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For the latest updates to Global Public Square, including show information and Fareed's Take, visit the new GPS site on CNN.com.
Blue troll is busy for now.
He went to Jack.Off with a picture of his mother in tights.
Actually. Blue troll went to Jack.Off with his mommies panties.
@chrissy. ..Nailed it!
........Nailed it!!
There is a big market for used condoms in India. These hindus are so cheap. They wash 'em and reuse 'em and then blow them as baloons
Hi. I'm Jessup. I eat kitty poop from Hammond Louisiana. It is very good.
Tastes like chicken
I am from Pakistan. I eat camel poop. Good mmmmm
Tastes like chicken
I drink the left over juice in used condoms which I find in alleys in Milwaukee.
Good juice. Much protein.
Tastes like liquid chicken
I drink man juice.
I drink s.p.e.r.m. very good.
Tastes like chicken
You dirty b as tard!
Highest and best use of hindus? As toilets. Mouth open turn them around and lay them down face up. Then take a big dump in their mouth. Use face as overflow
Hi. I eat horse poop from India. So so good. .
Tastes like chicken
If i ever see a hindu die on the roadside, i would walk right by him without calling for help. This is how much i dislike the DNA they are made of based on their acts and comments on these forums. And i am not even an interested party and probably more educated than most on this forum
I drink guy S.P.E.R.M.
Very nice. Sweet
Mother's milk is to babies what raypes and terrorism is to hinddoous
I like men from India. I smell their BO for my pleasure.
I drink their s.p.e.r.m
So...if no toilets in India's buildings how do women p ee standing up through an open window with wind blowing in her direction.
:::20% of women or 140 million women have been gang rayped in India
:::60% of men or 420 million men in India think that gang rayping and burning the wife alive for dowry by spraying kerosene and lighting her up is acceptable.
Hi. I drink cow p.p. and eat cow poo.poo. very good.
Tastes like chicken
Hi. I'm Casper. Tis true. Tis so. I eat piggy poo poo. Very good.
Tastes like chicken
Jack Mayflower drinks out of toilets in India. He eats piggy poop from Bombay
Tastes like chicken
Oh yea!??!
Casper Chattingham drinks donkey p.p. from toilet bowls in Milwaukee.
And he eats doggie poop
Ok guys. Come on. Let's get along.
You both eat doggie poop from Milwaukee
@Jesus Jimenez. Nailed it!
I eat Pepe's poop. LMFAO! !
On behalf of all jobless Hindus, I apologize for the caustic comments being made. You see for most of us this is the only form of entertainment we have. As you'll probably have also figured out our IQ level is very low due broken down school system in India and DNA
Apologies accepted, hindoo boy. Dont repeat.
I eat Jim's boogers. ..LMFAO !
Some purple colored, dhoti wearing hinddoou terrorist/raypists troll/s squatting in a cave in India. Rubbing mustard oil on his d ik trying to m asturbate looking at Durga Maa's photo. Incense made out of cow d ung is burning nearby. Suicide belt hangs on wall. Human feces all over the floor.
:::95% of India does not have toilets or plumbing
:::40% of raypes in India happen in bushes where women go to defecate and another 25% on rail tracks: SOURCE: Hallop Polls
:::73% of Indians admit to being seyxually abused by their fathers
Didn't Modi (Indian Prime Minister) raype his underage wife?
I pick my nose. I eat my moist salty gooey boogers. Great.
Tastes like chicken LMFAO
Hi. I'm Sanjay. I eat kitty poop from Milwaukee. Crunchy version. Excellent.
Tastes like chicken LMFAO
Howdy. Me Pepe. Me poop. Me eat me poop.
Tastes like chicken
We hindus are raipists. I gang raiped three girls in New Deli, India last night.
Good morning!
I eat piggy poop. Special. Imported from India. And I eat Anna's boogers.
Tastes like chicken LMFAO
Hi. Cook our today. My house.
Grilled kitty poop from India. Good
Tastes like chicken LMFAO

subset: commoncrawl


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"When you see a woman wearing McQueen, there's a certain hardness to the clothes that makes her look powerful." — Alexander McQueen
Alexander McQueen: Savage Beauty. By Andrew Bolton with contributions by Susannah Frankel and Tim Blanks. Photographs by Sølve Sundsbø. Metropolitan Museum of Art, 240 pp., $45.
By Janice Harayda
Americans know Alexander McQueen mainly through the wedding dress his design firm created after his death for Kate Middleton, a gown demure except for its plunging neckline. But he made his name with clothes that took more risks – anatomically correct bodices, trousers that showed "bum cleavage," a jacket imprinted with an image from the painting The Thief to the Left of Christ. On the cover of this catalog for a show at the Metropolitan Museum of Art, a hologram turns a portrait of McQueen into a skull. It's visual metaphor not just for his suicide at the age of 40 but for the difficulty of pinning down a man who made armadillo-shaped shoes fanciful enough for Lady Gaga and hand-carved wooden leg prostheses practical enough for a Paralympics champion.
Alexander McQueen suggests but does reconcile the contradictions of its subject. The London-born McQueen had Scottish roots and professed to deplore the romanticizing of the land of his ancestors. But he created romantic clothes for collections that invoked two of the greatest tragedies in Scottish history. In "Highland Rape," he used luxurious, torn fabrics as a lament for the eviction of thousands of Scots from their lands during the Highland Clearances, an event he called "genocide." And in "Widows of Culloden" he embellished tartans with jet beads in memory of the dead in the 1746 battle. If Scottish history isn't romantic, why honor it with "romantic" clothes? If the Clearances were genocide, what makes "Highland Rape" morally better than designs inspired by Nazi death camps? Any beauty in the clothes co-opts the tragedies that gave rise to them. It's as though Ralph Lauren's more aggressive and ghoulish younger brother had created collections called "Antietam" and "Widows of 9/11."
McQueen's contractions may reflect his early work as a costume-cutter for London shows that included, he says, Les Misérables. Many of his designs, such as a winged, hooded dress made of black duck feathers, suit the stage better than the street. They look more like costumes than clothes, even for women who attend events that justify spending $20,000 for a gown. And unlike Middleton's wedding dress, they are memorable less for their elegance than for their theatricality. Conventional elegance seems to have held little interest for McQueen, who said he wanted to "empower" women by making people afraid of them: "When you see a woman wearing McQueen, there's a certain hardness to the clothes that makes her look powerful." Middleton showed courage in choosing the firm of a designer who once said of his runway shows: "I don't want to do a cocktail party. I'd rather people left my shows and vomited."
Best line: A quote from McQueen: "[I design from the side,] that way I get the worst angle of the body. You've got all the lumps and bumps, the S-bend of the back, the bum. That way I get a cur and proportion and silhouette that works all the way round the body."
Worst line: More quotes from McQueen: "I hate it when people romanticize Scotland. There's nothing romantic about its history." And this one about "Highland Rape": "Fundamentally, this collection is luxurious, romantic but melancholic and austere at the same time."
Recommendation? This book doesn't include a photo or information on Kate Middleton's wedding dress, so it's not for anyone who is looking for those things. But it could make a good gift for people — and there were many of them — who couldn't get into the Met show or spend as much time as they wanted there.
Published: May 31, 2011
Furthermore: Alexander McQueen: Savage Beauty was the eighth most popular show in the history of the Met and drew more visitors than any exhibit mounted by its Costume Intsitute. Holland Cotter reviewed the show for the New York Times. The blog for the museum includes a brief video about McQueen and photographs of some of the clothes it displayed, which appear in the catalog.
You can also follow Jan Harayda (@janiceharayda) on Twitter at www.twitter.com/janiceharayda.
© 2011 Janice Harayda. All rights reserved.


