This article presents research targeted toward the isolation and detection of unique molecular structures from what is believed to be the world's most complex organic mixture: dissolved organic matter (DOM). Hydrophilic interaction chromatography (HILIC) was used to separate Suwannee River DOM (SRDOM) into 80 fractions, simplified to the extent that detection with nuclear magnetic resonance spectroscopy (NMR) results in many sharp signals that are indicative of individual compounds, some of which are identifiable with multidimensional NMR. Parallel factor analysis (PARAFAC) of fluorescence excitation-emission matrices (EEMs) was additionally employed on HILIC-simplified fractions to further confirm the effectiveness of the HILIC separations as well as draw insight into how structural characteristics relate to DOM fluorescence signals. Findings suggest that material believed to be derived from both cyclic and linear terpenoids was dominant in the most hydrophobic fractions as were the majority of the fluorescence signals, whereas hydrophilic material was highly correlated with carbohydrate-type structures as well as high contributions from amino acid fluorescence. NMR spectra of DOM, typically featureless mounds, are substantially more detailed with HILIC-simplified fractions to the point where hundreds of signals are present and 2D NMR correlations permit significant structural identifications.

In this paper we consider integral functionals of the formwith convex integrand satisfying (p, q) growth conditions. We prove local higher differentiability results for bounded minimizers of the functional F under dimension-free conditions on the gap between the growth and the coercivity exponents.As a novel feature, the main results are achieved through uniform higher differentiability estimates for solutions to a class of auxiliary problems, constructed adding singular higher order perturbations to the integrand.

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Background and Methods. The value of serum alpha‐L‐fucosidase activity in the diagnosis of hepatocellular carcinoma (HCC) was investigated by determining the enzyme activity levels in 21 patients with HCC, 76 patients with cirrhosis, 22 patients with other malignant neoplasms, and 23 healthy subjects. Results. The serum alpha‐L‐fucosidase activity level in patients with HCC (575.76 ± 212.86 nmol/ml/h) was significantly higher than that found in patients with cirrhosis (274.55 ± 138.97 nmol/ml/h; P < 0.001) or other neoplasms (257.91 ± 128.12 nmol/ml/h P < 0.001) and in controls (221.23 ± 114.45 nmol/ml/h; P < 0.001). No significant differences were found between controls and patients with cirrhosis and between controls and patients with other malignant neoplasms. When 443 nmol/ml/h is taken as the cutoff value (mean value of controls plus 2 standard deviations), alpha‐L‐fucosidase sensitivity and specificity were 76% and 90.9%, respectively. Conclusions. These results suggest that alpha‐L‐fucosidase is a useful marker for detecting HCC, in conjunction with alpha‐fetoprotein and ultrasonography.

We study nonlinear elliptic equations in divergence form(Formula presented.) When (Formula presented.) has linear growth in Du, and assuming that (Formula presented.) enjoys (Formula presented.) smoothness, local well-posedness is found in (Formula presented.) for certain values of (Formula presented.) and (Formula presented.). In the particular case (Formula presented.), G = 0 and (Formula presented.), (Formula presented.), we obtain (Formula presented.) for each (Formula presented.). Our main tool in the proof is a more general result, that holds also if (Formula presented.) has growth s−1 in Du, 2 ≤ s ≤ n, and asserts local well-posedness in Lq for each q > s, provided that (Formula presented.) satisfies a locally uniform VMO condition