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Home / Federal Supreme Court Rules on Refund of Dividend Withholding Tax
Federal Supreme Court Rules on Refund of Dividend Withholding Tax
In its decision of 27 November 2020 (case 2C_835/2017), the Swiss Federal Supreme Court decided a case relating to the refund of Swiss dividend withholding taxes by claiming the benefits under the Switzerland - United States Income Tax Treaty (1996) (as amended through 2009).
(a) Facts. The plaintiff, an individual, received from his participation in a Swiss corporation dividend distributions in the years 2008 and 2009. The distributing corporation deducted 35% anticipatory tax on the gross dividend payments and remitted it to the Federal Tax Administration. On 13 January 2011, the plaintiff filed a form requesting the refund of CHF 4,550,000, equalling 20% of the gross dividend distributions. On the refund form, he indicated a residence address in the United Kingdom. The Federal Tax Administration approved the request and remitted the full refund claimed to the plaintiff. On 12 August 2012, the plaintiff filed a further form requesting the refund of CHF 1,174,491.80 anticipatory tax deducted for dividend distributions he had received from various Swiss corporations in 2010. Again, he indicated a residence address in the United Kingdom. Upon request by the Federal Tax Administration, the plaintiff clarified that he was resident in the United Kingdom but not domiciled. He would benefit from a taxation on a remittance basis, i.e. he would only be taxed on income remitted to the United Kingdom. He added that, due to his US citizenship, he would be taxed in the United States on a worldwide basis and that he would also be entitled to benefits granted under the Switzerland - United States Income Tax Treaty (1996) (as amended through 2009). After a further exchange of letters, the Federal Tax Administration rejected the application and denied the refund. The Federal Tax Administration was not convinced that the plaintiff met the conditions of article 4(1)(a)(second sentence) of the Switzerland - United States Income Tax Treaty (1996) (as amended through 2009). Consequently, the plaintiff would not be entitled to treaty benefits. Moreover, in a formal decision, the Tax Administration obliged the plaintiff to pay back the refund of anticipatory tax for CHF 4,550,000 related to the years 2008 and 2009. In addition, the payment of debit interest of 5% per year would be due on the outstanding claim. Upon the plaintiff's objection, the Federal Administrative Court confirmed the decision of the Federal Tax Administration. The plaintiff filed an appeal to the Federal Supreme Court.
(b) Issue. Switzerland levies a withholding tax of 35% on dividend payments made by Swiss corporations (anticipatory tax, Verrechnungssteuer). A partial or full refund of withholding taxes is granted in accordance with applicable tax treaties. The issue was whether the recipient was entitled to claim the treaty benefits under the Switzerland - United States Income Tax Treaty (1996) (as amended through 2009) to obtain a refund of 20% anticipatory tax calculated on the gross dividends. The plaintiff never claimed the application of the Switzerland - United Kingdom Income Tax Treaty (1977) (as amended through 2017). Among other conditions, the application of the treaty to a US citizen that is not a resident of Switzerland requires a substantial presence, a permanent home or an habitual abode of the plaintiff in the United States (article 4(1)(a)(2nd sentence) of the Switzerland - Unite. The Federal Tax Administration held that the condition was not met, even though the plaintiff argued to dispose of a permanent home at the home address of his parents in said country. The tax administration argued that the effective arrangement in the home of his parents did not fulfil the requirement of having a permanent home in the United States.
(c) Decision. The Federal Supreme Court rejected the appeal and confirmed the decision taken by the Federal Administrative Court and the argumentation submitted by the Federal Tax Administration. The Court saw no reasons to deviate from the merits of the case prepared by the Federal Tax Administration.


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Oatmeal Raisin Cookie Bars are a quick and easy treat for your family and friends….perfect for a party, special dinner dessert or just because.
Here at the Carr home there are four seasons…winter, spring, summer and BAKING! We're officially in the Baking Season right now and I'm going through tons of "baking ingredients".
These Oatmeal Raisin Cookie Bars were made with the new I Can't Believe It's Not Butter…and it's true, I Can't Believe it! It's made with real, simple, non-GMO ingredients that you can actually read and pronounce and has 40% fewer calories and 70% less saturated fat than butter. It almost makes cookies "healthy", right? Ok, at least better!
We've used the I Can't Believe It's Not Butter spray and spreads for years on things like corn on the cob and baked potatoes but after making these cookie bars I realized you can substitute it in practically any recipe, without changing the flavor.
*At this point, I tasted the cookie dough. Yes, I live on the edge…I (and my children) eat raw cookie dough! I thought it would be good with chocolate chips, so I added some of those.
Visit http://clvr.li/thenewICB for more great recipes and leave a review to let others know your success story!
I'd love to hear how they liked them. Thanks for stopping by! Have a blessed week.
Oh my goodness! I love dessert like this!
I'd love for you to share this post at my Show Me Saturday linky party. The party goes live tomorrow morning at 7:00 am EST. My readers would love this!
Thanks Ashley, I'll plan to stop by.
These look AMAZING! I just pinned it to try later and shared it via Twitter! Can't wait to make it, maybe for Christmas cookie exchange!
Great recipe! They look wonderful!


FORMER Premier League boss Owen Coyle has told Arsenal to hold talks with Chelsea to sign Gary Cahill.
Arsenal, meanwhile, have a defensive crisis on their hands with Hector Bellerin, Rob Holding, Sokratis Papastathopoulos and Laurent Koscielny all out.
Ex-Burnley manager Coyle thinks the move makes sense - but he doesn't think it will come to fruition.
The club Coyle appears to be referring to is Crystal Palace after a move to Fulham hit the rocks.
The Cottagers held talks over Cahill but they have now switched attention to Scott Dann, who is out of Roy Hodgson's side.
Cahill has made just one Premier League appearance under Chelsea boss Maurizio Sarri.
That came came off the bench in the 0-0 draw at West Ham in September and he hasn't played a league match since.
In a nod to the fact he's likely to leave, Cahill's captain's notes now no longer appear in the matchday programme.
The transfer window slams shut at 11pm on Thursday.


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Home > Careers > Medical Sciences > Doctor
Doctor - scope, careers, colleges, skills, jobs, salary
Everything you need to know about making a career in the Doctor. Doctor careers, scope, colleges, skills required, job prospects and salary. Discover the complete information of Doctor here.
Have A Query
"Medicines cure diseases, but only doctors can cure patients." – CARL JUNG
Doctors are medical professionals who examine, diagnose, treat and counsel patients. They would prescribe treatments and medications or even surgeries accordingly. Doctors work in large hospitals to offer treatment in all branches covered under the medical specialties, in multi-specialty hospitals, clinics, nursing homes. They can also offer services for the Ministry of Defense or for government hospitals.
They also work towards educating and spreading awareness in public to prevent spreading of various diseases and illnesses.
Doctor Career Path
MBBS (Bachelor of Medicine and Bachelor of Surgery)
Level Under-Graduate
Duration 5 ½ years
Eligibility 10+2 (PCB [Physics, Chemistry & Biology]/Bio-technology & English) with aggregate of 50% to 60% marks (40% to 50% in case of reserved category); Applicants from NIOS (National Institute of Open Schooling) can also apply with the same criteria, Class XII candidates whose result is awaited can also apply, Age: 17-25 years (5 years relaxation for SC/ST/OBC), Medical entrance test is mandatory
Entrance Exam --
Specialization --
Average Course Fee Govt. colleges: INR 1,00,000 to INR 3,00,000, Private colleges: INR 20,00,000 to INR 50,00,000
Mode Regular
Goal General Physician, General Surgeon, General Practitioner, Junior Doctor, Medical Services under the Ministry of Defence, Higher Studies, Junior Resident, Teacher
BDS (Bachelor of Dental Surgery)
Duration 4 years and 1 year internship
Eligibility 10+2 (PCB [Physics, Chemistry & Biology]/Bio-technology & English) with aggregate of 50% to 60% marks (40% in case of reserved category); Applicants from NIOS (National Institute of Open Schooling) can also apply with the same criteria, Class XII candidates whose result is awaited can also apply, Age: 17-25 years (5 years relaxation for SC/ST/OBC), Medical entrance test is mandatory
Goal Dentist/Dental Surgeon, Teacher
MD (Doctor of Medicine)/ MS (Master of Surgery)
Level Post-Graduate
Duration 3-6 years
Eligibility MBBS with 50% to 55% marks from college recognized by Medical Council of India, PG entrance test is mandatory, Candidates should have obtained permanent registration with Medical Council of India/State Medical Councils
Entrance Exam National Eligibility Cum Entrance Test (NEET) -MDS
Specialization Doctor of Medicine (MD)- Obstetrics & Gynecology, Neurology, Anesthesiology, Cardiology, General Medicine, Pediatric, Psychiatry, Dermatology, Pathology, Orthopedic, Master of Surgery (MS)- Pediatric Surgery, General Surgery, Neurosurgery, Urology, Cardiac Surgery, Plastic Surgery, ENT, Ophthalmology, Gynecology & Obstetrics, Orthopedics
Goal Physician, Pathologist, Surgeon, Cardiologist, Resident Medical officer, Neurosurgeon, Lecturer, Anesthetist, Pediatrician, Super specialty courses/Doctoral Degree/Research
BHMS (Bachelor of Homoeopathic Medicine & Surgery)– 5 ½ years
BAMS (Bachelor of Ayurvedic Medicine & Surgery) – 5 ½ years
BUMS (Bachelor of Unani Medicine & Surgery) – 5 ½ years
BVSc & AH (Bachelor of Veterinary Sciences & Animal Husbandry) – 5 ½ years
MDS (Master of Dental Surgery) – 3 years
Super Specialty Courses– 3 years
PG- Diploma (Various Specializations)– 2 years
DNB (Diplomate of National Board)– 3 years
Ph.D. (Various Specializations) – 3 to 6 years
Colleges for Doctor
Aligarh Muslim University, Aligarh
All India Institute of Medical Sciences, New Delhi
Amrita College of Dentistry, Kerala
Armed Forces Medical College (AFMC), Pune
Christian Medical College (CMC), Vellore
Government Dental College & Research Institute, Bengaluru
Grant Medical College, Mumbai
Institute of Medical Sciences Banaras Hindu University, Varanasi
Jawaharlal Institute of Post Graduate Medical Education and Research, Puducherry
King George's Medical University (KGMU), Lucknow
Lady Hardinge Medical College, New Delhi
Mahatma Gandhi Institute of Medical Sciences, Wardha, Maharashtra
Maulana Azad Institute of Dental Sciences, New Delhi
Maulana Azad Medical College, Delhi
Post Graduate Institute of Medical Education & Research (PGIMER), Chandigarh
Sanjay Gandhi Post Graduate Institute of Medical Sciences (SGPGI), Lucknow
SDM College of Dental Sciences & Hospital, Dharwad
Sri Ramachandra University, Chennai
St. John's Medical College, Bangalore
Top Colleges for Doctor
Scholarship / Fellowship in Doctor
All India Institute of Medical Sciences (AIIMS) offers Merit-Cum-Means Based Scholarship to needy meritorious students for MBBS / BDS.
Ministry of Minority Affairs, Govt. of India offers Merit cum Means Scholarship (MOMA Scholarship) to the MBBS students belonging to the minority community and who are not financially strong.
All India Scholarship Entrance Examination (AISEE) is a non-government organization, which provide Medical Scholarship for college students.
The Kishore Vaigyanik Protsahan Yojana (KVPY) is an on-going National Program of Fellowship is initiated and funded by the Department of Science and Technology, Government of India. It attracts exceptionally highly motivated students for pursuing research career in science.
Manipal University offers Free-ship & Merit-cum-Means Scholarship to top performing students in NEET examinations, admitted through Directorate General of Health Services, New Delhi to MBBS and BDS programs at Manipal and Mangalore campuses.
Indian Oil awards IOCL Scholarship to the 1st year MBBS students.
Swiss Government provides Swiss Government Excellence Research Scholarship
National Thermal Power Corporation (NTPC) offers NTPC Scholarship for SC / ST & PH meritorious students who are studying at government medical colleges in India.
Prime Minister's Special Scholarship Scheme for the students of Jammu & Kashmir who are seeking admission in MBBS / BDS. Scholarship is awarded to students who are admitted through AICTE counseling process.
The Swami Dayanand Charitable Education Foundation (SDCEF) offers scholarships Merit-Cum-Means Scholarships to meritorious students pursuing medical courses.
Brainztorm Technical Excellence conducts All India Pre-Medical Scholarship Test (AIPMST) for studying MBBS / BDS in India.
The University Grants Commission (UGC), in association with the Ministry of Human Resource Development (MHRD) awards Ishan Uday Scholarship for the students of North Eastern region pursuing degree courses in medical science.
Loreal India awards scholarships for young women in Science program.
Narotam Sekhsaria Excellence Award and Certificate of Merit Scholarships for UG Studies in Medicine are merit based scholarships provided by Narotam Sekhsaria Foundation.
The Fair and Lovely Foundation Scholarship for women is a merit based scholarship provided by Fair and Lovely Foundation.
Postgraduate Institute of Medical Education & Research (PGIMER), Chandigarh offers Ph.D. fellowships for students pursuing Doctor of Philosophy (Ph.D.) in medical program.
Doctor Key Skills
Detail Oriented
Focus and hard work
Organization & Time Management
Passion for learning
Physical and mental strength
Doctor Career Prospects
Medical Professor or Lecturer
Medical Consultant / Advisor
Anesthetist
Sports Medicine Specialists
Jobs in Doctor
Government / Private Hospitals
Multi-Specialty hospitals
Medical Colleges / Educational Institutions
Own Venture
University research departments
Public health laboratories
Private medical organizations
Salary in Doctor
The salary depends upon how much knowledge & experience you have. The initial salary of a medical graduate doctor may be INR 30,000 to INR 40,000 per month. After getting the experience and good hands on in this field, the candidate may get the handsome salary as 10 to 15 lakh per annum.
Doctor Role Models
Dr. Naresh Trehan
Dr Naresh Trehan is an Indian cardiovascular and cardiothoracic surgeon. After graduating from King George Medical College, Lucknow, India, he went on to practice at New York University Medical Center Manhattan USA from 1971 to 1988. After a successful career in the US, he returned to India and started Escorts Heart Institute and Research Centre. At present, he serves as the chairman and managing director and chief cardiac surgeon of MedantaTM-The Medicity. He has served as personal surgeon to the President of India since 1991, has received numerous awards, including the Padma Shri, Padma Bhushan and Lal Bahadur Shastri National Award.
Dr. Devi Prasad Shetty
Devi Prasad Shetty (born 8 May 1953) is an Indian cardiac surgeon. He is chairman and Founder of Narayana Health, a chain of 21 medical centers in India. He has performed over 15,000 heart operations. In 2004 he was awarded the Padma Shri, the fourth highest civilian award followed by the Padma Bhushan in 2012, the third highest civilian award by the Government of India for his contribution to the field of affordable healthcare. He returned to India in 1989 and initially worked at B.M. Birla Hospital in Kolkata. He successfully performed the first neonatal heart surgery in the country in 1992, on a 9-day-old baby named "Ronnie". In Kolkata he operated on Mother Teresa after she had a heart attack and subsequently served as her personal physician.
Dr. A. G. K. Gokhale
Dr A. G. K. Gokhale (also known as Dr Alla Gopala Krishna Gokhale; Telugu born 2 October 1959; MBBS, M.S. (General Surgery), M.Ch (Cardio-thoracic surgery), DNB (Cardiothoracic Surgery), SMP (IIM-C)) is an Indian Cardiac Surgeon at Apollo Hospitals. He is known for being the first to perform a successful human-to-human heart transplant and first successful lung transplant in the state of Andhra Pradesh, India. He worked at Yashoda Hospitals and Global hospitals before this where he performed many of his historic achievements such as the first Heart Transplant, and Minimal access cardiac surgeries. He is also the Chairman of the charitable trust called "Sahrudaya Health, Medical and Educational Trust" that monetarily assists and provides moral support to poor heart patients and spread knowledge about prevention of heart diseases and is running a successful open heart surgery programme in Guntur Government General hospital. A heart surgeon by profession, and a philanthropist by nature, Dr. Gokhale along with his core team of professionals and generous donors, have dedicated their time, skills and resources in reaching out to those in need.For his contributions, he was honored by many associations including Indian Medical Association, Rotary and Lions clubs. He was felicitated by Government of Andhra Pradesh with Ugadi Puraskaram (2015) and in recognition of his contributions to the profession and society, he was honored by the Government of India with "Padma Sri"award(2016).
Dr.Aamod Rao
Dr. Aamod Rao Is An Experienced Aesthetic Surgeon Who Has Trained In Plastic Surgery At The Bombay Hospital And Research Centre, After Completing His Surgical Training At KIMS Hospital And Research Centre (Bangalore).He Has Also Completed A Fellowship In Aesthetic Surgery At The PUCRS University In Porto Alegre, Brazil. Additionally, Dr. Rao Is Trained In Aesthetic Medicine At The Empire Medical Training Centre, USA.His Main Areas Of Interest Are Facial Aesthetic Surgery And Body Contouring Surgery, Utilizing The Patient'S Own Body Fat For Breast And Buttock Augmentation And High Definition Liposculpting. Dr. Aamod Rao Has Been Featured In The Top 10 Successful Surgeons In India.Dr Aamod Rao has been featured in the top 10 successful surgeons in India.
Suniti Solomon
Suniti Solomon (1938 or 1939 – 28 July 2015) was an Indian physician and microbiologist who pioneered AIDS research and prevention in India after having diagnosed the first Indian AIDS cases in Chennai in 1985 along with her student Sellappan Nirmala . She founded the Y R Gaitonde Centre for AIDS Research and Education in Chennai. The Indian government conferred the National Women Bio-scientist Award on her. On 25 January 2017, Government of India announced "Padma Shri" award for her contribution towards Medicine. In her earlier career life abroad, Solomon had worked as a junior physician at King's College Hospital, London. After returning to India, Solomon worked as a microbiologist at Madras Medical College and rose to the rank of professor.
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Achievements are a great way for you to earn rewards.
There are 3 tiers for each achievement - once one tier of the achievement has been completed, the next tier will unlock.
Each tier is progressively more challenging to earn, but offers bigger rewards like diamonds, avatars and pets.


