bluuebunny/crossref_metadata_2025_split huggingface dataset:
$C^∞$ regularity of solutions of the Levi equation
Authors: Citti G. 
Published: July 2002

We will prove the

C^∞

regularity of the classical solutions of the equation

\mathcal{L}_{u} = q\frac{\left(1 + \left|\mathrm{grad}u\right|^{2}\right)^{3/ 2}}{1 + u_{t}^{2}}

where

\mathcal{L}u = u_{xx} + u_{yy} + 2\frac{u_{y} - u_{x}u_{t}}{1 + u_{t}^{2}}u_{xt} - 2\frac{u_{x} + u_{y}u_{t}}{1 + u_{t}^{2}}u_{yt} + \frac{u_{x}^{2} + u_{y}^{2}}{1 + u_{t}^{2}}u_{tt},

q \in C^{\infty }(\Omega )

and

q(ξ) ≠ 0

for every

ξ \in Ω

. This is a second order quasilinear equation, whose characteristic form has zero determinant at every point, and for every function

u

. However we will write it as a sum of squares of nonlinear vector fields, and we will extablish the result by means of a suitable freezing method.

Résumé

Nous prouvons la régularité

C^∞

des solutions classiques de l’équation

\mathcal{L}u = q\frac{\left(1 + \left|gradu\right|^{2}\right)^{3/ 2}}{1 + u_{t}^{2}}

où

\mathcal{L}u = u_{xx} + u_{yy} + 2\frac{u_{y} - u_{x}u_{t}}{1 + u_{t}^{2}}u_{xt} - 2\frac{u_{x} + u_{y}u_{t}}{1 + u_{t}^{2}}u_{yt} + \frac{u_{x}^{2} + u_{y}^{2}}{1 + u_{t}^{2}}u_{tt},

q \in C^{\infty }\left(\Omega \right)

et

q(ξ) ≠ 0

pour tout

ξ \in Ω

. Il s’agit d’une équation quasilinéaire du second ordre, dont le déterminant du symbole principal est nul en tout point

ξ

, et pour toute fonction

u

. Nous écrivons l’équation comme une somme de carrés de champs de vecteurs, et nous prouvons le résultat en employant une méthode « freesing å.
$ℤ_2$-equivariant Ljusternik–Schnirelman theory for non-even functionals
Authors: Ekeland I. , Ghoussoub N. 
Published: July 2002

We develop an equivariant Ljusternik–Schnirelman theory for non-even functionals. We show that if one applies a

ℤ_2

-equivariant min-max procedure to a non-symmetric functional

\varphi

, then one gets either the usual critical points, defined by

\varphi'(x) = 0

or an interesting new class of points

x

, defined by

\varphi (x) = \varphi(−x)

and

\varphi'(x) = λ\varphi'(−x)

for some

λ > 0

. We call them “

ℤ_2

-resonant points”; by a “virtual critical point” we understand a point which is either critical or

ℤ_2

-resonant. We extend the classical existence and multiplicity results of Ljusternik–Schnirelman theory for critical points of even functionals to virtual critical points of non-even functionals. As an application we prove a bifurcation-type result for a class of non-homogenous semi-linear elliptic boundary value problems.

Résumé

Nous construisons une théorie de Ljusternik–Schnirelman pour des fonctionnelles non symétriques. Plus précisément, nous montrons que si l’on applique une procédure de minimax

ℤ_2

-équivariante à une fonctionnelle non paire

\varphi

, l’on obtient d’une part les points critiques habituels, définis par

\varphi'(x) = 0

, et d’autre part des points d’un type nouveau, vérifiant,

\varphi(x) = \varphi(−x)

et

\varphi'(x) = λ\varphi,(−x)

pour certain

λ > 0

. Nous les baptisons «

ℤ_2

-résonants å, et nous appellerons « point critiques virtuels å les points qui sont, soit critiques au sens habituel, soit

ℤ_2

-résonants. Nous étendons alors la théorie classique de Ljusternik–Schnirelman pour les points critiques de fonctionnelles paires à la recherche des points critiques virtuels de fonctionnelles impaires. A titre d’application, nous obtenons un résultat de bifurcation pour une classe d’équations semi-linéaires elliptiques avec un second membre.
Complete blow up and global behaviour of solutions of ut − Δu = g(u)
Authors: Martel Yvan 
Published: July 2002

For

u_0 \in L^∞(\Omega)

,

u_0 ≥ 0

, we study the global behaviour of solutions of the nonlinear heat equation (1). The domain

\Omega

is smooth and bounded and the nonlinearity

g

is nonnegative, nondecreasing and convex.

