The Northern Ireland High Court in C (A Person under a Disability) v Chief Constable of the Police Service of Northern Ireland [2020] NIQB 3 has awarded damages of £16,500 for a breach of article 3 in respect of a failure by the police to conduct a proper investigation into the reported rape of a twenty-year-old woman with Asperger's syndrome.
The Claimant was diagnosed with Asperger's when twelve years old and lacked capacity to bring the proceedings in her own right. She alleged that she was raped and that the police failed in a number of respects. These included:
- The police failed to seize any relevant CCTV footage and did not conduct house-to-house inquiries to seek further witnesses;
- No attempt was made to follow up the Claimant's statement that she had left personal belongings in the place where she was raped;
- No attempt was made to retrieve the Claimant's diary, which her mother told the police might contain relevant information;
- There was no follow-up of the Claimant's mother's telling the police that her daughter had received text messages asking her not to proceed with the allegation;
- The police initially failed to take any statements from the people who were with the Claimant on the night of the rape;
- The Claimant was not interviewed until six months after she had been raped;
- The police failed to submit relevant evidence for analysis for over five months;
- The investigating officers had received inadequate training with respect to the investigation of rape relating to a vulnerable adult and were not aware of Achieving Best Evidence Guidelines.
The judge recounted the detailed history of the investigation. Without repeating all of that here, his conclusions were:
- There had been delay in conducting an ABE interview, due the inability of the police to assemble an appropriately credited and experienced team to conduct it. When an issue arose as to the Claimant's wishes to continue with the complaint, an officer should have visited her to ascertain whether she wanted to proceed [61].
- The investigating officer had no specific training in the investigation of serious sexual offences, particularly those involving vulnerable victims. He had no familiarity with policy documents and document on investigating child abuse and rape. The absence of training was a systemic failing [62].
- There were operational failures of a failure to obtain statements, a delay in obtaining statements, a failure to follow up investigative leads, a delay in following up investigative leads, a failure to secure and process evidence, delay in securing and processing evidence, a failure to reassess the overall strategy when it was clear that the interview of the Claimant was going to be delayed and a failure of supervising officers to direct a change in strategy [63].
The judge considered that these encompassed both operational and systemic failings. The operational failings could not be described as minor or insignificant but were serious. They resulted in the Ombudsman recommending misconduct proceedings for two officers, who accepted that they had failed to conduct a thorough investigation. Two more senior officers received advice and guidance for their supervisory failings. The combination of all the failings represented a failure to carry out an effective investigation and undoubtedly constituted a breach of article 3 [92].
The judge further considered that although the police's failures would have caused the Claimant some upset, distress and frustration, the significant and severe psychiatric and psychological deterioration which occurred following the incident would have occurred even had the police conducted the investigation in a flawless manner. In those circumstances, the judge awarded damages of £16,500 including interest.
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text:
加圧方式の床吹出し空調システムに関する研究 第1報, 均一な吹出し気流速度分布を得るための因子解析 Studies on a Pressurized Type Underfloor Air-Conditioning System (1th Report : Analysis of Controlled Factors for Uniform Air Velocity Profile)
Recently, a lower type free-access floor system which realizes improved ease of walking and less sense of confinement has been attracting attention. However, it is known that the lower the design of the air supply chamber, the larger the non-uniformity of the supplied air velocity at each diffuser and the greater the deterioration in room temperature distribution. In this report, an analytical model is proposed for predicting the non-uniformity of supplied air velocity at the design stage. The validity of the analytical model was confirmed by the good-coincidence of results obtained in scale model tests. It was found that the limit of the floor height at which a uniform supplied air velocity is obtained was 50 mm. Moreover, a relation was found whereby the inverse of coefficient of resistance at a diffuser up to a value of 1 is proportional to the maximum non-uniformity. This indicates the possibility that design work aimed at constructing a pressurized type under floor air-conditioning system with a uniform supplied air velocity profile may be readily performed from parameters of the coefficient of resistance at a diffuser by utilizing this relation.
日本冷凍協会論文集 13(2), 133-141, 1996-07-31

source: openbmb/Ultra-FineWeb


The Kingdom Name Generator!
Jump down to the Generator
A kingdom is a state, province or city ruled by a King or a Queen at the heart of a monarchy. There are some countries around the world that are still monarchies such as in Brunei (2012). Kingdoms also appear in many fictional fairytales, books, films and games, such as in The Lord of the Rings where the Kingdom Of Rohan is ruled by the King; Théoden.
Whether you are writing a fantasy book, film or game, the right kingdom name can be a great way to add a sense of consolidated power in the hands of a single character, this can create pivotal decision points in any story or plot line which can add a twist to the whole story and keep the reader on the edge of their seat, so to speak. I hope this name generator will help you find a good kingdom name that will positively add to your project.
In ancient and medieval times, there were many kingdoms in Europe, Africa and Asia. Some major kingdoms appeared in France, Germany, Israel and many other countries. Some cool kingdom names from medieval times include: Kingdom of Powys, Kingdom of Strathclyde, Kingdom of Aragon and Kingdom of Asturias. For a list of Kingdom Names, have a look at the: List Of Kingdoms Wiki
Kingdom Names Generated:
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Click on the names you like the best.
 Copy your names before you leave.


text:
Glossary of Korean Cooking Terms and Ingredients
Definition and translation of Namul
Translation of the Korean word "cha" into English
Translation of Pojangmacha
Definition of Pojangmacha in Korean
Definition and translation of Hwe in Korean food
Definition and translation of Daenjang in Korean food
Definition and translation of Gogi
Definition of Anju in Korean food
Definition of Jun in Korean food
Definition and translation of banchan, Korean side dishes.
Definition and translation of Korean kimchi, one of the most important parts of Korean cuisine.
Definition and Translation of Dubu in Korean food, a soft beancurd which is also known as Tofu in the West
Definition and Description of Korean kaenipperilla leaves, also used in Japanese (shiso) and Vietnamese cooking.
Translation and Definition of Namul.
Translation of Gui as used in Korean cooking.
Bap or Bop
Translation of Bap
Definition of Korean kochukaru.
Definition for Korean kochujang.
Definition of Chigae (Korean stew)

source: HuggingFaceFW/fineweb-edu


Clipboard Help+Spell 2.16 review
Clipboard Help+Spell
You may recall developer Mouser from other hits such as Find and Run Robot, Snapshot Captor, and Web Link Captor. And indeed, Clipboard Help+Spell carries his distinctive style: comprehensive Options dialog, multiple interface layouts, and other niceties that add up to the feeling that if you just dig deep enough, you can get Clipboard Help+Spell to do just about anything.
Much like competitor ArsClip, Clipboard Help+Spell features a powerful pop-up menu that lets you use most of the application's features without having to switch away from the program in use. The menu shows a list of recently copied text snippets, any of which take just a single keystroke to paste in at the cursor. You can also set aside a bunch of favorite clips so that you always have them handy, paste the current date and time in multiple formats, format selected text in various ways (such as title and sentence case), and many other features.
One of the nicest Clipboard Help+Spell features is called the Stack. At any point during your work, you can pop open the menu and set a "start stack" marker. Clipboard Help+Spell then records the series of items you copy, and lets you paste them back in the same sequence, one by one. This is very useful when transferring information manually from a text document into a spreadsheet, for example. You can just focus on finding and copying the information, and paste it into the spreadsheet later. That's much faster than having to constantly switch back and forth between the document and the spreadsheet.
Clipboard Help+Spell: built-in spell checker
Clipboard Help+Spell does have a built-in spell-checker, but you can't use it through the pop-up menu: You need to switch to the program's main window and select a clip to work on. You can then read through the clip and hunt for words with a red squiggly underline (just like in Microsoft Word), or execute a spell-check on the snippet, which pops open a spelling dialog on every error. So, spellchecking is available, but it isn't the star of the show.
In truth, most Clipboard Help+Spell users probably won't scratch the surface of this complex and powerful beast. But even if you only use 10% of what it has to offer, you'll still end up with a more powerful and flexible, clipboard. Try it out. See all: PC Advisor software downloads
Clipboard Help+Spell
Clipboard Help+Spell 2.16: Specs
 - Microsoft Windows 2000/7/8 Desktop/Vista/XP
Clipboard Help+Spell is simple and effective, and can save you time even if you use just a small subset of its features.
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Exercise 2 | Forward/Backward Moves & Spins (1-2-Whoosh)
1-2-Whoosh spins within forward/backward moves are a good challenge. They are more challenging than within side moves, yet great for building your stability and balance.
Start with feeling the music, finding its rhythm, and feeling the 1-2-Whoosh within you. When ready, get into your forward/backward moves, 1-2-Whoosh style. Feel poised and encourage your movement to rotate, aka bend. The more general rotation you have the more naturally spins happen.
Now, prepare your spin on the Whoosh of the previous move. Then feel yourself spin on the 1-2 and landing it on the Whoosh. Spinning as you travel straight forward or backward is challenging, so when you spin allow yourself to spin to the side if that feels better.
Incorporate all the elements of movement and use this exercise to solidify your 1-2-Whoosh timing and your stability. Explore and play with your spin possibilities.
Practice with the Spotify playlist and your favorite tunes.
Fun times ahead.