Because the early 90's the rave scene continues to be growing progressively bigger each year. Today the rave scene has changed right into a worldwide music movement using its own rave style and rave culture. The rave scene is much like the club scene and it is well-liked by more youthful adults because of its counter culture nature and energetic music. Many rave DJ's like Deadmouse, Mount Eden, and Avicci make the background music very popular through the U . s . States. It is very popular that you could even hear music on certain popular r / c.
These DJ's are exceeding expectations of electronic music and employ interesting busy rhythms that contain drum and bass, techno, and other kinds of electronic music like dubstep. Aside from the big bass and new sounds originating from music, ravers enjoy dancing and putting on vibrant rave clothing. Women put on all kinds of interesting and new clothing for his or her rave occasions that mostly incorporate comfortable clothing that enables these to dance.
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See Correspondents below
43 (as of 2011)
Jeff Fager
42 minutes (plus commercials)
Production company(s)
CBS News Productions
CBS Productions
480i (SDTV)
September 24, 1968 (1968-09-24) –
60 Minutes is a CBS television news program, which began in 1968. The program was created by Don Hewitt.
In February 2009, TV Guide named 60 Minutes 6th on TV Guide's 50 Greatest TV Shows of All Time.[1]
↑ "TV Guide Names Top 50 Shows". Archived from the original on 2012-09-04. Retrieved 2012-03-20.
This short article about television can be made longer. You can help Wikipedia by adding to it.
Retrieved from "https://simple.wikipedia.org/w/index.php?title=60_Minutes&oldid=7927113"
1968 television series debuts
1960s American television series
CBS network shows
English-language television programs
Television stubs


This should be a brief post.
I have enjoyed writing my reviews and personal views on film and culture at large. Film is something I genuinely love and I am a firm believer in free and open discussion (so long as one agrees with me...just kidding).
However, I have found that I have been neglecting my own writing. I also have been staying up far too late putting these posts together. Part of the problem is technical: sometimes my machine becomes slow, causing delays that keep me up longer than I should be up. As a result, I am behind on my own works and now struggle to wake up. When it took me well over an hour to actually wake up, I knew something was definitely wrong.
After some thought I have decided to cut back on posting. I had decided to do so after finishing my Spider-Man retrospective, and now that The Amazing Spider-Man is out I feel I can wrap up that assignment and devote more time to my own works.
No, I am not quitting blogging altogether. I will still write, but not to the degree that I once did, at least until I get some of my own writing done. Until I can get a better handle on coordinating my own writing with my reviews I will have to lessen my reviews.
I do have some previously written posts scheduled for publication, and on my sister site Gallifrey Exile I will still work to have my weekly Doctor Who review. I also will continue my James Bond retrospective. I have finally caught up to my original schedule, so now it should be two Bond films per month until Skyfall is released this November.
In short (but minus my height, when have I ever really been short) I will now turn my attention to my own writing and less to Rick's Cafe Texan.
This isn't good-bye by any stretch...just an intermission.


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Review: Power, Timothy, The Culture of Kitharoidia (Hellenic Studies Series 15), Cambridge, Mass.: Harvard University Press, 2010, 230 pp.
Title Review: Power, Timothy, The Culture of Kitharoidia (Hellenic Studies Series 15), Cambridge, Mass.: Harvard University Press, 2010, 230 pp.


Our body of work includes Commercials, Music videos, Title sequences, TV-billboards. We combine new and traditional techniques in our productions. 3D animation and High def video to cardboard cutouts and Super-8.
We did in 2011 also start to extend our tentacles into new adjacent multidimentional gracing grounds. Namely developing and producing content in the wonderful world of Transmedia Storytelling.
Mathias Erixon is the proprietor and creative chieftain of Oddity. He is as most people not that used to talking about himself in third person. But thats how it is.
His skillset include Motion Graphic Design & Animation; Concept Development, Directing & Production.
Though Oddity and as a freelancer Mathias has produced and/or worked on Commercials, Corporate films and Music videos for Absolut Vodka, Audi, Electrolux, Eurocities , Freephoo, Fotografiska, Friends Arena, Global fund, Grant Thornton, Guldägget, Handelsbanken, Kolmården, Metro International, the Nobel Foundation, the Rolling Stones, Southern Comfort, Fredrik "Benke" Rydmans´Svansjön, Telenor & Wasa Crispbread.
Over the years he has also directed musicvideos for the Endless, KVLR, Convoj, 2 x Nutmeg, Gopher and Psycho Sonic Cindy.
The first Nutmeg video was shown more than 86000 times on YouTube as it was released. It was also featured on YouTubes own startpage and was part of the lineup in filmfestivals in over 15 locations worldwide.
Grubs generally works chimerically through his venture GrubsGenius Innovations. He is an inventor, exo-antropologist and scientist.
Grubs has an unusual talent for bartering, promoting and selling the strangest of gadgets. Between his many travels he is working on finishing a web shop for all his strange contraptions. He has a newfound affection for Twitter and communicates his whereabouts, actions and findings via @GrubsMarlin.


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Dissertations and Theses (Ph.D. and Master's)
Alpha Alpha Alpha Male: Relations Among Fraternity Membership, Traditional Masculine Gender Roles, and Sexual Violence
Seabrook, Rita
Abstract: One in four women experiences sexual assault during her time in college (e.g., Cantor et al., 2015). Fraternity membership has been associated with greater acceptance and perpetration of sexual violence, as has endorsement of traditional masculinity (e.g., Murnen & Kohlman, 2007). In this dissertation, I explore mechanisms by which fraternity membership is associated with sexual violence, whether prospective fraternity membership is associated with sexual violence, and whether fraternity members are more likely than other college men to be excused for sexual violence. In Study 1, I used Structural Equation Modeling to test whether endorsement of traditional masculinity explains how fraternity membership is associated with greater rape myth acceptance and more sexually deceptive behavior in a sample of 365 undergraduate men. Assessments of traditional masculinity included conformity to masculine norms, pressure to uphold masculine norms, and acceptance of objectification of women. Results suggest that conformity to masculine norms, pressure to uphold masculine norms, and acceptance of objectification of women, together, mediate the relation between fraternity membership and acceptance of sexual violence. Universities should include discussions of masculinity and the pressure men feel to uphold it in their sexual assault prevention programs, especially those delivered to fraternity members. In Study 2, I surveyed 88 men interested in Greek life before the rush process (T1) and again 4 months later (T2) to examine predictors and consequences of fraternity membership. Participants completed measures of endorsement of traditional masculine gender roles, hostile and benevolent sexism, and acceptance of rape myths. Among men interested in joining a fraternity, none of the measures were associated with whether or not they joined a fraternity. From T1 to T2, men who joined a fraternity maintained similar levels of endorsement of masculine gender roles, benevolent sexism, and rape myth acceptance, whereas men who did not join a fraternity decreased in their endorsement. Results suggest that joining a fraternity prevented decreases in endorsement of traditional gender roles and acceptance of sexual violence. These results lend support to the hypothesis that fraternity membership is associated with sexual violence over time. In Study 3, I examined the influence of fraternity membership on perceptions of guilt in a sexual assault scenario. A sample of 408 undergraduate students listened to a podcast in which a female student describes an ambiguous sexual assault scenario. In the experimental condition, the female student reveals that the perpetrator is a fraternity member. In the control condition, no information is given about his fraternity affiliation. Participants then filled out measures of perceptions of the perpetrator and victim (perpetrator culpability, victim culpability, perpetrator guilt, and victim credibility), as well as semantic differentials for the perpetrator and victim (e.g., responsible, attractive, chaste). Results indicate that male participants rated a perpetrator as less guilty, and a victim as more culpable, less credible, and more negative when the perpetrator was a fraternity member compared to when no information was given about his fraternity status. There were no differences in perceptions of the victim and perpetrator among female participants. These results suggest that fraternity members are less likely to be blamed by other men for their sexual aggression. This leniency may contribute to high rates of sexual assault on college campuses by creating a cycle in which fraternity members perpetrate more sexual aggression, but are less likely to be punished, thus reinforcing sexually aggressive behaviors.
Handle: http://hdl.handle.net/2027.42/138689
Subject(s): sexual assault, fraternities, victim blame, masculinity
Name: rcbrook_1.pdf
Size: 1.3MB
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Where Danger and Love Collide
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End of Summer Sale!!!!
If you haven't already checked it out and grabbed up a lot of good reads, then do so now! Lots and lots of awesome reads in this! Check it out! Get It While It's Hot Sale! August 14th -18th, 2017 - $0.99 USD SALE Sale Page https://goo.gl/kmgwJk We've searched for the best deals from today's top authors so you didn't have to!*
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Beautiful three floor apartment in the heart of Amsterdam!
The finest luxury accommodations, located in the center of the city in the historic canal district in Amsterdam.
2 bedroom holiday cottage situated in the centre of Midden Holland.


