bluuebunny/crossref_metadata_2025 huggingface dataset:
A Novel Technology of Hydrogen Measurement Based on Directional Solidification in Molten Aluminum Alloy
Authors: Zeng Jian Min , Wang You Bin , Cheng Hai Feng
Published: December 2011

Hydrogen is a harmful element in aluminum. How to accurately measure hydrogen content in molten aluminum alloy has been significant for improving the metallurgical qualities of aluminum products. Currently, Reduced Pressure Test (RPT) based on the famous Sievert’ law is the most commonly used method to measure the hydrogen in aluminum. However, due to the changes in solidification morphology of alloys under different solidification conditions, hydrogen will be closed more or less in the sample by the developed dendrites, which results in the dispersion of test results. According to the principle of solute redistribution, an improved reduced pressure technology under directional solidification was proposed in this paper. The solidification interface was pushed on along the single direction by controlling the temperature gradient of solid-liquid interface. Hydrogen is released in front of the solid-liquid interface through the solute redistribution. The result shows that the hydrogen content increases and the mean variance decreases with the increasing of the temperature gradients. The method was proved to be of higher accuracy.
Study on Thermal Deformation Behavior of Cu-P Weathering Steel
Authors: Zhang Xin , Xiong Yi
Published: December 2011

Using thermal simulator (Gleeble 1500D), the thermal deformation behavior of Cu-P weathering steel containing Cr, Ni, Mo under the conditions of various deformation temperatures and strain rates was studied. The true stress-true strain curves at various thermal deformation conditions were got, and the thermal deformation equation was established. Then the microstructure features of the steel under various deformation temperatures and strain rates were analyzed when the true strains were same. The results show that with the same strains and strain rates, the higher the deformation temperature, the easier the recrystallization occurs, and the greater the size of the recrystal grains. And with the same strains and deformation temperatures, the lower the strain rate, the easier the recrystallization occurs, and the greater the proportion and size of the recrystal grains. Keywords:Weathering steel, Deformation temperature, Strain rate, Thermal deformation equation, Recrystallization
Analysis on the Critical Buckling Stress in the TC4 Thin Plate Weldment
Authors: Qi Xiu Ling , Zhang Yong
Published: December 2011

There exists a large amount of longitudinal tensile stress in the weld bead of the TC4 thin plate for the uneven heating of the welding thermal resource. Owing to the equilibrium of the internal stress, longitudinal compressive stress is also large on the edge of the thin plate. When the compressive stress is larger than the critical buckling stress, the buckling distortion can take place. Therefore, the value of the critical buckling stress is important to judge the distortion. Some theoretical formula and empirical equation can not give the suitable solution to the judge of the critical value of the certain TC4 thin plate weldment because of the difficulty in the analytic solution and difference in the feature of the material and boundary condition. Finite element method was utilized to estimate the value of the buckling stress in the thin plate. Based on the solution, the adjustment of welding longitudinal compressive stress model is done. Henceforth, the critical buckling stress can be determined by the method. Keywords: critical buckling stress, TC4 thin plate, welding longitudinal residual stress
Mismatch Simulation of Motion Detection Pointing Device
Authors: Mo Bing , Zheng Qi , Chen Si Hao , Kim Su Ki
Published: December 2011

A motion detection pointing device based on CMOS image sensor is presented in this paper. Mismatch of active pixel sensor and correlated double sampling circuit is analyzed by Monte Carlo method using H-SPICE. With a 3.3V supply voltage, the maximal offset voltage caused by all mismatch is 3.6043mV, less than 8-bit least significant bit. Therefore, the motion detection pointing device system could achieve 8bit precision. The contribution of each mismatch to the total maximal offset voltage is also analyzed, comparison shows photo diode current mismatch and saturation drain current mismatch are the main causes of offset voltage. Keywords: mismatch; offset voltage; Monte Carlo method
Coupling Analysis on Hydrauic Press and Forming Moulds of the Containment of Nuclear Power Reactor
Authors: Bi Da Sen , Zhou Yao Dong , Chu Liang
Published: December 2011

Based on actual production, the each mould in the production line of containment of nuclear power reactor and the frame of THP22-4000 hydraulic press was modeled by coupling method. By using the finite element analysis simulation software ANSYS Workbench, the stiffness and strength of each coupling models were analyzed by node-coupling method. According to the results having been analyzed formerly, the distribution of stress and strain of each coupling models were studied, and the influence rules of assembly area of mould on workbench and close-height of mould on coupling stiffness were drawn, so as to guide the mold and the hydraulic structure design and optimization. Under the prerequisite of ensuring the forming precision of containment, it would be possible to configure and optimize scientifically and rationally the structure of forming molds and equipments, lower the costs of productions, and obtain higher economic benefits.
Study on Welding of TIG Tailor Welded Galvanized Sheets and Formability of Stretch Forming
Authors: Li Yun Tao , Zhang Wen Jun , Ma Xu , Liu Guang Da , Yang Li Jun
Published: December 2011

In this study TIG welding of Tailor welded Galvanized Sheets and their formability of stretch forming have been carried out. It has been found that the microstructure of weld region is ferrites and pearlites, and the microstructure of heat-affected zone (HAZ) is blocky pearlites and ferrites. Stretch tests suggested that when the weld line parallels the tensile axis, σs , σb and the σs/σb is higher than that of the weld line perpendicular to the tensile axis. When the weld line parallels the tensile axis, the elongation of the specimen and n are lower than that of the specimen with the weld line perpendicular to the tensile axis. When the weld line perpendicular to the tensile axis, the fracture surface is basically the same as that of the base metal, when the weld line parallels the tensile axis, the fracture surface is dimples and cleavages.
Agriculture Auto Workpiece Injection Mold Design Based on CAE
Authors: Zhou Jian , Li Li Jun , Yan Yong Lin , Wang Zhi Wen , Zhou Dong Cheng
Published: December 2011

