Slope estimations at terminal values of three equidistant data

A new method is presented for estimating derivatives at the end points of three curvilinear data points. For first derivatives, the accuracy of the method is similar to that of the standard method, but it has the advantage that second derivatives are not necessarily all equal and can be more accurate than those predicted by conventional methods.     

The error function for fitting of models to immittance data

In statistical calculations for fitting a model to experimental immittance data (admittance and/or impedance data) the key issue is the error function, which as a result of calculations should attain its minimum value ( ? 0). Different formulae for the error function, recently used in calculations, are analyzed and a new formula is proposed. The principal feature of the new formula is that for the admittance data and the impedance data the same results of calculations are obtained; this formula takes into account the possibility of correlation of errors of the two components of the immittance vector.The usefulness of the proposed formula is experimentally verified and demonstrated on immittance data measured for two actual systems.     

对氧化还原滴定过程的理论探讨

提出了氧化还原的分布系数、滴定分数、缓冲容量和敏锐指数的新概念 ,并推导和讨论了它们的函数表达式 ,建立了氧化还原滴定过程的曲线方程。它有助于进一步对氧化还原滴定过程研究的计算机化和自动化。     

Remarks on the updated Hessian matrix methods

Optimizing a function with respect to a set of variables using the quasi‐Newton–Raphson method implies updating the Hessian matrix at each iteration. The Broyden–Fletcher–Goldfarb–Shanno update formula is used for minimization and the Murtagh–Sargent–Powell update formula for optimization of first‐order saddle points. Two new formulae are proposed to update the Hessian matrix. One of these formulae is derived using exponential weights and should be used to locate first‐order saddle points. The second formula is a modification of the TS–Broyden–Fletcher–Goldfarb–Shanno update and could used for both minimum and first‐order saddle point optimizations. These two update Hessian matrix formulae present a performance that is the same and in many cases better that the Broyden–Fletcher–Goldfarb–Shanno and Murtagh–Sargent–Powell formulae. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 324–332, 2003     

A new method for the calculation of molecular formulae from accurate mass data and vice versa

A calculator is described for the rapid manual conversion of accurate mass data into molecular formulae. The method uses any information available about the ion to simplify the process. Calculation of accurate masses from a molecular formula is even more rapidly determined.     

Nonlinear response of the surface electrostatic potential formed at metal oxide/electrolyte interfaces. A Monte Carlo simulation study

An analysis of surface potential nonlinearity (ψ₀) at metal oxide/electrolyte interfaces is presented. By using grand canonical Monte Carlo simulations of a simple lattice model of an interface, we show that a correlation exists between ionic strength, as well as surface site densities, and the non-Nernstian response of a metal-oxide electrode. We propose two approaches to deal with the ψ₀-nonlinearity: one based on perturbative expansion of the Gibbs free energy and another based on the assumption of the pH dependence of surface potential slope. The theoretical analysis based on our new potential form gives excellent performance in extreme pH regions, where classical formulae for ψ₀ are unjustified. The new formula is general and independent of any underlying assumptions. For this reason, it can be directly applied to experimental surface potential measurements, including those for individual surfaces of single crystals, as we present for data reported by Kallay and Preo?anin [6].     

A new mathematical treatment of spectrophotometric data for differentiating mononuclear and polynuclear complexes

A new mathematical approach to the treatment of spectrophotometric data for differentiation between mononuclear and polynuclear metal complexes in solution is presented. The slope of a straight line yields the total number of units in the complex, from which the true molecular formula can be obtained if the empirical formula is known. The formation constant is also given by the slope of a straight line. The method can be applied to complexes with any number of different ligands. Solutions are prepared in which the ratio of total concentrations of the reacting species is equal to the combining ratio. Spectrophotometric data must be obtained under conditions where only one complex is formed and the degree of dissociation is significant. The molar absorptivity must be obtained by direct measurement.     

Preliminary chemometric study of minerals and trace elements in Spanish infant formulae

The concentrations of minerals (Na, K, P, Ca and Mg) and trace elements (Fe, Zn, Cu, Mn, Se, Al, Cd and Pb) in a total of 105 different infant formulae (starter, follow-up, premature, specialised and soya formulae) marketed in Spain were determined by atomic spectrometry (flame and electrothermal) and inductively coupled plasma emission spectroscopy after acid-microwave decomposition. On the basis of the elements distribution, a preliminary chemometric study with the use of pattern recognition methods was carried out. Hierarchical cluster analysis (HCA), principal component analysis (PCA), as unsupervised exploratory techniques, and linear discriminant analysis (LDA), were applied to characterise, classify and distinguish the different types of infant formulae. The HCA results showed that mineral and trace element content data support adequate information to obtain the infant formula differentiation. PCA permitted the reduction of 13 variables to four principal components accounting for 61.9% of the total variability. This four-factor model interprets reasonably well the correlations of these studied elements. The obtained element associations may be attributed to the composition of matrix ingredients, the contamination during elaboration, the additives and mineral supplements added and the present tendency of standardization in the manufacture of infant formulae. The application of LDA gave a 77.1% of infant formulae correctly assigned with three clearly differentiated and two overlapped groups. The use of discriminant functions, as a complementary tool, to distinguish the different types depending on protein matrix of infant formula, is also discussed. This survey shows that HCA, PCA and LDA techniques appear useful tools for the characterisation and classification of infant formulae using their elemental profile.     

