... hand a choice ofa Cartan subalgebra t⊆b defines an
4
An action ofa Lie algebra
a
on a variety X is an action of
a
on O
X
by derivations.
Equivalently, it is a Lie algebra homomorphism from
a
to ... sufficiently large positive
characteristic. Next, one finds that for any smooth variety this algebra of
differential operators is an Azumaya algebra on the cotangent bundle. In the
case of the flag variety ... Azumaya
algebras
D
X
and τ
∗
ν
(
D
X
) are canonically equivalent.
Proof. Recall that to establish an equivalence between two Azumaya al-
gebras A, A
on a scheme Y (i.e. an equivalence between...
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... R
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+
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Annals of Mathematics
Formation of
singularities fora
transport equation with
nonlocal velocity
By Antonio C´ordoba, Diego C´ordoba, and
Marco A. Fontelos
1380 ANTONIO ... 715–724.
FORMATION OF SINGULARITIES FORA TRANSPORT EQUATION
1379
numerical results showed that, up to very high values of k, this asymptotic
behavior is compatible with the formation ofa curvature ... for the 1D analog (1.6).
The system (1.4) and (1.5) with σ = 0 has the very interesting property of
being ill-posed for general initial data. A linear analysis of small perturbations
of planar...
... determined.
Available epidemiological data addressing the impli-
cation of PAH, in general, as a causal factor in the
pathogeny of metabolic disorders are currently too
few to draw any definitive ... adenocarcinoma, lymphoreticular
tumours, hepatomas, mammary adenocarcinomas) [17].
B [a] P has also been shown to display immunotoxic
properties that affect macrophage function [18] and
increase local inflammatory ... incubated with the indicated concentrations of ACTH. In six separate experiments, the mean FFA concentration measured in
the incubation media in absence of any pharmacological agents (basal lipolysis)...
... frailty. Exploratory factor
analysis (EFA) reduced the data toa smaller number of factors and was subjected to confirmatory factor analysis
(CFA)which restricted the model by fitting the EFA-driven ... proposeafrailtymodeldevel-
oped from factor analysis (FA), a rob ust analytical tech-
nique which uses latent variables as a means of data
reduction to represent a wide range of attributes/varia-
bility ... variable
‘ angina’ has a factor loading of 0.550 on the general
(frailty) factor and a loading of 0.619 on its speci fic fac-
tor (Cardiovascular symptoms/disease) with both factors
independent of each...
... and polynomial decay fora quasilinear viscoelastic problem. Nonlinear Anal. 68,
785–793 (2007)
8. Messaoudi, SA: General decay of solutions ofa viscoelastic equation. J. Math. Anal. Appl. 341, ... Numerical Simulation of Large
Scale Complex Systems, School of
Mathematical Sciences, Nanjing
Normal University, Nanjing 210046,
PR China
Full list of author information is
available at the end of ... displacements of waves. This problem arises in the theory of vis-
coelastic and describes the interaction of two scalar fields, we can refer to Cavalcanti
et al. [1], Messaoudi and Tatar [2], Renardy et al....
... Mathematics, Nanjing University of Aeronautics and Astronautics,
Nanjing 210016, P. R. China
∗
Corresponding author: wang-fanglei@hotmail.com
Email address:
YA: anykna@nuaa.edu.cn
Abstract
This article ... continuous and f
has subcritical growth, the above functional is of class C
1
in H. We shall apply the
famous mountain pass theorem to show the existence ofa nontrivial critical point
of functional ... Provisional PDF corresponds to the article as it appeared upon acceptance. Fully formatted
PDF and full text (HTML) versions will be made available soon.
Existence and multiplicity of solutions for a...
... −div(|∇u|
p(x)−2
∇u) is said to be the p(x)-Laplacian, and becomes p-
Laplacian when p(x) ≡ p (a constant). The p(x)-Laplacian possesses more complicated
nonlinearities than the p-Laplacian; for example, it ... Theory and Nonlinear
Boundary Value Problems. Chapman and Hall/CRC, Boca Raton (2005)
[34] Zhao, JF: Structure Theory of Banach Spaces (in Chinese). Wuhan University Press,
Wuhan (1991)
[35] Garcia ... mathematical modeling of stationary thermo-rheological viscous
flows of non-Newtonian fluids and in the mathematical description of the pro cesses fil-
tration of an ideal baro-tropic gas through a porous...
... difference equations,” Journal of Mathematical Analysis and Applications, vol. 322, no. 2, pp.
930–956, 2006.
13 E. Thandapani and I. M. Arockiasamy, “Fourth-order nonlinear oscillations of difference ... Applicable Analysis, vol. 59, no. 1–4, pp. 225–231, 1995.
6 Z. Bai and H. Wang, “On positive solutions of some nonlinear fourth-order beam equations,” Journal
of Mathematical Analysis and Applications, ... existence of solutions for the boundary value problems of
fourth-order differential equations.
Because of applications in many areas for difference equations, in recent years, there
has been an increased...
... T
D
is
Headquarter
t
r
Pigeon Pigeon
Disaster areaA
Figure 1: System view of headquarter and disaster area.
also called the deadline ofa message in the following part of
this paper.
A key question ... fixed at 4 hours and the effect of
size of disaster area is shown. When the disaster area is very
small, ρ
Max
can be as large as 0.81; as the size of disaster
area increases, the incurred travel ... points of the arrival
of the tail message of k
th
trip and the head message of (k +
1)
th
trip. It is reasonable to estimate that the waiting of the
head message of the (k +1)
th
trip starts at 1/(2λ)...
... px,qx-Laplacian
S. Ogras, R. A. Mashiyev, M. Avci, and Z. Yucedag
Department of Mathematics, Dicle University, 21280 Diyarbakir, Turkey
Correspondence should be addressed to R. A. Mashiyev, mrabil@dicle.edu.tr
Received ... well-known p-Laplacian
operator. However, the px-Laplace operator possesses more complicated nonlinearity than
p-Laplace operator due to the fact that Δ
px
is not homogeneous. This fact implies ... of the calculus of variations and elasticity theory,” Izvestiya
Akademii Nauk SSSR. Seriya Matematicheskaya, vol. 50, no. 4, pp. 675–710, 1986 Russian.
14 C. O. Alves and M. A. Souto, “Existence...
... of
Mathematical Analysis and Applications, vol. 333, no. 2, pp. 591–603, 2007.
12 Q. Zhang, “Existence of radial solutions for px-Laplacian equations in
R
N
,” Journal of Mathematical
Analysis and ... Methods & Applications, vol. 52, no. 2, pp. 585–594, 2003.
6 X L. Fan, Q. Zhang, and D. Zhao, “Eigenvalues of px-Laplacian Dirichlet problem,” Journal of
Mathematical Analysis and Applications, ... Journal of Inequalities and Applications
The study of differential equations and variational problems with variable exponent
growth conditions is a new and interesting topic. Many results have...
... Department of Mathematics, Southeast University, Nanjing 210096, China;
College of Mathematics and Physics, Nanjing University of Information Science and Technology,
Nanjing 210044, China
Email ... “Periodic solutions of evolution m-laplacian equations with a nonlinear convec-
tion term,” International Journal of Mathematics and Mathematical Sciences, vol. 2007, Article
ID 27368, 10 pages, 2007.
Wenjun ... Mathematical Analysis and Applications, vol. 228, no. 2, pp.
483–494, 1998.
[7] S. L. Chen, “The extinction behavior of the solutions fora class of reaction-diffusion equations,”
Applied Mathematics and...
... Kovalevsky and F. Nicolosi, “On the sets of boundedness of solutions fora class of degen-
erate nonlinear elliptic four th-order equations with L
1
-data,” Fundamentalnaya I Prikladnaya
Matematika, ... Elliptic Equations of Higher Order, Naukova Dumka, Kiev, Ukraine,
1973.
[12] O. A. Ladyzhenskaya and N. N. Ural’tseva, Linear and Quasilinear Elliptic Equations,Academic
Press, New York, NY, USA, 1968.
S. ... S. Bonafede and S. DAsero, H
ă
older continuity of solutions fora class of nonlinear elliptic vari-
ational inequalities of high order,” Nonlinear Analysis. Theory, Methods & Applications,...