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(CNN) -- The Chinese air force have a new secret weapon: monkeys.
The People's Liberation Army Air Force has trained macaques to keep its troops safe by discouraging birds from nesting near the air force base, the PLA's website reported earlier this week.
The monkeys are used in an unidentified air force base in northern China, which is situated right on a major migratory route for birds.
When swarms of birds fly around the base, it poses a threat to military planes that are in mid-flight. The birds could potentially get sucked into plane engines, endangering the lives of both birds and pilots.
"Don't worry, we now have a secret weapon!" Su Chuang, a high-ranking officer, was quoted as saying on the PLA website. The officer was referring to the specially-trained monkeys that answer to the sound of a whistle.
When the nests of birds are discovered in tree tops, the monkey army is deployed to remove them.
The PLA have tried many different methods to remove the nests in the past, including opening fire on the nests, using long bamboo poles to topple them out of trees, and having soldiers climb the trees to pick them out.
None of these methods were very effective. Apart from being time-consuming and dangerous for the officers who had to climb the trees, the birds kept coming back.
However, when monkeys remove the nests, the birds do not return, as the macaques leave a scent on the branches that discourage the birds, according to the PLA's web posting.
"The monkeys are loyal bodyguards who defend the safety of our comrades," said the web report.
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Java Dynamic Management Kit 5.0 Tutorial
Defining Relation Types
We define a relation type in the relation service by associating a name for the relation type with a non-empty array of RoleInfo objects. These are the parameters to the service's createRelationType method that we call through the MBean server.
Example 15–3 Defining a Relation Type
try {
 String relTypeName = "myRelationType";
 Object[] params = new Object[2];
 params[0] = relTypeName;
 params[1] = roleInfoArray;
 String[] signature = new String[2];
 signature[0] = "java.lang.String";
 // get the string representing the "RoleInfo[]" object
 signature[1] = (roleInfoArray.getClass()).getName();
 server.invoke( relServObjName, "createRelationType",
 params, signature);
} catch (Exception e) {
 echo("\tCould not create the relation type " + relTypeName);
The relation type name given by the calling process must be unique among all relation type names already created in the relation service. Relations will refer to this name to define their type, and the service will verify that the roles of the relation match the role information in this type.
The relation service provides methods for managing the list of relation types it stores. The removeRelationType removes the type's definition from the relation service and also removes all relation instances of this type. This mechanism is further covered in Maintaining Consistency.
Other methods give the list of all currently defined relation types or the role information associated with a given type. Role information is always obtained through the name of the relation type where it is defined. Here we show the subroutine that our example uses to print out all role and type information.
Example 15–4 Retrieving Relation Types and Role Information
try {
 echo("\n-> Retrieve all relation types");
 Object[] params1 = new Object[0];
 String[] signature1 = new String[0];
 ArrayList relTypeNameList = (ArrayList)
 (server.invoke( relServObjName, "getAllRelationTypeNames",
 params1, signature1));
 for (Iterator relTypeNameIter = relTypeNameList.iterator();
 relTypeNameIter.hasNext(); ) {
 String currRelTypeName = (String)(relTypeNameIter.next());
 echo("\n-> Print role info for relation type " +
 Object[] params2 = new Object[1];
 params2[0] = currRelTypeName;
 String[] signature2 = new String[1];
 signature2[0] = "java.lang.String";
 ArrayList roleInfoList = (ArrayList)
 (server.invoke( relServObjName,"getRoleInfos",
 params2, signature2));
} catch (Exception e) {
 echo("\tCould not browse the relation types");


12 Types of Children in Ancient India
In Ancient India, 12 types of children were considered to be legal heir of his father. All of them need not be biological children of their legal father.
Manu Smriti and other dharma sastras describe 12 different ways a child can become legal heir of someone.
12 Types of Children in Manu Smriti
When a husband dies childless or is husband is either incapable of fatherhood, wife can opt for a method called 'Niyoga'.
She can request for appointment of a person for helping her bear a child. The man who was appointed must be or would most likely be a revered person. There were various clauses associated with this process, as follows:
1. The woman would agree to this only for the sake of rightfully having a child and not for pleasure.
2. The child, thus born would be considered the child of the husband-wife and not that of the appointed man.
3. The appointed man would not seek any paternal relationship or attachment to this child in the future.
4. To avoid misuse, a man was allowed a maximum of three times in his lifetime to be appointed in such a way.
5. The act will be seen as that of Dharma and while doing so, the man and the wife will have only Dharma in their mind and not passion nor lust. The man will do it as a help to the woman in the name of God, whereas the woman will accept it only to bear the child for herself and her husband.
In niyoga, the bodies were to be covered with ghee (so that lust may not take root in the minds of the participants but the actual act may take place for conception).
In Mahabharata, queen Satyavati compels her first son and sage Vyasa to perform niyoga with the widows of her third son Vichitravirya. The widows Ambika and Ambalika and one of their maids bear Dhritarashtra, Pandu and Vidura respectively.
Manu Smriti describes the child born by niyoga as a kshetraja child of the husband-wife.
12 Types of Children (Legal Heir) in Ancient India
 - Aurasa : Biological son through wife in a normal marriage, where son carries father's Y-Chromosome.
 - Putrikaputra : When there is no son, girl is treated as son and her son becomes legal heir (ex : Babruvahana, born to Arjuna and Chitrangada, but became legal heir of his maternal-grandfather.)
 - Kshetraja : Wife's womb but husband is not biological father. (ex: Kunti, Madri giving birth to pandavas). This can happen even after husband's death and still the children born will be treated as deceased father's heir
 - Dattaka : Adopted through legal method or vedic ritual.
 - Kritima : A child is nourished and brough up as a son, but no adoption rituals performed. Child grows up and assumes you as parent.
 - Gudhaja : Wife's secret son, without husband's knowledge. This child also is heir of father. Only difference with Kshetraja is, husband's approval or knowledge.
 - Apaviddha : Rejected child of some parent, but grew up with others. This child can claim property of person who nourished him, but cannot do pind-daan or death rituals to ancestors of that family (example : Karna did not or could not do pind-daan to ancestors of the adhirtha-radha)
 - Kanina : Son born to a lady before her marriage. But he becomes legal heir of his mother's future husband. (ex : Karna would have inherited the throne of Hastinapur after the death of Pandu being his eldest son as per this law, but birth of Karna was kept secret by Kunti and she revealed the truth only after the death of Karna. )
 - Sahodha : A son is brought along with the marriage. If a woman was pregnant at the time of her marriage, the son born to her after her marriage was deemed to be the son of the man who married her, even though the biological father was a different man.
 - Krita : He is a purchased son.
 - Paunarbhava : The son of a virgin widow. She after her marriage became a 'Punarbhu' ( married second time). Such marriages happened when husband dies during or immediately after marriage and wife is still a virgin. She can re-marry a person of her choice, but a son born from that marriage belongs to the family of 1st deceased husband. She can claim rights only from 2nd kid and so on..
 - Swayamdatta :Self Offered son' – When an orphaned boy went to some person and offered himself to be his son and the latter accepted his offer, the boy in such a case was called Swayamdatta.
Out of above 12, only 3 : Aurasa, Putrikaputra, Paunarbhava were entitled for full property of father and also his family's property (inherited from ancestors).
2 more : Kanina and Sahodha were also given rights to ancestral property, only if their biological father married their mother at a later stage.
Other 7 : Kshetraja, Dattaka, Kritima, Gudhaja, Apaviddha, Krita, Swayamdatta were entitled to claim only what was earned by their (social) father or his part of ancestral property, but not the entire family property. However, they can carry the surname, gotra etc.
Related Articles :


Installing example files in the Data Integration demo project - 7.2
Talend ESB Studio User Guide
Talend ESB
Talend Studio
Design and Development
After importing the Data Integration demo project and opening it for the first time, you are required to install the example files that are used in the example Jobs.
 1. Expand the Contexts node in the Repository tree view, and open the context group globalContext.
 2. If needed, change the value of the root variable to define the directory where the example files will be generated, C:\TalendDemoFiles\ being the default value.
 3. Change the value of the workspace variable according to the path of the local workspace of your actual Studio installation.
 4. Click Finish, and then click Yes to propagate the modifications.
 5. In the Update Detection dialog box, click OK to update the selected items.
 6. Open the beforeRunJobs Job, and press F6 to execute the Job.
All the example files are generated in directory you specified with the root variable.


Start New Discussion within our Software Development Community
I would like to seek help from all experts in VB.NET (VB Language) regarding copying file from source folder to destination folder.
I have a files named YYYYMMDDHHMMSS.txt. Now i want to build a small project to copy those file to destination folder. The project should work in following manner:
 1. Check Computer Date
 2. Look for the file in destination folder similar to computer date and then copy that file to destination folder. For example:
 Let say Computer Date is 26/12/2012. When the program starts, it should check the computer date and then look for the file named 20121226*.txt. If the file is present then it should start copying else it should give a message saying the file does not exists.
 3. It should create log file storing the copy information.
Can any one help me how to have above feature in my project.
Till now how far you wrote code for this? You want someone to write code for you?
That is not a question, that is a specification. As stated above, show what you have tried and described what is giving you problems.
For the date use the Date.Today() function.
To take the date from the format dd/mm/yyyy and put it in the form ddmmyyyy you will need to build a new string like this Date.Today.Day & Date.Today.Month & Date.Today.Year
To check if a file exists you need to use the System.IO.File.Exists(path) function
Hope this helps. Should be enough to complete your task


Unlock Alcatel Tetra
Forgot your Alcatel Tetra password or pattern lock? This article explains easy methods to unlock your Alcatel Tetra without reset or losing any data.
Let's get started!
Unlock Alcatel Tetra
There are basically multiple methods to unlock your Alcatel Tetra, and what method to opt for depends on you.
Unlock Alcatel Tetra by Answering Google Security Questions
If you have security questions set during under your Google account security, then you will be able to unlock your device by answering these questions.
Step 1: After multiple wrong attempts, you will get "Forgot Pattern" or "Forgot PIN/Password" option.
Step 2: Tap on it, and then select "Answer Questions" option.
Step 3: You will be presented with your Google security questions which you have added in your account. Answer them accordingly.
Step 4: If you answer the security questions correctly, you Alcatel Tetra will unlock.
Step 5: After successful unlock, you will be asked to create new PIN, Password or Pattern Lock for your Alcatel Tetra.
Unlock Alcatel Tetra Using your Gmail Account
To unlock Alcatel Tetra using your Gmail account, follow below-mentioned steps:
Step 2: Login with your Google (Gmail) account by entering its details such as username/password.
Step 3: Once you are logged in successfully, your smartphone will be unlocked.
Unlock Alcatel Tetra by Hard Reset (Factory Reset)
If none of the aforementioned methods works in your case, unfortunately, you are left with only option of doing factory reset/hard reset on your Alcatel Tetra. To do this, follow these steps:
Step 1: Turn Off your Alcatel Tetra.
Step 2: Now turn it ON by pressing "Power + Volume Up button" combinations for few seconds until you see Alcatel logo on the screen.
Step 3: Select "Yes" option to factory data reset message.
Please note that this will erase all the data and settings on your Alcatel Tetra.
Unlock Alcatel Tetra Using Googe Find My Device
While you may be able to unlock your Alcatel Tetra using Google Find My Device, this method will erase all the data on your phone.
Here's how you can do so:
Step 1: Open Google Find My Device and sign in with your Google account.
Step 2: After successful login, you need to select "Erase device" option followed by "Erase all data".
Step 3: As soon as you hit "Erase" button, the data deletion on your Android device will begin.
Caution: This is non-reversible process.
Alcatel Tetra Specifications
Alcatel Tetra was released in September 2018. It has 5 inches IPS LCD Asahi Dragontrail Glass protected screen.
Android 8.1 (Oreo) is the native OS featured in Alcatel Tetra. This phone runs a Quad-core processor at the core clock of 1.1 GHz and is powered by PowerVR GE8100 GPU.
Alcatel Tetra has 2 GB of memory.
This phone has a 5MP camera at the back and 2 MP at the front. Both are capable of running 720fps@30fps.
With the aforementioned methods, you can easily unlock your Alcatel Tetra when you have forgotten its password or pattern lock without losing any of your important data like photos, contacts and other important data.
But there's one catch! You will need to answer either the Google security questions or login with the Gmail account linked with your Alcatel Tetra that you want to unlock.