Progress of diffraction enhanced imaging at the Beijing Synchrotron Radiation Facility

A simple framework that allows a new general diffraction enhanced imaging (DEI) equation to be derived is presented. This latter equation may explain all open problems associated with the equation introduced by Chapman and those not explained by the first DEI equation, such as the noise background due to the small-angle scattering reflected by the analyzer. Combing the DEI equation with computed tomography (CT) theory, we propose a new DEI–CT formula that explains qualitatively the contour contrast caused by extinction of the refraction. Two formulae with a new method to extract the refraction angle are also introduced. Within this new theoretical framework the three components of the gradient of the refractive index can be reconstructed.     

Generalized Wiener indices in hexagonal chains

The Wiener index, or the Wiener number, also known as the “sum of distances” of a connected graph, is one of the quantities associated with a molecular graph that correlates nicely to physical and chemical properties, and has been studied in depth. An index proposed by Schultz is shown to be related to the Wiener index for trees, and Ivan Gutman proposed a modification of the Schultz index with similar properties. We deduce a similar relationship between these three indices for catacondensed benzenoid hydrocarbons (graphs formed of concatenated hexagons, or hexagonal chains, or sometimes acenes). Indeed, we may define three families of generalized Wiener indices, which include the Schultz and Modified Schultz indices as special cases, such that similar explicit formulae for all generalized Wiener indices hold on hexagonal chains. We accomplish this by first giving a more refined proof of the formula for the standard Wiener index of a hexagonal chain, then extending it to the generalized Wiener indices via the notion of partial Wiener indices. Finally, we discuss possible extensions of the result. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

A new approach to aid the characterisation and identification of metabolites of a model drug; partial isotope enrichment combined with novel formula elucidation software

This work describes the identification of ‘isotopically enriched’ metabolites of 4‐cyanoaniline using the unique features of the software package ‘Spectral Simplicity’. The software is capable of creating the theoretical mass spectra for partially isotope‐enriched compounds, and subsequently performing an elemental composition analysis to give the elemental formula for the ‘isotopically enriched’ metabolite. A novel mass spectral correlation method, called ‘FuzzyFit’, was employed. ‘FuzzyFit’ utilises the expected experimental distribution of errors in both mass accuracy and isotope pattern and enables discrimination between statistically probable and improbable candidate formulae. The software correctly determined the molecular formulae of ten previously described metabolites of 4‐cyanoaniline confirming the technique of partial isotope enrichment can produce results analogous to standard methodologies. Six previously unknown species were also identified, based on the presence of the unique ‘designer’ isotope ratio. Three of the unknowns were tentatively identified as N‐acetylglutamine, O‐methyl‐N acetylglucuronide and a putative fatty acid conjugate. The discovery of a significant number of unknown species of a model drug with a comprehensive history of investigation highlights the potential for enhancement to the analytical process by the use of ‘designer’ isotope ratio compounds. The ‘FuzzyFit’ methodology significantly aided the elucidation of candidate formulae, by provision of a vastly simplified candidate formula data set. Copyright © 2008 John Wiley & Sons, Ltd.     

New methods applicable for calibration of indicator electrodes

The new methods applicable for calibration of indicator electrodes, based on standard addition and standard subtraction methods, are suggested. Some of the methods enable the slope of an indicator electrode and equivalence volume V_eq to be determined simultaneously from a single set of potentiometric titration data. Some other methods known hitherto were also taken into account. A new model, based on a standard addition method, applicable also in nonlinear range for the ISE slope (S) is suggested, and its applicability was confirmed experimentally in calibration of calcium ISE.     

中药色谱指纹图谱相似度计算中保留时间校正方法的研究

从保留时间校正方法对线性推移、非线性推移和时间延迟的校正效果方面探讨了保留时间校正方法的适用范围。认为一点法校正仅能校正线性推移;两点法可以校正时间延迟和线性推移,并能部分校正非线性推移。多点法使用分段线性逼近的方法对非线性推移有良好的校正效果。     

Increased-valence formulae and the bonding of oxygen to haemoglobin

The molecular orbital configuration for the ground-state of O₂ generates the valence formula . “Increased-valence” formulae for triatomic and polyatomic molecules have been developed recently. In them, more electrons participate in bonding than is possible for the familiar valence-bond formulae. Using oxyhaemoglobin as an example of an oxygen carrier, various increased-valence formulae are generated for the FeO₂ groups. In the low-energy formulae, the iron is bonded to the above valence formula for O₂. Therefore, in contrast to the bonding schemes of Pauling and Coryell, Griffith and Weiss, little reorganization of O₂ need occur on formation of HbO₂. This conclusion is independent of the mode of co-ordination of iron to the O₂.     

