Buck Lake Conservation Area has several trails along the north side of Hwy 46, and today's trip was the first of several to come as I explored this spot. Today's hike was only about 3 miles; it is good for hiking and would be just as good for biking.
I started today's hike at the western trailhead and my first destination was the tower that overlooks Buck Lake. There has been a lot of rain over the past few weeks, so I was expecting to see some flooding. Luckily the trails were dry though, so all I really had to think about was making it back before the afternoon storms started again today.
The western trailhead has a parking area just off the highway that includes a trailhead kiosk with a map of the area. The smaller kiosk that can be seen in the first picture has information about the hunting seasons.
The main trail from this point is called "Forest Road 1", and it is wide and clear as it heads to the east for about a mile. The first landmark is a path that heads to the north shortly after passing the kiosks. The trail looks like it has been cleared recently. I took a look at this from Google Earth when I got home, and it doesn't look like it goes very far. This may be a spot intended for water runoff.
Beyond this spot, the road is surrounded by fields of Pink Hibiscus that seem to go on for as far as the eye can see. These plants grow to at least six feet tall, and love the wetlands. The wetlands here are bisected with canal that appears to aid in draining Buck Lake into the flood plain to the south of highway 46.
After about .6 miles, there is an intersection where Forest Road 5 connects to the main east-west road. The intersection is marked with a post identifying the direction (north) to the lookout tower and primitive campsite. The road itself is covered in soft grass; this path is also easy to hike and would be fine for a bicycle too.
From here, the lookout tower is a short (about .4 miles) hike away. Both sides of the trail are surrounded by forest, but there is still a nice breeze that keeps all of the bugs at bay.
When I arrived at the tower, I was surprised to see a small boat that appeared to be in good shape sitting next to the lake, complete with an oar. I suspect that this boat has been left here for anyone to use – I saw another photo taken back in 2011 that showed this boat and a canoe. The view from the top of the tower is beautiful (take a look at the panorama photo at the top of this page).
To the east of the lookout tower is a primitive campsite with a fire ring and a couple of picnic tables, and a good supply of firewood. Near this campsite I noticed a couple of trees that were "tagged" with pink plastic ribbons. This is a method that is normally used to mark trails before someone comes in to clear the underbrush and blaze the trees, so I wanted to take a look to see how far this "possible trail" went. After about 150 yards though, there didn't seem to be any more ribbons to follow.
From here I headed back the way I came all the way back to the main forest road to resume hiking to the east. The next spot I was looking for was the trail road that heads north about a mile from the parking area. At this intersection there is a hydrological monitoring station.
As I started to head north at this point the mosquitos and flies were thick, so I was about to spray myself with some Deep Woods Off until I looked off to the west. All of the white fluffy clouds that I had been seeing today were being pushed away by a wall of very dark storm clouds, so this seemed like a good opportunity to head back before the thunder and lightning arrived. All in all though, this was a nice short hike – with all of the trails in this area, I think I'll be exploring this spot for a several more weekends.


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My Job Free TELEVISION is a complimentary online streaming service where you can watch motion pictures and TV programs being aired every day. This site focuses on upgrading TELEVISION shows. The majority of people nowadays prefer viewing films in your home. Optimizing their house theater, this gives them the exact same experience of being in the movie theater. Lately, the site is experiencing downtime, and the majority of its users are not able to access the old domain of the website. That is why a growing number of similar websites like Project Free TELEVISION are becoming popular. Today, I will evaluate a few of the most gone to movie and TELEVISION streaming sites that can be thought about as Project Free TV alternatives to enjoy motion pictures and TV shows.
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If you're a Korean and currently outside the nation or you're simply someone who enjoys to see Korean shows, this website will be best for you. It has a large catalog of TELEVISION shows being aired on a weekly or daily basis. The only disadvantage discovers in this website are the pop-up advertisements.
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If you are a sports lover and desire to view live video games from all around the world, this site is for you. If you click the arranged game, the website will include another tab for Advertisement, so make sure to go back to the main web page to start viewing. Remember not to put any personal information from the website because it does not collect anything to be able to watch on their website.
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To show the procedure of downloading using this tool, we will download a video from among the site's reviews which is Kshow123. There are 2 ways for you to download videos using this tool.
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Today, I will examine some of the most checked out film and TV streaming websites that can be considered as Project Totally free TV alternatives to watch movies and TV programs.
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MILFORD, Del. (AP) - The Delaware Department of Natural Resources and Environmental Control says an equipment problem led to the release of a hazardous chemical from a poultry processing facility on Friday.
Environmental officials say that a mechanical failure in a pump led to the release of more than 200 pounds of anhydrous ammonia from a Perdue Farms facility in Milford.
Perdue spokesman Joe Forsthoffer says a part of the plant was evacuated as a precaution for about 20 minutes because people working there smelled ammonia but no one was injured. Forsthoffer says the area around the plant wasn't affected.


Soften cuticles with China Glaze Orange Cuticle Oil. The light refreshing and nourishing oil penetrates dry, damaged cuticles quickly, softening and giving natural nails increased flexibility and strength. It also rejuvenates artificial nails. A special blend of five nourishing oils, jojoba, rice bran, and antioxidant rich vitamins A, C and E help heal dry, damaged cuticles. Botanical extracts act as a natural soothing and antiseptic agent. Available as a 14ml bottle.


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All you need to know about live music, musicians and the venues that you love in New Braunfels and the greater Wurstplex area!
Chris Stapleton returns to River Road Ice House
When: Thursday, August 11, 2016
Where: River Road Ice House, New Braunfels, TX
Opener: Quaker City Night Hawks
Tickets: SOLD OUT
The entire country music loving world now knows who Chris Stapleton is, although that wasn't always the case... Last October, a very large percentage of hardcore music lovers that stay REALLY tuned in to what's going on bought tickets to see Stapleton perform on October 25, 2015 at River Road Ice House. The weather wasn't super cooperative, and a large rain storm early on that day forced the show inside, and those few lucky souls who were able to make it witnessed history in the making. I've had it described to me as "amazing" and "the best music I've ever heard live" as well as a few others, but they performed for a packed INDOOR crowd, with the knowledge that they would need to eventually return and perform a make-up date outside to make good on the ticket sales for a big show on the big stage.
Two weeks later, Chris Stapleton won CMA awards for album of the year, new artist of the year and male vocalist of the year. He then went on earler this year to win numerous ACM, Americana Music Honors & Awards, ACCM, Billboard, British CMA, CMT awards and last but not least, TWO Grammys for Best Country Album and Best County Solo Performance! Needless to say, options and opportunities are seemingly wide open compared to last October, so the option of NOT returning to New Braunfels for a "make good" show would certainly be the easy path.
Oh man did they ever make good at River Road Ice House last night?! The typical band is Chris, his wife Morgane singing harmonies, J.T. Cure on bass and Derek Mixon on drums. Members of the band that aren't at all shows but at many of them are Mickey Raphael on harmonica and Robby Turner on pedal steel. Raphael has played with Willie Nelson for 43 years and was there last night, and Robby Turner who toured with The Highwaymen and later Waylon Jennings until Waylon's death, but has also been a go to steel player for many over several decades.
THANK YOU River Road Ice House for being such a WORLD CLASS live music venue!
Enjoy a couple of songs from last night's show!
Tennessee Whiskey (Dean Dillon/Linda Hargrove):
Whiskey and You (Chris Stapleton):
Posted by Brian Strickland on 8/12/2016
Tags: Chris Stapleton, gratitude, press, River Road Ice House, shotoniphone, video
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Prophets and Outlaws FRIDAY NIGHT at River Road Ic...
Jazz, TX Grand Opening TONIGHT
Will Hoge at 502 Bar
Zane Williams' headliner debut at Gruene Hall
Music of New Braunfels 2017. Powered by Blogger.