For reducing the mold manufacturing time as soon as possible, CAE technology is used to build work-piece three-dimensional draw, parting surface, gating system is designed, the mold’s moving process being simulated, especially liquid flowing system is emulated. If the parameters are set reasonable, the ideal mold can be made. Keywords:Injection mold; parting surface; gating system; liquid flowing system analysis.
Effect of αk on Aluminium Trihydroxide Crystallization from Sodium Aluminate Soluntion under Ultrasound
Authors: Wu Yu Sheng , Qu Yan Ping , Zhang Lin Nan , Liu Mo
Published: December 2011

The ultrasound intensification crystallization process of aluminium trihydroxide from seeded sodium aluminate solution is investigated with various αk(the molecule ratio of Na2O/Al2O3). The experiment results indicate that ultrasound intensification can enhance precipitation ratio of seeded sodium aluminate solution, while large αkdoes not good to improvement of the precipitation under ultrasound. When αkis 1.45, 2.0 and 2.5, the precipitation ratio increase 2.5%, 2.0% and 0.9%, respectively under ultrasound intensification. The mechanism of enhancement on precipitation of alumina hydrate is acoustic cavitations that enhance or alter reactions process of aluminate ions, Al (OH)-4. The mass percentage of precipitation production grain size <45μm is increased by 4.3 % under ultrasound intensification with initial αkat 2.0, which is the biggest. Key words: ultrasound; sodium aluminate solution; precipitation; aluminium trihydroxide
Numerical Simulation of the Airliner Door under Explosion Impact Loading and Reinforcement Technique
Authors: Liu Ying , Zuo Dun Wen , Wang Yao Hua , Chen Xin Hua , He Ji Xian , Yan Hai Chun
Published: December 2011

This paper comprehensively uses a combination of methods of theoretical analysis, numerical simulation as well as the model test to do the structural analysis to some type of the passenger cabin doors, so as to set up the model for the descriptions of the part subjected to explosion impact loading; Through the tests, we gets the explosion impact loading and other important physical parameters. Aimed at the material of the door as well as the simplified models subjected to the explosion impact loading, the numerical simulation is put up by the finite element software ABAQUS. The necessity of the reinforcement is deeply analyzed as well as the difficulties during the process of the reinforcement, furthermore, the reinforcement measures are proposed to the airliner door. Keywords: Numerical simulation; Explosion impact loading; Explosion-combustion power equipments
A Study on Heat Transfer Model in Wood Particle during the Pyrolysis
Authors: Jing Liang Jing , Li Rui , Li Yu Yu
Published: December 2011

Heat transfer in wood particle controls the process of the pyrolysis. This paper makes a 2-D transient heat transfer model in cylindrical to predict the thermal behavior of wood particle in the process of fast pyrolysis. Wood anisotropy and thermophysical properties are considered in this model, as well as the influence of heat reaction on temperature distribution in wood particle. Based on the calculation of transient temperature in wood particle, and analysis of the temperature distribution during the process of wood fast pyrolysis at different time, this paper preliminarily discusses the optimization of parameters in wood particle fast pyrolysis. Keywords: pyrolysis, heat transfer, particle, wood
Effect of Annealing on Microstructure and Properties for Semi-Solid Magnesium Strips
Authors: Zhang Ying , Xu Jin Hua , Xie Shui Sheng , Geng Mao Peng , Guo Hong Min , Zhao Hai Bo
Published: December 2011

The experiment of the roll-casting for semi-solid AZ91D magnesium was carried out on the equipment made by ourselves in our laboratory. Parameters of annealing process and the effect of annealing temperature on structure and hardness of semi-solid magnesium were investigated. It was shown that annealing process can improve the structure and properties of roll-casting strips for semi-solid magnesium. In addition, it can relieve the eutectic structure segregation and make β-Mg17Al12 phase precipitate from primary α-Mg grain, which can cause dispersion strengthening process when the annealing temperature is about 420°C. With the increasing of annealing temperature, semi-solid primary α-Mg grain boundary become obscure gradually, grain growth is indistinct and β-Mg17Al12 phase is precipitated from the inner α-Mg grain. However, the aberrated eutectic α-Mg grain for non-equilibrium solidification increase continuously and separate gradually from β-Mg17Al12 phase, which makes the β-Mg17Al12 phase connect together and distribute on the α-Mg grain boundary closely approaching the equilibrium solidification structure. Hardness in eutectic structure area is higher than primary α-Mg grain. With the increasing of annealing temperature, hardness in eutectic structure area will increase and then decrease, when the temperature is over 400°C, the hardness will increase again, but hardness of primary α-Mg grain nearly unchanged. Keywords: casting-rolling; anneal; semi-solid; magnesium alloy; microstructure
Thermal Transfer Boundary Condition and Thermal Load of Piston for Torpedo Cam Engines
Authors: Xu Qin Chao , Wang Shu Zong , Lian Yong Qing
Published: December 2011

Piston of cam engines for torpedo works in terrible condition and always be caused fatigue breakdown by thermal load. In this paper, the thermal boundary condition of different piston parts are ascertained, such as the crown surface of piston and high-temp gas, the side of piston and cooling water, and the skirt of piston and cooling oil. Then the piston’s temperature field is obtained by using the finite element analysis software. This result provides the practical reference for further improving the structure and optimizing the design of the piston. Keywords: cam engine; piston; heat-transfer coefficient; temperature field.
Forces on a Circular Hole Located in Functionally Graded Material
Authors: Wang Xian Feng , Xing Feng , Hasebe Norio
Published: December 2011

