The value of two-person zero-sum repeated games with incomplete information and uncertain duration

Fix a zero-sum repeated game Γ with incomplete information on both sides. It is known that the value of the infinitely repeated game Γ_∞ need not exist (Aumann and Maschler 1995). It is proved that any number between the minmax and the maxmin of Γ_∞ is the value of a long finitely repeated game Γ _n where players’ information about the uncertain number of repetitions n is asymmetric.     

Order-disorder transition in Na3Bi(PO4)2

Na₃Bi(PO₄)₂ exhibits several phase transitions at about 575, 820 and 905°C. The structure was determined at ambient temperature (α-form) and above the first transition (β-form). The α-form cell is monoclinic with a = 19.86(1), b = 5.353(6), c = 13.96(3) Å, β = 110.64(7)°, Z = 8, space group P2₁/ _c ; the structure was solved from 3769 independent reflections to an R value, calculated on intensities, of 0.069. The β-form cell is orthorhombic with a = 18.71(3), b = 7.18(2), c = 5.429(7) Å, Z = 4, space group Pnam; the structure was solved to an R value, calculated on structure factors, of 0.055 using intensities of 858 unique reflections measured on a single crystal at 650°C. Both structures are related to that of glaserite. At high temperature, one of the PO₄ tetrahedra is statistically disordered over two positions related by the m-mirror. Below the transition, ordering of this ion leads to a unit cell of lower symmetry. At the transition, two individuals grow on the two sides of the m-mirror which disappears; thus, at ambient temperature, the crystals are systematically twinned. Above the second transition, the unit cell is hexagonal.     

Lights Out on graphs

Mathematische Semesterberichte - We model the Lights Out game on general simple graphs in the framework of linear algebra over the field $$\mathbb{F}_{2}$$ . Based upon a version of the Fredholm...     

Effect of silver coating on electrochemical performance of 0.5Li2MnO3.0.5 LiMn1/3Ni1/3Co1/3O2 cathode material for lithium-ion batteries

Journal of Solid State Electrochemistry - In this work, a Li-rich layered 0.5Li2MnO3.0.5LiMn1/3Ni1/3Co1/3O2 (LMNCO) pristine cathode material synthesized with a glycine-nitrate combustion method is...