redpajama_set_name: RedPajamaCommonCrawl


This sample shows how to dock your forms to the edges of your main form. The child form can float or be docked to any of the four edges. It also shows how to create ToolBar windows and ToolTip windows.
This sample gets a bit involved and I'll leave most of the details to the code. In general, A ToolBar Window is created to display images representing a controls menu. Tooltip windows are created to display tooltips denoting the names of the controls the cursor is hovering over. In real life you want real controls and not images but the docking concept is the same. The window displaying the forms is set to be a child of the main window and is subclassed to receive and handle various Window's messages. The child window is positioned and sized corresponding to the edge it is docked to.
Download the source code and run it. Right click on the child forms caption to display its menu. Dock the form to the desired edge. Then you can use its title bar to drag it to the center of the form to make it float.


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Q: TensorFlowNET: IndexOutOfRangeException in TransferLearningWithInceptionV3 example During the execution of TransferLearningWithInceptionV3 IndexOutOfRangeException is thrown.
The version of SciSharp-Stack-Examples is from 8 Jan 2022.
The screenshot with exception

A: In the framework, they use feature vector caching and store it in txt as the sequence of comma-separated floats.
But in my culture decimal separator is also a comma. So this file is read incorrectly.
The error can be fixed if to apply culture that separates decimal part with a dot:
static void Main(string[] args)
{
  Thread.CurrentThread.CurrentCulture = CultureInfo.CreateSpecificCulture("en-GB");

redpajama_set_name: RedPajamaStackExchange


Thank you for your interest in church planting. By completing this form, you will allow us to become acquainted with you as we begin the process of assessment you as a church planter with APEX and the Baptist Bible Fellowship International.
The purpose of APEX is to enlist, train, equip, qualify, and support candidates who have a desire to plant churches in emerging communities. Your answers and responses on this form will be evaluated with this in mind and will be kept confidential. The people who will have access to this information will be limited to those who may have a role in evaluation and assessment, those who will be coaching your ministry, and others whom you authorize.
Criminal background check ( a link will be sent after the application has been received and acknowledged by our admin team).
Spiritual gifts survey (Click here to begin).
A couple's assessment will be sent pending the acceptance of the application (look for email from Greg Baxter pastorgbb@gmail.com).
Full length video of a sermon ( a link will be sent to upload your sermon after application has been received).
The next APEX assessment event will be September 9th- 11th.
In order to be considered for the next assessment, pre-assessment packets must be complete by July 22nd.
Presentation of APEX approved church planters at a BBFI National meeting and addition of candidate information to the website.
Participation in a cohort led by APEX certified trainers at a church near your target area.
Connection with an experienced church planter coach.
Please be as clear as possible in your answers and responses to this form. Brevity is a virtue, but please use as much space as needed to give an accurate report.
If naturalized, when and where?
If you have had cross-cultural ministry experience, indicate the nature and some of your responsibilities.
If you have had experience as a church planter, list the place, length of time, effectiveness, present status of congregation, etc.
If so, when and what church?
Describe briefly your conversion and subsequent spiritual growth.
Describe briefly your call to ministry and target area.
What is your current debt to income ratio?
Please list the higher education institutions you have attended, degrees earned, and the major or focus of study for each. Attach transcripts from each institution.
Please give the names and email addresses for people who know you and your work and who will serve as references for you. These need to be people who can report to us about your employment, ministry, character, skills, communication, family relationships, etc. We will contact them after receiving permission from you to do so, and give them a form to use for their responses.
I hereby certify that all of the information given in this application is true and correct to the best of my knowledge.


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HOPE Buffalo Hosts Youth & Community Award Ceremony
Every Child Is One Caring Adult Away from Being A Success Story
ERIE COUNTY, NY—Despite national cuts to the U.S. Department of Health and Human Services' Teen Pregnancy Prevention funding, HOPE Buffalo continues to demonstrate its firm commitment to teen pregnancy prevention. HOPE Buffalo, a partnership between CAI and the Erie County Department of Health ("ECDOH") is a youth and community-led collaborative of over 40 diverse stakeholders: teens, adults, health care providers, educators, faith-based and community leaders. This collaboration works together to promote equitable access to high-quality and comprehensive sexuality education and reproductive health services.
On March 22nd, 2018, HOPE Buffalo will host their Annual Awards Ceremony to recognize youth, key community stakeholders and partners, health care providers, and representatives from the Buffalo Public School District and the Buffalo School Board of Education for their efforts in promoting adolescent health and wellness for teens in nine selected zip code areas in Buffalo (14201, 14204, 14206, 14207, 14208, 14209, 14211, 14213 & 14215).
HOPE Buffalo's primary objective is to reduce teen pregnancy in Buffalo by 30% over a five-year period among females ages 15 to19. If current trends continue, we estimate that by 2020 the teen pregnancy rate could be as low as 26.1 (26.1 pregnancies for every 1,000 adolescent females ages 15-19) in our nine targeted areas. However, this trend is threatened due to a loss in funding, and teen pregnancy rates could easily rise again," said Stan Martin, Director of HOPE Buffalo. "Today is a time for us to recognize our achievements, address the ongoing disparities and highlight the opportunities that exist to sustain our work for generations to come."
"The efforts of ECDOH and HOPE Buffalo have not only led to reducing teen pregnancy rates, these efforts also foster a sense of purpose and hope for the future in our youth," said Dr. Gale Burstein, Commissioner of Health, ECDOH.
PATCH Program
OAH Teen Pregnancy Prevention Program
National Campaign to Prevent Teen and Unplanned Pregnancy
The HOPE Buffalo project is supported through a grant from the U.S. Department of Health and Human Services Office of Adolescent Health to the Erie County Department of Health and CAI (Cicatelli Associates Inc.).
This publication was made possible by Grant number 5 TP1AH000106-02-00 from the HHS Office of Adolescent Health. Contents are solely the responsibility of the authors and do not necessarily represent the official views of the Department of Health and Human Services or the Office of Adolescent Health.


Are you looking for some fun activities to do with the kids this Easter? This activity pack includes fun games to practice sight words, identifying alphabet uppercase and lowercase, ABC order, CVC rhyming, positional words, alphabet order strips, ABC picture puzzles, ten frame number match, numbers to ten clipping cards, number order picture puzzles, number order strips.
- Sight words - write the room Dolch pre-primer sight words.
- Alphabet upper and lowercase matching cards.
- ABC order picture puzzles.
- Positional words activity cards.
- Alphabet order dry-erase strips.
- ABC order dry erase strips.
- Ten frame number matching cards.
- Numbers to ten counting and clipping cards.
- Number order picture puzzles.
Some of the graphics in this book were made by DJ Inkers. Link and commercial license number included in the file.