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The higher one's Speed, the faster one moves and the more attacks one can make in a given period of time. Logic asserts also that one's Speed is necessarily reduced by the weight one carries, and that attack speed must also be affected by the Speed Factor of one's chosen weapon. Speed is normally equal to Dexterity, or Dexterity plus five if the character's Dexterity is 20 or greater, but a few items change it independent of Dexterity. It can never be lower than 1.
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- Discrete Laplace operator
In mathematics, the discrete Laplace operator is an analog of the continuous Laplace operator, defined so that it has meaning on a graph or a discrete grid. For the case of a finite-dimensional graph (having a finite number of edges and vertices), the discrete Laplace operator is more commonly called the Laplacian matrix.
The discrete Laplace operator occurs in physics problems such as the Ising model and loop quantum gravity, as well as in the study of discrete dynamical systems. It is also used in numerical analysis as a stand-in for the continuous Laplace operator. Common applications include image processing, where it is known as the Laplace filter, and in machine learning for clustering and semi-supervised learning on neighborhood graphs.
There are various definitions of the discrete Laplacian for graphs, differing by sign and scale factor (sometimes one averages over the neighboring vertices, other times one just sums; this makes no difference for a regular graph). The traditional definition of the graph Laplacian, given below, corresponds to the negative continuous Laplacian on a domain with a free boundary.
where d(w,v) is the graph distance between vertices w and v. Thus, this sum is over the nearest neighbors of the vertex v. For a graph with a finite number of edges and vertices, this definition is identical to that of the Laplacian matrix. That is, φ can be written as a column vector; and so Δϕ is the product of the column vector and the Laplacian matrix, while (Δϕ)(v) is just the v'th entry of the product vector.
If the graph has weighted edges, that is, a weighting function is given, then the definition can be generalized to
where γwv is the weight value on the edge.
Closely related to the discrete Laplacian is the averaging operator:
Approximations of the continuous Laplacian
Approximations of the Laplacian, obtained by the finite difference method or by the finite element method can also be called Discrete Laplacians. For example, the Laplacian in two dimensions can be approximated using the five-point stencil finite difference method, resulting in
where the grid size is h in both dimensions, so that the five point stencil of a point (x, y) in the grid is
If the grid size h=1, the result is the negative discrete Laplacian on the graph, which is the square lattice grid. There are no constraints here on the values of the function f(x,y) on the boundary of the lattice grid, thus this is the case of the homogeneous Neumann boundary condition, i.e., free boundary. Other types of boundary conditions, e.g., the homogeneous Dirichlet boundary condition, where f(x,y)=0 on the boundary of the grid, are rarely used for graph Laplacians, but are common in other applications.
Multidimensional discrete Laplacians on rectangular cuboid regular grids have very special properties, e.g., they are Kronecker sums of one-dimensional discrete Laplacians, see Kronecker sum of discrete Laplacians, in which case all its eigenvalues and eigenvectors can be explicitly calculated.
Discrete Laplace operator is often used in image processing e.g. in edge detection and motion estimation applications. The discrete Laplacian is defined as the sum of the second derivatives Laplace operator#Coordinate expressions and calculated as sum of differences over the nearest neighbours of the central pixel.
Implementation in Image Processing
For one, two and three dimensional signals, the discrete laplacian can be given as convolution with the following kernels:
or, including the diagonals:
- 3D-Filter: is given by: first plane = ; second plane = ; third plane =
These kernels are deduced by using discrete differential quotients.
The spectrum of the discrete Laplacian is of key interest; since it is a self-adjoint operator, it has a real spectrum. For the convention Δ = I − M, the spectrum lies within [0,2] (as the averaging operator has spectral values in [ − 1,1]) and contains 0 (for constant functions). The smallest non-zero eigenvalue is denoted λ1 and is called the spectral gap. There is also the notion of the spectral radius, commonly taken as the largest eigenvalue.
The eigenvectors don't depend on the convention above (for regular graphs), and are the same as for the averaging operator (as they differ by adding a multiple of the identity), though the eigenvalues differ according to the convention.
If the graph is an infinite square lattice grid, then this definition of the Laplacian can be shown to correspond to the continuous Laplacian in the limit of an infinitely fine grid. Thus, for example, on a one-dimensional grid we have
This definition of the Laplacian is commonly used in numerical analysis and in image processing. In image processing, it is considered to be a type of digital filter, more specifically an edge filter, called the Laplace filter.
Discrete Schrödinger operator
Let be a potential function defined on the graph. Note that P can be considered to be a multiplicative operator acting diagonally on ϕ
Then H = Δ + P is the discrete Schrödinger operator, an analog of the continuous Schrödinger operator.
If the number of edges meeting at a vertex is uniformly bounded, and the potential is bounded, then H is bounded and self-adjoint.
The spectral properties of this Hamiltonian can be studied with Stone's theorem; this is a consequence of the duality between posets and Boolean algebras.
On regular lattices, the operator typically has both traveling-wave as well as Anderson localization solutions, depending on whether the potential is periodic or random.
Discrete Green's function
where δw is understood to be the Kronecker delta function on the graph: δw(v) = δwv; that is, it equals 1 if v=w and 0 otherwise.
For fixed and λ a complex number, the Green's function considered to be a function of v is the unique solution to
Certain equations involving the discrete Laplacian only have solutions on the simply-laced Dynkin diagrams (all edges multiplicity 1), and are an example of the ADE classification. Specifically, the only positive solutions to the homogeneous equation:
- Δϕ = ϕ,
- "Twice any label is the sum of the labels on adjacent vertices,"
are on the extended (affine) ADE Dynkin diagrams, of which there are 2 infinite families (A and D) and 3 exceptions (E). The resulting numbering is unique up to scale, and if the smallest value is set at 1, the other numbers are integers, ranging up to 6.
The ordinary ADE graphs are the only graphs that admit a positive labeling with the following property:
- Twice any label minus two is the sum of the labels on adjacent vertices.
In terms of the Laplacian, the positive solutions to the inhomogeneous equation:
- Δϕ = ϕ − 2.
The resulting numbering is unique (scale is specified by the "2"), and consists of integers; for E8 they range from 58 to 270, and have been observed as early as (Bourbaki 1968).
- Bourbaki, Nicolas (1968), "Chapters 4–6", Groupes et algebres de Lie, Paris: Hermann
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Eva Zmazek: Strong edge geodetic problem on grids
Date of publication: 28. 11. 2020
Discrete mathematics seminar
Torek, 1. 12. 2020, ob 10:15, na daljavo
Povzetek. Let G=(V(G),E(G)) be a simple graph. A set S ⊆ V(G) is a strong edge geodetic set if there exists an assignment of exactly one shortest path between each pair of vertices from S, such that these shortest paths cover all the edges E(G). The cardinality of a smallest strong edge geodetic set is the strong edge geodetic number of G. In this talk, the strong edge geodetic problem is studied on the Cartesian product of two paths.
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NASA has announced that Johnson Space Center and Texas A&M University will sign an agreement on Monday to begin the move of the primary space shuttle launch and landing trainer, the Shuttle Motion Simulator, to College Station:
The NASA-Texas A&M partnership will allow the university to house and showcase unique space shuttle training artifacts. The Shuttle Motion Simulator provided a full-motion simulation of shuttle launches and landings for every crew that flew on the shuttle. It began operations at JSC in 1977 and was used in training for all 135 space shuttle missions.
The facility that housed the shuttle simulators at JSC continues to be used for International Space Station training. This partnership will help ensure that this unique historical artifact and the space shuttle training technology it represents is preserved and used to inspire future engineers. JSC welcomes opportunities for such partnerships that find areas of common interest of benefit to both parties.


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Efficient Checking of Individual Rewards Properties in Markov Population Models
|Title||Efficient Checking of Individual Rewards Properties in Markov Population Models|
|Publication Type||Conference Paper|
|Year of Publication||2015|
|Authors||Bortolussi L, Hillston J|
|Conference Name||Quantitative Aspects of Programming Languages and Systems (QAPL)|
|Keywords||Markov population models, Rewards, Stochastic Approximation, Stochastic model checking|
In recent years fluid approaches to the analysis of Markov populations models have been demonstrated to have great pragmatic value. Initially developed to estimate the behaviour of the system in terms of the expected values of population counts, the fluid approach has subsequently been extended to more sophisticated interrogations of models through its embedding within model checking procedures. In this paper we extend recent work on checking CSL properties of individual agents within a Markovian population model, to consider the checking of properties which incorporate rewards.


