In recent years, there has been rapid progress in aerodynamic optimization methods which use adjoint ow analysis to e ciently calculate the sensitivity of steady-state objective functions to changes in the underlying design variables. This paper shows that the same adjoint approach can be used in turbomachinery applications in which the primary concern is blade vibration due to harmonic ow unst...

Abstract We produce a short and elementary algorithm to compute an upper bound for the canonical dimension of spit semisimple linear algebraic group. Using this we confirm previously known bounds by Karpenko [6–9] Devyatov [5] as well new (e.g., groups types $F_4$, adjoint $E_6$, some groups).

An adjoint sensitivity method is presented for parameter-dependent differentialalgebraic equation systems (DAEs). The adjoint system is derived, along with conditions for its consistent initialization, for DAEs of index up to two (Hessenberg). For stable linear DAEs, stability of the adjoint system (for semi-explicit DAEs) or of an augmented adjoint system (for fully implicit DAEs) is shown. In...

Let X be the wonderful compactification of the semisimple adjoint algebraic group G. We show that the basis of H0(X,L) constructed in [CM03] is compatible with all B×B-orbit closures in X by defining subsets using only combinatorics of the underlying paths. Furthermore, we construct standard monomials on X that have properties similar to classical standard monomials.

For linear di erential algebraic equations of tractability index the notion of the adjoint equation is analysed in full detail Its solvability is shown at the lowest possible smoothness The fundamental matrices of both equations are de ned and their relationships are characterized

Let G be an adjoint algebraic group of type B, C, or D over an algebraically closed field of characteristic 2. We construct a Springer correspondence for the Lie algebra of G. In particular, for orthogonal Lie algebras in characteristic 2, the structure of component groups of nilpotent centralizers is determined and the number of nilpotent orbits over finite fields is obtained.

Second-order sensitivity analysis of multibody systems described by differentialz/algebraic equations: adjoint variable approach Jie-Yu Ding ab; Zhen-Kuan Pan b; Li-Qun Chen ac a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, P.R. China b College of Information Engineering, Qingdao University, Qingdao, P.R. China c Department of Mechanics, Shanghai Unive...

The geometric multiplicity of each eigenvalue of a self-adjoint Sturm-Liouville problem is equal to its algebraic multiplicity. This is true for regular problems and for singular problems with limit-circle endpoints, including the case when the leading coefficient changes sign.

We classify extremal curves in free nilpotent Lie groups. The classification is obtained via an explicit integration of the adjoint equation in Pontryagin Maximum Principle. It turns out that abnormal extremals are precisely the horizontal curves contained in algebraic varieties of a specific type. We also extend the results to the nonfree case.

Given a parametrization of a rational plane algebraic curve C, some explicit adjoint pencils on C are described in terms of determinants. Moreover, some generators of the Rees algebra associated to this parametrization are presented. The main ingredient developed in this paper is a detailed study of the elimination ideal of two homogeneous polynomials in two homogeneous variables that form a re...