When it comes to garage door service in Hennepin County, Minnesota, local residents have known they can count on Custom Door Sales, Inc. since 1946. Whether you need garage door repair or garage door installation, our excellent teams in the field or in our office are here to help you.
Through more than 50 years of hard work, Custom Door Sales has built our reputation as one of the largest and most reliable garage door companies in the Midwest. We carefully train all our technicians and sales force so that we can provide customers with the knowledge and answers that they need. There's a lot of decisions that must be made when purchasing a garage door, and Custom Door Sales would like to make these decisions easy for you.
Need help with a broken garage door spring? This is a very common issue for homeowners in Minnesota. Springs have a very difficult job as they're responsible for the opening and closing of your garage door by expanding and contracting while supporting a lot of weight. These heavy-duty pieces of equipment do eventually wear out and break. The cold weather in Maple Grove and throughout the Minneapolis-St. Paul-Bloomington metro area puts additional strain on your door springs, which means that they're more likely to break during the winter months.


The post was edited 1 time, last by Wendolyn ( Dec 5th 2018 ).
Razor Will Lv 1 4 1 Y Y - 180 - 46 12 - Sacrifices some SP and Mpto increase chance to hit with physical, ranged, and magic attacks by 4% for 40 seconds.
Razor Will Lv 2 14 1 Y Y - 180 - 100 22 - Sacrifices some SP and Mpto increase chance to hit with physical, ranged, and magic attacks by 4% for 50 seconds.
Razor Will Lv 3 24 1 Y Y - 180 - 145 29 - Sacrifices some SP and Mpto increase chance to hit with physical, ranged, and magic attacks by 4% for 60 seconds.
Razor Will Lv 4 34 1 Y Y - 180 - 214 39 - Sacrifices some SP and Mpto increase chance to hit with physical, ranged, and magic attacks by 4% for 70 seconds.
Persist Barrier Lv 1 12 12 Y Y - 2 - - - - Every 1 seconds, 7% sustained MP reducing barrier is activated and every party member within 4m is not interrupted when the cast spell except caster. Moving, using skill or all of MP takes away the effect.
Persist Barrier Lv 2 30 12 Y Y - 2 - - - - Every 1 seconds, 7% sustained MP reducing barrier is activated and every party member within 4m is not interrupted when the cast spell except caster. Moving, using skill or all of MP takes away the effect.
Persist Barrier Lv 3 60 12 Y Y - 3 - - - - Every 1 seconds, 6% sustained MP reducing barrier is activated and every party member within 8m is not interrupted when the cast spell except caster. Moving, using skill or all of MP takes away the effect.
Persist Barrier Lv 4 80 12 Y Y - 3 - - - - Every 1 seconds, 5% sustained MP reducing barrier is activated and every party member within 10m is not interrupted when the cast spell except caster. Moving, using skill or all of MP takes away the effect.
The post was edited 2 times, last by Wendolyn ( Dec 17th 2018 ).
Hurls a water elemental cluster of razor-sharp ice that deals 44 additional damage and slows the target's movement speed for 2 seconds.
Ice Arrow Lv 2 10 2 Y Y 1.5 35 24 93 - Slow Hurls a water elemental cluster of razor-sharp ice that deals 124 additional damage and slows the target's movement speed for 2 seconds.
Ice Arrow Lv 3 18 2 Y Y 1.5 35 24 135 - Slow Hurls a water elemental cluster of razor-sharp ice that deals 236 additional damage and slows the target's movement speed for 2 seconds.
Ice Arrow Lv 4 26 2 Y Y 1.5 35 24 186 - Slow Hurls a water elemental cluster of razor-sharp ice that deals 338 additional damage and slows the target's movement speed for 2 seconds.
Ice Arrow Lv 5 34 2 Y Y 1.5 35 24 251 - Slow Hurls a water elemental cluster of razor-sharp ice that deals 480 additional damage and slows the target's movement speed for 3seconds.
Ice Arrow Lv 6 42 2 Y Y 1.5 35 24 320 - Slow Hurls a water elemental cluster of razor-sharp ice that deals 652 additional damage and slows the target's movement speed for 3 seconds.
Ice Arrow Lv 7 50 2 Y Y 1.5 35 24 408 - Slow Hurls a water elemental cluster of razor-sharp ice that deals 845 additional damage and slows the target's movement speed for 3 seconds.
Ice Arrow Lv 8 58 2 Y Y 1.5 35 24 645 - Slow Hurls a water elemental cluster of razor-sharp ice that deals 1099 additional damage and slows the target's movement speed for 3 seconds.
Ice Arrow Lv 9 66 2 Y Y 1.5 35 24 972 - Slow Hurls a water elemental cluster of razor-sharp ice that deals 1635 additional damage and slows the target's movement speed for 4 seconds.
Ice Arrow Lv 10 74 2 Y Y 1.5 35 24 1823 - Slow Hurls a water elemental cluster of razor-sharp ice that deals 2690 additional damage and slows the target's movement speed for 4 seconds.
Hydraulic Rush Lv 1 7 3 Y Y 3 28 24 91 - - Powerful water elemental magic that deals 102 additional damage to the target.
Hydraulic Rush Lv 2 15 3 Y Y 3 28 24 155 - - Powerful water elemental magic that deals 230 additional damage to the target.
Hydraulic Rush Lv 3 23 3 Y Y 2.75 28 24 191 - - Powerful water elemental magic that deals 321 additional damage to the target.
Hydraulic Rush Lv 4 31 3 Y Y 2.75 28 24 264 - - Powerful water elemental magic that deals 459 additional damage to the target.
Hydraulic Rush Lv 5 39 3 Y Y 2.5 28 24 335 - - Powerful water elemental magic that deals 628 additional damage to the target.
Hydraulic Rush Lv 6 47 3 Y Y 2.5 28 24 424 - - Powerful water elemental magic that deals 819 additional damage to the target.
Hydraulic Rush Lv 7 55 3 Y Y 2.25 28 24 556 - - Powerful water elemental magic that deals 1064 additional damage to the target.
Hydraulic Rush Lv 8 63 3 Y Y 2.25 28 24 834 - - Powerful water elemental magic that deals 1455 additional damage to the target.
Hydraulic Rush Lv 9 71 3 Y Y 2 28 24 1600 - - Powerful water elemental magic that deals 2333 additional damage to the target.
Hydraulic Rush Lv 10 79 3 Y Y 2 28 24 3074 - - Powerful water elemental magic that deals 3942 additional damage to the target.
Attempts to mesmerize the target with a 100% chance to instill Sleep for 7 seconds.
Attempts to mesmerize the target with a 100% chance to instill Sleep for 8 seconds.
Attempts to mesmerize the target with a 100% chance to instill Sleep for 9 seconds.
Attempts to mesmerize the target with a 100% chance to instill Sleep for 10 seconds.
Polar Storm Strike Lv 1 15 12 N Y - 160 6 385 - - 80% chance of freezing the target for 3 seconds and dealing 386 damage.
Polar Storm Strike Lv 2 30 12 N Y - 160 7 607 - - 85% chance of freezing the target for 4 seconds and dealing 686 damage.
Polar Storm Strike Lv 3 54 12 N Y - 160 8 1186 - - 90% chance of freezing the target for 3 seconds and dealing 1496 damage.
Polar Storm Strike Lv 4 80 12 N Y - 160 9 7121 - - 85% chance of freezing the target for 3 seconds and dealing 6018 damage.
Evolution Lv 1 17 1 Y Y 2 200 21 107 23 - Turns the target ally into a powerful monster, also bestowing the same abilities of that monster, for 1 minute.
Evolution Lv 2 43 1 Y Y 2 150 21 285 47 - Turns the target ally into a powerful monster, also bestowing the same abilities of that monster, for 1 minute.
Evolution Lv 3 72 1 Y Y 2 100 21 1372 208 - Turns the target ally into a powerful monster, also bestowing the same abilities of that monster, for 1 minute.
Detection Lv 1 10 3 Y Y 1.75 54 - 131 - - Detects hidden characters within a 10m radius. Only 1 player is shown.
Detection Lv 2 20 3 Y Y 1.5 52 - 157 - - Detects hidden characters within a 15m radius. Only 1 player is shown.
Detection Lv 3 30 3 Y Y 1.25 50 - 268 - - Detects hidden characters within a 20m radius. Only 1 player is shown.
Detection Lv 4 40 3 Y Y 1 48 - 403 - - Detects hidden characters within a 25m radius. Only 1 player is shown.
Detection Lv 5 50 3 Y Y .75 46 - 608 - - Detects hidden characters within a 30m radius. Only 1 player is shown.
Detection Lv 6 60 3 Y Y .5 44 - 1097 - - Detects hidden characters within a 35m radius. Only 1 player is shown.
Third Eye 10 3 Y Y .5 60 20 100 200 - Install the totem to reveal hidden players within 20m in your area. If the hidden player is in range, their hidden state will be removed.
Mass Dispel Lv 1 23 5 N Y 1 - - 265 - - Casts the Dispel effect on all party members within 11m range of the player. Player does not receive the effect.
Mass Dispel Lv 2 55 5 N Y .5 - - 1932 - - Casts the Dispel effect on all party members within 15m range of the player. Player does not receive the effect.


Preserve Gentry Parsons Chair Gentry Parsons Chair in Ivory (Set of 2) By Home Loft Concepts in Ivory (Set of 2) By Home Loft Concepts tools and spices within straightforward attain by developing your personal modular kitchen storage unit, with add-ons for hanging cups, spatulas, a hand towel, or something you require to keep organized although throwing down on the stove. In the kitchen, space is key. Creatively expand the seating arrangement by adding bar stools to your kitchen island for a stunning breakfast bar. Far more than a place to shop barware, , our bar carts on wheels are them portable and great for entertaining guests and serving the perfect pear and thyme fizz cocktail Shop our assortment of kitchen islands, bar carts and kitchen storage concepts to give new life and space to your kitchen.
They have provided clients with useful purchasing guides for all the home projects that you have ever dreamed of performing. This business has numerous buying guides that have all of the details you need to have to make your Gentry Parsons Chair in Ivory (Set of 2) By Home Loft Concepts obtain. The acquiring guides have installation articles, along with beneficial how-to ideas to aid you accomplish your ambitions in property improvement, decorating, recreation, and far more. By employing these valuable guides, you can explore the distinct options and the designs that you want for your residence. Much more than something else, you will uncover Gentry Parsons Chair in Ivory (Set of 2) By Home Loft Concepts all of the answers that you need in order Gentry Parsons Chair in Ivory (Set of 2) By Home Loft Concepts to be effective with your next home project.
Faq & Quation for Gentry Parsons Chair in Ivory (Set of 2) By Home Loft Concepts ?
The table is beautiful!! The butterfly leaf is an excellent characteristic and makes the table big more than enough to seat the whole family. My boy assembled it for me personally. He is in engineering and was impressed by the product quality and sturdiness of the desk. It was delivered regularly and all the portions were in the field. Little or nothing was broken or lacking. I will order from your company because of the price, quality, and superb service.
I ordered 3 stools plus they arrived 2 days afterwards. I took a risk and ordered the reddish afteroses reading other evaluations that the color was unique of how it looked in the online photographs. I think the colour is perfect and matches the web photos pretty close. They were very simple to assemble. I did smell the gasoline smell that other people commented about, but it was the plastic wrap/packaging, not the bar stools themselves.
It's an excellent set rather than difficult to put together. Do note the chair pads atento become screwed directly into the chair frame without predrilled holes. As well before you purchase end up being sure to check just about everywhere to get the very best price.