GRAY full form
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Meaning : Bitmap graphics (raw gray bytes)
Category : computers
Sub Category :graphics
Type : acronym
What does GRAY mean or stand for?
Bachelor of Music is a three year bachelors program offered by a university that teaches the advanced level of music theory,vocals or practicals.After doing this course there are many careers that can be chosen either as a performer,entertainment or even a music studio/company/record label.
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Can Horses Swim? Are They Good Swimmers?
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It depends. Like humans, horses can sink if they don't know how to swim. While most horses can stay afloat pretty well, this shouldn't be mistaken to mean that horses naturally are great swimmers even without prior training.
If you love horses and swimming, you may have thought of taking your horse for a swim or even for the sole purpose of fitness and rehabilitation. But this is never a good idea unless you have an experienced horse that knows how to swim.
You need to consider the fact that horses can sink. Horses also have a hard time turning in water. In fact, your horse can keep moving forward despite your best efforts to try to get your horse to move and make a turn.
This can also increase drowning risks, which will ultimately scare your horse from wanting to learn how to swim. If your horse hasn't been through a swimming or floating lesson or they are too nervous about getting inside water, it's not advisable to make them swim.
Wild horses couldn't live their entire lives in the wild without getting into the water. These types of horses naturally engage with water regularly. However, horses that aren't from the wild don't have the same instincts or capabilities when it comes to swimming.
Horses may, therefore, be among those animals that are genetically predisposed to swim. But it's not advisable to introduce swimming suddenly without unlocking your horse's genetic potential.
Your horse's first experience with water is critical, and you need to slowly introduce them to the idea of being in the water. Allow them to stand and walk around at their own pace and never ride them into deep water until your horse is fully trained and comfortable with that concept.
Do Horses Like To Swim? Are Horses Good Swimmers?
Like people, some horses seem to love swimming while others don't. Many different types of horses can become good swimmers once they become accustomed to the water.
But keep in mind, horses cannot hold their breath underwater, and you should never take your horse where there are big waves. This can be very dangerous and cause your horse a lot of unnecessary trauma.
It is also not recommended to ride your horse in the water if it is windy out. The water that gets blown in their face or causes their head to be submerged in the water can cause many issues, including water in their ears.
Horse Swimming
Teaching A Horse To Swim
If you want to get your horse into the water during the hot summer, you'll need to teach him/her how to swim better. As mentioned above, horses may be genetically predisposed to swimming; however, they need a progressive introduction.
You should start with shallow water to allow your horse to get comfortable with the idea of swimming, which can be an excellent exercise for horses.
Never guide your horse into deep water or attempt to force a swimming lesson. You can begin by visiting a shallow pond and try riding him/her in water that is at most 2 feet deep. Once he/she is used to this depth, you can venture deeper.
As you introduce your horse to deeper water, ensure there are no big stones underneath. You can do test runs on your own to make sure your horse doesn't trip on rocks.
However, before allowing your horse to venture into the deeper water, let them stand momentarily in the water until they are comfortable. You should watch out for signs of nervousness, like abrupt movements coupled with awkward stops.
When your horse is comfortable, you can venture deeper. Make sure you are in front of him/her to avoid being kicked as they may try to push forward inside the water. Also, remember to teach your horse how to turn while in water.
When your horse becomes familiar with the water around them, their natural swimming instinct will "kick in." Since they are heavy, you'll only see their head when they are swimming, similar to when larger dogs swim.
Their entire body will be submerged, and you'll only be able to see their head. If you look underneath, he/she will be busy paddling with their legs, just like how dogs swim.
In fact, horses look like they are running if you watch them swimming from underwater. But this happens over time when a horse gets comfortable in the water and learns how to swim.
Tip: It's advisable to guide your horse using a rope initially before he/she knows how to swim.
Horse Swimming Whilst Being Ridden
Is It Safe To Ride A Swimming Horse?
It can be dangerous and hard to ride a horse that is swimming. Since horses make different movements from those made when riding, your chances of slipping and falling are higher. What's more, horses tend to be more focused on swimming than the rider, which poses serious risks.
It's difficult to predict a horse's movement while they are swimming. Your horse is likely to make unexpected and/or rapid movements that pose serious risks.
There's also the risk of being kicked if you fall off your horse's back while he is swimming. While a horse kick underwater may not be as lethal as one on land, it can injure you seriously, making it impossible for you to swim.
You can also float away if you attempt to ride a swimming horse. If you don't know how to swim, don't try to ride a horse in any type of water. If your horse's head is the only part of its body above the water, your chances of drowning are higher if you don't know how to swim.
What To Do When Riding A Swimming Horse
If you must ride a swimming horse, there are some precautions you can take.
First and foremost, don't push your horse downwards into the water. Horses can't breathe underwater and will most probably get nervous making erratic movements and push you off his/her back.
Instead, you should swim as well to avoid exerting undue pressure on your horse. This is better than clamming on his/her neck and making them nervous.
You should also swim for short periods at a time. As mentioned above, horses are not meant to swim. They tend to get tired faster underwater, much more so than humans.
How Long Can Horses Swim?
To avoid tiring your horse and running the risk of allowing them to sink, don't subject your horse to swimming for more than 10 minutes at a time. It is also best to exit the water before you and your horse gets tired of swimming.
If you happen to get off your horse's back and start swimming beside them, be absolutely certain to stay away from their kicking legs. This can be extremely dangerous because a horse that kicks you underwater can be lethal.
Note: Avoid swimming around your horse because this tends to make them nervous and could cause them to make unnecessary movements that could tire them even faster.
Do Horses Enjoy Being In Water?
This is a tricky question because, just like humans, some horses might love splashing around in the water while others might be terrified of it.
You obviously can't ask your horse how they feel about being in the water, but there are sure signs that will allow you to understand how your horse is adapting to the experience.
You'll be able to see in their behavior whether they are enjoying the water or if they are hesitant to go near or in it.
When you guide your horse to water, make sure you don't immediately head for the deeper water. Your horse's head should never be submerged, and don't ever push your horse to go somewhere they don't want to go.
Give your buddy a chance to adapt by walking in shallow water and allowing them to explore the idea of being wet. This will give you a good indication as to whether or not your horse enjoys being in the water.
Unlike horses that have lived in the wild, your horse might not enjoy deep water because they are not a good swimmer.
Everybody thinks that horses can naturally swim and that you can immediately ride a horse into the ocean. However, that is just not the case, and every horse is different when it comes to whether or not they enjoy swimming.
Some horses, such as wild horses, will playfully paw at the water before rolling over in it. If your horse starts pawing at the water, you should make them stop immediately.
Riding a horse in water that begins to paw at it can be extremely dangerous for the rider. If that horse flips with you on it, you can get severely injured and even drown.
So always make sure you stop your horse from pawing at water regardless of how cute it looks!
Do Horses Need To Swim?
No. While horses need exercise, they can get all the training they need running or doing other ground exercises. However, if you want to expose your horse to various activities, swimming can be a good alternative when properly introduced.
Since horses rely heavily on their legs when swimming, this can be a great leg exercise. Swimming can also strengthen your horse's core muscles and improve his/her overall fitness.
In fact, swimming is common among horses with injuries because this type of exercise can heal serious injuries and boost muscle growth.
Like humans, horses must learn how to swim first before taking them out into deep waters for the first time. You should also ensure you know how to swim if you plan on riding him/her while they are in the water.
Keep in mind that there are many risks associated with horses and water. If your horse begins to panic, it may forget about you and head in a different direction. So always be alert!
The importance of teaching your horse how to swim can be the difference between having a happy horse who is comfortable strolling along the coast or having a companion that is terrified of water.
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The definition of affiant is a legal term used to identify someone who makes a sworn statement called an affidavit.(noun)
An example of an affiant is a person who gives testimony to the police and then swears to it and usually signs it.
See affiant in Webster's New World College Dictionary
Origin: < prp. of OFr afier: see affiance
See affiant in American Heritage Dictionary 4
Origin: From affy, to make affidavit
Origin:, from Middle English affien, to trust
Origin:, from Old French affier, to promise; see affiance.
Learn more about affiant


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Love and Money argues that we can't understand contemporary queer cultures without looking through the lens of social class. Resisting old divisions between culture and economy, identity and privilege, left and queer, recognition and redistribution, Love and Money offers supple approaches to capturing class experience and class form in and around queerness.
Contrary to familiar dismissals, not every queer television or movie character is like Will Truman on Will and Grace—rich, white, healthy, professional, detached from politics, community, and sex. Through ethnographic encounters with readers and cultural producers and such texts as Boys Don't Cry, Brokeback Mountain, By Hook or By Crook, and wedding announcements in the New York Times, Love and Money sees both queerness and class across a range of idioms and practices in everyday life. How, it asks, do readers of Dorothy Allison's novels use her work to find a queer class voice? How do gender and race broker queer class fantasy? How do independent filmmakers cross back and forth between industry and queer sectors, changing both places as they go and challenging queer ideas about bad commerce and bad taste?
With an eye to the nuances and harms of class difference in queerness and a wish to use culture to forge queer and class affinities, Love and Money returns class and its politics to the study of queer life.
1. The Class Character of Boys Don't Cry
2. Queer Visibility and Social Class
3. Every Queer Thing We Know
4. Recognition: Queers, Class, and Dorothy Allison
5. Queer Relay
6. Plausible Optimism
Conclusion: A Cultural Politics of Love and Solidarity
"In Love and Money Henderson attempts to look at contemporary queer cultures through the lens of social class. Henderson is critical of the distorted ways in which American media represents queer cultures and identity and seeks to study the difference that social class makes on queer subjectivity and representation."-Rohit K. Dasgupta,Transnational Cinemas
"Henderson's affective approach to the case history yields rich accounts of the resourceful survival strategies through which queer films and novels get made despite limited means. Exemplifying the values of love and solidarity that she finds in her cases, her critical practice offers innovative approaches to thinking queer and class together and fresh answers to longstanding questions about what it means to make art in a market economy."-Ann Cvetkovich,University of Texas, Austin
Throughout, Henderson grounds queer cultural criticism in the liminal movements and moments of everyday life, treating this criticism as art and understanding criticism as inside of, and a contributor to, cultural production. She also formulates a new kind of classed-queerness, one characterized by softness and slowness, of people trying hard to live and survive as best as they can. Summing Up: Highly recommended."-CHOICE
"It may be that the book is, at its core, an unusually intimate excavation of media-cultural experience. This much is evident in the carefully crafted prose and the frequent self-reflexive passages in which the author's various roles—as researcher, critic, fan, and consumer, but also as queer and classed subject—are laid more bare than is customary. Henderson reveals herself as voracious observer, situation her half-dozen primary objects in a jam-packed mediascape, where no one-off episode or festival favorite is too far off the mainstream radar. This is commendable, and invigorating, while the field tends to compartmentalize mainstream and experimental film and media as nonconversant tracks. Love and Money is also, irrefutably, hopeful. This may also be a suit that many of us are unaccustomed to wearing, especially as regards class politics at the current historical juncture. But in these pages, it might pay to try. It is, at least, as Henderson herself concludes, 'a place to start.'"-Cynthia Crisis,International Journal of Communication
"Drawn along disciplinary lines of queer theory, feminist theory, and critical cultural studies, Love and Money contributes vital scholarly debates over the emancipatory potential of cultural recognition versus economic redistribution. As a scholar of communication, Henderson adds valuable complexity to this discussion, highlighting the ways in which queer visibility depends on a class - race reduction mediated through tropes of bodily excess, disenfranchisement, and trauma. Through timely and profound analysis she weaves together disparate experiences and expressions from a variety of queer cultural texts to present a language of queer-class engagement that articulates the categories of race and gender while working to recenter class as a vital frame through which to understand the production of sexual difference." -Meg Rooney,QED: A Journal in GLBTQ Worldmaking
"Love and Money is at once fiercely intellectual and full of heart, formidable and invitingly funny. In this series of essays, Lisa Henderson offers some of the sharpest, most imaginative analysis of queerness and social class out there, shaking up entrenched ideas about how the two are and should be related."-Joshua Gamson,University of San Francisco


