Triskelion Symbolism: Learning its Inner Ways and Importance
triskelion symbolism
Triskelion Symbolism: How is this Emblem Important to You?
To fully comprehend the triskelion symbolism, you may need first to know the underlying meaning of the triskelion itself. It is an ancient symbol of the druids, a motif, that has triple spirals that are joint together in the middle some triangle. One can say the structure of the triskelion replicates the Archimedean spirals. In some circles, it is the representation of three human legs. This symbol comes from Sicily, and it means the Isle of Man.
Also, it has other names like Tree Cassyn Vannin. However, in the ancient lands of Brittany is the triskelion. So, like most of the other essential emblems in life, this too has meaning that is very important to us. In the Celtic culture, it bears the definition of passive and active. When you closely stare at the symbol, it seems like something that is always moving. The logo signifies the active parts of our life we invest through the aid of this symbol. Also, it represents how the cosmos gives us a response to our efforts.
On the other hand, the passive part represents the faith, belief, prayer and meditation that we invest in the hope that the universe can reply to us. It is a simple concept. The triskelion only shows you that you need the help of the heavenly beings at times. When this happens, there is a harmonious balance that will help you out.
Symbolic Meaning of the three Arms of the Triskelion
Just by the first look of the triskelion, you will notice that it has three extensions at the edges with spirals. They stand for various things depending on the culture and the belief that you hold about it. Some of these include the mind, spirit, and body. On the other hand, there is the symbolism of Father, the Son, and the Holy Spirit. However, in some of the cultures, they believe that it represents the past, present, and future. In short, there are several symbolic meaning of the triskelion that has a lot of purpose in life.
The combination of these arms is what brings harmony to give the life of any personal meaning. To understand this, people must know that they need to be both active and passive.
Moreover, you cannot work yourself to death or worry that much. Also, you need to have faith in the things that you are doing or working towards will work out. The moment that one of these is cut off from your life, then you will notice exact problems.
In Celtic culture, they understood that these arms of the triskelion needed to go hand in hand. Moreover, they would plant, hunt and even plunder. However, they would also take time to pray to their gods for guidance in life. Also, they knew that there is the presence of the supreme beings in their life and that they are always watching.
Representation of the Three Realms by the Triskelion
Like in most culture and beliefs the triskelion also has the three worlds that make up the entire universe. There is the spirit world that carries the life of the gods and goddesses.
On the other hand, there is the celestial world where the forces of the universe reside. Lastly, there is the world that we live in. The world of living souls, plants, and animals.
This is why the number three is always a significant number in the universe because it represents that lives of all the things in the cosmos. Also, the triskelion describes the phases of the moon and how they affect the three realms of the universe. You know that there are three primary phases of the moon those are the full, half and the new moon.
Association of the Triskelion Symbolism to the Lunar
When you are looking at the association of the triskelion symbolism to the lunar, there some of the traits that you cannot miss. Some of these are intuition, spirituality, illumination, subconscious, feminine, hidden desire and mastery. These some of the meaning of this symbolism as it touches on the matter of the lunar effect. This is one of the reasons why the triskelion's appearance is a lot in the life of the Celtic people. Moreover, it seeks to teach and guide them in ways that they can live full feelings lives.
Triskelion Symbolism in the Christian Faith
Early in the 5th Century, the Christians took up the teaching of the triskelion into the faith. This took place among the British and the Irish culture when the Romans went there to spread the word of Christianity. However, when you touch on the Christian side, the three arm stands for the Christian triplicates. Later, the triskelion would appear in most of the Celtic Christian arts. Some of these were the cross and Christian manuscripts. Moreover, there are some of the triskelia that would end up on the widows of the churches especially the roman catholic ones.
triskelion symbolism
Representation of the Triskelion in the Contemporary Society
Many people and countries adopted the symbol and are using it on things like their flags and logos. For example, the United States of America's Department of Transportation is using it on their logo. On the other hand, the flag of Sicily has it to represent the Isle of Man. Also, the coat of arm of the Füssen is also having the three extensions of the Triskelion. There are many more places that it appears meaning it represents a lot to the people that are using it.
Triskelion symbolism is an okay way to learn the inner working of the universe and how it represents itself. The people that are having belief on the methods and teaching of the triskelion are most likely to have a quiet life on this earth. Moreover, there is no way that one lifestyle can entirely work without the other.
alchemy planet symbolism
Alchemy Planet Symbols: Learning its Meaning and Significance
square symbolism
Square Symbolism: Spirit of its Significance in Our Lives


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The performance implications of perceptual differences of dependence in marketing channels: The mediating role of trust
Purpose – The purpose of this paper is to address two essential questions: do perceptual differences regarding dependence matter in determining channel performance, and if so, how? Design/methodology/approach – The paper conducted an empirical study of 347 cellular telephone supplier-retailer dyads in China. A questionnaire survey was employed. Findings – The results reveal that a retailer's perceptual difference of dependence exerts a significant effect on its evaluation of supplier performance only. Retailer trust partially mediates the effect of the perceptual differences on supplier performance and retailer performance. Therefore, the particular side of a dyadic relationship that researchers choose to study matters in an unbalanced dependence relationship. Practical implications – Managers, depending on their side, should pay close attention to perceptual differences and their consequences and deliberately employ different strategies to ensure effective channel management. Originality/value – Do differences in parties' perceptions of dependence influence channel performance? If they do, how do these perceived differences exert direct and indirect impacts? By answering these questions, the authors contribute not only to an understanding of the unique nature of dyadic channel relationships but also to methodological notions about whether to study one side in a dyad.
|Keywords||B2B marketing, Channel relationships, Marketing in China|
|Journal||Asia Pacific Journal of Marketing and Logistics|
Yang, Z. (Zhilin), Jia, F. (Fang), & Cai, S. (2014). The performance implications of perceptual differences of dependence in marketing channels: The mediating role of trust. Asia Pacific Journal of Marketing and Logistics, 26(3), 344–364. doi:10.1108/APJML-12-2013-0154

source: openbmb/Ultra-FineWeb


Referencing Grid Level Expressions from Advanced Query
Cory Fifield -
Trouble viewing images? Click on images to enlarge.
In this article we cover referencing Grid Level Expressions from Advanced Query.
How does it work?
Expressions are processed at the data grid level, after the query results have been processed and returned from the database. Expressions are then added to the resulting dataset and accessible throughout VDM's controls. If you're using Advanced Query, VDM needs to know where to place the Expressions in the resulting dataset. So you can add an expression to the Grid after you run an Advanced Query, but if they're not added to the Field Selection List in the Advanced Query, VDM doesn't know where to put them.
We don't recommend Grid Level Expressions be used with Advanced Query. We recommend Advanced Queries be used for SQL Scripting only, and additional calculations that need to be performed on the resulting dataset be configured and completed using Calculated Fields in Finished Reports or Visualize.
How to reference grid level expression in Advanced Query
1. Create your Advanced Query and run it.
2. Create the Grid Expressions. Make sure to have the correct datatypes used for the expression.
3. Add the new expression(s) to the select statement in the Advanced Query.
4. Save, run and preview the View with the new expression(s) added to the Advanced Query.
Have more questions? Submit a request


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GCWOK in a text message means "Gay Couple Without Kids".
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Community living: President can make motions, vote
President is permitted to make motions and cast votes
Q: Is an elected president allowed to make motions and vote?
A: This is a commonly asked question. Thinking that the president does not vote or make motions is incorrect. In fact, if you read the section on "Voting, Chairperson" in Robert's Rules of Order, it says: "The presiding officer, if a member of the assembly, can always vote in the case of a ballot at the same time other members do."
Thinking that the president only votes in case of a tie is wrong. The same is true if the president needs to make a motion or seconds a motion.
My recommendation is that the president asks other directors (at a board meeting) or members (at a members meeting) to make the motion. However, in some situations, it is important that the president make the motion and they would vote on the motion.
Most documents let board enter private property to make repairs
Q: A house in our gated community has been abandoned and the mortgage holder has not yet foreclosed on the property. The board has sent at least two certified letters to the last known address of the previous owner informing him that the lanai screen is broken, and the letters were returned marked not deliverable.
We are concerned about our HOA's responsibility if a child or pet wanders onto that property through the broken screen and falls into the pool. Since it is still private property, must we have a court order to allow us to go onto that property to repair this hazardous condition?
A: What you are referring to is called "Self-Help." Most documents allow the board to enter private property to make repairs. In this situation you describe, it involves making the property secure against a possible "attractive nuisance," which refers to objects or things on the premises that might attract children and therefore pose possible danger or harm.
There are two actions that I suggest. The first is to send a certified letter to the bank holding the mortgage, informing them of the problem. Ask them to make the necessary repairs or allow the board to enter the property and make the repairs.
The second action is to have your attorney send a letter to the previous owner. That letter should be a demand letter to make the property safe and should state if they do not make the repairs, the association will enter and make the property safe at the owner's expense.
Consult an attorney for further guidance.
Get creative with technology to let absent owners serve on board
Q: In a recent column you stated that part-time residents or landlord owners could serve on a board of directors. We are a small community with several homes rented and some owners who use the home as a vacation home. We do not have a clubhouse or common area building to hold our meeting. We meet at a local library where we would not have access to a speakerphone. How could any absent owner be informed of the needs of the association and serve on the board, much less serve as an officer?
A: Sometimes you must be creative. With today's electronic gadgets, there are several methods you can use.
Most libraries have wireless systems available. Using a laptop computer, there are several communication systems available to make connections with out-of-town directors. There are telephones that plug into computers, as well as Skype, which is a program used online that functions as a telephone and videophone. Cell phones can be used as a platform and serve as a speaker phone.
The problem is for the directors living out of town to keep advised of the necessary work and operations.
I would not restrict a person living out of town if they were willing to study and provide advice on solutions to problems. This can be done by e-mail and other electronic transmissions.
These solutions can be solved with limited expense and most of the equipment could be found from owners in your community.
The key words are communications, staying informed and a willingness to dedicate the time necessary.
Holding more than one officer position isn't a good idea
Q: Is it permissible for one person to hold the office of president and treasurer at the same time? I think the board should not let this happen — the board has other directors and we can have one person for each position. Why is there a need for our directors to allow this to take place?
A: The source for this answer can be found in your documents rather than the statutes. More than likely if your documents address this situation it would be in your bylaws, but most documents do not limit this situation.
It is not a good idea for a person to hold two officer positions, but in some situations it is necessary. The directors should not appoint one person to do most of the work unless there is no other option.
If directors do not have the time to serve as officers, they have two options. The first is to resign and let another owner fill the vacancy. The second is to engage professional management to do the work, and then the directors and officers would only need to supervise the manager's work.
Community living: President can make motions, vote 03/26/11 [Last modified: Saturday, March 26, 2011 5:30am]
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Utter French!
French Phrases: parts of the body
This page gives French words for the main parts of the body. Note that parts of the body in French are usually used with the definite article (le, la or les), even though in English, you'd often use a possessive (my, his etc).
Face and neck
la tête-the head
le visage-the face
les cheveux-the hair
le front-the forehead
les yeux-the eyes
un oeil-the eye
le nez-the nose
les joues (f)-the cheeks
les oreilles-the ears
les lèvres (f)-the lips
la bouche-the mouth
les dents (f)-the teeth
la langue-the tongue
le menton-the chin
le cou-the neck
la nuque-the nape, back of the neck
la gorge-the throat
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The upper body
le dos-the back
les épaules (f)-the shoulders
la poitrine-the chest
les seins (m)-the breasts
les bras-the arms
les coudes (m)-the elbows
le ventre-the belly
les mains (f)-the hands
les doigts (m)-the fingers
les ongles (m)-the fingernails
le pouce-the thumb
le poignet-the wrist
la hanche-the hip
l'abdomen-the abdomen
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The legs and lower body
les fesses (f)-the backside, buttocks
les jambes (f)-the legs
les cuisses (f)-the thighs
les genoux (m)-the knees
les chevilles (f)-the ankles
les talons (m)-the heels
les pieds (m)-the feet
les orteils (m)-the toes
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text:
Definition of a.c.
a.c.: Abbreviation on a prescription meaning before meals; from the Latin "ante cibum", before meals. This is one of a number of hallowed abbreviations of Latin terms that have traditionally been used in writing prescriptions.
Last Editorial Review: 4/27/2011 5:27:15 PM
- b.i.d. = twice a day (from "bis in die", twice a
- gtt. = drops (from "guttae", drops)
- p.c. = after meals (from "post cibum", after meals)
- p.o. = by mouth, orally (from "per os", by mouth)
- p.r.n. = when necessary (from "pro re nata", for an occasion that
has arisen, as circumstances require, as needed)
- q.d. = once a day (from "quaque die", once a day)
- q.i.d. = four times a day (from "quater in die", 4 times a day)
- q._h.: If a medicine is to be taken every so-many hours (from
"quaque", every and the "h" indicating the number of hours)
- q.h. = every hour
- q.2h. = every 2 hours
- q.3h. = every 3 hours
- q.4h. = every 4 hours
- t.i.d. = three times a day (from "ter in die", 3 times a day)
- ut dict. = as directed (from "ut dictum", as directed)
Back to MedTerms online medical dictionary A-Z List
Need help identifying pills and medications?
Use the pill finder tool on RxList.

