Search results for "General Mathematics"
showing 10 items of 3795 documents
A note on the uniqueness result for the inverse Henderson problem
2019
The inverse Henderson problem of statistical mechanics is the theoretical foundation for many bottom-up coarse-graining techniques for the numerical simulation of complex soft matter physics. This inverse problem concerns classical particles in continuous space which interact according to a pair potential depending on the distance of the particles. Roughly stated, it asks for the interaction potential given the equilibrium pair correlation function of the system. In 1974, Henderson proved that this potential is uniquely determined in a canonical ensemble and he claimed the same result for the thermodynamical limit of the physical system. Here, we provide a rigorous proof of a slightly more …
Rotation topological factors of minimal $\mathbb {Z}^{d}$-actions on the Cantor set
2006
In this paper we study conditions under which a free minimal Z d -action on the Cantor set is a topological extension of the action of d rotations, either on the product T d of d 1-tori or on a single 1-torus T 1 . We extend the notion of linearly recurrent systems defined for Z-actions on the Cantor set to Z d -actions, and we derive in this more general setting a necessary and sufficient condition, which involves a natural combinatorial data associated with the action, allowing the existence of a rotation topological factor of one of these two types.
A continuous decomposition of the Menger curve into pseudo-arcs
2000
It is proved that the Menger universal curve M admits a continuous decomposition into pseudo-arcs with the quotient space homeomorphic to M. Wilson proved [8] Anderson's announcement [1] saying that for any Peano continuum X the Menger universal curve M admits a continuous decomposition into homeomorphic copies of M such that the quotient space is homeomorphic to X. Anderson also announced (unpublished) that the plane admits a continuous decomposition into pseudo-arcs. This result was proved by Lewis and Walsh [4]. In a previous paper [6] the author has proved that each locally planar Peano continuum with no local separating point admits a continuous decomposition into pseudo-arcs. Applying…
IFS attractors and Cantor sets
2006
Abstract We build a metric space which is homeomorphic to a Cantor set but cannot be realized as the attractor of an iterated function system. We give also an example of a Cantor set K in R 3 such that every homeomorphism f of R 3 which preserves K coincides with the identity on K.
Microbubble PhoXonic resonators: Chaos transition and transfer
2022
We report the activation of optomechanical chaotic oscillations in microbubble resonators (MBRs) through a blue-side excitation of its optical resonances. We confirm the sequence of quasi-periodical oscillation, spectral continuum and aperiodic motion; as well as the transition to chaos without external feedback or modulation of the laser source. In particular, quasi periodic transitions and a spectral continuum are reported for MBRs with diameters up to 600 μm, whereas only an abrupt transition into a spectral con- tinuum is observed for larger microbubbles.
A model of capillary phenomena in RN with subcritical growth
2020
This paper deals with the nonlinear Dirichlet problem of capillary phenomena involving an equation driven by the p-Laplacian-like di¤erential operator in RN. We prove the existence of at least one nontrivial nonnegative weak solution, when the reaction term satisfies a sub-critical growth condition and the potential term has certain regularities. We apply the energy functional method and weaker compactness conditions.
Infinitely many solutions to boundary value problem for fractional differential equations
2018
Variational methods and critical point theorems are used to discuss existence of infinitely many solutions to boundary value problem for fractional order differential equations where Riemann-Liouville fractional derivatives and Caputo fractional derivatives are used. An example is given to illustrate our result.
Inverse estimation of terminal connections in the cardiac conduction system
2017
Modeling the cardiac conduction system is a challenging problem in the context of computational cardiac electrophysiology. Its ventricular section, the Purkinje system, is responsible for triggering tissue electrical activation at discrete terminal locations, which subsequently spreads throughout the ventricles. In this paper, we present an algorithm that is capable of estimating the location of the Purkinje system triggering points from a set of random measurements on tissue. We present the properties and the performance of the algorithm under controlled synthetic scenarios. Results show that the method is capable of locating most of the triggering points in scenarios with a fair ratio bet…
Systemic acidemia impairs cardiac function in critically Ill patients.
2021
Background: Acidemia, is associated with reduced cardiac function in animals, but no studies showing an effect of acidemia on cardiac function in humans are reported. In the present study, we examined the effect of acidemia on cardiac function assessed with transpulmonary thermodilution technique with integrated pulse contour analysis (Pulse Contour Cardiac Output, PiCCO™) in a large cohort of critically ill patients. Methods: This was a prospective multicenter observational cross-sectional study of 297 patients from 6 intensive care units in London, England selected from all patients admitted consecutively between May 2018 and March 2019. Measurements of lowest plasma pH and concurrent ass…
Indefinite integrals involving complete elliptic integrals of the third kind
2017
ABSTRACTA method developed recently for obtaining indefinite integrals of functions obeying inhomogeneous second-order linear differential equations has been applied to obtain integrals with respect to the modulus of the complete elliptic integral of the third kind. A formula is derived which gives an integral involving the complete integral of the third kind for every known integral for the complete elliptic integral of the second kind. The formula requires only differentiation and can therefore be applied for any such integral, and it is applied here to almost all such integrals given in the literature. Some additional integrals are derived using the recurrence relations for the complete …