text:
Youth E-cigarette Epidemic Prompts American Cancer Society Cancer Action Network to Seek Legislation Addressing Tobacco Addiction
ATLANTA, GA – January 17, 2020 – As lawmakers dive into the new year, the American Cancer Society Cancer Action Network (ACS CAN) is pursuing legislation that will ease the burden of cancer in Georgia. The latest edition of the ACS CAN's How Do You Measure Up? report
Matt Helder Joins American Cancer Society Cancer Action Network to Direct Government Relations in Washington State
OLYMPIA, Wash.— Matt Helder , who has had a successful career around the state legislature and local politics, joined the American Cancer Society Cancer Action Network (ACS CAN) as the Washington state government relations director. In his role, Helder will lead ACS CAN's policy agenda in the state to advance
NEW YORK KIDS CAN'T WAIT! LAWMAKERS MUST END THE SALE OF ALL FLAVORED TOBACCO PRODUCTS NOW
A diverse coalition brought the lifesaving message to the Capitol that the sale of all flavors of all tobacco must be prohibited.
Missouri Fails Again to Properly Fund Tobacco Control Programs and Protect Our Youth from a Lifetime of Addiction
Jefferson City, MO – January 15, 2020 – Eleven thousand Missourians will die this year from smoking-related diseases. And while Missouri has one of the highest adult smoking rates in the nation, Governor Mike Parson revealed that the state budget allocates virtually no additional funding for tobacco prevention and cessation programs.
Patient Groups Urge Supreme Court to Swiftly Take Up Health Care Case
Patient and health advocacy groups representing millions of Americans with pre-existing conditions filed an amicus curiae or friend of the court brief today urging the U.S. Supreme Court to immediately take up the case of Texas v. United States. The case is the latest court challenge to the health care law known as the Affordable Care Act.
American Cancer Society Cancer Action Network Champions Legislation To Protect Children From Skin Cancer
COLUMBIA, SC – January 14, 2020 – As lawmakers dive into the new year, the American Cancer Society Cancer Action Network (ACS CAN) is pursuing legislation that will ease the burden of cancer in South Carolina. The latest edition of the ACS CAN's How Do You Measure Up? report
Columbus, Ohio – As lawmakers dive into the new year, the American Cancer Society Cancer Action Network (ACS CAN) is pursuing legislation that will ease the burden of cancer in Ohio. The latest edition of the ACS CAN's How Do You Measure Up? report shows that Ohio can do
Nashville, TN – As lawmakers dive into the new year, the American Cancer Society Cancer Action Network (ACS CAN) is asking that legislators support legislation that will ease the burden of cancer in Tennessee. The latest edition of the ACS CAN's How Do You Measure Up? report shows that
Comprehensive Action Needed to Put Kids Over Tobacco Interests
Pierre, S.D. – Data from the 2019 National Youth Tobacco Survey show youth use of e-cigarettes in high schools has skyrocketed, with a 135% increase over the past two years. Survey results also show that 27.5% of high school students used e-cigarettes in the last 30 days. Nearly


text:
\subsubsection*{Acknowledgments}
The authors thank two anonymous referees for helpful comments and remarks.

\section{Jarn\'{\i}k's Fractal and Its Variations}

Let $a$ be a real number greater than~2.  As mentioned earlier, \citet{Jar1928} and \citet{Bes1934}
independently established that the set of real numbers with irrationality exponent greater than or
equal to~$a$ has Hausdorff dimension~$2/a$.  Jarn\'{\i}k\ exhibited a Cantor-like set $E^J(a)$ such that
every element of $E^J(a)$ has irrationality exponent greater than or equal to~$a$ and such that, for
every $d$ greater than~$a$, the set of real numbers with irrationality exponent~$d$ is null for the uniform measure~$\mu_J$
on $E^J(a)$.  The latter condition followed by application of the mass distribution principle
on~$E^J(a)$:

\begin{lemma}[Mass Distribution Principle, cf.~\citealp{Fal2003}]\label{3}
  Let $\mu$ be a measure on $E,$ a subset of the real numbers, and let $a$ be a positive real number.  If $\mu(E) >0$
  and there are positive constants $c$ and $\delta$ such that for every interval $I$ with
  $|I|<\delta$, $\mu(I) < c |I|^a$, then the Hausdorff dimension of $E$ is greater than or equal
  to~$a$.
\end{lemma}

For $b$ given so that $0\leq b<2/a$, we will define a subset $E$ of $E^J(a)$ with dimension~$b$.
$E$~will also be a Cantor-like set  and have its own uniform measure $\mu$.
Using $\mu_J$ as a guide, we will ensure that for any $d$ greater than $a$
the set of real numbers with irrationality exponent~$d$ is null with respect to~$\mu$.  Further, we
shall arrange that $\mu$ has the mass distribution property for exponent~$b$.

We fix some notation to be used in the final step of the construction.  For a positive
integer $p$,
\[
G_{p}(a)=\left\{x\in \left(\frac{1}{p^{a}}, 1-\frac{1}{p^{a}}\right): \exists q\in{\mathbb{N}},
  \left|\frac{q}{p} - x\right| \leq \frac{1}{p^a}\right\}.
\]
For $M$ a sufficiently large positive integer, and $p_1$ and $p_2$ primes such that
$M< p_1<p_2<2M$, the sets $G_{p_1}(a)$ and $G_{p_2}(a)$ are disjoint.  In fact, the distance between
any point in $G_{p_1}(a)$ and any point in $G_{p_2}(a)$ is greater than or equal to
\[
\frac{1}{4M^2}-\frac{2}{M^a} \geq \frac{1}{8 M^2}.
\]
For such $M,$ the set
\[
K_M(a)=\bigcup_{\substack{p \text{ prime}\\M<p< 2M}} G_p(a)
\]
is the disjoint union of the intervals composing the sets $G_p(a)$.  So $K_{M}(a)$ is made up of
intervals of length less than or equal to~$2/M^a$ which are separated by gaps of length at least~$1/(8M^2)$.

We obtain Jarn\'{\i}k's fractal by choosing a sequence $\vec{m}=(m_i:i\geq 1)$, which is sufficiently
fast growing in a sense to be determined below. Each number $m_i$ will play the role of an $M$ as described in the previous paragraph. We let $E^J_0(\vec{m},a)=[0,1]$ and for
$k=1,2,\ldots$ let $E^J_k(\vec{m},a)$ be the union of those intervals of $K_{m_k}(a)$ that are
completely contained in $E^J_{k-1}(\vec{m},a)$.  By discarding a negligible number of intervals, we
arrange that all intervals from $E^J_{k-1}(\vec{m},a)$ are split into the same number of intervals
in $E^J_k(\vec{m},a)$.  Let $i_k$ be the number of intervals from $E^J_k(\vec{m},a)$ which are
contained in a single interval of $E^J_{k-1}(\vec{m},a)$.  Let
$E^J(\vec{m},a)=\cap_{k\geq 1}E^J_k(\vec{m},a)$.  We define a mass distribution $\mu_J(\vec{m},a)$
on $E^J(\vec{m},a)$ by assigning a mass of $1/(i_1 \times \ldots \times i_{k})$ to each of the
$i_1 \times \ldots \times i_k$ many $k$-level intervals in $E^J_k(\vec{m},a).$ Then
$\mu_J(\vec{m},a)$ has the mass distribution property for
exponent~$2/a$,~\citep[see][Chapter~10]{Fal2003}.

There are two ways by which $E^J(\vec{m},a)$ can be thinned to a subset of lower Hausdorff
dimension.  First, we could use fewer numbers between $m_k$ and $2m_k$ when we define
$E^J_k(\vec{m},a)$.  However, even if we choose only one denominator at each level, the resulting set
has dimension~$1/a$ \citep[see][Example~4.7]{Fal2003}.  To obtain a dimension smaller than $1/a$,
not only do we choose just one denominator at each level, but we also choose only the intervals centered
on a uniformly spaced subset of the rational numbers with that denominator.

There is a further variation on Jarn\'{\i}k's construction and the above thinned version of it which
allows for approximating $a$ and~$b$.
To express it we  introduce the following definition.

\begin{definition}
The sequences of real numbers   $\vec{a}$ and $\vec{b}$
are \emph{appropriate} when $\vec{a}=(a_k:k\in{\mathbb{N}})$ is non-decreasing with $a_k \geq 1$ for all $k$ and limit $a$ greater than or
equal to~$2$ and $\vec{b}=(b_k:k\in{\mathbb{N}})$ is strictly increasing with limit $b$ less than or equal
to~$2/a$ such that if $1/a<b$ then $1/a<b_1$.
\end{definition}

For appropriate $\vec{a}$ and $\vec{b}$, we can
modify Jarn\'{\i}k's fractal to accommodate the specification of $a$ in the limit by substituting $a_k$
in place of $a$ in the definition of $E_k^J$.  That is, we let $E^J_k(\vec{m},\vec{a})$ be the
collection of intervals of $K_{m_k}(a_k)$ which are completely contained in
$E^J_{k-1}(\vec{m},\vec{a})$, adjusted by removing intervals so that every interval in
$E^J_{k-1}(\vec{m},\vec{a})$ contains the same number of intervals in $E^J_k(\vec{m},\vec{a})$.  By
construction, the intervals in $E_k^J(\vec{m},\vec{a})$ are of the form
$\left[\frac{q}{p}-\frac{1}{p^{a_k}},\frac{q}{p}+\frac{1}{p^{a_k}}\right].$
It follows that every real number in $E^J(\vec{m},\vec{a})$ has
irrationality exponent greater than or equal to~$a$.  Further, when the sequence $\vec{m}$ grows
sufficiently quickly, the uniform measure $\mu_J(\vec{m},\vec{a})$ on $E^J(\vec{m},\vec{a})$ has the
mass distribution property for exponent~$2/a$.  It follows that $\mu_J(\vec{m},\vec{a})$-almost
every real number has irrationality exponent exactly equal to~$a$.  Similarly, we can modify the way
that we thin $E^J(\vec{m},\vec{a})$ to reduce dimension from $2/a$ to $b$.  The construction is not
sensitive on this point and using $b_k$ to determine how to thin at step $k$ results in a fractal of
dimension~$b.$

\subsection{Irrationality exponent~$a$, Hausdorff Dimension $b$ and $0<b\leq 1/a$}

\begin{definition}[Family of fractals ${\mathcal{E}}(\vec{q},\vec{m},\vec{a})$ ]\label{5}
  Let $\vec{m}$ be an increasing sequence of positive integers; let $\vec{q}$ be a sequence of
  integers;

  let $\vec{h}$ be a sequence of integers such that for each $k,$ $h_k\in[0,q_k)$; and let $\vec{a}$
  be a non-decreasing sequence of real numbers greater than or equal to~$2$ with limit~$a$.
    \begin{itemize}
      \item Let ${\mathcal{E}}_{1}(\vec{h},\vec{q},\vec{m},\vec{a})$ be $[0,1]$.
      \item Given ${\mathcal{E}}_{k-1}(\vec{h},\vec{q},\vec{m},\vec{a}),$ let
        ${\mathcal{E}}_{k}(\vec{h},\vec{q},\vec{m},\vec{a})$ be the collection of intervals in  $G_{m_k}(a_k)$
        which are completely contained in intervals from
        ${\mathcal{E}}_{k-1}(\vec{h},\vec{q},\vec{m},\vec{a})$ and which are of the form
        $\left[\frac{r}{m_k}-\frac{1}{m_k^{a_k}},\frac{r}{m_k}+\frac{1}{m_k^{a_k}}\right]$
        such that $r\equiv h_k\mod{q_k}$.
        As usual, discard a negligible number of intervals so that each interval in
        ${\mathcal{E}}_{k-1}(\vec{h},\vec{q},\vec{m},\vec{a})$ has the same number of subintervals in
        ${\mathcal{E}}_{k}(\vec{h},\vec{q},\vec{m},\vec{a})$.  Further, ensure that this number of subintervals is
        independent of~$\vec{h}$.
    \end{itemize}
    Let ${\mathcal{E}}(\vec{q},\vec{m},\vec{a})$ be the family of fractals obtained by considering all
    possible sequences~$\vec{h}$.
\end{definition}