Sun & clouds behaviour chart as used in schools
Sun and Clouds Behaviour chart is an ideal chart for home so your child can instantly see how they are behaving it also encourages them to stay around the sun and not go in the black cloud.
Supplied with 1 x A4 fully laminated board, 5 x sun strips
To use, just write your childs name on the sun strips using a ball point pen or sharpie, then with blue tac (not supplied) just place the sun strip around the sun, if their behaviour deteriorates move the sun strip in to the grey could and if it continues to get bad into the black also if their behaviour improves move them back into the sun.
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Introduction The Dr Foster Global Comparators Network (GC) aims to improve quality in healthcare by promoting inter-hospital collaboration through sharing of outcome data and benchmarking standards.
This study aims to utilise the GC database to establish whether geographical differences in outcomes exist following high-risk emergency general surgery (EGS) admissions, whilst determining if structural differences between healthcare systems can be linked to high-quality care.
Method Discharge data for a cohort of EGS patients were collated using a pre-determined protocol. Hierarchical logistic regression analysis was performed to examine geographical and structural differences between GC hospitals.
Results 69,490 patients, admitted to 23 centres across Australia, England and the USA with high-risk EGS diagnoses from 2007–2012 were identified. Outcomes including: seven/thirty-day mortality, readmission and length of stay were all superior in the USA.
19,082 patients (27%) underwent emergency abdominal surgery. No geographical differences in mortality were seen at seven-days in this subgroup. Thirty-day mortality (OR = 1.47) readmission (OR = 1.42) and length of stay (OR = 1.98) were all worse in the UK.
Across this cohort, patient factors, (age, pathology and co-morbidity) were significantly associated with worse outcome as were structural factors including: low ITU bed ratios, high unit volume and inter-hospital transfers. Having dedicated EGS teams cleared of elective commitments with formalised handover of patients was associated with shorter length of stay.
Conclusion Post-operative outcomes were similar at seven but not at thirty-days. This may be attributable to better infrastructure and resource allocation towards EGS in the US. The costs associated with this healthcare gain were not measured.
Disclosure of interest None Declared.


- Research Paper on:
 Late Bill Payment Research Paper
 Number of Pages: 5
 Summary of the research paper:
 This 5 page paper uses data supplied by the student to examine if there is a correlation between the lateness of a bill and the amount of the bill. The paper presents a background to the research, hypothesises, data analysis and a conclusion. The bibliography cites 6 sources.
 Name of Research Paper File: TS14_TElatebill.rtf
 Buy This Research Paper »
 Unformatted Sample Text from the Research Paper:
 bill payments 5 Figure 3 Pattern of late residential bill payments 6 1. Background to the Problem The timing of payments on loans or amounts due are key to the cash flow of a company to whom the money is loaned. It is known that as loans become later it the payment may become increasingly difficult to collect and the potential for a default increases (Greenberg, 1997). For companies wishing to avoid taking on collections of more risky debts and for those who already have them, the ability to understand patterns of payments and the ability to predict the way in which these patterns will move will enable better decisions making to take place and increased the effectiveness of any risk assessments that take place (Howells and Bain, 2004). 2. Aims of Research The aim of the research is to look at the different patterns seen with overdue bill payments. The paper will seek to answer the following questions in order to increase the understanding with which late bill payment collections can be managed more efficiently and bill collections company can use to determine which risks they can afford to take on (Blazenko and Vandezande, 2003). The specific questions will include; * Is there any correlation between the amount and lateness of a bill? * Is there any difference between the residential ands the commercial bill payment patterns? * If there is a correlation for either the residential or the commercial costumers, to what extent does the correlation hold. The hypothesis is that First Hypothesis H1 There will be different patterns in payments seen with commercial bills being more likely to be paid later than the residential bills. H0 There is no difference between the bill paying patterns of
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International journal of environmental research and public health article relationship between burnout and body mass index in senior and middle managers from the mexican. How can i differentiate between a junior employee and a senior i am looking to see if there are definable attributes between a junior employee and senior.
Policy on consensual sexual relationships between senior and the university has taken a middle into an official counseling relationship 3 all other senior. Iii abstract deborah albright santiago a study of the relationship between middle school and high school teachers instructional and behavior management practices and demographic variables. Achieving coherence in district improvement focuses on a problem of practice faced by educational leaders across the nation: how to effectively manage the relationship between the central office and schools.
What's the difference between entry level/jr/sr developers [closed] what's the difference between junior, middle, and senior developers related 32. What is the grammatical difference between old english, middle english and early modern english can a modern english speaker understand spoken middle english. Leadership and innovation senior executives say that the top three ways they spend time making decisions about innovation involve largely middle managers.
Relations between senior officers and junior officers the twin foundations of military courtesy among officers are precedence and deference to seniors. Middle management is the intermediate management of a hierarchical organization that is a middle manager is a link between the senior management and the. Balancing teaching and management thinks that the key to a successful relationship between middle and senior management is cooperation.
Overcoming disconnect between middle & upper senior managers report to the executive officer of the what is the current relationship between management. What is a liaison between the upper management and the 3 the relationship between hr & a there might be several middle managers between an employee's. America's seniors have historically been late adopters to the world of technology compared to their younger compatriots, but their movement into digital life. Running head: self-efficacy and work experience 1 relationship between self-efficacy and work experience in baccalaureate junior and senior.
What are the differences between the middle and middle class is the vast space between that amount and a what is the relationship between poverty and. Recommended citation hopkins, treg, the relationship between well-being and technology among senior citizens in indiana (2018) doctoral dissertations and projects. The uneasy relationship between church and state dominated the middle ages and has continued into modern times.
The west and the middle east the china–north korea relationship by eleanor albert read foreign affairs in your inbox more from foreign. The present study sought to investigate the relationship between cultural capital of senior high school english teachers and their self-efficacy in iran's english language classrooms using a mixed methods approach. Read consumer reports' investigation of risky drivers and see what the similarities are between old than that for middle that the senior can. In a six-part series, the middle east and the west, a troubled history, npr's mike shuster examines the nearly 1,000-year history of western involvement in the middle east.Download


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Local Atomic Structure of a High-Entropy Alloy: An X-Ray and Neutron Scattering Study
- First Online:
- Cite this article as:
- Guo, W., Dmowski, W., Noh, JY. et al. Metall and Mat Trans A (2013) 44: 1994. doi:10.1007/s11661-_PHONE_-0
- 1.4k Downloads
By using high-energy synchrotron X-ray and neutron scattering, the local structure of a ternary high-entropy alloy Zr1/3Nb1/3Hf1/3 is characterized by means of pair distribution function (PDF) analysis. Results show that this alloy is a body center cubic (b.c.c.) phase in both bulk sample and in a thin film ~1.5 µm thick. The PDFs obtained from X-ray diffraction and neutron diffraction agree well with each other. The measured PDFs differ from the calculated PDF, particularly in the peak shape of the first two peaks, indicating local lattice distortion due to different atomic sizes in the solid solution.


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1519.1 What does good cause mean?
"Good cause" means that you did not file the lump-sum death payment application within the time limit because of:
Circumstances beyond your control, such as extended illness, communication difficulties, etc.;
Incorrect or incomplete information given to you by us;
Your efforts to get the evidence to support the claim, not realizing you could file the application within the time limit and submit the supporting evidence later; or
Unusual or unavoidable circumstances that show that you could not reasonably be expected to have been aware of the need to file the application within a specified period.
1519.2 When is good cause NOT established?
Good cause is not established if:
You were informed that an application for the lump-sum death payment had to be filed within the initial two-year period; and
You did not file the application because of neglect, or because you did not then want to claim the lump-sum death payment.


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- See also: Easter Eggs (Skyrim)
The card is considerably cheap, and is suggested to be picked during the start of a game. It is not suggested to use the card on a creature with 1 health unless it is an emergency, due to the Shackle attribute of the card going to waste.
Arrow in the Knee should be used on cards with high attack powers, as it will prevent them from attacking the next turn, saving you health or your creatures' defense. If possible with the deck and cards available in your hand, the card should be used on enemies with high defenses, and combined with a wound-related card (i.e. Finish Off) to easily destroy them.
- The phrase "Arrow to the Knee" originated from Skyrim as a line of dialogue from Hold Guards, who would say "I used to be an adventurer like you. Then I took an arrow in the knee" when passing by the player. Eventually, it became a widespread meme, becoming an iconic legacy of Skyrim on modern culture. It can therefore be considered an easter egg.
- During the closed beta, the card was previously named Arrow to the Knee. However, this changed at some point before the beta opened.


