In this article, we study geometric unitaries of JB-algebras (in particular, self-adjoint parts of C∗-algebras). We will show that the geometric unitaries of a JB algebra are precisely those central algebraic unitaries (or central symmetries). We will also show that the group of surjective isometries on a JB-algebra A (with point-norm topology) is the semi-direct product of the canonical action...

This article is based on the author’s talk at international conference dedicated to memory of Professor B. Yu. Sternin (Moscow, November 6–9, 2018). The Hochschild homology and cohomology a group algebra can be described via classifying space adjoint action groupoid under suitable assumption finiteness supports groups. difference between leads correction results in D. J. Benson’s book Represent...

In this paper, we find explicit solution to the operator equation $TXS^* -SX^*T^*=A$ in the general setting of the adjointable operators between Hilbert $C^*$-modules, when $T,S$ have closed ranges and $S$ is a self adjoint operator.

It is described how one can see the signs of action structure constants directly in the weight diagram of microweight and adjoint representations for groups of types E6, E7, and E8. This generalizes the results of the preceding paper, “A third look at weight diagrams”, where a similar algorithm was discussed for microweight representations of E6 and E7. The proofs are purely combinatorial and c...

The effective action of N = 2 gauge multiplets in general includes higher-dimension UV finite nonholomorphic corrections integrated with the full N = 2 superspace measure. By adding a hypermultiplet in the adjoint representation we study the effective action of N = 4 SYM. The nonanomalous SU(4) R-symmetry of the classical N = 4 theory must be also present in the on-shell effective action, and t...

2 Discretization 9 2.1 The Discontinuous Galerkin Method . . . . . . . . . . . . . . . . . . . . . 9 2.1.1 Conservation Equations . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.2 Solution Approximation . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.3 Weak Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1.4 Discrete System . . . . . . . . . . . . . . . . . ....

We investigate the behavior of adaptive time stepping numerical algorithms under the reverse mode of automatic differentiation (AD). By differentiating the time step controller and the error estimator of the original algorithm, reverse mode AD generates spurious adjoint derivatives of the time steps. The resulting discrete adjoint models become inconsistent with the adjoint ODE, and yield incor...

2 Discretization 9 2.1 The Discontinuous Galerkin Method . . . . . . . . . . . . . . . . . . . . . 9 2.1.1 Conservation Equations . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.2 Solution Approximation . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.3 Weak Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1.4 Discrete System . . . . . . . . . . . . . . . . . ....

The main purpose of this study is to estimate the step heat fluxes applied to the wall of a two-dimensional symmetric channel with turbulent flow. For inverse analysis, conjugate gradient method with adjoint problem is used. In order to calculate the flow field,   two equation model is used. In this study, adjoint problem is developed to conduct an inverse analysis of heat transfer in a channel...