By construction, if $\vec{h}$ and $\vec{g}$ have the same first $k$ values, then for all $j\leq k$,
${\mathcal{E}}_{j}(\vec{h},\vec{q},\vec{m},\vec{a})$ is equal to ${\mathcal{E}}_{j}(\vec{g},\vec{q},\vec{m},\vec{a})$.
So, ${\mathcal{E}}(\vec{q},\vec{m},\vec{a})$ is actually a finitely-branching tree of fractals.

\begin{lemma}\label{6}
  Suppose that $\vec{a}$ and $\vec{b}$ are appropriate sequences of reals  with limits $a$ and $b$ such that
  $a\geq 2$ and $b\leq 1/a$.  There is a function $f$, computable from $\vec{a}$ and $\vec{b},$ such that for any
  sequence of integers $\vec{m}=(m_k:k\in{\mathbb{N}})$ for which for all $k$, $m_{k+1}\geq f(k,m_k)$, there is a sequence
  of integers $\vec{q}$, such that for all $E\in {\mathcal{E}}(\vec{q},\vec{m},\vec{a})$ and for $\mu$ the uniform
  measure on $E$, the following conditions hold.
  \begin{itemize}
  \item For all $k$ greater than $2$ and all intervals $I$ such that
    $|I|\leq
   \frac{q_{k-1}}{m_{k-1}}-\frac{2}{m_{k-1}^a}$,
    \[\mu(I)<|I|^{b_k}.
     \]
  \item For all integers $k$,
   \[
   m_k^{a_k b_{k+1}-1}\leq \frac{1}{q_k}\leq m_k^{a_k b_{k+2}-1}.
   \]
    \end{itemize}
    Further, we can compute $q_k$ from $(a_1,\dots,a_k)$, $(b_1,\dots,b_{k+2})$ and
    $(m_1,\dots,m_k)$.
\end{lemma}

\begin{proof}
  We consider $E\in {\mathcal{E}}(\vec{q},\vec{m},\vec{a})$ and $\mu$ defined on $E$ as above from $\vec{a}$,
  an increasing sequence $\vec{m}=(m_k:k\geq 1)$ and $\vec{q}=(q_k: k\geq 1).$   For a given interval $I$, we
  estimate $\mu(I)$ and we deduce a sufficient growth rate on $\vec{m}$ and appropriate values for
  $\vec{q}$ in terms of $\vec{m}$ so as to ensure the desired inequality $\mu(I)<|I|^{b_k}$,
  for $I$ as specified.  The existence of $f$ follows by observing that these functions are
  computable from $\vec{a}$ and~$\vec{b}$.

  We follow a modified version of the proof of Jarn\'{\i}k's Theorem as presented in \cite{Fal2003}.  We
  take $m_1$ to be larger than $3 \times 2^a$ and sufficiently large so that $1/m_1>2m_1^{-a}$.

We let $E_0=[0,1]$ and for
$k\geq 1$ let $E_k$ consist of those intervals of $G_{m_k}(a_k)$ that are completely
contained in $E_{k-1}$ and are of the form $\left[\frac{r}{m_k}-\frac{1}{m_k^{a_k}},\frac{r}{m_k}+\frac{1}{m_k^{a_k}}\right]$ such that $r\equiv h_k\mod{q_k}$.
Thus, the intervals of $E_k$ are of length $2/m_k^{a_k}$ and are separated by gaps of length at least
  \[
  g_k=\frac{q_k}{m_k}-\frac{2}{m_k^{a_k}}.
  \]
  Let $i_k$ be the number of intervals of $E_{k}$ contained in a single interval of $E_{k-1}$.  By
  construction $i_1=m_1/q_1$ and for every~$k>1$,
  \begin{equation}
    \label{eq:1}
  i_k\geq \frac{1}{2} \frac{2}{(m_{k-1})^{a_{k-1}}}\,\frac{1}{q_k}\, m_k = \frac{\
    m_k}{(m_{k-1})^{a_{k-1}} q_k},
  \end{equation}
  which represents half of the product of the length of an interval in $E_{k-1}$ and the number of
  intervals with centers $p/m_k,$ where $p$ is an integer with fixed residue modulo $q_k$.  This
  estimate applies provided that $q_k$ is less than $m_k$ and $m_k$ is sufficiently large with
  respect to the value of~$m_{k-1}$.

  Now, we suppose that $S$ is a subinterval of $[0,1]$ of length $|S|\leq g_1$ and we estimate~$\mu(S)$.  Let
  $k$ be the integer such that $g_k\leq |S| < g_{k-1}$.  The number of $k$-level intervals that
  intersect~$S$~is
  \begin{itemize}
  \item  at most  $i_{k}$, since $S$ intersects at most one $(k-1)$-level interval,
  \item  at most $2+ |S|  {m_k}/{q_k} \leq 4|S|m_k/q_k$, by an
    estimate similar to that for the lower bound on~$i_k$.
  \end{itemize}

  Each $k$-level interval has measure $1/(i_1\times\ldots\times i_k)$.
  We have that
  \begin{align}
    \mu(S)&\ \leq \ \frac{\min(4|S| m_k/q_k,i_k)}{i_1\times\ldots\times i_k}\label{eq:2} \\
          & \ \leq \ \frac{ (4|S| m_k/q_k)^{ b_k} \  i_{k}^{1-b_k}}{i_1\times\ldots\times
            i_k}\nonumber \qquad \text{(as $b_k \in [0,1]$)}\\
          &\ =\  \frac{4^{b_k} m_k^{b_k}}{(i_1\times \ldots\times i_{k-1}) \ i_k^{b_k} q_k^{b_k} }
            |S|^{b_k}\nonumber\\
          &\ \leq\    1      \frac{ m_{1}^{a_1} q_2  }{m_2}\ \ \frac{m_2^{a_2} q_3  }
      {m_{3}}
      \ldots
      \frac
      { m_{k-2}^{a_{k-2}} q_{k-1}}
      {m_{k-1}}
      \ \
            \frac{4^{b_k}m_k^{{b_k}}}{i_k^{b_k} q_k^{b_k}} \ |S|^{b_k}\nonumber    \qquad \text{(by~\eqref{eq:1})}\\
    &\  \leq  \  \frac
      { m_{1}^{a_1} q_2  }
      {m_2}\ \
      \frac{m_2^{a_2} q_3  }
      {m_{3}}
      \ldots
      \frac
      { m_{k-2}^{a_{k-2}} q_{k-1}}
      {m_{k-1}}
      \ \
      \left(\frac{ m_{k-1}^{a_{k-1}} q_k  }{m_k}\right)^{b_k}
      \frac{m_k^{{b_k}}}{q_k^{b_k}}
      4^{b_k}\
      |S|^{b_k}\nonumber \\
    & \  = \ (q_2\cdots q_{k-1})
      \big(m_{1}^{a_1} m_{2}^{a_2-1}  \ldots m_{k-2}^{a_{k-2}-1}\big)
      4^{b_k} m_{k-1}^{a_{k-1} b_k-1 }
      |S|^{b_k}.\label{eq:3}
  \end{align}

  We want to ensure that for all such $S$, $\mu(S) < |S|^{b_k}$, from which we may infer that
  $\mu(S) < |S|^{s}$ for all $s$ in $[0,b_k]$.  Thus, it suffices to show that there is a suitable
  growth function $f$ for the sequence $\vec{m}$, and there is a suitable sequence of values for
  $\vec{q}$ such that
  \begin{equation*}
(q_2\cdots q_{k-2}    q_{k-1})
    \big(m_{1}^{a_1} m_{2}^{a_2-1}  \ldots m_{k-2}^{a_{k-2}-1}\big)
    4^{b_k} m_{k-1}^{a_{k-1}b_k-1}
    < 1.
  \end{equation*}
  Equivalently,
  \begin{equation*}
    (q_2\cdots q_{k-2})
    \big(m_{1}^{a_1} m_{2}^{a_2-1}  \ldots m_{k-2}^{a_{k-2}-1}\big)
    4^{b_k}m_{k-1}^{a_{k-1}b_k-1} <  \frac{1}{q_{k-1}}.
  \end{equation*}
  If we let $C$ be the term that does not depend on $m_{k-1}$ or on $q_{k-1}$, we can satisfy the
  first claim of the Lemma by satisfying the requirement
  \begin{equation*}
   C m_{k-1}^{a_{k-1}b_k-1} <  \frac{1}{q_{k-1}}.\label{eq:4}
 \end{equation*}
 Since $C$ is greater than $1$, this requirement on $m_{k-1}$ and $q_{k-1}$ also ensures part of the
 second claim of the lemma, that $m_{k-1}^{a_{k-1}b_k-1} < 1/q_{k-1}$.  Since
 $b_k<b \leq 1/a\leq 1/a_{k-1}$, by making $m_{k-1}$ sufficiently large and letting $q_{k-1}$ take
 the largest value such that $C m_{k-1}^{a_{k-1}b_k-1} < 1/q_{k-1}$, we may assume that
 \[
C m_{k-1}^{a_{k-1}b_k-1} > \frac{1}{2q_{k-1}}.
\]
Equivalently, we may assume that
 \[
2C m_{k-1}^{a_{k-1}b_k-1} > \frac{1}{q_{k-1}}.
\]
 The second clause in the second claim of the Lemma is that $1/q_{k-1} <m_{k-1}^{a_{k-1}b_{k+1}-1}$.
 Since $\vec{b}$ is strictly increasing, by choosing $m_{k-1}$ to be sufficiently large, we may
 ensure that
\[
2C<m_{k-1}^{a_{k-1}(b_{k+1}-b_k)}
\]
 and so
 $m_{k-1}^{a_{k-1}b_k-1}<1/q_{k-1}<m_{k-1}^{a_{k-1}b_{k+1}-1}, $ as required.  Further, by appropriateness of $\vec{a}$ and $\vec{b}$, $b_k$
 is less than or equal to~$1/a_{k-1}$, the value of~$1/q_{k-1}$ can be made arbitrarily small by
 choosing $m_{k-1}$ to be sufficiently large, so the above estimates apply.
\end{proof}

\begin{lemma}\label{7}
  Suppose that $\vec{a}$ and $\vec{b}$ are appropriate sequences with limits $a$ and $b$ such that
  $a\geq 2$ and $0\leq b\leq 1/a$.  Let $f$ be as in Lemma~\ref{6}, $\vec{m}$ be such that for
  all~$k$, $m_{k+1}\geq f(k,m_k)$, and $\vec{q}$ be defined from these sequences as in
  Lemma~\ref{6}.  For every $E$ in ${\mathcal{E}}(\vec{q},\vec{m},\vec{a}),$ $E$ has Hausdorff dimension~$b$.
\end{lemma}

\begin{proof}
  Let $E$ be an element of ${\mathcal{E}}(\vec{q},\vec{m},\vec{a})$ and let $\mu$ be the uniform measure on
  $E$.  By Lemma~\ref{6}, for every $\beta<b$, for all sufficiently small intervals $I$,
  $\mu(I)<|I|^\beta.$  Consequently, by application of the Mass Distribution Principle, the Hausdorff
  dimension of $E$ is greater than or equal to~$b$.  Next, consider a real number $\beta$ strictly bigger
  than~$b$.  For each $k\geq 1$, there are at most $m_k/q_k$ intervals in $E_k$, each
  with radius $1/m_k^{a_k}$.  Then, by Lemma~\ref{6} and the fact that $\vec{a}$ and $\vec{b}$ are appropriate,
\[
\sum_{j\leq {m_k}/{q_k}} \left(\frac{2}{m_k^{a_k}}\right)^\beta
\leq m_k\cdot \frac{2^\beta}{q_k}\cdot m_k^{-a_k\beta}
\leq 2^\beta \cdot  m_k^{ a_k b_{k+2}}\cdot m_k^{-a_k\beta}
\leq \frac{2^\beta}{m_k^{\beta-b_{k+2}}}
\leq\frac{2^\beta}{m_k^{\beta-b}},
\]
  which goes to 0 as $k$ goes to infinity.  It follows that $E$ has Hausdorff dimension less than or
  equal to~$b$, as required to complete the verification of the~Lemma.
\end{proof}

\subsection{Irrationality exponent~$a$, Hausdorff Dimension $b$ and $1/a\leq b\leq 2/a$}

\begin{definition}[Family of fractals ${\mathcal{F}}(\vec{q},\vec{m},\vec{a})$]\label{8}
  Let $\vec{m}$ be an increasing sequence of positive integers; let $\vec{q}$ be a sequence of
  integers such that for each $k,$ $q_k$ is between $1$ and the cardinality of the set of prime
  numbers in $[m_k,2m_k)$; let $\vec{H}$ be a sequence of subsets of primes such that, for each $k \geq 1$, $H_k$ contains exactly $q_k$ primes from the interval $[m_k, 2m_k )$; and let $\vec{a}$ be a
  non-decreasing sequence of real numbers greater than or equal to~$2$ with limit~$a$.
    \begin{itemize}
      \item Let ${\mathcal{F}}_1(\vec{H},\vec{q},\vec{m},\vec{a})$ be $[0,1]$.

