Notes on the complexity of sorting in abstract machines

The complexity of sorting with pointer machines and successor-predecessor random access machines is studied. The size of the problem is defined as the length of the problem string. A linear time algorithm is achieved for sorting by pointer machines. For successor-predecessor random access machines linear time is sufficient in a special case.     

Determination of antimony in geochemical samples by graphite furnace atomic absorption spectrometry using different matrix modifiers

Determination of antimony by graphite furnace atomic absorption spectrometry using five different matrix modifiers, viz. nitric acid, copper, nickel, molybdenum and palladium, together with L'vov platform was studied. Without matrix modification, antimony was lost in a 1.2-M HCl solution when the thermal pretreatment temperature exceeded 700°C. By using 1.4 M HNO₃ or $\text{1μg}\text{20μl}$ copper solution the thermal pretreatment temperature could be increased up to 900°C. The matrix modification with $\text{2μg}\text{20μl}$ palladium, $\text{4μg}\text{20μl}$ molybdenum, or $\text{20μg}\text{20μl}$ nickel allowed the use of 1300°C as the pretreatment temperature. The best results were obtained with palladium when its concentration exceeded $\text{0.8μg}\text{20μl}$. Chemical interferences were studied with standard solutions spiked with different metal chlorides. The severe interference caused by iron chloride was avoided with ascorbic acid (2.5 %, $\text{w}\text{v}$). The method was tested on some geochemical reference samples.     

NP-completeness of the hamming salesman problem

It is shown that the traveling salesman problem, where cities are bit strings with Hamming distances, is NP-complete.     

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.     

Photoabsorption spectra of boron nitride fullerenelike structures

Optical absorption spectra have been calculated for a series of boron nitride fullerenelike cage structures BnNn of sizes n=12-36. The method used is a real-time, real-space implementation of the time-dependent density-functional theory, involving the full time propagation of the time-dependent Kohn-Sham equations. The spectra are found to be a possible tool for distinguishing between different boron nitride fullerene species and isomers. The trends and differences in the spectra are found to be related to the general geometry of the molecules. Comparison between local-density and generalized-gradient approximations for electron exchange-correlation functionals shows that both of them produce essentially the same spectral characteristics.     

Prospects for constrained supersymmetry at $$\sqrt{s}={33}\,\text {TeV} $$ and $$\sqrt{s}={100}\,\text {TeV} $$ proton–proton super-colliders

Successful models of pure gravity mediation (PGM) with radiative electroweak symmetry breaking can be expressed with as few as two free parameters, which can be taken as the gravitino mass and \(\tan \beta \) . These models easily support a 125–126 GeV Higgs mass at the expense of a scalar spectrum in the multi-TeV range and a much lighter wino as the lightest supersymmetric particle. In these models, it is also quite generic that the Higgs mixing mass parameter, \(\mu \) , which is determined by the minimization of the Higgs potential is also in the multi-TeV range. For \(\mu >0\) , the thermal relic density of winos is too small to account for the dark matter. The same is true for \(\mu <0\) unless the gravitino mass is of order 500 TeV. Here, we consider the origin of a multi-TeV \(\mu \) parameter arising from the breakdown of a Peccei–Quinn (PQ) symmetry. A coupling of the PQ-symmetry breaking field, \(P\) , to the MSSM Higgs doublets, naturally leads to a value of \(\mu \sim \langle P \rangle ^2 /M_P \sim {\mathcal O}(100)\) TeV and of the order that is required in PGM models. In this case, axions make up the dark matter or some fraction of the dark matter with the remainder made up from thermal or non-thermal winos. We also provide solutions to the problem of isocurvature fluctuations with axion dark matter in this context.     

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).