In this second installment of Waiting on a Word's What to Watch, we talk ZOMBIES!
As you all know, I like me some sap. Beautiful stories about love and friendship and families warm my heart and make me cry. But guess what, Blogtropolis? I also love a good apocalyptic survivor story. I revel in watching drama unfold when characters find themselves in situations they never thought possible.
And that, my friends, is exactly what happens in The Walking Dead. Currently in its third season on AMC, TWD returns from mid-season hiatus this Sunday. Woo-hoo!
If you are in the minority of television viewers who aren't watching TWD, fire up your Netflix and get to watching Season One from the start. NOW! I can hear you fellow sap lovers whining: Zombies? Yuck. It's too gross. Trust me. TWD has something for everyone.
Without giving any spoilers I'll let you in on this tidbit. The series starts with our good guy, Rick (played by Andrew Lincoln), awaking from a coma to find that the world has been overrun with zombies.
Rick gets his act together pretty quickly and ventures out into the new zombie-infested world to find his wife and son, hoping they survived the outbreak. Lots of awesome stuff happens along the way. True, there's a bit of blood and guts, but I just cover my eyes for those parts. The story itself is worth the gory scenes.
TWD gives us drama, fear, suspense, intensity, hope, love. At its central core is humanity. The survivors' attempts to hold onto their humanity while fighting off "walkers." The process of accepting what the world has turned into. Inner struggles and fears versus the outer strength and strategies needed to survive in a changed world. As we follow this group of people through their journey, we wonder what we would do in the situations presented.
It's great television. Give it a try- one episode- it won't kill you (but maybe the walkers will… bah-hahahaha!). Not an episode goes by where I am not yelling at the television screen. Why are they going there? What are they doing? Oh my GOD don't they see that walker creeping up on them? They are the dumbest people on earth! Intensely awesome!
He's read all of The Walking Dead graphic novels and constantly compares them to the show. He keeps telling me how great they are, but I'm just not into the graphic novel format. If any of you are, definitely give them a read!
And, since this is my forum for writing about whatever I want, I'd like to put this out there for the record: Zombies are the BEST form of supernatural antagonistic creatures. Here's why.
Vampires are beautiful, charming and usually rich and cultured. However, us normal blood-pumping humans have little or no chance against vampires. Traditionally, they are faster and stronger and more cunning than us mortals. And if you're a pretty teenage girl with a mediocre personality, forget it! You're doomed to fall in love with an obsessed teenaged vampire and be turned into one eventually yourself. It's just the way the cookie crumbles.
Werewolves are somewhat normal until the full moon. Again, we have no chance against a man-turned-werewolf. They can sniff us out and overtake us, ripping us to pieces in mere minutes without giving us regular folks sufficient time to run away and hide.
Zombies, however, are totally beatable. The slow-moving, dumb-as-nails zombies drag their feet and take their time approaching, grunting and snorting so they can't even sneak up on you. If you have a weapon, you can shoot them in the head from a distance. If they happen to get close enough, you just swing something at them to knock through their brains. It's not pretty, but any schmuck who can swing an ax can defeat a zombie.
Also, when you kill a zombie, you don't feel bad about yourself. Essentially, you are doing them a favor by putting them out of their misery. They aren't people anymore and don't have human qualities like vampires and werewolves. They are creatures stuck in purgatory, and by killing them, you send them to a better place.
I think this is why people love a good zombie story. Usually, zombies are unlikeable and dim-witted (unlike vampires) and easily defeated (unlike werewolves). Average people can defeat zombies.
Average people defeating zombies is the premise of TWD. It's survival and drama and all the stuff that excellent television shows are made of. Try one episode! It's worth your hour.


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About 100+ WWC
Impact Journal
Member Tips & Tutorial Videos
Attend a Giving Circle
Previously Selected Charities
List of Nominated & Approved Charities
Charity Directory
Members – Nominate A Charity
Charities – Self Nomination Form
Q3 2018 = Going Strong!
Year FOUR is going strong! This quarter our groups touched the lives of individuals battling Parkinson's disease; mothers experiencing a tragic life event; first responders and their families; and disadvantaged youth and teens. Each of these organizations are doing important work in our community. Thanks to our members' giving hearts, we donated $28,500 this quarter and people's lives are being impacted on a daily basis. To date, our chapter has donated $322,800 to local charities.
Ahwatukee donated $11,300 to Banner Neuro Wellness, an organization under the umbrella of Banner Health Foundation. This organization provides complementary to current medical treatments and therapies for individuals and families who are affected by Parkinson's disease and other neurological conditions.
It costs $45 a month for individuals with Parkinson's disease to use the program and facilities. Our donations will be used to provide scholarships to people who cannot afford this vital resource.
Mother's Grace was the recipient of $8,800 in donations from our Scottsdale group. This charity is dedicated to the support of mothers and children who have endured life tragedies. By providing financial support and guidance, Mother's Grace empowers these women to reach their goals of making a difference in their communities by helping others inflicted with similar circumstances. Mother's Grace is committed to healing the world one mother at a time.
Our donations will be used to help between 5 and 10 Valley families with their immediate needs such as rent, utilities, car repairs, groceries, medical payments, and other acute needs that are explained in Mother's Grace. Our donation will be used for outreach and implementation of the program in our community.
Our West Valley sister group donated $2,600 to 100 Club of Arizona. This charity's mission is to provide financial assistance to families of first responders who are seriously injured or killed in the line of duty and provide resources to enhance their safety and welfare. They have proudly served the public safety community since 1968.
Our donations will be used in the general fund for whatever the most pressing need is at the time, including financial assistance to families and safety stipends.
Our East Valley group selected ICAN Positive Program for Youth and donated $5,700. ICAN is a free youth center in the East Valley that offers programming for youth, teens, families and the community. ICAN's nationally-recognized prevention programming teaches disadvantaged youth real-life skills including goal setting, positive decision making and how to avoid the risky behaviors that are prevalent in the community ICAN serves.
Our donations will be used to support the youth after-school programs offered in Chandler. Specifically, funding support staff to provide the program, supplies needed to facilitate program activities, food and transportation costs associated with the program and a portion of program training and development to ensure the highest quality programs are provided to kids.
Congratulations to our very own Kim Tarnopolski for receiving the First Runner Up award in the MASK Moms Making a Difference series. Kim was recognized for her work with our chapter and the impact she is making on children throughout the Valley of the Sun. Way to go, Kim!
Happy fall! See you in November!
Designed by Another Hand Advantage | Copyright 2014


Although he was officially in town to promote his new book, it's what Joe Biden said about 2020 that drew people's attention a recent event in Missoula, Montana. The former vice president expressed supreme confidence in his qualifications to be America's next Commander-In-Chief, and in fact, explicitly said that nobody is as qualified as him.
Of course, the first votes in the next Democratic presidential primary won't be cast for more than a year. But this hasn't stopped pollsters from asking Democrats which candidate they prefer to challenge Trump in 2020, and in those surveys, Biden regularly leads the pack. Most recently, a November Reuters/Ipsos poll found that 29 percent of Democrats support Biden in 2020, with Sen. Bernie Sanders in second with 22 percent.
But despite his strong position and obvious desire to become president, Biden stressed that "my family and I need to decide as a unit whether we're ready" for him to run in 2020.
"We do everything as a family," he said.
Biden said in Montana that he'll decide within the next two months whether or no to mount what would be his third presidential campaign, according to CNN.
Biden came close to running for president in 2016, but decided not to on account of the death of his son, Beau, from cancer. This was the third sudden death in Biden's immediate family during his political career; his first wife and daughter were killed in a car crash in 1972, after he won his first election to the Senate but before he had been sworn in.
If Biden runs in 2020, it will be his third presidential campaign after failed runs in 1988 and 2008. He acknowledged on Monday that his reputation as a "gaffe machine" could hurt him in another national election — but also said that, when running against Trump, his gaffes could be a source of strength.
"I may be a gaffe machine, but my god, what a wonderful thing compared to a guy who can't tell the truth," Biden joked. "No one doubts what I say — the problem is, I sometimes say all that I mean."
Sen. Elizabeth Warren, who could find herself running against Biden for the Democratic nomination in 2020, was asked Tuesday whether or not she agrees that Biden is the most qualified person in the country to be president.
"I think the vice president has many wonderful qualities," Warren responded. "I'm glad to hear he's out talking about them."


