Chen’ s theorem in arithmetical progressions

LetN be a sufficiently large even integer and

Optimization of the process variables for the synthesis of cardanol-based novolac-type phenolic resin using response surface methodology

Models capable of predicting the maximum extent of conversion (p) of cardanol-based novolac-type phenolic resin, have been developed using response surface methodology to determine the optimum reaction conditions. Three-dimensional response surface and their contour plot were drawn. The maximum extent of conversion (98.93%) was predicted when the cardanol was condensed with formaldehyde (molar ratio 1:0.652) at 119.84 °C for a time period of 3 h with the catalyst (e.g., citric acid) concentration of 1.988% of total volume of cardanol and formaldehyde. The pH of the reaction mixture was maintained at 3.0. These predicted values for optimum process conditions were in good agreement with experimental data.     

Crystal structure and magnetic structure of TbOOH

The monoclinic modification of terbium oxide hydroxide, TbOOH, was prepared using hydrothermal technique. The crystal structure was investigated by three-dimensional single-crystal X-ray analysis and was refined to a conventional R-value of 8.1%. The space group is $\text{P2}{}_1\text{m}$, No. 11, with a = 6.04 Å, b = 3.69 Å, c = 4.33 Å, and β = 109.0°. The terbium atom is seven coordinated with oxygen atoms, and the structure is not hydrogen bonded.The compound is antiferromagnetic with a Néel temperature of 10°K. Neutron diffraction powder patterns were measured at 300°K and 4.2°K. The magnetic super lattice reflections were indexed on the basis of a monoclinic unit cell with the dimensions a_M = 2a, b_M = b, c_M = c, and β_M = β, where a, b, c, and β are the dimensions of the chemical unit cell. The structure contains two independent magnetic atoms. A nonclinear antiferromagnetic arrangement of the spins describes the magnetic structure. The spin at one atom has an angle of 43° with the ac plane and the projection of the spin on the ac plane has an angle of 59° with the a axis. The spin on the other atom has an angle of ?43° with the ac plane, the projection having the same angle of 59° with the a axis.     

Shot noise sets the limit of quantification in electrochemical measurements

Detection of single molecules, particles, and rapid redox events is a challenge of electrochemical investigations and requires either an amplification strategy or significant averaging for the electrochemical current to exceed the noise level. We consider the minimum number of electrons required to reach the limit of quantification in these electrochemical measurements. A survey of the literature indicates that the state-of-the-art limit in current detection for different types of measurements (e.g. voltammetry, single-molecule redox cycling, ion channel recordings of single molecules, metal nanoparticle collision, and phase nucleation) is independent of the nature of the measurement and increases linearly with reciprocal response time, Δt^?1, over ～5 orders of magnitude (from ～10 to ～10⁶ s^?1). We demonstrate that the practical limit of quantification requires cumulative measurement of ～2100 electrons during Δt and is determined by statistics of counting electrons, that is, the shot noise in the current.     

Limit cycles of a class of Liénard systems derived from state-dependent impulses

Discontinuous phenomena, in which objects may behave continuously and sometimes discretely are not only found in nature and under laboratory conditions but also in simple, familiar contexts. For example, this phenomenon is skillfully incorporated into the internal structure of mechanical wristwatches. Unless an extremely small amount of state-dependent impulse is applied intermittently, the reciprocating rotational movement of the balance and hairspring, which is the heart of the mechanical wristwatch, cannot be maintained. The small amount of state-dependent impulse, which is often overlooked, can make a significant difference; however, very few studies have examined this subject. This study assumes the underlying cause of discontinuous behaviors as impulses generated when an object reaches a particular state, assuming that the continuous behavior follows the Liénard system, which is widely studied in the field of electrical circuits. The main theorem provides the conditions under which the effect of the impulses causes a stable limit cycle in the Liénard system, even if no limit cycle exists when there are no impulses. The Poincaré–Bendixson theorem for discontinuous dynamical systems and phase plane analysis are used to prove the main theorem. Several examples and their simulations are provided to illustrate the main theorem.     