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The rebirth of PBS
Honey Boo Boo, the management at PBS wants to thank you.
You, too, real housewives. And naked castaways, Long Island princesses, breakaway Amish, storage warriors, pawn stars and pickers. People at public television may not want to watch you, but they are happy to see you.
When Discovery, The Learning Channel, History, Bravo, A&E and similar networks emerged, there was a real fear it could lead to the death of PBS. Each specialized network would pick off a portion of PBS' audience for programs on science, nature, history and the arts. Founded as an alternative to commercial TV, PBS was losing what made it unique.
Yet in the past few years, these cable networks discovered that it was much more profitable to create reality TV stars. PBS' path was cleared, and it is making the most of its new chance.
"It is now once again something that the viewer can't get anywhere else," said Beth Hoppe, PBS' programming chief.
PBS' viewership slipped steadily starting in 1993, which hardly made it unusual in a world with an ever-increasing number of choices. Since 2009, that trend has reversed. PBS' average prime-time audience has ticked back up from 1.9 million four years ago to 2.1 million now, with the growth faster among young people. Certainly the sensation of "Downton Abbey" is a key factor, but the growth isn't just on Sunday.
Hoppe is trying to infuse PBS with new energy, make its projects more timely, and get her colleagues to treat it as a television network instead of just a public service.
Hoppe worked at PBS stations in New Hampshire, Boston and New York City, and remembers well the worries when new cable networks started.
"We were concerned that people would consider us irrelevant because we were no longer providing a service, or that we would no longer be perceived as providing a service that people couldn't get anywhere else," she said.
Maybe PBS' programs were better, but that might not matter, she said.
She left PBS to join the new wave, taking a job at Discovery to produce science programming for its networks. She knew it was time for something else when an executive asked her to go to Los Angeles to "add sex and celebrities" to the "Curiosity" series she was working on. Hoppe talked to old friend Paula Kerger, the president and CEO of the Public Broadcasting Service, to see if there was room for her if she returned.
There was, and by last December, she was made responsible for PBS' programming department.
Hoppe cites Animal Planet's mermaids shows as examples of something PBS would never do. "Mermaids: The Body Found" played like a documentary but was an admitted fake and was a huge success, spawning a sequel.
PBS, meanwhile, is a Snookie-free zone.
"It's not that the programming is bad," Kerger said. "It's just different, that's all. They're in a different business."
Hoppe has tried to make PBS more topical, ordering a lengthy examination of guns in America that ran a month after the Newtown, Conn., school shooting. She pushed PBS producers for programs looking at the Boston Marathon bombing, the meteorite that exploded over Russia in February and Superstorm Sandy.
"She comes to her job with a filmmaker's sensibility," said John Bredar, vice president of national programming at Boston's WGBH, the largest supplier of PBS programming. "She understands things from the ground up as a producer, as opposed to someone who just commissions work. She's someone who has a visceral understanding of what the market is like."
In October, PBS' "Frontline" is collaborating with ESPN for "Concussion Watch," an investigation into health issues caused by violent collisions in the National Football League.
PBS will aggressively mine anniversaries as programming hooks. This fall brings an "American Masters" special on Billie Jean King 40 years after her "Battle of the Sexes" tennis match with Bobby Riggs, and a show on "War of the Worlds" 75 years after the radio program incited panic.
As with other networks, the 50th anniversary of President John F. Kennedy's assassination will be given attention. PBS' programming will include a four-hour portrait of Kennedy, a "cold case" look at evidence in the shooting and a minute-by-minute recap of the killing from the firing of shots to when CBS' Walter Cronkite reported Kennedy's death.
That's what Hoppe means when she talks about thinking like a network instead of just a service, anticipating the interests of viewers. There's a difference between waiting to see what work producers will offer you and actively going out with some of your own ideas.
PBS also is trying to bring more consistency to a schedule that encompasses several genres. Programmers call it "flow," and in this case it means concentrating science programming on Wednesday, arts on Friday, with more history and news-oriented shows on Monday and Tuesday.
"I'm so delighted that she's in this job and really trying to help us become more timely, to bring more context in and really look to refresh what new genres we could bring to public television," Kerger said.
While there's much on cable TV that PBS doesn't want to emulate, Hoppe said the competition has pushed public broadcasting to be more innovative. She considers "Antiques Roadshow" to be an example. The success of miniseries like History's "Hatfields & McCoys" and "The Bible" is pushing PBS to get into that genre, with the first project under development involving the Civil War.
The system's crown jewel, "Downton Abbey," returns for its fourth season on Jan. 5. You'd have to look back two decades to Ken Burns' "The Civil War" to find a series as important to PBS.
The hope is that it doesn't exist in a vacuum, that some of the interest created by the series can be transferred to other things on the schedule. Programs on Henry VIII's palace and "Secrets of Chatsworth" were clearly aired to appeal to Anglophile "Downton" fans, and this fall will see documentaries on the Tower of London and Scotland Yard. Same thing with some British dramas, like "Call the Midwife" and "The Bletchley Circle."
"If we could look back in 10 years and say, 'that was a real turning point for PBS in terms of its perception in popular culture and being cool and hip — the first of many new hits for PBS of that sort of magnitude' — that would be awesome," Hoppe said.


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For the latest updates to Global Public Square, including show information and Fareed's Take, visit the new GPS site on CNN.com.
Guess what's left over if you boil a bunch of average Americans. Bobcat?
Hello darling Philip. Did you sukk Blue Saffron's dikk and eat his s hitte like Modi from India does?
Why do hindoos raype in India?
They should cut off Modi bollz and feed them to monkeys
Modi eats Blue's s hiet. Yummmy.
Modi is wonderful. No plebiscite will ever be needed.
Praise Shiva and Modi and India and Hinduism.
Blue Saffron eats cow poo poo from India
So true Philip. Modi is just a great leader. Many are jealous of him.
Long live Modi!
Blue Saffron eats bird sh it.
Thank you banasy for having the courage to tell it like it is.
Modi is a wonderful man.
Blue Saffron is worthless pig vomit mixed with cow poo poo and cow pee pee
Pig vomit mixed with cow poo poo. Yep sounds like Blue Saffron mixed with Philip Douglas. Lol
The BO of Philip and Blue Saffron combined is so toxic that it could knock out an elephant. LMFAO!
Kashore. I think you NAILED IT by George!
Philip and Blue Saffron are a pair of worthless pathetic rats from a New York sewer. They eat dog poo poo and drink cow pee pee .
Modi imports Blue Saffron's s hitt to devour each day. The creamy chocolate vanilla like steamy delicacy is transported in a jet to feed Modi. He calls it Saffron Pudding.
Modi even applies Blue Saffron's s hitt on his face as facial treatment. And also massages his body with this delicacy.
Hindoos raype to celebrate hindooism.
They eat Blue Saffron's excrete as a meal during diwali.
A water buffalo fukked Thackeray and Modi was born resembling a baboon. Go figure.
I love Blue Saffron's creme brulee s hitt. Yummy. Modi eats it like there is no tomorrow.
Modi is a goat fukker.
Looky looky a blue little troll. Ain't he cute?
Modi is a beautiful person.
India is truly amazing and beautiful.
We all love India. Blu Saffron is a Hindu boy from India.
He worships Modi and he loves India.
Blue Saffron loves India
Blue Saffron loves India
Blue Saffron and Philip eat Modi's poo poo and drink his pee pee
Yes yes. All true. I am a Hindu boy from India and eat Modi's poop and pee pee
We know that Blue Saffron. We know
@chrissy. You NAILED it!
Modi is a camel fukker.
Hindoos fukk goats
Modi loves to eat s hitt produced by Blue Saffron. He also uses that as facial mask and to color his facial hair. Mmmmm..
A donkey fukked Thackeray. Modi was born. A buffalo fukked Modi. Gandhi was born.
I admire Blue Saffron. He is my GOD. He invented hindooism.
Wonder if Modi received the latest shipment of Blue Saffron s hitt. Nice and chewy.
I admire Modi. He is my GOD. MY HERO.


