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Prove that the following polynomial has no integer roots:
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
A polynomial of degree 10 is unsolvable by any yardstick!
That's what I think!
To prove that it can be solved, you have to show how
I also believe, like Abel did, an equation in one variable of degree more than five, that is a quintic equation, cannot be solved manually! Maybe a supercomputer can do it,and even a supercomputer may take a long time!!!!
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
We can immediately rule out all integers from 0 to positive infinity. 0 can be ruled out by trial, and it can't be any positive integer since every coefficient is positive.
Looking at the negative integers we can rewrite the equation. All even powers will remain positive while all negative powers will become negative, so we can rewrite the equation as follows:
Using this new equation we will consider only positive integers for x, which is exactly equivalent to considering only negative integers of x for the original equation. Now, since the highest power is even we know that the equation will tend to positive infinity as x tends to positive infinity. What we do now is try, by trial and error, all integers from 1 up to the point that the equation is strictly increasing, at which point we'll be done.
Start with x = 1:
1 - 3 + 15 - 6 + 33 - 45 + 42 - 24 + 3 - 9 + 6 = 13
x = 2:
1024 - 1536 + 3840 - 768 + 2112 - 1440 + 672 - 192 + 12 - 18 + 6 = 3712
For x = 3, we'll look at prime factorizations. We'll further rewrite the equation as follows:
When x = 3 we can see that the first two terms will cancel out. The next two terms give us, which is greater than 0. Combining the next two terms gives us , again greater than 0. The next two terms clearly give us a term greater than 0, since the positive term has both a higher power of 3 and a larger coefficient. The final 3 terms give us 27 - 27 + 6 = 6. Since we were able to combine all of the terms to give us either 0 or a positive number we know that the equation is greater than 0 for x = 3.
We will use this same trick to show that all integer values of x greater than 3 result in a positive answer and thus are not roots.
Combine the first two terms to give us. Note that this is equivalent to . For all x > 3 this is clearly greater than 0, since both x^9 and x - 3 are greater than 0.
Combine the next two terms to give us. This term is clearly greater than 0 since the positive term has both a larger coefficient and a larger power than the negative term.
Combine the next 2 terms for. Again, this is positive for all x > 3 since 3x^5 and 11x - 15 will both be positive.
Combining the next 2 terms gives us, which again has a positive term with both a larger power and a larger coefficient, so this is positive.
Finally, combine the final 3 terms for. The 6 is obviously positive, and for all x > 3 so will 3x and x - 3. Therefore, this final term is positive.
Add it all up and we know that the equation is positive for all x > 0, which is equivalent to saying that the original equation is greater than 0 for all x < 0. Since we also know that 0 and x < 0 are not roots where x is an integer, we know that the equation has no integer roots.
Edit: Holy cow, your answer is way easier than mine. I don't quite understand how it works, though. Do you have a proof, or is this a well known theorem?
Last edited by TheDude (2007-11-07 02:45:57)
Wrap it in bacon
The result assumes that the polynomial is of degree at least 2. (Linear polynomial equations always have solutions.) It also assumes that none of the coefficients (except possibly the leading one) is ±1.
Last edited by JaneFairfax (2007-11-07 05:43:43)
Ganesh, be very careful. A polynomial of degree greater than 5 can not be solved in genera. However, many of them can be factored. For example:
(x - 1)(x-2)(x-3)(x-4)(x-5)(x-6)(x-7)(x-8)(x-9)(x-10)
Multiplying this out gives you a polynomial of degree 10 with roots 1 through 10.
Edit: Holy cow, your answer is way easier than mine. I don't quite understand how it works, though. Do you have a proof, or is this a well known theorem?
This is known as Eisenstein's criterion. It is proved in general for polynomial rings, and can even be applied to a ring's field of fractions. In this case, we may not only say that my given polynomial has no integer roots and is not reducible in the integers, but also that it is not reducible in the rationals as well (and hence, no rational roots either). A simple proof can be found on wikipedia.
It also assumes that none of the coefficients (except possibly the leading one) is ±1.
1 is not prime, so the preconditions can't be met if a coefficient is +/- 1
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
Very cool, thanks Jane and Ricky
Wrap it in bacon
This is great! Ricky (or anyone else) do you have any more "things they never teach you in algebra." I'm looking forward to learning new things like number theory and what not, but I love to expand on my pre-existing knowledge (like Algebra).
Everything TheDude said in his post could be followed by a good algebra II student, and that's what makes it genius, this stuff makes me all warm and fuzzy inside.
Also, TheDude, you have a really sweet sig.
There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.
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Here's what "They" are saying this morning, following the Astros 6-2 win over the Yankees.
New York Post: "And you thought Obamacare got off to a bad start..."
New York Daily News: "CC Sabathia insists there's a mechanical and reasonably explanation for getting lit up by the Triple-A Astros that has nothing to do with his diminished velocity...Whatever the explanation for Sabathia getting lit up in Houston, it's fair to wonder, now more than ever, if the big lefty can survive, never mind thrive, with his diminished fastball."
Poughkeepsie Journal: "CC said he wanted to pitch like a bully again, but he got beat up on his first day back at school."
Sabathia: "I didn't settle in because of the excitement of Opening Day. I backed off a little too much. Balls were up and the changeup was cutting...I wanted to start the season pitching so good, I wound up pitching bad."
Girardi: "It's not what you want, but I had a feeling we were going to lose a game at some point this year so we got it out of the way early."
Wednesday, April 2, 2014
What They're Saying: G1
2 comments:
like the quote from Giradi, bet he wont be so light if they lose the next one
- April 2, 2014 at 8:38 AM
My fav was the NY Post calling us "the awful Astros". Don't think a performance like that can come from an "awful" team.
- April 2, 2014 at 11:49 AM
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The Buccaneers found themselves with an open roster spot on Monday thanks to cornerback Eric Wright's suspension and injuries opened up two more of them on Tuesday.
The team announced that safety Cody Grimm and tackle Jeremy Trueblood are headed to injured reserve. Grimm has missed two of the last three games with a hamstring injury and Trueblood injured his shoulder in Sunday's loss to the Falcons.
Trueblood started the year as the starting right tackle, but was replaced by Demar Dotson after the first game of the season. Grimm has played a reserve role in nine games this season after starting 12 times in his first two years with the team.
Tampa got to work filling the empty roster spots by claiming wide receiver David Gilreath off of waivers from the Steelers. Gilreath, who had one catch in three games, was waived to make room for guard David DeCastro on the active roster in Pittsburgh.


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Dave and Connor in Season 24 Episode 8
At the Detour Decision Point, Father/son team David (left) and Connor (right) must choose between "Wooden Toy for Wooden Boy" or "Where's My Donkey?" on the All-Star edition of THE AMAZING RACE, Sunday, April 20 (8:00-9:00 PM, ET/PT) on the CBS Television Network. Photo: CBS ©2014 CBS Broadcasting, Inc. All Rights Reserved


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The Truth About Making Fast And Easy Money Online
I know, a lot of you are wondering whether making fast and easy money online is true or not? Well hopefully this article
will enlighten you! Many of us think that whenever an opportunity sounds too good to be true, it is a fraud! The reason for
such perception is valid because many of the so called 'Making Money' products claim to make its customer fast and easy
money. But when the customer finally tries out the product, it turns out totally opposite! Also, majority of the population
have job that requires them to break sweat, get stress and suffer just to earn an under valued salary.
It's in fact a norm to think that making money isn't easy. But if it's winning money, it's easy money except the occurrence
of it happening to an individual is extremely rare. With two factors opposing hopes and beliefs of making fast and easy
money, many are permanantly avoiding opportunities that are presented to them. It comes to a point where it doesn't even
matter whether the opportunity is legit and genuine. We rather just continue breaking sweat, stress up and suffering at work!
Now, what i've really come to understand is this! It is possible to make fast and easy money! Especially Online. Why?
Because it's a place where we can access millions of potential customers. If you got the right product and the right marketing
strategy, there's no doubt you'll make fast and easy money! Honestly, i can tell you, that there are many people making fast
and easy money online.
Have you even bought something online? Well, that person or merchant you made a purchase from is no doubt making fast and easy
money! The problem is we don't see it! We only see that we are the sole buyer ourselves! But from the seller or merchants view
it's like a profit explosion everyday! Waking up to 1000s of sales is a norm to them! We really have to open our eyes bigger!
It is really possible to make fast and easy money online!
You can ask 2 different types of person. Person A, a typical employee and Person B, a successful internet entrepreneur. Ask
them if it's possible to make 4 to 5 figures a day! Person A will definitely say No unless it's winnings from lottery or casino.
Person B, will say "OF COURSE!" and further explains how that can be achieved! The problem i'm trying to point out here is,
Whether you've exprience such of an occurrence! We only believe what we see! If someone tell you, that human beings can actually
float in the air, will you really believe it? You'll mostly give excuses saying it's probably a trick and illusion. But what
if, you actually saw a person float above you and at that point of time you're certain that it's no trick or illusion. When that
happens, you will believe 100% that a person can float and may even argue with skeptics that surround you.


