bluuebunny/crossref_metadata_2025 huggingface dataset:
Calculation of the total rate coefficients for non-equilibrium nitrogen thermal plasmas at atmospheric pressure
Authors: J Bacri  , A M Gomes
Published: July 2002

The total rate coefficients used in a simplified collisional radiative (SCR) model are calculated for thermal nitrogen plasmas at atmospheric pressure. Most of them cannot be considered as physical quantities depending on only a few parameters such as the electron temperature but are functions of the actual state of the plasma. The variations of these coefficients under the influence of radiative losses, the departure between electron and heavy-particle temperatures and the diffusion processes are studied. The use of these coefficients in a SCR model is discussed.
Electrode temperatures of carbon and graphite arcs
Authors: K R Hearne  , S A Nixon
Published: July 2002

Measurements of the electrode temperatures for arcs operating in room air over a current range of 5-30 A are given. A distinct difference in the peak temperatures of the radial distributions for graphite and carbon cathodes has been observed, the values being 4150 and 3500°K respectively. Using the Richardson-Dushman equation approximate values of the corresponding peak cathode electron current densities have been calculated and these are given as 4000 and 700 A cm−2. Radial temperature profiles for the graphite anode are also given for the same current range.
Yield of adhesive joints
Authors: B W Cherry  , C M Holmes
Published: July 2002

The yield strengths of polyethylene-stainless-steel lap joints and of polyethylene samples having the same thermal history have been measured over a range of strain rates at temperatures between 245 and 323°K. A yield mechanism based on the motion of dislocation loops through crystalline regions of the polymer is preferred to one based on the jumping of polymer segments into adjacent free volume in an amorphous region. The size of the dislocation loops may be derived from the time dependence of yield strength, and it is found that the ratio of these sizes for the polymer when in the joint and when free is constant under all conditions examined.
A theoretical and experimental analysis of high-strain-rate tensile tests using Malvern's theory
Authors: R Botte  , D Rousseau  , P Gobin
Published: July 2002

The theoretical behaviour of a cylindrical specimen of finite length during a high-strain-rate tensile test has been studied with the help of a strain-rate dependent theory. The behaviour is compared with experimental observations of tests on a specimen partially fixed at one extremity and submitted to a constant velocity impact at the other end. The chosen plasticity function is that introduced by Malvern which predicts a linear relationship between the stress and plastic strain rate. The calculations and experiments have been done in two cases: (i) ideal elastic-plastic material and (ii) highly work-hardened material.

The main results are as follows: two stages can be distinguished, a `transient' state at the beginning of the test, where the values of state variables are heterogeneous, and a `steady' state where stress and strain rate are uniform in the whole specimen. The strain distribution in the steady state depends markedly upon the `quasi-static' stress-strain relation σ=h(ϵ) and the parameter of the plasticity function. Malvern's theory is a good approximation of the experimental results in the `steady' state, but it cannot predict those of the `transient' state; in particular the theory gives too low values of the peak stress at the extremity of the specimen opposite to the impact section. The use of a more complex plasticity function is briefly investigated.
The steady-state equation for Brownian diffusion in the presence of particle coagulation
Authors: S Simons
Published: July 2002

A calculation is given of the spatial variation of phi , the volume fraction of particulate material, during one-dimensional steady-state diffusivity transport in an aerosol, taking coagulation of the particles into account. The effect of the latter is to modify the linear variation in phi which would otherwise exist, and detailed analytic results are obtained in the regimes Kn<<1 and Kn>>1. It is shown that if coagulation effects are sufficiently strong the spatial variation of phi can exhibit a maximum, while if they exceed a certain value in the Kn>>1 regime no steady state can be set up. Calculation of numerical values suggests that measurements of phi could provide useful experimental data on coagulation effects.
A calculation of the effect of a coaxial superconducting shield on the magnetic field distribution of an enclosed coaxial solenoid
Authors: TJ Sumner
Published: July 2002

An exact solution is obtained for the magnetic field distribution generated by a coaxial solenoid that is enclosed within a closed coaxial superconducting shield. The solution is compared with that obtained when using conventional high-permeability magnetic shielding and the consequences for field strength and homogeneity are discussed.
A critical evaluation of the data concerning thermal anomalies in the activation energy of the viscous flow of water
Authors: Z A Khan  , M A Chaudri
Published: July 2002

Thermal anomalies in the activation energy of the viscous flow for some liquids and solutions have been reported in the literature. Qurashi and Ahsanullah (1961) have claimed that the activation energy of the viscous flow versus temperature curve for water has periodic discontinuities. Their claim is based on the assumed accuracy of their measurements. A critical examination of their data shows that the extrapolation of their differential Beckman thermometer readings from one region of temperature to the other is untenable and therefore the conclusions of Qurashi and Ahsanullah are based on erroneous experimental results.
Electrons and holes in the solid electrolyte Ag2HgI4
Authors: T K Paul  , S Eswara Rao  , R C Bhuniya
Published: July 2002

The generation of electrons and holes in the polycrystalline super-ionic conductor Ag2HgI4has been demonstrated through the measurement of electrical conductivity with an ion-blocking electrode, magnetic susceptibility and thermoelectric power. The contribution of the electrons and holes to the electrical conductivity is very small compared to the ionic contribution. While the electrons take part in the transport phenomena at all temperatures, the holes do so only at elevated temperatures. Although the compound changes phase at 50 degrees C, the electrical conductivity does not show a sharp change at this temperature. The similar mechanism of conduction in both the phases is due to the same number of tetrahedral sites available to the cations in the two phases.
Modelling the propagation and scattering of elastic waves in inhomogeneous anisotropic media
Authors: J A G Temple
Published: July 2002