      \item Given ${\mathcal{F}}_{k-1}(\vec{H},\vec{q},\vec{m},\vec{a}),$ let
        ${\mathcal{F}}_{k}(\vec{H},\vec{q},\vec{m},\vec{a})$ be the collection of intervals in
\[
\bigcup_{p\in H_k} G_p(a_k) ,
\]
        which are completely contained in intervals from
        ${\mathcal{F}}_{k-1}(\vec{H},\vec{q},\vec{m},\vec{a})$.

      \item Let $s$ denote the function that maps $k$ to the ratio given by $q_k$, the number of
        retained denominators, divided by the number possible denominators, which is the number of
        primes in $[m_k,2m_k)$.  Discard a negligible number of intervals so that each interval in
        ${\mathcal{F}}_{k-1}(\vec{H},\vec{q},\vec{m},\vec{a})$ has the same number of subintervals in
        ${\mathcal{F}}_{k}(\vec{H},\vec{q},\vec{m},\vec{a})$, and further, so that this number of subintervals
        depends only on $k,\vec{q},\vec{m},\vec{a}$ and not on $\vec{H}$.
    \end{itemize}
    Let ${\mathcal{F}}(\vec{q},\vec{m},\vec{a})$ be the family of fractals obtained by considering all
    possible sequences~$\vec{H}$.
\end{definition}

\begin{lemma}\label{9}
  Suppose that $\vec{a}$ and $\vec{b}$ are appropriate sequences with limits $a$ and $b$ such that
  $a>2$ and $1/a\leq b\leq 2/a$.  There is a function~$f$, computable from $\vec{a}$
  and~$\vec{b},$ such that for any sequence $\vec{m}=(m_k:k\in{\mathbb{N}})$ for which for all~$k$,
  $m_{k+1}\geq f(k,m_k)$, there is a sequence $\vec{q}$, such that for all
  $E\in {\mathcal{F}}(\vec{q},\vec{m},\vec{a})$ and for $\mu$ the uniform measure on~$E$, the following conditions hold:
 \begin{itemize}
  \item For all $k>2$ and all intervals $I$ such that $|I|\leq    \frac{1}{4m_{k-1}^2}-\frac{2}{m_{k-1}^a},$
   \[
     \mu(I) <|I|^{b_k}.
   \]
 \item For all  integers $k,$
    \[
    \log(m_{k})m_k^{a_k b_{k+1}-2}\leq \frac{1}{q_k}\leq \log(m_{k})m_k^{a_k b_{k+2}-2}.
    \]
\end{itemize}
  Further, we can exhibit such an $\vec{q}$ for which $q_k$ is uniformly computable from
  $(a_1,\dots,a_k)$, $(b_1,\dots,b_k)$ and $(m_1,\dots,m_{k-1})$.
\end{lemma}

\begin{proof}
  The proof of Lemma~\ref{9} has the same structure as the proof of Lemma~\ref{6}, with fundamental
  difference as follows.  Lemma~\ref{6} refers to ${\mathcal{E}}$, the tree of subfractals of
  $E^J(\vec{m},\vec{a})$, where the subfractals are obtained by recursion during which at step $k$
  only $1/q_k$ of the $m_k$-many eligible intervals in $G_{m_k}(a_k)$ are used. Lemma~\ref{9}
  refers to ${\mathcal{F}}$, the tree of subfractals  of $E^J(\vec{m},\vec{a})$,
  where the subfractals are obtained by recursion during which at step $k$ for only $1/q_k$ of the
  eligible denominators $m$, all of the intervals in $G_{m}(a_k)$ are used.  The set of eligible
  denominators is the set of prime numbers between $m_k$ and $2m_k$.  By choosing $m_0$ large
  enough, the prime number theorem implies that this set of eligible denominators has  between
  $m_k/2\log(m_k)$ and $2m_k/\log(m_k)$ many elements and each contributes at least $m_k$ many
  eligible intervals.  Now, we give an abbreviated account to indicate how this difference
  propagates through the proof.

 We consider $E\in{\mathcal{F}}(\vec{q},\vec{m},\vec{a})$ and $\mu$ the uniform measure on $E$.  We let $i_k$
 be the number of intervals in $E_k$ contained in a single interval of $E_{k-1}$.  Now, we have the
 following version of Inequality~(\ref{eq:1}),
 \[
 i_k\geq
 \frac12\,\frac{2}{(2m_{k-1})^{a_{k-1}}}\,\frac{1}{q_k}\,\frac{m_k^2}{2\log(m_k)}>
  \frac{m_k^2}{2^{a+1}\,(m_{k-1})^{a_{k-1}}\,\,\log(m_k)\,q_k}.
 \]
The intervals in $E_k$ are separated by gaps of length at least $g_k=1/4m_k^2-(2/m_k^{a_k})$,
because given two
intervals with centers $c_1/d_1$ and $c_2/d_2$, the gap between them is
\[
\left|\frac{c_1d_2-c_2d_1}{d_1d_2}\right|-\left(\frac{1}{c^{a_k}}+\frac{1}{d^{a_k}}\right).
\]
The numerator in the first
fraction is at least $1$ and the denominator is no greater than~$(2m_k)^2$.  The denominators in
the second term are at least~$m_k^{a_k}$.

Now we suppose that $S$ is a subinterval of $[0,1]$ of length $|S|\leq g_1$ and we estimate~$\mu(S)$.
Let $k$ be the integer such that $g_k\leq |S| < g_{k-1}$.  The number of $k$-level intervals that
intersect~$S$~is
  \begin{itemize}
  \item  at most  $i_{k}$, since $S$ intersects at most one $(k-1)$-level interval,
  \item at most $2+ |S| {4m_k^2}/( q_k\log(m_k))$  which is less than $8|S|m^2_k/(q_k\log(m_k))$.
  This is because there are  at most $2m_k/\log{m_k}$ primes between $m_k$ and
  $2m_k$ and each prime contributes at most $2m_k$ many intervals in $[0,1]$.
  And we keep $1/q_k$ of these.
\end{itemize}
  As before, each $k$-level interval has measure $1/(i_1\times\ldots\times i_k)$.  Then, we have a version
  of Inequality~(\ref{2}).
  \[
  \mu(S)\leq \frac{\min\left(\frac{8|S|m^2_k}{q_k\log(m_k)}, i_k\right)}{i_1\times\ldots\times i_k}.
  \]
  Upon manipulation as before, we have a version of Inequality~(\ref{eq:3}).
  \[
  \mu(S)\leq 8^{b_k}2^{k(a+1)} (q_2\cdots q_{k-1})\,(\log(m_2)\cdots\log(m_{k-1})\,(m_1^{a_1}m_2^{a_2-2}\cdots m_{k-2}^{a_{k-2}-2})m_{k-1}^{a_{k-1}b_{k}-2}|S|^{b_k}.
  \]
 To ensure that $\mu(S)<|S|^{b_k}$, we must find a suitable growth function $f$ for the sequence
 $\vec{m}$ so that there is a suitable sequence of values for $\vec{q}$ such that
 \[
 8^{b_k}2^{k(a+1)} (q_2\cdots q_{k-1})\,(\log(m_2)\cdots\log(m_{k-1}))\,(m_1^{a_1}m_2^{a_2-2}\cdots
 m_{k-2}^{a_{k-2}-2})m_{k-1}^{a_{k-1}b_{k}-2}<1.
 \]
 Equivalently,
 \[
 8^{b_k}2^{k(a+1)} (q_2\cdots q_{k-2})\,(\log(m_2)\cdots\log(m_{k-1}))\,(m_1^{a_1}m_2^{a_2-2}\cdots
 m_{k-2}^{a_{k-2}-2})m_{k-1}^{a_{k-1}b_{k}-2}<1/q_{k-1}.
 \]
 Let $C$ be the term that does not depend on $m_{k-1}$ or $q_{k-1}$.  We can satisfy the first claim
 of Lemma~\ref{9} by satisfying the requirement
 \[
 C\log(m_{k-1}) m_{k-1}^{a_{k-1}b_k-2}<1/q_{k-1}.
 \]
 Since $C$ is greater than $1$, this requirement on $m_{k-1}$ and on $q_{k-1}$ also ensures part of
 the second claim of the lemma, that $\log(m_{k-1})m_{k-1}^{a_{k-1}b_k-2}<1/q_{k-1}$.  Since $b_{k}\leq
 2/a<2/a_{k-1}$, $a_{k-1}b_k-2$ is negative.  By making $m_{k-1}$ sufficiently large and letting
 $q_{k-1}$ take the largest value  such that $ C\log(m_{k-1}) m_{k-1}^{a_{k-1}b_k-2}<1/q_{k-1}$, we
 may assume that
 \[
 C\log(m_{k-1}) m_{k-1}^{a_{k-1}b_k-2}>1/2q_{k-1}.
 \]
 The second clause in the second claim of the lemma is that $1/q_{k-1} <m_{k-1}^{a_{k-1}b_{k+1}-2}$.
 Since $\vec{b}$ is strictly increasing, by choosing $m_{k-1}$ to be sufficiently large, we may
 ensure that
\[
2C<\log(m_{k-1})m_{k-1}^{a_{k-1}(b_{k+1}-b_k)}
\]
 and so
 $\log(m_{k-1})m_{k-1}^{a_{k-1}b_k-1}<1/q_{k-1}<\log(m_{k-1})m_{k-1}^{a_{k-1}b_{k+1}-2}, $ as
 required.  Further, since $b_k$
 is less than or equal to~$1/a_{k-1}$, the value of~$1/q_{k-1}$ can be made arbitrarily small by
 choosing $m_{k-1}$ to be sufficiently large, so the above estimates apply.
\end{proof}

\begin{lemma}\label{10}
  Suppose that $\vec{a}$ and $\vec{b}$ are appropriate sequences of real numbers with limits $a$ and $b$ such that
  $a>2$, $ 1/a \leq b\leq 2/a$ and $1/a_1\leq b_1$.  Let $f$ be as in Lemma~\ref{9}, $\vec{m}$ be
  such that for all~$k$, $m_{k+1}\geq f(k,m_k)$, and $\vec{q}$ be defined from these sequences as in
  Lemma~\ref{9}.  For every $E$ in ${\mathcal{F}}(\vec{q},\vec{m},\vec{a}),$ $E$ has Hausdorff dimension~$b$.
\end{lemma}

\begin{proof}
   Let $E$ be an element of ${\mathcal{F}}(\vec{q},\vec{m},\vec{a})$ and let $\mu$ be the uniform measure on
  $E$.  By Lemma~\ref{9}, for every $\beta<b$, for all sufficiently small intervals $I$,
  $\mu(I)<|I|^\beta.$  Consequently, by application of the Mass Distribution Principle, the Hausdorff
  dimension of $E$ is greater than or equal to~$b$.  Next, consider a real number $\beta$ greater
  than~$b$.  For each $k\geq 1$, there are at most $4m_k^2/(\log(m_k)q_k)$ intervals in $E_k$, each
  with radius less than or equal to $1/m_k^{a_k}$.  Then, by Lemma~\ref{9} and the fact that $a_k \geq 1$,
  \begin{eqnarray*}
\sum_{j\leq 4m_k^2/(\log(m_k)q_k)} \left(\frac{2}{m_k^{a_k}}\right)^\beta&\leq&
                                                                           \frac{4m_k^2}{\log(m_k)}\cdot
                                                                           \frac{1}{q_k}\cdot
                                                                           2^\beta m_k^{-a_k\beta}\\
&\leq& \frac{4m_k^2}{\log(m_k)}\cdot \log(m_{k})m_k^{a_k b_{k+2}-2}\cdot 2^\beta m_k^{-a_k\beta}\\
&\leq& \frac{4 \cdot 2^\beta}{m_k^{a_k(\beta-b_{k+2})}}\\
&\leq&\frac{4 \cdot 2^\beta}{m_k^{\beta-b}},
  \end{eqnarray*}
  which goes to 0 as $k$ goes to infinity.  It follows that $E$ has Hausdorff dimension less than or
  equal to~$b$, as required to complete the verification of the~Lemma.
\end{proof}

