An improved geometric inequality via vanishing moments, with applications to singular Liouville equations

We consider a class of singular Liouville equations on compact surfaces motivated by the study of Electroweak and Self-Dual Chern-Simons theories, the Gaussian curvature prescription with conical singularities and Onsager's description of turbulence. We analyse the problem of existence variationally, and show how the angular distribution of the conformal volume near the singularities may lead to improvements in the Moser-Trudinger inequality, and in turn to lower bounds on the Euler-Lagrange functional. We then discuss existence and non-existence results.Comment: some references adde

New improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces

We consider a singular Liouville equation on a compact surface, arising from the study of Chern-Simons vortices in a self dual regime. Using new improved versions of the Moser-Trudinger inequalities (whose main feature is to be scaling invariant) and a variational scheme, we prove new existence results.Comment: to appear in GAF

The Liouville Equation with Singular Data: A Concentration-Compactness Principle via a Local Representation Formula

AbstractFor a bounded domain Ω⊂R2, we establish a concentration-compactness result for the following class of “singular” Liouville equations:−Δu=eu−4π∑j=1mαjδpj in Ω where pj∈Ω, αj>0 and δpj denotes the Dirac measure with pole at point pj, j=1,…,m. Our result extends Brezis–Merle's theorem (Comm. Partial Differential Equations16 (1991) 1223–1253) concerning solution sequences for the “regular” Liouville equation, where the Dirac measures are replaced by Lp(Ω)-data p>1. In some particular case, we also derive a mass-quantization principle in the same spirit of Li–Shafrir (Indiana Univ. Math. J.43 (1994) 1255–1270). Our analysis was motivated by the study of the Bogomol'nyi equations arising in several self-dual gauge field theories of interest in theoretical physics, such as the Chern–Simons theory (“Self-dual Chern–Simons Theories” Lecture Notes in Physics, Vol. 36, Springer-Verlag, Berlin, 1995) and the Electroweak theory (“Selected Papers on Gauge Theory of Weak and Electromagnetic Interactions,” World Scientific, Singapore)

Primary-school class composition and the development of social capital

We study the development of social capital through adult civic engagement, in relation to social capital exposure having occurred during childhood based on experiences outside the family at primary school. We assume that the types of classmates in attendance at a child's school would have influenced her/his social capital. To identify the types of classmates, we take advantage of the heterogeneity in the ability levels of British primary-school classes during the 1960s. At that time, some schools were practicing a method of streaming, whereas others were not. Using British National Child Development data, we construct a single score of civic engagement and evaluate the effect on adult civic engagement of attending homogeneous-ability classes versus nonhomogeneous-ability classes and being in high-, average- or low-ability classes when enrolled in streamed schools. Our results show that children who were grouped in homogeneous-ability classes developed a lower interest in civic engagement than their peers who attended mixed-ability classes (nonstreamed schools). Moreover, among children who attended streamed schools, a lower attitude toward civic engagement was observed among low-ability students. Thus, streaming appears to be detrimental to social capital development, especially for low-ability individuals

LANDSAT-4/5 image data quality analysis

A LANDSAT Thematic Mapper (TM) quality evaluation study was conducted to identify geometric and radiometric sensor errors in the post-launch environment. The study began with the launch of LANDSAT-4. Several error conditions were found, including band-to-band misregistration and detector-to detector radiometric calibration errors. Similar analysis was made for the LANDSAT-5 Thematic Mapper and compared with results for LANDSAT-4. Remaining band-to-band misregistration was found to be within tolerances and detector-to-detector calibration errors were not severe. More coherent noise signals were observed in TM-5 than in TM-4, although the amplitude was generally less. The scan direction differences observed in TM-4 were still evident in TM-5. The largest effect was in Band 4 where nearly a one digital count difference was observed. Resolution estimation was carried out using roads in TM-5 for the primary focal plane bands rather than field edges as in TM-4. Estimates using roads gave better resolution. Thermal IR band calibration studies were conducted and new nonlinear calibration procedures were defined for TM-5. The overall conclusion is that there are no first order errors in TM-5 and any remaining problems are second or third order

Semilinear equations with exponential nonlinearity and measure data

We study the existence and non-existence of solutions of the problem [GRAPHICS] where Omega is a bounded domain in R-N, N >=, 3, and it is a Radon measure. We prove that if it 4 pi HN-2, then (0.1) has a unique solution. We also show that the constant 4 pi in this condition cannot be improved. (c) 2005 Elsevier SAS. All rights reserved

