Extensions,dilations, and spectral problems of singular Hamiltonian systems

In this paper, we construct a space of boundary values for minimal symmetric 1D Hamiltonian operator with defect index (1,1) (in limit‐point case at a(b) and limit‐circle case at b(a)) acting in the Hilbert space In terms of boundary conditions at a and b, all maximal dissipative, accumulative, and self‐adjoint extensions of the symmetric operator are given. Two classes of dissipative operators are studied. They are called “dissipative at a” and “dissipative at b.” For 2 cases, a self‐adjoint dilation of dissipative operator and its incoming and outgoing spectral representations are constructed. These constructions allow us to establish the scattering matrix of dilation and a functional model of the dissipative operator. Further, we define the characteristic function of the dissipative operators in terms of the Weyl‐Titchmarsh function of the corresponding self‐adjoint operator. Finally, we prove theorems on completeness of the system of root vectors of the dissipative operators.     

Activated aluminum oxide selectively retaining long chain n-alkanes: Part II. Integration into an on-line high performance liquid chromatography-liquid chromatography-gas chromatography-flame ionization detection method to remove plant paraffins for the determination of mineral paraffins in foods and environmental samples

Aluminum oxide activated by heating to 300-400 °C retains n-alkanes with more than about 20 carbon atoms, whereas iso-alkanes largely pass non-retained (with characteristics described in more detail in Part I). This property is useful for the analysis of mineral oil contamination of foods and other matrices: it enables the removal of plant n-alkanes, typically ranging from C₂₃ to C₃₃, when they disturb the analysis of mineral paraffins (usually almost exclusively consisting of iso-alkanes). An on-line HPLC-LC-GC-FID method is proposed in which a first silica gel HPLC column isolates the paraffins from the bulk of edible oils or extracts and is backflushed with dichloromethane. In a second separation step, a 10 cm × 2 mm i.d. column packed with activated aluminum oxide separates the long chain n-alkanes from the fraction of the iso-alkanes which is transferred to GC-FID by the on-column interface and the retention gap technique. The retained n-alkanes are removed by flushing with iso-octane.     

Variable ranking based on the estimated degree of separation for two distributions of data by the length of the receiver operating characteristic curve

Variable responses are fundamental for all experiments, and they can consist of information-rich, redundant, and low signal intensities. A dataset can consist of a collection of variable responses over multiple classes or groups. Usually some of the variables are removed in a dataset that contain very little information. Sometimes all the variables are used in the data analysis phase. It is common practice to discriminate between two distributions of data; however, there is no formal algorithm to arrive at a degree of separation (DS) between two distributions of data. The DS is defined herein as the average of the sum of the areas from the probability density functions (PDFs) of A and B that contain a ≥ percentage of A and/or B. Thus, DS90 is the average of the sum of the PDF areas of A and B that contain ≥90% of A and/or B. To arrive at a DS value, two synthesized PDFs or very large experimental datasets are required. Experimentally it is common practice to generate relatively small datasets. Therefore, the challenge was to find a statistical parameter that can be used on small datasets to estimate and highly correlate with the DS90 parameter. Established statistical methods include the overlap area of the two data distribution profiles, Welch’s t-test, Kolmogorov–Smirnov (K–S) test, Mann–Whitney–Wilcoxon test, and the area under the receiver operating characteristics (ROC) curve (AUC). The area between the ROC curve and diagonal (ACD) and the length of the ROC curve (LROC) are introduced. The established, ACD, and LROC methods were correlated to the DS90 when applied on many pairs of synthesized PDFs. The LROC method provided the best linear correlation with, and estimation of, the DS90. The estimated DS90 from the LROC (DS90–LROC) is applied to a database, as an example, of three Italian wines consisting of thirteen variable responses for variable ranking consideration. An important highlight of the DS90–LROC method is utilizing the LROC curve methodology to test all variables one-at-a-time with all pairs of classes in a dataset.     

The characteristic finite difference fractional steps methods for compressible two-phase displacement problem

For compressible two-phase displacement problem, a kind of characteristic finite difference fractional steps schemes is put forward and thick and thin grids are used to form a complete set. Some techniques, such as piecewise biquadratic interpolation, of calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates inL ² norm are derived to determine the error in the approximate solution. Project supported by the National Scaling Program, the National Tackling Key Problems Program and the Doctorate Foundation of the State Education Commission of China.     

On 8mm Microwave Radiometric Imaging System

This paper describes structure of imaging system, imaging mechanism of microwave radiometer, and the microwave radiation image features and recognition. Results of image experiments show: on microwave radiation image, the features of metal target, water surface and road among trees, grassland and jungle become extremely obvious.     

Ion-interaction chromatography of neutral molecules

Summary The chromatographic behavior of neutral molecules in ion-interaction chromatography (IIC) is investigated theoretically. The physical and chemical modification of the stationary phase in the presence of ion interaction Reagent (IIR) in the eluent, and adsorption competition between test analytes and IIR for inner layer sites are shown theoretically to change the partition coefficient of neutral molecules. The most reliable, literature experimental results, concerming retention behaviour of neutral molecules in IIC, were used to test the new theory. The wide variability among them was elucidated on the basis of the exhaustive retention model developed. Retention equations were compared to those which can be obtained, if the change of the analyte is zero, from the most important retention model in IIC.