The complex stress function method is used in this study to formulate the 2-dimensional problem for nonhomogeneous materials. The Young’s modulus E varies linearly with the coordinate x and the Poisson’s ratio of the material is assumed constant and. The stress components and the boundary conditions are expressed in terms of two complex stress functions in explicit forms. It is noted that the constant term in stress functions has an influence on the stress components, which is different from the homogeneous material case. Subsequently, the problem of a nonhomogeneous plane containing a circular hole subjected to a uniform internal pressure is studied.
Study on Simulation and Experiment of Drilling for Titanium Alloys
Authors: Wu Hong Bing , Jia Zhi Xin , Zhang Xue Chang , Liu Gang
Published: December 2011

To investigate the drilling process of titanium alloys, the three dimensional finite element model of two flutes twist drill was established. The drilling process of Ti6Al4V was simulated based on the presented model. In addition, the drilling experiments were carried out under the different spindle speed and feeding speed. The drilling forces of the experiment and simulation were achieved. The result of simulation agrees with the result of experiment well. It proves that the finite element model is correct. Simultaneously, the results show that more high drilling speed can improve the quality of hole in drilling process of Ti6Al4V obviously.
Microstructure and Fractrue Behaviors of Welded Joint of Particle Reinforced SiCp/ZC71 Magnesium Matrix Composites
Authors: Dong Xiao Ming , Wang Wen Yan , Xie Jing Pei , Xu Jing , Wang Ai Qin
Published: December 2011

The laser welding of particle reinforced SiCp/ZC71 magnesium matrix composite was carried out using a Nd:YAG laser welding experimental system. The mechanical properties of welded joint was studied by tensile test and the morphology of tensile fracture, microstructure as well ingredient of welded joint were observed by SEM. The results show that welding technology for composites is harsher. SiC particles distributed uniformly and the white magnesium intermetallic compound dots disappeared in the laser welded seam because the precipitation of the magnesium intermetallic compounds was prohibited owing to the rapid solidification and cooling of the laser-welded seam.. There is no evident heat affect zone in the weld seams；The mechanical properties of welded joint are worse than those of matrix metal. The weld zone is the weakest part in welded joint. The much lower tensile strength of the seam compared to the tensile strength of the ZC71/SiCp substrate attributed to the surface roughness of the seams and some solidification micron-sized pores (especially between SiC particles and magnesium alloy matrix)，The fracture morphology of welded joint indicated a brittle cleavage fracture.
LY12 Flange Squeeze Casting and the Die Design
Authors: Li Chun , Wang Jia Xuan , Miao Hua Qing , Xiong Hong Miao
Published: December 2011

In this paper, we introduce the squeeze casting process to produce flange. This article also introduces the optimized roughcast of flange, the cruces of the die design, the main structure parameters and the working traits of the die. The result shows that using squeeze casting method to produce flange not only can get the qualified part, which also greatly increase the material utilization together with enormously save processing time and processing costs at the same time.
The Effect of Hybrid Ultrasonic Pulse Current Parameters on VPTIG Arc Pressure and Weld Formation
Authors: Qi Bo Jin , Li Wei , Cong Bao Qiang , Yang Ming Xuan
Published: December 2011

Based on a novel arc welding device which can provide hybrid ultrasonic pulse current, the effect of hybrid pulsed current parameters on the arc pressure and weld formation during the aluminum alloy welding process was investigated. The experiment results show that, compared with normal VPTIG process, hybrid ultrasonic pulse VPTIG process gets greater arc pressure. Under the condition of keeping the RMS of positive current unchanged, lowering duty ratio has an evident effect on increasing arc pressure. At proper frequency range, increasing the pulse frequency and decreasing the pulse duty ratio can increase the depth and width of the weld, improve weld penetration rate correspondingly, and be beneficial to improve weld quality.
Microstructures and Mechanical Properties of TiAl-Based Alloys Prepared by High-Energy Ball Milling and Hot-Pressing Sintering
Authors: Wang Tian Guo , Qin Qun , Shi Qiu Yue , Zhang Wen Jun
Published: December 2011

TiAl-based alloy with a composition of Ti-47%Al-3%Cr (mole fraction) was prepared by high-energy ball milling and hot-pressing sintering. The relationship between microstructure and mechanical properties of Ti-47%Al-3%Cr alloy was studied by X-ray diffractometry (XRD), scanning electron microscopy (SEM) and mechanical testing. The results showed that the TiAl-based alloy with high density and uniform microstructure could be obtained by high-energy ball milling and hot-pressing sintering. The compactibility and sintering densification of the element powder could be promoted efficiently by high-energy ball milling. The main phase TiAl and few phases Ti3Al were observed in the hot pressing sintering bulk samples. In addition, the microstructure changed with ball milling times, as a result, the mechanical properties changed with the microstructure. The finer the microstructure was, the higher the strength at room temperature became. After the element powder was milled for 20 hours and hot-pressing sintered at 1300 °C for 2 hours, TiAl-based alloys were found to have good room temperature mechanical properties with the compressive strength of 2870 Mpa and the relative compressive ratio of 27.3%. Keywords: TiAl-based alloys; hot-pressing sintering; microstructure; mechanical properties
The Synthesis and Feature Rearch on the Thermosensitive Hydrogels (NIPA-co-AAm)
Authors: Zhu Xiu Fang , Yang Ming , Zhang Hong Xia , Nie Yu Jing
Published: December 2011