Pre-Shot Golf Routine
Home / Golf Tips / Pre-Shot Golf Routine
Pre-Shot Golf Routine
Pre-Shot Golf Routine: How Important Is It?
If you've read any golf psychology books you'll notice how each stresses the importance of a consistence pre-shot golf routine. Bob Rotella, a famous writer about golf psychology talks about the pre-shot golf routine in much detail. So if you're unfamiliar with a what a pre-shot routine in golf is, it is basically a sequence of steps or actions that you take before every single shot during your round. Every golfer has their own particular pre-shot routine, this can include alignment, the number of practice swings, waggles over the ball, as well as the timing of each movement or event. This all happens before actually hit your golf shot.
Why is a pre-shot golf routine important? A pre-shot routine basically makes you only focus on each step of your pre-shot routine. It helps to eliminate any bad or negative thoughts, nervousness, etc. before hitting your shot. A lot of golfers will step up to the tee and see white out of bounds stakes right or maybe there is a lake you need to carry and then you only start to focus on avoiding those obstacles. So if you see out of bounds stakes right, you may make a swing that overcompensates and you end up in the left woods. Or if you're thinking about hitting it over a lake 200 yards away when you're average carry is 220 yards away you may swing to hard to make sure you hit it over the lake when you really just needed to get up to the ball and take your normal swing. The pre-shot golf routine helps prevent these negative thoughts. It forces you to focus and only focus on the certain steps of your pre-shot routine and if you're focusing on those simple, yet relevant tasks you're not thinking about the lake you have to carry or preventing yourself from slicing the ball out of bounds to the right.
If you watch any golf professionals during a PGA Tournament on television you'll notice they all have a pre-shot routine. Each one has different steps and mannerisms before they step up and begin their actual backswing of the shot at hand.
Pre-Shot Golf Routine
So what can a pre-shot routine actually consist of? There can be very few steps you take during your pre-shot routine or there can be more. It all depends on the type of golfer. Once you have your club selection and you're confident you have the correct club you can start your pre-shot routine. This can start with alignment. Some golfers prefer 1-3 practice swings and some take their practice swings behind the ball, while others may take their practice swings right next to the ball lining up to the target. It can also include any current swing thoughts you have. Maybe you've been working on a move in your backswing that you repeat three times for muscle memory right before you step up to the ball. Once you step up and actually rest your club behind the ball, you may have a certain number of waggles, and you may also have a certain number of times you look at the target.
A good example of a pre-shot golf routine to start with if you've never had one before would be as follows. Choose your club selection and be confident with it before you start your pre-shot routine. If you go through your pre-shot routine and are about to swing but feel a wind gust, step back, re-think your golf club selection and start your pre-shot routine all over. This also includes any distractions during your pre-shot routine, just step back and start it over. So now that you have your club, take 1 or 2 practice swings. Then stand behind the ball and pick your alignment, a lot of golfers will pick a blade of grass 1 foot in front of the ball. That way when you step up to the ball you're only aligning your clubface to a blade of grass 1 foot in front of the ball. This is much easier than looking back and forth and at a target and trying to line up correctly. Then you take one waggle, one last look, at the target, visualize your perfect shot and take your swing.
This is just an example but it's a starting point to developing your own pre-shot golf routine. You can alter it in any way you want. You can also watch your favorite PGA Tour player on TV for tips as well. Also a lot of golfers will develop their pre-shot routine based how quickly they play. If you typically are a fast player on the course your pre-shot routine might be very simple. Sometimes this also helps with you giving you less time for negative thoughts. Or if you are a slower player who is very meticulous and likes to take your time, you may take a few more relaxed practice swings and take your time with each detail of your pre-shot routine. If you're that type of golfer a fast-paced, quick pre-shot routine probably doesn't make sense. You do not want to feel rushed during your pre-shot routine, you should feel relaxed and focused only on the next step of your routine.
It is also worthy to note that some players have different pre-shot routines for full swings, chipping, sand shots, or putting on the green. However, it's still important to have a solid consistent pre-shot routine for every type of shot. For chipping, one part of your pre-shot routine you may walk up to the green and determine exactly where you want the golf ball to land. You may take extra practice swings to get the feel of the shot so you hit it with the correct force and achieve the correct distance. For putting you may read a putt from behind the ball, then behind the hole. You may stand over the ball once to get a feel for the putt, then step back from the ball and focus on alignment. Regardless of all of this make sure all of your pre-shot routines are consistent and literally become second nature.
You may also find that over time you add steps or remove steps from your pre-shot routine. This is perfectly fine, you may be working on take your club back low and slow, so you add that move in and repeat it 3 times for added confidence and muscle memory. Developing a solid pre-shot routine may take some time before you are 100% comfortable and confident you have it perfected. You want it to mimic your style as a golfer, but once you have it down and consistently apply it to each shot you'll continually see improvement. You also should practice it and not only make sure you apply it to every single shot on the course but you should also go through your pre-shot routine while on the driving range. This will force you to not only solidify your pre-shot routine but also makes sure you are practicing properly on the range and thinking about every shot. It's important to practice with a purpose and rushing through a bucket of balls just to say you practiced today isn't helping. So start to begin forming and practicing your pre-shot routine today and you'll begin to notice a lot of improvement in your scores as well as your course management and the mental aspects of golf.
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This video teaches you
How to Plane Wood
Before you use your hand plane, make sure you sharpen the blade. To do so, place a piece of 220-grit sandpaper on a flat surface and hold the plane at a 25 degree angle so the bevel is flat against the sandpaper. Then, rub the blade in a circle until metal shavings form along its back. Place the blade back in your hand plane and adjust the angle of the blade with the depth adjustment wheel. The angle you choose will determine how thick the shavings you remove will be. If you're unsure what angle to choose, opt for a shallow angle, since you can always increase the depth of the cut if necessary. When you're ready, place your plane against the edge of your wood. Hold the knob with your non-dominant hand and press down so the plane is flush with the wood. Then, hold the back handle with your dominant hand and press forward so you're working across the surface smoothly and methodically. When you're done, lay a straight edge along your wood to check and confirm it's perfectly flat.


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Overview - TOUCH2 LEARN TEXTURE CARDS
Touch2 Learn Texture Cards are an excellent learning tool that contains five sets of cards (45 cards), each with its own texture and theme. Each set has cards for the numerals 1-9 and is designed to help you teach number recognition, numeral/quantity association, counting and vocabulary. The back of the cards show the numeral with TouchPoints and Touching/Counting Patterns. Perfect for tactile/kinesthetic learning.
- Forest Animals
- Sea Life
For Pre-K, K, RTI and Special Education.


Main Content
Bootstrapping a Default Probability Curve
This example shows how to bootstrap default probabilities from CDS market quotes. To bootstrap default probabilities from bond market data, see bondDefaultBootstrap. In a typical workflow, pricing a new CDS contract involves first estimating a default probability term structure using cdsbootstrap. This requires market quotes of existing CDS contracts, or quotes of CDS indices (e.g., iTraxx). The estimated default probability curve is then used as input to cdsspread or cdsprice. If the default probability information is already known, cdsbootstrap can be bypassed and cdsspread or cdsprice can be called directly.
The market information in this example is provided in the form of running spreads of CDS contracts maturing on the CDS standard payment dates closest to 1, 2, 3, 5, and 7 years from the valuation date.
Settle = '17-Jul-2009'; % valuation date for the CDS
MarketDates = datenum({'20-Sep-10','20-Sep-11','20-Sep-12','20-Sep-14',...
MarketSpreads = [140 175 210 265 310]';
MarketData = [MarketDates MarketSpreads];
ZeroDates = datenum({'17-Jan-10','17-Jul-10','17-Jul-11','17-Jul-12',...
ZeroRates = [1.35 1.43 1.9 2.47 2.936 3.311]'/100;
ZeroData = [ZeroDates ZeroRates];
[ProbData,HazData] = cdsbootstrap(ZeroData,MarketData,Settle);
The bootstrapped default probability curve is plotted against time, in years, from the valuation date.
ProbTimes = yearfrac(Settle,ProbData(:,1));
plot([0; ProbTimes],[0; ProbData(:,2)])
grid on
axis([0 ProbTimes(end,1) 0 ProbData(end,2)])
xlabel('Time (years)')
ylabel('Cumulative Default Probability')
title('Bootstrapped Default Probability Curve')
The associated hazard rates are returned as an optional output. The convention is that the first hazard rate applies from the settlement date to the first market date, the second hazard rate from the first to the second market date, and so on, and the last hazard rate applies from the second-to-last market date onwards. The following plot displays the bootstrapped hazard rates, plotted against time, in years, from the valuation date:
HazTimes = yearfrac(Settle,HazData(:,1));
stairs([0; HazTimes(1:end-1,1); HazTimes(end,1)+1],...
grid on
axis([0 HazTimes(end,1)+1 0.9*HazData(1,2) 1.1*HazData(end,2)])
xlabel('Time (years)')
ylabel('Hazard Rate')
title('Bootstrapped Hazard Rates')
See Also
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Related Topics


