A geometric quantization of a Kähler manifold, viewed as a symplectic manifold, depends on the complex structure compatible with the symplectic form. The quantizations form a vector bundle over the space of such complex structures. Having a canonical quantization would amount to finding a natural (projectively) flat connection on this vector bundle. We prove that for a broad class of manifolds,...

It is shown that the heat operator in the Hall coherent state transform for a compact Lie group K [Ha1] is related with a Hermitian connection associated to a natural one-parameter family of complex structures on T ∗K. The unitary parallel transport of this connection establishes the equivalence of (geometric) quantizations of T ∗K for different choices of complex structures within the given fa...

In this continuation paper the theory is further extended to reveal the connection between its formal aparatus, dealing with microscopic quantities, and the formal aparatus of thermodynamics, related to macroscopic properties of large systems. We will also derive the Born-Sommerfeld quantization rules from the formalism of the infinitesimal Wigner-Moyal transformations and, as a consequence of ...

Let us say that an infinite binary sequence q lies above an infinite binary sequence p if q can be obtained from p by replacing selected 0’s in p by 1’s. We show that above any infinite binary Martin-Löf random sequence p there exists an infinite binary nonrandom sequence q above which there exists an infinite binary random sequence r. This result is of interest especially in connection with th...

We consider tracefree meromorphic rank 2 connections over compact Riemann surfaces of arbitrary genus. By deforming the curve, the position of the poles and the connection, we construct the global universal isomonodromic deformation of such a connection. Our construction, which is specific to the tracefree rank 2 case, does not need any Stokes analysis for irregular singularities. It is thereby...

With the explosive growth of data in electronic commerce, rule finding becomes a crucial part in marketing. In this paper, we discuss the essential limitations of the existing metrics to quantify the interests of rules, and present the need of optimizing the interest metric. We describe the construction of the connection network that represents the relationships between items and propose a natu...

We have demonstrated the ability to trigger and guide high-voltage discharges with ionized filaments generated by femtosecond terawatt laser pulses. The plasma filaments extended over the whole gap, providing a direct ohmic connection between the electrodes. Laser-guided straight discharges have been observed for gaps of as much as 3.8 m at a high voltage reduced to 68% of the natural breakdown...

This paper details the development of the weak form formulations of finite element type methods using wavelets as basis functions. Such approaches are different from most wavelets based ones that are derived from the strong form. The advantages of the proposed formulation are that there is no need to enforce natural boundary conditions and that the lower order derivatives of the wavelet bases a...

In this article, we study digital repetitive control to track continuous-time periodic references. Sampled-data control gives a very natural platform for studying digital repetitive control, and in particular, sampled-data H∞ filtering is particularly suitable for this. The link is provided by introducing internal model control. This leads to a close connection between robust repetitive control...

Using natural lifting operations, we give a coordinate-free proof of the fact that connection used by Bordemann, Neumaier and Waldmann to construct Fedosov standard ordered star product on cotangent bundle Riemannian manifold is obtained symplectification complete lift corresponding Levi-Civita connection, in sense Yano Patterson. In terms local coordinates, this has already been shown Plebansk...