A finite-difference numerical model for studying the propagation and scattering of elastic waves in three-dimensional inhomogeneous and anisotropic media of arbitrary symmetry is presented. The model takes account of short pulses and finite-width beams and incorporates mode conversion at boundaries. The model, called SWAM3D (scattering of elastic waves in inhomogeneous anisotropic media in 3D), can handle a region of size equivalent to 250*250*250 nodes, that is a cube of side 25 shear wavelengths. It runs on a CRAY-2 supercomputer and represents a significant advance in the numerical treatment of wave propagation and scattering in inhomogeneous and anisotropic materials. As an indication of the power of the model, it is applied to the scattering of elastic waves of different polarisations from a cylindrical hole in a homogeneous transversely isotropic material. The propagation and scattering of elastic wave in inhomogeneous materials is an important problem in ultrasonic inspection of welds in liquid-metal-cooled fast reactors. A-scans and differential scattering cross sections are presented. They are used to explain some experimental results in the ultrasonic inspection of austenitic welds. The present results confirm the validity and applicability of the model.
Microporous materials with negative Poisson's ratios. II. Mechanisms and interpretation
Authors: K E Evans  , B D Caddock
Published: July 2002

For pt.I see ibid., vol.22, p.1877-82 (1989). In a previous paper the morphology of a microporous material made from expanded poly(tetrafluoroethylene) was described and results presented for its mechanical behaviour. The material was shown to be highly anisotropic and exhibited a large negative Poisson's ratio. In this paper a simple model for the microstructure is described to account for this effect. The model is based on an interconnected array of anisotropic particles that deforms so as to produce a large transverse displacement under longitudinal tensile loading. Very good agreement is found between the model and experimental results, providing an explanation for the variation of Poisson's ratio with tensile strain, in terms of changes in material morphology.
Simulation of gas-contact cooling for VUV laser oscillation in recombining plasmas
Authors: U Furukane  , K Sato  , T Oda
Published: July 2002

Possible rapid cooling of a higher temperature plasma is investigated in a gas-contact cooling method in which the effect of finite time for mixing the plasma and the contact gas is considered. The calculation has shown that cooling under these conditions is much more rapid than that achieved by radiative loss cooling and that the gain per unit length of the He II 164 nm line is approximately 2 cm-1for the laser oscillation under optimum conditions. The possibility of realising a laser at a shorter wavelength in a plasma with higher charge number Z is also discussed.
A collisional-radiative model applicable to argon discharges over a wide range of conditions. II. Application to low-pressure, hollow-cathode arc and low-pressure glow discharges
Authors: J Vlcek  , V Pelikan
Published: July 2002

For pt.I see ibid., vol.22, p.623 (1989). The extensive collisional-radiative model for an argon atom plasma is applied to a low-pressure, hollow-cathode arc discharge and to the positive column of a low-pressure glow discharge in order to clarify the mechanisms by which the excited levels in these discharges are populated, the results being compared with experimental investigations in the literature. Computations are carried out for various sets of input parameters, such as the electron kinetic temperature Te, the atom temperature Ta, the ion temperature Ti, the electron number density ne, the ground state atom population n1, the plasma column radius R and the escape factors lambdamnand lambdam, characterising the non-equilibrium plasmas under consideration. The predictions of the authors' model. i.e the populations in the excited levels as a function of the electron number density, the effective principal quantum number and the discharge current, are compared with the experimental results and in two cases also with the theoretical results of other authors. It is shown that all calculated dependences are fairly close to the corresponding experimental curves referring to both discharges. The results presented confirm the applicability of the so-called 'analytical top model' of van der Mullen et al. (1978, 1980) and Walsh's formula for Lambda1ninterpreted according to Mills and Hieftje (1984).
A fundamental plasma based model for energy transfer in laser material processing
Authors: B R Finke  , P D Kapadia  , J M Dowden
Published: July 2002

In most applications of lasers for material processing a plasma is detected above the hot surface of the workpiece. Since in certain ranges of temperature and density plasmas are able to absorb a significant part of the incident laser power, the physical processes which supply this energy into the workpiece are of special interest. In this paper the energy supply of a collisional plasma with a low degree of ionisation is considered in the steady state in a one-dimensional geometry. The dominant energy transport process is found to be the release of kinetic and ionisation energy of charged particles being absorbed and then recombining at the wall. Finally, a numerical example is given for the case of laser welding involving the presence of a plasma whose electron temperature and density are predicted.
Initial hydration steps in lipase studied by means of water sorption isotherms, FTIR spectroscopy and thermally stimulated depolarization currents
Authors: M G Bridelli  , R Capelletti  , F Maraia  , C Mora  , L Pirola
Published: July 2002

The role of water in lipases, a class of proteins endowed with a large external hydrophobic surface, is not yet fully understood. To analyse the water-related structural properties and the possible implications for the protein functionality, three experimental techniques such as water sorption isotherms, thermally stimulated depolarization currents (TSDCs), and Fourier transform infrared spectroscopy were applied to pellets and/or films of lipase fromCandida lipolytica, prepared at very low hydration degreesh, ranging between 0.003 and 0.457 gwater/gprotein. Two main broad TSDC bands (a weak one peaking atT≅160 K and a strong one atT≅260 K) were detected. The peak amplitudes and positions critically depend not only on the water content, but also on the previous hydration history of the sample. FTIR spectra monitored: (1) the amplitude and position changes of the characteristic optical absorption bands (amide A, B, I, and II) as a function of the humidity level, (2) the presence of a considerable amount of β-sheet structure at high hydration degrees, and (3) a conformational transition induced by drastic dehydration treatments. Complementary sorption isotherms, performed by means of a gravimetric method, showed a marked hysteresis in the lipase-aqueous solvent interaction. The whole set of results provides a model for the initial steps of the lipase hydration kinetics. Ath= 0.009, 13 water molecules are buried in the macromolecule, probably bound to the peptidic backbone. Ath= 0.037 all polar and charged free groups are hydrated. At higherha solution phase begins, and ath= 0.457 about 660 water molecules are accommodated around the protein, giving rise to three to four complete layer coverages.
Arc cathode current density measurements
Authors: C C lsanger  , P E Secker
Published: July 2002

