Different aspects of the monotonicity of a function

In this paper, we investigate which aspects are overriding in the concept images of monotonicity of Finnish tertiary mathematics students, i.e., on which aspects of monotonicity they base their argument in different types of exercises related to that concept. Further, we examine the relationship between the quality of principal aspects and the success in solving monotonicity exercises and a few other standard problems in calculus. Our findings indicate that a mathematics student's conception about monotone functions is often restricted to continuous or differentiable functions and the algebraic aspect – the nearest one to the formal definition of monotonicity – is rare.     

A generalization of the role expectation conflict theory with a methodological analysis

Gross’, Mason's and McEachern's role conflict theory with two incompatible role expectations is generalized by letting the number of incompatible role expectations increase. It is proved that the generalized theory is consistent and that its four axioms are independent. Three methodological results are proven. They show that the generalized theory is, in principle, testable from the point of view of three different well‐defined testing situations. Finally, it is shown that the original theory is a special case of the generalization.     

Determination of Bromine by Aluminium Monobromide Molecular Absorption Spectrometry Using Arsenic Atomic Lines

The present study was conducted to investigate the molecular absorption by AlBr in a carbon rod furnace for determination of bromine, by using the arsenic atomic line at 279.028 nm emitted from an As- hollow cathode lamp. A deuterium lamp was used for the simultaneous background correction. The interference caused by the other halogenides and some cations was also examined. The method was applied to determine bromine in organic matrice.     

Nonadiabatic Ehrenfest molecular dynamics within the projector augmented-wave method

We derive equations for nonadiabatic Ehrenfest molecular dynamics within the projector augmented-wave (PAW) formalism. The discretization of the electrons is time-dependent as the augmentation functions depend on the positions of the nuclei. We describe the implementation of the Ehrenfest molecular dynamics equations within the real-space PAW method. We demonstrate the applicability of our method by studying the vibration of NaCl, the torsional rotation of H(2)C=NH(2)(+) in both the adiabatic and the nonadiabatic regimes, and the hydrogen bombardment of C(40)H(16).     

Spectrophotometric determination of iron with 1-hydroxy-4-sulpho-2-naphthoic acid

1-Hydroxy-4-sulpho-2-naphthoic acid (H(3)L) is proposed as a spectrophotometric reagent for determination of iron. It gives a red-brown chelate, FeL(6-)(3), with lambda(max) 500-520 nm at pH 8 ( = 3.3 x 10(3) l. mole(-1). cm(-1)). In this wavelength region the reagent has no absorption. Most common cations and oxo-anions do not interfere. In the determination of iron in polymetallic iron ores and aluminium alloys the relative error and relative standard deviation of the method were found to be better than 1 and 0.5%, respectively. 1-Hydroxy-4-sulpho-2-naphthoic acid seems to be a more sensitive and accurate reagent for iron than 5-sulphosalicylic acid, and the number of interfering ions is smaller than in the 1,10-phenanthroline or thiocyanate methods.     

Complex formation between aluminium and 3-hydroxy-7-sulpho-2-naphthoic acid Potentiometric, absorption-spectrophotometric and spectrofluorometric studies in aqueous solution

The formation of chelates between aluminium(III) and 3-hydroxy-7-sulpho-2-naphthoic acid has been studied in aqueous solutions of various ionic strengths, at 298 K. The stability constants of AlL, AlL(2) and AlL(3) and the protonation constants of the ligand, obtained by potentiometry with the glass electrode, are compared with values found by absorption and fluorescence spectrophotometric methods.     

On the origin of residual dipolar couplings from denatured proteins

Effects of steric obstruction on random flight chains are examined. Spatial probability distributions are elaborated to calculate residual dipolar couplings and residual chemical shift anisotropy, parameters that are acquired by NMR spectroscopy from solutes dissolved in dilute liquid crystals. Calculations yield chain length and residue position-dependent values in good agreement with simulations to provide understanding of recently acquired data from denatured proteins.     

On the interpretation of residual dipolar couplings as reporters of molecular dynamics

The analysis of residual dipolar couplings from an ensemble of conformations to extract molecular dynamics is intricate. The very mechanism that is necessary to perturb overall molecular tumbling to generate nonvanishing residual dipolar couplings gives rise to convoluted data. The measured values are essentially weighted averages over conformations. However, the weights are not simply the populations of conformations. Consequently, the observed order parameter is not exactly the true measure of motion. In the case of paramagnetic alignment, the apparent order parameter is expected to depend on the number of torsions that separate the locus of interest from the paramagnetic site. In the case of alignment due to steric obstruction, the uneven selection of conformations by their differing Saupe order matrices leads to a bias in the residual dipolar couplings-probed molecular dynamics.     

Efficient decomposition of quantum gates

Optimal implementation of quantum gates is crucial for designing a quantum computer. We consider the matrix representation of an arbitrary multiqubit gate. By ordering the basis vectors using the Gray code, we construct the quantum circuit which is optimal in the sense of fully controlled single-qubit gates and yet is equivalent with the multiqubit gate. In the second step of the optimization, superfluous control bits are eliminated, which eventually results in a smaller total number of the elementary gates. In our scheme the number of controlled NOT gates is O(4(n)) which coincides with the theoretical lower bound.