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text:
Canada and the United States are countries of immigrants. Their electorates are diverse, and include people from different ethnic, cultural, religious, and sexual backgrounds. But the history of each nation includes just one example of the highest office in the land being held by someone other than a white man.
A new, bi-national public opinion poll from the Angus Reid Institute finds Americans and Canadians nearly unanimous in their willingness to vote for a woman for president or prime minister, and similarly enthusiastic about supporting a Jewish or Indigenous candidate.
Fewer than half of all Americans (47 per cent) say they could vote for a Muslim presidential candidate, and respondents in both countries are divided as to whether they could cast a ballot for a candidate who covers his or her head for religious reasons.
There are also significant gaps on both sides of the border, between those who say they could vote for diverse candidates, and those who say the chances of such candidates becoming head of government is probable in the next 25 years.
- Younger respondents on both sides of the border are more open to voting for diverse candidates than older age groups
- American respondents are deeply divided along political lines when it comes to these issues, while Canadians are divided along regional lines
- The vast majority of respondents in both nations say they could vote for a national leader who is a woman, but there are significant differences between countries on atheist and LGBTQ candidates
Link to the poll here: _URL_


text:
This post describes the simplest possible way to transform a form into a page in NAV 2009. Both Pages and Transformation is documented in more details elsewhere. Here, I just want to make the simples possible example, just to get a simple form transformed into a simple page.
You need to have at least a NAV 2009 classic client and the Transformation tool. To test the page, of course you also need the Rolebased client. But to just transform a form, you don't need it.
Import the tool:
1) Open a classic client, go to Object Designer and import the files DevTool.fob and TIF.fob from the folder TransformationTool\TIF Editor\
2) Create a new form in NAV, as simple as possible. For example a Card form based on the customer table, with just a few fields on it. This is the form you want to transform.
Setup and use the Transformation tool:
3) Run form 97000 "Transformation Forms"
4) Click Import -> "Import PageType – FormType mapping", and select the file TransformationTool\TIF Editor\FormToPagetypeMapping.txt.
5) Click Functions -> Get Forms. Filter on Type = Form, and ID = the new form, then click OK. This gets the form(s) that you want to transform.
6) In the FormType field, select "Card" ("Form with TabControl only and a source table").
Run the transformation:
7) Export the settings from form 97000: Click on Export -> "Transform Pages". You must export it to the TransformationTool folder, and it must be called TransformPages.xml.
8) From Object Designer, export the form (Tools -> Export) as xml.You must export it to the folder TransformationTool, and it must be called Forms.xml.
You now have the form you want to transform, and the meta-data that tells the TranformationTool how to transform it.
9) Run the file FormTransformation.exe from the TransformationTool folder. This generates a new file called Pages.xml. It also logs any progress or errors in the file Transformation.log.
Import the new page:
10) Back in NAV (classic client): Go to Object Designer, and import the file Pages.xml, and then compile it.
If all steps ran without any errors, you have now transformed your form into a page which can be displayed in the rolebased client.
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57. Piano Sound BoardRepairing Cracks
The sound board is a five eighths inch thick wooden board in the back of the piano. On the back of it, it has one inch ribs which stabilize it by running against the grain of the sound board. A sound board is made one of two ways.
The traditional sound board is made of several five eighths thick boards which are glued side by side across the whole inside of the piano. It is the best sounding board, but with age, it can crack.
More recently, sound boards have been made of laminated wood, or glorified plywood. They never crack, but they are slightly dead or muffled. Pay your money and take your chances.
"My sound board is cracked. Is the piano ruined?"
There is a myth still around that a piano is ruined if it has cracks in the sound board. The Steinway people did a test on this. They made a piano with a quarter inch "crack" in it. The cross ribs were tight and normal. When they tested it with Db meters, they found that the piano with a "crack" in it did just as well as a new piano with a perfect sound board.
So, what's the problem? When a piano develops cracks from old age, the cracks can cause buzzes. Also, the crack is much bigger than it would appear. When a crack develops, the spruce of the sound board warps and pulls away from the cross ribs. The effect is to widen the crack as far as acoustics are concerned. The illustrations will help you see what is happening.
While we are here, let's talk about the graphics at the left. You are looking at the front of the sound board area and the lower end of the treble bridge in the lower left an upright from the turn of the century from Leipzig.
The lower graphic shows a crack in the sound board at an angle to the upper left. The end of the bridge mounting board is also hanging in space. This prevents all the sound from transferring from the lowest strings shown into the sound board. The sound will have to travel up the bridge and find a way to the sound board by traveling far. This mutes the sound greatly at times.
The crack and the bridge mounting board separation call for an examination of the bridge to see if the main bridge is also separating. If so, go to Chapter Sever, Section 6-- Bridge Repair for instructions.
The crack here is not badly advanced, but it should be done at once. I also want you to see the severe deterioration of the varnish on the sound board. This sound board was over varnished I think, for the effect looks very think. Try to keep from adding so much varnish when refinishing a sound board. The weight is a real issue, and the cracking could slightly slow down the board.
The object of repairing the sound board is to return the warped sound board to be tight against the rib again.
All you need to buy is a box of 100 No. 10, inch and a quarter wood screws. I suggest Philips head. Also, if you don't have one, get a counter sinking bit for wood which will fit your drill motor.
If you are working on an upright, you will have to get it well away from the wall so that you can work behind it. If you have a grand, you will have to work under the thing. Extra light is essential in both cases.
Sturdy Philips Screw driver. Slow speed electric screw driver or drill with Philips bit. One drill bit the size of the shank of the screws you bought (see below). Counter sinking bit for wood.
First, clean the whole area behind the upright. The grand will be clean already.
Second, Determine which drill bit to use. The size of the bit must be exactly the same as the diameter of the screw shank. You are NOT going to drill a guide hole for the threads.
Third, Drill two holes on every rib-- One on either side of the crack wherever the rib crosses a crack. Drill them about a half inch from the crack. DO NOT DRILL INTO THE SOUND BOARD. DRILL ONLY THROUGH THE RIB. STOP SHORT OF GOING INTO THE SOUND BOARD. Are you getting the point?
You will bungle the whole job if you drill into the sound board. This hole you are drilling is to let the screw turn freely in the rib as it bites into the sound board. If you are unsure of yourself, go invest in one of those drill bits which have a stop on it. Set the stop so that the exposed part of the drill is only as long as the rib is deep.
The spruce sound board is five eighths of an inch thick, and it is not overly hard wood. Any error could put you all the way through the board.
If the crack has opened and warped a lot, drill four holes in the rib-- One on each side of the crack (totalfour at each point where a rib crosses a crack).
Fourth, Using the counter sinking bit, recess the tops of the holes just enough for the screw heads to be flush with the rib. This is neater work, and it is more secure.
Fifth, Put a screw into every hole. Take a look at your work, and see if you have missed any points that need doing. You will have to let some points go undrilled because they will be behind the wood frame of the piano. Don't worry about this.
Now, run the screws in with the electric drill motor and the Philips bit. The best drill motor is a battery operated one which runs slow. If you cannot control it, use the hand held screw driver for the whole process. You must not over tighten, or you will strip out the screw in the sound board. Leave the screw to be tightened the last couple of turns with the hand held screw driver so you have control.
As you can see in The illustration, the tip of the screw may just come through the other side of the sound board. This is good since the threads of the screw are getting a full bite in the wood this way. In the grand piano, you may not like the tips of the screws showing when you look into the piano. Sorry, but if you use a one inch screw, you will not get a good bite in the wood. Better to have the points showing than the loss of volume or a buzz, right?
If you had to put two holes on each side of a bad crack, tighten the outside holes first, then tighten the inside holes. This will bring the board up in stages and prevent stripping out the screws.
Don't cover the screws for cosmetic reasons as restoration shops do. You may want to snug the screws in a few years. You are done. It may not be real pretty, but your piano's sound board is now good for another fifty years.
You can run some Elmer's glue into all of the cracks, but it is not necessary. I usually don't bother.
There are toggle bolts made just for this repair, and you can get them from your tuner. But, they add too much weight to the sound board, and several cracks could cost quite a lot. I don't like them, and I won't tell you how to use them.
Last thought: If the sound board was severely broken up, and yet you got it all back together, you should do two more things.
First, work glue into the space between the sound board and the sides of the cabinet and the floor of the cabinet or the heavy wood frame in the rear. You want the sound board firmly anchored to the frame and cabinet.
Second, you should check the bearing of the strings over the bridge. This can be done with a bearing gage which we sell in the Catalog Tool Section. Sometimes a sound board warps or is different than when new because of repairs, and the sound will not get into the board through the bridges if there is no bearing or a negative bearing.
Filling Cracks in Sound Boards
Repairing the sound board from the back is essential, and filling the crack from above will not be enough alone to secure the sound board and stop the buzzing. Once the process above is complete, you may want to fill the cracks on the top side of the board for cosmetic purposes.
To accomplish this you must be doing a complete restoration and removing the harp for restringing. Once the harp is removed, you must deepen the grooves where the cracks are. Two "V" shaped tools are available, and either will work. The one with tools on each end and a handle in the middle has the most options for work. See this catalog page for sound board repair items.
The groove made by the tool is "V" shaped. This groove will then receive a spruce shim which is shaped the same way. Elmer's Carpenter's Glue must be used, and the spruce shim is tapped into the "V" groove and allowed to dry. The chisel end of the tool is then used to trim the excess of the spruce shim down level with the sound board You must avoid getting into the sound board Some very modest sanding is in order as a last step, and the sound board should then be lightly sanded and a coat of varnish or lacquer added.
Restoring the Crown and Down Bearing of a Sound Board
CAVEAT EMPTOR: This is strictly an act of desperation. If you use this technique, you must take 100% responsibility for the results. I have never done