text:
People Photographs
by Andrew D. Bernstein
LOS ANGELES, CA - DECEMBER 5: LeBron James #23 of the Los Angeles Lakers is seen during the National Anthem before the game against the San Antonio Spurs on December 5, 2018 at STAPLES Center in Los Angeles, California. NOTE TO USER: User expressly acknowledges and agrees that, by downloading and/or using this Photograph, user is consenting to the terms and conditions of the Getty Images License Agreement. Mandatory Copyright Notice: Copyright 2018 NBAE (Photo by Andrew D. Bernstein/NBAE via Getty Images)
Viewed 469 Times - Last Visitor from Viersen, 07 - Germany on 01/15/2021 at 3:29 PM
people nba california city of los angeles basketball sport usa horizontal match los angeles lakers national anthem staples center lebron james
There are no comments for Lebron James. Click here to post the first comment.

redpajama_set_name: RedPajamaCommonCrawl


The Mapping Clusters tools perform cluster analysis to identify the locations of statistically significant hot spots, cold spots, spatial outliers, and similar features. The Mapping Clusters toolset is particularly useful when action is needed based on the location of one or more clusters. An example would be the assignment of additional police officers to deal with a cluster of burglaries. Pinpointing the location of spatial clusters is also important when looking for potential causes of clustering; where a disease outbreak occurs can often provide clues about what might be causing it. Unlike the methods in the Analyzing Patterns toolset, which answer the question, "Is there spatial clustering?" with Yes or No, the Mapping Clusters tools allow visualization of the cluster locations and extent. These tools answer the questions, "Where are the clusters (hot spots/cold spots)?" , "Where are the spatial outliers?", and "Which features are most alike?".
Groups features based on feature attributes and optional spatial or temporal constraints.


text:
var fs = require('fs')

// Node modules
var sqwk = require('sqwk')

// App modules
var config = require('../config')
var util = require('./util')

// Begin module
module.exports = function(dir, callback) {

	// Read the directory
	if(config.log) sqwk.send([['Reading directory', dir]])

	// @todo Use async
	try {
		files = fs.readdirSync(dir)
	} catch(err) {
		callback(err)
	}

	var objects = {}

	files.forEach(function(file) {
		// If the file starts with our config.object_name and ends in .obj
		if(util.endsWith(file, config.object_ext) && util.startsWith(file, config.object_name)) {
			// Remove the sequential frame number from the end of the file
			var obj = file.substr(0,12)
			objects[obj] = obj
		}
	}); // files.foreach

	// Convert the object to an array
	var objects_array = []
	for(obj in objects) objects_array.push(obj)

	return callback(null, objects_array)
}

redpajama_set_name: RedPajamaGithub


text:
Pat Pat
Harms Keen?
Shots to defeat
The Pat Pat is one of only two tile based creatures to be given a name, the other being the Stranded Fish in Keen 3. It frequently appears in Keen 1, usually in little groups. One cannot be certain if it is a plant similar to a Venus Fly Trap or an animal similar to a mussel. Technically it is not a creature but a tile-based hazard which cannot move from the spot where it sits, and this argues for the identification as a plant. However, it should not be forgotten that the biology of Mars is very different from that of the Earth, so it may be neither of the two.
It is not known where the name "Pat Pat" originated from, possibly due to the creature's opening and closing its mouth.
The creature appears to have more animal characteristics than plant: it is not green, moves rapidly, even without prey and has a tongue. This is not a positive diagnosis however. Pat Pats do not like the cold, and are almost absent near the Mars polar caps. They also dislike darkness.
List of Keen 1 Creatures
List of Keen 1 Hazards
Retrieved from 'https://keenwiki.shikadi.net/w/index.php?title=Pat_Pat&oldid=16787'
Keen 1 enemies


A logistic function or logistic curve is a common sigmoid curve, given its name in 1844 or 1845 by Pierre Fran?ois Verhulst who studied it in relation to population growth. It can model the "S-shaped" curve (abbreviated S-curve) of growth of some population P. The initial stage of growth is approximately exponential; then, as saturation begins, the growth slows, and at maturity, growth stops.
Logistics is the management of the flow of the goods, information and other resources in a repair cycle between the point of origin and the point of consumption in order to meet the requirements of customers.
Logistics involves the integration of information, transportation, inventory, warehousing, material handling, and packaging, and occasionally security. Logistics is a channel of the supply chain which adds the value of time and place utility. Today the complexity of production logistics can be modeled, analyzed, visualized and optimized by plant simulation software.
The term logistics comes from the Greek logos, meaning "speech, reason, ratio, rationality, language, phrase", and more specifically from the Greek word logistiki , meaning accounting and financial organization. The word logistics has its origin in the French verb loger to lodge or to quarter. Its original use was to describe the science of movement, supplying & maintenance of military forces in the field. Later on it was used to describe the management of materials flow through an organization, from raw materials through to finished goods.
จากแนวความคิดการพัฒนาการขนส่งทางแม่น้ำและชายฝั่ง ผ่านการขนส่งโดยเรือ River Feeder Container ที่ทันสมัยล่าสุด เพื่อให้การบริการมีความครอบคลุมจากจุดเริ่มต้นไปสู่จุดหมายปลายทาง บริษัท เอส ซี จี โลจิสติกส์จำกัด จึงได้ต่อยอดการบริการเพิ่มขึ้น แบบ door to door โดยจัดตั้ง บริษัท Strategic Port Link หรือ SPL น้องใหม่ในกลุ่มบริษัทเอส ซี ให้บริการเชื่อมต่อการขนส่งทางบกกับการขนส่งทางน้ำ จัดหารถบรรทุกตู้คอนเทนเนอร์ตามแผนธุรกิจระยะที่ 1 จำนวน 30 คัน ขนส่งเชื่อมโยง (LINK) ระหว่างท่าเรือ ลานตู้คอนเทนเนอร์ (CY) และกลุ่มลูกค้าในนิคมอุตสาหกรรมทั่วประเทศไทย ด้วยงบลงทุนมากกว่าร้อยล้าน โดยคงเน้นย้ำนโยบายการประหยัดพลังงาน(CNG) และใส่ใจสิ่งแวดล้อมมุ่งสู่เป้า หมาย Green Logistics ตามนโยบายบริษัทในปี 2554.
Company Name : Strategic Port Link Co., LTD.


The associated pages of this site are work in general solely performed by Stephen Tate. I am a research scientist in field of biochemistry / proteomics and use astronomy as a relaxation method and also a means to better understand my position in everything.
The idea of sitting in a cold and dark field observing celestial objects is pure heaven.


text:
Q: Post request is not being sent thorugh JS to python I am making one online compiler-type web using python(flask), HTML, AJAX, JS.
here is my HTML code. I made one form which copy code from another EditText whose id is 'codebase'.And then assign value to codebase2 and send data to python code through Ajax in an async way.
            <form id="formRun" class="mr-auto" >
            <input type="hidden" id="codebase2" name ="codebase2" value="">
            <input type="hidden" id="input2" name ="input2" value="">
            <button  class="btn btn-outline-success my-2 my-sm-0 mr-auto runbtn"
            type="submit"  id="run">Run</button>
            </form>

JS code
//Assign value to hidden type.
document.getElementById("run").addEventListener('click', function(){

    document.getElementById("codebase2").value = document.getElementById("codebase").value;
    document.getElementById("input2").value = document.getElementById("input").value;

});

//Send data to python code
$(document).ready(function() {
    $('#formRun').on('submit', function(event) {
        $.ajax({
            data : {
                name : $('#codebase2').val(),

            },
            type : 'POST',
            url : '/QuickCode/process'
        })
        .done(function(data) {

                $('#output').text(data.output).show();

        });
        event.preventDefault();
    });
});

Python code
@app.route('/QuickCode/process', methods=['POST'])
def process():

    code = request.form['name']
    if code :
         program = {
                "script" : code,
                "language": "python3",
                "versionIndex": "0",
                "clientId": "98d1dddd58d....",
                "clientSecret":"5599cf7a4690......."
            }

         url = "https://api.jdoodle.com/v1/execute"

         response = requests.post(url, json=program)
         data_json = json.loads(response.text)

         outcode = data_json['output']
         print(outcode)
         return jsonify({'output': outcode})

But the problem is it does even not send post request so just my page refresh only happen.
Thank you in advance.

redpajama_set_name: RedPajamaStackExchange


text:
Katonah Classic Stage Film Festival Held as Drive-In: Filmmakers Young and Older From Around the World Present Different Views of our Changing World - Now Set for 8-31
The show must go on! The new local theater for classics Katonah Classic Stage in Katonah, NY (outside NYC ) is presenting its first Film Festival on Friday, August 28, at 8:00pm. This film festival will be shown in in a Drive-in set-up at the Bedford Playhouse in Bedford, NY at 8:30pm. Tickets are available on the website. UPDATE: Due to weather conditions, the festival will be held the same time but on August 31, 2020.
Though Katonah Classic Stage's mission is to present in-person productions of Shakespeare and other classics, because of the pandemic founder actor/director Trent Dawson and his team had to think out of the box. Hence, the KCS Film Festival was born.
Review of Uncut Gems on Netflix: Adam Sandler's Standout Performance Leads this Edge of Your Seat, Nail-biting Thriller.. and it's Better the Second Time Around
By Harry Sherer
With the Uncut Gems' arrival to Netflix, movie-watchers everywhere will have a second (and third and fourth) chance to watch the Safdie brother's explosive collaboration with Adam Sandler. One of Sandler's best acting performances in a decade, Uncut Gems was one of the best films 2019 had to offer, as well as indie-darling A24 Studio's most successful film in the box office, grossing over $50 million domestically. From the first month of the film's December 2019 release into early 2020, it felt like Uncut Gems was the film everyone was talking about.
With Sandler's killer performance, the world-class editing, Kevin Garnett's surprisingly polished acting chops, the ending that left theatres shocked, and everything in between, the film is an undisputed accomplishment for the Safdies, Sandler, and everyone else involved.
The film quickly arrived on Netflix only a month after theatrical release and hasn't left the trending page since. Given the boom of popularity surrounding the film's release and it's easy binge-watching access, this isn't a review of what it's like to watch Uncut Gems. This is a review of what it's like to watch Uncut Gems for the second time. If you keep reading I'll explain why this doesn't really matter, but for posterity's sake, I'll warn you once: spoilers abound.
Review of Netflix Series "Down To Earth" with Zac Efron: Zac Efron and Darien Olien Travel the World and Provide an Entertaining and Unique Glimpse into the Possibilities for a More Sustainable and Better World
By Julia Colucci
In his Netflix show Down to Earth, Zac Efron proves to be much more than Troy Bolton from High School Musical, or that hunky guy from Baywatch. Efron and his close friend Darin Olien (or as many people refer to him, the "Indiana Jones of Superfoods"), travel the world, learning how to live more sustainably. They tackle some of the world's biggest environmental problems and share ways that different countries are combatting them effectively.
Part of the show's appeal is getting to know the entertaining and humorous duo of Efron and Olien. The team visits eight incredible locations on their inspirational journey, and the ones that stood out to me the most include Iceland, France, Sardinia, and London.
In the pilot episode, Efron, Olien, and the crew explore the natural beauties of Iceland, a country that specializes in renewable energy. They tour a powerplant and learn that 100% of Iceland's electricity is generated from natural, renewable resources such as volcanic activity underground and their 10,000 extraordinary waterfalls.
The Reel Woman's Network: Crystal Chappell's New Platform Showcases Work by Females including Beacon Hill, Tainted Dreams, Venice the Series and more Original Works by Women
by Suzanne Ordas Curry
In a world where there are new streaming services popping up almost monthy- though I think 2020 has been espcially busy with the advent of Peacock and Disney and more, there are also other platforms being started by entreprenuers to serve specific audiences. The Reel Women's Network is one of them.
Started by Crystal Chappell of Open Books Productions in partnershsip with Jessica and Linda Hill of Bella Productions. the streaming network is dedicated to content created by women. There is free content on it but it is a subscription service and you can also buy just specific shows.
Are you a Fan of The Marvelous Mrs. Maisel? Listen to Rachel Brosnahan Dish on all the Details in a Live Event Sponsored by Temple Emanu-El Streicker
Review of Hulu's Little Fires Everywhere with Kerry Washington and Reese Witherspoon: This Twisted Tale of Two Families Is Addictive Yet Heavy so Take Your Time Binging It
Someone set fire to the house of a wealthy, prominent family in the small town of Shaker Heights, Ohio.
So begins the first scene of this Hulu original, which presents itself as a mystery, but quickly takes you back to the previous year, when everything started. With only one season and eight incredible, action-packed episodes, Little Fires Everywhere is easy to blow through in a week of binging. However, the content is very heavy and intense, so instead of watching it all at once, you might want to spread it out. I compare it to a rich slice of chocolate cake—it's delicious but best in small amounts.
Little Fires Everywhere follows two families—one being your typical upper-class, nuclear family, and the other being an underprivileged, single-parent family. The show never portrays one family-type as better than the other, but rather highlights the beauty and struggles that can come with both. The families are shown in their most vulnerable states, so over the course of the show you see how their conditions and experiences shape them as people. This is one of the reasons I found the show so interesting; it gives a very intimate view of lifestyles that are so different from my own.
Katonah Classic Stage Film Festival Held as Drive-...
Review of Uncut Gems on Netflix: Adam Sandler's St...
Review of Netflix Series "Down To Earth" with Zac ...
The Reel Woman's Network: Crystal Chappell's New P...
Are you a Fan of The Marvelous Mrs. Maisel? Liste...
Review of Hulu's Little Fires Everywhere with Kerr...


