bluuebunny/crossref_metadata_2025 huggingface dataset:
Studies of transformer repair workers exposed to PCBs: I. Study design, PCB concentrations, questionnaire, and clinical examination results
Authors: Emmett Edward A. , Maroni Marco , Schmith Joanne M. , Levin Barry K. , Jefferys Joan
Published: April 2007

A cross‐sectional study compared 55 transformer repairmen, 38 currently, and 17 previously exposed to polychlorinated biphenyls (PCBs) with 56 non‐exposed subjects. PCBs exposures occurred from air and contaminated surfaces, predominantly from Aroclor 1260 with some exposure to Aroclor 1242. Each worker underwent: a questionnaire; standardized medical examination; delayed hypersensitivity testing; and determination of serum and adipose tissue lipid total PCB concentrations.

Adipose and serum [PCBs] were significantly higher in the currently exposed, but previously exposed workers did not differ significantly from comparison subjects.

No subjects had a classical syndrome of PCB poisoning. A number of neurobehavioral and irritant symptoms were significantly more prevalent in the exposed group, but were probably not related to PCBs. Comedones were more frequent in the exposed group, but no evidence of classical chloracne was noted. Cutaneous delayed hypersensitivity responses to mumps and to trichophyton antigens did not differ between the groups. The association of PCBs with job functions were explored.
Study of mortality among chemical workers in the Kanawha Valley of West Virginia
Authors: Rinsky Robert A. , Ott Gerald , Ward Elizabeth , Greenberg Howard , Halperin William , Leet Terry
Published: April 2007

To assess the mortality experience of a cohort of chemical workers in the Kanawha Valley of West Virginia, 29,139 males who worked at any one of three facilities over a 39‐year period were followed‐up for vital status. The facilities include two chemical manufacturing plants and a research and development center. From this cohort, 5,785 men were found to have died as of the study end, December 31, 1978. This was less than the 6,148.5 men expected to have died, based upon the United States white male population (standardized mortality ratio (SMR) = 94, 95% confidence interval (CI) = 92–96). Eighty‐six specific causes of death were examined. Statistically significant increased deaths were observed for two causes; cancers of the liver (not specified as primary or secondary) (SMR = 174; CI = 102–280) and lympho‐ and reticulosarcoma (SMR = 140; CI = 104–187). When all biliary and liver cancer was examined by duration and time since initial employment, the SMR for those who worked at least 25 years and whose deaths occurred 30 years or more after first employment was 301 (95% confidence limit = 168–497). The identification and follow‐up of this complete cohort provides the basis for future study of subcohorts with specific chemical and process exposures and case control studies of specific causes of death.
Cancer mortality among northern georgia carpet and textile workers
Authors: O'Brien Thomas R. , Decouflé Pierre
Published: April 2007

Proportionate cancer mortality was analyzed among white male carpet and textile workers in five northwest Georgia counties for the years 1970–1984. Compared with other Georgians, carpet and textile workers had higher proportions of lymphocytic leukemia (proportionate cancer mortality ratio [PCMR] = 2.9; 95% CI = 1.4–5.4) and testicular cancer (PCMR = 3.2; 95% CI = 1.0–7.5). The excess mortality from lymphocytic leukemia was even higher when the analysis was limited to workers deemed most likely to work directly in production areas (PCMR = 4.2; 95% CI = 1.7–8.7). Further studies are needed to determine if the observed excesses are the result of workplace exposures.
Silicon Carbide in Lung Tissue of a Worker in the Abrasive Industry
Authors: Hayashi Hisato , Kajita Akira
Published: April 2007

Lung tissue of a worker in an abrasive manufacturing plant, whose duration of dust exposure was about 10 years, was analyzed by means of bulk analysis and in situ analytical electron microanalysis. The content of the total dust in the lung was 120 mg/g of the dried lung tissue. This value is close to the average concentration of the total dust in the lungs of coal miners with massive fibrosis. The lung dust composition in this case was approximately 43% silicon carbide, 24% aluminium oxide, 2.3% cristobalite, 2.0% quartz, and trace of talc and feldspar. Silicon carbide may be one of the major etiologic agents in this case of pneumoconiosis.
Health and socioeconomic consequences of occupational respiratory allergies: A pilot study using workers' compensation data
Authors: Yassi Annalee
Published: April 2007

Growing evidence suggests that individuals with occupational allergies have long‐term health and employment problems. Workers' compensation claims for allergic respiratory disease allowed in Ontario 1975‐1981 were reviewed for demographic, risk factor, and exposure data. Diagnoses listed in these 244 claims were reassessed for consistency with criteria for occupational respiratory allergies. Twenty‐eight percent of the 154 claimants who met the criteria were granted a permanent disability award from the workers' compensation board (WCB). In response to a questionnaire mailed 2‐8 years after claim allowance, 77% of those traced reported improvement, but 59% still required medication and 85% still suffered symptoms. Seventy‐six percent of claimants left their employer. Seventy‐five percent of those who left did so due to their allergic condition; 95% suffered long‐term income loss. The unemployment rate for this cohort was 36%, well above that for the general population. Older workers with longer duration of symptoms and longer duration of exposure prior to the claim had the worst prognoses. The data were consistent with previous studies in suggesting that occupational respiratory allergies may result in serious health and socioeconomic consequences. Exploring the feasibility, acceptability, and potential usefulness of WCB data, it is suggested that this source merits further consideration both for descriptive as well as prognostic studies.
Chronic respiratory disorders related to farming and exposure to grain dust in a rural adult community
Authors: Manfreda J. , Cheang M. , Warren C. P. W.
Published: April 2007