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text:
Q: Strange formula for area of a convex polygon Consider a convex $n-$gon in $\mathbb{R}^2$ with sides contained in the lines $y=k_ix+b_i, 1\leq i\leq n.$ Then its area equals to
$$
S=\frac{1}{2}\sum_{i=1}^{n} \frac{(b_{i+1}-b_i)^2}{k_{i+1}-k_i}.
$$
Of course, it is not hard to prove this formula, but it still looks a bit mysterious to me.
Question Has this expression appeared somewhere? It will be wonderful to see a pretty proof of it.
Remark Another expression for $S$ can be found here, formula (17). It is a toy analog of a MHV scattering amplitude in N=4 SYM.

A: Fedor's derivation is very slick and elegant - surely the best way to guess the formula if you didn't know it already.
It does however require additional justification to show that the oriented areas for all possible line positions will cancel appropriately to get the polygon area, especially if you are aiming to prove the formula for non-convex shapes as well (not asked by the OP but it does apply in this case as well.)
If you want to avoid this and derive it from a standard area formula for polygons  you can use Fedor's points of intersection $P_i$ and $P_{i+1}$ and plug them in to obtain:
\begin{equation}
\begin{aligned}
&\frac{1}{2}\sum_{i=1}^n \det|P_iP_{i+1}|\\
&=\frac{1}{2}\sum_{i=1}^n\frac{(b_{i+1}-b_i)(k_{i+1}b_{i+2}-k_{i+2}b_{i+1})-(b_{i+2}-b_{i+1})(k_{i}b_{i+1}-k_{i+1}b_{i})}
{(k_i-k_{i+1})(k_{i+1}-k_{i+2})}\\
&=\frac{1}{2}\sum_{i=1}^n\frac{b_{i+1}^2(k_i-k_{i+2})-b_{i}b_{i+1}(k_{i+1}-k_{i+2})-b_{i+1}b_{i+2}(k_i-k_{i+1})}
{(k_i-k_{i+1})(k_{i+1}-k_{i+2})}\\
&=\frac{1}{2}\sum_{i=1}^n\frac{b_{i+1}^2(k_i-k_{i+1}+k_{i+1}-k_{i+2})}
{(k_i-k_{i+1})(k_{i+1}-k_{i+2})}-\frac{1}{2}\sum_{i=1}^n\frac{b_{i}b_{i+1}}{(k_i-k_{i+1})}-\frac{1}{2}\sum_{i=1}^n\frac{b_{i+1}b_{i+2}}{(k_{i+1}-k_{i+2})}\\
&=\frac{1}{2}\sum_{i=1}^n\frac{b_{i+1}^2}
{(k_i-k_{i+1})}
+\frac{1}{2}\sum_{i=1}^n\frac{b_{i+1}^2}
{(k_{i+1}-k_{i+2})}
-\frac{1}{2}\sum_{i=1}^n\frac{b_{i}b_{i+1}}{(k_i-k_{i+1})}
-\frac{1}{2}\sum_{i=1}^n\frac{b_{i+1}b_{i+2}}{(k_{i+1}-k_{i+2})}\\
&=\frac{1}{2}\sum_{i=1}^n\frac{b_{i+1}^2}
{(k_i-k_{i+1})}
+\frac{1}{2}\sum_{i=1}^n\frac{b_{i}^2}
{(k_{i}-k_{i+1})}
-\frac{1}{2}\sum_{i=1}^n\frac{b_{i}b_{i+1}}{(k_i-k_{i+1})}
-\frac{1}{2}\sum_{i=1}^n\frac{b_{i}b_{i+1}}{(k_{i}-k_{i+1})}\\
&=\frac{1}{2}\sum_{i=1}^n\frac{b_{i+1}^2+b_{i}^2-2b_{i}b_{i+1}}
{(k_i-k_{i+1})}\\
&=\frac{1}{2}\sum_{i=1}^n\frac{(b_{i+1}-b_{i})^2}
{(k_i-k_{i+1})}
\end{aligned}
\end{equation}
Update: Actually I just realised that Fedor's method looks to be the exact dual of the method behind the formula I used:
"Sum the areas to a point between two points meeting at consecutive pairs of polygon sides" (The method I used)
$\Updownarrow$ "point-line duality"
"Sum the areas to a line between two lines joining consecutive pairs of polygon points" (Fedor's method)
So this might be a good way to justify it.

A: Denote $A_i=(0,b_i)$. It is a point on $\ell_i=\{(x,y):y=k_ix+b_i\}$, and let $$P_i=\ell_i\cap \ell_{i+1}=\left(\frac{b_{i+1}-b_i}{k_i-k_{i+1}},\frac{k_ib_{i+1}-k_{i+1}b_i}{k_i-k_{i+1}}\right)$$ be the vertex of the polygon. The (properly oriented) area of $\triangle A_iP_iA_{i+1}$ equals $\frac{(b_i-b_{i+1})^2}{2(k_{i+1}-k_{i})}$, and the sum of such oriented areas is the oriented area of the polygon.


text:
Hearing Health Tech Company, TympaHealth appoints Lord David Prior as Chairman
ByVisualast
Jul 7, 2022 Banking & Financial Services, Health Care & Hospitals, Medical Pharmaceuticals, Personnel Announcements, Tympa Health Technologies Ltd
LONDON and MIAMI, July 7, 2022 /PRNewswire/ — TympaHealth is pleased to announce Lord David Prior as their Chairman. David comes with many years of experience in health and banking. He has recently stepped down as Chairman of the UK National Health Service (NHS), a position he held from November 2018 – April 2022. Before that, he was a Minister in the Department of Health, Chairman of the Care Quality Commission, and Chairman of University College London Hospitals NHS Foundation Trust. He still serves as Deputy Chairman of Lazard in London and chairs the Cambridge Life Sciences Council.
David first became aware of TympaHealth a few years ago as a trailblazing NHS spin-out company and one of the case studies for the NHS England Clinical Entrepreneur Program. On meeting Dr. Krishan Ramdoo, an NHS ENT Surgeon, he was inspired by Krishan's vision to digitise the ear and hearing care pathway and take services safely out of the hospital setting into the community.
"We are thrilled to welcome David as our Chairman. He brings invaluable experience at a pivotal time for us as a company. Tympa has supported more than 200,000 patients to date and is now nearing 12,000 patient interactions per month through multiple sectors. David will help us develop and drive continued growth, not only in the UK but as we take the next steps into the US market and global stage." – Dr. Krishan Ramdoo | CEO TympaHealth
David said, "I am absolutely delighted to be joining the Tympa team to help them in this growth phase of their journey. They have developed exciting, world-class British technology which I am delighted to support. I am equally proud that it is a company born out of the NHS, one of the world's greatest universal healthcare systems".
Lord Prior joins an impressive team of investors, entrepreneurs, and executives backing TympaHealth as the next-generation platform for hearing care and wellness. "We're excited to have Lord Prior's leadership as Tympa builds on the tremendous clinical and patient-driven adoption to date," said Jim Breyer, CEO & Founder of Breyer Capital and a globally recognized technology investor who participated in Tympa's most recent financing. "David's experience in leading the NHS and its efforts to expand community access to care aligns well with Tympa's mission to improve hearing health awareness, access, and treatment globally."
For more information, please visit the Company's website at tympahealth.com
SOURCE Tympa Health Technologies Ltd
Considerations for coverage of digital therapeutics – Healthcare Economist
Physicians Immediate Care bought by TAG—The Aspen Group
By Visualast
A Father-Son Interview – The Health Care Blog
Hive hackers gang that targeted hospitals infiltrated by FBI


