In this paper we show how some metric properties of the unit sphere of a normed space can help to approach a solution to Tingley's problem. In our main result we show that if an onto isometry between ...the spheres of strictly convex spaces is the identity when restricted to some relative open subset, then it is the identity. This implies that an onto isometry between the unit spheres of strictly convex finite dimensional spaces is linear if and only if it is linear on a relative open set. We prove the same for arbitrary two-dimensional spaces and obtain that every two-dimensional, non strictly convex, normed space has the Mazur-Ulam Property. We also include some other less general, yet interesting, results, along with a generalisation of curvature to normed spaces.
Kinetic proofreading is used throughout natural systems to enhance the specificity of molecular recognition. At its most basic level, kinetic proofreading uses a supply of chemical fuel to drive a ...recognition interaction out of equilibrium, allowing a single free-energy difference between correct and incorrect targets to be exploited two or more times. Despite its importance in biology, there has been little effort to incorporate kinetic proofreading into synthetic systems in which molecular recognition is important, such as nucleic acid nanotechnology. In this article, we introduce a DNA strand displacement-based kinetic proofreading motif, showing that the consumption of a DNA-based fuel can be used to enhance molecular recognition during a templated dimerization reaction. We then show that kinetic proofreading can enhance the specificity with which a probe discriminates single nucleotide mutations, both in terms of the initial rate with which the probe reacts and the long-time behavior.
A Banach space X has the Mazur–Ulam property if any isometry from the unit sphere of X onto the unit sphere of any other Banach space Y extends to a linear isometry of the Banach spaces X,Y. A Banach ...space X is called smooth if the unit ball has a unique supporting functional at each point of the unit sphere. We prove that each non-smooth 2-dimensional Banach space has the Mazur–Ulam property.
There is a growing demand for accurate high-resolution land cover maps in many fields, e.g., in land-use planning and biodiversity conservation. Developing such maps has been traditionally performed ...using Object-Based Image Analysis (OBIA) methods, which usually reach good accuracies, but require a high human supervision and the best configuration for one image often cannot be extrapolated to a different image. Recently, deep learning Convolutional Neural Networks (CNNs) have shown outstanding results in object recognition in computer vision and are offering promising results in land cover mapping. This paper analyzes the potential of CNN-based methods for detection of plant species of conservation concern using free high-resolution Google Earth TM images and provides an objective comparison with the state-of-the-art OBIA-methods. We consider as case study the detection of Ziziphus lotus shrubs, which are protected as a priority habitat under the European Union Habitats Directive. Compared to the best performing OBIA-method, the best CNN-detector achieved up to 12% better precision, up to 30% better recall and up to 20% better balance between precision and recall. Besides, the knowledge that CNNs acquired in the first image can be re-utilized in other regions, which makes the detection process very fast. A natural conclusion of this work is that including CNN-models as classifiers, e.g., ResNet-classifier, could further improve OBIA methods. The provided methodology can be systematically reproduced for other species detection using our codes available through (https://github.com/EGuirado/CNN-remotesensing).
The paper deals with the interplay between boundedness, order and ring structures in function lattices on the line and related metric spaces. It is shown that the lattice of all Lipschitz functions ...on a normed space E is isomorphic to its sublattice of bounded functions if and only if E has dimension one. The lattice of Lipschitz functions on E carries a ``hidden'' f-ring structure with a unit, and the same happens to the (larger) lattice of all uniformly continuous functions for a wide variety of metric spaces. An example of a metric space whose lattice of uniformly continuous functions supports no unital f-ring structure is provided.
•Recycled aggregates are environmentally viable depending on the transport.•Mortar doped with crumb rubber has environmental advantages.•In the production of mortar, cement has the greatest ...environmental impact.•Crumb rubber in doped mortar behaves as a thermal and acoustic insulating material.
The construction sector is in a process of improvement towards sustainability. The study of the use of a waste as raw materials is an opportunity. This article aims to evaluate the environmental viability of incorporating recycled crumb rubber from end-of-life tires into a mortar. To this end, a life cycle assessment tool is implemented by applying the EPD methodology to assess the various categories of impact. A series of mortar alternatives were analyzed in which fine aggregate is replaced by a percentage of crumb rubber ranging from 10% to 40%: the proportion increases by 5% in each solution. The scope of the LCA is from cradle to gate as it is during the various stages that the greatest environmental impacts are incurred: including the extraction of raw materials, their transport, as well as the production process. The functional unit is that of producing 1 m3 of mortar. The results obtained in this study show that the primary contributor to environmental impact is the cement production phase. On the other hand, the various alternatives evaluated achieved a 37.04% reduction in emissions of kg of CO2, as well as a 41.83% reduction of abiotic depletion of fossil fuels when 40% of fine aggregate was replaced by crumb rubber. This study also demonstrates that the transport distance of recycled materials from their point of production to the mortar production plant is a decisive factor. Depending on that distance, the proposed solution can be rendered environmentally unviable. On a final note, it is important to underscore that the appropriate use of recycled aggregates in mortar is not only determined by strength but also environmentally. This research generates knowledge about the environmental benefits of using recycled materials in construction.