Detailed examination of the cathode arc tracks left by a discharge driven magnetically at high speed over prepared metal surfaces has yielded cathode root current density values of about 2 × 107A cm−2on copper and about 5 × 106A cm−2on brass. Individual electron emission sites on the cathode appear to have a lifespan not exceeding 10−7s, thereby accounting for the good correlation between current density values obtained for continuously burning arcs and those operating in multi-microsecond pulse modes.
Growth of ionization currents in dry air at high values of E/N
Authors: C Raja Rao  , G R Govinda Raju
Published: July 2002

Uniform field steady-state ionization currents were measured in dry air as a function ofNat constantE/N(Eis the electric field strength andNthe gas number density) and constant electrode separationdfor 14·13 × 10−16less-than-or-eq, slantE/Nless-than-or-eq, slant 282·5 × 10−16V cm2. Uniform field sparking potentials were also measured forNdrange 1·24 × 1016less-than-or-eq, slantNdless-than-or-eq, slant 245 × 1016cm−2. The ratio of the Townsend primary ionization coefficient α toN, α/N, was found to depend onE/Nonly. The secondary coefficients were also evaluated for aluminium and gold-plated electrodes for the above range ofE/N. Measurements of the sparking potentials showed that Paschen's law is not obeyed in air at values ofNdnear and below the Paschen minimum.
Nitrogen discharges of large cross section at high overvoltage in a homogeneous field
Authors: J Koppitz
Published: July 2002

Experiments on pulsed N2discharges at high overvoltage in a homogeneous field are described. Former investigations by different authors revealed that at high overvoltage a filamentary discharge develops according to the streamer mechanism. The number of primary electrons released at the cathode was low in these experiments. The discharges described here are initiated by a very high number (approximate 108) of primary electrons distributed uniformly over the cathode surface. Optical investigations with streak camera and image intensifier resolving the development in space and time show that the primary avalanches transform to a bright luminous layer which develops toward the anode first slowly (ν approximate 1·5 ν−, where ν− is the drift velocity of electrons), then very fast (ν>10ν−). Later a second luminous layer arises nearer to the cathode, spreading in both directions. The layers are homogeneous over a large area. In contrast to the single-streamer development the field distortions by space charge can be calculated easily using a one-dimensional approximation. Preliminary calculations show that the cathode-directed development is mostly due to secondary electrons from the cathode, while the fast development toward the anode is caused by a far-reaching process, probably gas-ionizing radiation, generating new electrons in the neutral gas.
An empirical treatment of energy dissipation of fast electrons at normal incidence in semi-infinite targets
Authors: Vilho Lantto
Published: July 2002

In an investigation of the penetration of a beam of fast electrons in a solid, a simple empirical method has been used for calculating the distribution of the energy dissipation by electrons in a semi-infinite target. The calculations are based on the values of the distribution function tabulated by Spencer for an infinite target. The method has been applied to obtain the distribution for 25, 50 and 100 keV electrons at normal incidence in aluminium, copper, tin and lead. The calculated differences in the dissipation distribution between the infinite and the semi-infinite cases agree fairly well with the results of the Monte Carlo calculations by Bishop. A comparison with the experimental distribution measured in a metal-oxide-semiconductor system is also presented.
A repetitively pulsed, Q-switched, inorganic liquid laser
Authors: H Brinkschulte  , J Perchermeier  , E Schimitschek
Published: July 2002

A circulating, inorganic liquid laser (Nd3+: POCl3/ZrCl4) delivering giant pulses in the 100 MW range was built. Repetition rates up to 10 pulses per second were achieved with very stable output properties after a warm-up time of a few minutes. The construction of the system and its performance are described in detail.
A theoretical model of the mercury and copper vapour arcs
Authors: A J T Holmes
Published: July 2002

A model of the vapour arc is proposed which reconciles the characteristics of very high current density and low voltage drop. Two methods of electron emission are suggested to account for the exceptional current density: emission by excited atom bombardment, and thermionic field emission. The relative importance of these two processes is examined. In addition, account is taken of the effects of the transfer of ion momentum to the gas in the arc spot and the overall energy balance. The relationships derived from these mechanisms enable a quantitative description of the parameters of the arc spot to be made which only depends on the basic constants of the cathode material. Values of the arc parameters calculated for the mercury and copper arcs agree well with experimental measurements.
The identification of species evolved in the evaporation of III-V compounds
Authors: C T Foxon  , B A Joyce  , R F C Farrow  , R M Griffiths
Published: July 2002

Methods are discussed for distinguishing between volatile species in a direct evaporation flux from those produced by various background interactions, using mass-spectrometric techniques. It is shown that while flux modulation methods are essential, phase-sensitive detection at a single frequency is inadequate, and that measurements must be made over a wide frequency range. The improvement over frequency domain methods which can be achieved using time representation of the pulsed signal with signal-averaging and fast Fourier transforms is illustrated. In addition, a means of minimizing mass discrimination effects in the mass spectrometer is described.

