Optimization of artificial neural networks used for retention modelling in ion chromatography

The aim of this work is the development of an artificial neural network model, which can be generalized and used in a variety of applications for retention modelling in ion chromatography. Influences of eluent flow-rate and concentration of eluent anion (OH-) on separation of seven inorganic anions (fluoride, chloride, nitrite, sulfate, bromide, nitrate, and phosphate) were investigated. Parallel prediction of retention times of seven inorganic anions by using one artificial neural network was applied. MATLAB Neural Networks ToolBox was not adequate for application to retention modelling in this particular case. Therefore the authors adopted it for retention modelling by programming in MATLAB metalanguage. The following routines were written; the division of experimental data set on training and test set; selection of data for training and test set; Dixon's outlier test; retraining procedure routine; calculations of relative error. A three-layer feed forward neural network trained with a Levenberg-Marquardt batch error back propagation algorithm has been used to model ion chromatographic retention mechanisms. The advantage of applied batch training methodology is the significant increase in speed of calculation of algorithms in comparison with delta rule training methodology. The technique of experimental data selection for training set was used allowing improvement of artificial neural network prediction power. Experimental design space was divided into 8-32 subspaces depending on number of experimental data points used for training set. The number of hidden layer nodes, the number of iteration steps and the number of experimental data points used for training set were optimized. This study presents the very fast (300 iteration steps) and very accurate (relative error of 0.88%) retention model, obtained by using a small amount of experimental data (16 experimental data points in training set). This indicates that the method of choice for retention modelling in ion chromatography is the artificial neural network.     

On the Interaction of Two Finite-Dimensional Quantum Systems

Interaction of quantum system S ^a described by the generalised × eigenvalue equation A| _s =E _s S ^a | _s (s=1,...,) with quantum system S ^b described by the generalised n×n eigenvalue equation B| _i = _i S ^b | _i (i=1,...,n) is considered. With the system S ^a is associated -dimensional space X ^a and with the system S ^b is associated an n-dimensional space X _n ^b that is orthogonal to X ^a . Combined system S is described by the generalised (+n)×(+n) eigenvalue equation [A+B+V]| _k = _k [S ^a +S ^b +P]| _k (k=1,...,n+) where operators V and P represent interaction between those two systems. All operators are Hermitian, while operators S ^a ,S ^b and S=S ^a +S ^b +P are, in addition, positive definite. It is shown that each eigenvalue _{k i} of the combined system is the eigenvalue of the × eigenvalue equation . Operator in this equation is expressed in terms of the eigenvalues _i of the system S ^b and in terms of matrix elements _s |V| _i and _s |P| _i where vectors | _s form a base in X ^a . Eigenstate | _k ^a of this equation is the projection of the eigenstate | _k of the combined system on the space X ^a . Projection | _k ^b of | _k on the space X _n ^b is given by | _k ^b =( _k S ^b –B)^–1(V– _k P})| _k ^a where ( _k S ^b –B)^–1 is inverse of ( _k S ^b –B) in X _n ^b . Hence, if the solution to the system S ^b is known, one can obtain all eigenvalues _{k i} } and all the corresponding eigenstates | _k of the combined system as a solution of the above × eigenvalue equation that refers to the system S ^a alone. Slightly more complicated expressions are obtained for the eigenvalues _{k i} } and the corresponding eigenstates, provided such eigenvalues and eigenstates exist.     

Über die quantitative Bestimmung von Quecksilber(II)ionen durch katalytische Zersetzung von Ferrocyanid.

Zusammenfassung Die unter katalytischer Wirkung von Quecksilber(II)ionen ablaufende Umsetzung von Ferrocyanid zu Berlinerblau wurde als quantitative kolorimetrische Methode zur Bestimmung von Quecksilber(II) in Konzentrationen von 5 bis 50g/ml ausgearbeitet.

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Summary The partial oxidation of ferrocyanide to Prussian blue accomplished under the catalytic action of mercury(II) ions has been developed into a quantitative method for the determination of mercury(II) in concentrations of 5 to 50g/ml.

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Résumé L'oxydation partielle du ferrocyanure en bleu de Berlin sous l'influence catalytique des ions Hg(II) a été mise au point comme méthode de dosage des ions Hg(II) à des concentrations de 5 à 50g/ml.

     

Influence of Aliphatic Chain Length on Structural,Thermal and Electrochemical Properties of n-alkylene Benzyl Alcohols: A Study of the Odd–Even Effect