Comparison of electrical mixture rules for composites

Firstly the basic theoretical methods of calculating the dielectric properties of heterogeneous mixtures are discussed. These are the mean field and effective medium theories and integral methods. Formulae are presented for systems containing parallel oriented ellipsoids and for randomly oriented ellipsoidal systems. Theoretical formulae are divided into two sub-groups: symmetric equations for statistical mixtures and asymmetric equations for matrix-inclusion type composites. In the former case only the relative amount of the components is important, in the second case phase inversion results in a change of the dielectric properties.Formulae are compared numerically using spherical and spheroidal systems with sharply different components (permittivity ratio is 1 100). In the case of asymmetric formulae the effect of phase inversion is studied as well. Percolation behaviour predicted by the equations is demonstrated and discussed. Functional shapes are compared in relation to the theoretical differences.Finally, experimental data are compared with the theoretical results, advantages and drawbacks of the various formulae are discussed. For spherical systems the simplest mean field formula yields somewhat worse values than effective medium or integral equations. The Looyenga equation does not work very well if the permittivity difference is high. For nonspherical systems the fit is better in general, even the simplest formula works satisfactorily. The shape independence predicted by the Looyenga theory for randomly oriented ellipsoids is in conflict with experimental data.     

Additivity rules using similarity models for chemical reactivity: calculation and interpretation of electrofugality and nucleofugality

A recently proposed, multi-parameter correlation: log k (25 degrees C)=s(f) (Ef + Nf), where Ef is electrofugality and Nf is nucleofugality, for the substituent and solvent effects on the rate constants for solvolyses of benzhydryl and substituted benzhydryl substrates, is re-evaluated. A new formula (Ef=log k (RCl/EtOH/25 degrees C) -1.87), where RCl/EtOH refers to ethanolysis of chlorides, reproduces published values of Ef satisfactorily, avoids multi-parameter optimisations and provides additional values of Ef. From the formula for Ef, it is shown that the term (sfxEf) is compatible with the Hammett-Brown (rho+sigma+) equation for substituent effects. However, the previously published values of N(f) do not accurately account for solvent and leaving group effects (e.g. nucleofuge Cl or X), even for benzhydryl solvolyses; alternatively, if the more exact, two-parameter term, (sfxNf) is used, calculated effects are less accurate. A new formula (Nf=6.14 + log k(BX/any solvent/25 degrees C)), where BX refers to solvolysis of the parent benzhydryl as electrofuge, defines improved Nf values for benzhydryl substrates. The new formulae for Ef and Nf are consistent with an assumption that sf=1.00(,) and so improved correlations for benzhydryl substrates can be obtained from the additive formula: log k(RX/any solvent/25 degrees C)=(Ef + Nf). Possible extensions of this approach are also discussed.     

New Temperature Integral Approximate Formula for Non-isothermal Kinetic Analysis

A new approximate formula for temperature integral is proposed. The linear dependence of the new fomula on x has been established. Combining this linear dependence and integration-by-parts, new equation for the evaluation of kinetic parameters has been obtained from the above dependence. The validity of this equation has been tested with data from numerical calculating. And its deviation from the values calculated by Simpson's numerical integrating was discussed. Compared with several published approximate formulae, this new one is much superior to all other approximations and is the most suitable solution for the evaluation of kinetic parameters from TG experiments. This revised version was published online in August 2006 with corrections to the Cover Date.     

How good is a Broyden–Fletcher–Goldfarb–Shanno-like update Hessian formula to locate transition structures? Specific reformulation of Broyden–Fletcher–Goldfarb–Shanno for optimizing saddle points

Based on a study of the Broyden–Fletcher–Goldfarb–Shanno (BFGS) update Hessian formula to locate minima on a hypersurface potential energy, we present an updated Hessian formula to locate and optimize saddle points of any order that in some sense preserves the initial structure of the BFGS update formula. The performance and efficiency of this new formula is compared with the previous updated Hessian formulae such as the Powell and MSP ones. We conclude that the proposed update is quite competitive but no more efficient than the normal updates normally used in any optimization of saddle points. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 349–362, 1998     

A novel method for estimation of transition temperature for polymorphic pairs in pharmaceuticals using heat of solution and solubility data

A novel method for thermodynamic stability studies of polymorphic drug substances has been developed. In order to estimate the transition temperature for an enantiotropic polymorphic pair, a formula for calculating the temperature at which the solubilities of each polymorph become equal has been derived with heat of solution and solubility as the variables. This formula is based on the assumption that van't Hoff plots (logarithmic solubility versus reciprocal of absolute temperature plots) of each polymorph show a straight line (heat of solution is independent of temperature) whose slope can be expressed as a function of heat of solution. The transition temperatures for seratrodast, acetazolamide and carbamazepine polymorphic pairs calculated by the formula were in good agreement with the results of previous studies. Furthermore, the calculated transition temperature for the indomethacin polymorphic pair was above the melting point, an unrealistic temperature range, suggesting that these polymorphs are monotropically related. Since this formula requires solubility data at only one arbitrary temperature other than heat of solution data for both polymorphs in a polymorphic pair, the proposed method is much faster than the conventional method requiring solubility data at five or more different temperatures for the preparation of van't Hoff plots.