Bentsen surname meaning, origin - danish surname Bentsen
The meaning of the surname Bentsen is: Means "son of BENT".
The surname Bentsen is present in the lists: Surnames, Danish surnames, Surnames start with letter B.
Number for the surname Bentsen
The number of the surname seven (7) characterizes talented people who are able to achieve great success both in the scientific field and in the Humanities. The ability to think, analyze, and plan their actions, and the ability to attract others, helps people with the surname Bentsen become the head of various groups of people and organizations.
Stones of the number 7 for the surname Bentsen: malachite, jade, carnelian (carnelian), pearl, jet, obsidian, hematite (Bloodstone), onyx, opal, amethyst, emerald, Selenite, flint, rhodonite, fluorite.
Planet number 7: Neptune.
Zodiac Signs number 7: Pisces, Virgo.
More: number of the surname Bentsen
Meaning of letters in the surname Bentsen
Compatible with the surname Bentsen danish surnames
Berntsen Danish surnames, Bjarnesen Danish surnames, Dahl Danish surnames, Hansen Danish surnames, Hermansen Danish surnames, Johannessen Danish surnames, Knudsen Danish surnames, Lang Danish surnames, Larson Danish surnames, Olesen Danish surnames, Ostergard Danish surnames, Paulsen Danish surnames, Riber Danish surnames, Sander Danish surnames, Vinter Danish surnames, Winther Danish surnames...
Also check the compatibility of other surnames with the surname Bentsen.
Famous people with the surname Bentsen
 1. Lloyd Bentsen
 Lloyd Millard Bentsen Jr. (February 11, 1921 – May 23, 2006) was an American politician who was a four-term United States Senator (1971–1993) from Texas...
 2. SS Edmund Fitzgerald
 SS Edmund Fitzgerald was an American Great Lakes freighter that sank in Lake Superior during a storm on November 10, 1975, with the loss of the entire...
 3. Bentsen-Rio Grande Valley State Park
 Bentsen-Rio Grande Valley State Park is located at 2800 S. Bentsen Palm Drive (FM 2062) south of the city of Mission in Hidalgo County in the U.S. state...
 4. Ken Bentsen Jr.
 Kenneth Bentsen Jr. (born June 3, 1959, in Houston, Texas) is a former congressman from Texas, serving four terms from 1995 to 2003. He is the nephew...
 5. Allan Bentsen
 Allan Bentsen (born August 21, 1968) is a Danish table tennis player. He won the European championship for national teams with Michael Maze and Finn Tugwell...
 6. William Bentsen
 William "Bill" Bentsen (February 18, 1930 – December 25, 2020) was an American sailor and Olympic champion. Bentsen was born in Chicago, Illinois. He received...
 7. Ivar Bentsen
 Ivar Bentsen (13 November 1876 – 21 May 1943) was a Danish architect and educator. He was a central figure in the Bedre-Byggeskik movement and succeeded...
 8. Beint Bentsen
 Beint Kristian Bentsen (25 July 1917 – 2003) was a Norwegian banker and politician for the Christian Democratic Party. He is best known as county mayor...
 9. Eldijana Aganović
 Eldijana Aganović (born 20 November 1971) is a Croatian table tennis player. She competed in the 1996 and 2000 Summer Olympics. Evans, Hilary; Gjerde,...
 10. Christen Bentsen Schaaning
 Christen Bentsen Schaaning (Kristen Bentsen Skaaning) (c. _PHONE_) was a Norwegian clergyman. He served as parish priest of Avaldsnes Church (Avaldsnes...


I'm unsure
{absolute_results} not working properly
Hi Low
I'm getting some strange behaviour when using the {absolute_results} variable in Low Alphabet with pagination.
What seems to happen is that when a paginated alpha group is first loaded it shows the correct number of entries... but at some stage when clicking up and down through the result pages, the tag stops working and displays the count of entries on the current page, rather than the total number of results across the entire paginated set.
So it starts off working okay, but then at some point stops working. Instead of {absolute_results} it starts to show {total_results} instead.
I hope that makes some kind of sense. It's a bit hard to explain... but I'd be interested to see if you can replicate this issue on your own system.
1 person has
this problem
 - Low (Official Rep) July 19, 2011 14:58
 Hey Andrew,
 That's pretty strange indeed. Let's narrow this down a bit.
 1. When it happens, does it happen at the same URL all the time? Or is it intermittent?
 2. What version of EE are you using?
 3. Can you replicate this behaviour with a regular channel:entries tag?
 Low Alphabet simply collects the entry_ids of the entries to display and then passes them on to the Channel module, which takes care of the parsing of variables etc. Including the {absolute_results} and {total_results} vars. So in theory, Low Alphabet shouldn't affect it...
 - (some HTML allowed)
 How does this make you feel?
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text:
Power flushing is a technique used to clear sludge from central heating system pipes, radiators, coils and heat exchangers. These are areas where scale and corrosion can collect, the symptoms are usually:
- Cold spots on radiators, even after bleeding
- Takes a long time for radiators to warm up
- Noisy boiler
- Radiators needing regular bleeding
- Inefficient central heating system
Once a power flush is complete, you can expect the following benefits:
- Pipes and radiators will get hotter quicker
- More cost efficient system
- Less stress on the boiler
- Increased life of the boiler
- Heat will be distributed more evenly throughout the home
Central heating boilers can fail early if there is excessive sludge in the system, modern condensing boilers are much more sensitive so it's recommended to have a full system flush before installing a new boiler. There is no point in paying for an expensive piece of kit that may fail early because of excessive sludge build up in the system!
You should also check the guarantee on any new boiler as most manufacturers will not accept a claim if the system hasn't been recently power flushed.


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I have a video file of 5 FPS / 8000Hz that I want to speed up 6 times. I want the pitch and playback to increase - can I do this by simply adjusting the file header?
I can't seem to figure out the right parameters to do this with ffmpeg since it actually creates new frames in order to stay at the same speed. I read some similar topics on this website, but can't seem to find anything simple to do with both sound and image.
Is there a way to do this with a command-line tool or can someone explain how to alter this in code?
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1 Answer 1
mencoder has an option to change the speed. A similar question was answered here.
The following command was suggested:
mencoder file.avi -speed 20 -vf scale=720:368,hqdn3d=3:2:3:2,expand=720:480 -ovc xvid -oac pcm -xvidencopts fixed_quant=2 -o out.avi )
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Your Answer


text: The finite-element method (FEM) was applied to analyze the vibration (inherent and the harmonic frequencies) of wine glasses (glass harp) as a musical instrument. FEM analysis for this problem was proven appropriate by confirming the coincidence between the experimental and analyzed inherent frequencies for several glass cups with different shapes. When using wine glasses as musical instruments, minute arrangement of the pitch is necessary. Even today, this is done by filling a certain quantity of water in the wine glasses. This method, however, is very troublesome because each time, just before a performance, a check has to be made to confirm that the correct water quantity had been filled in every vessel. Compounding the problem, the pitch sometimes changes during the performance because of water evaporation. In place of this water-filling method, minute pitch changes have been achieved by locally shaving a bottom part of each vessel. The pitch is found to decrease in proportion to the shaved glass quantity. The relationship between the shaved glass quantity and the changed pitch has been clarified experimentally and analytically through FEM analysis. With this procedure, the desired pitch can be obtained.


Australian Medicare Number Validation
Australian Medicare card numbers consist of 11 digits structured as follows:
First digit should be in the range 2-6
Digits are weighted (1,3,7,9,1,3,7,9)
Issue Number
Indicates how many times the card has been issued
Individual Reference Number (IRN)
The IRN appears on the left of the cardholder's name on the medicare card and distinguishes the individuals named on the card.
The IRN is not always considered part of the card number, but it is essential that it be included on Medicare claim forms.
It can be hard to find a definitive reference to the algorithm on the Medicare site. At the time of writing it could be found in this document:
Try It!
Sample Code
// ValidateMedicareNumber
// Checks medicare card number for validity
// using the published checksum algorithm.
// Returns: true if the number is valid, false otherwise.
// Note - this expects 11 digits including the IRN.
// To validate numbers without IRNs, change the length
// check to 10 digits.
// Source:
// Author: Guy Carpenter
// License: The author claims no rights to this code.
// Use it as you wish.
function ValidateMedicareNumber($MedicareNo)
 $medicareNo = preg_replace("/[^\d]/", "", $MedicareNo);
 // Check for 11 digits
 $length = strlen($medicareNo);
 if ($length==11) {
 // Test leading digit and checksum
 if (preg_match("/^([2-6]\d{7})(\d)/", $medicareNo, $matches)) {
 $base = $matches[1];
 $checkDigit = $matches[2];
 $sum = 0;
 $weights = array(1,3,7,9,1,3,7,9);
 foreach ($weights as $position=>$weight) {
 $sum += $base[$position] * $weight;
 return ($sum % 10) == intval($checkDigit);
 return false;
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text:
|Oracle Enterprise Manager Database Tuning with the Oracle Tuning Pack
Part Number A86647-01
The Outline Management tool allows you to manage stored outlines directly using a GUI-based tool. Specifically you can browse, sort, delete, and edit outlines with this tool. Outlines are preserved by Oracle's plan stability functionality, so before using Outline Management or Outline Editor to create or edit an outline, it is important to understand how plan stability works. Plan stability prevents certain database environment changes from affecting the performance characteristics of applications. Such changes include changes to the optimizer statistics, changes to the optimizer mode settings, and changes to parameters affecting the sizes of memory structures, such as
BITMAP_MERGE_AREA_SIZE. Plan stability is most useful when you cannot risk any performance changes in an application.
An outline consists primarily of a set of hints that is equivalent to the optimizer's results for the execution plan generation of a particular SQL statement. When you create an outline, plan stability examines the optimization results using the same data used to generate the execution plan. That is, Oracle uses the input to the execution plan to generate an outline, and not the execution plan itself.
As mentioned above, an outline is a means for modifying optimizer behavior. When the optimizer encounters the SQL text of the outline, it applies the supplied hints. The plans Oracle maintains in stored outlines remain consistent despite changes to a system's configuration or statistics. Using outlines also stabilizes the generated execution plan if the optimizer changes in subsequent Oracle releases. Plan stability facilitates migration from the rule-based optimizer to the cost-based optimizer when you upgrade to a new Oracle release.
For more information on plan stability, see the Oracle9i Database Performance Guide and Reference.
There are two ways to launch the Outline Management Tool:
The Outline Management tool provides an easy-to-use graphical interface for managing your stored outlines. The tool can tell you how many outlines exist in the database and whether or not the outlines have been used since the last database upgrade.
Specifically, the tool allows you to:
The Outline Management Tool can also be used to launch the Outline Editor to create a new outline or edit an existing outline. When you want to create a new outline, Outline Management gives you two options: Create and Create Like. The Create feature launches the Outline Editor which allows you to specify the name, category, and SQL text for your new outline. Use the Create Like feature to make a new outline similar to an existing one.
When you edit an existing outline, the Outline Editor lets you to see the SQL text and modify the graphical explain plan for the outline. For more information on using the Outline Editor, see Chapter 26, "Introduction to the Outline Editor".


