Krull dimension measures the depth of the spectrum Spec(R) of a commutative ring R. Since Spec(R) is a spectral space, Krull dimension can be defined for spectral spaces. Utilizing Stone duality, it can also be defined for distributive lattices. For an arbitrary topological space, the notion of Krull dimension is less useful. Isbell [23] remedied this by introducing the concept of graduated dim...

We present a new method for measuring the spectral phase of ultrashort pulses that utilizes spectral shearing interferometry with zero delay. Unlike conventional spectral phase interferometry for direct electric-field reconstruction, which encodes phase as a sensitively calibrated fringe in the spectral domain, two-dimensional spectral shearing interferometry robustly encodes phase along a seco...

Biometric recognition is more and more important due to security applications all over the world. Mobile phone becomes popular in recent years. Therefore, voice recognition on mobile devices for recognizing a speaker’s identity plays a potential role. This paper presents a speaker recognition method which combines a non-linear feature, named spectral dimension (SD), with Mel Frequency Cepstral ...

We characterize all equivariant odd spectral triples on the quantum SU(2) group having a nontrivial Chern character. It is shown that the dimension of an equivariant spectral triple is at least three, and there does exist a 3-summable equivariant spectral triple. We also show that given any odd spectral triple, there is an odd equivariant spectral triple that induces the same element in K. AMS ...

Quasisymmetry is a well-studied property of homeomorphisms between metric spaces, and the Ahlfors regular conformal dimension quasisymmetric invariant. In present paper, we consider metrics on infinite graphs, show that this notion coincides with critical exponent $p$-energies. Moreover, give relation spectral graph.