We extend classical results of Kostant and al. on multiplets of representations of finite-dimensional Lie algebras and on the cubic Dirac operator to the setting of affine Lie algebras and twisted affine cubic Dirac operator. We prove in this setting an analogue of Vogan’s conjecture on infinitesimal characters of Harish–Chandra modules in terms of Dirac cohomology. For our calculations we use ...

Based on the recent work [4] we put forward a new type of transformation for Lorentzian manifolds characterized by mapping every causal future-directed vector onto a causal future-directed vector. The set of all such transformations, which we call causal symmetries, has the structure of a submonoid which contains as its maximal subgroup the set of conformal transformations. We find the necessar...

In this paper, we introduce and investigate a general transformation or change of Finsler metrics, which is referred to as a generalized β-conformal change: L(x, y) −→ L(x, y) = f(eL(x, y), β(x, y)). This transformation combines both β-change and conformal change in a general setting. The change, under this transformation, of the fundamental Finsler connections, together with their associated g...

In this paper, we introduce and investigate a general transformation or change of Finsler metrics, which is referred to as a generalized β-conformal change: L(x, y) −→ L(x, y) = f(eL(x, y), β(x, y)). This transformation combines both β-change and conformal change in a general setting. The change, under this transformation, of the fundamental Finsler connections, together with their associated g...

Following the mathematical approach of Kelly (2003), rigorous version of infinitesimal deformation approach (ID) was applied to analyze fcc  bcc martensitic phase transformation observed in Fe-31wt Ni alloys considering the twinning shear system as the lattice invariant system (LIS). The expressions for crystallographical parameters associated with the martensitic phase transformation such as...

As the a's approach certain limiting values, one or more of which is infinite, Ta may have a definite finite transformation T as a limit. The transformation T may be regarded as a transformation of the family, and, if equivalent to a transformation Tb with finite parameters, can be generated by an infinitesimal transformation of the family (namely, bxXx + •" + brXr), but not otherwise.* Let it ...

Gregory S. Chirikjian Johns Hopkins University 2.1 Rotations in Three Dimensions Rules for Composing Rotations • Euler Angles • The Matrix Exponential 2.2 Full Rigid-Body Motion Composition of Motions • Screw Motions 2.3 Homogeneous Transforms and the Denavit-Hartenberg Parameters Homogeneous Transformation Matrices • The Denavit-Hartenberg Parameters in Robotics 2.4 Infinitesimal Motions and A...

Remark : An alternative approach, advocated in [4], is to use the infinitesimal invariance criteria, which requires solving a linear system of first order partial differential equations based on the prolonged infinitesimal generators of the transformation group. In contrast, the moving frame method is completely algebraic, typically much simpler, and, moreover provides significantly more inform...

We illustrate why a space-time structure as in General Relativity is not in contradiction with a dynamical origin of gravity from a scalar field. Further, we argue that the recently discovered gap-less mode of the singlet Higgs field represents the most natural dynamical agent of Newtonian gravity. 1. Following the original induced-gravity models [1], one may attempt to describe gravity as an e...

The main aim of this paper is to investigate the nature invariance rectifying curve under conformal transformation and obtain a sufficient condition for which such remains conformally invariant. It shown that normal component geodesic curvature homothetic