Isobaric analogue resonances in proton elastic scattering from 84Sr

The cross section for the reaction ⁸⁴Sr(p, p₀)⁸⁴Sr has been measured for proton energies in the range E_p = 4.18?6.73 MeV. Resonance parameters were determined for 15 isobaric analogue resonances. Spectroscopic factors calculated for the analogues by means of the R-matrix theory and the Green function method are compared with Spectroscopic factors determined from the ⁸⁴Sr(d, p)⁸⁵Sr reaction. Angular distributions were measured at E_p = 7 and 12 MeV in order to obtain optical model parameters.     

Structural information from EPR powder spectra of Mn(II)-doped Rb2MgCl4, Rb2MgCl3Br and Rb2MgCl2Br2

The structure of the compounds Rb₂MgCl₄, Rb₂MgCl₃Br and Rb₂MgCl₂Br₂ has been determined to be the tetragonal K₂NiF₄ structure. EPR spectra at X and Q-band frequencies of the polycrystalline samples of the Mn(II)-doped compounds, indicate that the Br^? ions prefer to order at special sites of the structure, as concluded from the fact that only octahedral groups [MgCl₆] and tetragonal groups [MgCl₄Br₂] are found.     

Fixed‐parameter decidability: Extending parameterized complexity analysis

We extend the reach of fixed‐parameter analysis by introducing classes of parameterized sets defined based on decidability instead of complexity. Known results in computability theory can be expressed in the language of fixed‐parameter analysis, making use of the landscape of these new classes. On the one hand this unifies results that would not otherwise show their kinship, while on the other it allows for further exchange of insights between complexity theory and computability theory. In the landscape of our fixed‐parameter decidability classes, we recover part of the classification of real numbers according to their computability. From this, using the structural properties of the landscape, we get a new proof of the existence of P ‐selective bi‐immune sets. Furthermore, we show that parameter values in parameterized sets in our uniformly fixed‐parameter decidability classes interact with both instance complexity and Kolmogorov complexity. By deriving a parameter based upper bound on instance complexity, we demonstrate how parameters convey a sense of randomness. Motivated by the instance complexity conjecture, we show that the upper bound on the instance complexity is infinitely often also an upper bound on the Kolmogorov complexity.     

Phase transitions in self-dual generalizations of the Baxter–Wu model

We study two types of generalized Baxter–Wu models, by means of transfer-matrix and Monte Carlo techniques. The first generalization allows for different couplings in the up- and down-triangles, and the second generalization is to a q-state spin model with three-spin interactions. Both generalizations lead to self-dual models, so that the probable locations of the phase transitions follow. Our numerical analysis confirms that phase transitions occur at the self-dual points. For both generalizations of the Baxter–Wu model, the phase transitions appear to be discontinuous.     

Linear-chain antiferromagnetism in Ni(N2H5)2(SO4)2

The compound dihydrazinium bis(sulfato) niccolate(II), Ni(N₂H₅)₂(SO₄)₂, containing sulfato-bridged chains of Ni(II) ions, can be described as an antiferromagnetic Heisenberg linear-chain system. A reasonable agreement of susceptibility measurements in the temperature region 2–80K, with a theory developed by Weng for antiferromagnetic Heisenberg linear chains with spin S=1, is obtained for a value of the intra-chain interaction $\text{J}\text{k}\text{=?3.35K}$. Preliminary results of specific heat measurements, on the other hand, do not fit quite well using this model. The origin of this discrepancy is suggested to be a zero-field splitting of the single ion.     

The synthesis of angular methyl substituted bicyclic enones via a unique regioselective enamine annulation reaction

Enamines of 2,4,4-trimethylcyclopentanone 5 and of 2,5,5-trimethylcyclohexanone 14 react with methyl vinyl ketone to afford the bicyclic enones 9 and 15 in yields up to 70%. The formation of these products bearing an angular Me group is the result of an anomalous enamine Robinson annulation reaction, due to an alkylation of the enamine in the first step at its most substituted α-position. The effect of substitution in the α- and β′-position in the cycloalkanone, its ringsize, the structure of the Michael acceptor (alkyl vinyl ketone) was illustrated in reactions of the enamines of 2,5-dimethylcyclohexanone 22, carvomenthone 19, menthone 26, dihydrocarvone 28 and tetrahydroeucarvone 32 with methyl- and/or ethyl vinyl ketone.     