text:
Dihedral Groups
|Dihedral Symmetry of Order 12
Dihedral Symmetry of Order 12
- Each snowflake in the main image has the dihedral symmetry of a natual regular hexagon. The group formed by these symmetries is also called the dihedral group of degree 6. Order refers to the number of elements in the group, and degree refers to the number of the sides or the number of rotations. The order is twice the degree.
- 1 Basic Description
- 2 A More Mathematical Explanation
- 3 Definition
- 4 Properties
- 5 Infinite Dihedral Groups
- 6 Subgroups
- 7 Why It's Interesting
- 8 Teaching Materials
- 9 Related Links
- 10 References
- 11 Future Directions for this Page
Basic Description
In mathematics, a dihedral group is the group of symmetries of a regular polygon, including both rotations and reflections. Dihedral groups are among the simplest examples of finite groups, and they play an important role in group theory, geometry, and chemistry.
Dihedral groups arise frequently in art and nature. Many of the decorative designs used on floor coverings, pottery, and buildings have one of the dihedral groups of symmetry. Chrysler's logo has as a symmetry group, and that Mercedes-Benz has . The ubiquitous five-pointed star has symmetry group .
There are two different kinds of notation for a dihedral group associated to a polygon with sides.
In geometry, we usually call it or , where indicates the number of the sides.
In algebra, we call it , where indicates the number of elements in the group.
On this page, we will use the notation to describe a dihedral group. For , we will call it the dihedral group of order or the group of symmetries of a regular -gon.
Below is an example of Dihedral symmetry of and .
A More Mathematical Explanation
- Note: understanding of this explanation requires: *Basic Abstract Algebra
ElementsThe dihedral group is the symmetry group of the regula [...]
The dihedral group is the symmetry group of the regular -sided polygon. The group consists of reflections, rotations, and the identity transformation.
Here is an example of . This group contains 12 elements, which are all rotations and reflections. The very first one is the identity transformation.
If is odd each axis of symmetry connects the mid-point of one side to the opposite vertex. If is even there are axes of symmetry connecting the mid-points of opposite sides and axes of symmetry connecting opposite vertices. In either case, there are n axes of symmetry altogether and elements in the symmetry group. Reflecting in one axis of symmetry followed by reflecting in another axis of symmetry produces a rotation through twice the angle between the axes. In Image 1, through to are the axes of symmetries. All the reflections can be described as reflections of the identity through six axes of symmetries.
There are several different way to define a Dihedral Group. We will introduce three of them.
We will use to represent the identity, , to represent the rotations, and , to represent the reflections.
Complex Plane Presentation
For , the dihedral group is defined as the rigid motions of the plane preserving a regular -gon, with the operation of composition. On complex plane, our model -gon will be an -gon centered at the origin, with vertices at the n-th roots of unity. is always an -th root of unity, but is such a root only if is even. In general, the roots of unity form a regular polygon with sides, and each vertex lies on the unit circle.
The -th roots of unity are roots of the cyclotomic equation .
Since a vector on the complex plane can be described as , a vector with an angle counterclockwise from x-axis can be described as , where is the magnitude of the vector.
Leonhard Euler's formula says that , so any point on the complex plane is .
For a regular -gon, the first angle counterclockwise from the x-axis is , so the primitive root of unity is .
Letting denote a primitive root of unity, and assuming the polygon is centered at the origin, the rotations , (Note: denotes the identity), are given by
Notation means a function. For example: .
For the reflections, , , the functions are given by
Matrix Representation
If we center the regular polygon at the origin, then the elements of the dihedral group act as linear transformations of the plane. This lets us represent elements of as matrices, with composition being matrix multiplication. This is an example of a (2-dimensional) group representation.
For example, the elements of the group can be represented by the following eight matrices:
If we represent the columns of each matrix as basis vectors, we can observe directly all the rotations and reflections.
In general, we can write any dihedral group as:
where is a rotation matrix, expressing a counterclockwise rotation through an angle of , and is a reflection across a line that makes an angle of with the x-axis.
Group Presentation
A presentation of a group is a description of a set and a subset of the free group generated by , written as , where the equation (the identity element) is often written in place of the element . A group presentation defines the quotient group of the free group by the normal subgroup generated by , which is the group generated by the generators subject to the relations .
We can use the presentation:
, or
to define a group, isomorphic to the dihedral group of finite order , which is the group of symmetries of a regular -gon.
We will use the second presentation, in which refers to a reflection, and refer to a primitive rotation.
- For , means an arbitrary mirror image of the -gon, and means the identity. This equation means that if we reflect the -gon once, you get . If reflect the -gon twice, the result will return to the identity.
- For , the equation means that is a rotation, and its th power equals the identity. That is, if we rotate the -gon times, we get back to the identity.
- For , means the mirror image of . Reflecting the -gon through the axis of symmetry of twice, the result is the identity.
Following the group presentation, we can label all the reflections and rotations in terms of and .
- Identity:
- Rotations: , and , which is the identity.
- Reflections: . There is not , because , and so is the reflection of the identity.
Cayley Table
As with any geometric object, the composition of two symmetries of a regular polygon is again a symmetry. This operation gives the symmetries of a polygon the algebraic structure of a finite group.
A Cayley table, named after the 19th century British mathematician Arthur Cayley, describes the structure of a finite group by arranging all the possible products of all the group's elements in a square table reminiscent of an addition or multiplication table.
Image 2 on the right shows the effect of composition in the group (the symmetries of a hexagon). denotes the identity; to denote counterclockwise rotations by 60, 120, 180, 240,and 300 degrees; and to denote reflections across the six diagonals. In general, denotes the entry at the intersection of the row with at the left and the column with at the top.
In the table, the same or different rotations and reflections work together and result in a new rotation or reflection. For example, look first at the vertical axis to find a element, . Then look at the horizontal axis to get the second element for our composition. We choose . Composing two elements is just the progression of a rotation or a reflection followed by another rotation or a reflection. In this case, our elements are and . First we rotate the hexagon counterclockwise 240 degrees, and then reflect it along the axis of symmetry of . The result is the same as reflecting the identity transformation through an angle of 60 degrees, which is . See Example 1 below.
Now, look back to Image 2, you will find that the intersection of in left column and in top row is . However, you will find the intersection of in left column and in top row is . If you like, you can create your own Cayley table for a dihedral group of any order and find the natual rule for it.
Explore the Cayley Table
Perhaps the most important feature of this table is that it has been completely filled in without introducing any new motions.
- Closure: Algebraically, this says that if and are in , then so is . This property is called closure, and it is one of the requirements for a mathematical system to be a group.
- identity: Notice that if is any element of , then . Thus, combining any element on either side with yields back again. An element with this property is called an identity, and every group must have one.
- Inverse: We see that for each element in , there exists an element such that . In this case, is said to be the inverse of and vise versa. The term inverse is a descriptive one, for if and are inverses of each other, then "un-does" whatever "does", in the sense that and taken together in either order produce , representing no change.
- Non-Abelian: Another property of deserves special comment. Obverse that , but . Thus in a group may or may not be the same as . If it happens that for all choices of group elements and , we say the group is commutative or --better yet-- Abelian (in honor of the great Norwegian mathematician Niel Abel). Otherwise, we say the group is non-Abelian. All dihedral groups are non-Abelian, except and .
- Associativity: For all dihedral groups, it holds true that for all a, b, c in the group.
If we want to know what is the composition of any two elements, it is convenient to use a Cayley map, because it tells us the result directly. But when we want to know the gradual change of the compositions, we will need another tool, a multi-colored Muplication Table.
Muptiplication Table
In a Multiplication Table, each color represents one rotation or reflection. In Image 3, pink colors represent rotations, and the deepest pink represents the identity transformation. Green colors represent all the six reflections.
From the changing of color, we can observe that the gradual change of the composition of two elements in . However, we cannot easily determine the exact result of composition by observing directly Image 3.
The abstract group structure is given by:
Uniqueness of the Identity
In a dihedral group , there is only one identity element.
PROOF: Suppose both and are identities of . Then,
The choices of in Eq. 1 and in Eq. 2 yield and .
Thus, and are both equal to and so are equal to each other.
In a dihedral group , the right and left cancellation laws hold; that is, implies , and implies .
PROOF: Suppose . Let be an inverse of .
Then, muliplying on the right by yields .
Associativity yields .
Then, and, therefore, as desired.
Similarly, one can prove that implies by multiplying by on the left.
A consequence of the cancellation property is the fact that in a Cayley table for a dihedral group, each group element occurs exactly once in each row and column. Another consequence of the cancellation property is the uniqueness of inverses.
Uniqueness of Inverses
For each element in a dihedral group , there is a unique element in such that .
PROOF: Suppose and are both inverses of .
Then and , so that .
Canceling the on both sides gives , as desired.
Sock-Shoes property
For dihedral group elements and , .
PROOF: Since and
we have by the Uniqueness of Inverses theorem that has only one inverse such that .
We get .
3D Rotational Symmetry
consists of rotations of multiples of about the origin, and reflections across lines through the origin, making angles of multiples of with each other.
If we put a dihedral group in three dimensions, the reflections are also rotations of
The proper symmetry group of a regular polygon embedded in three-dimensional space (if ). Such a figure may be considered as a degenerate regular solid with its face counted twice. Therefore it is also called a dihedron (Greek: solid with two faces), which explains the name dihedral group.
Infinite Dihedral Groups
The infinite dihedral group is denoted by . The infinite dihedral group can be described as the group of symmetries of a circle, which has infinite symmetries.
We use the group presentation:
, or
to represente the infinite dihedral group.
In the presentation, it says that because there are infinitely many symmetries, we can never rotate back to the identity, and so there are infinitely many rotations and reflections.
Definition: A subgroup is a subset of group elements of a group that satisfies the four group requirements. It must therefore contain the identity element. " is a subgroup of " is written as , or sometimes .[1]
Now we want to know exactly how many subgroups for , and what they are. Fortunately, mathematician Stephan A. Cavior had already proved this for us in 1975. In the theorem, for any dihedral group in order of , there are subgroups in total, including and . is just the identity itself.
Definitions of Terms
- : the number of divisors of ,
- e.g. .
- : the sum of divisors of ,
- e.g. .
- : the notation for the cyclic group of order , can be also written as . This is a quotient group presentation.
- : is a divisor of .
- : group is a subgroup generated by . It means .
- : the order of .
- : the index. means .
- : a set with elements looking like .
- : this means a group. is the index, which labels all the elements; is the order of the group.
This proof is complicated.
After we know what kind of group can be a subgroup of a dihedral group , the dihedral group of order , we will start to find all subgroups of .
A cyclic group of order is the group of all the rotations including the identity of the dihedral group of order .
- Lemma 2. Let be the element of order in and let be a subgroup of . Then either or and for some .
Proof. Let . Clearly is a normal subgroup of because . Thus is a subgroup of and hence the order of dihedral group is a divisor of , and we use the notation:
- Eq. 1 to represent.
On the other hand,
- Eq. 2 .
- Lemma 3. Given , let . For every let , where denotes a reflection and denotes a primitive rotation. Let . Then is a subgroup of and . We also have
Proof. If , for some , then and thus , because .
Therefore because .
So we have proved that .
Clearly and , because .
Thus .
Proving that is a subgroup of is very easy.
Just note that every element of is the inverse of itself (because they all have order two) and also note that , for all , because .Finally, the set has elements because clearly if and only if if and only if
Suppose that is a subgroup of . There are two disjoint cases to consider.
Case 1. .
- By Lemma 1. the number of these subgroups is .
Case 2. .
- In this case, by Lemma 2. we have and , for some .
- Let . Since is a subgroup of , which is a cyclic group of order , we have
- Let and be as were defined in Lemma 3.
- Now, since is not contained in , there exists some such that .
- Then, since is a subgroup, we must have , for all .
- Thus and so and therefore, by Eq. 1, we have .
- Thus, since , we must have .
- The converse is obvously true, i.e. given and , is a subgroup of , by Lemma 3., and because it contains .
- So the subgroups in this case are exactly the ones in the form , where and .
- Thus, by Lemma 3. the number of subgroups in this case is
So, by Case 1. and Case 2. the number of subgroups of is .
Why It's Interesting
In Music
The sequence of pitches which form a musical melody can be transposed or inverted. Since the 1970s, music theorists have modeled musical transposition and inversion in terms of an action of the dihedral group of order 24. More recently music theorists have found an intriguing second way that the dihedral group of order 24 acts on the set of major and minor chords.[3]
Dihedral groups as a kind of special symmetric groups are studied in music. In music, we use the operations Transposition and Inversion, which are denoted as and , to represente rotations and reflections in dihedral groups.
Musicians usually study , because 12 is the length of a normal cycle in music: C C♯ D E♭ E F F♯ G G♯ A B♭ B, and then C again.
Based on this 12 element cycle, is important in music theory. Musicians use Transpositions and Inversions (rotations and reflections) of a simple note to create other notes to complete a final composition.
A transposition of a sequence of pitch classes by semitones is the sequence in which each of the pitch classes in has been increased by semitones.
So for example if
- , where the numbers denote pitches,
- .
When doing the operation , add to each digit of , and use arithmetic modulo 12 (clock arithmetic) when the resulting digit is over 12. For instance, in adding 4 to 8, the result is 12, but
Turning to the next operation, inversion of a sequence just replaces each pitch class by its negative (in clock arithmetic).
So in the first example above with , we have
- .
To do the operation , we need to do subtraction in clock arithmetic. For instance, if we want to get 12 from 3, we need to add 9. 0 is already 12, so we need to add 0.
Teaching Materials
- There are currently no teaching materials for this page. Add teaching materials.
Related Links
Additional Resources
- An applet to explore dihedral groups: http://www.mathlearning.net/learningtools/Flash/Dihedral/dihedralExplorer.html
[1] Wikipedia. (n.d.). Dihedral groups. Retrieved from http://en.wikipedia.org/wiki/Dihedral_group
[2] de Cornulier, Yves. (n.d). Group Presentation. From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. http://mathworld.wolfram.com/GroupPresentation.html
[3] Wikipedia. (n.d.). Cayley table. Retrieved from http://en.wikipedia.org/wiki/Cayley_table
[4] Milson, Robert and Foregger, Thomas. dihedral group. From PlanetMath.org. June, 12. 2007. Retrieved from http://planetmath.org/encyclopedia/DihedralGroup.html
[5] Gallian, Joseph A. Contemporary Abstract Algebra Seventh Edition. Belmont: Brooks/Cole, Cengage Learning. 2010.
[6] Dahlke, Karl. (n.d). Groups, Dihedral and General Linear Groups. Retrieved from http://www.mathreference.com/grp,dih.html
[7] Sharifi, Yaghoub. Subgroups of dihedral groups (1)&(2). Feb, 17, 2011. Retrieved from http://ysharifi.wordpress.com/2011/02/17/subgroups-of-dihedral-groups-1/
[8] [1]Scott, W. R. Group Theory. New York: Dover, 1987.
[9] [2]Hungerford, Thomas W. Graduate Texts in Mathematics - Algebra. New York: Springer, 1974.
[10] [3]Crans, Alissa S., Fiore, Thomas M. and Satyendra, Ramon. Musical Actions of Dihedral Groups. University of South Florida. Nov 3, 2007. Retrieved from http://myweb.lmu.edu/acrans/MusicalActions.PDF
[11] Benson, Dave J. Music: A Mathematical Offering. Cambridge University Press. Nov 2006. Retrieved from http://www.maths.abdn.ac.uk/~bensondj/html/music.pdf
[12] Rowland, Todd and Weisstein, Eric W. (n.d). Root of Unity. From MathWorld--A Wolfram Web Resource. Retrieved from http://mathworld.wolfram.com/RootofUnity.html
[13] Conrad, Keith. (n.d). DIHEDRAL GROUPS. Retrieved from http://www.math.uconn.edu/~kconrad/blurbs/grouptheory/dihedral.pdf
Future Directions for this Page
- More information related to the other groups
- Add more about Dihedral Groups in 3D. I only talk about one property in 3D, but there must be some more.
- In the subgroups part, it is hard to explain only in words, so I use lots of notation, which is still not very clear. I hope can find a better way to illustrate it.
- Add more about applications
- Think about non-abelian in matrices which may relate to non-abelian in group theory.
Leave a message on the discussion page by clicking the 'discussion' tab at the top of this image page.


