Search results for "PD"

Zero Viscosity Limit for Analytic Solutions of the Navier-Stokes Equation on a Half-Space.¶ II. Construction of the Navier-Stokes Solution

1998

This is the second of two papers on the zero-viscosity limit for the incompressible Navier-Stokes equations in a half-space in either 2D or 3D. Under the assumption of analytic initial data, we construct solutions of Navier-Stokes for a short time which is independent of the viscosity. The Navier-Stokes solution is constructed through a composite asymptotic expansion involving the solutions of the Euler and Prandtl equations, which were constructed in the first paper, plus an error term. This shows that the Navier-Stokes solution goes to an Euler solution outside a boundary layer and to a solution of the Prandtl equations within the boundary layer. The error term is written as a sum of firs…

A remark on infinite initial values for quasilinear parabolic equations

2020

Abstract We study the possibility of prescribing infinite initial values for solutions of the Evolutionary p -Laplace Equation in the fast diffusion case p > 2 . This expository note has been extracted from our previous work. When infinite values are prescribed on the whole initial surface, such solutions can exist only if the domain is a space–time cylinder.

AAS “CBL Life” un tās nozares darbības analīze

2022

Bakalaura darba tēma ir AAS „CBL Life” un tās nozares darbības analīze. Tēma tika izvēlētā jo Latvijā dzīvības apdrošināšana nav viens no populārākajiem apdrošināšanas veidiem , pirmajā vietā ir OCTA , turpretī Eiropas Savienības attīstītajās valstīs dzīvības apdrošināšanas polises ir vienā no pirmajām vietām starp apdrošināšanas veidiem, kas tiek noslēgti. Apdrošināšana nozares finanšu dati ir komplicēti un specifiski ja salīdzina ar sabiedrībām ar ierobežotu atbildību. Autorei šķita interesanti noskaidrot kādas ir tendences, tirgus dati un kā tie ietekmē finanšu rādītājus un nozari kopumā. Bakalaura darba mērķis ir izpētīt galvenos apdrošināšanas tirgus rādītājus un pielietojot tos a…

Latwijas saimneeziba pee spehjigas un pee nespehjigas waldibas [Latvijas saimniecība pie spējīgas un nespējīgas valdības]

1928

Polarization tensors of planar domains as functions of the admittivity contrast

2014

(Electric) polarization tensors describe part of the leading order term of asymptotic voltage perturbations caused by low volume fraction inhomogeneities of the electrical properties of a medium. They depend on the geometry of the support of the inhomogeneities and on their admittivity contrast. Corresponding asymptotic formulas are of particular interest in the design of reconstruction algorithms for determining the locations and the material properties of inhomogeneities inside a body from measurements of current flows and associated voltage potentials on the body's surface. In this work we consider the two-dimensional case only and provide an analytic representation of the polarization t…

Dynamic Ordering of Firewall Rules Using a Novel Swapping Window-based Paradigm

2016

Designing and implementing efficient firewall strategies in the age of the Internet of Things (IoT) is far from trivial. This is because, as time proceeds, an increasing number of devices will be connected, accessed and controlled on the Internet. Additionally, an ever-increasingly amount of sensitive information will be stored on various networks. A good and effi- cient firewall strategy will attempt to secure this information, and to also manage the large amount of inevitable network traffic that these devices create. The goal of this paper is to propose a framework for designing optimized firewalls for the IoT. This paper deals with two fundamental challenges/problems encountered in such…

Everywhere differentiability of viscosity solutions to a class of Aronsson's equations

2017

For any open set $\Omega\subset\mathbb R^n$ and $n\ge 2$, we establish everywhere differentiability of viscosity solutions to the Aronsson equation $$ =0 \quad \rm in\ \ \Omega, $$ where $H$ is given by $$H(x,\,p)==\sum_{i,\,j=1}^na^{ij}(x)p_i p_j,\ x\in\Omega, \ p\in\mathbb R^n, $$ and $A=(a^{ij}(x))\in C^{1,1}(\bar\Omega,\mathbb R^{n\times n})$ is uniformly elliptic. This extends an earlier theorem by Evans and Smart \cite{es11a} on infinity harmonic functions.

Compact embeddings and indefinite semilinear elliptic problems

2002

Our purpose is to find positive solutions $u \in D^{1,2}(\rz^N)$ of the semilinear elliptic problem $-\laplace u = h(x) u^{p-1}$ for $2<p$. The function $h$ may have an indefinite sign. Key ingredients are a $h$-dependent concentration-compactness Lemma and a characterization of compact embeddings of $D^{1,2}(\rz^N)$ into weighted Lebesgue spaces.

Anisotropic elliptic equations with gradient-dependent lower order terms and L^1 data

2023

&lt;abstract&gt;&lt;p&gt;We prove the existence of a weak solution for a general class of Dirichlet anisotropic elliptic problems such as $ \mathcal Au+\Phi(x, u, \nabla u) = \mathfrak{B}u+f $ in $ \Omega $, where $ \Omega $ is a bounded open subset of $ \mathbb R^N $ and $ f\in L^1(\Omega) $ is arbitrary. The principal part is a divergence-form nonlinear anisotropic operator $ \mathcal A $, the prototype of which is $ \mathcal A u = -\sum_{j = 1}^N \partial_j(|\partial_j u|^{p_j-2}\partial_j u) $ with $ p_j &amp;gt; 1 $ for all $ 1\leq j\leq N $ and $ \sum_{j = 1}^N (1/p_j) &amp;gt; 1 $. As a novelty in this paper, our lower order terms involve a new class of operators $ \mathfrak B $ such…

TOF LiDAR with SiPM technology

2016

LiDAR (Light Detection And Ranging) systems measures the distance from the sensor to the target by determining the time between the release of the laser pulse to the receiving of the backscattered pulse. The interest in LiDAR technology has exploded in recent years since the applications are numerous. Here, we would highlight the Advanced Driver Assistance Systems (ADAS) and for rendezvous & docking operations between spacecraft. We built two LiDAR systems differing for the detector: a Silicon Photomultiplier (SiPM) and an Avalanche Photodiode (APD). The advantages of the SiPM approach has been extensively discussed in [1]. The comparison between these systems has been performed in terms of…