scholarly journals Yablo’s Paradox, the Liar, and Referential Contradictions from a Graph Theory Point of View

2021 ◽  
pp. 101-104
Author(s):  
Gustavo Bodanza
Keyword(s):  
Fixed Point ◽  
Graph Theory ◽  
Point Of View ◽  
Graph Theoretic ◽  
Admissible Sets ◽  
Special Cases ◽  
Theory Point ◽  
The One ◽  
The Liar

F -systems are useful digraphs to model sentences that predicate the falsity of other sentences. Paradoxes like the Liar and the one of Yablo can be analyzed with that tool to find graph-theoretic patterns. In this paper we studied this general model consisting of a set of sentences and the binary relation ‘... affirms the falsity of...’ among them. The possible existence of non-referential sentences was also considered. To model the sets of all the sentences that can jointly be valued as true we introduced the notion of conglomerate, the existence of which guarantees the absence of paradox. Conglomerates also enabled us to characterize referential contradictions, i.e., sentences that can only be false under a classical valuation due to the interactions with other sentences in the model. A Kripke-style fixed-point characterization of groundedness was offered, and complete (meaning that every sentence is deemed either true or false) and consistent (meaning that no sentence is deemed true and false) fixed points were put in correspondence with conglomerates. Furthermore, argumentation frameworks are special cases of F -systems. We showed the relation between local conglomerates and admissible sets of arguments and argued about the usefulness of the concept for the argumentation theory.

On the Dynamic Isotropy of Mechanisms With Two Degrees of Freedom

2005 ◽  
Author(s):  
Raffaele Di Gregorio ◽  
Alessandro Cammarata ◽  
Rosario Sinatra
Keyword(s):  
Finite Number ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Closed Curves ◽  
Special Cases ◽  
Dynamic Performances ◽  
Definition Of ◽  
Geometric Locus

The comparison of mechanisms with different topology or with different geometry, but with the same topology, is a necessary operation during the design of a machine sized for a given task. Therefore, tools that evaluate the dynamic performances of a mechanism are welcomed. This paper deals with the dynamic isotropy of 2-dof mechanisms starting from the definition introduced in a previous paper. In particular, starting from the condition that identifies the dynamically isotropic configurations, it shows that, provided some special cases are not considered, 2-dof mechanisms have at most a finite number of isotropic configurations. Moreover, it shows that, provided the dynamically isotropic configurations are excluded, the geometric locus of the configuration space that collects the points associated to configurations with the same dynamic isotropy is constituted by closed curves. This results will allow the classification of 2-dof mechanisms from the dynamic-isotropy point of view, and the definition of some methodologies for the characterization of the dynamic isotropy of these mechanisms. Finally, examples of applications of the obtained results will be given.

scholarly journals Detection Limits of DLS and UV-Vis Spectroscopy in Characterization of Polydisperse Nanoparticles Colloids

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Emilia Tomaszewska ◽  
Katarzyna Soliwoda ◽  
Kinga Kadziola ◽  
Beata Tkacz-Szczesna ◽  
Grzegorz Celichowski ◽  
...  
Keyword(s):  
Light Scattering ◽  
Dynamic Light Scattering ◽  
Point Of View ◽  
Spectroscopy Analysis ◽  
Force Microscopy ◽  
Atomic Force ◽  
Transmission Electron ◽  
Vis Spectroscopy ◽  
The One

Dynamic light scattering is a method that depends on the interaction of light with particles. This method can be used for measurements of narrow particle size distributions especially in the range of 2–500 nm. Sample polydispersity can distort the results, and we could not see the real populations of particles because big particles presented in the sample can screen smaller ones. Although the theory and mathematical basics of DLS technique are already well known, little has been done to determine its limits experimentally. The size and size distribution of artificially prepared polydisperse silver nanoparticles (NPs) colloids were studied using dynamic light scattering (DLS) and ultraviolet-visible (UV-Vis) spectroscopy. Polydisperse colloids were prepared based on the mixture of chemically synthesized monodisperse colloids well characterized by atomic force microscopy (AFM), transmission electron microscopy (TEM), DLS, and UV-Vis spectroscopy. Analysis of the DLS results obtained for polydisperse colloids reveals that several percent of the volume content of bigger NPs could screen completely the presence of smaller ones. The presented results could be extremely important from nanoparticles metrology point of view and should help to understand experimental data especially for the one who works with DLS and/or UV-Vis only.

scholarly journals Entropy-regularized 2-Wasserstein distance between Gaussian measures

2021 ◽  
Author(s):  
Anton Mallasto ◽  
Augusto Gerolin ◽  
Hà Quang Minh
Keyword(s):  
Fixed Point ◽  
Closed Form ◽  
Numerical Study ◽  
Wasserstein Distance ◽  
Iteration Algorithm ◽  
Probability Measures ◽  
Gaussian Distributions ◽  
Closed Form Solutions ◽  
Special Cases