text:
MENLO PARK, Calif. (AP) — With its new "Home" on Android gadgets, Facebook aims to put its social network at the center of people's mobile experiences.
If users choose to download Facebook's Home software starting on April 12, the social network will become the hub of their Android smartphones. A phone from HTC that comes pre-loaded with Home will also be available starting that day, with AT&T Inc. as the carrier.
The idea behind the software is to bring Facebook content right to the home screen, rather than requiring users to check apps. "Home" comes amid rapid growth in the number of people who access Facebook from phones and tablet computers. Of its 1.06 billion monthly users, 680 million log in to Facebook using a mobile gadget.
Eyes On Facebook Mobile Event As Company Evolves
The service is part of Facebook's move to shift its users' focus from "apps and tasks" to people, said CEO Mark Zuckerberg during Home's unveiling at the company's Menlo Park, Calif., headquarters on Thursday.
The new product, which resides on the home screen of Android phones, is a family of apps designed to help people share things with their Facebook friends. Rather than seeing a set of apps for email, maps and other services when they first turn on their phones, users will be greeted with photos and updates from their Facebook feeds. There will be ads too, eventually.
"We think this is the best version of Facebook there is," Zuckerberg said.
Zuckerberg says users can have an experience on Android phones that they can't have on other platforms. That's because Google makes the software available on an open-source basis, allowing others to adapt it to their needs.
Recognizing that text messaging is one of the most important tasks on a mobile phone, Facebook also showed off a feature called "chat heads." This lets users communicate with their friends directly from their phone's home screen – without opening a separate app.
The move that coincides with rapid growth among the number of users who access the social network from smartphones and tablet computers and Facebook's aim to evolve from its Web-based roots into a "mobile-first" company.
"What Facebook wants is to put itself at the front of the Android user experience for as many Facebook users as possible and make Facebook more elemental to their customers' experience," said Forrester analyst Charles Golvin.
The new Home service won't be available on Apple's iPhone and iPad devices. Apple's iOS and Mac operating systems include features that integrate Facebook's services, but Zuckerberg says doing something like Home would require a closer partnership.
Apple had no immediate comment.
The deeper mobile integration will likely help Facebook to attract more mobile advertisers. Though mobile ads were a big concern for Facebook's investors even before the company's initial public offering last May, some of the worry has subsided as the company muscles its way into the market.
Last year, Facebook began showing ads to its mobile audience by shoehorning corporate-sponsored content into users' news feeds, which also include updates from friends and brands they follow. Facebook now faces the challenge of showing people mobile ads without annoying or alienating them.
The mobile advertising market is growing quickly, thanks in large part to Facebook and Twitter, which also entered the space in 2012. Research firm eMarketer expects U.S. mobile ad spending to grow 77 percent this year to $7.29 billion, from $4.11 billion last year.
EMarketer said Wednesday that it expects Facebook Inc. to reap $965 million in U.S. mobile ad revenue in 2013. That's about 2.5 times the $391 million in 2012, the first year that Facebook started showing mobile ads. Clark Fredricksen, vice president at eMarketer, says "there are some clear reasons why a deeper integration with mobile operating systems and handsets make sense for Facebook. At the end of the day, the more deeply Facebook can engage consumers, no matter what device or operating system or handset," the better.
Facebook's stock rose 80 cents, or 3.1 percent, to $27.05 in afternoon trading following the announcement. It's still 23 percent below its initial public offering price of $35.
Barbara Ortutay reported from New York.


