Calculus and Fine Properties of Functions of Bounded Variation on RCD Spaces

We generalize the classical calculus rules satisfied by functions of bounded variation to the framework of RCD spaces. In the infinite dimensional setting, we are able to define an analogue of the distributional differential and, on finite dimensional spaces, we prove fine properties and suitable calculus rules, such as the Vol’pert chain rule for vector valued functions

Local vector measures

Consider a BV function on a Riemannian manifold. What is its differential? And what about the Hessian of a convex function? These questions have clear answers in terms of (co)vector/matrix valued measures if the manifold is the Euclidean space. In more general curved contexts, the same objects can be perfectly understood via charts. However, charts are often unavailable in the less regular setting of metric geometry, where still the questions make sense. In this paper we propose a way to deal with this sort of problems and, more generally, to give a meaning to a concept of ‘measure acting in duality with sections of a given bundle’, loosely speaking. Despite the generality, several classical results in measure theory like Riesz's and Alexandrov's theorems have a natural counterpart in this setting. Moreover, as we are going to discuss, the notions introduced here provide a unified framework for several key concepts in nonsmooth analysis that have been introduced more than two decades ago, such as: Ambrosio-Kirchheim's metric currents, Cheeger's Sobolev functions and Miranda's BV functions. Not surprisingly, the understanding of the structure of these objects improves with the regularity of the underlying space. We are particularly interested in the case of RCD spaces where, as we will argue, the regularity of several key measures of the type we study nicely matches the known regularity theory for vector fields, resulting in a very effective theory. We expect that the notions developed here will help creating stronger links between differential calculus in Alexandrov spaces (based on Perelman's DC charts) and in RCD ones (based on intrinsic tensor calculus)

A Note about the Strong Maximum Principle on RCD Spaces

We give a direct proof of the strong maximum principle on finite dimensional RCD spaces based on the Laplacian comparison of the squared distance

Random laser from engineered nanostructures obtained by surface tension driven lithography

The random laser emission from the functionalized thienyl-S,S-dioxide quinquethiophene (T5OCx) in confined patterns with different shapes is demonstrated. Functional patterning of the light emitter organic material in well defined features is obtained by spontaneous molecular self-assembly guided by surface tension driven (STD) lithography. Such controlled supramolecular nano-aggregates act as scattering centers allowing the fabrication of one-component organic lasers with no external resonator and with desired shape and efficiency. Atomic force microscopy shows that different geometric pattern with different supramolecular organization obtained by the lithographic process tailors the coherent emission properties by controlling the distribution and the size of the random scatterers

Role of magnetic resonance imaging in the detection and characterization of solid pancreatic nodules: an update

Pancreatic ductal adenocarcinoma is the most common malignant tumor of the pancreas. The remaining pancreatic tumors are a diverse group of pancreatic neoplasms that comprises cystic pancreatic neoplasms, endocrine tumors and other uncommon pancreatic tumors. Due to the excellent soft tissue contrast resolution, magnetic resonance imaging (MRI) is frequently able to readily separate cystic from noncystic tumors. Cystic tumors are often easy to diagnose with MRI; however, noncystic non-adenocarcinoma tumors may show a wide spectrum of imaging features, which can potentially mimic ductal adenocarcinoma. MRI is a reliable technique for the characterization of pancreatic lesions. The implementation of novel motion-resistant pulse sequences and respiratory gating techniques, as well as the recognized benefits of MR cholangiopancreatography, make MRI a very accurate examination for the evaluation of pancreatic masses. MRI has the distinctive ability of non-invasive assessment of the pancreatic ducts, pancreatic parenchyma, neighbouring soft tissues, and vascular network in one examination. MRI can identify different characteristics of various solid pancreatic lesions, potentially allowing the differentiation of adenocarcinoma from other benign and malignant entities. In this review we describe the MRI protocols and MRI characteristics of various solid pancreatic lesions. Recognition of these characteristics may establish the right diagnosis or at least narrow the differential diagnosis, thus avoiding unnecessary tests or procedures and permitting better management

An attributional Life Cycle Assessment application experience to highlight environmental hotspots in the production of foamy polylactic acid trays for fresh-food packaging usage

Food packaging systems mainly serve to contain and protect foods during their shelf-lives. However, it is well known that a package is responsible for several environmental impacts associated with its entire life-cycle. Therefore, package design should be developed taking into account not only cost, food shelf life and safety, as well as user-friendliness, but also environmental sustainability. To address and improve this latter issue, environmental evaluation methodologies need to be applied: Life Cycle Assessment (LCA) is one amongst them, and can be considered a valid tool for this purpose. Indeed, it has been long applied in the food packaging field to highlight both environmental hotspots and improvement potentials for more eco-friendly products.In this context, this paper reports upon an LCA application experience in the production of foamy Polylactic Acid (PLA) trays for fresh-food packaging applications.The study highlighted that the highest environmental impacts come from the production and transport of the granules, so remarking the need to search for alternative biopolymers. In this regard, the results of this study will form the base for another one regarding the assessment of second-generation PIA granules, namely those produced by processing both wastes and wastewaters from starchy crop cultivation systems and processing plants. (C) 2017 Elsevier Ltd. All rights reserved

Experimental evidence of replica symmetry breaking in random lasers

Spin-glass theory is one of the leading paradigms of complex physics and describes condensed matter, neural networks and biological systems, ultracold atoms, random photonics, and many other research fields. According to this theory, identical systems under identical conditions may reach different states and provide different values for observable quantities. This effect is known as Replica Symmetry Breaking and is revealed by the shape of the probability distribution function of an order parameter named the Parisi overlap. However, a direct experimental evidence in any field of research is still missing. Here we investigate pulse-to-pulse fluctuations in random lasers, we introduce and measure the analogue of the Parisi overlap in independent experimental realizations of the same disordered sample, and we find that the distribution function yields evidence of a transition to a glassy light phase compatible with a replica symmetry breaking.Comment: 10 pages, 5 figure

Quasi-Continuous Vector Fields on RCD Spaces

In the existing language for tensor calculus on RCD spaces, tensor fields are only defined m-a.e. In this paper we introduce the concept of tensor field defined \u20182-capacity-a.e.\u2019 and discuss in which sense Sobolev vector fields have a 2-capacity-a.e. uniquely defined quasi-continuous representative

The Abresch-Gromoll inequality in a non-smooth setting

We prove that the Abresch-Gromoll inequality holds on infinitesimally Hilbertian CD(K,N) spaces in the same form as the one available on smooth Riemannian manifolds

Effect of the (Nd,Dy)-double doping on the structural properties of ceria

The crystallographic properties of the Ce1-x(Nd0.63Dy0.37)xO2-x/2 system (0 64 x 64 0.6) were studied by means of synchrotron powder X-ray diffraction and compared to the ones of Sm-doped ceria. The aim of this work was to investigate the effect of substituting Sm3+ by a mixture of a smaller and a larger ion that ensures a more pronounced Ce4+/dopant size mismatch while having the same average ionic size as Sm3+. Two main findings came to light: (a) the compositional region of the CeO2-based solid solution widens up to x ranging between 0.4 and 0.5, and (b) the cell parameter is larger than the one of Sm-doped ceria at each composition. Both effects are expected to play a significant role on the ionic conductivity of the material. The results are discussed in terms of disorder and cation-vacancy association