\subsection{Irrationality Exponent 2, Hausdorff Dimension $b$, and $0< b\leq 1$}

The next case to consider is that in which the desired irrationality exponent is equal to  $2$ and
the desired effective Hausdorff dimension is equal to $b\in (0,1]$.  In fact, we need only consider
the case of $b<1$, since almost every real number with respect to Lebesgue measure has both irrationality
exponent equal to~$2$ and effective Hausdorff dimension equal to~$1$.

\begin{definition}[Family of fractals ${\mathcal{G}}(\vec{q},\vec{m})$]\label{11}
  Let $\vec{m}$ be an increasing sequence of positive integers such that for all $k$, $m_k$ divides
  $m_{k-1}$; let $\vec{q}$ be a sequence of
  integers;

  and let $\vec{h}$ be a sequence of integers such that for each $k,$ $h_k\in[0,q_k)$.
    \begin{itemize}
      \item Let ${\mathcal{G}}_{1}(\vec{h},\vec{q},\vec{m})$ be $[0,1]$.
      \item Given ${\mathcal{G}}_{k-1}(\vec{h},\vec{q},\vec{m}),$ let
        ${\mathcal{G}}_{k}(\vec{h},\vec{q},\vec{m})$ be the collection of intervals
        which are completely contained in intervals from
        ${\mathcal{G}}_{k-1}(\vec{h},\vec{q},\vec{m})$ and which are of the form
        $\left[\frac{r}{m_k},\frac{r}{m_k}+\frac{1}{m_k}\right]$ such that $r\equiv h_k\mod{q_k}$.
        As usual, discard a negligible number of intervals so that each interval in
        ${\mathcal{G}}_{k-1}(\vec{h},\vec{q},\vec{m})$ has the same number of subintervals in
        ${\mathcal{G}}_{k}(\vec{h},\vec{q},\vec{m})$.  Further, ensure that this number of subintervals is
        independent of~$\vec{h}$.
    \end{itemize}
    Let ${\mathcal{G}}(\vec{q},\vec{m})$ be the family of fractals obtained by considering all
    possible sequences~$\vec{h}$.
\end{definition}

In the following Lemma~\ref{12} is parallel to Lemmas \ref{6} and \ref{9}.  Likewise, the next
Lemma~\ref{13} is parallel to Lemmas \ref{7} and \ref{10}.  In fact, the estimates here are simpler
than the earlier ones. We leave the proofs for the interested reader.

\begin{lemma}\label{12}
  Suppose $\vec{b}$ is strictly increasing sequence of real numbers with limit $b$ such that
  $0< b<1$.  There is a function $f$, computable from $\vec{b},$ such that for any sequence
  $\vec{m}=(m_k:k\in{\mathbb{N}})$ for which for all $k$, $m_{k+1}\geq f(k,m_k)$, there is a sequence
  $\vec{q}$, such that for all $E\in {\mathcal{G}}(\vec{q},\vec{m})$ and for $\mu$ the uniform measure on $E$,
  the following conditions hold.
  \begin{itemize}
  \item For all $k$ greater than $2$ and all intervals $I$ such that
    $|I|\leq
    \frac{q_{k-1}-1}{m_{k-1}}$,
    \[\mu(I)<|I|^{b_k}.
     \]
  \item For all integers $k$,
   \[2
   m_k^{2b_{k+1}-1}\leq \frac{1}{q_k}\leq m_k^{2b_{k+2}-1}.
   \]
    \end{itemize}
    Further, we can compute $q_k$ from $(b_1,\dots,b_{k+2})$ and $(m_1,\dots,m_k)$.
\end{lemma}

\begin{lemma}\label{13}
  Suppose $\vec{b}$ is strictly increasing sequence of real numbers with limit $b$ such that
  $0< b<1$.  Let $f$ be as in Lemma~\ref{12}, $\vec{m}$ be such that for all~$k$,
  $m_{k+1}\geq f(k,m_k)$, and $\vec{q}$ be defined from these sequences as in Lemma~\ref{12}.  For
  every $E$ in ${\mathcal{G}}(\vec{q},\vec{m}),$ $G$ has Hausdorff dimension~$b$.
\end{lemma}

\section{Hausdorff Dimension and Irrationality Exponent}

In this section, we will put together the pieces and prove Theorem~\ref{1}.

In the proof we will use the following definition.

\begin{definition} For positive integers $d, d_1, d_2, a^*$, we let
\begin{eqnarray*}
    B(d_1,d_2,a^*)&=& \bigcup_{\substack{p,q \in {\mathbb{N}} \\ d_1\leq q\leq d_2 }}
\left[\frac{p}{q}-\frac1{q^{a^*}},\frac{p}{q}+\frac1{q^{a^*}}\right]
\\
    B(d,\infty,a^*)&=& \bigcup_{\substack{ p,q\in {\mathbb{N}} \\  d\leq q }}
\left[\frac{p}{q}-\frac1{q^{a^*}},\frac{p}{q}+\frac1{q^{a^*}}\right]
  \end{eqnarray*}
 \end{definition}

 \begin{proof}[Proof of Theorem \ref{1}]
  If $b=0$ the desired set $E$ is quite trivial:   for every $a$ greater than or equal to $2$, including
  $a=\infty$, there is a real number $x$ such that $a$ is the irrationality exponent of $x$.  Let
  $E=\{x\}$ and note that $E$ has Hausdorff dimension equal to~$0$ and the uniform measure on~$E$
  concentrates on a set of real numbers of irrationality exponent~$a$.

   Assume that $b>0$.  Let $\vec{a}$ be the constant sequence with values $a$ and let $\vec{b}$ be a
   strictly increasing sequence of positive rational numbers with limit $b$.  Thus, $\vec{a}$ and
   $\vec{b}$ are appropriate.  The desired set $E$ will be an element of ${\mathcal{E}}(\vec{q},\vec{m},\vec{a}),$
   ${\mathcal{F}}(\vec{q},\vec{m},\vec{a})$ or ${\mathcal{G}}(\vec{q},\vec{m})$, for $\vec{m}$ and $\vec{q}$ constructed
   according to Lemma~\ref{7},~\ref{10} or~\ref{12}, depending on whether $a>2$ and $b\in(0,1/a)$,
   or $a>2$ and $b\in[1/a,2/a)$, or $a=2$ and $b\in(0,1)$, respectively.  Since the first claim of the Theorem follows
   from Lemmas~\ref{7},~\ref{10} or~\ref{13}, we need only check the second claim.  We give a full
   account of the case $a>2$ and $0< b\leq1/a$.  We leave it to the reader to note that the same
   argument applies in the other cases.

  Suppose that $b\in(0,1/a)$ and let $f$ and $\vec{q}$ be the functions obtained in Lemma~\ref{6}.  Let
  $\vec{m}$ be the sequence defined by letting $m_1$ be sufficiently large in the sense of
  Lemma~\ref{6} and letting $m_k$ be the least $m$ such that $m$ is greater than $f(k,m_{k-1})$.
  Let $E^J(\vec{m},\vec{a})$ be the Jarn\'{\i}k-fractal determined from $\vec{m}$ and $\vec{a}$.  Let
  $E^J_k(\vec{m},\vec{a})$ denote the set of intervals used in the definition of
  $E^J(\vec{m},\vec{a})$ at step $k$.  Let $g_k$ denote the minimum gap between two intervals in
  $E^J_k(\vec{m},\vec{a})$.
  We define the sequence $k_s$, $E_{k_s}$ and $d_s$ by recursion on $s$.  Let $k_1=1,$ let
  $E_1=E^J_1(\vec{m},\vec{a})=[0,1],$ and let $d_1$ be the least integer $d$ such that
  $\mu_J(B(d,\infty,a+1/2))$ is less than $\mu_J(E_1)/2^1=1/2$.
  Now, suppose that $k_s$, $E_{k_s},$ and $d_s$ are defined so that $E_{k_s}$ is an initial segment of
  the levels of an element of ${\mathcal{E}}(\vec{q},\vec{m},\vec{a})$ and so that
  \[
  \mu_J\big(B\big(d_s,\infty,a+\frac{1}{2^s}\big)\cap E_{k_s}\big)< \frac{\mu_J(E_{k_s})}{2^s}.
  \]
  Let $d_{s+1}$ be the least $d$ such that
  \[
  \mu_J\big(B\big(d,\infty,a+\frac{1}{2^{s+1}}\big)\big)< \mu_J(E_{k_s})/(4\cdot 2^{s+1}).
  \]
  Let $c$ be the number of  intervals in $B(d_s,d_{s+1},a+1/2^s)$.
  Let $k_{s+1}$ be the least $k$ such that the union of $2c$
  many of the intervals in $E^J_k(\vec{m},\vec{a})$ has measure less than
  $\mu_J(E_{k_s})/(4\cdot 2^s),$ and
  let $C$ be the collection of intervals in $E^J_{k_{s+1}}$ which
  contain at least one endpoint of an interval in $B(d_s,d_{s+1},a+1/2^s)$.

  Consider the set
  $F_{s+1}$ of extensions of the branch in ${\mathcal{E}}(\vec{q},\vec{m},\vec{a})$ with endpoint $E_{k_s}$
  to branches of length $k_{s+1}$.  Each element $F_{s+1}$ specifies a set of intervals
  $S$ at level $k_{s+1}.$
  Distinct elements in   $F_{s+1}$ have empty intersection and identical $\mu_J$-measure.
  At most one-fourth of the elements $S$  in $F_{s+1}$ can be such that
  \[
  \mu_J\big(B\big(d_s,\infty,a+\frac{1}{2^s}\big)\cap S \big)\geq 4\cdot \frac{\mu_J(S)}{2^s}.
  \]
  Similarly, at most one-fourth of the $S$ in $F_{s+1}$ can be such that
  \[
  \mu_J\big(B\big(d_{s+1},\infty,a+\frac{1}{2^{s+1}}\big)\cap S\big)\geq
   4\cdot \frac{\mu_J(S)}{4\cdot 2^{s+1}} =
  \frac{\mu_J(S)}{2^{s+1}},
  \]
  and at most one-fourth of the $S$ in $F_{s+1}$ can have
  \[
    \mu_J(C\cap S)\geq 4\cdot \frac{\mu_J(S)}{4\cdot 2^s}= \frac{\mu_J(S)}{2^s}.
  \]
  Choose one element  $S$ of $F_{s+1}$ which does not belong to any of these fourths and define $E$ through its
  first $k_{s+1}$ levels so as to agree with that element.  Note that
  \[
  \mu_J\big(B\big(d_{s+1},\infty,a+\frac{1}{2^{s+1}}\big)\cap E_{k_{s+1}}\big)\leq  \frac{\mu_J(E_{k_{s+1}})}{2^{s+1}},
  \]
  which was the induction assumption on $E_{k_s}$.  Further note that at most $4/2^s$ of the
  intervals in $E_{k_s}$ can be contained in $B(d_s,d_{s+1},a+1/2^s)$ and at most $1/2^s$ of
  the intervals in~$E_{k_s}$ can contain an endpoint of an interval in $B(d_s,d_{s+1},a+1/2^s)$.
  Thus, the uniform measure $\mu$ on any element of ${\mathcal{E}}(\vec{q},\vec{m},\vec{a})$ extending the branch up to~$E_{k_{s+1}}$
  assigns $B(d_s,d_{s+1},a+1/2^s)$ a measure of less than $5/2^s$.

