scholarly journals Review on the Stability of the Peregrine and Related Breathers

2020 ◽  
Vol 8 ◽  
Author(s):  
Miguel A. Alejo ◽  
Luca Fanelli ◽  
Claudio Muñoz
Keyword(s):  
Spectral Properties ◽  
Lyapunov Functionals ◽  
Nonlinear Odes ◽  
First Variation ◽  
Standard Definition ◽  
Nonlinear Schrödinger ◽  
Open Questions ◽  
The First Variation ◽  
The Stability ◽  
Definition Of

In this note, we review stability properties in energy spaces of three important nonlinear Schrödinger breathers: Peregrine, Kuznetsov-Ma, and Akhmediev. More precisely, we show that these breathers are unstable according to a standard definition of stability. Suitable Lyapunov functionals are described, as well as their underlying spectral properties. As an immediate consequence of the first variation of these functionals, we also present the corresponding nonlinear ODEs fulfilled by these nonlinear Schrödinger breathers. The notion of global stability for each breather mentioned above is finally discussed. Some open questions are also briefly mentioned.

scholarly journals On the Stability Problem of Equilibrium Discrete Planar Curves

2021 ◽  
Author(s):  
Yoshiki Jikumaru
Keyword(s):  
Variational Methods ◽  
Stability Problem ◽  
Curvature Vector ◽  
Constraint Condition ◽  
Discrete Curvature ◽  
First Variation ◽  
Discrete Curvatures ◽  
Polygonal Curves ◽  
The First Variation ◽  
The Stability

AbstractWe study planar polygonal curves with the variational methods. We show a unified interpretation of discrete curvatures and the Steiner-type formula by extracting the notion of the discrete curvature vector from the first variation of the length functional. Moreover, we determine the equilibrium curves for the length functional under the area-constraint condition and study their stability.

scholarly journals A discrete time method to the first variation of fractional order variational functionals

Open Physics ◽  
2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Shakoor Pooseh ◽  
Ricardo Almeida ◽  
Delfim Torres
Keyword(s):  
Fractional Order ◽  
Fractional Derivatives ◽  
Variational Problems ◽  
Effective Solution ◽  
First Variation ◽  
First Order ◽  
Variational Functional ◽  
Discrete Nature ◽  
The First Variation ◽  
Definition Of

AbstractThe fact that the first variation of a variational functional must vanish along an extremizer is the base of most effective solution schemes to solve problems of the calculus of variations. We generalize the method to variational problems involving fractional order derivatives. First order splines are used as variations, for which fractional derivatives are known. The Grünwald-Letnikov definition of fractional derivative is used, because of its intrinsic discrete nature that leads to straightforward approximations.

Postmodern More

Moreana ◽  
2003 ◽  
Vol 40 (Number 153- (1-2) ◽  
pp. 219-239
Author(s):  
Anne Lake Prescott
Keyword(s):  
Human Language ◽  
Thomas More ◽  
The Stability ◽  
Definition Of ◽  
Recent Critic

Thomas More is often called a “humanist,” and rightly so if the word has its usual meaning in scholarship on the Renaissance. “Humanist” has by now acquired so many different and contradictory meanings, however, that it needs to be applied carefully to the likes of More. Many postmodernists tend to use the word, pejoratively, to mean someone who believes in an autonomous self, the stability of words, reason, and the possibility of determinable meanings. Without quite arguing that More was a postmodernist avant la lettre, this essay suggests that he was not a “humanist” who stalks the pages of much recent postmodernist theory and that in fact even while remaining a devout Catholic and sensible lawyer he was quite as aware as any recent critic of the slipperiness of human selves and human language. It is time that literary critics tightened up their definition of “humanist,” especially when writing about the Renaissance.

scholarly journals Influence of study model, baseline catalytic concentrations and analytical system on the stability of serum alanine aminotransferase

2020 ◽  
Vol 1 (2) ◽  
Author(s):  
Josep Miquel Bauça ◽  
Andrea Caballero ◽  
Carolina Gómez ◽  
Débora Martínez-Espartosa ◽  
Isabel García del Pino ◽  
...  
Keyword(s):  
Alanine Aminotransferase ◽  
Experimental Models ◽  
Individual Variability ◽  
Serum Samples ◽  
Multicentric Study ◽  
Different Temperatures ◽  
The Stability ◽  
Analytical System ◽  
Definition Of ◽  
Analytical Platforms