The polymer was prepared by the radical copolymerization. Tensile tests were conducted on a N-isopropylacrylamide (NIPA)-acrylamide (AAm) comonomer gel sensitive to variations in environmental temperature. and salinity Mechanical properties (Young’s modulus) were determined at different levels of swelling equilibrium. Shifts in the mechanical properties were observed between samples tested in the swollen and unswollen states. Additional tests were conducted to determine the effect of salinity on the LCST. Increasing the salinity from 0M to 1.0M resulted in a decrease in LCST (55centigrade to 28centigrade).It is found that adjustment of the salinity of the environment solution is an effective method of controlling the LCST of the gel. Keywords: Salinity, hydrogels, mechanical properties
Research on Preparation of Transparent Hydrophilic Antifogging Acrylate Resin
Authors: Hu Jing  , Wu Shao Long , Lou Bai Yang
Published: December 2011

Solution polymerization method was used to prepare hydrophilic antifogging acrylate resin. By means of comparison, the optimum synthesis technology conditions was obtained that ethyl acrylate was used as soft monomer , methylcrylate was used as hard monomer. The best functional monomers was acrylic acid and methyl acrylic acid. The accessory functional monoer was β-hydroxyl ethyl acrylate. Cross-linking agent methylol acrylamide belongs to self-cross-linking system. Crosslinker was N-hydroxymethyl acrylamide.The quality rate of cross-linking agent and carboxylic acid is 4 to 1 .The resin can be cured perfectly at the temperature of 100°C in 40 min. The prepared acrylate resin had excellent water-solubility and antifogging.
Effective Way to Improve the Magnetoresistance Effect in Perovskite at Room Temperature
Authors: Huang Bao Xin , Li Jian , Wang Jun Hua , Chen Ke Zheng , Liu Yi Hua , Mei Liang Mo
Published: December 2011

The magnetic and electrical properties of the La0.67Ca0.25Sr0.08MnO3/xAg composite system are systematically investigated as a function of Ag-added content. With increasing the Ag dopant amount, the magnetization decreases a little while Curie temperature (TC) is almost independent of Ag content around 312 K. The resistivity reduces rapidly with Ag addition ( x < 0.25 ) due to the decomposed metal Ag, and then it increases slightly which is probably induced by the less Ag content related to the volatilization of Ag during calcinations. At low temperature, the ρ – T curves ﬁt well by the expression of ρ =ρ0 +ρ2T2 +ρ4.5T4.5 while all data for the above TC can be ﬁtted by using the adiabatic small-polaron-hopping model ρ=ρ0T exp (E/kBT ). The enhancement of MR effect ( 41% ) at room temperature is mainly related to the coexistence of intrinsic MR properties and the spin dependent scattering of conduction electrons at the interfaces. These results indicate that combining the doping effect with the composite method is an effective selection in enhancement of MR at room temperature, which is very meaningful for the application research.
On Countable Dense and n-homogeneity
Authors: van Mill Jan
Published: December 2011

We prove that a connected, countable dense homogeneous space is n-homogeneous for every n, and strongly 2-homogeneous provided it is locally connected. We also present an example of a connected and countable dense homogeneous space which is not strongly 2-homogeneous. This answers in the negative Problem 136 ofWatson in the Open Problems in Topology Book.
A proof of the smoothing properties of the positive part of Boltzmann's kernel
Authors: Bouchut François , Desvillettes Laurent
Published: December 2011

We give two direct proofs of Sobolev estimates for the positive part of Boltzmanns kernel. The first deals with a cross section with separated variables; no derivative is needed in this case. The second is concerned with a general cross section having one derivative in the angular variable.
Unrectictifiable 1-sets have vanishing analytic capacity
Authors: David Guy
Published: December 2011

We complete the proof of a conjecture of Vitushkin that says that if

E

is a compact set in the complex plane with finite 1-dimensional Hausdorff measure, then

E

has vanishing analytic capacity (i.e., all bounded analytic functions on the complement of

E

are constant) if and only if

E

is purely unrectifiable (i.e., the intersection of

E

with any curve of finite length has zero 1-dimensional Hausdorff measure). As in a previous paper with P. Mattila, the proof relies on a rectifiability criterion using Menger curvature, and an extension of a construction of M. Christ. The main new part is a generalization of the

T(b)

-Theorem to some spaces that are not necessarily of homogeneous type.

On complète la démonstration d'une conjecture de Vitushkin si

E

est une partie compacte du plan complexe de mesure de Hausdorff unidimensionelle nulle, alors

E

est de capacité analytique nulle (toute fonction analytique bornée sur le complémantaire de

E

est consante) si et seulement si

E

est totalement non rectifiable (l'intersection de

E

avec toute courbe de longueur finie est de mesure de Hausdorff nulle). Comme dans un papier précédent avec P. Mattila, la démonstration sur un critère de rectifiabilité utilisant la courbure de Menger, et une extension d'une construction de M Christ. L'élément nouveau principal est une généralisation du théorème

T(b)

sur certains espaces qui ne sont pas nécessairement de type homogène.
Singular integral operators with non-smooth kernels on irregular domains
Authors: Duong Xuan Thinh , McIntosh Alan G.R.
Published: December 2011

Let

\chi

be a space of homogeneous type. The aims of this paper are as follows:

i) Assuming that

T

is a bounded linear operator on

L_2(\chi)

we give a sufficient condition on the kernel of

T

so that

T

is of weak type

(1,1)

, hence bounded on

L_p(\chi)

for

1 < p ≤ 2

; our condition is weaker than the usual Hörmander integral condition.

ii) Assuming that

T

is a bounded linear operator on

L_2(\Omega)

where

\Omega

is a measurable subset of

\chi

, we give a sufficient condition on the kernel of

T

so that

T

is of weak type

(1,1)

