Interval Oscillation for Second Order Nonlinear Differential Equations with a Damping Term

2000 Mathematics Subject Classification: 34C10, 34C15.

A fast two-grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half-plane

We consider the numerical treatment of second kind integral equations on the real line of the form ∅(s) = ∫_(-∞)^(+∞)▒〖κ(s-t)z(t)ϕ(t)dt,s=R〗 (abbreviated ϕ= ψ+K_z ϕ) in which K ϵ L_1 (R), z ϵ L_∞ (R) and ψ ϵ BC(R), the space of bounded continuous functions on R, are assumed known and ϕ ϵ BC(R) is to be determined. We first derive sharp error estimates for the finite section approximation (reducing the range of integration to [-A, A]) via bounds on (1-K_z )^(-1)as an operator on spaces of weighted continuous functions. Numerical solution by a simple discrete collocation method on a uniform grid on R is then analysed: in the case when z is compactly supported this leads to a coefficient matrix which allows a rapid matrix-vector multiply via the FFT. To utilise this possibility we propose a modified two-grid iteration, a feature of which is that the coarse grid matrix is approximated by a banded matrix, and analyse convergence and computational cost. In cases where z is not compactly supported a combined finite section and two-grid algorithm can be applied and we extend the analysis to this case. As an application we consider acoustic scattering in the half-plane with a Robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied. Our final result is that if z (related to the boundary impedance in the application) takes values in an appropriate compact subset Q of the complex plane, then the difference between ϕ(s)and its finite section approximation computed numerically using the iterative scheme proposed is ≤C_1 [kh log⁡〖(1⁄kh)+(1-Θ)^((-1)⁄2) (kA)^((-1)⁄2) 〗 ] in the interval [-ΘA,ΘA](Θ<1) for kh sufficiently small, where k is the wavenumber and h the grid spacing. Moreover this numerical approximation can be computed in ≤C_2 N log⁡N operations, where N = 2A/h is the number of degrees of freedom. The values of the constants C1 and C2 depend only on the set Q and not on the wavenumber k or the support of z.

Randomized phase II study of cetuximab plus cisplatin/vinorelbine compared with cisplatin/vinorelbine alone as first-line therapy in EGFR-expressing advanced non-small-cell lung cancer

Background: The Lung Cancer Cetuximab Study is an open-label, randomized phase II pilot study of cisplatin and vinorelbine combined with the epidermal growth factor receptor (EGFR)-targeted monoclonal antibody cetuximab versus cisplatin and vinorelbine alone, in patients with advanced EGFR-expressing, non-small-cell lung cancer (NSCLC). End points of the study are activity, safety and pharmacokinetics. Patients and methods: Following randomization, for a maximum of eight cycles, patients received three-weekly cycles of cisplatin (80 mg/m2, day 1) and vinorelbine (25 mg/m2 on days 1 and 8) alone or following cetuximab treatment (initial dose 400 mg/m, followed by 250 mg/m2 weekly thereafter). Results: Eighty-six patients were randomly allocated to the study (43 per arm). Confirmed response rates were 28% in the cisplatin/vinorelbine arm (A) and 35% in the cetuximab plus cisplatin/vinorelbine arm (B). Median progression-free survival (PFS) was 4.6 months in arm A and 5.0 months in arm B, with PFS rates at 12 months of 0% and 15%, respectively. Median survival was 7.3 months in arm A and 8.3 months in arm B. The 24-month survival rates were 0% and 16%, respectively. The cetuximab combination was well tolerated. Conclusion: In the first-line treatment of advanced NSCLC, the combination of cetuximab plus cisplatin/vinorelbine demonstrated an acceptable safety profile and the potential to improve activity over cisplatin/vinorelbine alone. © 2007 European Society for Medical Oncology.

Investigation of movement and factors influencing post-release survival of line-caught coral reef fish using recreational tag-recapture data

Six species of line-caught coral reef fish (Plectropomus spp., Lethrinus miniatus, Lethrinus laticaudis, Lutjanus sebae, Lutjanus malabaricus and Lutjanus erythropterus) were tagged by members of the Australian National Sportsfishing Association (ANSA) in Queensland between 1986 and 2003. Of the 14,757 fish tagged, 1607 were recaptured and we analysed these data to describe movement and determine factors likely to impact release survival. All species were classified as residents since over 80% of recaptures for each species occurred within 1 km of the release site. Few individuals (range 0.8-5%) were recaptured more than 20 km from their release point. L. sebae had a higher recapture rate (19.9%) than the other species studied (range 2.1-11.7%). Venting swimbladder gases, regardless of whether or not fish appeared to be suffering from barotrauma, significantly enhanced (P < 0.05) the survival of L. sebae and L. malabaricus but had no significant effect (P > 0.05) on L. erythropterus. The condition of fish on release, subjectively assessed by anglers, was only a significant effect on recapture rate for L. sebae where fish in "fair" condition had less than half the recapture rate of those assessed as in "excellent" or "good" condition. The recapture rate of L. sebae and L. laticaudis was significantly (P < 0.05) affected by depth with recapture rate declining in depths exceeding 30 m. Overall, the results showed that depth of capture, release condition and treatment for barotrauma influenced recapture rate for some species but these effects were not consistent across all species studied. Recommendations were made to the ANSA tagging clubs to record additional information such as injury, hooking location and hook type to enable a more comprehensive future assessment of the factors influencing release survival.