Results obtained by the application of various forms of data acquisition and signal processing to the Knudsen and Langmuir evaporation of InP, GaP and GaAs are presented, and some thermodynamic implications of the new vapour pressure values examined.
Stress and displacements in lamellar composites. I
Authors: R G C Arridge
Published: July 2002

A lamellar composite is approximated by a stack of very long longitudinal strips, of rectangular cross section, of elastic material bonded to rigid strips on their upper and lower faces and extended in a direction perpendicular to these faces. The lateral faces of the strips are assumed stress-free. The stresses and displacements in the cross section are calculated using two-dimensional stress analysis giving solutions in Fourier series. The effective modulus of the material is calculated for a range of thickness/width ratios and compared wth literature values. The analysis has relevance for the deformation of lamellar composites in polymeric and other materials.
Phase determination from a focal series and the corresponding diffraction pattern in electron microscopy for strongly scattering objects
Authors: P Schiske
Published: July 2002

The determination of the image forming wavefunction is considered for normal operation of the conventional transmission electron microscope. No assumption is made about the relative strengths of unscattered and scattered radiation. Spatial coherence and monochromaticity are assumed. For objects which are represented by a finite number of Fourier components, an algorithm for phase determination is given. Only the locations and not the intensities of the reflections in the diffraction pattern are needed. The main information used is contained in two or three images with different defocus. Combinations of defocus values which should be avoided since they yield insufficient information, can be determined beforehand from the diffraction pattern.
On Timoshenko's correction for shear in vibrating beams
Authors: T Kaneko
Published: July 2002

The note is a review of studies of the shear coefficient K occurring in Timoshenko's differential equation for flexural vibrations of beams. Expressions of K hitherto proposed for circular and rectangular cross sections are tabulated, together with new expressions hitherto overlooked and unknown, and compared with one another. It is pointed out that the expressions of K=(6+12 sigma +6 sigma2)/(7+12 sigma +4 sigma2) for the circle and K=(5+5 sigma )/(6+5 sigma ) for the rectangle, where sigma is Poisson's ratio, which have been found in Timoshenko's (1922) paper, will be the most probable ones at the present stage of theories and experiments.
Analysis of flashes accompanying discharges in air at dielectric surfaces
Authors: J S Brzosko  , A Konarzewski  , A Wojewodzka  , E Zukowski  , J Grudzinski
Published: July 2002

A new method of measuring discharges at the surface of a dielectric is presented. It is based on observations of the flash accompanying the discharges with a linear photomultiplier. The measurements were made for C4H4O6KNa.4H2O, KH2PO4, NH4H2PO4, glass (G) and organic glass (PG). The measured flash-energy spectra reveal two parts which vary strongly with the dielectric used, the applied electric field and the time. The flash energies, geometrical picture and flash-energy spectra are discussed.
Axial velocity variations in high-current free-burning arcs
Authors: D C Strachan  , M R Barrault
Published: July 2002

A simple method for estimating mean arc velocities in high-current free-burning arcs is presented. Typical results are presented for arcs burning to copper, graphite and steel cathodes employing experimental values of arc current, electric field, radius and radiation loss. These results are compared with laser-Doppler velocity measurements for the case of copper. The method has also been applied to the studies of Bowman (1972) where a direct comparison with measured velocities has also proved possible and successful. The velocity estimates reveal a number of interesting experimental phenomena. Of particular interest is the implied presence of large velocity gradients in both space and time. The spatial gradients indicate that great care will be necessary in plasma velocimetry techniques based on particle tracking.
The surface layer effect in TS, KDP and Rochelle salt
Authors: A Mansingh  , E Prasad
Published: July 2002

The surface layer effect in triglycine sulphate (TGS), potassium dihydrogen phosphate (KDP) and Rochelle salt (RS) has been investigated by measuring the thickness dependence of the dielectric constant. Measurements at and near the transition temperatures have been made at a frequency of 1 kHz. The sample thickness has been varied between about 3 and 0.2 mm. The measured dielectric constant is found to decrease with the sample thickness for all the three materials and the effect is more pronounced for the smaller thicknesses (less than 1 mm). The results can be explained by considering a single homogeneous surface layer of low dielectric constant and the thickness and dielectric constant of the surface layer are independent of temperature. The surface layer thickness is found to be of the order of 10-4cm for Rochelle salt and 10-5cm for KDP and TGS.
Miniature five-hole pressure probe for measurement of three mean velocity components in low-speed flows
Authors: P M Ligrani  , B A Singer  , L R Baun
Published: July 2002

A miniature five-hole pressure probe is described which has a probe tip diameter of 1.22 mm. The probe was developed to measure three mean velocity components using a non-nulling procedure at individual locations in a curved channel where differential pressures are low, flow is three-dimensional and laminar, and spatial resolution and flow blockage effects are important considerations. Calibration coefficients are presented for Reynolds numbers based on probe tip diameter ranging from 80 to 400. Coefficients for yaw angle, pitch angle, total pressure and total minus static pressure are independent of Reynolds number within experimental uncertainties. Experimental details unique to the use of the miniature probe are also given along with distributions of mean velocity and mean vorticity over a portion of the 12.7 mm*508.0 mm cross section of a curved channel. At a Dean number of 119 (mean streamwise velocity approximately 1.2 m s-1), structural characteristics of Dean vortices are evident from contours of the streamwise velocity, the total pressure and the streamwise component of mean vorticity determined from secondary flow vectors.
Simple method to obtain polar information with a normal microwave interferometer
Authors: C A J Hugenholtz
Published: July 2002