AbstractGaussian distributions are plentiful in applications dealing in uncertainty quantification and diffusivity. They furthermore stand as important special cases for frameworks providing geometries for probability measures, as the resulting geometry on Gaussians is often expressible in closed-form under the frameworks. In this work, we study the Gaussian geometry under the entropy-regularized 2-Wasserstein distance, by providing closed-form solutions for the distance and interpolations between elements. Furthermore, we provide a fixed-point characterization of a population barycenter when restricted to the manifold of Gaussians, which allows computations through the fixed-point iteration algorithm. As a consequence, the results yield closed-form expressions for the 2-Sinkhorn divergence. As the geometries change by varying the regularization magnitude, we study the limiting cases of vanishing and infinite magnitudes, reconfirming well-known results on the limits of the Sinkhorn divergence. Finally, we illustrate the resulting geometries with a numerical study.

Cohomology Ring of Symplectic Quotients by Circle Actions

2004 ◽  
Vol 56 (3) ◽  
pp. 553-565 ◽  
Author(s):  
Ramin Mohammadalikhani
Keyword(s):  
Fixed Point ◽  
Cohomology Ring ◽  
Circle Action ◽  
Fixed Point Set ◽  
Circle Actions ◽  
Generating Set ◽  
Special Cases ◽  
Symplectic Quotients ◽  
Point Set

AbstractIn this article we are concerned with how to compute the cohomology ring of a symplectic quotient by a circle action using the information we have about the cohomology of the original manifold and some data at the fixed point set of the action. Our method is based on the Tolman-Weitsman theorem which gives a characterization of the kernel of the Kirwan map. First we compute a generating set for the kernel of the Kirwan map for the case of product of compact connected manifolds such that the cohomology ring of each of them is generated by a degree two class. We assume the fixed point set is isolated; however the circle action only needs to be “formally Hamiltonian”. By identifying the kernel, we obtain the cohomology ring of the symplectic quotient. Next we apply this result to some special cases and in particular to the case of products of two dimensional spheres. We show that the results of Kalkman and Hausmann-Knutson are special cases of our result.

Studies on a Levonorgestrel-Releasing Trade Plastic Device and on a Similar Polyurethane Foam Used as a Levonorgestrel Carrier

2019 ◽  
Vol 56 (3) ◽  
pp. 543-547
Author(s):  
Flavius Olaru ◽  
Dana Stoian ◽  
Delia Berceanu Vaduva ◽  
Alina Corpade ◽  
Florin Birsasteanu ◽  
...  
Keyword(s):  
Skin Irritation ◽  
Oral Route ◽  
Point Of View ◽  
Intrauterine Devices ◽  
Daily Amount ◽  
Pu Foam ◽  
The One ◽  
Structural Point ◽  
Copper Iud

Hormonal Intrauterine Devices (IUD) were developed based on copper IUD with the role to release a daily amount of hormones. From a structural point of view Levonorgestrel-IUD (L-IUD) is a small T-shaped piece of plastic, which contains levonorgestrel. When compared with the oral route of L-IUD administration, it provides some advantages because it releases levonorgestrel directly into the uterus. Our aims were: (1) to compare the thickness of uterine jonctional zone (UJZ) in two groups of patients with and without inserted L-IUD, (2) to evaluate the changes in thickness of UJZ after the insertion of L-IUD in two patients with adenomyosis, and (3) to obtain and to characterize a similar T-shaped polyurethane (PU) foam used as a levonorgestrel delivery system. On the one hand, the results confirm that L-IUD is effective in thinning the UJZ and in the treatment of adenomyosis, while on the other hand, the characterization of the PU materials (Zetasizer measurements, their thermal degradation, UV-Vis spectra and skin irritation tests) revealed that this polymer can be used as a safety and prolonged levonorgestrel carrier.

scholarly journals An Extension of the Concept of Derivative: Its Application to Intertemporal Choice

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 696
Author(s):  
Salvador Cruz Rambaud ◽  
Blas Torrecillas Jover
Keyword(s):  
Behavioral Finance ◽  
Intertemporal Choice ◽  
Point Of View ◽  
Financial Mathematics ◽  
Economic Problems ◽  
Scientific Disciplines ◽  
The One ◽  
Novel Concept ◽  
Decreasing Impatience

The framework of this paper is the concept of derivative from the point of view of abstract algebra and differential calculus. The objective of this paper is to introduce a novel concept of derivative which arises in certain economic problems, specifically in intertemporal choice when trying to characterize moderately and strongly decreasing impatience. To do this, we have employed the usual tools and magnitudes of financial mathematics with an algebraic nomenclature. The main contribution of this paper is twofold. On the one hand, we have proposed a novel framework and a different approach to the concept of relative derivation which satisfies the so-called generalized Leibniz’s rule. On the other hand, in spite of the fact that this peculiar approach can be applied to other disciplines, we have presented the mathematical characterization of the two main types of decreasing impatience in the ambit of behavioral finance, based on a previous characterization involving the proportional increasing of the variable “time”. Finally, this paper points out other patterns of variation which could be applied in economics and other scientific disciplines.

