15 research outputs found
Boundary Value Problem for (III): Global Solution and Asymptotics
Based on the results in the previous papers that the boundary value problem
with the condition for
has a unique solution , and satisfies
, in this paper we show that ,
with the initial conditions has a unique solution by
using functional analysis method. So we get a globally well defined bounded
function . The asymptotics of as and as are obtained, and the connection formulas for
the parameters in the asymptotics and the numerical simulations are also given.
Then by the properties of , the solution to the boundary value problem
is well described by the asymptotics
and the connection formulas.Comment: 11 pages, 2 fingure
Boundary Value Problem for (I): Existence and Uniqueness
In this paper we study the equation with the
boundary conditions , and for .
The existence of the solution is proved by using topological shooting argument.
And the uniqueness is proved by variation method. Using the asymptotics of
as , in the following papers we will discuss the global
solution for , and give explicit asymptotics of as
and as , and the connection formulas for the parameters in the
asymptotics. Based on these results, we will solve the boundary value problem
, , which is the goal of this work. Once people discuss
the regular solution of this equation, this boundary value problem must be
considered.
This problem is useful to study the Yang-Mills potential related equations,
and the method used for this equation is applicible to other similar equations.Comment: 12 page
Boundary value problem for r
We study the equation r2d2f/dr2+f=f3 with the boundary conditions f(1)=0, f(∞)=1, and f(r)>0 for 1<r<∞. The existence of the solution is proved using a topological shooting argument. And the uniqueness is proved by a variation method
Orthonormal Polynomials on the Unit Circle and Spatially Discrete Painlev\'e II Equation
We consider the polynomials orthonormal with respect to the weight on the unit circle in the complex plane. The leading coefficient
is found to satisfy a difference-differential (spatially discrete)
equation which is further proved to approach a third order differential
equation by double scaling. The third order differential equation is equivalent
to the Painlev\'e II equation. The leading coefficient and second leading
coefficient of can be expressed asymptotically in terms of the
Painlev\'e II function.Comment: 16 page
The global burden of adolescent and young adult cancer in 2019 : a systematic analysis for the Global Burden of Disease Study 2019
Background In estimating the global burden of cancer, adolescents and young adults with cancer are often overlooked, despite being a distinct subgroup with unique epidemiology, clinical care needs, and societal impact. Comprehensive estimates of the global cancer burden in adolescents and young adults (aged 15-39 years) are lacking. To address this gap, we analysed results from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2019, with a focus on the outcome of disability-adjusted life-years (DALYs), to inform global cancer control measures in adolescents and young adults. Methods Using the GBD 2019 methodology, international mortality data were collected from vital registration systems, verbal autopsies, and population-based cancer registry inputs modelled with mortality-to-incidence ratios (MIRs). Incidence was computed with mortality estimates and corresponding MIRs. Prevalence estimates were calculated using modelled survival and multiplied by disability weights to obtain years lived with disability (YLDs). Years of life lost (YLLs) were calculated as age-specific cancer deaths multiplied by the standard life expectancy at the age of death. The main outcome was DALYs (the sum of YLLs and YLDs). Estimates were presented globally and by Socio-demographic Index (SDI) quintiles (countries ranked and divided into five equal SDI groups), and all estimates were presented with corresponding 95% uncertainty intervals (UIs). For this analysis, we used the age range of 15-39 years to define adolescents and young adults. Findings There were 1.19 million (95% UI 1.11-1.28) incident cancer cases and 396 000 (370 000-425 000) deaths due to cancer among people aged 15-39 years worldwide in 2019. The highest age-standardised incidence rates occurred in high SDI (59.6 [54.5-65.7] per 100 000 person-years) and high-middle SDI countries (53.2 [48.8-57.9] per 100 000 person-years), while the highest age-standardised mortality rates were in low-middle SDI (14.2 [12.9-15.6] per 100 000 person-years) and middle SDI (13.6 [12.6-14.8] per 100 000 person-years) countries. In 2019, adolescent and young adult cancers contributed 23.5 million (21.9-25.2) DALYs to the global burden of disease, of which 2.7% (1.9-3.6) came from YLDs and 97.3% (96.4-98.1) from YLLs. Cancer was the fourth leading cause of death and tenth leading cause of DALYs in adolescents and young adults globally. Interpretation Adolescent and young adult cancers contributed substantially to the overall adolescent and young adult disease burden globally in 2019. These results provide new insights into the distribution and magnitude of the adolescent and young adult cancer burden around the world. With notable differences observed across SDI settings, these estimates can inform global and country-level cancer control efforts. Copyright (C) 2021 The Author(s). Published by Elsevier Ltd.Peer reviewe
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Boundary Value Problem for (I): Existence and Uniqueness
In this paper we study the equation with the boundary
conditions , and f(r) > 0 for $
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Boundary Value Problem for (III): Global Solution and Asymptotics
Based on the results in the previous papers that the boundary value problem with the condition y(x) > 0 for
$