Application of Haar functions for transmission line and transformer differential protection

The development of algorithms, based on Haar functions, for extracting the desired frequency components from transient power-system relaying signals is presented. The applications of these algorithms to impedance detection in transmission line protection and to harmonic restraint in transformer differential protection are discussed. For transmission line protection, three modes of application of the Haar algorithms are described: a full-cycle window algorithm, an approximate full-cycle window algorithm, and a half-cycle window algorithm. For power transformer differential protection, the combined second and fifth harmonic magnitude of the differential current is compared with that of fundamental to arrive at a trip decision. The proposed line protection algorithms are evaluated, under different fault conditions, using realistic relaying signals obtained from transient analysis conducted on a model 400 kV, 3-phase system. The transformer differential protection algorithms are also evaluated using a variety of simulated inrush and internal fault signals.

The line transect method for estimating densities of large mammals in a tropical deciduous forest: An evaluation of models and field experiments

We have evaluated techniques of estimating animal density through direct counts using line transects during 1988-92 in the tropical deciduous forests of Mudumalai Sanctuary in southern India for four species of large herbivorous mammals, namely, chital (Axis axis), sambar (Cervus unicolor), Asian elephant (Elephas maximus) and gaur (Bos gauras). Density estimates derived from the Fourier Series and the Half-Normal models consistently had the lowest coefficient of variation. These two models also generated similar mean density estimates. For the Fourier Series estimator, appropriate cut-off widths for analysing line transect data for the four species are suggested. Grouping data into various distance classes did not produce any appreciable differences in estimates of mean density or their variances, although model fit is generally better when data are placed in fewer groups. The sampling effort needed to achieve a desired precision (coefficient of variation) in the density estimate is derived. A sampling effort of 800 km of transects returned a 10% coefficient of variation on estimate for chital; for the other species a higher effort was needed to achieve this level of precision. There was no statistically significant relationship between detectability of a group and the size of the group for any species. Density estimates along roads were generally significantly different from those in the interior af the forest, indicating that road-side counts may not be appropriate for most species.

Line removal and restoration of handwritten strokes

In document images, we often find printed lines over-lapping with hand written elements especially in case of signatures. Typical examples of such images are bank cheques and payment slips. Although the detection and removal of the horizontal lines has been addressed, the restoration of the handwritten area after removal of lines, persists to be a problem of interest. lit this paper, we propose a method for line removal and restoration of the erased areas of the handwritten elements. Subjective evaluation of the results have been conducted to analyze the effectiveness of the proposed method. The results are promising with an accuracy of 86.33%. The entire Process takes less than half a second for completion on a 2.4 GHz 512 MB RAM Pentium IV PC for a document image.

Performance of Tuned Half-Wave-Length Power Transmission Lines

The basic concepts of tuned half-wave lines were covered by Hubert and Gent [1]. In this paper the problem of overvoltages during faults and the stability of the system incorporating such tuned lines are discussed. The type of tuning bank and the line arrangements that will be satisfactory from the point of view of stability are suggested. The behavior of a line tuned by distributed capacitor is analyzed, and its performance is compared with the other type of tuned line.

Analysis of Natural Half-Wave-Length Power Transmission Lines

This paper provides additional theoretical information on half-wave-length power transmission. The analysis is rendered more general by consideration of a natural half-wave line instead of a short line tuned to half-wave. The effects of line loading and its power factor on the voltage and current profiles of the line and ganerator excitation have been included. Some of the operating problems such as charging of the line and synchronization of the half-wave system are also discussed. The inevitability of power-frequency overvoltages during faults is established. Stability studies have indicated that the use of switching stations is not beneficial. Typical swing curves are also presented.

Linewidths and line shapes in the vicinity of graphene

It is well known that graphene, by virtue of its pi-cloud delocalization, has a continuum of electronic energy states and thus behaves nearly like a metal. Instances involving quenching of electronic energy excitation in fluorophores placed in the proximity of graphene sheets are well documented. In this paper, we perform theoretical investigations on the broadening of vibrational and electronic transitions in the vicinity of graphene. We find that for CO vibrations in the vicinity of undoped graphene, the broadening at a distance of 5 angstrom is similar to 0.008 cm(-1)((kappa) over tilde = 2, (kappa) over tilde being the effective dielectric constant). In comparison, for electronic transitions, the linewidth is much larger, being of the order of several cm(-1). Also, if the transition dipole were parallel to the graphene sheet, the linewidth would be reduced to half the value for the case where it is perpendicular, an observation which should be easy to check experimentally for electronic transitions. This should be observable for the f - f transitions (which are rather narrow) of Lanthanide complexes placed within a distance of a few nanometers from a graphene sheet. Further the linewidth would have a (distance)(-4) dependence as one varies the distance from graphene. (C) 2014 AIP Publishing LLC.