We show in particular that any nondecreasing solution blowing up at the finite time

T_{\mathrm{max}}

blows up completely in

\Omega

after

T_{\mathrm{max}}

. We apply this result to the description of all possible global behaviours of the solutions of (1) according to the value of

λ

. We show similar results when we introduce a notion of complete blow up in infinite time.

Résumé

Pour

u_0 \in L^∞(\Omega)

,

u_0 ≥ 0

, on étudie le comportement global des solutions de l’équation de la chaleur non-linéaire

\tag{1}
\begin{cases}
u_{t} - \Delta u = \lambda g\left(u\right) & \text{dans }\left(0,T\right) \times \Omega , \\
u = 0 & \text{sur }\partial \Omega , \\
u\left(0\right) = u_{0} &\text{dans }\Omega .
\end{cases}

Le domaine

\Omega

est borné régulier, et la nonlinéarité

g

est positive, croissante et convexe.

On montre en particulier que toute solution croissante explosant au temps fini

T_{\mathrm{max}}

explose totalement dans

\Omega

après

T_{\mathrm{max}}

. On applique ce résultat à la description des comportements globaux possibles des solutions de (1) en fonction de

λ

. On montre des résultats similaires pour une notion d’explosion totale en temps infini que l’on introduit.
Multibump solutions for a class of Lagrangian systems slowly oscillating at infinity
Authors: Alessio Francesca , Montecchiari Piero 
Published: July 2002

We prove the existence of infinitely many homoclinic solutions for a class of second order hamiltonian systems of the form

- \"u + u = \alpha (t)\nabla W(u)

where

W

is superquadratic and

\.{\alpha} (t)\rightarrow 0

,

0<\lim \inf \alpha(t)<\lim \sup \alpha(t)

as

t → + ∞

. In fact we prove that such a kind of systems admit a “multibump” dynamics.

Résumé

On montre l’existence d’une infinité de solutions homoclines d’une classe de systèmes hamiltoniens du second ordre de la forme

- \"u + u = \alpha (t)\nabla W(u)

où

W

est superquadratique et

\.{\alpha} (t)\rightarrow 0

,

0<\lim \inf \alpha(t)<\lim \sup \alpha(t)

quand

t → + ∞

. On montre en particulier que cette famille des systèmes admet une dynamique “multi-bosses”.
A nonlinear oblique derivative boundary value problem for the heat equation Part 1: Basic results
Authors: Mehats Florian , Roquejoffre Jean-Michel 
Published: July 2002

We study the heat equation

B_t − ΔB = 0

in the half-plane with the nonlinear oblique derivative condition

B_X = KBB_Z

on the boundary, where

(B_X, B_Z)

are respectively the normal and the tangential derivatives of

B

. The ultimate goal is to let

K → +∞

in the equations.

In this first part, we introduce self-similar solutions which verify an elliptic equation with the same nonlinear boundary condition. The main part of this first paper concerns this self-similar problem. It is well-posed and its solution is shown to be smooth, by means of boundary integral estimates. The originality of the approach is the robustness of the estimates with respect to

K

. The evolution problem itself admits global classical solutions which converge, as times tends to

+∞

, to the self-similar solution.

Résumé

Nous étudions l’équation de la chaleur

B_t − ΔB = 0

dans le demi-plan, avec la condition aux limites

B_X = KBB_Z

sur la frontière. Il s’agit une condition oblique non linéaire,

B_X

et

B_Z

, étant respectivement les dérivées normale et tangentielle de
B
sur cet axe. Notre but final est de faire tendre

K

vers

+∞

dans les équations.

