Abstract. We first show that the canonical solution operator to ∂ restricted to (0, 1)forms with holomorphic coefficients can be expressed by an integral operator using the Bergman kernel. This result is used to prove that in the case of the unit disc in C the canonical solution operator to ∂ restricted to (0, 1)-forms with holomorphic coefficients is a Hilbert-Schmidt operator. In the sequel w...

\ Abstract: Edge detection plays an important role in object identification. Application ranges from machine vision, image processing to pattern recognition. There exist many algorithms for detecting edges such as sobel, prewitt, canny, morphological operators etc. Canny operator is more susceptible to noise. This paper analyses the advantages and disadvantages of Canny operator and Morphologic...

In recent years, Fourier multiplier theorems in vector–valued function spaces have found many applications in embedding theorems of abstract function spaces and in theory of differential operator equations, especially in maximal regularity of parabolic and elliptic differential–operator equations. Operator–valued multiplier theorems in Banach–valued function spaces have been discussed extensive...

In the context of standard abstract interpretation theory, we deene and study a systematic operator of reduced relative power for composing functionally abstract domains. The reduced relative power of two abstract domains D1 (the exponent) and D2 (the base) consists in a suitably deened lattice of monotone functions from D1 to D2, called dependencies, and it is a generalization of the Cousot an...

Plan Less abstract search Figure 1: The results of abstract problem-solving can serve to constrain search in more detailed spaces. Here, abstract operations are used to constrain information about which more detailed operations are considered at a search point. search. The utility of an abstraction mapping is that information obtained by less expensive problem-solving in an abstract space can t...

The rapid growth of computer industry requires creating large, highly complicated and sophisticated software. This implies increasing probability for errors, bugs and failures. Various software verification techniques are used to ensure quality of produced programs. Unfortunately, verification using formal methods is not very popular, because it is considered not practical and expensive. Theref...

‎In this short note‎, ‎we present some inequalities for relative operator entropy which are generalizations of some results obtained by Zou [Operator inequalities associated with Tsallis relative operator entropy‎, ‎{em Math‎. ‎Inequal‎. ‎Appl.}‎ ‎{18} (2015)‎, ‎no‎. ‎2‎, ‎401--406]‎. ‎Meanwhile‎, ‎we also show some new lower and upper bounds for relative operator entropy and Tsallis relative o...