Let Ωi, Ωo be bounded open connected subsets of
ℝn that contain the origin. Let
Ω(ϵ)≡Ωo\ϵΩi‾ for small ϵ > 0. Then, we consider a linear transmission problem for the Helmholtz equation in the pair ...of domains ϵΩi and Ω(ϵ) with Neumann boundary conditions on ∂Ωo. Under appropriate conditions on the wave numbers in ϵΩi and Ω(ϵ) and on the parameters involved in the transmission conditions on ϵ∂Ωi, the transmission problem has a unique solution (ui(ϵ, ·), uo(ϵ, ·)) for small values of ϵ > 0. Here, ui(ϵ, ·) and uo(ϵ, ·) solve the Helmholtz equation in ϵΩi and Ω(ϵ), respectively. Then, we prove that if x ∈ Ωo \ {0}, then uo(ϵ, x) can be expanded into a convergent power expansion of ϵ,
κnϵlogϵ,δ2,nlog−1ϵ for ϵ small enough. Here,
κn=1 if n is even and
κn=0 if n is odd, and δ2, 2 ≡ 1 and δ2, n ≡ 0 if n ≥ 3.
We prove the validity of regularizing properties of the boundary integral operator corresponding to the double layer potential associated to the fundamental solution of a
nonhomogeneous
second order ...elliptic differential operator with constant coefficients in Hölder spaces by exploiting an estimate on the maximal function of the tangential gradient with respect to the first variable of the kernel of the double layer potential and by exploiting specific imbedding and multiplication properties in certain classes of kernels of integral operators and a generalization of a result for integral operators on differentiable manifolds.
We prove that a condition of boundedness of the maximal function of a singular integral operator, that is known to be sufficient for the continuity of a corresponding integral operator in Hölder ...spaces, is actually also necessary in case the action of the integral operator does not decrease the regularity of a function. We do so in the frame of metric measured spaces with a measure satisfying certain growth conditions that include nondoubling measures. Then we present an application to the case of an integral operator defined on a compact differentiable manifold.
Let α ∈ 0 , 1 . Let Ω o be a bounded open domain of R n of class C 1 , α . Let ν Ω o denote the outward unit normal to ∂ Ω o . We assume that the Steklov problem Δ u = 0 in Ω o , ∂ u ∂ ν Ω o = λ u ...on ∂ Ω o has a multiple eigenvalue λ ˜ of multiplicity r. Then we consider an annular domain Ω ( ϵ ) obtained by removing from Ω o a small cavity of class C 1 , α and size ϵ > 0, and we show that under appropriate assumptions each elementary symmetric function of r eigenvalues of the Steklov problem Δ u = 0 in Ω ( ϵ ), ∂ u ∂ ν Ω ( ϵ ) = λ u on ∂ Ω ( ϵ ) which converge to λ ˜ as ϵ tend to zero, equals real a analytic function defined in an open neighborhood of ( 0 , 0 ) in R 2 and computed at the point ( ϵ , δ 2 , n ϵ log ϵ ) for ϵ > 0 small enough. Here ν Ω ( ϵ ) denotes the outward unit normal to ∂ Ω ( ϵ ), and δ 2 , 2 ≡ 1 and δ 2 , n ≡ 0 if n ⩾ 3. Such a result is an extension to multiple eigenvalues of a previous result obtained for simple eigenvalues in collaboration with S. Gryshchuk.
Background
Nutritional derangements are common hallmarks of pancreatic cancer (PC). Their early detection and management are usually overlooked in routine practice. This study aimed to explore ...preoperative nutritional status and its prognostic value in patients undergoing surgery for PC.
Methods
Data from 73 patients who underwent surgery for PC from November 2015 to January 2018 at the General and Pancreatic Surgery Unit, The Pancreas Institute, University Hospital of Verona Hospital, Verona, Italy, were retrospectively evaluated. The Nutritional Risk Screening (NRS)-2002 was used to evaluate the preoperative nutritional risk. Body composition was assessed using bioimpedance vectorial analysis (BIVA) on the day prior to surgery. The effect of clinical, pathological, and nutritional characteristics on overall survival (OS) was investigated using a Cox and logistic regression model. Kaplan–Meier curves were compared using the log-rank test.