Friction Welding Your 3D Prints
Friction Welding.jpg
A common technique to successfully 3D print complex objects is to print separate pieces and then glue them together. But are there other techniques for joining pieces together? Apparently yes.
There is a technique known as "friction welding", which uses the principle of friction-generated heat. If there is sufficient friction, the heat may be high enough to melt or soften 3D prints made of ABS and particularly of PLA as they have a lower melt temperature.
In this video friction welding is demonstrated. The approach is to insert a filament segment into a Dremel or similar tool and spin it at very high speed. The tip of the rotating filament touches the print and friction generates heat. Some of the filament's melted plastic is deposited on the print if you handle it carefully. You can also drill smooth holes in the print by simply pushing the filament through.
Is this approach useful for joining two pieces together? Maybe, but it would require a lot of very careful work to do so. Probably it's less effective for joining pieces than it is for welding holes closed and other small repairs.
But it's yet another approach to put in your 3D printing toolkit.
Via YouTube


Question: What Are Lava Stones Good For?
Do lava rocks help with anxiety?
It's an intense energy, but a calming one.
On a spiritual level, lava stones bring stability.
Are lava beads bad luck?
Lava Rock beads are, as their name suggests, a type of igneous rock. It's considered bad luck and illegal to take lava rocks from Hawaii's national parks because the volcano goddess, Pele, may place a curse on you.
Is lava stone toxic?
Lava rocks is a very broad term. If it is just a bubbly basalt, you should be fine. … The 'lava rocks' might be toxic because sometimes they are used as an industrial filter.
Is Tiger's Eye dangerous?
This stone is formed in part from the mineral crocidolite, which is a type of asbestos. During the formation of tiger's eye, crocidolite is completely replaced with quartz and iron ore, so if you ever wondered whether tiger's eye is dangerous – well, it isn't.
What does Tiger's Eye do?
Is lava rock good for fish tanks?
If you want the plants and fish in your aquarium to live in a healthy environment, lava rocks are a great idea. Lava rocks are covered by holes and pores that have beneficial bacteria, which is called denitrifying bacteria. These bacteria can help in keeping normal nitrogen cycles in your aquarium.
How can you tell if lava rock beads are fake?
Real lava beads should look spongy, ceramic ring-like, and with a rough texture. They should be lightweight and red, red, brown, or black in color. They also should not fade during the cleaning process. They should not burn, melt, shatter, or have an unusual odor.
Are lava rocks strong?
It was shiny, hard and heavy. Lava rock, for landscaping, is foamed obsidian. The gasses released in the volcanic eruption penetrated the lava, but did not escape before the lava cooled, leaving air pockets behind.
What side of your body do you wear crystals?
leftThe left side of your body deals with your internal self and controls stresses from your outside environment. Wear your Crystal Bracelet on the left side if you want to receive its healing energy and internal benefit.
Can lava rocks be cleaned?
Lava rocks are often used for gas barbeque grills and can become quite dirty with food and grease droppings. You cannot use a wire brush or wash them in water as you might ceramic briquettes found in other gas grills. Instead, you must burn them clean.
What rocks are bad for aquariums?
Rocks to avoid include:Shells or crushed coral (These are not ideal for most freshwater tanks, but may be used for African cichlid tanks, where higher pH and calcium hardness are desirable.)Limestone.Geodes.Marble.Dolomite.Dec 4, 2019
Can you shower with a lava stone bracelet?
Do not wear your Lava Stone Bracelet in the Bath or Shower they should be removed prior to bathing or showering.
Can lava stone get wet?
Answer: Hello, if it gets wet it will not effect the lava beads at all, the central bead you may want to pat dry once out of the water.
Is lava stone expensive?
How much do lava stone countertops cost? Lava stone's biggest deterrent is its price. At $250 to $350 per square foot, it's one of the most expensive countertop materials around, comparable to, or even exceeding, high-end marble.
Do lava stones really work?
Lava stones and the chakra Many users of lava stone believe it grounds and stabilizes the root chakra because of the stone's strong connection with the earth. When the root chakra is stabilized, the body and mind will feel positive, safe and anchored to the earth.
Does lava stone have healing properties?
Known for its grounding and calming healing properties, lava stone is great for stabilizing the root chakra. When the root chakra is stabilized, you feel safe, anchored and more positive.
How long do lava beads last?
2-3 daysThe lava beads are black or brown (if you ordered a bracelet with natural brown lava). They are porous with "craters" on them. You can drop one drop of oil on each bead (a little goes a long way, so you only have to put them on a couple of the beads) and it will last 2-3 days.
Do Chakra bracelets help anxiety?
Stone and Crystal Bracelet for Anxiety. Certain crystals and stones are seen as anxiety antidote since ancient times. They believed to offer a calming effect which assists in alleviating emotional disorders. Blue Agate is believed to be among the strongest crystal for stress and anxiety relief.
What do lava rocks do spiritually?
Will lava rock affect pH?
The lava rock is red due to the iron in it. It has no calcuim so it will have no affect on your ph.


The iBobber is a smart fishing tool that uses sonar to catch the fishes. After combining 19th and 21st century technology, iBobber has introduced an interesting twist of sonar and app connectivity to fishing.
What we need to do to catch a fish is just attach the bobber to the fishing line and it will detect where the fishes in water are and how deep the water is. It will communicate this information via Bluetooth to a Smartphone, which will allow you to adjust the casting and the depth resulting in increasing the chances of getting a bite.
Obviously, the sonar would not reach the Mariana Trench but it can detect the depth up to 135 feet and has a sonar angle of 42-degrees, means the detection diameter gets wide toward the bottom of the well over 20 feet.
It can also detect the height of a fish based on the scale size.
It also has an additional feature for those who love fishing; the iBobber will inform you about the temperature and also includes a lunar calendar which will help you to know the ideal fishing timing and locations. The iBobber app for iOS and android are available for free on play store.
The iBobber will notify you when the fish is caught in the hook.
The iBobber costs for $100.
The iBobber consists:-
Smallest on market Longest battery life
LED Beacon Strike alarm
Strike alarm Waterbed mapping


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Definition of "level of quantification"
65.1 In section 65, "level of quantification" means, in respect of a substance, the lowest concentration that can be accurately measured using sensitive but routine sampling and analytical methods.
Marginal note:Domestic Substances List
66. (1) The Minister shall, for the purposes of sections 73, 74 and 81, maintain a list to be known as the Domestic Substances List, and the List shall specify all substances that the Minister is satisfied were, between January 1, 1984 and December 31, 1986,
(a) manufactured in or imported into Canada by any person in a quantity of not less than 100 kg in any one calendar year; or
(b) in Canadian commerce or used for commercial manufacturing purposes in Canada.
Marginal note:Non-domestic Substances List
(2) The Minister shall, for the purpose of section 81, maintain a list to be known as the Non-domestic Substances List, and the List shall specify substances, other than
(a) the substances referred to in subsection (1); and
(b) living organisms within the meaning of Part 6.
Marginal note:Amendment of Lists
(3) Where a substance was not included on the Domestic Substances List and the Minister subsequently learns that, between January 1, 1984 and December 31, 1986, the requirements set out in paragraph (1)(a) or (b) were met in respect of the substance, the Minister shall add the substance to the List and, where necessary, delete it from the Non-domestic Substances List.
Marginal note:Amendment of Lists
(4) Where the Minister includes a substance on the Domestic Substances List and subsequently learns that, between January 1, 1984 and December 31, 1986, the requirements set out in paragraph (1)(a) or (b) were not met in respect of the substance, the Minister shall delete the substance from the List and may add it to the Non-domestic Substances List.
Marginal note:Publication of Lists
(5) The Minister shall publish in the Canada Gazette and in any other manner that the Minister considers appropriate the Domestic Substances List, the Non-domestic Substances List and any amendments to those Lists.
(6) The Minister may, by order, designate any person or class of persons to exercise the powers and perform the duties and functions set out in this section.
Marginal note:Regulation of criteria
67. (1) The Governor in Council may, on the recommendation of the Ministers, make regulations
(a) respecting a property or characteristic of a substance, including, without limiting the generality of the foregoing, persistence and bioaccumulation;
(b) prescribing the substances or groups of substances in respect of which the property or characteristic may be applicable;
(c) prescribing the conditions under which and the circumstances in which the property or characteristic may be applicable; and
(d) respecting the conditions, test procedures and laboratory practices to be followed for analysing, testing or measuring the property or characteristic.
(2) No regulation that is applicable to a mineral or metal may be made under subsection (1) unless, in the opinion of the Ministers, the natural occurrence, properties and characteristics of that mineral or metal in the environment have been taken into consideration.
- 1999, c. 33, s. 67;
- 2001, c. 34, s. 28(F).
- Date modified:


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|This article does not cite any references or sources. (December 2009)|
The barca-longa was a two or three-masted lugger found on the coasts of Spain and Portugal as well as more widely in the Mediterranean Sea. They were used in Spain and Portugal for fishing but were employed by the Royal Navy in Mediterranean waters, for shore raids or as dispatch boats. In general, they were not in Royal Navy ownership. The Oxford English Dictionary's earliest reference is from 1681. Others are 18th-century.
|This article about a type of ship or boat is a stub. You can help Wikipedia by expanding it.|


The main objective of this post is to give a brief introduction to Homing Missiles in Game (2D). A script for Homing missile is also included and explained in the article.
What is a Homing Missile?
What is the logic behind Homing Missiles?
How to use Homing Missiles in Unity?
Have these Questions in Your Mind?
No worries. You will get a satisfactory answer to all those questions, right here.
Let's, start with Introduction
You might have seen Homing Missiles in many movies.
Real life example of homing missile
Remembered these scenes from "Marvel's The Avengers" movie?
If you are not a Marvel fan don't worry, I am here to help you.
"Homing Missile is the missile which locks target and chases the target until or unless it reaches the target and blasts itself."
There are plenty of games which are using Homing Missiles.
Excited to implement Homing Missiles in your game?
I know you are.
Let's set the scene setup first
Scene Setup:
 1. Create two 2D Objects name them "Missile " and "Target".
 2. Add a Sprite to them. (You can download the project from below link).
 3. Add rigidBody 2D in missile and add Script also name it as "Homing Missile"
How it actually works?
You might think,
It is easy to Implement Homing Missile. Just use MoveToward/Lerp until it reaches the target. Then just write code and look at what is going on in your scene. (try it and then read further to understand)
Working of Homing Missile
It is reaching the target properly but there is no feel of a rocket. (Right Brain:-What is wrong with my code?)
Checkout an actual script for Homing Missiles.
public class HomingMissile : MonoBehaviour
 public Transform target;
 public Rigidbody2D rigidBody;
 public float angleChangingSpeed;
 public float movementSpeed;
 void FixedUpdate ()
 Vector2 direction = (Vector2)target.position - rb.position;
 direction.Normalize ();
 float rotateAmount = Vector3.Cross (direction, transform.up).z;
 rigidBody.angularVelocity = -angleChangingSpeed * rotateAmount;
 rigidBody.velocity = transform.up * movementSpeed;
I think script is short but not a sweet one. You can use this homing missile script for your code.
Don't be scared, I'll show you how to do it.
Let's start with the table to introduce variables:
Variable Name Variable Type Description
rigidBody RigidBody2D rigidBody of the missile to add velocity and change angle.
target Transform To get the position of the Target.
angleChangingSpeed float The speed to change the angle
movementSpeed float Speed of movement
Pure Mathematics: (Open your Brain's left part)
actual path of homing missile
You need to understand this Picture. That's How our Homing Missile Works.
First, what you need is "Direction".
direction= targetPosition (target.position) - missilePosition(rb.position);
vector substraction
This is how subtraction of two Vector happens (Pythagoras Theorem).
Normalization means converting vector to unit vector.
Vector A(3,4)
Normalized(A)=(3/3*3+4*4, 4/3*3+4*4)=(3/5,4/5)
Find Amount of rotation to do that.
Vector Cross Product
Blue Arrow(direction)
Red Arrow(Missile Transform)
green(Resulting Vector).
All three Vectors are perpendicular to each other.that's why we needed z-axis only.
Now we need to change angularVelocity of our rigidBody.
rb.angularVelocity = - angleChangingSpeed * rotationAmount.
Minus Sign(-) is used to reverse the direction of movement.
Adding Velocity to our rigidBody.(just changing the Angle is not Enough).
rb.velocity=tranform.up * movementSpeed.
Stop cheering just yet!
This is not the end!
Missile needs balancing between angleChangingSpeed and movementSpeed.
What if there is no balance between angleChangingSpeed and movementSpeed (Great question! Open right brain is needed here! )
Missile heading to the target
In the above Image, the missile is heading forward to the target, there is no problem here.
velocity force vs angular velocity
In the above Image, the target has moved to a new position. The missile continues to go toward the target due to angular velocity (in red), while still going to the place where the target used to be (in black) due to its velocity. (Thinking what is wrong.?)
velocity force vs angular velocity -2
In the above Image, the missile's velocity forces it to move at the side of the target (black) while the angular velocity tries to pull the missile to the target. (Now you might feel there is something suspicious).
orbit dead loop
In the above Image, the missile falls into a stable orbit around the target and never reaches its goal.
The black arrows indicate a velocity vector while the red lines indicates angular velocity. (That's why need a balance between angleChangingSpeed and velocity).
That is how whole Universe is trapped (Thank God for this error else there is no life!).
Now, How to Fix this Problem?
Well, There is no particular formula to balance them, but by Increasing angle or decreasing velocity will help you there.
 - Don't go with very small speed so your missile loses the feel of Homing Missile and Don't make it Extreme fast it will be trapped in the orbit.
 - Don't make angleChangingSpeed too small else it will fall in to trap and to high angleChangingSpeed loses the feel of your game.
That's It for Homing Missile from my side..!
But I'm Hoping to see your homing Missiles in my comment box as well as in your game.. ;)
Please, do Share our blogs with others if you like our content :)
Feel free to contact us if you really liked this blog. And don't forget to share your comments below!
TheAppGuruz is a leading Mobile Game development company in India. We are proficient in Unity and we have design & developed 500+ Android and iOS mobile games for various client across the globe. If you have any game project that need professional help feel free to contact us.
We provide mobile game development services in countries like US, UK, Australia, UAE, Kuwait, Qatar, India, China, Indonesia, Singapore and European countries
Tune in to our social media for the latest on Facebook | Twitter | Linkedin | YouTube.
I am the person who changed track from Machine Learning Engineer to Game Developer.So, There is Mathematical effect in my Game logic and optimization in Data.Always ready to accept challenges and train my Game.
face mask Belial The Demon Headgear Pocket Staff Magic


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Ariyalur to Cuddalore distance, location, road map and direction
Ariyalur is located in India
at the longitude of 79.08 and latitude of 11.14. Cuddalore is located in India
at the longitude of 79.77 and latitude of 11.74.
- Driving Distance : 126 KM and 354 meters / 78.5 miles.
- Straight Line Distance : 100 KM and 900 meters / 62.7 miles.
- Travel time : 2 hours and 26 minutes.
- Direction and bearing : North East side, 48 degree.
Distance between Ariyalur and Cuddalore
The total straight line distance between Ariyalur and Cuddalore is 100 KM
(kilometers) and 900 meters. The miles based distance from Ariyalur to Cuddalore is 62.7
miles. This is a straight line distance and so most of the time the actual travel distance between Ariyalur and Cuddalore may be higher or vary due to curvature of the road.
The driving distance or the travel distance between Ariyalur to Cuddalore is 126 KM and 354 meters. The mile based, road distance between these two travel point is 78.5 miles.
Time Difference between Ariyalur and Cuddalore
The sun rise time difference or the actual time difference between Ariyalur and Cuddalore is 0 hours, 2 minutes and 45 seconds
Ariyalur and Cuddalore time calculation is based on UTC time of the particular city. It may vary from country standard time, local time etc.
Ariyalur To Cuddalore travel time
Ariyalur is located around 100 KM away from Cuddalore so if you travel at the consistent speed of 50 KM per hour you can reach Cuddalore in 2 hours and 26 minutes. Your Cuddalore travel time may vary due to your bus speed, train speed or depending upon the vehicle you use.
Ariyalur to Cuddalore Bus
Bus timings from Ariyalur to Cuddalore is around 2 hours and 26 minutes
when your bus maintains an average speed of sixty kilometer per hour over the course of your journey. The estimated travel time from Ariyalur to Cuddalore by bus may vary or it will take more time than the above mentioned time due to the road condition and different travel route. Travel time has been calculated based on crow fly distance so there may not be any road or bus connectivity also.
Bus fare from Ariyalur to Cuddalore
may be around Rs.95.
Midway point between Ariyalur To Cuddalore
Mid way point or halfway place is a center point between source and destination location. The mid way point between Ariyalur and Cuddalore is situated at the latitude of 11.442536817488 and the longitude of 79.423003773107. If you need refreshment you can stop around this midway place, after checking the safety,feasibility, etc.
Ariyalur To Cuddalore road map
Cuddalore is located nearly North East
side to Ariyalur. The bearing degree from Ariyalur To Cuddalore is 48 ° degree
. The given North East direction from Ariyalur is only approximate. The given google map shows the direction in which the blue color line indicates road connectivity to Cuddalore. In the travel map towards Cuddalore you may find en route hotels, tourist spots, picnic spots, petrol pumps and various religious places. The given google map is not comfortable to view all the places as per your expectation then to view street maps, local places see our detailed map here.
Ariyalur To Cuddalore driving direction
The following diriving direction guides you to reach Cuddalore from Ariyalur. Our straight line distance may vary from google distance.
Travel Distance from Ariyalur
The onward journey distance may vary from downward distance due to one way traffic road. This website gives the travel information and distance for all the cities in the globe. For example if you have any queries like what is the distance between Ariyalur and Cuddalore? and How far is Ariyalur from Cuddalore?. Driving distance between Ariyalur and Cuddalore. Ariyalur to Cuddalore distance by road. Distance between Ariyalur and Cuddalore is 100 KM / 62.3 miles. distance between Ariyalur and Cuddalore by road. It will answer those queires aslo. Some popular travel routes and their links are given here :-
Travelers and visitors are welcome to write more travel information about Ariyalur and Cuddalore.
- It can be your previous travel experience between Ariyalur and Cuddalore.
- Available transport routes to reach Cuddalore like train routes, bus routes, air routes and cruise routes.
- Tourist places or any other important places on the routes between Ariyalur and Cuddalore.
- Hotels, restaurant information on the way to Cuddalore.
- Photos related to Ariyalur and Cuddalore or en route.
- Travel queries and other relavent information related to this page.