Precision Anti-Cancer Medicines by Oligonucleotide Therapeutics in Clinical Research Targeting Undruggable Proteins and Non-Coding RNAs

Cancer incidence and mortality continue to increase, while the conventional chemotherapeutic drugs confer limited efficacy and relevant toxic side effects. Novel strategies are urgently needed for more effective and safe therapeutics in oncology. However, a large number of proteins are considered undruggable by conventional drugs, such as the small molecules. Moreover, the mRNA itself retains oncological functions, and its targeting offers the double advantage of blocking the tumorigenic activities of the mRNA and the translation into protein. Finally, a large family of non-coding RNAs (ncRNAs) has recently emerged that are also dysregulated in cancer, but they could not be targeted by drugs directed against the proteins. In this context, this review describes how the oligonucleotide therapeutics targeting RNA or DNA sequences, are emerging as a new class of drugs, able to tackle the limitations described above. Numerous clinical trials are evaluating oligonucleotides for tumor treatment, and in the next few years some of them are expected to reach the market. We describe the oligonucleotide therapeutics targeting undruggable proteins (focusing on the most relevant, such as those originating from the MYC and RAS gene families), and for ncRNAs, in particular on those that are under clinical trial evaluation in oncology. We highlight the challenges and solutions for the clinical success of oligonucleotide therapeutics, with particular emphasis on the peculiar challenges that render it arduous to treat tumors, such as heterogeneity and the high mutation rate. In the review are presented these and other advantages offered by the oligonucleotide as an emerging class of biotherapeutics for a new era of precision anti-cancer medicine

A singular Sphere Covering Inequality: uniqueness and symmetry of solutions to singular Liouville-type equations

We derive a singular version of the Sphere Covering Inequality which was recently introduced in Gui and Moradifam (Invent Math. https://doi.org/10.1007/s00222-018- 0820-2, 2018) suitable for treating singular Liouville-type problems with superharmonic weights. As an application we deduce newuniqueness results for solutions of the singular mean field equation both on spheres and on bounded domains, as well as new self-contained proofs of previously known results, such as the uniqueness of spherical convex polytopes first established in Luo and Tian (Proc Am Math Soc 116(4):1119– 1129, 1992). Furthermore, we derive new symmetry results for the spherical Onsager vortex equation

Existence of Multistring Solutions of the Self-Gravitating Massive W−W-Boson

We consider a semilinear elliptic system which include the model system of the $W-$strings in the cosmology as a special case. We prove existence of multi-string solutions and obtain precise asymptotic decay estimates near infinity for the solutions. As a special case of this result we solve an open problem posed in \cite{yan}Comment: 12 page

MYCN Impact on High-Risk Neuroblastoma: From Diagnosis and Prognosis to Targeted Treatment

Simple Summary Neuroblastoma is one of the most diffuse and the deadliest cancer in children. While many advances have been made in the last few decades to improve patients' outcome, high-risk neuroblastoma (HR-NB) still shows a very aggressive pattern of development and poor prognosis, with only a 50% chance of 5-year survival. Moreover, while many factors contribute to defining the high-risk condition, MYCN status is well established as the major element in pathology disclosure. The aim of this review is to describe the current knowledge in the diagnosis, prognosis and therapeutic approaches of HR-NB, particularly in relation to MYCN. The review highlights how MYCN influences the HR-NB scenario and the new therapeutic approaches that are currently proposed to target it, in consideration of MYCN as a highly relevant target for HR-NB patient management. Among childhood cancers, neuroblastoma is the most diffuse solid tumor and the deadliest in children. While to date, the pathology has become progressively manageable with a significant increase in 5-year survival for its less aggressive form, high-risk neuroblastoma (HR-NB) remains a major issue with poor outcome and little survivability of patients. The staging system has also been improved to better fit patient needs and to administer therapies in a more focused manner in consideration of pathology features. New and improved therapies have been developed; nevertheless, low efficacy and high toxicity remain a staple feature of current high-risk neuroblastoma treatment. For this reason, more specific procedures are required, and new therapeutic targets are also needed for a precise medicine approach. In this scenario, MYCN is certainly one of the most interesting targets. Indeed, MYCN is one of the most relevant hallmarks of HR-NB, and many studies has been carried out in recent years to discover potent and specific inhibitors to block its activities and any related oncogenic function. N-Myc protein has been considered an undruggable target for a long time. Thus, many new indirect and direct approaches have been discovered and preclinically evaluated for the interaction with MYCN and its pathways; a few of the most promising approaches are nearing clinical application for the investigation in HR-NB