In a survey of chronic respiratory symptoms and airflow obstruction of a rural population aged 20–65 years, the effects of both farming and, in particular, the exposure to grain dust on the respiratory health of the people was examined. Of the 1,892 subjects (82% of the eligible population) studied, 924 were males and 968 females, with half living in the town. Three groups were identified: current, former, and never farmers. Almost all current farmers were exposed to grain for, on average, 2 months a year. There was no difference in atopic status between the groups. While there was a strong association between most symptoms and smoking, there was no association between symptoms and exposure to grain and farming category once age and smoking had been taken into account. Results of this study suggest that farmers do not have chronic respiratory symptoms or impairment of lung function because of their exposure to grain dust. Lung function of former farmers might have been affected by farming, and this may reflect more involvement with livestock in the past.
Parental occupational lead exposure and lead concentration of newborn cord blood
Authors: Wang Jung‐Der , Shy Wen‐Yi , Chen Jui‐San , Yang Kun‐Ho , Hwang Yaw‐Huei
Published: April 2007

The purpose of this study was to determine the influence of parental occupational lead exposure on the lead levels of newborn cord blood in the Taipei area. From September 1984 to June 1985, 5,000 pregnant women voluntarily participated in the study at the Taipei Municipal Maternal and Child Hospital. Each woman was interviewed regarding her and her husband's occupational exposures; 2,948 successfully delivered healthy newborns, and cord blood samples were obtained using Terumo Venoject, and 242 samples were analyzed by graphite furnace atomic absorption spectrometry using an Instrumentation Laboratory 251 instrument. Nine cord blood samples were from newborns with both parents exposed, 26 samples had maternal exposure only, 105 samples had paternal exposure only, and 102 were nonexposed. The results showed that the average lead level of cord blood with both parents exposed was 8.9 ± 2.9 μg%, maternal exposure 9.0 ± 3.8 μg%, paternal exposure 8.3 ± 3.4 μg%, and 6.9 ± 3.2 μg% in the nonexposed group. There were significant differences between the nonexposed and the maternal exposure groups, and also between the nonexposed and paternal exposure groups. All 26 maternal exposures were from lead soldering operations. Multivariate analysis revealed that, after control of father's exposure status, newborn cord blood lead level increased 0.27 μg% for each hour the mother spent on lead soldering during a normal working day, thus suggesting that soldering during pregnancy may be hazardous to newborns. Paternal contribution to the cord blood lead levels seemed to be through either working at home with the pregnant mother also at home or bringing work clothes home for laundering.
Gene–lifecourse interaction for alcohol consumption in adolescence and young adulthood: Five monoamine genes
Authors: Guo Guang , Wilhelmsen Kirk , Hamilton Nathan
Published: April 2007

Association analysis has suggested that common sequence variants of genes that affect monoamine function can affect substance use and abuse. Demonstration of these associations has been inconsistent because of limited sample sizes and phenotype definition. Drawing on the life course perspective, we predicted a stronger association between the polymorphisms in 5HTT, DAT1, DRD4, DRD2, and MAOA and alcohol consumption in young adulthood than adolescence. This analysis tested for the gene–lifecourse interaction for the frequency of alcohol consumption in a nationally representative non‐alcohol‐dependent sample of 2,466 individuals that were visited during adolescence and young adulthood for four times between 1994 and 2002. All five genes are significantly associated with the frequency of alcohol consumption, with the genotype effects ranging 7%–20% of the mean score of alcohol consumption and their P values being 0.014, 0.0003, 0.003, 0.007, 0.005, and 0.003, respectively. The association is only observed in the life stage of young adulthood and not in adolescence. This analysis has demonstrated the potential usefulness of the life course perspective in genetic studies of human behaviors such as alcohol consumption. © 2007 Wiley‐Liss, Inc.
Twenty‐five years of end‐user searching, Part 2: Future research directions
Authors: Markey Karen
Published: April 2007

This is the second part of a two‐part article that examines 25 years of published research findings on end‐user searching of online information retrieval (IR) systems. In Part 1 (Markey, 2007), it was learned that people enter a few short search statements into online IR systems. Their searches do not resemble the systematic approach of expert searchers who use the full range of IR‐system functionality. Part 2 picks up the discussion of research findings about end‐user searching in the context of current information retrieval models. These models demonstrate that information retrieval is a complex event, involving changes in cognition, feelings, and/or events during the information seeking process. The author challenges IR researchers to design new studies of end‐user searching, collecting data not only on system‐feature use, but on multiple search sessions and controlling for variables such as domain knowledge expertise and expert system knowledge. Because future IR systems designers are likely to improve the functionality of online IR systems in response to answers to the new research questions posed here, the author concludes with advice to these designers about retaining the simplicity of online IR system interfaces.
Mid-term survival after abdominal aortic aneurysm surgery predicted by cardiopulmonary exercise testing
Authors: Carlisle J , Swart M
Published: April 2007

Background

Cardiopulmonary exercise (CPX) testing measures how efficiently subjects meet increased metabolic demand. This study aimed to determine whether preoperative CPX testing predicted postoperative survival following elective abdominal aortic aneurysm (AAA) repair.

Methods

Some 130 patients had CPX testing before elective open AAA repair. Additional preoperative, operative and postoperative variables were recorded prospectively. Median follow-up was 35 months. The correlation of variables with survival was assessed by single and multiple regression analyses.

Results

CPX testing identified 30 of 130 patients who had been unfit before surgery. Two years after surgery the Kaplan–Meier survival estimate was 55 per cent for the 30 unfit patients, compared with 97 per cent for the 100 fit patients. The absolute difference in survival between these two groups at 2 years was 42 (95 per cent confidence interval 18 to 65) per cent (P < 0·001).

Conclusion

Preoperative CPX testing, combined with simple co-morbidity scoring, identified patients unlikely to survive in the mid-term, even after successful AAA repair.
51V NMR Chemical Shifts Calculated from QM/MM Models of Vanadium Chloroperoxidase
Authors: Waller Mark P. , Bühl Michael , Geethalakshmi K. R. , Wang Dongqi , Thiel Walter
Published: April 2007

51V NMR chemical shifts calculated from QM/MM‐optimized (QM=quantum mechanical; MM=molecular mechanical) models of vanadium‐dependent chloroperoxidase (VCPO) are presented. An extensive number of protonation states for the vanadium cofactor (active site of the protein) and a number of probable positional isomers for each of the protonation states are considered. The size of the QM region is increased incrementally to observe the convergence behavior of the 51V NMR chemical shifts. A total of 40 models are assessed by comparison to experimental solid‐state 51V NMR results recently reported in the literature. Isotropic chemical shifts are found to be a poor indicator of the protonation state; however, anisotropic chemical shifts and the nuclear quadrupole tensors appear to be sensitive to changes in the proton environment of the vanadium nuclei. This detailed investigation of the 51V NMR chemical shifts computed from QM/MM models provides further evidence that the ground state is either a triply protonated (one axial water and one equatorial hydroxyl group) or a doubly protonated vanadate moiety in VCPO. Particular attention is given to the electrostatic and geometric effects of the protein environment. This is the first study to compute anisotropic NMR chemical shifts from QM/MM models of an active metalloprotein for direct comparison with solid‐state MAS NMR data. This theoretical approach enhances the potential use of experimental solid‐state NMR spectroscopy for the structural determination of metalloproteins.
Wavelength shifts in solid‐state circular dichroism spectra: A possible explanation
Authors: Castiglioni Ettore , Abbate Sergio , Longhi Giovanna , Gangemi Roberto
Published: April 2007

We have devised an artificial sampling approach generating “absorption flattening” (AF) on the UV–Vis spectrum of a solution of a chiral compound: Tris (ethylendiamine)cobalt(III) chloride (Λ‐Co(en)3Cl3). We have observed a concomitant red shift of the CD maxima. Related CD and absorption spectra have been calculated from spectra recorded on diluted homogeneous solutions, thus monitoring the effect of AF on both types of data. Experimental data are in good agreement with calculated spectra. Simulations with suitable bandshapes show that the red shift of the CD spectrum is due to AF. On the basis of these results, we conclude that AF is an important cause of distortions in CD spectra for inhomogeneous samples. Plans to compensate or at least to take into account this effect are presented. Chirality, 2007. © 2007 Wiley‐Liss, Inc.
HPLC on chiral support with polarimetric detection: Application to conglomerate discovery
Authors: Roussel Christian , Vanthuyne Nicolas , Jobert Jean‐Laurent , Loas Andrei I. , Tanase Anca E. , Gherase Dragos
Published: April 2007

In conglomerates, each single crystal contains only one of the two possible enantiomeric forms—either dextrorotatory or levorotatory. The analysis of a single crystal by liquid chromatography on chiral support associated with chiroptical detection is a very efficient tool to reveal the occurrence of a conglomerate. In terms of rapidity and easiness, this method compares favorably with the classical methods used to show this occurrence. Two examples are provided. Chirality, 2007. © 2007 Wiley‐Liss, Inc.
A diophantine definition of integers in the rings of rational numbers
Authors: Shlapentokh Alexandra
Published: April 2007

The author considers rings of rational numbers which are integral at all the primes except, possibly, primes contained in a finite set. In such rings a Diophantine definition of ℤ is constructed to show that all the recursively enumerable subsets of the ring are Diophantine.
Central limit theorems for extreme Sojourns of stationary Gaussian processes
Authors: Berman Simeon M.
Published: April 2007

Let X(t), t ≧ 0, be a real stationary Gaussian process, and, for u > 0 and t >0, let Lt(u) be the time spent by X(s), 0 ≦ s ≦ t, above the level u. Here u is taken to be a function u(t) of t, and Lt is defined as Lt(u(t)). It is shown that the distribution of (Lt – ELt)/(Var Lt)1/2 converges, for t → ∞ and u(t) → ∞, to a standard normal distribution under various conditions relating the growth of u(t) to the decay of the covariance and other functions associated with it.
Electron transport in bifurcated tokamak equilibria
Authors: Garabedian Paul , Taylor Mark
Published: April 2007

Transport of ions and electrons is calculated by the Monte Carlo method in tokamak plasmas without axial symmetry. Turbulence is modeled by time‐averaged equations of electrostatics and magnetostatics that describe quasineutrality and equilibrium. Good agreement with experimental measurements is obtained by allowing for small three‐dimensional asymmetries in the electric and magnetic fields.
Time series transformations in clocked queueing networks
Authors: Percus Ora E. , Percus J. K.
Published: April 2007

We consider a network in which message packets arriving on a clock cycle are directed along paths which may have segments in common. When they do, the messages involved are queued and transmitted, one per cycle. The statistics of queue length are investigated by an expansion of the time series in a channel about the regime of independent arrivals. Results for the second stage of such a network are in good agreement with computer simulations.
Regularity for quasilinear second‐order subelliptic equations
Authors: Xu Chao‐Jiang
Published: April 2007

In this paper, we study the regularity of solutions of the quasilinear equation

where X = (X1,…,Xm) is a system of real smooth vector fields, Aij, B ϵ C∞(Ω × ℝ Rm+1). Assume that X satisfies the Hörmander condition and (Aij(x, z,ζ)) is positive definite. We prove that if u ϵ S2,α(Ω) (see Section 2) is a solution of the above equation, then u ϵ C∞ (Ω).
Removal of boundary singularities of pseudo‐holomorphic curves with Lagrangian boundary conditions
Authors: Oh Yong‐Geun
Published: April 2007

We give a proof of the theorem of removing isolated singularities of pseudo‐holomorphic curves with Lagrangian boundary conditions and bounded symplectic area. The proof is a combination of some Lp‐type estimates, standard techniques of geometric P.D.E., and some ideas from symplectic geometry and calibration theory.
Solution of a nonlinear heat equation with arbitrarily given blow‐up points
Authors: Merle Frank
Published: April 2007

We consider the equation

where I ⊂ ℝ u is scalar‐valued and p > 1.

It has been proven that if u(t) blows up at time T, the blow‐up points are finite in number and located in I°.

Our aim is to prove that this result is optimal. That is, for any given points x1,…,xk in I° there is a solution u such that its blow‐up points are exactly x1,…,xk.
Stability of viscous shock waves associated with a system of nonstrictly hyperbolic conservations laws
Authors: Liu Tai‐Ping , Xin Zhouping
Published: April 2007

We introduce a simple model of two conservation laws which is strictly hyperbolic except for a degenerate parabolic line in the state space. Besides classical shock waves, it also exhibits overcompressive, marginal overcompressive, and marginal undercompressive shock waves. Our purpose is to study the behavior of the corresponding viscous waves, in particular the manner in which these waves are stable. There are several basic differences between classical shock waves and other types of shock waves. A perturbation of an overcompressive shock wave gives rise to a new wave. Monotone marginal overcompressive waves behave distinctly from the nonmonotone ones. Analytical techniques used in our study include characteristic‐energy and weighted‐energy methods, and nonlinear superposition through time‐invariants. Although we carry out our analysis for a simple model, the general phenomena would hold for overcompressive waves which occur in other physical models.
Axially symmetric harmonic maps minimizing a relaxed energy
Authors: Hardt Robert , Lin Fang‐Hua , Poon Chi‐Cheung
Published: April 2007

Here we obtain various results on the class of axially symmetric harmonic maps from B3 to S2. We find some new classes of non‐minimizing harmonic maps exhibiting unusual singular behavior. Optimal partial regularity estimates are obtained for mappings which minimize, among axially symmetric maps, various relaxed energies which have been studied in [4]and [11].
Refined asymptotics for the blowup of ut — δu = up
Authors: Filippas Stathis , Kohn Robert V.
Published: April 2007

This work is concerned with positive, blowing‐up solutions of the semilinear heat equation ut — δu = up in Rn. Our main contribution is a sort of center manifold analysis for the equation in similarity variables, leading to refined asymptotics for u in a backward space‐time parabola near any blowup point. We also explore a connection between the asymptotics of u and the local geometry of the blowup set.
Phase transitions and generalized motion by mean curvature
Authors: Evans L. C. , Soner H. M. , Souganidis P. E.
Published: April 2007

We study the limiting behavior of solutions to appropriately rescaled versions of the Allen‐Cahn equation, a simplified model for dynamic phase transitions. We rigorously establish the existence in the limit of a phase‐antiphase interface evolving according to mean curvature motion. This assertion is valid for all positive time, the motion interpreted in the generalized sense of Evans‐Spruck and Chen‐Giga‐Goto after the onset of geometric singularities.
Solutions of superlinear elliptic equations and their morse indices
Authors: Bahri A. , Lions P. L.
Published: April 2007

We consider here solutions of semilinear second‐order elliptic equations with superlinear nonlinearities. And we present some relationships between their Morse Indices and some qualitative properties. In particular we show that for, “uo;subcritical” nonlinearities, bounds on solutions are equivalent to bounds on their Morse indices.
Morse theory for periodic solutions of hamiltonian systems and the maslov index
Authors: Salamon Dietmar , Zehnder Eduard
Published: April 2007

In this paper we prove Morse type inequalities for the contractible 1‐periodic solutions of time dependent Hamiltonian differential equations on those compact symplectic manifolds M for which the symplectic form and the first Chern class of the tangent bundle vanish over π2 (M). The proof is based on a version of infinite dimensional Morse theory which is due to Floer. The key point is an index theorem for the Fredholm operator which plays a central role in Floer homology. The index formula involves the Maslov index of nondegenerate contractible periodic solutions. This Maslov index plays the same role as the Morse index of a nondegenerate critical point does in finite dimensional Morse theory. We shall use this connection between Floer homology and Maslov index to establish the existence of infinitely many periodic solutions having integer periods provided that every 1‐periodic solution has at least one Floquet multiplier which is not equal to 1.
Undecidability results for restricted universally quantified formulae of set theory
Authors: Parlamento F. , Policriti A.
Published: April 2007

The problem of establishing whether there are sets satisfying a formula in the first order set theoretic language ℒ︁ϵ based on =,ϵ, which involves only restricted quantifiers and has an equivalent ∀∃‐prenex form ((∀∃)0‐formula), is neither decidable nor semidecidable. In fact, given any ω‐model of ZF – FA, where FA denotes the Foundation Axiom, the set of existential closures of (∀∃)0‐formulae true in the model is a productive set. Undecidability arises even when dealing with restricted universal quantifiers only, provided a predicate is_a_pair(x), meaning that x is a pair of distinct sets, is added to ℒ︁ϵ. If satisfiability refers to ω‐models of ZF – FA in which a form of Boffa's antifoundation axiom holds, then semidecidability fails as well; in fact, given any such model, the set of existential closures of formulae involving only restricted quantifiers and the predicate is_a_pair which are true in it, is a productive set. These results are all proved by making use of appropriate codings of Turing machine computations in the set theoretic language.
Solution of the inverse spectral problem for an impedance with integrable derivative part II
Authors: Coleman Carol Flynn , McLaughlin Joyce R.
Published: April 2007

The inverse eigenvalue problem for a Sturm‐Liouville equation in impedance form with Dirichlet boundary conditions on a unit interval is solved. The solution of this nonlinear problem requires the investigation of a combined map from the logarithmic derivative of the impedance, assumed to be square integrable, to two sequences of spectral data. The first is the sequence of Dirichlet eigenvalues, shown to be locally bounded with square roots differing from the sequence of integral multiples of π by a square summable sequence. The second sequence has as first term the mean of the logarithmic derivative of the impedance. Each term in the remainder of the sequence is the logarithm of the product of the impedance and the derivative of an eigenfunction evaluated at an endpoint. It is shown that this second sequence is a locally bounded square summable sequence.

The combined map is a real analytic isomorphism. A uniqueness result follows from the asymptotics and analyticity shown in the first paper and properties of Riesz bases. The existence is shown by giving a closed form of the solution.

It is also shown that the same map solves the inverse Sturm‐Liouville problem in impedance form with Neumann boundary conditions. © 1993 John Wiley & Sons, Inc.
On –δu = K(x)u5 in ℝ3
Authors: Li Yanyan
Published: April 2007

In this paper, we study the equation –Δu = K(x)u5 in ℝ3 and provide a large class of positive functions K(x) for which we obtain infinitely many positive solutions which decay at infinity at the rate of |x|−1. © 1993 John Wiley & Sons, Inc.
Decay rates for nonconvex systems of conservation laws
Authors: Zumbrun Kevin
Published: April 2007

We study decay of solutions for hyperbolic systems of conservation laws which are not genuinely nonlinear. For a generic class of such systems, we determine sharp (algebraic) rates of decay in the total variation of the wave speed, for solutions with compact initial support. Our analysis involves generalized characteristic arguments and the random choice difference scheme of Glimm. © 1993 John Wiley & Sons, Inc.
Space‐time large deviations for interacting particle systems
Authors: Pra P. Dai
Published: April 2007

We prove a process‐level large deviation principle for the space‐time empirical averages of continuous‐time systems on an infinite lattice. Our methods rely on the Donsker‐Varadhan large deviation theory for Markov processes, and allow us to express the rate function rather explicitly in terms of the Markov generator of the infinite particle system. We can prove our principle for a large class of spin systems with no particle exchange, as well as for infinite diffusion processes whose drift is the gradient of a finite range Hamiltonian. © 1993 John Wiley & Sons, Inc.
Stability of travelling waves for non‐convex scalar viscous conservation laws
Authors: Jones Christopher K. R. T. , Gardner Robert , Kapitula Todd
Published: April 2007

Travelling waves of a viscous conservation law (so‐called viscous profiles) are shown to be stable in polynomialy weighted L∞ spaces. There is no assumption of convexity on the nonlinear term and thus earlier results of Il'in and Oleǐnik, Sattinger, and Kawashima and Matsumura are generalized. The method uses the semigroup of the linearized equation with solutions of the full problem expressed by the variation of constants formula. Estimates are derived for the semigroup through a new technique for estimating the resolvent. © 1993 John Wiley & Sons, Inc.
Zero relaxation and dissipation limits for hyperbolic conservation laws
Authors: Chen Gui‐Qiang , Liu Tai‐Ping
Published: April 2007

We are interested in hyperbolic systems of conservation laws with relaxation and dissipation, particularly the zero relaxation limit. Such a limit is of interest in several physical situations, including gas flow near thermo‐equilibrium, kinetic theory with small mean free path, and viscoelasticity with vanishing memory. In this article we study hyperbolic systems of two conservation laws with relaxation. For the stable case where the equilibrium speed is subcharacteristic with respect to the frozen speeds, we illustrate for a model in viscoelasticity that no oscillation develops for the nonlinear system in the zero relaxation limit. For the marginally stable case where the equilibrium speed may equal one of the frozen speeds, we show for a model in phase transitions that no oscillation arises when the dissipation is present and goes to zero more slowly than the relaxation. Our analysis includes the construction of suitable entropy pairs to derive energy estimates. We need such energy estimates not only for the compactness properties but also for the deviation from the equilibrium of the solutions for the relaxation systems. The theory of compensated compactness is then applied to study the oscillation in the zero relaxation limit. © 1993 John Wiley & Sons, Inc.
Periodic limit of inverse scattering
Authors: Zhang Taiyan , Venakides Stephanos
Published: April 2007

I t is well known that a p‐periodic potential Q(x) can be reconstructed from spectral data of the corresponding Hill operator −(d2/dx2) + Q(x) in terms of a Riemann θ‐function. We regard the periodic potential Q(x) as the pointwise limit of a scattering potential QN,c(x) (defined to equal Q(x) when −Np ≦ x ≦ Np, to equal zero when x < Np) and to equal c2 when x > (Np) as N → ∞ and c2 → ∞. The scattering potential QN,c(x) can be recovered from the scattering data of the corresponding Schrödinger operator in terms of a Dyson determinant according to a well known‐theory. We derive the Riemann θ‐function corresponding to the periodic potential Q(x) by taking the above limit of the Dyson determinant for the scattering potential.

We first calculate the scattering data of the potential QN,c(x) through recursive formulas in terms of the left transmission and reflection coefficients T and R of the potential which is equal to Q(x) when 0 ≦ x ≦ p and equal to zero otherwise. We use these data to express the Dyson determinant of QN,c(x). We then expand the Dyson determinant into a Fredholm series and compute the main contributions to the expansion in the asymptotic limit N → ∞ and c2 → ∞ using a method developed by Lax, Levermore, and Venakides in their study of the small dispersion limit of the initial value problem of Korteweg‐de Vries equation. The computation of the leading order contributions reduces to a quadratic functional maximization problem constrained by a positivity condition and by a mass quantization condition. The solutions to this maximization problem constitute the differentials on a Riemann surface, the main ingredients for the Riemann θ‐function corresponding to the periodic potential. The limit of the Dyson determinant for QN,c(x) as N → ∞ and c2 → ∞ is shown to equal the exact Riemann θ‐function corresponding to the periodic potential Q(x) times an exponential function with exponent being a quadratic polynomial in x. Our calculation includes the correct phase shifts of the θ‐function. © 1993 John Wiley & Sons, Inc.
Sup‐norm stability for Glimm's scheme
Authors: Young Robin
Published: April 2007

We consider the Cauchy problem for a general N × N system of conservation laws. Existence of solutions was proved by Glimm using his celebrated random choice scheme. In this paper, we obtain a third‐order interaction estimate analagous to that obtained by Glimm for 2×2 systems. By using this estimate, and identifying a global cancellation effect, we obtain L∞‐stability for solutions generated by Glimm's scheme. As an immediate consequence we have L1‐stability and L∞‐decay, obtained by Temple for 2×2 systems. © 1993 John Wiley & Sons, Inc.
Analytic dependence of riemann mappings for bounded domains and minimal surfaces
Authors: Wu Sijue
Published: April 2007

In this paper, we prove that the functional which takes a closed Lavrentiev curve to the corresponding Riemann mapping is locally Lipl on the set Ω of all closed Lavrentiev curves. This set is a subset of BMO(T). It is, however, not open in BMO(T). We also prove that the previous functional is analytic for certain classes of closed Lavrentiev curves, including the class of curves which have some symmetry with respect to the unit circle. These classes of curves are submanifolds of BMO(T). Finally, we consider the functional which takes a Lavrentiev curve (closed or not) in n‐dimensional Euclidean space to the corresponding minimal surface, and we study the differentiability and analyticity of this functional on certain function spaces. © 1993 John Wiley & Sons, Inc.
Newton's method and periodic solutions of nonlinear wave equations
Authors: Craig Walter , Wayne C. Eugene
Published: April 2007

We prove the existence of periodic solutions of the nonlinear wave equation

satisfying either Dirichlet or periodic boundary conditions on the interval [O, π]. The coefficients of the eigenfunction expansion of this equation satisfy a nonlinear functional equation. Using a version of Newton's method, we show that this equation has solutions provided the nonlinearity g(x, u) satisfies certain generic conditions of nonresonance and genuine nonlinearity. © 1993 John Wiley & Sons, Inc.
Disorder of particle chains as a dynamical problem of transition to chaos: Analogy to simulation induced chaos
Authors: Beloshapkin V. V. , Tretyakov A. G. , Zaslavsky G. M.
Published: April 2007

The problem of the equilibria of particle chains with nearest and next‐to‐nearest neighbor interaction has been reduced to the dynamical system, given by 4D or 2D web‐maps. It is shown that at the same time these maps can represent difference schemes for differential equations used in computational simulation. An analogy between particle disordering, dynamical chaos, and simulation induced chaos is established. © 1994 John Wiley & Sons, Inc.
On the zeros of some continuous analogues of matrix orthogonal polynomials and a related extension problem with negative squares
Authors: Dym Harry
Published: April 2007

A new proof of a recent theorem of Ellis, Gohberg, and Lay, which identifies the number of roots of a “continuous” matrix orthogonal polynomial in the open upper halfplane with the number of negative eigenvalues of a related integral operator is presented. A related extension problem is then formulated and solved in assorted classes of functions which are analytic in the open upper half plane, apart from a finite number of poles. A discrete analogue of this extension problem is also formulated and solved. © 1994 John Wiley & Sons, Inc.
Sets of conductivity and elasticity tensors stable under lamination
Authors: Francfort Gilles A. , Milton Graeme W.
Published: April 2007

A complete characterization is obtained of any set of constitutive (conductivity or elasticity) tensors that is stable under lamination between any two of the elements of the set. The conditions are local and are expressed in terms of the curvature and tangent plane at points on the boundary of the set. They are checked to hold for several well‐known examples of sets stable under a more general process of homogenization. A companion paper investigates the link between these conditions and quasiconvexity. © 1994 John Wiley & Sons, Inc.
A Unified theory of tokamaks and stellarators
Authors: Garabedian P. R.
Published: April 2007

Computational methods are described to study the equilibrium, stability, and transport of a fusion plasma confined by a magnetic field with toroidal geometry. Misconceptions in conventional theories of transport are analyzed and new results more consistent with experimental observations are presented. Specifications are given for an advanced stellarator designed to compete with tokamaks as a fusion reactor. © 1994 John Wiley & Sons, Inc.
Surface energy and microstructure in coherent phase transitions
Authors: Kohn Robert V. , Müller Stefan
Published: April 2007

We study a variational problem involving a nonconvex function of Δu, regularized by a higher order term. The motivation comes from the theory of martensitic phase transformation—specifically, a model for the fine scale structure of twinning near an austenite‐twinned‐martensite interface. It is widely believed that the fine scale structure can be understood variationally, through the minimization of elastic and surface energy. Our problem represents the essence of this minimization.

Similar variational problems have been considered by many authors in the materials science literature. They have always assumed, however, that the twinning should be essentially one‐dimensional. This is in general false. Energy minimization can require a complex pattern of twin branching near the austenite interface. There are indications that the states of minimum energy may be asymptotically self‐similar. © 1994 John Wiley & Sons., Inc.
The τ‐function of the universal whitham hierarchy, matrix models and topological field theories
Authors: Krichever I. M.
Published: April 2007

The universal Whitham hierarchy is considered from the viewpoint of topological field theories. The τ‐function is defined for this hierarchy. It is proved that the algebraic orbits of Whitham hierarchy can be identified with various topological matter models coupled with topological gravity. © 1994 John Wiley & Sons, Inc.
Hyperbolic conservation laws with stiff relaxation terms and entropy
Authors: Chen Gui‐Qiang , Levermore C. David , Liu Tai‐Ping
Published: April 2007

We study the limiting behavior of systems of hyperbolic conservation laws with stiff relaxation terms. Reduced systems, inviscid and viscous local conservation laws, and weakly nonlinear limits are derived through asymptotic expansions. An entropy condition is introduced for N × N systems that ensures the hyperbolicity of the reduced inviscid system. The resulting characteristic speeds are shown to be interlaced with those of the original system. Moreover, the first correction to the reduced system is shown to be dissipative. A partial converse is proved for 2 × 2 systems. This structure is then applied to study the convergence to the reduced dynamics for the 2 × 2 case. © 1994 John Wiley & Sons, Inc.
Existence and positivity of solutions of a fourth‐order nonlinear PDE describing interface fluctuations
Authors: Bleher Pavel M. , Lebowitz Joel L. , Speer Eugene R.
Published: April 2007

We study the partial differential equation magnified image which arose originally as a scaling limit in the study of interface fluctuations in a certain spin system. In that application x lies in R, but here we study primarily the periodic case × R S1. We establish existence, uniqueness, and regularity of solutions, locally in time, for positive initial data in H1(S1), and prove the existence of several families of Lyapunov functions for the evolution. From the latter we establish a sharp connection between existence globally in time and positivity preservation: if [0], T*) is a maximal half open interval of existence for a positive solution of the equation, with T* < ∞, then limtT* w(t,·) exists in C1(S1) but vanishes at some point. We show further that if T* > (1 + √3)/16π2 √3 then T* = ∞ and limt∞ w(t,.) exists and is constant. We discuss also some explicit solutions and propose a generalization to higher dimensions. © 1994 John Wiley & Sons, Inc.
Decision algorithms for elementary topology I. Topological syllogistics with set and map constructs, connectedness, and cardinality comparison
Authors: Cantone Domenico , Cutello Vincenzo
Published: April 2007

In this paper we give a decision procedure for a topological syllogistic, denoted ℒ2,∞, involving, besides the standard Boolean set operators (∩, ∩, ′ (set complementation)) and predicates ( ϵ (membership), = (equality)), also the Kuratowski closure operator, continuous and closed maps with the notion of direct and inverse images, surjectivity and injectivity, as well as point evaluation, the singleton operator {·}, a predicate for comparing the cardinalities of two given sets, and a predicate expressing that a given set is topologically connected. Several examples are also discussed. © 1994 John Wiley & Sons, Inc.
Stability of solutions to a destabilized hopf equation
Authors: Hayes Brian T.
Published: April 2007