AbstractObjectivesThe stability of the analytes most commonly used in routine clinical practice has been the subject of intensive research, with varying and even conflicting results. Such is the case of alanine aminotransferase (ALT). The purpose of this study was to determine the stability of serum ALT according to different variables.MethodsA multicentric study was conducted in eight laboratories using serum samples with known initial catalytic concentrations of ALT within four different ranges, namely: <50 U/L (<0.83 μkat/L), 50–200 U/L (0.83–3.33 μkat/L), 200–400 U/L (3.33–6.67 μkat/L) and >400 U/L (>6.67 μkat/L). Samples were stored for seven days at two different temperatures using four experimental models and four laboratory analytical platforms. The respective stability equations were calculated by linear regression. A multivariate model was used to assess the influence of different variables.ResultsCatalytic concentrations of ALT decreased gradually over time. Temperature (−4%/day at room temperature vs. −1%/day under refrigeration) and the analytical platform had a significant impact, with Architect (Abbott) showing the greatest instability. Initial catalytic concentrations of ALT only had a slight impact on stability, whereas the experimental model had no impact at all.ConclusionsThe constant decrease in serum ALT is reduced when refrigerated. Scarcely studied variables were found to have a significant impact on ALT stability. This observation, added to a considerable inter-individual variability, makes larger studies necessary for the definition of stability equations.

scholarly journals On the explicit representation of the trace space $$H^{\frac{3}{2}}$$ and of the solutions to biharmonic Dirichlet problems on Lipschitz domains via multi-parameter Steklov problems

2021 ◽  
Author(s):  
Pier Domenico Lamberti ◽  
Luigi Provenzano
Keyword(s):  
Fourier Series ◽  
Dirichlet Problem ◽  
Lipschitz Domain ◽  
Spectral Properties ◽  
Explicit Representation ◽  
Lipschitz Domains ◽  
Dirichlet Problems ◽  
Trace Space ◽  
In Series ◽  
Definition Of

AbstractWe consider the problem of describing the traces of functions in $$H^2(\Omega )$$ H 2 ( Ω ) on the boundary of a Lipschitz domain $$\Omega $$ Ω of $$\mathbb R^N$$ R N , $$N\ge 2$$ N ≥ 2 . We provide a definition of those spaces, in particular of $$H^{\frac{3}{2}}(\partial \Omega )$$ H 3 2 ( ∂ Ω ) , by means of Fourier series associated with the eigenfunctions of new multi-parameter biharmonic Steklov problems which we introduce with this specific purpose. These definitions coincide with the classical ones when the domain is smooth. Our spaces allow to represent in series the solutions to the biharmonic Dirichlet problem. Moreover, a few spectral properties of the multi-parameter biharmonic Steklov problems are considered, as well as explicit examples. Our approach is similar to that developed by G. Auchmuty for the space $$H^1(\Omega )$$ H 1 ( Ω ) , based on the classical second order Steklov problem.

scholarly journals Existence Results for the Conformal Dirac–Einstein System

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Chiara Guidi ◽  
Ali Maalaoui ◽  
Vittorio Martino
Keyword(s):  
Perturbation Methods ◽  
Existence Of Solutions ◽  
Coupled System ◽  
Existence Results ◽  
First Variation ◽  
The First Variation

AbstractWe consider the coupled system given by the first variation of the conformal Dirac–Einstein functional. We will show existence of solutions by means of perturbation methods.

A practical metric for melanopic metrology

2019 ◽  
Vol 51 (8) ◽  
pp. 1178-1191 ◽  
Author(s):  
SM Berman ◽  
RD Clear
Keyword(s):  
Ganglion Cell ◽  
Retinal Ganglion Cell ◽  
Vision Research ◽  
Spectral Response ◽  
Retinal Ganglion ◽  
Standard Definition ◽  
Standard Unit ◽  
Vision Science ◽  
The Past ◽  
Definition Of

Over the past decade, there has been a growing interest in lighting research on the effects of the recently discovered melanopsin receptor (also referred to as the intrinsically photosensitive retinal ganglion cell) and its impacts on health and vision. Presently, there is not a generally accepted metrology for dealing with the spectral response of the melanopsin receptor as applied to both lighting and vision research. A proposition to handle this issue from a vision science perspective has been presented in 2014 in the journal Trends in Neurosciences and from a more lighting perspective in 2017 in Lighting Research and Technology. These propositions are complex, and do not retain the CIE standard definition of a lumen. In this paper, we propose an approach based on effective watts and melanopic/photopic ratios that is both simpler and more closely aligned with CIE standard unit definitions. In addition, we include some practical examples of how such ratios are accessible now, and can be used for both lighting and vision research as well as applications.

scholarly journals Reliable Learning with PDE-Based CNNs and DenseNets for Detecting COVID-19, Pneumonia, and Tuberculosis from Chest X-Ray Images

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 434
Author(s):  
Anca Nicoleta Marginean ◽  
Delia Doris Muntean ◽  
George Adrian Muntean ◽  
Adelina Priscu ◽  
Adrian Groza ◽  
...  
Keyword(s):  
Transfer Learning ◽  
Negative Impact ◽  
X Ray ◽  
Domain Specific ◽  
Direct Training ◽  
Public Data ◽  
Normal Chest ◽  
Chest X Ray ◽  
The Stability ◽  
Definition Of