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COMMENT: The airport at the end of the world
They call it the airport at the end of the world and no wonder. St Helena is a dot in the South Atlantic, 1,950km (1,210mi) west of the border between Namibia and Angola in south-west Africa and 4,000km (2,500mi) east of Rio de Janeiro. It is about 16km (10mi) long and 8km (5mi) wide and had a population as of the 2008 census of precisely 4,255, though presumably a few more now.
Put another way, St Helena is a very long way from the nearest major landmass, and until now could be reached only by sea. The voyage takes five days from Cape Town with a departure once every three weeks. According to the statisticians, this made St Helena one of the most remote populated places on earth in terms of travel time from major cities.
Now, finally, in a tribute to the triumph of vision and persistence, St Helena has an airport, an achievement that deserves a wider audience than hitherto apparent.
The airport is scheduled to open next month and for St Helena residents, known as 'Saints', who once counted the banished Napoleon among their number, it means their island will for the first time be linked to the rest of the world by air.
The idea of an airport was first mooted in 1943 by the South African Air Force, which undertook a survey but concluded the project was not feasible. Pressure began to build again from the 1960s and the island government took up the cause in 1999, succeeding eventually in securing an agreement from the UK government in 2005. After further delays caused by the 2008 credit crunch, construction contracts were signed in November 2011.
As reported in this issue, South Africa-based BA partner airline Comair and the island's own Atlantic Star Airlines will be ahead of the field providing the first aviation links with the outside world, Comair via scheduled service to Johannesburg and ASA operating a charter to Luton, both using the B737-800.
Officials say the airport will help St Helena towards self-sufficiency, encourage economic development and reduce dependence on UK government aid by kick-starting the tourism industry.
As exotic destinations go, it's certainly different and, perhaps surprisingly, offers a tropical and mild climate. Temperatures in the capital, Jamestown, range from 21-28C in summer (January-April) and 17-24C the rest of the time.
Next time you want to wind down after a business trip, St Helena could be just the place.
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The exotic destination has a terminal of exotic size, all paid for by the UK tax payer.
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text:
Review> Set Designer Harnesses Nostalgia for Detroit in AMC's New Series, "Low Winter Sun"
By Susan Morris • September 25, 2013
(Courtesy AMC)
Nostalgia (nóstos), meaning "homecoming", a Homeric word, and (álgos), meaning "pain, ache", and was coined by a 17th-century medical student to describe the anxieties displayed by Swiss mercenaries fighting away from home. Ruth Ammon, set designer for the AMC television series, Low Winter Sun, used this word to describe the series in its most honorable sense. This tale of morality uses the architecture of Detroit's heyday, to embody the pride of the city which elevated middle working class life.
It is poignant that the city's decline is also apparent in every frame, rather than pimping these noble structures like urban porn. Whether featuring Albert Kahn's Packard Automotive Plant, 1903-11 (the production offices were next door to this location, one of the largest parcels of unoccupied real estate in the Western hemisphere); Kahn's Detroit Police Headquarters at 1300 Beaubien St., 1923 (given the same role in the series, but now under threat since the PDP moved out); the art deco David Stott Building of 1929 by Donaldson and Meier; St. Hyacinth Roman Catholic Church, 1924 by Donaldson and Meier; or the Venetian Gothic Ransom Gillis House, 1876-78 (documented extensively by photographer Camilo Jose Vergara), these were deliberate choices.
The tale centers on the murder investigation of a deeply corrupt cop. We know from the opening scene who did it—two of his fellow officers. One is an honest cop, Frank Agnew (Mark Strong), who agrees to participate after being fed misleading information by another cop, whose motives are more ambiguous. When Frank is assigned to solve the case, he must find a way to investigate without revealing his own guilt.
The visual language reflects these moral ambiguities: the lone figure in a landscape usually backlit, which could almost be in a Western, but the vast expanses are downtown, a hallmark of contemporary Detroit. Buildings are often sited next to these open fields dotted with wildflowers among the debris, like the remaining few teeth in a withered mouth, but we always see a child on a bicycle, a man walking (who has money for gas?) or a dog (one has a rat in its mouth). These silhouetted figures are in wide shots, a rare luxury in an urban context; when you shoot in New York or Los Angeles, the picture has to be carefully cropped to eliminate unwanted surroundings. The visual vocabulary has pronounced darks and lights, and is often shot with available light, or motivated with a single light source indoors. In addition, mirrored surfaces and shots looking through glass partitions all contribute to the dark mood.
The most modern location is the Coleman A. Young Municipal Center, originally called the City-County Building, 1954, an international style building designed by Harley, Ellington and Day featuring white marble facing with black marble spandrels. It is here that the series will come to a head, with a faceoff among the protagonists as they enter this courthouse. Unusually for Cold Winter Sun, the building is wedged into a cityscape with the 3-mile long Detroit People Mover elevated train snaking its way across the screen. We've seen this public transit system before in other scenes where the Ren Cen and other downtown sites can be seen in the backdrop.
On a up-note, Campus Martius Park (from the Latin for Field of Mars, where Roman heroes walked), which is the point of origin in the Detroit coordinate system—8 Mile Road is 8 miles from this point—is a revitalized green space with new stages, sculptures, an ice-skating rink, mini sand beach, and restaurants. It is filled with lunch-time workers, and is the site of a meeting of two warring gangsters, chosen as neutral territory in the midst of a vibrant public space.
Many films have been shot in Detroit from 8 Mile, Beverly Hills Cop, Gran Torino, Robocop and the recent documentaries Searching for Sugarman and Detropia (one of its characters is Tommy Stephens, proprietor of the Raven Lounge, a location used in Low Winter Sun). But Low Winter Sun uses the city differently. We frequent Brush Park, Greektown, Boston-Edison, Indian Village, Klenk Island, Cass Corridor, MorningSide as well as downtown. It's almost a cliche to say that the city plays a character in the series, but (not having seen the British original) it feels that this story could only have been set in this American city at this point in its history. That's nostalgia.
Low Winter Sun, AMC, Sundays 10/9 PM and on demand. 10 episodes (season started 8.11.13).
AMC Detroit nostalgia Reviews Television
June 27, 2019 First-ever Detroit City of Design Competition brings kinetic energy generators and a nap room
June 13, 2019 Lorcan O'Herlihy renovates Detroit's African Bead Museum


