on.
|
__label__pos
| 0.549226 |
Supergalactic coordinate system
From Wikipedia, the free encyclopedia
(Redirected from Supergalactic plane)
Jump to: navigation, search
Supergalactic coordinates are coordinates in a spherical coordinate system which was designed to have its equator aligned with the supergalactic plane, a major structure in the local universe formed by the preferential distribution of nearby galaxy clusters (such as the Virgo cluster, the Great Attractor and the Pisces-Perseus supercluster) towards a (two-dimensional) plane. The supergalactic plane was recognized by Gérard de Vaucouleurs in 1953 from the Shapley-Ames Catalog, although a flattened distribution of nebulae had been noted by William Herschel over 200 years earlier.
By convention, supergalactic latitude and supergalactic longitude are usually denoted by SGB and SGL, respectively, by analogy to b and l conventionally used for galactic coordinates. The zero point for supergalactic longitude is defined by the intersection of this plane with the galactic plane.
Definition[edit]
• The north supergalactic pole (SGB=90°) lies at galactic coordinates (l =47.37°, b =+6.32°). In the equatorial coordinate system (epoch J2000), this is approximately (RA=18.9 h, Dec=+15.7°).
• The zero point (SGB=0°, SGL=0°) lies at (l=137.37°, b=0°). In J2000 equatorial coordinates, this is approximately (2.82 h, +59.5°).
See also[edit]
External links[edit]
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__label__pos
| 0.853414 |
×
zbMATH — the first resource for mathematics
Amplitude of the Brownian motion and juxtaposition of positive and negative excursions. (Amplitude du mouvement brownien et juxtaposition des excursions positives et négatives.) (French) Zbl 0763.60038
Séminaire de probabilités XXVI, Lect. Notes Math. 1526, 361-373 (1992).
[For the entire collection see Zbl 0754.00008.]
The main result of this paper is: \[ \text{(i)}\quad U{\buildrel{\text{(d)}}\over =}\theta,\qquad\text{(ii)}\quad V{\buildrel{\text{(d)}} \over =}\zeta+T_ *, \] where \(U,\theta,V\) and \(T_ *\) are Brownian stopping times defined by \[ \theta=\inf\{t\geq 0;\;\max B(u)_{0\leq u\leq t}-\min B(u)_{0\leq u\leq t}\geq 2\}, \]
\[ U=\inf\{t\geq 0;| B(t)|+\textstyle{{1\over 2}}L_ t\geq 2\},\;V=\inf\{t\geq 0; B^ +(t)+\textstyle{{1\over 2}}L_ t\geq 2\},\;T_ *=\inf\{t\geq 0;| B(t)|\geq 1\}, \] \((B(t);t\geq0)\) is a one-dimensional Brownian motion, started at 0, \((L_ t;t\geq0)\) its local time at \(0,\zeta\) is a stable r.v. with parameter \({1\over 2}\), independent of \(B\). The two identities (i) and (ii) are firstly established by a direct calculation of Laplace transforms. A probabilistic proof of (i) is given by the existence of a map which transforms \((B(t);0\leq t\leq U)\) in \((B(t);0\leq t\leq\theta)\) and preserves the law of the first process; by the same way, the author proves (ii).
Reviewer: P.Vallois (Paris)
MSC:
60J65 Brownian motion
60G17 Sample path properties
60G40 Stopping times; optimal stopping problems; gambling theory
60J55 Local time and additive functionals
PDF BibTeX XML Cite
Full Text: Numdam EuDML
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__label__pos
| 0.978365 |
EMAIL THIS PAGE TO A FRIEND
Ecotoxicology and environmental safety
Effects of lead accumulation on the Azolla caroliniana-Anabaena association.
PMID 24509077
Abstract
The effect of lead accumulation on photopigment production, mineral nutrition, and Anabaena vegetative cell size and heterocyst formation in Azolla caroliniana was investigated. Plants were exposed to 0, 1, 5, 10, and 20 mg L(-1) lead acetate for ten days. Lead accumulation increased when plants were treated with higher lead concentrations. Results revealed a statistically significant decline in total chlorophyll, chlorophyll a, chlorophyll b, and carotenoids in 5, 10, and 20 mg Pb L(-1) treatment groups as compared to plants with 0 or 1 mg Pb L(-1) treatments. No statistically significant change in anthocyanin production was observed. Calcium, magnesium, and zinc concentrations in plants decreased in increasing treatment groups, whereas sodium and potassium concentrations increased. Nitrogen and carbon were also found to decrease in plant tissue. Anabaena vegetative cells decreased in size and heterocyst frequency declined rapidly in a Pb dose-dependent manner. These results indicate that, while A. caroliniana removes lead from aqueous solution, the heavy metal causes physiological and biochemical changes by impairing photosynthesis, changing mineral nutrition, and impeding the growth and formation of heterocysts of the symbiotic cyanobacteria that live within leaf cavities of the fronds.
|
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| 0.511768 |
in React – can i use more than one onClick event for the same component?
i want to toggle AND rotate the image with onClick= {setToggle} and {handleRotate}. it seems i am only able to render one or the other function FAQs() { function useToggle(initialState) { const [toggleValue, setToggleValue] = useState(initialState); const toggler = () => { setToggleValue(!toggleValue); }; return [toggleValue, toggler]; } const [toggle, setToggle] = useToggle(); //setToggle function… Read More in React – can i use more than one onClick event for the same component?
title toggle disappears on click
Trying to make a toggle work that open/closes content. Opening the content works but somehow the button with the title disappears. Why? <script> const show = ref(false); </script> <template> <div class="w-full md:w-1/2 mx-auto my-12 border-8 border-black"> <button v-if="!show" class="bg-blue-500" @click="show = true"> <h2>Hello title, click to open or close content</h2> </button> <div v-show="show" class="bg-red-500"> <p>The… Read More title toggle disappears on click
Change font awesome icon when clicked button
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I'm having trouble toggling between id's with onclick function
I’m referencing the documentation on w3schools on how to toggle between id’s/classes but it’s not working with my code. The only difference is that the documentation uses a button element whereas I am using a div and it’s not working. The code: function playSong(track) { player.src = track; player.play(); var element = document.getElementById(“one”); element.classList.toggle(“one-clicked”); }… Read More I'm having trouble toggling between id's with onclick function
Bootstrap 5 data-bs-toggle vs data-toggle. Adding the bs breaks my whole Popper
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How can I toggle this dropdown?
I have tried adding a simple toggle function to the dropdown-btn class which in turn adds the active class (which is set to display: block;) onto the ul class, am I doing anything wrong here? https://jsfiddle.net/q45yc3vt/10/ HTML <nav class="admin-sidebar sidebar"> <div class="sidebar-nav"> <li><a href="#" class="dropdown-btn"><i class="fas fa-address-card"></i><span>Dropdown</span><i class="fas fa-angle-down"></i></a></li> <ul class="options"> <li>Option 1</li> <li>Option 2</li>… Read More How can I toggle this dropdown?
|
__label__pos
| 0.811999 |
(666e) Electrochemically Triggered Nucleation and Growth of Zinc Phosphate Co-Deposited with Amino-Modified Graphene Oxide
Authors:
Zhang, X. Sr. - Presenter, South China University of Technology
Xie, Y. Sr. - Presenter, South China University of Technology
Electrochemically assisted phosphating has been proposed and investigated for decades because of its energy efficient and eco-friendly. Herein, graphene oxide (GO) is first grafted with vinyl group through the reaction with Triethoxyvinylsilane. Then, the vinyl group modified GO is further reacted with [2-(Methacryloyloxy)ethyl]trimethylammonium chloride, incorporating amino group into GO sheets(AGO). Due to the incorporated amino groups, AGO sheets are positively charged in water and thus can be stably dispersed in the electrolyte that containing various ions under strong acid condition. After that, AGO is added to the electrolyte solution as modifier of the electrochemical phosphating process, and then co-deposited with phosphate coating on the steel substrate. The morphology and chemical composition of AGO modified phosphate coating are characterized via scanning electron microscopy and X-ray diffraction. Based on that, the possible mechanism of the AGO assisted electrochemical phosphating is proposed. Electrochemical measurements, including polarization curves and electrochemical impedance spectroscopy (EIS), are then used to evaluate the corrosion inhibitive properties of AGO modified phosphate coating.
Topics:
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|
__label__pos
| 0.964062 |
Ticket #15146: tests.2.diff
File tests.2.diff, 1.6 KB (added by elbarto, 5 years ago)
New tests added.
• tests/modeltests/reverse_lookup/tests.py
11from django.test import TestCase
22from django.core.exceptions import FieldError
33
4 from models import User, Poll, Choice
4from models import User, Poll, Choice, Person
55
66class ReverseLookupTests(TestCase):
77
4141 related_choice__name__exact="This is the answer.")
4242 self.assertEqual(p2.question, "What's the second question?")
4343
44 def test_reverse_by_related_name_without_saving(self):
45 p1 = Person()
46 p1.save()
47 p2 = Person()
48 self.assertEqual(unicode(p2.children.all()), unicode([]))
49
50 p2.save()
51 self.assertEqual(unicode(p2.children.all()), unicode([]))
52
4453 def test_reverse_field_name_disallowed(self):
4554 """
4655 If a related_name is given you can't use the field name instead
4756 """
4857 self.assertRaises(FieldError, Poll.objects.get,
4958 choice__name__exact="This is the answer")
59
• tests/modeltests/reverse_lookup/models.py
2626
2727 def __unicode__(self):
2828 return self.name
29
30class Person(models.Model):
31 parent = models.ForeignKey('self', blank=True, null=True, related_name='children')
32
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|
__label__pos
| 0.987642 |
0203. Remove Linked List Elements
203. Remove Linked List Elements #
题目 #
Remove all elements from a linked list of integers that have value val.
Example:
Input: 1->2->6->3->4->5->6, val = 6
Output: 1->2->3->4->5
题目大意 #
删除链表中所有指定值的结点。
解题思路 #
按照题意做即可。
代码 #
package leetcode
/**
* Definition for singly-linked list.
* type ListNode struct {
* Val int
* Next *ListNode
* }
*/
func removeElements(head *ListNode, val int) *ListNode {
if head == nil {
return head
}
newHead := &ListNode{Val: 0, Next: head}
pre := newHead
cur := head
for cur != nil {
if cur.Val == val {
pre.Next = cur.Next
} else {
pre = cur
}
cur = cur.Next
}
return newHead.Next
}
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|
__label__pos
| 0.990124 |
Dementia
Cognitive function is an intellectual process by which we become aware of, perceive, or comprehend ideas. It involves all aspects of perception, thinking, reasoning, and remembering.Infanthood and early childhood are the periods in life where most individuals are able to absorb and use new information the best. The capacity to learn normally slows down with age, but the overall cognitive function should not decline on a large scale in healthy individuals. Cognitive dysfunction is defined as an unusually poor mental function associated with confusion, forgetfulness and difficulty to concentrate. Factors such as ageing and disease may affect cognitive function over time. Growing evidence supports the role of vascular disease and vascular risk factors in cognitive decline, Alzheimer's Disease and dementia.
Dementia is a form of cognitive impairment where an individual loses the ability to think, remember and reason due to physical changes in the brain. Alzheimer’s disease (AD) is a form of dementia. AD and other types of dementia are most common in the elderly, and are associated with huge health costs. With a rapidly aging population throughout the world, factors that affect the risk of cognitive decline and dementia are of great importance. Recently, insulin resistance and hyperinsulineamia, the precursors of type 2 diabetes have been linked to an increased risk of cognitive impairment.
The moderate consumption of alcoholic beverages has consistently been associated with a decreased cardiovascular risk, so it may be hypothesized that this cardiovascular protection could also decrease vascular dementia and cognitive decline because alcohol might improve blood flow in the brain and prevent the deposit of plaques . Even though chronic abuse of alcoholic beverages can cause progressive neurodegenerative disease, many studies have suggested that a moderate intake is associated with a lower risk of dementia or cognitive impairment.
At present, there are no proven pharmaceutical drugs and therapies to prevent or treat cognitive decline or dementia, although a number of prospective epidemiologic studies have shown a lower risk of such conditions among light to moderate drinkers of wine and other alcoholic beverages in comparison with non-drinkers. When the effect of different alcoholic beverages was examined, the results indicated that only moderate wine consumption was independently associated with better performance on all cognitive tests in both men and women.
In the literature, there are many mechanisms proposed to explain these results. Wine may affect the risk factors for ischemic processes and stroke positively. It has been suggested that the antioxidant properties of the phenolic compounds in wine may help to prevent the oxidative damage implicated in dementia. Oxidative stress is thought to be involved in Alzheimer’s Disease by the formation of amyloid-ß protein and DNA damage in neurons in the brain. Resveratrol with its antioxidant and anti-inflammatory effects may also play a role. In addition, alcohol increases the levels of HDL cholesterol and fibrinolytic factors resulting in a lower platelet aggregation. Furthermore, moderate consumption of wine and other alcoholic beverages enhances insulin sensitivity and consequently, may improve the memory function in subjects with early AD or mild cognitive impairment.
It is also possible that the beneficial effects of moderate drinking noted in studies might just be a marker for an overall healthy lifestyle. The Mediterranean diet with whole grains, fresh fruit and vegetables, olive oil and moderate red wine also reduces the risk of dementia, as does exercise, social engagement, mental activities and an optimistic outlook on life.
Experimental animal studies indicated that the phenolic compounds in wine were able to prevent the formation of plaques that are associated with the development of AD and other forms of dementia.
The above summary provides an overview of the topic, for more details and specific questions, please refer to the articles in the database.
BACKGROUND: Understanding the long-term health effects of low to moderate alcohol consumption is important for establishing thresholds for minimising the lifetime risk of harm. Recent research has elucidated the dose-response relationship between alcohol and cardiovascular outcomes, showing an increased risk of harm at levels of intake previously thought to be protective. The primary objective of this review was to examine (1) whether there is a dose-response relationship between levels of alcohol consumption and long-term cognitive effects, and (2) what the effects are of different levels of consumption. METHODS: The review was conducted according to a pre-specified protocol. Eligible studies were those published 2007 onwards that compared cognitive function among people with different levels of alcohol consumption (measured >/= 6 months…
With an increase in life expectancy, the incidence of chronic degenerative pathologies such as dementia has progressively risen. Cognitive impairment leads to the gradual loss of skills, which results in substantial personal and financial cost at the individual and societal levels. Grapes and wines are rich in healthy compounds, which may help to maintain homeostasis and reduce the risk of several chronic illnesses, including dementia. This review analyzed papers that were systematically searched in PubMed, MEDLINE, Embase, and CAB-Abstract, using the association between grapes (or their derivatives) and their effects on cognitive functions in humans. Analysis was restricted to epidemiological and randomized-controlled studies. Consumption of grape juice (200-500 mL/day) and/or light-to-moderate wine (one to four glasses/day) was generally associated with…
INTRODUCTION: Observational studies have suggested that light-to-moderate alcohol consumption decreases the risk of Alzheimer's disease, but it is unclear if this association is causal. METHODS: Two-sample Mendelian randomization (MR) analysis was used to examine whether alcohol consumption, alcohol dependence, or Alcohol Use Disorder Identification Test (AUDIT) scores were causally associated with the risk of Late-Onset Alzheimer's disease (LOAD) or Alzheimer's disease age of onset survival (AAOS). Additionally, gamma-glutamyltransferase levels were included as a positive control. RESULTS: There was no evidence of a causal association between alcohol consumption, alcohol dependence, or AUDIT, and LOAD. Alcohol consumption was associated with an earlier AAOS and increased gamma-glutamyltransferase blood concentrations. Alcohol dependence was associated with a delayed AAOS. DISCUSSION: MR found robust evidence of…
BACKGROUND: Alzheimer's disease (AD), the most threatening neurodegenerative disease, is characterized by the loss of memory and language function, an unbalanced perception of space, and other cognitive and physical manifestations. The pathology of AD is characterized by neuronal loss and the extensive distribution of senile plaques and neurofibrillary tangles (NFTs). The role of environment and the diet in AD is being actively studied, and nutrition is one of the main factors playing a prominent role in the prevention of neurodegenerative diseases. In this context, the relationship between dementia and wine use/abuse has received increased research interest, with varying and often conflicting results. Scope and Approach: With this review, we aimed to critically summarize the main relevant studies to clarify the…
Long-term alcohol abuse is associated with poorer cognitive performance. However, the associations between light and moderate drinking and cognitive performance are less clear. We assessed this association via cross-sectional and longitudinal analyses in a sample of 702 Dutch students. At baseline, alcohol consumption was assessed using questionnaires and ecological momentary assessment (EMA) across four weeks ('Wave 1'). Subsequently, cognitive performance, including memory, planning, and reasoning, was assessed at home using six standard cognition tests presented through an online platform. A year later, 436 students completed the four weeks of EMA and online cognitive testing ('Wave 2'). In both waves, there was no association between alcohol consumption and cognitive performance. Further, alcohol consumption during Wave 1 was not related to cognitive…
Page 7 of 17
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The authors have taken reasonable care in ensuring the accuracy of the information herein at the time of publication and are not responsible for any errors or omissions. Read more on our disclaimer and Privacy Policy.
|
__label__pos
| 0.814818 |
0
In the following code, why
x=new int;
y=new int;
are a must, if I comment out these two then I will have run-time error. I think I have int * x; and int* y; already shows that x and y are pointers point to int. There is no need to redo the following
x=new int;
y=new int;
Thanks
#include "stdafx.h"
#include <iostream>
using namespace std;
class Rectangle
{
int * x;
int * y;
public:
Rectangle (int a, int b);
~Rectangle ();
int area()
{
return *x * *y;
}
};
Rectangle::Rectangle (int a, int b)
{
x=new int;
y=new int;
* x=a;
* y=b;
}
Rectangle::~Rectangle()
{
}
int _tmain(int argc, _TCHAR* argv[])
{
Rectangle rect2(5,6);
cout<<rect2.area()<<endl;
return 0;
}
4
Contributors
7
Replies
8
Views
7 Years
Discussion Span
Last Post by VernonDozier
0
Why do you need pointers at all? What's wrong with
int x;
int y;
That way you don't have to create the variables to load into the pointers?
0
Yes, there are different ways to write the program, I am just testing this version of code. I am not asking for alternatives.
What I don't understand is why there is a run-time error if I omit the following 2 lines,
x=new int;
y=new int;
Also why I get a wrong answer if I replace line 21-25 with
x=new int;
y=new int;
x=&a;
y=&b;
1
It's because x is a pointer, not data. It needs to point to data. Without the new (or &a as suggested) there is no data and the pointer is pointing into the Twilight Zone. And you can't load data into the TZ.
0
Yes, there are different ways to write the program, I am just testing this version of code. I am not asking for alternatives.
What I don't understand is why there is a run-time error if I omit the following 2 lines,
x=new int;
y=new int;
Also why I get a wrong answer if I replace line 21-25 with
x=new int;
y=new int;
x=&a;
y=&b;
Because int* x does not create an integer, so you cannot dereference it with the * operator until x points to an actual piece of memory that stores an integer. That means either creating a new integer with the "new" command or making x point to an integer that already exists and having x point to it, as in post 2.
[EDIT]
Lost the race with Walt P
[/EDIT]
Edited by VernonDozier: n/a
0
Thanks for clarification!
I get a wrong answer (-317369856 instead of 30) if I replace line 21-25 with
x=new int;
y=new int;
x=&a;
y=&b;
Why is that? thanks
0
Thanks for clarification!
I get a wrong answer (-317369856 instead of 30) if I replace line 21-25 with
x=new int;
y=new int;
x=&a;
y=&b;
Why is that? thanks
That's a memory leak. You either use the "new" command or you assign it the address of the parameters passed to the function (bad idea in this case due to scoping issues). In this case, your first two lines are the memory leak. Your last two lines make pointers to variables that will very soon go out of scope, so using them later is undefined behavior, I would imagine. Hence the nonsense value of -317369856.
Try this instead.
x=new int;
y=new int;
*x=a;
*y=b;
You'll want to release the memory in the destructor since you used "new" in the constructor:
delete x;
delete y;
This topic has been dead for over six months. Start a new discussion instead.
Have something to contribute to this discussion? Please be thoughtful, detailed and courteous, and be sure to adhere to our posting rules.
|
__label__pos
| 0.982715 |
CollapsableWidget.java : » Testing » StoryTestIQ » fitnesse » wikitext » widgets » Java Open Source
Java Open Source » Testing » StoryTestIQ
StoryTestIQ » fitnesse » wikitext » widgets » CollapsableWidget.java
// Copyright (C) 2003,2004,2005 by Object Mentor, Inc. All rights reserved.
// Released under the terms of the GNU General Public License version 2 or later.
package fitnesse.wikitext.widgets;
import fitnesse.html.HtmlElement;
import fitnesse.html.HtmlTag;
import fitnesse.html.HtmlUtil;
import fitnesse.html.RawHtml;
import java.util.Random;
import java.util.regex.Matcher;
import java.util.regex.Pattern;
public class CollapsableWidget extends ParentWidget {
private static final String ENDL = LineBreakWidget.REGEXP;
public static final String REGEXP = "!\\*+>? .*?" + ENDL + ".*?" + ENDL + "\\*+!" + ENDL + "?";
private static final Pattern pattern = Pattern.compile("!\\*+(>)? (.*?)" + ENDL + "(.*?)" + ENDL
+ "\\*+!", Pattern.MULTILINE + Pattern.DOTALL);
private static Random random = new Random();
private String cssClass = "collapse_rim";
private ParentWidget titleWidget;
public boolean expanded = true;
private static final String collapsableOpenCss = "collapsable";
private static final String collapsableClosedCss = "hidden";
private static final String collapsableOpenImg = "/files/images/collapsableOpen.gif";
private static final String collapsableClosedImg = "/files/images/collapsableClosed.gif";
public CollapsableWidget(ParentWidget parent) {
super(parent);
}
public CollapsableWidget(ParentWidget parent, String text) throws Exception {
this(parent);
Matcher match = pattern.matcher(text);
match.find();
expanded = match.group(1) == null;
String title = match.group(2);
String body = match.group(3);
init(title, body);
}
public CollapsableWidget(ParentWidget parent, String title, String body, String cssClass)
throws Exception {
this(parent);
init(title, body);
this.cssClass = cssClass;
}
private void init(String title, String body) throws Exception {
titleWidget = new BlankParentWidget(this, "!meta " + title);
addChildWidgets(body);
}
public String render() throws Exception {
HtmlElement titleElement = new RawHtml(" " + titleWidget.childHtml());
HtmlElement bodyElement = new RawHtml(childHtml());
HtmlElement html = makeCollapsableSection(titleElement, bodyElement);
return html.html();
}
public HtmlTag makeCollapsableSection(HtmlElement title, HtmlElement content) {
String id = random.nextLong() + "";
HtmlTag outerDiv = HtmlUtil.makeDivTag(cssClass);
HtmlTag image = new HtmlTag("img");
image.addAttribute("src", imageSrc());
image.addAttribute("class", "imageleft");
image.addAttribute("id", "img" + id);
HtmlTag anchor = new HtmlTag("a", image);
anchor.addAttribute("class", "anchoredimage");
anchor.addAttribute("href", "javascript:toggleCollapsable('" + id + "');");
outerDiv.add(anchor);
outerDiv.add(title);
HtmlTag collapsablediv = makeCollapsableDiv();
collapsablediv.addAttribute("id", id);
collapsablediv.add(content);
outerDiv.add(collapsablediv);
return outerDiv;
}
private HtmlTag makeCollapsableDiv() {
if (!expanded)
return HtmlUtil.makeDivTag(collapsableClosedCss);
else
return HtmlUtil.makeDivTag(collapsableOpenCss);
}
private String imageSrc() {
if (expanded)
return collapsableOpenImg;
else
return collapsableClosedImg;
}
}
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All other trademarks are property of their respective owners.
|
__label__pos
| 0.646914 |
Softer and Soft Handoff in an Orthogonal Frequency Division Wireless Communication System
- QUALCOMM Incorporated
Transmission patterns for pilot symbols transmitted from a mobile station or base station are provided. The patterns may be selected according to a location of the mobile station with respect to one or more antennas are provided. In some aspects, the pattern may be selected based upon the distance between the mobile station and the one or more antennas. In other aspect, the pattern may be based upon whether the mobile station is in handoff.
Skip to: Description · Claims · Patent History · Patent History
Description
RELATED APPLICATIONS
The present application for patent is a Divisional of U.S. application Ser. No. 11/132,765 entitled “Softer and Soft Handoff in an Orthogonal Frequency Division Wireless Communication System” filed May 18, 2005.
BACKGROUND
I. Field
The present document relates generally to wireless communication and amongst other things to handoff in a wireless communication system.
II. Background
An orthogonal frequency division multiple access (OFDMA) system utilizes orthogonal frequency division multiplexing (OFDM). OFDM is a multi-carrier modulation technique that partitions the overall system bandwidth into multiple (N) orthogonal frequency subcarriers. These subcarriers may also be called tones, bins, and frequency channels. Each subcarrier is associated with a respective sub carrier that may be modulated with data. Up to N modulation symbols may be sent on the N total subcarriers in each OFDM symbol period. These modulation symbols are converted to the time-domain with an N-point inverse fast Fourier transform (IFFT) to generate a transformed symbol that contains N time-domain chips or samples.
In a frequency hopping communication system, data is transmitted on different frequency subcarriers in different time intervals, which may be referred to as “hop periods”. These frequency subcarriers may be provided by orthogonal frequency division multiplexing, other multi-carrier modulation techniques, or some other constructs. With frequency hopping, the data transmission hops from subcarrier to subcarrier in a pseudo-random manner. This hopping provides frequency diversity and allows the data transmission to better withstand deleterious path effects such as narrow-band interference, jamming, fading, and so on.
An OFDMA system can support multiple mobile stations simultaneously. For a frequency hopping OFDMA system, a data transmission for a given mobile station may be sent on a “traffic” channel that is associated with a specific frequency hopping (FH) sequence. This FH sequence indicates the specific subcarrier to use for the data transmission in each hop period. Multiple data transmissions for multiple mobile stations may be sent simultaneously on multiple traffic channels that are associated with different FH sequences. These FH sequences may be defined to be orthogonal to one another so that only one traffic channel, and thus only one data transmission, uses each subcarrier in each hop period. By using orthogonal FH sequences, the multiple data transmissions generally do not interfere with one another while enjoying the benefits of frequency diversity.
An accurate estimate of a wireless channel between a transmitter and a receiver is normally needed in order to recover data sent via the wireless channel. Channel estimation is typically performed by sending a pilot from the transmitter and measuring the pilot at the receiver. The pilot signal is made up of pilot symbols that are known a priori by both the transmitter and receiver. The receiver can thus estimate the channel response based on the received symbols and the known symbols.
A code division multiple access (CDMA) system has a universal frequency reuse that makes it possible for mobile users to receive and send the same signal simultaneously from and to multiple base stations or sectors of a base station. Soft and softer handoff in CDMA systems are techniques whereby mobiles near cell, and sector in the case of softer handoff, boundaries communicate the same transmitted signals to more than one base station or sector of a base station. Soft and softer handoff provides enhanced communication quality and a smoother transition compared to the conventional hard handoff. Soft and softer handoff is intrinsic to a CDMA system, as transmitted signals of different users occupy the same time and frequency allocation. Different users can be separated based on the respective spreading signatures.
Supporting soft and softer handoff in orthogonal multiple-access systems such as TDMA, FDMA and OFDMA is far more difficult and often requires special planning Consider a reverse link transmission in FH-OFDMA. Each user is assigned a non-overlapping time and frequency resource. As such there is little or no intra-cell. However, it is often not possible to reliably detect the signal in a nearby sector or cell, as the interference is considerably large compared to the signal. Low signal-to-noise ratio causes the channel estimation to be inaccurate, further degrading the overall detection performance. Often, the post-detection signal-to-noise ratio (SNR) is too low for the signal observed in a nearby cell/sector to be useful. Techniques such as active set based restricted frequency (ASBR) hopping and common hopping sequence can be used to help improve the detection reliability of the signal observed in a nearby sector/cell. These techniques, however, result in smaller usable system resources (e.g., bandwidth) and often require significant planning
Therefore, there is a need to find efficient approaches to provide soft and softer handoff in OFDMA systems while minimizing the amount of overhead required to perform the soft and softer handoff.
SUMMARY
[To be Completed when Claims Finalized]
Various aspects and embodiments of the invention are described in further detail below. The invention further provides methods, processors, transmitter units, receiver units, base stations, terminals, systems, and other apparatuses and elements that implement various aspects, embodiments, and features of the invention, as described in further detail below.
BRIEF DESCRIPTION OF THE DRAWINGS
The features, nature, and advantages of the present embodiments may become more apparent from the detailed description set forth below when taken in conjunction with the drawings in which like reference characters identify correspondingly throughout and wherein:
FIG. 1 illustrates a multiple access wireless communication system according to one embodiment;
FIG. 2 illustrates a spectrum allocation scheme for a multiple access wireless communication system according to one embodiment;
FIG. 3A illustrates a block diagrams of a pilot assignment scheme according to one embodiment;
FIG. 3B illustrates a block diagrams of a pilot assignment scheme according to another embodiment;
FIG. 4A illustrates a pilot symbol scrambling scheme according to one embodiment;
FIG. 4B illustrates a pilot symbol scrambling scheme according to another embodiment;
FIG. 5A illustrates a pilot pattern assignment scheme according to one embodiment;
FIG. 5B illustrates a pilot pattern assignment scheme according to another embodiment;
FIG. 5C illustrates a pilot pattern assignment scheme according to a further embodiment;
FIG. 5D illustrates a pilot pattern assignment scheme according to an additional embodiment;
FIG. 6 illustrates a multiple access wireless communication system according to another embodiment;
FIG. 7 illustrates a pilot pattern assignment scheme according to yet another embodiment;
FIG. 8 illustrates a block diagram of an embodiment of a transmitter system and a receiver system in a multi-input multi-output multiple access wireless communication system according to an embodiment;
FIG. 9A illustrates a block diagram of a single-antenna mobile station according to an embodiment;
FIG. 9B illustrates a block diagram of a multi-antenna station according to an embodiment;
FIG. 10 illustrates a block diagram of a base station according to an embodiment;
FIG. 11 illustrates a flow chart of a method of pilot pattern assignment according to one embodiment;
FIG. 12 illustrates a flow chart of a method of pilot pattern assignment according to another embodiment; and
FIG. 13 illustrates a flow chart of a method of pilot pattern assignment according to an additional embodiment.
