Search results for "REPRESENTATION"
showing 10 items of 1710 documents
Scientific Instruments on Display
2016
Why and where are scientific instruments displayed? As this collective work convincingly demonstrates, the exhibition and representation of instruments depends on considerations that are shaped by ...
Module categories of finite Hopf algebroids, and self-duality
2017
International audience; We characterize the module categories of suitably finite Hopf algebroids (more precisely, $X_R$-bialgebras in the sense of Takeuchi (1977) that are Hopf and finite in the sense of a work by the author (2000)) as those $k$-linear abelian monoidal categories that are module categories of some algebra, and admit dual objects for "sufficiently many" of their objects. Then we proceed to show that in many situations the Hopf algebroid can be chosen to be self-dual, in a sense to be made precise. This generalizes a result of Pfeiffer for pivotal fusion categories and the weak Hopf algebras associated to them.
Sesquilinear forms associated to sequences on Hilbert spaces
2019
The possibility of defining sesquilinear forms starting from one or two sequences of elements of a Hilbert space is investigated. One can associate operators to these forms and in particular look for conditions to apply representation theorems of sesquilinear forms, such as Kato's theorems. The associated operators correspond to classical frame operators or weakly-defined multipliers in the bounded context. In general some properties of them, such as the invertibility and the resolvent set, are related to properties of the sesquilinear forms. As an upshot of this approach new features of sequences (or pairs of sequences) which are semi-frames (or reproducing pairs) are obtained.
Drawings, Gestures and Discourses: A Case Study with Kindergarten Students Discovering Lego Bricks
2020
This paper presents a study aimed at investigating the didactic potentiality of the use of an artefact, useful to construct mathematical meanings concerning the coordination of different points of view, in the observation of a real object/toy. In our view, the process of meaning construction can be fostered by the use of adequate artefacts, but it requires a teaching/learning model, which explicitly takes care of the evolution of meanings, from those personal, emerging through the activities, to the mathematical ones, aims of the teaching intervention. The main hypothesis of this study is that the alternation between different semiotic systems, graphical system, verbal system and system of …
Classification of Sequences with Deep Artificial Neural Networks: Representation and Architectural Issues
2021
DNA sequences are the basic data type that is processed to perform a generic study of biological data analysis. One key component of the biological analysis is represented by sequence classification, a methodology that is widely used to analyze sequential data of different nature. However, its application to DNA sequences requires a proper representation of such sequences, which is still an open research problem. Machine Learning (ML) methodologies have given a fundamental contribution to the solution of the problem. Among them, recently, also Deep Neural Network (DNN) models have shown strongly encouraging results. In this chapter, we deal with specific classification problems related to t…
Fully Dynamic Evaluation of Sequence Pair
2013
In the electronic design automation field, as well as in other areas, problem instances and solutions are often subject to discrete changes. The foundational significance of efficient updates of the criterion value after dynamic updates, instead of recomputing it from scratch each time, has attracted a lot of research. In this paper, motivated by the significance of the sequence pair (SP) representation for floorplanning, we develop a fully dynamic algorithm of SP evaluation, that efficiently updates a criterion value after insertions and deletions of SP elements and after modifications of element weights. Our result is based on a new data structure for the predecessor problem, which mainta…
Analytical representation of bimodality in bivariate distribution of chain length and chemical composition of copolymers
2022
Abstract Tuning the bimodality of microstructural features in polymers has provided novel properties and applications. A classic example is to overcome the trade-off between processability and mechanical properties in polyolefins. A recent example is to decrease the interfacial tension in blending incompatible polymers. Therefore, the development of a bimodality index (BI), especially for the chain length distribution (CLD) and the chemical composition distribution (CCD), is crucial for the quantitative design of materials. This study introduces quantitative expressions for the bimodality of univariate CLD on the linear scale, and CCD. Moreover, we develop a bimodality criterion for bivaria…
On the existence of the exponential solution of linear differential systems
1999
The existence of an exponential representation for the fundamental solutions of a linear differential system is approached from a novel point of view. A sufficient condition is obtained in terms of the norm of the coefficient operator defining the system. The condition turns out to coincide with a previously published one concerning convergence of the Magnus series expansion. Direct analysis of the general evolution equations in the SU(N) Lie group illustrates how the estimate for the domain of existence/convergence becomes larger. Eventually, an application is done for the Baker-Campbell-Hausdorff series.
On a projective representation of chain geometries
1984
We define a distance d on the set of r-spaces of an n-space. By the transfer of d to the GrasmannianG=G(n, r) we obtain a distinguished class of normal rational curves of order 1, the “1-distance lines’, 1=1,..., r, which are in 1–1-correspondence to the so-called “generalized reguli of type (r, 1)”.
The Kp Hierarchy
1989
As an application of the theory of infinite-dimensional Grassmannians and the representation theory of gl1 we shall study in this chapter certain nonlinear “exactly solvable” systems of differential equations. Exactly solvable means here that the nonlinear system can be transformed to an (infinite-dimensional) linear problem. A prototype of the equations is the Korteweg-de Vries equation $$\frac{{\partial u}}{{\partial t}} = \frac{3}{3}u\frac{{\partial u}}{{\partial x}} + \frac{1}{4}\frac{{{\partial ^3}u}}{{\partial {x^3}}}$$ . It turns out that it is more natural to consider an infinite system of equations like that above, for obtaining explicit solutions. The set of equations is called th…