text:
Consumers Warned About Amazon.com Scam
Email appears to be from online retailer, but isn't
Mark Huffman Reporter
Millions of consumers now use Amazon.com to purchase everything from books to cookware, so it's no surprise scammers have latched onto the online retailer as a tool in their phishing schemes.
The Better Business Bureau (BBB) said it has received reports of emails, appearing to come from Amazon.com customer service, with the subject line "Thank you for your order." The message has the Amazon.com logo and looks legitimate in other ways, at least on the surface.
The email lists an order number, total price, and a link to view the order. Someone receiving the message who had not ordered anything might click the link to see what he has mistakenly been charged for. Someone who had actually ordered something from Amazon might click the link because the price and item description is wrong.
Anyone who clicks on the link would be sent to a fake site where an attempt would be made to steal her personal information.
It goes without saying you shouldn't click on the link. Amazon.com requests that anyone receiving one of these bogus emails forward it to stop-spoofing@amazon.com.
Amazon.com said it never asks for Social Security numbers, tax identification numbers or other personal information as part of its transactions. It also said it never asks customers to confirm account information by clicking on an email link.
Take a Financial Relief Quiz. Get matched with an Authorized Partner.
Mark Huffman
Mark Huffman has been a consumer news reporter for ConsumerAffairs since 2004. He covers real estate, gas prices and the economy and has reported extensively on negative-option sales. He was previously an Associated Press reporter and editor in Washington, D.C., a correspondent for Westwoood One Radio Networks and Marketwatch.


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text:
Q: Quick question on abelian von Neumann algebras concerning chapter 4.4. in Murphy's book:
He proceeds by stating

(1)If $A$ is a von Neumann algebra acting non-degenerately on the Hilbert space $H$ and if $\zeta$ is separating for $A'$, then $\zeta$ is cyclic for $A$
(2)If $A$ is an abelian von Neumann algebra acting non-degenerately on a separable Hilbertspace $H$, then $A$ has a separating vector.
(3)If $A$ is maximal abelian von Neumann algebra on a separable Hilbert space then $A$ has a cyclic vector

He proves (3) by employing (2) to $M$ and since $M=M'$ we know that the separating vector found by (2) is cyclic for $M$.
My question is : Do maximal abelian von Neumann algebras always act non-degenerately on the Hilbert space (if so, why?) or, which would be a little horrifying, does (3) actually only hold for max. abelian algebras that act non-degenerately on the space. (That would be terrifying, because in my opinion then the proof, that every abelian von Neumann algebra that acts on a separable Hilbert space is isomorphic to $L^\infty(\Omega,\mu)$ ..., would only hold for algebras that act non-degenerately, too.
Thanks!

A: If your abelian algebra $A$ is degenerate, that means that $I_A\ne I_H$. Then $A+\mathbb C\,(I_H-I_A)$ is an abelian algebra that contains $A$. So $A$ is not a masa.


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text:
Иолаи или иолеи (в греческой передаче), илийцы () — народ, засвидетельствованный в античную эпоху (нурагический период) на юге острова Сардиния. Иолаи были воинственными пастухами. В период доминирования на острове Карфагена, а позднее Рима укрылись в центральной части Сардинии в области между горными массивами Лимбара, Гочано и Монти-ди-Ала и возвышенностью Ольястра.

В нурагический период их территория простиралась от Кампиданской равнины (также: Иолейская равнина, Piana Iolea) до реки Тирсо на севере, где начиналась территория баларов, и где была найдена надпись латинским алфавитом «ILI-IUR-IN NVRAC SESSAR». Согласно легенде, прежние обитатели Илиона, то есть Трои после захвата города ахейцами обосновались в этой части Сардинии под именем «илийцев». Ещё один миф говорит о происхождении их названия от имени Иолая, героя, который привёл на Сардинию поселенцев и основал колонию.

По окончании Первой Пунической войны (241 год до н. э.), в 238 году до н. э. римские войска оккупировали основные карфагенские крепости на Сардинии, и население внутренней части страны противостояло новым завоевателям, которые ответили на это жестокими репрессиями.

В 227 году до н. э. Сардиния и Корсика стала второй римской провинцией (первой была Сицилия). Начало Второй Пунической войны и первые победы Ганнибала спровоцировали новые восстания на Сардинии, где после поражения римлян в битве при Каннах сардо-пунический вождь Ампсикора, на стороне которого воевали карфагеняне и иолаи, организовал новое восстание. В 215 году до н. э. повстанцы были наголову разбиты в битве при Корнусе войсками Тита Манлия Торквата, и таким образом карфагеняне окончательно потеряли власть над островом.

Население острова (иолаи и балары) продолжало сопротивляться римлянам, и в 174 году до н. э. консул Тиберий Семпроний Гракх нанёс им сокрушительное поражение, обратив в рабство около 80000 жителей острова. Илийцы, однако, отказались покоряться римлянам, и в течение почти всего имперского периода укрывались в горном регионе, ныне известном как Барбаджа ().

Барбаджа и её население продолжали оставаться угрозой ещё через полтысячелетия и для вандалов, которые, захватив Карфаген, в 456 году оккупировали прибрежные города Сардинии, однако не смогли овладеть всем островом. Не смогла с ними справиться и Византийская империя, которая контролировала остров лишь частично, за исключением территорий илийцев и баларов, чьи набеги прекратились лишь в 594 году, когда их предводитель Госпитон по настоянию папы Григория I заключил мир с византийцами и позволил проповедовать христианство среди своего народа.

Античные источники
 Диодор Сицилийский (IV, 30): «С ними часто воевали сначала карфагеняне, затем римляне, но не смогли их одолеть».
 Павсаний (X, 17, 5): «Карфагеняне в то время, когда они были сильны благодаря своему флоту, покорили всех, кого они встретили на Сардинии, за исключением илийцев, которые проживали на окраине острова и в Goceano».
 , монах-августинец, в III книге своих «Рассуждений» (Componimento, 1830), пишет: «… Они — (обитатели Тортоли и Лотцораи) являются древними илийцами, которых столь хвалили Плиний Старший и другие авторы, о чём не следует больше сомневаться или рассуждать, поскольку я уже достаточно показал в другом месте, в своё время колонизировали Сардинию»

