Convex Regularization Method for Solving Cauchy Problem of the Helmholtz Equation

In this paper, we introduce the Convex Regularization Method (CRM) for regularizing the (instability) solution of the Helmholtz equation with Cauchy data. The CRM makes it possible for the solution of Helmholtz equation to depend continuously on the small perturbations in the Cauchy data. In addition, the numerical computation of the reg- ularized Helmholtz equation with Cauchy data is stable, accurate and gives high rate of convergence of solution in Hilbert space. Undoubtedly, the error estimated analysis associated with CRM is minimal.Mathematics Subject Classi cation: 44B28; 44B30Keywords: Convex Regularization Method, ill-posed Helmholtz equation with Cauchy data, stable solutio

A Two-Dimensional Chebyshev Wavelet Method for Solving Partial Di erential Equations

In this paper, we introduce a two-dimensional Chebyshev wavelet method (TCWM) for solving partial di erential equations (PDEs) in L2(R) space. In this method, the spatial variables appearing in the PDE each has its own kernel, as well as wavelet coecient for approxi- mating the unknown solution of the equation. The approximated solu- tion of the equation is fast and has higher number of vanishing moments as compared to the Chebyshev wavelet method with only one wavelet coecient for two or more separated kernels for the variables appearing in the PDE

The prevalence of, and factors associated with, paying for sex among men resident in Britain: findings from the third national survey of sexual attitudes and lifestyles (Natsal-3)

Objectives Men who pay for sex (MPS) are considered a bridging population for sexually transmitted infections (STI). However, the extent, characteristics and role of MPS in transmission is poorly understood. We investigate these questions using data from Britain's third National Survey of Sexual Attitudes and Lifestyles (Natsal-3). Methods We performed complex survey analyses of data from 6293 men aged 16–74 years resident in Britain who completed Natsal-3, a probability sample survey undertaken during 2010–2012, using computer-assisted personal interviewing and computer-assisted self-interview. Results 11.0% (95% CI10.1% to 11.9%) of all men reported ever paying for sex. Among MPS, 18.4% (95% CI 18.2% to 18.7%) of their lifetime sexual partners were paid. 3.6% (95% CI 3.1% to 4.2%) of men had paid for sex in the past 5 years. Partners of MPS constitute 14.7% of all reported partners and MPS report 15.6% of all reported STI diagnoses in the past 5 years. Paying for sex in the past 5 years was strongly associated with reporting larger numbers of sexual partners (adjusted OR, AOR for 5+ partners, past 5 years, 31.50, 95% CI 18.69 to 53.09). After adjusting for partner numbers, paying for sex remained strongly associated with reporting new foreign partners outside the UK (AOR 7.96; 95% CI 4.97 to 12.73) and STI diagnosis/es (AOR 2.34; 95% CI 1.44 to 3.81), all in the past 5 years. Among men ever paying for sex, 62.6% (95% CI 58.3% to 66.8%) reported paying for sex outside the UK, most often in Europe and Asia. Conclusions MPS in Britain remain at greater risk of STI acquisition and onward transmission than men who do not. They report high numbers of partners, but the minority are paid partners. They are an important core group in STI transmission

The prevalence of, and factors associated with, paying for sex among men resident in Britain: findings from the third National Survey of Sexual Attitudes and Lifestyles (Natsal-3)

Objectives Men who pay for sex (MPS) are considered a bridging population for sexually transmitted infections (STI). However, the extent, characteristics and role of MPS in transmission is poorly understood. We investigate these questions using data from Britain's third National Survey of Sexual Attitudes and Lifestyles (Natsal-3). Methods We performed complex survey analyses of data from 6293 men aged 16–74 years resident in Britain who completed Natsal-3, a probability sample survey undertaken during 2010–2012, using computer-assisted personal interviewing and computer-assisted self-interview. Results 11.0% (95% CI10.1% to 11.9%) of all men reported ever paying for sex. Among MPS, 18.4% (95% CI 18.2% to 18.7%) of their lifetime sexual partners were paid. 3.6% (95% CI 3.1% to 4.2%) of men had paid for sex in the past 5 years. Partners of MPS constitute 14.7% of all reported partners and MPS report 15.6% of all reported STI diagnoses in the past 5 years. Paying for sex in the past 5 years was strongly associated with reporting larger numbers of sexual partners (adjusted OR, AOR for 5+ partners, past 5 years, 31.50, 95% CI 18.69 to 53.09). After adjusting for partner numbers, paying for sex remained strongly associated with reporting new foreign partners outside the UK (AOR 7.96; 95% CI 4.97 to 12.73) and STI diagnosis/es (AOR 2.34; 95% CI 1.44 to 3.81), all in the past 5 years. Among men ever paying for sex, 62.6% (95% CI 58.3% to 66.8%) reported paying for sex outside the UK, most often in Europe and Asia. Conclusions MPS in Britain remain at greater risk of STI acquisition and onward transmission than men who do not. They report high numbers of partners, but the minority are paid partners. They are an important core group in STI transmission

Medicated sex in Britain: evidence from the third National Survey of Sexual Attitudes and Lifestyles

