Search results for "Principle"

Algebraic aspects and coherence conditions for conjoined and disjoined conditionals

2019

We deepen the study of conjoined and disjoined conditional events in the setting of coherence. These objects, differently from other approaches, are defined in the framework of conditional random quantities. We show that some well known properties, valid in the case of unconditional events, still hold in our approach to logical operations among conditional events. In particular we prove a decomposition formula and a related additive property. Then, we introduce the set of conditional constituents generated by $n$ conditional events and we show that they satisfy the basic properties valid in the case of unconditional events. We obtain a generalized inclusion-exclusion formula and we prove a …

Selective versions of chain condition-type properties

2015

We study selective and game-theoretic versions of properties like the ccc, weak Lindel\"ofness and separability, giving various characterizations of them and exploring connections between these properties and some classical cardinal invariants of the continuum.

Perturbed eigenvalue problems for the Robin p-Laplacian plus an indefinite potential

2020

AbstractWe consider a parametric nonlinear Robin problem driven by the negativep-Laplacian plus an indefinite potential. The equation can be thought as a perturbation of the usual eigenvalue problem. We consider the case where the perturbation$$f(z,\cdot )$$f(z,·)is$$(p-1)$$(p-1)-sublinear and then the case where it is$$(p-1)$$(p-1)-superlinear but without satisfying the Ambrosetti–Rabinowitz condition. We establish existence and uniqueness or multiplicity of positive solutions for certain admissible range for the parameter$$\lambda \in {\mathbb {R}}$$λ∈Rwhich we specify exactly in terms of principal eigenvalue of the differential operator.

Existence and multiplicity results for semilinear elliptic Dirichlet problems in exterior domains

1995

Markov extensions for multi-dimensional dynamical systems

1999

By a result of F. Hofbauer [11], piecewise monotonic maps of the interval can be identified with topological Markov chains with respect to measures with large entropy. We generalize this to arbitrary piecewise invertible dynamical systems under the following assumption: the total entropy of the system should be greater than the topological entropy of the boundary of some reasonable partition separating almost all orbits. We get a sufficient condition for these maps to have a finite number of invariant and ergodic probability measures with maximal entropy. We illustrate our results by quoting an application to a class of multi-dimensional, non-linear, non-expansive smooth dynamical systems.

Solutions and positive solutions for superlinear Robin problems

2019

We consider nonlinear, nonhomogeneous Robin problems with a (p − 1)-superlinear reaction term, which need not satisfy the Ambrosetti-Rabinowitz condition. We look for positive solutions and prove existence and multiplicity theorems. For the particular case of the p-Laplacian, we prove existence results under a different geometry near the origin.We consider nonlinear, nonhomogeneous Robin problems with a (p − 1)-superlinear reaction term, which need not satisfy the Ambrosetti-Rabinowitz condition. We look for positive solutions and prove existence and multiplicity theorems. For the particular case of the p-Laplacian, we prove existence results under a different geometry near the origin.

A multiplicity theorem for parametric superlinear (p,q)-equations

2020

We consider a parametric nonlinear Robin problem driven by the sum of a \(p\)-Laplacian and of a \(q\)-Laplacian (\((p,q)\)-equation). The reaction term is \((p-1)\)-superlinear but need not satisfy the Ambrosetti-Rabinowitz condition. Using variational tools, together with truncation and comparison techniques and critical groups, we show that for all small values of the parameter, the problem has at least five nontrivial smooth solutions, all with sign information.

Instruction-based clinical eye-tracking study on the visual interpretation of divergence : how do students look at vector field plots?

2018

Relating mathematical concepts to graphical representations is a challenging task for students. In this paper, we introduce two visual strategies to qualitatively interpret the divergence of graphical vector field representations. One strategy is based on the graphical interpretation of partial derivatives, while the other is based on the flux concept. We test the effectiveness of both strategies in an instruction-based eye-tracking study with N = 41 physics majors. We found that students’ performance improved when both strategies were introduced (74% correct) instead of only one strategy (64% correct), and students performed best when they were free to choose between the two strategies (88…

Anthropic space and design for all. New knowledge paths for urban planning strategies

2019

Abstract Nowadays city environment shows the presence of a mixed variety of elements, as natural, semi natural and anthropic components that build up both structure and connections of the urban context. This specific structure shapes and directs space and its functions strictly connected with their sustainable potential uses and sustainable development opportunities. The lack of rules and proper planning methods produces inefficient use conditions by resident citizens, entropy, functions' reduction of ecological networks and deep environmental impacts. The consequence comes out to be a great widespread life quality decrease in urban areas. These thoughts lead the authors to rethink the defi…

Evidence for the time-temperature superposition principle from Monte-Carlo simulations of the glass transition in two-dimensional polymer melts

1992

The bond fluctuation model on a square lattice with a bond-length dependent potential exhibits in simulations of slow cooling a kinetic glass transition where the system falls out of equilibrium. Extending previous work, the relaxation functions of gyration radius and end-to-end distance, and the bond autocorrelation function of the polymers are presented and related to the time-dependent displacements of inner monomeric units and center of gravity of the whole chains, respectively. Over a wide temperature range the data can be collapsed on master curves satisfying the time-temperature superposition principle for Rouse dynamics.