Antos Antler Dog Chew - Large
Antos Antlers are healthy chews for dogs. Antos antlers satisfy a dog's natural urge to chew, whilst also helping to strengthen and clean teeth.
Brand Antos
Manufacturer Antos
Species Dog
Out of stock
What are Antos Antler Dog Chews?
Antos Antlers satisfy a dog's natural urge to chew, whilst also helping to strengthen and clean teeth.
Antos antlers are a naturally grown chew so don't contain nylon like some long-lasting chews. They are not an 'empty' chew like rawhide and contain important minerals.
Even dogs who are losing weight can enjoy Antos antlers because they only contain a tiny amount of fat. Naturally, they don't contain additives or preservatives.
Antos antlers are sourced from naturally shed Red Deer and Fallow Deer antler, much of which is from Scottish highland herds.
Please Note:
Make sure your dog is gnawing on the antler chew and not trying to break it in half. Don't hold the antler chew for him as this may cause him to bear down on it. Leave it for him to work out how to enjoy it. Please don't leave Antos antler chew toys outside in the elements, where other creatures can get to them, to safeguard your dog's health.
Like any dog chew, the following is very important: To avoid a choking risk, take the Antos antler chew toys away from your dog once it gets worn down to a small enough size that your dog could easily swallow. Always supervise your dog when chewing the antos antler chew toy.
What are the benefits of using Antos Antler Dog Chews?
Naturally shed antler
Contain important minerals
Leaves no stains or mess
Helps with dental hygiene
No additives or preservatives
What is in Antos Antler dog chews?
100% Naturally shed deer antler
What size Antos Antler is best for my dog?
Just like with any chew, buying the right size for your dog is important. For example, whilst a toy dog could take on an extra large antler, it would serve no benefit at all and would be quite overwhelming for the dog. Likewise, a giant breed should not be given a small antler.
Size Guide:
Small (50 - 75g) - suitable for toy dogs
Medium (75 - 150g)- suitable for small to medium dogs
Large (150 - 220g) - suitable for medium to large dogs
Extra large (220 - 270g) - suitable for large to giant breeds or dogs with strong jaws
In the very unlikely event that your dog isn't interested in chewing the antler, try rubbing it with sandpaper or a nail file. If your dog still isn't interested in it, try smearing on a small amount of peanut butter or honey, or soaking it overnight in water in the refrigerator.
Remember, Antos antlers are incredibly long-lasting so you may find your dog leaves and goes back to the antler chew many times before it's finished.
Write Your Own Review


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18 TCP Redirect: tcp^ via Channels
The net/tcp-redirect library provides a function for directing some TCP port numbers to use buffered channels instead of the TCP support from racket/tcp.
Returns a unit that implements tcp^. For port numbers not listed in port-numbers, the unit's implementations are the racket/tcp implementations.
For the port numbers listed in port-numbers and for connections to "127.0.0.1", the unit's implementation does not use TCP connections, but instead uses internal buffered channels. Such channels behave exactly as TCP listeners and ports.


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Wind-driven wave heights in the German Bight
- First Online:
- 177 Downloads
Wind speed, friction velocity and significant wave height data from the FINO1 platform in the southern German Bight 45 km off the coast for the years 2004 to 2006 have been evaluated and related to each other. The data show a clear dependence of the hourly mean wave height to the hourly mean friction velocity and wind speed. Wave heights increase with decreasing stratification and increasing fetch. Synoptic weather patterns for the highest wave heights in the southern German Bight are determined. The analysis is made separately for four wind direction sectors. The two strongest storms in the evaluated period, "Britta" and "Erwin", are analysed in more detail. Finally, the 50-year extreme significant wave height has been estimated to be about 11 m most probably coming from northerly directions.


Raising Winter Chicks Part 2
In the last post on raising winter chicks, we talked about the benefits of starting chicks in the winter This post will touch on a few of the concerns people sometimes have about winter chicks: heating requirements, when you can move the chicks out of the brooder, and shipping chicks during cold, winter weather
The Cons of Raising Chicks in the Winter
 1. Where will you keep your chicks?
You will need to consider that baby chicks need a lot of heat, with temperatures around 90F for the first week, and slowly decreasing as


phrases, sayings, proverbs and idioms at
Home button Home | Search the website Search | Phrase Dictionary | Dollars to doughnuts
The meaning and origin of the expression: Dollars to doughnuts
Browse phrases beginning with:
Dollars to doughnuts
Other phrases about:
What's the meaning of the phrase 'Dollars to doughnuts'?
An outcome that is almost assured; a certainty.
What's the origin of the phrase 'Dollars to doughnuts'?
Dollars to doughnuts'Dollars to doughnuts' is one of several 'dollars to...' phrases, like 'dollars to buttons' and 'dollars to cobwebs', which date from 1884 (in G. W. Peck's Boss Book) and 1904 (in The Boston Herald) respectively. Buttons and cobwebs were presumably chosen for their obvious lack of value, but the expressions failed to catch on as they lacked the perky alliteration of 'dollars to doughnuts'.
This is, of course, an American phrase. It is occasionally spelled as 'dollars to donuts', which only emphasis its US origin as, outside the USA, a donut is most definitely a doughnut.
'Dollars to doughnuts' is a pseudo betting term, pseudo in that it didn't originate with actual betting involving doughnuts, but just as a pleasant-sounding alliterative phrase which indicated short odds - dollars are valuable but doughnuts aren't. The phrase parallels the earlier English betting expression 'a pound to a penny'.
The phrase appears to have originated in mid 19th century USA. The earliest citation I can find for it is in the newspaper The Daily Nevada State Journal, February 1876:
Whenever you hear any resident of a community attempting to decry the local paper... it's dollars to doughnuts that such a person is either mad at the editor or is owing the office for subscription or advertising.
It doesn't crop up again in print until some years later, apart from a similar citation in a March edition of the Nevada State Journal, which suggests that the (unnamed) author of those pieces either coined the term himself or appropriated some street slang that he had heard.


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To enable a Mac to boot from a network using the Parallels NetBoot service, the following requirements should be met:
The Mac must obtain its IPv4 address from the local DHCP server.
The following network traffic must be allowed from the Mac to the NetBoot host:
a. HTTP (TCP port 80)
b. TFTP (UDP port 69)
c. BootP/DHCP (UDP port 67)
Note: "Subnet" and "Broadcast domain" are used interchangeably in this document.
Configuration 1: Mac and NetBoot Server in the Same subnet
In this scenario, no specific configuration is required unless a firewall is enabled on the NetBoot server. If a firewall is running on a NetBoot server, then the following firewall rules must be created:
Inbound connections to TCP port 80 from any client must be enabled. This is usually done with the predefined "World Wide Web Services (HTTP Traffic-In)" rule.
- Inbound connections to UDP ports 67 and 69 from any client must be enabled. This is usually done with the predefined "Windows Deployment Services (UDP-In)" rule.
Configuration 2: Mac and NetBoot Server in Different subnets
In this scenario, the NetBoot server and the Mac are located in different subnets, which means that broadcast DHCP requests from the Mac can't reach the NetBoot server. To solve this issue, the administrator should set up DHCP Relay Agent on the client subnet's router (R1), which will forward broadcast UDP traffic as unicast to the NetBoot server.
Cisco has excellent documentation on DHCP Relay Agent feature here
Note: On the layer3-capable switch DHCP Relay Agent must be configured on Vlan interface with an IP address assigned, not a physical uplink interface.
Suppose we have the following network configuration:
FastEthernet0/0 – the network interface on the router R1 which serves the User subnet.
- 172.17.2.100 – IP address of the NetBoot server.
To setup the DHCP Relay 1, you need to enter the following commands on R1:
configure terminal no ip forward-protocol udp 37 no ip forward-protocol udp 49 no ip forward-protocol udp 53 no ip forward-protocol udp 137 no ip forward-protocol udp 138 interface FastEthernet0/0 ip helper-address 172.17.2.100 end
No other devices between the Mac and the NetBoot server require a specific configuration. The administrator should only ensure that HTTP (TCP port 80), TFTP (UDP port 69), and BootP/DHCP (UDP port 67) traffic to the NetBoot server is not blocked.
Configuration 3: Mac, DHCP Server and NetBoot Server in Different subnets
In this scenario, the NetBoot server, the DHCP server and the managed computer are located in different subnets, which means that broadcast DHCP requests from the Mac can't reach the NetBoot server.
If your DHCP server is already set up – you're already using DHCP Relay Agent. Just add a second server to forward DHCP packets to and make sure that the HTTP (TCP port 80), TFTP (UDP port 69), and BootP/DHCP (UDP port 67) traffic is not blocked by your firewall.
If you're planning deployment – you'll need to set up DHCP Relay Agent, and set it to forward DHCP requests to two servers: DHCP server and NetBoot server. See Configuration 2 for more details on setting up DHCP Relay Agent.


