Search results for "model."

Quantitative Approximation Properties for the Fractional Heat Equation

2017

In this note we analyse \emph{quantitative} approximation properties of a certain class of \emph{nonlocal} equations: Viewing the fractional heat equation as a model problem, which involves both \emph{local} and \emph{nonlocal} pseudodifferential operators, we study quantitative approximation properties of solutions to it. First, relying on Runge type arguments, we give an alternative proof of certain \emph{qualitative} approximation results from \cite{DSV16}. Using propagation of smallness arguments, we then provide bounds on the \emph{cost} of approximate controllability and thus quantify the approximation properties of solutions to the fractional heat equation. Finally, we discuss genera…

Gradient and Lipschitz Estimates for Tug-of-War Type Games

2021

We define a random step size tug-of-war game and show that the gradient of a value function exists almost everywhere. We also prove that the gradients of value functions are uniformly bounded and converge weakly to the gradient of the corresponding $p$-harmonic function. Moreover, we establish an improved Lipschitz estimate when boundary values are close to a plane. Such estimates are known to play a key role in the higher regularity theory of partial differential equations. The proofs are based on cancellation and coupling methods as well as an improved version of the cylinder walk argument. peerReviewed

An evolutionary Haar-Rado type theorem

2021

AbstractIn this paper, we study variational solutions to parabolic equations of the type $$\partial _t u - \mathrm {div}_x (D_\xi f(Du)) + D_ug(x,u) = 0$$ ∂ t u - div x ( D ξ f ( D u ) ) + D u g ( x , u ) = 0 , where u attains time-independent boundary values $$u_0$$ u 0 on the parabolic boundary and f, g fulfill convexity assumptions. We establish a Haar-Rado type theorem: If the boundary values $$u_0$$ u 0 admit a modulus of continuity $$\omega $$ ω and the estimate $$|u(x,t)-u_0(\gamma )| \le \omega (|x-\gamma |)$$ | u ( x , t ) - u 0 ( γ ) | ≤ ω ( | x - γ | ) holds, then u admits the same modulus of continuity in the spatial variable.

Assouad Type Dimensions in Geometric Analysis

2021

We consider applications of the dual pair of the (upper) Assouad dimension and the lower (Assouad) dimension in analysis. We relate these notions to other dimensional conditions such as a Hausdorff content density condition and an integrability condition for the distance function. The latter condition leads to a characterization of the Muckenhoupt Ap properties of distance functions in terms of the (upper) Assouad dimension. It is also possible to give natural formulations for the validity of Hardy–Sobolev inequalities using these dual Assouad dimensions, and this helps to understand the previously observed dual nature of certain cases of these inequalities. peerReviewed

Refined instability estimates for some inverse problems

2022

Many inverse problems are known to be ill-posed. The ill-posedness can be manifested by an instability estimate of exponential type, first derived by Mandache [29]. In this work, based on Mandache's idea, we refine the instability estimates for two inverse problems, including the inverse inclusion problem and the inverse scattering problem. Our aim is to derive explicitly the dependence of the instability estimates on key parameters. The first result of this work is to show how the instability depends on the depth of the hidden inclusion and the conductivity of the background medium. This work can be regarded as a counterpart of the depth-dependent and conductivity-dependent stability estim…

On some partial data Calderón type problems with mixed boundary conditions

2021

In this article we consider the simultaneous recovery of bulk and boundary potentials in (degenerate) elliptic equations modelling (degenerate) conducting media with inaccessible boundaries. This connects local and nonlocal Calderón type problems. We prove two main results on these type of problems: On the one hand, we derive simultaneous bulk and boundary Runge approximation results. Building on these, we deduce uniqueness for localized bulk and boundary potentials. On the other hand, we construct a family of CGO solutions associated with the corresponding equations. These allow us to deduce uniqueness results for arbitrary bounded, not necessarily localized bulk and boundary potentials. T…

Nutritional properties and plausible benefits of Pearl millet (Pennisetum glaucum) on bone metabolism and osteoimmunology : a mini-review

2020

Bone is a hard connective tissue that undergoes a systematic renewal. This highly dynamic organ is made up of four different types of cells, however, bone formation is commonly attributed to osteoblasts and bone resorption to osteoclasts. Bone tissue formation occurs during embryonic development and in certain post-birth pathological conditions. The immune system could influence the functions of bone cells, and the crosstalk between hematopoietic, immune, and bone cells is known as osteoimmunology. Indeed, cytokines produced by immune cells, including TNF-α and IL-6, are critically implicated in bone pathogenesis. It is well established that diet plays an important role in bone health and f…

Osteoporosi nell’anziano.

2009

Suite of Statistical Models Forecasting Latvian GDP

2014

Abstract We develop a suite of statistical models to forecast Latvian GDP. We employ various univariate and multivariate econometric techniques to obtain short-term GDP projections and to assess the performance of the models. We also comprise the information contained in components of GDP and obtain short-term GDP projections from disaggregated perspective. We run out-of-sample forecasting procedures to evaluate GDP projections and to assess forecasting accuracy of all individual statistical models. We conclude that factor and bridge models are among the best individually performing models in the suite. Forecasting accuracy obtained using disaggregated models of factor and bridge models is …

Information system implementation model and observations - Case health care, social services and other service processes in smaller municipalities

2012

Public sector in Finland is under heavy pressure to get more efficient and customer oriented. Information systems and their development is one possibility to improve municipalities’ own processes and their service offering to the inhabitants. In this study we investigated what is the status of Information Systems in municipal governance and architecture management. The situation with systems landscape and architecture is, based on our findings, very scattered and municipals do not make their decisions, for example outsourcing decisions, in a systematic way. Based on those findings, especially in small municipalities, we created a model, which municipal ICT responsible professionals can foll…