A simple method to obtain polar information from a microwave interferometer is described. The two paths in the microwave interferometer are made unequal in length so that the output is frequency dependent. Square-wave modulation of the repeller voltage of the klystron is used to obtain two signals with slightly different frequencies. An appropriate choice of the frequency difference can yield a ½π phase difference, so that a polar interferometer results.
A collisionless ion beam plasma
Authors: I L Freeston  , G W Gardiner  , A M Zavody
Published: July 2002

A laboratory plasma of density of the order of 3*1012 electrons/m3, electron temperature 0.15 eV mean free paths greater than 1 m, and which was designed to simulate the ionospheric plasma, is described. The plasma is formed by neutralizing an ion beam with electrons, the ions and electrons being produced from separate thermionic sources. Typical results obtained with a single electrode probe are interpreted by the standard Langmuir procedure, and show that the measured density agrees with the measured plasma frequency from measurements of the admittance of a parallel grid capacitor. The plasma is undisturbed by the application of a magnetic field, and is compared with the ionospheric plasma.
ECRF experiments for local heating and current drive by fundamental O-mode launch from the low-field side on JT-60U
Authors: Y. Ikeda  , S. Ide  , T. Suzuki  , A. Kasugai  , K. Takahashi  , K. Kajiwara  , A. Isayama  , T. Oikawa  , K. Hamamatsu  , Y. Kamada  , T. Fujita  , K. Sakamoto  , S. Moriyama  , M. Seki  , R. Yoshino  , T. Imai  , K. Ushigusa  , T. Fujii  , JT-60 Team
Published: July 2002

An electron cyclotron range of frequency (ECRF) program has been initiated to study the local heating and current drive in JT-60U. A frequency of 110 GHz was adopted to couple the fundamental O-mode from the low-field side with an oblique toroidal injection angle for the current drive. Experiments were performed at an injection power of ~1.5 MW by using three gyrotrons, each of which has generated the output power up to ~0.8 MW for 3 seconds. A strongly peakedTeprofile was observed and the central electron temperature increased up to ~15 keV when the O-mode was absorbed on the axis. The local electron heating clarified the significant difference in the heat pulse propagation between in the plasmas with internal transport barrier (ITB) and without. The driven current estimated by the Motional Stark Effect (MSE) diagnostic showed that the electron cyclotron (EC) waves drove the plasma current up to ~0.2 MA for an injected power of ~1.3 MW at the local electron temperature and density ofTe~6 keV,ne~0.7×1019 m-3. The measured driven current near the axis was consistent with the theoretical prediction using a Fokker-Planck code. In the case of co-electron cyclotron current drive (ECCD), the sawtooth activity in neutral beam (NB) heated plasma was completely suppressed for 1.5 s with the deposition at the inversion radius, while the sawtooth was enhanced for counter-ECCD at the same deposition condition.
On roughly transitive amenable graphs and harmonic Dirichlet functions
Authors: Elek Gábor , Tardos Gábor
Published: July 2002

We introduce the notion of rough transitivity and prove that there exist no non-constant harmonic Dirichlet functions on amenable roughly transitive graphs.
On the symmetry of the Goldie and CS conditions for prime rings
Authors: Huynh Dinh , Jain S. , López-Permouth S.
Published: July 2002

It is shown that: (a) If

R
R

is a prime right Goldie right CS ring with right uniform dimension at least 2, then

R
R

is left Goldie, left CS; (b) A semiprime ring

R
R

is right Goldie left CS iff

R
R

is left Goldie, right CS.
Superposition operator in Sobolev spaces on domains
Authors: Labutin Denis
Published: July 2002

For an arbitrary open set

Ω
⊂

R

n

\Omega \subset \mathbb {R}^n

we characterize all functions

G
G

on the real line such that

G
∘
u
∈

W

1
,
p

(
Ω
)

G\circ u\in W^{1,p}(\Omega )

for all

u
∈

W

1
,
p

(
Ω
)

u\in W^{1,p}(\Omega )

. New element in the proof is based on Maz’ya’s capacitary criterion for the imbedding

W

1
,
p

(
Ω
)
↪

L
∞

(
Ω
)

{W^{1,p}(\Omega )\hookrightarrow L^\infty (\Omega )}

.
Elementary proof of Brauer’s and Nesbitt’s theorem on zeros of characters of finite groups
Authors: Leitz Manfred
Published: July 2002

The following has been proven by Brauer and Nesbitt. Let

G
G

be a finite group, and let

p
p

be a prime. Assume

χ
\chi

is an irreducible complex character of

G
G

such that the order of a

p
p

-Sylow subgroup of

G
G

divides the degree of

χ
\chi

. Then

χ
\chi

vanishes on all those elements of

G
G

whose order is divisible by

p
p

. The two only known proofs of this theorem use profound methods of representation theory, namely the theory of modular representations or Brauer’s characterization of generalized characters. The purpose of this paper is to present a more elementary proof.
On the weak limit of mappings with finite distortion
Authors: Yan Baisheng
Published: July 2002

We give a new proof that the limit of a weakly convergent sequence of mappings with finite distortion also has finite distortion. The result has been recently proved by Gehring and Iwaniec using the biting convergence of Jacobians. We present a different proof using simply the lower semi-continuity of quasiconvex functionals.
The Lindelöf property and fragmentability
Authors: Cascales B. , Namioka I. , Vera G.
Published: July 2002

Let

K
K

be a compact Hausdorff space and

C
(
K
)

C(K)

the space of continuous real functions on

K
K

. In this paper we prove that any

t

p

(
K
)

t_{p}(K)

-Lindelöf subset of

C
(
K
)

C(K)

which is compact for the topology

t

p

(
D
)

t_{p}(D)

of pointwise convergence on a dense subset

D
⊂
K

D\subset K

is norm fragmented; i.e., each non-empty subset of it contains a non-empty

t

p

(
D
)

t_{p}(D)