Ce travail est divisé en deux parties. Dans cette première partie, nous introduisons des solutions autosemblables associées à ce problème.

Ces solutions autosemblables vérifient un système elliptique, avec la même condition aux limites non linéaire sur l’axe, et l’étude de ce problème constitue la majeure partie de ce premier article. Nous prouvons, au moyen d’estimations intégrales à la frontière, qu’il est bien posé et que sa solution est régulière. L’apport de cette approche est la robustesse des estimations vis-à-vis de

K

. Le problème d’évolution proprement dit admet des solution classiques, qui convergent en temps vers la solution autosemblable.
Ergodic problem for the Hamilton–Jacobi–Bellman equation. II
Authors: Arisawa Mariko 
Published: July 2002

We study the ergodic problem for the first-order Hamilton–Jacobi–Equations (HJBs), from the view point of controllabilities of underlying controlled deterministic systems. We shall give sufficient conditions for the ergodicity by the estimates of controllabilities.
Next, we shall give some results on the Abelian–Tauberian problem for the solutions of HJBs. Our solutions of HJBs satisfy the equations in the sense of viscosity solutions.

Résumé
Nous étudions le problème ergodique pour les équations de Hamilton–Jacobi–Bellmans (HJBs). Nous utiliserons les notions des contrôlabilités dans les systèmes déterministes contrôlés pour donner des conditions suffisantes pour la convergenće ergodique.
Ensuite, nous donnons des résultats du problème de Abel et de Tauber pour les solutions des HJBs. Nos solutions des HJBs satisfont les équations au sens de la solution de la viscosité.
Minoration du temps d’existence pour l’équation de Klein–Gordon non-linéaire en dimension 1 d’espace
Authors: Delort J.-M. 
Published: July 2002

Let

u

be a solution to the semilinear Klein–Gordon equation in one space dimension

\partial^2_tu-\partial^2_xu+u=F(u, \partial_tu,\partial_xu)

where

F

is a quadratic nonlinearity and the Cauchy data

u|_{t=0} = ϵu_0

,

∂_tu|_{t=0} = ϵu_1

are small in

C_0^∞

. Moriyama, Tonegawa and Tsutsumi have shown that the time of existence of the solution satisfies

\lim \inf_{ϵ→0}ϵ^2 \mathrm{log}\, T_ϵ > 0

. The aim of this paper is to prove that

\lim \inf_{ϵ→0}ϵ^2 \mathrm{log}\, T_ϵ ≥ A

for a constant

A

which can be explicitly computed from the Cauchy data and the nonlinearity.

Résumé

Soit

u

la solution de l’équation de Klein–Gordon semi-linéaire en dimension 1 d’espace

\partial^2_tu-\partial^2_xu+u=F(u, \partial_tu,\partial_xu)

avec une nonlinéarité

F

quadratique et des données de Cauchy petites,

C^∞

à support compact,

u|_{t=0} = ϵu_0

,

∂_tu|_{t=0} = ϵu_1

. Moriyama, Tonegawa et Tsutsumi ont montré que le temps d’existence

T_ϵ

de la solution vérifie alors

\lim \inf_{ϵ→0}ϵ^2 \mathrm{log}\, T_ϵ > 0

. Le but de cet article est de montrer que

\lim \inf_{ϵ→0}ϵ^2 \mathrm{log}\, T_ϵ ≥ A

, où

A

est une constante explicite s’exprimant en fonction de

u_0

,

u_1

et de la nonlinéarité.
Enhanced GABA release in cell‐damaging conditions in the adult and developing mouse hippocampus
Authors: Saransaari Pirjo , Oja Simo S. 
Published: July 2002

