Back‐propagation artificial neural network and attenuated total reflectance‐Fourier transform infrared spectroscopy for diagnosis of basal cell carcinoma by blood sample analysis

A diagnostic method for the cancer, based on investigation of infrared spectra of blood samples, has been developed. The two‐layer modified principal component feed forward back‐propagation artificial neural network (BP‐ANN) was used to classify the attenuated total reflectance‐Fourier transform infrared (ATR‐FTIR) spectra of blood samples obtained from healthy people and those with basal cell carcinoma (BCC). Results showed 98.33% of accuracy, in comparison with the current clinical methods. In the first step, 20 blood samples (10 normal and 10 cancer cases) were applied to construct the calibration model. Spectroscopic studies were performed in 900–1800 cm⁻¹ spectral region with 3.85 cm⁻¹ data space. In order to modify the capability of ANN in prediction of test samples, two different algorithms were applied. The obtained results confirmed the compatibility of the proposed network with the architecture of 20‐8‐2 (input‐hidden‐output) with the pattern model. It was concluded that analysis of blood samples by ATR‐FTIR spectroscopy and ANN chemometric technique would be a reliable approach for detection of BCC. Copyright © 2009 John Wiley & Sons, Ltd.     

Silicon nitride nanoparticles for surface-assisted laser desorption/ionization of small molecules

Conventional matrix-assisted laser desorption/ionization mass spectrometry is limited to analyses of higher molecular weight compounds due to high background noise generated by the matrix in the lower mass region. Surface-assisted laser desorption/ionization (SALDI) mass spectrometry is an alternative solution to this problem. Nanoparticles, structured silicon surfaces and carbon allotropes are commonly used as SALDI surfaces. Here, for the first time, we demonstrate the application of silicon nitride nanoparticles as a suitable medium for laser desorption/ionization of small drug molecules.     

The inverse Fermat–Weber problem

Given n points in the plane with nonnegative weights, the inverse Fermat–Weber problem consists in changing the weights at minimum cost such that a prespecified point in the plane becomes the Euclidean 1-median. The cost is proportional to the increase or decrease of the corresponding weight. In case that the prespecified point does not coincide with one of the given n points, the inverse Fermat–Weber problem can be formulated as linear program. We derive a purely combinatorial algorithm which solves the inverse Fermat–Weber problem with unit cost using O(n) greedy-like iterations where each of them can be done in constant time if the points are sorted according to their slopes. If the prespecified point coincides with one of the given n points, it is shown that the corresponding inverse problem can be written as convex problem and hence is solvable in polynomial time to any fixed precision.     

Calculation of radiative transition probabilities and radiative recombination rate coefficients for H2, OH, H 2+ and OH+ molecules

A method is presented to calculate the radiative transition probabilities and the radiative recombination rate coefficients between electronic molecular states. Total transition probabilities are determined from vibrational transition probabilities without considering the detailed rotational structure of the molecular electronic states. Radiative recombination rate coefficients are obtained from the computation of vibrational photo-ionisation cross sections. Concerning spontaneous emission, Lyman (B → X) and Werner (C → X) band systems of H₂ and Meinel (A → X), (B → A) and (B → X) band systems of OH are investigated. For radiative recombination, transitions between H₂⁺ (X) and H₂(X), and between OH⁺(X, a, A, b, and c) and OH(X) are considered. Transition probabilities and recombination rate coefficients are calculated as a function of temperature in the range 1500–15 000 K.     

The 3G-inequality for general Schrödinger operators on Lipschitz domains

In this paper we prove a new 3G-inequality for the Laplacian Green function on a bounded Lipschitz domain in ⁿ, n3. We exploit this inequality to prove the existence and comparison of perturbed continuous Green functions associated with – where is in a general class of signed Radon measures covering the well known Kato class.Mathematics Subject Classification (2000): 31B05, 35J10     

Pattern generation by convection in spherical shells

Summary The problem of pattern selection by thermal convection in thin spherical shells with nearly insulating boundaries is investigated for both non-singular and singular cases where the Rayleigh number attains its minimum value for a single and double values of the degreel of spherical harmonics, respectively. The number of distinct solutions for the singular case is found to be substantially larger than the number of distinct solutions for the non-singular case. While there is at least one stable solution for the non-singular case, there is an additional stable mixed mode solution in the singular case as is shown in the casel=1 andl ^*=2.

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Zusammenfassung Das Problem der Strukturselektion für thermische Konvektion in dünnen Kugelschalen mit nahezu thermisch isolierenden Rändern wird untersucht im nicht-singulären und im singulären Fall, wobei die Rayleighzahl im ersteren Fall ihr Minimum für einen einzigen Wert für den Gradl der spherischen Harmonischen erreicht, während dies im zweiten Fall für zwei benachbarte Werte vonl geschieht. Die Zahl der zu verschiedenen Strukturen gehörenden Lösungen ist im letzteren Fall wesentlich größer als im ersten Fall. Im nicht-singulären Fall existiert stets eine stabile Lösung, während im singulären Fall zusätzlich eine stabile gemischte Lösung existiert, wie im Falll=1,l ^*=2 gezeigt wird.

     

Strict directional solutions in vectorial problems: necessary optimality conditions

Journal of Global Optimization - We study directional strict efficiency in vector optimization and equilibrium problems with set-valued map objectives. We devise several possibilities to define a...     

Carleman estimate for Biot consolidation system in poro‐elasticity and application to inverse problems

In this paper, we consider a coupled system of mixed hyperbolic–parabolic type, which describes the Biot consolidation model in poro‐elasticity. We establish a local Carleman estimate for Biot consolidation system. Using this estimate, we prove the uniqueness and a Hölder stability in determining on the one hand a physical parameter arising in connection with secondary consolidation effects λ^? and on the other hand the two spatially varying densities by a single measurement of solution over ω × (0,T), where T > 0 is a sufficiently large time and a suitable subdomain ω satisfying ?ω??Ω. Copyright © 2016 John Wiley & Sons, Ltd.     

Removal of chromate from aqueous solution by reduction with nanoscale Fe–Al layered double hydroxide

Nanoscale layered double hydroxides of Fe^II and Al^III (Fe–Al LDH) have been applied for removal of chromate (Cr^VI) from aqueous solution. Given the reaction stoichiometry, Cr^VI was completely reduced to Cr^III and coprecipitated with Fe^III and Al^III oxyhydroxides. The extent of Cr^VI removal decreased with increasing initial pH and decreasing molar ratio of Cr^VI/structural Fe^II in the LDH. The chromate reduction rate at different initial concentrations of Cr^VI was well described by the pseudo-second-order model with reaction rate constant ranging from 197.4 to 13.53 (mmol min)^?1. Initial pH and substitution of various amounts of Fe^III in the LDH structure had little effect on the reaction rate. Backtransformation of Cr^III to Cr^VI by birnessite Mn oxide (δ-MnO₂) after 40 days of reaction was less than 1% of the initial Cr (as Cr^III solid), indicating high stability of the final reaction products and high efficiency of nanoscale Fe–Al LDHs for removal of chromate from aqueous solution.