We prove that the Shimizu L-function of a real quadratic field is obtained from a (Lorentzian) spectral triple on a noncommutative torus with real multiplication, as an adiabatic limit of the Dirac operator on a 3-dimensional solvmanifold. The Dirac operator on this 3-dimensional geometry gives, via the Connes–Landi isospectral deformations, a spectral triple for the noncommutative tori obtaine...

We present a model of (modified) gravity on spacetimes with fractal structure based on packing of spheres, which are (Euclidean) variants of the Packed Swiss Cheese Cosmology models. As the action functional for gravity we consider the spectral action of noncommutative geometry, and we compute its asymptotic expansion on a space obtained as an Apollonian packing of 3-dimensional spheres inside ...

We prove that the Shimizu L-function of a real quadratic field is obtained from a (Lorentzian) spectral triple on a noncommutative torus with real multiplication, as an adiabatic limit of the Dirac operator on a 3-dimensional solvmanifold. The Dirac operator on this 3dimensional geometry gives, via the Connes-Landi isospectral deformations, a spectral triple for the noncommutative tori obtained...

We report on some recent work on deformation of spaces, notably deformation of spheres, describing two classes of examples. The first class of examples consists of noncommutative manifolds associated with the so called θ-deformations which were introduced in [17] out of a simple analysis in terms of cycles in the (b,B)-complex of cyclic homology. These examples have non-trivial global features ...

Assignment of protein backbone resonances is most routinely carried out using triple resonance three dimensional NMR experiments involving amide 1 H and 15 N resonances. However for intrinsically unstructured proteins, alpha-helical proteins or proteins containing several disordered fragments, the assignment becomes problematic because of high degree of backbone shift degeneracy. In this backdr...

Clinical successes with dual energy CT, aggressive development of energy discriminating x-ray detectors, and novel, target-specific, nanoparticle contrast agents promise to establish spectral CT as a powerful functional imaging modality. Common to all of these applications is the need for a material decomposition algorithm which is robust in the presence of noise. Here, we develop such an algor...

let ‎x be an ‎‎n-‎‎‎‎‎‎square complex matrix with the ‎cartesian decomposition ‎‎x = a + i ‎b‎‎‎‎‎, ‎where ‎‎a ‎and ‎‎b ‎are ‎‎‎n ‎‎times n‎ ‎hermitian ‎matrices. ‎it ‎is ‎known ‎that ‎‎$vert x vert_p^2 ‎leq 2(vert a vert_p^2 + vert b vert_p^2)‎‎‎$, ‎where ‎‎$‎p ‎‎geq 2‎$‎ ‎and ‎‎$‎‎vert . vert_p$ ‎is ‎the ‎schatten ‎‎‎‎p-norm.‎ ‎‎ ‎‎in this paper‎, this inequality and some of its improvements ...

Wide free spectral range (FSR) optical filters are very much essential for modern commercial Dense Wavelength Division Multiplexing(DWDM) technique.Performance of a serially coupled integrated optic triple ring resonator (TRR) which can be used as optical filter has been investigated in this article. Delay line signal processing and Mason’s rule have been used to analyze the TRR architecture. F...