bluuebunny/crossref_metadata_2025 huggingface dataset:
Modelling of Thermo-Mechanical Behaviour of Magnesium Alloys during Indirect Extrusion
Authors: Ertürk Serkan , Steglich Dirk , Bohlen Jan , Letzig Dietmar , Brocks Wolfgang
Published: December 2009

A yield function for hexagonal closed packed (hcp) metals was modified with respect to strain rate and temperature and developed to capture the material behaviour during extrusion. Magnesium alloy ZEK100 was extruded indirectly at 300°C into a round bar. Compression tests were carried out at various strain rates, temperatures and sample orientation to characterise the material flow. These data were used as input data for fully thermo-mechanical coupled simulations of indirect extrusion. A successful prediction of the extrusion force and the temperature increase during extrusion is presented.
Creep-Fatigue Interaction in the AISI H11 Tool Steel
Authors: Reggiani Barbara , D’Ascenzo Marco , Donati Lorenzo , Zhou Jie , Tomesani Luca
Published: December 2009

The effect of process parameters on the creep-fatigue behavior of a hot-work tool steel for aluminum extrusion die was investigated through a technological test in which the specimen geometry resembled the mandrel of a hollow extrusion die. Tests were performed on a Gleeble thermomechanical simulator by heating the specimen using joule’s effect and by applying cyclic loading up to 6.30 h or till specimen failure. Displacements during the tests at 380, 490, 540 and 580°C and under the average stresses of 400, 600 and 800 MPa were determined. A dwell time of 3 min was introduced during each of the tests to understand the creep behavior. The results showed that the test could indeed physically simulate the cyclic loading on the hollow die during extrusion and reveal all the mechanisms of creep-fatigue interaction.
Prediction of the Extrusion Load and Exit Temperature Using Artificial Neural Networks Based on FEM Simulation
Authors: Zhou Jia , Li Luo Xing , Mo J. , Zhou Jie , Duczczyk Jurek
Published: December 2009

In the present study, the extrusion process for the AZ31B magnesium alloy was simulated using a DEFORM-3D software package to establish a database in order to provide input data for artificial neural networks (ANN). The network model was trained by taking extrusion ratio, ram speed, shape complexity and ram displacement as the input variables and the extrusion load and exit temperature as the output parameters. The data from FEM simulations were submitted for ANN as a training file and then ANN built were used to predict the target parameters. The ANN predicted results were found to be in agreement with the FEM simulated and experimental measured ones.
Contrasting Models to Determine the Approximate Extrusion Process Conditions for the First Billet
Authors: Sabater Marc , García-Romeu Maria Luisa
Published: December 2009

This paper is focused on determining extrusion process conditions for the first billet and, particularly, on selecting an adequate billet temperature and extrusion speed. It is important to predict these values before adjusting the die to avoid lengthy and unproductive preparation times, and to make die adjustment easier during the tests. With that in mind, this study employs two models to determine the first billet temperature (TFB) and the extrusion speed (SE) parameters: one that applies regression techniques and another that uses neural networks. The aim of this paper is to present the results obtained by comparing the performance of the two models to determine which one offers the best results. We also analyze whether changing the number of patterns for construction of the models will improve results. The models are based on extrusion process parameters taken from real industry contexts. The results indicate that the variables chosen as predictor variables for the extrusion speed output must be refined.
Numerical Design of Extrusion Process Using Finite Thermo-Elastoviscoplasticity with Damage. Prediction of Chevron Shaped Cracks
Authors: Labergère Carl , Saanouni Khemais , Lestriez Philippe
Published: December 2009

The influence of the initial temperature and its evolution with large plastic deformation on the formation of the fully coupled chevron shaped cracks in extrusion is numerically investigated. Fully coupled thermo-elasto-viscoplastic constitutive equations accounting for thermal effects, mixed and nonlinear isotropic and kinematic hardening, isotropic ductile damage with micro-cracks closure effects are used. These constitutive equations have been implemented in Abaqus/Explicit code thanks to the user subroutine vumat and used to perform various numerical simulations needed to investigate the problem. It has been shown that the proposed methodology is efficient to predict the chevron shaped cracks in extrusion function of the main process parameters including the temperature effect.
A New Constitutive Model for Work Hardening Based on Gain Boundary Energy Density
Authors: Luo Ji , Wang Zhi Rui
Published: December 2009

Recently, the necessity to grade grain size to ultrafine and nano scale for understanding the mechanical behavior of these materials has been recognized. However, the nature of such classification has remained unclear. As an example, ultrafine (100 nm -1 μm) and nano (<100 nm) grained FCC metals, compared to their coarse grained counterparts, exhibit a grain size strengthening that may deviate from the Hall-Petch relationship. To explain the mechanism of such deviation, previous dislocation theories seem insufficient. To solve this problem, a critical grain size criterion governing the shift of deformation mechanism is proposed in this work. This model employs an energetic approach; it relates the grain boundary energy density to certain critical energy values; and it permits, for the first time, a quantitative grading of grain sizes. Predictions based on this model were evaluated. The prediction on copper polycrystals of various grain sizes showed a very good agreement with experimental results. It is thus wished that the grain size theory on plastic deformation mechanism could be unified with the dislocation theory. In this study, such unification is attempted by using a parameter defined as the defect energy density. The possibility of such generalization is further reasoned upon the fact that the defect energy approach should be a unique but common form applicable for both dislocations and grain boundaries.
Nanostructure Formation and Properties in Some Al Alloys after SPD and Heat Treatment
Authors: Kvačkaj Tibor , Bidulská Jana , Fujda Martin , Kočiško Robert , Pokorný Imrich , Milkovic Ondrej
Published: December 2009