DETAILED DESCRIPTION
Referring to FIG. 1, a multiple access wireless communication system according to one embodiment is illustrated. A base station 100 includes multiple antenna groups 102, 104, and 106 each including one or more antennas. In FIG. 1, only one antenna is shown for each antenna group 102, 104, and 106, however, one or multiple antennas may be utilized for each antenna group that corresponds to a sector of base station 100. Mobile station 108 is in communication with antenna 104, where antenna 104 transmits information to mobile station 108 over forward link 114 and receives information from mobile station 108 over reverse link 112. Mobile station 110 is in communication with antenna 106, where antenna 106 transmits information to mobile station 110 over forward link 118 and receives information from mobile station 110 over reverse link 116.
Each group of antennas 102, 104, and 106 and/or the area in which they are designed to communicate is often referred to as a sector of the base station. In the embodiment, antenna groups 102, 104, and 106 each are designed to communicate to mobile stations in a sector, sectors 120, 122, and 124, respectively, of the areas covered by base station 100.
In order to facilitate handoff for a mobile station, e.g. mobile station 108, a specific pilot pattern is provided to those mobile stations in handoff. The specific arrangement of pilot symbols may be such that all of the mobile stations near the edge of a sector boundary are assigned to transmit a known pattern of pilot symbols so that two different sectors may simultaneously decode the pilot symbols. In other embodiments, a specific pilot pattern is assigned to those mobile stations for which handoff has been requested. The pilot pattern assigned to the mobile station may vary depending on the sectors between which the handoff is occurring, the cell or sector with which the mobile station is communicating.
In order to allow for efficient processing of data symbols, base station 100 may combine data symbols, from multiple sectors for a same mobile station. In an embodiment, this may be done by utilizing the pilot pattern of the mobile station to spatially separate the mobile stations in handoff. That is, since a pilot pattern is known for each mobile station a channel estimate and channel matrix may be obtained for each mobile station from symbols received at the antennas of each sector. This estimate may then be utilized to generate data symbols by combining the data symbols received in each sector. However, it should be noted that in other embodiments combining of data symbols is not performed and the data symbols received in each sector may be decoded independently.
A base station may be a fixed station used for communicating with the terminals and may also be referred to as, and include some or all the functionality of, an access point, a Node B, or some other terminology. A mobile station may also be referred to as, and include some or all the functionality of, a mobile station, a user equipment (UE), a wireless communication device, terminal, access terminal or some other terminology.
As used herein, in communication with antenna group or antenna generally refers to the antennas group or antenna that is responsible for transmission to a mobile station. In the case of transmission from a mobile station, multiple antenna groups may be utilized to receive transmissions including utilizing soft or other types of combining
Referring to FIG. 2, a spectrum allocation scheme for a multiple access wireless communication system is illustrated. A plurality of OFDM symbols 200 is allocated over T symbol periods and S frequency subcarriers. Each OFDM symbol 200 comprises one symbol period of the T symbol periods and a tone or frequency subcarrier of the S subcarriers.
In an OFDM frequency hopping system, one or more symbols 200 may be assigned to a given mobile station. In one embodiment of an allocation scheme as shown in FIG. 2, one or more hop regions, e.g. hop region 202, of symbols to a group of mobile stations for communication over a reverse link. Within each hop region, assignment of symbols may be randomized to reduce potential interference and provide frequency diversity against deleterious path effects.
Each hop region 202 includes symbols 204 that are assigned to the one or more mobile stations that are in communication with the sector of the base station and assigned to the hop region. During each hop period, or frame, the location of hop region 202 within the T symbol periods and S subcarriers varies according to a hopping sequence. In addition, the assignment of symbols 204 for the individual mobile stations within hop region 202 may vary for each hop period.
The hop sequence may pseudo-randomly, randomly, or according to a predetermined sequence, select the location of the hop region 202 for each hop period. The hop sequences for different sectors of the same base station are designed to be orthogonal to one another to avoid “intra-cell” interference among the mobile station communicating with the same base station. Further, hop sequences for each base station may be pseudo-random with respect to the hop sequences for nearby base stations. This may help randomize “inter-cell” interference among the mobile stations in communication with different base stations.
In the case of a reverse link communication, some of the symbols 204 of a hop region 202 are assigned to pilot symbols that are transmitted from the mobile stations to the base station. The assignment of pilot symbols to the symbols 204 should preferably support space division multiple access (SDMA), where signals of different mobile stations overlapping on the same hop region can be separated due to multiple receive antennas at a sector or base station, provided enough difference of spatial signatures corresponding to different mobile stations. To more accurately extract and demodulate signals of different mobile stations, the respective reverse link channels should be accurately estimated. Therefore, it may be desired that pilot symbols on the reverse link enable separating pilot signatures of different mobile stations at each receive antenna within the sector in order to subsequently apply multi-antenna processing to the pilot symbols received from different mobile stations.
Block hopping may be utilized for both the forward link and the reverse link, or just for the reverse link depending on the system. It should be noted that while FIG. 2 depicts hop region 200 having a length of seven symbol periods, the length of hop region 200 can be any desired amount, may vary in size between hop periods, or between different hopping regions in a given hop period.
It should be noted that while the embodiment of FIG. 2 is described with respect to utilizing block hopping, the location of the block need not be altered between consecutive hop periods or at all.
Referring to FIGS. 3A and 3B, block diagrams of pilot assignment schemes according to several embodiments are illustrated. Hop regions 300 and 320 are defined by N symbol periods by S subcarriers or tones. Hop region 300 includes pilot symbols 302 and hop region 320 includes pilot symbols 322, with the remaining symbols periods and tone combinations available for data symbols and other symbols. In one embodiment, pilot symbol locations for each hop regions, i.e. a group of NS contiguous tones over NT consecutive OFDM symbols, should have pilot tones located close to the edges of the hop region. This is generally because typical channels in wireless applications are relatively slow functions of time and frequency so that a first order approximation of the channel, e.g. a first order Taylor expansion, across the hop region in time and frequency provides information regarding channel conditions that is sufficient to estimate the channel for a given mobile station. As such, it is preferred to estimate a pair of channel parameters for proper receipt and demodulation of symbols from the mobile stations, namely the constant component of the channel, a zero order term of a Taylor expansion, and the linear component, a first order term Taylor expansion, of the channel across the time and frequency span of the channel. Generally estimation accuracy of the constant component is independent of pilot placement. The estimation accuracy of the linear component is generally preferably achieved with pilot tones located at the edges of the hop region.
Pilot symbols 302 and 322 are arranged in contiguous pilot symbol clusters 304, 306, 308, and 310 (FIG. 3A) and 324, 326, 328, and 330 (FIG. 3B). In one embodiment, each cluster 304, 306, 308, and 310 (FIG. 3A) and 324, 326, 328, and 330 (FIG. 3B) within a hop region, has a fixed number, and often the same number, of pilot symbols within a given hop region. The utilization of clusters 304, 306, 308, and 310 (FIG. 3A) and 324, 326, 328, and 330 (FIG. 3B) of contiguous pilot symbols may, in one embodiment take into account the effect of a multi-user interference caused by inter-carrier interference which results from high Doppler and/or symbol delay spreads. Further, if pilot symbols from mobile stations scheduled on a same hop region are received at substantially different power levels, signals of a stronger mobile station may create a significant amount of interference for a weaker mobile station. The amount of interference is higher at the edges, e.g. subcarrier 1 and subcarrier S, of the hop region and also at the edge OFDM symbols, e.g. symbol periods 1 and T, when the leakage is caused by excess delay spread, i.e. when the portion of channel energy concentrated in the taps that exceed cyclic prefix of the OFDM symbols becomes significant. Therefore, if pilot symbols are located exclusively at the edges of a hop region there may be degradation in channel estimation accuracy and a bias in interference estimation. Hence, as depicted in FIGS. 3A and 3B pilot symbols are placed close to the edges of the hop region, however, avoiding the situation where all the pilot symbols are at the edges of the hop region.
Referring to FIG. 3A, a hop region 300 is comprised of pilot symbols 302. In the case of channels with a pronounced frequency selectivity rather than time selectivity, pilot symbols 302 are located in contiguous pilot symbol clusters 304, 306, 308, and 310 with each pilot symbol cluster 304, 306, 308, and 310 spanning a multiple symbol periods and one frequency tone. The frequency tone is preferably chosen to be close to the edges of the frequency range of the hop region 300, however, not exactly at the edge. In the embodiment of FIG. 3A, none of the pilot symbols 302 in a given cluster are at the edge frequency tones and in each cluster only pilot symbol may be at an edge symbol period.
One rationale behind a “horizontal” shape of the contiguous pilot symbol clusters of pilot symbols 302 is that, for channels with higher frequency selectivity, the first order (linear) component may be stronger in the frequency domain than in the time domain.
It should be noted that one or more pilot symbols in each cluster, in the embodiment of FIG. 3A, may be at a different tone than one or more pilot symbols in a different cluster. For example, cluster 304 may be at tone S and cluster 306 may be at tone S-1.
Referring to FIG. 3B, in the case of channels with a pronounced time selectivity rather than frequency selectivity, pilot symbols 322 are arranged in clusters 324, 326, 328, and 330 of contiguous pilot symbols that each span multiple frequency tones but have a same symbol period of hop region 320. OFDM symbols at the edges of hop region 320, those that have a maximum tone, e.g. tone S, or minimum tone, e.g. tone 1, of the frequency range that defines the S subcarriers, may be included as part of the pilot symbols, since there may be pilot symbols 322 that are at the edges of the hop region 320. However, in the embodiment shown in FIG. 3B, only one pilot symbol in each cluster may be assigned to the maximum or minimum frequency subcarrier.
In the embodiment depicted in FIG. 3B, a channel with higher time selectivity may have a typical pattern that may be obtained by a 90° rotation of the pattern chosen for channels with higher frequency selectivity (FIG. 3A).
It should be noted that one or more pilot symbols in each cluster, in the embodiment of FIG. 3B, may be assigned to a different symbol period than one or more pilot symbols in a different cluster. For example, cluster 324 may be at different symbol period T than cluster 326.
Additionally, as depicted in the embodiments of FIGS. 3A and 3B, pilot patterns are provided so that the clusters, 304, 306, 308, and 310 (FIG. 3A) and 324, 326, 328, and 330 (FIG. 3B), are preferably symmetric with respect to the center of the hop region. The symmetry of the clusters with respect to the center of the hop region may provide improved simultaneous estimation of the channel with respect to time and frequency responses of the channel.
It should be noted that while FIGS. 3A and 3B depict four clusters of pilot symbols per hop region, a fewer or greater amount of clusters may be utilized in each hop region. Further, the number of pilot symbols per pilot symbol cluster may also vary. The total number of pilot symbols and pilot symbol clusters are a function of the number of pilot symbols required by the base station to successfully demodulate data symbols received on the reverse link and to estimate the channel between the base station and the mobile station. Also, each cluster need not have the same number of pilot symbols. The number of mobile stations that can be multiplexed over a single hop region can, in one embodiment, be equal to the number of pilot symbols in a hop region.
In addition, while FIGS. 3A and 3B depict pilot symbol clusters designed either for channels having frequency selectivity or time selectivity the pilot pattern may be such that there are clusters for frequency selective channels as well as clusters for time selective channels in the same pilot pattern, e.g. some clusters arranged in the pattern of clusters 304, 306, 308, or 310 and some clusters arranged in the pattern of clusters 324, 326, 328, or 330.
In some embodiments, pre-determined pilot patterns for those mobile stations in handoff or at the boundary between two or more sectors or cells will have a pilot pattern that indicates the condition. These pre-determined pilot patterns may be based upon different locations of the pilot symbols versus locations of pilot symbols for pilot patterns used for mobile stations in non-handoff communication with an antenna group of a sector of a base station.
Referring to FIGS. 4A and 4B, pilot allocation schemes according to further embodiments are illustrated. In FIG. 4A, hop regions 400 includes pilot symbols C1,q, C2,q, and C3,q, arranged in cluster 402; C4,q, C5,q, and C6,q, arranged includer 404; C7,q, C8,q, and C9,q, arranged in cluster 406; and C10,q, C11,q, and C12,q arranged in cluster 408. In one embodiment, in order to improve spatial diversity in hop regions where multiple mobile stations provide overlapping pilot symbols, the pilot symbols of different mobile stations should be multiplexed in such a way over the same OFDM symbol period and tone so that the pilot symbols are substantially orthogonal when received at the antennas of the cluster of the base station.
In FIG. 4A, each of the pilot symbols C1,q, C2,q, C3,q, C4,q, C5,q, C6,q, C7,q, C8,q, C9,q, C10,q, C11,q, and C12,q are assigned to multiple mobile stations of hop region 400, that is each symbol period includes multiple pilot symbols, from a number of different mobile station stations. Each of the pilot symbols in a pilot symbol cluster, e.g. cluster 402, 404, 406, and 408, are generated and transmitted in such a way that a receiver of the pilots symbols in the cluster, e.g. base station, can receive them so that they are orthogonal with respect to the pilot symbols from each other mobile station in the same cluster. This can be done by applying a predetermined phase shift, e.g. a scalar function to multiply, each of the samples constituting the pilot symbols transmitted by each of the mobile stations. To provide orthogonality, the inner products of vectors representing the sequence of the scalar functions in each cluster for each mobile station may be set to zero.
Further, in some embodiments, it is preferred that the pilot symbols of each cluster are orthogonal to the pilot symbols of each other cluster of the hop region. This can be provided in the same manner as orthogonality is provided for the pilot symbols within each cluster from a different mobile station, by utilizing a different sequence of scalar functions for the pilot symbols of each mobile station in each cluster of pilot symbols. Mathematical determination of orthogonality can be made by selecting a sequence of scalar multiples for each of the pilot symbols for a particular cluster for the particular mobile station the vector of which is orthogonal, e.g. the inner product is zero, with respect to a vector representing the sequence of scalar multiples used for the pilot symbols of the other mobile stations in all the clusters and the same mobile station in the other clusters.
In one embodiment the number of mobile stations that may be supported, where orthogonality of the pilot symbols across each of the clusters is provided, is equal to the number of pilot symbols that are provided per pilot symbol cluster.
In one embodiment, the exponential functions utilized to multiply the samples of the pilot symbols are generated utilizing a fast Fourier transform function.
In order to combat the intra-sector interference that may arise, scrambling codes may be used for the mobile stations. The scrambling code may be unique to individual mobile stations or may be the same for each of the mobile stations communicating with an individual sector.
In some embodiments, pre-determined scrambling sequences and/or codes may be assigned for pilot patterns for those mobile stations in handoff or at the boundary between two or more sectors or cells will have a pilot pattern that indicates the condition. These pre-determined sequences may be different than those for pilot symbols for pilot patterns used for mobile stations in non-handoff communication with an antenna group of a sector of a base station.
Referring to FIG. 5A, a pilot pattern assignment scheme according to one embodiment is illustrated. A base station 500 includes three sectors 502, 504, and 506. Within each sector, a different pilot pattern is assigned to mobile users for reverse link transmission to the base station in each sector. In the embodiment of FIG. 5A, pilot pattern a is assigned to those mobile stations that communicate with antennas for sector 502, pilot pattern b is assigned to those mobile stations that communicate with antennas for sector 504, and pilot pattern c is assigned to those mobile stations that communicate with antennas for sector 506. The determination as to which sector is in communication with which mobile station may be readily made using well known techniques.
In order to facilitate handoff, base station 500 can determine if pilot symbols received in sector 502 are in pilot pattern a, b, or c. If the pilot symbols are in pilot pattern a, then the base station 500 knows that the mobile station is assigned to that sector. If the pilot symbols are in pilot pattern b or c then the base can either ignore them, if no handoff has been requested or assigned, or demodulate and decode the pilot symbols, if a handoff has been requested or assigned. The base station may then combine data symbols, received at antenna groups for each sector, for those mobile stations in handoff, to provide softer handoff. This combination may be performed as discussed with respect to FIGS. 9A-10.
In the embodiment of FIG. 5A, pilot patterns a, b, and c may be orthogonal to each to provide a relatively simple approach for base station 500 to decode pilot symbols, especially in cases where mobile stations in different sectors are assigned overlapping time and frequency allocations, e.g. the same hop region is assigned in different sectors to different mobile stations. Further, the associated data symbols of the pilot symbols may be simultaneously processed at multiple sectors of the base station, e.g. the data symbols transmitted by a mobile station in sector 502 may be decoded at each of the antennas for sectors 502, 504, and 506 and then combined using maximum ratio combining (MRC) or other known techniques. The simultaneous processing may be provided due to the orthogonality of the pilot patterns with respect to each other, thus allowing estimation and identification of data symbols for the mobile station based upon the orthogonality of the pilot patterns. The orthogonality may be in accordance to any of the approaches described with respect to FIGS. 3A, 3B, 4A, and 4B, e.g. pilot symbol locations, scrambling sequences unique to each user to multiply the pilot symbols transmitted by each user, or scrambling sequences unique to each sector multiply the pilot symbols transmitted by each user.
Referring to FIG. 5B, a pilot pattern assignment scheme according to another embodiment is illustrated. A base station 510 includes three sectors 512, 514, and 516. Within each sector, a different pilot pattern is assigned to mobile users for reverse link transmission that are in non-handoff communication than those in non-handoff communication in another sector. In the embodiment of FIG. 5B, pilot pattern a is assigned to those mobile stations that communicate with antennas for sector 512, pilot pattern b is assigned to those mobile stations that communicate with antennas for sector 514, and pilot pattern c is assigned to those mobile stations that communicate with antennas for sector 516. The determination as to which sector is in communication with which mobile station may be readily made using well known techniques.
In addition, a specific pilot pattern is reserved for handoff, so that any sector that receives the specific pilot pattern knows that the mobile station is in softer handoff. In the embodiment, of FIG. 5B, those mobile stations that are assigned or request handoff between sectors 512 and 514 are assigned to transmit pilot symbols having pilot pattern c, those mobile stations that are assigned or request handoff between sectors 514 and 516 are assigned to transmit pilot symbols having pilot pattern a, and those mobile stations that are assigned or request handoff between sectors 516 and 512 are assigned to transmit pilot symbols having pilot pattern b. In this way, a sector is likely to have minimal interference for those mobile stations in softer handoff, since those sectors in handoff receive pilot symbols that will have low interference with those pilot symbols received at the same sector, since more distant sectors will be using the same pilot pattern. The base station may then combine pilot symbols and data symbols, for those mobile stations that transmit pilot symbols transmitted according to a pilot pattern reserved for handoff, received at antenna groups for each sector to provide softer handoff.
In the embodiment of FIG. 5B, pilot patterns a, b, and c may be orthogonal to each to provide a relatively simple approach for base station 510 to decode pilot symbols. The orthogonality may be in accordance to any of the approaches described with respect to FIGS. 3A, 3B, 4A, and 4B, e.g. pilot symbol locations, scrambling sequences unique to each user to multiply the pilot symbols transmitted by each user, or scrambling sequences unique to each sector multiply the pilot symbols transmitted by each user.
To decode the pilot symbols during handoff, the base station 510 may decide to separately extract the pilot symbols from each sector that uses one of the pilot patterns assigned for handoff, e.g. in sector 512 pilot symbols having pattern c are assumed to relate to a mobile station in handoff. This is possible because with respect to each sector, a handoff user is using a pilot sequence that is orthogonal to all other users in the sector. The base station may then combine data symbols, received at antenna groups for each sector, for those mobile stations in handoff, to provide softer handoff. This combination may be performed as discussed with respect to FIGS. 9A-10.
Alternatively, the base station may perform joint decoding using antennas from each of the sectors at the base station as described with respect to FIG. 5A and FIG. 5B for a pilot pattern assigned for handoff. In such embodiments, the base station may extract the data symbols of a user with the reserved pilot pattern for handoff from each sector and then combine it with signals having the same pilot pattern in the same hop region from other sectors. However, to provide orthogonality among handoff users at a same sector boundary, the hopping sequence of the user utilizing the pilot pattern reserved for handoff is the same in each of the two adjacent sectors. This is to provide that no two users, one from each of the adjacent sectors, are using the same pilot pattern over the same time-frequency, e.g. hop region, allocation at the same time.
Referring to FIG. 5C, a pilot pattern assignment scheme according to a further embodiment is illustrated. A base station 520 includes three sectors 522, 524, and 516. Within each sector, a same pilot pattern or patterns is assigned to mobile users for reverse link transmission to the base station in each sector. In the embodiment of FIG. 5B, pilot patterns a and b are assigned to those mobile stations that communicate with antennas for sector 512, sector 514, and sector 516.
In addition, similarly to FIG. 5C, a specific pilot pattern is reserved for handoff, so that any sector that receives the specific pilot pattern knows that the mobile station is in handoff. In the embodiment of FIG. 5C, a same pilot pattern is assigned to each mobile station in handoff. However, different pilot patterns may be utilized depending on the sector from, or to, which the mobile station is in handoff. The base station may then combine data symbols, received at antenna groups for each sector, for those mobile stations in handoff, to provide softer handoff. This combination may be performed as discussed with respect to FIGS. 9A-10.
In the embodiment of FIG. 5C, pilot patterns a, b, and c may be orthogonal to each to provide a relatively simple approach for base station 520 to decode pilot symbols. The orthogonality may be in accordance to any of the approaches described with respect to FIGS. 3A, 3B, 4A, and 4B, e.g. pilot symbol locations, scrambling sequences unique to each user to multiply the pilot symbols transmitted by each user, or scrambling sequences unique to each sector multiply the pilot symbols transmitted by each user.
The data symbols related to the pilot pattern reserved for handoff, e.g. pilot pattern c, may be simultaneously processed at multiple sectors of base station 520, e.g. the pilot symbols transmitted by a mobile station in sector 502 may be decoded at each of the antennas for sectors 502, 504, and 506 and then combined by utilizing MRC or other known techniques. The simultaneous processing may be provided due to the utilization of the specific pilot pattern for handoff that is orthogonal with respect to all pilot patterns used within the sectors. The orthogonality may be in accordance to any of the approaches described with respect to FIGS. 3A, 3B, 4A, and 4B, e.g. pilot symbol locations, scrambling sequences unique to each user to multiply the pilot symbols transmitted by each user, or scrambling sequences unique to each sector multiply the pilot symbols transmitted by each user.
Referring to FIG. 5D, a pilot pattern assignment scheme according to an additional embodiment is illustrated. A base station 530 includes three sectors 532, 534, and 536. Within each sector, a group of different pilot patterns is assigned to mobile users for reverse link transmission to the base station. In the embodiment of FIG. 5D, one of pilot patterns a, b, and c is assigned to those mobile stations that communicate with antennas for sector 532, one of pilot patterns d, e, and f is assigned to those mobile stations that communicate with antennas for sector 534, and one of pilot patterns g, h, and i is assigned to those mobile stations that communicate with antennas for sector 536. The determination as to which sector is in communication with which mobile station may be readily made using well known techniques.
In order to facilitate handoff, base station 530 can determine if pilot symbols received in sector 532 are in pilot pattern a, b, or c. If the pilot symbols are in pilot pattern a, b, or c, then the base station 500 knows that the mobile station is assigned to that sector. If the pilot symbols are in pilot pattern d, e, f g, h, or i then the base station can either ignore them, if no handoff has been requested or assigned to any mobile station, or demodulate and decode the pilot symbols, if a handoff has been requested or assigned to any mobile station in communication with the base station or a neighboring base station. The base station may then combine pilot symbols, and data symbols, received at antenna groups for each sector to provide softer handoff.
In the embodiment of FIG. 5D, pilot patterns a, b, c, d, e, f g, h, and i may be orthogonal to each to provide a relatively simple approach for base station 530 to decode pilot symbols, especially in cases where mobile stations in different sectors are assigned overlapping time and frequency allocations, e.g. the same hop region is assigned in different sectors to different mobile stations. Further, the data symbols associated with mobile stations in handoff may be simultaneously processed at multiple sectors of the base station, e.g. the pilot symbols transmitted by a mobile station in sector 532 may be decoded at each of the antennas for sectors 532, 534, and 536 and then combined by utilizing MRC or other known techniques. The simultaneous processing may be provided due to the orthogonality of the pilot patterns with respect to each other that allows users to be separated due to the orthogonality of the pilot patterns. The orthogonality may be in accordance to any of the approaches described with respect to FIGS. 3A, 3B, 4A, and 4B, e.g. pilot symbol locations, scrambling sequences unique to each user to multiply the pilot symbols transmitted by each user, or scrambling sequences unique to each sector multiply the pilot symbols transmitted by each user.
Referring to FIG. 6, a multiple access wireless communication system according to another embodiment is illustrated. A multiple access wireless communication system 600 includes multiple cells, e.g. cells 602, 604, and 606. In the embodiment of FIG. 6, each cell 602, 604, and 606 may include multiple sectors, not shown, which are in communication with mobile stations 620. For handoffs between cells, there are several approaches which may be utilized. In one embodiment, each cell assigns a same pilot pattern to each mobile station in handoff. In this way, soft handoff may operate similar to softer handoff described with respect to FIG. 5C for softer handoff. In other embodiments, an approach similar to that of FIG. 5A or 5D may be utilized, where a specific pilot pattern or patterns may be assigned to different cells, either in every cell in the network or reused in specific patterns between groups of cells, based upon some geographic planning algorithm. Both of these approaches provide the ability to decode pilot and data symbols from mobile stations communicating with one base station at multiple base stations. This is an efficient way to provide soft handoff without increasing processing overhead.
In order to process data symbols for those mobile stations in softer handoff, each base station may utilize the unique pilot symbols for those mobile stations in handoff to decode data symbols for those mobile stations in handoff. A base station controller 630 may then determine if one or more of the base stations has decoded transmission from those mobile stations in handoff. In an embodiment, if one or more base stations successfully decodes the data symbols then the decoded data symbols are combined from the base stations that successfully decoded the data symbols by the base station controller 630. In other embodiments, if one or more base stations successfully decodes the data symbols then the decoded data symbols from only one base station are utilized for transmission to the network.
Referring to FIG. 7, a pilot pattern assignment scheme according to yet another embodiment is illustrated. A plurality of base stations 702, 712, and 722 are controlled by a base station controller 730. Each of the base stations 702, 712, and 722 includes an antenna groups that correspond to a sector 704, 706, and 708, base station 702; sector 714, 716, and 718, base station 712; and sector 724, 726, and 728, base station 722. In order to facilitate soft handoff, in one embodiment, a different pilot pattern may be utilized at each base station with respect to an adjacent base station. For example, base station 702 utilizes pilot patterns a, b, and c for communication, base station 712 utilizes pilot patterns d, e, and f, and base station 722 utilizes pilot patterns g, h, and i. In order to facilitate soft handoff, in one embodiment, base station controller 730 may decode data symbols related to pilot symbols that are in a pilot pattern of an adjacent sector. In other embodiments, this information may be available may be available at each base station and decoded symbols may be generated at each base station for pilot symbols from neighboring cells. The decoded symbols may be provided to base station controller 730 which then can combine them or only use for communication to the network.
In order to achieve orthogonality between the pilot patterns of each base station the pilot patterns a, b, and c; d, e, and f, and g, h, and i may each be orthogonal to each other. Alternatively, a cell specific scrambling sequence may be utilized, in addition to the user specific scrambling and sector specific scrambling. A cell specific scrambling schema may be defined by Yc=[Y1,c, . . . , YNP,s]T which is a vector of scalar functions that multiply the respective sequence of pilot symbols for every mobile station in the cell. The overall sequences of pilot symbols Z(q,s,c)=[Z1,(q,s,c), . . . , ZNP,(q,s,c)]T which corresponds to a mobile station with q-th user specific scrambling in the s-th sector of the c-th cell may defined as follows. If sector specific scrambling is utilized:
Zk,(q,s,c)=Sk,q·Xk,s·Yk,c, 1=≦NP, 1≦s≦S, c=1,2, (1)
If sector specific scrambling is not utilized:
Zk,(q,s,c)=Sk,q·Yk,c, 1≦k≦NP, 1≦s≦S, c=1,2, (2)
Unlike user specific and sector specific scrambling, no particular optimization of cell specific scrambling sequences need be utilized. The two design parameters that may be utilized are that:
• All the elements of cell specific scrambling sequences have equal modulus.
• Cell specific scrambling sequences differ substantially for different cells.
Based on the above, the base station controller 730 may know each cell specific scrambling sequence and decode those pilot symbols which are not decoded by a specific base station.
Although FIG. 7 depicts having the same pilot pattern in each sector of each base station, an approach similar to FIGS. 5A, 5B, or 5C may be utilized for each base station.
Referring to FIG. 8, a block diagram of an embodiment of a transmitter system 810 and a receiver system 850 in a MIMO system 800 is illustrated. At transmitter system 810, traffic data for a number of data streams is provided from a data source 812 to transmit (TX) data processor 814. In an embodiment, each data stream is transmitted over a respective transmit antenna. TX data processor 814 formats, codes, and interleaves the traffic data for each data stream based on a particular coding scheme selected for that data stream to provide coded data.
The coded data for each data stream may be multiplexed with pilot data using OFDM techniques. The pilot data is typically a known data pattern that is processed in a known manner and may be used at the receiver system to estimate the channel response. The multiplexed pilot and coded data for each data stream is then modulated (i.e., symbol mapped) based on a particular modulation scheme (e.g., BPSK, QSPK, M-PSK, or M-QAM) selected for that data stream to provide modulation symbols. The data rate, coding, and modulation for each data stream may be determined by instructions performed on provided by processor 830.
The modulation symbols for all data streams are then provided to a TX processor 820, which may further process the modulation symbols (e.g., for OFDM). TX processor 820 then provides NT modulation symbol streams to NT transmitters (TMTR) 822a through 822t. Each transmitter 822 receives and processes a respective symbol stream to provide one or more analog signals, and further conditions (e.g., amplifies, filters, and upconverts) the analog signals to provide a modulated signal suitable for transmission over the MIMO channel. NT modulated signals from transmitters 822a through 822t are then transmitted from NT antennas 824a through 824t, respectively.