, hence bounded on

L_p(\Omega)

for

1 < p ≤2

.

iii) We establish sufficient conditions for the maximal truncated operator

T_*

, which is defined by

T_*u(x)

= sup

_{\epsilon>0} | T_\epsilon u(x) |

, to be

L_p

bounded,

1 < p < \infty

. Applications include weak

(1,1)

estimates of certain Riesz transforms and

L_p

boundedness of holomorphic functional calculi of linear elliptic operators on irregular domains.
Catching sets with quasicircles
Authors: MacManus Paul
Published: December 2011

We show how certain geometric conditions on a planar set imply that the set must lie on a quasicircle, and we give a geometric characterization of all subsets of the plane that are quasiconformally equivalent to the usual Cantor middle-third set.
$L^p$-estimates for the wave equation on the Heisenberg group
Authors: Müller Detlef , Stein Elias M.
Published: December 2011

Let

\mathcal L

denote the sub-Laplacian on the Heisenberg group

\mathbb H_m

. We prove that

e^{i\sqrt {–\mathcal L}}

/(1 – \mathcal L)^{\alpha/2}

extends to a bounded operator on

L^p (\mathbb H_m)

, for

1 ≤ p ≤ \infty

, when

\alpha > (d–1) | 1/p – 1/2|

.
Schiffer problem and isoparametric hypersurfaces
Authors: Shklover Vladimir E.
Published: December 2011

The Schiffer Problem as originally stated for Euclidean spaces (and later for some symmetric spaces) is the following: Given a bounded connected open set

\Omega

with a regular boundary and such that the complement of its closure is connected, does the existence of a solution to the Overdetermined Neumann Problem (N) imply that

\Omega

is a ball? The same question for the Overdetermined Dirichlet Problem (D). We consider the generalization of the Schiffer Problem to an arbitrary Riemannian manifold and also the possibility of replacing the condition on the domain to be a ball by more general condition; to have a homogeneous boundary (i.e., boundary, admitting a transitive group of isometries). We prove that if

\Omega

has a homogeneous boundary, then (N) and (D) always admit solutions (in fact, for infinitely many eigenvalues), but the converse statement is not always true. We show that in a number of spaces (symmetric and non-symmetric), many domains such that their boundaries are isoparametric hypersurfaces have eigenfunctions for (N) and (D) but fail the Schiffer Conjecture or even its generalization.

These ideas can be extended to other (essentially more complicated) overdetermined boundary value problems, including higher order equations and non-linear equations which, in a number of important cases, may also have solutions in domains with isoparametric (and not necessarily homogeneous) boundaries. Also, a number of initial/boundary value problems for time-dependent equations with some extra boundary conditions have solutions for domains with the above boundaries. If a time-dependent equation is non-linear and has blow-up, this blow-up occurs at the same time at all the points on the boundary.
Convexity and uniqueness in a free boundary problem arising in combustion theory
Authors: Petrosyan Arshak
Published: December 2011

We consider solutions to a free boundary problem for the heat equation describing the propagation of flames.
Parabolic equations involving 0th and 1st order terms with $L^1$ data
Authors: Goudon Thierry , Saad Mazen
Published: December 2011

This paper is devoted to general parabolic equations involving 0th and 1st order terms in linear and nonlinear expressions, while the data only belong to

L^1

. Existence and entropicuniqueness of solutions are proved.
Liouville type theorems for $\varphi$-subharmonic functions
Authors: Rigoli Marco , Setti Alberto G.
Published: December 2011

In this paper we presents some Liouville type theorems for solutions of differential inequalities involving the

\varphi

-Laplacian. Our results in particular improve and generalize known results for the Laplacian and the

p

-Laplacian and are new even in these cases. Phragmen-Lindeloff type results and a weak form of the Omori-Yau maximum principle are also discussed.
Weak slice conditions, product domains, and quasiconformal mappings
Authors: Buckley Stephen M. , Stanoyevitch Alexander
Published: December 2011

We investigate geometric conditions related to Hölder imbeddings and show among other things that the only bounded Euclidean domains of the form

U \times V

that are quasiconformally equivalent to inner uniform domains are inner uniform domains.
Quasicircles modulo bilipschitz maps
Authors: Rohde Steffen
Published: December 2011

We give an explicit construction of all quasicircles, modulo bilipschitz maps. More precisely, we construct a class

\mathcal S

of planar Jordan curves, using a process similar to the construction of the van Koch snowflake curve. These snowflake-like curves are easily seen to be quasicircles. We prove that for every quasicircle

\Gamma

there is a bilipschitz homeomorphism

f

of the plane and a snowflake-like curve

S \in \mathcal S

with

\Gamma = f(S)

. In the same fashion we obtain a construction of all bilipschitz-homogeneous Jordan curves, modulo bilipschitz map, and determine all dimension functions occuring for such curves. As a tool we construct a variant of the Konyagin–Volberg uniformly doubling measure on

\Gamma

.
Size properties of wavelet packets generated using finite filters
Authors: Nielsen Morten
Published: December 2011

We show that asymptotic estimates for the growth in

L^p(\mathbb{r})

-norm of a certain subsequence of the basic wavelet packets associated with a finite filter can be obtained in terms of the spectral radius of a subdivision operator associated with the filter. We obtain lower bounds for this growth for

p\gg 2

using finite dimensional methods. We apply the method to get estimates for the wavelet packets associated with the Daubechies, least asymmetric Daubechies, and Coiflet filters. A consequence of the estimates is that such basis wavelet packets cannot constitute a Schauder basis for

