In this article, we show that a finite dimensional Hilbert space can have an infinite Bessel sequence, but a normalized Bessel sequence in a finite dimensional Hilbert space must be of finite length. A relation between the dimension of a given finite dimensional Hilbert space and the bound of any finite normalized tight frame for the underlying space is obtained. Also some properties of the fra...

Inspired by Hintikka’s treatment of question embedding verbs in [8] and the variations of noncontingency operator, we propose a logic with strong noncontingency operator N as the only primitive modality. A proposition is strongly noncontingent, if no matter whether it is true or false, it does it necessarily; otherwise, it is weakly contingent. This logic is not a normal modal logic, since N(φ ...

Concept languages have been studied in order to give a formal account of the basic features of frame-based languages. The focus of research in concept languages was initially on the semantical reconstruction of frame-based systems and the computational complexity of reasoning. More recently, attention has been paid to the formalization of other aspects of frame-based languages, such as non-mono...

Restoration of image sequences is an important problem that can be encountered in many im age processing applications such as visual communications robot guidance and target tracking The independent restoration of each frame in an image sequence is a suboptimal approach be cause the between frame correlations are not explicitly taken into consideration In this paper we address this problem by p...

Restoration of image sequences is an important problem that can be encountered in many image processing applications, such as, visual communications, robot guidance and target tracking. The independent restoration of each frame in an image sequence is a suboptimal approach because the between-frame correlations are not explicitly taken into consideration. In this paper we address this problem b...

With help of direct calculation, it is revealed that an essential concept in deriving the Boltzmann collisional operator, the scattering cross section in the laboratory frame, cannot be well defined. Along this line, it is suggested that the collisional operator, as well as the entire Boltzmann equation, should be reconsidered.

The Schrödinger operator on the Newtonian space-time is defined in a way which is independent on the class of inertial observers. In this picture the Schrödinger operator acts not on functions on the space-time but on sections of certain one-dimensional complex vector bundle over spacetime. This bundle, constructed from the data provided by all possible inertial observers, has no canonical triv...

The nuclear magnetic resonance (NMR) spin relaxation rate constant in the rotating frame of reference R1 provides information on microsecond to millisecond ( s-ms) timescale kinetic processes that stochastically modulate the resonance frequencies of nuclear spins in molecules. Expressions for R1 are presented for two-site chemical exchange using both the conventional perturbation approach for e...

We consider Γ = (X, E) a dual polar graph and we give a tight frame on each eigenspace of the Laplacian operator associated to Γ. We compute the constants associated to each tight frame and as an application we give a formula for the product in the Norton algebra attached to the eigenspace corresponding to the second largest eigenvalue of the Laplacian.

This informal note presents generalized versions of the higherorder frame and anti-frame rules. The main insights reside in two successive generalizations of the “tensor” operator ⊗. In the first step, a form of “local invariant”, which allows implicit reasoning about “well-bracketed state changes”, is introduced. In the second step, a form of “local monotonicity” is added.