-relatively open subset of small supremum norm diameter. Several applications are given.
The Sobolev-type moment problem
Authors: Marcellán Francisco , Szafraniec Franciszek
Published: July 2002

We propose necessary and sufficient conditions for a bisequence of complex numbers to be a moment one of Sobolev type over the real line, the unit circle and the complex plane. We achieve this through converting the moment problem in question into a matrix one and utilizing some techniques coming from operator theory. This allows us to consider the Sobolev type moment problem in its full generality, not necessarily in the diagonal case and even of infinite order.
Finite representability of operators in the sense of Bellenot
Authors: Basallote Manuela , Díaz-Madrigal Santiago
Published: July 2002

We present several new results about the notion of finite representability of operators introduced by Bellenot.
Trace methods in twisted group algebras
Authors: Passman D.
Published: July 2002

In this brief note, we discuss trace methods in twisted group algebras. Specifically, we obtain information on the trace of idempotent and nilpotent elements. As is to be expected, if the ground field has positive characteristic, then the arguments used for ordinary group rings carry over to this context with little difficulty. On the other hand, lifting these results to characteristic zero algebras is not straightforward and requires a reduction to finitely presented groups.
Structure of closed finitely starshaped sets
Authors: Rodriguez Mabel , Toranzos Fausto
Published: July 2002

A set

S
S

is finitely starshaped if any finite subset of

S
S

is totally visible from some point of

S
S

. It is well known that in a finite-dimensional linear space, a closed finitely starshaped set which is not starshaped must be unbounded. It is proved here that such a set must admit at least one direction of recession. This fact clarifies the structure of such sets and allows the study of properties of their visibility elements, well known in the case of starshaped sets. A characterization of planar finitely starshaped sets by means of its convex components is obtained. Some plausible conjectures are disproved by means of counterexamples.
Operator semigroups with quasinilpotent commutators
Authors: Radjavi Heydar , Rosenthal Peter , Shulman Victor
Published: July 2002

It is shown that a multiplicative semigroup of operators is triangularizable if

S
T
−
T
S

ST-TS

is quasinilpotent for every pair

{
S
,
 
T
}

\{S,\ T\}

in the semigroup and certain other hypotheses are satisfied.
Subsemivarieties of 𝑄-algebras
Authors: Faroughi M.
Published: July 2002

A variety is a class of Banach algebras

V
V

, for which there exists a family of laws

{
‖
P
‖
≤

K
p

}
P

\{\|P\|\le K_p\}_P

such that

V
V

is precisely the class of all Banach algebras

A
A

which satisfies all of the laws (i.e. for all

P
P

,

‖
P

‖
A

≤

K
p

)

\|P\|_A\le K_p)

. We say that

V
V

is an

H
H

-variety if all of the laws are homogeneous. A semivariety is a class of Banach algebras

W
W

, for which there exists a family of homogeneous laws

{
‖
P
‖
≤

K
P

}
P

\{\|P\|\le K_P\}_P

such that

W
W

is precisely the class of all Banach algebras

A
A

, for which there exists

K
>
0

K>0

such that for all homogeneous polynomials

P
P

,

‖
P

‖
A

≤

K
i

⋅

K
P

\|P\|_A\le K^i\cdot K_P

, where

i
=
deg
⁡
(
P
)

i=\deg (P)

. However, there is no variety between the variety of all

I
Q

IQ

-algebras and the variety of all

I
R

IR

-algebras, which can be defined by homogeneous laws alone. So the theory of semivarieties and the theory of varieties differ significantly. In this paper we shall construct uncountable chains and antichains of semivarieties which are not varieties.
Divergent Laguerre series
Authors: Stempak Krzysztof
Published: July 2002

We prove failure of a.e. convergence of partial sums of Laguerre expansions of

L

p

L^{p}

functions for

p
>
4

p>4

. The idea which is used goes back to Stanton and Tomas. We follow Meaney’s paper (1983), where divergence results were proved in the Jacobi polynomial case.
Global existence and blowup of solutions for a parabolic equation with a gradient term
Authors: Chen Shaohua
Published: July 2002

The author discusses the semilinear parabolic equation

u
t

=
Δ
u
+
f
(
u
)
+
g
(
u
)

|

∇
u

|

2

u_t=\Delta u + f(u) + g(u)|\nabla u|^2

with

u

|

∂
Ω

=
0
,
 
u
(
x
,
0
)
=
ϕ
(
x
)

u|_{\partial \Omega }=0, \ u(x,0)=\phi (x)

. Under suitable assumptions on

f
f

and

g
g

, he proves that, if

0
≤
ϕ
≤
λ
ψ

0 \leq \phi \leq \lambda \psi

with

λ
>
1

\lambda > 1

, then the solutions are global, while if

ϕ
≥
λ
ψ

\phi \geq \lambda \psi

with

λ
>
1

\lambda > 1

, then the solutions blow up in a finite time, where

ψ
\psi

is a positive solution of

Δ
ψ
+
f
(
ψ
)
+
g
(
ψ
)

|

∇
ψ

|

2

=
0

\Delta \psi +f(\psi )+g(\psi )|\nabla \psi |^2=0

, with

ψ

|

∂
Ω

=
0

\psi |_{\partial \Omega }=0

.
Generalized frames and their redundancy
Authors: Askari-Hemmat A. , Dehghan M. , Radjabalipour M.
Published: July 2002

Let

h
h

be a generalized frame in a separable Hilbert space

H
H

indexed by a measure space

(
M
,

S

,
μ
)

(M,\mathcal { S},\mu )