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•PDMS-based coatings for deicing were prepared with wide-ranging properties.•Shear stresses developed on elastomeric surfaces allow to decrease ice adhesion strength.•Impact of the ...elasticity on ice adhesion is more noticeable under shear forces.•Impact of the hydrophobicity on ice adhesion is more noticeable under tensile forces.•Proper balance between surface and bulk properties leads to super low ice-adhesion.
Ice adhesion to rigid materials is reduced with low energy surfaces of high receding contact angles. However, their adhesion strength values are above the threshold value to be considered as icephobic materials. Surface deformability is a promising route to further reduce ice adhesion.
In this work, we prepared elastomer surfaces with a wide range of elastic moduli and hydrophobicity degree and we measured their ice adhesion strength. Moreover, we also explored the deicing performance of oil-infused elastomeric surfaces. The ice adhesion was characterized by two detachment modes: tensile and shear.
The variety of elastomeric surfaces allowed us to simultaneously analyze the ice adhesion dependence with deformability and contact angle hysteresis. We found that the impact of these properties depends on the detachment mode, being deformability more important in shear mode and hydrophobicity more relevant in tensile mode. In addition, oil infusion further reduces ice adhesion due to the interfacial slippage. From an optimal balance between deformability and hydrophobicity, we were able to identify surfaces with super-low ice adhesion.
Interactions involving charged particles in the presence of multivalent ions are relevant in wide-range of phenomena, including condensation of nucleic acids, cement hardening, or water treatment. ...Here, we study such interactions by combining direct force measurements with atomic force microscopy (AFM) and aggregation studies with time-resolved light scattering for particles originating from the same colloidal suspension for the first time. Classical DLVO theory is found to be only applicable for monovalent and divalent ions. For ions of higher valence, charge inversion and additional non-DLVO attractive forces are observed. These attractive forces can be attributed to surface charge heterogeneities, which leads to stability ratios that are calculated from direct force measurements to be higher than the experimental ones. Ion–ion correlations are equally important as they induce the charge inversion in the presence of trivalent or tetravalent ions, and they enhance the surface charge heterogeneities. Such heterogeneities therefore play an essential role in controlling interactions in particle suspensions containing multivalent ions.
In this paper, we show that the C1-differentiability of the norm of a two-dimensional normed space depends only on distances between points of the unit sphere in two different ways.
As a consequence, ...we see that any isometry between the spheres of normed planes τ:SX→SY is linear, provided that there exist linearly independent x,x‾∈SX where SX is not differentiable and that SX is piecewise differentiable.
We end this work by showing that the isometry τ:CX→CY is linear even if it is not an isometry between spheres: every isometry between (planar) Jordan piecewise C1-differentiable convex curves extends to X whenever X and Y are strictly convex and the amount of non-differentiability points of SX and SY is finite and greater than 2.
Force profiles and aggregation rates involving positively and negatively charged polystyrene latex particles are investigated in monovalent electrolyte solutions, whereby the counterions are varied ...within the Hofmeister series. The force measurements are carried out with the colloidal probe technique, which is based on the atomic force microscope (AFM), while the aggregation rates are measured with time-resolved multiangle light scattering. The interaction force profiles cannot be described by classical DLVO theory, but an additional attractive short-ranged force must be included. An exponential force profile with a decay length of about 0.5 nm is consistent with the measured forces. Furthermore, the Hamaker constants extracted from the measured force profiles are substantially smaller than the theoretical values calculated from dielectric spectra. The small surface roughness of the latex particles (below 1 nm) is probably responsible for this deviation. Based on the measured force profiles, the aggregation rates can be predicted without adjustable parameters. The measured absolute aggregation rates in the fast regime are somewhat lower than the calculated ones. The critical coagulation concentration (CCC) agrees well with the experiment, including the respective shifts of the CCC within the Hofmeister series. These shifts are particularly pronounced for the positively charged particles. However, the consideration of the additional attractive short-ranged force is essential to quantify these shifts correctly. In the slow regime, the calculated rates are substantially smaller than the experimental ones. This disagreement is probably related to surface charge heterogeneities.
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