L^p(\mathbb{R})

for

p\gg 2

. Finally, we show that the same type of results are true for the associated periodic wavelet packets in

L^p[0,1)

.
Rotation invariant subspaces of Besov and Triebel-Lizorkin space: compactness of embeddings, smoothness and decay of functions
Authors: Skrzypczak Leszek
Published: December 2011

Let

H

be a closed subgroup of the group of rotation of

\mathbb{R}^n

. The subspaces of distributions of Besov-Lizorkin-Triebel type invariant with respect to natural action of

H

are investigated. We give sufficient and necessary conditions for the compactness of the Sobolev-type embeddings. It is also proved that

H

-invariance of function implies its decay properties at infinity as well as the better local smoothness. This extends the classical Strauss lemma. The main tool in our investigations is an adapted atomic decomposition.
Nevanlinna theory, fuchsian functions and brownian motion windings
Authors: Gruet Jean-Claude
Published: December 2011

Atsuji proposed some integrals along Brownian paths to study the Nevanlinna characteristic function

T(f,r)

when

f

is meromorphic in the unit disk

D

. We show that his criterion does not apply to the basic case when

f

is a modular elliptic function. The divergence of similar integrals computed along the geodesic flow is also proved.
Multipliers and weighted $\overline{\partial}$ estimates
Authors: Ortega-Cerdà Joaquim
Published: December 2011

We study estimates for the solution of the equation

\overline{\partial} u=f

in one variable. The new ingredient is the use of holomorphic functions with precise growth restrictions in the construction of explicit solutions to the equation.
Outer and inner vanishing measures and division in $H^\infty + C$
Authors: Izuchi Keiji
Published: December 2011

Measures on the unit circle are well studied from the view of Fourier analysis. In this paper, we investigate measures from the view of Poisson integrals and of divisibility of singular inner functions in

H^\infty + C

. Especially, we study singular measures which have outer and inner vanishing measures. It is given two decompositions of a singular positive measure. As applications, it is studied division theorems in

H^\infty + C

.
On independent times and positions for Brownian motions
Authors: de Meyer Bernard , Roynette Bernard , Vallois Pierre , Yor Marc
Published: December 2011

Let

(B_t ; t \ge 0)

,

\big(\text{resp. }((X_t, Y_t) ; t \ge 0)\big)

be a one (resp. two) dimensional Brownian motion started at 0. Let

T

be a stopping time such that

(B_{t \wedge T} ; t \ge 0)

\big(resp.

(X_{t \wedge T} ; t \ge 0) ; (Y_{t \wedge T} ; t \ge 0)\big)

is uniformly integrable. The main results obtained in the paper are:

We also give a number of examples of stopping times

T

, with only some exponential moments, such that

T

and

B_T

are independent, and similarly for

X_T

and

Y_T

. We also exhibit bounded non-constant stopping times

T

such that

X_T

and

Y_T

are independent and Gaussian.
$L^p$ estimates for singular integrals with kernels belonging to certain block spaces
Authors: Al-Qassem Hussain , Pan Yibiao
Published: December 2011

We establish the

L^p

boundedness of singular integrals with kernels which belong to block spaces and are supported by subvarieties.
Algebro-Geometric Solutions of the Camassa–Holm hierarchy
Authors: Gesztesy Fritz , Holden Helge
Published: December 2011

We provide a detailed treatment of the Camassa-Holm (CH) hierarchy with special emphasis on its algebro-geometric solutions. In analogy to other completely integrable hierarchies of soliton equations such as the KdV or AKNS hierarchies, the CH hierarchy is recursively constructed by means of a basic polynomial formalism invoking a spectral parameter. Moreover, we study Dubrovin-type equations for auxiliary divisors and associated trace formulas, consider the corresponding algebro-geometric initial value problem, and derive the theta function representations of algebro-geometric solutions of the CH hierarchy.
On coincidence of $p$-module of a family of curves and $p$-capacity on the Carnot group
Authors: Markina Irina
Published: December 2011

The notion of the extremal length and the module of families of curves has been studied extensively and has given rise to a lot of applications to complex analysis and the potential theory. In particular, the coincidence of the

p

-module and the

p

-capacity plays an important role. We consider this problem on the Carnot group. The Carnot group

\mathbb{G}

is a simply connected nilpotent Lie group equipped with an appropriate family of dilations. Let

\Omega

be a bounded domain on

\mathbb{G}

and

K_0

,

K_1

be disjoint non-empty compact sets in the closure of

\Omega

. We consider two quantities, associated with this geometrical structure

(K_0,K_1;\Omega)

. Let

M_p(\Gamma(K_0,K_1;\Omega))

stand for the

p

-module of a family of curves which connect

K_0

and

K_1

in

\Omega

. Denoting by

\cap_p(K_0,K_1;\Omega)

the

p

-capacity of

K_0

and

K_1

relatively to

\Omega

, we show that

M_p(\Gamma(K_0,K_1;\Omega))=\cap_p(K_0,K_1;\Omega)

.
On global solutions to a defocusing semi-linear wave equation
Authors: Gallagher Isabelle , Planchon Fabrice
Published: December 2011

We prove that the 3D cubic defocusing semi-linear wave equation is globally well-posed for data in the Sobolev space

\dot{H}^{s}

where

s>3/4

. This result was obtained in [Kenig-Ponce-Vega, 2000] following Bourgain's method ([Bourgain, 1998]). We present here a different and somewhat simpler argument, inspired by previous work on the Navier-Stokes equations ([Calderon, 1990], [Gallagher-Planchon, 2002]).
A partial regularity result for a class of Stationary Yang-Mills Fields in high dimension
Authors: Meyer Yves , Rivière Tristan
Published: December 2011

