受迫耗散Boussinesq方程的可积性质和孤波解的探讨

考虑到耗散效应和地形外力,Rossby波的振幅可由受迫耗散Boussinesq方程来描述.当包含这两项时,模型比较复杂,不具有Painleve性质.通过将模型双线性化,双线性方法是一个可寻找孤波解和B(a|¨)cklund变换的方法.通过截断的Painleve展开式,得到了将方程双线性化的合适的因变量变换.然后得到了受迫耗散Boussinesq方程的单孤波解和B(a|¨)cklund变换.     

Reply to Comments on “Non-Darcian Forced Convection Flow of Viscous Dissipating Fluid over a Flat Plate Embedded in a Porous Medium”

In this note, we reply to the comments by Rees and Magyari (2007) on our article (Aydin and Kaya 2007). They mainly stated that the thermal boundary conditions we defined at the edge of the boundary layer were incompatible with the energy equation. This is questionable and therefore we will discuss it below. They disclosed that our results were in error. However, this is quite misleading. Scientifically, they cannot reach such a conclusion without comparing our results with what they thought to be correct. In fact, this misleading and unproven statement will be shown not to be correct in the following.     

强迫二阶非线性泛函微分方程解的振动性与渐近性

本文讨论强迫二阶非线性泛函微分方程（ａ（ｔ）ｘ＇（ｔ））＇＋ｐ（ｔ）ｆ（ｘ（ｔ），ｘ（ｑ（ｔ）））＝ｒ（ｔ）解的振动性与渐近性。所得结论改进和推广了已知的一些结果。     

Estimation of forced-selection word intelligibility by comparing objective distances between candidates

We proposed and evaluated an estimation method for the forced selection speech intelligibility tests. Our proposal takes into account the forced selection manner of the Diagnostic Rhyme Test (DRT), which forces selection from a pair of rhyming words. A distance measure is calculated between the test word and the two candidate words, respectively, and the distance is compared to select the most likely word. We compared two distance measures. The first objective distance measure used here was based on the Articulation index Band Correlation (ABC). The ABC is the correlation of time–frequency (T–F) patterns between the test word and the template word speech of the two words in the candidate word pair. The word with the higher correlation was decided to be the likely candidate word. The T–F pattern was calculated in the Articulation Index (AI) bands, and the correlation was calculated between the corresponding bands of the test and candidate word sample. In order to estimate the intelligibility, we calculate the ratio of the number of bands in which higher correlation is seen for the correct word vs. the total number of bands (named ABC-est). This ratio quantifies how well the test word matches the correct word in the word pair. For the second objective distance, we used a measure based on the frequency-weighted segmental SNR (fwSNR_seg). Segmental SNR (SNR_seg) was calculated in AI bands, and compared among the candidate word templates. We then calculated the frequency-weighted ratio of the number of bands in which higher SNR_seg was observed for the correct word vs. the total number of bands (named fwSNR_seg-est), again to quantify how well the test word matches the selected candidate word in the pair. We estimated a logistic mapping function from the above two ratios to intelligibility scores using speech mixed with known noise. The mapping functions were then used to estimate the intelligibility of speech mixed with unknown noise. This estimation was compared to another measure that we previously evaluated, the conventional fwSNR_seg, which directly maps the measure to intelligibility. Both proposed measures were proven to be significantly more accurate than conventional fwSNR_seg. For most cases, the accuracy was comparable between the two proposed distance measures, ABC-est and fwSNR_seg-est, with the latter showing correlation between the subjective and estimated intelligibility as high as 0.97, and root mean square as low as 0.11 for one of the test sets, but not as accurate for other sets. The ABC-est showed more stable accuracy for all sets. However, both measures show practical accuracies in all conditions tested. Thus, it should be possible to “screen” the intelligibility in many of the noise conditions to be tested, and cut down on the scale of the subjective test needed.     