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September 24th, 2013
Video chat may help language learning
As a graduate student studying how children develop language, Sarah Roseberry made an interesting observation. Parents would come into her lab at Temple University and talk about how they Skyped with grandparents in places like the Dominican Republic.
"The parents would swear their children were learning Spanish," recalls Roseberry, now a postdoctoral fellow at the University of Washington. "The more we thought about it, the more we realized this made sense."
Roseberry decided to take her theory into the research lab. What she found was intriguing: Language can be learned via video chat, as long as the conversation allows for meaningful back-and-forth exchanges.
For the study, Roseberry and her colleagues gathered a group of 36 children between the ages of 2 and 2-and a-half, the time when children are still just learning language from others and not from videos.
They were divided into three groups: the first group worked one-on-one with adults in the room, the second group worked one-on-one with an adult via video chat and the third group of toddlers were shown a video of an adult communicating in a video chat with another child.
The researchers then introduced the children to nonsense words which required an action. So for example "meeping" was used to refer to turning and "blicking" referred to bouncing. After learning the words, the researchers showed the children a split screen on a computer. On one side Sesame Street characters were performing the action and on the other side, they were doing something else. Researchers then asked the children to point out which characters were performing the nonsense words.
They found the children who learned the words through live interactions and video chat, were the only ones who could do it. The kids only watching the video and not engaging with the adult, didn't pick up the concepts. "It's the difference between the child being an active learner versus a passive learner," says Roseberry.
So what's the take away for parents? Roseberry thinks the message is nuanced.
"Screen time isn't all good or all bad," says Roseberry.
For those of us with children who love their iPads and tablets, she suggests looking for games that encourage learning versus entertainment. "All screens are not created equal," says Roseberry.
The study appears in the most recent edition of the journal Child Development.
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Monday, October 24, 2011
Gingered Acorn Squash Soup + Book Giveaway
I have to mention what Robb Walsh wrote in the Forward of this book. His first introduction to Louis Lambert and his cooking was by way of an article in Martha Stewart Living in 1996. The article was about West Texas food and Marfa. I remember that article too, and I remember the recipes. I still have them in my files. The dishes in this new book are just as memorable. This is Texas food with some influences from Mexico here and ideas inherited from Louisiana there, and everything has been given some kind of fresh, new twist. The red grapefruit and avocado salad is reminiscent of Lambert's grandmother's salad from years ago, but here, it's been updated with watercress, pine nuts, and goat cheese. The fried green tomatoes are topped with a crab salad made with a Creole remoulade. There's a posole recipe, but this version is made with shrimp and green chiles, and wild Texas ducks are used for duck rillettes. Of course, there's a meat chapter including adobo-grilled t-bone with red chile and cheese enchiladas, bock-braised beef short ribs, and crispy wild boar ribs with fresh plum barbecue sauce. But, it's not a red meat-heavy kind of book. There's also a Poultry chapter, a Seafood chapter, Tex-Mex, Vegetables and Sides, Breads, and Desserts. I appreciated how every once in a while a recipe caught me by surprise, and that was the case with the gingered acorn squash soup.
With ginger in the title of the recipe, I knew there would be a nice spice flavor in the soup. Then, I read about the pineapple in it which adds just a hint of fruitiness. The roasted acorn squash, sauteed onions, and homemade stock give the soup a rich savoriness, and then the ginger and pineapple add little punches of different flavors. Sometimes, when making a soup, the garnishes can seem like a step or two too many but not here. The sour cream with honey, buttery brioche croutons, and a sprinkling of an anise-flavored herb like tarragon or Mexican mint marigold were so well-suited to this soup I urge you not to skip them. This was a hearty, fall soup, and in small portions would be a lovely way to start a Thanksgiving feast. In fact, the entire Thanksgiving meal could come from this book by using the Mexican chocolate chile rub on turkey instead of chicken, whipping up a big bowl of the loaded garlic mashed potatoes, baking the ricotta spinach gratin, and for dessert, I'd pick the gingered pear fried pies.
Gingered Acorn Squash Soup
Reprinted with permission from Big Ranch, Big City Cookbook: Recipes from Lambert's Texas Kitchens by Louis Lambert and June Naylor, copyright 2011. Published by Ten Speed Press, a division of Random House, Inc.
Makes 8 servings
2 acorn squash (approximately 6 cups cooked squash), quartered and seeded
3 tablespoons unsalted butter, melted
2 tablespoons brown sugar
1/4 teaspoon ground allspice
2 tablespoons olive oil
1 small white onion, diced small
3 tablespoons finely diced fresh ginger
1/2 cup small-diced fresh or canned pineapple
1 teaspoon salt
1/4 teaspoon white pepper
4 cups chicken stock
1 cup heavy cream
1/2 cup sour cream
2 tablespoons honey
Fresh chopped tarragon, for garnish
Preheat your oven to 400°F.
Arrange the cut squash on a baking sheet and brush the cut sides with the melted
butter. Season each piece by sprinkling on the brown sugar and allspice. Bake the
squash until the flesh is tender, about 30 minutes. When the squash has cooled enough to handle, scoop out the flesh and set aside.
Heat a heavy soup pot over medium-high heat and add the olive oil. Add the onion
and ginger to the pot and cook until the onion becomes soft, about 4 minutes. Add the pineapple, salt, and white pepper and cook for another 2 minutes. Stir in the chicken stock, heavy cream, and squash and bring to a simmer. Slowly cook the soup, stirring occasionally, for 20 minutes. Remove the soup from the heat and, using an immersion blender, puree the soup until smooth. You can also blend the soup in batches in a blender or food processor.
To make the garnish, stir together the sour cream and honey in a small bowl. To
serve, ladle the hot soup into warmed bowls and drizzle the top of each with the sour cream mixture. Garnish with freshly chopped tarragon.
(Note: When I made this soup, I made one small change to the ingredients by using only one half cup of cream instead of a full cup.)
You can follow information about Louis Lambert and Big Ranch, Big City on Facebook and Twitter. Two lucky people who comment on this post by Friday, October 28th 2011 at noon CST and who can provide a US mailing address, will be chosen to each receive one copy of the book. Just leave a comment, including your email address so I can contact you, and I'll randomly pick two winners on Friday.
UPDATE: The winners were #7 and #11. Thank you everyone who entered!
Posted by lisa is cooking at Monday, October 24, 2011
36 comments:
That soup looks and sounds fabulous! Great flavors.ReplyDelete
What gorgeous photos! I am salivating! Would love a chance in your drawing. email@example.com
- AnonymousOctober 24, 2011 at 7:12 PM
Wasn't sure about the ginger, but after reading all the ingredients I can't wait for my CSA box to arrive this week. firstname.lastname@example.com
Mmm, that looks delicious!ReplyDelete
Sounds tasty, I love the spiciness of ginger! I'm eager to see what the rest of the book holds! firstname.lastname@example.com
Hi Lisa,ReplyDelete
I am not familiar with this cookbook, but the recipe is on my list! Thank you for posting it!
(you have my email!)
Wow Lisa, this acorn soup looks delicious, so flavorful...beautifully done!ReplyDelete
Hope you have a great week ahead :-)
- AnonymousOctober 24, 2011 at 9:47 PM
Lovely! I love the suggestion to use Mexican mint marigold. Thanks for the giveaway!ReplyDelete
I love the idea of traditional Texan food with a gourmet twist. This soup looks downright decadent and the croutons are definitely the icing on the proverbial cake.ReplyDelete
You don't need to put me in the running for the book, but I just had to comment. I LOVE this book! Chef Lambert's voice comes through so clearly in the book. There are great technique blocks in addition to the fab recipes. I think my first recipe will be the Shrimp Posole Verde.ReplyDelete
Looks like a great book. travisdoran at gmail.comReplyDelete
This soup looks like heaven!ReplyDelete
I moved from Austin to Phoenix in June and would LOVE to have this cookbook as a piece of "home" in the desert. We have southwestern influences here, but they're not the same as Texas -- I miss it!ReplyDelete
I missed Lou's demo at the Texas Book Festival and now I regret it. This soup looks amazing- the ginger and pineapple must really add some complexity to the flavor. Also, I can't wait to try that sour cream and honey combination- sounds terrific!ReplyDelete
Sounds like a great book with a unique perspective.ReplyDelete
- AnonymousOctober 25, 2011 at 8:18 PM
Sounds like a good book, would love to read!ReplyDelete
gemini1077 at gmail dot com
What a fantastic book -thank you for sharing with us. Love the soup you highlighted. email@example.com
Yum Lisa, this looks amazing. I made a thai sweet potato soup for lunch today :) cold weather can go away now please!ReplyDelete
I love acorn squash baked with brown sugar and some butter. The ingredients in this soup are stirring up thoughts of glorious goodness. I've never thought of myself as a ginger lover but I'm discovering I enjoy many recipes with ginger and HEY...I think I must love ginger. This cookbook sounds intriguing.ReplyDelete
I, too, would love to enter your contest. On the dismal side of things, though, I have had very poor luck with cooking acorn squash. It seems to take forever and never really get done. I've had better luck with butternut squash.ReplyDelete
I just came here because of your farro/roasted cauliflower recipe, though. I just had a similar salad at a friends house, and it was so GREAT! I'll be trying your version except that I'm not a fan of pine nuts, so I'll probably put in pecans--this is Texas after all :) email@example.com
It really is interesting recipe. Wow, that pineapple sounds bit unusual.ReplyDelete
Really nice soup recipe,i never eat this king of soupe.ReplyDelete
I w'll try it soon.
Thank for the visit,great website.
creole cuisine
This looks awesome! I am more of a butternut squash girl myself, but I have some acorns this year that I was wondering what to do with.ReplyDelete
Squash soup is already one of my favorite things to eat. And now you're going to add ginger, pineapple, and tarragon, more ingredients that I love? Now _this_ is my kind of cooking.ReplyDelete
I just happened across your blog. It looks nice and I am going to follow it for a while. Looks like you may have a fondness for cookbooks. My new book is reviewed at http://jennsfoodjourney.blotspot.comReplyDelete
And she's giving one away.
If you care to, check me out at http://theobsessivechef.blogspot.com
Don't enter me in the contest because my shelves are already groaning, but just had to comment on what looks like a delicious soup. I love winter squash but am a little afraid of the acorn. Such tough skin! But I'm willing to go in for this!ReplyDelete
Interesting squash soup. Printed the recipe and plan to fix it when the weather gets cooler. A cold front is on the way but I plan to to try Shrimp Pozole Verde first. I have two pork chops in Lamberts Citrus Brine from Valley Grilled Poterhouse Pork Chop recipe. Going to fix for dinner tomorrow night. I would like to have his book to try some of the other recipes. email@example.com
I would love to try this soup. I steer clear of strong ginger flavors due to an unfortunate ginger incident in my past :P but this sounds very good and I am trying to learn to love it again.... the cookbook sounds fantastic!ReplyDelete
confession: acorn squash is probably my least favorite of the winter squash. that said, this is a fabulous way to prepare it--the aroma must be amazing!ReplyDelete
I am in a mood for soups, as I imagine most people in this hemisphere anyway... I rarely cook acorn squash, afraid of losing fingers while cutting it, but this soup would be worth the risk ;-)ReplyDelete
The pork chops were very tasty. Looking forward to trying the Shrimp Pozole Verde tonight. firstname.lastname@example.com
This says Fall to me! Would love that cookbook, another addict right here!ReplyDelete
- Kris Cacciapaglia-EnrightOctober 28, 2011 at 9:14 AM
The soup look delish! I love trying new dishes, thanks for posting.ReplyDelete
This recipe looks delish! your pictures are SO pretty Lisa! firstname.lastname@example.com
I'm definitely making this soup today (w/our first "cold front" going through central TX). My only thought is to use slightly less brown sugar and honey, as I generally love the naturally sweet flavor of the squash itself. Have really enjoyed your site, and I'd love a copy of the cookbook! firstname.lastname@example.com
Hi Lisa, Your Gingered Acorn Squash Soup recipe has been selected to be featured in a Recipe Guessing Game. Please share the following link with your friends and fans. To play, go here: http://knapkins.com/guess_games/308?source=blog Congrats again!! :)ReplyDelete