Rigid ground state structure of 1,2-dihydro-3H-benz[e]inden-3-one deformed in the lowest electronic triplet state

The X-ray diffraction of crystalline 1,2-dihydro-3H-benz[e]inden-3-one (DHBI) reveals that the molecular geometry is fully planar in the electronic ground state. Glassy solutions of naphthaldehyde, 2-acetonaphthone and methyl 2-naphthoate in the mixtures methylcyclohexane/iso-pentane (MIP) and methanol/ethanol (ME) are phosphorescent. DHBI in ME shows phosphorescence, but in MIP it is non-phosphorescent. The phosphorescence spectra of these compounds and of naphthalene have a strong resemblance. This is in accordance with a molecular distortion in the lowest triplet state, which decouples the π electron systems of the carbonyl group and the naphthyl group. The absence of phosphorescence of DHBI in MIP, indicates a geometry of the triplet state, having a non-planar naphthalene ring, when the molecule is in the non-hydrogen bonded form.     

Antiferromagnetic interaction in dichlorobis (pyrazole) manganese (II); three independent determinations

The value of the antiferromagnetic interaction in the supposed linear chain compound, Mn(pyrazole)₂Cl₂, has been determined with the aid of low-temperature susceptibility and specific heat measurements, and paramagnetic resonance linewidth studies. The results of the measurements are consistent with each other and yield a $\text{J}\text{k}$ value of ?0.85 ± 0.05 K.     

Linear-chain antiferromagnetism in the compounds MII(N2H5)2(SO4)2 with M = Mn,Fe, Co,Ni, and Cu

Powder-susceptibility measurements in the temperature region 2–80° K on the chain compounds M^II(N₂H₅)₂(SO₄)₂, with M = Mn, Fe, Co, Ni, and Cu, show that the magnetic properties of these compounds can be interpreted in terms of antiferromagnetic linear-chain systems. The experimental results provide information on the magnitude of the intrachain interactions. In addition, ESR linewidth experiments were used for a determination of the intrachain interaction in Mn(N₂H₅)₂ (SO₄)₂. For the interpretation of the data on Fe(N₂H₅)₂(SO₄)₂, the parallel susceptibility of Ising chains with S = 2 is calculated theoretically. An estimate for the ratio between the intra- and interchain coupling is given. Use is made of preliminary results of specific heat measurements on these compounds for the interpretation of the magnetic data.     

Program equilibrium—a program reasoning approach

The concept of program equilibrium, introduced by Howard (Theory and Decision 24(3):203–213, 1988) and further formalised by Tennenholtz (Game Econ Behav 49:363–373, 2004), represents one of the most ingenious and potentially far-reaching applications of ideas from computer science in game theory to date. The basic idea is that a player in a game selects a strategy by entering a program, whose behaviour may be conditioned on the programs submitted by other players. Thus, for example, in the prisoner’s dilemma, a player can enter a program that says “If his program is the same as mine, then I cooperate, otherwise I defect”. It can easily be shown that if such programs are permitted, then rational cooperation is possible even in the one-shot prisoner’s dilemma. In the original proposal of Tennenholtz, comparison between programs was limited to syntactic comparison of program texts. While this approach has some considerable advantages (not the least being computational and semantic simplicity), it also has some important limitations. In this paper, we investigate an approach to program equilibrium in which richer conditions are allowed, based on model checking—one of the most successful approaches to reasoning about programs. We introduce a decision-tree model of strategies, which may be conditioned on strategies of others. We then formulate and investigate a notion of “outcome” for our setting, and investigate the complexity of reasoning about outcomes. We focus on coherent outcomes: outcomes in which every decision by every player is justified by the conditions in his program. We identify a condition under which there exist a unique coherent outcome. We also compare our notion of (coherent) outcome with that of (supported) semantics known from logic programming. We illustrate our approach with many examples.