  Let $E$ be the set defined as above and for each $k$, let $E_k$ denote the level-$k$ of~$E$, and let
  $\mu$ denote the uniform measure on~$E$.  The first claim of the theorem, that the Hausdorff
  dimension of~$E$ is equal to~$b,$ follows from Lemma~\ref{7}.  For the second claim, every element
  of~$E^J$, and hence of~$E$, has irrationality exponent greater than or equal to~$a$.  So, it is
  sufficient to show that for every positive $\epsilon$,  there is an $s$ such
  that $\mu(B(d_s,\infty, a+\epsilon))<\epsilon$.  Let $s$ be sufficiently large so that
  $5/2^{s-1} < \epsilon$.   Then, since
  \begin{align*}
    B(d_s,\infty, a+\epsilon)&=\bigcup_{t\geq s}B(d_t,d_{t+1},a+\epsilon)\\
    &\subseteq\bigcup_{t\geq s}B\big(d_t,d_{t+1},a+\frac{1}{2^s}\big)\\
    &\subseteq \bigcup_{t\geq s}B\big(d_t,d_{t+1},a+\frac{1}{2^t}\big),
  \end{align*}
  we have
  \begin{align*}
    \mu(B(d_s,\infty, a+\epsilon))&\leq \sum_{t\geq s}\mu\big(B\big(d_t,d_{t+1},a+\frac{1}{2^t}\big)\big)\\
    &\leq \sum_{t\geq s}\frac{5}{2^t}\\
    &\leq \frac{5}{2^{s-1}}.
  \end{align*}
  The desired result follows.
\end{proof}

\section{Effective Hausdorff Dimension and Irrationality Exponent}

This section is devoted to the proof of Theorem~\ref{2}.

\begin{proof}[Proof of Theorem~\ref{2}] As in our discussion of Theorem~\ref{1}, we will consider
  the case $a>2$ and $b\in[0,1/a]$ in detail.  We leave it to the reader to note that with
  straightforward modifications the argument applies to the other two cases.  For $b=0$, the
  argument reduces to finding a singleton set $E$, so the tree of subfractals ${\mathcal{E}}$ is just the tree
  of elements of $E^J$.  For $a>2$ and $b\in[1/a,2/a]$, ${\mathcal{F}}$ replaces ${\mathcal{E}}$.  For $a=2$ and
  $b\in(0,1]$, ${\mathcal{G}}$ replaces ${\mathcal{E}}$.

  Our proof follows the outline of the proof of Theorem~\ref{1}.  That is, we will produce a version
  of $E^J$ and $E$ so that the uniform measure $\mu$ on $E$ concentrates on real numbers with
  irrationality exponent~$a$ and so that every element of $E$ has effective Hausdorff dimension $b$.
  However, since we are not assuming that $a$ and $b$ are computable real numbers, we must work with
  rational approximations when ensuring the condition on effective Hausdorff dimension.  This change
  to add effectiveness to the representation of dimension leads us to weaken our conclusions
  elsewhere: we must settle for showing that $x$ has irrationality exponent greater than or equal
  to~$a$ by showing that for every $a^*<a$ there are infinitely many $p$ and $q$ such that
  $|p/q-x|<1/q^{a^*}$.  A similar modification of Jarn\'{\i}k's construction appears
  in~\cite*{BugBecSla2014}, for different purpose.

  We will construct $\vec{a}$ and $\vec{b}$ so that $\vec{a}$ is non-decreasing with limit $a$ and
  so that $\vec{b}$ is strictly increasing with limit $b$.  Simultaneously, we will construct
  $\vec{m}$, $\vec{q}$ and $E$ in ${\mathcal{E}}(\vec{q},\vec{m},\vec{a})$ as in the proof of
  Theorem~\ref{1}.  In Theorem~\ref{1}, we began with $E^J(\vec{m},\vec{a})$ and
  ${\mathcal{E}}(\vec{q},\vec{m},\vec{a})$.  We defined a sequence of integers $d_k$ and an element of
  ${\mathcal{E}}(\vec{q},\vec{m},\vec{a})$.    At step $k$, we ensured that the set of real numbers with
  irrationality exponent greater than $a+1/2^k$ had small measure with respect to $\mu$.  It would
  have been sufficient to ensure the same fact for the set of numbers with irrationality exponent
  less than $a+\epsilon_k$, provided that $\epsilon_k$ was a non-increasing sequence with limit
  zero, which is how we will proceed now.  Thus, we will construct $(\overline{\alpha}_s:s\in{\mathbb{N}})$ to be a
  non-increasing sequence with limit $a$ to stand in for $(a+1/2^s:s\in{\mathbb{N}})$.

  Consider the problem of ensuring that for a non-negative integer $k$ and for every element $x$ of $E$,
  the sequence $\sigma$ consisting of the first $\log(m_{k})a_{k}$ digits in the base-2 expansion of
  $x$ has Kolmogorov complexity less than $\log(m_{k})a_{k} b$.  For this, it would be sufficient
  to exhibit an uniformly computable map taking binary sequences of length less than
  $\log(m_{k})a_{k} b$ onto the set of intervals in $E_k$.  For large enough $m_{k}$, we can use a
  binary sequence of length $\log(m_{k})(b-b_k)a_k$ to describe the first $k-1$ steps of the definition
  of $E^J$ and any initial conditions imposed at the beginning of step $k$.  It will then be
  sufficient to show that this information is enough to compute a map taking binary sequences of
  length less than $\log(m_{k})a_{k} b_k$ onto the set of intervals in $E_k$.

  We proceed by recursion on $s$. For each $s$, we specify three integers, $\ell_s,$ $k_s,$ and
  $d_s$.  We specify $d_s$ as we did in Theorem~\ref{1}.  We will specify rational numbers
  $\alpha_s$, $\overline\alpha_s$ and $\beta_s$ and use them to specify the values of $\vec{a}$, of
  up to $\ell_s$, specify the levels of $E^J$ up to $\ell_s$, which means that we also
  specify sequence of numbers $\vec{m}$ up to $\ell_s$, and we specify the values of $\vec{b}$ up to
  $\ell_s+2$.    This determines the values of $\vec{q}$ up to $\ell_s$.  Finally, we specify the first $k_s$ many
  levels of $E$.

  \subparagraph{Initialization of the recursion.}  Let $\beta_0$ be a positive rational number less
  than $b$.  Let $\epsilon_0$ be a rational number such that $\beta_0+\epsilon_0<b$.  Let
  $\alpha_0$ and $\overline{\alpha}_0$ be positive rational numbers such that
  $\alpha_0<a<\overline{\alpha}_0$ and $\overline\alpha_0-\alpha_0<1$.
   Let $E_0=E^J_0=[0,1]$; let $m_1$ be sufficiently large in the
  sense of Lemma~\ref{6} for the constant sequence $\vec{\alpha}$ with value $\alpha_0$ and the
  sequence $\vec{\beta}$ with values $\beta_0+(1-1/2^n)\epsilon_0$, respectively; let
  $E^J_1=G_{m_1}(\alpha_0)$, the collection of intervals centered at rational numbers
  $p/m_1\in(0,1)$ with diameter $2/m_1^{\alpha_0}$;
   let    $  g_1=\frac{q_1}{m_1}-\frac{2}{m_1^{\alpha}}$, which is the minimum distance between two intervals in $E_1^J$;
   and
   let $d_0$ be the least integer $d$ such that
  $2/d^{\alpha_0}$ is less than $g_1$
  and such that
  \[
  \sum_{j\geq d}\frac{ j}{ (2 j)^{\overline{\alpha}_0}}< \frac{1}{2}.
  \]
  Since $\overline{\alpha}_0 > 2$, $d_0$ is well-defined.
  Since we will define $E^J$ so that
  Lemma~\ref{6} applies, this sum is an upper bound on $\mu_J(B(d_0,\infty,\alpha_0))$.  So, this
  choice of $d_0$ ensures that $\mu_J(B(d_0,\infty,\alpha_0))$ is less than $1/2$.

  Let $\ell_0=1$; let the first two values of $\vec{a}$ be equal to those in $\vec{\alpha}$ and the
  first $3$ values of $\vec{b}$ be the same as those in $\vec{\beta}$.
  Note that these choices
  determine $q_1$.  Let $k_0=0$ and let $E_1=E^J_1$.

  \subparagraph{Recursion: stage $s+1$.}  Now, suppose that our construction is defined through
  stage~$s$.  Following the proof of Theorem~\ref{1}, we may assume that we have ensured
\[
  \mu_J(B(d_{s},\infty,\alpha_s)\cap E_{k_s})) \ < \ \frac{\mu_J(E_{k_s})}{2^{s}},
\] subject to our satisfying the hypotheses of~Lemma~\ref{6}.

  We ensure that stage $s+1$ of the construction of $E$ is uniformly computable from the
  construction up to step $s$ and parameters set during the initialization of stage $s+1$ by
  continuing the construction of $E^J$ recursively in these parameters until the definition of
  $E_{k_{s+1}}$ is evident.

  \subsubparagraph{Initialization of stage $s+1$.} Let $\alpha_{s+1},$ $\overline{\alpha}_{s+1}$ be rational
  numbers such that
  \[
  \alpha_{s}<\alpha_{s+1}<a<\overline{\alpha}_{s+1}\leq \overline{\alpha}_{s}
  \]
  and such that
 \[
  |\overline{\alpha}_{s+1}-\alpha_{s+1}|<\frac{1}{s+1}.
  \]
  Let $\beta_{s+1}$ be a rational number
  strictly between $\beta_{s}+\epsilon_s$ and $b$ such that
  \[
  |b-\beta_{s+1}|<\frac{1}{s+1},
  \]
 and let
  $\epsilon_{s+1}$ be a rational number such that
  \[
   \beta_{s+1}+\epsilon_{s+1} <b.
  \]
  Let $d_{s+1}$ be the least integer $d$ such that $2/d^{\overline{\alpha}_{s+1}}<g_{\ell_s}$
   such that  $2/d^{\overline{\alpha}_{s+1}}$  is less than the minimum gap length
   $g_{\ell_s}= \frac{q_{\ell_s}}{m_{\ell_s}}-\frac{2}{m_{\ell_s}^{\overline{\alpha}_s}}$
  and
  \[
  \sum_{j\geq d} \frac{j}{(2 j)^{\overline{\alpha}_{s+1}}}<\frac{\mu_J(E_{k_{s}})}{4\cdot 2^{s+1}}.
  \]
  Since $2/d_{s+1}^{\overline{\alpha}_{s+1}}<g_{\ell_s}$ and we ensure that our construction of
  $E^J$ satisfies the hypotheses of Lemma~\ref{6}, this sum is an upper bound on
  $\mu_J(B_{d_{s+1}},\infty,\overline{\alpha}_{\ell_{s+1}})$.  Thus, we have ensured that
  \[
    \mu_J(B_{d_{s+1}},\infty,\overline{\alpha}_{\ell_{s+1}}) < \frac{\mu_J(E_{k_{s}})}{4\cdot 2^{s+1}},
  \]
  which is analogous to how we chose $d_{s+1}$ in the proof of Theorem~\ref{1}.

  Let $m_{\ell_s+1}$ be greater than $f(\ell_{s},m_{\ell_s})$  and  sufficiently large so  that a binary
  sequence of length $\log(m_{\ell_{s+1}})a(b-\beta_{s+1})$ can  describe these
  parameters together with the first $s$ steps of the construction.

  \subsubparagraph{Subrecursion: substage $\ell$.}  Proceed by recursion on substages $\ell$
  starting with initial value $\ell_{s}+1$.  Suppose that the termination condition for stage $s+1$
  was not realized during substage $\ell-1$.  Define $a_{\ell}$ to be equal to $\alpha_{s+1}$ and
  define $b_{\ell+2}$ to be equal $\beta_{s+1}+\epsilon_{s+1}(1-1/2^{\ell-\ell_{s}})$.
  If~$\ell=\ell_s+1$, then value of $m_{\ell_s+1}$ was assigned in the previous
  paragraph.  Otherwise, let $m_\ell$ be larger than $f(\ell,m_{\ell-1})$.  Note that $f$ is defined in
  terms the values of $\vec{q}$ and $\vec{a}$ up to $\ell$ and that the values of $\vec{q}$ are
  defined in terms of $\vec{a}$ and $\vec{m}$ up to $\ell$ and $\vec{b}$ up to $\ell+2$, all of
  which have been determined before the evaluation of~$f$.

\subsubparagraph{Termination of the subrecursion.}  Note that $\mu_J(E_{k_s})$
  is determined at the end of step $s$, since it is equal to the number of level-$k_s$ intervals in
  $E_{k_s}$
  divided by the number of level-$(k_s)$ intervals in $E^J$.
  We say that step $\ell$ satisfies the termination condition for stage $s+1$ when
  there is a $k$ between $\ell_{s}$ and $\ell$ such that there is an $S$ in  the level $k$ of ${\mathcal{E}}(\vec{q}, \vec{m}, a)$
  satisfying the following conditions.
  \begin{itemize}
  \item There is a $d^*$ in $(d_{s},d_s+\ell)$ such that the $\mu_J$-measure of the set of intervals in
    $E_\ell^J$ which have non-empty intersection with $B(d_{s},d^*,\overline{\alpha}_{s})\cap S$ is
    less than \[
    4\cdot\frac{\mu_J(S)}{2^{s}}- \sum_{j\geq d^*} \frac{j}{ (2 j)^{\overline{\alpha}_{s+1}}}.
   \]

  \item There is a $d^*$ in $(d_{s+1},d_{s+1}+\ell)$ such that the $\mu_J$-measure of the set of intervals in
    $E_\ell^J$ which have non-empty intersection with $B(d_{s+1},d^*,\overline{\alpha}_{s+1})$ is
    less than
   \[
    4\cdot\frac{\mu_J(S)}{2^{s+1}}- \sum_{j\geq d^*} \frac{j}{ (2 j)^{\overline{\alpha}_{s+1}}}.
    \]

  \item The $\mu_J$ measure of the union of the set of intervals in $S$
   which contain at least one endpoint of an interval in $B(d_{s},d_{s+1},\overline{\alpha}_{s+1})$ is less than
    \[
    \frac{\mu_J(S)}{  2^{s+1}}.
    \]
  \end{itemize}

  If the termination condition is realized for $\ell$, then we set $\ell_{s+1}$ equal to~$\ell$, and
  set $k_{s+1}$ and $E_{k_{s+1}}$ to have values equal to those in the least pair $k$ and $S$
  which satisfy the termination condition.