Seleno-Nucleobases and Their Water-Soluble Ruthenium-Arene Half-Sandwich Complexes: Chemistry and Biological Activity

Half-sandwich organometallic ruthenium complexes of seleno-nucleobases, 3 and 4, were synthesized and characterized. The structures of both complexes were determined by X-ray crystallography and are the first crystal structures of ruthenium complexes with seleno-nucleobases. Interestingly, 3 self-assembles aided by adventitious water in DMF to give a tetranuclear square 3a center dot 6H(2)O. Complex 4 is active against Jurkat and Molt-4 cell lines but inactive against the K562 cell line, whereas 3 is completely inactive against all three cell lines. The free ligand 6-selenopurine (1) and 6-selenoguanine (2) are highly active against these cell lines. Compound 2, like its thio analogue, is unstable under UVA light, whereas 4 is stable under similar conditions, which suggests that the ruthenium complex could reduce problems associated with the instability of the free ligand, 2, under irradiation.

Phase diagram of the half-filled ionic Hubbard model

We study the phase diagram of the ionic Hubbard model (IHM) at half filling on a Bethe lattice of infinite connectivity using dynamical mean-field theory (DMFT), with two impurity solvers, namely, iterated perturbation theory (IPT) and continuous time quantum Monte Carlo (CTQMC). The physics of the IHM is governed by the competition between the staggered ionic potential Delta and the on-site Hubbard U. We find that for a finite Delta and at zero temperature, long-range antiferromagnetic (AFM) order sets in beyond a threshold U = U-AF via a first-order phase transition. For U smaller than U-AF the system is a correlated band insulator. Both methods show a clear evidence for a quantum transition to a half-metal (HM) phase just after the AFM order is turned on, followed by the formation of an AFM insulator on further increasing U. We show that the results obtained within both methods have good qualitative and quantitative consistency in the intermediate-to-strong-coupling regime at zero temperature as well as at finite temperature. On increasing the temperature, the AFM order is lost via a first-order phase transition at a transition temperature T-AF(U,Delta) or, equivalently, on decreasing U below U-AF(T,Delta)], within both methods, for weak to intermediate values of U/t. In the strongly correlated regime, where the effective low-energy Hamiltonian is the Heisenberg model, IPT is unable to capture the thermal (Neel) transition from the AFM phase to the paramagnetic phase, but the CTQMC does. At a finite temperature T, DMFT + CTQMC shows a second phase transition (not seen within DMFT + IPT) on increasing U beyond U-AF. At U-N > U-AF, when the Neel temperature T-N for the effective Heisenberg model becomes lower than T, the AFM order is lost via a second-order transition. For U >> Delta, T-N similar to t(2)/U(1 - x(2)), where x = 2 Delta/U and thus T-N increases with increase in Delta/U. In the three-dimensional parameter space of (U/t, T/t, and Delta/t), as T increases, the surface of first-order transition at U-AF(T,Delta) and that of the second-order transition at U-N(T,Delta) approach each other, shrinking the range over which the AFM order is stable. There is a line of tricritical points that separates the surfaces of first- and second-order phase transitions.

Asymptotic analysis based on K-S constitutive law for a rubber wedge compressed by a line load at its tip

In the present paper, a rubber wedge compressed by a line load at its tip is asymptotically analyzed using a special constitutive law proposed by Knowles and Sternberg (K-S elastic law) [J. Elasticity 3 (1973) 67]. The method of dividing sectors proposed by Gao [Theoret. Appl. Fract, Mech. 14 (1990) 219] is used. Domain near the wedge tip can be divided into one expanding sector and two narrowing sectors. Asymptotic equations of the strain-stress field near the wedge tip are derived and solved numerically. The deformation pattern near a wedge tip is completely revealed. A special case. i.e. a half space compressed by a line load is solved while the wedge angle is pi.

Split-aperture laser pulse compressor design tolerant to alignment and line-density differences

We introduce a four-pass laser pulse compressor design based on two grating apertures with two gratings per aperture that is tolerant to some alignment errors and, importantly, to grating-to-grating period variations. Each half-beam samples each grating in a diamond-shaped compressor that is symmetric about a central bisecting plane. For any given grating, the two half-beams impinge on opposite sides of its surface normal. It is shown that the two split beams have no pointing difference from paired gratings with different periods. Furthermore, no phase shift between half-beams is incurred as long as the planes containing a grating line and the surface normal for each grating of the pair are parallel. For grating pairs satisfying this condition, gratings surfaces need not be on the same plane, as changes in the gap between the two can compensate to bring the beams back in phase. © 2008 Optical Society of America.