We prove, for arbitrary dimension of the base

n\ge 4

, that stationary Yang-Mills Fields satisfying some approximability property are regular apart from a closed subset of the base having zero

(n-4)

-Hausdorff measure.
Nonassociative Algebras: Some Applications
Authors: González Santos , Martínez Consuelo
Published: December 2011

Nonassociative algebras can be applied, either directly or using their particular methods, to many other branches of Mathematics and other Sciences. Here emphasis will be given to two concrete applications of nonassociative algebras. In the first one, an application to group theory in the line of the Restricted Burnside Problem will be considered. The second one opens a door to some applications of non-associative algebras to Error correcting Codes and Cryptography.
The Pressure Equation in the Fast Diffusion Range
Authors: Chasseigne Emmanuel , Vázquez Juan Luis
Published: December 2011

We consider the following degenerate parabolic equation

v_{t}=v\Delta v-\gamma|\nabla v|^{2}\quad\text{in $\mathbb{R}^{N} \times(0,\infty)$,}

whose behaviour depends strongly on the parameter

\gamma

. While the range

\gamma < 0

is well understood, qualitative and analytical novelties appear for

\gamma>0

. Thus, the standard concepts of weak or viscosity solution do not produce uniqueness. Here we show that for

\gamma>\max\{N/2,1\}

the initial value problem is well posed in a precisely defined setting: the solutions are chosen in a class

\mathcal{W}_s

of local weak solutions with constant support; initial data can be any nonnegative measurable function

v_{0}

(infinite values also accepted); uniqueness is only obtained using a special concept of initial trace, the

p

-trace with

p=-\gamma < 0

, since the standard concepts of initial trace do not produce uniqueness. Here are some additional properties: the solutions turn out to be classical for

t>0

, the support is constant in time, and not all of them can be obtained by the vanishing viscosity method. We also show that singular measures are not admissible as initial data, and study the asymptotic behaviour as

t\to \infty

.
Calderón-Zygmund theory for non-integral operators and the $H^{\infty}$ functional calculus
Authors: Blunck Sönke , Kunstmann Peer Christian
Published: December 2011

We modify Hörmander's well-known weak type (1,1) condition for integral operators (in a weakened version due to Duong and McIntosh) and present a weak type

(p,p)

condition for arbitrary operators. Given an operator

A

on

L_2

with a bounded

H^\infty

calculus, we show as an application the

L_r

-boundedness of the

H^\infty

calculus for all

r\in(p,q)

, provided the semigroup

(e^{-tA})

satisfies suitable weighted

L_p\to L_q

-norm estimates with

2\in(p,q)

. This generalizes results due to Duong, McIntosh and Robinson for the special case

(p,q)=(1,\infty)

where these weighted norm estimates are equivalent to Poisson-type heat kernel bounds for the semigroup

(e^{-tA})

. Their results fail to apply in many situations where our improvement is still applicable, e.g. if

A

is a Schrödinger operator with a singular potential, an elliptic higher order operator with bounded measurable coefficients or an elliptic second order operator with singular lower order terms.
Two–microlocal Besov spaces and wavelets
Authors: Moritoh Shinya , Yamada Tomomi
Published: December 2011

We give a characterization of the two-microlocal Besov spaces in terms of the local Besov type conditions. As an easy consequence, we obtain the inclusions between the two-microlocal Besov spaces and the local Besov spaces. These results are natural extensions of those obtained by Jaffard and Meyer, who treated the pointwise Hölder regularity in terms of two-microlocal estimates. The Daubechies wavelets play a key role throughout the paper.
Maximal and Fractional Operators in Weighted $L^{p(x)}$ Spaces
Authors: Kokilashvili Vakhtang , Samko Stefan
Published: December 2011

We study the boundedness of the maximal operator, potential type operators and operators with fixed singularity (of Hardy and Hankel type) in the spaces

L^{p(\cdot)}(\rho,\Omega)

over a bounded open set in

\mathbb{R}^n

with a power weight

\rho(x)=|x-x_0|^\gamma

,

x_0\in \overline{\Omega}

, and an exponent

p(x)

satisfying the Dini-Lipschitz condition.
Nonresonant smoothing for coupled wave + transport equations and the Vlasov-Maxwell system
Authors: Bouchut François , Golse François , Pallard Christophe
Published: December 2011

Consider a system consisting of a linear wave equation coupled to a transport equation:

\begin{align*}
\Box_{t,x}u &=f ,\\
(\partial_t + v(\xi) \cdot \nabla_x)f &=P(t,x,\xi, D_\xi)g ,
\end{align*}

Such a system is called
nonresonant
when the maximum speed for particles governed by the transport equation is less than the propagation speed in the wave equation. Velocity averages of solutions to such nonresonant coupled systems are shown to be more regular than those of either the wave or the transport equation alone. This smoothing mechanism is reminiscent of the proof of existence and uniqueness of

C^1

solutions of the Vlasov–Maxwell system by R. Glassey and W. Strauss for time intervals on which particle momenta remain uniformly bounded, see “Singularity formation in a collisionless plasma could occur only at high velocities”,
Arch. Rational Mech. Anal.
92
(1986), no. 1, 59–90. Applications of our smoothing results to solutions of the Vlasov-Maxwell system are discussed.
A multiple set version of the $3k-3$ Theorem
Authors: Hamidoune Yahya ould , Plagne Alain
Published: December 2011

In 1959, Freiman demonstrated his famous

3k-4

Theorem which was to be a cornerstone in inverse additive number theory. This result was soon followed by a