At receiver system 850, the transmitted modulated signals are received by NR antennas 852a through 852r and the received signal from each antenna 852 is provided to a respective receiver (RCVR) 854. Each receiver 854 conditions (e.g., filters, amplifies, and downconverts) a respective received signal, digitizes the conditioned signal to provide samples, and further processes the samples to provide a corresponding “received” symbol stream.
An RX data processor 860 then receives and processes the NR received symbol streams from NR receivers 854 based on a particular receiver processing technique to provide NT “detected” symbol streams. The processing by RX data processor 860 is described in further detail below. Each detected symbol stream includes symbols that are estimates of the modulation symbols transmitted for the corresponding data stream. RX data processor 860 then demodulates, deinterleaves, and decodes each detected symbol stream to recover the traffic data for the data stream. The processing by RX data processor 818 is complementary to that performed by TX processor 820 and TX data processor 814 at transmitter system 810.
RX processor 860 may derive an estimate of the channel response between the NT transmit and NR receive antennas, e.g., based on the pilot information multiplexed with the traffic data. RX processor 860 may identify the pilot symbols according to pilot patterns stored in memory, e.g. memory 872 that identify the frequency subcarrier and symbol period assigned to each pilot symbol. In addition, the user specific and sector specific scrambling sequences may be stored in memory so that they may be utilized by RX processor 860 to multiple the received symbols so that the proper decoding can occur.
To decode the pilot and data symbols during handoff, the RX processor 860 and processor 870 may separately extract the pilot symbols from each sector that uses one of the pilot patterns assigned for handoff. The pilot symbols, and associated data symbols, that are transmitted according one of the pilot patterns assigned for handoff are decoded for each sector and may then be combined from all of the sectors. The combining may be performed, as previously stated, by utilizing maximum ratio combining (MRC) or other known techniques.
The channel response estimate generated by RX processor 860 may be used to perform space, space/time processing at the receiver, adjust power levels, change modulation rates or schemes, or other actions. RX processor 860 may further estimate the signal-to-noise-and-interference ratios (SNRs) of the detected symbol streams, and possibly other channel characteristics, and provides these quantities to a processor 870. RX data processor 860 or processor 870 may further derive an estimate of the “operating” SNR for the system. Processor 870 then provides channel state information (CSI), which may comprise various types of information regarding the communication link and/or the received data stream. For example, the CSI may comprise only the operating SNR. The CSI is then processed by a TX data processor 878, modulated by a modulator 880, conditioned by transmitters 854a through 854r, and transmitted back to transmitter system 810.
In addition the SNR estimates may be utilized to determine a location of a mobile station, which is transmitting the pilot symbols, within a cluster of a cell or a cell. This information then can be utilized to determine a pilot pattern to assign to the mobile station. In some embodiments, memories 832 and 872 may contain identifiers that correspond to the different pilot patterns that may be utilized within the wireless communication systems. The memories can identify the pilot patterns based upon whether they are to be used for handoff or if the location of the mobile station indicates that it is near a cell or sector boundary. The pilot patterns may also have the same pilot symbol locations but have user specific and/or sector specific scrambling sequences, depending on how the different pilot patterns are distinguished from each other. These identifiers may then be transmitted from the transmitter to the receiver and then utilized by the receiver to modulate the pilot symbols according to the identified pilot pattern.
At transmitter system 810, the modulated signals from receiver system 850 are received by antennas 824, conditioned by receivers 822, demodulated by a demodulator 840, and processed by a RX data processor 842 to recover the CSI reported by the receiver system. The reported CSI is then provided to processor 830 and used to (1) determine the data rates and coding and modulation schemes to be used for the data streams and (2) generate various controls for TX data processor 814 and TX processor 820.
Processors 830 and 870 direct the operation at the transmitter and receiver systems, respectively. Memories 832 and 872 provide storage for program codes and data used by processors 830 and 870, respectively. The memories 832 and 872 store the pilot patterns in terms of cluster locations, user specific scrambling sequences, sector specific scrambling sequences, if utilized, and cell specific scrambling sequences, if utilized.
Processors 830 and 870 then can select which of the pilot patterns, user specific scrambling sequences, sector specific scrambling sequences, and cell specific scrambling sequences are to be utilized in transmission of the pilot symbols.
At the receiver, various processing techniques may be used to process the NR received signals to detect the NT transmitted symbol streams. These receiver processing techniques may be grouped into two primary categories (i) spatial and space-time receiver processing techniques (which are also referred to as equalization techniques); and (ii) “successive nulling/equalization and interference cancellation” receiver processing technique (which is also referred to as “successive interference cancellation” or “successive cancellation” receiver processing technique).
While FIG. 8 discusses a MIMO system, the same system may be applied to a multi-input single-output system where multiple transmit antennas, e.g. those on a base station, transmit one or more symbol streams to a single antenna device, e.g. a mobile station. Also, a single output to single input antenna system may be utilized in the same manner as described with respect to FIG. 8.
Referring to FIGS. 9A, 9B, and 10, if a base station is equipped with multiple antennas for data reception, then the data transmissions from multiple users may be separated using various receiver spatial processing techniques. If a single antenna mobile station (FIG. 9A) is utilized, a single-input multiple-output (SIMO) channel is formed between single-antenna mobile station 910a and multi-antenna base station 1000 (FIG. 10). The SIMO channel may be characterized by an R×1 channel response vector ha(k,t) for each subband, which may be expressed as:
h _ a ( k , t ) = [ h a , 1 ( k , t ) h a , 2 ( k , t ) h a , R ( k , t ) ] , for k = 1 K , Eq ( 1 )
where k is an index for subband, and ha,i(k,t), for i=1 . . . R , is the coupling or complex channel gain between the single antenna at mobile station 910a and the R antennas at base station 1000 for subband k in hop period t.
A multiple-input multiple-output (MIMO) channel is formed between multi-antenna mobile station 910u (FIG. 9B) and multi-antenna base station 1000. The MIMO channel for mobile station 910u may be characterized by an R×T channel response matrix Hu(k,t) for each subband, which may be expressed as:
Hu(k,t)=[hu,1(k,t) hu,2(k,t) . . . hu,T(k,t)], for k=1 . . . K, Eq (2)
where hu,j(k,t), for j=1 . . . T , is the channel response vector between antenna j at mobile station 910u and the R antennas at base station 1000 for subband k in hop period t. Each channel response vector hu,j(k,t) contains R elements and has the form shown in equation (4).
In general, each mobile station may be equipped with one or multiple antennas and may be assigned S subbands in each hop period, where S≦1. Each mobile station may then have one set of channel response vectors for each antenna, with each vector set containing S channel response vectors for the S subbands assigned to the mobile station for hop period t. For example, if mobile station m is assigned S subbands with indices k through k+S−1 in hop period t, then the vector set for each antenna j of mobile station m would contain S channel response vectors hm,j(k,t) through hm,j(k+S−1, t) for subbands k through k+S−1, respectively. These S channel response vectors are indicative of the channel response between antenna j at mobile station m and the R antennas at the base station for the S subbands assigned to mobile station m. The subband index k for mobile station m changes in each hop period and is determined by the FH sequence assigned to mobile station m.
The channel response vectors for the multiple mobile stations selected for simultaneous data transmission are typically different from one another and may be viewed as “spatial signatures” for these U mobile stations. The base station may estimate the channel response vectors for each mobile station based on pilot symbols received from the mobile stations, which may be time division multiplexed with data symbols as depicted in FIGS. 3A, 3B, 4A, and 4B.
For simplicity, the following description assumes that L=U/N and L single-antenna mobile stations m1 through mL are assigned to each subband group in each hop period. An R×L channel response matrix H(k,t) may be formed for each subband k in each hop period t based on the L channel response vectors for the L mobile stations using subband k in hop period t, as follows:
H _ ( k , t ) = [ h _ m 1 ( k , t ) h _ m 2 ( k , t ) h _ m L ( k , t ) ] , = [ h m 1 , 1 ( k , t ) h m 2 , 1 ( k , t ) h m L , 1 ( k , t ) h m 1 , 2 ( k , t ) h m 2 , 2 ( k , t ) h m L , 2 ( k , t ) h m 1 , R ( k , t ) h m 2 , R ( k , t ) h m L , R ( k , t ) ] , Eq ( 3 ) for k = 1 K ,
where hml(k,t), for l=1. . . L , is the channel response vector for the l-th mobile station using subband k in hop period t. The channel response matrix H(k,t) for each subband in each hop period is dependent on the specific set of mobile stations assigned to that subband and hop period.
The “received” symbols at the base station for each subband k in each symbol period n of each hop period t may be expressed as:
r(k,t,n)=H(k,tx(k,t,n)+n(k,t,n), for k=1 . . . K, Eq (4)
where x(k,t,n) is a vector with L “transmit” symbols sent by the L mobile stations on subband k in symbol period n of hop period t; r(k,t,n) is a vector with R received symbols obtained via the R antennas at the base station for subband k in symbol period n of hop period t; and n(k,t,n) is a noise vector for subband k in symbol period n of hop period t.
For simplicity, the channel response matrix H(k,t) is assumed to be constant for an entire hop period and is not a function of symbol period n. Also for simplicity, the noise may be assumed to be additive white Gaussian noise (AWGN) with a zero mean vector and a covariance matrix of φnn2·I, where σ2 is the variance of the noise and I is the identity matrix.
K transmit symbol vectors, x(k,t,n) for k=1. . . K, are formed for the K subbands in each symbol period of each hop period. Because different sets of mobile stations may be assigned to different subbands in a given hop period, as determined by their FH sequences, the K transmit symbol vectors x(k,t,n) for each symbol period of each hop period may be formed by different sets of mobile stations. Each vector x(k,t,n) contains L transmit symbols sent by the L mobile stations using subband k in symbol period n of hop period t. In general, each transmit symbol may be a data symbol, a pilot symbol, or a “zero” symbol (which is a signal value of zero).
K received symbol vectors, r(k,t,n) for k=1 . . . K, are obtained for the K subbands in each symbol period of each hop period. Each vector r(k,t,n) contains R received symbols obtained via the R antennas at the base station for one subband in one symbol period. For a given subband k, symbol period n, and hop period t, the j-th transmit symbol in the vector x(k,t,n) is multiplied by the j-th vector/column of the channel response matrix H(k,t) to generate a vector rj(k,t,n). The L transmit symbols in x(k,t,n), which are sent by L different mobile stations, are multiplied by the L columns of H(k,t) to generate L vectors r1(k,t,n) through rL(k,t,n), one vector rj(k,t,n) for each mobile station. The vector r(k,t,n) obtained by the base station is composed of the L vectors r1(k,t,n) through rL(k,t,n), or
r _ ( k , t , n ) = j = 1 L r _ j ( k , t , n ) .
Each received symbol in r(k,t,n) thus contain a component of each of the L transmit symbols in x(k,t,n). The L transmit symbols sent simultaneously by the L mobile stations on each subband k in each symbol period n of each hop period t thus interfere with one another at the base station.
The base station may use various receiver spatial processing techniques to separate out the data transmissions sent simultaneously by the L mobile stations on each subband in each symbol period. These receiver spatial processing techniques may include a zero-forcing (ZF) technique, a minimum mean square error (MMSE) technique, a maximal ratio combining (MRC) technique, or other known techniques.
For the zero-forcing technique, the base station may derive a spatial filter matrix Mzf(k,t) for each subband k in each hop period t, as follows:
Mzf(k,t)=[HH(k,tH(k,t)]1·HH(k,t), Eq (5)
where “H” denotes a conjugate transpose. The base station estimates the channel response matrix H(k,t) for each subband, e.g., based on pilots transmitted by the mobile stations. The spatial processing of pilot symbols may be any manner as previously described herein.
The base station then uses the estimated channel response matrix Ĥ(k,t) to derive the spatial filter matrix. For clarity, the following description assumes no estimation error so that Ĥ(k,t)=H(k,t). Because H(k,t) is assumed to be constant across hop period t, the same spatial filter matrix Mzf(k,t) may be used for all symbol periods in hop period t.
The base station may perform zero-forcing processing for each subband k in each symbol period n of each hop period t, as follows:
x _ ^ zf ( k , t , n ) = M _ zf ( k , t ) · r _ ( k , t , n ) , = [ H _ H ( k , t ) · H _ ( k , t ) ] - 1 · H _ H ( k , t ) · [ H _ ( k , t ) · x _ ( k , t , n ) + n _ ( k , t , n ) ] , = x _ ( k , t , n ) + n _ zf ( k , t , n ) , Eq . ( 6 )
where {circumflex over (x)}zf(k,t,n) is a vector with L “detected” data symbols for subband k in symbol period n of hop period t; and nzf(k,t,n) is the noise after the zero-forcing processing. A detected data symbol is an estimate of a data symbol sent by a mobile station.
For the MMSE technique, the base station may derive a spatial filter matrix Mmmse(k,t) for each subband k in each hop period t, as follows:
Mmmse(k,t)=[HH(k,t)+σ2·I]−1·HH(k,t). Eq (7)
If the covariance matrix φnn of the noise is known, then this covariance matrix may be used in place of σ2·I in equation (10).
The base station may perform MMSE processing for each subband k in each symbol period n of each hop period t, as follows:
x _ ^ mmse ( k , t , n ) = D _ mmse - 1 ( k , t ) · M _ mmse ( k , t ) · r _ ( k , t , n ) , = D _ mmse - 1 ( k , t ) · M _ mmse ( k , t ) · [ H _ ( k , t ) · x _ ( k , t , n ) + n _ ( k , t , n ) ] , x _ ( k , t , n ) + n _ mmse ( k , t , n ) , Eq . ( 8 )
where Dmmse(k,t) is a diagonal vector containing the diagonal elements of a matrix [Mmmse(k,t)·H(k,t)], or Dmmse(k,t)=diag[Mmmse(k,t)·H(k,t)]; and nmmse(k,t,n) is the noise after the MMSE processing.
The symbol estimates from the spatial filter Mmmse(k,t) are unnormalized estimates of the transmit symbols in x(k,t,n). The multiplication with the scaling matrix Dmmse−1(k,t) provides normalized estimates of the transmit symbols.
For the MRC technique, the base station may derive a spatial filter matrix Mmrc(k,t) for each subband k in each hop period t, as follows:
Mmrc(k,t)=HH(k,t). Eq (9)
The base station may perform MRC processing for each subband k in each symbol period n of each hop period t, as follows:
x _ ^ mrc ( k , t , n ) = D _ mrc - 1 ( k , t ) · M _ mrc ( k , t ) · r _ ( k , t , n ) , = D _ mrc - 1 ( k , t ) · H _ H ( k , t ) · [ H _ ( k , t ) · x _ ( k , t , n ) + n _ ( k , t , n ) ] , x _ ( k , t , n ) + n _ mrc ( k , t , n ) , Eq ( 10 )
where Dmrc(k,t) is a diagonal vector containing the diagonal elements of a matrix [HH(k,t)·H(k,t)], or Dmrc(k,t)=diag[HH(k,t)·H(k,t)]; and nmrc(k,t,n) is the noise after the MRC processing.
As shown above, the multiple data transmissions sent simultaneously from up to L mobile stations on each subband k in each symbol period n of each hop period t may be separated by the base station based on their uncorrelated spatial signatures, which are given by their channel response vectors hml(k,t). This allows a higher capacity when the number of antennas used for data reception increases. Furthermore, this approach may reduce the amount of intra-cell interference observed on each subband in each hop period so that better utilization of the additional capacity created in the spatial dimension can be achieved.
At each base station, the above processing techniques may be performed by generated the estimated matrices utilizing symbol data received at each antenna group, i.e. those for different sectors. For example, if a mobile station is in handoff its pilot and data symbols are received at multiple antenna groups. Since the pilot symbols received at each the decoded data symbols may be generated by combining the data symbols received at each antenna group.
In the case of a soft handoff across multiple cells, each cell or sector within a cell may decode the data symbols. Then a base station controller that controls the cells may combine the decoded symbols or may use a symbol decoded at one of the cells without regard to decoding performed at the other cell or cells for that mobile station. Alternatively, it may combine the decoded symbols from multiple base stations.
FIGS. 9A and 9B illustrate block diagrams of embodiments of single-antenna mobile station 910a and multi-antenna mobile station 910u respectively. At single-antenna mobile station 910a, an encoder/modulator 914a receives traffic/packet data (denoted as {da}) from a data source 912a and possibly overhead/signaling data from a controller 940a, processes (e.g., encodes, interleaves, and symbol maps) the data based on one or more coding and modulation schemes selected for mobile station 910a, and provides data symbols (denoted as {xa}) for mobile station 910a. Each data symbol is a modulation symbol, which is a complex value for a point in a signal constellation for a modulation scheme (e.g., M-PSK or M-QAM).
A symbol-to-subband mapper 920a receives the data symbols and pilot symbols and provides these symbols onto the proper subband(s) in each symbol period of each hop period, as determined by an FH control from an FH generator 922a. FH generator 922a may generate the FH control based on an FH sequence or a traffic channel assigned to mobile station 910a. FH generator 922a may be implemented with look-up tables, PN generators, and so on. Mapper 920a also provides a zero symbol for each subband not used for pilot or data transmission. For each symbol period, mapper 920a outputs K transmit symbols for the K total subbands, where each transmit symbol may be a data symbol, a pilot symbol, or a zero symbol.
An OFDM modulator 930a receives K transmit symbols for each symbol period and generates a corresponding OFDM symbol for that symbol period. OFDM modulator 930a includes an inverse fast Fourier transform (IFFT) unit 932 and a cyclic prefix generator 934. For each symbol period, IFFT unit 932 transforms K transmit symbols to the time domain using a K-point IFFT to obtain a “transformed” symbol that contains K time-domain samples. Each sample is a complex value to be transmitted in one sample period. Cyclic prefix generator 934 repeats a portion of each transformed symbol to form an OFDM symbol that contains N+C samples, where C is the number of samples being repeated. The repeated portion is often called a cyclic prefix and is used to combat ISI caused by frequency selective fading. An OFDM symbol period (or simply, a symbol period) is the duration of one OFDM symbol and is equal to N+C sample periods. OFDM modulator 930a provides a stream of OFDM symbols to a transmitter unit (TMTR) 936a. Transmitter unit 936a processes (e.g., converts to analog, filters, amplifies, and frequency upconverts) the OFDM symbol stream to generate a modulated signal, which is transmitted from an antenna 938a.
At multi-antenna mobile station 910u, an encoder/modulator 914u receives traffic/packet data (denoted as {du}) from a data source 912u and possibly overhead/signaling data from a controller 940u, processes the data based on one or more coding and modulation schemes selected for mobile station 910u, and provides data symbols (denoted as {xu}) for mobile station 910u. A demultiplexer (Demux) 916u demultiplexes the data symbols into T streams for the T antennas at mobile station 910u, one data symbol stream {xu,j} for each antenna, and provides each data symbol stream to a respective symbol-to-subband mapper 920u. Each mapper 920u receives the data symbols and pilot symbols for its antenna and provides these symbols onto the proper subband(s) in each symbol period of each hop period, as determined by an FH control generated by an FH generator 922u based on an FH sequence or a traffic channel assigned to mobile station 910u. Up to T different data symbols or pilot symbols may be sent from the T antennas in each symbol period on each subband assigned to mobile station 910u. Each mapper 920u also provides a zero symbol for each subband not used for pilot or data transmission and, for each symbol period, outputs K transmit symbols for the K total subbands to a corresponding OFDM modulator 930u.
Each OFDM modulator 930u receives K transmit symbols for each symbol period, performs OFDM modulation on the K transmit symbols, and generates a corresponding OFDM symbol for the symbol period. T OFDM modulators 930ua through 930ut provide T streams of OFDM symbols to T transmitter units 936u a through 936u t, respectively. Each transmitter unit 936u processes its OFDM symbol stream and generates a corresponding modulated signal. T modulated signals from transmitter units 536ua through 536ut are transmitted from T antennas 938ua through 938ut, respectively.
Controllers 940a and 940u direct the operation at mobile stations 910a and 910u, respectively. Memory unit 942a and 942u provide storage for program codes and data used by controllers 940a and 940u, respectively.
Referring to FIG. 10, a block diagram of an embodiment of base station 1000 is illustrated. The modulated signals transmitted by the U mobile stations selected for data transmission are received by R antennas 1012a through 1012r, and each antenna provides a received signal to a respective receiver unit (RCVR) 1014. Each receiver unit 1014 processes (e.g., filters, amplifies, frequency downconverts, and digitizes) its received signal and provides a stream of input samples to an associated OFDM demodulator (Demod) 1020. Each OFDM demodulator 1020 processes its input samples and provides received symbols. Each OFDM demodulator 1020 typically includes a cyclic prefix removal unit and a fast Fourier transform (FFT) unit. The cyclic prefix removal unit removes the cyclic prefix in each received OFDM symbol to obtain a received transformed symbol. The FFT unit transforms each received transformed symbol to the frequency domain with a K-point FFT to obtain K received symbols for the K subbands. For each symbol period, R OFDM demodulators 1020a through 1020r provide R sets of K received symbols for the R antennas to a receive (RX) spatial processor 1030.
Receive (RX) spatial processor 1030 includes K subband spatial processors 1032a through 1032k for the K subbands. Within RX spatial processor 1030, the received symbols from OFDM demodulators 1020a through 1020r for each symbol period are demultiplexed into K vectors of received symbols, r(k,t,n) for k=1 . . . K, which are provided to the K spatial processors 1032. Each spatial processor 10632 also receives a spatial filter matrix M(k,t) for its subband, performs receiver spatial processing on r(k,t,n) with M(k,t) as described above, and provides a vector {circumflex over (x)}(k,t,n) of detected data symbols. For each symbol period, K spatial processors 1032 through 10632k provide K sets of detected data symbols in K vectors {circumflex over (x)}(k,t,n) for the K subbands to a subband-to-symbol demapper 1040.
Demapper 1040 obtains the K sets of detected data symbols for each symbol period and provides detected data symbols for each mobile station m onto a stream {{circumflex over (x)}m} for that mobile station, where m ∈ {a . . . u}. The subbands used by each mobile station are determined by an FH control generated by an FH generator 1042 based on the FH sequence or traffic channel assigned to that mobile station. A demodulator/decoder 10650 processes (e.g., symbol demaps, deinterleaves, and decodes) the detected data symbols {{circumflex over (x)}m} for each mobile station and provides decoded data {{circumflex over (d)}m} for the mobile station.
A channel estimator 1034 obtains received pilot symbols from OFDM demodulators 1020a through 1020r and derives a channel response vector for each antenna of each mobile station transmitting to base station 1000 based on the received pilot symbols for the mobile station. A spatial filter matrix computation unit 1036 forms a channel response matrix H(k,t) for each subband in each hop period based on the channel response vectors of all mobile stations using that subband and hop period. Computation unit 1036 then derives the spatial filter matrix M(k,t) for each subband of each hop period based on the channel response matrix H(k,t) for that subband and hop period and further using the zero-forcing, MMSE, or MRC technique, as described above. Computation unit 1036 provides K spatial filter matrices for the K subbands in each hop period to K subband spatial processors 1032a through 1032k.
A controller 1060 directs the operation at base station 1000 and other base stations, which are generally proximate to base station 1000. A memory unit 1062 provides storage for program codes and data used by controller 1060. In the case of a soft handoff across multiple cells, controller 1060 may combine the decoded symbols or may use a symbol decoded at base station without regard to decoding performed at the other cell or cells for that mobile station. Alternatively, it may combine the decoded symbols from multiple base stations.
Referring to FIG. 11, a flow chart of a method of pilot symbol assignment according to one embodiment is illustrated. A determination is made with which antenna group, or within which sector, an access terminal is communicating, block 1100. This determination may be made using known techniques, or may be assigned by the access point. Based upon the information, a pilot pattern is assigned to the access terminal, block 1102. The pilot pattern may be an only pilot pattern for the sector or one of many pilot patterns assigned to the sector.
Referring to FIG. 12 a flow chart of a method of pilot symbol assignment according to another embodiment is illustrated. A determination is made as to the location of an access terminal, block 1200. This may be based upon determining a distance between the access terminal and one or more antenna groups of the access point, for example by determining signal strength or signal-to-noise ratios. Further, the determination may be made based upon whether the access terminal is near a boundary between one or more sectors of the access point. In other embodiments, this may be done by utilizing quality of service requirements to select the indicator of the plurality of indicators, channel quality information received from the access terminal, or other signal quality indicators such as SNR or the like.
Based upon the information, a pilot pattern is assigned to the access terminal, block 1202. The pilot pattern assigned may be unique to the boundary between two or more sectors, the same for all boundaries for all the sectors of an access point, or a mix thereof Further, the specific pilot pattern assigned to those access terminals near the boundary may vary over time or based upon other system parameters. Those access terminal not near a boundary, may be assigned one or more of one or more pilot patterns allocated for access terminals that communicate with only one sector or antenna group.
Referring to FIG. 13, a flow chart of a method of pilot symbol assignment according to an additional embodiment is illustrated. A determination is made as to the location of an access terminal, block 1300. This may be based upon determining a location of the access terminal and one or more antenna groups of the access point or by determining whether a request has been made for handoff
Based upon the information, a pilot pattern is assigned to the access terminal, block 1302. The pilot pattern assigned for those in handoff may different than those not in handoff. For example, the pilot pattern may be unique to a handoff between any combination of sectors, the same for all for all handoffs between all the sectors of an access point, or a mix thereof. Further, the specific pilot pattern assigned to those access terminals for handoff may vary over time or based upon other system parameters. Those access terminal not in handoff, may be assigned one or more of one or more pilot patterns allocated for access terminals that communicate with only one sector or antenna group.
The pilot patterns assigned in FIGS. 11-13, may comprise pilot symbol locations and either, both, or neither of user scrambling sequences and sector specific scrambling sequences. Also, the methods may be altered to apply to cells by substituting cells for sectors with respect to any of the blocks described with respect to FIGS. 11-13.
The techniques described herein may be implemented by various means. For example, these techniques may be implemented in hardware, software, or a combination thereof. For a hardware implementation, the processing units within a base station or a mobile station may be implemented within one or more application specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field programmable gate arrays (FPGAs), processors, controllers, micro-controllers, microprocessors, other electronic units designed to perform the functions described herein, or a combination thereof.
For a software implementation, the techniques described herein may be implemented with modules (e.g., procedures, functions, and so on) that perform the functions described herein. The software codes may be stored in memory units and executed by processors. The memory unit may be implemented within the processor or external to the processor, in which case it can be communicatively coupled to the processor via various means as is known in the art.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments may be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A wireless communication apparatus, comprising:
a plurality of antenna groups;
a memory that stores a plurality of pilot pattern indicators each corresponding to a plurality of pilot symbols and corresponding to one or more of the plurality of antenna groups; and
a circuit coupled with the plurality of antenna groups that selects a pilot pattern indicator of the plurality of pilot pattern indicators to be transmitted to a wireless communication device based upon whether the wireless communication device is in handoff.
2. The wireless communication apparatus of claim 1, wherein the memory stores a number of pilot pattern indicators equal to the number of antenna groups.
3. The method of claim 1, wherein the memory stores a number of pilot pattern indicators equal to three times the number of antenna groups.
4. The wireless communication apparatus of claim 1, wherein the wireless communication apparatus transmits signals according to an OFDM communication protocol.
5. The wireless communication apparatus of claim 1, wherein the circuit comprises a processor.
6. The wireless communication apparatus of claim 1, wherein the circuit determines whether the wireless communication device is in handoff based upon channel quality information received from the wireless communication device.
7. The wireless communication apparatus of claim 1, wherein each group of the plurality of pilot symbols corresponds to a different scrambling sequence of a plurality of scrambling sequences and wherein the pilot pattern indicator corresponds to a pre-determined handoff scrambling sequence.
8. The wireless communication apparatus of claim 1, wherein each group of the plurality of pilot symbols corresponds to pilot symbol locations of a plurality of patterns of pilot symbol locations and wherein a group corresponding to the pilot pattern indicator corresponds to a pre-determined handoff pilot pattern.
9. The wireless communication apparatus of claim 1, wherein the circuit selects the pilot pattern indicator of the plurality of pilot pattern indicators to be transmitted to the wireless communication device based upon whether the wireless communication device is in handoff and based upon the antenna group with which the wireless communication device is currently communicating.
10. The wireless communication apparatus of claim 1, wherein each of the plurality of pilot symbols corresponding to each of the plurality of pilot pattern indicators is orthogonal with respect to each other plurality of pilot symbols corresponding to each other of the plurality of pilot pattern indicators.
11. The wireless communication apparatus of claim 1, wherein the circuit decodes data symbols received at each of the plurality of antenna groups associated with each of the groups of the plurality of pilot symbols corresponding to a pilot symbol indicator of the plurality of pilot symbol indicators and then combines decoded data symbols for a same group of the plurality of pilot symbols received at each of the plurality of antenna groups.
12. A method of selecting a pilot pattern for a wireless communication device comprising:
determining whether a wireless communication device is in handoff;
selecting a pilot pattern of a plurality of pilot patterns to be utilized for transmission by the wireless communication device based upon whether the wireless communication device is in handoff; and
transmitting an indicator of the pilot pattern to the wireless communication device.
13. The method of claim 12, further comprising determining which antenna group the wireless communication device is in communication, and wherein selecting the pilot pattern further comprises selecting the pilot pattern based upon the antenna group the wireless communication device is in communication.
14. The method of claim 12, wherein determining whether the wireless communication device is in handoff further comprises determining whether the wireless communication device is in handoff based upon channel quality information.
15. The method of claim 12, wherein each of the plurality of pilot patterns corresponds to a different scrambling sequence of a plurality of scrambling sequences and wherein the indicator corresponds to a pre-determined handoff scrambling sequence.
16. The method of claim 12, wherein each of the plurality of pilot patterns corresponds to pilot symbol locations of a plurality of patterns of pilot symbol locations and wherein the indicator corresponds to a pre-determined handoff pilot pattern.
17. The method of claim 14, wherein determining whether the wireless communication device is in handoff further comprises determining whether the wireless communication device is in handoff based upon channel quality information received from the wireless communication device.
