Formal proofs of operator identities by a single formal computation

A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials.     

Linear Quadratic Gaussian Homing for Markov Processes with Regime Switching and Applications to Controlled Population Growth/Decay

Methodology and Computing in Applied Probability - The problem of optimally controlling one-dimensional diffusion processes until they enter a given stopping set is extended to include Markov...     

Perturbative manifolds and the Noether generators of nth-order Poisson equations

A manifold that contains small perturbations will induce a perturbed partial differential equation. The partial differential equation that we select is the Poisson equation – in order to explore the interplay between the geometry of the manifold and the perturbations. Specifically, we show how the problem of symmetry determination, for higher-order perturbations, can be elegantly expressed via geometric conditions.     

Path integral quantization corresponding to the deformed Heisenberg algebra

In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized uncertainty principle and doubly special relativity, has been analyzed. It has been observed that, though this algebra can give rise to fractional derivative terms in the corresponding quantum mechanical Hamiltonian, a formal meaning can be given to them by using the theory of harmonic extensions of function. Depending on this argument, the expression of the propagator of the path integral corresponding to the deformed Heisenberg algebra, has been obtained. In particular, the consistent expression of the one dimensional free particle propagator has been evaluated explicitly. With this propagator in hand, it has been shown that, even in free particle case, normal generalized uncertainty principle and doubly special relativity show very much different result.     

Investigation on Ochratoxin A stability using different extraction techniques

The stability of Ochratoxin A during its extraction using different extraction techniques has been evaluated. Microwave-assisted extraction and pressurised liquid extraction, in addition to two other reference methods of extraction, i.e. ultrasound-assisted and magnetic stirring-assisted extraction, were evaluated. The effect of extraction temperature using the cited techniques was checked.The results show that Ochratoxin A can be extracted using microwave-assisted extraction at temperatures up to 150 °C without degradation. Pressurised liquid extraction can be used at temperatures up to 100 °C, for extraction times of less than 30 min. Further, both ultrasound-assisted extraction and magnetic stirring extraction can be applied at temperatures up to 65 °C.High-performance liquid chromatography combined with fluorescence detection using a Chromolith RP-18e column at a flow rate of 5 mL min⁻¹ was used to quantify the Ochratoxin A. The retention time for the Ochratoxin A was 1.3 min. The limits of detection (LOD) and of quantification (LOQ) were 0.03 and 0.10 μg L⁻¹, respectively.     

Normal forms for nonlinear control systems with scalar output

We propose a normal form for nonlinear control systems with scalar output. We follow an approach proposed by Poincaré and adapted for control systems by Kang and Krener which consists of analyzing, step-by-step, the action of the change of coordinates on the system. To cite this article: I.A. Tall, M. Balde, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Adsorption of Molybdenum on Titania from Aqueous Solutions

The adsorption of Mo from dilute aqueous solutions (10(-3) to 3x10(-2) M) is effected on three samples of titania, two are anatase and the third is P25, which is composed of rutile and anatase. The adsorption isotherms at 298, 318, and 338 K are analyzed using a Langmuir linear equation. The isotherms on P25 showed a distinct inflection point that is reproduced by two linear portions, indicating different adsorption regimes. This adsorption behavior is explained as follows: with low amount adsorbed the adsorption is initiated by protonation of the basic hydroxyls on which the negatively charged MoO(4)(2-')s are adsorbed, and this is accompanied by an increase in the pH of the impregnating solution. At higher adsorption the coordinatively unsaturated Ti(4+) sites participate in the process, leading to a decline in the initial increase in pH. In the case of the two anatase samples the low surface area resulted in poor distribution of adsorption sites; consequently, the distinction between the two modes of adsorption was not entirely clear. The higher adsorption site density in the case of anatase is accompanied by a lower surface coverage, θ, than that for P25. The heat of adsorption, Q, on the three titania samples showed a linear increase with θ, which is represented by the regression equation: -Q=95.77θ-4.25 (R(2)=0.993). Copyright 2001 Academic Press.     

Polarographic behaviour of salicylaldehyde-2-pyridylhydrazone and its copper(II) complex

The polarographic behaviour of salicylaldehyde-2-pyridylhydrazone (SAPH) has been studied in aqueous buffer solution containing 40% ethanol using DC and DP polarographic methods. In the pH range 1.8–7.5 the observed single irreversible reduction wave is assigned to the splitting of the N-N bond and reduction of C=N centre. In alkaline medium, a second wave appears at a more negative potential due to the reduction of the salicylaldehyde which is formed by hydrolytic decomposition of the SAPH molecule. The effect of pH on the limiting current andE _1/2 as well as the reduction mechanism are discussed and compared with similar compounds. The kinetic parameters of the electrode reaction have been calculated.The analytical properties of the copper(II)-SAPH system is described. The complex gave rise to a single irreversible well-defined wave (E _1/2=–0.58 V at pH=5.2). The reaction process is diffusion controlled. A method is suggested for the determination of Cu(II) in presence of different metal ions as the difference in theirE _1/2 values is sufficient for the purpose.This work is taken partly from the M. Sc. Thesis of Jamal S. Shalabi     

Adsorption of Some Essential Amino Acids on Hydroxyapatite

Samples of synthetic hydroxyapatite, Ca(10)(PO(4))(6)(OH)(2), obtained by wet method and calcined at 1173 K in air were used in an adsorption study of some essential amino acids, mainly histidine, methionine, and tryptophan. Adsorption isotherms were obtained using aqueous solutions of concentration range 2.7x10(-2)-1.3x10(-3) M at 303, 318, and 343 K, under near neutral conditions. The mode of adsorption was studied using IR spectroscopy. The results are discussed in terms of the dependence of the adsorption process both on the functional groups on the hydroxyapatite and on the solution chemistry of the aqueous amino acids solutions. Copyright 2001 Academic Press.     

Simultaneous determination of carbaryl and azinphos-methyl in water by first-derivative synchronous spectrofluorimetry

A method is proposed for the simultaneous determination of the pesticides carbaryl (CBL) and azinphos-methyl (AZM) in water by first-derivative synchronous spectrofluorimetry. It is based on the alkaline hydrolysis of both pesticides to their metabolites 1-naphthol (from CBL) and anthranilic acid (from AZM). The constant wavelength difference chosen to optimize the determination is Δλ=λ_em?λ_ex=103 nm. CBL is measured at 302/405 nm and AZM at 333/436 nm. The calibration graphs are linear between 2.0 and 500.0 ng/ml for CBL and between 1.2 and 500.0 ng/ml for AZM with detection limits of 0.62 ng/ml and 0.35 ng/ml, respectively. The precision of the method (RSD) is 2.4% at the 80.0 ng/ml level for CBL and 2.5% at the 80.0 ng/ml level for AZM. The method is applied to the determination of both analytes in samples of natural waters.