Beginning with the self-dual two-forms approach to the Einstein equations, we show how, by choosing basis spinors which are proportional to solutions of the Dirac equation, we may rewrite the vacuum Einstein equations in terms of a set of divergence-free vector fields, which obey a particular set of chiral equations. Upon imposing the Jacobi identity upon these vector fields, we reproduce a pre...

Single voltage vectors applied in the conventional model predictive torque control (MPTC) for multiphase motors do not only suffer from serious and stator flux ripples but also cause large harmonic current. To address aforementioned challenges, an MPTC using a modified dual virtual vector modulation method is proposed to improve operational performance of three-phase permanent magnet synchronou...

Vector fields whose flow preserves a symplectic form up to a constant, such as simple mechanical systems with friction, are called “conformal”. We develop a reduction theory for symmetric conformal Hamiltonian systems, analogous to symplectic reduction theory. This entire theory extends naturally to Poisson systems: given a symmetric conformal Poisson vector field, we show that it induces two r...

Some modified connection structures of the Finslerian gravitational field are considered by modifying the Finslerian independent variables (x, y) (i, j = 1, 2, 3, 4) in the following forms: (x, y, pj) (pj : co-vector dual to y); (x, y , z) (z: another vector chosen at one more microscopic level than the y−level); (x, ψ) (ψ: spinor). Mathematics Subject Classification: 53FB40, 83D05.

The triality properties of Dirac spinors are studied, including a construction of the algebra of (complexified) biquaternion. It is proved that there exists a vector-representation of Dirac spinors. The massive Dirac equation in the vector-representation is actually self-dual. The Dirac’s idea of non-integrable phases is used to study the behavior of massive term.

I. Positive energy representations of LSU(N) ................................................................. 477 II. Local loop groups and their von Neumann algebras ................................................. 491 III. The basic ordinary di€erential equation ..................................................................... 505 IV. Vector and dual vector primary ®elds ..................

We show that an inflationary background might be realized by using any pform non-minimally coupled to gravity. Standard scalar field inflation corresponds to the 0-form case and vector inflation to the 1-form. Moreover, we show that the 2and 3-form fields are dual to a new vector and scalar inflationary theories where the kinetic terms are non-minimally coupled to gravity.