18. The method of claim 12, wherein determining whether the wireless communication device is in handoff comprises determining whether the wireless communication device is in handoff is based upon whether a request for handoff has been provided.
19. The method of claim 12, wherein each pilot pattern of the plurality of pilot patterns is orthogonal with respect to each other pilot pattern of the plurality of pilot patterns.
20. The method of claim 12, wherein each pilot pattern of the plurality of pilot patterns is assigned a different scrambling sequence of a plurality of scrambling sequence than each other pilot pattern of the plurality of pilot patterns.
21. A wireless communication apparatus, comprising:
a plurality of antenna groups each of which corresponds to one of a plurality of sectors of a cell in which a wireless communication apparatus is capable of communication;
a memory that stores a plurality of indicators each corresponding to a pilot pattern of a plurality of pilot patterns, at least one of the plurality of pilot patterns corresponding to a handoff; and
a circuit coupled with the plurality of antenna groups and the memory, the circuit determining if a pilot pattern received at one or more of the antenna groups corresponds to the at least one pilot pattern and combining processed data symbols, associated with the at least one pilot pattern, received at the one or more antenna groups.
22. The wireless communication apparatus of claim 21, wherein the circuit performs combining by using maximum ratio combining
23. The wireless communication apparatus of claim 21, wherein the circuit assigns the at least one pilot pattern to a wireless communication device based upon a determination as to whether the wireless communication device is in handoff.
24. The wireless communication apparatus of claim 21, wherein the circuit determines whether the wireless communication device is in handoff based upon a request for handoff.
25. The wireless communication apparatus of claim 21, wherein the circuit determines whether the wireless communication device is in handoff based upon a location of the wireless communication device.
26. The wireless communication apparatus of claim 21, wherein the circuit determines the location of the wireless communication device based upon a signal to noise ratio.
27. The wireless communication apparatus of claim 21, wherein the circuit comprises a processor.
28. The wireless communication apparatus of claim 21, wherein the wireless communication apparatus transmits signals according to an OFDM communication protocol.
29. The wireless communication apparatus of claim 21, wherein the plurality of groups of pilot symbols are each orthogonal to each other.
Patent History
Publication number: 20100254354
Type: Application
Filed: Jun 17, 2010
Publication Date: Oct 7, 2010
Patent Grant number: 8045988
Applicant: QUALCOMM Incorporated (San Diego, CA)
Inventors: Arak Sutivong (San Diego, CA), Ayman Fawzy Naguib (Cupertino, CA), Dhananjay Gore (San Diego, CA), Alexei Gorokhov (San Diego, CA), Tingfang Ji (San Diego, CA)
Application Number: 12/818,078
Classifications
Current U.S. Class: Using Multiple Antennas At A Station (370/334); Hand-off Control (370/331)
International Classification: H04W 36/00 (20090101);
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| 0.749569 |
Capturing mouse click events with Python and OpenCV
In this article, we will learn how to capture mouse click events with Python and OpenCV?
Submitted by Abhinav Gangrade, on July 12, 2020
Modules used:
In this article, we will use Python-openCV(cv2) and NumPy modules.
Python-opencv(cv2):
Python-opencv(cv2) is a python library that will help us to solve the open-source computer vision problems.
NumPy:
Numpy stands for Numerical Python. This library is used for scientific computing. In this article, we will use this module to create a blank black image.
How we can download these modules?
The general way to download these modules:
• python-opencv(cv2): pip install opencv-python
• Numpy: pip install numpy
• Pycharm users: Pycharm users can go to the project interpreter and install this module from there.
What we will do in this Article?
In this article, we will check the mouse click event, we will create a blank image with the help of NumPy and after that when we click the left button it will create a circle on the image and when we will click the right button it also create a circle of any color on the image. In this way, we will check the mouse clicking event of the mouse.
Important Function we will use in this Article:
1. np.zeros((<size with layer>),np.uint8): This Function will create a blank Image.
2. cv2.setMouseCallback(<Image Frame>,<Event Capturing Function>): This Function will check the mouse clicking function and do the following actions according to the Event capturing Function.
Program:
# import modules
import cv2 ,numpy as np
# set the window name
window="Include Help"
# create a blank image
# the image size is (512,512) and 3 layered
image=np.zeros((512,512,3),np.uint8)
# set the name to the window
cv2.namedWindow(window)
# Create the Event Capturing Function
def capture_event(event,x,y,flags,params):
# event= click of the mouse
# x,y are position of cursor
# check the event if it was right click
if event==cv2.EVENT_RBUTTONDOWN:
# create a circle at that position
# of radius 30 and color red
cv2.circle(image,(x,y),30,(0,0,255),-1)
# Check if the event was left click
if event==cv2.EVENT_LBUTTONDBLCLK:
# create a circle at that position
# of radius 30 and color greeen
cv2.circle(image,(x,y),30,(0,255,0),-1)
# check if the event was scrolling
if event==cv2.EVENT_MBUTTONDBLCLK:
# create a circle at that position
# of radius 30 and color blue
cv2.circle(image,(x,y),30,(255,0,0),-1)
# set the mouse settin function
cv2.setMouseCallback(window,capture_event)
# create a loop untill we press the button
while True:
cv2.imshow(window,image)
if cv2.waitKey(1)==13:
break
cv2.destroyAllWindows()
Output:
Capturing mouse click events with Python and OpenCV
In this way, we can capture the mouse click event with the help of Python-opencv(cv2).
Comments and Discussions!
Load comments ↻
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| 0.992078 |
SheafSystem 0.0.0.0
poset_bounds.cc
1
2 //
3 // Copyright (c) 2014 Limit Point Systems, Inc.
4 //
5 // Licensed under the Apache License, Version 2.0 (the "License");
6 // you may not use this file except in compliance with the License.
7 // You may obtain a copy of the License at
8 //
9 // http://www.apache.org/licenses/LICENSE-2.0
10 //
11 // Unless required by applicable law or agreed to in writing, software
12 // distributed under the License is distributed on an "AS IS" BASIS,
13 // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14 // See the License for the specific language governing permissions and
15 // limitations under the License.
16 //
17
18 // Implementation for class poset_bounds
19
20 #include "SheafSystem/poset_bounds.h"
21
22 #include "SheafSystem/assert_contract.h"
23
24 // ===========================================================
25 // ANY FACET
26 // ===========================================================
27
30 clone() const
31 {
32 poset_bounds* result;
33
34 // Preconditions:
35
36
37 // Body:
38
39 result = new poset_bounds(*this);
40
41 // Postconditions:
42
43 // Exit:
44
45 return result;
46 }
47
48 bool
50 invariant() const
51 {
52 bool result = true;
53
54 // Preconditions:
55
56 // Body:
57
58 // Must satisfy base class invariant
59
60 result = result && any::invariant();
61
62 if(invariant_check())
63 {
64 // Prevent recursive calls to invariant
65
67
68 // Finished, turn invariant checking back on.
69
71 }
72
73 // Postconditions:
74
75 // Exit
76
77 return result;
78 }
79
80 bool
82 is_ancestor_of(const any* other) const
83 {
84
85 // Preconditions:
86
87 require(other != 0);
88
89 // Body:
90
91 // True if other conforms to this
92
93 bool result = dynamic_cast<const poset_bounds*>(other) != 0;
94
95 // Postconditions:
96
97 return result;
98
99 }
100
101 // ===========================================================
102 // POSET_BOUNDS FACET
103 // ===========================================================
104
107 {
108
109 // Preconditions:
110
111 // Body:
112
113 _lb = 0;
114 _lb_is_singleton = false;
115 _bounded_below = false;
116
117 _ub = 0;
118 _ub_is_singleton = false;
119 _bounded_above = false;
120
121 // Postconditions:
122
123 ensure(invariant());
124
125 // Exit:
126
127 return;
128 }
129
132 : _descriptor(xother._descriptor)
133 {
134 // Preconditions:
135
136 // Body:
137
138 switch(_descriptor.mode())
139 {
140 case poset_bounds_descriptor::MEMBER_MEMBER:
141 _lb = (xother._lb != 0) ? new zn_to_bool(*xother._lb) : 0;
142 _lb_is_singleton = true;
143
144 _bounded_below = (lb_id() != BOTTOM_INDEX);
145
146 _ub = (xother._ub != 0) ? new zn_to_bool(*xother._ub) : 0;
147 _ub_is_singleton = true;
148
149 _bounded_above = (ub_id() != TOP_INDEX);
150
151 break;
152
153 case poset_bounds_descriptor::MEMBER_SUBPOSET:
154 _lb = (xother._lb != 0) ? new zn_to_bool(*xother._lb) : 0;
155 _lb_is_singleton = true;
156
157 _bounded_below = (lb_id() != BOTTOM_INDEX);
158
159 _ub = xother._ub;
160 _ub_is_singleton = false;
161 _bounded_above = true;
162
163 break;
164
165 case poset_bounds_descriptor::SUBPOSET_MEMBER:
166 _lb = xother._lb;
167 _lb_is_singleton = false;
168 _bounded_below = true;
169
170 _ub = (xother._ub != 0) ? new zn_to_bool(*xother._ub) : 0;
171 _ub_is_singleton = true;
172
173 _bounded_above = (ub_id() != TOP_INDEX);
174
175 break;
176
177 case poset_bounds_descriptor::SUBPOSET_SUBPOSET:
178 _lb = xother._lb;
179 _lb_is_singleton = false;
180 _bounded_below = true;
181
182 _ub = xother._ub;
183 _ub_is_singleton = false;
184 _bounded_above = true;
185
186 break;
187
188 default:
189 post_fatal_error_message("unrecognized specification mode");
190 break;
191 }
192
193 // Postconditions:
194
195 ensure(invariant());
196 }
197
200 : _descriptor(xdesc)
201 {
202 // Preconditions:
203
204
205 // Body:
206
207 switch(_descriptor.mode())
208 {
209 case poset_bounds_descriptor::MEMBER_MEMBER:
210 _lb = 0;
211 _lb_is_singleton = true;
212
213 _bounded_below = (lb_id() != BOTTOM_INDEX);
214
215 _ub = 0;
216 _ub_is_singleton = true;
217
218 _bounded_above = (ub_id() != TOP_INDEX);
219
220 break;
221
222 case poset_bounds_descriptor::MEMBER_SUBPOSET:
223 _lb = 0;
224 _lb_is_singleton = true;
225
226 _bounded_below = (lb_id() != BOTTOM_INDEX);
227
228 _ub = 0;
229 _ub_is_singleton = false;
230 _bounded_above = true;
231
232 break;
233
234 case poset_bounds_descriptor::SUBPOSET_MEMBER:
235 _lb = 0;
236 _lb_is_singleton = false;
237 _bounded_below = true;
238
239 _ub = 0;
240 _ub_is_singleton = true;
241
242 _bounded_above = (ub_id() != TOP_INDEX);
243
244 break;
245
246 case poset_bounds_descriptor::SUBPOSET_SUBPOSET:
247 _lb = 0;
248 _lb_is_singleton = false;
249 _bounded_below = true;
250
251 _ub = 0;
252 _ub_is_singleton = false;
253 _bounded_above = true;
254
255 break;
256
257 default:
258 post_fatal_error_message("unrecognized specification mode");
259 break;
260 }
261
262 // Postconditions:
263
264 // Exit:
265
266 return;
267 }
268
271 {
272
273 // Preconditions:
274
275 // Body:
276
277 // Postconditions:
278
279 // Exit:
280
281 return;
282 }
283
284
287 descriptor() const
288 {
289 return _descriptor;
290 }
291
294 mode() const
295 {
296 return _descriptor.mode();
297 }
298
299
302 lb_id() const
303 {
304 return _descriptor.lb_id();
305 }
306
307 void
310 {
311 // Preconditions:
312
313 require(lb_is_singleton());
314
315 // Body:
316
317 _descriptor.put_lb_id(xlb_id);
318
319 // Postconditions:
320
321 ensure(lb_id() == xlb_id);
322
323 // Exit
324
325 return;
326 }
327
328 void
330 put_lb_id(const scoped_index& xlb_id)
331 {
332 // Preconditions:
333
334 require(lb_is_singleton());
335
336 // Body:
337
338 _descriptor.put_lb_id(xlb_id.hub_pod());
339
340 // Postconditions:
341
342 ensure(lb_id() == xlb_id.hub_pod());
343
344 // Exit
345
346 return;
347 }
348
349 bool
352 {
353
354 // Preconditions:
355
356 // Body:
357
358 // Postconditions:
359
360 // Exit
361
362 return _lb_is_singleton;
363 }
364
365 bool
368 {
369 // Preconditions:
370
371 // Body:
372
373 // Postconditions:
374
375 // Exit
376
377 return _bounded_below;
378 }
379
382 ub_id() const
383 {
384 return _descriptor.ub_id();
385 }
386
387 void
390 {
391 // Preconditions:
392
393 require(ub_is_singleton());
394
395 // Body:
396
397 _descriptor.put_ub_id(xub_id);
398
399 // Postconditions:
400
401 ensure(ub_id() == xub_id);
402
403 // Exit
404
405 return;
406 }
407
408 void
410 put_ub_id(const scoped_index& xub_id)
411 {
412 // Preconditions:
413
414 require(ub_is_singleton());
415
416 // Body:
417
418 _descriptor.put_ub_id(xub_id.hub_pod());
419
420 // Postconditions:
421
422 ensure(ub_id() == xub_id.hub_pod());
423
424 // Exit
425
426 return;
427 }
428
429 bool
432 {
433
434 // Preconditions:
435
436 // Body:
437
438 // Postconditions:
439
440 // Exit
441
442 return _ub_is_singleton;
443 }
444
445 bool
448 {
449 bool result;
450
451 // Preconditions:
452
453 // Body:
454
457
458 result = !_ub_is_singleton;
459
460 // Postconditions:
461
462 // Exit
463
464 return result;
465 }
466
467 bool
470 {
471 // Preconditions:
472
473 // Body:
474
475 // Postconditions:
476
477 // Exit
478
479 return _bounded_above;
480 }
481
482
483
484 // PROTECTED MEMBER FUNCTIONS
485
virtual bool invariant() const
Class invariant, intended to be redefined in each descendant. See below for template for invariant in...
Definition: any.cc:153
bool _bounded_below
True if the lower bound is not the bottom.
Definition: poset_bounds.h:202
pod_index_type ub_id() const
The index of the upper bound member, if the upper bound contains a single member. ...
bool lb_is_singleton() const
True if the lower bound contains a single member.
bool bounded_below() const
True if the lower bound is not the bottom.
bool _bounded_above
True if the upper bound is not the top.
Definition: poset_bounds.h:217
void put_lb_id(pod_index_type xlb_id)
Sets the index of the lower bound member to xlb_ib, if the lower bound contains a single member...
pod_index_type ub_id() const
The index of the upper bound member, if the upper bound contains a single member. ...
A (lower, upper) bounds pair for a poset. Specifies a portion of a poset for a bounded i/o operation...
Definition: poset_bounds.h:50
void put_lb_id(pod_index_type xlb_id)
Sets the index of the lower bound to xlb_id.
poset_bounds_descriptor::specification_mode mode() const
The specification mode.
void put_ub_id(pod_index_type xub_id)
Sets the index of the upper bound member to xub_ib, if the upper bound contains a single member...
Abstract base class with useful features for all objects.
Definition: any.h:39
A map from Zn (the integers mod n) to bools. A characteristic function used to represent subsets of Z...
Definition: zn_to_bool.h:52
specification_mode
Enumeration for mode of specifying the lower and upper bounds.
virtual ~poset_bounds()
Destructor.
bool _ub_is_singleton
True if the upper bound contains a single member.
Definition: poset_bounds.h:212
An index within the external ("client") scope of a given id space.
Definition: scoped_index.h:116
bool _lb_is_singleton
True if the lower bound contains a single member.
Definition: poset_bounds.h:197
pod_index_type lb_id() const
The index of the lower bound.
bool ub_is_decomposition() const
True if the join of the members of the upper bound is equal to the external schema.
bool ub_is_singleton() const
True if the upper bound contains a single member.
void disable_invariant_check() const
Disable invariant check. Intended for preventing recursive calls to invariant and for suppressing inv...
Definition: any.h:97
zn_to_bool * _lb
The lower bound.
Definition: poset_bounds.h:192
zn_to_bool * _ub
The upper bound.
Definition: poset_bounds.h:207
A description of a (lower, upper) bounds pair for a poset. Specifies a portion of a poset for a bound...
bool bounded_above() const
True if the upper bound is not the top.
bool invariant_check() const
True if invariant checking is enabled.
Definition: any.h:79
int_type pod_index_type
The plain old data index type.
Definition: pod_types.h:49
virtual bool is_ancestor_of(const any *other) const
Conformance test; true if other conforms to this.
Definition: poset_bounds.cc:82
pod_index_type lb_id() const
The index of the lower bound member, if the lower bound contains a single member. ...
poset_bounds()
Default constructor.
virtual poset_bounds_descriptor descriptor() const
A descriptor for this.
poset_bounds_descriptor _descriptor
A descriptor for this.
Definition: poset_bounds.h:187
void enable_invariant_check() const
Enable invariant checking.
Definition: any.h:87
void put_ub_id(pod_index_type xub_id)
Sets the index of the upper bound to xub_id.
virtual poset_bounds * clone() const
Virtual constructor; makes a new instance of the same type as this.
Definition: poset_bounds.cc:30
specification_mode mode() const
Specification mode for this.
virtual bool invariant() const
Class invariant.
Definition: poset_bounds.cc:50
pod_type hub_pod() const
The pod value of this mapped to the unglued hub id space.
Definition: scoped_index.h:710
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| 0.99357 |
Wednesday, November 2, 2011
BMC: Change Temperature Thresholds
This post shows how to update a server's Baseboard Management Controller (or iDRAC or maybe an iLO or something else) to power the server off at a different temperature threshold than the manufacturer default. This is done using ipmitool and freeipmi commands. We use it to lower the set points for some of our servers in a less-capable room that we have. The servers will then do a hard shutdown if the thermal threshold we set is reached.
Background
A smaller server room we have is shared with a college on campus. We have compute nodes (part of our HPC lab) in that room and they have critical college infrastructure in there. We don't like having our equipment go down, but we do like to help them keep their servers up. As a a result, we will shut our equipment down first in the event of server room problems.
All of the servers in the room are on UPS power (unlike our main server room where no compute nodes are on UPS). Unfortunately, the chillers are on wall power and are off for the duration of any power outages. Thus, if the power goes out for an hour or a chiller decides to stop chilling at 3 AM, we end up in a situation where there is still a normal heat load from the servers but no more cooling.
We used to take care of everything manually by watching the temperatures climb, hope the power would come back or the chiller get fixed ASAP (the latter of which usually takes an hour our two if we're very lucky), and finally power off our servers in the room. Sometimes the effect of us powering off our compute nodes, which are normally operating around 100% utilization, would be enough to save the college from having their operations interrupted.
Since I don't really like getting woken up to an "it's hot in here" or "on battery" notification from our room sensors when an automated response is just as good, I decided to do something about it. I already automated the cleanup of systems after a power outage, so that wasn't a concern. What was a concern, however, was helping out the college we share the room with. That normally required manual intervention (again, not the best use of anyone's time at 3 AM). Since we already have a process we follow manually, why not automate it?
Code
Notes:
• All IPMI commands (ipmitool and freeipmi) listed below can be done locally or remotely. See the man pages for details (it's really quite simple if the servers are setup correctly).
• These were only tested on some models of Dell PowerEdge and HP ProLiant servers. Double-check the fields or you may end up telling the server to power off based on the wrong temperature sensor.
• Be sure to test this first. An easy way to do so is to set a limit 1-2 degrees above the current temperature and then add some heat in front of the server. Change it to the intended thresholds after testing is complete.
Fetch current ambient temperature sensor value:
Dell iDRAC/BMC
ipmitool sensor get 'Ambient Temp' |grep 'Sensor Reading' | awk '{print $4}' #usually faster on Dell than:
ipmitool sdr entity 7.1 | grep Ambient | sort | awk -F '|' '{print $5}' | awk '{print $1;}'
HP iLO/BMC (only tested on one model of server)
ipmitool sdr entity 39.1 | grep Temp | sort | awk -F '|' '{print $5}' | awk '{print $1;}' #usually faster on HP than:
ipmitool sensor get 'Temp 9' |grep 'Sensor Reading' | awk '{print $4}' #double check that this corresponds to ambient
Others. After finding the right entity, use that for faster access:
ipmitool sdr type Temperature # figure out which sensor corresponds to ambient (planar is probably not what you want)
Find which values to change
ipmi-sensors-config -L |grep Ambient
ipmi-sensors-config -L |grep Temp #may be necessary on non-Dell
This will return something like "3_Ambient_Temp" on all Dell systems I have tried (but not HP). This is the section to use when modifying the temperature values.
You can also use this dynamically if you have a variety of Dell servers (and maybe other non-HP servers). Instead of specifying "7_Ambient_Temp" or another value, replace it with "$(ipmi-sensors-config -L |grep Ambient)".
Example:
ipmi-sensors-config -o -e "$(ipmi-sensors-config -L |grep Ambient):Upper_Critical_Threshold"
Fetch current thresholds
ipmi-sensors-config -o -S "$(ipmi-sensors-config -L |grep Ambient)" #grab all set points for the ambient temperature sensor
ipmi-sensors-config -o -S 3_Ambient_Temp #same as above, but specify the section (assuming 3 is correct)
ipmi-sensors-config -o -S "$(ipmi-sensors-config -L |grep Ambient):Upper_Critical_Threshold" #fetch the upper critical threshold value
ipmitool sensor list | grep Ambient
ipmitool sensor get "Ambient Temp"
Set temperature thresholds (Dell and possibly other non-HP servers):
ipmi-sensors-config -c -e "$(ipmi-sensors-config -L |grep Ambient):Upper_Non_Critical_Threshold=30" #warning
ipmi-sensors-config -c -e "$(ipmi-sensors-config -L |grep Ambient):Upper_Critical_Threshold=33" #critical
Set the server to actually power off at the critical threshold instead of just alerting (Dell):
I don't have a great way of querying the correct value programmatically, so you'll just have to find this information manually using "ipmi-pef-config". On Dells, the value you want (in my experience) has always been "Event_Filter_9". Then set "$SECTION:Event_Filter_Action_Power_Off=Yes"
The way to find it manually is to use "ipmi-pef-config -o" and look for an Event_Filter section that has "Event_Severity Critical" and "Sensor_Type Temperature". Assuming the section is Event_Filter_9, run the following:
ipmi-pef-config -c -e 'Event_Filter_9:Event_Filter_Action_Power_Off=Yes'
(Theoretically) set temperature thresholds on HP ProLiant BL460c G1... BROKEN:
ipmi-sensors-config -c -e '13_Temp_9:Upper_Critical_Threshold=30' #warning
ipmi-sensors-config -c -e '13_Temp_9:Upper_Non_Recoverable_Threshold=33' #critical
This will return "ERROR: `13_Temp_9:Upper_Non_Recoverable_Threshold' is not writeable". There's probably a non-industry standard, HP-specific way to do this, but we have so few HP servers it isn't worth looking up how to do it. HP only recently added the ability to do IPMI over LAN, so that doesn't surprise me. Meanwhile, Dell has had great BMC/IPMI support on every one of their servers I have ever managed.
Before IPMI over LAN support was added, I called HP to ask why that functionality wasn't available. The excuse was something like "vendors implement it so differently that it's hard to implement." Of course, my response was "if you're the vendor who implements it, why can't you implement it in an industry-standard way?" They finally did get around to it but apparently don't have a complete implementation yet. Maybe newer servers do, but I don't have access to any.
Comment below if you have any questions. I might be able to answer them. If you figure out how to make this work with HP or other vendors (if it doesn't work using the methods above), please let me know and I'll update this post.
2 comments:
1. Hi Ryan,
Good stuff.....trying to do something similar in my lab. So if I understand correctly.....I have to configure IPMI on the iDRACS then use the ipmitool to issue the commands to gather the server metrics. Correct? One other question.....once I get the metrics can I then send them to a network management platform with the ipmitool? Thanks
ReplyDelete
2. ugg, nearly 2 years later, on a G8 server, I'm still getting not writable erros (though CPU maybe they don't want me tweaking the threshold :) ERROR: `16_03-CPU_2:Upper_Critical_Threshold' is not writeable. Thanks for the good info though.
ReplyDelete
Please leave any comments, questions, or suggestions below. If you find a better approach than what I have documented in my posts, please list that as well. I also enjoy hearing when my posts are beneficial to others.
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__label__pos
| 0.504777 |
Physics 523 and 524
Class meets on Mondays and Wednesdays at 5:30 in room 184. (Last semester class met on Tuesdays and Thursdays at 5:30 in room 5.)
The grader is Mr. Zhixian Yu, his email address.
Videos of lectures of Sidney Coleman.
Notes on Lie groups.
Notes on groups.
Class notes.
Notes on general relativity.
Notes on the renormalization group.
Notes on functional derivatives.
Derivation of one of Glauber's dentities.
Note on why \(u\) and \(v\) spinors are so different.
Kinoshita's five-loop calculation of the magnetic moment of the electron.
Notes on spontaneous symmetry breaking
Notes on effective field theories and on the Hawking temperature of an accelerating frame
Notes on maximally symmetric spaces and conformal algebra
Notes on Monte Carlo methods
Solutions to some Monte Carlo problems.
Basic remarks about Wilson loops.
Basic remarks about Grassmann variables and fermionic path integrals.
Please tell me of any typos or errors in these notes.
Weinberg on Dirac brackets.
Weinberg on Dirac brackets and QED.
Weinberg on axial-gauge quantization of nonabelian gauge theories.
First homework assignment: Derive Feynman's trick $$ \frac{1}{AB} ={} \int_0^1 \frac{dx}{[ (1-x)A + x B ]^2} . $$ Due Thursday, Feb. 14th.
Second homework assignment: Use SW's pseudounitarity condition (class notes 1.209, SW's 5.4.32) \begin{equation} \beta D^\dagger(\Lambda) \beta = D^{-1}(\Lambda) \label {class notes 1.209, SW's (5.4.32)} \end{equation} to show that \begin{equation} \overline u(\vec p,s') u(\vec p,s) ={} \frac{m}{p^0} \, \delta_{s s'} . \end{equation} Hint: The definition of the spinors (class notes 1.211, SW's 5.5.12 & 13) helps here.
Due Thursday, Feb. 21st.
Third homework assignment: Show that \begin{equation} \overline L_\ell {\gamma^a D^\ell_a} L_\ell = [\frac{1}{2} ( 1 + \gamma_5 ) L ]^\dagger i \gamma^0 {\gamma^a D^\ell_a} \frac{1}{2} ( 1 + \gamma_5 ) L = \overline L {\gamma^a D^\ell_a} \frac{1}{2} ( 1 + \gamma_5 ) L . \end{equation} Due Thursday, March 7.
Fourth homework assignment: Using the differential forms \begin{equation} \begin{split} P_i ={}& \partial_i, \quad J_{ik} ={} (x_i \, \partial_k - x_k \, \partial_i ), \\ D ={}& x^i \, \partial_i, \quad \mbox{and} \quad K^i ={} ( \eta^{ik} \, x^j \, x_j - 2 x^i \, x^k) \, \partial_k \end{split} \end{equation} of the generators of the conformal algebra in flat space, show that \begin{equation} [ K^i, K^j] ={} 0, \quad [ D, P^i ] ={} - P^i, \quad [ D, J_{ij}] = 0, \quad \end{equation} \begin{equation} [D,K^i]= K^i, \quad [J^{ij}, K^\ell] = - \eta^{i \ell} K^j + \eta^{j \ell} K^i, \quad \mbox{and} \quad [K^i,P^j] ={} 2 J^{i j} + 2 \eta^{ij} D. \end{equation}
Due Thursday 4 April 2019.
Videos of lectures of 524 for 2019.
Lecture 1: The Landau-Ginzburg theory of phase transitions. Order parameters. First-order phase transitions (discontinuous). Second-order phase transitions (continuous). Use of the Gibbs free energy. In an ideal ferromagnet at temperatures below the critical temperature, the magnetization is proportional to the square root of \( T - T_c \). Landau and Ginzburg represented the spin density as a field and showed that the correlation function of spins is a Yukawa potential with a range that diverges as \( (T-T_c)^{-1/2} \). The basic ideas about functional differentiation. These are in the online notes. Video of first lecture.
Lecture 2: The Landau-Ginzburg theory of phase transitions. Susceptibility diverges as \( 1/|T - T_c| \). One of Glauber's identities. Derivation posted in online notes. S-matrix for electromagnetic field radiated by a classical current. Video of lecture 2.
Lecture 3: Renormalization and counterterms. Derivation of the one-loop correction to the phton propagator. Vacuum polarization. A Feynman trick. Use of trace identities. The Wick rotation. Video of lecture 3.
Lecture 4: Renormalization and counterterms. More about the one-loop correction to the phton propagator. Vacuum polarization. The Wick rotation. Dimensional regularization. Use of counterterms. How to take the limit in which the dimension of spacetime goes to 4. Video of lecture 4.
Lecture 5: How the Dirac field and its spinors \(u\) and \( v\) transform. More about vacuum polarization and its effects. Video of lecture 5.
Lecture 6: Effective field theories. Integrating over fields with masses huge compared to those of the standazrd model. The linear sigma model. Goldstone's theorem. Video of lecture 6.
Lecture 7: Goldstone's theorem for \(SU(2)\) and \(SU(3)\). The abelian Higgs mechanism. The \(SU(2)\) and \(SO(n)\) Higgs mechanisms. Video of lecture 7.
Lecture 8: Review of effective field theory. Goldstone's theorem and the Higgs mechanism for \(SO(n)\). Majorana masses. Hypercharge. The Glashow-Weinberg-Salam-Ward model and the standard model. Video of lecture 8.
Lecture 9: How the gauge bosons get their masses. Identification of the electric charge as \(Q = T_3 + Y/2\) and the cosine of the the weak mixing angle as \( \cos \theta_w = M_W/M_Z\). Electroweak interactions of the quarks and leptons. Masses of the quarks and leptons. Video of lecture 9.
