Game Theoretical Methods in Nonlinear PDEs

Nonlinear PDEs, mean value properties, and stochastic differential games are intrinsically connected. In this short expository note, we will describe how the solutions to certain PDEs (of $p$-Laplacian type) can be interpreted as limits of values of a specific Tug-of-War game, when the step-size $\epsilon$ determining the allowed length of move of a token, decreases to $0$.Comment: to appear in Bollettino dell'Unione Matematica Italian

On the existence of traveling waves in the 3D Boussinesq system

We extend earlier work on traveling waves in premixed flames in a gravitationally stratified medium, subject to the Boussinesq approximation. For three-dimensional channels not aligned with the gravity direction and under the Dirichlet boundary conditions in the fluid velocity, it is shown that a non-planar traveling wave, corresponding to a non-zero reaction, exists, under an explicit condition relating the geometry of the crossection of the channel to the magnitude of the Prandtl and Rayleigh numbers, or when the advection term in the flow equations is neglected.Comment: 15 pages, to appear in Communications in Mathematical Physic

A case of multiple abnormalities of the azygos venous system: a praeaortic interazygos vein

The posterior thoracic wall, an area drained by the azygos venous system, is a common site for surgical intervention. Since the venous part of the cardiovascular system is subject to most common variation, abnormalities in the azygos venous system are often reported. Some of the anatomical variants have significant clinical implications for computed tomography image assessment and mediastinal surgery. During dissection of the posterior mediastinum in a 76 year-old Caucasian male cadaver we found a rare variation in the azygos venous system. The hemiazygos vein drained the left 9th to 11th left posterior intercostal veins. While passing ventrally to the aorta at the level of the body of the eighth thoracic vertebra it was joined by two separate vessels found to be the continuations of the 7th and 8th left posterior intercostal veins. The resultant dilated vessel, termed the "interazygos vein", then opened into the azygos vein on the right side of the vertebral column. Variation in the azygos venous system has often been reported, but the abnormality observed by us appears to be extremely rare. The interazygos vein passing ventrally to the aorta may mimic enlarged lymph nodes and cause misinterpretation of a computed tomography image or, if accidentally damaged during mediastinal surgery, may lead to intraoperative haemorrhage. To the best of our knowledge this report provides new data of potential clinical significance

On the variational limits of lattice energies on prestrained elastic bodies

We study the asymptotic behaviour of the discrete elastic energies in presence of the prestrain metric $G$, assigned on the continuum reference configuration $\Omega$. When the mesh size of the discrete lattice in $\Omega$ goes to zero, we obtain the variational bounds on the limiting (in the sense of $\Gamma$-limit) energy. In case of the nearest-neighbour and next-to-nearest-neibghour interactions, we derive a precise asymptotic formula, and compare it with the non-Euclidean model energy relative to $G$

Existence and stability of viscoelastic shock profiles

We investigate existence and stability of viscoelastic shock profiles for a class of planar models including the incompressible shear case studied by Antman and Malek-Madani. We establish that the resulting equations fall into the class of symmetrizable hyperbolic--parabolic systems, hence spectral stability implies linearized and nonlinear stability with sharp rates of decay. The new contributions are treatment of the compressible case, formulation of a rigorous nonlinear stability theory, including verification of stability of small-amplitude Lax shocks, and the systematic incorporation in our investigations of numerical Evans function computations determining stability of large-amplitude and or nonclassical type shock profiles.Comment: 43 pages, 12 figure

Psychosocial outcomes of three triage methods for the management of borderline abnormal cervical smears: an open randomised trial

Objective To assess which of three triage strategies for women with borderline abnormal cervical smear results in the best psychosocial outcomes

Why place matters in residential care: the mediating role of place attachment in the relation between adolescents’ rights and psychological well-being

Little evidence exists on the relationship between rights’ perceptions and well-being outcomes during the adolescence, and particularly in care, as well as on the mediating role of place attachment. Young people in residential care are psychologically and socially vulnerable, showing greater difficulties than their peers do in the family. Youth’s rights fulfilment in residential care may positively affect their psychological functioning together with positive attachments to this place. A sample of 365 adolescents in residential care settings (M = 14.71, SD = 1.81) completed a set of self-reported measures, specifically, the Rights perceptions scale, the Place attachment scale and Scales of psychological well-being. Results revealed significant mediating effects of place attachment (Global scale and subscales of Friends Bonding and Place Dependence) on the relationship between Participation and Protection rights in residential care and Psychological well-being (Positive Relations with others, Personal Growth and Self-Acceptance). The positive role of rights fulfilment in residential care, specifically participation opportunities, as well as the role of youth’s attachment to the care setting are discussed based on previous evidence and theoretical assumptions. A set of practical implications is described.info:eu-repo/semantics/acceptedVersio

Measurement of psychological entitlement in 28 countries

This article presents the cross-cultural validation of the Entitlement Attitudes Questionnaire, a tool designed to measure three facets of psychological entitlement: active, passive, and revenge entitlement. Active entitlement was defined as the tendency to protect individual rights based on self-worthiness. Passive entitlement was defined as the belief in obligations to and expectations toward other people and institutions for the fulfillment of the individual’s needs. Revenge entitlement was defined as the tendency to protect one’s individual rights when violated by others and the tendency to reciprocate insults. The 15-item EAQ was validated in a series of three studies: the first one on a general Polish sample (N = 1,900), the second one on a sample of Polish students (N = 199), and the third one on student samples from 28 countries (N = 5,979). A three-factor solution was confirmed across all samples. Examination of measurement equivalence indicated partial metric invariance of EAQ for all national samples. Discriminant and convergent validity of the EAQ was also confirmed

Relative entropy and the stability of shocks and contact discontinuities for systems of conservation laws with non BV perturbations

We develop a theory based on relative entropy to show the uniqueness and L^2 stability (up to a translation) of extremal entropic Rankine-Hugoniot discontinuities for systems of conservation laws (typically 1-shocks, n-shocks, 1-contact discontinuities and n-contact discontinuities of large amplitude) among bounded entropic weak solutions having an additional trace property. The existence of a convex entropy is needed. No BV estimate is needed on the weak solutions considered. The theory holds without smallness condition. The assumptions are quite general. For instance, strict hyperbolicity is not needed globally. For fluid mechanics, the theory handles solutions with vacuum.Comment: 29 page