Search results for "generalization"
showing 10 items of 250 documents
Contextuality-by-Default 2.0: Systems with Binary Random Variables
2017
The paper outlines a new development in the Contextuality-by-Default theory as applied to finite systems of binary random variables. The logic and principles of the original theory remain unchanged, but the definition of contextuality of a system of random variables is now based on multimaximal rather than maximal couplings of the variables that measure the same property in different contexts: a system is considered noncontextual if these multimaximal couplings are compatible with the distributions of the random variables sharing contexts. A multimaximal coupling is one that is a maximal coupling of any subset (equivalently, of any pair) of the random variables being coupled. Arguments are …
Critical path analysis in the network with fuzzy activity times
2001
A natural generalization of the criticality notion in a network with fuzzy activity times is given. It consists in direct application of the extension principle of Zadeh to the notion of criticality of a path (an activity, an event) treated as a function of the activities duration times in the network. There are shown some relations between the notion of fuzzy criticality, introduced in the paper, and the notion of interval criticality (criticality in the network with interval activity times) proposed by the authors in another paper. Two methods of calculation of the path degree of criticality (according to the proposed concept of fuzzy criticality) are presented.
The exterior derivative as a Killing vector field
1996
Among all the homogeneous Riemannian graded metrics on the algebra of differential forms, those for which the exterior derivative is a Killing graded vector field are characterized. It is shown that all of them are odd, and are naturally associated to an underlying smooth Riemannian metric. It is also shown that all of them are Ricci-flat in the graded sense, and have a graded Laplacian operator that annihilates the whole algebra of differential forms.
Upper bounds for the tightness of the $$G_\delta $$-topology
2021
We prove that if X is a regular space with no uncountable free sequences, then the tightness of its $$G_\delta $$ topology is at most the continuum and if X is, in addition, assumed to be Lindelof then its $$G_\delta $$ topology contains no free sequences of length larger then the continuum. We also show that, surprisingly, the higher cardinal generalization of our theorem does not hold, by constructing a regular space with no free sequences of length larger than $$\omega _1$$ , but whose $$G_\delta $$ topology can have arbitrarily large tightness.
The effect of long context exposure on cued conditioning and c-fos expression in the rat forebrain
2004
The c-fos expression was used to study the neural substrates of the cued fear conditioning acquisition, preceded by a short exposure versus a long exposure to the conditioning context. A long-context exposure (either during the night or during the day) prior to conditioning, was associated with low freezing in the learning test. Differences in the c-fos expression of CA1, CA3, BL Amygdala, LS and BNST were found between the short- or long-context groups with a pre-exposure before cued conditioning. Ce Amygdala showed no differences in the c-fos expression labeling. We reported the hippocampal c-fos activation during the cued fear conditioning acquisition. Specifically, the CA1 activation co…
Shear capacity in concrete beams reinforced by stirrups with two different inclinations
2014
Abstract A model for the estimation of shear capacity in Reinforced Concrete (RC) beams with web reinforcement is provided by introducing a generalization of classical plastic Nielsen’s model, which is based on the variable-inclination stress-field approach. The proposed model is able to predict the shear capacity in RC beams reinforced by means of stirrups having two different inclinations and longitudinal web bars. A numerical comparison with the results of experimental tests and those provided by a Finite Element Model (FEM) based on the well known theory of Modified Compression Field Theory (MCFT) is carried out for validating the robustness of the proposed model. Finally, a set of para…
Diffraction by m-bonacci gratings
2015
We present a simple diffraction experiment with m-bonacci gratings as a new interesting generalization of the Fibonacci ones. Diffraction by these nonconventional structures is proposed as a motivational strategy to introduce students to basic research activities. The Fraunhofer diffraction patterns are obtained with the standard equipment present in most undergraduate physics labs and are compared with those obtained with regular periodic gratings. We show that m-bonacci gratings produce discrete Fraunhofer patterns characterized by a set of diffraction peaks which positions are related to the concept of a generalized golden mean. A very good agreement is obtained between experimental and …
Shape optimization for monge-ampére equations via domain derivative
2011
In this note we prove that, if $\Omega$ is a smooth, strictly convex, open set in $R^n$ $(n \ge 2)$ with given measure, the $L^1$ norm of the convex solution to the Dirichlet problem $\det D^2 u=1$ in $\Omega$, $u=0$ on $\partial\Omega$, is minimum whenever $\Omega$ is an ellipsoid.
Leveraging Specific Contexts and Outcomes to Generalize in Combinatorial Settings
2018
International audience; Generalization is a fundamental aspect of mathematics, and it is a practice with which undergraduate students should engage and gain fluency. It is important for students in combinatorial settings to be able to generalize, but combinatorics lends itself to engagement with specific examples, concrete outcomes, and particular contexts. In this paper, we seek to inform the nature of generalization in combinatorial settings by demonstrating ways in which students leverage specific, concrete settings to engage in generalizing activity in combinatorics. We provide two data examples that highlight ways in which concrete and specific ideas can be leveraged to help students d…
Mappings of finite distortion: The zero set of the Jacobian
2003
This paper is part of our program to establish the fundamentals of the theory of mappings of finite distortion [6], [1], [8], [13], [14], [7] which form a natural generalization of the class of mappings of bounded distortion, also called quasiregular mappings. Let us begin with the definition. We assume that Ω ⊂ Rn is a connected open set. We say that a mapping f : Ω → Rn has finite distortion if: