bluuebunny/crossref_metadata_2025 huggingface dataset:
THE ASPECT OF VECTOR CONTROL USING THE ASYNCHRONOUS TRACTION MOTOR IN LOCOMOTIVES
Authors: Liudvinavičius Lionginas , Lingaitis Leonas Povilas , Dailydka Stasys , Jastremskas Virgilijus
Published: December 2009

The article examines curves controlling asynchronous traction motors increasingly used in locomotive electric drives the main task of which is to create a tractive effort‐speed curve of an ideal locomotive Fk = f(v), including a hyperbolic area the curve of which will create conditions showing that energy created by the diesel engine of diesel locomotives (electric locomotives and in case of electric trains, electricity taken from the contact network) over the entire range of locomotive speed is turned into efficient work. Mechanical power on wheel sets is constant Pk = Fkv = const, the power of the diesel engine is fully used over the entire range of locomotive speed. Tractive effort‐speed curve Fk(v) shows the dependency of locomotive traction power Fk on movement speed v. The article presents theoretical and practical aspects relevant to creating the structure of locomotive electric drive and selecting optimal control that is especially relevant to creating the structure of locomotive electric drive using ATM (asynchronous traction motor) that gains special popularity in traction rolling stock replacing DC traction motors having low reliability. __e frequency modes of asynchronous motor speed regulation are examined. To control ATM, the authors suggest the method of vector control presenting the structural schemes of a locomotive with ATM and control algorithm.
A Novel in Vitro Model to Investigate Behavior of Articular Chondrocytes in Osteoarthritis
Authors: RANKIN KENNETH S. , LAKEY RACHEL L. , GERRAND CRAIG H. , SPROWSON ANDREW P. , McCASKIE ANDREW W. , BIRCH MARK A.
Published: December 2009

Objective.

To investigate in vivo simulation of the microenvironment in which osteoarthritis (OA) chondrocytes are cultured in vitro.

Methods.

Human articular chondrocytes were cultured under normoxic and hypoxic conditions. Cells were cultured on standard culture plastic or a porous polyHEMA surface that closely resembles the in vivo cartilage microarchitecture. Morphological changes to the cells were demonstrated by fluorescent staining with DAPI and vinculin. Proteoglycan and type II collagen protein levels were assessed using established techniques. Matrix metalloproteinase-1 (MMP-1) production was assessed by ELISA. The gene expression of type II collagen and SOX9 was measured using real-time polymerase chain reaction.

Results.

Cells grown on culture plastic were seen to be flat and hexagonal. Cells cultured on the porous polyHEMA surface exhibited morphology in keeping with the in vivo microenvironment. Glycosaminoglycan release in hypoxia was high from cells cultured on standard culture plastic. Transcriptional expression of type II collagen was upregulated in hypoxia and by culture on the polyHEMA surface. Transcriptional expression of SOX9 in hypoxia was upregulated compared to normoxia; no significant effect was seen by varying the culture surface. Translational expression of type II collagen was upregulated at 20% oxygen on the polyHEMA surface compared to culture plastic and this was related to MMP-1 expression.

Conclusion.

Culture of chondrocytes in hypoxia and on a porous surface simulates the in vivo microenvironment and illustrates the molecular mechanisms of OA.
Negative Relationship Between Expression of Glucocorticoid Receptor α and Disease Activity: Glucocorticoid Treatment of Patients with Systemic Lupus Erythematosus
Authors: LI XIU , ZHANG FENG-SHAN , ZHANG JI-HUI , WANG JING-YUAN
Published: December 2009

Objective.

Glucocorticoid receptor α (GRα) is crucial for glucocorticoids (GC) to carry out their physiological and pharmacological roles. Studies have shown the disorder of GR-GC systems in autoimmune diseases. Our study was performed to test the relationship between GRα expression and disease activity of systemic lupus erythematosus (SLE).

Methods.

The responses of 55 patients with SLE to GC were screened. We examined GRα mRNA and protein expression in peripheral blood mononuclear cells from SLE patients and healthy volunteers by reverse transcriptase-polymerase chain reaction and Western blotting.

Results.

Expression of GRα in patients with SLE was lower than that in controls (p < 0.05). Expression of GRα obviously decreased after administration of GC in the steroid-sensitive group with SLE (p < 0.05). Expression of GRα was negatively correlated with SLE Disease Activity Index scores in the steroid-sensitive group with SLE.

Conclusion.

The expression of GRα in patients with SLE was low and there was a negative correlation between GRα expression and disease activity; these findings might provide insight into the pathogenesis of SLE and help to screen whether the patient is sensitive to GC treatment. (Heilungkiang Provincial Health Department Guiding Projects Funding. Trial registration No. 2006-094.)
Stromal Interaction Molecules 1 and 2 Are Key Regulators of Autoreactive T Cell Activation in Murine Autoimmune Central Nervous System Inflammation
Authors: Schuhmann Michael K. , Stegner David , Berna-Erro Alejandro , Bittner Stefan , Braun Attila , Kleinschnitz Christoph , Stoll Guido , Wiendl Heinz , Meuth Sven G. , Nieswandt Bernhard
Published: December 2009

Calcium (Ca2+) signaling in T lymphocytes is essential for a variety of functions, including the regulation of differentiation, gene transcription, and effector functions. A major Ca2+ entry pathway in nonexcitable cells, including T cells, is store-operated Ca2+ entry (SOCE), wherein depletion of intracellular Ca2+ stores upon receptor stimulation causes subsequent influx of extracellular Ca2+ across the plasma membrane. Stromal interaction molecule (STIM) 1 is the Ca2+ sensor in the endoplasmic reticulum, which controls this process, whereas the other STIM isoform, STIM2, coregulates SOCE. Although the contribution of STIM molecules and SOCE to T lymphocyte function is well studied in vitro, their significance for immune processes in vivo has remained largely elusive. In this study, we studied T cell function in mice lacking STIM1 or STIM2 in a model of myelin-oligodendrocyte glycoprotein (MOG35–55)-induced experimental autoimmune encephalomyelitis (EAE). We found that STIM1 deficiency significantly impaired the generation of neuroantigen-specific T cell responses in vivo with reduced Th1/Th17 responses, resulting in complete protection from EAE. Mice lacking STIM2 developed EAE, but the disease course was ameliorated. This was associated with a reduced clinical peak of disease. Deficiency of STIM2 was associated with an overall reduced proliferative capacity of lymphocytes and a reduction of IFN-γ/IL-17 production by neuroantigen-specific T cells. Neither STIM1 nor STIM2 deficiency altered the phenotype or function of APCs. These findings reveal a crucial role of STIM-dependent pathways for T cell function and activation under autoimmune inflammatory conditions, establishing them as attractive new molecular therapeutic targets for the treatment of inflammatory and autoimmune disorders.
Quiver varieties of type A
Authors: Maffei Andrea
Published: December 2009

We prove a conjecture of Nakajima describing the relation between quiver varieties of type A and the geometry of partial flag varieties and of the nilpotent variety.
Triangulations of 3-manifolds, hyperbolic relative handlebodies, and Dehn filling
Authors: Costantino Francesco , Frigerio Roberto , Martelli Bruno , Petronio Carlo
Published: December 2009

We establish a bijective correspondence between the set

\mathcal{T}_n

of 3-dimensional triangulations with

n

tetrahedra and a certain class

\mathcal H_n

of relative handlebodies (i.e. handlebodies with boundary loops, as defined by Johannson) of genus

n + 1

.

We show that the manifolds in

\mathcal H_n

are hyperbolic (with geodesic boundary, and cusps corresponding to the loops), have least possible volume, and simplest boundary loops.

Mirroring the elements of

\mathcal H_n

in their geodesic boundary we obtain a set

\mathcal{D}_n

of cusped hyperbolic manifolds, previously considered by

D

. Thurston and the first named author. We show that also

\mathcal{D}_n

corresponds bijectively to

\mathcal{T}_n

, and we study some Dehn fillings of the manifolds in

\mathcal{D}_n

. As consequences of our constructions, we also show that:
Lower algebraic $K$-theory of hyperbolic 3-simplex reflection groups
Authors: Lafont Jean-François , Ortiz Ivonne J.
Published: December 2009

A hyperbolic 3-simplex reflection group is a Coxeter group arising as a lattice in

O^+(3,1)

, with fundamental domain a geodesic simplex in

ℍ^3

(possibly with some ideal vertices). The classification of these groups is known, and there are exactly 9 cocompact examples, and 23 non-cocompact examples. We provide a complete computation of the lower algebraic

K

-theory of the integral group ring of all the hyperbolic 3-simplex reflection groups.
Counting tropical elliptic plane curves with fixed $j$-invariant
Authors: Kerber Michael , Markwig Hannah
Published: December 2009

In complex algebraic geometry, the problem of enumerating plane elliptic curves of given degree with fixed complex structure has been solved by R. Pandharipande [8] using Gromov–Witten theory. In this article we treat the tropical analogue of this problem, the determination of the number

E_{\mathrm{trop}}(d)

of tropical elliptic plane curves of degree

d

and fixed “tropical

j

-invariant” interpolating an appropriate number of points in general position and counted with multiplicities. We show that this number is independent of the position of the points and the value of the

j

-invariant and that it coincides with the number of complex elliptic curves (with

j

-invariant

j ∉ \{ 0, 1728 \}

). The result can be used to simplify G. Mikhalkin's algorithm to count curves via lattice paths (see [6]) in the case of rational plane curves.
The length of the second shortest geodesic
Authors: Nabutovsky Alexander , Rotman Regina
Published: December 2009

According to the classical result of J. P. Serre ([S]) any two points on a closed Riemannian manifold can be connected by infinitely many geodesics. The length of a shortest of them trivially does not exceed the diameter

d

of the manifold. But how long are the shortest remaining geodesics? In this paper we prove that any two points on a closed

n

-dimensional Riemannian manifold can be connected by two distinct geodesics of length

≤ 2qd ≤ 2nd

, where

q

is the smallest value of

i

such that the

i

th homotopy group of the manifold is non-trivial.
The structure of homotopy Lie algebras
Authors: Félix Yves , Halperin Steve , Thomas Jean-Claude
Published: December 2009

In this paper we consider a graded Lie algebra,

L

, of finite depth

m

, and study the interplay between the depth of

L

and the growth of the integers

\dim\, L_i

. A subspace

W

in a graded vector space

V

is called full if for some integers

d

,

N

,

q

,

\dim\, V_k ≤ d \sum^{k + q}_{i =k} \dim\, W_i

,

i ≥ N

. We define an equivalence relation on the subspaces of

V

by

U ∼ W

if

U

and

W

are full in

U + W

. Two subspaces

V,W

in

L

are then called

L

-equivalent (

V\sim_L W

) if for all ideals

K ⊂ L

,

V ∩ K ∼ W ∩ K

. Then our main result asserts that the set

\mathcal L

of

L

-equivalence classes of ideals in

L

is a distributive lattice with at most

2^m

elements. To establish this we show that for each ideal

I

there is a Lie subalgebra

E ⊂ L

such that

E ∩ I = 0

,

E\oplus I

is full in

L

, and

\mathrm{depth}\, E + \mathrm{depth}\, I ≤ \mathrm{depth}\, L

.
The symplectic topology of Ramanujam's surface
Authors: Seidel Paul , Smith Ivan
Published: December 2009

Ramanujam's surface

M

is a contractible affine algebraic surface which is not homeomorphic to the affine plane. For any

m>1

the product

M^m

is diffeomorphic to Euclidean space

{mathbb R}^{4m}

. We show that, for every

m>0

,

M^m

cannot be symplectically embedded into a subcritical Stein manifold. This gives the first examples of exotic symplectic structures on Euclidean space which are convex at infinity. It follows that any exhausting plurisubharmonic Morse function on

M^m

has at least three critical points, answering a question of Eliashberg. The heart of the argument involves showing a particular Lagrangian torus

L

inside

M

cannot be displaced from itself by any Hamiltonian isotopy, via a careful study of pseudoholomorphic discs with boundary on

L

.
Zero entropy and bounded topology
Authors: Paternain Gabriel P. , Petean Jimmy
Published: December 2009

We study the existence of Riemannian metrics with zero topological entropy on a closed manifold

M

with infinite fundamental group. We show that such a metric does not exist if there is a finite simply connected CW complex which maps to

M

in such a way that the rank of the map induced in the pointed loop space homology grows exponentially. This result allows us to prove in dimensions four and five, that if

M

admits a metric with zero entropy then its universal covering has the rational homotopy type of a finite elliptic CW complex. We conjecture that this is the case in every dimension.
Sur la représentation conforme des surfaces de Riemann à bord et une caractérisation des courbes séparantes
Authors: Gabard Alexandre
Published: December 2009

On présente une démonstration simplifiée d'un théorème d'Ahlfors: étant donné une courbe algébrique réelle séparante, il est toujours possible d'exhiber un morphisme vers la droite dont les fibres au-dessus des points réels sont toutes exclusivement formées de points réels. Ensuite, on montre comment notre méthode, basée sur l'usage du théorème d'Abel, conduit à une meilleure borne sur le degré d'un tel morphisme que celle obtenue par Ahlfors. [We present a simplified proof of a theorem due to Ahlfors: given a dividing real algebraic curve, it is always possible to find a morphism to the line such that the fibers over real points consist only of real points. Then in a second part, we show how our method - which is quite elementary, relying only on the use of Abel's theorem - even leads to a better bound on the degree of such a morphism than the one obtained by Ahlfors.]
A free-boundary problem for Stokes equations: classical solutions
Authors: Antontsev Stanislav , Meirmanov Anvarbek , Yurinsky Vadim
Published: December 2009

The problem considered is that of evolution of the free boundary separating two immiscible viscous fluids with different constant densities. The motion is described by the Stokes equations driven by the gravity force. For flows in a bounded domain

\Omega \subset \mathbb R^n

,

n \geq 2

, we prove existence and uniqueness of classical solutions, and concentrate on the study of properties of the moving boundary separating the two fluids.
A remark on the homotopical dimension of some moduli spaces of stable Riemann surfaces
Authors: Mondello Gabriele
Published: December 2009

Using a result of Harer, we prove certain upper bounds for the homotopical/cohomological dimension of the moduli spaces of Riemann surfaces of compact type, of Riemann surfaces with rational tails and of Riemann surfaces with at most

k

rational components. These bounds would follow from conjectures of Looijenga and Roth-Vakil.
Spaces of geometrically generic configurations
Authors: Feler Yoel
Published: December 2009

Let

X

denote either

\Bbb{CP}^m

or

\Bbb{C}^m

. We study certain analytic properties of the space

\mathcal{E}^n(X,gp)

of ordered geometrically generic

n

-point configurations in

X

. This space consists of all

q=(q_1,...,q_n)\in X^n

such that no

m+1

of the points

q_1,...,q_n

belong to a hyperplane in

X

. In particular, we show that for a big enough

n

any holomorphic map

f\colon\mathcal{E}^n(\Bbb{CP}^m,gp)\to\mathcal{E}^n(\Bbb{CP}^m,gp)

commuting with the natural action of the symmetric group

\mathbf{S}(n)

in

\mathcal{E}^n(\Bbb{CP}^m,gp)

is of the form

f(q)=\tau(q)q=(\tau(q)q_1,...,\tau(q)q_n)

,

q\in \mathcal{E}^n(\Bbb{CP}^m,gp)

, where

\tau\colon\mathcal{E}^n(\Bbb{CP}^m,gp) \to{\mathbf{PSL}(m+1,\mathbb C)}

is an

\mathbf{S}(n)

-invariant holomorphic map. A similar result holds true for mappings of the configuration space

\mathcal{E}^n(\Bbb{C}^m,gp)

.
On the global regularity of subcritical Euler–Poisson equations with pressure
Authors: Tadmor Eitan , Wei Dongming
Published: December 2009

We prove that the one-dimensional Euler–Poisson system driven by the Poisson forcing together with the usual

\gamma

-law pressure,

\gamma \geq 1

, admits global solutions for a large class of initial data. Thus, the Poisson forcing regularizes the generic finite-time breakdown in the 2x2 p-system. Global regularity is shown to depend on whether or not the initial configuration of the Riemann invariants and density crosses an intrinsic critical threshold.
Non-generic blow-up solutions for the critical focusing NLS in 1-D
Authors: Krieger Joachim , Schlag Wilhelm
Published: December 2009

We consider the
L2
-critical focussing nonlinear Schrödinger equation in
1+1
-D. We demonstrate the existence of a large set of initial data close to the ground state soliton resulting in the pseudo-conformal type blow up behavior. More specifically, we prove a version of a conjecture of Perelman, establishing the existence of a co-dimension one stable blow up manifold in the measurable category.
Toric structures on near-symplectic 4-manifolds
Authors: Gay David T. , Symington Margaret
Published: December 2009

A near-symplectic structure on a 4-manifold is a closed 2-form that is symplectic away from the 1-dimensional submanifold along which it vanishes and that satisfies a certain transversality condition along this vanishing locus. We investigate near-symplectic 4-manifolds equipped with singular Lagrangian torus fibrations which are locally induced by effective Hamiltonian torus actions. We show how such a structure is completely characterized by a singular integral affine structure on the base of the fibration whenever the vanishing locus is nonempty. The base equipped with this geometric structure generalizes the moment map image of a toric 4-manifold in the spirit of earlier work by the second author on almost toric symplectic 4-manifolds. We use the geometric structure on the base to investigate the problem of making given smooth torus actions on 4-manifolds symplectic or Hamiltonian with respect to near-symplectic structures and to give interesting constructions of structures which are locally given by torus actions but have nontrivial global monodromy.
Stability of closed characteristics on compact convex hypersurfaces in $\mathbb{R}^6$
Authors: Wang Wei
Published: December 2009

Let Σ ⊂
ℝ6
be a compact convex hypersurface. We prove that if Σ carries only finitely many geometrically distinct closed characteristics, then at least two of them must have irrational mean indices. Moreover, if Σ carries exactly three geometrically distinct closed characteristics, then at least two of them must be elliptic.
Singular Dynamics for Semiconcave Functions
Authors: Cannarsa Piermarco , Yu Yifeng
Published: December 2009

Semiconcave functions are a well-known class of nonsmooth functions that possess deep connections with optimization theory and nonlinear pde’s. Their singular sets exhibit interesting structures that we investigate in this paper. First, by an energy method, we analyze the curves along which the singularities of semiconcave solutions to Hamilton–Jacobi equations propagate—the socalled generalized characteristics. This part of the paper improves the main result in [P. Albano, P. Cannarsa,
Propagation of singularities for solutions of nonlinear ﬁrst order partial differential equations
, Arch. Ration. Mech. Anal. 162 (2002), 1–23] and simpliﬁes the construction therein. As applications, we recover some known results for gradient ﬂows and conservation laws. Then we derive a simple dynamics for the propagation of singularities of general semiconcave functions. This part of the work is also used to study the singularities of generalized solutions to Monge–Ampère equations. We conclude with a global propagation result for the singularities of solutions e in weak KAM theory.
Asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces
Authors: Kohlenbach Ulrich , Leuştean Laurentiu
Published: December 2009

This paper provides a ﬁxed point theorem for asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces as well as new effective results on the Krasnosel’skiĭ–Mann iterations of such mappings. The latter were found using methods from logic and the paper continues a case study in the general program of extracting effective data from prima-facie ineffective proofs in the ﬁxed point theory of such mappings.
The speed of propagation for KPP type problems. I: Periodic framework
Authors: Berestycki Henri , Hamel François , Nadirashvili Nikolai
Published: December 2009

This paper is devoted to some nonlinear propagation phenomena in periodic and more general domains, for reaction-diffusion equations with Kolmogorov–Petrovsky–Piskunov (KPP) type nonlinearities. The case of periodic domains with periodic underlying excitable media is a follow-up of the article [7]. It is proved that the minimal speed of pulsating fronts is given by a variational formula involving linear eigenvalue problems. Some consequences concerning the influence of the geometry of the domain, of the reaction, advection and diffusion coefficients are given. The last section deals with the notion of asymptotic spreading speed. The main properties of the spreading speed are given. Some of them are based on some new Liouville type results for nonlinear elliptic equations in unbounded domains.
Singular principal G-bundles on nodal curves
Authors: Schmitt Alexander H.W.
Published: December 2009

In the present paper, we give for the first time a general construction of compactified moduli spaces for semistable

G

-bundles on an irreducible complex projective curve

X

with exactly one node,

G

a semisimple linear algebraic group over the complex numbers.
Energy and Morse index of solutions of Yamabe type problems on thin annuli
Authors: Ben Ayed Mohammed , El Mehdi Khalil , Ould Ahmedou Mohameden , Pacella Filomena
Published: December 2009

In this paper we consider the following Yamabe type family of problem

(P_\varepsilon) : \quad -\Delta u_\varepsilon = u_\varepsilon ^{\frac{n+2}{n-2}}, \, \, u_\varepsilon > 0

in

A_\varepsilon

,

u_\varepsilon =0

on

\partial A_\varepsilon

, where

A_\varepsilon

is an annulus-shaped domain of

\mathbb R^n

,

n\geq 3

, which becomes thinner when

\varepsilon\to 0

. We show that for every solution

u_\varepsilon

, the energy

\int_{A_\varepsilon} \, |\nabla u_\varepsilon|^2

, as well as the Morse index tends to infinity as

\varepsilon\to 0

. Such a result is proved through a fine blow-up analysis of some appropriate scalings of solutions whose limiting profiles are regular as well as singular solutions of some elliptic problem on

\mathbb R^n

, a half space or an infinite strip. Our argument involves also a Liouville-type theorem for regular solutions on the infinite strip.
Energy quantization and mean value inequalities for nonlinear boundary value problems
Authors: Wehrheim Katrin
Published: December 2009

We give a unified statement and proof of a class of well known mean value inequalities for nonnegative functions with a nonlinear bound on the Laplacian. We generalize these to domains with boundary, requiring a (possibly nonlinear) bound on the normal derivative at the boundary. These inequalities give rise to an energy quantization principle for sequences of solutions of boundary value problems that have bounded energy and whose energy densities satisfy nonlinear bounds on the Laplacian and normal derivative: One obtains local uniform bounds on the complement of finitely many points, where some minimum quantum of energy concentrates.
On two problems studied by A. Ambrosetti
Authors: Arcoya David , Carmona José
Published: December 2009

We study the Ambrosetti-Prodi and Ambrosetti-Rabinowitz problems. We prove for the first one the existence of a continuum of solutions with shape of a reflected C (

\supset

-shape). Next, we show that there is a relationship between these two problems.
On bifurcation and uniqueness results for some semilinear elliptic equations involving a singular potential
Authors: Chaves Manuela , García-Azorero Jesús
Published: December 2009

We will present some results concerning the problem

\left\{ \begin{array}{ll} & -\Delta u = \lambda \frac {u}{|x|^2}+u^q \, , \, \, u > 0 \text{ in }\Omega,\\ & u|_{\partial \Omega}=0, \end{array} \right.

where

0<q<\frac{N+2}{N-2}

,

q\neq 1

,

\lambda \ge 0

and

\Omega

is a smooth bounded domain containing the origin. In particular, bifurcation and uniqueness results are discussed.
The periodic Ambrosetti-Prodi problem for nonlinear perturbations of the p-Laplacian
Authors: Mawhin Jean
Published: December 2009

We prove an Ambrosetti-Prodi-type result for the periodic solutions of equation

\left(|u'|^{p-2}u')\right)' + f(u)u' + g(x,u) = t ,

when

f

is arbitrary and

g(x,u) \to +\infty

or

g(x,u)\to - \infty

when

|u| \to \infty.

The proof uses upper and lower solutions and Leray-Schauder degree.
A weighted symmetrization for nonlinear elliptic and parabolic equations in inhomogeneous media
Authors: Reyes Guillermo , Vázquez Juan Luis
Published: December 2009

In the theory of elliptic equations, the technique of Schwarz symmetrization is one of the tools used to obtain a priori bounds for classical and weak solutions in terms of general information on the data. A basic result says that, in the absence of lower-order terms, the symmetric rearrangement of the solution

u

of an elliptic equation, that we write

u^*

, can be compared pointwise with the solution of the symmetrized problem. The main question we address here is the modification of the method to take into account degenerate equations posed in inhomogeneous media. Moreover, the equations we want to deal with involve weights that make them of non-divergence form, at least when written in terms of the natural variables. We find comparison results covering the elliptic case and the corresponding evolution models of parabolic type, with emphasis on equations of porous medium type. More specifically, we obtain a priori bounds and decay estimates for wide classes of solutions of those equations.
Upper bounds for singular perturbation problems involving gradient fields
Authors: Poliakovsky Arkady
Published: December 2009

We prove an upper bound for the Aviles–Giga problem, which involves the minimization of the energy

E_\varepsilon(v)=\varepsilon\int_\Omega\big|\nabla^2v\big|^2dx+\frac{1}{\varepsilon}\int_\Omega\big(1-|\nabla v|^2\big)^2dx

over

v\in H^2(\Omega)

, where

\varepsilon>0

is a small parameter. Given

v\in W^{1,\infty}(\Omega)

such that

\nabla v\in BV

and

|\nabla v| =1

a.e., we construct a family

\{v_\varepsilon\}

satisfying:

v_\varepsilon\to v

in

W^{1,p}(\Omega)

and

E_\varepsilon(v_\varepsilon)\to\frac{1}{3}\int_{J_{\nabla v}}|\nabla^+v-\nabla^-v|^3\,d{\mathcal H}^{N-1}

, as

\varepsilon

goes to

0

.
Rational string topology
Authors: Félix Yves , Thomas Jean-Claude , Vigué-Poirrier Micheline
Published: December 2009

We use the computational power of rational homotopy theory to provide an explicit cochain model for the loop product and the string bracket of a 1-connected closed manifold

M

. We prove that the loop homology of

M

is isomorphic to the Hochschild cohomology of the cochain algebra

C^\ast(M)

with coefficients in itself. Some explicit computations of the loop product and the string bracket are given.
A nonlinear elliptic equation with singular potential and applications to nonlinear field equations
Authors: Badiale Marino , Benci Vieri , Rolando Sergio
Published: December 2009

We study existence and asymptotic properties of solutions to a semilinear elliptic equation in the whole space. The equation has a cylindrical symmetry and we find cylindrical solutions. The main features of the problem are that the potential has a large set of singularities (i.e. a subspace), and that the nonlinearity has a double power-like behaviour, subcritical at infinity and supercritical near the origin. We also show that our results imply the existence of solitary waves with nonvanishing angular momentum for nonlinear evolution equations of Schrodinger and Klein-Gordon type.
Even sets of nodes on sextic surfaces
Authors: Catanese Fabrizio , Tonoli Fabio
Published: December 2009

We determine the possible even sets of nodes on sextic surfaces in

\mathbb P 3

, showing in particular that their cardinalities are exactly the numbers in the set

\{ 24, 32, 40, 56 \}

. We also show that all the possible cases admit an explicit description. The methods that we use are an interplay of coding theory and projective geometry on one hand, of homological and computer algebra on the other.

We give a detailed geometric construction for the new case of an even set of 56 nodes , but the ultimate verification of existence relies on computer calculations. Moreover, computer calculations have been used more than once in our research in order to get good guesses. The construction gives a maximal family, unirational and of dimension 27, of nodal sextics with an even set of 56 nodes.

As in [Ca-Ca] (where the other cases were described) each such nodal surface

F

is given as the determinant of a symmetric map

\varphi : \mathcal E^\vee \to \mathcal E

, for an appropriate vector bundle

\mathcal E

depending on

F

. The first difficulty here is to show the existence of such vector bundles. This leads us to the investigation of a hitherto unknown moduli space of rank 6 vector bundles which we show elsewhere to be birational to a moduli space of plane representations of cubic surfaces in

\mathbb P^3

. The resulting picture shows a very rich and interesting geometry. The main difficulty is to show the existence of "good" maps

\varphi

, and the interesting phenomenon which shows up is the following: the "moduli space" of such pairs

(\mathcal E, \varphi )

is (against our initial hope) reducible, and for a general choice of

\mathcal E

the determinant of

\varphi

is the double of a cubic surface

G

. Only when the vector bundle

\mathcal E

corresponds to a reducible cubic surface, then we get an extra component of the space of such pairs

(\mathcal E, \varphi )

, and a general choice in this component yields one of our desired nodal sextic surfaces.
Statistics in Finance
Authors: Davis Richard A. , Klüppelberg Claudia
Published: December 2009

The Statistics in Finance Workshop, organized by Richard A. Davis (Ft. Collins) and Claudia Klüppelberg (Technische Universität München), was held January 11–17. This meeting was well attended with over 40 participants with broad geographic representation from Europe, England, Australia, the Far East, and the US. This workshop was a nice blend of researchers with various backgrounds including statistics, probability, and econometrics. Approximately 33 talks, of varying lengths, were delivered during the five days. The talks were given by both leading experts in the field as well as by up and coming stars.

There were several major themes in the various sessions. These included, continuous time models, Levy processes, stochastic volatility models, GARCH models, extreme value theory with applications to financial risk, theory of copulas, and option pricing. This meeting generated a great deal of discussion and often smaller groups of people met in the evenings for expanded and detailed lectures. A number of important research contacts were made which we fully expect to stimulate many new collaborative research projects.

In addition to the excellent scientific program, there were two scheduled social activities. The inclement weather cleared up just in time for the traditional Wednesday afternoon hike to Oberwolfach for coffee and Black Forest Cake. The second activity, which most considered the highlight of the week, was a piano recital performed by Peter Brockwell and Gernot Müller.

For many of the participants, this was their first trip to Oberwolfach, and they came away very impressed from the experience. There was a strong consensus that the “Statistics in Finance Workshop” should become a regular Oberwolfach event.
Mini-Workshop: Nonlinear Spectral and Eigenvalue Theory
Authors: Appell Jürgen , Drábek Pavel , Chiappinelli Raffaele
Published: December 2009

What is the state-of-the-art of abstract spectral and eigenvalue theory for nonlinear operators, and how may this theory be applied to nonlinear equations involving the p-Laplace operator? These two questions have provided the main focus of the Mini-Workshop. Accordingly, the main topics covered by the talks on this Mini-Workshop have been

Of course, these three topics are not mutually independent, but there are various interconnections between them which are of particular interest. For example, sets of eigenvalues (point spectra) may be regarded, as in the linear case, as an important part of the spectrum; conversely, nonlinear eigenvalue theory is one of the historical roots of nonlinear spectral theory. Moreover, the p-Laplace operator is one of the most interesting homogeneous (though nonlinear) operators which may not only serve as a “model operator” in nonlinear eigenvalue problems, but also occurs quite frequently in various applications to physics, mechanics, and elasticity.

The aim and scope of the Mini-Workshop was to bring together experts on nonlinear spectral analysis and operator theory, on the one hand, and more application-oriented specialists in eigenvalue problems for nonlinear partial differential equations (like the p-Laplace equation), on the other. As a result, 15 leading experts in the field from 10 different countries discussed recent progress and open problems in the theory, methods, and applications of spectra and eigenvalues of nonlinear operators.
Self-Adaptive Methods for PDE
Authors: Rannacher Rolf , Süli Endre , Verfürth Rüdiger
Published: December 2009

This conference was on theoretical and practical aspects of error control and self-adaptivity in the numerical solution of partial differential equations. The organizers were Endre Süli (Oxford), Rolf Rannacher (Heidelberg) and Rüdiger Verfürth (Bochum), and the 44 participants came from 11 different countries.

Many processes in sciences and engineering are formulated in terms of partial differential equations. With the incorporation of more and more complete physics these models become increasingly complex and their accurate numerical simulation requires the use of efficient self-adaptive methods. Such “self-adptivity” is usually based on
it a posteriori
estimates for the discretization and iteration errors in terms of local quantities (residuals) obtained from the computed solution. During the last few years, these approaches have seen a rapid development from simple model situations towards real-life applications. The conference's focus was on basic questions of the rigorous mathematical understanding of these methods and their applications. The frame of the conference was set by six invited one-hour survey lectures on the topics:

Additionally 18 shorter talks have been given on more specialized aspects not treated in the survey lectures and on other subjects. Important topics addressed by these talks were “adaptivity for nonlinear, nondifferentiable PDEs”, “adaptivity for coupled problems”, “anisotropic and moving mesh adaptation”, “local and global recovery techniques”, “parallelization of adaptive methods”, and “mesh generation”. The talks showed that much progress has been made in extending the concept of a posteriori error estimation and mesh adaptation from simple elliptic problems to real-life situations including coupled models, multiple scales and nonlinearity. Thanks to the restricted number of talks, there was left plenty of time for discussion which was extensively used by the participants. The discussions concentrated on question related to the convergence and asymptotic complexity of adaptive finite element methods and the various strategies of using “duality-based” a posteriori error estimates. The recent extension of these concepts to optimization problems and to model calibration has opened a whole new world of applications and will significantly affect the future development of PDE numerics.
Hyperbolic Conservation Laws
Authors: Dafermos Constantine , Kröner Dietmar , Leveque Randy
Published: December 2009

The conference was organized by Constantine Dafermos (Providence), Dietmar Kröner (Freiburg), Randy LeVeque (Seattle).

44 scientists from 9 countries participated in this workshop. During the conference we had 22 main lectures and on Tuesday and Thursday evening 10 short informal contributions. On Wednesday evening the whole group came together for a roundtable discussion on open problems. The main feature of this workshop was characterised by the collaboration of people from numerical and theoretical analysis. In the field of hyperbolic conservation laws, progress is mainly based on the input from numerical analysis to mathematical theory and vice versa. This has been shown for many new results obtained in the past and was confirmed during this workshop.

The abstracts are listed in two groups, first about “Theory” and second about “Numerics” and in each group in alphabetical order.
Cohomological Aspects of Hamiltonian Group Actions and Toric Varieties
Authors: Guillemin Victor W. , Puppe Volker , Vergne Michèle
Published: December 2009

The meeting brought together people with different mathematical background, who all use cohomological methods to study symmetries of manifolds. The main aim was the exchange of ideas, recent results, and the discussion of open problems and questions from diverse viewpoints. Altogether there were 27 talks (including an evening talk on computer programs), and a Hausmusik evening with an artistic juggling intermission.

All talks reflected the central theme of the workshop, namely the use of (equivariant) cohomology in studying Lie group actions on manifolds. Contribution to the following subjects were given:

Especially the informal discussions among participants both with similar and with diverse mathematical background were a very important aspect of the workshop. We believe that the meeting has stimulated further cooperation in the study of actions of Lie groups between mathematicians from different areas.
Calculus of Variations
Authors: Dal Maso Gianni , Friesecke Gero , Rivière Tristan
Published: December 2009

The workshop continued the longstanding biannual series at Oberwolfach on Calculus of Variations. This Oberwolfach series provides an imporant service to the mathematics community, being currently the only periodic international meeting in this very active area. The main themes of the workshop were variational methods in differential geometry and in nonlinear partial differential equations theory, where exciting topics included geometric flows, condensation and singularity formation in geometric problems, and mass transportation phenomena in partial differential equations. Among the many traditional and non-traditional application areas of the calculus of variations, the talks covered aspects of general relativity, discrete systems, phase transitions and microstructure, fluid dynamics, quantum chemistry, and approximation theory for rough function spaces.
Phasenübergänge
Authors: Alt Hans Wilhelm , Luckhaus Stephan , Presutti Errico , Salje Ekhard K.H.
Published: December 2009

This workshop, as an established intention, brings together different groups working on phase transitions. Mathematicians working in statistical mechanics, and others working in PDE and continuum mechanics met with physicists with a strong experimental background. There were many younger participants, and they specifically stated that this workshop gave them an excellent opportunity for contact with the fields different from their own. There was a wide range of subjects presented in the talks and also in the discussion groups, with an emphasis on free energies, scalings and microstructures. The modelling aspect was very important always with the aim to get rigorous results, describe qualitative behaviour and the relationship between different classes of models in precise terms, e.g. via singular perturbation theory. This meant that the discussion of mathematical technical tools, many inspired by phase transition problems, played a large role in the workshop.
Thermodynamische Materialtheorien
Authors: Hutter Kolumban , Müller Ingo , Truskinovsky Lev
Published: December 2009

The workshop was well-attended with 46 participants of which 9 gave keynote lectures and 25 gave short contributions. After most lectures there were lively discussions to which all attendants contributed.

The overall theme was thermodynamics which, as a universal theory, may be – and was – applied to different types of phenomena and materials, viz.

The participants had a varied background: Some were physicists and engineers, others applied mathematicians. The former were mostly interested in modelling of material properties and simulation of observed processes. They generally tended to make their models as simple as possible. The mathematicians took an interest in the properties of the model equations, provided that they offered a challenge to the analyst, or that they permitted the application of their analytical tools.

This dichotomy of the audience was intended by the organizers, of course, and it led to lively discussions. Thus it was hotly debated whether good mathematics should be wasted on bad physics. Or whether it is justifiable to construct mutilated, or arbitrarily extended physical models such that they be amenable for the analytical toolbox. The question arose of what value an existence and uniqueness proof is for non-realistic models.

Another case in point is the regularization of originally hyperbolic equations as they occur in the kinetic theory of gases and in extended thermodynamics. It was debated whether it is worthwhile to smooth out solutions artificially, rather than investigate how nature manages the problem of avoiding jumps.

It could not be expected that such discussions reach an agreeable conclusion but - perhaps - they served to break up questionable ideas in both groups of participants; ideas, that have become all too comfortable and well-accommodated in their minds. The dialogue will be continued in the future between communities that ordinarily do not overlap; this may in fact be an important outcome of the meeting.

There was an evening lecture by Prof. W. Bürger on toys – boomerangs, spinning tops and rattlebacks. Everybody seems to have enjoyed that lecture.
Graph Theory
Authors: Diestel Reinhard , Schrijver Alexander , Seymour Paul
Published: December 2009

This conference was one of a series of Oberwolfach conferences, held every two years or so, with focus on graph structure, decomposition, and representation. There were 49 participants, including over a dozen graduate students and postdocs.

At the request of the Oberwolfach Director, the conference schedule was designed to promote informal collaboration. In particular, there were fewer formal talks than usual, and instead there were a number of discussion groups or “workshops”. Also, the first day (except for one plenary talk) was devoted to having the participants introduce themselves – we asked all participants to give a five-minute presentation of their current interests.

We were fortunate in that several of the plenary talks described major new results. For instance, Ron Aharoni and Eli Berger have just solved the Erdős–Menger conjecture; Bertrand Guenin has proved a major extension of the four-colour theorem; and Stephan Brandt and Stéphan Thomassé have settled a long-standing question about the chromatic number of dense graphs.

But probably the most distinctive feature of the meeting were the workshops. Some of these were planned before the conference, and others were held spontaneously. They were each on a topic with a chairman, but made as informal as possible. Some were more or less a sequence of talks on the topic, some were monologues, and some were genuine discussions. There were several different topics: infinite graphs and Ramsey theory, matroid theory, connectivity, graph minors and width, and topological methods. Three topics in particular gave rise to particularly active and long-running workshops: the proof of the Erdős–Menger conjecture, the prospects of extending the graph minors project to matroids, and the use of topological methods for combinatorial problems.

Our thanks to the organizers of the workshops for making them run successfully, to the Director for encouraging us to try out new ways of informal collaboration, and to all the participants for making this a highly stimulating meeting.
Gemischte und nicht-standard Finite-Elemente-Methoden mit Anwendungen
Authors: Braess Dietrich , Carstensen Carsten , Hackl Klaus
Published: December 2009

Mixed finite element methods (MFEM) form a general mathematical framework for the spatial discretisation of partial differential equations, mainly applied to elliptic equations of second order. They become increasingly important for the solution of nonlinear problems. In contrast to standard finite element schemes the mixed finite element discretisation of problems in divergence form, i.e.

f +{\rm div} \, \sigma = 0

where

\sigma = A (\nabla \, u)

,

\sigma \in L

and

u \in H

, allows more flexibility in the design of the discrete approximation spaces contained in

L

and

H

, i.e. in the spaces for the direct variables and the Lagrange multipliers.

The workshop focuses on new developments in the field of mixed and non-standard finite element methods. The main points are

The workshop aimed at bridging the gap between the computational engineering community and applied mathematicians and in consequence to unify the scientific language and foster later collaboration. Nonlinear mixed schemes were of particular concern for problems in elasticity and plasticity, but electromagnetics and mathematically related topics were also included.

Mixed finite element methods for elliptic problems are based on a variational description in saddle-point form. Side conditions such as divergence free velocity fields in incompressible fluid dynamics are usually treated in this framework. The appearance of ‘soft’ side conditions is typical for structural mechanics as is the case with nearly incompressible materials or plates and shells with small thickness parameters. We also mention materials which almost satisfy the Kirchhoff condition, i.e. problems with a high but finite shear stiffness. In such cases, which are by no means ‘soft’ from the mathematical point of view, mixed methods lead to a more robust discretisation.

The arising stability conditions and computational techniques cannot be understood fully by intuitive mechanical principles; however, from the mathematician's point of view their reasoning is natural, clear and insightful.

Mixed and non-standard finite element methods gain increasing prominence in the prevention of locking phenomena. We highlight a topic which is currently actively investigated: the development of stable and efficient plate and shell elements with regard to shear locking, which is more intricate than volume locking. Here it is important to understand how techniques based on heuristic ideas are consistent with more modern mathematical methods.

Availability of fast solvers is decisive for the competitiveness of numerical techniques. For a variety of applications, multigrid methods are crucial for the efficiency of the implementation.

Methods have been proposed which do not appear plausible if one wants to deduce the algorithms directly from the physical model. The advanced methods depend on rigorous error estimators in order to guarantee that the numerical solutions represent the exact solutions of the physical model.