The second order hypergeometric q-difference operator is studied for the value c = −q. For certain parameter regimes the corresponding recurrence relation can be related to a symmetric operator on the Hilbert space l(Z). The operator has deficiency indices (1, 1) and we describe as explicitly as possible the spectral resolutions of the self-adjoint extensions. This gives rise to one-parameter o...

This paper proposes an inductive method to construct bases for spaces of spherical harmonics over the unit sphere Ω2q of Cq. The bases are shown to have many interesting properties, among them orthogonality with respect to the inner product of L(Ω2q). As a bypass, we study the inner product [f, g] = f(D)(g(z))(0) over the space P(Cq) of polynomials in the variables z, z ∈ Cq, in which f(D) is t...

Single-carrier (SC) transmission with space-time block coded (STBC) transmit diversity can achieve good bit error rate (BER) performance. However, in a high mobility environment, the STBC codeword orthogonality is distorted and as consequence, the BER performance is degraded by the interference caused by the orthogonality distortion of STBC codeword. In this paper, we proposed a novel frequency...

This paper presents a spectral analysis of signed networks from both theoretical and practical aspects. On the theoretical aspect, we conduct theoretical study based on matrix perturbation theorem for analyzing community structures of complex signed networks and show how the negative edges affect distributions and patterns of node spectral coordinates in the spectral space. We prove and demonst...

We describe a perceptual space for timbre, define an objective metric that takes into account perceptual orthogonality and measure the quality of timbre interpolation. We discuss two timbre representations and using these two representations, measure perceived relationships between pairs of sounds on a equivalent range of timbre variety. We determine that a timbre space based on Mel-frequency c...

In this second recitation, we will address the following topics: • Review of the projection theorem. • Derivation of the projection operator on the range of a matrix, using completion of squares. • Solutions of under and over constrained linear equations. Notice that this recitation note is an alternative discussion of the least-squares problem which is more difficult than the one you can find ...

Linear modal analysis is a useful and effective tool for the design of structures. However, comprehensive basis nonlinear remains to be developed. In current work, machine learning scheme proposed with view performing analysis. The focussed on defining one-to-one mapping from latent ‘modal’ space natural coordinate space, whilst also imposing orthogonality mode shapes. achieved via use recently...

In the downlink of DS-CDMA, frequency-selectivity destroys the orthogonality of the user signals and introduces multiuser interference (MUI). Space-time chip equalization is an efficient tool to restore the orthogonality of the user signals and suppress the MUI. Furthermore, multiple-input multiple-output (MIMO) communication techniques can result in a significant increase in capacity. This pap...