Parameter determination of a thermal desorption model

A new method for the analysis of thermal desorption spectra is presented, based on the experimental peak maximum functions for temperatureT _m(β) and pressureP _m(β) and a rigorous mathematical treatment. The resonant heating rate β_r is determined, satisfyingT _m(β_r)=T _r, whereT _r is the resonant temperature defined byA exp(−E _d/(RT _r))=1. Desorption energyE _d and frequency factorA can be determined simultaneously with relatively high robustness towards statistical experimental errors as demonstrated by computer-simulated thermal desorption spectra.     

Use of biopartitioning micellar chromatography and RP-HPLC for the determination of blood–brain barrier penetration of α-adrenergic/imidazoline receptor ligands,and QSPR analysis

For this study, 31 compounds, including 16 imidazoline/α-adrenergic receptor (IRs/α-ARs) ligands and 15 central nervous system (CNS) drugs, were characterized in terms of the retention factors (k) obtained using biopartitioning micellar and classical reversed phase chromatography (log k_BMC and log k_wRP, respectively). Based on the retention factor (log k_wRP) and slope of the linear curve (S) the isocratic parameter (φ₀) was calculated. Obtained retention factors were correlated with experimental log BB values for the group of examined compounds. High correlations were obtained between logarithm of biopartitioning micellar chromatography (BMC) retention factor and effective permeability (r(log k_BMC/log BB): 0.77), while for RP-HPLC system the correlations were lower (r(log k_wRP/log BB): 0.58; r(S/log BB): –0.50; r(φ₀/P_e): 0.61). Based on the log k_BMC retention data and calculated molecular parameters of the examined compounds, quantitative structure–permeability relationship (QSPR) models were developed using partial least squares, stepwise multiple linear regression, support vector machine and artificial neural network methodologies. A high degree of structural diversity of the analysed IRs/α-ARs ligands and CNS drugs provides wide applicability domain of the QSPR models for estimation of blood–brain barrier penetration of the related compounds.     

Isopiestic Determination of the Osmotic and Activity Coefficients of K<Subscript>2</Subscript>HPO<Subscript>4</Subscript>(aq), Including Saturated and Supersaturated Solutions,at <Emphasis Type="Italic">T</Emphasis>=298.15 K

The osmotic coefficients of K₂HPO₄(aq) have been measured at T=298.15 K by the isopiestic vapor pressure method over the range of molalities from 1.3846 mol⋅kg⁻¹ to 13.939 mol⋅kg⁻¹ (oversaturation) with CaCl₂(aq) as the reference solution. The molalities and osmotic coefficients of saturated solutions in equilibrium with K₂HPO₄⋅xH₂O(cr) were measured simultaneously by the same method. Available literature osmotic coefficients of K₂HPO₄(aq) at T=298.15 K, and our new experimental data, were combined and modeled using an extended form of Pitzer’s equation and the Clegg-Pitzer-Brimblecombe equation based on the mole-fraction-composition scale. These equations were used to calculate the activity coefficients of K₂HPO₄(aq) at T=298.15 K.     

Analysis of a fast method for solving the high frequency Helmholtz equation in one dimension

We propose and analyze a fast method for computing the solution of the high frequency Helmholtz equation in a bounded one-dimensional domain with a variable wave speed function. The method is based on wave splitting. The Helmholtz equation is split into one-way wave equations with source functions which are solved iteratively for a given tolerance. The source functions depend on the wave speed function and on the solutions of the one-way wave equations from the previous iteration. The solution of the Helmholtz equation is then approximated by the sum of the one-way solutions at every iteration. To improve the computational cost, the source functions are thresholded and in the domain where they are equal to zero, the one-way wave equations are solved with geometrical optics with a computational cost independent of the frequency. Elsewhere, the equations are fully resolved with a Runge–Kutta method. We have been able to show rigorously in one dimension that the algorithm is convergent and that for fixed accuracy, the computational cost is asymptotically just O(w^{1/ p})\mathcal {O}(\omega^{1/ p}) for a pth order Runge–Kutta method, where ω is the frequency. Numerical experiments indicate that the growth rate of the computational cost is much slower than a direct method and can be close to the asymptotic rate.     

Diagnosis of suspicious breast lesions using an empirical mathematical model for dynamic contrast-enhanced MRI

The purpose of this study was to test whether an empirical mathematical model (EMM) of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) can distinguish between benign and malignant breast lesions. A modified clinical protocol was used to improve the sampling of contrast medium uptake and washout. T(1)-weighted DCE magnetic resonance images were acquired at 1.5 T for 22 patients before and after injection of Gd-DTPA. Contrast medium concentration as a function of time was calculated over a small region of interest containing the most rapidly enhancing pixels. Then the curves were fitted with the EMM, which accurately described contrast agent uptake and washout. Results demonstrate that benign lesions had uptake (P<2.0 x 10(-5)) and washout (P<.01) rates of contrast agent significantly slower than those of malignant lesions. In addition, secondary diagnostic parameters, such as time to peak of enhancement, enhancement slope at the peak and curvature at the peak of enhancement, were derived mathematically from the EMM and expressed in terms of primary parameters. These diagnostic parameters also effectively differentiated benign from malignant lesions (P<.03). Conventional analysis of contrast medium dynamics, using a subjective classification of contrast medium kinetics in lesions as "washout," "plateau" or "persistent" (sensitivity=83%, specificity=50% and diagnostic accuracy=72%), was less effective than the EMM (sensitivity=100%, specificity=83% and diagnostic accuracy=94%) for the separation of benign and malignant lesions. In summary, the present research suggests that the EMM is a promising alternative method for evaluating DCE-MRI data with improved diagnostic accuracy.     

Some notes on the threshold graphs

In this paper we consider threshold graphs (also called nested split graphs) and investigate some invariants of these graphs which can be of interest in bounding the largest eigenvalue of some graph spectra.     

Alkali hydrolysis of trinitrotoluene

Data for alkali hydrolysis of 2,4,6-trinitrotoluene (TNT) in aqueous solution at pH 12.0 under static (pH-controlled) as well as dynamic (pH-uncontrolled) conditions are reported. The experiments were conducted at two different molar ratios of TNT to hydroxyl ions at room temperature. The TNT disappeared rapidly from the solution as a first-order reaction. The complete disappearance of aromatic structure from the aqueous solution within 24 h was confirmed by the ultraviolet-visible (UV-VIS) spectra of the samples. Cuvet experiments in a UV-VIS spectrophotometer demonstrated the formation of Meisenheimer complex, which slowly disappeared via formation of aromatic compounds with fewer nitro groups. The known metabolites of TNT were found to accumulate only in very small quantities in the liquid phase.     

Relations between (κ, τ)-regular sets and star complements

Let G be a finite graph with an eigenvalue µ of multiplicity m. A set X of m vertices in G is called a star set for µ in G if µ is not an eigenvalue of the star complement G\X which is the subgraph of G induced by vertices not in X. A vertex subset of a graph is (κ, τ)-regular if it induces a κ-regular subgraph and every vertex not in the subset has τ neighbors in it. We investigate the graphs having a (κ, τ)-regular set which induces a star complement for some eigenvalue. A survey of known results is provided and new properties for these graphs are deduced. Several particular graphs where these properties stand out are presented as examples.