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Many U.S. boy bands have tried to recreate the success the Backsteet Boys, 'N Sync and 98 Degrees enjoyed in the late 1990s and early 2000s (Ever heard of LMNT, which included "Glee" star Matthew Morrison, or Audio, formerly the Diddy-produced B5?) but nearly all have failed to make a real impact, for one reason or another.
Big Time Rush could change that.
The quartet's self-titled show on Nickelodeon, which formed the band in 2009, has been renewed for a third season (the band members play fictional versions of themselves on the show, much like The Monkees did in the 1960s). Big Time Rush also followed up its 2010 debut album, "BTR," which peaked at No. 3 on the Billboard 200 and featured a Snoop Dogg cameo, with November's "Elevate," which peaked at No. 12 on the Billboard 200.
Not bad for four guys who didn't exactly have boy band aspirations.
"I don't think we ever envisioned being in a boy band," said Big Time Rush's James Maslow over the phone last week from Las Vegas. "We had our own bands and projects before this. Once we saw where this could go, we got together and made this the best it could be."
The audition process lasted two years and included more than 1,500 aspiring singers and actors. Fellow band member Logan Henderson described it as a triple-threat "boot camp" because it involved choreography, singing and acting.
"The waiting period was miserable," said Henderson, also on the phone. "We couldn't go out and audition outside of that. It was a tough decision to stick with it but we're glad we did."
How did their friends react to their decision to join a boy band?
"They were supportive," Maslow said. "I think they were stoked that their friend was on TV and had a record deal. … They even have this drinking game for me: Every time my character does something silly, take a drink."
(Most of Big Time Rush's fans aren't legally old enough to drink, but all of the band members are: Maslow and Kendall Schmidt are 21, and Henderson and Carlos Pena Jr. are 22).
Big Time Rush played the B96 SummerBash in June at Toyota Park and return for a sold-out show at the Akoo (formerly Rosemont) Theatre Friday. Henderson expects the shows on this tour to be vastly different from the band's past concerts, from the stage design and lighting to the wardrobes and choreography. The band had been working on the latter for days when we spoke over the phone.
"I can't feel my legs," joked Henderson.
Fans can also catch the band in its first original TV movie, "Big Time Movie," which airs March 10 on Nickelodeon. The guys are called into action to save the world in the James Bond-like special, which takes place in London, and cover a few Beatles songs along the way. And yes, they're aware some overly protective Beatles fans might not be thrilled with the idea.
"We're sharing the Beatles with fans who are on the younger side and might not know The Beatles unless their parents listen to them," Maslow said. "You can't hate on the fact that we're spreading their music to a new generation."
Twitter @aboutluisgomez


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Lighting Designer: Tillotson Design Associates
Architecture Firm: Diller, Scofidio + Renfro
Photo: Iwan Baan
Date: 2010
Fixtures used: MICROLUX U
Description: Lincoln combines high-concept design with the impeccable contemporary Italian cuisine of Chef Jonathan Benno. Designed by the architectural firm of Diller, Scofidio + Renfro, Lincoln's unique design features glass curtain walls, a signature sloping lawn roof and a spectacular view of the reflecting pool and the Henry Moore sculpture. The restaurant's environment is both comfortable and refined – with an open kitchen, bar, lounge, two dining rooms and private dining accommodations.


text: Just upgraded to 3.5.2 OS: centos 5.9 php:5.3.23 apache:2.2.23 Just can't get the panel up. I get a 503 error error_log: [Wed Apr 10 09:26:23 2013] [error] (13)Permission denied: mod_fcgid: couldn't bind unix domain socket /etc/httpd/run/mod_fcgid/15487.447 [Wed Apr 10 09:26:23 2013] [warn] (13)Permission denied: mod_fcgid: spawn process /var/www/php-fcgi-scripts/ispconfig/.php-fcgi-starter error [Wed Apr 10 09:26:23 2013] [warn] [client 220.127.116.11] mod_fcgid: can't apply process slot for /var/www/php-fcgi-scripts/ispconfig/.php-fcgi-starter Any thoughts on the subject. Thanks korbynn


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This month's puzzles mark the
8th year
of our joint Monthly Interactive & Printable Logic Problems project. To
celebrate, we've posted
an extra, bonus puzzle as our little
anniversary gift for everyone who likes our puzzles and enjoys solving them.
Happy Puzzling Birthday!
In Mrs. Smith's 4th grade class, five boys have crushes on a girl. Fortunately, each boy really liked a different girl. Yesterday was Valentine's Day and to celebrate, each boy screwed up his courage and gave the girl he liked a Valentine. Not realizing that the other boys were doing the same thing, they still managed to give their Valentine's in a different place and at a different time during the school day. Determine the full name of each boy, the full name of each girl that received a Valentine, and when each girl received it.
1. During lunch, Norman gave his Valentine to the girl whose last name was Guest.
2. Rick, whose last name wasn't Smith, gave his Valentine to Heather, whose last name wasn't Fields.
3. Rebecca, whose last name wasn't Willis, wasn't given a Valentine at recess. Sara didn't receive a Valentine during gym.
4. Greg, whose last name wasn't Jeffries, gave his Valentine to a girl during recess but it wasn't Abigail. Melissa received her Valentine during homeroom but not from a boy named Foley.
5. Sam's last name was Bow. Bill, who didn't like Sara, gave his Valentine to the girl whose last name was Grant.
6. The five boys were represented by Norman, the boy whose last name was Jeffries, the boy who gave his Valentine during math class, the boy whose last name was Marsh, and the boy who gave a Valentine to Abigail Lewis.
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Last Update
April 2, 2010


