We quantize the Hamilton equations instead of condition. The resulting equation has simple form ??u=0 in a fiber bundle, where Laplacian is Wheeler–DeWitt metric provided n?4. Using then separation variables, solutions u can be expressed as products temporal and spatial eigenfunctions, eigenfunctions are symmetric space SL(n,R)/SO(n). Since one define Schwartz tempered distributions SL(n,R)/SO(...

Quantization is instrumental in enabling the rich feature set of JPEG 2000. Several quantization options are provided within JPEG 2000. Part I of the standard includes only uniform scalar dead-zone quantization, while Part II allows both generalized uniform scalar dead-zone quantization and trellis coded quantization (TCQ). In this paper, an overview of these quantization methods is provided. I...

We consider the problem of stabilizing uncertain systems with quantization. The plant uncertainty is dealt with by the supervisory adaptive control framework, which employs switching among a finite family of candidate controllers. For a static quantizer, we quantify a relationship between the quantization range and the quantization error bound that guarantees closed loop stability. For a dynami...

In [23] a nice looking formula is conjectured for a deformed product of functions on a symplectic manifold in case it concerns a hermitian symmetric space of non-compact type. We derive such a formula for simply connected symmetric symplectic spaces using ideas from geometric quantization and prequantization of symplectic groupoids. We compute the result explicitly for the natural 2-dimensional...

In this paper we develop a way to count zero momentum modes in front-form quantization and apply it to several such approaches: canonical light-cone quantization; Dirac light-cone quantization; reduced phase space quantization ; and Penrose quantization. We also examine which of these light-cone methods are consistent with the Atiyah-Singer index theorem.

We raise the problem of constructing quantum observables that have classical counterparts without quantization. Specifically we seek to define and motivate a solution to the quantum-classical correspondence problem independent from quantization and discuss the general insufficiency of prescriptive quantization, particularly the Weyl quantization. We demonstrate our points by constructing time o...

This paper studies quantization error in the context of Matching Pursuit coded streams and proposes a new coefficient quantization scheme taking benefit of the Matching Pursuit properties. The coefficients energy in Matching Pursuit indeed decreases with the iteration number, and the decay rate can be upper-bounded with an exponential curve driven by the redundancy of the dictionary. The redund...

We solve for the critical coupling in symmetric phase of two-dimensional $\phi^4$ field theory using Discretized Light-Cone Quantization. adopt periodic boundary conditions, neglect zero mode, and obtain a consistent with reported conformal truncation light-front quantization. find 17% dfference from quantization polynomial basis.