This men's cotton waffle sweatshirt looks great solo or layered with a jacket. Classic crew design has traditional drop shoulders, while zigzag stitching on the front zip pockets adds updated flair. 3-Stripes accent sleeves above the cuffs.


I moved from abroad directly to the Maison du Sport International (MSI) 10 years ago, right after it was built up. This is the ideal place to share best practices and advice! As a "small" federation, it is very valuable to be surrounded by a variety of sports organisations which we can easily reach in the next minute!


The perfect mid-weight full-zip layering piece. Made with double jersey knit polyester and spandex stretch knit for multi-directional movement. The new go-to piece in your closet when there's a little chill in the air.


This really is awesome images ideas about Employee Update Form - Customer Update Form Template Customer Information Update Form. Hopefully these provides you with some inspirations. This Images belongs to our Employee Update Form Inspirations pictures gallery. A curated listing of images which get you Good ideas and Inspiration.
Title "Employee Update Form - Customer Update Form Template Customer Information Update Form".


Smoky Joe gets an idea. A bad idea.
A new poney is supposed to arrive.
I'm not sure when in 2017, but I'm really excited about this. Let's hope it will be a good movie.
The main character countdown results.
arc en ciel Dash feels better after eating the cupcakes with vodka baked into them.
Last Hope Arc 1 Artem.
Something bad happens to arc en ciel Dash, and Pinkie Pie has to help out.


text:
import { mount } from "enzyme"
import { InquiryLogin } from "../../Views/InquiryLogin"
import { login } from "Utils/auth"
import { useArtworkInquiryRequest } from "../../Hooks/useArtworkInquiryRequest"
import { flushPromiseQueue } from "DevTools"
import { useInquiryContext } from "../../Hooks/useInquiryContext"
import { fill } from "../util"
import { useTracking } from "react-tracking"

jest.mock("Utils/auth")
jest.mock("../../Hooks/useArtworkInquiryRequest")
jest.mock("../../Hooks/useInquiryContext")
jest.mock("Utils/wait", () => ({ wait: () => Promise.resolve() }))
jest.mock("react-tracking")

describe("InquiryLogin", () => {
  const next = jest.fn()
  const submitArtworkInquiryRequest = jest.fn()
  const trackEvent = jest.fn()

  beforeAll(() => {
    ;(useArtworkInquiryRequest as jest.Mock).mockImplementation(() => ({
      submitArtworkInquiryRequest,
    }))
    ;(useInquiryContext as jest.Mock).mockImplementation(() => ({
      artworkID: "example",
      engine: { decide: jest.fn().mockReturnValue(false) },
      inquiry: { email: "example@example.com", message: "Hello world" },
      next,
      setContext: jest.fn(),
      setRelayEnvironment: jest.fn(),
    }))
    ;(useTracking as jest.Mock).mockImplementation(() => ({ trackEvent }))
  })

  afterEach(() => {
    next.mockReset()
    submitArtworkInquiryRequest.mockReset()
    trackEvent.mockClear()
  })

  it("renders correctly", () => {
    const wrapper = mount(<InquiryLogin />)

    expect(wrapper.html()).toContain(
      "We found an Artsy account associated with example@example.com."
    )
  })

  describe("without two-factor auth", () => {
    beforeAll(() => {
      ;(login as jest.Mock).mockImplementation(() =>
        Promise.resolve({ user: { id: "example-id", access_token: "token" } })
      )
    })

    it("logs in and sends the message", async () => {
      const wrapper = mount(<InquiryLogin />)

      expect(submitArtworkInquiryRequest).not.toBeCalled()
      expect(next).not.toBeCalled()

      // Enter password
      fill(wrapper, "password", "secret")

      // Submit form
      wrapper.find("form").simulate("submit")
      await flushPromiseQueue()

      expect(submitArtworkInquiryRequest).toBeCalledWith({
        artworkID: "example",
        contactGallery: true,
        message: "Hello world",
      })
      expect(next).toBeCalled()
      expect(trackEvent).toBeCalledTimes(1)
      expect(trackEvent).toBeCalledWith({
        action: "successfullyLoggedIn",
        auth_redirect: "http://localhost/",
        context_module: "inquiry",
        intent: "inquire",
        service: "email",
        trigger: "click",
        type: "login",
        user_id: "example-id",
      })
    })
  })

  describe("with two-factor auth", () => {
    it("logs in and sends the message", async () => {
      const wrapper = mount(<InquiryLogin />)

      expect(submitArtworkInquiryRequest).not.toBeCalled()
      expect(next).not.toBeCalled()

      // Enter password
      fill(wrapper, "password", "secret")

      // Login will error asking for 2fa code
      ;(login as jest.Mock).mockImplementation(() =>
        Promise.reject(new Error("missing two-factor authentication code"))
      )

      // Submit form
      wrapper.find("form").simulate("submit")
      await flushPromiseQueue()
      wrapper.update()

      // Input two factor auth code
      fill(wrapper, "authenticationCode", "code")

      // Login works now
      ;(login as jest.Mock).mockImplementation(() =>
        Promise.resolve({ user: { id: "id", access_token: "token" } })
      )

      // Submit form again
      wrapper.find("form").simulate("submit")
      await flushPromiseQueue()

      expect(submitArtworkInquiryRequest).toBeCalled()
      expect(next).toBeCalled()
    })
  })

  describe("with on-demand auth", () => {
    it("logs in and sends the message", async () => {
      const wrapper = mount(<InquiryLogin />)

      expect(submitArtworkInquiryRequest).not.toBeCalled()
      expect(next).not.toBeCalled()

      // Enter password
      fill(wrapper, "password", "secret")

      // Login will error asking for 2fa code
      ;(login as jest.Mock).mockImplementation(() =>
        Promise.reject(new Error("missing on-demand authentication code"))
      )

      // Submit form
      wrapper.find("form").simulate("submit")
      await flushPromiseQueue()
      wrapper.update()

      expect(wrapper.text()).toContain(
        "Your safety and security are important to us. Please check your email for a one-time authentication code to complete your login."
      )

      // Input two factor auth code
      fill(wrapper, "authenticationCode", "code")

      // Login works now
      ;(login as jest.Mock).mockImplementation(() =>
        Promise.resolve({ user: { id: "id", access_token: "token" } })
      )

      // Submit form again
      wrapper.find("form").simulate("submit")
      await flushPromiseQueue()

      expect(submitArtworkInquiryRequest).toBeCalled()
      expect(next).toBeCalled()
    })
  })
})


Thus, I have set out to make some basics, and I started with this T-shirt. I'm told the next on my list of makes should be a White button down dress shirt/blouse, a good "day dress", a black jacket with pencil skirt, a dressy jacket (this is where the Chanel-like jacket fits into the plan.) a Little Black Dress, a pair of nice black dress slacks, and well fitted jeans. From this arsenal, I should be able to run to the closet and mix-n-match a manner of outfits just by adding choice accessories and colored pieces to match any season, spring, summer, fall, or holiday.
Pairing it with shorts or a nice skirt changes the entire ensemble from casual to business. So, there, is it really just another ole' t-shirt? I think not. I just need to wrap my head around the idea of making the simple pieces needed to build a versatile wardrobe.
McCalls 6355: view C, I cut a size 16 based on the finished bust and graded the shoulders, neckline, and sleeve cap back to my normal size 14, including added 1/2" at the shoulder/neckline to narrow the opening, it was way too wide even for the size 14. The short sleeves were lengthened 1.5 inches from the pattern. I lowered the front neckline by 1.5" and lowered the bust dart by 1" and angle it up a tad to taste. The fabric is ponte knit from Hancock, so it only has 25% stretch. Next one I will lengthen at the hem another 1.5" or so, it falls just a teeny bit to high on the hip or maybe just take in the side seams. We shall see what happens with a different fabric.
I follow a lot of "idea" cites and get wardrobe planning tips from various sources all the time. What are some of the special places you all check to help you sew with a plan or purpose?
Great basic tee. I refer to the catalogues that I get, one of them is chadwick, the loft/ann taylor is my definite go-to, random online shops, and of course people watching.
Love this top! I need to make some basic, solid color tees too.
Love your white t-shirt! Very classic! I really like it with the maxi skirt.
Great job, can't wait to see more.


text:
\section{Introduction}
In this short note, we readdress the problem of the presence of arbitrage opportunities for the market models based
on fractional Brownian motion with the Hurst parameter $H\in (1/2,1)$. Statistical properties of these models make them important for financial applications; however, the presence  of arbitrage represents a certain obstacle from the theoretical point of view. This problem was intensively studied; see, e.g., \cite{BKiev,BPS,B11,Bj,C,G,Ma,R,Shi,Sal}. As can be seen from Example \ref{ex1} below, there is a discontinuity with respect to $H\to 1/2+0$   at the point $H=1/2$ of the wealth process   for some portfolio strategies.  The market where $H=1/2$ is arbitrage free, and the market with $H\in(1/2,1)$ allows arbitrage.
One of possible  some solutions  of this problem  is to use different constructions  of stochastic integral that are not based on Riemann sums
such as Wick integral (see \cite{BKiev,Bj}).  Another approach is to include proportional transaction costs in the model \cite{G,BPS}.
In addition,  it was suggested in \cite{C} that additional restrictions on the admissible strategies also can remove arbitrage. It was shown
in Theorem 4.3 \cite{C} that arbitrage cannot be achieved in the class of piecewise constant strategies with a minimal amount of
time between two consecutive transactions. The restrictions on the times between transactions were relaxed in \cite{B11}, Theorem 3.21.

