Search results for "analysis."
showing 10 items of 26008 documents
Molecular Characterization of a Variant of Bacillus anthracis-Specific Phage AP50 with Improved Bacteriolytic Activity▿ †
2008
ABSTRACT The genome sequence of a Bacillus anthracis -specific clear plaque mutant phage, AP50c, contains 31 open reading frames spanning 14,398 bp, has two mutations compared to wild-type AP50t, and has a colinear genome architecture highly similar to that of gram-positive Tectiviridae phages. Spontaneous AP50c-resistant B. anthracis mutants exhibit a mucoid colony phenotype.
Game-Theoretic Approach to Hölder Regularity for PDEs Involving Eigenvalues of the Hessian
2021
AbstractWe prove a local Hölder estimate for any exponent $0<\delta <\frac {1}{2}$ 0 < δ < 1 2 for solutions of the dynamic programming principle $$ \begin{array}{@{}rcl@{}} u^{\varepsilon} (x) = \sum\limits_{j=1}^{n} \alpha_{j} \underset{\dim(S)=j}{\inf} \underset{|v|=1}{\underset{v\in S}{\sup}} \frac{u^{\varepsilon} (x + \varepsilon v) + u^{\varepsilon} (x - \varepsilon v)}{2} \end{array} $$ u ε ( x ) = ∑ j = 1 n α j inf dim ( S ) = j sup v ∈ S | v | = 1 u ε ( x + ε v ) + u ε ( x − ε v ) 2 with α1,αn > 0 and α2,⋯ ,αn− 1 ≥ 0. The proof is based on a new coupling idea from game theory. As an application, we get the same regularity estimate for viscosity solutions of the PDE $…
Equivalence of viscosity and weak solutions for a $p$-parabolic equation
2019
AbstractWe study the relationship of viscosity and weak solutions to the equation $$\begin{aligned} \smash {\partial _{t}u-\varDelta _{p}u=f(Du)}, \end{aligned}$$ ∂ t u - Δ p u = f ( D u ) , where $$p>1$$ p > 1 and $$f\in C({\mathbb {R}}^{N})$$ f ∈ C ( R N ) satisfies suitable assumptions. Our main result is that bounded viscosity supersolutions coincide with bounded lower semicontinuous weak supersolutions. Moreover, we prove the lower semicontinuity of weak supersolutions when $$p\ge 2$$ p ≥ 2 .
Hölder regularity for the gradient of the inhomogeneous parabolic normalized p-Laplacian
2018
In this paper, we study an evolution equation involving the normalized [Formula: see text]-Laplacian and a bounded continuous source term. The normalized [Formula: see text]-Laplacian is in non-divergence form and arises for example from stochastic tug-of-war games with noise. We prove local [Formula: see text] regularity for the spatial gradient of the viscosity solutions. The proof is based on an improvement of flatness and proceeds by iteration.
Regularity for nonlinear stochastic games
2015
We establish regularity for functions satisfying a dynamic programming equation, which may arise for example from stochastic games or discretization schemes. Our results can also be utilized in obtaining regularity and existence results for the corresponding partial differential equations. peerReviewed
Remarks on regularity for p-Laplacian type equations in non-divergence form
2018
We study a singular or degenerate equation in non-divergence form modeled by the $p$-Laplacian, $$-|Du|^\gamma\left(\Delta u+(p-2)\Delta_\infty^N u\right)=f\ \ \ \ \text{in}\ \ \ \Omega.$$ We investigate local $C^{1,\alpha}$ regularity of viscosity solutions in the full range $\gamma>-1$ and $p>1$, and provide local $W^{2,2}$ estimates in the restricted cases where $p$ is close to 2 and $\gamma$ is close to 0.
Passive Control of Linear Structures Equipped with non-Linear Viscous Dampers and Amplification Mechanism
2008
Fluid damper devices in civil structures such as buildings or bridges are commonly used as energy absorbers for seismic protection. The problem in the response analysis of structures with filled dampers mainly consists in the fact that, due to the strongly nonlinear behavior of such equipments, the response spectrum technique fails. Moreover, in order to enhance the damping effect various toggle brace configurations have been recently proposed. In this paper by using the concept of power spectral density function compatible with the elastic response spectrum and the stochastic linearization technique, the equivalent damping ratio is obtained. It is shown that once the system is linearized r…
Fractional Hardy inequalities and visibility of the boundary
2013
We prove fractional order Hardy inequalities on open sets under a combined fatness and visibility condition on the boundary. We demonstrate by counterexamples that fatness conditions alone are not sufficient for such Hardy inequalities to hold. In addition, we give a short exposition of various fatness conditions related to our main result, and apply fractional Hardy inequalities in connection to the boundedness of extension operators for fractional Sobolev spaces.
The ALICE experiment at the CERN LHC
2008
Journal of Instrumentation 3(08), S08002 (2008). doi:10.1088/1748-0221/3/08/S08002
Visual Contrast Modulates Operant Learning Responses in Larval Zebrafish.
2018
The larval zebrafish is a promising vertebrate model organism to study neural mechanisms underlying learning and memory due to its small brain and rich behavioral repertoire. Here, we report on a high-throughput operant conditioning system for zebrafish larvae, which can simultaneously train 12 fish to associate a visual conditioned pattern with electroshocks. We find that the learning responses can be enhanced by the visual contrast, not the spatial features of the conditioned patterns, highlighted by several behavioral metrics. By further characterizing the learning curves as well as memory extinction, we demonstrate that the percentage of learners and the memory length increase as the co…