3k-3

Theorem, proved again by Freiman. This result describes the sets of integers

\mathcal{A}

such that

| \mathcal{A}+\mathcal{A} | \leq 3 | \mathcal{A} | -3

. In the present paper, we prove a

3k-3

-like Theorem in the context of multiple set addition and describe, for any positive integer

j

, the sets of integers

\mathcal{A}

such that the inequality

|j \mathcal{A} | \leq j(j+1)(| \mathcal{A} | -1)/2

holds. Freiman's

3k-3

Theorem is the special case

j=2

of our result. This result implies, for example, the best known results on a function related to the Diophantine Frobenius number. Actually, our main theorem follows from a more general result on the border of

j\mathcal{A}

.
Quasiconformal groups of compact type
Authors: Bonfert-Taylor Petra , Martin Gaven J.
Published: December 2011

We establish that a quasiconformal group is of compact type if and only if its limits set is purely conical and find that the limit set of a quasiconformal group of compact type is uniformly perfect. A key tool is the result of Bowditch-Tukia on compact-type convergence groups. These results provide crucial tools for studying the deformations of quasiconformal groups and in establishing isomorphisms between such groups and conformal groups.
A note on lifting of Carnot groups
Authors: Bonfiglioli Andrea , Uguzzoni Francesco
Published: December 2011

We prove that every homogeneous Carnot group can be lifted to a free homogeneous Carnot group. Though following the ideas of Rothschild and Stein, we give simple and self-contained arguments, providing a constructive proof, as shown in the examples.
Random walks on graphs with volume and time doubling
Authors: Telcs András
Published: December 2011

This paper studies the on- and off-diagonal upper estimate and the two-sided transition probability estimate of random walks on weighted graphs.
Wavelets on Fractals
Authors: Dutkay Dorin E. , Jorgensen Palle E.T.
Published: December 2011

We show that there are Hilbert spaces constructed from the Hausdorff measures

\mathcal{H}^{s}

on the real line

\mathbb{R}

with

0 < s < 1

which admit multiresolution wavelets. For the case of the middle-third Cantor set

\mathbf{C}\subset \lbrack 0,1]

, the Hilbert space is a separable subspace of

L^{2}(\mathbb{R},(dx)^{s})

where

s=\log _{3}(2)

. While we develop the general theory of multi-resolutions in fractal Hilbert spaces, the emphasis is on the case of scale

3

which covers the traditional Cantor set

\mathbf{C}

. Introducing

\psi_{1}(x)=\sqrt{2}\chi _{\mathbf{C}}(3x-1) \qquad\text{and}\qquad \psi _{2}(x)=\chi _{\mathbf{C}}(3x)- \chi_{\mathbf{C}}(3x-2)

we first describe the subspace in

L^{2}(\mathbb{R},(dx)^{s})

which has the following family as an orthonormal basis (ONB):

\psi_{i,j,k}(x)=2^{j/2}\psi_{i}(3^{j}x-k)\text{,}

where

i=1,2,j

,

k\in \mathbb{Z}

. Since the affine iteration systems of Cantor type arise from a certain algorithm in

\mathbb{R}^d

which leaves gaps at each step, our wavelet bases are in a sense gap-filling constructions.
SAK Principle for a class of Grushin-type operators
Authors: Maniccia Lidia , Mughetti Marco
Published: December 2011

We prove Fefferman's SAK Principle for a class of hypoelliptic operators on

\mathbb R^2

whose nonnegative symbol vanishes anisotropically on the characteristic manifold.
Riesz transforms for symmetric diffusion operators on complete Riemannian manifolds
Authors: Li Xiang-Dong
Published: December 2011

Let

(M, g)

be a complete Riemannian manifold,

L=\Delta -\nabla \phi \cdot \nabla

be a Markovian symmetric diffusion operator with an invariant measure

d\mu(x)=e^{-\phi(x)}d\nu(x)

, where

\phi\in C^2(M)

,

\nu

is the Riemannian volume measure on

(M, g)

. A fundamental question in harmonic analysis and potential theory asks whether or not the Riesz transform

R_a(L)=\nabla(a-L)^{-1/2}

is bounded in

L^p(\mu)

for all

1
0

and

p\geq 2

provided that

L

generates a ultracontractive Markovian semigroup

P_t=e^{tL}

in the sense that

P_t 1=1

for all

t\geq 0

,

\|P_t\|_{1, \infty} < Ct^{-n/2}

for all

t\in (0, 1]

for some constants

C>0

and

n > 1

, and satisfies

(K+c)^{-}\in L^{{n\over 2}+\epsilon}(M, \mu)

for some constants

c\geq 0

and

\epsilon>0

, where

K(x)

denotes the lowest eigenvalue of the Bakry-Emery Ricci curvature

Ric(L)=Ric+\nabla^2\phi

on

T_x M

, i.e.,

K(x)=\inf\limits\{Ric(L)(v, v): v\in T_x M, \|v\|=1\}, \quad\forall\ x\in M.

Examples of diffusion operators on complete non-compact Riemannian manifolds with unbounded negative Ricci curvature or Bakry-Emery Ricci curvature are given for which the Riesz transform

R_a(L)

is bounded in

L^p(\mu)

for all

p\geq 2

and for all

a>0

(or even for all

a\geq 0

).
Time-Frequency Analysis of Sjöstrand’s Class
Authors: Gröchenig Karlheinz
Published: December 2011

We investigate the properties an exotic symbol class of pseudodifferential operators, Sjöstrand's class, with methods of time-frequency analysis (phase space analysis). Compared to the classical treatment, the time-frequency approach leads to striklingly simple proofs of Sjöstrand's fundamental results and to far-reaching generalizations.