Примечания

См. также
 Нурагическая культура
 Балары
 Протосардский язык

Доисторическая Сардиния
Пунические войны
Исчезнувшие народы Европы

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text:
Enzyme_catalysis
Enzyme catalysis
Enzyme catalysis is the catalysis of chemical reactions by specialized proteins, enzymes. Catalysis of biochemical reactions in the cell is vital due to the very low reaction rates of the uncatalysed reactions.
The mechanism of enzyme catalysis is similar in principle to other types of chemical catalysis. By providing an alternative reaction route and by stabilizing intermediates the enzyme reduces the energy required to reach the highest energy transition state of the reaction. The reduction of activation energy (ΔG) increases the number of reactant molecules with enough energy to reach the activation energy and form the product.
Daily Sensitivity Test
1 Induced fit
1.1 Catalysis by induced fit
2 Mechanisms of transition state stabilization
2.1 Catalysis by bond strain
2.2 Catalysis by proximity and orientation
2.3 Catalysis Involving Proton donors or acceptors
2.4 Electrostatic catalysis
2.5 Covalent Catalysis
2.6 Quantum Tunneling
3 Examples of catalytic mechanisms
3.1 Triose phosphate isomerase
3.2 Trypsin
3.3 Aldolase
The favored model for the enzyme-substrate interaction is the induced fit model.[1] This model proposes that the initial interaction between enzyme and substrate is relatively weak, but that these weak interactions rapidly induce conformational changes in the enzyme that strengthen binding.
Catalysis by induced fit
The advantages of the induced fit mechanism arise due to the stabilising effect of strong enzyme binding. There are two different mechanisms of substrate binding; uniform binding which has strong substrate binding, and differential binding which has strong transition state binding. The stabilizing effect of uniform binding increases both substrate and transition state binding affinity and differential binding increases only transition state binding affinity. Both are used by enzymes and have been evolutionarily chosen to minimize the ΔG of the reaction. Enzymes which are saturated, ie. have a high affinity substrate binding, require differential binding to reduce the ΔG, whereas largely substrate unbound enzymes may use either differential or uniform binding.
These effects have led to most proteins using the differential binding mechanism to reduce the ΔG, so most proteins have high affinity of the enzyme to the transition state. Differential binding is carried out by the induced fit mechanism - the substrate first binds weakly, then the enzyme changes conformation increasing the affinity to the transition state and stabilizing it, so reducing the activation energy to reach it.
It is important to clarify, however, that the induced fit concept cannot be used to rationalize catalysis. That is, the chemical catalysis is defined as the reduction of ΔG‡ (when the system is already in the ES‡) relative to ΔG‡ in the uncatalyzed reaction in water (without the enzyme). The induced fit only suggests that the barrier is lower in the closed form of the enzyme but does not tell us what the reason for the barrier reduction is.
Mechanisms of transition state stabilization
These conformational changes also bring catalytic residues in the active site close to the chemical bonds in the substrate that will be altered in the reaction. After binding takes place, one or more mechanisms of catalysis lowers the energy of the reaction's transition state, by providing an alternative chemical pathway for the reaction. There are six possible mechanisms of "over the barrier" catalysis as well as a "through the barrier" mechanism:
Catalysis by bond strain
This is the principal effect of induced fit binding, where the affinity of the enzyme to the transition state is greater than to the substrate itself. This induces structural rearrangements which strain substrate bonds into a position closer to the conformation of the transition state, so lowering the energy difference between the substrate and transition state and helping catalyze the reaction.
However, the strain effect is, in fact, a ground state destabilization effect, rather than transition state stabilization effect [2] [3]. Furthermore, enzymes are very flexible and they cannot apply large strain effect [4].
In addition to bond strain in the substrate, bond strain may also be induced within the enzyme itself to activate residues in the active site.
Substrate, bound substrate, and transition state conformations of lysozyme.
The substrate, on binding, is distorted from the typical 'chair' hexose ring into the 'sofa' conformation, which is similar in shape to the transition state.
Catalysis by proximity and orientation
This increases the rate of the reaction as enzyme-substrate interactions align reactive chemical groups and hold them close together. This reduces the entropy of the reactants and thus makes reactions such as ligations or addition reactions more favorable, there is a reduction in the overall loss of entropy when two reactants become a single product.
This effect is analogous to an effective increase in concentration of the reagents. The binding of the reagents to the enzyme gives the reaction intramolecular character, which gives a massive rate increase.
Similar reactions will occur far faster if the reaction is intramolecular.
The effective concentration of acetate in the intramolecular reaction can be estimated as k2/k1 = 2 x 105 Molar.
However, the situation might be more complex, since modern computational studies have established that traditional examples of proximity effects cannot be related directly to enzyme entropic effects [5] [6] [7]. Also, the original entropic proposal [8] has been found to largely overestimate the contribution of orientation entropy to catalysis [9].
Catalysis Involving Proton donors or acceptors
See also: Protein pKa calculations
Proton donors and acceptors, i.e. acids and bases, may donate and accept protons in order to stabilize developing charges in the transition state. This typically has the effect of activating nucleophile and electrophile groups, or stabilizing leaving groups. Histidine is often the residue involved in these acid/base reactions, since it has a pKa close to neutral pH and can therefore both accept and donate protons.
Many reaction mechanisms involving acid/base catalysis assume a substantially altered pKa. This alteration of pKa is possible through the local environment of the residue.
Hydrophobic environment
Increase pKa Decrease pKa
Adjacent residues of like charge
Salt bridge (and hydrogen
bond) formation
Decrease pKa Increase pKa
The pKa is can be modified significantly by the environment, to the extent that residues which are basic in solution may act as proton donors, and vice versa.
Serine protease catalytic mechanism
The initial step of the serine protease catalytic mechanism involves the histidine of the active site accepting a proton from the serine residue. This prepares the serine as a nucleophile to attack the amide bond of the substrate. This mechanism includes donation of a proton from serine (a base, pKa 14) to histidine (an acid, pKa 6), made possible due to the local environment of the bases.
It is important to clarify that the modification of the pKa's is a pure part of the electrostatic mechanism [3]. Furthermore, the catalytic effect of the above example is mainly associated with the reduction of the pKa of the oxy anion and the increase in the pKa of the histidine, while the proton transfer from the serine to the histidine is not catalyzed significantly since, it is not the rate determining barrier [10].
Electrostatic catalysis
Stabilization of charged transition states can also be by residues in the active site forming ionic bonds (or partial ionic charge interactions) with the intermediate. These bonds can either come from acidic or basic side chains found on amino acids such as lysine, arginine, aspartic acid or glutamic acid or come from metal cofactors such as zinc. Metal ions are particularly effective and can reduce the pKa of water enough to make it an effective nucleophile.