 We suggest one more alternative class of strategies allowing to exclude arbitrage for a
 a  market based on a fractional Brownian motion with $H\ge 1/2$ with stochastic integrals generated by the Riemann  sums.
 We suggest to use admissible strategies that are not necessary piecewise constant and that
 they are constructed  using current observations processed with an arbitrarily small time delay.
   It can be noted that this is a natural restrictions on the class of the portfolio strategies;  in practice, certain delay in information transfer and execution is inevitable for practical implementation of a portfolio  strategy.
\par
We found that a simple  Bachelier type market of with these strategies is arbitrage free (Theorem \ref{ThNA}); this result is similar to
 to the results for piecewise constant strategies from  Theorem 4.3 \cite{C} and Theorem 3.21 \cite{B11}.
 \par
The most interesting result of this paper is that it appears  the  discontinuity with respect to $H$ at  $H=1/2$ of the expectations of stochastic integrals vanishes for our class strategies (Lemma \ref{ThE} and Theorem \ref{ThNA}(ii)).
\par
The proofs are based on a useful representation for
the fractional Brownian motion $B_H(t)$  with the zero mean.  We found that the increment  of $B_H(t)$ can be  represented as the sum of a two independent Gaussian
processes  one of  which is smooth in the sense that it is differentiable  in mean square sense,
with the derivative that is square integrable on the finite time intervals. Similarly to the drift part of the diffusion processes, expectations of the
integrals by
this process are non-zero for the processes adapted to it.
 This process can be considered as an analog of the drift. It has to be noted that  the term "drift" is usually applied to
 $\mu$ presented  for the process $\mu t+B_H(t)$; see
\cite{CNS},\cite{Mu},\cite{Es}, where  and estimation of $\mu$ was studied.
In  \cite{Mu}, the term "drift" was also used for a representation for $B_H$ after linear integral transformation and random time change via a standard Brownian motion process with constant in time drift.
 Our representation is for $B_H$ itself, i.e, without an integral transformation.
\section{The  main result}
\subsection*{The fractional Brownian motion and stochastic integration}
 We are
given a standard probability space $(\Omega,{\cal F},{\bf P})$, where $\Omega$ is
a set of elementary events, ${\cal F}$ is a complete $\sigma$-algebra of
events, and ${\bf P}$ is a probability measure.

 We  assume that $\{B_H(t)\}_{t\in{\bf R}}$ is a fractional Brownian motion such that $B_H(0)=0$
 with the Hurst parameter $H\in  (1/2,1)$ defined as described in \cite{Ma,GN}
 such that
 \begin{eqnarray}
 B_H(t)-B_H(s)=c_H\int_s^t(t-q)^{H-1/2}dB(q)+c_H  \int_{-\infty}^s\left[(t-q)^{H-1/2}-(s-q)^{H-1/2}\right]dB(q),
 \label{BBH}
 \end{eqnarray}
 where $t>s>0$,
 $c_H=\sqrt{2H\Gamma (3/2-H)/[\Gamma(1/2+H)\Gamma(2-2H)]}$ and  $\Gamma$ is the gamma function. Here
$\{B(t)\}_{t\in{\bf R}}$ is  standard Brownian motion such that $B(0)=0$.
\par
Let $\{{\cal G}_t\}$ be the filtration generated by the process $B(t)$.

For a given $T>s$, let ${\rm A}_0(s,T)$ be the set of all  processes  $\gamma(t)$, $t\in[s,T]$,
that are progressively
measurable with respect to the filtration $\{{\cal G}_t\}$ and such that ${\bf E}\int_0^T\gamma(t)^2dt<+\infty$.

Let ${\rm A}_\varepsilon[s,T]$  be the set of all  $\gamma\in{\rm A}_0[s,T]$
such that there exists an integer $n>0$ and a set of non-random times
${\cal T}=\{T_k\}_{k=1}^n\subset [s,T]$, where $n>0$ is an integer, $T_0=s$, $T_n=T$,
and $T_{k+1}-T_k\ge \varepsilon$, such that $\gamma(t)$ is ${\cal G}_{T_k}$-measurable for $t\in[T_k,T_{k+1})$.
In particular, this set includes all $\gamma\in{\rm A}_0[s,T]$ such that $\gamma(t)$ is ${\cal G}_{t-\varepsilon}$-measurable for all $t\in[s,T]$.
Let ${\rm A}^d[s,T]=\cup_{\varepsilon>0}{\rm A}_\varepsilon[s,T]$.

Let $\widehat{\rm A}_\varepsilon$ the set of all  $\gamma\in{\cal A}_0$ such that $\gamma(t)$ is ${\cal G}_{t-\varepsilon}$-adapted, and let $\widehat{\rm A}^d=\cup_{\varepsilon>0}\widehat{\cal A}_\varepsilon$.

\begin{lemma}\label{lemmaI} For any $\gamma\in{\rm A}^d[s,T]$, the integral $\int_s^T\gamma(t)dB_H(t)$ converge as a sequence of the corresponding
Riemann sums  in $L_1(\Omega,{\cal G}_{T},{\bf P})$.
\end{lemma}
The following lemma establishes continuity in $L_1(\Omega,{\cal G}_{T},{\bf P})$  of the stochastic integrals with respect to
the Hurst parameter $H$ at  $H=1/2$.
 \begin{lemma}\label{ThE}
For any $\gamma\in\widehat{\rm A}^d$, \begin{eqnarray}
{\bf E}\left|\int_s^T\gamma(t)dB_H(t)-\int_s^T\gamma(t)dB(t)\right|\to 0 \quad\hbox{as}\quad H\to 1/2+0.
\label{lim}\end{eqnarray} \end{lemma}
\par
This continuity does not take place for some $\gamma$, as can be seen from the following example
\cite{Shi}.
\begin{example}\label{ex0}
For any $H\in(1/2,1)$ and $T>s$,
\begin{eqnarray*}
(B_H(T)-B_H(s))^2=2\int_0^T(B_H(t)-B_H(s))dB_H(t).
\label{sqB}\eaaa
The integral converges  as a sequence of the corresponding
Riemann sums.
\end{example}
A  consequence of  Example  \ref{ex0} is that
\begin{eqnarray*}
{\bf E}\int_s^T\gamma(t)dB_H(t)\nrightarrow 0={\bf E}\int_s^T\gamma(t)dB(t) \quad\hbox{as}\quad H\to 1/2+0.
\eaaa
Therefore, the stochastic integrals by $dB_H$
depends discontinuously in $H\to 1/2+0$ for some $g\in{\rm A}_0[s,T]$.

By Lemma \ref{ThE}, it also follows from Example  \ref{ex0}
that,  for $\gamma_\varepsilon(t)={\bf E}\{g(t)|{\cal G}_{t-\varepsilon}\}$,
\begin{eqnarray*}
{\bf E}\int_s^T\gamma_\varepsilon(t)dB_H(t)\nrightarrow {\bf E}\int_s^T\gamma(t)dB_H(t) \quad\hbox{as}\quad \varepsilon\to 0+.
\eaaa
Therefore, the stochastic integrals by $dB_H$
depends discontinuously in $\varepsilon$ with these $g_\varepsilon$.

\subsection*{The market model}
The rules for the operations of the agents on the market define the
class of admissible strategies  where the optimization problems have
to be solved.

Let $X(0)>0$ be the initial wealth at time $t=0$ and let $X(t)$ be
the wealth at time $t>0$.
\par
We assume that the wealth $X(t)$ at time $t\in[0,T]$ is
\begin{equation}
\label{X} X(t)=\beta(t)b(t)+\gamma(t)S(t).
\end{equation}
Here $\beta(t)$ is the quantity of the bond portfolio, $\gamma(t)$ is the
quantity of the stock  portfolio, $t\ge 0$. The pair $(\beta(\cdot),
\gamma(\cdot))$ describes the state of the bond-stocks securities
portfolio at time $t$. Each of  these pairs is  called a strategy.

\par
 Let $\theta\in(0,+\infty]$ be given; the case where $\theta=+\infty$ is note excluded.

 Let $\{{\cal F}_t\}_{t\ge -\theta}$
be a filtration such that ${\cal F}_t\subseteq {\cal G}_t$ for all $t$.

\par  A pair $(\beta(\cdot),\gamma(\cdot))$  is said to be an admissible
strategy if the processes $\beta(t)$ and $\gamma(t)$ are progressively
measurable with respect to the filtration $\{{\cal F}_t\}$.

 In particular, the agents are not supposed to know the
future (i.e., the strategies have to be adapted to the flow of
current market information).

In addition, we require that  $$ {\bf E}\int_0^{T}\left[\beta(t)^2+
\gamma(t)^2\right]dt<+\infty.$$
This restriction bounds the risk to be accepted and  pays the same role as exclusion of doubling strategies; see examples and
discussion  on doubling strategies in \cite{B11}.

\begin{definition}\label{defS}
\begin{enumerate}
\item
Let ${\cal A}_0$ be the set of all $\gamma$ that are progressively measurable  with respect to $\{{\cal G}_t\}$
 such as described above.
\item
Let ${\cal A}_\varepsilon$ be the set of all  $\gamma\in{\cal A}_0$ such that there exists a finite set of non-random times ${\cal T}=\{T_k\}_{k=1}^n\subset [0,T]$, where $n>0$ is an integer, $T_0=0$, $T_n=T$,
and $T_{k+1}-T_k\ge \varepsilon$, such that  $\gamma(t)$ is ${\cal G}_{T_k}$-measurable for $t\in[T_k,T_{k+1})$.
\item
Let ${\cal A}^d=\cup_{\varepsilon>0}{\cal A}_\varepsilon$.
\item
Let $\widehat{\cal A}_\varepsilon$ the set of all  $\gamma\in{\cal A}_0$ such that $\gamma(t)$ is ${\cal G}_{t-\varepsilon}$-adapted.
\item
Let $\widehat{\cal A}^d=\cup_{\varepsilon>0}\widehat{\cal A}_\varepsilon$.
\end{enumerate}
\end{definition}

Note that $\widehat A_\varepsilon\subset {\cal A}_\varepsilon$ for any $\varepsilon>0$, and
the set ${\cal A}^d$  is wider than  the class of piecewise constant functions  considered in \cite{C}.

Suppose that, for some $\gamma\in{\cal A}_0$, the integral $\int_0^t\gamma(s)dS(s)$ converge as a sequence of the corresponding
Riemann sums. In this case, an  admissible
pair $(\beta(\cdot),\gamma(\cdot))$  is said to be an admissible
self-financing strategy if
 $$
dX(t)=\beta(t)db(t)+\gamma(t)dS(t)=\gamma(t)dS(t),
$$
meaning that
 $$
X(t)=X(0)+\int_0^t\beta(s)db(s)+\int_0^t\gamma(s)dS(s)=\int_0^t\gamma(s)dS(s),
$$
 Under this condition, the process
$\gamma(t)$ alone defines the strategy.