AbstractThe release of [3H]GABA from hippocampul slices from adult (3‐month‐old) and developing (7‐day‐old) mice was studied in cell‐damaging conditions in vitro using a superfusion system. Cell damage was induced by modified superfusion media, including hypoxia, hypoglycemia, ischemia, the presence of free radicals and oxidative stress. The basal release of GABA from the immature and mature hippocampus was generally markedly increased in all cell‐damaging conditions. In 7‐day‐old mice the release was enhanced most in the presence of free radicals, 1.0 mM NaCN and ischemia, whereas in the adults 1.0 mM NaCN provoked the largest release of GABA, followed by ischemia and free radical‐containing media. Potassium stimulation (50mM K+) was still able to potentiate the release in all cell‐damaging conditions in both age groups. It was shown by superfusing the slices in Ca‐ and Na‐free media that ischemia‐induced GABA release was Ca‐independent, occurring by a reversed operation of Na‐dependent cell membrane carriers in both adult and developing hippocampus. Glutamate and its receptor agonists,N‐methyl‐d‐aspartate (NMDA), kainate and 2‐amino‐3‐hydroxy‐5‐methyl‐4‐isoxazolepropionate (AMPA), potentiated GABA release only in the immature hippocampus by a receptor‐mediated mechanism. The enhancement by kainate and AMPA receptors also operated under ischemic conditions. The massive amount of GABA released simultaneously with excitatory amino acids in the mature and immature hippocampus may be an important protective mechanism against excitotoxicity, counteracting harmful effects that lead to neuronal death. The GABA release induced by activation of presynaptic glutamate receptors may contribute particularly to the maintenance of homeostasis in the hippocampus upon impending hyper‐excitation.
IL‐1β and ICE mRNA are not altered upon β‐amyloid25–35 induced neurotoxicity in human neuroblastoma cells
Authors: Diana A. , Eriksson C. , Winblad B. , Schultzberg M. 
Published: July 2002

AbstractThe specific β‐amyloid25–35 fragment induced cellular degradation of the human neuroblastoma cell line SH‐SY5Y, but did not elicit an effect on the levels of interleukin‐1β and interleukin‐1β converting enzyme, as determined by semiquantitative reverse transcription‐polymerase chain reaction and immunocytochemical analysis. The assays revealed constitutive expression of these proteins both at mRNA and protein level.It is conceivable that in the absence of glial elements, such as in the present neuroblastoma cell line, β‐amyloid triggers the toxicity through a direct action and/or through the production of other harmful molecules.
Dependence on zolpidem: a case report
Authors: Sakkas P. , Psarros C. , Masdrakis V. , Liappas J. , Christodoulou G.N. 
Published: July 2002

SummaryWe report the case of a patient with a history of zolpidem dependence. The patient, after a stressful life event, started using zolpidem. She rapidly developed tolerance and dependence, taking 50-100 mg, and sometimes up to 300 mg, of zolpidem daily. Also, our patient suffered episodes of altered consciousness, accompanied by visual hallucinations.
Effects of rifampin on the pharmacokinetics and pharmacodynamics of glyburide and glipizide
Authors: Niemi Mikko , Backman Janne T. , Neuvonen Mikko , Neuvonen Pertti J. , Kivistö Kari T. 
Published: July 2002

ObjectiveTo study the effects of rifampin (INN, rifampicin) on the pharmacokinetics and pharmacodynamics of glyburide (INN, glibenclamide) and glipizide, 2 sulfonylurea antidiabetic drugs.MethodsTwo separate, randomized, 2‐phase, crossover studies with an identical design were conducted. In each study, 10 healthy volunteers received 600 mg rifampin or placebo once daily for 5 days. On day 6, a single dose of 1.75 mg glyburide (study I) or 2.5 mg glipizide (study II) was administered orally. Plasma glyburide and glipizide and blood glucose concentrations were measured for 12 hours.ResultsIn study I, rifampin decreased the area under the plasma concentration–time curve [AUC(0‐∞)] of glyburide by 39% (P < .001) and the peak plasma concentration by 22% (P = .01). The elimination half‐life of glyburide was shortened from 2.0 to 1.7 hours (P < .05) by rifampin. The blood glucose decremental AUC(0–7) (net area below baseline) and the maximum decrease in the blood glucose concentration were decreased by 44% (P = .05) and 36% (P < .001), respectively, by rifampin. In study II, rifampin decreased the AUC(0‐∞) of glipizide by 22% (P < .05) and shortened its half‐life from 3.0 to 1.9 hours (P = .01). No statistically significant differences in the blood glucose concentrations were found between the phases; however, 4 subjects had moderate hypoglycemia during the placebo phase but only 1 subject had moderate hypoglycemia during the rifampin phase.ConclusionsRifampin moderately decreased the plasma concentrations and effects of glyburide but had only a slight effect on glipizide. The mechanism underlying the interaction between rifampin and glyburide is probably induction of either CYP2C9 or P‐glycoprotein or both. Induction of CYP2C9 would explain the increased systemic elimination of glipizide. It is probable that the blood glucose–lowering effect of glyburide is reduced during concomitant treatment with rifampin. In some patients, the effects of glipizide may also be reduced by rifampin.Clinical Pharmacology & Therapeutics (2001) 69, 400–406; doi: 10.1067/mcp.2001.115822
Comprehension, Utility, and Acceptability of a Multidomain Physical Functioning Report for Systemic Lupus Erythematosus Patients and Their Providers
Authors: Plantinga Laura C. , Xu Grace , Hoge Courtney , Vandenberg Ann , Dunlop‐Thomas Charmayne , Jones Brian D. , Johnson Jeremy , Drenkard Cristina , Lim S. Sam , Bowling C. Barrett 
Published: July 2021