text:
This article was originally published in the September/October 1999 issue of Home Energy Magazine. Some formatting inconsistencies may be evident in older archive content.
| Back to Contents Page | Home Energy Index | About Home Energy |
Home Energy Magazine Online September/October 1999
in energy
Weather Data Getting CloudyIn the last two decades, researchers have relied increasingly on computer programs such as DOE-2 and BLAST to analyze building energy use. For example, simulations can be used to extrapolate building energy performance from limited measured energy data, or to weather normalize predicted savings in energy management or shared savings contracts. In order to do a computer simulation, however, one needs detailed, preferably hourly, weather information. The major sources of this weather information are the surface weather observations reported by the National Weather Service (NWS) or the Federal Aviation Administration (FAA) at airports and other sites and archived at the National Climatic Data Center (NCDC). Unfortunately, beginning in 1992, the NWS and the FAA have been changing the method that is used to collect these observations and the types of data that are collected. Credible building energy simulations can no longer be completed using the weather data currently being reported from these sites.
For building energy simulations, the following weather data are needed at a minimum: dry-bulb temperature, some measure of humidity (either wet-bulb or dew point temperature), station pressure, wind direction and speed, and some measure of solar radiation. All of these parameters except the last are generally available in the surface observation data. If measured solar radiation is unavailable, as is the case in most instances, researchers use analytical and empirical models to estimate the amount of total, direct, and diffuse solar radiation from reported conditions of cloud type, cloud cover, and sky cover.
In 1992, the NWS, the FAA, and the Department of Defense began replacing manual observations with automated sensors and reporting systems called variously Automated Surface Observing System (ASOS) or Automated Weather Observation System (AWOS). As of February 1999, there are 694 commissioned NWS and FAA ASOS/AWOS stations in the United States. When the planned 900-plus nationwide NWS/FAA stations are all in place at the end of this year, they will be the primary source of surface observations in the United States.
The ASOS instrumentation was designed primarily to meet aviation needs; data recorded include ambient and dew point temperatures, wind conditions, precipitation accumulation, cloud height to 12,000 ft, and other weather phenomena such as lightning or freezing rain. A laser beam ceilometer provides the only information on sky conditions. In addition to reporting ceiling heights to 12,000 ft, ASOS uses an algorithm that analyzes 80 ceilometer readings over an hour to deduce five levels of sky cover: Clear, Few, Scattered, Broken, or Overcast. Data on cloud cover above 12,000 ft and minutes of sunshine may be included in the future through additional instrumentation or manual augmentation.
ASOS data are reported on a one-minute interval in the Aviation Routine Weather Report (METAR) format. (Information on ASOS can be found on-line at www.nws.noaa.gov/asos.) Hourly data for previous periods of record can be obtained from the NCDC.
The reported ASOS data present major difficulties for those of us who perform building energy calculations because of the very limited information on solar conditions. Furthermore, the automated methods used to determine cloud height and sky cover are incompatible with previously developed solar models. There is a plan to upgrade the ASOS/AWOS network to record minutes of sunshine. But even if this plan is implemented, a new solar model would have to be developed to make such data usable for building energy simulations.
For the present, procedures are urgently needed to estimate solar radiation from the weather elements now being reported by the automated weather stations. For predicting average year energy use, the older weather data are adequate. But for running weather normalization calculations, current data are necessary. (If all you need is average daily temperature data, you may be able to find that information on a Web site maintained by the University of Dayton, where current data, updated daily, is available for 159 U.S. cities--www.engr.udayton.edu/weather.) And only with the development of new procedures can the currently available data be made usable for this type of building energy simulation.
--Joe Huang
Joe Huang is a staff scientist in the Building Technologies Department at Lawrence Berkeley National Laboratory.
| Back to Contents Page | Home Energy Index | About Home Energy |
Home Energy can be reached at: email@example.com
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The NIH Library is pleased to present a one-day bioinformatics workshop and several bioinformatics classes this month, all offered online.
Announcements & News
Electronic Lab Notebook Forum: March 11, 2019
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Unlikely harmony for Eastwood in 'Jersey Boys'
Amid the swirl of an early 1960s party scene in Clint Eastwood's latest, an adaptation of "Jersey Boys," the hit Broadway musical about Frankie Valli and the Four Seasons, a television screen flashes an unexpected face: young Clint, himself, in black-and-white.
The period-appropriate shot from the TV Western "Rawhide" — a wry Hitchcockian cameo — condenses in a moment the almost unfathomable breadth of Eastwood's career: fresh-faced cowboy to steadfast Oscar-winning director. Does it feel like a lifetime ago to Eastwood?
"Several lifetimes ago," chuckles the 84-year-old director. "Seeing myself in 1959 or '60 or '61 or whenever that episode was done, it was kind of like: Wow. I've traveled a long road since then."
That road — from Sergio Leone's spaghetti Westerns to Eastwood's own "Unforgiven," from "Make my day" to "Get off my lawn" — has made an unlikely detour down the New Jersey Turnpike. "Jersey Boys" — Eastwood's 12th film as director since turning 70 — only adds to what's by now one of the most remarkable late chapters of any filmmaker. How has he done it?
"I just never let the old man in," said Eastwood in a recent interview. "I was always looking for new things to do. I rightfully or wrongly always thought I could do anything."
Such an attitude explains many of his accomplishments. Who else would have thought a tragic story about a female boxer ("Million Dollar Baby") could be such a success? Who else would have come to Iwo Jima to make the World War II drama "Flags of Our Fathers" and, out of curiosity and empathy, opted to also make a film ("Letters from Iwo Jima") about the other side of the battle field?
And who would have expected the man — "a tall, chiseled piece of lumber, a totem pole with feet," as James Wolcott called him — mythologized as both The Man With No Name and Dirty Harry would be taken by the story of the guys behind "Big Girls Don't Cry"?
"The whole secret in life in any profession, regardless of whether it's entertainment or anything else, is just being interested," Eastwood says. "Are you interested in life? Are you interested in what's going on? Are you interested in new kinds of music?"
Eastwood, a piano player and jazz fan, has long been known for his passion for music. He made a film about Charlie Parker ("Bird"), sang in "Paint Your Wagon" and "Gran Torino," produced a documentary on Thelonious Monk ("Straight No Chaser") and has composed most of his scores over the last decade.
But the falsetto-rich pop confections of Valli (played by John Lloyd Young, who originated the role on Broadway) and the Four Seasons would seem a higher register than Eastwood's natural pitch.
"So many times you'd look off to the wings or even between shots and see him standing there trying to figure it out for himself, going (in a high voice) "Ooooo," says Michael Lomenda, who plays the Four Seasons' Nick Massi in the film.
Though the "Jersey Boys" sensation on Broadway immediately brought interest from Hollywood, earlier adaption attempts flat-lined before Eastwood revived it with Warner Bros.
"I couldn't understand quite why after nine years on Broadway, somebody didn't want to do it," says Eastwood.
Eastwood favored a faithful adaptation written by the musical's writers, Marshall Brickman and Rick Elice, and cast veterans of the Broadway and touring productions over more famous options. Erich Bergen, who plays songwriter Bob Gaudio, and Lomenda both come from touring shows. Vincent Piazzo of HBO's "Boardwalk Empire" was the lone outsider.
"We knew there was no chance in hell it would be turned into fluff," Young says of hearing that Eastwood would direct "Jersey Boys."
Instead, Eastwood's film, which opens Friday, has more melancholy than your average musical, and gravitates toward the group's tumultuous offstage personal lives. Eastwood's famously efficient style of filmmaking — usually just one or two takes, always on time and under budget — was an education for the actors, most of them unseasoned in moviemaking.
"His fearlessness is somehow contagious," says Piazza. "The harmony that you walk into and the space he creates for you as an actor is a rare, rare thing."
Though Eastwood may seem like cinema's answer to a chunk of Mt. Rushmore, he has a warm presence and is quick to smile. He has a habit of pulling taut the skin of his cheek, as if making age an idle plaything. He chases a publicist who has come in to wrap up the interview with a scowl and a good-natured "Get out!"
He recently finished shooting the Navy SEAL drama "American Sniper," with Bradley Cooper, which he calls "a love story and a military story about a guy who's very talented at shooting people." It's two films in one year for Eastwood in what he notes is his 60th year in movies.
"It's fashionable to pigeonhole everybody," he says. "You're 60, you're a senior. At 60, I felt like I was about 40. At 40, I felt like I was about 18. It's just all mental attitude."


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Two more getting their first direction. First is a hawthorn with great bark and second is an unusual variety of privet.
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A homeowner is 'short' when they owe an amount on their property that, when combined with closing costs, is higher than current market value.
A short sale occurs when a negotiation is entered into with the homeowner's mortgage company or companies to accept less than the full balance of the loan at closing.
The majority of Realtors at The Group, Inc. have completed extensive training from the premier short sale experts in the nation. They have been shown how to process a short sale completely, correctly, and ethically. In addition, The Group, Inc. has highly skilled short sale specialists on our staff to assist our Realtors and their customers with the short sale process.
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Bermudez Anniversario
Rum Review: Ron Bermudez Anniversario 91.5/100
a review by Chip Dykstra (Aka Arctic Wolf)
Posted June 14, 2010 (Revised November 2012)
This is the third review I have published with respect to the rums of Ron Bermudez . I previously reviewed the Ron Anejo Bermudez 5 Anos and the Bermudez 1852 Ron Anejo 10 Anos Don Armando based upon sample bottles provided to my by Westway L. LTD. My sample bottle of the Ron Bermudez Anniversario rum was also supplied by Westway, as they are introducing the Bermudez rums into my home Province of Alberta. The Anniverario is a well aged rum full of character and oak flavour, and it was a delight to cap off my reviews of the Bermudez range with this outstanding rum.
In the Bottle 4/5
The Ron Bermudez Anniversario arrives with elegant style in a bold black box with gold trim and fonts. Although the bottle looks black in the picture it is actually a dark green. The label is entirely in Spanish; but fortunately my Spanish is just good enough that I can report that the bottle does not include an age statement. (The supplier of the spirit has informed me that the age of the spirit is 15 years, but other statements I have seen online indicate a 12 year old spirit. I am not sure of course; but it is very possible that Bermudez has recently changed the age of their Anniversario from 12 to 15 years) The spirit is bottled at 40 % alcohol by volume.
I am disappointed in the black metal screw cap, however as this may be considered a premium spirit, it is not priced as such, so I have not deducted a major penalty for the inferior cap, (just a minor penalty).
In the Glass 9/10
In the glass the rum is a nice clean amber brown colour. A thick layer of oil coated the side of my glass when I tilted it, and I watched as long legs slowly formed, and then slowly crawled down back into the rum.
I found the aroma of the Ron Bermudez Anniversario to be very consistent with the aroma from the Ron Bermudez Anejo 1852, which I reviewed earlier. Initially, I receive a soft caramel and vanilla from the glass. This is followed by stronger aromas of oak tannin and spice. As I allow the glass to decant, an aroma of fragrant baking spices became more assertive over time expressing a rich molasses and a spicy toffee. There also appears to be a gentle smoke in the air with vague scents of dried fruit. Although this is consistent with the aroma of the younger 5 Anos Bermudez rum, it is not really the same. The Anniversario is richer and deeper with more oak character and spice.
In the Mouth 56/60
In the younger versions of the Ron Bermudez rums, the flavours of rich caramel and butterscotch (and soft ripe fruit) tended to lead out and perhaps define the characteristic flavour of those rums. However, in the case of the Ron Bermudez Anniversario these flavours are no longer as dominant. Instead the oak tannin spices and the citrus zests have taken command. The rum is spicy with hints of cinnamon and orange peel. Toffee and caramel sit in the background supporting the spicier flavour of the oak. There is also a firm leathery smoke in the rum which is full of the flavours of dried fruits (raisins, dates, and prunes). When I sampled the younger 5-year-old Bermudez rum, I had a vague impression that there was a metallic taste in the rum; but now, in the older Ron Bermudez Anniversario, this metallic element is more identifiable. To me it similar to a flavour I have noted in other Dominican rums and identified as a hint of iodine and a dash of musty ocean brine.
I find that the combinations of flavours that I receive from the Anniversario is providing a complex, but inviting character which I am enjoying immensely.
In the Throat 13.5/15
The rum exits the mouth with a rush of oak spice tempered by a long finish of sweet molasses and caramel. It is just a little spicy as it swarms the tonsils on the way down but the burn is appealing. A real feeling of richness and style seems to follow with the exit of the rum.
The Afterburn 9/10
This is a really great rum. It is full of oaky spices and flavour without the oak turning bitter. It has an elegant style reminiscent of cognac but it fully retains its character as rum. I have found this to be a completely unexpected treat.
If you are interested in comparing more scores, here is a link to my other published Rum Reviews.
You may (loosely) interpret the scores as follows.
0-25 A spirit with a rating this low would actually kill you.
26-49 Depending upon your fortitude you might actually survive this.
50 -59 You are safe to drink this…but you shouldn't.
60-69 Substandard swill which you may offer to people you do not want to see again.
70-74 Now we have a fair mixing rum or whisky. Accept this but make sure it is mixed into a cocktail.
75-79 You may begin to serve this to friends, again probably still cocktail territory.
80-84 We begin to enjoy this spirit neat or on the rocks. (I will still primarily mix cocktails)
85-89 Excellent for sipping or for mixing!
90-94 Definitely a primary sipping spirit, in fact you may want to hoard this for yourself.
95-97.5 The Cream of the Crop
98+ I haven't met this bottle yet…but I want to.
Very loosely we may put my scores into terms that you may be familiar with on a Gold, Silver, and Bronze medal scale as follows:
70 – 79.5 Bronze Medal (Recommended only as a mixer)
80 – 89.5 Silver Medal (Recommended for sipping and or a high quality mixer)
90 – 95 Gold Medal (Highly recommended for sipping and for sublime cocktails.)
95.5+ Platinum Award (Highest Recommendation)
11 Responses to "Bermudez Anniversario"
January 24, 2014 at 5:40 pm
This definitely has the "Dominican tang" you mention, more so than the Brugal, I found. At the first sip I found the tang a little too prominent and bitter, and worried that it would ruin the bottle for me. A week and a third of the bottle later, I find that not only am I getting used to the tang, I'm getting the rest of the flavour profile through. The 'Dominican tang' may be a bit of an acquired taste, but once you get it, it seems, it adds an extra dimension to the drink. Challenging, but welcomingly so. Could do without the tacky plastic seal on the bottle though, it makes it look like a prop from my little nephew's adventure pirate kit 😀
December 21, 2011 at 5:04 am
Where can this rum be purchased in the US? I'm located in NJ in the NYC Vicinity. Please advise!!
November 22, 2011 at 6:48 pm
Gentlemen, any idea where to purchase the 1852 Aniversario? I would love to purchase a few bottles of a quality rum that bears my name…
Thanks! Mario Bermudez
November 29, 2011 at 8:42 pm
Hello, Mario,
if you live in Alberta you are the luckiest among Canadians: only AB is capable to carry it. So far I found that LiquorConnect.com of Alberta has it in it's catalogue as well as ZYN.ca of Inglewood. Otherwise it's nowhere to be fount in Canada nor USA 😦
PS. Ontario's LCBO must be privatized.
- November 29, 2011 at 8:42 pm
November 21, 2011 at 6:55 pm
Hello, Arctic Wolf,
it was a real treat to read your review of the Bermudez Aniversario 1852.
Here is my concern: I just returned from a vacation in DR and brought a range of premium rums which I purchased from highly recommended and reputable chain stores of Columbus Plaza (one in S.Domingo and another in La Romana). I was excited by the richness and luxury of Barcelo Imperial and Bermudez Don Armando (my favourite). Not so much by Brugal Extra Viejo (too much old musty oak in it).
But my real disappointment came from the Aniversario 1852! When I uncorcked it, a powerfull whiff of rubbing alcohol hit me in the nose. The color was pale and unimpressive compared to oily amberness of the Don Armando. The taste is thin and far from Don Armando's fruitiness and carameliness.
Is it a real Aniversario or I got a fake? Mind you, other rums from the same store are superb. I'm puzzled.
Could you give a brief comparision Aniversario vs. Don Armando?
Thanks in advance.