The century-old, well-known odd–even effect phenomenon is still a very attractive and intriguing topic in supramolecular and nano-scale organic chemistry. As a part of our continuous efforts in the study of supramolecular chemistry, we have prepared three novel aromatic alcohols (1,2-bis[2-(hydroxymethyl)phenoxy]butylene (Do4OH), 1,2-bis[2-(hydroxymethyl)phenoxy]pentylene (Do5OH) and 1,2-bis[2-(hydroxymethyl)phenoxy]hexylene (Do6OH)) and determined their crystal and molecular structures by single-crystal X-ray diffraction. In all compounds, two benzyl alcohol groups are linked by an aliphatic chain of different lengths (CH₂)_n; n = 4, 5 and 6. The major differences in the molecular structures were found in the overall planarity of the molecules and the conformation of the aliphatic chain. Molecules with an even number of CH₂ groups tend to be planar with an all-trans conformation of the aliphatic chain, while the odd-numbered molecule is non-planar, with partial gauche conformation. A direct consequence of these structural differences is visible in the melting points—odd-numbered compounds of a particular series display systematically lower melting points. Crystal and molecular structures were additionally studied by the theoretical calculations and the melting points were correlated with packing density and the number of CH₂ groups. The results have shown that the generally accepted rule, higher density = higher stability = higher melting point, could not be applied to these compounds. It was found that the denser packaging causes an increase in the percentage of repulsive H‧‧‧H interactions, thereby reducing the stability of the crystal, and consequently, the melting points. Another interesting consequence of different molecular structures is their electrochemical and antioxidative properties—a non-planar structure displays the highest oxidation peak of hydroxyl groups and moderate antioxidant activity.     

Axiomatic Geometric Formulation of Electromagnetism with Only One Axiom: The Field Equation for the Bivector Field <Emphasis Type="Italic">F</Emphasis> with an Explanation of the Trouton-Noble Experiment

In this paper we present an axiomatic, geometric, formulation of electromagnetism with only one axiom: the field equation for the Faraday bivector field F. This formulation with F field is a self-contained, complete and consistent formulation that dispenses with either electric and magnetic fields or the electromagnetic potentials. All physical quantities are defined without reference frames, the absolute quantities, i.e., they are geometric four-dimensional (4D) quantities or, when some basis is introduced, every quantity is represented as a 4D coordinate-based geometric quantity comprising both components and a basis. The new observer-independent expressions for the stress-energy vector T(n) (1-vector), the energy density U (scalar), the Poynting vector S and the momentum density g (1-vectors), the angular momentum density M (bivector) and the Lorentz force K ((1-vector) are directly derived from the field equation for F. The local conservation laws are also directly derived from that field equation. The 1-vector Lagrangian with the F field as a 4D absolute quantity is presented; the interaction term is written in terms of F and not, as usual, in terms of A. It is shown that this geometric formulation is in a full agreement with the Trouton-Noble experiment.     

The Difference Between the Standard and The Lorentz Transformations of the Electric and the Magnetic Fields

In this paper it is shown by using the Clifford algebra formalism that the usual Lorentz transformations of the three-dimensional (3D) vectors of the electric and magnetic fields E and B (which will be named as standard transformations (ST)) are different than the Lorentz transformations (LT) of well-defined quantities from the 4D spacetime. This difference between the ST and the LT is obtained regardless of the used algebraic objects (1-vectors or bivectors) for the representation of the electric and magnetic fields in the usual observer dependent decompositions of F. The LT correctly transform the whole 4D quantity, e.g., E_f : F · γ₀, whereas the ST are the result of the application of the LT only to the part of E_f, i.e., to F, but leaving γ₀ unchanged. The new decompositions of F in terms of 4D quantities that are defined without reference frames, i.e., the absolute quantities, are introduced and discussed. It is shown that the LT of the 4D quantities representing electric and magnetic fields correctly describe the motional electromotive force (emf) for all relatively moving inertial observers, whereas it is not the case with the ST of the 3D E and B.     

Indirect optical crosstalk reduction by highly-doped backside layer in single-photon avalanche diode arrays

A method of reducing indirect optical crosstalk in single-photon avalanche diode arrays is investigated by TCAD simulations. The reduction is accomplished by taking advantage of an enhanced optical absorption in a highly-doped Si layer on the backside of the wafer. A simulation environment was developed to give information about optical crosstalk by incorporating the experimental optical constants of the materials constituting the crosstalk-reduction layer. It is shown that the indirect optical crosstalk is greatly reduced by increasing the thickness and doping of the layer. A crosstalk reduction of 5 orders of magnitude is gained with addition of 1-μm-thick \(\hbox {PureB}/\upalpha \hbox {-Si}\) stack for the array processed on a p-type substrate, while the same reduction is achieved with a 1-μm-thick highly-doped Si layer (As, \(1.1\times 10^{20}\, \hbox {cm}^{-3}\)) for an array processed on an n-type substrate.     

The Proof That the Standard Transformations of E and B Are Not the Lorentz Transformations

In this paper it is exactly proved that the standard transformations of the three-dimensional (3D) vectors of the electric and magnetic fields E and B are not relativistically correct transformations. Thence the 3D vectors E and B are not well-defined quantities in the 4D space-time and, contrary to the general belief, the usual Maxwell equations with the 3D E and B are not in agreement with the special relativity. The 4-vectors E ^a and B ^a , as well-defined 4D quantities, are introduced instead of ill-defined 3D E and B. The proof is given in the tensor and the Clifford algebra formalisms.     

Bose-Einstein correlations for pions produced inp p collisions at 360 GeV/c

Zeitschrift für Physik C Particles and Fields - Correlations among identically charged pions were measured for pions produced inp p collisions at 360 GeV/c using the EHS spectrometer. The...