ObjectivePatient‐provider discussions about functioning are often outside the scope of usual care for systemic lupus erythematosus (SLE), and tools to facilitate such discussions are lacking. The present study was undertaken to assess the comprehension, utility, and acceptability of a novel, individualized functioning report, the purpose of which is to facilitate patient–provider communication about functioning, in a predominantly Black SLE patient population.MethodsIndividualized reports (including sections with pictorial representations of participants' measured activities of daily living, falls, physical performance, perceived physical functioning, and community mobility from a previous pilot study visit) and surveys were emailed or mailed to 59 SLE patients. Ease of interpretation was dichotomized (“very easy” versus all other responses). Utility and acceptability were assessed by items relating to usefulness for care planning and comfort with discussing the report.ResultsAmong 47 (79.7%) SLE patients who completed the survey (78.7% Black, 91.5% female, mean age 49.6 years), the reported ease of interpretation ranged from 70.2% to 85.1% across the report sections. Ease of interpretation was lower among those who were older, Black, and female and who had lower cognitive scores (P > 0.05 for all). Most reported that physical functioning domains of the report were useful for treatment or other care planning (70.2–80.5%) and that they felt comfortable discussing the report with a health care provider (93.2–100%).ConclusionWe found that a novel functioning report for SLE patients was associated with high comprehension, utility, and acceptability. Future studies can help determine how an individualized functioning report could improve patient–provider communication in the clinic setting.
Predictive Value of Magnetic Resonance Imaging in Patients With Juvenile Idiopathic Arthritis in Clinical Remission
Authors: Mazzoni Marta , Pistorio Angela , Magnaguagno Francesca , Viola Stefania , Urru Alessia , Magnano Gian Michele , Ravelli Angelo , Malattia Clara 
Published: July 2021

ObjectiveTo define the prevalence of subclinical synovitis on magnetic resonance imaging (MRI) in a large cohort of patients with juvenile idiopathic arthritis (JIA) in clinical remission and to evaluate its predictive value in terms of disease flare and joint deterioration.MethodsNinety patients with clinically inactive JIA who underwent a contrast‐enhanced (CE)–MRI of a previously affected joint were retrospectively included. Each joint was evaluated for synovitis, tenosynovitis, and bone marrow edema. Baseline and follow‐up radiographs were assessed to evaluate structural damage progression.ResultsCE‐MRI was acquired in 45 wrists, 30 hips, 13 ankles, and 2 knees. Subclinical synovitis was detected in 59 (65.5%) of 90 patients and bone marrow edema in 42 (46.7%) of 90 patients. Fifty‐seven of 90 (63.3%) patients experienced a disease flare during follow‐up. Forty‐four of 59 (74.6%) patients with subclinical synovitis experienced a disease flare versus 13 (41.9%) of 31 patients with no residual synovitis on MRI (P = 0.002). The presence of subclinical synovitis was the best predictor of disease flare on multivariable regression analysis (hazard ratio [HR] 2.45, P = 0.003). Baseline and follow‐up radiographs were available for 54 patients, and 17 (31.5%) of 54 patients experienced radiographic damage progression. The presence of bone marrow edema (HR 4.40, P = 0.045) and being >17 years old (HR 3.51, P = 0.04) were strong predictors of joint damage progression in the multivariable analysis.ConclusionMRI‐detected subclinical inflammation was present in a large proportion of patients with JIA despite clinical remission. Subclinical synovitis and bone marrow edema have been shown to play a role in predicting the risk of disease relapse and joint deterioration, with potential implications for patients' management of the disease.
A Self‐Healable Polyelectrolyte Binder for Highly Stabilized Sulfur, Silicon, and Silicon Oxides Electrodes
Authors: Jin Biyu , Wang Dongyun , Zhu Juan , Guo Hongyu , Hou Yang , Gao Xiang , Lu Jianguo , Zhan Xiaoli , He Xiaojun , Zhang Qinghua 
Published: July 2021