It has recently been shown that the interpretation by partial differential equations (PDEs) of a class of convolutional neural networks (CNNs) supports definition of architectures such as parabolic and hyperbolic networks. These networks have provable properties regarding the stability against the perturbations of the input features. Aiming for robustness, we tackle the problem of detecting changes in chest X-ray images that may be suggestive of COVID-19 with parabolic and hyperbolic CNNs and with domain-specific transfer learning. To this end, we compile public data on patients diagnosed with COVID-19, pneumonia, and tuberculosis, along with normal chest X-ray images. The negative impact of the small number of COVID-19 images is reduced by applying transfer learning in several ways. For the parabolic and hyperbolic networks, we pretrain the networks on normal and pneumonia images and further use the obtained weights as the initializers for the networks to discriminate between COVID-19, pneumonia, tuberculosis, and normal aspects. For DenseNets, we apply transfer learning twice. First, the ImageNet pretrained weights are used to train on the CheXpert dataset, which includes 14 common radiological observations (e.g., lung opacity, cardiomegaly, fracture, support devices). Then, the weights are used to initialize the network which detects COVID-19 and the three other classes. The resulting networks are compared in terms of how well they adapt to the small number of COVID-19 images. According to our quantitative and qualitative analysis, the resulting networks are more reliable compared to those obtained by direct training on the targeted dataset.

scholarly journals Analysis of Urban Effects in Oklahoma City using a Dense Surface Observing Network

2016 ◽  
Vol 55 (3) ◽  
pp. 723-741 ◽  
Author(s):  
Xiao-Ming Hu ◽  
Ming Xue ◽  
Petra M. Klein ◽  
Bradley G. Illston ◽  
Sheng Chen
Keyword(s):  
Metropolitan Area ◽  
Land Surface ◽  
Critical Role ◽  
Central Business District ◽  
Temperature Inversion ◽  
Oklahoma City ◽  
Near Surface ◽  
Open Questions ◽  
The Stability ◽  
Business District

AbstractMany studies have investigated urban heat island (UHI) intensity for cities around the world, which is normally quantified as the temperature difference between urban location(s) and rural location(s). A few open questions still remain regarding the UHI, such as the spatial distribution of UHI intensity, temporal (including diurnal and seasonal) variation of UHI intensity, and the UHI formation mechanism. A dense network of atmospheric monitoring sites, known as the Oklahoma City (OKC) Micronet (OKCNET), was deployed in 2008 across the OKC metropolitan area. This study analyzes data from OKCNET in 2009 and 2010 to investigate OKC UHI at a subcity spatial scale for the first time. The UHI intensity exhibited large spatial variations over OKC. During both daytime and nighttime, the strongest UHI intensity is mostly confined around the central business district where land surface roughness is the highest in the OKC metropolitan area. These results do not support the roughness warming theory to explain the air temperature UHI in OKC. The UHI intensity of OKC increased prominently around the early evening transition (EET) and stayed at a fairly constant level throughout the night. The physical processes during the EET play a critical role in determining the nocturnal UHI intensity. The near-surface rural temperature inversion strength was a good indicator for nocturnal UHI intensity. As a consequence of the relatively weak near-surface rural inversion, the strongest nocturnal UHI in OKC was less likely to occur in summer. Other meteorological factors (e.g., wind speed and cloud) can affect the stability/depth of the nighttime boundary layer and can thus modulate nocturnal UHI intensity.

The Humdrum Use of Ultimate Authority: Defining and Analysing Chapter VII Resolutions

2009 ◽  
Vol 78 (3) ◽  
pp. 309-342 ◽  
Author(s):  
Patrik Johansson
Keyword(s):  
Cold War ◽  
United Nations ◽  
Security Council ◽  
Security Council Resolution ◽  
Post Cold War ◽  
Standard Definition ◽  
The Status ◽  
Definition Of ◽  
The Cold War ◽  
Business As Usual

AbstractUnder Chapter VII of the Charter of the United Nations, the Security Council has the unique authority to make decisions that are binding on member states. However, the lack of a standard definition of what makes a Security Council resolution "a Chapter VII resolution" has caused disagreement regarding the status of several resolutions. This is unfortunate as the international community should never have to doubt whether a Security Council resolution is in fact adopted under Chapter VII or not. It is also unnecessary. This article addresses this problem by proposing a definition of Chapter VII resolutions, based on two criteria referred to as "Article 39 determinations" and "Chapter VII decisions". On the basis of the proposed definition, the article describes and analyses a dramatic increase in the use of Chapter VII during the post-Cold War era. It concludes that as Chapter VII has come to constitute the majority of Security Council resolutions in recent years, the resort to Chapter VII no longer signifies exceptional determination and resolve, which it did during the Cold War; instead Chapter VII today implies business as usual. An appendix lists all Chapter VII resolutions from 1946–2008.

Sign in / Sign up

Export Citation Format

Share Document