, and assume its analysing operator is surjective. It is shown that

h
h

is essentially discrete; that is, the corresponding index measure space

(
M
,

S

,
μ
)

(M,\mathcal { S},\mu )

can be decomposed into atoms

E
1

,

E
2

,
⋯

E_1,E_2,\cdots

such that

L
2

(
μ
)

L^2(\mu )

is isometrically isomorphic to the weighted space

ℓ
w
2

\ell ^2_w

of all sequences

{

c
i

}

\{c_i\}

of complex numbers with
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue EndAbsoluteValue left-brace c Subscript i Baseline right-brace StartAbsoluteValue EndAbsoluteValue squared equals sigma-summation StartAbsoluteValue c Subscript i Baseline EndAbsoluteValue squared w Subscript i Baseline greater-than normal infinity">

|

|

{

c
i

}

|

|

2

=
∑

|

c
i

|

2

w
i

>
∞

||\{c_i\}||^2=\sum |c_i|^2 w_i>\infty

, where

w
i

=
μ
(

E
i

)
,
 
i
=
1
,
2
,
⋯
.

w_i=\mu (E_i),\ i=1,2,\cdots .

This provides a new proof for the redundancy of the windowed Fourier transform as well as any wavelet family in

L
2

(

R

)

L^2(\mathbb {R})

.
Characteristic classes for complex bundles with trivial real reduction
Authors: Haibao Duan
Published: July 2002

This note concerns itself with a theory of characteristic classes for those complex bundles whose real reductions are trivial.
Conformal metrics and Ricci tensors in the pseudo-Euclidean space
Authors: Pina Romildo , Tenenblat Keti
Published: July 2002

We consider constant symmetric tensors

T
T

on

R
n

R^n

,

n
≥
3

n\geq 3

, and we study the problem of finding metrics

g
¯

\bar {g}

conformal to the pseudo-Euclidean metric

g
g

such that

Ric

g
¯

=
T

\mbox {Ric}\,\bar {g} = T

. We show that such tensors are determined by the diagonal elements and we obtain explicitly the metrics

g
¯

\bar {g}

. As a consequence of these results we get solutions globally defined on

R
n

R^n

for the equation

−
φ

Δ
g

φ
+
n

|

|

∇
g

φ

|

|

2

/

2
+
λ

φ
2

=
0.

- \varphi \Delta _g \varphi +n ||\nabla _g \varphi ||^2/2 + \lambda \varphi ^2 = 0.

Moreover, we show that for certain unbounded functions

K
¯

\overline {K}

defined on

R
n

R^n

, there are metrics conformal to the pseudo-Euclidean metric with scalar curvature

K
¯

\overline {K}

.
An inequality for the norm of a polynomial factor
Authors: Pritsker Igor
Published: July 2002

Let

p
(
z
)

p(z)

be a monic polynomial of degree

n
n

, with complex coefficients, and let

q
(
z
)

q(z)

be its monic factor. We prove an asymptotically sharp inequality of the form

‖
q

‖

E

≤

C
n

‖
p

‖
E

\|q\|_{E} \le C^n \, \|p\|_E

, where

‖
⋅

‖
E

\|\cdot \|_E

denotes the sup norm on a compact set

E
E

in the plane. The best constant

C
E

C_E

in this inequality is found by potential theoretic methods. We also consider applications of the general result to the cases of a disk and a segment.
Signs in the 𝑐𝑑-index of Eulerian partially ordered sets
Authors: Bayer Margaret
Published: July 2002

A graded partially ordered set is Eulerian if every interval has the same number of elements of even rank and of odd rank. Face lattices of convex polytopes are Eulerian. For Eulerian partially ordered sets, the flag vector can be encoded efficiently in the

c
d

cd

-index. The

c
d

cd

-index of a polytope has all positive entries. An important open problem is to give the broadest natural class of Eulerian posets having nonnegative

c
d

cd

-index. This paper completely determines which entries of the

c
d

cd

-index are nonnegative for all Eulerian posets. It also shows that there are no other lower or upper bounds on

c
d

cd

-coefficients (except for the coefficient of

c
n

c^n

).
Uniqueness of left invariant symplectic structures on the affine Lie group
Authors: Agaoka Yoshio
Published: July 2002

We show the uniqueness of left invariant symplectic structures on the affine Lie group

A
(
n
,

R

)

A(n,\mathbf {R})

under the adjoint action of

A
(
n
,

R

)

A(n,\mathbf {R})

, by giving an explicit formula of the Pfaffian of the skew symmetric matrix naturally associated with

A
(
n
,

R

)

A(n,\mathbf {R})

, and also by giving an unexpected identity on it which relates two left invariant symplectic structures. As an application of this result, we classify maximum rank left invariant Poisson structures on the simple Lie groups

S
L
(
n
,

R

)

SL(n,\mathbf {R})

and

S
L
(
n
,

C

)

SL(n, \mathbf {C})

. This result is a generalization of Stolin’s classification of constant solutions of the classical Yang-Baxter equation for

s
l

(
2
,

C

)

\mathfrak {sl}(2, \mathbf {C})

and

s
l

(
3
,

C

)

\mathfrak {sl}(3,\mathbf {C})

.
Hypercentral units in integral group rings
Authors: Li Yuanlin , Parmenter M.
Published: July 2002

In this note, we show that when

G
G

is a torsion group the second center of the group of units

U
(

Z

G
)

U({\mathbb Z}G)

of the integral group ring

Z

G

{\mathbb Z}G

is generated by its torsion subgroup and by the center of

U
(

Z

G
)

U({\mathbb Z}G)