AbstractLarge volume change, poor conductivity, and electrolyte soluble active materials intermediates have long been daunting challenges for sulfur, silicon, and silicon oxides electrode materials. A self‐healable polyelectrolyte binder is exploited by crosslinking polydopamine, phytic acid and poly(acrylamide‐co‐2‐(Dimethylamino)ethyl acrylate) in situ at room temperature through reconfigurable hydrogen bonds and ionic bonds. Therefore, the crosslinked binder network can readily recover its mechanical strength without extra stimulus, offering a reliable strategy for electrodes plagued by large volume change issue. Sulfur (S) and silicon (Si) electrodes prepared using the self‐healable polyelectrolyte binder can effectively maintain its structure integrity after long‐term cycling. In addition, the polar groups, especially negative‐charged phosphate ions empower the polyelectrolyte binder as a more effective binder than commercial poly(vinylidene fluoride) in terms of restraining lithium polysulfides shuttling and accelerating lithium ion transportation, as evidenced by in situ UV‐visible spectroscopy, density functional theory calculation and cyclic voltammetry. Consequently, high‐active materials loading S cathode, Si and SiO‐graphite anodes all achieve high area capacity and satisfying cycling stability by conveniently applying the advanced binder. This facile strategy for constructing multiuse binder illuminates versatile development in many energy storage systems.
A Stretchable and Transparent Electrode Based on PEGylated Silk Fibroin for In Vivo Dual‐Modal Neural‐Vascular Activity Probing
Authors: Cui Yajing , Zhang Fan , Chen Geng , Yao Lin , Zhang Nan , Liu Zhiyuan , Li Qingsong , Zhang Feilong , Cui Zequn , Zhang Keqin , Li Peng , Cheng Yuan , Zhang Shaomin , Chen Xiaodong 
Published: July 2021

AbstractTransparent electrodes that form seamless contact and enable optical interrogation at the electrode–brain interface are potentially of high significance for neuroscience studies. Silk hydrogels can offer an ideal platform for transparent neural interfaces owing to their superior biocompatibility. However, conventional silk hydrogels are too weak and have difficulties integrating with highly conductive and stretchable electronics. Here, a transparent and stretchable hydrogel electrode based on poly(3,4‐ethylenedioxythiophene):polystyrene sulfonate (PEDOT:PSS) and PEGylated silk protein is reported. PEGylated silk protein with poly(ethylene glycol) diglycidyl ether (PEGDE) improves the Young's modulus to 1.51–10.73 MPa and the stretchability to ≈400% from conventional silk hydrogels (<10 kPa). The PEGylated silk also helps form a robust interface with PEDOT:PSS thin film, making the hydrogel electrode synergistically incorporate superior stretchability (≈260%), stable electrical performance (≈4 months), and a low sheet resistance (≈160 ± 56 Ω sq−1). Finally, the electrode facilitates efficient electrical recording, and stimulation with unobstructed optical interrogation and rat‐brain imaging are demonstrated. The highly transparent and stretchable hydrogel electrode offers a practical tool for neuroscience and paves the way for a harmonized tissue–electrode interface.