Wavelet transformation is one of the most practical mathematical transformations in the field of image processing, especially image and signal processing. Depending on the nature of the multiresolution analysis, Wavelet transformation become more accessible and powerful tools. In this paper, we refer to the mathematical foundations of this transformation.   Introduction: The...

the synthesis of diethyl/methyl 1,3-diaryl-1,2,3,6-tetrahydro-pyrimidine-4,5-dicarboxylates can be achieved using one-pot reaction from dialkylacetylene dicarboxylate, amines, and formaldehyde by employing hydrated phosphomolybdic acid (h3[p(mo3o10)4].xh2o) as catalyst at room temperature. the effect of various solvent and catalyst amount was investigated. the salient features of the present me...

In strong-coupling regimes, quantum dynamical effects can alter conventional physics described by perturbation theories, but the simulations of these systems using matrix product states---such as multilevel vibronic that are relevant to energy and electron transfer reactions---suffer from rapid entanglement growth during their real-time evolution, impeding explorations spectra, dynamics, kineti...

Theories of fuzzy sets and type-2 fuzzy sets are powerful mathematical tools for modeling various types of uncertainty. In this paper we introduce the concept of type-2 fuzzy finite state automata and discuss the algebraic study of type-2 fuzzy finite state automata, i.e., to introduce the concept of homomorphisms between two type-2 fuzzy finite state automata, to associate a type-2 fuzzy trans...

In general, a tensor is a multilinear transformation defined over an underlying finite dimensional vector space. In this brief introduction, tensor spaces of all integral orders will defined inductively. Initially the underlying vector space, V, will be assumed to be an inner product space in order to simplify the discussion. Subsequently, the presentation will be generalized to vector spaces w...

To address current software engineering challenges resulting from the diversity of software environnements and usages, Software Product Lines (SPL) promise greater productivity by proposing to develop applications based on a set of common assets thus fostering reuse. However, software product line derivation fails to meet efficiently unforeseen, customer-specific, requirements. In this paper, w...

We introduce the notion of a transformation digroup and prove that every digroup is isomorphic to a transformation digroup. The purpose of this paper is to show how to choose a class of non-bijective transformations on a Cartesian product of two sets to define a transformation digroup on the Cartesian product. The main result of this paper is that every digroup is isomorphic to a transformation...

Let X denote either a vector space over the real numbers R or a module over the integers Z . A symmetric positive definite bilinear form f on X is an inner product if, for any linear form g on X, there exists a unique x ∈ X such that g(y) = f(x, y) for all y ∈ X. This nondegeneracy condition is superfluous whenX is a finite-dimensional vector space [1, 2]. The pair (X, f) is called an inner pro...

Product characterization is critical to understanding the way in which the registered products were made and the unique characteristics that need to be assessed for each Bt plant-incorporated protectant. The product characterization data provide information on the specific transformation systems used for each product, on the actual DNA inserted into the plant, on the inheritance and stability o...

We show that the braided tensor product algebra A1⊗A2 of two module algebras A1,A2 of a quasitriangular Hopf algebraH is equal to the ordinary tensor product algebra of A1 with a subalgebra of A1⊗A2 isomorphic to A2, provided there exists a realization of H within A1. In other words, under this assumption we construct a transformation of generators which ‘decouples’ A1,A2 (i.e. makes them commu...