Results
Most patients (80.8%) were at preoperative risk of malnutrition (NRS-2002 ≥ 3) despite a mean BMI of 24.1 kg/m
2
(± 4.3). Twenty-four patients (32.9%) received neoadjuvant therapy prior to surgery. Preoperative NRS-2002 was significantly higher in this subset of patients (
p
= 0.026), with a significant difference by chemotherapy regimens (in favor of FOLFIRINOX,
p
= 0.035). In a multivariate analysis, the only independent prognostic factor for OS was the NRS-2002 score (HR 5.24,
p
= 0.013). Particularly, the likelihood of 2-year survival was higher in NRS < 3 (
p
= 0.009).
Conclusions
Our analysis confirms that preoperative malnutrition has a detrimental impact on OS in PC patients undergoing radical surgery for PC. Careful preoperative nutritional evaluation of PC patients should be mandatory, especially in those who are candidates for neoadjuvant therapy.
Introduction:
Although the literature supports the importance of physical activity in the oncological context, in Italy a large number of patients are not sufficiently active.
Methods:
The present ...study aimed to explore factors influencing an active lifestyle in cancer patients during oncological treatments. Semi-structured focus groups, including 18 patients with different cancer types, were conducted at the Oncology Unit in the University Hospital Trust of Verona (Italy). The interviews were audio-recorded, transcribed verbatim, and analyzed with content analysis.
Results:
According to the Health Belief Model, transcripts were categorized into the following themes: benefits, barriers, and cues to action. Patients reported a series of physical, physiological, and psychological benefits deriving from an active lifestyle. The main barriers hampering the physical activity participation were represented by treatment-related side effects, advanced disease, and some medical procedures, for example, ileostomy. Several strategies that can trigger patients to exercise were identified. Medical advice, social support from family and friends, features such as enjoyment, setting goals, and owning an animal can motivate patients to perform physical activity. At the same time, an individualized program based on patients’ characteristics, an available physical activity specialist to consult, more detailed information regarding physical activity in the oncological setting, and having accessible structures were found important facilitators to implementing active behavior.
Conclusions:
Overall, patients have a positive view regarding physical activity, and a variety of obstacles and cues to action were recognized. Considering this information may help to improve adherence to a physical activity program over time, consequently increasing the expected benefits.
We consider a nonlinear integral operator which involves a Nemytskij type operator and which appears in the applications as a pull-back of layer potential operators. We prove an analyticity result in ...Schauder spaces by splitting the operator into the composition of a nonlinear operator acting into Roumieu classes and a composition operator.
Nowadays, it is widely acknowledged that low physical activity levels are associated with an increase in terms of both disease recurrence and mortality in cancer survivors. In this light, deciphering ...those factors able to hamper or facilitate an active lifestyle is crucial in order to increase patients' adherence to physical activity. The purpose of this study was to explore barriers and motivations in a sample of female oncological patients, practising running using the ecological model and compare them with healthy controls. Focus group interviews were conducted at Verona University. Participants were 12 female cancer survivors and 7 matched healthy controls who had participated at "Run for Science" project. The interviews were transcribed verbatim and analyzed using content analysis. Transcripts were categorized according to the ecological model, identifying barriers and motivations as themes. About motivations, three sub-themes were included: personal, interpersonal and environmental/organizational factors. Regarding barriers, another sub-theme was recognized: community/policy factors. Compared to healthy controls, survivors expressed motivations and barriers specifically related to their oncological disease. Running was a challenge with their cancer and a hope to give to other patients. Main barriers were represented by treatment-related side effects, inexperienced trainers and external factors, e.g. delivery of incorrect information. Running programs dedicated to oncological patients should consider intrinsic obstacles, related to cancer and its treatment. The interventions should offer a personalized program performed by qualified trainers, together with a motivational approach able to improve participants' adherence to an active lifestyle.
PDF