Lecture 10: Electroweak interactions of the quarks and leptons. Beta decay. Masses of the quarks and leptons. The CKM matrix. A CP-breaking phase. How a high-energy theory naturally explains the lightness of the masses of the neutrinos. Video of lecture 10.
Lecture 11: How derivatives transform under variations. More about how a high-energy theory naturally explains the lightness of the masses of the neutrinos. The Majorana condition on Dirac spinors. How that condition leads to the Majorana condition on Majorana fields. Interactions of neutrinos going thru matter. Quantization of fields in flat and curved space. Bogoliubov transformations. How curved space makes particles. Video of lecture 11.
Lecture 12: What we mean by a field. Action and equation of motion for a scalar field in curved space. Expansion of scalar field in terms of solutions of its equation of motion. A scalar product for mode functions in flat and curved space. Properties of the scalar product: hermiticity and other properties. Expansion of mode functions in terms of solutions of the equation of motion. Expansion of the field in terms of solutions of the equation of motion in different coordinate systems. Relations between the annihilation and creation operators in different coordinate systems. Bogoliubov coefficients. Bogoliubov transformations. How curved space makes particles. Equation of motion in an accelerated frame of reference. Video of lecture 12.
Lecture 13: Lorentz transformation to an accelerated coordinate system. Rindler coordinates. Mean value of two massless scalar fields in the vacuum. Mean value of two massless scalar fields at a nonzero temperature. Mean value of two massless scalar fields in the vacuum of an inertial frame that instantaneously is the rest frame of the accelerating frame. A comparison of the two reveals that a detector in a frame uniformly accelerating with acceleration \( \alpha \) feels a temperature \( T = \hbar \alpha/(2 \pi c k_B) \), a result due to Hawking, Davies, and Unruh. (The missing factor of 2 in the last formulas of the lecture is due to my failure to properly latex Mathematica's formula for \(B_\beta\).)
Notes on Hawking radiation. Video of lecture 13.
Lecture 14:
Summary of lecture on acceleration and temperature. Computation of the temperature due to the surface gravity of the Earth. Isometries. Two forms of Wilhelm Killing's characterization of an isometry. Maximally symmetric spaces. Examples of the 2-sphere and the 2-hyperboloid in 3-space and of the 3-sphere and the 3-hyperboloid in 4-space. Connection with \(\Lambda CDM\) cosmologies. The Lie derivative. Properties of maximally symmetric spaces in 2, 3, and 4 dimensions. Killing's condition that two metrics be conformally related. Characterization of a conformal transformation.
Notes on maximally symmetric spaces with the typo in \(y_2\) fixed. Video of lecture 14.
Lecture 15:
A conformal relation between two metrics. Condition on Killing vectors for conformal symmetry. Formula for conformal factor. Condition on Killing vectors for conformal symmetry in flat space. Formula for conformal factor in flat space. Conformal symmetries of flat space: translations, Lorentz transformations, dilations, and conformal transformations. Differential forms of the generators of conformal symmetries. Their Lie algebra.
Notes on maximally symmetric spaces and on conformal symmetry. Video of lecture 15.
Lecture 16:
Review of Killing's condition for a conformal symmetry in flat space. The commutation relations of the conformal group. Isomorphism between the conformal group of Minkowski space and the group \(SO(d,2)\). Derivation of the conformal invariance of Maxwell's action. Remarks about the conformal invarince of pure (no matter) nonabelian gauge theory and of the theory of a free massless scalar field.
Notes on maximally symmetric spaces and on conformal symmetry. Video of lecture 16.
Lecture 17:
Review of Killing's condition for conformal symmetry in flat space. Derivation of the conditions for a Killing vector in 1, 2, and 3 or more dimensions. In 1 dimension the Killing vector is completely arbitrary. In 2-d euclidian space, the two new coordinates can be the real and imaginary parts of an arbitrary analytic or antianalytic function of the old coordinates. Light-cone coordinates. In 2-d Minkowski space, the new coordinates can be arbitrary functions of the light-cone coordinates. In 3 or more dimensions, a Killing vector must be a quadratic function of the old coordinates. The parameters of the quadratic function are those of a translation, a dilation, a Lorentz transformation, and of a special conformal transformation.
Notes on maximally symmetric spaces and on conformal symmetry.
The book Conformal Field Theory by Di Francesco, Mathieu, and Sénéchal is the best reference I know of for conformal field theory.
Video of lecture 17.
Lecture 18:
Finite conformal transformations in two-dimensional euclidian space. Analytic and antianalytic functions. Quantum statistical mechanics in euclidian space. The Monte Carlo method. The Metropolis step. Why it works. Quantum field theory on a spacetime lattice. Michael Creutz's website. Video of lecture 18.
Lecture 19:
Some remarks about Wilson lines and Wilson loops. Video of lecture 19.
Lecture 20:
More about Wilson loops, Wilson lines, and the Wilson action. The class notes basic remarks about Wilson loops fill in some gaps in the video. The notes on Creutz's examples are here: Solutions to some Monte Carlo problems. Video of lecture 20.
Lecture 21:
Announcement of Paul Steinhardt's talk on May 11th at Bookworks on Rio Grande in Albuquerue and brief summary of his theory of a cyclic universe. Sign conventions for and more details about gauge fields and Faraday tensor. Yet more about Wilson loops, Wilson lines, and the Wilson action. A scalar field on a lattice. Grassmann variables and how to integrate over them. The notes are on lattice field theory and on Grassmann variables. The notes on Creutz's examples are here: Solutions to some Monte Carlo problems. Video of lecture 21.
Lecture 22:
More about the use of Grassmann variables and how to integrate over them. Video of lecture 22.
Lecture 23:
Gauge fixing in abelian and nonabelian gauge theories. The Coulomb or radiation gauge, axial gauges, the temporal gauge. Gauss's law generates gauge transformations. Physical states are invariant under gauge transformations. Wilson's loop in the temporal gauge. Some of the history of lattice gauge theory. Speculation about confinement of quarks and gluons. Video of lecture 23.
Lecture 24:
Constraints and Dirac brackets. Video of lecture 24.
Lecture 25:
Constraints and Dirac brackets. Application to QED. Images of Weinberg's equations 8.2.1-8.2.5. Images of Weinberg's equations 8.2.6-8.3.3. Images of Weinberg's equations 8.3.4-8.3.10. Images of Weinberg's equations 8.3.11-8.4.13. Images of Weinberg's section 8.4.14-8.5.2. Video of lecture 25.
Lecture 26:
More about Dirac brackets and the quantization of abelian and nonableian gauge theories. Vector and axial-vector currents and the U(1) anomaly. Anomalies and the measure of path integration. Forms and nonabelian gauge theory. Solitons, instantons, and homotopy groups. Video of lecture 26.
Lectures by Chatterjee on anomalies. Adel Bilal's notes on anomalies.
Because pdf's of textbooks often are available for free online at addresses that you probably know better than I do, I have decided to use two books this autumn. One is the first volume of Steven Weinberg's trilogy The Quantum Theory of Fields.
The other is Anthony Zee's Quantum Field Theory in a Nutshell.
I encourage students to read the first chapter of Weinberg's book before the first class or during the first week of classes. That chapter is a history of the invention of quantum field theory. It reads like a novel with equations.
I plan to cover the first eight or nine chapters in class during the fall, but I will let you read chapter 1 by yourselves and will skip or discuss lightly the starred sections and others that can be left to a second reading. The key chapters are 2, 5, and 6.
First homework assignment: Weinberg defines linear, unitary and antilinear, antiunitary operators and their adjoints on page 51. Show that the adjoint of an operator \(X\) that is either linear & unitary or antilinear & antiunitary is the inverse \(X^{-1}\).
Solutions.
Second homework assignment: (A) Suppose \( | \vec p, \vec k \rangle = a^\dagger(\vec p) a^\dagger(\vec k) | 0 \rangle \), where \( |0\rangle\) is the vacuum and \( \vec p \ne \vec k \), is a state consisting of two spin-zero bosons of momenta \( \vec p\) and \( \vec k \). Simplify the expressions \( a(\vec q) | \vec p, \vec k \rangle \) and \( \langle \vec p, \vec k | a^\dagger( \vec q) \).
The commutation relations for spin-zero bosons are \( [ a(p), a^\dagger(p') ] = \delta^{(3)}(\vec p -\vec p') \).
(B) Now work the same problem for fermions. Suppose \( | \vec p, +; \vec k, + \rangle = a^\dagger(\vec p,+) a^\dagger(\vec k,+) | 0 \rangle \), where \( |0\rangle\) is the vacuum and \( \vec p \ne \vec k \), is a state consisting of two spin-one-half fermions of momenta \( \vec p\) and \( \vec k \) with spins in the +z direction. Simplify the expressions \( a(\vec q,+) | \vec p, +; \vec k, + \rangle \) and \( \langle \vec p, +; \vec k, + | a^\dagger( \vec q, +) \).
The anticommutation relations for fermions are \( \{ a(p, s), a^\dagger(p',s') \} = [ a(p, s), a^\dagger(p',s') ]_+ = \delta_{s s'} \delta^{(3)}(\vec p -\vec p') \).
Third homework assignment: Use the commutation relations $$ [ a_i(\pmb p), a^\dagger_j(\pmb p') ] = \delta_{i j} \, \delta^3( \pmb p - \pmb p'), \qquad [ a_i(\pmb p), a_j(\pmb p') ] = 0, \qquad [ a^\dagger_i(\pmb p), a^\dagger_j(\pmb p') ] = 0 $$ for \( i,j = 1,2 \) to derive the commutation relations for the complex operators $$ a(\pmb p) = ( a_1(\pmb p) + i a_2(\pmb p) )/\sqrt{2} \quad \mbox{and} \quad b(\pmb p) = ( a_1(\pmb p) - i a_2(\pmb p) )/\sqrt{2} $$ and their adjoints. Due Thursday 20 September.
Fourth homework assignment: Gamma matrices obey the anticommutation relations \begin{equation} \{ \gamma^a , \gamma^b \} ={} 2 \, \eta^{a b} . \end{equation} Define the matrices \( \mathcal{J}^{a b} \) as \begin{equation} \mathcal{J}^{a b} ={} - \frac{i}{4} \, [ \gamma^a , \gamma^b ] . \end{equation} Show that \begin{equation} [ \mathcal{J}^{a b}, \gamma^c ] ={} -i \, \gamma^a \, \eta^{ b c} + i \, \gamma^b \, \eta^{ a c} . \end{equation} Due Tuesday 2 October.
Fifth homework assignment: The hamiltonian for a free real field \begin{equation} \phi(x) ={} \int \frac{d^3 p}{\sqrt{(2\pi)^3 2p^0}} \Big[ a(p) e^{i p \cdot x} + a^\dagger(p) e^{-i p \cdot x} \Big] \label {free real field} \end{equation} is \begin{equation} H ={} \frac{1}{2} \int \pi^2(x) + (\nabla \phi(x))^2 + m^2 \phi^2(x) \, d^3x \label {H} \end{equation} where \( \pi(x) ={} \dot \phi(x) \) is the momentum conjugate to the field. Show that \begin{equation} H ={} \int d^3p \, \sqrt{\vec p^2 + m^2} \, \Big( a^\dagger(p) a(p) + \frac{1}{2} \delta^3( \vec 0) \Big) . \label {H =} \end{equation}
Due to my misstatement of the problem, HW5 will be due on Tuesday 30 October.
Sixth homework assignment: Derive the second and third terms in the amplitude for boson-boson scattering, equation (53) of sw6.pdf. Follow the method outlined 30-50 minutes into my lecture of 16 October. Due Thursday 1 November.
Seventh homework assignment: Show that Belinfante's energy-momentum tensor (3.49) is symmteric. Due Thursday 8 November.
Eighth homework assignment: For the theory of spin-zero bosons with Lagrange density $$ L ={} \frac{1}{2} \left[ \partial_a \phi \partial^a \phi - m^2 \phi^2 \right] - \frac{g}{4!} \phi^4 , $$ to lowest order in the coupling constant \(g\) find the differential and total cross-sections for the scattering of bosons with momenta \( p \) and \( k \) into momenta \( p' \) and \( k' \). Due Thursday 6 December 2018.
Ninth homework assignment: Read section ( 6.2) of the Class notes on the abelian Higgs mechanism. What are the masses of the particles of the two scalar fields in the theory with lagrangian (6.5)? What are the masses of the physical fields of the theory with lagrangian (6.11)? The equation numbers refer to those of the Class notes. Due Thursday 13 December 2018.
Extra-credit problem: Find a group whose structure constants are imaginary or complex. Videos of lectures of 523 for 2018.
Lecture one: The very few, very basic principles of quantum field theory: quantum mechanics, special relativity, and the simplest implementation of the concepts of field and particle. Basic ideas of quantum mechanics and of Lie groups. Structure constants.
Video of first lecture.
Lecture two: Structure constants of the rotation group and of the Lorentz group. Demonstration of the structure constants of the rotation group. Representations of the Lorentz group.
Video of lecture 2.
Lecture three: How the quantum states of particles transform under Lorentz transformations. The little group. How the states of massive particles transform under Lorentz transformations. The little group for massive particles. The little group for massless particles is ISO(2).
Video of lecture 3.
Lecture 4: The Wigner rotation \(W\) of a Lorentz transformation \(\Lambda\) that is a rotation, i.e., \( \Lambda = R\), is the rotation \(R\), that is, \( W = R\). The little group for massless particles. A word about representations of the group of translations. Creation and annihilation operators. States of many particles. The S matrix. Normal ordering.
Video of lecture 4.
Lecture 5: How fields transform under Lorentz transformations and translations. (Much of this material will be done more clearly in lecture 6. See the notes on section 5.1 above.) Why certain quantities are Lorentz invariant.
Video of lecture 5.
Lecture 6: How fields transform under Lorentz transformations and translations. States. Creation and annihilation operators. How fields transform. Translations. Boosts. Rotations.
Video of lecture 6.
Lecture 7: How fields transform under Lorentz transformations and translations. Conditions on spinors from Poincaré covariance under translations, boosts, and rotations. Application to spin-zero fields. Why spin-zero fields describe bosons.
Video of lecture 7.
Lecture 8: Review of particles and antiparticles as arising from two fields of the same kind having the same mass. Example of the interaction of a spin-zero charged boson with the electromagnetic field. How the process \( a + b \to \gamma + \gamma\) can arise. The commutation relations of charged fields with the charge operator. Parity for charged spin-zero fields. The parity of a state of a spin-zero boson and its antiparticle is even, i.e., positive. Why the way fields transform under rotations is related to their statistics.
Video of lecture 8.
Lecture 9: How scalar fields transform under charge conjugation and time reversal. How massive vector fields transform under Lorentz transformations and translations and how that leads to explicit formulas for their spinors.
Video of lecture 9.
Lecture 10: How massive vector fields transform under Lorentz transformations and translations and how that leads to explicit formulas for their spinors. Expansion of field of a spin-one boson. The spin-statistics theorem for spin-one bosons. The battery failed ater 55 minutes.
Video of lecture 10.
Lecture 11: The Lorentz group and its (1/2,1/2) representation. Clifford algebras. Dirac matrices.
Video of lecture 11.
Lecture 12: Derivation of formulas for Dirac spinors. Spin-statistics theorem for spin-one-half particles.
Video of lecture 12.
Lecture 13: Rest of derivation of formulas for Dirac spinors. Spin-statistics theorem for spin-one-half particles. Parity of Majorana neutrinos.
Video of lecture 13.
Lecture 14: Dyson's expansion of the S matrix. First steps to Feynman diagrams.
Video of lecture 14.
Lecture 15: Time-dependent perturbation theory. A real scalar field that interacts with itself cubically. Lowest-order scattering of 2 bosons into 2 bosons. In 2d-order perturbation theory, there are 3 amplitudes which we add together. The Feynman propagator for scalar fields.
Video of lecture 15.
Lecture 16: The Feynman propagator for spin-one-half fields. More about the \(\phi^3\) theory and 2-to-2 scattering.
Video of lecture 16.
Lecture 17: More about the Feynman propagator for spin-one-half fields. Application to fermion-boson scattering. Feynman's propagator for spin-one fields.
Video of lecture 17.
Lecture 18: The Feynman rules. Application to fermion-antifermion scattering. Canonical variables.
Video of lecture 18.
Lecture 19: The principle of least action in field theory. Noether's theorem linking a symmetry of the action density to the conservation of a physical quantity.
A camera was not avaliable; there is no video of lecture 19.
Lecture 20: More about the principle of least action in field theory and Noether's theorem linking a symmetry of the action density to the conservation of a physical quantity. Internal symmetry. Energy-momentum tensor and the conservation of energy and momentum. The Belinfante energy-momentum tensor, which is symmetric. Conservation of angular momentum.
Video of lecture 20.
Lecture 21: Global \(U(1)\) symmetry. Abelian gauge invariance. Coulomb-gauge quantization.
A memory card for the camera was not avaliable; there is no video of lecture 21.
Lecture 22: Feynman rules for QED. Application to electron-positron scattering.
Video of lecture 22.
Lecture 23: Application of Feynman rules for QED to electron-positron scattering. Why there's a minus sign in the t-channel amplitude. Gamma-matrix trace identities. Application to electron-positron to muon-anti-muon scattering.
Video of lecture 23.
Lecture 24: Application of gamma-matrix trace identities to electron-positron to muon-anti-muon scattering. Interpretation of squared delta function. Box normalization of states. Density of final states. Flux of incoming particles. Evaluation of energy delta function. Calculation of differential and total cross-sections.
Video of lecture 24.
Lecture 25: Comparison of \(e^+ e^-\to \mu^+ \mu^- \) pair production with \( e^- \mu^- \to e^- e^- \mu^-\mu^- \) elastic scattering. Crossing symmetry. Nonabelian gauge theory. Covariant derivatives. The Yang-Mills-Faraday field strength tensor. Action for a nonabelian gauge theory. QCD.
Video of lecture 25.
Lecture 26: Action for a nonabelian gauge theory. QCD. The standard model. The Higgs mechanism. The Glashow-Salam-Weinberg model of the electroweak interactions.
Video of lecture 26.
Lecture 27: The Glashow-Salam-Weinberg model of the electroweak interactions. Path integrals for transition amplitudes. Gaussian integrals and Trotter's formula. Path integrals in quantum mechanics. Path integrals for quadratic actions.
Video of lecture 27.
Lecture 28: Bohm-Aharanov effect. Path integrals in statistical mechanics. Mean values of time-ordered products. Quantum field theory on a lattice.
Video of lecture 28.
Lecture 29: Quantum field theory on a lattice. Finite-temperature field theory. Perturbation theory. Application to quantum electrodynamics.
Video of lecture 30.
Lecture 30: Grassmann variables and fermionic path integrals. Spontaneous symmetry breaking. Goldstone bosons. Abelian Higgs mechanism. Scattering of spinless bosons in \( \lambda \phi^4 \) theory.
Video of lecture 30.
Lecture 31: Renormalization group. Renormalization and interpolation. Renormalization group in quantum field theory. Renormalization group in lattice field theory. Renormalization group in condensed-matter physics.
Video of lecture 31.
Kevin Cahill, [email protected], 505-205-5448
Last modified: Thu Nov 21 19:04:06 MST 2019
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Skip to main content
Geosciences LibreTexts
7. Basis of wind-driven circulation: Ekman spiral and transports
• Page ID
1277
• [ "article:topic" ]
In Section 6, it was mentioned that the large-scale currents at the ocean surface are all driven by the wind. This seems logical enough at first sight, but the Arctic explorer Fridtjof Nansen noticed something strange: icebergs tend to drift at an angle to the right of the prevailing wind direction. To explain this remarkable observation, Ekman (1905) formulated a theory that is still a cornerstone of physical oceanography. The central assumption is that near the ocean surface, the largest deviations from geostrophic balance occur as a result of the wind stress which leads to momentum diffusion in the vertical direction. This means that to a good approximation, the horizontal momentum balance equations \((1.2a)\) and \((1.2b)\) in Section 1 become:
\[\dfrac{\left(\frac{dp}{dx}\right)}{\rho}=f \times v +K_v\dfrac{d^2u}{dz^2} \tag{7.1a}\]
\[\dfrac{\left(\frac{dp}{dy}\right)}{\rho}=-f \times u +K_v\dfrac{d^2v}{dz^2} \tag{7.1b}\]
We now split the velocity up in a geostrophic part (\(u_g,v_g\)) and an ageostrophic Ekman velocity (\(u_E,v_E\)):
\[\dfrac{\left(\frac{dp}{dx}\right)}{\rho}=f \times (v_g+v_E) +K_v\dfrac{d^2(u_g+u_E)}{dz^2} \tag{7.2a}\]
\[\dfrac{\left(\frac{dp}{dy}\right)}{\rho}=-f \times (u_g+u_E) +K_v\dfrac{d^2(v_g+v_E)}{dz^2} \tag{7.2b}\]
From equations \((5.1a)\) and \((5.1b)\) in Section 5, we can see that the geostrophic velocities cancel against the pressure gradient terms on the lefthand side; the terms \(K_v\dfrac{d^2u_g}{dz^2}\) and \(K_v\dfrac{d^2v_g}{dz^2}\) can be neglected. Therefore, the equations simplify to:
\[f \times v_E =-K_v\dfrac{d^2 u_E}{dz^2} \tag{7.3a}\]
\[f \times u_E =K_v\dfrac{d^2 v_E}{dz^2} \tag{7.3b}\]
which can be reformulated through substitution into one fourth-order ordinary differential equation:
\[u_E =-\left(\dfrac{K_v}{f}\right)^2 \dfrac{d^4 u_E}{dz^4} \tag{7.4}\]
with the (real) solution:
\[u_E = A_1 \cos\left(\sqrt{\frac{f}{2K_v}}z+\phi_1\right)e^{\sqrt{\frac{f}{2K_v}}z}+A_2 \cos\left(\sqrt{\frac{f}{2K_v}}z+\phi_2\right)e^{-\sqrt{\frac{f}{2K_v}}z} \tag{7.5}\]
To determine the different coefficients, we use two boundary conditions:
1) The direct impact of the wind stress disappears in the deep ocean: \(u_E \rightarrow 0\) for \(z \rightarrow -\infty\). Therefore, \(A_2\) must be equal to \(0\).
2) In Section 6, we argued that close to the ocean-atmosphere interface, the wind stress is linearly proportional to the vertical velocity gradient; this means that if the wind is blowing in the zonal (West-East) direction, \(\dfrac{du_E}{dz}=\dfrac{\tau_w}{\rho K_v}\) (equation \(6.1\)), \(\dfrac{dv_E}{dz}=0\) for \(z=0\). This leads to \(\phi_1=-\dfrac{\pi}{4}\), \(A_1=\dfrac{\tau_w}{\rho \sqrt{f K_v}}\).
Overall, we have:
\[u_E = \dfrac{\tau_w}{\rho \sqrt{f K_v}} \cos\left(\sqrt{\frac{f}{2K_v}}z-\frac{\pi}{4}\right)e^{\sqrt{\frac{f}{2K_v}}z} \tag{7.6a}\]
\[v_E = -\dfrac{K_v}{f}\dfrac{d^2 u_E}{dz^2}=\dfrac{\tau_w}{\rho \sqrt{f K_v}} \sin\left(\sqrt{\frac{f}{2K_v}}z-\frac{\pi}{4}\right)e^{\sqrt{\frac{f}{2K_v}}z} \tag{7.6b}\]
The Ekman transports per unit area in the zonal and meridional directions are respectively:
\(M_{E,x}=\rho\int_{-\infty}^0 u_E\, dz\), \(M_{E,y}=\rho\int_{-\infty}^0 v_E\, dz\)
These could be calculated by integrating \((7.6a)\) and \((7.6b)\), but it is much easier to use \((7.3a)\) and \((7.3b)\):
\[M_{E,x}=\dfrac{K_v \rho}{f}\int_{-\infty}^0 \dfrac{d^2 v_E}{dz^2}\, dz=\dfrac{K_v \rho}{f}\left(\dfrac{dv_E}{dz}(z=0)-\dfrac{dv_E}{dz}(z\rightarrow-\infty)\right) =0 \tag{7.7a}\]
\[M_{E,y}=-\dfrac{K_v \rho}{f}\int_{-\infty}^0 \dfrac{d^2 u_E}{dz^2}\, dz=-\dfrac{K_v \rho}{f}\left(\dfrac{du_E}{dz}(z=0)-\dfrac{du_E}{dz}(z\rightarrow-\infty)\right) =-\dfrac{\tau_w}{f} \tag{7.7b}\]
What does all this mean? At the ocean surface, \(u_E=\dfrac{\tau_w}{\rho \sqrt{2f K_v}}\) and \(v_E=-\dfrac{\tau_w}{\rho \sqrt{2f K_v}}\) (from equations \(7.6a\) and \(7.6b\)), that is, the Ekman velocity is at an angle of \(45^{\circ}\) to the right of the wind direction in the Northern Hemisphere (and to the left of the wind in the Southern Hemisphere) due to the Coriolis force. Going deeper, the Coriolis force keeps turning the direction of the flow further to the right, while the water speed decreases exponentially with depth. As illustrated in the Figure below (courtesy of NOAA), the overall flow pattern forms a so-called Ekman spiral. Furthermore, \((7.7a)\) and \((7.7b)\) imply that the net Ekman transport is at \(90^{\circ}\) to the right of the wind direction in the Northern Hemisphere.
NOAAekman_spiral.gif
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Thread: Skeleton Window: Message Handler in a Class?
1. #1
Registered User
Join Date
Jun 2003
Posts
361
Skeleton Window: Message Handler in a Class?
Hello hello
I'm on my quest to incorporate classes and skeleton windows into one handy, uh, class I'm one error message away from a functional app
Here's the layout (my beautiful Main.cpp file):
Code:
#define WIN32_LEAN_AND_MEAN
#include <windows.h>
#include "Game.h"
int APIENTRY WinMain(HINSTANCE MyInstance, HINSTANCE PrevInstance, LPSTR kposzArgs, int nWinMode)
{
MSG Msg;
Game MyGame(MyInstance);
while(GetMessage(&Msg, NULL, 0, 0))
{
TranslateMessage(&Msg);
DispatchMessage(&Msg);
}
return Msg.wParam;
}
That is all the code in my Main.cpp file.
The code in my Game.h file (relevant portions) looks like:
Code:
#pragma once
class Game
{
public:
Game(void);
Game(HINSTANCE hInstance);
~Game(void);
LRESULT CALLBACK WinFunc(HWND hWnd, unsigned int Msg, WPARAM wParam, LPARAM lParam);
private:
HWND MainWindow;
HINSTANCE MainInstance;
};
The key thing to note here is that my LRESULT CALLBACK... function is a method in my Game Class.
Finally, Game.cpp looks like:
Code:
#include "Game.h"
#using <mscorlib.dll>
Game::Game(HINSTANCE hInstance)
{
MainInstance = hInstance; //I'm hoping I can do that
Fullscreen = GetScreenMode(); //Works fine
InitWindow(); //Current problem lies inside here (below)
}
void Game::InitWindow(void)
{
WNDCLASS WCL;
DWORD Style;
WCL.cbClsExtra = 0;
WCL.cbWndExtra = 0;
WCL.hbrBackground = (HBRUSH)GetStockObject(BLACK_BRUSH);
WCL.hCursor = LoadCursor(MainInstance, IDC_ARROW);
WCL.hIcon = LoadIcon(MainInstance, IDI_APPLICATION);
WCL.hInstance = MainInstance;
WCL.lpfnWndProc = WinFunc; //Have also tried Game::WinFunc
WCL.lpszClassName = "MyClass";
WCL.lpszMenuName = NULL;
WCL.style = CS_OWNDC;
if (!RegisterClass(&WCL)) exit(10);
if (Fullscreen)
{
Width = GetSystemMetrics(SM_CXSCREEN);
Height = GetSystemMetrics(SM_CYSCREEN);
Style = WS_POPUP;
}
else
{
Width = GetSystemMetrics(SM_CXSCREEN);
Height = GetSystemMetrics(SM_CYSCREEN);
Style = WS_OVERLAPPED|WS_SYSMENU;
}
MainWindow = CreateWindow("MyClass", "RPG", Style, 0, 0, Width, Height, NULL, NULL, MainInstance, NULL);
if (!MainWindow) exit(10);
ShowWindow(MainWindow, SW_SHOW);
UpdateWindow(MainWindow);
SetFocus(MainWindow);
}
LRESULT CALLBACK Game::WinFunc(HWND hWnd, unsigned int Msg, WPARAM wParam, LPARAM lParam)
{
switch(Msg)
{
case WM_DESTROY:
PostQuitMessage(0);
break;
default:
return DefWindowProc(hWnd, Msg, wParam, lParam);
}
return 0;
}
Those last two functions are usually what appear in the WinMain function, but I've moved them into the class. So, my problem comes from the line:
WCL.lpfnWndProc = WinFunc;
I get an error saying:
error C2440: '=' : cannot convert from 'LRESULT (__stdcall Game::* )(HWND,unsigned int,WPARAM,LPARAM)' to 'WNDPROC'
So then, my question is:
Is there no way I can pass a Message Handling Function that is within a Class to be the default handler?
Even if you don't know the answer, I really appreciate you atleast reading that all and getting down here to the bottom If any ideas or advice can be given (am I doing something else wrong?) on how (if at all possible) to use my "Game::WinFunc" function, I'm open to any insight.
Last edited by Epo; 12-28-2003 at 10:16 PM.
2. #2
Skunkmeister Stoned_Coder's Avatar
Join Date
Aug 2001
Posts
2,572
The problem your having is because your wndproc has to be declared as _stdcall and member functions are called using the _thiscall declarator. This basically means that to pass a class func off as a wndproc then that func must be static.
Free the weed!! Class B to class C is not good enough!!
And the FAQ is here :- http://faq.cprogramming.com/cgi-bin/smartfaq.cgi
3. #3
Registered User
Join Date
Jun 2003
Posts
361
How would I go about making a function static? I've seen the word but have never gotten around to using it...ever
Would you call this a good idea? Or is this more of a roundabout way that may have reprecussions?
Thanks so far though, you're making it sound much simpler than what I thought it would be
4. #4
Registered User
Join Date
Jun 2003
Posts
361
I'm gonna answer this question myself before anyone else so that I can save atleast a bit of my dignity.