By Lemma \ref{lemmaI}, for any $\gamma\in{\cal A}^d$, the integral $\int_0^T\gamma(s)dS(s)$ converge as a sequence of the corresponding
Riemann sums  in $L_1(\Omega,{\cal G}_{T},{\bf P})$.

Let ${\cal A}$ be a set of admissible $\gamma$  (we will consider  ${\cal A}={\cal A}_0$, ${\cal A}={\cal A}^d$,  or ${\cal A}=\widehat{\cal A}^d$).

For  $H\in [1/2,1)$, we denote by ${\cal M}_{H}({\cal A})$ the market model described above with  ${\cal A}$ as the set of admissible $\gamma$ .

\begin{definition}\label{defNA} We say that the market model ${\cal M}_{H}({\cal A})$ allows arbitrage if there exists a strategy $\gamma\in{\cal A}$ such that the
integral $\int_0^t\gamma(s)dS(s)$ converges  as a sequence of the corresponding
Riemann sums, and   ${\bf P}(X(T)\ge 0)=1$ and ${\bf P}(X(T)>0)>0$ for the corresponding self-financing strategy with the wealth $X(T)=\int_0^t\gamma(s)dS(s)$ at time $T$ with the initial wealth $X(0)=0$.
\end{definition}

It is known that the market model ${\cal M}_{1/2}({\cal A}_0)$ does not allow  arbitrage.
On the other hand,  the market model ${\cal M}_{H}({\cal A}_0)$ allows arbitrage for any $H\in (1/2,1)$.
This can be seen from
 the following version of Example \ref{ex0} \cite{Shi}.
\begin{example}\label{ex1}
For any $H\in(1/2,1)$,
\begin{eqnarray}
X(T)=(S(T)-S(0))^2=2\int_0^T(S(t)-S(0))dS(t)=\int_0^T\gamma(t)dS(t),
\label{sq}\end{eqnarray}
is the wealth for an admissible strategy with $\gamma(t)$ selected as $2(S(t)-S(0))$. In this case, the integral integral $\int_0^T\gamma(s)dS(s)$ converges  as a sequence of the corresponding
Riemann sums.
\end{example}

A consequence of  Example  \ref{ex1} is that the stochastic integrals by $dB_H$
depends discontinuously in $H\to 1/2+0$, since it is not true that
\begin{eqnarray*}
{\bf E}\int_0^T\gamma(t)dB_H(t)\to 0={\bf E}\int_0^T\gamma(t)dB(t) \quad\hbox{as}\quad H\to 1/2+0.
\eaaa
This is an undesired feature; small deviations of the evolution
law for $B_H$  cause large changes of the wealth for a strategy.
In addition, it implies that non-arbitrage model ${\cal M}_{1/2}({\cal A}_0)$ and arbitrage allowing model ${\cal M}_{H}({\cal A}_0)$ are
statistically indistinguishable  for the case where $H\approx 1/2$.
\begin{theorem}\label{ThNA}
\begin{enumerate}
\item
For any $H\in [1/2,1)$, the market model ${\cal M}_{H}({\cal A}^d)$ is arbitrage-free.
\item
For any $\gamma\in\widehat{\cal A}^d$, \begin{eqnarray*}
{\bf E}\left|\int_0^T\gamma(t)dB_H(t)-\int_0^T\gamma(t)dB(t)\right|\to 0 \quad\hbox{as}\quad H\to 1/2+0.
\label{lim2}\eaaa
\end{enumerate}
\end{theorem}
\section{Proofs}
Let $s\ge 0$ be fixed.
By (\ref{BBH}), we have that
\begin{eqnarray*}
 B_H(t)-B_H(s)=W_H(t)+R_H(t),
 \eaaa
where
 \begin{eqnarray*}
 W_H(t)=c_H\int_{s}^t(t-q)^{H-1/2}dB(q),\qquad
R_H(t)=c_H  \int_{-\infty}^{s}f(t,q)dB(q),
\label{BBHa}\eaaa
and where $f(t,q)=(t-q)^{H-1/2}-(s-q)^{H-1/2}$.

Let $s\ge 0$ and $T>s$ be fixed.
For $\tau\in [s,T]$ and  $g\in L_2(s,T)$, set \begin{eqnarray*}
G_H(\tau,s,T,g)=c_H(H-1/2)\int_{\tau}^T(t-\tau)^{H-3/2}g(t)dt.
\eaaa
\begin{lemma}\label{ThM}
The processes $W_H(t)$ and $R_H(t)$, where $t>s$, are independent Gaussian $\{{\cal G}_t\}$-adapted processes with zero mean and such that
 the following holds.
 \begin{enumerate}
 \item
 $W_H(t)$ is independent on ${\cal G}_s$ for all $t>s$ and has an It\^o's differential in $t$ in the following sense:  for any $T>s$,
 there exists a function $h(\cdot,s,T)\in L_2(s,T)$ such that
 \begin{eqnarray*}
 \int_{s}^T\gamma(t)dW_H(t)=\int_{s}^TG_H(\tau,s,T,\gamma)d B(\tau)
\eaaa
for any $\gamma\in L_2(\Omega,{\cal G}_s,{\bf P},L_2(s,T))$.
\item
 $R_H(t)$ is ${\cal G}_s$-measurable for all $t>s$ and differentiable in $t>s$ in mean square sense. More precisely,
 there exits a process   ${\cal D} R_H$ such that
 \subitem(a)  ${\cal D} R_H(t)$ is ${\cal G}_s$-measurable for all $t>s$;
\subitem(b) for any $t>s$, \begin{eqnarray*} {\bf E} {\cal D} R_H(t)^2=c_H^2\frac{H-1/2}{2}(t-s)^{2H-2},\qquad
{\bf E}\int_{s}^t {\cal D} R_H(q)^2dq<+\infty;
\eaaa
\subitem(c)
for any $t>s$,  \begin{eqnarray}
\lim_{\delta\to 0} {\bf E}\left|\frac{R_H(t+\delta)-R_H(t)}{\delta} -{\cal D} R_H(t)\right|=0.\label{deflim}
\end{eqnarray}
\end{enumerate}
\end{lemma}
For $s\ge 0$, $T>s$, $\tau\in [s,T]$,  $g\in L_2(s,T)$, set \begin{eqnarray}
G_H(\tau,s,T,g)=c_H(H-1/2)\int_{\tau}^T(\tau-s)^{H-3/2}g(t)dt.
\label{GH}\end{eqnarray}
 \begin{corollary}\label{corr} Let $\gamma(t)$ be a process such that $\gamma(t)$ is ${\cal G}_s$-measurable for all $t$,
and that ${\bf E}\int_s^T\gamma(t)^2dt<+\infty$ for any $T>s$.
Then
\begin{eqnarray*}
\int_{s}^T\gamma(t)dB_H(t)=\int_{s}^T\gamma(t)dW_H(t)+\int_{s}^T\gamma(t){\cal D} R_H(t)dt\\
=\int_{s}^TG_H(\tau,s,T,\gamma)d B(\tau)+\int_{s}^T\gamma(t){\cal D} R_H(t)dt,
\eaaa
and the integrals here converge  in $L_1(\Omega,{\cal G}_{T},{\bf P})$.
\end{corollary}

\par
{\em Proof of Lemma \ref{ThM}} and Corollary \ref{corr} can be found in \cite{D15}.

{\em Proof of Lemma \ref{lemmaI}}. Suppose  that $\gamma\in{\rm A}_\varepsilon(s,T)$, where $\varepsilon>$.
Let ${\cal T}_\varepsilon=\{T_k\}_{k=1}^n$  be the set such as in the definition of ${\rm A}_\varepsilon(s,T)$.
By Corollary \ref{corr}, the integrals $\int_{T_{k-1}}^{T_k}\gamma(t)dB_H(t)$ converge as required for all $k$.
Then the proof follows. $\Box$.

{\em Proof of Lemma \ref{ThE}.}
 Let $\Theta$ denotes a finite set of non-random times $\{T_k\}_{k=1}^n\subset [s,T]$, where $n>0$ is an integer, $T_0=s$, $T_n=T$,
and $T_{k+1}\in(T_k,T_k+\varepsilon)$; this times are not necessarily equally spaced.
For $\delta\in(0,\varepsilon)$, let ${\cal T}_\d=\cup_{k=0}^n(T_k,(T_k+\delta)\land T)$.   Let ${\rm A}_{\varepsilon,\Theta,\delta}$ be the set of all $\gamma\in{\rm A}_\varepsilon$
such that $\gamma=0$ for $t\in{\cal T}_\d$.

  Let $I_k= \int_{T_k}^{T_{k+1}}\gamma_\varepsilon(t)dB_H(t)$ and let $\bar I_k=\int_{T_k}^{T_{k+1}}\gamma_\varepsilon(t)dB(t)$.

Let ${\cal T}_\varepsilon=\{T_k\}_{k=1}^n$  be the set such as in Definition \ref{defS}(ii),   and let
\begin{eqnarray*}
I_k=\int_{T_{k-1}}^{T_k}\gamma(t)dB_H(t)=I_{W,k}+I_{R,k},
\eaaa
where
\begin{eqnarray*}
I_{W,k}=\int_{T_{k-1}}^{T_k}\gamma(t)dW_{H,k}(t),\quad  I_{R,k}=\int_{T_{k-1}}^{T_k}\gamma(t)dR_{H,k}(t)
\eaaa
and where $W_{H,k}(t)$ and $R_{H,k}$ are defined similarly to $W_H$ and $R_H$ with $[s,T]$ replaced by $[T_{k-1},T_k]$.

Let us prove first the theorem statement for $\gamma\in {\rm A}_{\varepsilon,\delta}$.

It suffices to show that
\begin{eqnarray}
{\bf E} |I_k-\bar I_k|\to 0 \quad\hbox{as}\quad H\to 1/2+0, \quad k=0,1,...,n.
\label{limk}
\end{eqnarray}
Let us prove (\ref{limk}). Let again $R_{H,k}(t)$ and ${\cal D} R_{H,k}(t)$ be defined similarly to $R_H(t)$ and ${\cal D} R_H(t)$, with the interval $[s,T]$ replaced by the interval $[T_{k-1},T_k]$.
 We have that
$I_k=I_{W,k}+I_{R,k}$, where $I_{W,k}$ and $I_{R,k}$ are defined similarly to the proof of Lemma \ref{ThE}
with the interval $[T_{k-1},T_k]$. Clearly, ${\bf E} J_{W,k}=0$.

