Existence and Uniqueness results for linear second-order equations in the Heisenberg group

In this manuscript, we prove uniqueness and existence results of viscosity solutions for a class of linear second-order equations in the Heisenberg group. We state uniqueness by proving a comparison result to our class of equations, and existence via an application of Perron’s method adapted to our framework. We also provide the explicit construction of the appropriate sub- and supersolutions employed by Perron’s method for a variety of domains in the Heisenberg group.Fil: Ochoa, Pablo Daniel. Universidad Nacional de Cuyo. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Ruiz, Julio Alejo. Universidad Nacional de Cuyo. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Existence and multiplicity of solutions to magnetic Kirchhoff equations in Orlicz-Sobolev spaces

In this paper, we study the existence and multiplicity of weak solutions to a general type of Kirchhoff equations in magnetic fractional Orlicz-Sobolev spaces. Specifically, we appeal to Critical Point Theory to prove the existence of non-trivial solutions under the so-called Ambrosetti-Rabinowitz condition. We also state the existence of ground-state solutions. Moreover, multiplicity results which yield the existence of an unbounded sequence of solutions are also provided. Finally, we show existence under a weak-type Ambrosetti-Rabinowitz condition formulated in the framework of Orlicz spaces

Mexican American Parents of Elementary Students and Literacy Engagement: A Case Study of a Bilingual (Spanish/English) Parent Book Club Using Children\u27s Literature

This qualitative case study explored what occurred when seven Latinx parents and a bilingual coordinator engaged in a book club using the same historical fiction text as the school\u27s fifth grade classroom. Research questions focused on Book Club participation, connections to the focal text(s), and new learning. Data included audiotapes of the sessions, parent written/artistic artifacts, participant interviews, retrospective field notes, and reflective journal entries. Study findings suggest that positive partnerships between schools and parents can occur within familial text engagement opportunities built on existing relationships with school personnel; use of relevant literature, literacy activities that allow for parent choice and voice, drawing on cultural Funds of Knowledge and life experiences, the autonomy to ask questions and make inferences and connections, and facilitate learning for one another. Finally, the study improved perceptions that parents could better assist their children in learning due to new learning in literacy instruction and reading

Equivalence of solutions for non-homogeneous p(x)-Laplace equationsy

We establish the equivalence between weak and viscosity solutions for non-homogeneous p(x)-Laplace equations with a right-hand side term depending on the spatial variable, the unknown, and its gradient. We employ inf- and sup-convolution techniques to state that viscosity solutions are also weak solutions, and comparison principles to prove the converse. The new aspects of the p(x)- Laplacian compared to the constant case are the presence of log-terms and the lack of the invariance under translations.Fil: Medina, Maria. Universidad Autónoma de Madrid; EspañaFil: Ochoa, Pablo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina. Universidad Nacional de Cuyo. Facultad de Ingeniería; Argentin

Natural History of MYH7-Related Dilated Cardiomyopathy.

Background Variants in myosin heavy chain 7 (MYH7) are responsible for disease in 1% to 5% of patients with dilated cardiomyopathy (DCM); however, the clinical characteristics and natural history of MYH7-related DCM are poorly described. Objectives We sought to determine the phenotype and prognosis of MYH7-related DCM. We also evaluated the influence of variant location on phenotypic expression. Methods We studied clinical data from 147 individuals with DCM-causing MYH7 variants (47.6% female; 35.6 ± 19.2 years) recruited from 29 international centers. Results At initial evaluation, 106 (72.1%) patients had DCM (left ventricular ejection fraction: 34.5% ± 11.7%). Median follow-up was 4.5 years (IQR: 1.7-8.0 years), and 23.7% of carriers who were initially phenotype-negative developed DCM. Phenotypic expression by 40 and 60 years was 46% and 88%, respectively, with 18 patients (16%) first diagnosed at <18 years of age. Thirty-six percent of patients with DCM met imaging criteria for LV noncompaction. During follow-up, 28% showed left ventricular reverse remodeling. Incidence of adverse cardiac events among patients with DCM at 5 years was 11.6%, with 5 (4.6%) deaths caused by end-stage heart failure (ESHF) and 5 patients (4.6%) requiring heart transplantation. The major ventricular arrhythmia rate was low (1.0% and 2.1% at 5 years in patients with DCM and in those with LVEF of ≤35%, respectively). ESHF and major ventricular arrhythmia were significantly lower compared with LMNA-related DCM and similar to DCM caused by TTN truncating variants. Conclusions MYH7-related DCM is characterized by early age of onset, high phenotypic expression, low left ventricular reverse remodeling, and frequent progression to ESHF. Heart failure complications predominate over ventricular arrhythmias, which are rare.pre-print1333 K

