In this paper, firstly, in $E_1^3$, we defined normal Fermi-Walker derivative and applied for the adapted frame. Normal Fermi-Walker parallelism, normal non-rotating frame, and Darboux vector expressions of normal Fermi-Walker derivative by normal Fermi-Walker derivative are given for adapted frame. Being conditions of normal Fermi-Walker derivative and normal non-rotating frame are examined fo...

In this paper, we focus on the structured multi-frame vectors in Hilbert $C^*$-modules. More precisely, it will be shown that the set of all complete multi-frame vectors for a unitary system can be parameterized by the set of all surjective operators, in the local commutant. Similar results hold for the set of all complete wandering vectors and complete multi-Riesz vectors, when the surjective ...

How to extend standard support vector machines to solve multi-class classification problem and yield the outputs in the frame of Dempster-Shafer theory is useful. The multi-class probability support vector machine is proposed, firstly. The Dempster-Shafer theory based multi-class support vector machine is designed by constructing probability support vector machines for binary classification usi...

In this paper, we provide a review of LPC parameter quantisation for wideband speech coding as well as evaluate our contributions, namely the switched split vector quantiser (SSVQ) and multi-frame GMM-based block quantiser. We also compare the performance of various quantisation schemes on the two popular LPC parameter representations: line spectral frequencies (LSFs) and immittance spectral pa...

Vector-valued discrete Fourier transforms (DFTs) and ambiguity functions are defined. The motivation for the definitions is to provide realistic modeling of multi-sensor environments in which a useful time-frequency analysis is essential. The definition of the DFT requires associated uncertainty principle inequalities. The definition of the ambiguity function requires a component that leads to ...