Analytical solutions of N‐person games

The possibility of analytical solutions of N‐person games is presented. A simple formula provides valuable information about the outcomes of such games with linear payoff functions and Pavlovian agents. Experiments performed with our simulation tool for the multiagent stag hunt dilemma game are presented. For the case of Pavlovian agents the game has nontrivial but remarkably regular solutions. If both payoff functions are linear and the real solutions of Eq. (2) are both positive, then the analytical solutions are remarkably accurate. © 2012 Wiley Periodicals, Inc. Complexity, 2012     

Open retractions onto n-ods

We characterize dendrites which admit an open retraction onto an arbitrary n-od. The paper contains also several corollaries and two problems concerning the subject     

Spin crossover of spiro-biphenalenyl neutral radical molecular conductors

We present ab initio molecular and solid-state calculations at the level of density functional theory (DFT) for the ethyl-substituted spiro-biphenalenyl neutral radical organic conductor. We find that the phase transition of this material is accompanied by a spin crossover (low-spin, LS, to high-spin, HS), and consequently a different band becomes the conduction band. The energy gap (Eg) increases from 0.12 eV of the low-temperature polymorph to 0.23 eV of the high-temperature polymorph corresponding to a different occupancy causing a change in the number of the available charge carriers, explaining the change of conductivity by 2 orders of magnitude at the phase transition. These gap values are also consistent with structural, IR, electrical conductivity, and magnetic susceptibility data of Itkis et al. The proximity of the monomers in the stacking dimers is closely related to the spin crossover in this material.     

Higher order Peierls distortion of one-dimensional carbon skeletons

In some one-dimensional chains with metallic band structures the energetically most advantageous distortion opens an energy gap non-linear in the distortion. The absence of a linear Peierls effect is due to the symmetry of the degenerate pair of orbitals at the Fermi level: they do not interact directly in the distorted system. The effect provides a natural bridging of the one-dimensional polyacetylene (linearly Peierls-distorted) to the two-dimensional graphite (not distorted) carbon skeletons. The simple explanation bears some generality.     

Determination of the expected decrease in strength of high alumina cement concrete by derivatography

Methods involving the use of the derivatograph in the determination of the expected decrease in strength of high alumina cement are described. In a series of steps the strength, porosity and the cement content of the concrete are determined by physico-chemical measurements. The actual phase composition of the cement component of concrete is determined by derivatography. Methods of separating the two overlapping peaks due to the dehydration of the calcium aluminate hydrates present in the cement are described.     

Desorption electrospray ionization–mass spectrometric analysis of low vapor pressure chemical particulates collected from a surface

The collection of a low vapor pressure chemical simulant triethyl phosphate sorbed onto silica gel (TEP/SG) from a surface with subsequent analysis of the TEP/SG particulates using desorption electrospray ionization–mass spectrometry (DESI–MS) is described. Collection of TEP/SG particulates on a surface was accomplished using a sticky screen sampler composed of a stainless steel screen coated with partially polymerized polydimethylsiloxane (PDMS). DESI–MS analysis of TEP/SG particulates containing different percentages of TEP sorbed onto silica gel enabled the generation of response curves for the TEP ions m/z 155 and m/z 127. Using the response curves the calculation of the mass of TEP in a 25 wt% sample of TEP/SG was calculated, results show that the calculated mass of TEP was 14% different from the actual mass of TEP in the sample using the m/z 127 TEP ion response curve. Detection limits for the TEP vapor and TEP/SG particulates were calculated to be 4 μg and 6 particles, respectively.     

On the growth of Betti numbers of locally symmetric spaces

We announce new results concerning the asymptotic behavior of the Betti numbers of higher rank locally symmetric spaces as their volumes tend to infinity. Our main theorem is a uniform version of the Lück Approximation Theorem (Lück, 1994 [10]) which is much stronger than the linear upper bounds on Betti numbers given by Gromov in Ballmann et al. (1985) [3].The basic idea is to adapt the theory of local convergence, originally introduced for sequences of graphs of bounded degree by Benjamini and Schramm, to sequences of Riemannian manifolds. Using rigidity theory we are able to show that when the volume tends to infinity, the manifolds locally converge to the universal cover in a sufficiently strong manner that allows us to derive the convergence of the normalized Betti numbers.