Search results for "first"

Stochastic integro-differential and differential equations of non-linear systems excited by parametric Poisson pulses

1997

Abstract The connection between stochastic integro-differential equation and stochastic differential equation of non-linear systems driven by parametric Poisson delta correlated processes is presented. It is shown that the two different formulations are fully equivalent in the case of external excitation. In the case of parametric type excitation the two formulation are equivalent if the non-linear argument in the integral representation is related by means of a series to the corresponding non-linear parametric term in the stochastic differential equation. Differential rules for the two representations to find moment equations of every order of the response are also compared.

Hydrodynamics and Stochastic Differential Equation with Sobolev Coefficients

2013

In this chapter, we will explain how the Brenier’s relaxed variational principle for Euler equation makes involved the ordinary differential equations with Sobolev coefficients and how the investigation on stochastic differential equations (SDE) with Sobolev coefficients is useful to establish variational principles for Navier–Stokes equations. We will survey recent results on this topic.

A Scenario Simulation Model of Stock's Volatility Based on a Stationary Markovian Process

2013

In this paper we discuss univariate statistical properties of volatility. We present a parsimonious univariate model that well reproduces two stylized facts of volatility: the power-law decay of the volatility probability density function with exponent α and the power-law decay of the autocorrelation function with exponent β. Such model also reproduces, at least qualitatively, the empirical observation than when the probability density function decays faster, then the autocorrelation decays slower. Another important feature investigated within the model is the mean First Passage Time (mFPT) Tx0 (Λ) of volatility time-series. We show that the proposed model allows to obtain the mFPT in terms…

Stochastic model of memristor based on the length of conductive region

2021

Abstract We propose a stochastic model of a voltage controlled bipolar memristive system, which includes the properties of widely used dynamic SPICE models and takes into account the fluctuations inherent in memristors. The proposed model is described by rather simple equations of Brownian diffusion, does not require significant computational resources for numerical modeling, and allows obtaining the exact analytical solutions in some cases. The noise-induced transient bimodality phenomenon, arising under resistive switching, was revealed and investigated theoretically and experimentally in a memristive system, by finding a quite good qualitatively agreement between theory and experiment. B…

TCT-43 First-in-human experience of a novel transradial device for embolic deflection during transcatheter aortic valve replacement

2018

The average stroke rate in contemporary transcatheter aortic valve replacement (TAVR) studies is 4.4%. The majority of the TAVR studies are non-randomized registries, hence, neurological outcomes may be underreported. Over 50% of all TAVR related strokes occur during the procedure or on the same day

A Concept for Quantitative Comparison of Mathematical and Natural Language and its possible Effect on Learning

2017

Starting with the question whether there is a connection between the mathematical capabilities of a person and his or her mother tongue, we introduce a new modeling approach to quantitatively compare natural languages with mathematical language. The question arises from educational assessment studies that indicate such a relation. Texts written in natural languages can be deconstructed into a dependence graph, in simple cases a dependence tree. The same kind of deconstruction is also possible for mathematical texts. This gives an idea of how to quantitatively compare mathematical and natural language. To that end, we develop algorithms to define the distance between graphs. In this paper, w…

Topical Depth and Writing Quality in Student EFL Compositions

1992

ABSTRACT This study tests a method to describe the relationship between coherence and writing quality by using topical structure analysis. Originally the method was used to examine short professional texts written in the mother tongue (L1) but in the present study it is applied to short compositions written in English by students learning this foreign language (EFL). The analyses showed that what characterized good writers was the ability to develop the topics in their compositions more evenly across several topic levels than mid‐quality writers and especially the poor writers. Good writers were more homogeneous (measured by the size of standard deviation) as a group in handling topics at h…

Existence, nonexistence and uniqueness of positive solutions for nonlinear eigenvalue problems

2017

We study the existence of positive solutions for perturbations of the classical eigenvalue problem for the Dirichlet $p-$Laplacian. We consider three cases. In the first the perturbation is $(p-1)-$sublinear near $+\infty$, while in the second the perturbation is $(p-1)-$superlinear near $+\infty$ and in the third we do not require asymptotic condition at $+\infty$. Using variational methods together with truncation and comparison techniques, we show that for $\lambda\in (0, \widehat{\lambda}_1)$ -$\lambda>0$ is the parameter and $\widehat{\lambda}_1$ being the principal eigenvalue of $\left(-\Delta_p, W^{1, p}_0(\Omega)\right)$ -we have positive solutions, while for $\lambda\geq \widehat{\…

A journey into the information Typhoon: Typhoon Haiyan DRL Field Report Findings and Research Insights:

2013

Dispersive interactions between atoms and nonplanar surfaces

2009

We calculate the dispersive force between a ground state atom and a non planar surface. We present explicit results for a corrugated surface, derived from the scattering approach at first order in the corrugation amplitude. A variety of analytical results are derived in different limiting cases, including the van der Waals and Casimir-Polder regimes. We compute numerically the exact first-order dispersive potential for arbitrary separation distances and corrugation wavelengths, for a Rubidium atom on top of a silicon or gold corrugated surface. We discuss in detail the inadequacy of the proximity force approximation, and present a simple but adequate approximation for computing the potentia…