Application of Laplace transform technique to the solution of certain third-order non-linear systems

A number of papers have appeared on the application of operational methods and in particular the Laplace transform to problems concerning non-linear systems of one kind or other. This, however, has met with only partial success in solving a class of non-linear problems as each approach has some limitations and drawbacks. In this study the approach of Baycura has been extended to certain third-order non-linear systems subjected to non-periodic excitations, as this approximate method combines the advantages of engineering accuracy with ease of application to such problems. Under non-periodic excitations the method provides a procedure for estimating quickly the maximum response amplitude, which is important from the point of view of a designer. Limitations of such a procedure are brought out and the method is illustrated by an example taken from a physical situation.

Facile synthesis, ex-vivo and in vitro screening of 3-sulfonamide derivative of 5-(4-chlorophenyl)-1-(2,4-dichlorophenyl)-4-methyl-1H-pyrazole-3-carboxylic acid piperidin-1-ylamide (SR141716) a potent CB1 receptor antagonist

Facile synthesis of biaryl pyrazole sulfonamide derivative of 5-(4-chlorophenyl)-1-(2,4-dichlorophenyl)-4-methyl-1H-pyrazole-3-carboxylic acid piperidin-1-ylamide (SR141716, 1) and an investigation of the effect of replacement of the –CO group in the compound 1 by the –SO2 group in the aminopiperidine region is reported. Primary ex-vivo pharmacological testing and in vitro screening of sulfonamide derivative 2 showed the loss of CB1 receptor antagonism.

The pulse response of non-linear third order systems

The response of a third order non-linear system subjected to a pulse excitation is analysed. A transformation of the displacement variable is effected. The transformation function chosen is the solution of the linear problem subjected to the same pulse. With this transformation the equation of motion is brought into a form in which the method of variation of parameters is applicable for the solution of the problem. The method is applied to a single axis gyrostabilized platform subjected to an exponentially decaying pulse. The analytical results are compared with digital and analog computer solutions.

The curvature invariant for a class of homogeneous operators

For an operator T in the class B-n(), introduced by Cowen and Douglas, the simultaneous unitary equivalence class of the curvature and the covariant derivatives up to a certain order of the corresponding bundle E-T determine the unitary equivalence class of the operator T. In a subsequent paper, the authors ask if the simultaneous unitary equivalence class of the curvature and these covariant derivatives are necessary to determine the unitary equivalence class of the operator T is an element of B-n(). Here we show that some of the covariant derivatives are necessary. Our examples consist of homogeneous operators in B-n(). For homogeneous operators, the simultaneous unitary equivalence class of the curvature and all its covariant derivatives at any point w in the unit disc are determined from the simultaneous unitary equivalence class at 0. This shows that it is enough to calculate all the invariants and compare them at just one point, say 0. These calculations are then carried out in number of examples. One of our main results is that the curvature along with its covariant derivative of order (0, 1) at 0 determines the equivalence class of generic homogeneous Hermitian holomorphic vector bundles over the unit disc.

Suppression of the zero-order term in off-axis digital holography through nonlinear filtering

We present experimental validation of a new reconstruction method for off-axis digital holographic microscopy (DHM). This method effectively suppresses the object autocorrelation,namely, the zero-order term,from holographic data,thereby improving the reconstruction bandwidth of complex wavefronts. The algorithm is based on nonlinear filtering and can be applied to standard DHM setups with realistic recording conditions.We study the robustness of the technique under different experimental configurations,and quantitatively demonstrate its enhancement capabilities on phase signals.

Induced higher-order aberrations after laser in situ keratomileusis (LASIK) performed with wavefront-guided IntraLase femtosecond laser in moderate to high astigmatism