Influence of SPD process realized by ECAP on structural formation and mechanical properties was searched. Samples after ECAP were heat treated at various temperature and time conditions. Investigation material bases were high purity aluminium and aluminium alloys EN AW 6082, EN AW 2014. The best material properties are describing in dependence on experimental conditions.
The Effect of Grain Size and Strain Rate on the Tensile Ductility of Bulk Nanostructured Metals and Alloys
Authors: Wang Guo Yong , Lian Jian She , Jiang Qing
Published: December 2009

The nanostructured metals and alloys are under intensive research worldwide and being developed into bulk forms for application. While these new materials offer record-high strength, their ductility is often inadequate and sometime rendering them unusable. Besides tailoring the nanostructure to achieve coexisting high strength and high ductility, to uncover the coherent property of this material is also important. This article reviews the recent researches finished in our lab. A set of nanostructured metals and alloys were synthesized by a direct current electrodeposition technique, and the effect of grain size and strain rate on the mechanical properties stressing on tensile ductility was systemically studied by tensile test at room temperature.
Strength and Ductility in Electrodeposited Nanocrystalline Nickel
Authors: Yang Heather W. , Mohamed Farghalli A.
Published: December 2009

Electrodeposited nanocrystalline (nc) Ni having an average grain size of 20 nm was annealed at 443 K for different holding times. An examination of the microstructure following annealing showed three important features. First, all annealed samples exhibited abnormal grain growth, which was manifested by the presence of large grains that were surrounded by regions of small grains (bimodal grain distributions). Second, annealing twins existed in the large grains of the samples that showed a bimodal grain distribution. Third, by estimating the density of annealing twin, it was found that annealing nc-Ni at 443 K resulted in a maximum twin density after 5h. Following annealing treatment, specimens with different volume fractions of twins were tested under uniaxial tension at 393 K and a strain rate of 10-4 s-1. The results showed that both strength and ductility in nc-Ni attained maximum values after annealing for 5h. The role of both bimodal grain distributions and annealing twins in enhancing ductility and strength was discussed.
Nanostructured Ti2448 Biomedical Titanium Alloy
Authors: Hao Yu Lin , Li Shi Jian , Sui M.L. , Yang Rui
Published: December 2009

It is generally accepted that grain refinement by the mechanisms of dislocation interaction, deformation twinning and/or stress-induced martensitic transformation is of relatively low efficiency. Rapid production of nanostructured metallic materials by conventional processing technologies remains a challenge. A new mechanism of fast grain refinement, through highly localized plastic deformation, was recently found in a -type biomedical titanium alloy (Ti2448). This mechanism leads to rapid grain refinement to tens nanometers and even amorphous transition during conventional cold processing. Since such grain refinement induces little strengthening, this process was previously termed soft nanostructuring. Here we review the research into this new way of nanostructuring and discuss the mechanism of grain refinement as well as dispersion strengthening of Ti2448 alloy by the precipitation of a second phase from the nano-sized  matrix.
Effect of Grain Size on the Superplastic Behavior of a Nanostructured Nickel-Based Superalloy
Authors: Mukhtarov Shamil Kh.
Published: December 2009

The present paper deals with the review of earlier studies and original investigation of microcrystalline (MC) and nanostructured (NS) nickel based INCONEL® alloy 718 processed by severe plastic deformation (SPD) via multiple isothermal forging (MIF). The alloy with a mean grain size of 1 µm - 80 nm has been studied in terms of its thermal stability, superplastic and mechanical properties. It was established that the NS state with the 80 nm grain size can be considered as thermally stable up to the temperature 600°C (0.56Tm). The increase of annealing temperature beyond 600°C causes static recrystallization. Investigations of mechanical properties at room temperature have shown that the decrease of a mean grain size provides the enhancement of strength and reduction of plasticity. Thus, the alloy with a grain size of 80 nm has shown the ultimate strength - 1920 MPa and ductility - 4.8%. Mechanical properties of the NS state of the alloy after annealing are discussed. It has been established that alloy 718 with a grain size of 80 nm displays superplasticity at 600°C and a strain rate of 1.510-4s-1. The values of relative elongation and strain rate sensitivity coefficient m are 350% and 0.37, respectively.
Nano-Grained Structure Induced by Mechanical Twinning during Multi-Directional Forging and the Mechanical Properties
Authors: Miura Hiromi , Nakao Y.
Published: December 2009

A bulky SUS316 austenitic stainless steel (SUS316) was multi-directionally forged (MDFed) at 77 K and 300 K up to a cumulative strain of = 6 at maximum. With increasing cumulative strain, the grains were subdivided by mechanical twinning and martensitic transformation. Especially, mechanical twins accelerated grain fragmentation by subdivision of the initial grains and by intersection of the previously formed twins during MDF. The intersection of twins caused finally evolution of packet grains, which were composed of lamellar structured twins. The packet size and the lamellar twin spacing decreased down to 35 nm and 15 nm by MDF to  = 6 at 77 K. The average grain size achieved was estimated to be about 10 nm. Twinning appeared more frequently and uniformly at 77 K than at 300 K. Tensile test at 300 K revealed ultimate tensile strength of 2.1 GPa and fracture strain of about 0.2. The fracture strain, however, appeared to be constant over ∑Δε = 2.4 independent of cumulative strain. The observed excellent balance of strength and ductility of the nano-grained SUS316 is discussed in relation with the effects of twins on grain fragmentation and mechanical properties.
Ultrahigh Strength and Ductility of Cu-Nb Nanolayered Composites
Authors: Mara Nathan A. , Bhattacharyya D. , Dickerson Patricia O. , Hoagland R.G. , Misra Amit
Published: December 2009

In recent years, the high strength of nanomaterials has gathered much interest in the materials community. Nanomaterials (polycrystalline and composites) have already been used, largely by the semiconductor community, as critical length scales for chip design have decreased to tens of nanometers. However, to ensure reliability of nanomaterials, the mechanisms underlying their structural integrity must be well understood. For these materials to be put into service, not only should their strength be considered, but also ductility, toughness, formability, and fatigue resistance. While some progress has been made into constructing models for the deformation mechanisms governing these behaviors, the body of experimental knowledge is still limited, especially for length scales below 10 nanometers. The results described here show stress-strain curves for nanolaminate composites with individual layer thickness of 40 nm and 5 nm. Nanolaminate composites fabricated via magnetron sputtering comprised of alternating 5 nm thick Cu and Nb multilayers (two relatively soft metals) exhibit strengths on par with hardened tool steel and deformability in compression in excess of 25% [1]. The deformability of nanoscale composites is found to be limited by the onset of geometric instability.
Magnetically Anisotropic Ni2MnGa Thin Films: Coating Glass and Si Micro-Cantilevers Substrates
Authors: Madurga Vicente , Favieres C. , Vergara J.
Published: December 2009

Ni2MnGa thin films, with thickness between 30 and 60 nm, were pulsed-laser deposited at room temperature on Si micro-cantilevers and glass substrates. Two different deposition processes were performed: normal deposition and off¬-normal. After annealing in an inert atmosphere, in-plane isotropic magnetic hysteresis loops were measured for the normal deposited films. In contrast, in-plane anisotropic hysteresis loops were obtained from the off-normal deposited ones. An in-plane easy direction for the magnetisation, perpendicular to the incidence plane of the plasma during deposition, was measured with an anisotropy field of ≈100 Oe and an easy coercive field of ≈24 Oe. The mechanical behaviour of the magnetically anisotropic coated micro-cantilevers and their response to a decreasing temperature permitted observing the martensitic transformation of the Ni2MnGa thin films.
Fabrication and Magnetic Properties of CoNiAl Ferromagnetic Shape Memory Alloy Thin Films
Authors: Kanth Rajini B. , Bhattacharjya D. , Mukhopadhyay P.K.
Published: December 2009

Study o Ferromagnetic shape memory alloys (FSMAs) is an interesting topic of present day research because of their large magnetic field induced shape recovery. They are important materials for the development of sensors and actuator based applications. Attempt for miniaturization of these actuators and sensors have led to the study of thin films. Bulk CoNiAl alloys are promising FSMAs because of their higher ductility and large range of control over the magnetic and structural transformation temperatures. To investigate the physical properties in thin film form we fabricated CoNiAl alloy films by D.C. sputtering method on glass substrates (kept at room temperature) under various conditions. They were annealed in vacuum at 500 0C for 1h. The samples were characterized by X-ray diffraction, scanning electron microscopy, energy dispersive X-ray analysis and ellipsometry. Thickness of the films was found to be lying between 70 and 272 nm. Fine grained microstructure was found for all the deposited films. The transformation temperatures of the samples were taken from the resistivity measurement done between 80 and 350 K. Magnetization measurements were also done between 80 and 400 K by using a vibrating sample magnetometer, but the Curie temperatures of the present films were not found to be below 400 K and magnetoelastic couplings were found to be rather weak.
Simulation of an Improved Microactuator with Discrete MSM Elements
Authors: Spasova Berta , Gatzen Hans Heinrich
Published: December 2009

Magnetic Shape Memory (MSM) alloys are a new class of “smart” materials. In the martensite state, they exhibit a reversible strain due to a reorientation of twin variants, based on twin boundary motion driven by an external magnetic field occurring in the martensite state. This effect allows for the development of linear microactuators.
This work presents the simulation results for the fabrication of a microactuator based on an MSM alloy with an optimized design. A stator element consists of a NiFe45/55 flux guide, two poles, and double-layer Cu coils wound around each pole for generating the magnetic field. The MSM material applied is NiMnGa. The integrated microactuator is subjected to dynamic simulation, using a “checkerboard” pattern to locally switch the magnetic properties when the relative permeability µr is changed. The model is described with the Ansys Parametric Design Language (APDL). Design, modeling, and simulation of the magnetic system including MSM material, are conducted by Finite Element Method (FEM) analysis using the software tool ANSYS™.
Extruded Rods with <001> Axial Texture of Polycrystalline Ni-Mn-Ga Alloys
Authors: Morawiec Henryk , Lelątko Józef , Goryczka Tomasz , Prusik Krystian , Piechota S. , Stróż Danuta
Published: December 2009

The Ni-Mn-Ga alloys extruded at high temperature with a relatively large reduction rate were the subject of the studies. The microscopic observations of the transient zone in the extruded rods revealed rotation of the columnar grains in the ingot along the rod axis - giving the preferred <001> orientations. Comparison of the texture, magnetization and magneto-crystalline anisotropy constant for samples cut out from the columnar grain zone and these cut from the extruded rods was carried out for two alloys which differ in chemical composition and Ms temperature. Both alloys have the 5M martensitic structure at room temperature. The samples cut out of the ingot and the extruded rods have shown the axial <001> orientation, similar magnetization curves and magnetocrystalline anisotropy constant Ku = 1.5-1.6 J/m3•105.
Nano-Positioning with Ferromagnetic Shape Memory Alloy Actuators
Authors: Asua Estibalitz , Feuchtwanger Jorge , García-Arribas Alfredo , Etxebarria Victor , Barandiarán José M.
Published: December 2009

Ferromagnetic shape memory alloy-based actuators offer distintive features that make them advantageous competitors to traditional electromechanical devices. The production of force and motion without contact is one of the most important features. However, the largely non-linear and hysteretic nature of the response of such materials makes them of little use apart from on-off or continuous actuation.
In this work we present the results obtained in a laboratory prototype of linear position FSMA actuator, where the active element is a 12 mm long Ni-Mn-Ga single crystal. The crystal expands a maximum of 12 micrometers and in control experiments, is commanded to expand and contract alternatively to reach positions at 5 µm and 8 µm. It shows that the commanded position could be controlled within 20 nm.
NiMn-Based Metamagnetic Shape Memory Alloys
Authors: Kainuma Ryosuke , Ito K. , Ito W. , Umetsu R.Y. , Kanomata T. , Ishida Kiyohito
Published: December 2009

The magnetic properties of the parent and martensite phases of the Ni2Mn1+xSn1-x and Ni2Mn1+xIn1-x ternary alloys and the magnetic field-induced shape memory effect obtained in NiCoMnIn alloys are reviewed, and our recent work on powder metallurgy performed for NiCoMnSn alloys is also introduced. The concentration dependence of the total magnetic moment for the parent phase in the NiMnSn alloys is very different from that in the NiMnIn alloys, and the magnetic properties of the martensite phase with low magnetization in both NiMnSn and NiMnIn alloys has been confirmed by Mössbauer examination as being paramagnetic, but not antiferromagnetic. The ductility of NiCoMnSn alloys is drastically improved by powder metallurgy using the spark plasma sintering technique, and a certain degree of metamagnetic shape memory effect has been confirmed.
Structural Relation between the X-Phase and other Phases in Ni2MnGa
Authors: Kakeshita Tomoyuki , Fukuda Takashi , Terai Tomoyuki , Osakabe Toyotaka , Kakurai Kazuhisa
Published: December 2009

We have investigated stress and temperature dependences of the structure of the X-phase in Ni2MnGa to understand structural relation between the X-phase and other phases. Position and intensity of satellites of the X-phase are different from those of the intermediate (I-) phase under compressive stress, but they approach those of the I-phase with decreasing stress. That is, the structure change associated with the I → X transformation is discontinuous under a compressive stress, while it is continuous under zero stress. In addition, the transformation from the X-phase to the L21-type parent phase is continuous regardless of applied stress. These results strongly suggest the existence of multi-critical point in Ni2MnGa. On the other hand, the transformation from the X-phase to the martensite phase is discontinuous regardless of applied stress.
Study of Co-Ni-Al Alloys with Magnetically Controlled Shape Memory Effect
Authors: Kositsyna Irina I. , Zavalishin V.A.
Published: December 2009

The methods of electron microscopy, resistometry and magnetometry are used to study
ten (36-38)Co - (32-36)Ni - (27-30)Al (at. %) alloys. Cast coarse-crystalline and microcrystalline
alloys made by melt spinning in a helium atmosphere are considered. It is shown that the martensite
start temperature Ms becomes 30-50°C lower as grains are refined to 1 m m. Replacement of 1 at. %
cobalt by nickel and 1 at. % aluminum by nickel makes the temperature interval of the В2«L10
martensite transformation (30-60)°C and (100-110)°C higher respectively. The martensite
transformation hysteresis is about 100 degrees. The melt-spun Co38Ni34Al28 alloy with the
transformation temperatures Мs = 31°С, Мf = –34°С, Аs = –6°С, Аf = 70°С and Тс = 98°С is a
material possessing the magnetically controlled shape memory effect.
Magnetic and Martensitic Transitions in Ni2Mn1+xSn1-x Alloys
Authors: Chatterjee Subham , Majumdar S.
Published: December 2009

The magnetic phase diagram of Ni2Mn1+xSn1−x based ferromagnetic (FM) shape memory alloys for varied concentrations of x have been studied. With increasing concentration of Mn, the FM Curie temperature (TC) decreases, while the martensitic transition temperature (TM) goes higher. For x = 0.44 and 0.48, TM is close to the onset of ferromagnetism, and two distinct magnetic transitions are observed corresponding to the TC’s of the FM phases of martensite and austenite respectively. The isothermal magnetization at 5 K indicates saturating behaviour at high fields and the saturation moment drops linearly with x. The samples show reasonably large negative magnetoresistance around TM, however the magnitude drops with increasing x. The magnetoresistance is found to be highly irreversible with respect to the applied magnetic field and field induced arrested state is observed for all the FM samples studied around the first order martensitic transition. The present investigation clearly indicates complex magnetic ground state of the Ni2Mn1+xSn1−x samples with competing magnetic interactions.
Uterine Adenocarcinoma with Pulmonary, Liver and Mesentery Metastasis in a Holstein Cow
Authors: Stilwell George , Peleteiro Maria C.
Published: December 2009

The clinical and pathology features of a cow with uterine adenocarcinoma and multiple metastasis are described. Weight loss, inappetence, mild respiratory signs, and reduced milk yield were evident on clinical examination. Grossly deformed uterus, enlarged iliac lymph nodes, and rosary arranged nodules in the mesentery were felt by rectal palpation. Right side laparotomy revealed numerous small masses covering the omentum, and mesentery. Euthanasia was performed. Necropsy and histopathology exam revealed a uterine adenocarcinoma with multiple pulmonary, liver and mesentery metastasis. Uterine adenocarcinoma with metastasis should be included in the differential diagnosis of cows showing weight loss and mild respiratory distress and palpation of numerous firm nodules in the mesentery should be suggestive of neoplasias' metastasis.
Explicit units and the equivariant Tamagawa number conjecture, II
Authors: Burns David , Hayward Anthony
Published: December 2009

We show that a special case of the equivariant Tamagawa number conjecture implies explicit restrictions on the structure of ideal class groups that are in general much finer than those which can be obtained by using the method of Thaine.
Links with no exceptional surgeries
Authors: Futer David , Purcell Jessica S.
Published: December 2009

We show that if a knot admits a prime, twist-reduced diagram with at least 4 twist regions and at least 6 crossings per twist region, then every non-trivial Dehn filling of that knot is hyperbolike. A similar statement holds for links. We prove this using two arguments, one geometric and one combinatorial. The combinatorial argument further implies that every link with at least 2 twist regions and at least 6 crossings per twist region is hyperbolic and gives a lower bound for the genus of a link.
Inégalités de Milnor–Wood géométriques
Authors: Besson Gérard , Courtois Gilles , Gallot Sylvestre
Published: December 2009

Nous prouvons une généralisation de la célèbre inégalité de Milnor–Wood. Si Y est une variété riemannienne fermée, nous considérons une représentation de son groupe fondamental dans le groupe d'isométries d'une espace symétrique X de même dimension. Lorsque X est le produit d'espaces symétriques de courbure strictement négative et de dimension strictement supérieure à 2, nous démontrons une majoration du volume de cette représentation par un nombre calculé à l'aide des entropies volumiques de Y et X. Le cas d'égalité est étudié et donne un théorème de rigidité. Ensuite nous décrivons des exemples de représentations de volume non nul. En dimension 3 l'inégalité ci-dessus donne une preuve simple d'un théorème dû à Soma montrant la finitude du nombre de variétés hyperboliques fermées dominées par une même variété fermée.

We prove a generalisation of the celebrated Milnor–Wood inequality. If Y is a closed Riemannian manifold, we consider a representation of its fundamental group into the isometry group of a symmetric space of the same dimension. When X is the product of symmetric spaces of negative curvature and of dimension greater than 2, we prove an upper bound of the volume of this representation computed in terms of the volume entropies of Y and X. The case of equality is studied and gives rise to a rigidity theorem. We then describe examples of representations of non-zero volume. In dimension 3 the inequality gives a simple proof of a theorem due to Soma showing the finiteness of the number of closed hyperbolic manifolds dominated by the same closed manifold.
Arithmetically Cohen–Macaulay bundles on hypersurfaces
Authors: Mohan Kumar N. , Rao A. P. , Ravindra G. V.
Published: December 2009

We prove that any rank two arithmetically Cohen–Macaulay vector bundle on a general hypersurface of degree at least three in

ℙ^5

must be split.
On symplectic 4-manifolds with prescribed fundamental group
Authors: Baldridge Scott , Kirk Paul
Published: December 2009

In this article we study the problem of minimizing

aχ + bσ

on the class of all symplectic 4-manifolds with prescribed fundamental group

G

(

χ

is the Euler characteristic,

σ

is the signature, and

a, b \in ℝ

), focusing on the important cases

χ

,

χ + σ

and

2χ + 3σ

. In certain situations we can derive lower bounds for these functions and describe symplectic 4-manifolds which are minimizers. We derive an upper bound for the minimum of

χ

and

χ + σ

in terms of the presentation of

G

.
Dense subgroups with Property (T) in Lie groups
Authors: de Cornulier Yves
Published: December 2009

We characterize connected Lie groups that have a dense, finitely generated subgroup with Property (T).
Théorie d'Iwasawa des représentations cristallines II
Authors: Benois Denis , Berger Laurent
Published: December 2009

Let

K

be a finite unramified extension of

ℚ_p

and let

V

be a crystalline representation of

\mathrm{Gal}(\bar ℚ_p/K)

. In this article, we give a proof of the

C_{\mathrm{EP}}(L,V)

conjecture for

L⊂ ℚ_p^{\mathrm{ab}}

as well as a proof of its equivariant version

C_{\mathrm{EP}}(L/K,V)

for

L⊂ \bigcup_{n = 1}^∞ K(ζ_{p^n})

. The main ingredients are the

δ_{ℤ_p(V)}

conjecture about the integrality of Perrin–Riou's exponential, which we prove using the theory of

(φ,Γ)

-modules, and Iwasawa-theoretic descent techniques used to show that

δ_{ℤ_p(V)}

implies

C_{\mathrm{EP}}(L/K,V)

.

Soit

K

une extension finie non-ramifiée de

ℚ_p

et

V

une représentation cristalline de

\mathrm{Gal}(\bar ℚ_p/K)

. Dans cet article, on montre la conjecture

C_{\mathrm{EP}}(L,V)

pour

L⊂ ℚ_p^{\mathrm{ab}}

et sa version équivariante

C_{\mathrm{EP}}(L/K,V)

pour

L⊂ \bigcup_{n = 1}^∞ K(ζ_{p^n})

. Les principaux ingrédients sont la conjecture

δ_{ℤ_p(V)}

sur l'intégralité de l'exponentielle de Perrin–Riou, que nous démontrons en utilisant la théorie des

(φ,Γ)

-modules, et des techniques de descente en théorie d'Iwasawa pour montrer que

δ_{ℤ_p(V)}

implique

C_{\mathrm{EP}}(L/K,V)

.
Magnetic flows on homogeneous spaces
Authors: Bolsinov Alexey V. , Jovanović Božidar
Published: December 2009

We consider magnetic geodesic flows of the normal metrics on a class of homogeneous spaces, in particular adjoint orbits of compact Lie groups. We give the proof of the non-commutative integrability of flows and show, in addition, for the case of adjoint orbits, the usual Liouville integrability by means of analytic integrals. We also consider the potential systems on adjoint orbits, which are generalizations of the magnetic spherical pendulum. The complete integrability of such system is proved for an arbitrary adjoint orbit of a compact semisimple Lie group.
Genus-one helicoids from a variational point of view
Authors: Hoffman David , White Brian
Published: December 2009

In this paper, we use variational methods to prove existence of a complete, properly embedded, genus-one minimal surface that is asymptotic to a helicoid at infinity. We also prove some new properties of such helicoid-like surfaces.
Relations between tautological cycles on Jacobians
Authors: Moonen Ben
Published: December 2009

We study tautological cycle classes on the Jacobian of a curve. We prove a new result about the ring of tautological classes on a general curve that allows, among other things, easy dimension calculations and leads to some general results about the structure of this ring. Further we lift a result of Herbaut and van der Geer–Kouvidakis to the Chow ring (as opposed to its quotient modulo algebraic equivalence) and we give a method to obtain further explicit cycle relations. As an ingredient for this we prove a theorem about how Polishchuk’s operator

\mathcal{D}

lifts to the tautological subalgebra of CH(J).
Relatively hyperbolic groups: geometry and quasi-isometric invariance
Authors: Druţu Cornelia
Published: December 2009

In this paper it is proved that relative hyperbolicity is a quasi-isometry invariant. As byproducts of the arguments, simplified definitions of relative hyperbolicity are provided. In particular we obtain a new definition very similar to the one of hyperbolicity, relying on the existence of a central left coset of a peripheral subgroup for every quasi-geodesic triangle.
Intersection de sous-groupes et de sous-variétés III
Authors: Rémond Gaël
Published: December 2009

We elucidate the structure of various exceptional subsets appearing in parts I and II in order to prove new results on the Zilber–Pink conjecture for abelian varieties. In particular, we obtain boundedness of height on the intersection of interest for all non-degenerate varieties (in a precise sense). The main idea to prove that our exceptional subsets are closed comes from a result of Bombieri, Masser and Zannier on tori and we follow the same approach through so-called anomalous subvarieties but we have to allow extra generality in the definition. We also use in a crucial way a theorem of Ax on analytic subgroups of algebraic groups.
Two theorems on harmonic manifolds
Authors: Nikolayevsky Yuri
Published: December 2009

A Riemannian manifold is called
harmonic
, if for any point

x

it admits a nonconstant harmonic function depending only on the distance to

x

. A.Lichnerowicz conjectured that any harmonic manifold is two-point homogeneous. This conjecture is proved in dimension

n \le 4

and also for some classes of manifolds, but disproved in general, with the first counterexample of dimension

7

. We prove the Lichnerowicz Conjecture in dimension

5

: a five-dimensional harmonic manifold has constant sectional curvature. We also obtain a functional equation for the volume density function

\theta(r)

of a harmonic manifold and show that

\theta(r)

is an exponential polynomial, a finite linear combination of the terms of the form

\mathrm{Re} (c e^{\lambda r} r^m)

, with

c, \lambda

complex constants.
Une caractérisation des endomorphismes de Lattès par leur mesure de Green
Authors: Berteloot F. , Dupont Christophe
Published: December 2009

We show that the Lattès endomorphisms are the only holomorphic endomorphisms of the complex

k

-dimensional projective space whose measure of maximal entropy is absolutely continuous with respect to the Lebesgue measure. As a consequence, Lattès endomorphisms are also characterized by other extremal properties as the maximality of the Hausdorff dimension of their measure of maximal entropy or the minimality of their Liapounov exponents. Our proof uses a linearization method which is of independant interest and a previous characterization by the regularity of the Green current.
Arithmetic properties of $φ(n)/λ(n)$ and the structure of the multiplicative group modulo $n$
Authors: Banks William D , Luca Florian , Shparlinski Igor E.
Published: December 2009

For a positive integer

n

, we let

\varphi(n)

and

\lambda(n)

denote the Euler function and the Carmichael function, respectively. We define

\xi(n)

as the ratio

\varphi(n)/\lambda(n)

and study various arithmetic properties of

\xi(n)

.
Présentations duales des groupes de tresses de type affine $Ã$
Authors: Digne François
Published: December 2009

Artin–Tits groups of spherical type have two well-known Garside structures, coming respectively from the divisibility properties of the classical Artin monoid and of the dual monoid. For general Artin–Tits groups, the classical monoids have no such Garside property. In the present paper we define dual monoids for all Artin–Tits groups and we prove that for the type

\tilde A_n

we get a (quasi)-Garside structure. Such a structure provides normal forms for the Artin–Tits group elements and allows to solve some questions such as to determine the centralizer of a power of the Coxeter element in the Artin–Tits group. More precisely, if

W

is a Coxeter group, one can consider the length

l_R

on

W

with respect to the generating set

R

consisting of all reflections. Let

c

be a Coxeter element in

W

and let

P_c

be the set of elements

p\in W

such that

c

can be written

c=pp'

with

l_R(c)=l_R(p)+l_R(p')

. We define the monoid

M(P_c)

to be the monoid generated by a set

\underline P_c

in one-to-one correspondence,

p\mapsto \underline p

, with

P_c

with only relations

\underline{pp'}=\underline p.\underline p'

whenever

p

,

p'

and

pp'

are in

P_c

and

l_R(pp')=l_R(p)+l_R(p')

. We conjecture that the group of quotients of

M(P_c)

is the Artin–Tits group associated to

W

and that it has a simple presentation (see 1.1 (ii)). These conjectures are known to be true for spherical type Artin–Tits groups. Here we prove them for Artin–Tits groups of type

\tilde A

. Moreover, we show that for exactly one choice of the Coxeter element (up to diagram automorphism) we obtain a (quasi-) Garside monoid. The proof makes use of non-crossing paths in an annulus which are the counterpart in this context of the non-crossing partitions used for type

A

.
Applications of Hofer's geometry to Hamiltonian dynamics
Authors: Schlenk Felix
Published: December 2009

We prove that for every subset

A

of a tame symplectic manifold

(W,\omega)

meeting a semi-positivity condition, the

\pi_1

-sensitive Hofer–Zehnder capacity of

A

is not greater than four times the stable displacement energy of

A

,

c_{HZ}^\circ(A,W)\le 4e (A\times S^1, W\times T^*S^1).

This estimate yields almost existence of periodic orbits near stably displaceable energy levels of time-independent Hamiltonian systems. Our main applications are:

The proof of the above energy-capacity inequality combines a curve shortening procedure in Hofer geometry with the following detection mechanism for periodic orbits: If the ray

\{\varphi_F^t \}

,

t \ge 0

, of Hamiltonian diffeomorphisms generated by a compactly supported time-independent Hamiltonian stops to be a minimal geodesic in its homotopy class, then a non-constant contractible periodic orbit must appear.
Pointwise taut Riemannian manifolds
Authors: Leitschkis Michael
Published: December 2009

In the present work, we investigate pointwise taut Riemannian manifolds by using methods from Riemannian geometry, Morse theory and topology. Using ideas of Terng and Thorbergsson, we extend a result of Warner and show that a compact simply connected pointwise taut

n

-dimensional manifold is homeomorphic to a compact rank one symmetric space, if the first conjugate locus of a point is of constant multiplicity. We apply this result to study compact simply connected pointwise taut manifolds in dimensions three and four.
On invariance and Ricci-flatness of Hermitian metrics on open manifolds
Authors: Koehler Bert , Kühnel Marco
Published: December 2009

We discuss a technique to construct Ricci-flat hermitian metrics on complements of (some) anticanonical divisors of almost homogeneous complex manifolds and inquire into when this metric is complete and Kähler. This construction has a strong interplay with invariance groups of the same dimension as the manifold acting with an open orbit. Lie groups of this type we call divisorial. As an application we describe compact manifolds admitting a divisorially invariant Kähler metric on an open subset. Finally, we see a connection between the reducibility of the anticanonical divisor and the non-triviality of the Kähler cone on the complement.
Cluster algebras as Hall algebras of quiver representations
Authors: Caldero Philippe , Chapoton Frédéric
Published: December 2009

Recent articles have shown the connection between representation theory of quivers and the theory of cluster algebras. In this article, we prove that some cluster algebras of type A-D-E can be recovered from the data of the corresponding quiver representation category. This also provides some explicit formulas for cluster variables.
The canonical subgroup: a "subgroup-free" approach
Authors: Goren Eyal Z. , Kassaei Payman L.
Published: December 2009

Beyond the crucial role they play in the foundations of the theory of overconvergent modular forms, canonical subgroups have found new applications to analytic continuation of overconvergent modular forms. For such applications, it is essential to understand various "numerical" aspects of the canonical subgroup, and in particular, the precise extent of its overconvergence. In this paper, we develop a theory of canonical subgroups for a general class of curves (including the unitary and quaternionic Shimura curves), using formal and rigid geometry. In our approach, we use the common geometric features of these curves rather than their (possible) specific moduli-theoretic description; it allows us to reproduce, for the classical cases, the optimal radii of definition for the canonical subgroup, usually derived by employing the theory of formal groups.
Reflections in abstract Coxeter groups
Authors: Franzsen W. N. , Howlett R. B. , Mühlherr Bernhard
Published: December 2009

Let

W

be a Coxeter group and

r\in W

a reflection. If the group of order 2 generated by

r

is the intersection of all the maximal finite subgroups of

W

that contain it, then any isomorphism from

W

to a Coxeter group

W'

must take

r

to a reflection in

W'

. The aim of this paper is to show how to determine, by inspection of the Coxeter graph, the intersection of the maximal finite subgroups containing

r

. In particular we show that the condition above is satisfied whenever

W

is infinite and irreducible, and has the property that all rank two parabolic subgroups are finite. So in this case all isomorphisms map reflections to reflections.
A weak Kellogg property for quasiminimizers
Authors: Björn Anders
Published: December 2009

The Kellogg property says that the set of irregular boundary points has capacity zero, i.e. given a bounded open set

\Omega

there is a set

E \subset \partial\Omega

with capacity zero such that for all

p

-harmonic functions

u

in

\Omega

with continuous boundary values in Sobolev sense,

u

attains its boundary values at all boundary points in

\partial\Omega \setminus E

. In this paper, we show a weak Kellogg property for quasiminimizers: a quasiminimizer with continuous boundary values in Sobolev sense takes its boundary values at quasievery boundary point. The exceptional set may however depend on the quasiminimizer. To obtain this result we use the potential theory of quasisuperminimizers and prove a weak Kellogg property for quasisuperminimizers. This is done in complete doubling metric spaces supporting a Poincaré inequality.
A pinching theorem for the first eigenvalue of the Laplacian on hypersurfaces of the Euclidean space
Authors: Colbois Bruno , Grosjean Jean-Francois
Published: December 2009

In this paper, we give pinching theorems for the first nonzero eigenvalue

λ_1(M)

of the Laplacian on the compact hypersurfaces of the Euclidean space. Indeed, we prove that if the volume of

M

is

1

then, for any

ε > 0

, there exists a constant

C_ε

depending on the dimension

n

of

M

and the

L_∞

-norm of the mean curvature

H

, so that if the

L_{2p}

-norm

\Vert H \Vert_{2p}

(

p ≥ 2

) of

H

satisfies

n\Vert H \Vert_{2p}^2 − C_ε < λ_1(M)

, then the Hausdorff-distance between

M

and a round sphere of radius

(n/λ_1(M))^{1/2}

is smaller than

ε

. Furthermore, we prove that if

C

is a small enough constant depending on

n

and the

L_∞

-norm of the second fundamental form, then the pinching condition

n\Vert H \Vert_{2p}^2 − C < λ_1(M)

implies that

M

is diffeomorphic to an

n

-dimensional sphere.
Asymptotic non-degeneracy of the solution to the Liouville–Gel’fand problem in two dimensions
Authors: Sato Tomohiko , Suzuki Takashi
Published: December 2009

In this paper we study the asymptotic non-degeneracy of the solution to the Liouville–Gel’fand problem

− Δv = λ V (x )e^v \text{ in }Ω, \quad   v = 0 \text{ on } ∂ Ω,

where

Ω ⊂ ℝ^2

is a smooth bounded domain,

V (x )

is a positive-valued

C^1(\bar Ω)

function, and

λ  > 0

is a constant.
Conjugacy in Garside groups I: cyclings, powers and rigidity
Authors: Birman Joan S. , Gebhardt Volker , González-Meneses Juan
Published: December 2009

In this paper a relation between iterated cyclings and iterated powers of elements in a Garside group is shown. This yields a characterization of elements in a Garside group having a rigid power, where ‘rigid’ means that the left normal form changes only in the obvious way under cycling and decycling. It is also shown that, given

X

in a Garside group, if some power

X^m

is conjugate to a rigid element, then

m

can be bounded above by

\Vert Δ\Vert^3

. In the particular case of braid groups

\{B_n ; n \in ℕ\}

, this implies that a pseudo-Anosov braid has a small power whose ultra summit set consists of rigid elements. This solves one of the problems in the way of a polynomial solution to the conjugacy decision problem (CDP) and the conjugacy search problem (CSP) in braid groups. In addition to proving the rigidity theorem, it will be shown how this paper fits into the authors’ program for finding a polynomial algorithm to the CDP/CSP, and what remains to be done.
Fillings, finite generation and direct limits of relatively hyperbolic groups
Authors: Groves Daniel , Manning Jason Fox
Published: December 2009

We examine the relationship between finitely and infinitely generated relatively hyperbolic groups. We observe that direct limits of relatively hyperbolic groups are in fact direct limits of finitely generated relatively hyperbolic groups. We combine this observation with known results to prove the Strong Novikov Conjecture for some exotic groups constructed by Osin.
Presentations of finite simple groups: profinite and cohomological approaches
Authors: Guralnick Robert M. , Kantor William M. , Kassabov Martin , Lubotzky Alexander
Published: December 2009

We prove the following three closely related results:
Separating quasi-convex subgroups in 7-systolic groups
Authors: Haglund Frédéric , Świątkowski Jacek
Published: December 2009

Let Γ be a group acting without inversions and simply transitively on the top-dimensional simplices of some simply-connected simplicial complex X with “simplicial negative curvature”. Then the quasi-convex subgroups of Γ are convex-cocompact. Furthermore, if the action of Γ on X satisfies some additional condition called “extra-tilability”, the quasi-convex subgroups of Γ are separable, i.e., every such subgroup is the intersection of finite index subgroups. The latter result applies to a large class of “simplicially negatively curved” groups recently constructed by Januszkiewicz and the second author.
Weak amenability of hyperbolic groups
Authors: Ozawa Narutaka
Published: December 2009

We prove that hyperbolic groups are weakly amenable. This partially extends the result of Cowling and Haagerup showing that lattices in simple Lie groups of real rank one are weakly amenable. We take a combinatorial approach in the spirit of Haagerup and prove that for the word length distance d of a hyperbolic group, the Schur multipliers associated with the kernel r d have uniformly bounded norms for 0 < r < 1. We then combine this with a Bożejko–Picardello type inequality to obtain weak amenability.
On the complexity of the quasi-isometry and virtual isomorphism problems for finitely generated groups
Authors: Thomas Simon
Published: December 2009

We study the Borel complexity of the quasi-isometry and virtual isomorphism problems for the class of finitely generated groups.
Contraction groups in complete Kac–Moody groups
Authors: Baumgartner Udo , Ramagge Jacqui , Rémy Bertrand
Published: December 2009

Let G be an abstract Kac–Moody group over a finite field and G the closure of the image of G in the automorphism group of its positive building. We show that if the Dynkin diagram associated to G is irreducible and neither of spherical nor of affine type, then the contraction groups of elements in G which are not topologically periodic are not closed. (In such groups there always exist elements that are not topologically periodic.)