Large deviations for martingales with some applications

Let(X _i ) be a martingale difference sequence. LetY be a standard normal random variable. We investigate the rate of uniform convergence

Optimisation of the chlorthalidone chiral separation by capillary electrochromatography using an achiral stationary phase and cyclodextrin in the mobile phase

The separation of chlorthalidone enantiomers in capillary electrochromatography on an achiral stationary phase when adding a chiral selector, hydroxypropyl-β-cyclodextrin, to the mobile phase, was optimised. The goal was to investigate the feasibility of modelling retention times and resolution when during the optimisation procedure regular replacement of columns is required due to their fragility. Therefore, it is essential that the packing procedure delivers reproducible columns. The optimisation of an existing chlorthalidone separation was chosen as case study. The influence of two factors, chiral selector concentration and organic modifier content, on the responses was modelled. The experiments performed prior to modelling were defined by a central composite design. Results on different columns, obtained under identical experimental conditions, were found comparable and thus modelling was possible in situations where several columns were required to complete a design. A second-order polynomial model was built for both responses. Optimal separations were also predicted using Derringer’s desirability functions. The optimum was found at 33 mM cyclodextrin and 16% (v/v) acetonitrile on two types of columns (with different packing times) leading to a strong reduction in analysis time for an equally good separation compared to the initial conditions. Measured and predicted responses were found comparable, indicating that acceptable models were obtained.     

Evaluation of the limit of performance of an analytical method based on a statistical calculation of its critical concentrations according to ISO standard 11843: Application to routine control of banned veterinary drug residues in food according to European Decision 657/2002/EC

Traceability of the measurement of analytical parameters capable of evaluating the performance of methods is an important concept for the assessment of quality for the routine control, especially for residue monitoring of non-authorized medicinal substances in food from animal origin. The European Decision no. 657/2002/EC recommends to calculate two statistical limits, CCα and CCβ, which allow to evaluate the critical concentrations above which the method reliably distinguish and quantify a substance taking into account the variability of the method and the statistical risk to take a wrong decision. The calculation, which can be derived from the ISO standard no. 11843 is applied on a routine basis. An example displays a very simple way for evaluating the performance of an LC-MSMS method which has been validated a few years ago and is qualified onto a Micromass Quattro LCZ tandem mass spectrometer to monitor and confirm the nitrofuran metabolite residues in food from animal origin. Community Reference Laboratory for Antimicrobial Veterinary Drug Residue Control in Food from Animal Origin     

APPLICATION OF THE MOMENT METHODS TO ANALYSIS OF X-RAY DIFFRACTION LINE PROFILE FOR PA1010-BMI SYSTEM

Pure X-ray diffraction profiles have been analysed for polyamide 1010 and PA1010--BMI system by means of multipeak fitting resolution of X-ray diffraction.The methods ofvariance and fourth moment have been applied to determine the particle size and strainvalues for theparacrystalline materials.The results indicated that both variance and fourthmoment of X-ray diffraction line profile yielded approximately the same values of theparticle size and the strain.The particle sizes of(100)reflection have been found todecrease with increasing BMI content,whereas the strain values increased.     

Low detection limit spectrophotometry

An efficient, more sensitive and accurate spectrophotometric process is possible and can be used to obtain qualitative or quantitative results for analytes at limiting concentrations lower than usual. Transmission measurements (incident light power, P₀, or transmitted, P) are performed with a fluorescence spectrometer. One cell only is used to measure standards or unknown solutions, placed between the standard holder cuvette and the emission monochromator of the instrument. The source of the radiant power (P₀) is not the xenon lamp but the fluorescence or scattered radiation from the holder cuvette filled with an appropriate solution. The analyte concentration is found from a calibration graph, based upon Beer’s law or the approximate formula P₀−P=2.303P₀εbc, which is valid for dilute solutions. Determination of iron in a reference material, using 1,10-phenanthroline as the chromogenic reagent, was chosen as an example to demonstrate the suitability of the proposed method and clarify several important statistical questions. Also discussed is why and to what extent molecular fluorescence methods are more sensitive than molecular absorption methods.