You put the word "static" infront of the declaration.
Hah
Um, just wondering though, what does static mean? I haven't had an explanation yet that I can understand.
5. #5
Skunkmeister Stoned_Coder's Avatar
Join Date
Aug 2001
Posts
2,572
The downside is a class member static function can only access static members.
Free the weed!! Class B to class C is not good enough!!
And the FAQ is here :- http://faq.cprogramming.com/cgi-bin/smartfaq.cgi
6. #6
Registered User
Join Date
Jun 2003
Posts
361
It's funny you mention that, cause I was just about to ask why I was getting this error:
error C2597: illegal reference to non-static member 'Game::bRunning'
Which...well...you just told me....this is gonna take some messing around with, thanks for your help eh
Edit:
Any thoughts on why I get this though?
New error LNK2020: unresolved token (0A00000E) ?bRunning@Game@@0_NA
if I declare bRunning as a Private Member of my Game Class?
static bool bRunning;
Last edited by Epo; 12-28-2003 at 10:16 PM.
7. #7
erstwhile
Join Date
Jan 2002
Posts
2,227
These kind of questions come up up periodically and a search of this board should give you some answers to your questions:
static window procedures
I attached a quick and dirty example (using dialog) to the last post in this thread that might be of some interest to you.
Good luck.
CProgramming FAQ
Caution: this person may be a carrier of the misinformation virus.
8. #8
Registered User
Join Date
Jun 2003
Posts
361
That's exactly what I was looking for
I'm wondering, are there any side effects to using this method though? Like...your computer locking up into a turtle slow speed when you try to click the X button?
I seem to still be having troubles with receiving messages...
Main.cpp
Code:
#define WIN32_LEAN_AND_MEAN
#include <windows.h>
#include "Game.h"
int APIENTRY WinMain(HINSTANCE MyInstance, HINSTANCE PrevInstance, LPSTR kposzArgs, int nWinMode)
{
Game MyGame(MyInstance); //Can I use the Instance like this?
while (MyGame.bRunning)
{
MyGame.MessagePump();
MyGame.RenderScene();
}
return 0;
}
Game.h
Code:
#include <D3DX8.h>
#pragma comment(lib,"D3D8.lib")
#pragma comment(lib,"D3DX8.lib")
#pragma once
class Game
{
public:
Game(HINSTANCE hInstance);
~Game(void);
void MessagePump(void);
void RenderScene(void);
bool bRunning;
static LRESULT CALLBACK SWinFunc(HWND hWnd, unsigned int Msg, WPARAM wParam, LPARAM lParam);
protected: //What does "Protected" mean?
LRESULT CALLBACK WinFunc(HWND hWnd, unsigned int Msg, WPARAM wParam, LPARAM lParam);
private:
D3DFORMAT Get16BitMode(void);
bool GetScreenMode(void);
bool InitWindow(void);
bool InitD3D(void);
bool InitScene(void);
void KillScene(void);
void KillD3D(void);
void KillWindow(void);
unsigned long Width, Height;
bool Fullscreen;
HWND MainWindow;
HINSTANCE MainInstance;
LPDIRECT3D8 D3D;
IDirect3DDevice8 *D3DDevice;
};
And Finally, the Game.cpp
Code:
Game::Game(HINSTANCE hInstance)
{
MainInstance = hInstance;
Fullscreen = GetScreenMode();
bRunning = InitWindow();
if (bRunning) bRunning = InitD3D();
if (bRunning) bRunning = InitScene();
}
Game::~Game(void)
{
KillScene();
KillD3D();
KillWindow();
}
bool Game::InitWindow(void)
{
WNDCLASS WCL;
DWORD Style;
WCL.cbClsExtra = 0;
WCL.cbWndExtra = 0;
WCL.hbrBackground = (HBRUSH)GetStockObject(BLACK_BRUSH);
WCL.hCursor = LoadCursor(NULL, IDC_ARROW);
WCL.hIcon = LoadIcon(NULL, IDI_APPLICATION);
WCL.hInstance = MainInstance; //The only important thing about this function is that I'm using the Private Member that
//had the original Instance passed into it from the Main.cpp file. Is that okay to do?
WCL.lpfnWndProc = SWinFunc;
WCL.lpszClassName = "MyClass";
WCL.lpszMenuName = NULL;
WCL.style = CS_OWNDC;
if (!RegisterClass(&WCL)) return false;
if (Fullscreen)
{
Width = GetSystemMetrics(SM_CXSCREEN);
Height = GetSystemMetrics(SM_CYSCREEN);
Style = WS_POPUP;
}
else
{
Width = GetSystemMetrics(SM_CXSCREEN);
Height = GetSystemMetrics(SM_CYSCREEN);
Style = WS_OVERLAPPED|WS_SYSMENU;
}
MainWindow = CreateWindow("MyClass", "RPG", Style, 0, 0, Width, Height, NULL, NULL, MainInstance, this);
if (!MainWindow) return false;
ShowWindow(MainWindow, SW_SHOW);
UpdateWindow(MainWindow);
SetFocus(MainWindow);
return true;
}
//My Two Message Handling Functions
LRESULT CALLBACK Game::SWinFunc(HWND hWnd, unsigned int Msg, WPARAM wParam, LPARAM lParam)
{
if (Msg == WM_NCCREATE)
{
LPCREATESTRUCT LPC = (LPCREATESTRUCT)lParam;
SetWindowLong(hWnd, GWL_USERDATA, (long)LPC->lpCreateParams);
SetWindowLong(hWnd, 0, 1);
return DefWindowProc(hWnd, Msg, wParam, lParam);
}
Game *pMyGame;
if (GetWindowLong(hWnd, 0))
{
pMyGame = (Game *)GetWindowLong(hWnd, GWL_USERDATA);
return pMyGame->WinFunc(hWnd, Msg, wParam, lParam);
}
return DefWindowProc(hWnd, Msg, wParam, lParam);
}
LRESULT CALLBACK Game::WinFunc(HWND hWnd, unsigned int Msg, WPARAM wParam, LPARAM lParam)
{
switch(Msg)
{
case WM_KEYDOWN:
bRunning = false;
return 0;
break;
case WM_CLOSE:
bRunning = false;
return 0;
break;
case WM_DESTROY:
PostQuitMessage(0);
return 0;
break;
}
return (DefWindowProc(hWnd,Msg,wParam,lParam));
}
It seems that my second Message Handler (the non-static one) never fires because if I press a key once the app is running, nothing happens. I think the reason behind my lock-ups is that bRunning is always true and the loop in Main.cpp starts going ridiculously quickly once the window is closed, and hence the lockup.
I'm wondering if anyone sees something that's causing my Message Handler #2 not to be fired?
9. #9
Registered User
Join Date
Oct 2003
Posts
13
I'm working on something exactly like this but I'm using a thunk class to redirect the calls to the proper WndProcs.
Code:
#pragma warning(push)
#pragma warning(disable : 4355)
#if defined(_M_IX86)
#pragma pack(push, 1)
template<typename W>
class Thunk
{
const DWORD m_mov; /* mov dword ptr [esp+0x4], m_this */
const W *m_this;
const BYTE m_jmp; /* jmp WndProc */
const ptrdiff_t m_relproc; /* relative jmp */
public:
Thunk(WNDPROC proc, W *obj) :
m_mov(0x042444C7),
m_this(obj),
m_jmp(0xE9),
m_relproc((int) proc - ((int) this + sizeof(Thunk)))
{
::FlushInstructionCache(GetCurrentProcess(), this, sizeof(Thunk));
}
operator::WNDPROC() const
{
return(WNDPROC) (this);
}
};
#pragma pack(pop)
#else
#error Only X86 supported
#endif
#pragma warning(pop)
Code:
class Window
{
protected:
HWND m_hWnd; /* Window handle */
Thunk<Window> m_thunk; /* Our thunk object */
WNDPROC m_oldProc;
virtual LRESULT CALLBACK InternalWndProc(UINT uMsg, WPARAM wParam, LPARAM lParam) = 0;
static LRESULT CALLBACK wndProc(HWND pThis, UINT uMsg, WPARAM wParam, LPARAM lParam)
{
// This is where the correct MessageHandler is called
Window *p = (Window *) pThis;
return p->InternalWndProc(uMsg, wParam, lParam);
}
public:
Window() : m_hWnd(NULL), m_thunk(wndProc, this), m_oldProc(NULL)
{
}
const HWND GetHWND(){ return m_hWnd; }
#pragma warning(push)
#pragma warning(disable : 4355)
HWND Create(DWORD dwExStyle, LPCTSTR pClassName, LPCTSTR pWindowName, DWORD dwStyle, int iX, int iY, int iWidth,
int iHeight, HWND pParentWindow, HMENU hMenu,
HINSTANCE hInstance, LPVOID lpParam)
{
/* Create the window */
m_hWnd = CreateWindowEx(dwExStyle, pClassName, pWindowName,
dwStyle, iX, iY, iWidth, iHeight,
pParentWindow, hMenu, hInstance, lpParam);
if (m_hWnd) m_oldProc = windowProcedure(m_thunk);
return m_hWnd;
}
/* Return the current message handler */
WNDPROC windowProcedure () const
{
return reinterpret_cast < ::WNDPROC > (::GetWindowLong(m_hWnd, GWL_WNDPROC));
}
/* Set the message handler, returning the previous. */
::WNDPROC windowProcedure (::WNDPROC newProc)
{
return reinterpret_cast < ::WNDPROC > (::SetWindowLong(m_hWnd, GWL_WNDPROC, reinterpret_cast < ::LONG > (newProc)));
}
#pragma warning(pop)
};
now all u have to do is derive your control from Window and code the InternalWndProc function. call RegisterClassEx using DefWindowProc as the default Window procedure. the Thunk will redirect it correctly.
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Website Security Test
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__label__pos
| 0.89394 |
Leibniz formula for determinants
From Wikipedia, the free encyclopedia
Jump to: navigation, search
In algebra, the Leibniz formula expresses the determinant of a square matrix
A = (a_{ij})_{i,j = 1, \dots, n}
in terms of permutations of the matrix elements. Named in honor of Gottfried Leibniz, the formula is
\det(A) = \sum_{\sigma \in S_n} \sgn(\sigma) \prod_{i = 1}^n a_{\sigma(i), i}
for an n×n matrix, where sgn is the sign function of permutations in the permutation group Sn, which returns +1 and −1 for even and odd permutations, respectively.
Another common notation used for the formula is in terms of the Levi-Civita symbol and makes use of the Einstein summation notation, where it becomes
\det(A)=\epsilon^{i_1\cdots i_n}{a}_{1i_1}\cdots {a}_{ni_n},
which may be more familiar to physicists.
Directly evaluating the Leibniz formula from the definition requires \Omega(n! \cdot n) operations in general—that is, a number of operations asymptotically proportional to n factorial—because n! is the number of order-n permutations. This is impractically difficult for large n. Instead, the determinant can be evaluated in O(n3) operations by forming the LU decomposition A = LU (typically via Gaussian elimination or similar methods), in which case \det A = (\det L) (\det U) and the determinants of the triangular matrices L and U are simply the products of their diagonal entries. (In practical applications of numerical linear algebra, however, explicit computation of the determinant is rarely required.) See, for example, Trefethen and Bau (1997).
Formal statement and proof[edit]
Theorem. There exists exactly one function
F : M_n (\mathbb K) \rightarrow \mathbb K
which is alternate multilinear w.r.t. columns and such that F(I) = 1.
Proof.
Uniqueness: Let F be such a function, and let A = (a_i^j)_{i = 1, \dots, n}^{j = 1, \dots , n} be an n \times n matrix. Call A^j the j-th column of A, i.e. A^j = (a_i^j)_{i = 1, \dots , n}, so that A = \left(A^1, \dots, A^n\right).
Also, let E^k denote the k-th column vector of the identity matrix.
Now one writes each of the A^j's in terms of the E^k, i.e.
A^j = \sum_{k = 1}^n a_k^j E^k.
As F is multilinear, one has
\begin{align}
F(A)& = F\left(\sum_{k_1 = 1}^n a_{k_1}^1 E^{k_1}, \dots, \sum_{k_n = 1}^n a_{k_n}^n E^{k_n}\right)\\
& = \sum_{k_1, \dots, k_n = 1}^n \left(\prod_{i = 1}^n a_{k_i}^i\right) F\left(E^{k_1}, \dots, E^{k_n}\right).
\end{align}
From alternation it follows that any term with repeated indices is zero. The sum can therefore be restricted to tuples with non-repeating indices, i.e. permutations:
F(A) = \sum_{\sigma \in S_n} \left(\prod_{i = 1}^n a_{\sigma(i)}^i\right) F(E^{\sigma(1)}, \dots , E^{\sigma(n)}).
Because F is alternating, the columns E can be swapped until it becomes the identity. The sign function \sgn(\sigma) is defined to count the number of swaps necessary and account for the resulting sign change. One finally gets:
\begin{align}
F(A)& = \sum_{\sigma \in S_n} \sgn(\sigma) \left(\prod_{i = 1}^n a_{\sigma(i)}^i\right) F(I)\\
& = \sum_{\sigma \in S_n} \sgn(\sigma) \prod_{i = 1}^n a_{\sigma(i)}^i
\end{align}
as F(I) is required to be equal to 1.
Therefore no function besides the function defined by the Leibniz Formula is a multilinear alternating function with F\left(I\right)=1.
Existence: We now show that F, where F is the function defined by the Leibniz formula, has these three properties.
Multilinear:
\begin{align}
F(A^1, \dots, cA^j, \dots) & = \sum_{\sigma \in S_n} \sgn(\sigma) ca_{\sigma(j)}^j\prod_{i = 1, i \neq j}^n a_{\sigma(i)}^i\\
& = c \sum_{\sigma \in S_n} \sgn(\sigma) a_{\sigma(j)}^j\prod_{i = 1, i \neq j}^n a_{\sigma(i)}^i\\
&=c F(A^1, \dots, A^j, \dots)\\
\\
F(A^1, \dots, b+A^j, \dots) & = \sum_{\sigma \in S_n} \sgn(\sigma)\left(b_{\sigma(j)} + a_{\sigma(j)}^j\right)\prod_{i = 1, i \neq j}^n a_{\sigma(i)}^i\\
& = \sum_{\sigma \in S_n} \sgn(\sigma)
\left( \left(b_{\sigma(j)}\prod_{i = 1, i \neq j}^n a_{\sigma(i)}^i\right) + \left(a_{\sigma(j)}^j\prod_{i = 1, i \neq j}^n a_{\sigma(i)}^i\right)\right)\\
& = \left(\sum_{\sigma \in S_n} \sgn(\sigma) b_{\sigma(j)}\prod_{i = 1, i \neq j}^n a_{\sigma(i)}^i\right)
+ \left(\sum_{\sigma \in S_n} \sgn(\sigma) \prod_{i = 1}^n a_{\sigma(i)}^i\right)\\
&= F(A^1, \dots, b, \dots) + F(A^1, \dots, A^j, \dots)\\
\\
\end{align}
Alternating:
\begin{align}
F(\dots, A^{j_1}, \dots, A^{j_2}, \dots)
& = \sum_{\sigma \in S_n} \sgn(\sigma) \left(\prod_{i = 1, i \neq j_1, i\neq j_2}^n a_{\sigma(i)}^i\right) a_{\sigma(j_1)}^{j_1} a_{\sigma(j_2)}^{j_2}\\
\end{align}
For any \sigma \in S_n let \sigma' be the tuple equal to \sigma with the j_1 and j_2 indices switched.
\begin{align}
F(A) & = \sum_{\sigma\in S_{n},\sigma(j_{1})<\sigma(j_{2})}\left[\sgn(\sigma)\left(\prod_{i = 1, i \neq j_1, i\neq j_2}^na_{\sigma(i)}^{i}\right)a_{\sigma(j_{1})}^{j_{1}}a_{\sigma(j_{2})}^{j_{2}}+\sgn(\sigma')\left(\prod_{i = 1, i \neq j_1, i\neq j_2}^na_{\sigma'(i)}^{i}\right)a_{\sigma'(j_{1})}^{j_{1}}a_{\sigma'(j_{2})}^{j_{2}}\right]\\
& =\sum_{\sigma\in S_{n},\sigma(j_{1})<\sigma(j_{2})}\left[\sgn(\sigma)\left(\prod_{i = 1, i \neq j_1, i\neq j_2}^na_{\sigma(i)}^{i}\right)a_{\sigma(j_{1})}^{j_{1}}a_{\sigma(j_{2})}^{j_{2}}-\sgn(\sigma)\left(\prod_{i = 1, i \neq j_1, i\neq j_2}^na_{\sigma(i)}^{i}\right)a_{\sigma(j_{2})}^{j_{1}}a_{\sigma(j_{1})}^{j_{2}}\right]\\
& =\sum_{\sigma\in S_{n},\sigma(j_{1})<\sigma(j_{2})}\sgn(\sigma)\left(\prod_{i = 1, i \neq j_1, i\neq j_2}^na_{\sigma(i)}^{i}\right)\left(a_{\sigma(j_{1})}^{j_{1}}a_{\sigma(j_{2})}^{j_{2}}-a_{\sigma(j_{1})}^{j_{2}}a_{\sigma(j_{2})}^{j_{_{1}}}\right)\\
\\
\end{align}
Thus if A^{j_1} = A^{j_2} then F(\dots, A^{j_1}, \dots, A^{j_2}, \dots)=0.
Finally, F(I)=1:
\begin{align}\\
F(I) & = \sum_{\sigma \in S_n} \sgn(\sigma) \prod_{i = 1}^n I_{\sigma(i)}^i\\
& = \sum_{\sigma = (1,2,\dots,n)} \prod_{i = 1}^n I_{i}^i\\
& = 1
\end{align}
Thus the only functions which are multilinear alternating with F(I)=1 are restricted to the function defined by the Leibniz formula, and it in fact also has these three properties. Hence the determinant can be defined as the only function
\det : M_n (\mathbb K) \rightarrow \mathbb K
with these three properties.
See also[edit]
References[edit]
|
__label__pos
| 0.9989 |
Is bentonite clay good for cancer patients?
Published by Anaya Cole on
Is bentonite clay good for cancer patients?
Although a study reported the genotoxic effect of bentonite on human B lymphoblast cells (57), recently bentonite has been shown to inhibit the growth of human cancer cell lines U251 (central nervous system, glioblastoma). It seems that bentonite clay surfaces controls the levels of metabolic growth components (58).
What are the side effects of clay?
Side effects are usually mild but may include constipation, vomiting, or diarrhea. Clay is POSSIBLY UNSAFE when taken by mouth for a long period of time. Eating clay long-term can cause low levels of potassium and iron.
How long should you take bentonite clay internally?
How often should you use bentonite clay? Internally, you can take 1/2 to 1 teaspoon once per day, as many days of the week as you’d like. Most experts recommend that you don’t consume BC internally for more than four weeks in a row.
How often drink bentonite clay?
While many sources recommend drinking 1-3 teaspoons (or more) of clay mixed with water daily, there are some who remind us that after the below solution is mixed (see Recipe), it’s appropriate to drink just 1 ounce of the clay water daily for the first week. Week 2 the patient may increase to 2 ounces daily.
How long does bentonite clay take to work?
After consuming bentonite clay and water, wait 60 minutes to eat, allowing it to sweep through the stomach and do its good work, unaffected by the acidity required for digestion. (Ideally, use Betaine HCl or Digestive Bitters to create the optimum pH for digestion directly before eating.
When is the best time to drink bentonite clay?
When to take it — It’s recommended by most to take bentonite clay before a meal, by 30-60 minutes. The main reason is that clay is very alkaline (it has an 8.5-10 pH). Ideally, for digestion, the stomach should have a 1-2 pH, (which is why many of us take bitters or Betaine HCl).
How long does it take for bentonite clay to work?
Which country eats clay?
In Haiti, one of the poorest countries in the Western Hemisphere, the scarcity of food have made the Haitians turn to mud platters for their survival. No, not to hold food but to eat them. They have got so used to eating mud platters that now this has become a normal practice for them.
Is bentonite a carcinogen?
Bentonite itself is probably not more toxic than any other particulate not otherwise regulated and is not classified as a carcinogen by any regulatory or advisory body, but some bentonite may contain variable amounts of respirable crystalline silica, a recognized human carcinogen.
Does bentonite clay have side effects?
There’s no known serious side effect to using calcium bentonite clay. It’s possible to consume too much of this product, so always follow package instructions and don’t consume the clay for more than four weeks in a row without taking a break.
Is bentonite clay anti inflammatory?
Benefits of Bentonite Clay for Skin Has anti-inflammatory properties: Another boon for those battling breakouts, bentonite clay is naturally anti-inflammatory and can help calm inflammatory acne, explains Fahs. It’s also sometimes used to soothe dermatitis and even diaper rash, adds Jeffy.
What is the benefits of eating clay?
Clay can help absorb toxins, so many support earth eating as a way of relieving stomach issues, such as food poisoning. Although geophagia may not begin as a mental health concern, over time, eating dirt could come to resemble an addiction.
What is clay therapy for cancer?
Learning About Clay Therapy for Cancer. It is weathered volcanic ash and it is rich in a variety of minerals. When mixed with water, a very powerful electromagnetic field is purported to be created, which is said to attract and hold toxic and unwanted substances so that they can then be removed from the body.
Can clay help fight bacteria in wounds?
Now Mayo Clinic researchers and their collaborators at Arizona State University have found that at least one type of clay may help fight disease-causing bacteria in wounds, including some treatment-resistant bacteria. The findings appear in the International Journal of Antimicrobial Agents.
What are the side effects of green clay?
When green clay is applied to the skin, it’s important to note that some people have reported heightened sensitivity, rashes, dryness, or flakiness — particularly if it’s applied in excess. When ingested, green clay may cause constipation.
What are the health benefits of dried clay?
The ingestion of dried clay minerals or a clay suspension is commonly used as a source of dietary elements, as a detoxifying agent, and as an allopathic treatment of gastrointestinal illnesses and acute and chronic diarrhea ( Carretero, 2002 ). For example in Ghana, the iron, copper, calcium, zinc,…
Categories: News
|
__label__pos
| 0.999748 |
Quick Start (SOAP mode): Passing documents to the Output Service using the Java API
The following Java quick start retrieves the file Loan.xdp from Content Services. This XDP file is located in the space /Company Home/Form Designs. The XDP file is returned in a com.adobe.idp.Document instance. The com.adobe.idp.Document instance is passed to the Output service. The non-interactive form is saved as a PDF file named Loan.pdf on the client computer. Because the File URI option is set, the PDF file Loan.pdf is also saved on the J2EE application server hosting LiveCycle. (See Passing Documents located in Content Services (deprecated) to the Output Service.)
/*
* This Java Quick Start uses the SOAP mode and contains the following JAR files
* in the class path:
* 1. adobe-output-client.jar
* 2. adobe-livecycle-client.jar
* 3. adobe-usermanager-client.jar
* 4. adobe-utilities.jar
* 5. jbossall-client.jar (use a different JAR file if the LiveCycle Server is not deployed
* on JBoss)
* 6. activation.jar (required for SOAP mode)
* 7. axis.jar (required for SOAP mode)
* 8. commons-codec-1.3.jar (required for SOAP mode)
* 9. commons-collections-3.1.jar (required for SOAP mode)
* 10. commons-discovery.jar (required for SOAP mode)
* 11. commons-logging.jar (required for SOAP mode)
* 12. dom3-xml-apis-2.5.0.jar (required for SOAP mode)
* 13. jaxen-1.1-beta-9.jar (required for SOAP mode)
* 14. jaxrpc.jar (required for SOAP mode)
* 15. log4j.jar (required for SOAP mode)
* 16. mail.jar (required for SOAP mode)
* 17. saaj.jar (required for SOAP mode)
* 18. wsdl4j.jar (required for SOAP mode)
* 19. xalan.jar (required for SOAP mode)
* 20. xbean.jar (required for SOAP mode)
* 21. xercesImpl.jar (required for SOAP mode)
* 22. adobe-contentservices-client.jar
*
* These JAR files are located in the following path:
* <install directory>/sdk/client-libs/common
*
* The adobe-utilities.jar file is located in the following path:
* <install directory>/sdk/client-libs/jboss
*
* The jbossall-client.jar file is located in the following path:
* <install directory>/jboss/client
*
* SOAP required JAR files are located in the following path:
* <install directory>/sdk/client-libs/thirdparty
*
* If you want to invoke a remote LiveCycle Server instance and there is a
* firewall between the client application and the server, then it is
* recommended that you use the SOAP mode. When using the SOAP mode,
* you have to include these additional JAR files
*
* For information about the SOAP
* mode, see "Setting connection properties" in Programming
* with LiveCycle
*/
import com.adobe.livecycle.contentservices.client.CRCResult;
import com.adobe.livecycle.contentservices.client.impl.DocumentManagementServiceClientImpl;
import com.adobe.livecycle.output.client.*;
import java.util.*;
import java.io.File;
import java.io.FileInputStream;
import com.adobe.idp.Document;
import com.adobe.idp.dsc.clientsdk.ServiceClientFactory;
import com.adobe.idp.dsc.clientsdk.ServiceClientFactoryProperties;
public class CreatePDFFFromContentServicesSoap {
public static void main(String[] args) {
try{
//Set connection properties required to invoke LiveCycle using SOAP mode
Properties connectionProps = new Properties();
connectionProps.setProperty(ServiceClientFactoryProperties.DSC_DEFAULT_SOAP_ENDPOINT, "http://hiro-xp:8080");
connectionProps.setProperty(ServiceClientFactoryProperties.DSC_TRANSPORT_PROTOCOL,ServiceClientFactoryProperties.DSC_SOAP_PROTOCOL);
connectionProps.setProperty(ServiceClientFactoryProperties.DSC_SERVER_TYPE, "JBoss");
connectionProps.setProperty(ServiceClientFactoryProperties.DSC_CREDENTIAL_USERNAME, "administrator");
connectionProps.setProperty(ServiceClientFactoryProperties.DSC_CREDENTIAL_PASSWORD, "password");
//Create a ServiceClientFactory object
ServiceClientFactory myFactory = ServiceClientFactory.createInstance(connectionProps);
//Create an OutputClient object
OutputClient outClient = new OutputClient(myFactory);
//Reference form data
FileInputStream fileInputStream = new FileInputStream("C:\\Adobe\Loan.xml");
Document inXMData = new Document (fileInputStream);
//Set PDF run-time options
PDFOutputOptionsSpec outputOptions = new PDFOutputOptionsSpec();
outputOptions.setFileURI("C:\\Adobe\Loan.pdf"); // this PDF form is saved on the server
//Get the form design from Content Services
Document formDesign = GetFormDesign(myFactory);
//Set rendering run-time options
RenderOptionsSpec pdfOptions = new RenderOptionsSpec();
pdfOptions.setLinearizedPDF(true);
pdfOptions.setAcrobatVersion(AcrobatVersion.Acrobat_9);
//Create a non-interactive PDF document
OutputResult outputDocument = outClient.generatePDFOutput2(
TransformationFormat.PDF,
"C:\\Adobe",
formDesign,
outputOptions,
pdfOptions,
inXMData
);
//Save the non-interactive PDF form as a PDF file on the client computer
Document pdfForm = outputDocument.getGeneratedDoc();
File myFile = new File("C:\\Adobe\Loan.pdf");
pdfForm.copyToFile(myFile);
}
catch (Exception ee)
{
ee.printStackTrace();
}
}
//Retrieve the form design from Content Services ES2
private static Document GetFormDesign(ServiceClientFactory myFactory)
{
try{
//Create a DocumentManagementServiceClientImpl object
DocumentManagementServiceClientImpl docManager = new DocumentManagementServiceClientImpl(myFactory);
//Specify the name of the store and the content to retrieve
String storeName = "SpacesStore";
String nodeName = "/Company Home/Form Designs/Loan.xdp";
//Retrieve /Company Home/Form Designs/Loan.xdp
CRCResult content = docManager.retrieveContent(
storeName,
nodeName,
"");
//Return the Document instance
Document doc =content.getDocument();
return doc;
}
catch(Exception e)
{
e.printStackTrace();
}
return null;
}
}
// Ethnio survey code removed
|
__label__pos
| 0.946965 |
Can't Use Absolute Path for installDist
I’m trying to use installDist to dump a runnable build to a network drive and every time I give it into 'file:// ... it tries to append that path to the project path. I have tried to overwrite destinationDir property, but it seems it’s missing or has been removed?
distributions.main {
contents {
into 'file://C:\\Users\\etc\\etc\\etc'
}
}
Results in:
FAILURE: Build failed with an exception.
* What went wrong:
Execution failed for task ':subproject:installDist'.
> Could not normalize path for file 'C:\path\to\workspace\and\project\src\submodule\build\install\subproject\C:'.
I believe all strings are treated as relative paths. You could try something like this:
into(new File('C:\\Users\\etc\\etc\\etc'))
Actually, the syntax I was using was just fine for a custom Copy or
Sync type task. I remember reading that contents{} closures had the
same methods as a Copy type task, but apparently they aren’t quite the
same?
It should work the same. In the end this CopySpec is just being passed to a regular archive task.
Anyone look into this? I’m pretty sure it is a bug of some kind …
It’s not been fixed for 7 years???
1. There is nothing to fix on the Gradle side. The contents { ... } is a copy spec, yes, furthermore it also is just used as a child copy spec. If you want to define a destination directory, you do that on the respective task. You cannot use an arbitrary destination in a child copy spec.
