Software entities should be open for extension, but closed to modification. Unfortunately, unanticipated requirements emerging during software evolution makes it difficult to always enforce this principle. This situation poses a dilemma that is particularly important when considering component-based systems: On the one hand, violating the open/closed principle by allowing for modification compr...

The extension principles play an important role in characterizing and constructing of wavelet frames. The common extension principles, the unitary extension principle (UEP) or the oblique extension principle (OEP), are based on the unitarity of the modulation matrix. In this paper we state the UEP and OEP for refinable function vectors in the polyphase representation. Finally, we apply our resu...

We propose a reflection principle for holomorphic objects in Cn . Our construction generalizes the classical principle of H.Lewy, S.Pinchuk and S.Webster. Key-words: reflection principle, generic manifold, maximum modulus set, holomorphic extension. A.M.S. Classification: 32D15, 32D99, 32F25, 32H99.

We study a fuzzy fractional differential equation (FFDE) and present its solution using Zadeh's extension principle. The proposed study extends the case of fuzzy differential equations of integer order. We also propose a numerical method to approximate the solution of FFDEs. To solve nonlinear problems, the proposed numerical method is then incorporated into an unconstrained optimisation techni...

a new simple model is introduced for a liquid and an equation of state is derived based on this model and the statistical mechanical calculations. this equation of state works well for the non-polar and slightly polar liquids. the important conclusion that may be deduced from this equation of state is that if the reduced variables of state are chosen and defined appropriately, then, the princip...

The fuzzy extension principle has been widely used to extend the domain of mathematical functions and relations from elements of a referential set to fuzzy subsets of that referential set. However, there are restrictions associated with the fuzzy extension principle. This paper addresses the question how restricted is the family of “fuzzy set to fuzzy set mappings” obtained by the fuzzy extensi...

An important tool for the construction of tight wavelet frames is the Unitary Extension Principle first formulated in the Fourierdomain by Ron and Shen. We show that the time-domain analogue of this principle provides a unified approach to the construction of tight frames based on many variations of multiresolution analyses, e.g., regular refinements of bounded L-shaped domains, refinements of ...