DSpace Collection:
http://hdl.handle.net/11368/2829331
Wed, 27 May 2020 05:59:13 GMT2020-05-27T05:59:13ZRegular versus singular solutions in a quasilinear indefinite problem with an asymptotically linear potential
http://hdl.handle.net/11368/2961235
Title: Regular versus singular solutions in a quasilinear indefinite problem with an asymptotically linear potential
Abstract: The aim of this paper is analyzing the positive solutions of the quasilinear
problem
egin{equation*}
label{P}
-(u'/sqrt{1+(u')^2})' = lambda a(x) f(u) ; ; ext{in } (0,1),
u'(0)=0,;u'(1)=0,
end{equation*}
where $lambdain R$ is a parameter, $ain L^infty(0,1)$ changes sign once in $(0,1)$
and satisfies $int_0^1a(x),dx<0$, and $f in mc{C}^1(R)$ is positive and increasing in $(0,+infty)$ with a potential, $F(s)=int_0^{s}f(t),dt$, quadratic at zero and linear at $+infty$.
The main result of this paper establishes that
this problem possesses a component of positive bounded variation solutions, $mathscr{C}_{l_0}^+$, bifurcating from $(l,0)$ at some $l_0>0$ and from $(l,infty)$ at some $l_infty>0$.
It also establishes that $mathscr{C}_{l_0}^+$ consists of regular solutions, if, and only if,
centerline{
$
int_0^z left( int_x^z a(t),dt
ight)^{-rac{1}{2}}dx =+infty, quad hbox{or}quad
int_z^1 left( int_x^z a(t),dt
ight)^{-rac{1}{2}}dx =+infty.
$}
Equivalently, the small positive regular solutions of $mathscr{C}_{l_0}^+$ become singular
as they are sufficiently large if, and only if,
centerline{
$
left( int_x^z a(t),dt
ight)^{-rac{1}{2}}in L^1(0,z) quad ext{and} quad
left( int_x^z a(t),dt
ight)^{-rac{1}{2}}in L^1(z,1).
$}
This is achieved by providing a very sharp description of the asymptotic profile, as $l ol_infty$, of the solutions.
According to the mutual positions of $l_0$ and $l_infty$, as well as the bifurcation direction, the occurrence of multiple solutions can also be detected.Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/11368/29612352020-01-01T00:00:00ZRecursive approach for non-Markovian time-convolutionless master equations
http://hdl.handle.net/11368/2965928
Title: Recursive approach for non-Markovian time-convolutionless master equations
Abstract: We consider a general open system dynamics and we provide a recursive method to derive the associated non-Markovian master equation in a perturbative series. The approach relies on a momenta expansion of the open system evolution. Unlike previous perturbative approaches of this kind, the method presented in this paper provides a recursive definition of each perturbative term. Furthermore, we give an intuitive diagrammatic description of each term of the series, which provides a useful analytical tool to build them and to derive their structure in terms of commutators and anticommutators. We eventually apply our formalism to the evolution of the observables of the reduced system, by showing how the method can be applied to the adjoint master equation, and by developing a diagrammatic description of the associated series.Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/11368/29659282018-01-01T00:00:00ZErratum: Exact non-Markovian master equation for the spin-boson and Jaynes-Cummings models (Physical Review A (2017) 95 (020101(R)) DOI: 10.1103/PhysRevA.95.020101)
http://hdl.handle.net/11368/2965930
Title: Erratum: Exact non-Markovian master equation for the spin-boson and Jaynes-Cummings models (Physical Review A (2017) 95 (020101(R)) DOI: 10.1103/PhysRevA.95.020101)
Abstract: n/aSun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/11368/29659302017-01-01T00:00:00ZMetformin and aspirin treatment could lead to an improved survival rate for Type 2 diabetic patients with stage II and III colorectal adenocarcinoma relative to non-diabetic patients
http://hdl.handle.net/11368/2965749
Title: Metformin and aspirin treatment could lead to an improved survival rate for Type 2 diabetic patients with stage II and III colorectal adenocarcinoma relative to non-diabetic patients
Abstract: Metformin, the drug of choice in the treatment of type 2 diabetes mellitus (DM2), in addition to aspirin (ASA), the drug prescribed for cardioprotection of diabetic and non‐diabetic patients, have an inhibitory effect on cancer cell survival. The present population‐based study conducted in the province of Trieste (Italy), aimed to investigate the prevalence of DM2 in patients with colorectal adenocarcinoma (CRC) and survival for CRC in diabetic and nondiabetic patients. All permanent residents diagnosed with a CRC between 2004 and 2007 were ascertained through the regional health informa‐ tion system. CRC‐speci c and relative survival probabilities were computed for each group of patients de ned by CRC stage, presence or absence of DM2 treated with metformin, and presence or absence of daily ASA therapy. A total of 515 CRC patients without DM2 and 156 with DM2 treated with metformin were enrolled in the study. At the time of CRC diagnosis, 71 (14%) nondiabetic and 39 (25%) diabetic patients were taking ASA daily. The five‐year relative survival for stage III CRC was 101% [95% con dence interval (CI)=76‐126] in the 18 patients with DM2 treated with metformin and ASA, 55% (95% CI=31‐78) in the 23 without DM2 treated with ASA, 55% (95% CI=45‐65) in the 150 without DM2 not taking ASA, and 29% (95% CI=13‐45) in the 43 with DM2 treated with metformin, however not with ASA. The ndings support the hypothesis of a possible inhibitory effect of metformin and ASA on CRC cells. Randomized controlled trials are required to verify this hypothesis.Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/11368/29657492018-01-01T00:00:00Z