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I'm a Drama major an that was inspired by the Twilight Series to write my own play version of the books. Random interesting writing fact: I like to listen to Vanessa Carlton and Muse while writing because i found it's the best Twilight music that i can find... I am currently attending college and love to write to relax. I'm on Twitter @katie1989 I'm also co-hosting a writing contest called Twisted Twilight Tales.
Stories Written (3)
|The Happily Ever After
|Ever wonder what happed after breaking dawn. The Cullens move to a small town in Alaska six years after the Volturi leaves them in Forks but will it be the last that the cullens hear from them? Or will Renesmee's new friend bring them back to haunt the Cullens? Join the whole family on this next adventure. *Rated Teen because i'm not exactly sure how this is going to turn out... If you have read this story before...I've gone back and edited...it's the same story only better i think.
|Did you wonder what would have happend if Bella had never jumped off the cliff? If Alice never came? If Jacob had kissed her that day at her house before the funeral? Edward finally comes back, but will Bella take him back? How will Jake take it? What will happen when they recieve an unexpected visitor... CHAPTER 3 IS HERE!!!
|Truth In Music
|AU-AH. Slightly OOC. Bella Swan had always had a simple existence. School, work, and her music. She no longer had any living family members and the band was all she had left. That is all she had and that was all she ever wanted. After years of toiling away her and her band mates get their big break with Volterra records. The famous and dashing Carlisle Cullen and his equally famous and dashing son Emmett take them under their wings, knowing that their band Twilight is the next big thing. They had made their big break. Soon enough the Cullen's fall in love with the lovely shy girl from small town Washington, well all but one Cullen. Edward. When Bella met Edward they both felt sparks. But that only lasted until Edward opened his mouth. Edward Cullen left the music business in his past to move on to a life in the film, but was that what he really holds in his heart. Can this girl from Forks help him find out what it really is that he wants? More importantly in the hard world of Hollywood can they have a happily ever after? Especially when Edward's past comes back to haunt them. From Chapter four: "What?" I asked him wanting to know what he found humorous. "Nothing." He said taking another sip of his wine. "No. What?" I pressed. He had been so standoffish I wanted to know why now he would suddenly find the conversation at hand laughable. "It just sound cliché don't you think?" "What does?" "The over told discovery story…it was out of the blue…unexpected…" "It was." "I'm not doubting that it was. However god knows the world doesn't really need another band." "Edward…" Esme tired to intercede. "What?" He asked his mother. "Don't be rude." She said quietly. "I'm being honest." He said bluntly. "There are far too many bands out there already as far as I'm concerned, and each is less inventive in their 'sound' as the next." "Excuse me?" I asked getting very deffesive. "Look I'm not saying that you aren't very talented at what you do, but…" "Have you even heard us?" "No." "Then you talk pretty big for someone who knows absolutely nothing about us." I stood up. Unable to sit and listen to him any longer. "Carlisle, Esme, thank you for a lovely evening. It was a pleasure meeting you." I said to Esme before turning to Emmett. "Em. Do you think you could drive me home now, before I do something I might regret." I didn't even wait for him to answer I just left the room and headed out to the car.
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Join the American Academy of Sleep Medicine and receive a subscription to JCSM with your membership
To translate, back-translate and cross-language validate (English/Spanish) the Sleep
Heart Health Study Sleep Habits Questionnaire for use with Spanish-speakers in clinical
and research settings.
Following rigorous translation and back-translation, this cross-sectional cross-language
validation study recruited bilingual participants from academic, clinic, and community-based
settings (N = 50; 52% women; mean age 38.8 ± 12 years; 90% of Mexican heritage).
Participants completed English and Spanish versions of the Sleep Habits Questionnaire,
the Epworth Sleepiness Scale, and the Acculturation Rating Scale for Mexican Americans
II one week apart in randomized order. Psychometric properties were assessed, including
internal consistency, convergent validity, scale equivalence, language version intercorrelations,
and exploratory factor analysis using PASW (Version18) software. Grade level readability
of the sleep measure was evaluated.
All sleep categories (duration, snoring, apnea, insomnia symptoms, other sleep symptoms,
sleep disruptors, restless legs syndrome) showed Cronbach α, Spearman-Brown
coefficients and intercorrelations ≥ 0.700, suggesting robust internal consistency,
correlation, and agreement between language versions. The Epworth correlated significantly
with snoring, apnea, sleep symptoms, restless legs, and sleep disruptors) on both
versions, supporting convergent validity. Items loaded on 4 factors accounted for
68% and 67% of the variance on the English and Spanish versions, respectively.
The Spanish-language Sleep Habits Questionnaire demonstrates conceptual and content
equivalency. It has appropriate measurement properties and should be useful for
assessing sleep health in community-based clinics and intervention studies among
Spanish-speaking Mexican Americans. Both language versions showed readability at
the fifth grade level. Further testing is needed with larger samples.
Baldwin CM; Choi M; McClain DB; Celaya A; Quan SF. Spanish translation and cross-language
validation of a Sleep Habits Questionnaire for use in clinical and research settings.
J Clin Sleep Med 2012;8(2):137-146.
Sleep research over the past two decades has shown associations between sleep disorders
and chronic disease,1–7 poorer health-related quality
of life,8,9
increased health and work-related costs, and travel and work-related accidents.10,11
Prevalence rates for insomnia, the most commonly reported sleep complaint, range
from 20% to 40% of the population, depending on the defined severity and frequency,12 and is suggested to have a bidirectional
relationship with several chronic conditions including depression and cardiovascular
Prevalence rates for obstructive sleep apnea syndrome range from 2% to 4%,7 and rates for restless legs syndrome range from
5% to 15% in the general population.15
Snoring (48%), feeling unrested (26.5%), and insufficient sleep (26%) are leading
sleep problems identified in a population-based study.5
These and other sleep disruptions can contribute to excessive daytime sleepiness,16 making sleep disorders significant
contributors to disability, morbidity, and mortality.1,5,7,11,17,18
Despite the growing clinical and public health concerns regarding sleep disorders,
few studies have examined associations between sleep and race/ethnicity in the United
States. A majority of extant racial/ethnic studies compared African Americans with
and without sleep disorders, or comparing African and Caucasian Americans on sleep
disordered breathing, snoring, sleep architecture, insomnia symptoms, sleep quality,
daytime sleepiness, comorbid conditions, and health-related quality of life.8,19–23
Recent reviews reported the need for studies of sleep among Hispanics.24,25
This research need is time-critical because Hispanic Americans (e.g., Cuban, Mexican,
Puerto Rican) are the second largest and fastest growing minority group and currently
constitute 15% of the population; Mexican Americans represent the largest subgroup,
comprising 66.7% of the Hispanic American population.26
Many factors combine to make sleep disorders research a high priority among Hispanics
in the United States. Hispanics experience the following: higher rates of unemployment
and less earned income when employed; greater likelihood of living in poverty; less
likelihood of graduating from high school; greater food insecurity; are under- or
uninsured; reduced leisure-time physical activity; acculturation pressures, immigration
bias, limited access to care, diverse cultural constructions of health and illness;
and higher rates of chronic conditions, including obesity, type 2 diabetes, and
hypertension.27,28 These factors are associated with disordered or disrupted
sleep in other cultural and racial/ethnic groups; thus studying sleep in Hispanics
should enrich the overall understanding of their social, emotional, and physical
Current Knowledge/Study Rationale: Limited knowledge of sleep and health
of Hispanics of Mexican descent, the largest Hispanic group in the United States,
is partly due to the need for precisely translated and validated sleep measures
to assess Spanish-speaking Mexican Americans in clinical and research settings.
Study Impact: This first-of-its-kind study to rigorously translate and cross-language
validate the Sleep Heart Health Study Sleep Habits Questionnaire demonstrated conceptual
and content equivalency and acceptable psychometric characteristics with items loading
on 4 factors that accounted for 68% and 67% of the variance on the English and Spanish
versions respectively. This Spanish-language version of the Sleep Habits Questionnaire
may be applied in clinical and research settings as a first step toward addressing
sleep health disparities of Spanish-speaking Mexican Americans.
A major issue in the adequate and appropriate assessment of sleep disorders of Hispanics
is that of language.29 Spanish is the
second most common language in the United States and is the primary language spoken
at home by more than 34 million people aged 5 or older.26 Disparities in quality and access to care have reportedly
been narrowing for all groups except Hispanics due, in part, to language barriers.30 The aim of this paper is to report
the psychometrics of a rigorously translated, back-translated, and cross-language
validated version of the Sleep Heart Health Study Sleep Habits Questionnaire.31 The development of the Spanish version was guided
by Brislin's Translation Model to ensure that the instrument was linguistically
and conceptually equivalent and suitable for use in clinical and research settings
with Spanish-speaking Mexican Americans.32–34
Translators and back translators (N = 6) provided written informed consent (English
and Spanish) prior to participating in the study and completed demographic information,
including age, sex, race/ethnicity, years of education, current occupation and a
questionnaire listing prior translation experience. Each translator was compensated
$250 for their time.
Bilingual men and women volunteers (N = 50) were recruited by flyers posted in community,
college and university settings, libraries, places of worship, community centers,
and primary care clinics in neighborhoods with a high census of Mexican American/Hispanic
residents. Participants completed demographic and health history data in English.
English and Spanish versions of the Sleep Habits Questionnaire, the Epworth and
an acculturation rating scale were completed 7 to 10 days apart in counterbalanced
(randomized) order.35 Participants were
provided written informed consent (English and Spanish) prior to participation and
were compensated $30 for their time. All facets of this study were reviewed and
approved by the university institutional review board.
Demographic information included age, sex, race/ethnicity, educational level, marital
status, smoking status, alcohol, caffeine, prescription and other drug use, health
history, and self-reported height and weight to calculate body mass index (BMI).
The Sleep Habits Questionnaire was developed to survey Sleep Heart Health Study
(SHHS) participants; a description of the study has been previously published.31 The Sleep Habits Questionnaire includes
validated questions and response scales selected from the instruments of the Wisconsin
Sleep Cohort Study36 and the Cleveland
Family Study.37 The Cleveland study has
demonstrated the validity and internal consistency of these questions among Caucasian
and African American adults.38 The Sleep
Habits Questionnaire includes instructions to complete it without discussing the
questions with anyone, including a spouse. The questionnaire addresses several categories
of sleep disorders examined in this study: (1) sleep duration (2 items); (2) snoring
(3 items); (3) breathing pauses/apnea (4 items); (4) insomnia symptoms (3 items);
(5) sleep symptoms, including insufficient sleep, daytime sleepiness, nightmares,
leg jerks, leg cramps, and need for sleep aids (12 items); (6) sleep quality, including
perception of depth and duration of sleep (3 items); and (7) restless legs syndrome
(10 items). There is an additional category that assesses potential sleep disruptors,
including sinusitis, room noise, temperature, pain, and frequent toileting (9 items).
The questionnaire can be used in its entirety for a comprehensive overview of subjective
reports of sleep disorders, or in categories (e.g., snoring, insomnia symptoms,
restless legs syndrome) for focused assessment in clinical and research settings.
Snoring is ascertained by the question "Have you ever snored (now or at any
time in the past)?" with possible responses "yes," "no,"
or "don't know." Participants answering "yes" were asked,
"How often do you snore now?" with possible responses including "rarely-less
than one night a week," "sometimes-1 or 2 nights a week," "frequently-3
to 5 nights a week," "always or almost always-6 or 7 nights a week,"
or "don't know." Breathing pauses during sleep are ascertained by the
question, "Are there times when you stop breathing during sleep?" with
possible responses "yes," "no," or "don't know,"
or if a physician ever told them they have sleep apnea. Participants are also asked
how often there is someone nearby while they are sleeping, with possible responses
of "never," "sometimes," and "always." The questionnaire
includes "Sleep Symptoms" containing 2 somnolence statements, "Feel
excessively (overly) sleepy during the day," and "Feel unrested during
the day, no matter how many hours of sleep you had," as well as "Not
getting enough sleep," the insomnia statements, "Trouble falling asleep,"
"Wake up during the night and have difficulty resuming sleep," and "Wake
up too early in the morning and be unable to resume sleep," and "Bad
dreams or nightmares," rated on a 5-point scale from "Never" to
"Almost Always." These symptom questions have been widely used (e.g.,
the World Health Organization).39
Questions used to identify RLS were drawn from SHHS-29
and reflect NIH diagnostic criteria for the syndrome including description, frequency,
time of day, active/at rest status, and degree of discomfort.40
The Epworth Sleepiness Scale is a validated self-completion tool that asks subjects
to rate the likelihood of falling asleep in several common situations and was included
with the sleep habits items.41 Sleepiness
using the Epworth is assessed by the question, "What is the chance that you
would doze off or fall asleep in each of the following situations?" followed
by a list of 8 situations including "riding as a passenger in a car,"
