This paper describes improved piecewise cubic convolution for two-dimensional image reconstruction. Piecewise cubic convolution is one of the most popular methods for image reconstruction, but the traditional approach uses a separable two-dimensional convolution kernel that is based on a onedimensional derivation. The traditional approach is suboptimal for the usual case of non-separable scenes...

Convolution is a ubiquitous operation in mathematics and computing. The Kripke semantics for substructural and interval logics motivates its study for quantalevalued functions relative to ternary relations. The resulting notion of relational convolution leads to generalised binary and unary modal operators for qualitative and quantitative models, and to more conventional variants, when ternary ...

In this work, a general definition of Convolution between two arbitrary Tempered Ultradistributions is given. When one of the Tempered Ultradistributions is rapidly decreasing this definition coincides with the definition of J. Sebastiao e Silva. The product of two arbitrary distributions of exponential type is defined via the Convolution of its corresponding Fourier Transforms. Several example...

This paper explores the utility of a discrete singular convolution algorithm for vibration analysis. A number of di!erent realizations of singular convolution kernels are selected to illustrate the present algorithm. Vibration analysis of strings, rods, beams, diatomic molecules, membranes, waveguides and thin plates are utilized to test numerical accuracy and speed of convergence of the presen...

This paper proposes a novel convolution–non-convolution parallel deep network (CNCP)-based method for electricity theft detection. First, the load time series of normal residents and thieves were analyzed it was found that, compared with thieves, residents’ present more obvious periodicity in different scales, e.g., weeks years; second, times converted into 2D images according to periodicity, t...