Search results for "PROB"

Global Synchronization via Homogeneous Nucleation in Oscillating Surface Reactions

1999

The mechanism leading to globally synchronized oscillations in the $\mathrm{CO}+{\mathrm{O}}_{2}/\mathrm{Pt}\left(110\right)$ reaction system is investigated by means of Monte Carlo simulations. The model considers the reconstruction of the surface via phase border propagation and spontaneous phase nucleation. The reason for global oscillations turns out to be the spontaneous phase nucleation. This nucleation, which is modeled as a weak noise process, results in a random creation of dynamic defects and leads to global synchronization via stochastic resonance. The mechanism of global coupling via the gas phase, as it is proposed to date, does not occur.

Symmetry of minimizers with a level surface parallel to the boundary

2015

We consider the functional $$I_\Omega(v) = \int_\Omega [f(|Dv|) - v] dx,$$ where $\Omega$ is a bounded domain and $f$ is a convex function. Under general assumptions on $f$, G. Crasta [Cr1] has shown that if $I_\Omega$ admits a minimizer in $W_0^{1,1}(\Omega)$ depending only on the distance from the boundary of $\Omega$, then $\Omega$ must be a ball. With some restrictions on $f$, we prove that spherical symmetry can be obtained only by assuming that the minimizer has one level surface parallel to the boundary (i.e. it has only a level surface in common with the distance). We then discuss how these results extend to more general settings, in particular to functionals that are not differenti…

On the arithmetic of a family of degree-two K3 surfaces

2018

Let $\mathbb{P}$ denote the weighted projective space with weights $(1,1,1,3)$ over the rationals, with coordinates $x,y,z,$ and $w$; let $\mathcal{X}$ be the generic element of the family of surfaces in $\mathbb{P}$ given by \begin{equation*} X\colon w^2=x^6+y^6+z^6+tx^2y^2z^2. \end{equation*} The surface $\mathcal{X}$ is a K3 surface over the function field $\mathbb{Q}(t)$. In this paper, we explicitly compute the geometric Picard lattice of $\mathcal{X}$, together with its Galois module structure, as well as derive more results on the arithmetic of $\mathcal{X}$ and other elements of the family $X$.

Printing Life-Inspired Subcellular Scale Compartments with Autonomous Molecularly Crowded Confinement.

2019

A simple, rapid, and highly controlled platform to prepare life-inspired subcellular scale compartments by inkjet printing has been developed. These compartments consist of fL-scale aqueous droplets (few µm in diameter) incorporating biologically relevant molecular entities with programmed composition and concentration. These droplets are ink-jetted in nL mineral oil drop arrays allowing for lab-on-chip studies by fluorescence microscopy and fluorescence life time imaging. Once formed, fL-droplets are stable for several hours, thus giving the possibility of readily analyze molecular reactions and their kinetics and to verify molecular behavior and intermolecular interactions. Here, this pla…

2021

Abstract We extend the classical Carathéodory extension theorem to quasiconformal Jordan domains (Y, dY ). We say that a metric space (Y, dY ) is a quasiconformal Jordan domain if the completion ̄Y of (Y, dY ) has finite Hausdorff 2-measure, the boundary ∂Y = ̄Y \ Y is homeomorphic to 𝕊1, and there exists a homeomorphism ϕ: 𝔻 →(Y, dY ) that is quasiconformal in the geometric sense. We show that ϕ has a continuous, monotone, and surjective extension Φ: 𝔻 ̄ → Y ̄. This result is best possible in this generality. In addition, we find a necessary and sufficient condition for Φ to be a quasiconformal homeomorphism. We provide sufficient conditions for the restriction of Φ to 𝕊1 being a quasi…

A multi-methodology and sustainability-supporting framework for implementation and assessment of a holistic building renovation

La ristrutturazione degli edifici in futuro dovrà essere condotta secondo una prospettiva più olistica legata alla sostenibilità vista in una più ampia gamma di obiettivi/criteri e facilitata dagli scenari di ristrutturazione possibili. La ristrutturazione degli edifici dovrebbe servire a migliorarne le performance al fine di soddisfare le esigenze degli utenti, rendendo questi ultimi meno vulnerabili in relazione ai futuri costi energetici. Vi è un grande potenziale per ridurre il consumo di energia negli edifici esistenti. Tuttavia, ciò non deve comprometterè i valori architettonici e di qualità che rendono particolari. Pertanto, non possono essere semplicemente rinnovati, ma devono subir…

How can we apply the models of the quality of life and the quality of life management in an economy based on knowledge?

2017

The scientific substantiations of quality have been applied to models that pertain to mathematical statistics, the probability theory, the information theory, fuzzy systems, graphic methods, time series, and algebraic and numerical methods. To these, this article aims to present a new method of applying mathematical modelling in an economy based on knowledge, by using the concept of the definite integral, the composite function, and mathematical optimisation. The research methods used in the realisation of this article are bibliographic research, creation of new models, and problem-solving. Mathematical modelling, the simulation of the quality of life, etc. are methods and techniques of bot…

Janas Egles personības un stāstu krājuma „Svešie jeb miļeņkij ti moi” apguve literatūras stundās 10. klasē

2022

Diplomdarba „Janas Egles personības un stāstu krājuma „Svešie jeb miļeņkij ti moi” apguve literatūras stundās 10. klasē” mērķis ir izstrādāt metodisko apdari, kas rosinātu skolēnu interesi par Janas Egles personību un daiļradi, veicinātu izpratni par viņas stāstiem un tajos ietvertajām problēmām un vērtībām personības veidošanas kontekstā. Diplomdarba saturu veido ievads, piecas nodaļas ar apakšnodaļām, secinājumi un pielikumi. Pirmajā nodaļā apskatīta literatūras mācību priekšmeta specifika. Otrā nodaļa veltīta ieskatam Janas Egles personībā un daiļradē literatūras mācību priekšmeta kontekstā. Trešajā nodaļā aprakstīta skolotājas gatavošanās darbam klasē, tajā raksturotas 10. klases skolēn…

THE GROUP OF AUTOMORPHISMS OF THE SEMIGROUP OF ENDOMORPHISMS OF FREE COMMUTATIVE AND FREE ASSOCIATIVE ALGEBRAS

2007

Let W(X) be a free commutative or a free associative algebra. The group of automorphisms of the semigroup End (W(X)) is studied.

Fusing optical and SAR time series for LAI gap filling with multioutput Gaussian processes

2019

The availability of satellite optical information is often hampered by the natural presence of clouds, which can be problematic for many applications. Persistent clouds over agricultural fields can mask key stages of crop growth, leading to unreliable yield predictions. Synthetic Aperture Radar (SAR) provides all-weather imagery which can potentially overcome this limitation, but given its high and distinct sensitivity to different surface properties, the fusion of SAR and optical data still remains an open challenge. In this work, we propose the use of Multi-Output Gaussian Process (MOGP) regression, a machine learning technique that learns automatically the statistical relationships among…