"watching TV," and others. For each situation, possible responses include
4 ordinal categories ranging from "no chance" to "high chance."
The Epworth is a unitary scale, with a Cronbach α of 0.88 and test-retest reliability
over 5 months of r = 0.82 in previous studies.41
The Epworth was used in tandem with the Sleep Habits Questionnaire to examine convergent
validity. The Epworth measure, translated for this study in the same manner as the
Sleep Habits Questionnaire, also demonstrated high reliability for the English (0.780)
and Spanish (0.771) versions. The Spearman-Brown and intraclass coefficient for
the English/Spanish translated Epworth demonstrated robust correlations as well
(0.928 and 0.907, respectively).
Language serves as a general indicator of level of acculturation.28–30 The 30-item Acculturation Rating Scale for Mexican Americans
II (ARSMA-II; English and Spanish versions) identifies language familiarity, usage,
preference, ethnic identity, generation, reading, writing, cultural exposure, and
ethnic interaction. It has an internal reliability of 0.88 and test-retest reliability
of 0.72.42 Persons who score high in the
"Traditional" category are more likely to identify with the Mexican
culture, whereas persons with high scores in the "Assimilated" category
identify more with the United States culture. High scores in the "Bicultural"
category suggest the person identifies with both the Mexican and United States cultures.
This English to Spanish translation of the Sleep Habits Questionnaire was guided
by the adaptation of Brislin's Translation Model to address cultural and functional
equivalence, to make the translation and validation process more efficient and to
ensure the integrity of the process.32,33 Cultural equivalence implies similarity
of meaning and construct relevance across cultures.34
The translation and validation model is displayed in Figure 1.
In Step 1, 3 independent translations were made simultaneously in a blinded
fashion from source (English) to target (Spanish) language by 3 bilingual health
providers of Mexican heritage with Spanish as their first language. During Step 2,
each target language version of the questionnaire was back-translated in a blinded
fashion to the source language by 3 new volunteer bilingual health providers of
Mexican heritage with Spanish as their first language. In Step 3, a team
member whose first language was Spanish completed a content analysis of the translations
and back-translations to aid in assuring credibility, trustworthiness, and transferability
of translation. Where differences in meanings were identified in the back-translations,
the principal investigator and bilingual team members met with the translators and
back-translators involved in Steps 1 and 2 to review differences and adapt the target
language version (Spanish) in order to achieve the most accurate culturally equivalent
meanings. In Step 4, two additional native Spanish speakers independently
back-translated the version of the questionnaire revised in Step 3. Because bilingual
speakers and certified translators may introduce bias due to using and understanding
languages differently than the population to be tested, the back-translators in
Step 4 were lay people from local clinics who were more representative of the population
under study. Blinded data were reviewed by lay bilingual experts to determine the
need for linguistic adjustments based on early comments in this step. Step 5
consisted of a second meeting of the bilingual experts, who reviewed and compared
the back-translations of the expert and lay translators. At this point, the team
agreed on culturally equivalent meanings in both the English and Spanish language
versions of the Sleep Habits Questionnaire. Step 6 assisted in assuring that
both linguistic and cultural equivalence of translation was achieved (cross-language
validation).43,44 During this step, bilingual participants completed English
and Spanish language version packets 7 to 10 days apart in counterbalanced (randomized)
order. These data were examined for psychometric properties of the rigorously translated
Flow chart for translation and validation of the spanish-translated SHHS SHQ
Flow chart for translation and validation of the spanish-translated SHHS SHQ
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The Spanish translated instrument was assessed for grade level readability using
the Huerta Reading Ease Score.45 Readability
scores may range from 0 (most difficult) to 100 (least difficult) to read. Scores
from 90 to 100 indicate very easy reading at an estimated 5th grade level;
scores from 80 to 90 suggest easy reading at an estimated 6th grade level;
while scores from 0 to 30 indicate very difficult reading at an estimated graduate
college level.
Differences in demographic and health history variables for the cross-language validation
participants included analysis of variance for continuous variables and χ2
for nominal variables. Internal consistency reliability and conceptual equivalence
were evaluated using Cronbach α, Spearman-Brown, and intraclass coefficients.
We used a standardized item α to measure the Spearman-Brown coefficients. Intraclass
coefficients are used for test-retest reliability to determine the stability between
English and Spanish versions when sample size is small.46 Spearman-Brown and intraclass coefficients will approach
1.0 when there is no variance within items. Spearman-Brown and intraclass coefficients
of 0.80 to 0.89 are considered adequate, while coefficients ≥ 0.90 suggest
good reliability.46,47 A one-way random effects model was used for intraclass correlations,
which conceptualizes each observed subject as a component of subject factor; therefore,
the intraclass correlation is interpreted as the proportion of subject variance
associated with differences among the scores of the subject. Inter-correlations
among sleep variables were conducted using correlation coefficients to determine
convergent validity with the Epworth Sleepiness Scale. The criterion level for coefficient
α was set at ≥ 0.70 to retain an item in an adequate scale. Exploratory
factor analysis utilized principal component analysis without rotation to reduce
the number of items to validate item consistency between the 2 language versions.
For exploratory purposes, analysis included communalities ≥ 0.400 to determine
central factors.48,49 All data analyses were performed using PASW (Version 18).
All 6 translators were of Mexican American heritage with Spanish as their first
language. Two men and one woman translated the Sleep Habits Questionnaire from English
to Spanish; then 2 other women and one other man reverse-translated the questionnaire
from Spanish back to English. Translators and back-translators were 19 to 55 years
of age. Their current occupations included physician, nurse, clinic staff members
who work with Spanish-speaking patients, and 2 certified hospital translators (one
translator and one back-translator). The bilingual experts and lay translators who
reviewed the final translated version were no-cost volunteers of Mexican descent
with Spanish as their first language.
Characteristics of the cross-language validation participants are displayed in Table 1. Ethnic distribution for the bilingual participants
(N = 50; 52% women; mean age 38.8 ± 12 years) showed 90% to be of Mexican
origin, 4% Central or South American, and 6% non-Hispanic white. The mean education
level was 14.9 ± 3.4 years. The range of 6 to 22 years for education suggests
a broad sampling for educational achievement. The largest subgroups of participants
(n = 23 on the English and n = 25 on the Spanish versions) scored in the "Traditional"
category on the ARSMA II,42 suggesting
strong identification with Mexican culture. The remainder of the participants (n
= 12 and n = 11 on the English and Spanish versions, respectively) scored in the
"Bicultural" category, indicating strong identification with the cultures
of both Mexico and the United States, and "Assimilated" (n = 13 and
n = 12 on the English and Spanish versions, respectively), indicating strong identification
with United States culture. Given the higher levels of education seen in this predominantly
Mexican American sample, education (as a proxy for socioeconomic status) and acculturation
were stratified by sleep disorder categories (duration, snoring, apnea, insomnia
symptoms, other sleep symptoms, restless legs, and sleep disruptors). Neither education
nor acculturation differed significantly for any sleep category for either language
version. Figure 2 portrays the number of participants in each
acculturation category for English and Spanish. The acculturation differences between
versions were not significant. Participants were also assessed for English and Spanish
language fluency, including speaking, reading, writing, and comprehension (Table 2). The ratings ranged from 1 (poor) to 5 (excellent).
All participants scored ≥ 4. In addition, a majority of participants reported
having lived (n = 34) or studied (n = 26) in a Latin American country, predominantly
Characteristics of the cross-language validation studied sample (N = 50)
Characteristics of the cross-language validation studied sample (N = 50)
Acculturation between English (n = 48) and Spanish (n = 48) versions (number of
participants in each category)
Acculturation between English (n = 48) and Spanish (n = 48) versions (number of
participants in each category)
Language fluency for bilingual participants (N = 50) in the cross-language validation
Language fluency for bilingual participants (N = 50) in the cross-language validation
Internal consistency and correlation results for the Sleep Habits Questionnaire
are displayed in Table 3. All sleep variables except sleep
quality showed robust Cronbach α ≥ 0.700.46,47 The 3-item sleep quality category
examines short versus long, light versus deep, and non-restful versus tranquil sleep
on a 5-point Likert-type scale and showed a Cronbach α of 0.583 and 0.685 for
the English and Spanish versions, respectively, suggesting moderate reliability.
All categories of sleep variables for both language versions were highly correlated,
with Spearman-Brown and intraclass correlations > 0.800, suggesting strong and
comparable translation of the English to Spanish measures.46,47
Reliability of English and Spanish sleep scales
ξ Spearman-Brown Coefficient;
φ Intraclass Coefficient between English and Spanish versions.
Reliability of English and Spanish sleep scales
Table 4 displays the proportion of cross-language validation
participants with and without sleep disorders by categories. Proportions were consistent
between English and Spanish language versions, respectively, for short (18% vs.
20%) and long (14% each) sleep duration on weekdays, short (4% vs. 2%) and long
(40% vs. 44%) sleep duration on weekends, snoring (56% vs. 54%), sleep apnea (8%
each), insomnia symptoms (24% each), sleep symptoms (22% vs. 26%), sleep quality
(28% vs. 32%), and restless legs (10% vs. 12%).
Proportion of participants (N = 50) with and without sleep complaints on English
and Spanish versions
# Numbers of items for each category are listed in Table 3.
Yes = Presence of sleep disorder.
+ Poor to below average sleep quality.
^ Monthly to weekly disrupted sleep.
Proportion of participants (N = 50) with and without sleep complaints on English
and Spanish versions
The means and standard deviations for the Epworth were 7.3 ± 4.8 (range 0-19)
for the English version and 7.2 ± 4.5 (range 0-18) for the Spanish version.
Proportions of participants with an Epworth score > 10 designating excessive
daytime somnolence were 10% and 12% for the English and Spanish versions, respectively.
Correlations for both language versions are displayed in Table 5.
Correlations for the English language version are shown below the diagonal. For
the English version, weekday sleep duration (average in h) was significantly negatively
correlated with insomnia symptoms (r = −0.426, p < 0.01), sleep symptoms
(r = −0.538, p < 0.01), sleep disruptors (r = −0.466, p < 0.01),
and restless legs (r = −0.327, p < 0.05), and significantly positively
correlated with sleep quality (r = 0.354, p < 0.05). Weekend sleep duration (in
h) was negatively correlated with sleep symptoms (r = −304) and sleep disruptors
(r = −328, each p < 0.05) and restless legs (r = −0.462, p < 0.01).
Snoring was significantly positively correlated with apnea (r = 0.412, p < 0.01),
sleep symptoms (r = 0.291, p < 0.05), and sleep disruptors (r = 0.306, p <
0.05). Apnea was negatively correlated sleep quality (r = −0.317, p < 0.05).
Insomnia symptoms were positively correlated with other sleep symptoms (r = 0.805,
p < 0.01), sleep disruptors (r = 0.675, p < 0.01), and restless legs (r =
0.403, p < 0.01), and negatively correlated with sleep quality (r = −0.401,
p < 0.01). Sleep symptoms (e.g., insufficient sleep) were positively correlated
with sleep disruptors (r = 0.824, p < 0.01) and restless legs (r = 0.540, p <
0.01) and negatively correlated with sleep quality (r = −405, p < 0.01).
Sleep quality was negatively correlated with sleep disruptors (r = −0.347,
p < 0.01). Sleep disruptors were positively correlated with restless legs (r
= 0.586, p < 0.05) and negatively correlated with sleep quality (r = −347,
p < 0.05).
Intercorrelations among sleep variables and comparisons with Epworth for convergent
{ label (or @symbol) needed for fn } Bolded are significant
between the Epworth and items from the Sleep Habits Questionnaire for construct
* Correlation is significant at the p < 0.05 level (2-tailed).
** Correlation is significant at the p < 0.01 level (2-tailed). Correlations
for English are below the diagonal and correlations for Spanish are above the diagonal.
Intercorrelations among sleep variables and comparisons with Epworth for convergent
(more ...)
Correlations for the Spanish language version are shown above the diagonal in Table 5. Weekday sleep duration (in h) was negatively correlated
with insomnia symptoms (r = −0.399, p < 0.01), sleep symptoms (r = −0.426,
p < 0.01), and sleep disruptors (r = −0.334, p < 0.05), and positively
correlated with sleep quality (r = 0.415, p < 0.01). Weekend sleep duration was
negatively correlated with insomnia symptoms (r = −0.295, p < 0.05), sleep
symptoms (r = −0.301, p < 0.05), and restless legs (r = −0.411, p
< 0.01), and positively correlated with sleep quality (r = 0.295, p < 0.01).
Snoring was positively correlated with sleep disruptors (r = 0.312, p < 0.05).
As with the English version, apnea was negatively correlated with sleep quality
(r = −0.319, p < 0.05). Insomnia symptoms were positively correlated with
other sleep symptoms (r = 0.748, p < 0.01), sleep disruptors (r = 0.640, p <
0.01), restless legs (r = 0.396, p < 0.01), and negatively correlated with sleep
quality (r = −0.426, p < 0.01). Consonant with the English version, sleep
symptoms were positively correlated with sleep disruptors (r = 0.820, p < 0.01)
and restless legs (r = 0.609, p < 0.01) and negatively correlated with sleep
quality (r = −456, p < 0.01); sleep disruptors were positively correlated
with restless legs (r = 0.622, p < 0.01) and negatively correlated with sleep
quality (r = −385, p < 0.01).
Approximately 87% (39 of 45) of the correlations between the English and Spanish
versions were consistent in direction and magnitude of the relationships. Differences