We have by Lemma \ref{ThM} and by the property of the Riemann--Liouville integral that
$\|\gamma-G_H(\cdot,T_{k-1},T_k,\gamma)\|_{L_2(T_{k-1},T_k)}\to 0$ a.s. as $H\to 1/2+0$. In addition,
there exists $c>0$ such that
 \begin{eqnarray*}
 \|G_H(\cdot,T_{k-1},T_k,\gamma)\|_{L_2(T_{k-1},T_k)}\le c\|\gamma\|_{L_2(T_{k-1},T_k)}\eaaa a.s. for all $H$. Therefore,
 \begin{eqnarray*}
 \|\gamma(t)-G_H(t,T_{k-1},T_k,\gamma)\|_{L_2(T_{k-1},T_k)}\le 2c\|\gamma\|_{L_2(T_{k-1},T_k)}\eaaa a.s.  for all $H$.
It follows that
\begin{eqnarray*}
{\bf E}|I_{W,k} -\bar I_k|^2={\bf E}\int_{T_{k-1}}^{T_k}|\gamma(t)-G_H(t,T_{k-1},T_k,\gamma)|^2dt\to 0 \quad\hbox{as}\quad H\to 1/2+0.
\label{II}
\eaaa

For $t\in[T_k\land (T_{k-1}+\delta),T_k]$,  we have by Lemma \ref{ThM} that \begin{eqnarray*}
{\bf E} {\cal D} R_{H,k}(t)^2\le c_H^2\frac{H-1/2}{2}(T_k-T_{k-1}+\delta)^{2H-2}=c_H^2\frac{H-1/2}{2}\delta^{2H-2}.
\label{DR2}
\eaaa Hence
\begin{eqnarray*}
{\bf E}|I_{R,k}|\le \left({\bf E}\int_{T_{k-1}}^{T_k}\gamma(t)^2dt\right)^{1/2} \left({\bf E}\int_{T_k\land (T_{k-1}+\delta)}^{T_k}{\cal D} R_H(t)^2dt\right)^{1/2}\to 0\quad\hbox{as}\quad H\to 1/2+0.
\eaaa
Since it holds for all $k$, the theorem statement follows for all $\Theta$, $\delta$ and $\gamma_\varepsilon\in{\cal A}_{\varepsilon,\Theta,\delta}$.
Since any  $\gamma_\varepsilon\in{\cal A}_{\varepsilon}$ can be represented as $\gamma_\varepsilon=\gamma^{(1)}+\gamma^{(2)}$, where $\gamma^{(k)}\in{\cal A}_{\varepsilon,\Theta_k,\delta_k}$, $\kappa=1,2$,
with an appropriate choice of $\Theta_k$ and $\delta_k$.
This completes the proof of Lemma \ref{ThE}.
$\Box$

\index{Let us observe that, for any admissible $\gamma$ such that ${\bf E}_{t-\varepsilon}\int_{T-\varepsilon}^T\gamma(t)^2dt>0$
the conditional distribution of $X(T)$ given ${\cal F}_{T-\varepsilon}$ is Gaussian.}

{\em Proof of Theorem \ref{ThNA} (i).} Suppose  that a strategy $\gamma\in{\cal A}_\varepsilon$ delivers an arbitrage with the corresponding wealth process $X(t)$ such that $X(0)=0$.

Let  $A_k=\{\int_{T_{k-1}}^{T_k}\gamma(t)^2dt>0\}$. Let $I_{W,k}$ and $I_{R,k}$ are defined similarly to the proof of Lemma \ref{ThE}
with the interval $[T_{k-1},T_k]$.

  By the definitions, $A_k\in{\cal G}_{T_{k-1}}$. Suppose that
${\bf P}(A_{n}>0)$.

The value $I_{R,n}$ is ${\cal G}_{T_{n-1}}$-measurable, and  the values $\{W_H(t)\}_{t\in [T_{n-1},T]}$ are independent from ${\cal G}_{T_{n-1}}$.
 Since $\gamma(t)$ is ${\cal G}_{T_{n-1}}$-measurable for $t\in[T_{n-1},T]$ and ${\cal G}_{T_{n-1}}\subset {\cal G}_{T_{n-1}}$, it follows that $I_{W,n}$ and  $I_n$
both have  Gaussian distributions conditionally given ${\cal G}_{T_{n-1}}$. Hence $I_n$ has support on the entire interval $(-\infty,+\infty)$ given $A_n$.

Hence ${\bf P}(X(T)<0|A_n)>0$ and $${\bf P}(X(T)<0)={\bf P}(X(T)<0|A_n){\bf P}(A_n)>0.$$ This would be inconsistence with with the supposition that $\gamma$
delivers an arbitrage. Hence  ${\bf P}(A_n)=0$ and  $X(T)=X(T_{n-1})$. Similarly, we obtain that  ${\bf P}(A_k)=0$ for all $k$ and $X(T)=0$. This is inconsistence with with the supposition that $\gamma$
delivers an arbitrage. This completes the proof of Theorem \ref{ThNA}.  $\Box$

{\em Proof of Theorem \ref{ThNA} (ii)} follows from Lemma \ref{ThE}.

\section{Discussion and future developments}
The model presented above  represents a simplest possible model
that allows to illustrate that the arbitrage opportunities vanish for strategies with an arbitrarily small
time delay in information processing.
We leave for future research development of more comprehensive models  and detailed analysis  such as the following.
\begin{enumerate}
\item It could be interesting to investigate if the  discontinuity with respect to $H$ at  $H=1/2$ of stochastic integrals vanishes for piecewise continuous strategies presented in no-arbitrage results obtained in Theorem 4.3 \cite{C} and Theorem 3.21 \cite{B11}.
\item It could be interesting to extend our approach on a more mainstream model with $S(t)=\exp(\mu t+\sigma B_H(t))$. It is unclear yet how to do this for a setting
with ${\cal F}_{t-\varepsilon}$-measurable
quantity of shares $\gamma(t)$ for admissible strategies. However, it is straightforward to consider a model with this prices in a setting with
$\gamma(t)=\pi(t)/S(t)$, where $\pi(t)$ is ${\cal F}_{t-\varepsilon}$-adapted.
\end{enumerate}
\subsection*{Acknowledgment} This work  was
supported by ARC grant of Australia DP120100928 to the author.

redpajama_set_name: RedPajamaArXiv


text:
O Cinturão Médio (Middle Belt) é um termo geográfico humano que designa a região do centro da Nigéria povoada em grande parte por grupos étnicos minoritários e alongam-se para todo o país longitudinalmente. O Cinturão Médio é indeterminado, que carece designar  "fronteiras" e é caracterizado por uma heterogeneidade e diversidade de povos e culturas. A eminência de grupos minoritários múltiplos em algum grau constitui uma barreira etno-linguística no país, desenhando uma separação entre o Norte islâmico e o Sul cristão.

A região é uma convergência desses domínios culturais e mantém um enorme grau de diversidade etno-linguístico, com línguas das famílias afro-asiática, nilo-saariana, e níger-congo, três dos principais grupos de línguas africanas, todas as que estão sendo faladas.

Dinâmica
Minorias na Nigéria tendem a ser dominadas pelos três maiores grupos étnicos, os hauçás do Norte e dos ibos e iorubás do Sul. Rodeado por histórias religiosas, econômicas e culturais divergentes, o Cinturão Médio tem sido o caldeirão onde pequenos e grandes grupos étnico-religiosos na Nigéria há muito tempo coexistiram, mas onde também colidiram cada vez mais sobre a terra, recursos, identidade e poder político.

O resultado é uma mistura de conflitos recorrentes e unidade política ocasional e solidariedade entre esses povos altamente diferenciados. Um exemplo para o último foi o Congresso do Cinturão Médio Unido que surgiu após a independência da Nigéria da Grã-Bretanha em 1960.

Em particular, a cidade de Jos no estado de Plateau tem sido um centro para disputas étnico-religiosos e violência desde a década de 1990. O Jos Forum Inter-Communal Dialogue process durou 16 meses, de  agosto de 2013 a dezembro de 2014, e refere-se a um processo de paz empreendido por comunidades que vivem em Jos que concluíram em uma "Declaração de Compromisso para a Paz".

Áreas da Nigéria, que são geralmente referidas como pertencentes ao Cinturão Médio são: os estados de Kwara, Kogi, Benue, Plateau, Nasarawa, Níger, Taraba, Adamawa, bem como as partes do sul dos estados de Kaduna, Kebbi, Bauchi, Gombe e Borno.

A definição das áreas de Cinturão Médio estão sujeitas a grande debate, devido à presença de número significativo de etnias hauçás, fulas e grupos canúris. Além disso, os iorubás de Kwara e Kogi têm uma forte afinidade com os demais iorubás e frequentemente preferem não ser associados com a identidade do Cinturão Médio.

Geografia da Nigéria
Demografia da Nigéria
Regiões de cinturão

redpajama_set_name: RedPajamaWikipedia


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Shia LaBeouf Plastic Surgery Before and After Gallery – Shia Saide LaBeouf (born June 11, 1986)is an American actor, performance artist, and filmmaker.He became known among younger audiences as Louis Stevens in the Disney Channel series Even Stevens, a role for which LaBeouf received a Young Artist Award nomination in 2001 and won a Daytime Emmy Award in 2003. He made his film debut in The Christmas Path (1998). In 2004, he made his directorial debut with the short film Let's Love Hateand later directed a short film titled Maniac (2011), starring American rappers Cage and Kid Cudi.
American actor, performance artist, and filmmaker, pictures are revealing the main difference between her natural and plastic parts. So if you are searching for Shia Saide LaBeouf plastic surgery before and after pictures. You are here on the right way to get all about Shia Saide LaBeouf plastic surgery including before and after pictures, reasons and results and her statement that why she got admitted to go under knife.
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Summary: 97 years old residential co-educational institution nestling in the hills of Sahyadris, offering a rewarding and enriching experience, (rewarding salary with VIth Pay commission, free accommodati..
"Sanjeewan Vidyalaya" in Panchgani is a co-educational English Medium residential school, situated on one of the mountain ranges of the Sahyadris. The bracing and the beautiful environment makes Panchgani a perfect setting for a residential school. The small township-from which the school is about a mile away-has all the civic, communications.


As the new millennium kicked-in about 17 years back, it ushered in lots of things unheard before in our generation (my generation). I will not be surprised if after some time you start hearing the words like new-era and old-era referring to pre-millennium and post-millennium periods. To a certain extent, the trend has already started in a veiled manner. The generation that has hit the job market in the new-era is being referred to as millennials. Rightly so, certain traits have already been identified and tagged with this generation. Companies and organizations are already putting in their people and human resource strategies considering this millennial generation.
One trait that can be clearly tagged with this generation is that it is a generation which is "On-the-Go". With the streaming internet access in hands, this generation believes in doing the things on the go. For example, the generation believes trainings are supposed to be done not gone to somewhere. When I started my career, all the corporate trainings used to be classroom-based which we would go to whereas in the new-era no training strategy can exclude the online trainings as the millennial generation believes in doing the training online rather than going to a class room. This gets reflected in the success of various MOOC platforms that have arrived on the scene during last decade.
There are many such examples. Even the Bollywood has not remained unaffected by this millennial generation. If you look at the cult of movies that have been made in the recent past and are being made in this new era, reflects and captures the emerging trend. While the movies in the old-era mostly reflected the social trends, the current trend reflects the movies on contemporary topics, off-beat themes and the living legends. The millennials with access to internet are exposed to global cinema much more than the earlier generation was and consuming movies more than it ever has been. This makes them look for idols and heroes and expect more from celluloid stories than the typical stereotypical themes.
This has led to a cult that has started unfolding around the movies on sports arena catering to the millennials. The initial trend started with movies like Lagaan, Chak De India, Goal, Iqbal, Jo Jeeta Wohi Sikandar and few more which chronicled stories surrounding sports themes. This trend seems to be coming of age during last couple of years with the bio-pics of our contemporary sports legends being made which have been well received by the audience across the age bands. Last 5 years have given us six such movies with three movies coming in last one year. As a nation we indeed are exploring and looking around for success stories.
Pan Singh Tomar (2012), directed by Tigmanshu Dhulia, Bhag Milkha Bhag (2013), directed by Rakeyesh Omprakash Mehra, Mary Kom (2014), directed by Omung Kumar, MS Dhoni (2016), directed by Neeraj Pandey, Dangal (2016),directed by Nitesh Tiwari, Sachin (2017), directed by James Erskine.
As I have listed only few names here, this does not mean that we do not have other legends. There are uncountable many more legendary players who brought laurels to the country as well as given joy to the nation over the years. This has given us reasons to celebrate. Their success not only popularized their games but also motivated the whole new generation to follow on their footsteps.
• The respective sports federations, Indian Olympic Association and other sports bodies can work alongside National Film Development Corporation (NFDC) by providing funding to make movies on such success stories.
• The authorities can pick up the list of players on whom they would want to make the movies. I have given a name of few of the players above but there are many more.
• It shall be ensured that these movies do not end up just being documentaries. The movies shall be independently made by established directors or movie houses so that movie retains the soul of a movie.
• All this apart, the Directorate of Film Festivals and other organizations like Filmfare, Zee, Screen, etc which are involved in promoting Indian Cinema shall explore organizing Sports Film Festivals regularly.
• These movies shall be taken to our schools so that each and every child in the impressionable age sees them.
I strongly feel this investment will go a long way towards playing a role of a powerful catalyst in fulfilling our dream around Mission Olympics.