Objectives: To describe the prevalence of medication use to assist sexual performance in Britain and to identify associated factors. / Methods: Cross-sectional probability sample, undertaken in 2010–2012, of 15 162 people aged 16–74 years, resident in Britain, of whom, 5617 men and 8095 women reported sexual experience (ever) and 4817 men were sexually-active (reported sex in the last year). / Results: Ever use of medication to assist sexual performance (medicated sex) was more commonly reported by men than women (12.9% (95% CI 11.9% to 13.9%) vs 1.9% (95% CI 1.7% to 2.3%)) and associated with older age in men and younger age in women. It was associated with reporting smoking, and use of alcohol and recreational drugs, as well as unsafe sex (≥2 partners and no condom use in the last year) in both men and women. Among men, the proportion reporting medicated sex in the last year was higher among those reporting erectile difficulties (ED) than those not doing so (28.4% (95% CI 24.4% to 32.8%) vs 4.1% (95% CI 3.4% to 4.9%)). In all men, medicated sex was associated with more frequent sexual activity, meeting a partner on the internet, unsafe sex and recent sexually transmitted infections diagnosis; associations that persisted after adjusting for same-sex behaviour and ED. However, there were significant interactions with reporting ED, indicating that among men with ED, medicated sex is not associated with same-sex behaviour and ever use of recreational drugs. / Conclusions: A substantial minority of people in Britain report medicated sex, and the association between medicated sex and risky sexual behaviour is not confined to high-risk groups

Consistency in reporting sensitive sexual behaviours in Britain: change in reporting bias in the second and third National Surveys of Sexual Attitudes and Lifestyles (Natsal-2 and Natsal-3).

OBJECTIVES: Britain's second National Survey of Sexual Attitudes and Lifestyles (Natsal-2) was conducted in 1999-2001 and the third (Natsal-3) was conducted in 2010-2012 to update prevalence estimates of sexual behaviours and assess changes over time. We investigated whether there was a change in reporting bias between these two cross-sectional surveys. METHODS: We analysed data from the 'common birth cohort' of participants born during 1956-1983, who were eligible to take part in Natsal-2 (n=10 764) and Natsal-3 (n=6907). We compared estimates for outcomes that occurred before Natsal-2 and expected these to be consistent between surveys if no change in reporting bias had occurred. RESULTS: A greater proportion of non-white men and women were in Natsal-3 consistent with demographic changes in Britain. Reporting behaviours was largely consistent between surveys for men. Fewer women in Natsal-3 reported early first intercourse or having child(ren) before age 20; they were also more likely to report not discussing sex with their parents at age 14. Men and women in Natsal-3 were more likely to report tolerant attitudes towards same-sex partnerships but less tolerance towards unfaithfulness in marriage and one-night-stands. CONCLUSIONS: We found little evidence of change in reporting bias among men since Natsal-2. Among women, a modest change in reporting bias was observed for a small number of experiences, possibly due to changes in participation, social acceptability and methodological differences between surveys. Changes in the reporting of sexual behaviours and attitudes over time observed in the wider Natsal-3 study are therefore likely to largely reflect real changes in the population

Sexual identity, attraction and behaviour in Britain: The implications of using different dimensions of sexual orientation to estimate the size of sexual minority populations and inform public health interventions.

BACKGROUND: Sexual orientation encompasses three dimensions: sexual identity, attraction and behaviour. There is increasing demand for data on sexual orientation to meet equality legislation, monitor potential inequalities and address public health needs. We present estimates of all three dimensions and their overlap in British men and women, and consider the implications for health services, research and the development and evaluation of public health interventions. METHODS: Analyses of data from Britain's third National Survey of Sexual Attitudes and Lifestyles, a probability sample survey (15,162 people aged 16-74 years) undertaken in 2010-2012. FINDINGS: A lesbian, gay or bisexual (LGB) identity was reported by 2·5% of men and 2·4% of women, whilst 6·5% of men and 11·5% of women reported any same-sex attraction and 5·5% of men and 6·1% of women reported ever experience of same-sex sex. This equates to approximately 547,000 men and 546,000 women aged 16-74 in Britain self-identifying as LGB and 1,204,000 men and 1,389,000 women ever having experience of same-sex sex. Of those reporting same-sex sex in the past 5 years, 28% of men and 45% of women identified as heterosexual. INTERPRETATION: There is large variation in the size of sexual minority populations depending on the dimension applied, with implications for the design of epidemiological studies, targeting and monitoring of public health interventions and estimating population-based denominators. There is also substantial diversity on an individual level between identity, behaviour and attraction, adding to the complexity of delivering appropriate services and interventions

Men who have sex with men in Great Britain: comparing methods and estimates from probability and convenience sample surveys

OBJECTIVE: To examine sociodemographic and behavioural differences between men who have sex with men (MSM) participating in recent UK convenience surveys and a national probability sample survey. METHODS: We compared 148 MSM aged 18-64 years interviewed for Britain's third National Survey of Sexual Attitudes and Lifestyles (Natsal-3) undertaken in 2010-2012, with men in the same age range participating in contemporaneous convenience surveys of MSM: 15 500 British resident men in the European MSM Internet Survey (EMIS); 797 in the London Gay Men's Sexual Health Survey; and 1234 in Scotland's Gay Men's Sexual Health Survey. Analyses compared men reporting at least one male sexual partner (past year) on similarly worded questions and multivariable analyses accounted for sociodemographic differences between the surveys. RESULTS: MSM in convenience surveys were younger and better educated than MSM in Natsal-3, and a larger proportion identified as gay (85%-95% vs 62%). Partner numbers were higher and same-sex anal sex more common in convenience surveys. Unprotected anal intercourse was more commonly reported in EMIS. Compared with Natsal-3, MSM in convenience surveys were more likely to report gonorrhoea diagnoses and HIV testing (both past year). Differences between the samples were reduced when restricting analysis to gay-identifying MSM. CONCLUSIONS: National probability surveys better reflect the population of MSM but are limited by their smaller samples of MSM. Convenience surveys recruit larger samples of MSM but tend to over-represent MSM identifying as gay and reporting more sexual risk behaviours. Because both sampling strategies have strengths and weaknesses, methods are needed to triangulate data from probability and convenience surveys