text:
Celebrate Mental Health Week – May 7-13, 2012
CMHA's Mental Health Week is an annual national event that takes place during the first week in May to encourage people from all walks of life to learn, talk, reflect and engage with others on all issues relating to mental health.
This year's Mental Health Week theme is Mental Health for All. Mental Health Week 2012 will focus on key topics that will help the public have a broader understanding of mental health, including: Kids Have Stress Too!; Resiliency: at Home, at School, and at Work; and Mental Health is Everyone's Concern. Local events and activities are planned in communities across Canada. Find an event near you or plan your own!
For more information, visit _URL_.
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Bayad Name Meaning
Bayad is a Muslim Girl Name. Bayad name meaning is Awareness. It has multiple Islamic meaning. The name is originated from. The lucky number of Bayad name is 8.
Name Bayad
Meaning Awareness
Gender Girl
Lucky Number 8
Religion Muslim
Lucky Days Thursday, Friday
Lucky Colors Light Green, Peach
Lucky Stones Sapphire
Lucky Metals Silver, Copper
Bayad Name Meaning and History
Bayad is a Muslim Girl name Acording to Numerology Predictions, lucky number for Bayad is 8. Bayad name meaning in english are Awareness.
People believes to have their Lucky Days according to their names, Thursday, Friday are Favourable and Lucky Days for name Bayad and lucky metals are Silver, Copper for Bayad name holders.
Lucky colors for Bayad are Light Green, Peach and Bayad name is famous in our names dictionary, and has been searched 48276 times, which is Forty-eight thousand two hundred seventy-six times.
Bayad is listed in the Girls directory of Girls Islamic names meaning section, and can be searched easily online or you can check in alphabetic "B" of the Girls Muslim names area. There are almost 462 baby Girl names which start with alphabet B in our names section. You can also check the Bayad Name meaning in Urdu in our Muslim Urdu names area.
Q. What does Bayad name mean?
Bayad name meaning in Urdu is "بیداری،جاگنا ، ہوشیاری". In English, Bayad name meaning is "Awareness".
Q. What is the Lucky Number of Bayad?
The lucky number associated with the name Bayad is "8".
Q. What is the religion of the name Bayad?
The religion of the name Bayad is Muslim.
Q. What is the origin of Bayad name?
The origin of the name Bayad is.
Q. What is the auspicious color of the name Bayad?
For the name Bayad, the lucky color is Light Green, peach.
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text: Many products and processes have multidimensional characteristics and criteria. As these responses involve common parameters and processes, the response data are correlated. The quality and reliability improvement of such products and processes will typically involve multiple-response optimizations to find optimal operating conditions. Many of the current multiple-response optimization approaches assume a single-response uncertainty in the response models, and the uncertainty in the parameter estimates of the models. In this paper, we consider a Bayesian Model Average (BMA) approach to the modeling and optimization of variability of the predictions and the uncertainty of the model parameters. We further propose a Mahalanobis distance (MD) approach to account for the correlations among the response and the variation in the estimation of the response model.


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An old theorem of A. J. Wilkie (Some results and problems on weak systems of arithmetic, Logic Colloquium '77) asserts that a discretely ordered ring $R$ can be extended to a model of open induction if and only if for all $n>1$, there is a homomorphism from $R$ onto $\mathbb{Z}/n\mathbb{Z}$.
Wilkie's proof proceeds by adjoining transcendental elements to $R$, but it is not clear that this is ever necessary:
Does every ring that extends to a model of open induction have an algebraic extension to a model of open induction?
Does anyone know anything about this? I know of no place in the literature where the question is even mentioned, although it has come up more than once in conversation.
Here is simple test-case: Let $R$ be the ring $\mathbb{Z}[t,\sqrt{2}t-r]$, where $r$ is a real transcendental and $t$ is an indeterminate. Order $R$ by declaring $t$ positive infinite. It is not hard to show that $R$ extends to a model of true arithmetic. I don't know if $R$ has an algebraic extension to a model of open induction.
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Can you please explain what it means for a ring to "model open induction"? – Andrej Bauer May 7 '10 at 13:31
2 Answers 2
Andrej Bauer asked in a comment, "What is a model of open induction?" Let me give the most modern and relevant answer and then explain the term "open induction", which is somewhat archaic.
Let $F$ be an ordered field. An (ordered) subring $R$ of $F$ is called an "integer part" of $F$ if
 1. $R$ is discretely ordered: This means the inequality $x < y < x+1$ has no solution in $R$. Equivalently, nothing in $R$ lies between 0 and 1.
 2. For all $x\in F$ there is some $r\in R$ such that $r\le x < r+1$.
Item 2 is equivalent to saying that every element of $F$ is a finite distance from some element of $R$, where "finite" means bounded by an element of $\mathbb{Z}$. Remember that $F$ can and usually will be nonarchimedian.
Items 1 and 2 together imply that there is a unique function $\lfloor\cdot\rfloor$ from $F$ to $R$ given by the inequality $\lfloor x \rfloor \le x < 1+\lfloor x \rfloor$. Think of this as an abstract analog of the integer part operator.
A "model of open induction" is an integer part of a real closed field. Mourges and Ressayre proved that every real closed field has an integer part. The term "open induction" comes from a paper of Shepherdson, who started this whole topic by proving that an ordered ring $R$ is an integer part of its real closure if and only if the positive semiring of $R$ satisfies the axioms of Peano Arithmetic, with the induction axioms restricted to quantifier-free (i.e. open) formulas. Shepherdson also gave recursively presentable nonstandard models of open induction, which is interesting because according to Tennenbaum's Theorem there are no such models of Peano Arithmetic.
Since then there have been many successful attempts to build recursive nonstandard models of theories a little stronger than open induction. The champ, to-date, is a recursive nonstandard normal model of open induction, given in a paper by Otero and Berarducci. Here "normal" means integrally closed in its quotient field.
The main unsolved problems concerning open induction, in my opinion, are (1) Is the universal theory of open induction decidable (i.e. is it decidable whether a diophantine equation has a solution in some model of open induction) and (2) Is there a recursive non-standard diophantine correct model of open induction, where "diophantine correct" means "extends to a model of true arithmetic".
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Interesting. In Brouwerian intuitionism the following is called "open induction", where $A \subseteq [0,1]$ is an open subset of the unit interval: $(\forall x \in [0,1]. (\forall y < x. y \in A) \implies x \in A) \implies [0,1] = A$. This seems unrelated to what you are talking about. – Andrej Bauer May 7 '10 at 15:27
I think this should have been edited into the question instead of posted as an answer. In any case, this should be community wiki. – François G. Dorais May 7 '10 at 22:42
I think that the answer in general is "no", and that this follows from results in a paper "Limit computable integer parts" by D'Aquino, Knight, and Lange (_URL_ Namely, by Theorem 3.5 and Remark 3, there exists a real-closed field $R$ with an element $r\in R$ and a $\mathbb Z$-ring $I\subseteq R$ such that no discretely ordered subring $I\subseteq J\subseteq R$ intersects $[r,r+1)$, but $b/i\in[r,r+1)$ for some $b,i\in I$. Then $I$ (being a $\mathbb Z$-ring) can be extended to a model of $\mathit{IOpen}$, but no such extension can be found in its real closure $\operatorname{rcl}(I)\subseteq R$ (since no discretely ordered $I\subseteq J\subseteq \operatorname{rcl}(I)$ can contain an integer part of $b/i$).
Caveat: the paper is so far an unpublished preprint, and I have actually serious doubts about its correctness. Namely, the claim "$\frac{p(a)}n+z$ cannot be in $(0,1)$" in the proof of the widely used Proposition 3.1 is unjustified, and in fact, I think that this proposition directly contradicts Example 2 (take $I=(x^2+1)\mathbb Q[x^2]+\mathbb Z$, $R=\operatorname{rcl}(\mathbb Q(x))$, and $a=x$; then conditions 2 and 3 hold as $I[x]=I+xI$ is easily seen to be discretely ordered, but condition 1 does not). However, I think that this does not affect the proof of Theorem 3.5, since all the elements which 3.1 is applied on there are (or can be taken to be) transcendental.
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Emil, Thanks very much for the reference. I'm not sure that Example 2 DIRECTLY contradicts Proposition 3.1, because (in the example you gave) $\mathbb{Z}[(x^2+1)/4]$ is not a Z-ring, as Prop. 3.1 requires it to be. But I'll have to think about this. – SJR Feb 3 '11 at 17:12
Fair enough, thanks for pointing it out. Hopefully it's correct now. – Emil Jeřábek Feb 3 '11 at 18:25
Your Answer


text:
Given that p is prime, when is 8p+1 square?
Let 8p + 1 = k2. As LHS is odd, k must be odd; let k = 2m + 1.
Therefore 8p + 1 = 4m2 + 4m + 1, leading to 2p = m2 + m = m(m + 1).
As m and m + 1 are consecutive integers, one of them must be even. However, after dividing through by 2 we can see that LHS is prime, so RHS must be prime. This can only happen when m = 2; that is, p = 3.
Hence 8p + 1 can only be square when p = 3.
Triangle Search: When is 8p+1 a triangle number?


text:
My pdf currently displays 11 decimal places for a field number (using "no format") and I would like for it to only display 6 decimal places. I see that under "Format" in the field map there is an option to only display 2 decimal places for a number and that works fine. Is there any way to display 6 decimal places? Thanks!
Use the Formidable: Dynamic option under the "Webform Data Field ID" dropdown then enter [125 decimal=2 dec_point="." thousands_sep=","] into the text box that appears below the dropdown. (Change 125 to your field ID)