An Alternate Method for Fourier Transform Infrared (FTIR) Spectroscopic Determination of Soil Nitrate Using Derivative Analysis and Sample Treatments

This study aimed at examining effective sample treatments and spectral processing for an alternate method of soil nitrate determination using the attenuated total reflectance (ATR) of Fourier transform infrared (FTIR) spectroscopy. Prior to FTIR measurements, soil samples were prepared as paste to enhance adhesion between the ATR crystal and sample. The similar nitrate peak heights of soil pastes and their supernatants indicated that the nitrate in the liquid portion of the soil paste mainly responded to the FTIR signal. Using a 0.01-M CaSO4 solution for the soil paste, which has no interference bands in the characteristic spectra of the analyte, increased the concentration of the nitrates to be measured. Second-order derivatives were used in the prediction model to minimize the interference effects and enhance the performance. The second-order derivative spectra contained a unique nitrate peak in a range of 1,400-1,200 cm(-1) without interference of carbonate. A partial least square regression model using second-order derivative spectra performed well (R (2) = 0.995, root mean square error (RMSE) = 23.5, ratio of prediction to deviation (RPD) = 13.8) on laboratory samples. Prediction results were also good for a test set of agricultural field soils with a CaCO3 concentration of 6% to 8% (R (2) = 0.97, RMSE = 18.6, RPD = 3.5). Application of the prediction model based on soil paste samples to nitrate stock solution resulted in an increased RMSE (62.3); however, validation measures were still satisfactory (R (2) = 0.99, RPD = 3.0

Topological Test Spaces

A test space is the set of outcome-sets associated with a collection of experiments. This notion provides a simple mathematical framework for the study of probabilistic theories -- notably, quantum mechanics -- in which one is faced with incommensurable random quantities. In the case of quantum mechanics, the relevant test space, the set of orthonormal bases of a Hilbert space, carries significant topological structure. This paper inaugurates a general study of topological test spaces. Among other things, we show that any topological test space with a compact space of outcomes is of finite rank. We also generalize results of Meyer and Clifton-Kent by showing that, under very weak assumptions, any second-countable topological test space contains a dense semi-classical test space.Comment: 12 pp., LaTeX 2e. To appear in Int. J. Theor. Phy

Blowup Criterion for the Compressible Flows with Vacuum States

We prove that the maximum norm of the deformation tensor of velocity gradients controls the possible breakdown of smooth(strong) solutions for the 3-dimensional compressible Navier-Stokes equations, which will happen, for example, if the initial density is compactly supported \cite{X1}. More precisely, if a solution of the compressible Navier-Stokes equations is initially regular and loses its regularity at some later time, then the loss of regularity implies the growth without bound of the deformation tensor as the critical time approaches. Our result is the same as Ponce's criterion for 3-dimensional incompressible Euler equations (\cite{po}). Moreover, our method can be generalized to the full Compressible Navier-Stokes system which improve the previous results. In addition, initial vacuum states are allowed in our cases.Comment: 17 page

Second Order General Slow-Roll Power Spectrum

Recent combined results from the Wilkinson Microwave Anisotropy Probe (WMAP) and Sloan Digital Sky Survey (SDSS) provide a remarkable set of data which requires more accurate and general investigation. Here we derive formulae for the power spectrum P(k) of the density perturbations produced during inflation in the general slow-roll approximation with second order corrections. Also, using the result, we derive the power spectrum in the standard slow-roll picture with previously unknown third order corrections.Comment: 11 pages, 1 figure ; A typo in Eq. (38) is fixed ; References expanded and a note adde

A New delta N Formalism for Multi-Component Inflation

The delta N formula that relates the final curvature perturbation on comoving slices to the inflaton perturbation on flat slices after horizon crossing is a powerful and intuitive tool to compute the curvature perturbation spectrum from inflation. However, it is customarily assumed further that the conventional slow-roll condition is satisfied, and satisfied by all components, during horizon crossing. In this paper, we develop a new delta N formalism for multi-component inflation that can be applied in the most general situations. This allows us to generalize the idea of general slow-roll inflation to the multi-component case, in particular only applying the general slow-roll condition to the relevant component. We compute the power spectrum of the curvature perturbation in multi-component general slow-roll inflation, and find that under quite general conditions it is invertible.Comment: 24 pages, no figur

A Blow-Up Criterion for Classical Solutions to the Compressible Navier-Stokes Equations

In this paper, we obtain a blow up criterion for classical solutions to the 3-D compressible Naiver-Stokes equations just in terms of the gradient of the velocity, similar to the Beal-Kato-Majda criterion for the ideal incompressible flow. In addition, initial vacuum is allowed in our case.Comment: 25 page

Impact of cyclooxygenase inhibitors in the Women's Health Initiative hormone trials: secondary analysis of a randomized trial.

OBJECTIVES: We evaluated the hypothesis that cyclooxygenase (COX) inhibitor use might have counteracted a beneficial effect of postmenopausal hormone therapy, and account for the absence of cardioprotection in the Women's Health Initiative hormone trials. Estrogen increases COX expression, and inhibitors of COX such as nonsteroidal anti-inflammatory agents appear to increase coronary risk, raising the possibility of a clinically important interaction in the trials. DESIGN: The hormone trials were randomized, double-blind, and placebo-controlled. Use of nonsteroidal anti-inflammatory drugs was assessed at baseline and at years 1, 3, and 6. SETTING: The Women's Health Initiative hormone trials were conducted at 40 clinical sites in the United States. PARTICIPANTS: The trials enrolled 27,347 postmenopausal women, aged 50-79 y. INTERVENTIONS: We randomized 16,608 women with intact uterus to conjugated estrogens 0.625 mg with medroxyprogesterone acetate 2.5 mg daily or to placebo, and 10,739 women with prior hysterectomy to conjugated estrogens 0.625 mg daily or placebo. OUTCOME MEASURES: Myocardial infarction, coronary death, and coronary revascularization were ascertained during 5.6 y of follow-up in the estrogen plus progestin trial and 6.8 y of follow-up in the estrogen alone trial. RESULTS: Hazard ratios with 95% confidence intervals were calculated from Cox proportional hazard models stratified by COX inhibitor use. The hazard ratio for myocardial infarction/coronary death with estrogen plus progestin was 1.13 (95% confidence interval 0.68-1.89) among non-users of COX inhibitors, and 1.35 (95% confidence interval 0.86-2.10) among continuous users. The hazard ratio with estrogen alone was 0.92 (95% confidence interval 0.57-1.48) among non-users of COX inhibitors, and 1.08 (95% confidence interval 0.69-1.70) among continuous users. In a second analytic approach, hazard ratios were calculated from Cox models that included hormone trial assignment as well as a time-dependent covariate for medication use, and an interaction term. No significant interaction was identified. CONCLUSIONS: Use of COX inhibitors did not significantly affect the Women's Health Initiative hormone trial results

Essential nonlinearities in hearing

Our hearing organ, the cochlea, evidently poises itself at a Hopf bifurcation to maximize tuning and amplification. We show that in this condition several effects are expected to be generic: compression of the dynamic range, infinitely shrap tuning at zero input, and generation of combination tones. These effects are "essentially" nonlinear in that they become more marked the smaller the forcing: there is no audible sound soft enough not to evoke them. All the well-documented nonlinear aspects of hearing therefore appear to be consequences of the same underlying mechanism.Comment: 4 pages, 3 figure