  \paragraph{Verification.}  We first note that by inspection of our construction, it satisfies the hypotheses
  of Lemma~\ref{6}.
  Next, we observe that for every stage the subrecursion for that stage eventually realizes its
  termination condition.  For the sake of a contradiction, suppose that there is a stage in the main
  recursion of the construction whose subrecursion never terminates.  Then $E^J$ is defined using
  an eventually constant sequence $\vec{a}$ and an increasing sequence $\vec{b}$.  By the same
  reasoning as in the proof of Theorem~\ref{1}: first, there must be a $k$ and an $S$ such that
  the three sets in question have sufficiently small relative measure in $S$; and second, for
  any such $k$ and $S$, for any $\delta>0$, there is an $\ell$ such that the measures of the
  intersections of those three sets with $S$ is approximated to within $\delta$ by the measure
  of their smallest covers using intervals in $E_\ell^J$.  But, then the termination condition would
  apply, a contradiction.  Thus, both $E$ and $E^J$ are well-defined, as are their uniform measures
  $\mu$ and~$\mu_J$.

  By the same argument as in the proof of Theorem~\ref{1}, $\mu$-almost every real number~$x$ has
  exponent of irrationality equal to~$a$.  By Lemma~\ref{3}, the Mass Distribution Principle applied
  to~$\mu$, if $B$ is a subset of the real numbers and the Hausdorff dimension of~$B$ is less than
  $b$, then $\mu(B)=0$.  So, $\mu$-almost every~$x$ has effective Hausdorff dimension greater than
  or equal to~$b$.

  In order to conclude that every element of $E$ has effective Hausdorff dimension less than or
  equal to $b$, it remains to show that for every $x\in E$ and for every $n\in{\mathbb{N}}$, there is an $m>n$
  such that the Kolmogorov complexity of the first $m$ digits in the binary expansion of $x$ is less
  than or equal to~$b\cdot m$.  Let such $x$ and $n$ be given, and consider a stage $s+1$ such that
  $m_{s+1}$ is greater than $n$.  Then, the first $s$ many steps of the construction together with
  the values of $a_{\ell_{s+1}},$ $b_{\ell_{s+1}}$ and $m_{s+1}$ can be effectively described by a
  sequence of length $m_{s+1}$.  The result of stage $s+1$ of the construction is effectively
  determined from these parameters; in particular, $E_{\ell_{s+1}}$ is effectively defined from
  these parameters.  By definition, there are at most $m_{\ell_{s+1}}/q_{\ell_{s+1}}$ many intervals
  in $E_{\ell_{s+1}}$.  By Lemma~\ref{6},
  \[
  \frac{1}{q_{\ell_{s+1}}}<
   m_{\ell_{s+1}}^{a_{\ell_{s+1}}(b_{\ell_{s+1}}+(1-2^{\ell_{s+1}-\ell_s})\epsilon_{s+1})-1}<
   m_{\ell_{s+1}}^{a_{\ell_{s+1}}(b_{\ell_{s+1}}+\epsilon_{s+1})-1},
    \]
    and so
    \[
     \frac{m_{\ell_{s+1}}}{q_{\ell_{s+1}}}<
     m_{\ell_{s+1}}^{a_{\ell_{s+1}}(b_{\ell_{s+1}}+\epsilon_{s+1})}=
     2^{\log(m_{\ell_{s+1}})a_{\ell_{s+1}}(b_{\ell_{s+1}}+\epsilon_{s+1})}.
     \]
    Thus, we can read off a surjection from the set of binary sequences of length
    \[\log(m_{\ell_{s+1}})a_{\ell_{s+1}}(b_{\ell_{s+1}}+\epsilon_{s+1})\]
     to the set of intervals in
    $E_{\ell_{s+1}}$.  Each interval $I$ in $E_{\ell_{s+1}}$ has length
    $2/m_{\ell_{s+1}}^{a_{\ell_{s+1}}}$.  Computably, each such interval $I$ restricts the first
    $\log(m_{\ell_{s+1}})a_{\ell_{s+1}}$ digits in the base-2 expansions of its elements to at most
    two possibilities.  Thus, for each $x$ in $E$, the sequence of the first
    $\log(m_{\ell_{s+1}})a_{\ell_{s+1}}$ digits in its base-2 expansion can be uniformly computably
    described using the information encoded by three sequences, one of length
    $\log(m_{\ell_{s+1}}) a_{\ell_{s+1}}(b-(b_{\ell_{s+1}}+\epsilon_{s+1}))$ to describe the
    construction up to stage $s$, one of length
    $ \log(m_{\ell_{s+1}}) a_{\ell_{s+1}}(b_{\ell_{s+1}}+\epsilon_{s+1})$ to describe the interval
    within $E_{\ell_{s+1}}$ that contains $x$, and one of length $1$ to describe which of the two
    possibilities within that interval apply to $x$.  By the choice of $m_{\ell_{s+1}}$, this sum
    is less than or equal to $\log(m_{\ell_{s+1}})a_{\ell_{s+1}} b$, as required.
\end{proof}

redpajama_set_name: RedPajamaArXiv


text:
`tbomb` is a utility to stress-test bittorrent trackers via UDP.

It (already!) has some cool features:

- Pre-allocated packets (performance)
- can reuse connection IDs (much like HTTP keepalive)
- reports what errors occurred, and how many of them
- random peer IDs
- random infohashes
- checks transaction IDs
- can finish after either a specified time or a specified number of requests

Planned features:

- Scrape mode (with multi-scrape)
- Some way to limit the amount of infohashes/peerIDs generated
- IPv6 mode? Maybe when IPv6 for UDP trackers is defined.
- configure timeout
- configure additional announce options? (downloaded, uploaded, left, event, ...)

It was inspired by [gobench](https://github.com/cmpxchg16/gobench).

## How to get it
To get it, simply

    go get -u github.com/mrd0ll4r/tbomb

That should download and install it.

## Usage
The basic usage is

    tbomb [options] (-r <requests per client>|-t <timeout>) -u <target>

The options and arguments are:

    -u <target>: specifies the target to test, e.g. 127.0.0.1:12345 or tracker.example.org:1337
    -t <timeout>: specifies the period of testing in seconds
    -r <requests>: specifies the number of requests to send _per_client_
    -c <clients>: specifies the number of concurrent clients to use
    -k: enables keep-alive mode (reusing connectionIDs)
    -e: enables detailed error reports (has some impact on performance)
    (-s: enables scrape-mode (not yet implemented))

This is what a typical call might look like:

    tbomb -c 200 -u localhost:6882 -t 30 -k -e

This is what a typical report might look like:

    Dispatching 400 clients
    Waiting for results...

    Requests:                           504547
    Successful requests:                499834
    failed requests:                      4713
    Connect attempts:                      460
    Failed connects:                        60
    Successful requests rate:            16658 hits/sec
    Approximate concurrency:            105.99 clients running
    Test time:                           30.01 sec
    Errors encountered:
        announce: I/O timeout on receive        4351
        connect: I/O timeout on receive          60

Note: To have the test results as accurate as possible, we set the read timeout to zero as soon as the test time is over.
This causes all blocking read operations to return immediately, so we don't get the two second delay (because we had
two seconds of timeout) any more. But it also causes all blocking read operations to return a timeout. We don't count them
in the errors encountered and we don't use them to calculate the approximate concurrency. But you will see more failed
requests/connects than errors encountered. Now you know why. The successful requests rate and test time are more accurate,
the approximate concurrency is less accurate (because we cancel *real* timeouts as well). This only applies if you
specify a timeout for the test.

This is another typical report, it's from an older version. I keep it here to show how the approximate concurrency is
computed:

    Dispatching 200 clients
    Waiting for results...

    Requests:                           571644
    Successful requests:                569970
    failed requests:                      1674
    Connect attempts:                      254
    Failed connects:                        54
    Successful requests rate:            18054 hits/sec
    Approximate concurrency:             90.53 clients running
    Test time:                           31.57 sec
    Errors encountered:
        announce: I/O timeout on receive        1674
        connect: I/O timeout on receive          54

Note that the test actually took about two seconds longer than specified - this is due to the receive timeout being two
seconds. (no longer applies)
Note about the approximate concurrency: If 1674 + 54 = 1728 timeouts occurred, each after two seconds, 3456 seconds in
total were timed out. With 200 concurrent clients over 31.57 seconds (=6914 seconds of work), about half of the time
was actually blocked due to timeouts. The `approximate concurrency` value therefore indicates how many clients were
working full-time, (without waiting for I/O), on average. The value is experimental. The value will only be shown if you
use a timeout for the test.

## License
MIT


text:
Heresy never prospers. What's the reason?
By Phil Lawler ( bio - articles - email ) | Aug 28, 2003
So now we have a Catholic bishop arguing that women should hear confessions.
Oh, of course he's not challenging the definitive Church teaching that women cannot be ordained as priests. And he's not suggesting that sacramental confession need not involve an ordained minister. Oh, no; nothing like that. He's just giving us a "gentle invitation to reflect." Right.
It would be refreshing if Bishop Vincent Malone could make the candid admission that he does not believe the Church's teaching regarding the ministerial priesthood or the sacraments. Failing that, it would be still more refreshing if the Holy See made that observation for him-- and took the necessary further step of relieving him from his pastoral duties.
Phil Lawler has been a Catholic journalist for more than 30 years. He has edited several Catholic magazines and written eight books. Founder of Catholic World News, he is the news director and lead analyst at CatholicCulture.org. See full bio.


Our boogie boards are home but we're amped at Piscataqua's harbor. After hours on red brick, the idea of dinner is is looking good so we tube into a high top in the bar. For openers, Jim's got a pomegranate martini. It looks like a Cosmospolitan but that comes with cranberry juice. Who knew all you have to do to a martini is add fruit to make it a health drink? One taste and I want one but I know better.
Roseanna and I are having salmon that's been marinated in miso, plated on rice cake with shitakes. She takes hers with ponzu and I take mine without: light on sauce, heavy on flavor. Ponzu is citrus-y bringing out the salmon's warmth and depth. Mine is great all by itself and it's just the fish, which has no trouble taking the challenge. Mushroomed rice is always creative. We're happy someone took time to sliver asparagus which not only makes for a better picture but you can see that they're roasted. And we're partial to the plate pile. There's a little mixing but not too much plus the carbs stay hot. Yes, yes I know but it's Saturday.


text:
Q: Flask request parameter string limit? I want to use Python and Flask to serve static html pages which will read arguments from the URL parameters.
I don't know how much data will be passed in with the query strings, and I would like to know what kind of limits there are on Flask's handling of URL parameters? Can I have as many URL parameters as I want, and send as large strings as I want with them?
(The HTML will primarily be requested by a Chrome/Chromium browser)

redpajama_set_name: RedPajamaStackExchange


text:
The Great Glorious Goddamn of It All (Hardcover)
By Josh Ritter
(FC-Fiction-general)
NATIONAL BESTSELLER
From singer-songwriter Josh Ritter, a lyrical, sweeping novel about a young boy's coming-of-age during the last days of the lumberjacks.
In the tiny timber town of Cordelia, Idaho, ninety-nine year old Weldon Applegate recounts his life in all its glory, filled with tall tales writ large with murder, mayhem, avalanches and bootlegging. It's the story of dark pine forests brewing with ancient magic, and Weldon's struggle as a boy to keep his father's inherited timber claim, the Lost Lot, from the ravenous clutches of Linden Laughlin.
Ever since young Weldon stepped foot in the deep Cordelia woods as a child, he dreamed of joining the rowdy ranks of his ancestors in their epic axe-swinging adventures. Local legend says their family line boasts some of the greatest lumberjacks to ever roam the American West, but at the beginning of the twentieth century, the jacks are dying out, and it's up to Weldon to defend his family legacy.
Braided with haunting saloon tunes and just the right dose of magic, The Great Glorious Goddamn of It All is a novel bursting with heart, humor and an utterly transporting adventure that is sure to sweep you away into the beauty of the tall snowy mountain timber.
Publisher: Hanover Square Press


I am a Line Dance Instructor & Choreographer from Scotland.
I have been teaching for the past 7 years.
I have classes within the Glasgow area ranging from Absolute Beginner to Intermediate Level.
We dance to a variety of music genres including Country, Pop, Jazz etc.