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...

The aim of this article is to study a multiplier family of univalent harmonic meromorphic functions using the sequences {cn} and {dn} of positive real numbers. By specializing {cn} and {dn}, representation theorms, bounds, convolution, geometric convolution, integral convolution and convex combinations for such functions have been determined. The theorems presented, in many cases, confirm or ge...

Abstract. We introduce the mixed convolution bodies of two convex symmetric bodies. We prove that if the boundary of a body K is smooth enough then as δ tends to 1 the δ–M∗–convolution body of K with itself tends to a multiple of the Euclidean ball after proper normalization. On the other hand we show that the δ–M∗–convolution body of the n–dimensional cube is homothetic to the unit ball of ln 1 .

We introduce the mixed convolution bodies of two convex symmetric bodies. We prove that if the boundary of a body K is smooth enough then as δ tends to 1 the δ-M∗-convolution body of K with itself tends to a multiple of the Euclidean ball after proper normalization. On the other hand we show that the δ-M∗-convolution body of the n-dimensional cube is homothetic to the unit ball of `1 .