noted showed snoring to be negatively (English) and positively (Spanish) associated
with weekend sleep duration; however, neither finding was significant. Snoring was
significantly positively associated with apnea and sleep symptoms in English, while
the Spanish version showed trends toward significance for apnea (r = 0.259, p =
0.07) and sleep symptoms (r = 0.247, p = 0.08).
The Epworth scale provided convergent validity for 5 of 8 of the sleep categories
(63%) for both language versions. For the English and Spanish versions, respectively,
the Epworth was significantly positively correlated with snoring (r = 0.325 and
r = 0.309, each p < 0.05), apnea (r = 0.340 and r = 0.354, each p < 0.05),
sleep symptoms (r = 0.477 and r = 0.510, each p < 0.01), sleep disruptors (r
= 0.505, p < 0.01 and r = 0.344, p < 0.05), and restless legs (r = 0.330 and
r = 0.303, each p < 0.05). The Epworth was also noted to be significantly negatively
correlated with weekday sleep duration (r = −0.334, p < 0.05) and positively
associated with insomnia symptoms (r = 0.290, p < 0.05) on the English, but not
the Spanish versions; however the directions of the correlations for both versions
were the same.
Exploratory factor analysis was conducted using principal components analysis without
rotation that resulted in 4 factors. The factor loadings for items in the questionnaire
are displayed in Table 6. Items 4 and 5 from each language
version loaded on Factor 1 (Sleep Duration); Items 13, 14, 15 (Snoring) and 17,
18, 19 (Breathing Pauses/Apnea) loaded on Factor 2 (Snoring and Apnea); Items 21
a-e and h-j loaded on Factor 3 (Sleep Symptoms); Items 24 a-b, 25, 26, 27, 28, 29,
30, 30a, and 32 loaded on Factor 4 (Restless Legs). The bedtime, time to sleep,
time arising in the morning, napping, reasons for napping, sleep quality, insufficient
sleep, use of sleep aids, nightmares/bad dreams, sleep disruptors, age at onset
of restless legs, and physician diagnosed restless legs did not centrally load on
any of the factors. Based on these factor loadings, the structure of the Spanish
version of the Sleep Habits Questionnaire is similar to the structure of the English
version which supports construct validity across language. Categories included in
Factors 2, 3, and 4 also correlated strongly with the Epworth Sleepiness Scale,
which provided convergent validity. The Epworth was significantly negatively correlated
with sleep duration on the English version, but not the Spanish version, or for
weekend sleep duration on both language versions.
Exploratory factor analysis of the Sleep Habits Questionnaire in English and Spanish
Exploratory factor analysis of the Sleep Habits Questionnaire in English and Spanish
The Spanish-translated instrument was assessed in sections of sleep categories.
Readability scores for the instrument were 89.1 (6th to near 5th
grade reading level) for the snoring category, 91.7 for the sleep quality category,
95.7 for the for sleep duration category, 99.1 for the apnea category, and 99.7
each for the restless legs syndrome category and the Epworth Sleepiness Scale (all
5th grade reading level).45
Readability scores could not be calculated for the sleep items that address insomnia
symptoms, sleep symptoms (e.g., unrefreshing sleep, leg jerks), or sleep disruptors
(e.g., nighttime toileting, noise in the surroundings). These categories, arranged
with Likert-type scales for frequency of symptoms, do not provide enough words or
sentences with punctuation marks to allow for readability calculations.
Overall, the Spanish-translated version of the Sleep Habits Questionnaire demonstrated
acceptable psychometric characteristics. Both language versions showed high levels
of content validity and conceptual equivalency. The rigorous translation process
and review of the Spanish version by experts found the items and content to be conceptually
similar to the English version. The Spearman-Brown and intraclass correlation coefficients,
which measure the homogeneity of the scales, indicated strong correlation and agreement
between language versions. The Epworth provided convergent validity for a majority
of sleep categories on both language versions, and exploratory factor analyses provided
construct validity across language. Thus, the Sleep Habits Questionnaire is suitable
for use with clinic patients and in community-based studies that examine various
categories of self-identified sleep disorders.
All Sleep Habits Questionnaire categories except for sleep quality demonstrated
strong internal consistency reliability for both language versions, ranging from
0.734 (English) and 0.731 (Spanish) for the 2-item sleep duration variable to 0.900
(English) and 0.890 (Spanish) for the 10 restless legs items. The 3-item sleep quality
category that assessed perception of length, depth, and satisfaction with sleep
showed only moderate internal consistency for the English (0.583) and Spanish (0.685)
versions. The quality of sleep items are determined by using a 5-point scale with
short/long, light/deep, and poor/good anchors. This scaling feature may not provide
enough definition or information for persons whose first language is not English
to respond adequately to these items. Future studies will need to examine these
items with additional bilingual and Spanish-only speakers to determine if the psychometrics
for the sleep quality items remain consistent or fluctuate with other groups. Nevertheless,
the coefficients between language versions are robust, suggesting good correlation
and agreement. Furthermore, the readability scores45
suggest that each of the sleep categories, as well as the Epworth, are suitable
to a fifth- to sixth-grade reading level. Translation issues and years of schooling
have been posited as barriers to adequate health assessment of Spanish-speaking
Hispanics in the United States.27–29
Proportions of participants with the presence of sleep disorders by categories showed
consistency in reporting between language versions. Percentages of participants
who report sleep disorders provide a foundation for prevalence rates among Spanish-speaking
Mexican Americans. A majority of these rates are consistent with population studies
undertaken in the United States, including the rates for insomnia symptoms, weekday
short sleep duration, and, in particular, the high rates for snoring among the Hispanics
in this study with Hispanics in other studies.4,5,8,16,24,25 Age, education, and acculturation
category were not significantly associated with any of the sleep categories. Future
studies will need to determine if these and other socioeconomic status variables,
including naturalization or U.S.-born status,50
may play roles in the type and severity of sleep disorder category among Mexican
American Hispanics.
Intercorrelations for both language versions show similar and consistent relationships
and directions among variables that support what might be expected in clinical and
research settings for persons with sleep disturbances, suggesting good criterion
validity. For example, persons who snore would be more likely to have apnea and
report daytime sleepiness (positive correlations). Persons who experience more sleep
disruption due to noisy nighttime environment, pain, or the need for frequent toileting
would be more likely to report shorter weekday and weekend sleep durations and poor
sleep quality (negative correlations) and greater reports of insomnia symptoms,
other sleep symptoms, and daytime somnolence (positive correlations). Likewise,
significant correlations between the Epworth with the sleep symptoms, sleep disruptors,
restless legs, and, in particular, the snoring and apnea categories on both language
versions support the convergent validity of the Spanish-translated measure. Notably,
the comprehensiveness of this questionnaire relevant to the number and type of sleep
categories have identified variables and their direction for both English and Spanish
speakers that can be examined in future clinical and research studies. These covariates
include insomnia symptoms, other sleep symptoms (e.g., insufficient or unrefreshing
sleep), restless legs, daytime somnolence, and sleep disruptors.
Reasons for the limited number of English and Spanish variables (6 of 45) that did
not significantly correlate are not known, but the lack of power due to the small
sample size may have contributed to the lack of significance. In addition, there
may have been unexpected circumstances that could have affected these few correlations.
For example, snoring showed a positive correlation in English and a negative correlation
in Spanish with weekend sleep duration. Weekend events or changes in weekend activities
might possibly have influenced differences in snoring responses during the 7- to
10-day time frame. Future studies of this sort will need to include a brief question
regarding change in lifestyle habits in repeated measures studies.
Items in the Spanish version loaded on the same factors in the English version (Sleep
Duration, Snoring and Apnea, Sleep Symptoms, and Restless Legs). The four factors
explained 68% of the variance on the English version and 67% of the variance on
the Spanish version. Loadings for inclusion in this exploratory factor analysis
were set at ≥ 0.400 to determine central factors, while loadings > 0.600
are considered high.48,49 Findings from this analysis suggest strong loadings for the
measured variables most associated with each of the four extracted factors. Factor
loadings and variance accounted for are consistent between language versions, supporting
the construct validity between the English and Spanish versions.
Limitations to this study include sample size and bilingual Spanish speakers of
predominantly Mexican heritage residing in the Southwest. This sample of 50 bilingual
volunteers is sufficient for initial analyses of reliability and validity, but is
not adequate to demonstrate the critical relationships between sleep health and
other comorbid conditions that should be studied in the Hispanic population. The
design of a cross-language validation study is not appropriate for establishing
the test-retest reliability of the Spanish version, providing normative data, or
assessing cultural equivalence across other Spanish-speaking ethnic groups from
Central and South America, Cuba, and Puerto Rico. Education and acculturation, included
as a prelude to examining sociocultural factors on the development of this Spanish
language version did not have an impact on the sleep categories for either language
version. Future studies will need to examine if these and other socioeconomic, immigration,
and access to care factors may be linked to type and severity of sleep disorder
category among Mexican American Hispanics.50
Acculturation status, age, and recruitment locations (clinics, community-based neighborhood
centers and programs, and academic milieus) suggest the participants are representative
of the general Mexican American population residing in Maricopa County, Arizona,
who are clinic patients or would participate in community-based research studies.
Notably, however, the high educational achievement reflected in their mean years
of education (14.9) is not representative of academic levels generally seen among
Mexican Americans (10th grade).27–29
Nevertheless, their range of education (6 to 22 years) suggests that the translated
measure is relevant to a broad span of Spanish-speaking learners with a minimum
of sixth grade education. These shortcomings will need to be addressed in future
studies to determine the settings and populations in which use of the new instrument
is most appropriate. Future studies will also need to determine item equivalence
with confirmatory factor analysis.
This study examined the psychometric properties of the English to Spanish translated,
back-translated, and cross-language validated Sleep Habits Questionnaire with bilingual
community-dwelling adults predominantly of Mexican American heritage with Spanish
as their first language. Results demonstrate that the Sleep Habits Questionnaire
is a psychometrically sound measure with robust correlations within and between
language versions for a broad range of subjective sleep disorder categories that
can be self-administered in community and clinic settings. The Epworth provided
convergent validity for the snoring, apnea, sleep symptoms, restless legs, and sleep
disruptors categories, while loadings from exploratory factor analysis supported
the structure of both English and Spanish versions of the instrument. The English
version of the Sleep Habits Questionnaire has been used ubiquitously in clinical
and population-based studies. Findings indicate that the Spanish-language version
has robust and appropriate measurement properties and may be useful for assessing
sleep health in community-based and intervention studies among Spanish speakers
residing in the Southwest.
This was not an industry supported study. The authors have indicated no financial
conflicts of interest.
The authors gratefully acknowledge Mary Z. Mays, Ph.D. and Janice Jirsak, M.S. for
data coordination and data integrity. Funding: NIH Grant #1R03HD051678 and, in part,
the ASU CONHI Dean's Research Award.
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Gottlieb DJ, Punjabi NM, Newman AB, et al., authors. Association of sleep time
with diabetes mellitus and impaired glucose tolerance. Arch Intern Med. 2005;165:863–8.
Gottlieb DJ, Redline S, Nieto FJ, et al., authors. Association of usual sleep
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disorders and sleep habits in the United States. Sleep Breath. 2009;14:63–70.
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and mortality: a prospective cohort study. PLoS Med. 2009;6:e1000132[PubMed Central][PubMed]
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review. Behav Sleep Med. 2006;4:29–44. [PubMed]
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in older African Americans and Caucasians at risk for sleep-disordered breathing.
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in a population-based study. Sleep. 2007;30:1096–103. [PubMed Central][PubMed]
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of sleep-disordered breathing among middle-aged adults. New Engl J Med. 1993;328:1230–5.
Redline S, Kump K, Tishler PV, Browner I, Ferrette V, authors. Gender differences
in sleep disordered breathing in a community-based sample. Am J Respir Crit Care
Med. 1993;149:722–6
Kump K, Whalen C, Tishler PV, et al., authors. Assessment of the validity and
utility of a sleep-symptom questionnaire. Am J Respir Crit Care Med. 1994;150:735–41.
Zielinski J, Zgierska A, Polakowska M, et al., authors. Snoring and excessive
daytime somnolence among Polish middle-aged adults. Eur Respir J. 1999;14:946–50.
Allen RP, Picchietti D, Hening WA, Trenkwalder C, Walters AS, Montplaisir J,
authors; Restless legs syndrome diagnosis and epidemiology workshop at the National
Institutes of Health; International Restless Legs Syndrome Study Group. Restless
legs syndrome: diagnostic criteria, special considerations, and epidemiology. A
report from the restless legs syndrome diagnosis and epidemiology workshop at the
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conceptually equivalent health definitions across multiple cultural groups. Eighth
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address the Hispanic Paradox. Sleep. 2011;34:1021–31. [PubMed Central][PubMed]