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C is for Coven Board Book
C is for Coven is a reinterpretation of a classic alphabet book, matching each letter of the ABCs with a rhyming phrase that teaches kids about witchcraft. Instead of A is for Apple and D is for Dog, A is for Altar and D is for Drawing Down the Moon. This bewitching and adorable board book will make learning the ABCs fun, magical, and memorable for the whole family.
Founded by children's book author Andrea Stein, Moon Dust Press is dedicated to creating resources for children being raised in homes practicing alternative spiritualities, breaking down stereotypes about witchcraft and Pagan practices in children's literature, and providing needed diverse representation.
Moon Dust Press is committed to producing high quality, beautifully illustrated, and entertaining books that allow children and parents to find the magic in every day life


All Policies Include Enhanced COVID-19 Cover
Coronavirus FAQs
Animal therapy used to treat mental health inpatients
10 October 2017 13:05
Stroking rats provokes curiosity and questions
Stroking rats provokes curiosity and questions
Animals are successfully being used to treat Schizophrenia and bipolar disorder at a Manchester hospital.
A seven-week "animal magic" course of therapy uses dogs, rabbits and rats to treat patients with severe and long-term mental health conditions at North Manchester General Hospital.
Noah's ART (Animal Rescue Therapy) assists people in opening up about their problems.
Anyone with long-term mental health issues is reminded of the importance of pre-existing medical travel insurance.
Novel and engaging
Sharon Hall, 54, who set up the scheme, says: "A lot of the time the animals can be a real comfort - and the simple physical connection of holding or cuddling an animal can bring profound relaxation even at a time of major mental or emotional anguish."
Noah's Art is one of 35 mental health and well-being initiatives funded by £330,000 in grants from Manchester Health and Care Commissioning.
Ms Hall, a former mental health nurse, says the project helps patients break down barriers and start conversations.
"A lot of the session is non-verbal - and people can just sit and spend time with the animals enjoying a quiet bond," she says, adding that the feedback so far has been "quite magical".
The novel therapy even appeals to disengaged patients.
Occupational therapists at the hospital say the sessions are attracting men who wouldn't normally get involved in group activities.
'A ray of light'
Playing with Moose - a King Charles Cavalier Spaniel puppy - helped Ms Hall cope with the grief of losing her parents, prompting her to set up Noah's ART.
Moose is now used in the sessions along with Maggie - a Jack Russell - rabbits, guinea pigs, rats and even a mouse.
"When people can enjoy animals it can be that small ray of light that gives hope for enjoying other things in life too," Ms Hall added.


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In 70-80% of cases, as a rule, the breakdown is insignificant and charge will be about $165-195
We will not charge you for labor if the problem will be just with circuit breakers, lost power, damaged power outlet, clogged sewerage and etc.
We Service All Major Brands & Models
Microwave Oven Common Problems
If the microwave door does not open, the door opening mechanism has failed. To find the place of breakdown, it is best to give the microwave oven to a service center or go to specialists from Fuse Appliance Repair. I do not advise you to try to open the door with effort. You can damage both the door itself and cause additional damage to the mechanism of its opening.
- Rotary table.
The small power of the electric motor of constant rotation of the turntable in the microwave oven is not uncommon for these motors, since they wear out with age.
Sometimes the breakdown will be unexpected and the turntable will stop. But sometimes the engine starts to make strange noises, which indicate the impending trouble.
- Failure of the exhaust fan.
Like the rotary table, the exhaust fan is powered by a small motor that runs constantly. Sometimes the fan motor and the table are common. The failure of the electric motor of the fan often occurs suddenly, and sometimes they break down gradually, making some strange and unusual sounds in the process of work.
- Malfunction of mixer motor.
The mixer in your microwave oven is a small metal blade that continuously rotates, while the oven is running. The purpose of the mixer is to make sure that the microwave energy in the oven is evenly distributed. This helps to prevent uneven cooking or heating food.
As with the exhaust fan and the turntable, the mixer motor breaks down gradually, producing unusual sounds during operation. The impending breakdown of the mixer motor can often be accompanied by a strange grinding noise.
- Problems with the magnetron.
Magnetron can be considered the heart of a microwave oven. It generates microwave radiation, which prepares food. This happens by converting electricity into microwave energy of the appropriate frequency.
A good magnetron works almost silently. But as soon as the end of their working life comes to an end, they start to make strange sounds. The noise of a defective magnetron can range from a rather shrill howling to growling or rumbling.
You should know that if the furnace magnetron has already begun to emit these noises, then this is not dangerous. But it is a sure sign of an impending breakdown. Call the wizard as soon as you start to notice these sounds, and he will help you avoid the failure of the microwave oven at an inconvenient time.
This problem begins to manifest itself due to untimely care of the microwave, traces of fat and food accumulate on the walls of the microwave and it starts to spark, all microwaves have a mica plate that is a dielectric, that is, a material through which any radio waves easily pass. For the mica is installed magnetron, with the help of which our food is heated. As a rule, when the microwave begins to spark, then the mica and the magnetron cup are burnt, but there are also cases when the magnetron itself breaks down, so if your microwave sparkled, do not turn it on any more, and replace the mica and Check the magnetron cap.
The paint on the inside of the microwave oven can be chamfered. If the paint is beveled, the inner metal will be opened, resulting in a microwave sparking or blowing. Check the inside of the microwave oven in any places where the paint has broken away. If there are damaged spots, touch them with the microwave oven's paint.
Most microwave ovens have internal lighting that turns on when they are warmed up or when the door is opened. This light is not necessary for microwave operation, but it is much more convenient to use with it. If the bulb in the microwave is burnt out, you can carefully disassemble the microwire and replace the bulb or consult technicians from Fuse Appliance Repair.
Every thing, be it an electrical appliance or some kind of mechanism, has its expiry date and resource of work. In our world there is nothing eternal and the magnetron is no exception. The resource of operation of the magnetron directly depends on the mode of its operation. The more intensive the microwave oven, the less the magnetron will serve. In the course of long operation, the magnetron "ages and wears out", resulting in such a malfunction as the loss of cathode emission, i.e. The cathode region is depleted with time, and it loses its ability to emit electrons into the working region, which causes the magnetron to stop working. The second malfunction that can occur during long operation is a break in the filament. In this case, you can give an example of an ordinary incandescent lamp, no matter how much it would not shine to you, sooner or later, it will still burn out. As a result of the breakage of the filament, approximately the same situation arises as in the first case. The cathode is not heated, hence – there is no emission. These two malfunctions are often encountered in practice, and if we theorize theoretically, we can assume that a third malfunction occurs as a result of a prolonged operation of the furnace – this is a failure of the magnetic system of the magnetron. In the event of a malfunctioning of the magnetic system, the electrons will simply fly from the cathode to the anode, they will not "circulate" along the anode surface and the microwave oscillations in the resonators will not arise. In practice, it was in magnetrons that I did not see this, but it was found in other devices containing permanent magnets. From time or under the influence of external factors, a permanent magnet can lose its properties (demagnetize).
Warning: A microwave oven can store a deadly amount of electricity (up to 5000 volts) in its high-voltage capacitor even after the microwave oven is disconnected from the mains. It is therefore extremely important to replace the electronic components in the microwave oven, only a licensed technical can lock them).
Another very common malfunction of the magnetron is the breakdown of the pass-through capacitors of the magnetron filter. Check it out, the same simple, by the same tester. In the resistance measurement mode, you need to touch the probes of the device with one of the power terminals of the magnetron and its housing. If the device shows "infinity" – the capacitors are in good order (bottom picture). If the device shows any resistance, then one of the capacitors is broken or in a leak. If there are other serviceable capacitors, they can simply be replaced, if not, then it is better to replace the magnetron with a known good.
- Door switch
There are many reasons why your microwave oven does not turn on, one of which can be a faulty door switch. A door switch, known as a lock switch, signals to other microwave components to start the power supply when the door is closed and stop when the door is opened. For this reason, everything else can appear in working order, but the microwave will not start to heat up. To access the door switch or the lock switch, turn off the microwave oven and remove the cabinet. The switches have terminals designated C for general and NO for normally open. Check each terminal with a multimeter to ensure continuity. If at the time there is, then it means that the switch is working. If there is no circuit, replace the switch. You can also take this opportunity to make sure that the door hooks work correctly.
- Ceramic fuse
If your microwave oven does not start and the display is empty and does not respond, the problem may be related to the ceramic fuse. This part protects other microwave components from power fluctuations and leads to a total loss of power when it fails, that is, your microwave oven will not work. To access the ceramic fuse located inside the cabinet next to the power cord, first turn off the microwave oven. Use a multimeter to check the integrity of the fuse. If you are aware of the cause of a fuse failure, such as opening or closing a microwave door, you can also check the door switch to make sure it works. If you do not know the cause of the fuse failure, you can test other microwave parts, such as a magnetron, a high voltage diode, a capacitor and a transformer.
- Thermal fuse or cut-out
The problem with a thermal fuse or cutout can be the reason that your microwave oven does not turn on. Thermoswitches, also known as thermal fuses, help to keep the furnace from overheating. When the heat outputs do not work, your microwave oven does not turn on as a precaution so that it does not heat up. To access the thermal switches, first turn off the microwave oven, and then remove the cabinet. After you find the thermal fuse, disconnect its wires from the terminals. Use the multimeter to check for continuity and replace the thermal cutouts if there is no continuity. Take this opportunity to also check if the cooling fan is working, or to cause the microwave to overheat, shutting off the airflow.
- Door Latch
Your microwave oven may not start due to a problem with the door latch. Most of the door latches are made of plastic hooks that stick out of the door and lock the door switch when the door is closed, signaling the rest of the controls to turn on the microwave. If the hooks are damaged or do not have tension due to worn springs, the switch will not click, which means that the microwave oven does not turn on. To gain access to the door latch, first unplug the microwave oven from the power source and remove the inner door panel


text:
1. Dial your office extension (701-845-7XXX) from any phone off campus and wait for it to get to voicemail.
2. When your voicemail greeting begins press the star key (*) on your phone.
3. When prompted enter your extension 37XXX followed by the pound or hashtag key (#)
4. When prompted enter you voicemail PIN follow by the pound or hashtag key (#).
5. Your are now at the Unity Connections voicemail menu. Press 4 on your phone keypad to begin setup options.
6. Press 1 on your phone keypad to change your greetings.
7. Press 1 on your phone keypad to rerecord your standard greeting or Press 3 on your phone keypad to edit all other greetings.
8. If you press 3, follow the menu options to edit the other greetings.