Isolation and characterization of degradation products of citalopram and process-related impurities using RP-HPLC

A reversed-phase high-performance liquid chromatographic method for simultaneous separation and determination of citalopram hydrobromide and its process impurities in bulk drugs and pharmaceutical formulations was developed. The separation was accomplished on an Inertsil ODS 3V (250x4.6 mm; particle size 5 mum) column using 0.3% diethylamine (pH = 4.70) and methanol/acetonitrile (55:45 v/v) as mobile phase in a gradient elution mode. The eluents were monitored by a photodiode array detector set at 225 nm. The chromatographic behavior of all the related substances was examined under variable conditions of different solvents, buffer concentrations, and pH. The method was validated in terms of accuracy, precision, and linearity. The method could be of use not only for rapid and routine evaluation of the quality of citalopram in bulk drug manufacturing units but also for the detection of its impurities in pharmaceutical formulations. Three unknown impurities were consistently observed during the analysis of different batches of citalopram. Forced degradation of citalopram was carried out under thermal, photo, acidic, alkaline, and peroxide conditions. The degradation products and unknown impurities were isolated and characterized by ESI-MS/MS, (1)H NMR, and FT-IR spectroscopy.     

Surface effect on the nonlinear forced vibration of cantilevered nanobeams

The nonlinear forced vibration behavior of a cantilevered nanobeam is investigated in this paper, essentially considering the effect due to the surface elastic layer. The governing equation of motion for the nano-cantilever is derived, with consideration of the geometrical nonlinearity and the effects of additional flexural rigidity and residual stress of the surface layer. Then, the nonlinear partial differential equation (PDE) is discretized into a set of nonlinear ordinary differential equations (ODEs) by means of the Galerkin’s technique. It is observed that surface effects on the natural frequency of the nanobeam is of significance, especially for the case when the aspect ratio of the nanobeam is large. The nonlinear resonant dynamics of the nanobeam system is evaluated by varying the excitation frequency around the fundamental resonance, showing that the nanobeam would display hardening-type behavior and hence the frequency-response curves bend to the right in the presence of positive residual surface stress. However, with the negative residual surface stress, this hardening-type behavior can be shifted to a softening-type one which becomes even more evident with increase of the aspect ratio parameter. It is also demonstrated that the combined effects of the residual stress and aspect ratio on the maximum amplitude of the nanobeam may be pronounced.     

Oscillation criteria for second order forced ordinary differential equations with mixed nonlinearities

We present new oscillation criteria for the second order forced ordinary differential equation with mixed nonlinearities:

     

Consideration of the masses of helical springs in forced vibrations of damped combined systems

The common point about many systems modeled as Bernoulli-Euler beams with attachments is that the own masses of the helical springs are neglected. Some researchers accounted for the masses of the springs during free vibrations of those systems. Further to these studies, the present study deals with the investigation of the effect of not taking into account the masses of the helical springs in damped combined systems during their forced vibrations. It is shown that the spring mass effect may be important in regions near to the resonance frequencies. Further, this effect influences the phase angles more than the amplitudes.     

Interval oscillation criteria for a forced second-order nonlinear differential equations with damping

In this paper, we are concerned with the oscillations in a class of forced second-order differential equations with nonlinear damping terms. By using classical variational principle and averaging technique, several new interval oscillation criteria for the equations are established, which improve and extend some known results. Example is also given to illustrate the results.     

FEM modelling of the time-harmonic dynamical stress field problem for a pre-stressed plate-strip resting on a rigid foundation

In this paper, the FEM modelling of the time-harmonic dynamical stress field problem for the pre-stressed plate-strip with finite length resting on a rigid foundation is developed. The mathematical formulation of the considered problem is made by the use of the equations and relations of the Three-dimensional Linearized Theory of Elastic Waves in Initially Stressed Bodies. The proposed modelling is tested on the concrete problems as an example. The numerical results testing the validity of the developed FEM modelling are presented. Moreover, the numerical results attained for the various values of the problem parameters are also presented.