Cotangent

SInaA Coiina A Tangent A Cotangent A Secant A Cosecant A... 

The dissipation factor is a ratio of the real power (in-phase power) to the reactive power (power 90° out of phase). It is also defined as (1) IT is the ratio of conductance of a capacitor in which the material is the dielectric to its susceptance, (2) IT is the ratio of its parallel reactance to its parallel resistance it is the tangent of the loss angle and the cotangent... 

The graphic interpretation of the above conditions consists in selecting the branch of the cotangent curve in Eq. (A 1.83) that intersects the straight line y = ml Am at the inflection point (see Fig. A 1.3 where the inflection points are connected by a dotted line). For the Debye spectrum, we have... 

Obviously Z(12)(Jf) is isomorphic to the Grassmannian bundle Grass(2,Tfr) of two-dimensional quotients of the cotangent bundle of X. We put... 

The Semple bundle varieties were first introduced in [Semple (1)]. In [Collino (1)], [Colley-Kennedy (1),(2)] they are considered for arbitrary smooth surfaces. The construction of Fn(X) for an arbitrary smooth projective variety X is an obvious generalisation. For our purposes it appears to be slightly more practical to use the tangent bundles instead of the cotangent bundles in the construction. 

Hilbert scheme on the cotangent bundle of a Riemann surface... 

The Hilbert scheme of points on the cotangent bundle of a Riemann surface has a natural holomorphic symplectic structure together with a natural C -action. In this case, the unstable manifold is very important since it becomes a Lagrangian submanifold. The same kind of situation appears in many cases, for example when one studies the moduli space of Higgs bundle or the quiver varieties [62], and it is worth explaining this point before studying the specific example. 

Now we shall study the Hilbert scheme of points on the cotangent bundle of a Riemann surface. Let E be a Riemann surface and T E its cotangent bundle. There exists a natural holomorphic symplectic form uc on T E. The multiplication by a complex number on each fiber gives a natural C -action on T E, and with respect to this action we have "(p uJc = tuc for t E C, where we denote the action of t by T E T E. As explained in Theorem 1.10, the Hilbert scheme inherits a holomorphic symplectic form and... 

HILBERT SCHEME ON THE COTANGENT BUNDLE OF A RIEMANN SURFACE... 

Tangent of the loss angle and the cotangent of the phase angle... 

L. Illusie, Complexe cotangent et deformations I,II. Lecture Notes in Math. 239 283, Springer-Verlag (1971, 1972). 

CTMTN ccn cyclotrimethylenetrinitramine (RDX) cotangent(see also cot) c si Czecho-Slovakia D... 

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