On the dependence of the reflection operator on boundary conditions for biharmonic functions

The biharmonic equation arises in areas of continuum mechanics including linear elasticity theory and the Stokes flows, as well as in a radar imaging problem. We discuss the reflection formulas for the biharmonic functions $u(x,y)\in\mathbb{R}^2$ subject to different boundary conditions on a real-analytic curve in the plane. The obtained formulas, generalizing the celebrated Schwarz symmetry principle for harmonic functions, have different structures. In particular, in the special case of the boundary, $\Gamma_0 :=\{y=0\}$, reflections are point to point when the given on $\Gamma_0$ conditions are $u=\partial_nu=0$, $u=\Delta u=0$ or $\partial_nu=\partial n\Delta u=0$, and point to a continuous set when $u=\partial_n\Delta u=0$ or $\partial_nu=\Delta u=0$ on $\Gamma_0$.Comment: 18 page

Integrative Neuropsychological Characteristics of Subcortical-Frontal Brain Regions as a Schizophrenia Liability Factor

Para estudiar las características de las regiones cerebrales subcórtico-frontal, se investigaron la función y la evaluación de su relación con la vulnerabilidad a la esquizofrenia en 59 pacientes y 23 controles, empleando los métodos neuropsicológicos de Luria. El análisis estableció anormalidades bilaterales de la función de las zonas lobulares prefrontal y frontal profunda en pacientes comparados con los controles. Estas anormalidades eran más predominantes en el hemisferio izquierdo. Las coeficientes de correlación punto-biserial de algunos indicadores neuropsicológicos integrativos con la vulnerabilidad a la esquizofrenia eran de 0,39 ± 0,11 y 0,28 ± 0,09, respectivamente. Los datos obtenidos llevan a la discusión de los indicadores neuropsicológicos integrativos de regiones subcortical-frontales del cerebro que se revelan como marcadores potenciales de vulnerabilidad a la esquizofrenia y confirma el papel de la asimetría estructural y funcional del cerebro en la patogénesis de la esquizofrenia.In order to study neuropsychological characteristics of subcortical-frontal brain regions function and assessment of their relation with vulnerability to schizophrenia 59 patients and 23 controls were investigated using Luria’s neuropsychological methods. The analysis established bilateral abnormalities of the function of prefrontal and profound frontal lobe zones in patients as compared with controls. These abnormalities were more predominate in the left hemisphere. Point biserial correlation coefficients of determined integrative neuropsychological indicators with liability to schizophrenia were 0.39 ± 0.11 and 0.28 ± 0.09, for the left and right brain zones respectively. The obtained data permits discussion of the integrative neuropsychological indicators of subcorticalfrontal brain regions as potential markers of liability to schizophrenia and confirms the role of structural and functional brain asymmetry in the pathogenesis of schizophrenia

Defining Kawasaki disease and pediatric inflammatory multisystem syndrome-temporally associated to SARS-CoV-2 infection during SARS-CoV-2 epidemic in Italy: results from a national, multicenter survey

Background: There is mounting evidence on the existence of a Pediatric Inflammatory Multisystem Syndrome-temporally associated to SARS-CoV-2 infection (PIMS-TS), sharing similarities with Kawasaki Disease (KD). The main outcome of the study were to better characterize the clinical features and the treatment response of PIMS-TS and to explore its relationship with KD determining whether KD and PIMS are two distinct entities. Methods: The Rheumatology Study Group of the Italian Pediatric Society launched a survey to enroll patients diagnosed with KD (Kawasaki Disease Group - KDG) or KD-like (Kawacovid Group - KCG) disease between February 1st 2020, and May 31st 2020. Demographic, clinical, laboratory data, treatment information, and patients' outcome were collected in an online anonymized database (RedCAP®). Relationship between clinical presentation and SARS-CoV-2 infection was also taken into account. Moreover, clinical characteristics of KDG during SARS-CoV-2 epidemic (KDG-CoV2) were compared to Kawasaki Disease patients (KDG-Historical) seen in three different Italian tertiary pediatric hospitals (Institute for Maternal and Child Health, IRCCS "Burlo Garofolo", Trieste; AOU Meyer, Florence; IRCCS Istituto Giannina Gaslini, Genoa) from January 1st 2000 to December 31st 2019. Chi square test or exact Fisher test and non-parametric Wilcoxon Mann-Whitney test were used to study differences between two groups. Results: One-hundred-forty-nine cases were enrolled, (96 KDG and 53 KCG). KCG children were significantly older and presented more frequently from gastrointestinal and respiratory involvement. Cardiac involvement was more common in KCG, with 60,4% of patients with myocarditis. 37,8% of patients among KCG presented hypotension/non-cardiogenic shock. Coronary artery abnormalities (CAA) were more common in the KDG. The risk of ICU admission were higher in KCG. Lymphopenia, higher CRP levels, elevated ferritin and troponin-T characterized KCG. KDG received more frequently immunoglobulins (IVIG) and acetylsalicylic acid (ASA) (81,3% vs 66%; p = 0.04 and 71,9% vs 43,4%; p = 0.001 respectively) as KCG more often received glucocorticoids (56,6% vs 14,6%; p < 0.0001). SARS-CoV-2 assay more often resulted positive in KCG than in KDG (75,5% vs 20%; p < 0.0001). Short-term follow data showed minor complications. Comparing KDG with a KD-Historical Italian cohort (598 patients), no statistical difference was found in terms of clinical manifestations and laboratory data. Conclusion: Our study suggests that SARS-CoV-2 infection might determine two distinct inflammatory diseases in children: KD and PIMS-TS. Older age at onset and clinical peculiarities like the occurrence of myocarditis characterize this multi-inflammatory syndrome. Our patients had an optimal response to treatments and a good outcome, with few complications and no deaths

Search for stop and higgsino production using diphoton Higgs boson decays

Results are presented of a search for a "natural" supersymmetry scenario with gauge mediated symmetry breaking. It is assumed that only the supersymmetric partners of the top-quark (stop) and the Higgs boson (higgsino) are accessible. Events are examined in which there are two photons forming a Higgs boson candidate, and at least two b-quark jets. In 19.7 inverse femtobarns of proton-proton collision data at sqrt(s) = 8 TeV, recorded in the CMS experiment, no evidence of a signal is found and lower limits at the 95% confidence level are set, excluding the stop mass below 360 to 410 GeV, depending on the higgsino mass

Search for supersymmetry in events with one lepton and multiple jets in proton-proton collisions at root s=13 TeV

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