text:
|The Field Description of Igneous Rocks, Second Edition|
|by ||Dougal Jerram|
|Year Published: ||2011|
|Total Pages: ||256|
|Product Code: ||ROCKS|
|The Second Edition of this unique pocket field guide has been thoroughly revised and updated to include advances in physical volcanology, emplacement of magmas and interpreting structures and textures in igneous rocks. The book integrates new field based techniques (AMS and geophysical studies of pluton shape) with new topics on magma mixing and mingling, sill emplacement and magma sediment interaction. Part of the successful Field Guide series, this book includes revised sections on granitic and basaltic rocks and for the first time a new chapter on the engineering properties of igneous rocks.
The Geological Field Guide Series is specifically designed for scientists and students to use in the field when information and resources may be more difficult to access.
Many editions have been updated for 2011 and the guides are:
- Student-friendly in design and cost


Indian sub-continent voters to play a decisive role in general election
Over 25 constituencies have 40 per cent voters from ethnic minorities
14th April 2010: Indian sub-continent voters will play a more decisive role in the 2010 general election than ever before.
A new research suggests nothing less than 25 parliamentary constituencies have more than 40 per cent of their voting population from ethnic minorities. In fact, the voters are from the Indian, Pakistani and Bangladeshi communities.
The parliamentary constituencies where over 40 per cent of the population was categorised as being from an ethnic minority in the 2001 census include East Harrow 66.3 per cent, Birmingham Ladywood 64.9 per cent, Birmingham Sparkbrook and Small Heath 64.8 per cent, and Brent South 64.6 per cent.
The research, by Prof. Muhammad Anwar of the University of Warwick, even suggests they are more likely to turn out to vote than their white neighbours.
Prof. Anwar has asserted that ethnic minorities voter registration is approaching levels of white voters; and their turnout is now higher than the national average.
In the previous general election held in 2005, the national average turnout was 61.4 per cent, but for Bangladeshi voters it was 76 per cent, Pakistanis 70 per cent and Indians 67 per cent.
The higher levels of turn-out among Asians and particularly Muslim groups are likely to continue in future.
The findings come just about for weeks before the general elections.
The research says the minorities are still 'massively undervalued and under-represented', even though the ethnic minority vote will be more important than ever before.
Prof. Anwar says in recent years Muslims in Britain and elsewhere have become a focus of attention for politicians and the media. As such, Muslims themselves have become more conscious of their rights and responsibilities as British citizens, including participation in the electoral process.
UKIP calls for end to mass uncontrolled immigration
Let illegal immigrants become British citizens: Lib-dem


Duct designform >
Fan, AHU calculation
If calculating to ACH:
If calculating to recommended fresh air to occupants:
FAN DUTY SELECTION (ventilation only) Free to download and use! Importantly select either Metric or Imperial units,
 Enter dimensions of area, amount of air changes required, select "Enter" the tool will return the necessary VOLUME of air required.
If the user requires VOLUME of air per person, simply enter required Volume M3/m / CFM then number of occupants, select "Enter" the tool will return necessary VOLUME.
Also included the conversion of the most used units to cubic Meters per Hour.
Please support this site
 Having determined the VOLUME the calculation of the Duct size requires the VELOCITY, The Velocity is obtained with either experience or recommendations by HVAC organisations. Depending on the application the VELOCITY can vary between as little as 200 FPM/60 MPM (low pressure) to above 5,800CFM/ 1800 MPM (high pressure). For the same VOLUME of air the smaller the Duct will result in higher VELOCITY creating more FRICTION loss through the Duct.


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Is there a command that ignores the following character, in the same way that \^ puts a hat over the following character?
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2 Answers 2
up vote 5 down vote accepted
I don't know if one exists already, but issuing the directive
will do the trick: \?abc gives bc, and so on.
Edit: Here is a discussion of the question Tim N raised in the comments: getting a \caption to drop the final period in a figure number. It does not work, even in the default article class, to just let
which gives a few errors, the first of which is actually "Argument of \? has an extra }" and not "Paragraph ended before \? was complete" (that's the second). A little \tracingmacros-trawling reveals the following phenomenon: when \caption is called, it first increments the figure counter, which calls \refstepcounter so it can be referenced, which sets up (using \edef) the current label \_USER_ for \ref, which (finally) must contain the value of \thefigure! And guess what: the extra period does not appear after \thefigure in this context, so the \? gobbles the closing brace of the \edef command. Hence the error.
Let's see if we can get what you want. The caption line is constructed in several stages, which in article consist of the following discrete steps:
 - Generate the caption "number" (the text "Figure 1.2.", for example);
 - Attach it to the caption "text" (the argument of \caption) by, for example, inserting a colon and a space between them.
These correspond to the internal macros \fnum@figure and \_USER_, which are defined by the document class, and obviously vary; it seems that Tim N's packages are putting extra periods in, but who knows whether it's in the first stage or the second? Or even in \thefigure itself? Depending on where it happens, you need a different workaround:
 - If someone erroneously defined \thefigure to contain an extra period, and you know how the rest of the number ought to look, then you can just redefine it. Since there's no way to gobble the previous character, if my solution below doesn't work for you, then you should try this.
 - If \fnum@figure somehow puts a period after the value of \thefigure, then under some circumstances you will be able to remove it using \?. For example, if they modified the default article definition (see below) then putting \? right after \thefigure will do the trick. However, if they produce the period by some clever device, you will have to be equally clever to unravel it.
Here is that definition:
% The default def'n doesn't have the period
 - Finally, suppose that the period is inserted in \_USER_. Then you may be able to catch it with \?, but only if the command that produces the "number" is dropped in as-is and not fully expanded first. This is the case in the article class and, we hope, also in whatever your situation is.
So it appears the goal is to stick \? right after \thefigure as it appears in \fnum@figure only. You want to patch a command, and there are several ways to go about this, but the etoolbox package is generally useful so I'll go with it. See the following minimal document:
% Cute but not necessary here:
% \def\?#1{}
% BAD:
% \renewcommand\thefigure{\arabic{figure}\?}
 \caption{A figure}
Since we are going with \makeatletter anyway, I figure the internal \_USER_ command that Yiannis pointed out is probably the wiser course, though \? is nice if you are putting it in ordinary text.
share|improve this answer
In the LaTeX kernel you find \_USER_. – Yiannis Lazarides Jan 10 '12 at 0:03
_USER_: Oops, yes. Though it does need to be swaddled in \makeatletter...\makeatother. – Ryan Reich Jan 10 '12 at 0:08
My goal was an ugly hack, to \renewcommand \thefigure to end with this, because for some interaction between packages, my figure captions started showing up as "Figure 1.2.:" with an extra period. The period can be made invisible by ending with \color{white}, but trying to \? it results in:! Paragraph ended before \? was complete. – Tim N Jan 10 '12 at 0:12
I should add that ending with \^ does put a hat over the dot. – Tim N Jan 10 '12 at 0:12
You mention "because for some interaction between packages". There could be other ways around this, for which one would need to see a minimal working example (MWE) that illustrates your problem. However, for now, this question is most likely "answered". You could post a follow-up question. See I've just been told I have to post a follow-up question, why and how? – Werner Jan 10 '12 at 0:27
You could try the following:
It simply consumes its argument but doesn't use it.
share|improve this answer
My goal was an ugly hack, to \renewcommand \thefigure to end with this, because for some interaction between packages, my figure captions started showing up as "Figure 1.2.:" with an extra period. The period can be made invisible by ending with \color{white}, but trying to \swallow it results in:! Argument of \swallow has an extra }. – Tim N Jan 10 '12 at 0:10
_USER_: Then the dot is added outside of the current brace group. You might want to use the caption package instead to change the caption format. – Martin Scharrer Jan 10 '12 at 0:28
_USER_: I see. Still, \^ does what it does, so I suppose it's not impossible to solve? – Tim N Jan 10 '12 at 0:33
Your Answer