Background Wavefront-guided Laser-assisted in situ keratomileusis (LASIK) is a widespread and effective surgical treatment for myopia and astigmatic correction but whether it induces higher-order aberrations remains controversial. The study was designed to evaluate the changes in higher-order aberrations after wavefront-guided ablation with IntraLase femtosecond laser in moderate to high astigmatism. Methods Twenty-three eyes of 15 patients with moderate to high astigmatism (mean cylinder, −3.22 ± 0.59 dioptres) aged between 19 and 35 years (mean age, 25.6 ± 4.9 years) were included in this prospective study. Subjects with cylinder ≥ 1.5 and ≤2.75 D were classified as moderate astigmatism while high astigmatism was ≥3.00 D. All patients underwent a femtosecond laser–enabled (150-kHz IntraLase iFS; Abbott Medical Optics Inc) wavefront-guided ablation. Uncorrected (UDVA), corrected (CDVA) distance visual acuity in logMAR, keratometry, central corneal thickness (CCT) and higher-order aberrations (HOAs) over a 6 mm pupil, were assessed before and 6 months, postoperatively. The relationship between postoperative change in HOA and preoperative mean spherical equivalent refraction, mean astigmatism, and postoperative CCT were tested. Results At the last follow-up, the mean UDVA was increased (P < 0.0001) but CDVA remained unchanged (P = 0.48) and no eyes lost ≥2 lines of CDVA. Mean spherical equivalent refraction was reduced (P < 0.0001) and was within ±0.50 D range in 61 % of eyes. The average corneal curvature was flatter by 4 D and CCT was reduced by 83 μm (P < 0.0001, for all), postoperatively. Coma aberrations remained unchanged (P = 0.07) while the change in trefoil (P = 0.047) postoperatively, was not clinically significant. The 4th order HOAs (spherical aberration and secondary astigmatism) and the HOA root mean square (RMS) increased from −0.18 ± 0.07 μm, 0.04 ± 0.03 μm and 0.47 ± 0.11 μm, preoperatively, to 0.33 ± 0.19 μm (P = 0.004), 0.21 ± 0.09 μm (P < 0.0001) and 0.77 ± 0.27 μm (P < 0.0001), six months postoperatively. The change in spherical aberration after the procedure increased with an increase in the degree of preoperative myopia. Conclusions Wavefront-guided IntraLASIK offers a safe and effective option for vision and visual function improvement in astigmatism. Although, reduction of HOA is possible in a few eyes, spherical-like aberrations are increased in majority of the treated eyes.

Clinical aspects of exhaled nitric oxide in adults : Associations with atopy, bronchial hyperresponsiveness, smoking and chronic obstruction

Measurement of fractional exhaled nitric oxide (FENO) has proven useful in assessment of patients with respiratory symptoms, especially in predicting steroid response. The objective of these studies was to clarify issues relevant for the clinical use of FENO. The influence of allergic sensitization per se on FENO in healthy asymptomatic subjects was studied, the association between airway inflammation and bronchial hyperresponsiveness (BHR) in steroid-naive subjects with symptoms suggesting asthma was examined, as well as the possible difference in this association between atopic and nonatopic subjects. Influence of smoking on FENO was compared between atopic and nonatopic steroid-naive asthmatics and healthy subjects. The short-term repeatability of FENO in COPD patients was examined in order to assess whether the degree of chronic obstruction influences the repeatability. For these purposes, we studied a random sample of 248 citizens of Helsinki, 227 army conscripts with current symptoms suggesting asthma, 19 COPD patients, and 39 healthy subjects. FENO measurement, spirometry and bronchodilatation test, structured interview. skin prick tests, and histamine and exercise challenges were performed. Among healthy subjects with no signs of airway diseases, median FENO was similar in skin prick test-positive and –negative subjects, and the upper normal limit of FENO was 30 ppb. In atopic and nonatopic subjects with symptoms suggesting asthma, FENO associated with severity of exercise- or histamine-induced BHR only in atopic patients. FENO in smokers with steroid-naive asthma was significantly higher than in healthy smokers and nonsmokers. Among atopic asthmatics, FENO was significantly lower in smokers than in nonsmokers, whereas no difference appeared among nonatopic asthmatics. The 24-h repeatability of FENO was equally good in COPD patients as in healthy subjects. These findings indicate that allergic sensitization per se does not influence FENO, supporting the view that elevated FENO indicates NO-producing airway inflammation, and that same reference range can be applied to both skin prick test-positive and -negative subjects. The significant correlation between FENO and degree of BHR only in atopic steroid-naive subjects with current asthmatic symptoms supports the view that pathogenesis of BHR in atopic asthma is strongly involved in NO-producing airway inflammation, whereas in development of BHR in nonatopic asthma other mechanisms may dominate. Attenuation of FENO only in atopic but not in nonatopic smokers with steroid-naive asthma may result from differences in mechanisms of FENO formation as well as in sensitivity of these mechanisms to smoking in atopic and nonatopic asthma. The results suggest, however, that in young adult smokers, FENO measurement may prove useful in assessment of airway inflammation. The short-term repeatability of FENO in COPD patients with moderate to very severe disease and in healthy subjects was equally good.

