A5004451209- Nonlinear Partial Differential Equations
- Geometric Analysis and Curvature Flows
- Advanced Mathematical Modeling in Engineering
- Spectral Theory in Mathematical Physics
- Advanced Harmonic Analysis Research
- Advanced Topics in Algebra
- Advanced Mathematical Physics Problems
- Numerical methods in inverse problems
- Geometry and complex manifolds
- advanced mathematical theories
- Algebraic structures and combinatorial models
- Mathematics and Applications
- Stability and Controllability of Differential Equations
- Nonlinear Waves and Solitons
- semigroups and automata theory
- Homotopy and Cohomology in Algebraic Topology
- Numerical methods for differential equations
- Advanced Differential Equations and Dynamical Systems
- Functional Equations Stability Results
- Point processes and geometric inequalities
- Cardiovascular Health and Disease Prevention
- Quantum chaos and dynamical systems
- Stochastic processes and financial applications
- Differential Equations and Boundary Problems
- Algebraic and Geometric Analysis
University of Bologna
2014-2023
Policlinico S.Orsola-Malpighi
2014-2017
Technion – Israel Institute of Technology
2015
Small changes of bilirubin and liver enzymes are often detected during the acute phase stroke, but their origin significance still poorly understood.On days 0, 3, 7, 14 after admission, 180 patients with ischemic stroke underwent serial determinations bilirubin, GOT, GPT, γGT, alkaline phosphatase, C-reactive protein (CRP) complete blood count. On 0 7 common bile duct diameter was measured by ultrasound, on day 3 cerebral infarct volume (IV) calculated from CT scan slices.During first week...
In this paper, we are concerned with existence, qualitative properties, and uniform Gaussian estimates of the global fundamental solutions a family heat operators on Carnot groups. As byproduct, obtain existence uniqueness theorems Thychonov type for Cauchy problem. Our effort here is also to provide simple direct proofs relying few basic tools such as invariant Harnack inequalities maximum principles. our study, thoroughly exploit some structural properties groups pointed out in previous paper [4].
A reduced prevalence of cardiovascular diseases has been reported in liver cirrhosis. However, studies focusing on supraortic district cirrhotic patients are lacking.By ultrasound duplex scanning, the presence and severity atherosclerotic plaques flow pattern abnormalities were assessed carotid vertebral arteries 118 cirrhotics aged 60.7 +/- 12.8 (1 standard deviation) years, 236 controls matched with according to age, sex cigarette smoking.Previous ischemic strokes significantly less...
In this paper we furnish mean value characterizations for subharmonic functions related to linear second order partial differential operators with nonnegative characteristic form, possessing a well-behaved fundamental solution \Gamma . These are based on suitable average the level sets of Asymptotic also considered, extending classical results Blaschke, Privaloff, Radó, Beckenbach, Reade and Saks. We analyze as well notion function in weak sense distributions, show how approximate by smooth...
We construct the fundamental solutions<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Gamma"><mml:semantics><mml:mi mathvariant="normal">Γ</mml:mi><mml:annotation encoding="application/x-tex">\Gamma</mml:annotation></mml:semantics></mml:math></inline-formula>and<inline-formula alttext="gamma"><mml:semantics><mml:mi>γ</mml:mi><mml:annotation...
If $\mathcal{L}=\sum_{j=1}^m X_j^2+X_0$ is a Hörmander partial differential operator in $\mathbb{R}^N$, we give sufficient conditions on the $X_j$'s for existence of Lie group structure $\mathbb{G}=(\mathbb{R}^N,*)$, not necessarily nilpotent, such that $\mathcal{L}$ left invariant $\mathbb{G}$. We also investigate global fundamental solution $\Gamma$ $\mathcal{L}$, providing results ensuring suitable invariance property $\Gamma$. Examples are given operators to which our apply: some new,...
We prove lower bounds for the fundamental solutions of non-divergence form operators<disp-formula content-type="math/mathml">\[<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma-summation Underscript i comma j Endscripts a Subscript Baseline left-parenthesis x t right-parenthesis upper X minus partial-differential and sigma-summation comma"><mml:semantics><mml:mrow><mml:mrow class="MJX-TeXAtom-ORD"><mml:mstyle displaystyle="false"...
The aim of this paper is to study some classes second-order divergence-form partial differential operators ℒ sub-Riemannian type. Our main assumption the C∞-hypoellipticity ℒ, together with existence a well-behaved fundamental solution Γ(x, y) for ℒ. We consider mean-integral operator Mr naturally associated mean-value theorem ℒ-harmonic functions and we investigate following topics: positivity set kernel Mr; role in solving homogeneous Dirichlet problem related Perron–Wiener–Brelot sense;...
We study convexity properties of the average integral operators naturally associated with divergence-form second-order subelliptic ᏸ nonnegative characteristic form.When is classical Laplace operator, these are usual integrals over Euclidean spheres.In our setting, (weighted) level sets ∂ r (x) = {y : (x, y) 1/r } fundamental solution ᏸ.We shall obtain characterizations ᏸ-subharmonic functions u (that is, weak solutions to -ᏸu ≤ 0) in terms (w.r.t. a power ) (x), as function radius .Solid...
Objectives The ultrasound investigation of carotid and vertebral arteries is routinely performed in stroke patients to determine the etiopathogenetic classification possible need revascularization. However, medium long-term prognostic implications ischemic are not yet known. Methods This study included 309 (mean age 76.3; 160 men). They all had undergone (carotid stenoses were measured according European Carotid Surgery Trial [ECST] method). After a median interval 9.4 months, telephone...