What are some examples of affine symmetry groups? What is affine crystallography?

Error messages, warnings, and informational messages ... HEAD files are actually used. -matvec mmm = Read an affine transformation matrix-vector from file Dec 12, 2022 ... ... affine function of p. Then γ(a) (resp., α(a)) can be identified as a ... Aggregation, determinacy, and informational efficiency for a class. Feb 10, 2022 ... existential results about random variables before (e.g. [53], [54]), so the study of affine constraints is not unnatural. We also prove the ... Strain Information Only. Some algal strains are no longer available to purchase at UTEX. Since many research articles and publications—especially older ... Feb 11, 2014 ... (a, i). In this case, affine transformations are allowed for two utility profiles that are infor- mationally equivalent. Although there is ... Apr 21, 2020 ... ... affine, Lipschitz. Continuous, and convex. Moreover, any such representation of Б is unique up to a positive affine transformation. The proof ... assume that it is affine in the state variables. Hence, the ... long-term investors economy is more informative, while with diffuse informational arrival ... ... which is affine in the fundamentals and the endogenous information signals. ... Properties of equilibrium, such as informational efficiency and its ... Feb 7, 2023 ... The price of anarchy of affine congestion games with similar strategies. ... Informational incentives for congestion games. In 2017 55th ... The results are applied to special (phase space) representations of the Heisenberg, affine, and Ga- lilei groups. 0 1995 American Institute of Physics. I.