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Normal Breast Development and Changes
What is normal breast development?
Breast development is a vital part of reproduction in the human female. Unlike other mammals, however, human females develop full breasts long before they are needed to nurse their offspring.
Breast development occurs in distinct stages throughout a woman's life, first before birth, again at puberty, and during the childbearing years. Changes also occur to the breasts during the menstrual cycle and when a woman reaches menopause.
When does breast development begin?
Breasts begin to form during fetal development with a thickening in the chest area called the mammary ridge or milk line. By the time a female infant is born, nipples and the beginnings of the milk-duct system have formed.
Breast changes continue to occur over the lifespan, with lobes, or small subdivisions of breast tissue, developing first. Mammary glands develop next and consist of 15 to 24 lobes. Mammary glands are influenced by hormones activated in puberty. Involution or shrinkage of the milk ducts is the final major change that occurs within the breast tissue. A gradual shrinking of the mammary glands (involution) typically begins around the age of 35.
What breast changes happen at puberty?
As a girl approaches adolescence, the first outward signs of breast development begin to appear. When the ovaries start to secrete estrogen, fat in the connective tissue begins to accumulate causing the breasts to enlarge. The duct system also begins to grow. Usually the onset of these breast changes is also accompanied by the appearance of pubic hair and hair under the arms.
Once ovulation and menstruation begin, the maturing of the breasts begins with the formation of secretory glands at the end of the milk ducts. The breasts and duct system continue to grow and mature, with the development of many glands and lobules. The rate at which breasts grow varies greatly and is different for each young woman.
Female breast developmental stages
Stage 1
(Preadolescent) only the tip of the nipple is raised
Stage 2
Buds appear, breast and nipple raised, and the areola (dark area of skin that surrounds the nipple) enlarges
Stage 3
Breasts are slightly larger with glandular breast tissue present
Stage 4
The areola and nipple become raised and form a second mound above the rest of the breast
Stage 5
Mature adult breast; the breast becomes rounded and only the nipple is raised
What cyclical changes occur to the breasts during the menstrual cycle?
Each month, women experience fluctuations in hormones that make up the normal menstrual cycle. Estrogen, which is produced by the ovaries in the first half of the menstrual cycle, stimulates the growth of milk ducts in the breasts. The increasing level of estrogen leads to ovulation halfway through the cycle, and then the hormone progesterone takes over in the second half of the cycle, stimulating the formation of the milk glands. These hormones are believed to be responsible for the cyclical changes such as the swelling, pain, and tenderness that many women experience in their breasts just before menstruation.
During menstruation, many women also experience changes in breast texture, with breasts feeling particularly lumpy. These are the glands in the breast enlarging to prepare for a possible pregnancy. If pregnancy does not occur, the breasts return to normal size. Once menstruation begins, the cycle begins again.
What happens to the breasts during pregnancy and lactation?
Many doctors believe the breasts are not fully mature until a woman has given birth and produced milk. Breast changes are one of the earliest signs of pregnancy--a result of the hormone progesterone. In addition, the areolas (the dark areas of skin that surround the nipples of the breasts) begin to swell followed by the rapid swelling of the breasts themselves. Most pregnant women experience tenderness down the sides of the breasts and tingling or soreness of the nipples because of the growth of the milk duct system and the formation of many more lobules.
By the fifth or sixth month of pregnancy, the breasts are fully capable of producing milk. As in puberty, estrogen controls the growth of the ducts, and progesterone controls the growth of the glandular buds. Many other hormones, such as follicle stimulating hormone (FSH), luteinizing hormone (LH), prolactin, oxytocin, and human placental lactogen (HPL) also play vital roles in milk production.
Other physical changes, such as the prominence of the blood vessels in the breast and the enlargement and darkening of the areola occur. All of these changes are in preparation for breastfeeding the baby after birth.
What happens to the breasts at menopause?
By the time a woman reaches her late 40s and early 50s, menopause is beginning or is well underway. At this time, the levels of estrogen and progesterone begin to fluctuate, with levels of estrogen dramatically decreasing. This leads to many of the symptoms commonly associated with menopause. With this reduction in the stimulation by estrogen to all tissues of the body, including the breast tissue, there is a reduction in the glandular tissue of the breasts. Without estrogen, the connective tissue of the breast becomes dehydrated and inelastic, and the breast tissue, which was prepared to make milk, shrinks and loses shape. This leads to the "sagging" of the breasts often associated with women of this age.
Women who are taking hormone therapy may experience some of the premenstrual breast symptoms that they experienced while they were still menstruating, which can include tenderness and swelling. However, if there was sagging of the breasts before menopause, this is not reversed with hormone therapy.


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There are questions about the safety of seafood in the Gulf following the BP oil disaster. Gary Tuchman reports.
Post by: Gary Tuchman
Filed under: Environmental issues • Gulf Oil Spill
So the shrimp in the Gulf has become the proverbial "canary in the coal mine" as evidence of the ecological disaster from the BP oil spill??? If anyone thinks this is evidence as the sole cause for low shrimp numbers, then what about the devasting drought throughout the entire state of Texas which has virtually eliminated the normal and natural flow of freshwater into the gulf for over a year? Come on let's see some rational thoughts and reporting about low shrimp numbers in the Gulf rather than simply shouting the "sky is falling" and the Gulf has beomce some kind of toxic soup. It is this kind of hyper-emotional comments that give credence to those who view environmentalists as extremists and simply acting on feelings rather the firing of synapses between nuerons.
I have an anti-immune disease and would not even think of eating Gulf Seafood. The dispersant is the reason! I eat out quite a bit and most restaurants have only Gulf Seafood and seafood from foreign ports. Which is worse? The filthy, unregulated seafood from Asia or the oil and dispersant laden seafood from the Gulf Coast. Do you for any minute think I believe any of our elected officials when they claim the seafood is safe? No way! How much are they receiving from the big oil companies to keep their jobs? From NOAA, our governor, USCG, DMR, DEQ and the list goes on; I don't believe the first one. When the oil was coming ashore, our Lt Governor claimed we were smelling our lawnmower gas. And recently Mississippians elected him as our next governor. Now, you can understand why Mississippi is labeled number 50 in most subjects.
This report should be an embarrassment to everyone involved in it. The FDA, the EPA, the CDC, the NIH, and the Coast Guard have played with the numbers on this disaster since it started. The disaster in the Gulf of Mexico is UNPRECEDENTED and on a scale which has no yardstick! The ramifications of the spraying of COREXIT will go on for decades. The ecology of the Gulf of Mexico has been damaged to it's core. Shame on you CNN. We used to trust you Anderson, but you have lost your nerve. One day the truth about what has happened in the Gulf will come out, and after seeing this report I am sure it won't be coming from CNN.
Anderson Cooper goes beyond the headlines to tell stories from many points of view, so you can make up your own mind about the news. Tune in weeknights at 8 and 10 ET on CNN.
Questions or comments? Send an email
Want to know more? Go behind the scenes with AC361°