An investigation of first-order transition across charge ordered and ferromagnetic phases in Gd0.5Sr0.5MnO3 single crystals by magnetic and magnetotransport studies

Gadolinium strontium manganite single crystals of the composition Gd0.5Sr0.5MnO3 were grown using the optical float zone method. We report here the magnetic and magnetotransport properties of these crystals. A large magnetoresistance similar to 10(9)% was observed at 45 K under the application of a 110 kOe field. We have observed notable thermomagnetic anomalies such as open hysteresis loops across the broadened first-order transition between the charge order insulator and the ferromagnetic metallic phase while traversing the magnetic field-temperature (H-T) plane isothermally or isomagnetically. In order to discern the cause of these observed anomalies, the H-T phase diagram for Gd0.5Sr0.5MnO3 is formulated using the magnetization-field (M-H), magnetization-temperature (M-T) and resistance-temperature (R-T) measurements. The temperature dependence of the critical field (i.e. H-up, the field required for transformation to the ferromagnetic metallic phase) is non-monotonic. We note that the non-monotonic variation of the supercooling limit is anomalous according to the classical concepts of the first-order phase transition. Accordingly, H-up values below similar to 20 K are unsuitable to represent the supercooling limit. It is possible that the nature of the metastable states responsible for the observed open hysteresis loops is different from that of the supercooled ones.

Charge-order-driven multiferroic properties of Y1-xCaxMnO3

Dielectric measurements on the charge-ordered insulators, Y1-xCaxMnO3 (x = 0.4. 0.45 and 0.5), show maxima in the dielectric constant around the charge ordering transition temperature while magnetic measurements show the presence of weak ferromagnetic interactions at low temperatures. Besides the magnetic field dependence of the dielectric constant, these manganites also exhibit second harmonic generation. Thus, the charge-ordered Y1-xCaxMnO3 compositions are multiferroic and magnetoelectric, in accordance with theoretical predictions. Magnetoelectric properties are retained in small particles of Y0.5Ca0.5MnO3. (C) 2008 Elsevier Ltd. All rights reserved.

A Combinatorial Optimization Problem for High Order PODs with Few Sensors

Experimental characterization of high dimensional dynamic systems sometimes uses the proper orthogonal decomposition (POD). If there are many measurement locations and relatively fewer sensors, then steady-state behavior can still be studied by sequentially taking several sets of simultaneous measurements. The number required of such sets of measurements can be minimized if we solve a combinatorial optimization problem. We aim to bring this problem to the attention of engineering audiences, summarize some known mathematical results about this problem, and present a heuristic (suboptimal) calculation that gives reasonable, if not stellar, results.

Energy identities in water wave theory for free-surface boundary condition with higher-order derivatives

A modified form of Green's integral theorem is employed to derive the energy identity in any water wave diffraction problem in a single-layer fluid for free-surface boundary condition with higher-order derivatives. For a two-layer fluid with free-surface boundary condition involving higher-order derivatives, two forms of energy identities involving transmission and reflection coefficients for any wave diffraction problem are also derived here by the same method. Based on this modified Green's theorem, hydrodynamic relations such as the energy-conservation principle and modified Haskind–Hanaoka relation are derived for radiation and diffraction problems in a single as well as two-layer fluid.

Constructing commutative semifields of square order

The projection construction has been used to construct semifields of odd characteristic using a field and a twisted semifield [Commutative semi-fields from projection mappings, Designs, Codes and Cryptography, 61 (2011), 187{196]. We generalize this idea to a projection construction using two twisted semifields to construct semifields of odd characteristic. Planar functions and semifields have a strong connection so this also constructs new planar functions.

Polymer melt dynamics: Microscopic roots of fractional viscoelasticity

The rheological properties of polymer melts and other complex macromolecular fluids are often successfully modeled by phenomenological constitutive equations containing fractional differential operators. We suggest a molecular basis for such fractional equations in terms of the generalized Langevin equation (GLE) that underlies the renormalized Rouse model developed by Schweizer [J. Chem. Phys. 91, 5802 (1989)]. The GLE describes the dynamics of the segments of a tagged chain under the action of random forces originating in the fast fluctuations of the surrounding polymer matrix. By representing these random forces as fractional Gaussian noise, and transforming the GLE into an equivalent diffusion equation for the density of the tagged chain segments, we obtain an analytical expression for the dynamic shear relaxation modulus G(t), which we then show decays as a power law in time. This power-law relaxation is the root of fractional viscoelastic behavior.