We prove that $QH^*_{\\mathrm{aff}}(G/B)$ is a Frobenius algebra, and that the new quantum product determines a flat Dubrovin connection. We further develop an analogue of Givental and Kim formalism for this ring and we deduce a presentation of $QH^*_{\\mathrm{aff}}(G/B)$ by ...
Using the Frobenius norm to compute the representation error facilitates the use of the kernel trick; see (9). However, the Frobenius norm implicitly assumes that the noise follows a Gaussian distribution. How can the kernel trick be applied on non-Gaussian noise models including, e.g., gross...
In Section 5, we give the definitions of exponential families and curved exponential families. In Sections 6 Statistical inference on curved exponential families, 7 Bayesian statistics of curved exponential families, we give brief summaries of geometry of statistical inferences and Bayesian statistics. ...
Keywords. Affine semigroup, factorizations, Frobenius problem, gluing semigroup, semigroup ideal. Introduction An affine semigroup S ⊂ Nq is a set containing 0 and closed under addition. A finite set A = {a1, . . . , ah} ⊂ Nq is a generating set of S if S = h i=1 λiai ...
N. E. Belova, “Bundles of biaxial spaces generated by the algebra of antiquaternions,” in: Motions in Generalized Space [in Russian], Penza (2000), pp. 17–30. K. M. Budanov and A. V. Voevodin, “On Frobenius Weil algebras of width 2,” Differ. Geom. Mnogoobr. Figur, 37,...
As a consequence we prove that (O, f ) saturates when G = Zcl( ) is a Q-morphic image of SL2 or the unit group of a quaternion algebra over Q. This already has a number of classical appli- cations (see Sect. 6). 1Unless indicated otherwise, the Zariski closure is in affine ...