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Bloggers in the Limelight: Jean and Rosz
I do this every single day where in I pop in and out of my fellow blogger's site updating myself on their food adventures, fashion and beauty finds and basically their day-to-day life. While most of the ones listed in my browser's bookmark tab consists that of fellow food and travel bloggers website, one continues to stand out as this is actually the only fashion blog that I regularly follow.
Meet Jean and Rosz.
I am a fan of accessories and I love browsing through photos of the hippest and cutest bracelets, necklaces and cocktail rings against their crisp white background. I love how they would post magazine photos of celebrities wearing the latest accessories and guess what, they actually have these available for sale! They boasts to be the first blog on trend spotting and I'd have to save they are pretty good at it. It surely is amazing that these two girls really have to nose and eyes for the latest trends.
Frannywanny: Who are Jean and Rosz?
Jean: Jean and Rosz are best friends from way back in high school. We are different in so many ways but has one thing in common -- our love for all things beautiful! And through Jean & Rosz the brand, we are able to share that with everyone.
Rosz: "Jean & Rosz" is our usual selves sharing our passion in the excessively fun side of fashion. Accessorizing.
Frannywanny: What inspired you to start this trend-setting blog?
Jean: We got inspired because there's no trend-spotting blog yet that focuses on accessories here in the Philippines. Through our blog we talk about different fashion trends esp. on accessories and try to make them available locally.
Rosz: In the country today, a lot of beauty, fashion and food blogs have developed. I thought why not discuss usual topics with a twist of incorporating accessory elements. Not just fashion accessories but anything accessory that captures my fancy, whether it would be for home, for the body, the car or even for the parks. I think of weird things all the time like how did the inventor of fork designed such a thing, or how safari has transformed to a well-known dress print to bangle, and i thought i could share these in our accessory trend spotting blog.
Frannywanny: If you were to style anyone in this world, who would it be and why?
Jean: Mariah Carey because I admit I like her music but I think she could dress so much better to make her look sexy and classy at the same time.
Rosz: Lately, i've been contemplating on whether lady gaga would allow me to play with her, but definitely, Madonna.
Frannywanny: Describe your personal fashion preference?
Jean: I actually don't have a particular fashion preference because I usually dress according to my mood. Fashion is fun so I experiment with my looks a lot!
Rosz: I like anything basic but with a modern twist, I love fashion elements that are strikingly noticeable but never over the top. I love fashion from the 1920's and the 1950's, if only i could live in it.
Frannywanny: Tell us about your dream shopping trip? Where would this be and share where you will be shopping and what you will be buying?
Jean: My dream shopping trip will be at Christie's in New York or London to bid and be able to buy some of their bling! I always loved jewelries and I drool over their pieces, for me they have some of the finest jewels in the world. I remember that my childhood dream was to have my own jewelry store so that i can have endless choices of jewelries to wear everyday! =)
Rosz: I don't really shop but i loooove looking around because I always know exactly what I want. But my dream shopping trip is literally a "dream" in which i will be given a certain time frame, say 30 minutes in 5th Avenue in New York, Canton Road in Hk, Champs Elysees in Paris and rush to get all the bags, watches and diamonds that i want.
After which, I will use it for a while and auction them to set-up an organization which can send less-fortunate kids to school. That way, there is lesser guilt in loving these frivolous things, at least i get to help.haha. Can you just imagine the adrenaline rush in that 30 mins? Add also the exhiliration I would get once these kids earn their degrees. That for me is my definition of a shopping spree.
Frannywanny: In 5 words: what makes your blog different?
Jean: We are accessory trend-spotters
Rosz: We're not unique, we're genuine.
Jean and Rosz will raffle off 5 exciting prizes :
Jean and Rosz Double Wing Necklace
How to win any of these prizes:
1) Leave me a comment and answer this question -- "Who's your favorite fashion icon and is there a particular fashion trend that you love?"
2) Kindly include your name and email address to make it easier for me to contact you.
3) Lastly, subscribe to Jean and Rosz' mailing list to get fresh updates on the latest trends!
Jean and Rosz will help me choose the five lucky winners and we'll send the products straight to your doorstep!
This contest will run from August 8- 29, 2010! The list of winners will be published right after.


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Search for mental health solutions
Summit focuses on link between crime and mental health
ROCKFORD — Stakeholders from across Winnebago County met Thursday to discuss new ways to support a population of people with mental health issues that are overrepresented in the criminal justice system.
About 17 percent of men and 34 percent of women in jail have a major mental health condition such as bipolar disorder, depression, post traumatic stress disorder or schizophrenia, national statistics show. Those rates are between three to six times higher than rates of mental illness in the general population.
Once they're in jail, the mentally ill tend to stay behind bars longer than those without such illnesses who face the same charges, Jail Superintendent Andrea Tack said Thursday.
Those at Thursday's forum, the second in a series of public safety summits called by Winnebago County Board Chairman Scott Christiansen, shared strategies used by other counties across the country and looked for ways to improve services already offered.
"This is another area that seriously impacts the criminal justice system in many ways. It not only affects the lives of people with behavior disorder issues, it is also costly to the taxpayers of Winnebago County," Christiansen said. "We need to find more effective ways to address this issue and we are hopeful this summit will do just that."
Nearly 150 attendees, including law enforcement, prosecutors, public defenders, judges and mental health professionals gathered at the University of Illinois School of Medicine at Rockford. A small focus group worked in the afternoon to pin down ways to improve services. They plan to release an action plan in the coming weeks that shows new strategies for service.
"The hope is that we can identify persons with behavioral health issues earlier, get them into the services they need earlier ... and actually get them into treatments and services prior to their involvement in the criminal justice system," said Michelle Rock, director of the Illinois Center of Excellence for Behavioral Health and Justice, which is located in Rockford.
The summit's keynote speaker was Patricia Griffin, a senior consultant for Policy Research Associates and the Pennsylvania Mental Health and Justice Center of Excellence. She said Winnebago County's services are already ahead of the curve because of its nationally recognized specialty courts, rehabilitative programs for inmates, crisis intervention training for law enforcement and the triage center operated by Rosecrance Health Network.
"There are a number of things I see as real strengths here in the county," Griffin said. "They're proud of what their strengths are, but they want to keep doing more."
Kevin Haas: 815-987-1410; firstname.lastname@example.com; @KevinMHaas


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Lidocaine is a topic covered in the Guide to Diagnostic Tests.
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Nicoll, Diana, et al. "Lidocaine." Guide to Diagnostic Tests, 7th ed., McGraw-Hill Education, 2017. Emergency Central, emergency.unboundmedicine.com/emergency/view/GDT/619270/all/Lidocaine.
Nicoll DD, Lu CMC, McPhee SJS. Lidocaine. Guide to Diagnostic Tests. McGraw-Hill Education; 2017. https://emergency.unboundmedicine.com/emergency/view/GDT/619270/all/Lidocaine. Accessed April 1, 2023.
Nicoll, D., Lu, C. M., & McPhee, S. J. (2017). Lidocaine. In Guide to Diagnostic Tests (7th ed.). McGraw-Hill Education. https://emergency.unboundmedicine.com/emergency/view/GDT/619270/all/Lidocaine
Nicoll DD, Lu CMC, McPhee SJS. Lidocaine [Internet]. In: Guide to Diagnostic Tests. McGraw-Hill Education; 2017. [cited 2023 April 01]. Available from: https://emergency.unboundmedicine.com/emergency/view/GDT/619270/all/Lidocaine.
* Article titles in AMA citation format should be in sentence-case
TY - ELEC T1 - Lidocaine ID - 619270 A1 - Lu,Chuanyi Mark, AU - Nicoll,Diana, AU - McPhee,Stephen J, BT - Guide to Diagnostic Tests UR - https://emergency.unboundmedicine.com/emergency/view/GDT/619270/all/Lidocaine PB - McGraw-Hill Education ET - 7 DB - Emergency Central DP - Unbound Medicine ER -


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Ashima Sends V13 in Colorado
Twelve-year-old Ashima Shiraishi has just climbed her fifth V13 by sending The Automator in Colorado's Rocky Mountain National Park.
Photo by Eddie GianelloniTwelve-year-old Ashima Shiraishi has just climbed her fifth V13 by sending The Automator in Colorado's Rocky Mountain National Park. Shiraishi needed only two sessions to send the problem, which was first climbed in August of 2000 by Dave Graham. The Automator sits in an area know as Lower Chaos Canyon and became the first problem of the grade to be completed by a female climber when Angie Payne topped it out in 2010.
This is the second V13 send for Shiraishi this month. The young globe-trotting climber from New York City was recently spending time in Magic Wood, Switzerland, where she sent One Summer in Paradise. Since she started climbing in 2007 at the age of six, Shiraishi has become the number one female climber in the world. In a mere six years of climbing, she has sent two 5.14c's (Lucifer and Southern Smoke in the Red River Gorge), five V13's (Fragile Steps and Steady Plums Direct in Rocklands, Crown of Aragorn in Hueco Tanks, One Summer in Paradise, and now The Automator) and flashed the V11 Black Demon in Rocklands, South Africa. She now plans to try Jade (v14), which is also located in RMNP.
Click HERE to read a Rock and Ice interview with Shiraishi from earlier this year.