Systematic computer simulation studies established that electrostatic effects give, by far, the largest contribution to catalysis [3]. In particular, it has been found that enzyme provides an environment which is more polar than water, and that the ionic transition states are stabilized by fixed dipoles. This is very different from transition state stabilization in water, where the water molecules must pay with "reorganization energy" [11] in order to stabilize ionic and charged states. Thus, the catalysis is associated with the fact that the enzyme polar groups are preorganized [12].
Carboxypeptidase catalytic mechanism
The tetrahedral intermediate is stabilised by a partial ionic bond between the Zn2+ ion and the negative charge on the oxygen.
Covalent Catalysis
Covalent catalysis involves the substrate forming a transient covalent bond with residues in the active site. This adds an additional covalent intermediate to the reaction, and helps to reduce the energy of later transition states of the reaction. The covalent bond must, at a later stage in the reaction, be broken to regenerate the enzyme. This mechanism is found in enzymes such as proteases like chymotrypsin and trypsin, where an acyl-enzyme intermediate is formed. Schiff base formation using the free amine from a lysine residue is another mechanism, as seen in the enzyme aldolase during glycolysis.
It is important to clarify that covalent catalysis does correspond in most cases to simply the use of a specific mechanism rather than to true catalysis [3]. For example, the energetics of the covalent bond to the serine molecule in chymotrypsin should be compared to the well-understood covalent bond to the nucleophile in the uncatalyzed solution reaction. A true proposal of a covalent catalysis (where the barrier is lower than the corresponding barrier in solution) would require, for example, a partial covalent bond to the transition state by an enzyme group (e.g., a very strong hydrogen bond), and such effects do not contribute significantly to catalysis.
Quantum Tunneling
These traditional "over the barrier" mechanisms have been challenged in some cases by models and observations of "through the barrier" mechanisms (quantum tunneling). Some enzymes operate with kinetics which are faster than what would be predicted by the classical ΔG‡. In "through the barrier" models, a proton or an electron can tunnel through activation barriers. [13][14] Quantum tunneling for protons has been observed in tryptamine oxidation by aromatic amine dehydrogenase.[15]
Interestingly, quantum tunneling does not appear to provide a major catalytic advantage, since the tunneling contributions are similar in the catalyzed and the uncatalyzed reactions in solution [14] [16] [17].
Examples of catalytic mechanisms
In reality, most enzyme mechanisms involve a combination of several different types of catalysis.
Triose phosphate isomerase
Triose phosphate isomerase (EC 5.3.1.1) catalyses the reversible interconvertion of the two triose phosphates isomers dihydroxyacetone phosphate and D-glyceraldehyde 3-phosphate.
Trypsin (EC 3.4.21.4) is a serine protease that cleaves protein substrates at lysine and arginine amino acid residues.
Aldolase (EC 4.1.2.13) catalyses the breakdown of fructose 1,6-bisphosphate (F-1,6-BP) into glyceraldehyde 3-phosphate and dihydroxyacetone phosphate (DHAP).
^ Koshland DE (Feb 1958). "Application of a Theory of Enzyme Specificity to Protein Synthesis.". Proc. Natl. Acad. Sci. U.S.A. 44 (2): 98-104. PMID 16590179.
^ Jencks W.P. "Catalysis in Chemistry and Enzymology" 1987, Dover, New York
^ a b c d Warshel A., Sharma P.K., Kato M., Xiang Y., Liu H. and Olsson M.H.M. "Electrostatic Basis of Enzyme Catalysis", Chem. Rev., 2006, 106: 3210-3235
^ Warshel A. and Levitt M. "Theoretical Studies of Enzymatic Reactions: Dielectric Electrostatic and Steric Stabilization of the Carbonium Ion in the Reaction of Lysozyme" J. Mol. Biol., 1976, 103: 227
^ Stanton R.V., Perakyla M., Bakowies D. and Kollman P.A. "Combined ab initio and Free Energy Calculations To Study Reactions in Enzymes and Solution: Amide Hydrolysis in Trypsin and Aqueous Solution" J. Am. Chem. Soc. 1998; 120:3448-3457
^ Kuhn B.; Kollman P.A. "QM-FE and Molecular Dynamics Calculations on Catechol O-Methyltransferase: Free Energy of Activation in the Enzyme and in Aqueous Solution and Regioselectivity of the Enzyme-Catalyzed Reaction" J. Am. Chem. Soc. 2000; 122:2586-2596
^ Bruice T.C. and Lightstone F.C. "Ground State and Transition State Contributions to the Rates of Intramolecular and Enzymatic Reactions" Acc. Chem. Res. 1999; 32:127-136
^ Page M.I. and Jencks W.P. "Entropic Contributions to Rate Accelerations in Enzymic and Intramolecular Reactions and the Chelate Effect" Proc. Natl. Acad. Sci. USA 1971, 68:1678-1683
^ Warshel A. and Parson W.W. "Dynamics of Biochemical and Biophysical Reactions: Insight from Computer Simulations" Quart. Rev. Biophys. 2001 34: 563-679
^ Warshel A., Naray-Szabo G.,Sussman F.and Hwang J.-K. "How do Serine Proteases Really Work?" Biochemistry, 1989, 28: 3629
^ Marcus R. A. "On the Theory of Electron-Transfer Reactions. VI. Unified Treatment for Homogeneous and Electrode Reactions" J. Chem. Phys. 1965 43:679-701
^ Warshel A. "Energetics of Enzyme Catalysis", Proc. Natl. Acad. Sci. USA, 1978 75: 5250
^ Garcia-Viloca M, Gao J, Karplus M, Truhlar DG. How enzymes work: analysis by modern rate theory and computer simulations. Science. 2004 Jan 9;303(5655):186-95. PMID 14716003
^ a b Olsson MH, Siegbahn PE, Warshel A. Simulations of the large kinetic isotope effect and the temperature dependence of the hydrogen atom transfer in lipoxygenase. J Am Chem Soc. 2004 Mar 10;126(9):2820-8. PMID 14995199
^ Masgrau L, Roujeinikova A, Johannissen LO, Hothi P, Basran J, Ranaghan KE, Mulholland AJ, Sutcliffe MJ, Scrutton NS, Leys D. Atomic Description of an Enzyme Reaction Dominated by Proton Tunneling. Science. 2006 April 14;312(5771):237-41. PMID 16614214
^ Ball, P. " Enzymes: By chance, or by design?" Nature, 2004, 431: 396
^ Olsson M.H.M., Parson W.W. and Warshel A. "Dynamical Contributions to Enzyme Catalysis: Critical Tests of A Popular Hypothesis" Chem. Rev. 2006, 105: 1737-1756
Alan Fersht, Structure and Mechanism in Protein Science : A Guide to Enzyme Catalysis and Protein Folding. W. H. Freeman, 1998. ISBN 0-7167-3268-8
Concepts in asymmetric synthesis
Chirality, Stereocenter, Stereoisomer, Enantiomer, Diastereomer, Meso compound, Planar chirality, Chiral ligand, Axial chirality
Optical rotation, Enantiomeric excess, Diastereomeric excess, Chiral derivitizing agents
Chiral resolution
Crystallization, Kinetic resolution, Chiral column chromatography
Asymmetric induction, Chiral pool synthesis, Chiral auxiliaries, Asymmetric catalytic reduction, Asymmetric catalytic oxidation, Organocatalysis, Biocatalysis
Proteins: enzymes
Active site - Allosteric regulation - Binding site - Catalytically perfect enzyme - Coenzyme - Cofactor - Cooperativity - EC number
Enzyme catalysis - Enzyme inhibitor - Enzyme kinetics - Lineweaver-Burk plot - Michaelis-Menten kinetics - List of enzymes
EC1 Oxidoreductases/list - EC2 Transferases/list - EC3 Hydrolases/list - EC4 Lyases/list - EC5 Isomerases/list - EC6 Ligases/list
Categories: Enzymes | Catalysts
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Enzyme_catalysis". A list of authors is available in Wikipedia.
https://www.chemeurope.com/en/encyclopedia/Enzyme_catalysis.html


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Alfa Romeo Tipo A Monoposto was the first monoposto (single-seater) racing car, designed by Alfa Romeo. The car had two 6C 1750 straight-6 engines and gearboxes assembled side by side. Producing 230 bhp (172 kW), the car had top speed of 149 mph (240 km/h).
The car's best racing achievement was in the Coppa Acerbo of 1931; Tazio Nuvolari was third with Giuseppe Campari winning. Luigi Arcangeli was killed at Monza in 1931 while practising with this car for the Italian GP. The car's complex design ultimately led to it being very unreliable; Jano started to design a new car, the Tipo B (P3), to fix this problem. The Tipo A was made only four examples and only one replica exist today in Alfa Romeo Historical Museum in Arese.
Last updated on 10 March 2014 at 23:08.