We consider perturbations of Dirac type operators on complete, connected metric spaces equipped with a doubling measure. Under a suitable set of assumptions, we prove quadratic estimates for such operators and hence deduce that these operators have a bounded functional calculus. In particular, we deduce a Kato square root type estimate.

The quality of a test suite can be measured using mutation analysis. Groups of OO mutation operators are proposed for testing object-oriented features. The OO operators applied to UML specification and C++ code are illustrated by an example. Experimental results demonstrate effectiveness of different mutation operators and the reduction of functional test suite.

The statistical analysis of covariance operators in a functional data analysis setting is considered. Many suitable distances to compare covariance operators are presented and in particular the problem of estimating the average covariance operators among different groups is addressed. Finally, an applied problem in which this methodology has proved useful is introduced, namely, exploring phonet...

In the present paper we prove direct approximation theorems for discrete type operators (Lnf)(x) = ∞ ∑ k=0 un,k(x)λn,k(f), f ∈ C[0,∞), x ∈ [0,∞) using a modified K−functional. As applications we give direct theorems for Baskakov type operators, Szász-Mirakjan type operators and Lupaş operator.

This paper discusses identification of parameters of generalized ordered weighted averaging (GOWA) operators from empirical data. Similarly to ordinary OWA operators, GOWA are characterized by a vector of weights, as well as the power to which the arguments are raised. We develop optimization techniques which allow one to fit such operators to the observed data. We also generalize these methods...

Recursion is a simple but powerful programming technique used extensively in functional languages. For a number of reasons, however, it is often desirable to use structured forms of recursion in programming, encapsulated in so-called recursion operators, in preference to unrestricted recursion. In particular, using recursion operators has proved invaluable for transforming and reasoning about f...

We consider a certain class of Herglotz-Nevanlinna matrix-valued functions which can be realized as the Weyl-Titchmarsh matrix-valued function of some symmetric operator and its self-adjoint extension. New properties of Weyl -Titchmarsh matrixvalued functions as well as a new version of the functional model in such realizations are presented. In the case of periodic Herglotz-Nevanlinna matrix-v...

The homogeneous functional calculus on vector lattices is a useful tool in a variety of areas. One of the interesting application is the study of powers of Banach lattices initiated by G. Ya. Lozanovskĭı [18]. Recently G. Buskes and A. van Rooij [8] introduced the concept of squares of Archimedean vector lattices which allows to represent orthoregular bilinear operators as linear regular operat...

In this paper we explain how recursion operators can be used to structure and reason about program semantics within a functional language. In particular, we show how the recursion operator fold can be used to structure denotational semantics, how the dual recursion operator unfold can be used to structure operational semantics, and how algebraic properties of these operators can be used to reas...

This study introduces (p,q)-hybrid Durrmeyer-Stancu type linear positive operators, which are generalized forms of q-hybrid Durrmeyer-Stancu-type operators and examines their approximation properties. The first modulus continuity on a finite interval is introduced using Peetre’s K-functional. Then, the weighted theorem in space provided Gadzhiev’s Korovkin-type theorem. Finally, these operators...