. This extends a result of Arora and Passi (1993) from finite groups to torsion groups, and completes the characterization of hypercentral units in

Z

G

{\mathbb Z}G

when

G
G

is a torsion group.
Convex polytopes all of whose reverse lexicographic initial ideals are squarefree
Authors: Ohsugi Hidefumi , Hibi Takayuki
Published: July 2002

A compressed polytope is an integral convex polytope any of whose reverse lexicographic initial ideals is squarefree. A sufficient condition for a

(
0
,
1
)

(0,1)

-polytope to be compressed will be presented. One of its immediate consequences is that the class of compressed

(
0
,
1
)

(0,1)

-polytopes includes (i) hypersimplices, (ii) order polytopes of finite partially ordered sets, and (iii) stable polytopes of perfect graphs.
An infinitely generated intersection of geometrically finite hyperbolic groups
Authors: Susskind Perry
Published: July 2002

Two discrete, geometrically finite subgroups of the isometries of hyperbolic n-space (

n
≥
4

n \ge 4

) are defined whose intersection is infinitely generated. This settles, in dimensions 4 and above, a long-standing question in Kleinian and hyperbolic groups reiterated at a problem session chaired by Bernard Maskit at the AMS meeting 898, March 3–5, 1995, a conference in honor of Bernard Maskit’s 60th birthday.
Automorphisms of Coxeter groups of rank three
Authors: Franzsen W. , Howlett R.
Published: July 2002

If

W
W

is an infinite rank

3
3

Coxeter group, whose Coxeter diagram has no infinite bonds, then the automorphism group of

W
W

is generated by the inner automorphisms and any automorphisms induced from automorphisms of the Coxeter diagram. Indeed

Aut
⁡
(
W
)

\operatorname {Aut}(W)

is the semi-direct product of

Inn
⁡
(
W
)

\operatorname {Inn}(W)

and the group of graph automorphisms.
On birational morphisms between pencils of Del Pezzo surfaces
Authors: Vologodsky Vitaly
Published: July 2002

Let

X

/

S

X/S

and

X
′

/

S
′

X’/S’

be two Del Pezzo fibrations of degrees

d
d

,

d
′

d’

respectively. Assume that

X
X

and

X
′

X’

differ by a flop. Then we prove that

d
=

d
′

d=d’

and give a short list of values of other basic numerical invariants of

X
X

and

X
′

X’

.
On the solutions of the congruence 𝑛²≡1(𝑚𝑜𝑑𝜙²(𝑛))
Authors: Luca Florian , Křǐžek Michal
Published: July 2002

In this note, we show that if

n
n

is a positive integer satisfying the congruence

n

2

≡
1
 
(
m
o
d
 

ϕ

2

(
n
)
)

n^{2}\equiv 1~ (mod~\phi ^{2}(n))

, then

n
≤
3

n\le 3

.
The Fucik spectrum and critical groups
Authors: Perera Kanishka , Schechter Martin
Published: July 2002

We compute critical groups of zero for variational functionals arising from semilinear elliptic boundary value problems with jumping nonlinearities when the asymptotic limits of the nonlinearity fall in certain parts of Type (II) regions between curves of the Fucik spectrum.
A random variational principle with application to weak Hadamard differentiability of convex integral functionals
Authors: De Blasi Francesco , Georgiev Pando
Published: July 2002

We present a random version of the Borwein-Preiss smooth variational principle, stating that under suitable conditions, the set of minimizers of a perturbed function depending on a random variable, admits a measurable selection. Two applications are given. The first one shows that if

E
E

is a superreflexive Banach space, then any convex continuous integral functional on

L
1

(
T
,
μ
;
E
)

L^1(T, \mu ; E)

from a certain class (in particular the usual

L
1

L^1

norm), is weak Hadamard differentiable on a subset whose complement is

σ
\sigma

-very porous. The second application is a random version of the Caristi fixed point theorem for multifunctions.
An example on the Mann iteration method for Lipschitz pseudocontractions
Authors: Chidume C. , Mutangadura S.
Published: July 2002

An example of a Lipschitz pseudocontractive map with a unique fixed point is constructed for which the Mann iteration sequence fails to converge. This resolves a long standing open problem.
On the volume and the Gauss map image of spacelike hypersurfaces in de Sitter space
Authors: Aledo Juan , Alías Luis
Published: July 2002

In this paper we prove that a complete spacelike hypersurface

M
n

M^n

in de Sitter space such that its image under the Gauss map is contained in a hyperbolic geodesic ball of radius

ϱ
\varrho

is necessarily compact and its

n
n

-dimensional volume satisfies
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="omega Subscript n Baseline slash normal c normal o normal s normal h left-parenthesis rho right-parenthesis less-than-or-equal-to normal v normal o normal l left-parenthesis upper M right-parenthesis less-than-or-equal-to omega Subscript n Baseline normal c normal o normal s normal h Superscript n Baseline left-parenthesis rho right-parenthesis">

ω
n

/

c
o
s
h

(
ϱ
)
≤

v
o
l

(
M
)
≤

ω
n

c
o
s
h

n

(
ϱ
)

\omega _n/\mathrm {cosh}(\varrho )\leq \mathrm {vol}(M)\leq \omega _n\mathrm { cosh}^{n}(\varrho )

, where

ω
n

\omega _n

denotes the volume of a unitary round

n
n

-sphere. We also characterize the case where these inequalities become equalities. As an application of our result, we also conclude that Goddard’s conjecture is true under the assumption that the hyperbolic image of the hypersurface is bounded.
On perfectly meager sets
Authors: Bartoszynski Tomek
Published: July 2002

We show that it is consistent that the product of perfectly meager sets is perfectly meager.