text:
In probability theory, a conditional expectation (also known as conditional expected value or conditional mean) is the expected value of a real random variable with respect to a conditional probability distribution.
The concept of conditional expectation is extremely important in Kolmogorov's measure-theoretic definition of probability theory. In fact, the concept of conditional probability itself is actually defined in terms of conditional expectation.
Let X and Y be discrete random variables, then the conditional expectation of X given the event Y=y is a function of y over the range of Y
where is the range of X.
A problem arises when we attempt to extend this to the case where Y is a continuous random variable. In this case, the probability P(Y=y) = 0, and the Borel–Kolmogorov paradox demonstrates the ambiguity of attempting to define conditional probability along these lines.
However the above expression may be rearranged:
and although this is trivial for individual values of y (since both sides are zero), it should hold for any measurable subset B of the domain of Y that:
In fact, this is a sufficient condition to define both conditional expectation and conditional probability.
Formal definition
Note that is simply the name of the conditional expectation function.
A couple of points worth noting about the definition:
- This is not a constructive definition; we are merely given the required property that a conditional expectation must satisfy.
- The required property has the same form as the last expression in the Introduction section.
- Existence of a conditional expectation function is determined by the Radon–Nikodym theorem, a sufficient condition is that the (unconditional) expected value for X exist.
- Uniqueness can be shown to be almost sure: that is, versions of the same conditional expectation will only differ on a set of probability zero.
- The σ-algebra controls the "granularity" of the conditioning. A conditional expectation over a finer-grained σ-algebra will allow us to condition on a wider variety of events.
- To condition freely on values of a random variable Y with state space, it suffices to define the conditional expectation using the pre-image of Σ with respect to Y:
- This suffices to ensure that the conditional expectation is σ(Y)-measurable. Although conditional expectation is defined to condition on events in the underlying probability space Ω, the requirement that it be σ(Y)-measurable allows us to condition on as in the introduction.
Definition of conditional probability
For any event, define the indicator function:
which is a random variable with respect to the Borel σ-algebra on (0,1). Note that the expectation of this random variable is equal to the probability of A itself:
Then the conditional probability given is a function such that is the conditional expectation of the indicator function for A:
In other words, is a -measurable function satisfying
A conditional probability is regular if is also a probability measure for all ω ∈ Ω. An expectation of a random variable with respect to a regular conditional probability is equal to its conditional expectation.
- For the trivial sigma algebra the conditional probability is (almost surely) a constant function,
- For, as outlined above,.
Conditioning as factorization
In the definition of conditional expectation that we provided above, the fact that Y is a real random variable is irrelevant: Let U be a measurable space, that is, a set equipped with a σ-algebra of subsets. A U-valued random variable is a function such that for any measurable subset of U.
We consider the measure Q on U given as above: Q(B) = P(Y−1(B)) for every measurable subset B of U. Then Q is a probability measure on the measurable space U defined on its σ-algebra of measurable sets.
Theorem. If X is an integrable random variable on Ω then there is one and, up to equivalence a.e. relative to Q, only one integrable function g on U (which is written ) such that for any measurable subset B of U:
There are a number of ways of proving this; one as suggested above, is to note that the expression on the left hand side defines, as a function of the set B, a countably additive signed measure μ on the measurable subsets of U. Moreover, this measure μ is absolutely continuous relative to Q. Indeed Q(B) = 0 means exactly that Y−1(B) has probability 0. The integral of an integrable function on a set of probability 0 is itself 0. This proves absolute continuity. Then the Radon–Nikodym theorem provides the function g, equal to the density of μ with respect to Q.
The defining condition of conditional expectation then is the equation
and it holds that
We can further interpret this equality by considering the abstract change of variables formula to transport the integral on the right hand side to an integral over Ω:
This equation can be interpreted to say that the following diagram is commutative in the average.
E(X|Y)= goY Ω ───────────────────────────> R Y g=E(X|Y= ·) Ω ──────────> R ───────────> R ω ──────────> Y(ω) ───────────> g(Y(ω)) = E(X|Y=Y(ω)) y ───────────> g( y ) = E(X|Y= y )
The equation means that the integrals of X and the composition over sets of the form Y−1(B), for B a measurable subset of U, are identical.
Conditioning relative to a subalgebra
There is another viewpoint for conditioning involving σ-subalgebras N of the σ-algebra M. This version is a trivial specialization of the preceding: we simply take U to be the space Ω with the σ-algebra N and Y the identity map. We state the result:
Theorem. If X is an integrable real random variable on Ω then there is one and, up to equivalence a.e. relative to P, only one integrable function g such that for any set B belonging to the subalgebra N
where g is measurable with respect to N (a stricter condition than the measurability with respect to M required of X). This form of conditional expectation is usually written: E(X | N). This version is preferred by probabilists. One reason is that on the Hilbert space of square-integrable real random variables (in other words, real random variables with finite second moment) the mapping X → E(X | N) is self-adjoint
and a projection (i.e. idempotent)
Basic properties
Let (Ω, M, P) be a probability space, and let N be a σ-subalgebra of M.
- Conditioning with respect to N is linear on the space of integrable real random variables.
- More generally, for every integrable N–measurable random variable Y on Ω.
- for all B ∈ N and every integrable random variable X on Ω.
- Conditioning is a contractive projection
- for any s ≥ 1.
See also
- Law of total probability
- Law of total expectation
- Law of total variance
- Law of total cumulance (generalizes the other three)
- Conditioning (probability)
- Joint probability distribution
- Disintegration theorem
- Loève (1978), p. 7
||This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. (November 2010)|
- Kolmogorov, Andrey (1933). Grundbegriffe der Wahrscheinlichkeitsrechnung (in German). Berlin: Julius Springer.[page needed]
- Loève, Michel (1978). "Chapter 27. Concept of Conditioning". Probability Theory vol. II (4th ed.). Springer. ISBN 0-387-90262-7.[page needed]
- William Feller, An Introduction to Probability Theory and its Applications, vol 1, 1950[page needed]
- Paul A. Meyer, Probability and Potentials, Blaisdell Publishing Co., 1966[page needed]
- Grimmett, Geoffrey; Stirzaker, David (2001). Probability and Random Processes (3rd ed.). Oxford University Press. ISBN 0-19-857222-0., pages 67-69


text:
Toybox Shape Sorting House
Let's match up the shapes and slot them through the holes with the Early Learning Centre Shape Sorting House.
The perfect addition to your toy box, this sorting house is both fun and educational! Choose a shape and figure out where it fits. Can you match the colours and shapes and name each of them. When you're done, lift the roof or open the door and start all over again.
Sorting the shapes helps children develop with fine motor skills.


text:
Juan Marichal (historian)
Juan Marichal (February 2, 1922 – August 9, 2010) was a Spanish-Canarian historian, literary critic and essayist. Marichal also served as a professor at Harvard University. Marichal spent years in exile during the Franco dictatorship following the end of the Spanish Civil War.
Marichal was born on February 2, 1922, in Santa Cruz de Tenerife, Canary Islands, Spain. He moved with his family to Madrid in 1935. However, he soon relocated to both Valencia and Barcelona before attending school in Paris, France. He graduated from French lycee in Casablanca, near the end of the Spanish Civil War.
In 1941, Marichal boarded a ship with other exiles from the Spanish Civil War and sailed from Casablanca to Mexico at just 19 years old. He enrolled at the National Autonomous University of Mexico, where he studied literature and philosophy. He worked at a box factory as a student to pay for his tuition.
Marichal became a professor at Luis Vives Institute, an organization in Mexico founded by Spaniard exiles. He moved to the United States, where he enrolled as a doctoral student at Princeton University in New Jersey due to a scholarship obtained for him by Edmundo O'Gorman, a Mexican historian and philosopher. Marichal received his doctorate in literature from Princeton University in 1949.
Marichal taught literature at Harvard University in Massachusetts after obtaining his doctorate, where his courses, which focused on Spain and the Spanish-language, included El Cid. He later spent more than 10 years writing his most famous work, The Complete Works of Manuel Azaña, a Spanish politician. He also published the writings and works of his father-in-law, Spanish poet Pedro Salinas, Three Voices of Pedro Salinas, in 1976. Marichal was a recipient of the Spain National Prize in Literature in 1996 for his work as a historian and was awarded the Canary Prize for Literature in 1987.
Juan Marichal died on August 9, 2010, at his home in Cuernavaca, Morelos, Mexico, at the age of 88. His death was announced by the regional government of the Canary Islands. He was predeceased by his wife, Solita, the daughter of poet Pedro Salinas.. The couple had one son.
- "Historian and Essayist Juan Marichal Dies". Latin American Herald Tribune. 2010-08-09. Retrieved 2010-08-21.
- "The Canary Islands mourn the death of Juan Marichal". Tenerife News (Canary Island News). 2010-08-11. Retrieved 2010-08-21.
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think you know) it's not too hard to show that $\mathcal{T} \to Hom(\mathcal{S}, \mathbb{Z})$ and $\mathcal{S} \to Hom(\mathcal{T}, \mathbb{Z})$ are injections. This alone is enough to imply that the pairing is nondegenerate, hence becomes perfect after extending scalars to $\mathbb{Q}$.
So it suffices to show either that $\mathcal{T} \to Hom(\mathcal{S},\mathbb{Z})$ is surjective, or that $\mathcal{S} \to Hom(\mathcal{T},\mathbb{Z})$ is surjective (because the cokernels of these maps are finite groups of the same order, equal to the det of the matrix of the pairing with respect to $\mathbb{Z}$-bases of either side).
You seem to be trying to do the first, but the second is (I think) easier. Let $\phi \in Hom(\mathcal{T},\mathbb{Z})$ and consider the formal power series $f = \sum_{n \ge 1} \phi(T_n) q^n$. It's clear that $f \in \mathbb{Z}[[q]]$; but also that $f \in S_k(\Gamma, \mathbb{Q})$, so $f \in \mathcal{S}$. Clearly we have $(T_n, f) = a_n(f) = \phi(T_n)$ and thus we're done.
Now you can construct a "Miller-like" basis as follows. [EDIT: This doesn't actually work, see comments.] The $T_n$'s generate $\mathcal{T}$, so there is some finite subset which is a $\mathbb{Z}$-basis of $\mathcal{T}$; let these be $T_{n_1}, \dots, T_{n_d}$. Then there is a dual basis $f_1, \dots, f_d$ of $\mathcal{S}$ such that $(T_{n_i}, f_j) = \delta_{ij}$, and there are your Miller-like basis. (You can't necessarily take the $n_i$ to be $\{1, \dots, rk(\mathcal{S})\}$ though, as your example above shows.)
share|cite|improve this answer
Thank you for this nice answer... I have one comment on the last sentence though: take $n, m$ with $n \neq 1, m \neq 1$ and $(n,m)=1$ then $\mathbb{Z} = \mathbb{Z}n + \mathbb{Z}m$ but there is no subset of $\{n, m\}$ that is a basis for $\mathbb{Z}$, so... how precisely do you want to find these $T_{n_1},..., T_{n_d}$? – Fabian Werner Jan 24 '12 at 14:17
Maybe another comment: Isnt it true that Shimura also proves that there exists a basis $f_1,..., f_n$ of modular forms for $\Gamma(N)$ such that all the Fourier coefficients are integers? Furthermore, the Hecke algebra of $\Gamma(N)$ is commutative and looks quite similar to the one for $\Gamma_0(N)$, so i dont see a reason why the result should not hold for $\Gamma(N)$ as well... (?) – Fabian Werner Jan 24 '12 at 14:36
Yes, you are quite right; my argument does not, in fact, show that there is a finite subset of the $T_n$ that is a basis for $\mathcal{T}$. Sorry, dumb mistake. – David Loeffler Jan 24 '12 at 14:52
As for your second comment: everything I said for $\Gamma_0(N)$ goes over verbatim to any group $\Gamma$ intermediate between $\Gamma_0(N)$ and $\Gamma_1(N)$. Since we can conjugate $\Gamma(N)$ to a subgroup intermediate between $\Gamma_0(N^2)$ and $\Gamma_1(N^2)$, this covers the $\Gamma(N)$ case as well. But if you take some totally generic congrence subgroup $\Gamma$ of level $N$ it's not even clear how to define $T_p$ for $p$ dividing $N$; you can certainly take the double coset $\Gamma \begin{pmatrix} 1 0 0 p \Gamma$ but this might not do anything remotely nice on $q$-expansions. – David Loeffler Jan 24 '12 at 14:54
Sorry, that should say $\Gamma \begin{pmatrix} 1 & 0 \\ 0 & p \end{pmatrix} \Gamma$, obviously. – David Loeffler Jan 24 '12 at 14:55
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- Boy Names
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Abiodun - Name Meaning, Origin & Popularity
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- A-B-I-O-D-U-N, is a 7-letter male given name.
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- ah BEE o doon
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