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Original Communication | Published: 08 May 2002
Estimation of carotenoid accessibility from carrots determined by an in vitro digestion method
E Hedrén1 na1 na2,
V Diaz2 na2 &
U Svanberg1 na2
European Journal of Clinical Nutritionvolume 56, pages425–430 (2002) | Download Citation
Objective: To develop an in vitro digestion method to assess the impact of heat treatment, particle size and presence of oil on the accessibility (available for absorption) of α- and β-carotene in carrots.
Design: Raw and cooked carrots were either homogenized or cut into pieces similar to chewed items in size. The carrot samples, with or without added cooking oil, were exposed to an in vitro digestion procedure. Adding a pepsin–HCl solution at pH 2.0 simulated the gastric phase. In the subsequent intestinal phase, pH was adjusted to 7.5 and a pancreatin–bile extract mixture was added. Carotenoids released from the carrot matrix during the digestion were extracted and quantified on high-performance liquid chromatography (HPLC).
Results: Three percent of the total β-carotene content was released from raw carrots in pieces. When homogenized (pulped) 21% was released. Cooking the pulp increased the accessibility to 27%. Addition of cooking oil to the cooked pulp further increased the released amount to 39%. The trends for α-carotene were similar to those for β-carotene.
Conclusion: The described in vitro digestion method allows a rapid estimation of carotene accessibility in processed carrots, which may reliably predict in vivo behavior.
Sponsorship: This study was supported by the Swedish International Development Cooperation Agency (SIDA) and the International Program in the Chemical Sciences (IPICS), Uppsala University, Sweden.
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Vitamin A deficiency is a major public health problem in developing countries (WHO/UNICEF, 1995). Preschool children and women of reproductive age are predominantly affected. For these population groups the primary source of vitamin A is derived from provitamin A carotenoids in plant foods. Food-based strategies for combatting vitamin A deficiency include promotion of a higher production and consumption of dark-green leafy vegetables, yellow and red fruit and vegetables and red palm oil, which are all rich in provitamin A carotenoids (Bloem et al, 1998). However, some studies have indicated that β-carotene may be poorly absorbed from certain vegetables (Brown et al, 1989; Micozzi et al, 1992; de Pee et al, 1995) and thus the justification of such strategies has been questioned. Some epidemiological studies have suggested a lowered risk of developing certain types of cancer or chronic diseases following a diet containing food products rich in carotenoids, due to their anti-oxidative properties (Block et al, 1992; van Poppel, 1993; Steinmetz & Potter, 1996). However, our knowledge about the content of carotenoids in vegetable foods as well as the bioavailability of these is limited.
Bioavailability is defined as the fraction of an ingested nutrient from food that is available for absorption in the intestine and metabolic process and storage (Jackson, 1997). A number of factors have been identified that may affect the bioavailability of carotenoids from foods, eg the matrix in which the carotenoids are incorporated, the content of dietary fat and fiber, the particle size, and the food processing method applied. In carrots the carotenoids are present in crystalline form or associated with proteins embedded in chromoplasts (Byrant et al, 1992), which limit their release during the digestion process. Cooking may enhance the carotenoid release by softening or breaking down the cell walls and by dissociating the protein complex (Poor et al, 1993; Zhou et al, 1996; Rock et al, 1998). Another way of reducing matrix effects is by homogenization or particle size reduction (van Zeben & Hendriks, 1948; Gärtner et al, 1997; Castenmiller et al, 1999; van het Hof et al, 1999). Dietary fat, as well, has a documented positive effect on bioavailability of carotenoids (Roels et al, 1958; Dimitrov et al, 1988; Shiau et al, 1994; Jalal et al, 1998), although the amount of fat required to optimize carotenoid bioavailability has not been clearly identified.
Existing methods to estimate the carotenoid bioavailability include both short- and long-term studies in humans (Micozzi et al, 1992; de Pee et al, 1995; Castenmiller et al, 1999) as well as appropriate animal models, such as ferret (White et al, 1993) and preruminant calves (Poor et al, 1993). The most commonly applied method includes measuring increases in plasma concentrations of carotenoids or retinol in humans following administration of an acute or chronic dose of an isolated carotenoid or a carotenoid-containing food (Brown et al, 1989; Micozzi et al, 1992; Castenmiller et al, 1999; van het Hof et al, 1999). This is a relative measure, as the plasma is highly dynamic and individual responses have been reported to be highly variable (Dimitrov et al, 1988; Törrönen et al, 1996). To obtain a quantitative measure of carotenoid bioavailability, the oral–faecal balance method is a better approach (Roels et al, 1958; Shiau et al, 1994).
However, studies based on humans or animals are tedious and costly and are not useful to screen a large number of food samples. There is therefore a need for an in vitro model that simulates the human digestion tract. Such a method should quantitatively assess the amount of carotenoids that becomes accessible both from different food sources and from foods subjected to different food treatments. In connection with this, we use the term bioaccessibility to be defined as the fraction of a nutrient available for absorption, ie the amount of a nutrient that is released from its food matrix during digestion and made accessible for absorption into mucosa. In the present paper the proposed in vitro digestion method therefore measures the amount of carotenoids accessible for absorption from carrots, and is defined as 'in vitro accessibility'. The objective of the present study was to investigate how different parameters, ie cooking/heating, particle size and presence of fat affect the accessibility of carotenoids from carrots using an in vitro method simulating the human digestion system.
One batch of carrots (Nandrin) cultivated on Gotland in Sweden was purchased in a local store in Gothenburg, Sweden. All carrots were washed and the excess of water was carefully removed from the surface. The samples were peeled and cut into pieces (about 10×10×40 mm). Half of the samples were boiled in water for 20 min, water:carrot (70:30). The samples were then rapidly frozen at −40°C for 24 h before they were freeze-dried (Lyovac GT 2). The material was stored in amber flasks filled with nitrogen and kept in a freezer at −18°C.
Prior to digestion, the freeze-dried carrots were either finely ground to pass a 250 µm aperture sieve or cut into small pieces. The pieces were fractionated between two sieves of 4.0 and 2.8 mm aperture. An internal standard 20 µg β-apo-8-carotenal (Fluka 10829) dissolved in 100 µl hexane was added to a conical flask and the solvent was evaporated with a flush of nitrogen. About 0.5 g of carrot sample (finely ground or in small pieces) was accurately weighed in the flask and suspended in 10 ml distilled water with 1% (w/vol) ascorbic acid (Merck 100127). Nitrogen was blown into the flask before it was screw capped and left for 30 min to absorb moisture. Different amounts (0, 20, 40 and 60% of dry weight of sample) of a cooking oil (rapeseed oil) stabilized with 1% (w/vol) DL-α-tocopherol (Merck 108283) were then added.
In vitro digestion
The digestion started with addition of 5 ml of 0.5% porcine pepsin solution (Sigma p 6887) in 0.1 mol HCl/l with physiological amounts (Diem & Lentner, 1975) of calcium (3.6 mmol added as CaCl2·2H2O, Merck), magnesium (1.5 mmol added as MgCl2·6H2O, Merck), sodium (49 mmol added as NaCl, Merck), potassium (12 mmol added as KCl, Merck) and phosphate (6.4 mmol added as KH2PO4, Merck). If necessary the pH was adjusted to 2.0 with 2 mol HCl/l. Nitrogen was blown into the flask before the mixture was incubated at 37°C in a water bath (Lab-line 4645-1) with orbital shaking (13 mm diameter) at 250 rpm for 1 h. The pH was adjusted to about 5 by adding 2 mol NaOH/l before 3 ml of a mixture of porcine pancreatin (4 g/l, Sigma P 1750) and porcine bile salt (25 g/l, Sigma B 8631) dissolved in 0.1 mol NaHCO3/l stabilized with 1% (w/vol) DL-α-tocopherol was added. The pH was further increased to 7.5 by adding 2 mol NaOH/l. The mixture was then, after nitrogen had been blown into the flask, incubated again for 30 min. After the incubation the sample was immediately centrifuged (Labofuge M) at 5000 g for 20 min in a centrifuge tube of glass.
To validate the method some critical steps in the digestion procedure were more carefully examined, ie the impact of addition of pancreatic enzymes and different amounts of bile salts (25 and 50 g/l), as well as the shaking conditions (reciprocal and orbital) for the micellarization process.
Extraction and quantification
After centrifugation the supernatant was collected with a plastic pipette in a separatory funnel containing 20 ml of 25% (w/vol) NaCl water. Twenty milliliters of 95% ethanol and 15 ml of petroleum ether (stabilized with 0.1% (w/vol) butyl hydroxytoluene, BHT) were added and the funnel was swirled before being left to allow the two layers to separate. The lower phase was drawn off and re-extracted with 15 ml petroleum ether and 10 ml 95% ethanol. This procedure was repeated until the organic phase was colorless. The upper organic phases were combined and evaporated in a rotary vacuum evaporator with nitrogen flush at 35°C to dryness. The residue was dissolved in a tert-butyl-ether and methanol solution (1:1, stabilized with 0.1% (w/vol) BHT), made up to 10 ml and passed through a disposable cellulose membrane filter with 0.45 µm pore size (Sartorius Filtration AB) into an amber vial. The preparation procedure was made in dim light.
The carotenes were separated and quantified by high-performance liquid chromatography, Water 600 HPLC with a multi-solvent delivery system, provided with a 996 photodiode array detector with a Millennium Chromatography manager to acquire and process spectral and chromatographic data. A YMC carotenoid column (YMC Inc., Wilmington, NC, USA) was used prepared on high purity silica (5 µm) with a C30 polymer ligand. The column is made of stainless steel 4.8×250 mm in size. The isocratic mobile phase was methanol:tert-butyl methyl ether:water (56:40:4; Lichrosolv grade, Merck). The flow rate was 1 ml/min and injections were made with a 20 µl loop. Analysis of each sample was performed in duplicate.
Determination of total α- and β-carotene content of carrots
The freeze-dried carrot samples were ground into a fine powder and 0.25 g was accurately weighed and put into a conical flask and mixed with 10 ml of 1% (w/vol) ascorbic acid dissolved in distilled water. One hundred microliters of internal standard (200 µg β-apo-8-carotenal/ml) were added before the flask was left for 30 min. The flask was swirled vigorously after 10 ml of a mixture of acetone and 95% ethanol (1:1) had been added. The upper phase was decanted into a separatory funnel with 20 ml 25% (w/vol) NaCl water. Another 10 ml of the acetone and ethanol mixture was added and decanted until the residue was colorless. The carotenoids were extracted with petroleum ether (stabilized with 0.1% (w/vol) BHT) and prepared for quantification on the HPLC in the same manner as the in vitro samples.
Differences in mean values of in vitro accessible carotenes were tested by analysis of variance (ANOVA) and determination of the significance of difference among samples using P-values obtained by Tukey's HSD multiple rank test.