The Hopf, or inviscid Burgers equation, destabilized by a linear source term is studied for periodic data. It is shown that for mean‐zero initial data whose integral has a unique minimum in each period, the stationary solution is a global attractor.
The relaxation schemes for systems of conservation laws in arbitrary space dimensions
Authors: Jin Shi , Xin Zhouping
Published: April 2007

We present a class of numerical schemes (called the relaxation schemes) for systems of conservation laws in several space dimensions. The idea is to use a local relaxation approximation. We construct a linear hyperbolic system with a stiff lower order term that approximates the original system with a small dissipative correction. The new system can be solved by underresolved stable numerical discretizations without using either Riemann solvers spatially or a nonlinear system of algebraic equations solvers temporally. Numerical results for 1‐D and 2‐D problems are presented. The second‐order schemes are shown to be total variation diminishing (TVD) in the zero relaxation limit for scalar equations. ©1995 John Wiley & Sons, Inc.
Symmetry of the blow‐up set of a porous medium type equation
Authors: Gui Changfeng
Published: April 2007

We study the blow‐up set of a porous medium type equation with source. Under some technical conditions, we prove that if the blow‐up set is a bounded smooth region, then it must be a ball with a certain radius. This problem can be reduced to a sublinear elliptic equation coupled with an overdetermined boundary condition. Roughly speaking, the overdetermined boundary condition forces the domain to be a ball. Because the nonlinear term is sublinear and then non‐Lipschitz, many difficulties arise if one wants to use the moving plane method to reach the goal. In particular, the Hopf boundary lemma is not applicable to this problem. Instead, we investigate various related problems in a half space and a problem in the first quadrant of the entire space, and then use the symmetry results obtained for these problems to overcome the obstacles encountered. ©1995 John Wiley & Sons, Inc.
On the alexandroff‐bakelman‐pucci estimate and the reversed hölder inequality for solutions of elliptic and parabolic equations
Authors: Cabré Xavier
Published: April 2007

The constant appearing in the classical Alexandroff‐Bakelman‐Pucci estimate for subsolutions of second‐order uniformly elliptic equations in nondivergence form was known to depend on the diameter of the domain. Using the Krylov‐Safonov boundary weak Harnack inequality due to Trudinger, we show that the dependence on the diameter may be replaced by dependence on a more precise geometric quantity of the domain. As a consequence, we get dependence on the measure instead of the diameter. We also give new bounds for subsolutions in some unbounded domains, such as domains contained in cones.

We apply the Fabes and Stroock reversed Hölder inequality for the Green's function to improve our estimates. We also give a new proof of the reversed Hölder inequality for the Green's function based on the Krylov‐Safonov Harnack inequality.

Finally, we find new bounds for subsolutions of uniformly parabolic equations in cylindrical and noncylindrical domains. The constant in the (Alexandroff‐Bakelman‐Pucci‐) Krylov‐Tso estimate was known to depend on the diameter of the base of the cylinder. We get dependence either on the measure of the base or on the height of the cylinder. We also give bounds for subsolutions in noncylindrical domains. ©1995 John Wiley & Sons, Inc.
Compressible helical flows
Authors: Morgulis A. , Yudovich V. I. , Zaslavsky G. M.
Published: April 2007

Helical (Beltrami) flow with nonuniform coefficient is considered for the case of compressible fluid and a class of exact solutions is proposed. A paradox of helical flow is discussed and the compressibility is considered as a possible resolution of the paradox. Examples with different symmetries are given for the compressible helical flow and, in particular, the generalization of the ABC (Arnold‐Beltrami‐Childress) flow for the compressible case is proposed. ©1995 John Wiley & Sons, Inc.
Forced lattice vibrations: Part I
Authors: Deift Percy , Kriecherbauer Thomas , Venakides Stephanos
Published: April 2007

This is the First part of a two‐part series on forced lattice vibrations in which a semi‐infinite lattice of one‐dimensional particles {xn}n≧1 magnified image is driven from one end by a particle x0. This particle undergoes a given, periodically perturbed, uniform motion, x0(t) = at + h(yt), where a and γ are constants and h(·) has period 2π. For a wide variety of restoring forces F (i.e., F′ > 0), numerical calculations indicate the existence of a sequence of thresholds γ1 = γ1(a, h, F) > γ2 = γ2(a,h,F) > … > γk = γk(a,h,F) > …, γk → 0, as k → ∞. If γk > γ > γk+1, a k‐phase wave that is well described by the wave form, magnified image emerges and travels through the lattice.

The goal of this series is to describe the emergence and calculate some properties of these wave forms. In Part I the authors first consider the case where F(x) = ex (i.e., Toda forces) but h is arbitrary, and show how to compute a basic diagnostic (see J(λ), formula (1.26)) for the system in terms of the solution of an associated scalar Riemann‐Hilbert problem, once a certain finite set of numbers is known. In another direction, the authors consider the case where F(x) is restoring but arbitrary, and h is small. Here the authors prove a general result, asserting that if there exists a sufficiently ample family of traveling‐wave solutions of the doubly infinite lattice, magnified image then it is possible to construct time‐periodic k‐phase wave solutions with asymptotics in n of type (iii) for the driven system (i).

In Part II, the authors prove that sufficiently ample families of traveling‐wave solutions of the system (iv) exist in the cases γ > γ1 and γ1 > γ > γ2 for general restoring forces F. In the case with Toda forces, F(x) = ex, the authors prove that sufficiently ample families of traveling‐wave solutions.