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Trace Adkins Says He's Come a Long Way on His New Album, 'Proud to Be Here'
Trace Adkins named his new album 'Proud to Be Here,' and that sums up his career outlook pretty nicely.
Adkins might be riding high on the charts now, with a string of bestselling records and hit singles to his credit, but he still remembers how he felt when he was just starting out — and, as he proved during a recent interview with Taste of Country, he knows how far he's come.
"I can't hardly go back and listen to [my earlier albums], especially that first album, because that sounds to me like a inexperienced guy that's in the studio scared to death," Adkins reflected. "That's exactly what it was. I did the best I could, and I had some great songs to work with. I know in my opinion I have evolved and I have grown and I have gotten better [since then]. Now I can listen to this stuff and go, 'This is about as good as I can do it.' I think I've just grown and gotten a little better at what I do."
Plenty of Adkins' hits have played up his sense of humor (including 'Honky Tonk Badonkadonk' and the Blake Shelton duet 'Hillbilly Bone'), but his latest hit, 'Just Fishin',' is a more thoughtful, family-oriented song about a man spending some quality time with his daughter.
"There's probably been a song in this vein on every album I've done," says of 'Just Fishin'.' "A couple of times [those songs] in the past have been singles. I don't know if I'm going to do it any more or any less, but it's just something that I've always done, and this time they thought enough of the song to put it out as a single. I didn't have a problem with that."