2. Whether something changed or not you cannot tell from this thread. This is a community forum where mainly users talk with users, not the bug tracker. :wink:
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View | Details | Raw Unified | Return to bug 54239
Collapse All | Expand All
(-)org/apache/jasper/compiler/Generator.java (-4 / +7 lines)
Lines 124-129 Link Here
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private GenBuffer charArrayBuffer;
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private GenBuffer charArrayBuffer;
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private final DateFormat timestampFormat;
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private final DateFormat timestampFormat;
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private ELInterpreter elInterpreter;
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/**
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/**
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* @param s
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* @param s
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}
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}
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return v;
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return v;
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} else if (attr.isELInterpreterInput()) {
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} else if (attr.isELInterpreterInput()) {
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v = JspUtil.interpreterCall(this.isTagFile, v, expectedType,
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v = elInterpreter.interpreterCall(ctxt, this.isTagFile, v, expectedType,
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attr.getEL().getMapName(), false);
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attr.getEL().getMapName(), false);
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if (encode) {
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if (encode) {
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return "org.apache.jasper.runtime.JspRuntimeLibrary.URLEncode("
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return "org.apache.jasper.runtime.JspRuntimeLibrary.URLEncode("
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n.setBeginJavaLine(out.getJavaLine());
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n.setBeginJavaLine(out.getJavaLine());
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if (!pageInfo.isELIgnored() && (n.getEL() != null)) {
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if (!pageInfo.isELIgnored() && (n.getEL() != null)) {
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out.printil("out.write("
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out.printil("out.write("
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+ JspUtil.interpreterCall(this.isTagFile, n.getType() +
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+ elInterpreter.interpreterCall(ctxt, this.isTagFile, n.getType() +
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"{" + n.getText() + "}", String.class,
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"{" + n.getText() + "}", String.class,
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n.getEL().getMapName(), false) + ");");
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n.getEL().getMapName(), false) + ");");
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} else {
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} else {
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// run attrValue through the expression interpreter
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// run attrValue through the expression interpreter
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String mapName = (attr.getEL() != null) ? attr.getEL()
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String mapName = (attr.getEL() != null) ? attr.getEL()
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.getMapName() : null;
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.getMapName() : null;
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attrValue = JspUtil.interpreterCall(this.isTagFile, attrValue,
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attrValue = elInterpreter.interpreterCall(ctxt, this.isTagFile, attrValue,
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c[0], mapName, false);
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c[0], mapName, false);
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}
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}
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} else {
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} else {
Lines 3424-3430 Link Here
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ctxt = compiler.getCompilationContext();
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ctxt = compiler.getCompilationContext();
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fragmentHelperClass = new FragmentHelperClass("Helper");
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fragmentHelperClass = new FragmentHelperClass("Helper");
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pageInfo = compiler.getPageInfo();
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pageInfo = compiler.getPageInfo();
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elInterpreter = ELInterpreterFactory.getELInterpreter(compiler.getCompilationContext().getServletContext());
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/*
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/*
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* Temporary hack. If a JSP page uses the "extends" attribute of the
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* Temporary hack. If a JSP page uses the "extends" attribute of the
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* page directive, the _jspInit() method of the generated servlet class
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* page directive, the _jspInit() method of the generated servlet class
Return to bug 54239
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How Many Calories Do You Burn While You’re Asleep?
How many calories do you burn while you’re asleep? The act of burning calories is directionally proportionate to the amount of energy that is used up while performing a task. According to this fact, no matter what you do you, you will use up energy and burn calories. Digesting food, breathing, and even sleeping uses the energy in our body and burns calories.
The process takes a healthy part in losing weight as well; however, it is not something to be counted as exercise and to be dependent upon. Read on to find out everything there is to know about the burning calories during sleeping.
Does Sleeping Actually Burn Calories, or is it A Myth?
Our body cells have mitochondria which are the powerhouse of the cell. It stores energy that is used up in all kinds’ activities that we do. The process of losing weight is similar to this concept where a certain amount of calories are taken in and some are burned.
While sleeping the human body breathes in heavier and continues pumping blood and oxygen all throughout the body. The positions that we change during sleeping also take up energy and eventually burn a few calories.
Our brain is actually the most active when we are sleeping, it needs to take care of our subconscious which we can see usually in our dreams, it helps the dead cells replace in our body, and the brain needs to make sure that we do not miss a heartbeat in the whole process. All these activities take up energy and hence, burn calories in our body.
if you build more muscle, you'll burn more calories
Calories Burned Sleeping Calculator?
If you are tracking your food and your calories then you would want to track the number of calories burned in while you sleep as well.
The process of calculation depends on the weight and the amount of sleep you get. For every pound, a person burns about 0.42 calories in an hour. To find out the total, you need to multiply your weight in pounds with 0.42 and you will get the result for one hour. Multiply the answer with the number of hours that you have spent sleeping. The result is the number of calories that you have managed to burn during one cycle of sleep.
Calories burned while sleeping = 0.42 x Weight in pounds x no. of hours you sleep
Keep in mind that these calculations are very tentative and may vary from person to person as well.
Can You Increase how many Calories do you Burn while you’re asleep?
There are several tricks and tips that you can follow to help in burning a few extra calories while you are sleeping. Follow these for results
how to burn more calories while sleeping
• A person with a higher metabolism will have the advantage of having more calories burned when they are in deep sleep. To increase your metabolism, it is ideal to eat small frequent meals throughout the day instead of eating three or four full meals. The body will constantly run and the system will eventually increase.
• Never go to bed hungry! When you are hungry for a long time, your body tends to go into the starvation mode. In this mode, your body will slow down your metabolism process so that the energy is preserved. Hence, you will not lose many calories.
• Do not eat heavy during before going to bed as well. As much as being hungry is not recommended, having a fat snack is also not enough. You do not want your body to be working on digesting your food all night instead of recharging you.
• Keep your exercise routine. You do not want to increase your metabolism without making your muscles strong enough. Make sure to take plenty of exercises all through the day so that body remains in running mode during sleeping as well which will help to increase the energy consumption. Keep in mind to never over workout yourself since that can be hazardous to your health and your sleep as well. Extra workouts can cause a hormone to be released into the body that does not allow the body to rest and recharge for the next day.
• People who have muscles in their body are most likely to increase the process of burning calories. The more the body fat, the less energy you will be consuming. Since muscles reply on energy consumption to survive, your body will be losing calories all the time instead of only when you are asleep.
How Does Drinking Water Help In The Process?
the relationship between drinking water and calories
Water is an essential part of the human body. The body is made from 70% water which helps in detoxifying the system. This detoxification is important to remove the waste from the body and to keep it clean and help it remain cool during different processes like digestion.
The metabolism of the body increases with the right amount of water. Drinking a glass before bed allows the system to cool down from the processes. Just like pouring cool water on a grill after a barbecue is important to cool it down, the water acts as a cooling agent to the body and helps in repairing the body cells easier. The better system allows more calories to burn easily throughout the night.
How Does Weight Loss Contribute To Sleep Consumption Of Energy?
The right way to lose weight is to eat healthily and eat in a portion-controlled systematic way. A person using this method will find out that every single calorie they burn is important. The best way to track this is to write it down or put it into a calorie counter.
A healthy person can eat up to 1500 calories a day and the minimum amount should be about 1200 calories. Making a habit to burn at least 150 calories a day will help in eating with a more free approach and having to eat much better food. When you follow different steps to increase your metabolism, you will find calories to burn more while you are sleeping and you can lose weight faster. However, it is to be kept in mind that this is not a way of losing weight entirely, it is just an advantage.
Also read: Sleeping After Eating, Good or Bad?
How Do People With Muscles Constantly Lose Calories While Sleeping?
Building muscles help in losing weight because muscles use up more energy than body mass or body fat does. Once you have made muscles, you are consuming a lot more energy than an average person does. Muscles require excessive energy to survive which makes it fine to burn calories while sleeping as well as working out.
Building muscles will also help in keeping you fit and fine and will allow the body to revive from a day shock much more easily than usual.
Things The Body Does While Sleeping That Burn Calories
If the body is consuming energy while sleeping, it is doing a lot of things which help in burning those calories. The following are a few things that the body necessarily does while you are sleeping. Each thing requires energy usage from the body
Cell replacement
The worn out cells and tissues in the body are revived when we are sleeping. The reason behind this is that when we sleep, the brain has to focus on the internal body system only and not something that we do during the day. The focal point hence becomes the replacement of the worn out parts of the body and making the immune system stronger. It is almost like recharging the body.
Breathing
While you are sleeping, your brain needs to make sure that in no way is there any compromise in losing a heartbeat or a breath. The constant pumping of blood and acquiring oxygen also burns calories. The brain also ensures that necessary measures are taken in case of a mishap. For example, sometimes we wake up coughing because we were close to choking in our sleep.
Tossing and turning
Even though we are dead asleep, our body ensures that we are constantly comfortable, or the blood flow in one end is not restricted. Hence, we tend to toss and turn all night without even knowing it. For this process, we require energy which our body consumes while we are sleeping.
Does Sleeping In The Cold Burn More Calories?
Does Sleeping In The Cold Burn More Calories
Yes, sleeping in the cold burns relatively more calories than usual. All the functions that our body performs create heat energy which is then released or we are cooled down with sweat or otherwise. However, if you are in a cooler environment, you will need to make your body warm first and then continue with all the procedure. It may not burn a huge sum of calories, but it will burn a little extra.
The same is the case with drinking cold water; the temperature of the water needs to rise before the body starts using it, which is why a little extra is burned in the process.
There are several books that have supported the idea of sleeping the cold to help in reducing much more than sleeping in the warm will help you.
Conclusion
Contrary to popular belief, our body is actually the most active when it is asleep. The brain has far more responsibilities when we go to sleep which is why; most energy is consumed at that time.
Over time, there have been umpteenth research studies about how important sleep is for weight loss and to be healthy. All the thesis have been proved with the facts that the body tends to work and release energy while it is sleeping so that it can recharge for the coming day.
In the end, make sure to remember that an optimum eight hours of sleep is important but oversleeping actually slows your metabolism and causes reversal reactions in the body. The body tends to save calories because it does not know when you will be collecting them again.
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You get up exhausted and you don’t really understand why. You start yawning an hour after waking up or maybe you have trouble falling asleep despite your best efforts to get to bed early. Sound familiar? What you need is a sleep diary!
A sleep log allows you to track your sleep cycles. It will give you a better idea of your sleep habits, which will allow you to be proactive in changing them. It may even help your doctor diagnose a health problem you’re facing and explore the positive or negative impacts of treatment.
What to write in a good sleep diary:
In order to be effective, it is important to include the following:
• Sleep time
• Time(s) of awakening
• Total hours of sleep
• Sleep quality (on a scale from 1 to 5, 5 being excellent)
• Any disturbances you experience through the night
• What you did if you woke up at night
• What you ate before going to bed (type and quantity)
• What you did before you went to bed
• Your mood before bedtime
• Medications taken before bedtime (if applicable, name, type and time)
• The time of your last physical activity before bedtime
• The amount of alcohol or caffeine consumed during the day
• The number of naps and their duration during the day
• How you feel when you wake up
How to make an effective sleep diary
There are several ways to do this, whether it’s an Excel file, on a note sheet, in a note-taking application or in a nice notebook. A little tip, however, it’s recommended to move away from the screens an hour before bedtime, so the paper option would be best!
For an effective diary, a weekly structure can be particularly useful. You can use the “bullet journal” model as a basis and create your own template. Write down the days and the “boxes” to be filled. Then each day, you just fill them in with the day’s sleep information. You then copy this template for each week. Start on a day that suits you. It doesn’t have to be a Monday.tips & advices
How long you should keep a sleep diary? The answer is simple: as long as you feel the need. However, recording your sleep over a two week period will give you a much more accurate overview than just one week of information. The larger the sample, the more answers it will give to your sleep problems.
In the end, a sleep diary allows you to understand your cycles and to identify what might need to change. You ultimately optimize your sleep, adjust your schedule, change bad habits and recover energy where you thought it was impossible. In any case, we wish you the best of luck!
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> > > SERVER UPGRADED MAY 2013 < < <
The Creation Wiki is now operating on a new and improved server.
Neutrino
From CreationWiki, the encyclopedia of creation science
Jump to: navigation, search
A neutrino is an electrically neutral, weakly interacting elementary subatomic particle with a disputed but small non-zero mass. It is able to pass through ordinary matter almost unaffected. The neutrino (meaning "small neutral one" in Italian) is denoted by the Greek letter ν (nu).
Neutrinos do not carry electric charge, which means that they are not affected by the electromagnetic forces that act on charged particles such as electrons and protons. Neutrinos are affected only by the weak sub-atomic force, of much shorter range than electromagnetism, and gravity, which is relatively weak on the subatomic scale.
Most neutrinos passing through the Earth emanate from the Sun. About 65 billion (6.5×1010) solar neutrinos per second pass through every square centimeter perpendicular to the direction of the Sun in the region of the Earth.
In September 2011, neutrinos apparently moving faster than light (aka FTL neutrinos) were detected. If this finding is confirmed, it would change generally-accepted understanding of the theory of relativity and could have significant impact on radioactive decay methods for the age of the earth and universe and arguments built around the speed of light.
External Links
Personal tools
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| 0.922794 |
Chapter 1
FUNDAMENTALS OF CHEMISTRY
LEARNING OUTCOMES
UNDERSTANDING: Students will be able to: Identify and provide example of different branches of chemistry. (Applying) Differentiate between branches of chemistry. (Understanding) Distinguish between matter and a substance. (Analyzing) Define ions, molecular ions, formula units and free radicals. (Remembering) Define atomic number, atomic mass, atomic mass unit. (Remembering) Differentiate among elements, compounds and mixtures. (Remembering) Define relative atomic mass based on C-12 scale. (Remembering) Differentiate between empirical and molecular formula.(Understanding) Distinguish between atoms and ions. (Analyzing) Differentiate between molecules and molecular ions.(Analyzing) Distinguish between ion and free radical. (Analyzing) Classify the chemical species from given examples.(Understanding) Identify the representative particles of elements and compounds. (Remembering) Relate gram atomic mass, gram molecular mass and gram formula mass to mole. (Applying) Describe how Avogadro’s number is related to a mole of any substance. (Understanding) Distinguish among the terms gram atomic mass, gram molecular mass and gram formula mass. (Analyzing) Change atomic mass, molecular mass and formula mass into gram atomic mass, gram molecular mass and gram formula mass. (Applying)
Major Concepts: 1.1 1.2 1.3 1.4 1.5 Branches of Chemistry Basic Definitions Chemical Species Avogadro’s Number and Mole Chemical Calculations
1
Chapter 1
INTRODUCTION What are the simplest components of wood, rocks and living organisms? This is an age-old question. Ancient Greek Philosophers believed that everything was made of an elemental substance. Some believed that substance to be water, other thought it was air. Some other believed that there were four elemental substances. As 19th century began, John Dalton proposed an atomic theory. This theory led to rapid progress in chemistry. By the end of the century however, further observations exposed the need for a different atomic theory. 20th century led to a picture of an atom with a complex internal structure. A major goal of this chapter is to acquaint you with the fundamental concepts about matter. In this chapter you will learn some basic definitions to understand matter. This knowledge will help you in grade XI. (a) (b) 1.1
Society, Technology and Science
Do you know the debate going on for centuries about the corpuscular nature of matter? An ancient Greek philosopher, Empedocles thought that all materials are made up of four things called elements: 1. Earth 2. Air 3. Water 4. Fire Plato adopted Empedocles theory and coined the term element to describe these four substances. His successor, Aristotle also adopted the concept of four elements. He introduced the idea that elements can be differentiated on the basis of properties such as hot versus cold and wet versus dry. For example, heating clay in an oven could be though of as driving of water and adding fire, transforming clay into a pot. Similarly water (cold & wet) falls from the sky as rain, when air (hot and wet) cools down. The Greek concept of four elements existed for more than two thousand years.
to understand quantitative relationships between amounts of reactants and products in chemical reactions. balancing of Redox chemical equations. BRANCHES OF CHEMISTRY:
Chemistry is defined as the science that examines the materials of the universe and changes that these materials undergo. The study of chemistry is commonly divided into eight major branches: 1. Physical Chemistry The branch of Chemistry that deals with laws and theories to understand the structure and changes of matter is called Physical Chemistry. 2. Organic Chemistry: The branch of Chemistry that deals with substances containing carbon is called Organic Chemistry. However, some carbon compounds such as CO2, CO, carbonates and bicarbonates are studied in Inorganic Chemistry.
2
Chapter 1
3. Inorganic Chemistry: The branch of Chemistry that deals with elements and their compounds except organic compounds is called Inorganic Chemistry. 4. Biochemistry: The branch of Chemistry that deals with physical and chemical changes that occur in living organisms is called Biochemistry. 5. Industrial Chemistry: The branch of Chemistry that deals with the methods and use of technology in the large scale production of useful substances is called industrial chemistry. 6. Nuclear Chemistry: The branch of Chemistry that deals with the changes that occur in atomic nuclei is called nuclear chemistry. 7. Environmental Chemistry: The branch of Chemistry that deals with the chemicals and toxic substances that pollute the environment and their adverse effects on human beings is called environmental chemistry. 8. Analytical Chemistry: The branch of Chemistry that deals with the methods and instruments for determining the composition of matter is called Analytical Chemistry.
Society, Technology and Science
Archimedes was a Greek philosopher and mathematician and inventor of many war machines. Greek emperor gave him the task to determine whether his crown was made of pure gold or impure gold. Archimedes took the task and started thinking on it. He knew that the volume of an object determines the volume of the liquid it displaces, when submerged in the liquid. One day when he was taking bath, he observed that more water overflowed the bath tank as he sank deeper into the water. He also noticed that he felt weightless as he submerged deeper in the bath tank. From these observations he concluded that the loss in weight is equal to the weight of water overflowed. Thinking this he at once designed an experiment in his mind to check the purity of crown. He thought, he should weigh the crown and equal weight of the pure gold. Both should be dipped in water in separate containers, since every substance has different mass to volume ratio. If the crown was made of pure gold, it would displace same weight of water as an equal weight of pure gold. If the crown is impure, it would displace different mass of water than the pure gold. Thinking this, he was so excited that he ran from the bath shouting “Eureka” which means I have found it. Like Archimedes discovery, science developed through observations and experiments rather than by speculation alone.
1.1.1 DIFFERENTIATION BETWEEN BRANCHES OF CHEMISTRY Vinegar contains 5% acetic acid. Acetic acid (CH3COOH) is a colourless liquid that has characteristic vinegar like smell. It is used to flavour food. Various types of studies on this compound can help you to differentiate between various branches of chemistry. 1. Since this is a carbon compound, its method of preparations and study of its chemical characteristics is organic chemistry.
3
7. The study of the effect of radioactive radiations or neutron on this compound or its component elements is nuclear chemistry. 8. During chemical reaction atoms combine or separate or re-arrange. They combine in simple ratios. on the human is environmental chemistry. However. However. Thus some of the postulates of Dalton’s atomic theory were found defective and were changed. Dalton was able to explain quantitative results that scientists of his time had obtained in their experiments. series of experiment that were performed in 1850’s and beginning of twentieth century clearly demonstrated that atom is divisible and consists of subatomic particles. Atoms can neither be created nor destroyed. The method and instruments used to determine its percentage composition. Use of technology and ways to obtain acetic acid on the large scale is industrial chemistry. the British chemist John Dalton presented a scientific theory on the existence and nature of matter. metal carbonates. carbon. His brilliant work became the main stimulus for the rapid progress of the chemistry during nineteenth century. protons and neutrons. They have same mass and same volume. Main postulates of his theory are as follows: 3. The study of any adverse effects of this compound or the compounds that are derived from it. The study of chemical reactions that acetic acid undergoes in the bodies of human beings is biochemistry. 1. In 1803. some carbon compounds such as CO2. boiling point etc is analytical chemistry. Example 1. CO. This is because inorganic chemistry deals with elements and their compounds except carbon compounds. Technology and Science Theories are tentative. He nicely explained the law of chemical combinations. applications of laws and theories to understand its structure is physical chemistry. hydrogen carbonates and carbides are studied in inorganic chemistry. 2. 4. 4.1: Identifying examples of different branches of chemistry Identify the branch of chemistry in each of the following examples: 4 . 3. electrons. 6. This theory is called Dalton’s atomic theory. Atoms of a particular element are identical. melting point. Explanation of its transformation into gaseous state or solid state.Chapter 1 2. The work of scientists help to change existing theories of the time. 5. All elements are composed of tiny indivisible particles called atoms. hydrogen and oxygen is inorganic chemistry. They may change if they do not adequately provide explanation of the observed facts. But the study of its component elements. Also the atoms of an element may differ in masses (such atoms are called isotopes). Society.
Problem Solving strategy: Concentrate on the basic definition of each branch of chemistry and identify branch of chemistry in each example. 8. It is highly soluble in water. A chemist performed an experiment to check the percentage purity of a sample of glucose (C6H12O6). 5. Nuclear chemistry. 6. since depletion of ozone layer is environmental problem. since photosynthesis is a chemical reaction that occurs in plants (living organism). 7. α-particles (He++) when bombard on nitrogen atom. 4. Environmental chemistry. 2. since nuclear change can emit protons. Plantation helps in overcoming green house effect. Hair contain a special class of proteins called keratins. 5 . 2. 6. Solution: 1. Environmental chemistry. Haber’s process converts large quantities of hydrogen and nitrogen into ammonia (NH3).1 Identify the branch of chemistry that is related to the following information: 1. SELF ASSESSMENT EXERCISE 1. whether organic or inorganic in nature. 3. An analyst determines that NO2 is responsible for acid rain. Chlorofluorocarbon compounds are responsible for the depletion of ozone layer. Inorganic chemistry. Environmental chemistry. Analytical chemistry. a proton is emitted. since green house effect is an environmental problem. Photosynthesis produces glucose and oxygen from carbon dioxide and water in presence of chlorophyll and sunlight. 3.Chapter 1 1. 8. 4. 5. Industrial chemistry. 7. since it deals with properties of inorganic compounds. since acid rain is an environmental problem. since large scale production of any substance is the subject of industrial chemistry. Ammonia is a colourless gas with pungent irritating odour. which are present in nails and wool. Biochemistry. since it deals with analysis of a compound.
Any matter that has a particular set of characteristics that differ from the characteristics of another kind of matter is called a substance. White lead is a pigment used by artists for centuries. copper. DNA. For example substances like oxygen. A substance that cannot be converted to other simpler substances is called an element. Living things contain thousand of different substances such as carbohydrates. Hydrocarbons are the compounds of carbon and hydrogen.2. fats.Chapter 1 2. other substances exist as polyatomic molecules. Element radium decays by emitting αparticles and is converted into another element radon. galena (PbS). the metal Pb in the compound is extracted from its ore. Most of the components of these mixtures are elements and compounds that exist as molecules. water. carbon dioxide. For instance. milk and eggs. aluminium etc are elements. Technology and Science Molecularity of the physical world World is composed of a few more than a hundred elements. Some examples of complete protein food are meat. Elements are building blocks of all the substances that make up all living and non-living things. Acetylene is the simplest hydrocarbon that contains carbon-carbon triple bond. RNA etc. 3. hydrogen. Society.2 BASIC DEFINITIONS Some of the important definitions used to understand matter are given below: 1. common salt etc are different substances. 7. A careful observation of the physical world reveals that matter usually occurs as mixtures. iron. 6. CO2. 8. Gases can be compressed by applying pressure. glucose. The same elements that make up earth also make up moon. This means elements are building blocks for everything in the universe. Air consists of many elements and compounds all existing in molecular form. N2. Petroleum and coal that are complex mixtures also contain hundred of thousands of molecular compounds. 5. proteins. COMPOUNDS AND MIXTURES Anything that occupies space and has mass is called matter. Calorimeter is a device that measures the amount of heat. Rocks and earth are mixtures of numerous compounds. lipids. Only noble gases exist as monoatomic molecules. H2O and the noble gases. An element is now defined 6 . Clay and sand consists of long chains of atoms called giant molecules. 1. It also fills the empty spaces under the earth. urea. oxygen. Water a molecular substance cover 70% of the earth’s crust. Sulphuric acid (H2SO4) is weaker than hydrochloric acid. For instance O2. a substance absorbs on heating or emits on cooling.1 ELEMENTS. 4. All these substances are molecular in nature.
Homogeneous mixtures also have uniform composition throughout. sugar mixed in water. Science Tit Bits Bad breath may be good for you. A mixture consists of only one phase is called a homogeneous mixture.2. sodium chloride etc are compounds. table salt dissolved in water. therefore its atomic number is 1. A compound is a pure substance that consists of two or more elements held together in fixed proportions by natural forces called chemical bonds. The chemistry of garlic is not simple. MASS NUMBER The number of protons in the nucleus of an atom is known as its atomic number. Do you think atomic number of He is 2? What is the mass number of C-atom? The total number of protons and neutrons in an atom is known as its mass number. Examples of mixture are air. People who eat a lot of garlic have a lower chance of getting stomach cancer. there is only one proton in the nucleus of H-atom. For example. salt + sand etc. For example sand + salt. A mixture can be converted into two or more pure substances by a physical method. All the atoms of a given element have the same number of protons and therefore the same atomic number. salt dissolved in water. water. water containing dissolved oxygen. An impure substance that contains two or more pure substances that retain their individual chemical characteristics is called a mixture. For example. Garlic contains more than 200 compounds. P=1 P=2 N=2 P=6 N=6 H-atom He-atom C-atom Some atoms of an element have different number of neutrons such atoms are called isotopes. Elements and compounds have uniform composition throughout. Most of its components are made up of molecules. oil floating on water etc. The properties of compounds are different from the properties of the elements from which they are formed. For example. No. In fact the entire physical world is made up of mixture of elements and compounds. 1. suffering from heart disease or having a stroke than do people who eat little or no garlic. A mixture that consists of two or more visibly different components is called a heterogeneous mixture. of neutrons = mass number – atomic number 7 .2 ATOMIC NUMBER. carbon dioxide. copper sulphate. We will discuss isotopes in section 2.2.Chapter 1 as a substance whose all the atoms have the same atomic number.
nineteenth century chemists calculated relative atomic masses. This can be done by assigning a value to the mass of one atom of a given element. By international agreement in 1961. By observing the proportions in which elements combine to form various compounds.40% as massive as the standard C-12 atom.Chapter 1 Example 1. However. light isotope of carbon C-12 has been chosen as a standard. Thus “the mass of an atom of an element relative to the mass of an atom of C-12 is called relative atomic mass”. This value has been determined accurately using mass spectrometer. therefore we cannot determine the mass of a single atom. Lavoisier. One atomic mass unit (amu) is defined as a mass exactly equal to one-twelfth the mass of one C-12 atom. How many protons and neutrons are in the nucleus of an atom of this element? Problem Solving strategy: Number of protons are equal to atomic number and Number of neutrons = mass number – atomic number Solution: Number of protons = atomic number = 17 Number of neutrons= mass number – atomic number = 35-17 = 18 1. The mass of atoms of all other elements are compared to the mass C-12. Mass of one C-12 atom = 12 amu 1amu= mass of one C-12 atom 12 A hydrogen atom is 8. 8 . relative atomic mass of hydrogen. This isotope of carbon(C-12) has been assigned a mass of exactly 12 atomic mass unit. An atom is extremely small particles. Avogadro and Berzelius. Gay Lussac. Therefore. it is possible to determine the mass of one atom of an element relative to another experimentally.2.3 RELATIVE ATOMIC MASS AND ATOMIC MASS UNIT The first quantitative information about atomic masses came from the work of Dalton.2: Determining the number of protons and neutrons in an atom Atomic number of an element is 17 and mass number is 35. so that it can be used as standard.
So the empirical formula of hydrogen peroxide is written as HO.9994 amu. 9 . In a chemical formula element’s symbol and numerical subscripts show the type and the number of each atom in a compound.008 amu = Similarly. relative atomic masses of O. Therefore.40 x 12 amu 100 =1.0067amu 15.4 EMPIRICAL FORMULA.1 shows the relative atomic masses of some elements. What is the empirical formula of glucose? 2.9898 amu Element Al S Cl Fe Relative atomic mass 26. H and O atoms in a glucose molecule is 6 : 12 : 6. 1. The actual ratio between C.1 relative atomic masses of some elements Element H N O Na Relative atomic mass 1.9815 amu respectively.06 amu 35. EMPIRICAL FORMULA The empirical formula of a compound is the chemical formula that gives the simplest whole-number ratio of atoms of each element. MOLECULAR FORMULA A molecular formula gives the actual whole number ratio of atoms of each element present in a compound. So molecular formula of hydrogen peroxide is H2 O2. For example in compound hydrogen peroxide there is one H atom for every O atom. Table 1. 26. Table 1. The simplest ratio between C.008 amu 14. H and O atoms in glucose in 1 : 2 : 1.9898 amu. simplest ratio of hydrogen to oxygen is 1 : 1.2. Na. 22.847 amu 1. For example there are actually two H atoms and two O atoms in each molecule of hydrogen peroxide.9815 amu 32. Therefore. Al are 15. Here you will learn about two types of chemical formulas.9994amu 22. What is the molecular formula of glucose? An empirical formula shows the simplest number of atoms of each element in a compound whereas the molecular formula shows the actual number of aotms of each element in a molecule of a compound.Chapter 1 8. actual ratio of hydrogen to oxygen atoms is 2 : 2. There are several types of chemical formulas for a compound.453 amu 55. MOLECULAR FORMULA Recall that the chemical formula of a compound tells us which elements are present in it and the whole number ratio of their atoms.
eight hydrogen atoms and four oxygen atoms.008) + 16. Can you show it why? SELF ASSESSMENT EXERCISE 1.00 = 18. sulphur dioxide (SO2) etc.016amu 10 . 3. Write its empirical and molecular formulas. SELF ASSESSMENT EXERCISE 1. empirical and molecular formulas are same. Write the empirical formula for caffeine. All you have to do is to add up the atomic masses of all the atoms in the compound.2 Write the empirical formulas for the compound containing carbon to hydrogen in the following ratios: (a) 1:4 (c) 2:2 (b) (d) 2:6 6:6 For many compounds. There are nine carbon atoms. This contains 2 carbon atoms.00 = 2. Identify empirical and molecular formula for benzene from the following formulas. C6 H6 . in this compound. four hydrogen atoms and 2 oxygen atoms.2. ammonia (NH3).016 + 16. Caffeine (C8H10N4O2) is found in tea and coffee. There are actually six C atoms and six hydrogen atoms in each molecule of benzene. For example.5 MOLECULAR MASS AND FORMULA MASS Molecular mass is the sum of atomic masses of all the atoms present in the molecule.Chapter 1 Benzene in a compound of carbon and hydrogen. Vinegar is 5% acetic acid. Aspirin is used as a mild pain killer. CH Molecular formulas for water and carbon dioxide are H2O and CO2 respectively. 1. For example water (H2O). Molecular mass of water H2O = 2(atomic mass of H) + atomic mass of oxygen = 2(1. carbon dioxide (CO2).3 1. 2. Write its empirical and molecular formulas. It contains one C atom for every H atom. What are empirical formulas for these compounds? For many compounds empirical and molecular formulas are same. methane (CH4).