The total amount of α- and β-carotene in the cooked carrots was 468±11 and 1357±52 µg/g dry matter (n=4), respectively. All samples were performed in duplicates and replicated once or twice. In samples without added cooking oil, raw carrot pieces released about 3% of the total β-carotene after in vitro digestion and about 6% was released from cooked pieces (Table 1). When the carrots were homogenized (pulped) the percentage accessible β-carotene increased to 21% in the raw sample and to 27% in the cooked sample. The amount of released β-carotene after digestion was 40±9 and 82±18 µg/g dry matter from raw and cooked carrot pieces, respectively, and from pulped samples 290±28 and 367±23 µg/g dry matter of β-carotene were released, respectively (Figure 1). Addition of 20% oil per gram dry matter carrot resulted in a significant increase (P<0.05) of the amount of accessible β-carotene in the homogenized samples. The percentage increase in the raw pulped sample was 30% and in the cooked pulped sample 39%. Increasing the amount of added oil (up to 60%) resulted in a further slight increase of accessible β-carotene, although not significant. Adding oil to the carrot piece samples had no significant effect on the amount of released β-carotene, although there was a tendency for a slight increase.
Table 1 Percentage in vitro accessible β-carotene in the carrotsa,b
In vitro accessible β-carotene in carrots exposed to three treatments; heat (raw or cooked), particle size reduction (pieces or pulped) and addition of dietary oil (0, 20, 40 or 60% of dry weight of sample).
The released amounts of α-carotene are shown in Figure 2. The trends for α-carotene were similar to those for β-carotene, except that the absolute values were about 60% lower.
In vitro accessible α-carotene in carrots exposed to three treatments; heat (raw or cooked), particle size reduction (pieces or pulped) and addition of dietary oil (0, 20, 40 or 60% of dry weight of sample).
In this study an in vitro method that simulates the human intestinal digestion process was developed in order to estimate the amount of carotenoids from carrots that becomes accessible for absorption by the human mucosa. Garrett et al (1999) developed an in vitro digestion method with subsequent examination of uptake of micellarized carotenes by cultures of Caco-2 human intestinal cells. In contrast to that method, the present method estimates the maximum amount of carotenoids released, not necessarily micellarized, from the food matrix that at optimal physiological and dietary conditions could be absorbed by the human mucosa.
In vitro method considerations
Carotenoids are susceptible to oxidation owing to the numerous double bonds. To avoid oxidation of carotenoids during the in vitro digestion, ascorbic acid and DL-α-tocopherol were added to serve as antioxidants. The ascorbic acid would serve as an antioxidant in the water phase and the α-tocopherol is thought to be located at the surface of the oil droplets and bile salt micelles where the carotenoids are incorporated. During extraction of the digesta with organic solvents the carotenoids were protected by BHT. As an extra precaution against oxidation, the analyses were performed under dim light and whenever possible nitrogen gas was used to minimize the contact with oxygen.
Some critical steps in the present in vitro method were investigated more carefully, ie the significance of bile salts and pancreatic enzymes, as well as shear forces for the micellarization process. A mixture of homogenized cooked carrots with added cooking oil (40% of dry weight) was used to study the significance of bile salts and pancreatin enzymes. The amount of released β-carotene decreased by ∼80% when bile salts were omitted from the digestion mixture and was probably dissolved within lipid droplets originating from the carrot mixture. The pancreatin mixture with bile salts is necessary for the formation of bile salt micelles and carotenoid absorption is also known to be minimal when intraluminal bile salts are below the concentration required for aggregation into micelles (El-Gorab & Underwood, 1973). However, adding the double amount of bile salts into the pancreatin mixture (from 25 to 50 g/l) revealed no further increase in carotenoid accessibility. Remarkably, pancreatin showed less importance, since the amount of β-carotene released into the aqueous phase was only about 10% lower with pancreatin absent in the digestion mixture. From samples only subjected to the gastric phase, the amount of β-carotenes released into the aqueous phase was ∼90% lower, which means that the intestinal phase with bile salts is of major importance.
Once the lipophilic carotenoids are released from the food matrix in the stomach, they dissolve in an oily phase of lipid droplets. The formation of bile salt micelles requires mechanical disruption of the large lipid droplets into smaller droplets. This disruption is, in the in vitro method, brought about by shaking during incubation. Different shaking conditions were tested with cooked and homogenized carrot samples with added cooking oil (60% of dry weight sample). With the use of a waterbath (Heto, TB VS-02) with reciprocal shaking set at a moderate speed of ∼100 rpm, the coefficient of variation for β-carotene could be as high as 30% between assays. When we changed to a waterbath with orbital shaking set at a speed of 250 rpm we received reproducible results. The coefficient of variation within one assay was 3.7% (n=2) and the coefficient of day-to-day variation was 5.9% (n=4).
Parameters affecting the bioaccessibility of carotenoids
The effects of heat treatment, particle size and fat content on accessibility of carotenoids from carrots were studied with the present in vitro method. The in vitro accessibility of each carotenoid is expressed as percentage of the total amount present in the carrot and is thus an estimation of the amount accessible for absorption. The obtained values are compared with results from other studies in order to validate the in vitro method.
In the present in vitro study 3% of the β-carotene content was released from raw carrots in pieces, which is in agreement with results from a balance study in humans conducted by Roels et al (1958), where less than 5% of the carotene content in raw grated carrots was absorbed. However, cooking may bring about a more efficient release of carotenoids from the food matrix by softening the cell structure so that the digestive enzymes may work more efficiently. In the present study the heat treatment improved the release of β-carotene from carrots in pieces about two-fold and about 1.3 times in homogenized carrots. In a study on preruminant calves, accumulation of β-carotene in different tissues was 1.6 times higher after consumption of cooked carrots compared with consumption of raw carrots (Poor et al, 1993). Consumption of thermally processed carrots and spinach resulted in a plasma β-carotene response in women three times that associated with the consumption of these vegetables in the raw form (Rock et al, 1998).
To make carotenoids accessible for absorption, mechanical as well as chemical disruption of the food matrix is important (Furr & Clark, 1997). By mechanical disruption, the surface area for the digestive enzymes to attack enlarges and thereby the carotenoids are more easily released from their matrix. A seven-fold and an almost five-fold improvement of the β-carotene accessibility were shown in the present study after homogenization of raw and cooked carrot samples, respectively. Van Zeben and Hendriks (1948) showed an almost five-fold increase in concentration of plasma carotenes when women consumed cooked carrots homogenized in a mixer compared with unhomogenized carrots. In a study conducted by Törönnen et al (1996), the serum β-carotene response in women was almost twice as high after consumption of carrot juice compared with raw carrots. Huang et al (2000) evaluated the relative bioavailability of β-carotene in adult males after a single ingestion of stir-fried (with oil) shredded carrots using the serum response method. Compared with pure β-carotene in a capsule the bioavailability from the carrot meal was 33%. This figure is comparable with our in vitro measurement of cooked homogenized carrot with added oil (20, 40 and 60% of dry weight) that had a β-carotene accessibility of 38–45% (Table 1). Improved carotenoid (lycopene and β-carotene) bioavailability after disruption of the food matrix has been shown in human studies using other vegetable sources than carrots. The peak lycopene concentration in chylomicrons was reported to be about twice as high after consumption of tomato paste compared with fresh tomatoes (Gärtner et al, 1997). The plasma β-carotene response was twice as high in humans after consumption of enzymatically liquefied spinach compared with whole spinach (Castenmiller et al, 1999).
Ingestion of fat along with carotenoids is thought to be crucial in the absorption process (Prince & Frisoli, 1993). Dietary fat provides a hydrophobic environment for the released carotenoids that would be dissolved into small lipid droplets facilitated by mechanical mixing. With addition of bile salts these lipid droplets are transformed into mixed bile salt micelles from which the carotenoids are thought to be absorbed in the intestine. A positive effect of adding oil was measureable with the present in vitro method. Depending on the carrot sample, a 30–60% increase of in vitro β-carotene accessibility was obtained when cooking oil was added. Adding 20% oil per gram dry matter, which meant about 2 g per 100 g fresh sample, as the water content of the carrots was about 90%, was enough to detect a significant improving effect. Roels et al (1958) showed a five-fold increase in absorbed carotenes after supplementation of oil to raw grated carrots in a human balance study. In the present in vitro study, addition of 6 g instead of 2 g of cooking oil to the carrot samples had no improving effect on accessible β-carotene, although there was a slight increase (see Figure 1). From highly soluble β-carotene in the form of beadlets, about 17% was absorbed when added to meals containing no fat. Added to a low-fat diet, on average 32% was absorbed measured by the total wash-out method in young men (Shiau et al, 1994). Doubling the amount of fat in the meal had no further effect on the carotene absorption. No significant difference in plasma β-carotene response was shown in humans when spinach was ingested with 5 or 10 g of oil (Jayarajan et al, 1980) or when a β-carotene capsule was ingested with a low-fat (3 g) or a high-fat (32 g) diet (Roodenburg et al, 2000).
Although results of β-carotene accessibility using the in vitro digestion method are not strictly comparable with results using animal models or plasma β-carotene as a biomarker, still the trends found are comparable. Human balance studies reveal results similar to those obtained with the present in vitro method.
In conclusion, with the described in vitro digestion method, it has been shown that pulping is more important than cooking for release of carotenoids in carrots, and addition of oil is more effective in enhancing accessibility when carrot is pulped rather than in pieces. The in vitro digestion method described in the present paper appears to be useful for rapid screening of carotenoid accessibility in plant foods. The method gives an estimation of the amount of carotenoids that are released from the food matrix after digestion and absorbed into the human mucosa. Effects of different processing and preparation methods as well as dietary factors on carotenoid accessibility can be compared with the proposed in vitro digestion method.
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E Hedrén: Guarantor: E Hedrén.
E Hedrén, V Diaz and U Svanberg: Contributors: EH and VD were responsible for the laboratory analyses. EH, VD and US contributed to the conception and design of the study, developed the in vitro method and were jointly responsible for writing the article.
Department of Food Science, Chalmers University of Technology, Göteborg, Sweden
E Hedrén
& U Svanberg
Instituto de Investigación Tecnológica, Escuela Politécnica Nacional, Quito, Ecuador
V Diaz
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Correspondence to E Hedrén.
https://doi.org/10.1038/sj.ejcn.1601329
carotene bioavailability
β-carotene
α-carotene
in vitro accessibility
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