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- This event has passed.
Monday Specials
March 12, 2018
|Recurring Event (See all)
An event every week that begins at 12:00am on Monday, repeating indefinitely
Event Navigation
Happy Hour 4pm to 7pm Blowout Monday Night 7pm to 12am -2 for 1 Poke Bowls (Asian Chicken. Ahi Tuna & Steak) -$3 Sangria of the Week -$3 Craft Cocktail of the Week on Tap -$3 Craft Beer of the Week on Tap


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Judge Orders $300K Forfeiture in Counterfeit Case
SIOUX FALLS - Two people have been ordered to forfeit about $300,000 in bank accounts and other items in a trademark violation case.
Thirty-four-year-old Ravaye Meltzer and 29-year-old Bar Braver were convicted in federal court of trafficking in counterfeit goods and services.
Authorities say Meltzer and Braver intentionally sold counterfeit goods near Rapid City, Keystone, Deadwood, Hill City and Sturgis between February 2010 and August 2011.
U.S. District Judge Jeffrey Viken also ordered the two defendants to serve one year of probation.
Copyright 2013 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.


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Update on My Investigation into Cousin Nunna's Death
Several weeks ago, I discovered that the death of my 3rd cousin twice removed (my maternal grandmother's first cousin), Nunna Pierce Jackson, was ruled a homicide. (Refer to Murder in the Family for information on Cousin Nunna.) I set out to determine exactly what happened. What were the events that lead to Cousin Nunna being murdered? Sadly, as of today I must say that I've not discovered any other details surrounding her death.
My first steps were to 1) contact the Walton Tribune and 2) contact the Monroe – Walton County Public Library. The Walton Tribune was unable to assist and directed me toward the library, which of course I had already contacted. Sadly, the library did not have copies of the Walton Tribune from the time period in question.
This past week, I contacted both the Monroe Police Department and the Walton County Sheriff's Department for assistance and am awaiting a reply. I'm hopeful they can provide assistance.
In the meantime, after setting up a memorial for Cousin Nunna on FindAGrave then submitting a photo request, I was able to obtain a picture of Cousin Nunna's tombstone as well as updated images that better display the current state of Sheats Family Cemetery, which is the final resting place for Cousin Nunna, her sister Moode Pierce, and my great grandfather Cornelius Pierce.
Nunna Pierce Jackson
1898- 1929
Daughter of Great Grand Uncle Lon(nie) Pierce
Picture obtained via photo request at FindAGrave.com and is posted at http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GSmid=47152179&GRid=51051421.


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Man Singing, Brick Lane, London
One of a series of images taken in the East End of London between 1976 and 1978
Printed on Canson museum grade traditional fibre based Baryta paper offering maximum longevity.
Image size 12 x 10 inches
Black wood frame and white mount included in price
Edition of 10
Signed and numbered Certificate of Authenticity is supplied with the print.
Free worldwide delivery


text:
Get the Flash Playerto see this player.
|Boobs And Bottoms
Short review: There's more movement here than could even be measured on the Richter scale. Once the boobs start flopping and the butts start jiggling, you'll be losing your load just watching the action. Boobs and Bottoms is a nice site, and they need to keep adding updates on a regular basis, it's worth it. They do include 40+ bonus sites, a third party feed of dating and live chat, it's good, and high quality
Content Amount: I wish the numbers were doubled in how much this site holds, but alas, I guess we'll just have to wait for that to happen. For what is here, it's not extremely low, and they offer plenty of extras to spruce things up for the membership fee.


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Skate Parks
Bray Park, Wyndham Avenue, Boyne Island
The first of the region's skate parks was Riverside Skateway, built in August 1999. This is a regionally significant skate park, approximately 1500 square metres in size, with a total construction cost of $164,000. This cost included construction of the park, landscaping, seating, signage and irrigation.
The park has a 6m x 1.8m steel half pipe, start ramp, ¼ pipe, mogul, fun box, grind boxes and wedge ramp. It also has a "jelly mould" surrounding an established fig tree.
Later this year, work will begin on an upgrade to the skate park and a new pump track will also be added to the facility. The concept plans for these projects can be found here and here.
Bunting Park, Archer Street, Calliope
The Calliope Skate Park is located in Bunting Park, Archer Street Calliope. The course combines skateboarding, rollerblading and BMX trick riding facilities.
Bunting Park already has an established basketball facility, toilet facilities, Girl Guide Hall and Scout Hall, adjoins the cricket, soccer and rugby league fields and has ample open space oportunities.
Memorial Park, Yarroon Street, Gladstone
The Gladstone Skate Park is located at Memorial Park in Yaroon Street (next to the PCYC). The Gladstone Skate Park provides a safe and supervised venue for skating and BMX enthusiasts of all ages and skill levels to enjoy.
The project included many years of planning with the help of the Gladstone Sk8 committee. The final plan was designed by D-Brand skate design and construction undertaken by Bechtel and Golding Contractors. Total project cost was $425,000 with a further $65,000 added to incorporate shading for the facility. The project was made possible thanks to funding and support from Bechtel Corporation, Qld Government Department of Sport, Recreation and Planning, the Australian Government through the Regional Partnerships program, Parmac Property Group, Goldings and Cement Australia. Many local companies also offered their support and services towards the project.
The skate park measures 730 sq/m in size and caters for skate, bmx, blade and scooter. Some of the parks elements include, Vert wall, 3/4 bowl, stairs, fun box, mini ramp and grind box/rails. One of the parks great benefits is that it caters from first timers to professionals.
Yarwun Recreation Grounds, Calliope River Road, Yarwun
Yarwun Skateway was built in March 2000 and approximately half the size of the Riverside Park. This facility cost $54,000 to construct, including the refurbishment of the amenities building, seating, signage, landscaping and construction.
This facility includes a concrete half pipe, quarter pipe, wedge ramp, mogul, grind rails and a flat skating space with basketball hoop. ConQuest Skate Parks undertook the design and construction of this facility.
Agnes Water Skate & BMX Facility, Springs Road, Agnes Water (Captain Cook Lions Park)
Springs Road, Agnes Water is where you will find the Captain Cook Lions Park. Home to the area's skate and BMX facility, and conveniently located close to the Agnes Water School, it is a popular stop-off for local youth. A shaded playground incorporating fitness stations, amenities block and ample seating are also located in the Park; along with picnic table, barbeque and plenty of off-street parking.
Safety information can be found at Queensland Transport Department's website.


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Color: White
Interior: Cloth
Drive Train: FWD
Transmission: Automatic
Vin: NM0LS7F76G1238148
Engine: 2.5L
Mileage: 55,225
Stock #: 13949
West Coast Car & Truck Sales Inc.
West Coast Car & Truck Sales, Inc.
8391 US 19 North
Pinellas Park,
I hereby consent to receive text messages from or on behalf of dealer at the mobile phone number I provided above. I understand that I am opting in to receive text messages from dealer or their employees. I include consent to receive phone calls at the mobile phone number I provided. I understand that message and data rates may apply.