scholarly journals Development and application of methods to characterize micro semi-finished products and micro components

2018 ◽  
Vol 190 ◽  
pp. 15012
Author(s):  
Bernd Köhler ◽  
Brigitte Clausen ◽  
Hans-Werner Zoch
Keyword(s):  
Mechanical Testing ◽  
Electron Backscatter Diffraction ◽  
Decisive Role ◽  
Point Of View ◽  
X Ray ◽  
Analysis Techniques ◽  
Microhardness Testing ◽  
The One ◽  
Backscatter Diffraction

In the production of semi-finished products for the production of microcomponents and the components themselves, the characterization of their physical properties is of particular importance. Due to the often oligocrystalline character of these semi-finished products and components, it is necessary to use a suitable testing technique for static and dynamic investigations, as the mechanical properties are not transferable from the macroscopic point of view. In addition, the micro semi-finished products and components often show inhomogeneities induced by the manufacturing process. On the one hand, these are directly reflected in the microstructure and on the other hand they have an effect on quantities such as hardness or residual stresses, which play a decisive role in the application. Mechanical testing, conventional metallography, scanning electron microscopy (SEM), electron backscatter diffraction (EBSD), ultra-microhardness testing and X-ray residual stress analysis were used as measuring and analysis techniques suitable for the sub-millimeter range. In the following, the possibilities and limitations of two these methods are illustrated using the example of mechanical testing and EBSD. In this paper several examples for possible characterization techniques are given.

scholarly journals Fixed-Point Study of Generalized Rational Type Multivalued Contractive Mappings on Metric Spaces with a Graph

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 31
Author(s):  
Binayak S. Choudhury ◽  
Nikhilesh Metiya ◽  
Debashis Khatua ◽  
Manuel de la Sen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Metric Spaces ◽  
Graph Theoretic ◽  
Contractive Mappings ◽  
Control Functions ◽  
Special Cases ◽  
Multivalued Contractions ◽  
Rational Type ◽  
Type Contraction

The main result of this paper is a fixed-point theorem for multivalued contractions obtained through an inequality with rational terms. The contraction is an F-type contraction. The results are obtained in a metric space endowed with a graph. The main theorem is supported by illustrative examples. Several results as special cases are obtained by specific choices of the control functions involved in the inequality. The study is broadly in the domain of setvalued analysis. The methodology of the paper is a blending of both graph theoretic and analytic methods.

scholarly journals THE THICKNESS OF SCHUBERT CELLS AS INCIDENCE STRUCTURES

2019 ◽  
Vol 109 (2) ◽  
pp. 145-156
Author(s):  
JOHN BAMBERG ◽  
ARUN RAM ◽  
JON XU
Keyword(s):  
Representation Theory ◽  
Lattice Theory ◽  
Finite Geometry ◽  
Point Of View ◽  
Short Paper ◽  
Flag Varieties ◽  
Modern Language ◽  
Incidence Structures ◽  
Theory Point

This paper explores the possible use of Schubert cells and Schubert varieties in finite geometry, particularly in regard to the question of whether these objects might be a source of understanding of ovoids or provide new examples. The main result provides a characterization of those Schubert cells for finite Chevalley groups which have the first property (thinness) of ovoids. More importantly, perhaps this short paper can help to bridge the modern language barrier between finite geometry and representation theory. For this purpose, this paper includes very brief surveys of the powerful lattice theory point of view from finite geometry and the powerful method of indexing points of flag varieties by Chevalley generators from representation theory.

Understanding functional illiteracy from a policy, adult education, and cognition point of view: Towards a joint referent framework

2019 ◽  
Vol 30 (2) ◽  
pp. 109-122
Author(s):  
Aleksandar Bulajić ◽  
Miomir Despotović ◽  
Thomas Lachmann
Keyword(s):  
Adult Education ◽  
Operational Definition ◽  
Literacy Skills ◽  
Point Of View ◽  
Industrialized Countries ◽  
Functional Illiteracy ◽  
Scale Levels ◽  
Components Of Reading ◽  
The One ◽  
Definition Of

Abstract. The article discusses the emergence of a functional literacy construct and the rediscovery of illiteracy in industrialized countries during the second half of the 20th century. It offers a short explanation of how the construct evolved over time. In addition, it explores how functional (il)literacy is conceived differently by research discourses of cognitive and neural studies, on the one hand, and by prescriptive and normative international policy documents and adult education, on the other hand. Furthermore, it analyses how literacy skills surveys such as the Level One Study (leo.) or the PIAAC may help to bridge the gap between cognitive and more practical and educational approaches to literacy, the goal being to place the functional illiteracy (FI) construct within its existing scale levels. It also sheds more light on the way in which FI can be perceived in terms of different cognitive processes and underlying components of reading. By building on the previous work of other authors and previous definitions, the article brings together different views of FI and offers a perspective for a needed operational definition of the concept, which would be an appropriate reference point for future educational, political, and scientific utilization.

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