4: Determining formula mass 1. and in the preparation of large number of compounds.096 amu 2. Determine its formula mass. the common salt consists of Na+ and Cl ions.00) + 12(1. also called as table salt is used to flavour food. Solution: 1. Ionic compounds consist of arrays of oppositely charged ions rather than separate molecules.5amu 11 . Solution: 1. Whereas. For example. The sum of the atomic masses of all the atoms in the formula unit of a substance is called formula mass.Chapter 1 Example 1. Milk of magnesia which contains Mg(OH)2.008) + 6(16.3: Determining molecular mass 1. Determine the molecular mass of naphthalene C10H8. the term formula mass is used for ionic compounds. It has one Na+ ion for every Cl ion. Molecular mass of C6H12O6 = 6(12. hydrogen and oxygen by their subscripts and add. Example 1. preserve meat.00) =180. which is used in mothballs. Molecular mass of C10H8 = 12 x 10 + 1 x 8 = 120 + 8 = 128 amu The term molecular mass is used for molecular compounds. Sodium Chloride.5 = 58. Formula mass of NaCl = 1 x Atomic mass of Na + 1 x Atomic mass of Cl = 1 x 23 + 1 x 35. 2. Problem solving strategy: Multiply atomic masses of carbon. A formula unit indicates the simplest ratio between cations and anions in an ionic compound. So formula unit for common salt is NaCl. 2. So we represent an ionic compound by its formula unit. Problem solving strategy: Add the atomic masses of all the atoms in the formula unit. is used to treat acidity. Determine its formula mass. Determine the molecular mass of glucose C6H12O6 which is also known as blood sugar.
Following compounds are used as fertilizers. MOLECULAR IONS AND FREE RADICALS ATOMS AND IONS Atom is the smallest particle of an element that can not exist in free state.Chapter 1 2. (i) Urea. On the other hand an ion is a charged species formed from an atom or chemically bonded groups of atoms by adding or removing electrons. 12 . Figure 1. Determine the formula masses of baking soda and carbon dioxide. Ca forms Ca+2 by losing two electrons. 2. 3. ANIONS). For example Na forms Na+ by losing one electron. Calculate its formula mass.1 view of surface atoms of gold The image has been drawn by computer from signal sent to it by an instrument called a scanning tunneling microscope. however. which is responsible for the rising of cookies and bread. Positively charged ions are called cations. 1. Potassium Chlorate (KClO3) is used commonly for the laboratory preparation of oxygen gas.1 shows an image of gold atoms on the surface. Determine their formula masses. It is electrically neutral. NaHCO3 is heated it releases carbon dioxide. Today. Most of the matter is composed of molecules or ions formed by atoms. The computer has drawn gold atoms as topped peaks. the negatively charged ions are called anions. When baking soda. (NH2)2CO (ii) Ammonium nitrate.1 IONS (CATION.3 CHEMICAL SPECIES Figure 1. The Non-metal atoms usually gain one or more electrons and form anions. Metal atoms generally lose one or more electrons and form cations. Formula mass of Mg(OH)2 = 24 + 16x2 + 1x2 = 24 + 32 + 2 = 58 amu SELF ASSESSMENT EXERCISE 1. we have sophisticated instruments to weigh atoms and even visualize them. NH4NO3. whereas. 1.4 1. Important information Many scientists regarded atom as a merely a convenient mental construct and nothing more.3. An ionic compound contains anions and cations in such number that the compound is electrically neutral. This is because atom is so small that it cannot be seen with the naked eye.
Thus its nucleus has a total charge of +11.1. Molecular ions do not form ionic compounds. O-atom gains two electrons and forms O-2 ion.ion. Let us understand why an ion acquires a net positive or negative charge. The charge on the ion is +11 + (-10) = +1 SELF ASSESSMENT EXERCISE 1.2 Na+ ion Figure 1. Similarly N2-. For example O2 when loses one electron it forms O2+ ion. Mg+2 has +2 charge. S-2 has –2 charge.5 Explain Why? 1.2 shows the sodium ion. the resulting species is called a molecular ion. Around the nucleus. Consider the formation of Na+ ion. Fig. 3. These are short lived species and only exist at high temperature. FREE RADICALS A free radical is an atom which has an unpaired electron and bears no electrical charge. in the ion are 10 electrons. Note that sodium has a nucleus of 11 protons and 12 neutrons. with a total charge of -10.ion. Sulphide ion. 2. N2+ etc are examples of molecular ions. MOLECULAR ION When a molecule loses or gains electrons. Magnesium ion. For example 13 . An oxide ion has –2 charge. These ions are called molecular ions.Chapter 1 For example chlorine atom gains one electron and forms Cl. but when it absorbs an electrons it forms O2.
Dot (. For instance water exists as molecules. so it has odd number of electrons.6 Identify ions. Whereas an ion has even number of electrons. their molecules split up into free radicals. 14 . A free radical is an electrically neutral species. DIFFERENCE BETWEEN ION AND FREE RADICAL Chlorine free radical Chloride ion Which species has even number of electrons? Which species has odd number of electrons? A free radical has an unpaired electron. These species are atoms. SELF ASSESSMENT EXERCISE 1. molecules or formula units.5: Identifying representative particles of elements and compounds Figure 1.Chapter 1 are free radicals When substances like halogens are exposed to sun light. 1. molecular ions and free radicals from the following species.3.) indicates an unpaired electron. carbon exists as atoms. Identify particles of elements and compounds.2 REPRESENTIATIVE PARTICLES OF ELEMENTS AND COMPOUNDS The term representative particles refer to species present in a substance. so it has no unpaired electrons.3 shows some molecules. Example 1.
C.Chapter 1 Fig 1. Kr. d) A mixture of an element and a compound. SELF ASSESSMENT EXERCISE 1. H2. Solution: Particles of elements are A. Ar. For example. Rn.7 1. Ne. Particles of compounds are B and F. NH3 etc are polyatomic molecules. A molecule that contains only one atom is called monoatomic.3 Some common molecules Problem Solving Strategy: Elements have atoms of same sizes and compounds have atoms of different sizes. f) A mixture of two compounds. D and E. Inert gases consist of monoatomic molecules such as He. Molecules can also be classified as monoatomic or polyatomic. e) A mixture of two elements. b) An element whose particles are molecules. 15 . Molecules that contain two or more similar or different atoms are called polyatomic molecules. c) A compound. O2. Observe the given figure and identify the diagrams that represents the particles of : a) An element whose particles are atoms. HCl.
Chapter 1 2. Chemists also use a practical unit for counting atoms. A mole of a substance contains 6. 1. They could not succeed and wasted their time and money. These processes are still in use today. a compound or a mixture. It is represented by NA. oranges etc. Society. a mole of a substance represents 6. Chemical history was dominated by a pseudo-science called alchemy. Observe the given figure and decide which diagram represents particles in an element. A mole is an amount of a substance that contains 6. sublimation and extraction. a ream of paper represent 500 papers. Therefore. the works of earlier alchemists handicapped progress of science.022 x 1023 representative particles of a substance. Technology and Science During 600 – 1600 AD. so you would most likely count them by pairs rather than individually. Such processes are contributing a lot in the progress of science. Earlier alchemists were obsessed with the idea of turning cheap metals into gold. during that period they discovered many new processes such as distillation. molecules or ions of that substance. are counted in dozens. Thus. They searched for ways to change less valued metals such as lead into gold. This experimentally determined number is known as Avogadro’s number. However. For example a mole of 16 . molecules and ions. Just as a dozen eggs represent twelve eggs. Similarly eggs. This means the works of different scientists at the same time handicap or promote the growth of science. the counting unit depends on what you are counting.022 x 1023 atoms.4 AVOGADRO’S NUMBER AND MOLE How do you count shoes? As shoes come in pairs. They use a counting unit called mole to measure the amount of a substance. but paper by ream.022 x 1023 particles of that substance.
A mole of sulphur is 6. therefore.022 x 1023 molecules. So an easy way is to weigh them.022 x 1023 molecules. molecules.022 x 1023 C-atoms) A pair of Shoes & a dozen eggs Figure 1. when counting a pile of coins. For instance water exists as molecules. Just as 6. Society. 17 . They need about one million year to count them. The concept of mole has given a very simple method to count large number of items.022 x 1023atoms.02 x 10 carbon atoms weigh 12 23 g. A mole of S-atoms (6.02 x 10 coins will also have a definite mass. formula units or ions.022 x 1023 atoms. it would not be convenient to count them one by one. so one mole of hydrogen contain 6. one mole of water contains 6. you can count them by weighing.4 A mole of S-atoms. 6. A mole of water is 6. a mole of C-atoms & pair of Shoes & a dozen eggs What is the mass of one mole C-atoms? How many atoms are there in 32. So.022 x 1023 molecules of water. Technology and Science Size of the Mole Entire population can not count 1 mole of coins in a year. Mole is not only a 23 number but also represents definite amount of a substance.Chapter 1 carbon is 6.1 g of S-atoms? Does a dozen eggs have same mass as a dozen bananas? Does a mole of carbon atoms have a different mass than a mole of sulphur atoms? The mass of one mole of substance is called as molar mass.022 x 1023 atoms. If you know the mass of one coin.022 x 1023 S-atoms) A mole of C-atoms (6. Hydrogen exists as H2 molecules. What are the molar masses of carbon and sulphur? The term representative particles in a substance are atoms. Carbon exists as atoms so 1 mole of carbon contains 6.
022 x 1023 S-atoms? Is this mass of S-atoms equal to its atomic mass? What is the mass of one mole of C-atoms? Is this mass of C-atoms equal to its atomic mass? Atomic mass of an element expressed in grams is called gram atomic mass. Is gram atomic mass of C-atoms 12 g? What is the gram atomic mass of S-atoms? If each of the carbon and sulphur sample shown above contains one mole of atoms. why do the samples have different masses? Atomic mass of C Atomic mass of Na Atomic mass of Zn = 12amu = 23amu gram gram atomic mass of C = 12g atomic mass of C = 23g = 63.022 x 1023 C-atoms) What is the mass of 6.Chapter 1 1. GRAM MOLECULAR MASS AND GRAM FORMULA MASS A mole of S-atoms (6.54g Gram atomic mass of an element contains 1 mole of atoms.022 x 1023 S-atoms) A mole of C.4. Mass of 1 mole of C-atoms = 12g Mass of 1 mole of Na-atoms = 23g Mass of 1 mole of Zn-atoms = 63. Therefore.3 GRAM ATOMIC MASS.atoms (6.54g 18 .54amu gram atomic mass of C = 63.
096amu So. KCl. An ionic compound is represented by the formula unit that represents the simplest ratio between the ions of a compound. gram molecular mass of H2O = 18. gram formula mass of NaCl = 58. Molecular mass of H2O = 2 x 1.008 + 16 x 6 = 180. For example NaCl. Formula mass of NaCl = 23 + 35.022 x 1023 C6H12 O6 180.022 x 1023 molecules of glucose? is this mass of glucose molecules equal to molecular mass of glucose? Molecular mass of a substance expressed in grams is called gram molecular mass.5 = 58.022 x 1023 H2O-molecules) molecules) 18. 19 .008 + 16 = 18.5g = mole of NaCl formula unit.096g What is the mass of one mole of water molecules? Is this mass of water molecules equal to molecular mass of water? what is the mass of 6.016g Molecular mass of C6H12 O6 = 6 x 12 + 12 x 1.5amu Therefore.096g Formula mass of a substance expressed in gram is called gram formula mass. CuSO4 etc.Chapter 1 A mole of H2O-molecules (6.016g A mole of C6H12 O6 .016amu So. gram molecular mass of C6H12 O6 = 180.molecules (6.
5 = 74. (ii) (iii) All of these quantities represent molar mass.022 23 x 1023 molecules whereas gram formula mass contain 6.5amu So.Chapter 1 Formula mass of KCl = 39 + 35. GRAM MOLECULAR MASS AND GRAM FORMULA MASS (i) Gram atomic mass represents one mole of atom of an element.5: Calculating mass of one mole of a substance Calculate the molar masses of (a) Na (b) Nitrogen (c) Surcose C12H22O11 Problem solving strategy: If an element is a metal then its molar mass is its atomic mass expressed in grams ( gram atomic mass).5g DIFFERENCE BETWEEN THE TERMS GRAM ATOMIC MASS. If an element exists as molecule.5 CHEMICAL CALCULATIONS In this section. Mass of one mole of a substance expressed in grams is called molar mass.1 MOLE-MASS CALCULATIONS Example 1. its molar mass is its molecular mass expressed in grams (gram molecular mass). gram molecular mass contains 6. 1.022 x 1023 atoms. mole can be defined as atomic mass.5. Solution: a) 1 mole of Na = 23g b) Nitrogen occurs as diatomic molecules. Gram atomic mass contains 6. you will learn about the chemical calculations based on the concept of mole and Avogadro’s number. Molecular mass of N2 = 14 x 2 20 . gram molecular mass represents one mole of molecules of a compound or an element that exists in molecular state whereas gram formula mass represents one mole of an ionic compound.022 x 10 formula units. “Therefore. gram molecular mass of KCl = 74. 1. molecular mass or formula mass expressed in grams”.
05 moles of ozone is formed in a storm? Problem solving strategy: Ozone is a molecular substance. mass of 1mole of sucrose = 342g SELF ASSESSMENT EXERCISE 1.05 moles of O3 = 48 g x 9.5(a): Calculating the mass of a given number of moles of a substance Oxygen is converted to ozone (O3) during thunder storms. what mass of CO2 is produced? Problem solving strategy: Carbon dioxide is a molecular substance. mass of 1 mole of N2 = 28 g c) Its molecular mass expressed in grams. Molecular mass of C12H22O11 = 12x12 + 1x22 + 16x11 = 144 + 22 + 176 Therefore. Determine its molar mass and use it to convert moles to mass in grams.Chapter 1 = 28amu Therefore.6: When natural gas burns CO2 is formed.25 moles of CO2 is formed. 9. Calculate the mass of ozone if 9. Determine its molar mass and use it to convert moles to mass in grams 21 .05 = 434.8 Calculate the mass of one mole of (a) Copper (b) Iodine (c) Potassium (d) Oxygen Example 1. 9. If 0.4g of O3 Example 1.05 moles of O3 ? g of O3 Solution: 1 mole of O3 = 16 x 3 = 48 g 1 mole of O3 = 48 g So.
mass ? moles Solution: a) Molar mass of H2 = 1.25 moles of CO2 ? g of CO2 Solution: Molar mass of CO2= 12 + 16 x 2 = 44g 1 mole of CO2 = 44g of CO2 So.016 5g of H2 = 22 .008 x 2 = 2.016g = 1 mole of H2 = 1 moles of H2 2.Chapter 1 0. 0. 2. (b) A block of ice that weighs 100g.016g of H2 1g of H2 = 2. Problem solving strategy: Hydrogen and ice both are molecular substances.7: Converting grams to moles How many moles of each of the following substance are present? (a) A balloon filled with 5g of hydrogen. Use the molar mass of each to convert masses in grams to moles.016g 1 mole of H2 So.25 moles of CO2 = 44 x 0. Determine their molar masses.016 1 x5 moles of H2 2.25 = 11g of CO2 Example 1.
of moles of this compound that would exactly weigh 30g.5.016g 1 mole of H2O So.016 + 16 = 18. 1.25 moles of Zn.2 MOLE-PARTICLES CALCULATIONS Example 1.5grams of this salt. Calculate (a) Mass of this compound that would contain 2.Chapter 1 = 2. people are required to swallow suspensions of barium sulphate (BaSO4). NaCl contains 12.2 moles of aluminium? 23 . 2. 2. (b) No.48 moles of H2O b) 1 mole of H2O = 2 x 1. Before the digestive systems X-rayed. How many atoms are present in a foil that contains 0.8: Calculating number of atoms in given moles 1. Zn is a silvery metal that is used to galvanize steel to prevent corrosion. Calculate the number of moles it contains.016 1 x100 moles 18. A thin foil of aluminium (Al) is used as wrapper in food industries. A spoon of table salt. The molecular formula of a compound used for bleaching hair is H2O2.016 100g of H2O = = 5.008 + 16 = 2.5 moles. 3.016g of H2O 1g of H2O = 18.9 1. 18. Calculate mass of one mole of BaSO4.55 moles of H2O SELF ASSESSMENT EXERCISE 1. How many atoms are there in 1.016g = 1 mole = 1 moles 18.
53 x 1023 Zn atoms 2. Solution: 1. How many molecules are there in 0.25 moles of SO2. thus 1 mole of methane will have 6. 1 mole of Zn contains 6. 1 mole of Al contains 6.25 = 1.25 = 7.022 x 1023x 0. Solution: 1. How many molecules are present in 0.Chapter 1 Problem solving strategy: Remember that symbols Zn and Al stand for one mole of Zn and Al atoms respectively.022 x 1023x0. its one mole will also have 6. Similarly.5 23 = 3.5055 x 1023 molecules 24 .2 moles of Al will contain = 6.022 x 10 molecules So. Methane (CH4) is the major component of natural gas. 0. Problem solving strategy: Remember that CH4 is a molecular compound.2044 x 1023 atoms Example 1. 1 mole of CH4 contains = 6.022 x 1023 molecules. 23 1 mole of SO2 contains = 6.2 = 1. Sulphur dioxide reacts with water to form acid rain.022x1023 molecules. 0.022 x 1023 x 0.9: Calculating number of molecules in given moles of a substance 1. SO2 is a molecular compound.022 x 1023 x 1.5 moles of CH4 will contain = 6.022 x 1023 atoms 1.011 x 10 molecules 2.5 moles of a pure sample of methane? 2.022 x 1023 molecules So. At high temperature hydrogen sulphide (H2S) gas given off by a volcano is oxidized by air to sulphur dioxide (SO2).25 moles of Zn contain = 6.022 x 1023 atoms So 0.25 moles of SO2 will contain= 6.
Its molecular formula is CH2O.5 moles of Ti Example 1.022 x 1023 molecules = 1 mole of compound 3.022 x 1023 atoms. aircrafts and jet engines. Thus.011 x 1022 molecules of this compound.011 x 1023 Ti-atoms.022 x 1023 1 x 3.022 x 1023 molecules. Problem solving strategy: Remember that 1 mole of an element contains 6. 6. Calculate the number of moles of this metal in a sample containing 3.011 x 1023 atoms ? moles Solution: 6.Chapter 1 Example 1.022 x 1023 atoms = 1 mole 3. Thus. Calculate the number of moles that would contain 3. Problem Solving Strategy: Remember that 1 mole of any compound contains 6.022 x 1023 3. 6.011 x 1022 molecules ? moles 25 .011 x 1023 Ti atoms = = 0.11: Calculating number of moles in the given number of molecules Formaldehyde is used to preserve dead animals.022 x 1023 Ti atoms = 1 mole of Ti 1 Ti atoms = 1 moles of Ti 6.011 x 1023 moles of Ti 6.10: Calculating number of moles in the given number of atoms Titanium is corrosion resistant metal that is used in rockets.
A method used to prevent rusting in ships and underground pipelines involves connecting the iron to a block of a more active metal such as magnesium. The total number of protons and neutrons in an atom is called its mass number. It is used as a painkiller. The branch of Chemistry that deals with laws and theories to understand the structure and changes of matter is called Physical Chemistry. Physical and chemical changes that occur in living organisms are studied in biochemistry.022 x 10 = 0.011 x 1022 molecules = 1 moles of formaldehyde 6. How many moles of magnesium are present in 1 billion (1 x 109) atoms of magnesium. Industrial chemistry is concerned with the large scale production of chemical substances.Chapter 1 Solution: 6. hydrogen and oxygen. How many moles of this compound are present in the tablet? 2. A compound consists of two or more elements held together in fixed proportions by chemical bonds. 26 . This method is called cathodic protection. An impure substance that contains two or more pure substances that retain their individual chemical characteristics is called a mixture.022 x 1023 1 x 3. An element is a substance whose all the atoms have the same atomic number.05 moles of formaldehyde SELF ASSESSMENT EXERCISE 1.022 x 1023 molecules = 1 mole of formaldehyde 1 molecule = 3. An aspirin tablet contains 1. The number of protons in the nucleus of an atom is known as its atomic number. Aspirin is a compound that contains carbon. Organic chemistry deals with carbon compounds. The branch of Chemistry that deals with elements and their compounds except organic compounds is called Inorganic Chemistry.011 x 1022 moles of formaldehyde 23 6. Chemistry is the science of materials of the universe.10 1.25 x 1030 molecules.
molecular mass or formula mass expressed in grams. Molecular mass is the sum of atomic masses of all the atoms present in the molecule. Chemical formula of a compound that gives the simplest whole-number ratio between atoms is called empirical formula. The amount of matter that contains as many atoms. One atomic mass unit is defined as the mass exactly equal to one-twelfth the mass of one C12 atom. When a molecule loses or gains electrons. Mole can also be defined as atomic mass. REFERENCES FOR ADDITIONAL INFORMATION Zumdahl.Chapter 1 Atoms of an element that have different number of neutrons are called isotopes. The mass of an atom of an element relative to the mass of an atom of C-12 is called relative atomic mass. Molecular formula of a compound gives the exact number of atoms presents in a molecule. 27 . Molecular mass of an element or a compound expressed in grams is its gram molecular mass. The number of representative particles in one mole of the substance is known as Avogadro’s number. Introductory Chemistry. ions or molecules as the number of atoms in exactly 12g of C-12 is called mole. Gram formula mass is the formula mass of a substance in grams. Positively charged ions are called cations and negatively charged ions are called anions. Essential Chemistry. the resulting species is called molecular ion. Free radical is an atom or group of atoms that contains an unpaired electron. Raymond Chang. Atomic mass of an element expressed in grams is called gram atomic mass.
oxygen. H=1) a. c. a. d. water. (iii) a. d. 16 (v) How many moles of molecules are there in 16g oxygen. water. which box represent the particles in nitrogen. 23 c.008g (vii) What is the mass of carbon present in 44g of carbon dioxide. Air.Chapter 1 Q. (Atomic masses: Cu=63. 1 b.05 (vi) What is the mass of 4 moles of hydrogen gas. brass Air. a.5 249. 0. earth Calcium. 12 d. O=16.1: Encircle the correct answer: (i) Which of the following lists contains only elements? a. 106 b. 8. S=32.5 185. 1. fire. 159.5 149. b. 4.5 c. 1g d. What is the formula mass of CuSO4. b. c. b. sulphur. d.1 d. 0. Atomic mass of the element X is a.5.064g b.032g c.5 (iv) A compound with chemical formula Na2CX3 has formula mass 106amu.5H2O. 28 . oxygen Hydrogen. c. 0. carbon (ii) The diagrams below represent particles in four substances.
mass c. (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) Q.5x Q. An atom of this element will form an ion that will have charge. 6g c. Calculate the number of moles of each substance in samples with the following a. 2. b. What is mole? Differentiate between empirical formula and molecular formula. 2x d. +2 c.Chapter 1 a. atoms d. atomic number. 0. What is the number of molecules in 9. molecular ion. molecules (x) If one mole of carbon contains x atoms. free radical. x b. 12g b. formula unit.5x c. -1 (ix) Which term is the same for one mole of oxygen and one mole of water? a. 24g d. d. c. atomic mass unit.4: Q. 1. +3 d. 44g (viii) The electron configuration of an element is 1s22s2. what is the number of atoms contained in 12g of Mg. +1 b. a.4 g of He 250mg of carbon 15g of sodium chloride 40g of sulphur 29 masses: . Differentiate between (a) atom and ion (b) molecular ion and free radical. mass number. volume b.3: Q. Describe how Avogadro’s number is related to a mole of any substance.6: Differentiate between an ion and a free redical What do you know about corpuscular nature of matter? Differentiate between analytical chemistry and environmental chemistry.5: Q.2: Give short answers. a.0 g of steam? What are the molar masses of uranium -238 and uranium -235? Why one mole of hydrogen molecules and one mole of H-atoms have different masses? Define ion.
6 H-atoms.5kg of MgO Q. a.25 moles of steam 1. C6H6 0. 3.10: TNT or trinitrotoluene is an explosive compound used in bombs. the dye used to colour blue jeans is derived from a compound known as indoxyl (C8H7ON). Also determine the molar mass of this molecule. Q. It contains 7 C-atoms.13: Identify the substance that has formula mass of 133.01 moles of acetic acid.2 moles of K 75moles of H2 0. c. b.09 moles of benzene.05 moles of CuSO4. 5g of H atoms 30 . Calculate the molar masses of these compounds. Q.4 moles of nitrogen atoms b. b.5H2O 0.5 moles of carbon dioxide 3.12: Indigo (C16H10N2O2). 5 N-atoms and 6 O-atoms. d. 23g of Na c. MgCl2 S2Cl2 BCl3 AlCl3 Q. NH3 1. e.11: A molecule contains four phosphorus atoms and ten oxygen atoms.14: Calculate the number of atoms in each of the following samples: a. 1.8: 1. d. Also write their empirical formulas. 2.15moles of H2SO4 Calculate the number of molecules present in each of the following samples: a. c. Write its empirical formula.9: Decide whether or not each of the following is an example of empirical formula: a. c. b. d. c. b. Write the empirical formula of this compound. Q.7: Calculate the mass in grams of each of the following samples: a. Q. d.4 moles of ammonia.Chapter 1 e. CH3COOH Q.5amu. Al2Cl6 Hg2Cl2 NaCl C2H6O Q.
A silver article tarnishes in air. Dynamite (C3H5N3O9) explodes to form a mixture of gases. Purple iodine vapour appears when solid iodine is warmed. 4. Sulphur dioxide is the major source of acid rain. 8. 3. 6. Ice floats on water. 10. In Pakistan most of the factories use wet process for the production of cement. 7. A cornstalk grows from a seed. Many other light chlorinated hydrocarbons in drinking water are carcinogens. Carbon-14 is continuously produced in the atmosphere when high energy neutrons from space collide with nitrogen-14. c. 2. b. 3. 5.Chapter 1 Q. d.15: Calculate the mass of following: a. 31 .16: Identify the branch of chemistry that deals with the following examples: 1.24 x 1018 atoms of iron 2 x 1010 molecules of nitrogen gas 1 x 1025 molecules of water 3 x 106 atoms of Al Q. 9. Gasoline ( a mixture of hydrocarbons) fumes are ignited in an auto mobile engine.
00g of carbon. What mass of oxygen contains the same number of molecules as 42g of nitrogen. It shows particles in a sample of air. 2. Calculate the total number of atoms present in 18g H2O. e) What is the most common substance in air? 5.Chapter 1 1. 32 . What mass of sodium metal contains the same number of atoms as 12. Calculate the mass of one hydrogen atom in grams. 4. 6. d) Decide whether each substance in air is an element or a compound. a) Count the substances shown in the sample b) Is air a mixture or pure substance? Explain? c) Identify the formula of each substance in air. Observe the given figure. Calculate the number of H-atoms present in 18g H2O. 3.
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Often the main problem is variable bowel habit - there is sometimes diarrhoea and other days constipation. This is the main symptoms of irritable bowel syndrome (IBS)...
FAQ: How useful are breath tests for IBS?
There is some recent interest in breath tests to evaluate IBS. These are breath hydrogen tests after a meal of fructose, lactose and lactulose. Each sugar needs to be tested separately and the test takes 2-3 hours for each sugar. Often just the fructose test is performed. The concept is that response to a FODMAP diet can be predicted by a positive fructose breath test - i.e showing failure of normal absoprtion of fructose (malabsorption). In practice a positive test is very common and has minimal predictive value.
Positive breath tests for lactose may be found in 10-15% of people with IBS and 5% of the general population. Knowledge of a positive test can be helpful although a trial of diary exclusion for a month is perhaps more informative as symptoms from diary products may be due to factors other than the lactose.
Some groups have proposed that bacterial overgrowth in the small bowel causes many of the symptoms of IBS particularly bloating. Tests for this possible abnormality are difficult. A simple test is the lactulose breath test but this is difficult to interpret. There is a relatively high rate of positive tests making it difficult to know if this is a genuine finding. There is an antibiotic called rifaxamin that is claimed to treat this problem. This antibiotic is expensive and has limited availability and is not used in NZ for IBS. There may be some people who will benefit from this treatment if cheaper alternatives are available. it is not clear if repeated courses - perhaps every 3 months - will continue to maintain the improvement in symptoms.
Some tests also check for methane as well as H2 (hydrogen). About 40% of people are methane producers and this will give some extra information. Methane actually slows down the bowel - ? cause or effect. There is debate as to what to do with a positive test (as applies for hydrogen tests)
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Coded Illumination for Lensless Imaging
Abstract
It is common knowledge that conventional camera has a lens and a sensor array as a set. As light passes through the lens, it will be collected and form an image of the photograph subject. Because of the special property of lens, whatever is displayed in front of the sensor will be directly recorded on the sensor array. For lensless camera, the lens is replaced with a binary mask. Unlike the lens can collect light, mask can only project a shadow that human eyes can not recognize on the sensor array and further computational algorithm is required to recover a meaningful image from the shadow. Without the physical constraints of the lens, lensless camera can be extremely flat, light-weight and flexible, which makes it an alternative option to conventional cameras. However, despite these advantages, the quality of images recovered from the lensless cameras is often poor, especially when sensor to mask distance is small or number of sensor pixels is less than the number of scene pixels.
This thesis presents a new method to address the problem of poor reconstruction results by combining coded illumination patterns with the mask-based lensless imaging. Instead of using uniform illumination, the object is illuminated with multiple random generated binary patterns and the camera acquires a sequence of images for different illumination patterns. Apart from solving this problem in a naive way, a low-complexity and recursive algorithm is proposed to avoid storing all the measurements or creating a large system matrix. The results of simulation are presented on standard test images under various extreme conditions and demonstrate that the quality of the image improves significantly with only a small number of illumination patterns.
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