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While we understand that ads are annoying, you should know that advertising-income is what pays for the awesome content we provide [for free to you]. Would you consider disabling adblock on our site? You can also create an account for an ad-light experience!
Thank you for visiting our website! Below you will be able to find the answer to Two lady followers crossword clue which was last seen on Universal Crossword, September 11 2017. Our site contains over 2.8 million crossword clues in which you can find whatever clue you are looking for. Since you landed on this page then you would like to know the answer to Two lady followers. Without losing anymore time here is the answer for the above mentioned crossword clue:
We found 3 possible solutions in our database matching the query Two lady followers
|Universal September 11 2017
|Universal September 11 2017
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|Wheel cover
|Sigourney Weaver horror sequel
|Gold measurement units
|Utmost boundaries
|Cash, in slang (var.)
|Remain firmly attached
|Sign on a bathroom door
|Yoko of music
|Hank Hill's TV town
|Gambler's "wheel"
|List-shortening letters
|What it doesn't hurt to do
|Plane type
|"New" as a prefix
|St. ___ (Caribbean isle)
|Sideways look
|Positive response
|File folder projections
|Drexler or Barrow
|British WWII fliers
|Kitten comment
|Stage objects
|It can move mountains
|Gets closer to retirement
|Animal's den
|New York hockey player
|"Three" prefix
|Pea container
|Airport necessity
|Worsted fabrics
|Bulgarian currency
|War's opposite
|___ Lanka
|Author Bagnold
|Cash dispenser
|Eggs, to a scientist
|Kind of mattress
|Cod cousin
|Latin American dance
|___ Bator
|Common theater name
|Two lady followers
|Wriggly fish
|Builder of tiny hills
|Pitch for the road
|Whispered attention-getter
|Pale brown shade
|Golfer's peg
|Concert equipment
|Produces milk
|Two lady followers
|Security protection
|Concluded a hunger strike
|Marina construction
|Gravy sucker-uppers
|Talks as if from Dixie
|Raises the ante
|Prefix with "game"
|Formerly named
|Respectful one
|Two lady followers
|Attachment to "sacro"
|Dusty little bit
|The ___ of Avon (Shakespeare)
|Change color again
|Negative replies
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Sports cancellations for April 23
The Standish-Sterling baseball games scheduled for today, April 23 at Dow Diamond against Tawas has been cancelled due to the rain and thunderstorms in the forecast and has been rescheduled for Thursday, May 23.
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Edroma is one page HTML5&CSS3 landing page template. It's perfect for product or service presentation. Minimalistic design and well-considered page layout will certainly provide your page high attention of viewers.
- Features:
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- Used Google Fonts
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- Skeleton grid
Zip File Contents:
- HTML files
- Documentation
I am available for help, suggestions at firstname.lastname@example.com or via themeforest
Don't forget to rate it


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McLEAN, VA -- Sport & Health Clubs, which has 23 clubs in the Virginia, Maryland and Washington, DC, areas, has received $25 million in financing through Pittsburgh-based PNC Mezzanine Capital and Wynnewood, PA-based CMS Mezzanine Fund.
The financing will enable Sport & Health Clubs to restructure senior debt and allow the company to acquire and construct new clubs in the Washington, DC, area, according to a company press release. The company plans to add three new clubs per year.
One of the new clubs will be a 43,000-square-foot facility with indoor and outdoor pools. Several more clubs will receive new flat-screen TVs, cardio equipment with personal viewing screens and entertainment packages. Other clubs will expand and receive locker room renovations.
"Our priority remains to strengthen our position as the Washington metropolitan area's preeminent family of health clubs, offering our members the best in fitness equipment and programming," Jonathan Adler, Sport & Health CEO, said in a statement.
Mark Fisher, president and COO of Sport & Health, added: "While the turbulent economy has many industries tightening budgets and cutting back on expansion plans, Sport & Health is swimming against the current: expanding now to meet the needs of our members and to grow our footprint in the Washington, DC, area."
Sport & Health Clubs ranked 13th on Club Industry's Fitness Business Pro's Top 100 clubs list last year, reporting $85.5 million in revenue in 2007.


text:
The Romance Angels are a group of cherubic angels who are focused upon all things love related. Anyone can call upon these beings, and they're able to help unlimited numbers of people simultaneously.
This beautifully illustrated card deck by Doreen Virtue will allow you to receive angelic guidance about your romantic status, as well as conduct accurate and trustworthy readings for your friends and clients.
The Romance Angels Oracle Cards can offer you more clarity about soul-mate relationships, healing from the past, and attracting more love into your life. Whether you're seeking answers for yourself or someone else, these cards can yield valuable insights. The Romance Angels are happy to guide you to a lifetime of love!
Doreen Virtue holds B.A., M.A., and Ph.D. degrees in counseling psychology; and is a lifelong clairvoyant who works with the angelic realm. Doreen is the author of Healing with the Angels, How to Hear Your Angels, Messages from Your Angels, Archangels & Ascended Masters, Solomon's Angels, and the Archangel Oracle Cards, among other works. Her products are available in most languages worldwide.
Doreen has appeared on Oprah, CNN, The View, and other television and radio programs; and writes regular columns for Womans World, New Age Retailer, and Spirit & Destiny magazines. For more information on Doreen and the workshops she presents, please visit www.AngelTherapy.com.


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pmeeks needed a new logo design and created a contest on 99designs.
A winner was selected from 362 designs submitted by 67 freelance designers.
Productive Technology. http://pm6.com Tagline: Helping you make your business more productive
First - I'm committed to being very involved in this contest, and giving lots of feedback to help you help me.
I have an Independent Technology Consulting company serving the Charlotte, NC, USA region. Services include onsite consulting and offsite solution development.
Philosophy: Experience and best practices result in a productive use of client resources. Our deliverables help our clients to make their business more productive.
Differentiator: A rare combination of business acumen, communication, and solution delivery, at a reasonable value.
Website: http://pm6.com - don't laugh; I am going to get a new website as soon as the logo is done. You can see the old logo there - I made it myself, and it sucks, so don't use as basis for new logo. The designer chosen for the logo would be the natural choice to do the website.
I target the small to mid-size business market. The Fortune 1000 companies usually prefer larger companies and do not talk to independent consultants as much as the smaller companies do.
Primary audiences are IT Managers (larger businesses) and company owners (smaller businesses.) Developers and other non-buyers can recommend me, and may someday hire me, so they are a secondary target audience.
Many IT folks are business casual on the outside, but creative and whimsical on the inside. An excellent logo will have a similar construction.
The target audience will expect an image of credibility, and skill. They will also value creativity in a brand image, as developers and IT people are usually open to new ideas and concepts.
• Logo delivery must be in vector format.
• Iconic - feature an icon people will associate with the company. Logo should contain the word "Productive" but the icon should be prominent.
• Colors: I'm open, so try what you like. To me, light green seems attractive; blues should trend to the lighter side. Gradients are nice. Must look good on website with dark background, and on white business card.
• Emphasize the word Productive, not Technology. You can use just the word Productive in your design, or both words, but make Productive stand out if you use both.
• Logo image must convey skill, trust, integrity, commitment, and professionalism. I don't like cliché symbols of productivity, like bees. I like an abstract image, as long as it conveys the proper message.
• Logo should be clean, modern, and meaningful to the target audience.
• Tagline is long, so design need not include it, but you can try if you want.
See the following for examples of designs I like:
• http://99designs.com/contests/23641/entries/293
• http://99designs.com/contests/23577/entries/32
• http://99designs.com/contests/23646/entries/35
• http://99designs.com/contests/23657/entries/4
• http://99designs.com/contests/23677/entries/54
• http://99designs.com/contests/23724/entries/2
• http://99designs.com/contests/23772/entries/39
Find out how a design contest works or learn more about our logo design services.


text:
What is
Office 365
Office 365 is a cloud-based subscription service that brings together the best tools for the way people work today. By combining best-in-class apps like Excel and Outlook with powerful cloud services like OneDrive and Microsoft Teams, Office 365 lets anyone create and share anywhere on any device.
Learn more about Office 365
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Augmented reality (AR) goes way beyond Google Glass. Indeed, the sector is broad and exciting. It extends from what now is mundane – superimposing street names on a GPS display, for instance – to the truly exciting and innovative.
This slideshow presents examples of AR. More is on the way, including direct competitors to Google Glass. The bottom line is that AR can be integrated into applications, both consumer and business, in almost limitless ways. Google's project indeed is a big deal – and these apps are as well.
Related Topics : In Their Own Words: The Four Dark Horses for the Third Major Mobile OS Speak, HTC, Mobile Search, 3G, Location-Based Services
Wearables are revolutionizing the workplace, with innovations that create a safer work environment or enhance the way professionals are able to go about their job. ... More >>
Here are the top 10 strategic technology trends that will impact most organizations in 2017. Strategic technology trends are defined as those with substantial disruptive potential or those reaching the tipping point over the next five years. ... More >>
Digital innovation is by far the biggest influencer, changing the way we do just about everything, from shopping to communication to running a business. ... More >>