Clinical Risk Score to Predict Pathogenic Genotypes in Patients With Dilated Cardiomyopathy.

Background Although genotyping allows family screening and influences risk-stratification in patients with nonischemic dilated cardiomyopathy (DCM) or isolated left ventricular systolic dysfunction (LVSD), its result is negative in a significant number of patients, limiting its widespread adoption. Objectives This study sought to develop and externally validate a score that predicts the probability for a positive genetic test result (G+) in DCM/LVSD. Methods Clinical, electrocardiogram, and echocardiographic variables were collected in 1,015 genotyped patients from Spain with DCM/LVSD. Multivariable logistic regression analysis was used to identify variables independently predicting G+, which were summed to create the Madrid Genotype Score. The external validation sample comprised 1,097 genotyped patients from the Maastricht and Trieste registries. Results A G+ result was found in 377 (37%) and 289 (26%) patients from the derivation and validation cohorts, respectively. Independent predictors of a G+ result in the derivation cohort were: family history of DCM (OR: 2.29; 95% CI: 1.73-3.04; P < 0.001), low electrocardiogram voltage in peripheral leads (OR: 3.61; 95% CI: 2.38-5.49; P < 0.001), skeletal myopathy (OR: 3.42; 95% CI: 1.60-7.31; P = 0.001), absence of hypertension (OR: 2.28; 95% CI: 1.67-3.13; P < 0.001), and absence of left bundle branch block (OR: 3.58; 95% CI: 2.57-5.01; P < 0.001). A score containing these factors predicted a G+ result, ranging from 3% when all predictors were absent to 79% when ≥4 predictors were present. Internal validation provided a C-statistic of 0.74 (95% CI: 0.71-0.77) and a calibration slope of 0.94 (95% CI: 0.80-1.10). The C-statistic in the external validation cohort was 0.74 (95% CI: 0.71-0.78). Conclusions The Madrid Genotype Score is an accurate tool to predict a G+ result in DCM/LVSD.post-print1456 K

Phenotype and clinical outcomes of Glu89Lys hereditary transthyretin amyloidosis: a new endemic variant in Spain.

Background The p.Glu109Lys variant (Glu89Lys) is a rare cause of hereditary transthyretin amyloidosis (ATTRv) for which clinical spectrum remains unresolved. We sought to describe the clinical characteristics and outcomes of ATTR Glu89Lys amyloidosis and assess a potential founder effect in Spain. Methods Patients with the p.Glu109Lys ATTRv variant from 14 families were recruited at 7 centres. Demographics, complementary tests and clinical course were analysed. Haplotype analysis was performed in 7 unrelated individuals. Results Thirty-eight individuals (13 probands, mean age 40.4 ± 13.1 years) were studied. After median follow-up of 5.1 years (IQR 1.7–9.6), 7 patients died and 7 required heart transplantation (median age at transplantation 50.5 years). Onset of cardiac and neurological manifestations occurred at a mean age of 48.4 and 46.8 years, respectively. Median survival from birth was 61.6 years and no individual survived beyond 65 years. Patients treated with disease-modifying therapies exhibited better prognosis (p < 0.001). Haplotype analysis revealed a common origin from an ancestor who lived ∼500 years ago in southeast Spain. Conclusions Glu89Lys ATTRv is a TTR variant with a founder effect in Spain. It is associated with near complete penetrance, early onset and mixed cardiac and neurologic phenotype. Patients have poor prognosis, particularly if not treated with disease-modifying therapies.post-print2555 K